LMFDB - Embedded newform 27.9.f.a.2.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,9,Mod(2,27)]

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([1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, 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:	$10.9992224717$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.13
Character	$\chi$	$=$	27.2
Dual form			27.9.f.a.14.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.99728 + 0.352174i) q^{2} +(77.6955 + 22.9000i) q^{3} +(-236.696 - 86.1504i) q^{4} +(67.5893 + 80.5497i) q^{5} +(147.115 + 73.1000i) q^{6} +(3385.55 - 1232.24i) q^{7} +(-892.041 - 515.020i) q^{8} +(5512.18 + 3558.45i) q^{9} +(106.627 + 184.683i) q^{10} +(5656.92 - 6741.66i) q^{11} +(-16417.4 - 12113.8i) q^{12} +(4915.16 + 27875.3i) q^{13} +(7195.84 - 1268.82i) q^{14} +(3406.79 + 7806.14i) q^{15} +(47796.6 + 40106.1i) q^{16} +(115312. - 66575.1i) q^{17} +(9756.17 + 9048.46i) q^{18} +(56477.6 - 97822.1i) q^{19} +(-9058.73 - 24888.7i) q^{20} +(291260. - 18210.4i) q^{21} +(13672.7 - 11472.7i) q^{22} +(-141378. + 388433. i) q^{23} +(-57513.6 - 60442.5i) q^{24} +(65911.4 - 373802. i) q^{25} +57405.7i q^{26} +(346783. + 402705. i) q^{27} -907504. q^{28} +(-970128. - 171060. i) q^{29} +(4055.19 + 16790.8i) q^{30} +(-23816.5 - 8668.51i) q^{31} +(250836. + 298934. i) q^{32} +(593901. - 394253. i) q^{33} +(253755. - 92359.3i) q^{34} +(328083. + 189419. i) q^{35} +(-998151. - 1.31715e6i) q^{36} +(-54478.7 - 94360.0i) q^{37} +(147252. - 175488. i) q^{38} +(-256457. + 2.27834e6i) q^{39} +(-18807.6 - 106663. i) q^{40} +(-4.20215e6 + 740952. i) q^{41} +(588140. + 66202.9i) q^{42} +(-3.87489e6 - 3.25142e6i) q^{43} +(-1.91977e6 + 1.10838e6i) q^{44} +(85931.9 + 684518. i) q^{45} +(-419167. + 726019. i) q^{46} +(917770. + 2.52155e6i) q^{47} +(2.79515e6 + 4.21060e6i) q^{48} +(5.52741e6 - 4.63805e6i) q^{49} +(263287. - 723374. i) q^{50} +(1.04838e7 - 2.53196e6i) q^{51} +(1.23806e6 - 7.02141e6i) q^{52} +4.76381e6i q^{53} +(550801. + 926441. i) q^{54} +925386. q^{55} +(-3.65467e6 - 644417. i) q^{56} +(6.62818e6 - 6.30700e6i) q^{57} +(-1.87737e6 - 683308. i) q^{58} +(1.05864e7 + 1.26163e7i) q^{59} +(-133873. - 2.14118e6i) q^{60} +(-1.05057e6 + 382376. i) q^{61} +(-44515.4 - 25701.0i) q^{62} +(2.30466e7 + 5.25498e6i) q^{63} +(-7.59072e6 - 1.31475e7i) q^{64} +(-1.91313e6 + 2.27998e6i) q^{65} +(1.32503e6 - 578276. i) q^{66} +(-1.51350e6 - 8.58350e6i) q^{67} +(-3.30293e7 + 5.82395e6i) q^{68} +(-1.98795e7 + 2.69419e7i) q^{69} +(588565. + 493864. i) q^{70} +(-9.87592e6 + 5.70186e6i) q^{71} +(-3.08442e6 - 6.01317e6i) q^{72} +(1.01458e7 - 1.75731e7i) q^{73} +(-75578.1 - 207649. i) q^{74} +(1.36811e7 - 2.75334e7i) q^{75} +(-2.17954e7 + 1.82886e7i) q^{76} +(1.08444e7 - 2.97949e7i) q^{77} +(-1.31459e6 + 4.46016e6i) q^{78} +(-3.73057e6 + 2.11571e7i) q^{79} +6.56074e6i q^{80} +(1.77216e7 + 3.92297e7i) q^{81} -8.65380e6 q^{82} +(8.64355e6 + 1.52409e6i) q^{83} +(-7.05089e7 - 2.07818e7i) q^{84} +(1.31564e7 + 4.78855e6i) q^{85} +(-6.59417e6 - 7.85863e6i) q^{86} +(-7.14573e7 - 3.55065e7i) q^{87} +(-8.51829e6 + 3.10040e6i) q^{88} +(-1.19561e7 - 6.90285e6i) q^{89} +(-69439.4 + 1.39744e6i) q^{90} +(5.09895e7 + 8.83163e7i) q^{91} +(6.69273e7 - 7.97608e7i) q^{92} +(-1.65193e6 - 1.21890e6i) q^{93} +(945017. + 5.35946e6i) q^{94} +(1.16968e7 - 2.06247e6i) q^{95} +(1.26432e7 + 2.89700e7i) q^{96} +(-5.38212e7 - 4.51614e7i) q^{97} +(1.26732e7 - 7.31687e6i) q^{98} +(5.51718e7 - 1.70314e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17}+ \cdots + 228876057 q^{99}+O(q^{100}) $ 138 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 447 * q^5 - 774 * q^6 - 6 * q^7 - 9 * q^8 - 12960 * q^9 - 3 * q^10 + 28668 * q^11 + 77421 * q^12 - 6 * q^13 - 120975 * q^14 + 105507 * q^15 - 774 * q^16 - 9 * q^17 - 241317 * q^18 - 3 * q^19 + 137913 * q^20 + 1164372 * q^21 - 185478 * q^22 + 68376 * q^23 - 2624256 * q^24 + 507585 * q^25 + 3500568 * q^27 - 12 * q^28 - 943980 * q^29 - 1533627 * q^30 + 920739 * q^31 - 3005136 * q^32 - 1245285 * q^33 + 660474 * q^34 + 6225408 * q^35 + 4021128 * q^36 - 3 * q^37 - 23716884 * q^38 - 5699685 * q^39 - 975273 * q^40 + 16694382 * q^41 + 1594134 * q^42 + 4412514 * q^43 + 17341119 * q^44 + 12986721 * q^45 - 3 * q^46 - 11341869 * q^47 - 26229183 * q^48 + 11347482 * q^49 - 40948977 * q^50 - 16497396 * q^51 + 14465511 * q^52 + 34106454 * q^54 - 12 * q^55 + 52215771 * q^56 + 26766582 * q^57 - 19078611 * q^58 + 76116738 * q^59 - 24031170 * q^60 + 34059450 * q^61 - 223709616 * q^62 - 149069421 * q^63 + 100663293 * q^64 + 20396037 * q^65 + 83336805 * q^66 - 103603884 * q^67 + 101921427 * q^68 + 38038563 * q^69 + 135373629 * q^70 + 125718795 * q^71 + 183269700 * q^72 - 7632642 * q^73 - 66643887 * q^74 - 167459145 * q^75 - 203790342 * q^76 - 343269159 * q^77 - 344470788 * q^78 - 68767890 * q^79 + 151392924 * q^81 - 12 * q^82 + 383244663 * q^83 + 836800692 * q^84 + 170435619 * q^85 + 71426730 * q^86 - 145695735 * q^87 - 192774918 * q^88 + 135692730 * q^89 - 821329020 * q^90 + 77546796 * q^91 - 1343159175 * q^92 - 414573177 * q^93 - 44451609 * q^94 + 881099997 * q^95 + 1578184830 * q^96 + 31339344 * q^97 + 1293135102 * q^98 + 228876057 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	1.99728	+	0.352174i	0.124830	+	0.0220109i	0.235714	−	0.971822i	$-0.424257\pi$
$2$	1.99728	+	0.352174i	0.124830	+	0.0220109i	−0.110884	+	0.993833i	$0.535368\pi$
$3$	77.6955	+	22.9000i	0.959204	+	0.282716i
$3$	77.6955	+	22.9000i	0.959204	+	0.282716i
$4$	−236.696	−	86.1504i	−0.924595	−	0.336525i
$5$	67.5893	+	80.5497i	0.108143	+	0.128880i	0.817401	−	0.576070i	$-0.195414\pi$
$5$	67.5893	+	80.5497i	0.108143	+	0.128880i	−0.709258	+	0.704949i	$0.750970\pi$
$6$	147.115	+	73.1000i	0.113514	+	0.0564043i
$7$	3385.55	−	1232.24i	1.41006	−	0.513219i	0.478910	−	0.877864i	$-0.341032\pi$
$7$	3385.55	−	1232.24i	1.41006	−	0.513219i	0.931146	+	0.364645i	$0.118810\pi$
$8$	−892.041	−	515.020i	−0.217783	−	0.125737i
$9$	5512.18	+	3558.45i	0.840144	+	0.542364i
$10$	106.627	+	184.683i	0.0106627	+	0.0184683i
$11$	5656.92	−	6741.66i	0.386375	−	0.460464i	−0.537440	−	0.843302i	$-0.680609\pi$
$11$	5656.92	−	6741.66i	0.386375	−	0.460464i	0.923816	+	0.382838i	$0.125053\pi$
$12$	−16417.4	−	12113.8i	−0.791734	−	0.584193i
$13$	4915.16	+	27875.3i	0.172093	+	0.975991i	0.941445	+	0.337165i	$0.109468\pi$
$13$	4915.16	+	27875.3i	0.172093	+	0.975991i	−0.769352	+	0.638825i	$0.779421\pi$
$14$	7195.84	−	1268.82i	0.187314	−	0.0330284i
$15$	3406.79	+	7806.14i	0.0672947	+	0.154195i
$16$	47796.6	+	40106.1i	0.729318	+	0.611971i
$17$	115312.	−	66575.1i	1.38063	−	0.797106i	0.388395	−	0.921493i	$-0.373030\pi$
$17$	115312.	−	66575.1i	1.38063	−	0.797106i	0.992234	+	0.124386i	$0.0396963\pi$
$18$	9756.17	+	9048.46i	0.0929371	+	0.0861956i
$19$	56477.6	−	97822.1i	0.433373	−	0.750624i	−0.563788	−	0.825919i	$-0.690657\pi$
$19$	56477.6	−	97822.1i	0.433373	−	0.750624i	0.997161	+	0.0752952i	$0.0239899\pi$
$20$	−9058.73	−	24888.7i	−0.0566171	−	0.155554i
$21$	291260.	−	18210.4i	1.49763	−	0.0936359i
$22$	13672.7	−	11472.7i	0.0583664	−	0.0489752i
$23$	−141378.	+	388433.i	−0.505208	+	1.38805i	0.380920	+	0.924608i	$0.375607\pi$
$23$	−141378.	+	388433.i	−0.505208	+	1.38805i	−0.886128	+	0.463440i	$0.846615\pi$
$24$	−57513.6	−	60442.5i	−0.173351	−	0.182179i
$25$	65911.4	−	373802.i	0.168733	−	0.956933i
$26$			57405.7i			0.125621i
$27$	346783.	+	402705.i	0.652534	+	0.757760i
$28$	−907504.			−1.47644
$29$	−970128.	−	171060.i	−1.37163	−	0.241855i	−0.561195	−	0.827684i	$-0.689658\pi$
$29$	−970128.	−	171060.i	−1.37163	−	0.241855i	−0.810435	+	0.585828i	$0.800769\pi$
$30$	4055.19	+	16790.8i	0.00500641	+	0.0207294i
$31$	−23816.5	−	8668.51i	−0.0257888	−	0.00938637i	0.329094	−	0.944297i	$-0.393257\pi$
$31$	−23816.5	−	8668.51i	−0.0257888	−	0.00938637i	−0.354882	+	0.934911i	$0.615479\pi$
$32$	250836.	+	298934.i	0.239215	+	0.285086i
$33$	593901.	−	394253.i	0.500793	−	0.332444i
$34$	253755.	−	92359.3i	0.189889	−	0.0691139i
$35$	328083.	+	189419.i	0.218631	+	0.126227i
$36$	−998151.	−	1.31715e6i	−0.594273	−	0.784196i
$37$	−54478.7	−	94360.0i	−0.0290683	−	0.0503478i	0.851125	−	0.524963i	$-0.175921\pi$
