LMFDB - Embedded newform 27.10.e.a.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,10,Mod(4,27)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.9059675764$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	27.4
Dual form			27.10.e.a.7.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-28.3865 - 10.3319i) q^{2} +(136.675 - 31.6686i) q^{3} +(306.833 + 257.464i) q^{4} +(180.775 - 1025.22i) q^{5} +(-4206.93 - 513.146i) q^{6} +(4261.26 - 3575.62i) q^{7} +(1683.47 + 2915.86i) q^{8} +(17677.2 - 8656.62i) q^{9} +(-15724.0 + 27234.8i) q^{10} +(12927.0 + 73312.5i) q^{11} +(50090.0 + 25471.9i) q^{12} +(98368.2 - 35803.1i) q^{13} +(-157905. + 57472.8i) q^{14} +(-7759.98 - 145847. i) q^{15} +(-53273.1 - 302127. i) q^{16} +(92814.6 - 160760. i) q^{17} +(-591233. + 63093.1i) q^{18} +(-192015. - 332579. i) q^{19} +(319426. - 268030. i) q^{20} +(469174. - 623647. i) q^{21} +(390502. - 2.21465e6i) q^{22} +(-1.53236e6 - 1.28581e6i) q^{23} +(322430. + 345212. i) q^{24} +(816933. + 297339. i) q^{25} -3.16225e6 q^{26} +(2.14189e6 - 1.74296e6i) q^{27} +2.22809e6 q^{28} +(-1.09582e6 - 398845. i) q^{29} +(-1.28660e6 + 4.22028e6i) q^{30} +(369610. + 310140. i) q^{31} +(-1.30994e6 + 7.42905e6i) q^{32} +(4.08850e6 + 9.61062e6i) q^{33} +(-4.29563e6 + 3.60446e6i) q^{34} +(-2.89549e6 - 5.01513e6i) q^{35} +(7.65272e6 + 1.89510e6i) q^{36} +(9.41026e6 - 1.62991e7i) q^{37} +(2.01447e6 + 1.14246e7i) q^{38} +(1.23107e7 - 8.00858e6i) q^{39} +(3.29374e6 - 1.19882e6i) q^{40} +(-1.41224e7 + 5.14012e6i) q^{41} +(-1.97617e7 + 1.28557e7i) q^{42} +(-4.09140e6 - 2.32035e7i) q^{43} +(-1.49089e7 + 2.58229e7i) q^{44} +(-5.67938e6 - 1.96880e7i) q^{45} +(3.02137e7 + 5.23317e7i) q^{46} +(-1.66670e7 + 1.39852e7i) q^{47} +(-1.68490e7 - 3.96061e7i) q^{48} +(-1.63405e6 + 9.26718e6i) q^{49} +(-2.01178e7 - 1.68809e7i) q^{50} +(7.59442e6 - 2.49111e7i) q^{51} +(3.94006e7 + 1.43407e7i) q^{52} +6.54021e7 q^{53} +(-7.88089e7 + 2.73468e7i) q^{54} +7.74985e7 q^{55} +(1.75997e7 + 6.40578e6i) q^{56} +(-3.67759e7 - 3.93744e7i) q^{57} +(2.69856e7 + 2.26436e7i) q^{58} +(-2.27818e7 + 1.29202e8i) q^{59} +(3.51694e7 - 4.67488e7i) q^{60} +(-7.92211e7 + 6.64744e7i) q^{61} +(-7.28763e6 - 1.26225e7i) q^{62} +(4.43744e7 - 1.00095e8i) q^{63} +(3.54030e7 - 6.13198e7i) q^{64} +(-1.89237e7 - 1.07322e8i) q^{65} +(-1.67628e7 - 3.15054e8i) q^{66} +(-4.61270e7 + 1.67889e7i) q^{67} +(6.98683e7 - 2.54300e7i) q^{68} +(-2.50156e8 - 1.27210e8i) q^{69} +(3.03772e7 + 1.72278e8i) q^{70} +(1.63168e8 - 2.82615e8i) q^{71} +(5.50006e7 + 3.69711e7i) q^{72} +(3.39022e6 + 5.87204e6i) q^{73} +(-4.35524e8 + 3.65448e8i) q^{74} +(1.21071e8 + 1.47678e7i) q^{75} +(2.67106e7 - 1.51483e8i) q^{76} +(3.17223e8 + 2.66182e8i) q^{77} +(-4.32200e8 + 1.00144e8i) q^{78} +(2.59150e8 + 9.43227e7i) q^{79} -3.19378e8 q^{80} +(2.37546e8 - 3.06050e8i) q^{81} +4.53992e8 q^{82} +(-4.22014e8 - 1.53600e8i) q^{83} +(3.04525e8 - 7.05605e7i) q^{84} +(-1.48036e8 - 1.24217e8i) q^{85} +(-1.23594e8 + 7.00939e8i) q^{86} +(-1.62402e8 - 1.98092e7i) q^{87} +(-1.92007e8 + 1.61113e8i) q^{88} +(3.94983e8 + 6.84131e8i) q^{89} +(-4.21954e7 + 6.17552e8i) q^{90} +(2.91154e8 - 5.04294e8i) q^{91} +(-1.39132e8 - 7.89056e8i) q^{92} +(6.03382e7 + 3.06834e7i) q^{93} +(6.17611e8 - 2.24792e8i) q^{94} +(-3.75679e8 + 1.36736e8i) q^{95} +(5.62310e7 + 1.05685e9i) q^{96} +(2.10383e8 + 1.19314e9i) q^{97} +(1.42132e8 - 2.46180e8i) q^{98} +(8.63151e8 + 1.18406e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17}+ \cdots + 5248107342 q^{99}+O(q^{100}) $ 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−28.3865	−	10.3319i	−1.25452	−	0.456608i	−0.372593	−	0.927995i	$-0.621531\pi$
$2$	−28.3865	−	10.3319i	−1.25452	−	0.456608i	−0.881926	+	0.471387i	$0.843753\pi$
$3$	136.675	−	31.6686i	0.974191	−	0.225727i
$3$	136.675	−	31.6686i	0.974191	−	0.225727i
$4$	306.833	+	257.464i	0.599284	+	0.502859i
$5$	180.775	−	1025.22i	0.129352	−	0.733590i	−0.849276	−	0.527949i	$-0.822961\pi$
$5$	180.775	−	1025.22i	0.129352	−	0.733590i	0.978628	−	0.205641i	$-0.0659278\pi$
$6$	−4206.93	−	513.146i	−1.32521	−	0.161644i
$7$	4261.26	−	3575.62i	0.670806	−	0.562873i	−0.242498	−	0.970152i	$-0.577967\pi$
$7$	4261.26	−	3575.62i	0.670806	−	0.562873i	0.913304	+	0.407279i	$0.133522\pi$
$8$	1683.47	+	2915.86i	0.145312	+	0.251688i
$9$	17677.2	−	8656.62i	0.898095	−	0.439802i
$10$	−15724.0	+	27234.8i	−0.497237	+	0.861240i
$11$	12927.0	+	73312.5i	0.266213	+	1.50977i	0.765558	+	0.643367i	$0.222463\pi$
$11$	12927.0	+	73312.5i	0.266213	+	1.50977i	−0.499345	+	0.866403i	$0.666426\pi$
$12$	50090.0	+	25471.9i	0.697325	+	0.354606i
$13$	98368.2	−	35803.1i	0.955234	−	0.347677i	0.183070	−	0.983100i	$-0.441397\pi$
$13$	98368.2	−	35803.1i	0.955234	−	0.347677i	0.772164	+	0.635423i	$0.219174\pi$
$14$	−157905.	+	57472.8i	−1.09855	+	0.399840i
$15$	−7759.98	−	145847.i	−0.0395776	−	0.743855i
$16$	−53273.1	−	302127.i	−0.203221	−	1.15252i
$17$	92814.6	−	160760.i	0.269523	−	0.466828i	−0.699216	−	0.714911i	$-0.746467\pi$
$17$	92814.6	−	160760.i	0.269523	−	0.466828i	0.968739	+	0.248083i	$0.0798006\pi$
$18$	−591233.	+	63093.1i	−1.32749	+	0.141663i
$19$	−192015.	−	332579.i	−0.338020	−	0.585468i	0.646040	−	0.763304i	$-0.276424\pi$
$19$	−192015.	−	332579.i	−0.338020	−	0.585468i	−0.984060	+	0.177835i	$0.943091\pi$
$20$	319426.	−	268030.i	0.446411	−	0.374583i
$21$	469174.	−	623647.i	0.526438	−	0.699765i
$22$	390502.	−	2.21465e6i	0.355403	−	2.01559i
$23$	−1.53236e6	−	1.28581e6i	−1.14179	−	0.958077i	−0.142295	−	0.989824i	$-0.545448\pi$
$23$	−1.53236e6	−	1.28581e6i	−1.14179	−	0.958077i	−0.999496	+	0.0317477i	$0.989893\pi$
$24$	322430.	+	345212.i	0.198374	+	0.212391i
$25$	816933.	+	297339.i	0.418270	+	0.152238i
$26$	−3.16225e6			−1.35711
$27$	2.14189e6	−	1.74296e6i	0.775641	−	0.631175i
$28$	2.22809e6			0.685049
$29$	−1.09582e6	−	398845.i	−0.287705	−	0.104716i	0.194136	−	0.980975i	$-0.437810\pi$
$29$	−1.09582e6	−	398845.i	−0.287705	−	0.104716i	−0.481841	+	0.876259i	$0.660032\pi$
$30$	−1.28660e6	+	4.22028e6i	−0.289999	+	0.951252i
$31$	369610.	+	310140.i	0.0718813	+	0.0603156i	0.678020	−	0.735043i	$-0.262838\pi$
$31$	369610.	+	310140.i	0.0718813	+	0.0603156i	−0.606139	+	0.795359i	$0.707283\pi$
$32$	−1.30994e6	+	7.42905e6i	−0.220840	+	1.25244i
$33$	4.08850e6	+	9.61062e6i	0.600138	+	1.41071i
$34$	−4.29563e6	+	3.60446e6i	−0.551279	+	0.462578i
$35$	−2.89549e6	−	5.01513e6i	−0.326148	−	0.564906i
$36$	7.65272e6	+	1.89510e6i	0.759372	+	0.188049i
$37$	9.41026e6	−	1.62991e7i	0.825456	−	1.42973i	−0.0761142	−	0.997099i	$-0.524251\pi$
$37$	9.41026e6	−	1.62991e7i	0.825456	−	1.42973i	0.901570	−	0.432633i	$-0.142415\pi$
$38$	2.01447e6	+	1.14246e7i	0.156724	+	0.888824i
$39$	1.23107e7	−	8.00858e6i	0.852100	−	0.554325i
$40$	3.29374e6	−	1.19882e6i	0.203432	−	0.0740431i
$41$	−1.41224e7	+	5.14012e6i	−0.780513	+	0.284083i	−0.701386	−	0.712781i	$-0.747435\pi$
$41$	−1.41224e7	+	5.14012e6i	−0.780513	+	0.284083i	−0.0791263	+	0.996865i	$0.525213\pi$
$42$	−1.97617e7	+	1.28557e7i	−0.979945	+	0.637493i
$43$	−4.09140e6	−	2.32035e7i	−0.182501	−	1.03501i	−0.929125	−	0.369766i	$-0.879438\pi$
$43$	−4.09140e6	−	2.32035e7i	−0.182501	−	1.03501i	0.746624	−	0.665246i	$-0.231673\pi$
$44$	−1.49089e7	+	2.58229e7i	−0.599664	+	1.03865i
$45$	−5.67938e6	−	1.96880e7i	−0.206464	−	0.715723i
$46$	3.02137e7	+	5.23317e7i	0.994934	+	1.72328i
$47$	−1.66670e7	+	1.39852e7i	−0.498214	+	0.418052i	−0.856959	−	0.515384i	$-0.827649\pi$
$47$	−1.66670e7	+	1.39852e7i	−0.498214	+	0.418052i	0.358745	+	0.933436i	$0.383205\pi$
$48$	−1.68490e7	−	3.96061e7i	−0.458131	−	1.07690i
$49$	−1.63405e6	+	9.26718e6i	−0.0404934	+	0.229649i
$50$	−2.01178e7	−	1.68809e7i	−0.455215	−	0.381971i
$51$	7.59442e6	−	2.49111e7i	0.157191	−	0.515618i
$52$	3.94006e7	+	1.43407e7i	0.747289	+	0.271991i
$53$	6.54021e7			1.13855			0.569273	−	0.822149i	$-0.307225\pi$
$53$	6.54021e7			1.13855			0.569273	+	0.822149i	$0.307225\pi$
$54$	−7.88089e7	+	2.73468e7i	−1.26126	+	0.437657i
$55$	7.74985e7			1.14199
$56$	1.75997e7	+	6.40578e6i	0.239144	+	0.0870414i
$57$	−3.67759e7	−	3.93744e7i	−0.461452	−	0.494058i
$58$	2.69856e7	+	2.26436e7i	0.313117	+	0.262736i
$59$	−2.27818e7	+	1.29202e8i	−0.244768	+	1.38815i	0.576263	+	0.817265i	$0.304511\pi$
$59$	−2.27818e7	+	1.29202e8i	−0.244768	+	1.38815i	−0.821031	+	0.570884i	$0.806601\pi$
$60$	3.51694e7	−	4.67488e7i	0.350336	−	0.465682i
$61$	−7.92211e7	+	6.64744e7i	−0.732582	+	0.614710i	−0.930834	−	0.365441i	$-0.880918\pi$
$61$	−7.92211e7	+	6.64744e7i	−0.732582	+	0.614710i	0.198252	+	0.980151i	$0.436474\pi$
$62$	−7.28763e6	−	1.26225e7i	−0.0626359	−	0.108489i
$63$	4.43744e7	−	1.00095e8i	0.354895	−	0.800536i
$64$	3.54030e7	−	6.13198e7i	0.263773	−	0.456868i
$65$	−1.89237e7	−	1.07322e8i	−0.131491	−	0.745723i
$66$	−1.67628e7	−	3.15054e8i	−0.108742	−	2.04379i
$67$	−4.61270e7	+	1.67889e7i	−0.279653	+	0.101785i	−0.478039	−	0.878339i	$-0.658652\pi$
$67$	−4.61270e7	+	1.67889e7i	−0.279653	+	0.101785i	0.198386	+	0.980124i	$0.436430\pi$
$68$	6.98683e7	−	2.54300e7i	0.396269	−	0.144230i
$69$	−2.50156e8	−	1.27210e8i	−1.32859	−	0.675616i
$70$	3.03772e7	+	1.72278e8i	0.151219	+	0.857607i
$71$	1.63168e8	−	2.82615e8i	0.762030	−	1.31987i	−0.179773	−	0.983708i	$-0.557536\pi$
$71$	1.63168e8	−	2.82615e8i	0.762030	−	1.31987i	0.941803	−	0.336166i	$-0.109130\pi$
$72$	5.50006e7	+	3.69711e7i	0.241196	+	0.162131i
$73$	3.39022e6	+	5.87204e6i	0.0139725	+	0.0242011i	0.872927	−	0.487851i	$-0.162219\pi$
$73$	3.39022e6	+	5.87204e6i	0.0139725	+	0.0242011i	−0.858955	+	0.512052i	$0.828886\pi$
$74$	−4.35524e8	+	3.65448e8i	−1.68838	+	1.41672i
$75$	1.21071e8	+	1.47678e7i	0.441839	+	0.0538939i
$76$	2.67106e7	−	1.51483e8i	0.0918378	−	0.520838i
$77$	3.17223e8	+	2.66182e8i	1.02839	+	0.862919i
$78$	−4.32200e8	+	1.00144e8i	−1.32209	+	0.306336i
$79$	2.59150e8	+	9.43227e7i	0.748564	+	0.272455i	0.688001	−	0.725710i	$-0.258488\pi$
$79$	2.59150e8	+	9.43227e7i	0.748564	+	0.272455i	0.0605624	+	0.998164i	$0.480711\pi$