$37$	−54478.7	−	94360.0i	−0.0290683	−	0.0503478i	−0.880194	+	0.474615i	$0.842587\pi$
$38$	147252.	−	175488.i	0.0706198	−	0.0841614i
$39$	−256457.	+	2.27834e6i	−0.110855	+	0.984827i
$40$	−18807.6	−	106663.i	−0.00734674	−	0.0416654i
$41$	−4.20215e6	+	740952.i	−1.48708	+	0.262213i	−0.857405	−	0.514642i	$-0.827925\pi$
$41$	−4.20215e6	+	740952.i	−1.48708	+	0.262213i	−0.629679	+	0.776855i	$0.716814\pi$
$42$	588140.	+	66202.9i	0.189010	+	0.0212755i
$43$	−3.87489e6	−	3.25142e6i	−1.13341	−	0.951041i	−0.134204	−	0.990954i	$-0.542848\pi$
$43$	−3.87489e6	−	3.25142e6i	−1.13341	−	0.951041i	−0.999203	+	0.0399123i	$0.987292\pi$
$44$	−1.91977e6	+	1.10838e6i	−0.512198	+	0.295718i
$45$	85931.9	+	684518.i	0.0209558	+	0.166930i
$46$	−419167.	+	726019.i	−0.0936172	+	0.162150i
$47$	917770.	+	2.52155e6i	0.188080	+	0.516745i	0.997514	−	0.0704651i	$-0.0224483\pi$
$47$	917770.	+	2.52155e6i	0.188080	+	0.516745i	−0.809434	+	0.587210i	$0.800226\pi$
$48$	2.79515e6	+	4.21060e6i	0.526551	+	0.793194i
$49$	5.52741e6	−	4.63805e6i	0.958821	−	0.804547i
$50$	263287.	−	723374.i	0.0421259	−	0.115740i
$51$	1.04838e7	−	2.53196e6i	1.54966	−	0.374262i
$52$	1.23806e6	−	7.02141e6i	0.169328	−	0.960309i
$53$			4.76381e6i			0.603742i	0.953349	+	0.301871i	$0.0976111\pi$
$53$			4.76381e6i			0.603742i	−0.953349	+	0.301871i	$0.902389\pi$
$54$	550801.	+	926441.i	0.0647768	+	0.108954i
$55$	925386.			0.101128
$56$	−3.65467e6	−	644417.i	−0.371618	−	0.0655262i
$57$	6.62818e6	−	6.30700e6i	0.627906	−	0.597480i
$58$	−1.87737e6	−	683308.i	−0.165897	−	0.0603816i
$59$	1.05864e7	+	1.26163e7i	0.873652	+	1.04118i	0.998797	+	0.0490398i	$0.0156161\pi$
$59$	1.05864e7	+	1.26163e7i	0.873652	+	1.04118i	−0.125144	+	0.992139i	$0.539939\pi$
$60$	−133873.	−	2.14118e6i	−0.0103297	−	0.165215i
$61$	−1.05057e6	+	382376.i	−0.0758761	+	0.0276166i	−0.379679	−	0.925118i	$-0.623966\pi$
$61$	−1.05057e6	+	382376.i	−0.0758761	+	0.0276166i	0.303803	+	0.952735i	$0.401743\pi$
$62$	−44515.4	−	25701.0i	−0.00301262	−	0.00173933i
$63$	2.30466e7	+	5.25498e6i	1.46300	+	0.333587i
$64$	−7.59072e6	−	1.31475e7i	−0.452442	−	0.783653i
$65$	−1.91313e6	+	2.27998e6i	−0.107175	+	0.127726i
$66$	1.32503e6	−	578276.i	0.0698313	−	0.0304761i
$67$	−1.51350e6	−	8.58350e6i	−0.0751076	−	0.425956i	−0.999056	−	0.0434394i	$-0.986168\pi$
$67$	−1.51350e6	−	8.58350e6i	−0.0751076	−	0.425956i	0.923948	−	0.382517i	$-0.124943\pi$
$68$	−3.30293e7	+	5.82395e6i	−1.54477	+	0.272384i
$69$	−1.98795e7	+	2.69419e7i	−0.877021	+	1.18859i
$70$	588565.	+	493864.i	0.0245133	+	0.0205691i
$71$	−9.87592e6	+	5.70186e6i	−0.388637	+	0.224380i	−0.681569	−	0.731754i	$-0.738702\pi$
$71$	−9.87592e6	+	5.70186e6i	−0.388637	+	0.224380i	0.292932	+	0.956133i	$0.405369\pi$
$72$	−3.08442e6	−	6.01317e6i	−0.114774	−	0.223755i
$73$	1.01458e7	−	1.75731e7i	0.357270	−	0.618810i	−0.630234	−	0.776406i	$-0.717041\pi$
$73$	1.01458e7	−	1.75731e7i	0.357270	−	0.618810i	0.987504	+	0.157595i	$0.0503742\pi$
$74$	−75578.1	−	207649.i	−0.00252040	−	0.00692474i
$75$	1.36811e7	−	2.75334e7i	0.432390	−	0.870190i
$76$	−2.17954e7	+	1.82886e7i	−0.653298	+	0.548182i
$77$	1.08444e7	−	2.97949e7i	0.308492	−	0.847575i
$78$	−1.31459e6	+	4.46016e6i	−0.0355150	+	0.120496i
$79$	−3.73057e6	+	2.11571e7i	−0.0957782	+	0.543185i	0.898728	+	0.438507i	$0.144492\pi$
$79$	−3.73057e6	+	2.11571e7i	−0.0957782	+	0.543185i	−0.994506	+	0.104678i	$0.966619\pi$
$80$			6.56074e6i			0.160174i
$81$	1.77216e7	+	3.92297e7i	0.411682	+	0.911327i
$82$	−8.65380e6			−0.191404
$83$	8.64355e6	+	1.52409e6i	0.182129	+	0.0321143i	0.263969	−	0.964531i	$-0.414968\pi$
$83$	8.64355e6	+	1.52409e6i	0.182129	+	0.0321143i	−0.0818395	+	0.996646i	$0.526079\pi$
$84$	−7.05089e7	−	2.07818e7i	−1.41621	−	0.417413i
$85$	1.31564e7	+	4.78855e6i	0.252036	+	0.0917335i
$86$	−6.59417e6	−	7.85863e6i	−0.120550	−	0.143666i
$87$	−7.14573e7	−	3.55065e7i	−1.24730	−	0.619770i
$88$	−8.51829e6	+	3.10040e6i	−0.142044	+	0.0516997i
$89$	−1.19561e7	−	6.90285e6i	−0.190559	−	0.110019i	0.401685	−	0.915778i	$-0.368425\pi$
$89$	−1.19561e7	−	6.90285e6i	−0.190559	−	0.110019i	−0.592244	+	0.805759i	$0.701758\pi$
$90$	−69439.4	+	1.39744e6i	−0.00105837	+	0.0212991i
$91$	5.09895e7	+	8.83163e7i	0.743558	+	1.28788i
$92$	6.69273e7	−	7.97608e7i	0.934225	−	1.11337i
$93$	−1.65193e6	−	1.21890e6i	−0.0220831	−	0.0162944i
$94$	945017.	+	5.35946e6i	0.0121040	+	0.0686451i
$95$	1.16968e7	−	2.06247e6i	0.143606	−	0.0253217i
$96$	1.26432e7	+	2.89700e7i	0.148858	+	0.341085i
$97$	−5.38212e7	−	4.51614e7i	−0.607948	−	0.510129i	0.286041	−	0.958217i	$-0.407661\pi$
$97$	−5.38212e7	−	4.51614e7i	−0.607948	−	0.510129i	−0.893989	+	0.448088i	$0.852105\pi$
$98$	1.26732e7	−	7.31687e6i	0.137398	−	0.0793270i
$99$	5.51718e7	−	1.70314e7i	0.574350	−	0.177300i
$100$	−4.78041e7	+	8.27992e7i	−0.478041	+	0.827992i
$101$	3.11081e7	+	8.54689e7i	0.298943	+	0.821340i	0.994677	+	0.103040i	$0.0328570\pi$
$101$	3.11081e7	+	8.54689e7i	0.298943	+	0.821340i	−0.695734	+	0.718299i	$0.744921\pi$
$102$	2.18307e7	−	1.36492e6i	0.201682	−	0.0126097i
$103$	9.97579e7	−	8.37069e7i	0.886336	−	0.743725i	−0.0811355	−	0.996703i	$-0.525855\pi$
$103$	9.97579e7	−	8.37069e7i	0.886336	−	0.743725i	0.967472	+	0.252979i	$0.0814102\pi$
$104$	9.97179e6	−	2.73973e7i	0.0852393	−	0.234193i
$105$	2.11529e7	+	2.22301e7i	0.174025	+	0.182887i
$106$	−1.67769e6	+	9.51466e6i	−0.0132889	+	0.0753650i
$107$			5.29085e7i			0.403637i	0.979423	+	0.201818i	$0.0646850\pi$
$107$			5.29085e7i			0.403637i	−0.979423	+	0.201818i	$0.935315\pi$
$108$	−4.73891e7	−	1.25194e8i	−0.348324	−	0.920214i
$109$	1.60893e7			0.113981			0.0569903	−	0.998375i	$-0.481850\pi$
$109$	1.60893e7			0.113981			0.0569903	+	0.998375i	$0.481850\pi$
$110$	1.84825e6	+	325897.i	0.0126238	+	0.00222592i
$111$	−2.07191e6	−	8.57891e6i	−0.0136483	−	0.0565119i
$112$	2.11238e8	+	7.68843e7i	1.34245	+	0.488613i
$113$	−1.27906e8	−	1.52432e8i	−0.784469	−	0.934894i	0.214657	−	0.976690i	$-0.431137\pi$
$113$	−1.27906e8	−	1.52432e8i	−0.784469	−	0.934894i	−0.999126	+	0.0417953i	$0.986692\pi$
$114$	1.54595e7	−	1.02626e7i	0.0915326	−	0.0607626i
$115$	−4.08438e7	+	1.48659e7i	−0.233526	+	0.0849964i
$116$	2.14889e8	+	1.24066e8i	1.18681	+	0.685206i
$117$	−7.20995e7	+	1.71144e8i	−0.384759	+	0.913309i
$118$	1.67008e7	+	2.89266e7i	0.0861407	+	0.149200i
$119$	3.08356e8	−	3.67484e8i	1.53767	−	1.83253i
$120$	981322.	−	8.71797e6i	0.00473246	−	0.0420427i
$121$	2.37739e7	+	1.34828e8i	0.110907	+	0.628984i
$122$	−2.23294e6	+	393728.i	−0.0100795	+	0.00177728i
$123$	−3.43456e8	−	3.86605e7i	−1.50055	−	0.168907i
$124$	4.89049e6	+	4.10361e6i	0.0206855	+	0.0173572i
$125$	7.01359e7	−	4.04930e7i	0.287277	−	0.165859i
$126$	4.41798e7	+	1.86121e7i	0.175284	+	0.0738435i
$127$	−2.28221e8	+	3.95290e8i	−0.877285	+	1.51950i	−0.0229765	+	0.999736i	$0.507314\pi$
$127$	−2.28221e8	+	3.95290e8i	−0.877285	+	1.51950i	−0.854309	+	0.519766i	$0.826019\pi$
$128$	−4.46981e7	−	1.22807e8i	−0.166513	−	0.457492i
$129$	−2.26604e8	−	3.41356e8i	−0.818294	−	1.23267i
$130$	−4.62401e6	+	3.88001e6i	−0.0161899	+	0.0135850i
$131$	−1.50031e8	+	4.12206e8i	−0.509442	+	1.39968i	0.372373	+	0.928083i	$0.378544\pi$
$131$	−1.50031e8	+	4.12206e8i	−0.509442	+	1.39968i	−0.881814	+	0.471597i	$0.843678\pi$
$132$	−1.74539e8	+	4.21534e7i	−0.574906	+	0.138847i
$133$	7.06674e7	−	4.00775e8i	0.225846	−	1.28084i
$134$		−	1.76766e7i		−	0.0548253i
$135$	−8.99892e6	+	5.51518e7i	−0.0270929	+	0.166045i
$136$	−1.37150e8			−0.400904
$137$	−5.04185e8	−	8.89014e7i	−1.43122	−	0.252363i	−0.596314	−	0.802751i	$-0.703369\pi$
$137$	−5.04185e8	−	8.89014e7i	−1.43122	−	0.252363i	−0.834909	+	0.550388i	$0.814480\pi$
$138$	−4.91932e7	+	4.68095e7i	−0.135640	+	0.129068i
$139$	1.27574e8	+	4.64331e7i	0.341745	+	0.124385i	0.507191	−	0.861834i	$-0.330684\pi$
$139$	1.27574e8	+	4.64331e7i	0.341745	+	0.124385i	−0.165445	+	0.986219i	$0.552906\pi$
$140$	−6.13375e7	−	7.30992e7i	−0.159667	−	0.190283i
$141$	1.35631e7	+	2.16930e8i	0.0343149	+	0.548837i
$142$	−2.17330e7	+	7.91016e6i	−0.0534523	+	0.0194550i
$143$	2.15730e8	+	1.24552e8i	0.515901	+	0.297856i
$144$	1.20748e8	+	3.91154e8i	0.280821	+	0.909699i
$145$	−5.17914e7	−	8.97054e7i	−0.117162	−	0.202930i
$146$	2.64529e7	−	3.15253e7i	0.0582186	−	0.0693822i
$147$	5.35667e8	−	2.33778e8i	1.14716	−	0.500650i