$80$	−3.19378e8			−0.871766
$81$	2.37546e8	−	3.06050e8i	0.613149	−	0.789967i
$82$	4.53992e8			1.10888
$83$	−4.22014e8	−	1.53600e8i	−0.976057	−	0.355256i	−0.195751	−	0.980654i	$-0.562714\pi$
$83$	−4.22014e8	−	1.53600e8i	−0.976057	−	0.355256i	−0.780306	+	0.625398i	$0.784937\pi$
$84$	3.04525e8	−	7.05605e7i	0.667369	−	0.154634i
$85$	−1.48036e8	−	1.24217e8i	−0.307597	−	0.258104i
$86$	−1.23594e8	+	7.00939e8i	−0.243644	+	1.38177i
$87$	−1.62402e8	−	1.98092e7i	−0.303916	−	0.0370707i
$88$	−1.92007e8	+	1.61113e8i	−0.341306	+	0.286390i
$89$	3.94983e8	+	6.84131e8i	0.667303	+	1.15580i	0.978655	+	0.205509i	$0.0658849\pi$
$89$	3.94983e8	+	6.84131e8i	0.667303	+	1.15580i	−0.311352	+	0.950295i	$0.600782\pi$
$90$	−4.21954e7	+	6.17552e8i	−0.0677913	+	0.992161i
$91$	2.91154e8	−	5.04294e8i	0.445079	−	0.770900i
$92$	−1.39132e8	−	7.89056e8i	−0.202480	−	1.14832i
$93$	6.03382e7	+	3.06834e7i	0.0836409	+	0.0425333i
$94$	6.17611e8	−	2.24792e8i	0.815905	−	0.296965i
$95$	−3.75679e8	+	1.36736e8i	−0.473217	+	0.172237i
$96$	5.62310e7	+	1.05685e9i	0.0675702	+	1.26997i
$97$	2.10383e8	+	1.19314e9i	0.241289	+	1.36842i	0.828955	+	0.559316i	$0.188936\pi$
$97$	2.10383e8	+	1.19314e9i	0.241289	+	1.36842i	−0.587665	+	0.809104i	$0.699953\pi$
$98$	1.42132e8	−	2.46180e8i	0.155659	−	0.269610i
$99$	8.63151e8	+	1.18406e9i	0.903084	+	1.23884i
$100$	1.74108e8	+	3.01564e8i	0.174108	+	0.301564i
$101$	−4.78675e8	+	4.01656e8i	−0.457714	+	0.384068i	−0.842289	−	0.539026i	$-0.818793\pi$
$101$	−4.78675e8	+	4.01656e8i	−0.457714	+	0.384068i	0.384575	+	0.923094i	$0.374348\pi$
$102$	−4.72957e8	+	6.28677e8i	−0.432635	+	0.575078i
$103$	3.06242e8	−	1.73679e9i	0.268100	−	1.52047i	−0.491958	−	0.870619i	$-0.663719\pi$
$103$	3.06242e8	−	1.73679e9i	0.268100	−	1.52047i	0.760059	−	0.649854i	$-0.225170\pi$
$104$	2.69997e8	+	2.26554e8i	0.226313	+	0.189899i
$105$	−5.54563e8	−	5.93748e8i	−0.445245	−	0.476705i
$106$	−1.85654e9	−	6.75725e8i	−1.42833	−	0.519869i
$107$	1.19638e9			0.882354			0.441177	−	0.897420i	$-0.354561\pi$
$107$	1.19638e9			0.882354			0.441177	+	0.897420i	$0.354561\pi$
$108$	1.10595e9	+	1.66623e7i	0.782221	+	0.0117849i
$109$	−1.06171e9			−0.720423			−0.360212	−	0.932871i	$-0.617296\pi$
$109$	−1.06171e9			−0.720423			−0.360212	+	0.932871i	$0.617296\pi$
$110$	−2.19991e9	−	8.00704e8i	−1.43265	−	0.521440i
$111$	7.69981e8	−	2.52569e9i	0.481423	−	1.57916i
$112$	−1.30730e9	−	1.09696e9i	−0.785046	−	0.658732i
$113$	4.11298e8	−	2.33259e9i	0.237303	−	1.34581i	−0.600405	−	0.799696i	$-0.704994\pi$
$113$	4.11298e8	−	2.33259e9i	0.237303	−	1.34581i	0.837709	−	0.546118i	$-0.183895\pi$
$114$	6.37130e8	+	1.49767e9i	0.353310	+	0.830507i
$115$	−1.59525e9	+	1.33857e9i	−0.850528	+	0.713678i
$116$	−2.33545e8	−	4.04512e8i	−0.119759	−	0.207429i
$117$	1.42894e9	−	1.48443e9i	0.704982	−	0.732360i
$118$	1.98160e9	−	3.43222e9i	0.940906	−	1.62970i
$119$	−1.79308e8	−	1.01691e9i	−0.0819671	−	0.464858i
$120$	4.12207e8	−	2.68157e8i	0.181468	−	0.118052i
$121$	−2.99187e9	+	1.08895e9i	−1.26884	+	0.461821i
$122$	2.93562e9	−	1.06848e9i	1.19972	−	0.436662i
$123$	−1.76740e9	+	1.14976e9i	−0.696243	+	0.452934i
$124$	3.35590e7	+	1.90322e8i	0.0127471	+	0.0722923i
$125$	1.46916e9	−	2.54466e9i	0.538238	−	0.932255i
$126$	−2.29380e9	+	2.38289e9i	−0.810754	+	0.842240i
$127$	1.45764e9	+	2.52471e9i	0.497204	+	0.861182i	0.999995	−	0.00322582i	$-0.00102681\pi$
$127$	1.45764e9	+	2.52471e9i	0.497204	+	0.861182i	−0.502791	+	0.864408i	$0.667693\pi$
$128$	1.32022e9	−	1.10779e9i	0.434711	−	0.364766i
$129$	−1.29402e9	−	3.04177e9i	−0.411420	−	0.967104i
$130$	−5.71653e8	+	3.24201e9i	−0.175545	+	0.995564i
$131$	2.86011e9	+	2.39992e9i	0.848519	+	0.711992i	0.959463	−	0.281835i	$-0.0909429\pi$
$131$	2.86011e9	+	2.39992e9i	0.848519	+	0.711992i	−0.110944	+	0.993827i	$0.535387\pi$
$132$	−1.21990e9	+	4.00150e9i	−0.349736	+	1.14720i
$133$	−2.00740e9	−	7.30634e8i	−0.556291	−	0.202473i
$134$	1.48285e9			0.397306
$135$	−1.39972e9	−	2.51100e9i	−0.362693	−	0.650646i
$136$	6.25003e8			0.156660
$137$	1.32783e9	+	4.83292e8i	0.322033	+	0.117211i	0.497978	−	0.867189i	$-0.334076\pi$
$137$	1.32783e9	+	4.83292e8i	0.322033	+	0.117211i	−0.175945	+	0.984400i	$0.556298\pi$
$138$	5.78674e9	+	6.19562e9i	1.35824	+	1.45422i
$139$	2.02843e9	+	1.70206e9i	0.460887	+	0.386730i	0.843457	−	0.537197i	$-0.180517\pi$
$139$	2.02843e9	+	1.70206e9i	0.460887	+	0.386730i	−0.382571	+	0.923926i	$0.624961\pi$
$140$	4.02782e8	−	2.28429e9i	0.0886123	−	0.502545i
$141$	−1.83507e9	+	2.43926e9i	−0.390990	+	0.519722i
$142$	−7.55171e9	+	6.33663e9i	−1.55865	+	1.30786i
$143$	3.89642e9	+	6.74879e9i	0.779208	+	1.34963i
$144$	−3.55711e9	−	4.87959e9i	−0.689393	−	0.945697i
$145$	−6.07001e8	+	1.05136e9i	−0.114034	+	0.197512i
$146$	−3.55676e7	−	2.01714e8i	−0.00647839	−	0.0367408i
$147$	7.01439e7	+	1.31834e9i	0.0123897	+	0.232863i
$148$	7.08380e9	−	2.57829e9i	1.21364	−	0.441727i
$149$	−6.81545e8	+	2.48062e8i	−0.113281	+	0.0412308i	−0.398039	−	0.917369i	$-0.630309\pi$
$149$	−6.81545e8	+	2.48062e8i	−0.113281	+	0.0412308i	0.284758	+	0.958599i	$0.408087\pi$
$150$	−3.28420e9	−	1.67009e9i	−0.529687	−	0.269358i
$151$	−1.05193e9	−	5.96578e9i	−0.164661	−	0.933837i	−0.949414	−	0.314028i	$-0.898321\pi$
$151$	−1.05193e9	−	5.96578e9i	−0.164661	−	0.933837i	0.784753	−	0.619809i	$-0.212790\pi$
$152$	6.46502e8	−	1.11977e9i	0.0982367	−	0.170151i
$153$	2.49068e8	−	3.64524e9i	0.0367457	−	0.537792i
$154$	−6.25471e9	−	1.08335e10i	−0.896116	−	1.55212i
$155$	3.84778e8	−	3.22867e8i	0.0535449	−	0.0449295i
$156$	5.83924e9	+	7.12250e8i	0.789397	+	0.0962879i
$157$	−1.74829e9	+	9.91507e9i	−0.229650	+	1.30241i	0.623944	+	0.781469i	$0.285529\pi$
$157$	−1.74829e9	+	9.91507e9i	−0.229650	+	1.30241i	−0.853594	+	0.520939i	$0.825582\pi$
$158$	−6.38183e9	−	5.35499e9i	−0.814682	−	0.683600i
$159$	8.93884e9	−	2.07119e9i	1.10916	−	0.257000i
$160$	7.37963e9	+	2.68597e9i	0.890215	+	0.324012i
$161$	−1.11274e10			−1.30520
$162$	−9.90518e9	+	6.23339e9i	−1.12991	+	0.711061i
$163$	−8.26333e9			−0.916877			−0.458438	−	0.888726i	$-0.651591\pi$
$163$	−8.26333e9			−0.916877			−0.458438	+	0.888726i	$0.651591\pi$
$164$	−5.65661e9	−	2.05884e9i	−0.610603	−	0.222241i
$165$	1.05921e10	−	2.45427e9i	1.11251	−	0.257777i
$166$	1.03925e10	+	8.72037e9i	1.06227	+	0.891350i
$167$	−7.17537e8	+	4.06935e9i	−0.0713871	+	0.404857i	0.928085	+	0.372368i	$0.121454\pi$
$167$	−7.17537e8	+	4.06935e9i	−0.0713871	+	0.404857i	−0.999472	+	0.0324882i	$0.989657\pi$
$168$	2.60831e9	+	3.18152e8i	0.252620	+	0.0308137i
$169$	2.70926e8	−	2.27334e8i	0.0255482	−	0.0214375i
$170$	2.91884e9	+	5.05557e9i	0.268034	+	0.464248i
$171$	−6.27329e9	−	4.21687e9i	−0.561064	−	0.377144i
$172$	4.71868e9	−	8.17300e9i	0.411096	−	0.712038i
$173$	1.02989e9	+	5.84082e9i	0.0874149	+	0.495754i	0.996809	+	0.0798196i	$0.0254344\pi$
$173$	1.02989e9	+	5.84082e9i	0.0874149	+	0.495754i	−0.909394	+	0.415935i	$0.863454\pi$
$174$	4.40536e9	+	2.24023e9i	0.364342	+	0.185276i
$175$	4.54434e9	−	1.65401e9i	0.366269	−	0.133311i
$176$	2.14610e10	−	7.81116e9i	1.68594	−	0.613633i
$177$	9.77940e8	+	1.83802e10i	0.0748915	+	1.40757i
$178$	−4.14386e9	−	2.35010e10i	−0.309396	−	1.75467i
$179$	−1.06016e10	+	1.83625e10i	−0.771849	+	1.33688i	0.164699	+	0.986344i	$0.447335\pi$
$179$	−1.06016e10	+	1.83625e10i	−0.771849	+	1.33688i	−0.936548	+	0.350538i	$0.885999\pi$
$180$	3.32632e9	−	7.50316e9i	0.236177	−	0.532743i
$181$	−3.62734e9	−	6.28273e9i	−0.251208	−	0.435106i	0.712650	−	0.701519i	$-0.247495\pi$
$181$	−3.62734e9	−	6.28273e9i	−0.251208	−	0.435106i	−0.963859	+	0.266414i	$0.914161\pi$
$182$	−1.34752e10	+	1.13070e10i	−0.910359	+	0.763882i
$183$	−8.72241e9	+	1.15942e10i	−0.574919	+	0.764208i
$184$	1.16954e9	−	6.63278e9i	0.0752201	−	0.426594i
$185$	−1.50090e10	−	1.25941e10i	−0.942063	−	0.790485i
$186$	−1.39578e9	−	1.49440e9i	−0.0855081	−	0.0915500i
$187$	1.29855e10	+	4.72633e9i	0.776553	+	0.282642i
$188$	−8.71468e9			−0.508793
$189$	2.89501e9	−	1.50858e10i	0.165033	−	0.859984i
$190$	1.20770e10			0.672305
$191$	−2.92777e10	−	1.06562e10i	−1.59179	−	0.579365i	−0.614068	−	0.789253i	$-0.710468\pi$
$191$	−2.92777e10	−	1.06562e10i	−1.59179	−	0.579365i	−0.977725	+	0.209888i	$0.932690\pi$
$192$	2.89680e9	−	9.50206e9i	0.153838	−	0.504617i
$193$	2.83500e10	+	2.37885e10i	1.47077	+	1.23412i	0.915414	+	0.402514i	$0.131863\pi$
$193$	2.83500e10	+	2.37885e10i	1.47077	+	1.23412i	0.555359	+	0.831611i	$0.312581\pi$
$194$	6.35532e9	−	3.60428e10i	0.322129	−	1.82688i
$195$	−5.98513e9	−	1.40689e10i	−0.296427	−	0.696795i
$196$	−2.88735e9	+	2.42277e9i	−0.139748	+	0.117263i
$197$	1.99270e10	+	3.45145e10i	0.942634	+	1.63269i	0.760420	+	0.649432i	$0.224993\pi$
$197$	1.99270e10	+	3.45145e10i	0.942634	+	1.63269i	0.182215	+	0.983259i	$0.441673\pi$
$198$	−1.22684e10	−	4.25292e10i	−0.567275	−	1.96650i
$199$	7.00042e9	−	1.21251e10i	0.316436	−	0.548083i	−0.663306	−	0.748348i	$-0.730847\pi$
$199$	7.00042e9	−	1.21251e10i	0.316436	−	0.548083i	0.979742	+	0.200266i	$0.0641805\pi$
$200$	5.08285e8	+	2.88263e9i	0.0224632	+	0.127395i
$201$	−5.77274e9	+	3.75540e9i	−0.249459	+	0.162283i
$202$	1.77378e10	−	6.45602e9i	0.749580	−	0.272825i
$203$	−6.09568e9	+	2.21865e9i	−0.251936	+	0.0916972i
$204$	8.74394e9	−	5.68828e9i	0.353485	−	0.229956i
$205$	2.71681e9	+	1.54078e10i	0.107440	+	0.609323i
$206$	−2.66374e10	+	4.61373e10i	−1.03060	+	1.78505i
$207$	−3.82186e10	−	9.46436e9i	−1.44680	−	0.358282i
$208$	−1.60575e10	−	2.78123e10i	−0.594828	−	1.03027i
$209$	2.19000e10	−	1.83763e10i	0.793937	−	0.666192i
$210$	9.60761e9	+	2.25841e10i	0.340901	+	0.801339i
$211$	−3.59377e9	+	2.03813e10i	−0.124819	+	0.707881i	0.856597	+	0.515986i	$0.172574\pi$
$211$	−3.59377e9	+	2.03813e10i	−0.124819	+	0.707881i	−0.981415	+	0.191895i	$0.938537\pi$
$212$	2.00675e10	+	1.68387e10i	0.682312	+	0.572528i
$213$	1.33510e10	−	4.37938e10i	0.444432	−	1.45782i
$214$	−3.39611e10	−	1.23608e10i	−1.10693	−	0.402890i
$215$	−2.45284e10			−0.782882
$216$	8.68803e9	+	3.31124e9i	0.271569	+	0.103502i
$217$	2.68395e9			0.0821685
$218$	3.01383e10	+	1.09695e10i	0.903785	+	0.328951i
$219$	6.49318e8	+	6.95198e8i	0.0190748	+	0.0204226i
$220$	2.37791e10	+	1.99531e10i	0.684375	+	0.574259i
$221$	3.37431e9	−	1.91367e10i	0.0951525	−	0.539637i
$222$	−4.79521e10	+	6.37401e10i	−1.32501	+	1.76126i
$223$	−4.38346e10	+	3.67816e10i	−1.18698	+	0.995998i	−0.187077	+	0.982345i	$0.559901\pi$
$223$	−4.38346e10	+	3.67816e10i	−1.18698	+	0.995998i	−0.999907	+	0.0136523i	$0.995654\pi$
$224$	2.09815e10	+	3.63410e10i	0.556827	+	0.964453i
$225$	1.70151e10	−	1.81575e9i	0.442601	−	0.0472318i
$226$	−3.57753e10	+	6.19646e10i	−0.912210	+	1.57999i
$227$	−2.48471e9	−	1.40915e10i	−0.0621097	−	0.352241i	−0.999986	−	0.00527201i	$-0.998322\pi$
$227$	−2.48471e9	−	1.40915e10i	−0.0621097	−	0.352241i	0.937876	−	0.346969i	$-0.112789\pi$
$228$	−1.14658e9	−	2.15499e10i	−0.0280995	−	0.528126i
$229$	3.11387e10	−	1.13336e10i	0.748240	−	0.272337i	0.0603749	−	0.998176i	$-0.480770\pi$
$229$	3.11387e10	−	1.13336e10i	0.748240	−	0.272337i	0.687865	+	0.725839i	$0.258548\pi$
$230$	5.91136e10	−	2.15156e10i	1.39287	−	0.506965i
$231$	5.17861e10	+	2.63344e10i	1.19663	+	0.608513i
$232$	−6.81802e8	−	3.86669e9i	−0.0154512	−	0.0876281i
$233$	1.23522e10	−	2.13946e10i	0.274562	−	0.475556i	−0.695462	−	0.718563i	$-0.744800\pi$
$233$	1.23522e10	−	2.13946e10i	0.274562	−	0.475556i	0.970025	+	0.243007i	$0.0781337\pi$
$234$	−5.58996e10	+	2.73743e10i	−1.21881	+	0.596860i
$235$	1.13250e10	+	1.96155e10i	0.242234	+	0.419561i
$236$	−4.02551e10	+	3.37781e10i	−0.844728	+	0.708811i
$237$	3.84064e10	+	4.68468e9i	0.790744	+	0.0964522i
$238$	−5.41661e9	+	3.07191e10i	−0.109429	+	0.620601i
$239$	−1.81220e10	−	1.52062e10i	−0.359266	−	0.301460i	0.445232	−	0.895415i	$-0.353121\pi$
$239$	−1.81220e10	−	1.52062e10i	−0.359266	−	0.301460i	−0.804498	+	0.593955i	$0.797566\pi$
$240$	−4.36510e10	+	1.01142e10i	−0.849266	+	0.196781i
$241$	7.95360e10	+	2.89487e10i	1.51875	+	0.552781i	0.960836	−	0.277116i	$-0.0893787\pi$
$241$	7.95360e10	+	2.89487e10i	1.51875	+	0.552781i	0.557916	+	0.829897i	$0.311601\pi$
$242$	9.61796e10			1.80266
$243$	2.27745e10	−	4.93521e10i	0.419007	−	0.907983i
$244$	−4.14224e10			−0.748137
$245$	9.20554e9	+	3.35054e9i	0.163231	+	0.0594111i
$246$	6.20494e10	−	1.43773e10i	1.08026	−	0.250305i
$247$	−3.07955e10	−	2.58405e10i	−0.526442	−	0.441737i
$248$	−2.82095e8	+	1.59984e9i	−0.00473547	+	0.0268562i
$249$	−6.25431e10	−	7.62879e9i	−1.03106	−	0.125765i
$250$	−6.79954e10	+	5.70549e10i	−1.10090	+	0.923768i
$251$	−6.20532e10	−	1.07479e11i	−0.986808	−	1.70920i	−0.633609	−	0.773653i	$-0.718427\pi$
$251$	−6.20532e10	−	1.07479e11i	−0.986808	−	1.70920i	−0.353198	−	0.935548i	$-0.614906\pi$
$252$	3.93864e10	−	1.92877e10i	0.615239	−	0.301286i
$253$	7.44568e10	−	1.28963e11i	1.14252	−	1.97889i
$254$	−1.52925e10	−	8.67280e10i	−0.230529	−	1.30740i
$255$	−2.41666e10	−	1.22893e10i	−0.357919	−	0.182010i
$256$	−8.29884e10	+	3.02053e10i	−1.20764	+	0.439545i
$257$	−6.34372e10	+	2.30893e10i	−0.907079	+	0.330150i	−0.753086	−	0.657922i	$-0.771436\pi$
$257$	−6.34372e10	+	2.30893e10i	−0.907079	+	0.330150i	−0.153993	+	0.988072i	$0.549213\pi$
$258$	5.30545e9	+	9.97150e10i	0.0745476	+	1.40111i
$259$	−1.81797e10	−	1.03102e11i	−0.251037	−	1.42370i
$260$	2.18250e10	−	3.78020e10i	0.296193	−	0.513021i
$261$	−2.28236e10	+	2.43561e9i	−0.304440	+	0.0324882i
$262$	−5.63930e10	−	9.76755e10i	−0.739383	−	1.28065i
$263$	−4.61861e10	+	3.87548e10i	−0.595266	+	0.499487i	−0.889920	−	0.456117i	$-0.849240\pi$
$263$	−4.61861e10	+	3.87548e10i	−0.595266	+	0.499487i	0.294654	+	0.955604i	$0.404795\pi$
$264$	−2.11403e10	+	2.81007e10i	−0.267852	+	0.356040i
$265$	1.18230e10	−	6.70518e10i	0.147273	−	0.835226i
$266$	4.94344e10	+	4.14804e10i	0.605427	+	0.508013i
$267$	7.56498e10	+	8.09951e10i	0.910977	+	0.975345i
$268$	−1.84758e10	−	6.72465e9i	−0.218775	−	0.0796275i
$269$	7.16484e10			0.834298			0.417149	−	0.908838i	$-0.363029\pi$
$269$	7.16484e10			0.834298			0.417149	+	0.908838i	$0.363029\pi$
$270$	1.37899e10	+	8.57403e10i	0.157916	+	0.981856i
$271$	1.38630e11			1.56133			0.780667	−	0.624947i	$-0.214879\pi$
$271$	1.38630e11			1.56133			0.780667	+	0.624947i	$0.214879\pi$
$272$	−5.35143e10	−	1.94776e10i	−0.592802	−	0.215762i
$273$	2.38233e10	−	7.81450e10i	0.259579	−	0.851469i
$274$	−3.26993e10	−	2.74379e10i	−0.350478	−	0.294086i
$275$	−1.12382e10	+	6.37351e10i	−0.118495	+	0.672019i
$276$	−4.40042e10	−	1.03438e11i	−0.456460	−	1.07298i
$277$	−1.24350e11	+	1.04342e11i	−1.26908	+	1.06488i	−0.274423	+	0.961609i	$0.588487\pi$
$277$	−1.24350e11	+	1.04342e11i	−1.26908	+	1.06488i	−0.994653	+	0.103272i	$0.967069\pi$
$278$	−3.99948e10	−	6.92730e10i	−0.401607	−	0.695604i
$279$	9.21843e9	+	2.28283e9i	0.0910831	+	0.0225556i
$280$	9.74894e9	−	1.68857e10i	0.0947865	−	0.164175i
$281$	−8.20100e9	−	4.65102e10i	−0.0784673	−	0.445010i	−0.998576	−	0.0533470i	$-0.983011\pi$
$281$	−8.20100e9	−	4.65102e10i	−0.0784673	−	0.445010i	0.920109	−	0.391663i	$-0.128100\pi$
$282$	7.72932e10	−	5.02824e10i	0.727814	−	0.473472i
$283$	−7.16741e9	+	2.60872e9i	−0.0664237	+	0.0241763i	−0.375018	−	0.927017i	$-0.622364\pi$
$283$	−7.16741e9	+	2.60872e9i	−0.0664237	+	0.0241763i	0.308595	+	0.951194i	$0.400141\pi$
$284$	1.22828e11	−	4.47059e10i	1.12038	−	0.407786i
$285$	−4.70158e10	+	3.05856e10i	−0.422125	+	0.274610i
$286$	−4.08782e10	−	2.31832e11i	−0.361281	−	2.04893i
$287$	−4.18000e10	+	7.23997e10i	−0.363670	+	0.629895i
$288$	4.11544e10	+	1.42665e11i	0.352492	+	1.22194i
$289$	4.20649e10	+	7.28585e10i	0.354715	+	0.614384i
$290$	2.80931e10	−	2.35729e10i	0.233243	−	0.195714i
$291$	6.65393e10	+	1.56410e11i	0.543951	+	1.27864i
$292$	−4.71604e8	+	2.67460e9i	−0.00379624	+	0.0215296i
$293$	−4.06758e10	−	3.41310e10i	−0.322427	−	0.270548i	0.467179	−	0.884163i	$-0.345270\pi$
$293$	−4.06758e10	−	3.41310e10i	−0.322427	−	0.270548i	−0.789606	+	0.613614i	$0.789715\pi$
$294$	1.16298e10	−	3.81479e10i	0.0907838	−	0.297788i
$295$	1.28343e11	+	4.67129e10i	0.986671	+	0.359119i
$296$	6.33677e10			0.479794
$297$	1.55469e11	+	1.34496e11i	1.15941	+	1.00301i
$298$	2.19096e10			0.160939
$299$	−1.96772e11	−	7.16191e10i	−1.42378	−	0.518213i
$300$	3.33464e10	+	3.57026e10i	0.237686	+	0.254480i
$301$	−1.00402e11	−	8.42469e10i	−0.705004	−	0.591568i
$302$	−3.17770e10	+	1.80216e11i	−0.219827	+	1.24670i
$303$	−5.27031e10	+	7.00554e10i	−0.359207	+	0.477474i
$304$	−9.02518e10	+	7.57302e10i	−0.606072	+	0.508555i
$305$	5.38299e10	+	9.32362e10i	0.356184	+	0.616929i
$306$	−4.47322e10	+	1.00902e11i	−0.291658	+	0.657892i
$307$	−1.18264e11	+	2.04839e11i	−0.759854	+	1.31611i	0.183071	+	0.983100i	$0.441396\pi$
$307$	−1.18264e11	+	2.04839e11i	−0.759854	+	1.31611i	−0.942925	+	0.333006i	$0.891937\pi$
$308$	2.88025e10	+	1.63347e11i	0.182369	+	1.03427i
$309$	−1.31458e10	−	2.47074e11i	−0.0820305	−	1.54175i
$310$	−1.42583e10	+	5.18961e9i	−0.0876883	+	0.0319159i
$311$	−2.28732e10	+	8.32517e9i	−0.138645	+	0.0504628i	−0.410411	−	0.911901i	$-0.634615\pi$
$311$	−2.28732e10	+	8.32517e9i	−0.138645	+	0.0504628i	0.271765	+	0.962364i	$0.412392\pi$
$312$	4.40765e10	+	2.24139e10i	0.263337	+	0.133913i
$313$	2.84980e10	+	1.61620e11i	0.167828	+	0.951801i	0.946100	+	0.323874i	$0.104985\pi$
$313$	2.84980e10	+	1.61620e11i	0.167828	+	0.951801i	−0.778272	+	0.627927i	$0.783903\pi$
$314$	1.52069e11	−	2.63391e11i	0.882790	−	1.52904i
$315$	−9.45982e10	−	6.35883e10i	−0.541359	−	0.363898i
$316$	5.52311e10	+	9.56630e10i	0.311596	+	0.539700i
$317$	5.96848e10	−	5.00815e10i	0.331969	−	0.278555i	−0.461533	−	0.887123i	$-0.652700\pi$
$317$	5.96848e10	−	5.00815e10i	0.331969	−	0.278555i	0.793502	+	0.608568i	$0.208256\pi$
$318$	−2.75142e11	−	3.35609e10i	−1.50881	−	0.184040i
$319$	1.50747e10	−	8.54929e10i	0.0815062	−	0.462245i
$320$	−5.64666e10	−	4.73811e10i	−0.301035	−	0.252598i
$321$	1.63516e11	−	3.78877e10i	0.859581	−	0.199171i
$322$	3.15867e11	+	1.14966e11i	1.63739	+	0.595963i
$323$	−7.12870e10			−0.364417
$324$	1.51684e11	−	3.27466e10i	0.764692	−	0.165087i
$325$	9.10060e10			0.452475
$326$	2.34567e11	+	8.53755e10i	1.15024	+	0.418653i
$327$	−1.45110e11	+	3.36229e10i	−0.701830	+	0.162619i
$328$	−3.87625e10	−	3.25256e10i	−0.184918	−	0.155165i
$329$	−2.10164e10	+	1.19190e11i	−0.0988953	+	0.560863i
$330$	−3.26031e11	−	3.97681e10i	−1.51337	−	0.184596i
$331$	−2.51436e11	+	2.10980e11i	−1.15133	+	0.966085i	−0.999750	−	0.0223595i	$-0.992882\pi$
$331$	−2.51436e11	+	2.10980e11i	−1.15133	+	0.966085i	−0.151585	+	0.988444i	$0.548438\pi$
$332$	−8.99414e10	−	1.55783e11i	−0.406292	−	0.703718i
$333$	2.52524e10	−	3.69583e11i	0.112539	−	1.64707i
$334$	6.24123e10	−	1.08101e11i	0.274417	−	0.475305i
$335$	8.87375e9	+	5.03255e10i	0.0384951	+	0.218316i
$336$	−2.13415e11	−	1.08526e11i	−0.913477	−	0.464524i
$337$	2.68559e10	−	9.77474e9i	0.113424	−	0.0412830i	−0.284685	−	0.958621i	$-0.591889\pi$
$337$	2.68559e10	−	9.77474e9i	0.113424	−	0.0412830i	0.398109	+	0.917338i	$0.369667\pi$
$338$	−1.00394e10	+	3.65406e9i	−0.0418393	+	0.0152283i
$339$	−1.76555e10	−	3.31832e11i	−0.0726075	−	1.36464i
$340$	−1.34410e10	−	7.62278e10i	−0.0545477	−	0.309356i
$341$	−1.79592e10	+	3.11062e10i	−0.0719269	+	0.124581i
$342$	1.34509e11	+	1.84517e11i	0.531659	+	0.729321i
$343$	1.38410e11	+	2.39733e11i	0.539938	+	0.935200i
$344$	6.07704e10	−	5.09924e10i	0.233980	−	0.196333i
$345$	−1.75640e11	+	2.33469e11i	−0.667480	+	0.887245i
$346$	3.11114e10	−	1.76441e11i	0.116702	−	0.661848i
$347$	−2.13686e10	−	1.79304e10i	−0.0791213	−	0.0663907i	0.602369	−	0.798218i	$-0.294223\pi$
$347$	−2.13686e10	−	1.79304e10i	−0.0791213	−	0.0663907i	−0.681491	+	0.731827i	$0.738668\pi$
$348$	−4.47301e10	−	4.78907e10i	−0.163491	−	0.175043i
$349$	3.49950e11	+	1.27371e11i	1.26267	+	0.459576i	0.884666	−	0.466226i	$-0.154387\pi$
$349$	3.49950e11	+	1.27371e11i	1.26267	+	0.459576i	0.378009	+	0.925802i	$0.376609\pi$
$350$	−1.46087e11			−0.520362
$351$	1.48291e11	−	2.48138e11i	0.521473	−	0.872592i
$352$	−5.61576e11			−1.94969