$148$	4.76577e6	+	2.70280e7i	0.00993313	+	0.0563336i
$149$	−5.85971e8	+	1.03322e8i	−1.18886	+	0.209628i	−0.732877	−	0.680361i	$-0.761823\pi$
$149$	−5.85971e8	+	1.03322e8i	−1.18886	+	0.209628i	−0.455983	+	0.889989i	$0.650712\pi$
$150$	3.70214e7	−	5.01737e7i	0.0731288	−	0.0991085i
$151$	−7.38513e8	−	6.19686e8i	−1.42053	−	1.19197i	−0.951056	−	0.309018i	$-0.899999\pi$
$151$	−7.38513e8	−	6.19686e8i	−1.42053	−	1.19197i	−0.469473	−	0.882947i	$-0.655556\pi$
$152$	−1.00761e8	+	5.81742e7i	−0.188763	+	0.108982i
$153$	8.72522e8	+	4.33562e7i	1.59225	+	0.0791198i
$154$	3.21523e7	−	5.56895e7i	0.0571649	−	0.0990126i
$155$	−911496.	−	2.50431e6i	−0.00157917	−	0.00433872i
$156$	2.56982e8	−	5.17181e8i	0.433915	−	0.873260i
$157$	6.15909e8	−	5.16809e8i	1.01372	−	0.850611i	0.0248938	−	0.999690i	$-0.492075\pi$
$157$	6.15909e8	−	5.16809e8i	1.01372	−	0.850611i	0.988825	+	0.149079i	$0.0476308\pi$
$158$	−1.49020e7	+	4.09428e7i	−0.0239120	+	0.0656976i
$159$	−1.09091e8	+	3.70127e8i	−0.170687	+	0.579111i
$160$	−7.12528e6	+	4.04095e7i	−0.0108723	+	0.0616600i
$161$			1.48927e9i			2.21651i
$162$	2.15792e7	+	8.45936e7i	0.0313311	+	0.122822i
$163$	−3.83046e8			−0.542626			−0.271313	−	0.962491i	$-0.587458\pi$
$163$	−3.83046e8			−0.542626			−0.271313	+	0.962491i	$0.587458\pi$
$164$	1.05847e9	+	1.86636e8i	1.46319	+	0.258000i
$165$	7.18983e7	+	2.11913e7i	0.0970025	+	0.0285905i
$166$	1.67268e7	+	6.08807e6i	0.0220283	+	0.00801765i
$167$	−8.19824e8	−	9.77028e8i	−1.05403	−	1.25615i	−0.965590	−	0.260068i	$-0.916255\pi$
$167$	−8.19824e8	−	9.77028e8i	−1.05403	−	1.25615i	−0.0884438	−	0.996081i	$-0.528189\pi$
$168$	−2.69194e8	−	1.33760e8i	−0.337932	−	0.167915i
$169$	1.36645e7	−	4.97349e6i	0.0167513	−	0.00609697i
$170$	2.45906e7	+	1.41974e7i	0.0294425	+	0.0169986i
$171$	6.59410e8	−	3.38240e8i	0.771207	−	0.395586i
$172$	6.37061e8	+	1.10342e9i	0.727893	+	1.26075i
$173$	2.82308e8	−	3.36442e8i	0.315166	−	0.375600i	−0.585085	−	0.810972i	$-0.698939\pi$
$173$	2.82308e8	−	3.36442e8i	0.315166	−	0.375600i	0.900251	+	0.435372i	$0.143383\pi$
$174$	−1.30216e8	−	9.60818e7i	−0.142058	−	0.104820i
$175$	−2.37467e8	−	1.34674e9i	−0.253193	−	1.43593i
$176$	5.40763e8	−	9.53511e7i	0.563581	−	0.0993745i
$177$	5.33599e8	+	1.22266e9i	0.543653	+	1.24570i
$178$	−2.14486e7	−	1.79975e7i	−0.0213658	−	0.0179280i
$179$	−1.38419e9	+	7.99161e8i	−1.34829	+	0.778435i	−0.988007	−	0.154409i	$-0.950653\pi$
$179$	−1.38419e9	+	7.99161e8i	−1.34829	+	0.778435i	−0.360281	+	0.932844i	$0.617319\pi$
$180$	3.86317e7	−	1.69426e8i	0.0368005	−	0.161395i
$181$	9.08248e6	−	1.57313e7i	0.00846233	−	0.0146572i	−0.861763	−	0.507311i	$-0.830640\pi$
$181$	9.08248e6	−	1.57313e7i	0.00846233	−	0.0146572i	0.870226	+	0.492654i	$0.163973\pi$
$182$	7.07374e7	+	1.94349e8i	0.0644709	+	0.177132i
$183$	−9.03808e7	+	5.65087e6i	−0.0805883	+	0.00503861i
$184$	3.26166e8	−	2.73685e8i	0.284555	−	0.238770i
$185$	3.91849e6	−	1.07660e7i	0.00334528	−	0.00919107i
$186$	−2.87010e6	−	3.01625e6i	−0.00239797	−	0.00252009i
$187$	2.03481e8	−	1.15400e9i	0.166402	−	0.943712i
$188$		−	6.75908e8i		−	0.541073i
$189$	1.67028e9	+	9.36055e8i	1.30901	+	0.733591i
$190$	2.40882e7			0.0184837
$191$	2.92953e8	+	5.16555e7i	0.220122	+	0.0388135i	0.282621	−	0.959232i	$-0.408796\pi$
$191$	2.92953e8	+	5.16555e7i	0.220122	+	0.0388135i	−0.0624992	+	0.998045i	$0.519907\pi$
$192$	−2.88687e8	−	1.19533e9i	−0.212433	−	0.879596i
$193$	1.23554e9	+	4.49699e8i	0.890485	+	0.324110i	0.746433	−	0.665460i	$-0.231765\pi$
$193$	1.23554e9	+	4.49699e8i	0.890485	+	0.324110i	0.144052	+	0.989570i	$0.453987\pi$
$194$	−9.15913e7	−	1.09154e8i	−0.0646617	−	0.0770608i
$195$	−2.00853e8	+	1.33334e8i	−0.138912	+	0.0922150i
$196$	−1.70789e9	+	6.21620e8i	−1.15727	+	0.421212i
$197$	1.12925e9	+	6.51972e8i	0.749765	+	0.432877i	0.825609	−	0.564243i	$-0.190832\pi$
$197$	1.12925e9	+	6.51972e8i	0.749765	+	0.432877i	−0.0758442	+	0.997120i	$0.524165\pi$
$198$	1.16191e8	−	1.45863e7i	0.0755986	−	0.00949037i
$199$	−3.99362e8	−	6.91715e8i	−0.254656	−	0.441077i	0.710146	−	0.704054i	$-0.248629\pi$
$199$	−3.99362e8	−	6.91715e8i	−0.254656	−	0.441077i	−0.964802	+	0.262977i	$0.915296\pi$
$200$	−2.51311e8	+	2.99501e8i	−0.157069	+	0.187188i
$201$	7.89696e7	−	7.01558e8i	0.0483811	−	0.429813i
$202$	3.20317e7	+	1.81661e8i	0.0192386	+	0.109108i
$203$	−3.49520e9	+	6.16298e8i	−2.05820	+	0.362916i
$204$	−2.69959e9	−	3.03875e8i	−1.55875	−	0.175458i
$205$	−3.43703e8	−	2.88401e8i	−0.194611	−	0.163298i
$206$	2.28724e8	−	1.32054e8i	0.127011	−	0.0733300i
$207$	−2.16152e9	+	1.63803e9i	−1.17727	+	0.892153i
$208$	−8.83040e8	+	1.52947e9i	−0.471767	+	0.817124i
$209$	−3.39993e8	−	9.34124e8i	−0.178191	−	0.489575i
$210$	3.44193e7	+	5.18491e7i	0.0176980	+	0.0266603i
$211$	−1.03228e9	+	8.66188e8i	−0.520797	+	0.437001i	−0.864910	−	0.501928i	$-0.832624\pi$
$211$	−1.03228e9	+	8.66188e8i	−0.520797	+	0.437001i	0.344112	+	0.938928i	$0.388180\pi$
$212$	4.10404e8	−	1.12758e9i	0.203174	−	0.558216i
$213$	−8.97887e8	+	2.16851e8i	−0.436218	+	0.105352i
$214$	−1.86330e7	+	1.05673e8i	−0.00888439	+	0.0503859i
$215$		−	5.31883e8i		−	0.248921i
$216$	−1.01944e8	−	5.37829e8i	−0.0468324	−	0.247075i
$217$	−9.13136e7			−0.0411810
$218$	3.21348e7	+	5.66623e6i	0.0142282	+	0.00250881i
$219$	1.19071e9	−	1.13301e9i	0.517642	−	0.492559i
$220$	−2.19035e8	−	7.97223e7i	−0.0935025	−	0.0340321i
$221$	2.42257e9	+	2.88711e9i	1.01557	+	1.21030i
$222$	−1.11692e6	−	1.78641e7i	−0.000459842	−	0.00735479i
$223$	2.22382e9	−	8.09406e8i	0.899251	−	0.327301i	0.149298	−	0.988792i	$-0.452298\pi$
$223$	2.22382e9	−	8.09406e8i	0.899251	−	0.327301i	0.749953	+	0.661492i	$0.230076\pi$
$224$	1.21757e9	+	7.02966e8i	0.483619	+	0.279217i
$225$	1.69347e9	−	1.82592e9i	0.660766	−	0.712446i
$226$	−2.01781e8	−	3.49494e8i	−0.0773474	−	0.133970i
$227$	9.99253e8	−	1.19086e9i	0.376333	−	0.448496i	−0.544320	−	0.838877i	$-0.683212\pi$
$227$	9.99253e8	−	1.19086e9i	0.376333	−	0.448496i	0.920653	+	0.390382i	$0.127657\pi$
$228$	−2.11222e9	+	9.21823e8i	−0.781626	+	0.341121i
$229$	3.39844e8	+	1.92735e9i	0.123577	+	0.700841i	0.982143	+	0.188137i	$0.0602449\pi$
$229$	3.39844e8	+	1.92735e9i	0.123577	+	0.700841i	−0.858566	+	0.512704i	$0.828644\pi$
$230$	−8.68118e7	+	1.53073e7i	−0.0310218	+	0.00546999i
$231$	1.52487e9	−	2.06659e9i	0.535530	−	0.725782i
$232$	7.77295e8	+	6.52228e8i	0.268308	+	0.225137i
$233$	1.94723e9	−	1.12424e9i	0.660685	−	0.381447i	−0.131853	−	0.991269i	$-0.542093\pi$
$233$	1.94723e9	−	1.12424e9i	0.660685	−	0.381447i	0.792538	+	0.609823i	$0.208759\pi$
$234$	−2.04275e8	+	3.16430e8i	−0.0681322	+	0.105539i
$235$	−1.41079e8	+	2.44356e8i	−0.0462584	+	0.0801219i
$236$	−1.41885e9	−	3.89826e9i	−0.457392	−	1.25667i
$237$	−7.74346e8	+	1.55838e9i	−0.245438	+	0.493947i
$238$	7.45291e8	−	6.25373e8i	0.232283	−	0.194909i
$239$	6.06245e8	−	1.66565e9i	0.185805	−	0.510494i	−0.811460	−	0.584408i	$-0.801327\pi$
$239$	6.06245e8	−	1.66565e9i	0.185805	−	0.510494i	0.997265	+	0.0739138i	$0.0235490\pi$
$240$	−1.50241e8	+	5.09740e8i	−0.0452838	+	0.153640i
$241$	−1.62275e8	+	9.20306e8i	−0.0481042	+	0.272813i	−0.999367	−	0.0355681i	$-0.988676\pi$
$241$	−1.62275e8	+	9.20306e8i	−0.0481042	+	0.272813i	0.951263	+	0.308381i	$0.0997870\pi$
$242$			2.77662e8i			0.0809571i
$243$	4.78528e8	+	3.45379e9i	0.137240	+	0.990538i
$244$	2.81607e8			0.0794483
$245$	7.47188e8	+	1.31749e8i	0.207379	+	0.0365666i
$246$	−6.72361e8	−	1.98172e8i	−0.183596	−	0.0541130i
$247$	3.00441e9	+	1.09352e9i	0.807183	+	0.293791i
$248$	1.67809e7	+	1.99987e7i	0.00443616	+	0.00528681i
$249$	6.36664e8	+	3.16352e8i	0.165620	+	0.0822950i
$250$	1.54342e8	−	5.61757e7i	0.0395114	−	0.0143810i
$251$	−5.42483e7	−	3.13203e7i	−0.0136676	−	0.00789097i	0.493151	−	0.869944i	$-0.335845\pi$
$251$	−5.42483e7	−	3.13203e7i	−0.0136676	−	0.00789097i	−0.506818	+	0.862053i	$0.669178\pi$
$252$	−5.00232e9	−	3.22931e9i	−1.24042	−	0.800769i
$253$	1.81892e9	+	3.15045e9i	0.443946	+	0.768938i
$254$	−5.95032e8	+	7.09131e8i	−0.142957	+	0.170369i
$255$	9.12538e8	+	6.73331e8i	0.215819	+	0.159246i
$256$	6.28850e8	+	3.56639e9i	0.146416	+	0.830364i
$257$	4.07519e9	−	7.18565e8i	0.934146	−	0.164715i	0.314198	−	0.949358i	$-0.398265\pi$
$257$	4.07519e9	−	7.18565e8i	0.934146	−	0.164715i	0.619949	+	0.784642i	$0.287153\pi$