$353$	1.52542e11	+	5.55206e10i	0.522880	+	0.190313i	0.589957	−	0.807435i	$-0.299145\pi$
$353$	1.52542e11	+	5.55206e10i	0.522880	+	0.190313i	−0.0670763	+	0.997748i	$0.521367\pi$
$354$	1.62141e11	−	5.31854e11i	0.548755	−	1.80002i
$355$	−2.60247e11	−	2.18373e11i	−0.869677	−	0.729746i
$356$	−5.49449e10	+	3.11608e11i	−0.181302	+	1.02821i
$357$	−5.67111e10	−	1.33308e11i	−0.184783	−	0.434359i
$358$	4.90661e11	−	4.11714e11i	1.57873	−	1.32471i
$359$	1.24439e11	+	2.15534e11i	0.395395	+	0.684844i	0.993151	−	0.116834i	$-0.0372745\pi$
$359$	1.24439e11	+	2.15534e11i	0.395395	+	0.684844i	−0.597757	+	0.801678i	$0.703941\pi$
$360$	4.78463e10	−	4.97044e10i	0.150137	−	0.155967i
$361$	8.76047e10	−	1.51736e11i	0.271484	−	0.470225i
$362$	3.80552e10	+	2.15822e11i	0.116473	+	0.660552i
$363$	−3.74428e11	+	2.43581e11i	−1.13185	+	0.736314i
$364$	2.19173e11	−	7.97726e10i	0.654382	−	0.238176i
$365$	6.63302e9	−	2.41422e9i	0.0195611	−	0.00711966i
$366$	3.67389e11	−	2.39001e11i	1.07019	−	0.696201i
$367$	−9.31324e9	−	5.28180e10i	−0.0267981	−	0.151979i	0.968473	−	0.249120i	$-0.0801414\pi$
$367$	−9.31324e9	−	5.28180e10i	−0.0267981	−	0.151979i	−0.995271	+	0.0971408i	$0.969030\pi$
$368$	−3.06843e11	+	5.31467e11i	−0.872169	+	1.51064i
$369$	−2.05148e11	+	2.13115e11i	−0.576034	+	0.598405i
$370$	2.95934e11	+	5.12573e11i	0.820895	+	1.42183i
$371$	2.78696e11	−	2.33853e11i	0.763744	−	0.640857i
$372$	1.06139e10	+	2.49496e10i	0.0287364	+	0.0675491i
$373$	−4.90216e10	+	2.78016e11i	−0.131129	+	0.743668i	0.846349	+	0.532629i	$0.178796\pi$
$373$	−4.90216e10	+	2.78016e11i	−0.131129	+	0.743668i	−0.977478	+	0.211039i	$0.932315\pi$
$374$	−3.19781e11	−	2.68328e11i	−0.845144	−	0.709160i
$375$	1.20212e11	−	3.94318e11i	0.313911	−	1.02969i
$376$	−6.88374e10	−	2.50548e10i	−0.177615	−	0.0646465i
$377$	−1.22073e11			−0.311233
$378$	−2.38043e11	+	3.98323e11i	−0.599713	+	1.00351i
$379$	−9.16424e10			−0.228150			−0.114075	−	0.993472i	$-0.536390\pi$
$379$	−9.16424e10			−0.228150			−0.114075	+	0.993472i	$0.536390\pi$
$380$	−1.50475e11	−	5.47686e10i	−0.370202	−	0.134743i
$381$	2.79178e11	+	2.98904e11i	0.678763	+	0.726723i
$382$	7.20994e11	+	6.04985e11i	1.73239	+	1.45365i
$383$	−5.92326e10	+	3.35925e11i	−0.140659	+	0.797715i	0.830092	+	0.557626i	$0.188288\pi$
$383$	−5.92326e10	+	3.35925e11i	−0.140659	+	0.797715i	−0.970751	+	0.240089i	$0.922823\pi$
$384$	1.45359e11	−	1.93217e11i	0.341154	−	0.453477i
$385$	3.30242e11	−	2.77106e11i	0.766053	−	0.642795i
$386$	−5.58980e11	−	9.68181e11i	−1.28160	−	2.21980i
$387$	−2.73189e11	−	3.74755e11i	−0.619103	−	0.849275i
$388$	−2.42638e11	+	4.20262e11i	−0.543521	+	0.941406i
$389$	−1.30765e10	−	7.41607e10i	−0.0289547	−	0.164210i	0.966902	−	0.255149i	$-0.0821245\pi$
$389$	−1.30765e10	−	7.41607e10i	−0.0289547	−	0.164210i	−0.995857	+	0.0909384i	$0.971013\pi$
$390$	2.45390e10	+	4.61205e11i	0.0537113	+	1.00949i
$391$	−3.48931e11	+	1.27001e11i	−0.754996	+	0.274796i
$392$	−2.97727e10	+	1.08364e10i	−0.0636841	+	0.0231791i
$393$	4.66908e11	+	2.37433e11i	0.987335	+	0.502083i
$394$	−2.09059e11	−	1.18563e12i	−0.437054	−	2.47866i
$395$	1.43550e11	−	2.48635e11i	0.296698	−	0.513896i
$396$	−4.00080e10	+	5.85538e11i	−0.0817558	+	1.19654i
$397$	−3.60178e11	−	6.23847e11i	−0.727714	−	1.26044i	−0.957847	−	0.287278i	$-0.907250\pi$
$397$	−3.60178e11	−	6.23847e11i	−0.727714	−	1.26044i	0.230134	−	0.973159i	$-0.426084\pi$
$398$	−3.23992e11	+	2.71862e11i	−0.647233	+	0.543093i
$399$	−2.97500e11	−	3.62880e10i	−0.587637	−	0.0716779i
$400$	4.63136e10	−	2.62658e11i	0.0904563	−	0.513003i
$401$	−6.40054e11	−	5.37069e11i	−1.23614	−	1.03724i	−0.997816	−	0.0660572i	$-0.978958\pi$
$401$	−6.40054e11	−	5.37069e11i	−1.23614	−	1.03724i	−0.238323	−	0.971186i	$-0.576598\pi$
$402$	2.02668e11	−	4.69596e10i	0.387051	−	0.0896825i
$403$	4.74618e10	+	1.72747e10i	0.0896338	+	0.0326240i
$404$	−2.50285e11			−0.467433
$405$	−2.70827e11	−	2.98864e11i	−0.500200	−	0.551984i
$406$	1.95958e11			0.357928
$407$	1.31657e12	+	4.79192e11i	2.37831	+	0.865635i
$408$	8.54224e10	−	1.97930e10i	0.152616	−	0.0353623i
$409$	−4.98795e11	−	4.18539e11i	−0.881389	−	0.739573i	0.0850755	−	0.996375i	$-0.472887\pi$
$409$	−4.98795e11	−	4.18539e11i	−0.881389	−	0.739573i	−0.966464	+	0.256802i	$0.917331\pi$
$410$	8.20702e10	−	4.65443e11i	0.143436	−	0.813466i
$411$	1.96787e11	+	2.40034e10i	0.340179	+	0.0414939i
$412$	5.41125e11	−	4.54058e11i	0.925252	−	0.776378i
$413$	3.64899e11	+	6.32024e11i	0.617160	+	1.06895i
$414$	9.87110e11	+	6.63530e11i	1.65145	+	1.11009i
$415$	−2.33764e11	+	4.04891e11i	−0.386867	+	0.670073i
$416$	1.37126e11	+	7.77683e11i	0.224492	+	1.27316i
$417$	3.31138e11	+	1.68391e11i	0.536287	+	0.272714i
$418$	−8.11527e11	+	2.95372e11i	−1.30020	+	0.473233i
$419$	−8.52995e11	+	3.10465e11i	−1.35202	+	0.492095i	−0.913578	−	0.406664i	$-0.866692\pi$
$419$	−8.52995e11	+	3.10465e11i	−1.35202	+	0.492095i	−0.438443	+	0.898759i	$0.644470\pi$
$420$	−1.72899e10	−	3.24961e11i	−0.0271126	−	0.509577i
$421$	9.06300e10	+	5.13988e11i	0.140606	+	0.797414i	0.970791	+	0.239927i	$0.0771234\pi$
$421$	9.06300e10	+	5.13988e11i	0.140606	+	0.797414i	−0.830185	+	0.557487i	$0.811765\pi$
$422$	3.12591e11	−	5.41424e11i	0.479811	−	0.831058i
$423$	−1.73560e11	+	3.91500e11i	−0.263584	+	0.594566i
$424$	1.10103e11	+	1.90703e11i	0.165444	+	0.286558i
$425$	1.23623e11	−	1.03732e11i	0.183802	−	0.154228i
$426$	−8.31459e11	+	1.10521e12i	−1.22320	+	1.62593i
$427$	−9.98945e10	+	5.66530e11i	−0.145417	+	0.824702i
$428$	3.67090e11	+	3.08025e11i	0.528780	+	0.443699i
$429$	7.46268e11	+	7.98998e11i	1.06374	+	1.13891i
$430$	6.96276e11	+	2.53424e11i	0.982140	+	0.357470i
$431$	−4.10577e11			−0.573122			−0.286561	−	0.958062i	$-0.592512\pi$
$431$	−4.10577e11			−0.573122			−0.286561	+	0.958062i	$0.592512\pi$
$432$	−6.40699e11	−	5.54270e11i	−0.885069	−	0.765675i
$433$	7.57211e10			0.103519			0.0517597	−	0.998660i	$-0.483517\pi$
$433$	7.57211e10			0.103519			0.0517597	+	0.998660i	$0.483517\pi$
$434$	−7.61880e10	−	2.77302e10i	−0.103082	−	0.0375188i
$435$	−4.96670e10	+	1.62917e11i	−0.0665068	+	0.218155i
$436$	−3.25769e11	−	2.73353e11i	−0.431738	−	0.362271i
$437$	−1.33396e11	+	7.56525e11i	−0.174975	+	0.992332i
$438$	−1.12492e10	−	2.64429e10i	−0.0146046	−	0.0343302i
$439$	−4.08458e11	+	3.42737e11i	−0.524876	+	0.440423i	−0.866328	−	0.499476i	$-0.833526\pi$
$439$	−4.08458e11	+	3.42737e11i	−0.524876	+	0.440423i	0.341452	+	0.939899i	$0.389081\pi$
$440$	1.30467e11	+	2.25975e11i	0.165944	+	0.287424i
$441$	5.13370e10	+	1.77963e11i	0.0646333	+	0.224056i
$442$	−2.93502e11	+	5.08361e11i	−0.365773	+	0.633537i
$443$	−8.08411e10	−	4.58473e11i	−0.0997276	−	0.565583i	−0.993196	−	0.116457i	$-0.962846\pi$
$443$	−8.08411e10	−	4.58473e11i	−0.0997276	−	0.565583i	0.893468	−	0.449127i	$-0.148265\pi$
$444$	8.86528e11	−	5.76722e11i	1.08260	−	0.704277i
$445$	7.72790e11	−	2.81272e11i	0.934203	−	0.340022i
$446$	1.62433e12	−	5.91209e11i	1.94387	−	0.707512i
$447$	−8.52945e10	+	5.54875e10i	−0.101050	+	0.0657372i
$448$	−6.83951e10	−	3.87888e11i	−0.0802184	−	0.454941i
$449$	5.60284e11	−	9.70440e11i	0.650578	−	1.12683i	−0.332405	−	0.943137i	$-0.607860\pi$
$449$	5.60284e11	−	9.70440e11i	0.650578	−	1.12683i	0.982983	−	0.183697i	$-0.0588066\pi$
$450$	−5.01758e11	−	1.24254e11i	−0.576817	−	0.142842i
$451$	−5.59394e11	−	9.68899e11i	−0.636683	−	1.10277i
$452$	7.26756e11	−	6.09821e11i	0.818966	−	0.687194i
$453$	−3.32700e11	−	7.82061e11i	−0.371203	−	0.872567i
$454$	−7.50589e10	+	4.25680e11i	−0.0829184	+	0.470254i
$455$	−4.64381e11	−	3.89662e11i	−0.507953	−	0.426223i
$456$	5.28991e10	−	1.73519e11i	0.0572937	−	0.187934i
$457$	−8.78620e11	−	3.19792e11i	−0.942276	−	0.342961i	−0.175212	−	0.984531i	$-0.556061\pi$
$457$	−8.78620e11	−	3.19792e11i	−0.942276	−	0.342961i	−0.767064	+	0.641570i	$0.778283\pi$
$458$	−1.00102e12			−1.06303
$459$	−8.13981e10	−	5.06101e11i	−0.0855968	−	0.532207i
$460$	−8.34111e11			−0.868587
$461$	6.04861e11	+	2.20151e11i	0.623737	+	0.227022i	0.634503	−	0.772920i	$-0.281205\pi$
$461$	6.04861e11	+	2.20151e11i	0.623737	+	0.227022i	−0.0107661	+	0.999942i	$0.503427\pi$
$462$	−1.19794e12	−	1.28259e12i	−1.22334	−	1.30978i
$463$	3.64530e11	+	3.05877e11i	0.368654	+	0.309338i	0.808229	−	0.588868i	$-0.200426\pi$
$463$	3.64530e11	+	3.05877e11i	0.368654	+	0.309338i	−0.439575	+	0.898206i	$0.644871\pi$
$464$	−6.21241e10	+	3.52323e11i	−0.0622199	+	0.352866i
$465$	4.23649e10	−	5.63133e10i	0.0420211	−	0.0558564i
$466$	−5.71680e11	+	4.79697e11i	−0.561586	+	0.471227i
$467$	−5.66452e10	−	9.81124e10i	−0.0551109	−	0.0954548i	0.837154	−	0.546968i	$-0.184218\pi$
$467$	−5.66452e10	−	9.81124e10i	−0.0551109	−	0.0954548i	−0.892265	+	0.451513i	$0.850885\pi$
$468$	8.20635e11	−	8.75735e10i	0.790758	−	0.0843853i
$469$	−1.36529e11	+	2.36475e11i	−0.130301	+	0.225687i
$470$	−1.18814e11	−	6.73826e11i	−0.112312	−	0.636953i
$471$	7.50477e10	+	1.41051e12i	0.0702657	+	1.32063i
$472$	−4.15088e11	+	1.51080e11i	−0.384947	+	0.140109i
$473$	1.64822e12	−	5.99902e11i	1.51405	−	0.551068i
$474$	−1.04182e12	−	5.29791e11i	−0.947963	−	0.482061i
$475$	−5.79743e10	−	3.28788e11i	−0.0522533	−	0.296343i
$476$	2.06799e11	−	3.58187e11i	0.184637	−	0.319800i
$477$	1.15613e12	−	5.66161e11i	1.02252	−	0.500734i
$478$	3.57313e11	+	6.18884e11i	0.313057	+	0.542230i
$479$	1.35280e12	−	1.13513e12i	1.17415	−	0.985226i	0.174147	−	0.984720i	$-0.444283\pi$
$479$	1.35280e12	−	1.13513e12i	1.17415	−	0.985226i	1.00000		0.000506151i	$-0.000161113\pi$
$480$	1.09367e12	+	1.33402e11i	0.940377	+	0.114704i
$481$	3.42114e11	−	1.94023e12i	0.291419	−	1.65272i
$482$	−1.95866e12	−	1.64351e12i	−1.65290	−	1.38695i
$483$	−1.52083e12	+	3.52388e11i	−1.27151	+	0.294618i
$484$	−1.19837e12	−	4.36171e11i	−0.992628	−	0.361287i
$485$	1.26127e12			1.03507
$486$	−1.15639e12	+	1.16563e12i	−0.940245	+	0.947760i
$487$	2.24333e11			0.180723			0.0903613	−	0.995909i	$-0.471198\pi$
$487$	2.24333e11			0.180723			0.0903613	+	0.995909i	$0.471198\pi$
$488$	−3.27196e11	−	1.19090e11i	−0.261168	−	0.0950573i