$258$	−3.32375e8	−	7.61587e8i	−0.0750153	−	0.171886i
$259$	−3.00714e8	−	2.52329e8i	−0.0668274	−	0.0560749i
$260$	6.49253e8	−	3.74846e8i	0.142076	−	0.0820276i
$261$	−4.73881e9	−	4.39507e9i	−1.02119	−	0.947117i
$262$	−4.44821e8	+	7.70452e8i	−0.0944018	+	0.163509i
$263$	4.28068e8	+	1.17611e9i	0.0894726	+	0.245824i	0.976356	−	0.216170i	$-0.0693565\pi$
$263$	4.28068e8	+	1.17611e9i	0.0894726	+	0.245824i	−0.886883	+	0.461994i	$0.847134\pi$
$264$	−7.32832e8	+	4.58187e7i	−0.150865	+	0.00943252i
$265$	−3.83724e8	+	3.21982e8i	−0.0778100	+	0.0652903i
$266$	2.82285e8	−	7.75572e8i	0.0563847	−	0.154916i
$267$	−7.70859e8	−	8.10114e8i	−0.151681	−	0.159405i
$268$	−3.81231e8	+	2.16207e9i	−0.0739008	+	0.419112i
$269$		−	9.92958e9i		−	1.89636i	−0.317728	−	0.948182i	$-0.602920\pi$
$269$		−	9.92958e9i		−	1.89636i	0.317728	−	0.948182i	$-0.397080\pi$
$270$	−3.73964e7	+	1.06984e8i	−0.00703679	+	0.0201310i
$271$	8.78328e8			0.162847			0.0814235	−	0.996680i	$-0.474053\pi$
$271$	8.78328e8			0.162847			0.0814235	+	0.996680i	$0.474053\pi$
$272$	8.18157e9	+	1.44263e9i	1.49472	+	0.263560i
$273$	1.93921e9	+	8.02944e9i	0.349119	+	1.44556i
$274$	−9.75689e8	−	3.55122e8i	−0.173105	−	0.0630050i
$275$	−2.14719e9	−	2.55892e9i	−0.375439	−	0.447431i
$276$	7.02647e9	−	4.66442e9i	1.21088	−	0.803825i
$277$	−4.06954e9	+	1.48119e9i	−0.691236	+	0.251589i	−0.663664	−	0.748030i	$-0.731000\pi$
$277$	−4.06954e9	+	1.48119e9i	−0.691236	+	0.251589i	−0.0275717	+	0.999620i	$0.508777\pi$
$278$	2.38448e8	+	1.37668e8i	0.0399222	+	0.0230491i
$279$	−1.00435e8	−	1.32532e8i	−0.0165755	−	0.0218728i
$280$	−1.95109e8	−	3.37939e8i	−0.0317428	−	0.0549801i
$281$	−6.16482e9	+	7.34695e9i	−0.988770	+	1.17837i	−0.00480818	+	0.999988i	$0.501530\pi$
$281$	−6.16482e9	+	7.34695e9i	−0.988770	+	1.17837i	−0.983961	+	0.178381i	$0.942914\pi$
$282$	−4.93079e7	+	4.38046e8i	−0.00779687	+	0.0692666i
$283$	−1.44765e9	−	8.21005e9i	−0.225693	−	1.27997i	−0.861355	−	0.508003i	$-0.830384\pi$
$283$	−1.44765e9	−	8.21005e9i	−0.225693	−	1.27997i	0.635662	−	0.771968i	$-0.280727\pi$
$284$	2.82881e9	−	4.98795e8i	0.434841	−	0.0766742i
$285$	9.56021e8	+	1.07613e8i	0.144907	+	0.0163111i
$286$	3.87009e8	+	3.24739e8i	0.0578438	+	0.0485367i
$287$	−1.33135e10	+	7.68657e9i	−1.96230	+	1.13293i
$288$	3.18908e8	+	2.54037e9i	0.0463549	+	0.369255i
$289$	5.37662e9	−	9.31257e9i	0.770758	−	1.33499i
$290$	−7.18500e7	−	1.97406e8i	−0.0101586	−	0.0279106i
$291$	−3.14747e9	−	4.74134e9i	−0.438925	−	0.661194i
$292$	−3.91541e9	+	3.28542e9i	−0.538575	+	0.451918i
$293$	−3.69863e9	+	1.01619e10i	−0.501845	+	1.37881i	0.387626	+	0.921817i	$0.373295\pi$
$293$	−3.69863e9	+	1.01619e10i	−0.501845	+	1.37881i	−0.889471	+	0.456992i	$0.848927\pi$
$294$	1.15221e9	−	2.78272e8i	0.154220	−	0.0372460i
$295$	−3.00718e8	+	1.70546e9i	−0.0397074	+	0.225192i
$296$			1.12231e8i			0.0146199i
$297$	4.67662e9	−	5.98256e7i	0.601044	−	0.00768884i
$298$	−1.20673e9			−0.153019
$299$	−1.15226e10	−	2.03174e9i	−1.44166	−	0.254204i
$300$	−5.61027e9	+	5.33841e9i	−0.692626	+	0.659063i
$301$	−1.71252e10	−	6.23305e9i	−2.08626	−	0.759337i
$302$	−1.25678e9	−	1.49777e9i	−0.151088	−	0.180060i
$303$	4.59726e8	+	7.35293e9i	0.0545417	+	0.872348i
$304$	6.62270e9	−	2.41047e9i	0.775427	−	0.282232i
$305$	−1.01807e8	−	5.87785e7i	−0.0117647	−	0.00679234i
$306$	1.72740e9	+	3.93874e8i	0.197019	+	0.0449233i
$307$	−8.84641e9	−	1.53224e10i	−0.995895	−	1.72494i	−0.576339	−	0.817211i	$-0.695519\pi$
$307$	−8.84641e9	−	1.53224e10i	−0.995895	−	1.72494i	−0.419556	−	0.907730i	$-0.637814\pi$
$308$	−5.13368e9	+	6.11808e9i	−0.570460	+	0.679848i
$309$	9.66763e9	−	4.21919e9i	1.06044	−	0.462802i
$310$	−938556.	−	5.32282e6i	−0.000101628	−	0.000576361i
$311$	1.20968e10	−	2.13299e9i	1.29309	−	0.228007i	0.515561	−	0.856853i	$-0.327584\pi$
$311$	1.20968e10	−	2.13299e9i	1.29309	−	0.228007i	0.777530	+	0.628846i	$0.216473\pi$
$312$	1.40216e9	−	1.90029e9i	0.147972	−	0.200540i
$313$	1.15186e10	+	9.66527e9i	1.20012	+	1.00702i	0.999627	+	0.0273201i	$0.00869734\pi$
$313$	1.15186e10	+	9.66527e9i	1.20012	+	1.00702i	0.200488	+	0.979696i	$0.435747\pi$
$314$	1.41215e9	−	8.15304e8i	0.145265	−	0.0838689i
$315$	1.13442e9	+	2.21158e9i	0.115221	+	0.224626i
$316$	2.70570e9	−	4.68642e9i	0.271351	−	0.469994i
$317$	3.85001e9	+	1.05778e10i	0.381263	+	1.04751i	0.970825	+	0.239789i	$0.0770783\pi$
$317$	3.85001e9	+	1.05778e10i	0.381263	+	1.04751i	−0.589562	+	0.807723i	$0.700699\pi$
$318$	−3.48234e8	+	7.00827e8i	−0.0340536	+	0.0685334i
$319$	−6.64116e9	+	5.57260e9i	−0.641330	+	0.538140i
$320$	5.45978e8	−	1.50006e9i	0.0520685	−	0.143057i
$321$	−1.21160e9	+	4.11075e9i	−0.114114	+	0.387170i
$322$	−5.24481e8	+	2.97448e9i	−0.0487873	+	0.276686i
$323$		−	1.50400e10i		−	1.38178i
$324$	−8.14979e8	−	1.08122e10i	−0.0739548	−	0.981150i
$325$	1.07438e10			0.962995
$326$	−7.65049e8	−	1.34899e8i	−0.0677359	−	0.0119437i
$327$	1.25007e9	+	3.68445e8i	0.109331	+	0.0322241i
$328$	4.13009e9	+	1.50323e9i	0.356832	+	0.129876i
$329$	6.21430e9	+	7.40592e9i	0.530407	+	0.632114i
$330$	1.36138e8	+	6.76457e7i	0.0114795	+	0.00570406i
$331$	6.63184e9	−	2.41379e9i	0.552487	−	0.201089i	−0.0506641	−	0.998716i	$-0.516134\pi$
$331$	6.63184e9	−	2.41379e9i	0.552487	−	0.201089i	0.603151	+	0.797627i	$0.293912\pi$
$332$	−1.91460e9	−	1.10539e9i	−0.157589	−	0.0909838i
$333$	3.54786e7	−	7.13989e8i	0.00288529	−	0.0580650i
$334$	−1.29333e9	−	2.24012e9i	−0.103926	−	0.180005i
$335$	5.89102e8	−	7.02064e8i	0.0467747	−	0.0557439i
$336$	1.46516e10	+	1.08109e10i	1.14955	+	0.848213i
$337$	3.94099e7	+	2.23505e8i	0.00305553	+	0.0173287i	0.986297	−	0.164977i	$-0.0527550\pi$
$337$	3.94099e7	+	2.23505e8i	0.00305553	+	0.0173287i	−0.983242	+	0.182306i	$0.941644\pi$
$338$	2.90434e7	−	5.12114e6i	0.00222526	−	0.000392374i
$339$	−6.44700e9	−	1.47723e10i	−0.488157	−	1.11854i
$340$	−2.70154e9	−	2.26686e9i	−0.202160	−	0.169633i
$341$	−1.93168e8	+	1.11526e8i	−0.0142863	+	0.00824817i
$342$	1.43614e9	−	4.43333e8i	0.104977	−	0.0324060i
$343$	2.61335e9	−	4.52646e9i	0.188809	−	0.327026i
$344$	1.78202e9	+	4.89605e9i	0.127256	+	0.349633i
$345$	−3.51381e9	+	2.19693e8i	−0.248029	+	0.0155074i
$346$	6.82334e8	−	5.72546e8i	0.0476094	−	0.0399490i
$347$	8.18317e8	−	2.24831e9i	0.0564421	−	0.155074i	−0.908267	−	0.418391i	$-0.862594\pi$
$347$	8.18317e8	−	2.24831e9i	0.0564421	−	0.155074i	0.964709	+	0.263317i	$0.0848165\pi$
$348$	1.38548e10	+	1.45603e10i	0.944676	+	0.992783i
$349$	−7.45944e8	+	4.23046e9i	−0.0502811	+	0.285158i	−0.999572	−	0.0292395i	$-0.990691\pi$
$349$	−7.45944e8	+	4.23046e9i	−0.0502811	+	0.285158i	0.949291	+	0.314398i	$0.101803\pi$
$350$		−	2.77345e9i		−	0.184820i
$351$	−9.52100e9	+	1.16460e10i	−0.627269	+	0.767272i
$352$	3.43427e9			0.223699
$353$	−2.16757e10	−	3.82200e9i	−1.39596	−	0.246146i	−0.575479	−	0.817817i	$-0.695184\pi$
$353$	−2.16757e10	−	3.82200e9i	−1.39596	−	0.246146i	−0.820483	+	0.571671i	$0.806295\pi$
$354$	6.35156e8	+	2.62991e9i	0.0404452	+	0.167467i
$355$	−1.12679e9	−	4.10118e8i	−0.0709462	−	0.0258223i
$356$	2.23528e9	+	2.66390e9i	0.139165	+	0.165851i
$357$	3.23733e10	−	2.14905e10i	1.99303	−	1.32304i
$358$	−3.04605e9	+	1.10867e9i	−0.185441	+	0.0674949i
$359$	1.28604e10	+	7.42496e9i	0.774242	+	0.447009i	0.834386	−	0.551181i	$-0.185823\pi$
$359$	1.28604e10	+	7.42496e9i	0.774242	+	0.447009i	−0.0601437	+	0.998190i	$0.519156\pi$
$360$	2.75886e8	−	6.54875e8i	0.0164255	−	0.0389895i
$361$	2.11234e9	+	3.65868e9i	0.124376	+	0.215425i
$362$	2.36804e7	−	2.82212e7i	0.00137897	−	0.00164339i
$363$	−1.24044e9	+	1.10200e10i	−0.0714415	+	0.634679i
$364$	−4.46053e9	−	2.52969e10i	−0.254086	−	1.44099i
$365$	2.10126e9	−	3.70509e8i	0.118388	−	0.0208750i
$366$	−1.82506e8	−	2.05434e7i	−0.0101707	−	0.00114485i
$367$	−4.22342e9	−	3.54387e9i	−0.232809	−	0.195350i	0.518919	−	0.854824i	$-0.326335\pi$
$367$	−4.22342e9	−	3.54387e9i	−0.232809	−	0.195350i	−0.751728	+	0.659474i	$0.770779\pi$
$368$	−2.23359e10	+	1.28956e10i	−1.21790	+	0.703156i
$369$	−2.57996e10	−	1.08689e10i	−1.39158	−	0.586245i
$370$	1.16178e7	−	2.01226e7i	0.000619894	−	0.00107369i
$371$	5.87015e9	+	1.61281e10i	0.309851	+	0.851310i
$372$	2.85996e8	+	4.30824e8i	0.0149344	+	0.0224972i
$373$	−9.87507e9	+	8.28617e9i	−0.510158	+	0.428074i	−0.861185	−	0.508292i	$-0.830277\pi$