$489$	−1.12939e12	+	2.61688e11i	−0.893213	+	0.206964i
$490$	−2.26696e11	−	1.90221e11i	−0.177649	−	0.149065i
$491$	−7.49609e10	+	4.25124e11i	−0.0582060	+	0.330103i	−0.999981	−	0.00614067i	$-0.998045\pi$
$491$	−7.49609e10	+	4.25124e11i	−0.0582060	+	0.330103i	0.941775	+	0.336243i	$0.109156\pi$
$492$	−8.38318e11	−	1.02255e11i	−0.645009	−	0.0786759i
$493$	−1.65826e11	+	1.39144e11i	−0.126427	+	0.106085i
$494$	6.07197e11	+	1.05170e12i	0.458731	+	0.794546i
$495$	1.36996e12	−	6.70875e11i	1.02561	−	0.502248i
$496$	7.40112e10	−	1.28191e11i	0.0549073	−	0.0951022i
$497$	−3.15224e11	−	1.78772e12i	−0.231748	−	1.31431i
$498$	1.69656e12	+	8.62741e11i	1.23606	+	0.628563i
$499$	−2.03616e11	+	7.41101e10i	−0.147014	+	0.0535087i	−0.414479	−	0.910059i	$-0.636036\pi$
$499$	−2.03616e11	+	7.41101e10i	−0.147014	+	0.0535087i	0.267465	+	0.963568i	$0.413814\pi$
$500$	1.10594e12	−	4.02531e11i	0.791350	−	0.288028i
$501$	3.08012e10	+	5.78903e11i	0.0218423	+	0.410522i
$502$	6.51015e11	+	3.69209e12i	0.457535	+	2.59481i
$503$	−6.07371e11	+	1.05200e12i	−0.423056	+	0.732755i	−0.996237	−	0.0866745i	$-0.972376\pi$
$503$	−6.07371e11	+	1.05200e12i	−0.423056	+	0.732755i	0.573181	+	0.819429i	$0.305709\pi$
$504$	3.66567e11	−	3.91179e10i	0.253055	−	0.0270046i
$505$	3.25255e11	+	5.63358e11i	0.222542	+	0.385455i
$506$	−3.44600e12	+	2.89153e12i	−2.33689	+	1.96088i
$507$	2.98296e10	−	3.96508e10i	0.0200498	−	0.0266512i
$508$	−2.02768e11	+	1.14996e12i	−0.135087	+	0.766116i
$509$	7.97957e11	+	6.69565e11i	0.526926	+	0.442143i	0.867038	−	0.498242i	$-0.166021\pi$
$509$	7.97957e11	+	6.69565e11i	0.526926	+	0.442143i	−0.340113	+	0.940385i	$0.610465\pi$
$510$	5.59035e11	+	5.98536e11i	0.365909	+	0.391764i
$511$	3.54428e10	+	1.29001e10i	0.0229951	+	0.00836952i
$512$	1.78544e12			1.14823
$513$	−9.90945e11	−	3.77675e11i	−0.631715	−	0.240763i
$514$	2.03932e12			1.28870
$515$	−1.72523e12	−	6.27933e11i	−1.08072	−	0.393352i
$516$	3.86100e11	−	1.26648e12i	0.239759	−	0.786456i
$517$	−1.24075e12	−	1.04111e12i	−0.763793	−	0.640898i
$518$	−5.49178e11	+	3.11454e12i	−0.335142	+	1.90069i
$519$	3.25732e11	+	7.65680e11i	0.197064	+	0.463227i
$520$	2.81077e11	−	2.35852e11i	0.168582	−	0.141457i
$521$	−2.55142e11	−	4.41918e11i	−0.151709	−	0.262768i	0.780147	−	0.625596i	$-0.215144\pi$
$521$	−2.55142e11	−	4.41918e11i	−0.151709	−	0.262768i	−0.931856	+	0.362829i	$0.881811\pi$
$522$	6.73048e11	+	1.66672e11i	0.396761	+	0.0982528i
$523$	1.19962e12	−	2.07781e12i	0.701111	−	1.21436i	−0.266966	−	0.963706i	$-0.586021\pi$
$523$	1.19962e12	−	2.07781e12i	0.701111	−	1.21436i	0.968077	−	0.250653i	$-0.0806454\pi$
$524$	2.59685e11	+	1.47275e12i	0.150472	+	0.853371i
$525$	5.68719e11	−	3.69974e11i	0.326724	−	0.212547i
$526$	1.71147e12	−	6.22925e11i	0.974842	−	0.354813i
$527$	8.41631e10	−	3.06329e10i	0.0475307	−	0.0172997i
$528$	2.68582e12	−	1.74723e12i	1.50392	−	0.978358i
$529$	3.82075e11	+	2.16686e12i	0.212128	+	1.20304i
$530$	−1.02838e12	+	1.78121e12i	−0.566127	+	0.980561i
$531$	7.15735e11	+	2.48115e12i	0.390685	+	1.35434i
$532$	−4.27826e11	−	7.41016e11i	−0.231561	−	0.401075i
$533$	−1.20516e12	+	1.01125e12i	−0.646803	+	0.542732i
$534$	−1.31061e12	−	3.08077e12i	−0.697488	−	1.63955i
$535$	2.16275e11	−	1.22656e12i	0.114134	−	0.647286i
$536$	−1.26608e11	−	1.06236e11i	−0.0662549	−	0.0555945i
$537$	−8.67460e11	+	2.84544e12i	−0.450158	+	1.47661i
$538$	−2.03385e12	−	7.40260e11i	−1.04664	−	0.380947i
$539$	−7.00524e11			−0.357498
$540$	2.17011e11	−	1.13084e12i	0.109827	−	0.572305i
$541$	1.68290e12			0.844636			0.422318	−	0.906448i	$-0.361216\pi$
$541$	1.68290e12			0.844636			0.422318	+	0.906448i	$0.361216\pi$
$542$	−3.93523e12	−	1.43231e12i	−1.95872	−	0.712917i
$543$	−6.94732e11	−	7.43821e11i	−0.342940	−	0.367171i
$544$	1.07271e12	+	9.00110e11i	0.525154	+	0.440657i
$545$	−1.91931e11	+	1.08849e12i	−0.0931880	+	0.528496i
$546$	−1.48364e12	+	1.97213e12i	−0.714435	+	0.949659i
$547$	2.05235e12	−	1.72213e12i	0.980186	−	0.822474i	−0.00393113	−	0.999992i	$-0.501251\pi$
$547$	2.05235e12	−	1.72213e12i	0.980186	−	0.822474i	0.984118	+	0.177518i	$0.0568069\pi$
$548$	2.82993e11	+	4.90159e11i	0.134049	+	0.232180i
$549$	−8.24964e11	+	1.86087e12i	−0.387578	+	0.874259i
$550$	9.77516e11	−	1.69311e12i	0.455504	−	0.788955i
$551$	7.77654e10	+	4.41029e11i	0.0359422	+	0.203838i
$552$	−5.02039e10	−	9.43574e11i	−0.0230150	−	0.432564i
$553$	1.44157e12	−	5.24688e11i	0.655499	−	0.238582i
$554$	4.60792e12	−	1.67715e12i	2.07831	−	0.756444i
$555$	−2.45020e12	−	1.24598e12i	−1.09618	−	0.557434i
$556$	1.84173e11	+	1.04450e12i	0.0817314	+	0.463522i
$557$	3.05209e11	−	5.28638e11i	0.134354	−	0.232707i	−0.790997	−	0.611820i	$-0.790438\pi$
$557$	3.05209e11	−	5.28638e11i	0.134354	−	0.232707i	0.925350	+	0.379113i	$0.123771\pi$
$558$	−2.38093e11	−	1.60045e11i	−0.103967	−	0.0698857i
$559$	−1.23322e12	−	2.13600e12i	−0.534181	−	0.925228i
$560$	−1.36095e12	+	1.14198e12i	−0.584786	+	0.490694i
$561$	1.92447e12	+	2.34740e11i	0.820311	+	0.100059i
$562$	−2.47739e11	+	1.40499e12i	−0.104756	+	0.594102i
$563$	−5.43936e11	−	4.56416e11i	−0.228171	−	0.191458i	0.521534	−	0.853231i	$-0.325360\pi$
$563$	−5.43936e11	−	4.56416e11i	−0.228171	−	0.191458i	−0.749705	+	0.661773i	$0.769804\pi$
$564$	−1.19108e12	+	2.75981e11i	−0.495661	+	0.114848i
$565$	−2.31707e12	−	8.43345e11i	−0.956580	−	0.348167i
$566$	2.30411e11			0.0943689
$567$	−8.20703e10	−	2.15353e12i	−0.0333474	−	0.875040i
$568$	1.09875e12			0.442928
$569$	−2.06256e12	−	7.50709e11i	−0.824899	−	0.300239i	−0.105135	−	0.994458i	$-0.533528\pi$
$569$	−2.06256e12	−	7.50709e11i	−0.824899	−	0.300239i	−0.719763	+	0.694219i	$0.755750\pi$
$570$	1.65062e12	−	3.82460e11i	0.654953	−	0.151757i
$571$	9.39308e11	+	7.88173e11i	0.369782	+	0.310284i	0.808675	−	0.588255i	$-0.200185\pi$
$571$	9.39308e11	+	7.88173e11i	0.369782	+	0.310284i	−0.438893	+	0.898539i	$0.644629\pi$
$572$	−5.42019e11	+	3.07394e12i	−0.211705	+	1.20064i
$573$	−4.33900e12	−	5.29256e11i	−1.68149	−	0.205102i
$574$	1.93458e12	−	1.62330e12i	0.743846	−	0.624161i
$575$	−8.69519e11	−	1.50605e12i	−0.331721	−	0.574558i
$576$	9.50040e10	−	1.39043e12i	0.0359617	−	0.526319i
$577$	2.72719e11	−	4.72364e11i	0.102429	−	0.177413i	−0.810256	−	0.586077i	$-0.800672\pi$
$577$	2.72719e11	−	4.72364e11i	0.102429	−	0.177413i	0.912685	+	0.408664i	$0.134005\pi$
$578$	−4.41312e11	−	2.50281e12i	−0.164464	−	0.932722i
$579$	4.62809e12	+	2.35349e12i	1.71139	+	0.870280i
$580$	−4.56934e11	+	1.66310e11i	−0.167659	+	0.0610230i
$581$	−2.34753e12	+	8.54431e11i	−0.854709	+	0.311089i
$582$	−2.72810e11	−	5.12742e12i	−0.0985615	−	1.85245i
$583$	8.45451e11	+	4.79479e12i	0.303096	+	1.71894i
$584$	−1.14147e10	+	1.97708e10i	−0.00406075	+	0.00703343i
$585$	−1.26356e12	−	1.73333e12i	−0.446062	−	0.611900i
$586$	8.02007e11	+	1.38912e12i	0.280957	+	0.486631i
$587$	1.58490e12	−	1.32989e12i	0.550972	−	0.462321i	−0.324298	−	0.945955i	$-0.605128\pi$
$587$	1.58490e12	−	1.32989e12i	0.550972	−	0.462321i	0.875270	+	0.483634i	$0.160684\pi$
$588$	−3.17903e11	+	4.22571e11i	−0.109672	+	0.145781i
$589$	3.21754e10	−	1.82476e11i	0.0110155	−	0.0624721i
$590$	−3.16058e12	−	2.65204e12i	−1.07382	−	0.901043i
$591$	3.81655e12	+	4.08622e12i	1.28685	+	1.37777i
$592$	−5.42569e12	−	1.97479e12i	−1.81555	−	0.660805i
$593$	2.78234e12			0.923983			0.461992	−	0.886884i	$-0.347135\pi$
$593$	2.78234e12			0.923983			0.461992	+	0.886884i	$0.347135\pi$
$594$	−3.02362e12	−	5.42416e12i	−0.996525	−	1.78770i
$595$	−1.07497e12			−0.351618
$596$	−2.72988e11	−	9.93593e10i	−0.0886206	−	0.0322553i
$597$	5.72799e11	−	1.87889e12i	0.184552	−	0.605365i
$598$	4.84571e12	+	4.06603e12i	1.54954	+	1.30022i
$599$	1.97745e11	−	1.12147e12i	0.0627603	−	0.355931i	−0.937214	−	0.348755i	$-0.886605\pi$
$599$	1.97745e11	−	1.12147e12i	0.0627603	−	0.355931i	0.999974	−	0.00717632i	$-0.00228431\pi$
$600$	1.60759e11	+	3.77887e11i	0.0506400	+	0.119037i
$601$	−2.02299e12	+	1.69749e12i	−0.632498	+	0.530729i	−0.901704	−	0.432354i	$-0.857683\pi$
$601$	−2.02299e12	+	1.69749e12i	−0.632498	+	0.530729i	0.269206	+	0.963083i	$0.413239\pi$
$602$	1.97963e12	+	3.42881e12i	0.614326	+	1.06404i
$603$	−6.70062e11	+	6.96084e11i	−0.206389	+	0.214404i
$604$	1.21321e12	−	2.10133e12i	0.370910	−	0.642434i
$605$	5.75564e11	+	3.26419e12i	0.174660	+	0.990549i
$606$	2.21986e12	−	1.44411e12i	0.668650	−	0.434984i
$607$	−1.33549e12	+	4.86078e11i	−0.399292	+	0.145331i	−0.533858	−	0.845574i	$-0.679258\pi$
$607$	−1.33549e12	+	4.86078e11i	−0.399292	+	0.145331i	0.134566	+	0.990905i	$0.457036\pi$
$608$	2.72227e12	−	9.90827e11i	0.807915	−	0.294057i
$609$	−7.62867e11	+	4.96276e11i	−0.224735	+	0.146199i
$610$	−5.64743e11	−	3.20282e12i	−0.165145	−	0.936586i
$611$	−1.13878e12	+	1.97243e12i	−0.330565	+	0.572555i
$612$	1.01494e12	−	1.05435e12i	0.292455	−	0.303812i
$613$	−1.24550e11	−	2.15726e11i	−0.0356263	−	0.0617065i	0.847662	−	0.530536i	$-0.178009\pi$
$613$	−1.24550e11	−	2.15726e11i	−0.0356263	−	0.0617065i	−0.883289	+	0.468829i	$0.844676\pi$
$614$	5.47348e12	−	4.59279e12i	1.55420	−	1.30412i
$615$	8.59263e11	+	2.01982e12i	0.242208	+	0.569345i
$616$	−2.42112e11	+	1.37309e12i	−0.0677492	+	0.384225i
$617$	2.14716e12	+	1.80168e12i	0.596461	+	0.500490i	0.890306	−	0.455363i	$-0.150491\pi$
$617$	2.14716e12	+	1.80168e12i	0.596461	+	0.500490i	−0.293845	+	0.955853i	$0.594935\pi$
$618$	−2.17956e12	+	7.14939e12i	−0.601065	+	1.97161i
$619$	1.30675e12	+	4.75616e11i	0.357753	+	0.130211i	0.514643	−	0.857405i	$-0.327925\pi$
$619$	1.30675e12	+	4.75616e11i	0.357753	+	0.130211i	−0.156890	+	0.987616i	$0.550147\pi$
$620$	2.01189e11			0.0546818
$621$	−5.52326e12	−	8.32135e10i	−1.49033	−	0.0224534i
$622$	7.35306e11			0.196975
$623$	4.12932e12	+	1.50295e12i	1.09820	+	0.399713i
$624$	−3.07543e12	−	3.29274e12i	−0.812036	−	0.869414i
$625$	−1.04253e12	−	8.74791e11i	−0.273294	−	0.229321i
$626$	8.60877e11	−	4.88228e12i	0.224056	−	1.27068i
$627$	2.41124e12	−	3.20513e12i	0.623069	−	0.828211i
$628$	−3.08920e12	+	2.59215e12i	−0.792553	+	0.665031i