$373$	−9.87507e9	+	8.28617e9i	−0.510158	+	0.428074i	0.351027	+	0.936365i	$0.385833\pi$
$374$	8.12818e8	−	2.23320e9i	0.0415439	−	0.114141i
$375$	6.37654e9	−	1.54001e9i	0.322448	−	0.0778752i
$376$	4.79962e8	−	2.72200e9i	0.0240135	−	0.136187i
$377$		−	2.78834e10i		−	1.38032i
$378$	3.00636e9	+	2.45779e9i	0.147256	+	0.120386i
$379$	−2.46521e10			−1.19481			−0.597403	−	0.801941i	$-0.703801\pi$
$379$	−2.46521e10			−1.19481			−0.597403	+	0.801941i	$0.703801\pi$
$380$	−2.94628e9	−	5.19508e8i	−0.141299	−	0.0249148i
$381$	−2.67839e10	+	2.54860e10i	−1.27108	+	1.20949i
$382$	5.66916e8	+	2.06341e8i	0.0266235	+	0.00969017i
$383$	3.85665e9	+	4.59618e9i	0.179232	+	0.213600i	0.848179	−	0.529710i	$-0.177699\pi$
$383$	3.85665e9	+	4.59618e9i	0.179232	+	0.213600i	−0.668947	+	0.743310i	$0.733255\pi$
$384$	−6.60562e8	−	1.05651e10i	−0.0303801	−	0.485904i
$385$	3.13293e9	−	1.14030e9i	0.142596	−	0.0519008i
$386$	2.30934e9	+	1.33330e9i	0.104025	+	0.0600590i
$387$	−9.78909e9	−	3.17110e10i	−0.436414	−	1.41373i
$388$	8.84861e9	+	1.53262e10i	0.390434	+	0.676252i
$389$	1.83348e10	−	2.18505e10i	0.800714	−	0.954254i	−0.198954	−	0.980009i	$-0.563755\pi$
$389$	1.83348e10	−	2.18505e10i	0.800714	−	0.954254i	0.999668	+	0.0257550i	$0.00819897\pi$
$390$	−4.48117e8	+	1.95569e8i	−0.0193701	+	0.00845361i
$391$	9.55745e9	+	5.42030e10i	0.408917	+	2.31908i
$392$	−7.31937e9	+	1.29060e9i	−0.309977	+	0.0546573i
$393$	−2.10962e10	+	2.85908e10i	−0.884370	+	1.19855i
$394$	2.02582e9	+	1.69986e9i	0.0840650	+	0.0705389i
$395$	−1.95635e9	+	1.12950e9i	−0.0803632	+	0.0463977i
$396$	−1.45262e10	−	7.21817e8i	−0.590707	−	0.0293526i
$397$	−4.82759e9	+	8.36163e9i	−0.194343	+	0.336611i	−0.946685	−	0.322161i	$-0.895591\pi$
$397$	−4.82759e9	+	8.36163e9i	−0.194343	+	0.336611i	0.752342	+	0.658773i	$0.228924\pi$
$398$	−5.54032e8	−	1.52219e9i	−0.0220802	−	0.0606648i
$399$	1.46683e10	−	2.95201e10i	0.578746	−	1.16473i
$400$	1.81421e10	−	1.52230e10i	0.708675	−	0.594649i
$401$	7.24584e9	−	1.99078e10i	0.280228	−	0.769920i	−0.717107	−	0.696963i	$-0.754534\pi$
$401$	7.24584e9	−	1.99078e10i	0.280228	−	0.769920i	0.997335	−	0.0729567i	$-0.0232435\pi$
$402$	4.04795e8	−	1.37340e9i	0.0155000	−	0.0525886i
$403$	1.24575e8	−	7.06499e8i	0.00472292	−	0.0267850i
$404$		−	2.29101e10i		−	0.860008i
$405$	−1.96215e9	+	4.07897e9i	−0.0729310	+	0.151611i
$406$	−7.19793e9			−0.264913
$407$	−9.44324e8	−	1.66510e8i	−0.0344147	−	0.00606823i
$408$	−1.06559e10	−	3.14073e9i	−0.384549	−	0.113342i
$409$	2.74242e9	+	9.98159e8i	0.0980032	+	0.0356703i	0.390556	−	0.920579i	$-0.372283\pi$
$409$	2.74242e9	+	9.98159e8i	0.0980032	+	0.0356703i	−0.292553	+	0.956249i	$0.594505\pi$
$410$	−5.84904e8	−	6.97061e8i	−0.0206990	−	0.0246681i
$411$	−3.71371e10	−	1.84531e10i	−1.30149	−	0.646697i
$412$	−3.08237e10	+	1.12189e10i	−1.06978	+	0.389369i
$413$	5.13869e10	+	2.96683e10i	1.76625	+	1.01975i
$414$	−4.89403e9	+	2.51036e9i	−0.166596	+	0.0854545i
$415$	4.61446e8	+	7.99248e8i	0.0155571	+	0.0269457i
$416$	−7.09997e9	+	8.46142e9i	−0.237074	+	0.282533i
$417$	8.84860e9	+	6.52908e9i	0.292638	+	0.215927i
$418$	−3.50087e8	−	1.98544e9i	−0.0114676	−	0.0650358i
$419$	−1.09072e10	+	1.92323e9i	−0.353880	+	0.0623985i	−0.347762	−	0.937583i	$-0.613058\pi$
$419$	−1.09072e10	+	1.92323e9i	−0.353880	+	0.0623985i	−0.00611745	+	0.999981i	$0.501947\pi$
$420$	−3.09168e9	−	7.08410e9i	−0.0993567	−	0.227661i
$421$	3.98726e10	+	3.34571e10i	1.26925	+	1.06502i	0.994633	+	0.103469i	$0.0329943\pi$
$421$	3.98726e10	+	3.34571e10i	1.26925	+	1.06502i	0.274613	+	0.961555i	$0.411450\pi$
$422$	−2.36680e9	+	1.36647e9i	−0.0746298	+	0.0430876i
$423$	−3.91391e9	+	1.71651e10i	−0.122250	+	0.536148i
$424$	2.45346e9	−	4.24951e9i	0.0759128	−	0.131485i
$425$	−1.72856e10	−	4.74917e10i	−0.529820	−	1.45567i
$426$	−1.86970e9	+	1.16899e8i	−0.0567719	+	0.00354954i
$427$	−3.08557e9	+	2.58910e9i	−0.0928162	+	0.0778820i
$428$	4.55809e9	−	1.25232e10i	0.135834	−	0.373200i
$429$	1.39090e10	+	1.46173e10i	0.410646	+	0.431558i
$430$	1.87315e8	−	1.06232e9i	0.00547898	−	0.0310728i
$431$		−	2.63476e10i		−	0.763540i	−0.924257	−	0.381770i	$-0.875315\pi$
$431$		−	2.63476e10i		−	0.763540i	0.924257	−	0.381770i	$-0.124685\pi$
$432$	4.24148e8	+	3.31560e10i	0.0121782	+	0.951979i
$433$	3.69739e10			1.05183			0.525913	−	0.850539i	$-0.323724\pi$
$433$	3.69739e10			1.05183			0.525913	+	0.850539i	$0.323724\pi$
$434$	−1.82379e8	−	3.21583e7i	−0.00514062	−	0.000906429i
$435$	−1.96971e9	−	8.15573e9i	−0.0550104	−	0.227775i
$436$	−3.80828e9	−	1.38610e9i	−0.105386	−	0.0383573i
$437$	3.00126e10	+	3.57676e10i	0.822959	+	0.980764i
$438$	2.77720e9	−	1.84360e9i	0.0754589	−	0.0500923i
$439$	4.82865e10	−	1.75748e10i	1.30007	−	0.473188i	0.403052	−	0.915177i	$-0.367949\pi$
$439$	4.82865e10	−	1.75748e10i	1.30007	−	0.473188i	0.897020	+	0.441989i	$0.145727\pi$
$440$	−8.25482e8	−	4.76592e8i	−0.0220240	−	0.0127156i
$441$	4.69724e10	−	5.89675e9i	1.24190	−	0.155904i
$442$	3.82179e9	+	6.61953e9i	0.100133	+	0.173436i
$443$	2.10019e10	−	2.50291e10i	0.545311	−	0.649876i	−0.421059	−	0.907033i	$-0.638341\pi$
$443$	2.10019e10	−	2.50291e10i	0.545311	−	0.649876i	0.966370	+	0.257157i	$0.0827859\pi$
$444$	−2.48662e8	+	2.20909e9i	−0.00639850	+	0.0568436i
$445$	−2.52080e8	−	1.42962e9i	−0.00642834	−	0.0364569i
$446$	4.72665e9	−	8.33435e8i	0.119458	−	0.0210636i
$447$	−4.78934e10	−	5.39103e9i	−1.19962	−	0.135034i
$448$	−4.18996e10	−	3.51579e10i	−1.04015	−	0.872793i
$449$	−4.98804e9	+	2.87985e9i	−0.122728	+	0.0708572i	−0.560107	−	0.828420i	$-0.689240\pi$
$449$	−4.98804e9	+	2.87985e9i	−0.122728	+	0.0708572i	0.437379	+	0.899277i	$0.355907\pi$
$450$	4.02538e9	−	3.05048e9i	0.0981649	−	0.0743905i
$451$	−1.87760e10	+	3.25209e10i	−0.453833	+	0.786062i
$452$	1.71427e10	+	4.70992e10i	0.410701	+	1.12839i
$453$	−4.31883e10	−	6.50587e10i	−1.02559	−	1.54494i
$454$	2.41518e9	−	2.02657e9i	0.0568494	−	0.0477023i
$455$	−3.66752e9	+	1.00764e10i	−0.0855710	+	0.235104i
$456$	−9.16084e9	+	2.21246e9i	−0.211873	+	0.0511700i
$457$	−3.51560e9	+	1.99380e10i	−0.0806000	+	0.457105i	0.917620	+	0.397460i	$0.130108\pi$
$457$	−3.51560e9	+	1.99380e10i	−0.0806000	+	0.457105i	−0.998220	+	0.0596455i	$0.981003\pi$
$458$			3.96914e9i			0.0902059i
$459$	6.67982e10	+	2.33493e10i	1.50492	+	0.526046i
$460$	1.09483e10			0.244520
$461$	6.14335e10	+	1.08324e10i	1.36020	+	0.239839i	0.805688	−	0.592340i	$-0.201796\pi$
$461$	6.14335e10	+	1.08324e10i	1.36020	+	0.239839i	0.554507	+	0.832179i	$0.312907\pi$
$462$	3.77338e9	−	3.59053e9i	0.0828252	−	0.0788118i
$463$	1.91395e10	+	6.96622e9i	0.416493	+	0.151591i	0.541762	−	0.840532i	$-0.317757\pi$
$463$	1.91395e10	+	6.96622e9i	0.416493	+	0.151591i	−0.125270	+	0.992123i	$0.539980\pi$
$464$	−3.95083e10	−	4.70841e10i	−0.852347	−	1.01579i
$465$	−1.34704e7	−	2.15447e8i	−0.000288116	−	0.00460817i
$466$	4.28509e9	−	1.55965e9i	0.0908692	−	0.0330737i
$467$	5.46491e10	+	3.15517e10i	1.14899	+	0.663369i	0.948641	−	0.316356i	$-0.102459\pi$
$467$	5.46491e10	+	3.15517e10i	1.14899	+	0.663369i	0.200348	+	0.979725i	$0.435793\pi$
$468$	3.18098e10	−	3.42977e10i	0.663098	−	0.714960i
$469$	−1.57009e10	−	2.71948e10i	−0.324515	−	0.562076i
$470$	−3.67830e8	+	4.38362e8i	−0.00753799	+	0.00898342i
$471$	5.96882e10	−	2.60494e10i	1.21284	−	0.529315i
$472$	−2.94580e9	−	1.67065e10i	−0.0593520	−	0.336602i
$473$	−4.38399e10	+	7.73016e9i	−0.875841	+	0.154434i
$474$	−2.09541e9	+	2.83982e9i	−0.0415102	+	0.0562571i
$475$	−3.28436e10	−	2.75590e10i	−0.645173	−	0.541364i
$476$	−1.04646e11	+	6.04172e10i	−2.03842	+	1.17688i
$477$	−1.69518e10	+	2.62590e10i	−0.327448	+	0.507230i
$478$	1.79744e9	−	3.11325e9i	0.0344304	−	0.0596352i
$479$	−7.35383e9	−	2.02045e10i	−0.139692	−	0.383801i	0.850043	−	0.526713i	$-0.176576\pi$
$479$	−7.35383e9	−	2.02045e10i	−0.139692	−	0.383801i	−0.989735	+	0.142912i	$0.954353\pi$
$480$	−1.47898e9	+	2.97647e9i	−0.0278610	+	0.0560707i
$481$	2.36254e9	−	1.98240e9i	0.0441365	−	0.0370350i
$482$	−6.48216e8	+	1.78096e9i	−0.0120097	+	0.0329963i
$483$	−3.41042e10	+	1.15709e11i	−0.626642	+	2.12608i
$484$	5.98832e9	−	3.39615e10i	0.109125	−	0.618878i
$485$		−	7.38771e9i		−	0.133519i
$486$	−2.60583e8	+	7.06671e9i	−0.00467090	+	0.126670i