$629$	−1.74682e12	−	3.02558e12i	−0.444959	−	0.770691i
$630$	2.02833e12	+	2.78243e12i	0.512986	+	0.703706i
$631$	−2.21893e12	+	3.84330e12i	−0.557201	+	0.965100i	0.440528	+	0.897739i	$0.354791\pi$
$631$	−2.21893e12	+	3.84330e12i	−0.557201	+	0.965100i	−0.997729	+	0.0673608i	$0.978542\pi$
$632$	1.61239e11	+	9.14434e11i	0.0402017	+	0.227995i
$633$	1.54267e11	+	2.89942e12i	0.0381906	+	0.717786i
$634$	−2.21168e12	+	8.04986e11i	−0.543652	+	0.197873i
$635$	2.85190e12	−	1.03801e12i	0.696069	−	0.253348i
$636$	3.27599e12	+	1.66592e12i	0.793937	+	0.403735i
$637$	1.71055e11	+	9.70101e11i	0.0411631	+	0.233448i
$638$	−1.31122e12	+	2.27110e12i	−0.313316	+	0.542679i
$639$	4.37861e11	−	6.40832e12i	0.103892	−	1.52051i
$640$	−8.97075e11	−	1.55378e12i	−0.211358	−	0.366083i
$641$	−3.02140e12	+	2.53526e12i	−0.706883	+	0.593145i	−0.923723	−	0.383062i	$-0.874870\pi$
$641$	−3.02140e12	+	2.53526e12i	−0.706883	+	0.593145i	0.216840	+	0.976207i	$0.430425\pi$
$642$	−5.03309e12	−	6.13919e11i	−1.16930	−	0.142628i
$643$	−5.65796e11	+	3.20879e12i	−0.130530	+	0.740273i	0.847339	+	0.531053i	$0.178204\pi$
$643$	−5.65796e11	+	3.20879e12i	−0.130530	+	0.740273i	−0.977869	+	0.209220i	$0.932908\pi$
$644$	−3.41425e12	−	2.86489e12i	−0.782183	−	0.656330i
$645$	−3.35242e12	+	7.76780e11i	−0.762676	+	0.176717i
$646$	2.02359e12	+	7.36526e11i	0.457168	+	0.166396i
$647$	5.72090e11			0.128350			0.0641749	−	0.997939i	$-0.479558\pi$
$647$	5.72090e11			0.128350			0.0641749	+	0.997939i	$0.479558\pi$
$648$	1.29230e12	+	1.77426e11i	0.287923	+	0.0395303i
$649$	−9.76664e12			−2.16095
$650$	−2.58334e12	−	9.40260e11i	−0.567639	−	0.206604i
$651$	3.66829e11	−	8.49968e10i	0.0800478	−	0.0185476i
$652$	−2.53546e12	−	2.12751e12i	−0.549469	−	0.461059i
$653$	−5.68044e11	+	3.22154e12i	−0.122257	+	0.693352i	0.860643	+	0.509209i	$0.170062\pi$
$653$	−5.68044e11	+	3.22154e12i	−0.122257	+	0.693352i	−0.982899	+	0.184143i	$0.941049\pi$
$654$	4.46655e12	+	5.44814e11i	0.954712	+	0.116452i
$655$	2.97748e12	−	2.49841e12i	0.632068	−	0.530368i
$656$	2.30531e12	+	3.99291e12i	0.486029	+	0.841826i
$657$	1.10762e11	+	7.44533e10i	0.0231924	+	0.0155898i
$658$	1.82803e12	−	3.16624e12i	0.380161	−	0.658458i
$659$	2.60845e11	+	1.47933e12i	0.0538763	+	0.305548i	0.999824	−	0.0187720i	$-0.00597567\pi$
$659$	2.60845e11	+	1.47933e12i	0.0538763	+	0.305548i	−0.945947	+	0.324320i	$0.894865\pi$
$660$	3.88190e12	+	1.97404e12i	0.796337	+	0.404956i
$661$	7.66331e12	−	2.78922e12i	1.56139	−	0.568298i	0.590332	−	0.807161i	$-0.298997\pi$
$661$	7.66331e12	−	2.78922e12i	1.56139	−	0.568298i	0.971053	+	0.238863i	$0.0767747\pi$
$662$	9.31721e12	−	3.39119e12i	1.88549	−	0.686264i
$663$	−1.44847e11	−	2.72237e12i	−0.0291137	−	0.547187i
$664$	−2.62571e11	−	1.48912e12i	−0.0524192	−	0.297284i
$665$	−1.11195e12	+	1.92596e12i	−0.220490	+	0.381899i
$666$	−4.53530e12	+	1.02303e13i	−0.893248	+	2.01490i
$667$	1.16635e12	+	2.02018e12i	0.228173	+	0.395207i
$668$	−1.26788e12	+	1.06387e12i	−0.246367	+	0.206726i
$669$	−4.82628e12	+	6.41530e12i	−0.931525	+	1.23823i
$670$	2.68061e11	−	1.52025e12i	0.0513922	−	0.291459i
$671$	−5.89749e12	−	4.94858e12i	−1.12309	−	0.942387i
$672$	4.01852e12	+	4.30246e12i	0.760159	+	0.813870i
$673$	−4.81771e12	−	1.75350e12i	−0.905259	−	0.329488i	−0.152901	−	0.988241i	$-0.548862\pi$
$673$	−4.81771e12	−	1.75350e12i	−0.905259	−	0.329488i	−0.752358	+	0.658754i	$0.771084\pi$
$674$	−8.63337e11			−0.161143
$675$	2.26803e12	−	7.87011e11i	0.420516	−	0.145920i
$676$	1.41660e11			0.0260907
$677$	6.84175e12	+	2.49019e12i	1.25175	+	0.455600i	0.880993	−	0.473129i	$-0.156876\pi$
$677$	6.84175e12	+	2.49019e12i	1.25175	+	0.455600i	0.370758	+	0.928729i	$0.379098\pi$
$678$	−2.92726e12	+	9.60197e12i	−0.532020	+	1.74513i
$679$	5.16273e12	+	4.33204e12i	0.932106	+	0.782130i
$680$	1.12985e11	−	6.40768e11i	0.0202642	−	0.114924i
$681$	−7.85855e11	−	1.84727e12i	−0.140017	−	0.329131i
$682$	8.31183e11	−	6.97445e11i	0.147118	−	0.123447i
$683$	−2.90528e12	−	5.03209e12i	−0.510852	−	0.884821i	−0.999921	−	0.0125764i	$-0.995997\pi$
$683$	−2.90528e12	−	5.03209e12i	−0.510852	−	0.884821i	0.489069	−	0.872245i	$-0.337337\pi$
$684$	−8.39163e11	−	2.90902e12i	−0.146586	−	0.508153i
$685$	7.35520e11	−	1.27396e12i	0.127640	−	0.221079i
$686$	−1.45209e12	−	8.23523e12i	−0.250343	−	1.41977i
$687$	3.89697e12	−	2.53513e12i	0.667454	−	0.434206i
$688$	−6.79244e12	+	2.47225e12i	−1.15579	+	0.420672i
$689$	6.43349e12	−	2.34160e12i	1.08758	−	0.395846i
$690$	7.39799e12	−	4.81269e12i	1.24249	−	0.808290i
$691$	−6.33947e11	−	3.59529e12i	−0.105780	−	0.599906i	−0.990906	−	0.134555i	$-0.957039\pi$
$691$	−6.33947e11	−	3.59529e12i	−0.105780	−	0.599906i	0.885127	−	0.465350i	$-0.154072\pi$
$692$	−1.18779e12	+	2.05732e12i	−0.196908	+	0.341055i
$693$	7.91185e12	+	1.95927e12i	1.30310	+	0.322697i
$694$	4.21326e11	+	7.29759e11i	0.0689447	+	0.119416i
$695$	2.11168e12	−	1.77191e12i	0.343318	−	0.288078i
$696$	−2.15638e11	−	5.06889e11i	−0.0348324	−	0.0818788i
$697$	−4.84438e11	+	2.74738e12i	−0.0777482	+	0.440932i
$698$	−8.61788e12	−	7.23126e12i	−1.37420	−	1.15309i
$699$	1.01070e12	−	3.31528e12i	0.160130	−	0.525258i
$700$	1.82020e12	+	6.62500e11i	0.286536	+	0.104290i
$701$	−8.36387e12			−1.30821			−0.654103	−	0.756406i	$-0.726954\pi$
$701$	−8.36387e12			−1.30821			−0.654103	+	0.756406i	$0.726954\pi$
$702$	−6.77319e12	+	5.51166e12i	−1.05263	+	0.856574i
$703$	−7.22763e12			−1.11608
$704$	4.95316e12	+	1.80280e12i	0.759986	+	0.276612i
$705$	2.16905e12	+	2.32231e12i	0.330688	+	0.354054i
$706$	−3.75650e12	−	3.15208e12i	−0.569065	−	0.477502i
$707$	−6.03589e11	+	3.42312e12i	−0.0908561	+	0.515271i
$708$	−4.43217e12	+	5.89144e12i	−0.662929	+	0.881195i
$709$	1.65540e12	−	1.38905e12i	0.246034	−	0.206447i	−0.511428	−	0.859326i	$-0.670883\pi$
$709$	1.65540e12	−	1.38905e12i	0.246034	−	0.206447i	0.757462	+	0.652879i	$0.226439\pi$
$710$	5.13131e12	+	8.88769e12i	0.757819	+	1.31258i
$711$	5.39756e12	−	5.75997e11i	0.792107	−	0.0845292i
$712$	−1.32989e12	+	2.30343e12i	−0.193934	+	0.335904i
$713$	−1.67598e11	−	9.50493e11i	−0.0242865	−	0.137736i
$714$	2.32515e11	+	4.37007e12i	0.0334818	+	0.629284i
$715$	7.62339e12	−	2.77469e12i	1.09087	−	0.397042i
$716$	−7.98060e12	+	2.90470e12i	−1.13482	+	0.413041i
$717$	−2.95838e12	−	1.50441e12i	−0.418041	−	0.212583i
$718$	−1.30552e12	−	7.40396e12i	−0.183325	−	1.03969i
$719$	−1.68778e10	+	2.92332e10i	−0.00235524	+	0.00407940i	−0.867201	−	0.497959i	$-0.834083\pi$
$719$	−1.68778e10	+	2.92332e10i	−0.00235524	+	0.00407940i	0.864845	+	0.502038i	$0.167416\pi$
$720$	−5.64571e12	+	2.76473e12i	−0.782928	+	0.383404i
$721$	−4.90512e12	−	8.49591e12i	−0.675990	−	1.17085i
$722$	−4.05451e12	+	3.40213e12i	−0.555291	+	0.465944i
$723$	1.17874e13	+	1.43778e12i	1.60433	+	0.195691i
$724$	5.04588e11	−	2.86166e12i	0.0682516	−	0.387074i
$725$	−7.76617e11	−	6.51659e11i	−0.104396	−	0.0875991i
$726$	1.31454e13	−	3.04587e12i	1.75613	−	0.406909i
$727$	8.71148e11	+	3.17072e11i	0.115661	+	0.0420972i	0.399202	−	0.916863i	$-0.369287\pi$
$727$	8.71148e11	+	3.17072e11i	0.115661	+	0.0420972i	−0.283541	+	0.958960i	$0.591509\pi$
$728$	1.96060e12			0.258701
$729$	1.54980e12	−	7.46645e12i	0.203237	−	0.979130i
$730$	−2.13232e11			−0.0277907
$731$	−4.10993e12	−	1.49589e12i	−0.532361	−	0.193763i
$732$	−5.66142e12	+	1.31179e12i	−0.728828	+	0.168875i
$733$	−3.04011e12	−	2.55095e12i	−0.388974	−	0.326388i	0.427239	−	0.904139i	$-0.359486\pi$
$733$	−3.04011e12	−	2.55095e12i	−0.388974	−	0.326388i	−0.816213	+	0.577751i	$0.803931\pi$
$734$	−2.81337e11	+	1.59554e12i	−0.0357763	+	0.202897i
$735$	1.36428e12	+	1.66410e11i	0.172429	+	0.0210322i
$736$	1.15596e13	−	9.69968e12i	1.45209	−	1.21845i
$737$	−1.82712e12	−	3.16466e12i	−0.228119	−	0.395115i
$738$	8.02531e12	−	3.93003e12i	0.995882	−	0.487689i
$739$	−6.78004e12	+	1.17434e13i	−0.836243	+	1.44841i	0.0567720	+	0.998387i	$0.481919\pi$
$739$	−6.78004e12	+	1.17434e13i	−0.836243	+	1.44841i	−0.893015	+	0.450028i	$0.851414\pi$
$740$	−1.36275e12	−	7.72856e12i	−0.167061	−	0.947449i
$741$	−5.02731e12	−	2.55650e12i	−0.612567	−	0.311504i
$742$	−1.03273e13	+	3.75884e12i	−1.25075	+	0.455236i
$743$	7.67068e12	−	2.79190e12i	0.923388	−	0.336086i	0.163803	−	0.986493i	$-0.447624\pi$
$743$	7.67068e12	−	2.79190e12i	0.923388	−	0.336086i	0.759586	+	0.650407i	$0.225402\pi$
$744$	1.21093e10	+	2.27592e11i	0.00144891	+	0.0272320i
$745$	1.31113e11	+	7.43579e11i	0.0155935	+	0.0884349i
$746$	4.26397e12	−	7.38541e12i	0.504068	−	0.873072i
$747$	−8.78968e12	+	9.37986e11i	−1.03283	+	0.110218i
$748$	2.76752e12	+	4.79349e12i	0.323247	+	0.559879i
$749$	5.09810e12	−	4.27781e12i	0.591889	−	0.496654i
$750$	−7.48644e12	+	9.95131e12i	−0.863971	+	1.14843i
$751$	1.40176e12	−	7.94980e12i	0.160803	−	0.911961i	−0.792483	−	0.609894i	$-0.791212\pi$
$751$	1.40176e12	−	7.94980e12i	0.160803	−	0.911961i	0.953287	−	0.302067i	$-0.0976768\pi$
$752$	5.11322e12	+	4.29050e12i	0.583061	+	0.489246i
$753$	−1.18849e13	−	1.27246e13i	−1.34715	−	1.44234i
$754$	3.46524e12	+	1.26124e12i	0.390447	+	0.142111i
$755$	−6.30642e12			−0.706353
$756$	4.77233e12	−	3.88347e12i	0.531352	−	0.432386i
$757$	6.06107e12			0.670838			0.335419	−	0.942069i	$-0.391122\pi$
$757$	6.06107e12			0.670838			0.335419	+	0.942069i	$0.391122\pi$
$758$	2.60141e12	+	9.46835e11i	0.286218	+	0.104175i
$759$	6.09232e12	−	1.99840e13i	0.666338	−	2.18572i
$760$	−1.03115e12	−	8.65236e11i	−0.112114	−	0.0940748i
$761$	−2.52061e12	+	1.42951e13i	−0.272442	+	1.54510i	0.474528	+	0.880241i	$0.342619\pi$
$761$	−2.52061e12	+	1.42951e13i	−0.272442	+	1.54510i	−0.746970	+	0.664858i	$0.768492\pi$
$762$	−4.83665e12	−	1.13693e13i	−0.519694	−	1.22162i
$763$	−4.52424e12	+	3.79629e12i	−0.483265	+	0.405507i
$764$	−6.23978e12	−	1.08076e13i	−0.662597	−	1.14765i
$765$	−3.69216e12	−	9.14317e11i	−0.389766	−	0.0965206i
$766$	5.15213e12	−	8.92376e12i	0.540702	−	0.936523i
$767$	2.38483e12	+	1.35251e13i	0.248816	+	1.41111i
$768$	−1.03859e13	+	6.75644e12i	−1.07725	+	0.700797i
$769$	4.61098e10	−	1.67826e10i	0.00475471	−	0.00173057i	−0.339642	−	0.940555i	$-0.610306\pi$
$769$	4.61098e10	−	1.67826e10i	0.00475471	−	0.00173057i	0.344396	+	0.938824i	$0.388084\pi$
$770$	−1.22374e13	+	4.45406e12i	−1.25453	+	0.456613i
$771$	−7.93909e12	+	5.16469e12i	−0.809144	+	0.526381i
$772$	2.57406e12	+	1.45982e13i	0.260820	+	1.47918i
$773$	7.04257e12	−	1.21981e13i	0.709452	−	1.22881i	−0.255608	−	0.966780i	$-0.582276\pi$
$773$	7.04257e12	−	1.21981e13i	0.709452	−	1.22881i	0.965061	−	0.262027i	$-0.0843910\pi$
$774$	3.88296e12	+	1.34606e13i	0.388891	+	1.34812i
$775$	2.09730e11	+	3.63263e11i	0.0208835	+	0.0361712i
$776$	−3.12486e12	+	2.62207e12i	−0.309352	+	0.259577i
$777$	−5.74981e12	−	1.35158e13i	−0.565925	−	1.33029i
$778$	−3.95020e11	+	2.24027e12i	−0.0386555	+	0.219226i
$779$	4.42119e12	+	3.70982e12i	0.430151	+	0.360940i
$780$	1.78580e12	−	5.85777e12i	0.172746	−	0.566639i
$781$	2.28285e13	+	8.30888e12i	2.19557	+	0.799122i
$782$	1.12171e13			1.07263
$783$	−3.04229e12	+	1.05568e12i	−0.289250	+	0.100370i
$784$	2.88691e12			0.272905
$785$	9.84911e12	+	3.58478e12i	0.925728	+	0.336938i
$786$	−1.08008e13	−	1.15639e13i	−1.00938	−	1.08070i
$787$	1.40617e13	+	1.17992e13i	1.30663	+	1.09639i	0.988958	+	0.148193i	$0.0473458\pi$
$787$	1.40617e13	+	1.17992e13i	1.30663	+	1.09639i	0.317673	+	0.948200i	$0.397099\pi$
$788$	−2.77198e12	+	1.57207e13i	−0.256107	+	1.45246i
$789$	−5.08519e12	+	6.75946e12i	−0.467155	+	0.620963i
$790$	−6.64374e12	+	5.57476e12i	−0.606863	+	0.509218i
$791$	−6.58781e12	−	1.14104e13i	−0.598338	−	1.03635i
$792$	−1.99945e12	+	4.51015e12i	−0.180571	+	0.407313i
$793$	−5.41285e12	+	9.37533e12i	−0.486067	+	0.841893i
$794$	3.77872e12	+	2.14302e13i	0.337406	+	1.91352i
$795$	−5.07519e11	−	9.53873e12i	−0.0450609	−	0.846912i
$796$	5.26973e12	−	1.91803e12i	0.465243	−	0.169335i
$797$	−6.25528e12	+	2.27674e12i	−0.549141	+	0.199871i	−0.601665	−	0.798749i	$-0.705496\pi$
$797$	−6.25528e12	+	2.27674e12i	−0.549141	+	0.199871i	0.0525235	+	0.998620i	$0.483274\pi$
$798$	8.07007e12	+	4.10382e12i	0.704473	+	0.358241i
$799$	7.01325e11	+	3.97741e12i	0.0608777	+	0.345255i
$800$	−3.27909e12	+	5.67954e12i	−0.283040	+	0.490240i
$801$	1.29045e13	+	8.67430e12i	1.10763	+	0.744540i
$802$	1.26200e13	+	2.18585e13i	1.07715	+	1.86567i
$803$	−3.86668e11	+	3.24453e11i	−0.0328185	+	0.0275380i
$804$	−2.73815e12	−	3.33990e11i	−0.231103	−	0.0281891i
$805$	−2.01154e12	+	1.14080e13i	−0.168829	+	0.957480i
$806$	−1.16880e12	−	9.80737e11i	−0.0975509	−	0.0818550i
$807$	9.79255e12	−	2.26900e12i	0.812765	−	0.188323i
$808$	−1.97701e12	−	7.19572e11i	−0.163176	−	0.0593914i
$809$	−6.62977e12			−0.544164			−0.272082	−	0.962274i	$-0.587712\pi$
$809$	−6.62977e12			−0.544164			−0.272082	+	0.962274i	$0.587712\pi$
$810$	4.60001e12	+	1.12819e13i	0.375471	+	0.920870i
$811$	1.99109e13			1.61621			0.808105	−	0.589038i	$-0.200493\pi$
$811$	1.99109e13			1.61621			0.808105	+	0.589038i	$0.200493\pi$
$812$	−2.44158e12	−	8.88662e11i	−0.197092	−	0.0717356i
$813$	1.89473e13	−	4.39022e12i	1.52104	−	0.352435i
$814$	−3.24219e13	−	2.72052e13i	−2.58838	−	2.17191i
$815$	−1.49380e12	+	8.47176e12i	−0.118600	+	0.672612i
$816$	−7.93090e12	−	9.67383e11i	−0.626205	−	0.0763823i
$817$	−6.93139e12	+	5.81613e12i	−0.544278	+	0.456704i
$818$	9.83479e12	+	1.70344e13i	0.768024	+	1.33026i
$819$	7.81313e11	−	1.14349e13i	0.0606803	−	0.888088i
$820$	−3.13334e12	+	5.42710e12i	−0.242016	+	0.419185i
$821$	2.91273e11	+	1.65189e12i	0.0223747	+	0.126893i	0.993949	−	0.109841i	$-0.0350341\pi$
$821$	2.91273e11	+	1.65189e12i	0.0223747	+	0.126893i	−0.971575	+	0.236734i	$0.923923\pi$
$822$	−5.33810e12	−	2.71455e12i	−0.407815	−	0.207383i
$823$	−8.37838e12	+	3.04948e12i	−0.636591	+	0.231700i	−0.640098	−	0.768294i	$-0.721106\pi$
$823$	−8.37838e12	+	3.04948e12i	−0.636591	+	0.231700i	0.00350637	+	0.999994i	$0.498884\pi$
$824$	5.57977e12	−	2.03087e12i	0.421642	−	0.153465i
$825$	4.82415e11	+	9.06691e12i	0.0362559	+	0.681422i
$826$	−3.82825e12	−	2.17111e13i	−0.286147	−	1.62282i
$827$	6.42068e12	−	1.11209e13i	0.477316	−	0.826736i	−0.522346	−	0.852734i	$-0.674943\pi$
$827$	6.42068e12	−	1.11209e13i	0.477316	−	0.826736i	0.999662	+	0.0259981i	$0.00827639\pi$
$828$	−9.29002e12	−	1.27439e13i	−0.686879	−	0.942249i
$829$	−2.06311e12	−	3.57341e12i	−0.151714	−	0.262777i	0.780143	−	0.625601i	$-0.215146\pi$
$829$	−2.06311e12	−	3.57341e12i	−0.151714	−	0.262777i	−0.931858	+	0.362824i	$0.881813\pi$
$830$	1.08190e13	−	9.07825e12i	0.791292	−	0.663973i
$831$	−1.36912e13	+	1.81990e13i	−0.995950	+	1.32386i
$832$	1.28709e12	−	7.29946e12i	0.0931225	−	0.528124i
$833$	1.33812e12	+	1.12282e12i	0.0962928	+	0.0807993i
$834$	−7.66007e12	−	8.20132e12i	−0.548259	−	0.586998i
$835$	4.04228e12	+	1.47127e12i	0.287765	+	0.104738i
$836$	1.14509e13			0.810794
$837$	1.33222e12	+	2.00713e10i	0.0938237	+	0.00141355i
$838$	2.74212e13			1.92083
$839$	−1.47298e13	−	5.36120e12i	−1.02628	−	0.373536i	−0.226618	−	0.973984i	$-0.572767\pi$
$839$	−1.47298e13	−	5.36120e12i	−1.02628	−	0.373536i	−0.799664	+	0.600447i	$0.794989\pi$
$840$	7.97693e11	−	2.61659e12i	0.0552814	−	0.181334i
$841$	−1.00714e13	−	8.45089e12i	−0.694236	−	0.582533i
$842$	2.73778e12	−	1.55267e13i	0.187713	−	1.06457i
$843$	−2.59379e12	−	6.09708e12i	−0.176893	−	0.415812i
$844$	−6.35013e12	+	5.32839e12i	−0.430766	+	0.361456i
$845$	−1.84092e11	−	3.18856e11i	−0.0124216	−	0.0215149i
$846$	8.97170e12	−	9.32012e12i	0.602154	−	0.625539i
$847$	−8.85545e12	+	1.53381e13i	−0.591201	+	1.02399i
$848$	−3.48417e12	−	1.97597e13i	−0.231376	−	1.31220i
$849$	−8.96992e11	+	5.83530e11i	−0.0592522	+	0.0385459i
$850$	−4.58099e12	+	1.66734e12i	−0.301005	+	0.109557i
$851$	−3.53774e13	+	1.28763e13i	−2.31229	+	0.841605i
$852$	1.53718e13	−	9.99999e12i	0.999418	−	0.650162i
$853$	−4.02900e12	−	2.28496e13i	−0.260571	−	1.47777i	−0.781356	−	0.624086i	$-0.785472\pi$
$853$	−4.02900e12	−	2.28496e13i	−0.260571	−	1.47777i	0.520785	−	0.853688i	$-0.325639\pi$
$854$	8.68896e12	−	1.50497e13i	0.558994	−	0.968207i
$855$	−5.45728e12	+	5.66922e12i	−0.349244	+	0.362807i
$856$	2.01408e12	+	3.48848e12i	0.128216	+	0.222077i
$857$	−7.05429e12	+	5.91925e12i	−0.446724	+	0.374846i	−0.838219	−	0.545334i	$-0.816403\pi$
$857$	−7.05429e12	+	5.91925e12i	−0.446724	+	0.374846i	0.391494	+	0.920181i	$0.371958\pi$
$858$	−1.29288e13	−	3.03911e13i	−0.814454	−	1.91449i
$859$	5.29751e12	−	3.00437e13i	0.331973	−	1.88271i	−0.123316	−	0.992367i	$-0.539353\pi$
$859$	5.29751e12	−	3.00437e13i	0.331973	−	1.88271i	0.455289	−	0.890344i	$-0.349536\pi$
$860$	−7.52613e12	−	6.31517e12i	−0.469168	−	0.393679i
$861$	−3.42022e12	+	1.12190e13i	−0.212100	+	0.695728i
$862$	1.16549e13	+	4.24203e12i	0.718993	+	0.261692i
$863$	−2.15230e13			−1.32085			−0.660427	−	0.750890i	$-0.729625\pi$
$863$	−2.15230e13			−1.32085			−0.660427	+	0.750890i	$0.729625\pi$
$864$	1.01428e13	+	1.81954e13i	0.619219	+	1.11084i
$865$	6.17433e12			0.374988
$866$	−2.14946e12	−	7.82339e11i	−0.129867	−	0.0472677i
$867$	8.05655e12	+	8.62581e12i	0.484242	+	0.518458i
$868$	8.23525e11	+	6.91019e11i	0.0492422	+	0.0413192i
$869$	−3.56502e12	+	2.02182e13i	−0.212067	+	1.20269i
$870$	3.09311e12	−	4.11150e12i	0.183045	−	0.243312i
$871$	−3.93634e12	+	3.30298e12i	−0.231745	+	0.194457i
$872$	−1.78736e12	−	3.09581e12i	−0.104686	−	0.181322i
$873$	1.40476e13	+	1.92702e13i	0.818534	+	1.12285i
$874$	1.16030e13	−	2.00969e13i	0.672616	−	1.16500i
$875$	−2.83827e12	−	1.60966e13i	−0.163688	−	0.928322i
$876$	2.02442e10	+	3.80486e11i	0.00116153	+	0.0218308i
$877$	−2.51471e12	+	9.15280e11i	−0.143546	+	0.0522463i	−0.412794	−	0.910824i	$-0.635447\pi$
$877$	−2.51471e12	+	9.15280e11i	−0.143546	+	0.0522463i	0.269248	+	0.963071i	$0.413225\pi$
$878$	1.51358e13	−	5.50898e12i	0.859568	−	0.312857i
$879$	−6.64025e12	−	3.37672e12i	−0.375175	−	0.190785i
$880$	−4.12859e12	−	2.34144e13i	−0.232076	−	1.31617i
$881$	6.65666e11	−	1.15297e12i	0.0372276	−	0.0644801i	−0.846811	−	0.531893i	$-0.821481\pi$
$881$	6.65666e11	−	1.15297e12i	0.0372276	−	0.0644801i	0.884039	+	0.467413i	$0.154814\pi$
$882$	3.81412e11	−	5.58217e12i	0.0212220	−	0.310595i
$883$	−9.43072e12	−	1.63345e13i	−0.522061	−	0.904237i	−0.999671	−	0.0256645i	$-0.991830\pi$
$883$	−9.43072e12	−	1.63345e13i	−0.522061	−	0.904237i	0.477609	−	0.878572i	$-0.341504\pi$
$884$	5.96235e12	−	5.00301e12i	0.328384	−	0.275547i
$885$	1.90206e13	+	2.32007e12i	1.04227	+	0.127132i
$886$	−2.44207e12	+	1.38497e13i	−0.133140	+	0.755072i
$887$	1.09131e13	+	9.15716e12i	0.591958	+	0.496712i	0.888849	−	0.458199i	$-0.151505\pi$
$887$	1.09131e13	+	9.15716e12i	0.591958	+	0.496712i	−0.296891	+	0.954911i	$0.595950\pi$
$888$	8.66079e12	−	2.00676e12i	0.467411	−	0.108302i
$889$	1.52388e13	+	5.54648e12i	0.818264	+	0.297824i
$890$	−2.48429e13			−1.32723
$891$	2.55080e13	+	1.34588e13i	1.35590	+	0.715414i
$892$	−2.29198e13			−1.21219
$893$	7.85150e12	+	2.85771e12i	0.413163	+	0.150379i
$894$	2.99450e12	−	6.93847e11i	0.156785	−	0.0363283i
$895$	1.69092e13	+	1.41885e13i	0.880884	+	0.739149i
$896$	1.66474e12	−	9.44121e12i	0.0862900	−	0.489375i
$897$	−2.91619e13	−	3.55706e12i	−1.50401	−	0.183453i
$898$	−2.59309e13	+	2.17586e13i	−1.33068	+	1.11658i
$899$	−2.81327e11	−	4.87273e11i	−0.0143646	−	0.0248802i
$900$	5.68827e12	+	3.82363e12i	0.288994	+	0.194260i
$901$	6.07027e12	−	1.05140e13i	0.306864	−	0.531504i
$902$	5.86874e12	+	3.32833e13i	0.295199	+	1.67416i
$903$	−1.63904e13	−	8.33489e12i	−0.820341	−	0.417162i
$904$	7.49390e12	−	2.72756e12i	0.373207	−	0.135836i
$905$	−7.09693e12	+	2.58307e12i	−0.351684	+	0.128002i
$906$	1.36407e12	+	2.56374e13i	0.0672603	+	1.26415i
$907$	4.09987e12	+	2.32515e13i	0.201158	+	1.14082i	0.903372	+	0.428858i	$0.141084\pi$
$907$	4.09987e12	+	2.32515e13i	0.201158	+	1.14082i	−0.702214	+	0.711966i	$0.747805\pi$
$908$	2.86566e12	−	4.96346e12i	0.139906	−	0.242325i
$909$	−4.98465e12	+	1.12439e13i	−0.242157	+	0.546233i
$910$	9.15624e12	+	1.58591e13i	0.442620	+	0.766640i
$911$	−1.42123e13	+	1.19255e13i	−0.683645	+	0.573647i	−0.917069	−	0.398729i	$-0.869452\pi$