$487$	−2.63994e10			−0.469330			−0.234665	−	0.972076i	$-0.575399\pi$
$487$	−2.63994e10			−0.469330			−0.234665	+	0.972076i	$0.575399\pi$
$488$	1.13408e9	+	1.99969e8i	0.0199970	+	0.00352601i
$489$	−2.97609e10	−	8.77175e9i	−0.520489	−	0.153409i
$490$	1.44594e9	+	5.26280e8i	0.0250823	+	0.00912920i
$491$	−5.15419e10	−	6.14253e10i	−0.886818	−	1.05687i	−0.998009	−	0.0630696i	$-0.979911\pi$
$491$	−5.15419e10	−	6.14253e10i	−0.886818	−	1.05687i	0.111191	−	0.993799i	$-0.464533\pi$
$492$	7.79640e10	+	3.87396e10i	1.33056	+	0.661142i
$493$	−1.23255e11	+	4.48613e10i	−2.08650	+	0.759423i
$494$	5.61554e9	+	3.24213e9i	0.0942940	+	0.0544406i
$495$	5.10089e9	+	3.29294e9i	0.0849621	+	0.0548483i
$496$	−7.90689e8	−	1.36951e9i	−0.0130641	−	0.0226277i
$497$	−2.64093e10	+	3.14734e10i	−0.432844	+	0.515844i
$498$	1.16018e9	+	8.56060e8i	0.0188629	+	0.0139183i
$499$	−8.53818e9	−	4.84224e10i	−0.137709	−	0.780988i	−0.972935	−	0.231080i	$-0.925774\pi$
$499$	−8.53818e9	−	4.84224e10i	−0.137709	−	0.780988i	0.835225	−	0.549908i	$-0.185337\pi$
$500$	−2.00894e10	+	3.54230e9i	−0.321430	+	0.0566768i
$501$	−4.13227e10	−	9.46846e10i	−0.655900	−	1.50289i
$502$	−9.73187e7	−	8.16601e7i	−0.00153243	−	0.00128586i
$503$	−7.47465e10	+	4.31549e10i	−1.16767	+	0.674153i	−0.953129	−	0.302563i	$-0.902158\pi$
$503$	−7.47465e10	+	4.31549e10i	−1.16767	+	0.674153i	−0.214538	+	0.976716i	$0.568824\pi$
$504$	−1.78521e10	−	1.65571e10i	−0.276673	−	0.256603i
$505$	−4.78192e9	+	8.28253e9i	−0.0735253	+	0.127350i
$506$	2.52337e9	+	6.93291e9i	0.0384928	+	0.105758i
$507$	1.17557e9	−	7.34998e7i	0.0177916	−	0.00111238i
$508$	8.80735e10	−	7.39024e10i	1.32248	−	1.10970i
$509$	−2.04132e10	+	5.60848e10i	−0.304116	+	0.835553i	0.689658	+	0.724136i	$0.257761\pi$
$509$	−2.04132e10	+	5.60848e10i	−0.304116	+	0.835553i	−0.993774	+	0.111417i	$0.964461\pi$
$510$	1.58546e9	+	1.66620e9i	0.0234355	+	0.0246290i
$511$	1.26950e10	−	7.19967e10i	0.186186	−	1.05591i
$512$			4.08008e10i			0.593729i
$513$	5.89789e10	−	1.11793e10i	0.851583	−	0.161415i
$514$	8.39234e9			0.120235
$515$	1.34851e10	+	2.37779e9i	0.191702	+	0.0338022i
$516$	2.42284e10	+	1.00320e11i	0.341764	+	1.41510i
$517$	2.21912e10	+	8.07693e9i	0.310612	+	0.113054i
$518$	−5.11746e8	−	6.09875e8i	−0.00710781	−	0.00847075i
$519$	2.96386e10	−	1.96752e10i	0.408496	−	0.271174i
$520$	2.88083e9	−	1.04854e9i	0.0394007	−	0.0143407i
$521$	4.74442e10	+	2.73919e10i	0.643921	+	0.371768i	0.786123	−	0.618070i	$-0.212085\pi$
$521$	4.74442e10	+	2.73919e10i	0.643921	+	0.371768i	−0.142203	+	0.989838i	$0.545418\pi$
$522$	−7.91690e9	−	1.04471e10i	−0.106629	−	0.140706i
$523$	5.33114e10	+	9.23381e10i	0.712547	+	1.23417i	0.963898	+	0.266272i	$0.0857918\pi$
$523$	5.33114e10	+	9.23381e10i	0.712547	+	1.23417i	−0.251351	+	0.967896i	$0.580875\pi$
$524$	7.10233e10	−	8.46423e10i	0.942054	−	1.12270i
$525$	1.23903e10	−	1.10074e11i	0.163096	−	1.44893i
$526$	4.40777e8	+	2.49977e9i	0.00575805	+	0.0326555i
$527$	−3.32343e9	+	5.86010e8i	−0.0430868	+	0.00759736i
$528$	4.41984e10	+	4.97511e9i	0.568684	+	0.0640128i
$529$	−7.09026e10	−	5.94943e10i	−0.905397	−	0.759719i
$530$	−8.79797e8	+	5.07951e8i	−0.0111501	+	0.00643752i
$531$	1.34593e10	+	1.07215e11i	0.169296	+	1.34858i
$532$	−5.12536e10	+	8.87739e10i	−0.639850	+	1.10825i
$533$	−4.13084e10	−	1.13494e11i	−0.511835	−	1.40626i
$534$	−1.25432e9	−	1.88950e9i	−0.0154256	−	0.0232371i
$535$	−4.26177e9	+	3.57605e9i	−0.0520205	+	0.0436504i
$536$	−3.07057e9	+	8.43631e9i	−0.0372014	+	0.102210i
$537$	−1.25846e11	+	3.03933e10i	−1.51336	+	0.365495i
$538$	3.49694e9	−	1.98321e10i	0.0417406	−	0.236723i
$539$		−	6.35010e10i		−	0.752360i
$540$	6.88136e9	−	1.22790e10i	0.0809281	−	0.144406i
$541$	−1.25068e11			−1.46001			−0.730007	−	0.683440i	$-0.760483\pi$
$541$	−1.25068e11			−1.46001			−0.730007	+	0.683440i	$0.760483\pi$
$542$	1.75427e9	+	3.09324e8i	0.0203282	+	0.00358440i
$543$	1.06591e9	−	1.01426e9i	0.0122609	−	0.0116668i
$544$	4.88258e10	+	1.77711e10i	0.557512	+	0.202918i
$545$	1.08746e9	+	1.29599e9i	0.0123262	+	0.0146898i
$546$	1.04538e9	+	1.67200e10i	0.0117626	+	0.188133i
$547$	1.19145e11	−	4.33652e10i	1.33084	−	0.484387i	0.423926	−	0.905697i	$-0.360652\pi$
$547$	1.19145e11	−	4.33652e10i	1.33084	−	0.484387i	0.906917	+	0.421310i	$0.138430\pi$
$548$	1.11680e11	+	6.44783e10i	1.23838	+	0.714976i
$549$	−7.15159e9	−	1.63067e9i	−0.0787251	−	0.0179505i
$550$	−3.38735e9	−	5.86706e9i	−0.0370177	−	0.0641165i
$551$	−7.15240e10	+	8.52389e10i	−0.775970	+	0.924765i
$552$	3.16090e10	−	1.37949e10i	0.340451	−	0.148581i
$553$	1.34406e10	+	7.62253e10i	0.143720	+	0.815077i
$554$	−8.64964e9	+	1.52517e9i	−0.0918246	+	0.0161912i
$555$	5.50990e8	−	7.46734e8i	0.00580726	−	0.00787035i
$556$	−2.61960e10	−	2.19811e10i	−0.274117	−	0.230012i
$557$	1.23761e10	−	7.14536e9i	0.128577	−	0.0742340i	−0.434332	−	0.900753i	$-0.643015\pi$
$557$	1.23761e10	−	7.14536e9i	0.128577	−	0.0742340i	0.562909	+	0.826519i	$0.309682\pi$
$558$	−1.53921e8	−	3.00074e8i	−0.00158768	−	0.00309523i
$559$	7.15885e10	−	1.23995e11i	0.733156	−	1.26986i
$560$	8.08440e9	+	2.22117e10i	0.0822045	+	0.225855i
$561$	4.22362e10	−	8.50009e10i	0.426416	−	0.858168i
$562$	−1.49003e10	+	1.25028e10i	−0.149365	+	0.125332i
$563$	−5.56583e10	+	1.52920e11i	−0.553983	+	1.52206i	0.274243	+	0.961660i	$0.411573\pi$
$563$	−5.56583e10	+	1.52920e11i	−0.553983	+	1.52206i	−0.828226	+	0.560395i	$0.810649\pi$
$564$	1.54783e10	−	5.25150e10i	0.152970	−	0.519000i
$565$	3.63331e9	−	2.06055e10i	0.0356541	−	0.202204i
$566$		−	1.69076e10i		−	0.164746i
$567$	1.08337e11	+	1.10977e11i	1.04821	+	1.07374i
$568$	1.17463e10			0.112852
$569$	−6.79582e9	−	1.19829e9i	−0.0648325	−	0.0114317i	0.141138	−	0.989990i	$-0.454924\pi$
$569$	−6.79582e9	−	1.19829e9i	−0.0648325	−	0.0114317i	−0.205970	+	0.978558i	$0.566035\pi$
$570$	1.87154e9	+	5.51618e8i	0.0177296	+	0.00522564i
$571$	3.97562e10	+	1.44701e10i	0.373991	+	0.136121i	0.522175	−	0.852838i	$-0.325121\pi$
$571$	3.97562e10	+	1.44701e10i	0.373991	+	0.136121i	−0.148185	+	0.988960i	$0.547343\pi$
$572$	−4.03323e10	−	4.80662e10i	−0.376764	−	0.449009i
$573$	2.15782e10	+	1.07220e10i	0.200169	+	0.0994621i
$574$	−2.92978e10	+	1.06635e10i	−0.269891	+	0.0982322i
$575$	1.35878e11	+	7.84495e10i	1.24302	+	0.717660i
$576$	4.94336e9	−	9.94827e10i	0.0449089	−	0.903770i
$577$	−6.78404e10	−	1.17503e11i	−0.612047	−	1.06010i	−0.990895	−	0.134638i	$-0.957013\pi$
$577$	−6.78404e10	−	1.17503e11i	−0.612047	−	1.06010i	0.378848	−	0.925459i	$-0.376320\pi$
$578$	1.40182e10	−	1.67063e10i	0.125598	−	0.149682i
$579$	8.56976e10	+	6.32333e10i	0.762525	+	0.562642i
$580$	4.53068e9	+	2.56948e10i	0.0400361	+	0.227056i
$581$	3.11412e10	−	5.49103e9i	0.273294	−	0.0481892i
$582$	−4.61660e9	−	1.05782e10i	−0.0402374	−	0.0921979i
$583$	3.21160e10	+	2.69485e10i	0.278001	+	0.233271i
$584$	−1.81010e10	+	1.04506e10i	−0.155615	+	0.0898444i
$585$	−1.86587e10	+	5.75989e9i	−0.159316	+	0.0491803i
$586$	−1.09659e10	+	1.89936e10i	−0.0929941	+	0.161070i
$587$	−4.72536e10	−	1.29828e11i	−0.398000	−	1.09350i	−0.963257	−	0.268581i	$-0.913445\pi$
$587$	−4.72536e10	−	1.29828e11i	−0.398000	−	1.09350i	0.565257	−	0.824915i	$-0.308777\pi$
$588$	−1.46930e11	+	9.18650e9i	−1.22914	+	0.0768495i
$589$	−2.19307e9	+	1.84021e9i	−0.0182218	+	0.0152899i
$590$	−1.20124e9	+	3.30037e9i	−0.00991334	+	0.0272367i
$591$	7.28074e10	+	7.65151e10i	0.596796	+	0.627187i
$592$	1.18051e9	−	6.69502e9i	0.00961133	−	0.0545086i
$593$		−	1.47786e11i		−	1.19513i	−0.801821	−	0.597564i	$-0.796135\pi$
$593$		−	1.47786e11i		−	1.19513i	0.801821	−	0.597564i	$-0.203865\pi$
$594$	9.36158e9	+	1.52750e9i	0.0751975	+	0.0122697i
$595$	5.04423e10			0.402464
$596$	1.47598e11	+	2.60256e10i	1.16976	+	0.206260i
$597$	−1.51883e10	−	6.28885e10i	−0.119568	−	0.495078i
$598$	−2.22982e10	−	8.11589e9i	−0.174368	−	0.0634646i
$599$	2.98197e9	+	3.55377e9i	0.0231630	+	0.0276046i	0.777502	−	0.628881i	$-0.216487\pi$
$599$	2.98197e9	+	3.55377e9i	0.0231630	+	0.0276046i	−0.754339	+	0.656486i	$0.772042\pi$
$600$	−2.63843e10	+	1.75149e10i	−0.203583	+	0.135145i
$601$	1.14595e11	−	4.17093e10i	0.878354	−	0.319695i	0.136809	−	0.990598i	$-0.456315\pi$
$601$	1.14595e11	−	4.17093e10i	0.878354	−	0.319695i	0.741545	+	0.670903i	$0.234093\pi$
$602$	−3.20086e10	−	1.84802e10i	−0.243714	−	0.140708i
$603$	2.22013e10	−	5.26995e10i	0.167922	−	0.398600i
$604$	1.21417e11	+	2.10300e11i	0.912287	+	1.58013i
$605$	−9.25352e9	+	1.10279e10i	−0.0690694	+	0.0823137i
$606$	−1.67131e9	+	1.48477e10i	−0.0123927	+	0.110096i
$607$	−6.96919e9	−	3.95242e10i	−0.0513367	−	0.291145i	0.948321	−	0.317313i	$-0.102781\pi$
$607$	−6.96919e9	−	3.95242e10i	−0.0513367	−	0.291145i	−0.999658	+	0.0261682i	$0.991669\pi$
$608$	4.34090e10	−	7.65417e9i	0.317662	−	0.0560124i
$609$	−2.85674e11	−	3.21564e10i	−2.07684	−	0.233775i
$610$	−1.82637e8	−	1.53251e8i	−0.00131908	−	0.00110684i
$611$	−6.57779e10	+	3.79769e10i	−0.471971	+	0.272493i
$612$	−2.02788e11	−	8.54304e10i	−1.44556	−	0.608985i
$613$	−1.34667e11	+	2.33249e11i	−0.953714	+	1.65188i	−0.216430	+	0.976298i	$0.569441\pi$
$613$	−1.34667e11	+	2.33249e11i	−0.953714	+	1.65188i	−0.737284	+	0.675583i	$0.763892\pi$
$614$	−1.22726e10	−	3.37186e10i	−0.0863500	−	0.237245i
$615$	−2.00998e10	−	3.02783e10i	−0.140505	−	0.211656i
$616$	−2.50186e10	+	2.09931e10i	−0.173756	+	0.145799i
$617$	7.45509e10	−	2.04827e11i	0.514413	−	1.41334i	−0.362180	−	0.932108i	$-0.617968\pi$
$617$	7.45509e10	−	2.04827e11i	0.514413	−	1.41334i	0.876594	−	0.481231i	$-0.159810\pi$
$618$	2.07948e10	−	5.02221e9i	0.142561	−	0.0344303i
$619$	−4.72166e10	+	2.67779e11i	−0.321612	+	1.82395i	0.210875	+	0.977513i	$0.432369\pi$
$619$	−4.72166e10	+	2.67779e11i	−0.321612	+	1.82395i	−0.532487	+	0.846438i	$0.678742\pi$
$620$			6.71287e8i			0.00454299i
$621$	−2.05451e11	+	7.77684e10i	−1.38147	+	0.522922i
$622$	2.49119e10			0.166435
$623$	−4.89838e10	−	8.63717e9i	−0.325162	−	0.0573349i
$624$	−1.03633e11	+	9.86114e10i	−0.683534	+	0.650412i
$625$	−1.31325e11	−	4.77984e10i	−0.860652	−	0.313252i
$626$	1.96020e10	+	2.33608e10i	0.127645	+	0.152121i
$627$	−5.02453e9	−	8.03631e10i	−0.0325106	−	0.519980i
$628$	−1.90306e11	+	6.92659e10i	−1.22353	+	0.445329i
$629$	−1.25641e10	−	7.25386e9i	−0.0802652	−	0.0463411i
$630$	1.48688e9	+	4.81665e9i	0.00943875	+	0.0305761i
$631$	−7.03626e10	−	1.21872e11i	−0.443838	−	0.768750i	0.554132	−	0.832428i	$-0.313050\pi$
$631$	−7.03626e10	−	1.21872e11i	−0.443838	−	0.768750i	−0.997970	+	0.0636786i	$0.979717\pi$
$632$	1.42241e10	−	1.69517e10i	0.0891575	−	0.106254i
$633$	−1.00039e11	+	4.36596e10i	−0.623098	+	0.271935i
$634$	3.96431e9	+	2.24827e10i	0.0245364	+	0.139153i
$635$	−4.72658e10	+	8.33424e9i	−0.290705	+	0.0512591i
$636$	5.77080e10	−	7.82093e10i	0.352702	−	0.478002i
$637$	1.56455e11	+	1.31281e11i	0.950237	+	0.797343i
$638$	−1.52268e10	+	8.79118e9i	−0.0919021	+	0.0530597i
$639$	−7.47276e10	−	3.71326e9i	−0.448206	−	0.0222716i
$640$	6.87096e9	−	1.19008e10i	0.0409541	−	0.0709346i
$641$	5.53171e10	+	1.51982e11i	0.327663	+	0.900246i	0.988702	+	0.149894i	$0.0478934\pi$
$641$	5.53171e10	+	1.51982e11i	0.327663	+	0.900246i	−0.661039	+	0.750351i	$0.729884\pi$
$642$	−3.86761e9	+	7.78362e9i	−0.0227668	+	0.0458186i
$643$	5.46145e10	−	4.58270e10i	0.319495	−	0.268088i	−0.468908	−	0.883247i	$-0.655353\pi$
$643$	5.46145e10	−	4.58270e10i	0.319495	−	0.268088i	0.788403	+	0.615159i	$0.210908\pi$
$644$	1.28301e11	−	3.52504e11i	0.745910	−	2.04937i
$645$	1.21801e10	−	4.13249e10i	0.0703740	−	0.238766i
$646$	5.29670e9	−	3.00391e10i	0.0304141	−	0.172487i
$647$		−	1.04773e11i		−	0.597905i	−0.954268	−	0.298952i	$-0.903363\pi$
$647$		−	1.04773e11i		−	0.597905i	0.954268	−	0.298952i	$-0.0966372\pi$
$648$	4.39570e9	−	4.41214e10i	0.0249303	−	0.250236i
$649$	1.44941e11			0.816983
$650$	2.14583e10	+	3.78369e9i	0.120211	+	0.0211964i
$651$	−7.09466e9	−	2.09108e9i	−0.0395009	−	0.0116425i
$652$	9.06655e10	+	3.29996e10i	0.501709	+	0.182607i
$653$	1.52339e11	+	1.81551e11i	0.837837	+	0.998495i	0.999931	+	0.0117197i	$0.00373059\pi$
$653$	1.52339e11	+	1.81551e11i	0.837837	+	0.998495i	−0.162095	+	0.986775i	$0.551825\pi$
$654$	2.36697e9	+	1.17613e9i	0.0129385	+	0.00642900i
$655$	−4.33435e10	+	1.57757e10i	−0.235483	+	0.0857087i
$656$	−2.30565e11	−	1.33117e11i	−1.24502	−	0.718815i
$657$	1.18459e11	−	6.07627e10i	0.635779	−	0.326119i
$658$	9.80352e9	+	1.69802e10i	0.0522972	+	0.0905814i
$659$	−2.38359e10	+	2.84065e10i	−0.126383	+	0.150618i	−0.825525	−	0.564365i	$-0.809121\pi$
$659$	−2.38359e10	+	2.84065e10i	−0.126383	+	0.150618i	0.699142	+	0.714983i	$0.253565\pi$
$660$	−1.51924e10	−	1.12100e10i	−0.0800665	−	0.0590784i
$661$	2.29243e10	+	1.30010e11i	0.120085	+	0.681038i	0.984106	+	0.177582i	$0.0568274\pi$
$661$	2.29243e10	+	1.30010e11i	0.120085	+	0.681038i	−0.864021	+	0.503456i	$0.832061\pi$
$662$	1.40957e10	−	2.48545e9i	0.0733930	−	0.0129412i
$663$	1.22108e11	+	2.79792e11i	0.631962	+	1.44804i
$664$	−6.92546e9	−	5.81115e9i	−0.0356268	−	0.0298944i
$665$	3.70587e10	−	2.13958e10i	0.189497	−	0.109406i
$666$	3.22309e8	−	1.41354e9i	0.00163823	−	0.00718474i
$667$	2.03600e11	−	3.52645e11i	1.02867	−	1.78170i
$668$	1.09878e11	+	3.01887e11i	0.551829	+	1.51614i
$669$	1.91316e11	−	1.19617e10i	0.955098	−	0.0597154i
$670$	1.42385e9	−	1.19475e9i	0.00706586	−	0.00592896i
$671$	−3.36514e9	+	9.24564e9i	−0.0166002	+	0.0456086i
$672$	7.85021e10	+	8.24997e10i	0.384950	+	0.404553i
$673$	2.55164e10	−	1.44710e11i	0.124382	−	0.705407i	−0.857291	−	0.514833i	$-0.827854\pi$
$673$	2.55164e10	−	1.44710e11i	0.124382	−	0.705407i	0.981673	−	0.190574i	$-0.0610349\pi$
$674$			4.60280e8i			0.00223040i
$675$	1.73389e11	−	1.03085e11i	0.835229	−	0.496572i
$676$	−3.66281e9			−0.0175399
$677$	−1.14383e11	−	2.01689e10i	−0.544513	−	0.0960124i	−0.105376	−	0.994432i	$-0.533605\pi$
$677$	−1.14383e11	−	2.01689e10i	−0.544513	−	0.0960124i	−0.439137	+	0.898420i	$0.644716\pi$
$678$	−7.67403e9	−	3.17749e10i	−0.0363166	−	0.150371i
$679$	−2.37864e11	−	8.65753e10i	−1.11905	−	0.407300i
$680$	−9.26987e9	−	1.10474e10i	−0.0433549	−	0.0516683i
$681$	1.04908e11	−	6.96418e10i	0.487777	−	0.323804i
$682$	−4.25087e8	+	1.54719e8i	−0.00196490	+	0.000715166i
$683$	1.13839e11	+	6.57249e10i	0.523128	+	0.302028i	0.738213	−	0.674567i	$-0.235670\pi$
$683$	1.13839e11	+	6.57249e10i	0.523128	+	0.302028i	−0.215086	+	0.976595i	$0.569003\pi$
$684$	−1.85219e11	+	2.32518e10i	−0.846179	+	0.106226i
$685$	−2.69165e10	−	4.66207e10i	−0.122252	−	0.211747i
$686$	6.81370e9	−	8.12025e9i	0.0307671	−	0.0366668i
$687$	−1.77320e10	+	1.57529e11i	−0.0796031	+	0.707186i
$688$	−5.48048e10	−	3.10814e11i	−0.244605	−	1.38722i
$689$	−1.32792e11	+	2.34149e10i	−0.589246	+	0.103900i
$690$	−7.09542e9	−	7.98683e8i	−0.0313027	−	0.00352353i
$691$	1.59975e11	+	1.34235e11i	0.701681	+	0.588780i	0.922251	−	0.386591i	$-0.126348\pi$
$691$	1.59975e11	+	1.34235e11i	0.701681	+	0.588780i	−0.220571	+	0.975371i	$0.570792\pi$
$692$	−9.58058e10	+	5.53135e10i	−0.417799	+	0.241216i
$693$	1.65800e11	−	1.25645e11i	0.718872	−	0.544770i
$694$	2.42620e9	−	4.20230e9i	0.0104590	−	0.0181155i
$695$	4.88245e9	+	1.34144e10i	0.0209266	+	0.0574953i
$696$	4.54563e10	+	6.84752e10i	0.193712	+	0.291807i
$697$	−4.35227e11	+	3.65199e11i	−1.84410	+	1.54738i
$698$	−2.97972e9	+	8.18671e9i	−0.0125532	+	0.0344895i
$699$	1.77036e11	−	4.27565e10i	0.741572	−	0.179099i
$700$	−5.98148e10	+	3.39227e11i	−0.249125	+	1.41286i
$701$		−	1.31996e11i		−	0.546626i	−0.961925	−	0.273313i	$-0.911881\pi$
$701$		−	1.31996e11i		−	0.546626i	0.961925	−	0.273313i	$-0.0881195\pi$
$702$	−2.31175e10	+	1.99073e10i	−0.0951903	+	0.0819718i
$703$	−1.23073e10			−0.0503897
$704$	−1.31576e11	−	2.32004e10i	−0.535657	−	0.0944507i
$705$	−1.65569e10	+	1.57547e10i	−0.0670230	+	0.0637753i
$706$	−4.19463e10	−	1.52672e10i	−0.168840	−	0.0614527i
$707$	2.10636e11	+	2.51026e11i	0.843053	+	1.00471i
$708$	−2.09682e10	−	3.35369e11i	−0.0834504	−	1.33472i
$709$	4.05092e11	−	1.47441e11i	1.60313	−	0.583492i	0.623065	−	0.782170i	$-0.285887\pi$
$709$	4.05092e11	−	1.47441e11i	1.60313	−	0.583492i	0.980065	+	0.198678i	$0.0636648\pi$
$710$	−2.10608e9	−	1.21595e9i	−0.00828784	−	0.00478499i
$711$	−9.58501e10	+	1.03347e11i	−0.375072	+	0.404407i
$712$	7.11021e9	+	1.23152e10i	0.0276670	+	0.0479207i
$713$	6.73427e9	−	8.02558e9i	0.0260575	−	0.0310541i
$714$	7.22268e10	−	3.15216e10i	0.277911	−	0.121287i
$715$	4.54842e9	+	2.57954e10i	0.0174035	+	0.0987001i
$716$	3.96480e11	−	6.99101e10i	1.50858	−	0.266004i
$717$	8.52458e10	−	1.15530e11i	0.322549	−	0.437138i