$911$	−1.42123e13	+	1.19255e13i	−0.683645	+	0.573647i	0.233424	+	0.972375i	$0.425007\pi$
$912$	−9.93690e12	+	1.32086e13i	−0.475636	+	0.632236i
$913$	5.80547e12	−	3.29245e13i	0.276515	−	1.56820i
$914$	2.16369e13	+	1.81556e13i	1.02551	+	0.860501i
$915$	1.03099e13	+	1.10384e13i	0.486249	+	0.520606i
$916$	1.24724e13	+	4.53957e12i	0.585355	+	0.213052i
$917$	2.07689e13			0.969954
$918$	−2.91835e12	+	1.52075e13i	−0.135627	+	0.706748i
$919$	−3.57972e13			−1.65550			−0.827750	−	0.561097i	$-0.810380\pi$
$919$	−3.57972e13			−1.65550			−0.827750	+	0.561097i	$0.810380\pi$
$920$	−6.58866e12	−	2.39807e12i	−0.303216	−	0.110361i
$921$	−9.67679e12	+	3.17417e13i	−0.443162	+	1.45366i
$922$	−1.48953e13	−	1.24987e13i	−0.678830	−	0.569606i
$923$	5.93204e12	−	3.36423e13i	0.269027	−	1.52573i
$924$	9.10955e12	+	2.14133e13i	0.411124	+	0.966408i
$925$	1.25339e13	−	1.05172e13i	0.562923	−	0.472348i
$926$	−7.18747e12	−	1.24491e13i	−0.321238	−	0.556400i
$927$	−9.62119e12	−	3.33525e13i	−0.427927	−	1.48344i
$928$	4.39849e12	−	7.61842e12i	0.194688	−	0.337209i
$929$	−2.95102e12	−	1.67361e13i	−0.129987	−	0.737195i	−0.978220	−	0.207571i	$-0.933444\pi$
$929$	−2.95102e12	−	1.67361e13i	−0.129987	−	0.737195i	0.848233	−	0.529624i	$-0.177667\pi$
$930$	−1.78441e12	+	1.16083e12i	−0.0782208	+	0.0508858i
$931$	3.39583e12	−	1.23598e12i	0.148140	−	0.0539186i
$932$	9.29838e12	−	3.38433e12i	0.403678	−	0.146927i
$933$	−2.86255e12	+	1.86221e12i	−0.123676	+	0.0804564i
$934$	5.94278e11	+	3.37032e12i	0.0255522	+	0.144914i
$935$	7.19299e12	−	1.24586e13i	0.307792	−	0.533111i
$936$	6.73399e12	+	1.66759e12i	0.286768	+	0.0710145i
$937$	−1.30382e13	−	2.25828e13i	−0.552573	−	0.957084i	−0.998088	−	0.0618095i	$-0.980313\pi$
$937$	−1.30382e13	−	2.25828e13i	−0.552573	−	0.957084i	0.445515	−	0.895274i	$-0.353020\pi$
$938$	6.31880e12	−	5.30210e12i	0.266515	−	0.223633i
$939$	9.01326e12	+	2.11870e13i	0.378344	+	0.889353i
$940$	−1.57539e12	+	8.93449e12i	−0.0658132	+	0.373245i
$941$	−8.89701e11	−	7.46548e11i	−0.0369906	−	0.0310388i	0.624105	−	0.781341i	$-0.285464\pi$
$941$	−8.89701e11	−	7.46548e11i	−0.0369906	−	0.0310388i	−0.661096	+	0.750302i	$0.729908\pi$
$942$	1.24428e13	−	4.08148e13i	0.514861	−	1.68884i
$943$	2.82498e13	+	1.02821e13i	1.16336	+	0.423427i
$944$	4.02491e13			1.64961
$945$	−1.49430e13	−	5.69516e12i	−0.609528	−	0.232307i
$946$	−5.29853e13			−2.15102
$947$	5.36176e12	+	1.95152e12i	0.216637	+	0.0788494i	0.448059	−	0.894004i	$-0.352116\pi$
$947$	5.36176e12	+	1.95152e12i	0.216637	+	0.0788494i	−0.231422	+	0.972854i	$0.574338\pi$
$948$	1.05782e13	+	1.13257e13i	0.425378	+	0.455435i
$949$	5.43727e11	+	4.56241e11i	0.0217612	+	0.0182598i
$950$	−1.75130e12	+	9.93214e12i	−0.0697598	+	0.395628i
$951$	6.57143e12	−	8.73504e12i	0.260524	−	0.346300i
$952$	2.66330e12	−	2.23478e12i	0.105088	−	0.0881795i
$953$	1.43873e11	+	2.49196e11i	0.00565019	+	0.00978641i	0.868837	−	0.495099i	$-0.164868\pi$
$953$	1.43873e11	+	2.49196e11i	0.00565019	+	0.00978641i	−0.863186	+	0.504885i	$0.831535\pi$
$954$	−3.86679e13	+	4.12642e12i	−1.51141	+	0.161289i
$955$	−1.62177e13	+	2.80898e13i	−0.630918	+	1.09278i
$956$	−1.64540e12	−	9.33151e12i	−0.0637104	−	0.361320i
$957$	−6.47101e11	−	1.21621e13i	−0.0249384	−	0.468713i
$958$	−5.01292e13	+	1.82455e13i	−1.92285	+	0.699861i
$959$	7.38632e12	−	2.68840e12i	0.281997	−	0.102638i
$960$	−9.21807e12	−	4.68760e12i	−0.350283	−	0.178127i
$961$	−4.55077e12	−	2.58087e13i	−0.172119	−	0.976137i
$962$	−2.97576e13	+	5.15416e13i	−1.12024	+	1.94031i
$963$	2.11487e13	−	1.03566e13i	0.792437	−	0.388061i
$964$	1.69510e13	+	2.93601e13i	0.632193	+	1.09499i
$965$	2.95135e13	−	2.47648e13i	1.09559	−	0.919308i
$966$	4.68120e13	+	5.70997e12i	1.72966	+	0.210978i
$967$	−6.84793e12	+	3.88366e13i	−0.251849	+	1.42831i	0.552184	+	0.833722i	$0.313795\pi$
$967$	−6.84793e12	+	3.88366e13i	−0.251849	+	1.42831i	−0.804033	+	0.594585i	$0.797317\pi$
$968$	−8.21195e12	−	6.89065e12i	−0.300613	−	0.252244i
$969$	−9.74316e12	+	2.25756e12i	−0.355012	+	0.0822587i
$970$	−3.58031e13	−	1.30312e13i	−1.29852	−	0.472621i
$971$	1.27040e13			0.458621			0.229310	−	0.973353i	$-0.426353\pi$
$971$	1.27040e13			0.458621			0.229310	+	0.973353i	$0.426353\pi$
$972$	1.96944e13	−	9.27926e12i	0.707691	−	0.333438i
$973$	1.47296e13			0.526846
$974$	−6.36803e12	−	2.31777e12i	−0.226720	−	0.0825194i
$975$	1.24383e13	−	2.88203e12i	0.440797	−	0.102136i
$976$	2.43040e13	+	2.03935e13i	0.857342	+	0.719396i
$977$	5.08942e12	−	2.88636e13i	0.178708	−	1.01350i	−0.755069	−	0.655645i	$-0.772397\pi$
$977$	5.08942e12	−	2.88636e13i	0.178708	−	1.01350i	0.933777	−	0.357856i	$-0.116492\pi$
$978$	3.47632e13	+	4.24030e12i	1.21505	+	0.148208i
$979$	−4.50494e13	+	3.78009e13i	−1.56735	+	1.31516i
$980$	1.96192e12	+	3.39815e12i	0.0679461	+	0.117686i
$981$	−1.87681e13	+	9.19084e12i	−0.647009	+	0.316843i
$982$	6.52020e12	−	1.12933e13i	0.223748	−	0.387543i
$983$	1.89206e12	+	1.07304e13i	0.0646313	+	0.366542i	0.999920	+	0.0126565i	$0.00402878\pi$
$983$	1.89206e12	+	1.07304e13i	0.0646313	+	0.366542i	−0.935289	+	0.353886i	$0.884860\pi$
$984$	−6.32791e12	−	3.21789e12i	−0.215170	−	0.109419i
$985$	3.89874e13	−	1.41903e13i	1.31966	−	0.480316i
$986$	6.14484e12	−	2.23654e12i	0.207045	−	0.0753582i
$987$	9.02154e11	+	1.69558e13i	0.0302589	+	0.568711i
$988$	−2.79609e12	−	1.58574e13i	−0.0933567	−	0.529452i
$989$	−2.35657e13	+	4.08170e13i	−0.783244	+	1.35662i
$990$	−4.58197e13	+	4.88962e12i	−1.51598	+	0.161777i
$991$	−1.26571e13	−	2.19228e13i	−0.416873	−	0.722046i	0.578750	−	0.815505i	$-0.303541\pi$
$991$	−1.26571e13	−	2.19228e13i	−0.416873	−	0.722046i	−0.995623	+	0.0934592i	$0.970208\pi$
$992$	−2.78821e12	+	2.33959e12i	−0.0914162	+	0.0767073i
$993$	−2.76836e13	+	3.67983e13i	−0.903549	+	1.20104i
$994$	−9.52239e12	+	5.40041e13i	−0.309391	+	1.75464i
$995$	−1.11654e13	−	9.36890e12i	−0.361136	−	0.303029i
$996$	−1.72262e13	−	1.84434e13i	−0.554654	−	0.593845i
$997$	−2.92836e13	−	1.06584e13i	−0.938635	−	0.341635i	−0.173008	−	0.984920i	$-0.555349\pi$
$997$	−2.92836e13	−	1.06584e13i	−0.938635	−	0.341635i	−0.765627	+	0.643285i	$0.777571\pi$
$998$	6.54564e12			0.208864
$999$	−8.25278e12	−	5.13125e13i	−0.262153	−	1.62997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.e.a.4.6	✓	156
3.2	odd	2		81.10.e.a.64.21		156
27.7	even	9	inner	27.10.e.a.7.6	yes	156
27.20	odd	18		81.10.e.a.19.21		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.6	✓	156	1.1	even	1	trivial
27.10.e.a.7.6	yes	156	27.7	even	9	inner
81.10.e.a.19.21		156	27.20	odd	18
81.10.e.a.64.21		156	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-28.3865 - 10.3319i) q^{2} +(136.675 - 31.6686i) q^{3} +(306.833 + 257.464i) q^{4} +(180.775 - 1025.22i) q^{5} +(-4206.93 - 513.146i) q^{6} +(4261.26 - 3575.62i) q^{7} +(1683.47 + 2915.86i) q^{8} +(17677.2 - 8656.62i) q^{9} +(-15724.0 + 27234.8i) q^{10} +(12927.0 + 73312.5i) q^{11} +(50090.0 + 25471.9i) q^{12} +(98368.2 - 35803.1i) q^{13} +(-157905. + 57472.8i) q^{14} +(-7759.98 - 145847. i) q^{15} +(-53273.1 - 302127. i) q^{16} +(92814.6 - 160760. i) q^{17} +(-591233. + 63093.1i) q^{18} +(-192015. - 332579. i) q^{19} +(319426. - 268030. i) q^{20} +(469174. - 623647. i) q^{21} +(390502. - 2.21465e6i) q^{22} +(-1.53236e6 - 1.28581e6i) q^{23} +(322430. + 345212. i) q^{24} +(816933. + 297339. i) q^{25} -3.16225e6 q^{26} +(2.14189e6 - 1.74296e6i) q^{27} +2.22809e6 q^{28} +(-1.09582e6 - 398845. i) q^{29} +(-1.28660e6 + 4.22028e6i) q^{30} +(369610. + 310140. i) q^{31} +(-1.30994e6 + 7.42905e6i) q^{32} +(4.08850e6 + 9.61062e6i) q^{33} +(-4.29563e6 + 3.60446e6i) q^{34} +(-2.89549e6 - 5.01513e6i) q^{35} +(7.65272e6 + 1.89510e6i) q^{36} +(9.41026e6 - 1.62991e7i) q^{37} +(2.01447e6 + 1.14246e7i) q^{38} +(1.23107e7 - 8.00858e6i) q^{39} +(3.29374e6 - 1.19882e6i) q^{40} +(-1.41224e7 + 5.14012e6i) q^{41} +(-1.97617e7 + 1.28557e7i) q^{42} +(-4.09140e6 - 2.32035e7i) q^{43} +(-1.49089e7 + 2.58229e7i) q^{44} +(-5.67938e6 - 1.96880e7i) q^{45} +(3.02137e7 + 5.23317e7i) q^{46} +(-1.66670e7 + 1.39852e7i) q^{47} +(-1.68490e7 - 3.96061e7i) q^{48} +(-1.63405e6 + 9.26718e6i) q^{49} +(-2.01178e7 - 1.68809e7i) q^{50} +(7.59442e6 - 2.49111e7i) q^{51} +(3.94006e7 + 1.43407e7i) q^{52} +6.54021e7 q^{53} +(-7.88089e7 + 2.73468e7i) q^{54} +7.74985e7 q^{55} +(1.75997e7 + 6.40578e6i) q^{56} +(-3.67759e7 - 3.93744e7i) q^{57} +(2.69856e7 + 2.26436e7i) q^{58} +(-2.27818e7 + 1.29202e8i) q^{59} +(3.51694e7 - 4.67488e7i) q^{60} +(-7.92211e7 + 6.64744e7i) q^{61} +(-7.28763e6 - 1.26225e7i) q^{62} +(4.43744e7 - 1.00095e8i) q^{63} +(3.54030e7 - 6.13198e7i) q^{64} +(-1.89237e7 - 1.07322e8i) q^{65} +(-1.67628e7 - 3.15054e8i) q^{66} +(-4.61270e7 + 1.67889e7i) q^{67} +(6.98683e7 - 2.54300e7i) q^{68} +(-2.50156e8 - 1.27210e8i) q^{69} +(3.03772e7 + 1.72278e8i) q^{70} +(1.63168e8 - 2.82615e8i) q^{71} +(5.50006e7 + 3.69711e7i) q^{72} +(3.39022e6 + 5.87204e6i) q^{73} +(-4.35524e8 + 3.65448e8i) q^{74} +(1.21071e8 + 1.47678e7i) q^{75} +(2.67106e7 - 1.51483e8i) q^{76} +(3.17223e8 + 2.66182e8i) q^{77} +(-4.32200e8 + 1.00144e8i) q^{78} +(2.59150e8 + 9.43227e7i) q^{79} -3.19378e8 q^{80} +(2.37546e8 - 3.06050e8i) q^{81} +4.53992e8 q^{82} +(-4.22014e8 - 1.53600e8i) q^{83} +(3.04525e8 - 7.05605e7i) q^{84} +(-1.48036e8 - 1.24217e8i) q^{85} +(-1.23594e8 + 7.00939e8i) q^{86} +(-1.62402e8 - 1.98092e7i) q^{87} +(-1.92007e8 + 1.61113e8i) q^{88} +(3.94983e8 + 6.84131e8i) q^{89} +(-4.21954e7 + 6.17552e8i) q^{90} +(2.91154e8 - 5.04294e8i) q^{91} +(-1.39132e8 - 7.89056e8i) q^{92} +(6.03382e7 + 3.06834e7i) q^{93} +(6.17611e8 - 2.24792e8i) q^{94} +(-3.75679e8 + 1.36736e8i) q^{95} +(5.62310e7 + 1.05685e9i) q^{96} +(2.10383e8 + 1.19314e9i) q^{97} +(1.42132e8 - 2.46180e8i) q^{98} +(8.63151e8 + 1.18406e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17}+ \cdots + 5248107342 q^{99}+O(q^{100}) \) 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

Introduction

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