$718$	2.30709e10	+	1.93588e10i	0.0868095	+	0.0728418i
$719$	5.28838e10	−	3.05325e10i	0.197882	−	0.114247i	−0.397785	−	0.917479i	$-0.630221\pi$
$719$	5.28838e10	−	3.05325e10i	0.197882	−	0.114247i	0.595667	+	0.803231i	$0.296888\pi$
$720$	−2.33461e10	+	3.61640e10i	−0.0868729	+	0.134570i
$721$	2.34588e11	−	4.06319e11i	0.868091	−	1.50358i
$722$	2.93044e9	+	8.05131e9i	0.0107841	+	0.0296291i
$723$	−3.36830e10	+	6.77876e10i	−0.123270	+	0.248083i
$724$	−3.50505e9	+	2.94108e9i	−0.0127567	+	0.0107042i
$725$	−1.27885e11	+	3.51361e11i	−0.462879	+	1.27175i
$726$	−6.35846e9	+	2.15731e10i	−0.0228879	+	0.0776544i
$727$	4.11431e10	−	2.33334e11i	0.147285	−	0.835296i	−0.818219	−	0.574907i	$-0.805038\pi$
$727$	4.11431e10	−	2.33334e11i	0.147285	−	0.835296i	0.965504	−	0.260389i	$-0.0838508\pi$
$728$		−	1.05042e11i		−	0.373972i
$729$	−4.19123e10	+	2.79302e11i	−0.148399	+	0.988928i
$730$	4.32729e9			0.0152379
$731$	−6.63284e11	−	1.16955e11i	−2.32290	−	0.409589i
$732$	2.18796e10	+	6.44880e9i	0.0762071	+	0.0224613i
$733$	1.40249e11	+	5.10464e10i	0.485829	+	0.176827i	0.573310	−	0.819339i	$-0.305659\pi$
$733$	1.40249e11	+	5.10464e10i	0.485829	+	0.176827i	−0.0874803	+	0.996166i	$0.527881\pi$
$734$	−7.18728e9	−	8.56547e9i	−0.0247617	−	0.0295099i
$735$	5.50361e10	+	2.73469e10i	0.188581	+	0.0937042i
$736$	−1.51578e11	+	5.51700e10i	−0.516566	+	0.188015i
$737$	−6.64287e10	−	3.83526e10i	−0.225157	−	0.129995i
$738$	−4.77013e10	−	3.07941e10i	−0.160807	−	0.103811i
$739$	−2.69209e11	−	4.66284e11i	−0.902634	−	1.56341i	−0.824062	−	0.566500i	$-0.808297\pi$
$739$	−2.69209e11	−	4.66284e11i	−0.902634	−	1.56341i	−0.0785724	−	0.996908i	$-0.525036\pi$
$740$	−1.85498e9	+	2.21068e9i	−0.00618605	+	0.00737225i
$741$	2.08388e11	+	1.53762e11i	0.691193	+	0.510008i
$742$	6.04442e9	+	3.42796e10i	0.0199406	+	0.113089i
$743$	−3.59160e10	+	6.33296e9i	−0.117851	+	0.0207803i	−0.232263	−	0.972653i	$-0.574613\pi$
$743$	−3.59160e10	+	6.33296e9i	−0.117851	+	0.0207803i	0.114412	+	0.993433i	$0.463502\pi$
$744$	8.45829e8	+	1.93809e9i	0.00276052	+	0.00632531i
$745$	−4.79279e10	−	4.02163e10i	−0.155583	−	0.130550i
$746$	−2.26414e10	+	1.30720e10i	−0.0731053	+	0.0422074i
$747$	4.22214e10	+	3.91587e10i	0.135597	+	0.125761i
$748$	−1.47581e11	+	2.55618e11i	−0.471437	+	0.816553i
$749$	6.51959e10	+	1.79124e11i	0.207154	+	0.569150i
$750$	1.32781e10	−	8.30183e8i	0.0419653	−	0.00262379i
$751$	1.20638e11	−	1.01227e11i	0.379248	−	0.318227i	−0.433159	−	0.901318i	$-0.642601\pi$
$751$	1.20638e11	−	1.01227e11i	0.379248	−	0.318227i	0.812407	+	0.583090i	$0.198157\pi$
$752$	−5.72634e10	+	1.57330e11i	−0.179063	+	0.491971i
$753$	−3.49761e9	−	3.67573e9i	−0.0108791	−	0.0114331i
$754$	9.81980e9	−	5.56908e10i	0.0303821	−	0.172305i
$755$		−	1.01371e11i		−	0.311980i
$756$	−3.14707e11	−	3.65456e11i	−0.963428	−	1.11879i
$757$	−3.98668e11			−1.21403			−0.607013	−	0.794692i	$-0.707632\pi$
$757$	−3.98668e11			−1.21403			−0.607013	+	0.794692i	$0.707632\pi$
$758$	−4.92372e10	−	8.68184e9i	−0.149148	−	0.0262987i
$759$	6.91762e10	+	2.86429e11i	0.208444	+	0.863078i
$760$	−1.14963e10	−	4.18429e9i	−0.0344589	−	0.0125420i
$761$	−8.36046e10	−	9.96361e10i	−0.249282	−	0.297083i	0.626864	−	0.779129i	$-0.284338\pi$
$761$	−8.36046e10	−	9.96361e10i	−0.249282	−	0.297083i	−0.876146	+	0.482046i	$0.839894\pi$
$762$	−6.24704e10	+	4.14701e10i	−0.185291	+	0.123003i
$763$	5.44711e10	−	1.98258e10i	0.160719	−	0.0584970i
$764$	−6.48906e10	−	3.74646e10i	−0.190462	−	0.109963i
$765$	5.54808e10	+	7.32119e10i	0.161993	+	0.213765i
$766$	6.08415e9	+	1.05381e10i	0.0176720	+	0.0306088i
$767$	−2.99650e11	+	3.57109e11i	−0.865830	+	1.03186i
$768$	−3.28113e10	+	2.91493e11i	−0.0943147	+	0.837882i
$769$	−2.40087e10	−	1.36160e11i	−0.0686537	−	0.389354i	−0.999701	−	0.0244556i	$-0.992215\pi$
$769$	−2.40087e10	−	1.36160e11i	−0.0686537	−	0.389354i	0.931047	−	0.364899i	$-0.118896\pi$
$770$	6.65893e9	−	1.17415e9i	0.0189427	−	0.00334010i
$771$	3.33079e11	+	3.74924e10i	0.942604	+	0.106103i
$772$	−2.53705e11	−	2.12884e11i	−0.714266	−	0.599341i
$773$	2.26195e11	−	1.30594e11i	0.633528	−	0.365767i	−0.148589	−	0.988899i	$-0.547473\pi$
$773$	2.26195e11	−	1.30594e11i	0.633528	−	0.365767i	0.782117	+	0.623132i	$0.214140\pi$
$774$	−8.38373e9	−	6.67832e10i	−0.0233600	−	0.186082i
$775$	−4.81009e9	+	8.33131e9i	−0.0133336	+	0.0230944i
$776$	2.47517e10	+	6.80048e10i	0.0682588	+	0.187539i
$777$	−1.75858e10	−	2.64912e10i	−0.0482479	−	0.0726804i
$778$	4.43149e10	−	3.71846e10i	0.120957	−	0.101495i
$779$	−1.64846e11	+	4.52910e11i	−0.447639	+	1.22988i
$780$	5.90280e10	−	1.42560e10i	0.159470	−	0.0385140i
$781$	−1.74273e10	+	9.88350e10i	−0.0468409	+	0.265648i
$782$			1.11624e11i			0.298492i
$783$	−2.67538e11	−	4.49996e11i	−0.711767	−	1.19719i
$784$	4.50206e11			1.19164
$785$	8.32576e10	+	1.46806e10i	0.219253	+	0.0386602i
$786$	−5.22039e10	+	4.96743e10i	−0.136777	+	0.130149i
$787$	−3.29394e11	−	1.19889e11i	−0.858650	−	0.312523i	−0.125088	−	0.992146i	$-0.539921\pi$
$787$	−3.29394e11	−	1.19889e11i	−0.858650	−	0.312523i	−0.733562	+	0.679622i	$0.762144\pi$
$788$	−2.11121e11	−	2.51605e11i	−0.547555	−	0.652550i
$789$	6.32613e9	+	1.01181e11i	0.0163241	+	0.261091i
$790$	−4.30515e9	+	1.56694e9i	−0.0110530	+	0.00402296i
$791$	−6.20863e11	−	3.58455e11i	−1.58595	−	0.915649i
$792$	−5.79870e10	−	1.32219e10i	−0.147377	−	0.0336042i
$793$	−1.58225e10	−	2.74054e10i	−0.0400114	−	0.0693017i
$794$	−1.25868e10	+	1.50003e10i	−0.0316689	+	0.0377415i
$795$	−3.71870e10	+	1.62293e10i	−0.0930942	+	0.0406286i
$796$	3.49359e10	+	1.98131e11i	0.0870201	+	0.493516i
$797$	4.01383e11	−	7.07747e10i	0.994777	−	0.175406i	0.347516	−	0.937674i	$-0.387025\pi$
$797$	4.01383e11	−	7.07747e10i	0.994777	−	0.175406i	0.647262	+	0.762268i	$0.275914\pi$
$798$	3.96929e10	−	5.37941e10i	0.0978816	−	0.132655i
$799$	2.73702e11	+	2.29663e11i	0.671570	+	0.563514i
$800$	1.28275e11	−	7.40597e10i	0.313172	−	0.180810i
$801$	−4.13407e10	−	8.05949e10i	−0.100426	−	0.195784i
$802$	2.14830e10	−	3.72096e10i	0.0519274	−	0.0899409i
$803$	−6.10777e10	−	1.67810e11i	−0.146899	−	0.403603i
$804$	−7.91313e10	+	1.59253e11i	−0.189376	+	0.381121i
$805$	−1.19960e11	+	1.00659e11i	−0.285663	+	0.239699i
$806$	4.97621e8	−	1.36720e9i	0.00117912	−	0.00323961i
$807$	2.27387e11	−	7.71484e11i	0.536132	−	1.81900i
$808$	1.62685e10	−	9.22631e10i	0.0381682	−	0.216462i
$809$			6.91423e11i			1.61417i	0.590434	+	0.807086i	$0.298957\pi$
$809$			6.91423e11i			1.61417i	−0.590434	+	0.807086i	$0.701043\pi$
$810$	−5.35547e9	+	7.45582e9i	−0.0124411	+	0.0173203i
$811$	1.41013e11			0.325968			0.162984	−	0.986629i	$-0.447888\pi$
$811$	1.41013e11			0.325968			0.162984	+	0.986629i	$0.447888\pi$
$812$	8.80395e11	+	1.55237e11i	2.02513	+	0.357085i
$813$	6.82421e10	+	2.01137e10i	0.156203	+	0.0460394i
$814$	−1.82744e9	−	6.65133e8i	−0.00416241	−	0.00151499i
$815$	−2.58898e10	−	3.08542e10i	−0.0586811	−	0.0699334i
$816$	6.02635e11	+	2.99444e11i	1.35923	+	0.675390i
$817$	−5.36906e11	+	1.95418e11i	−1.20506	+	0.438607i
$818$	5.12585e9	+	2.95941e9i	0.0114486	+	0.00660985i
$819$	−3.32062e10	+	6.68259e11i	−0.0738047	+	1.48528i
$820$	5.65074e10	+	9.78737e10i	0.124983	+	0.216476i
$821$	3.09207e11	−	3.68498e11i	0.680575	−	0.811078i	−0.309606	−	0.950865i	$-0.600197\pi$
$821$	3.09207e11	−	3.68498e11i	0.680575	−	0.811078i	0.990182	+	0.139787i	$0.0446418\pi$
$822$	−6.76743e10	−	4.99346e10i	−0.148230	−	0.109374i
$823$	−2.05735e10	−	1.16678e11i	−0.0448444	−	0.254325i	0.954141	−	0.299357i	$-0.0967722\pi$
$823$	−2.05735e10	−	1.16678e11i	−0.0448444	−	0.254325i	−0.998986	+	0.0450318i	$0.985661\pi$
$824$	−1.32099e11	+	2.32926e10i	−0.286543	+	0.0505253i
$825$	−1.08228e11	−	2.47987e11i	−0.233627	−	0.535320i
$826$	9.21856e10	+	7.73529e10i	0.198035	+	0.166171i
$827$	1.48258e11	−	8.55968e10i	0.316954	−	0.182993i	−0.333080	−	0.942899i	$-0.608088\pi$
$827$	1.48258e11	−	8.55968e10i	0.316954	−	0.182993i	0.650034	+	0.759905i	$0.274755\pi$
$828$	6.52740e11	−	2.01499e11i	1.38873	−	0.428697i
$829$	−1.14122e11	+	1.97665e11i	−0.241630	+	0.418516i	−0.961179	−	0.275926i	$-0.911015\pi$
$829$	−1.14122e11	+	1.97665e11i	−0.241630	+	0.418516i	0.719549	+	0.694442i	$0.244349\pi$
$830$	6.40162e8	+	1.75883e9i	0.00134889	+	0.00370605i
$831$	−3.50104e11	+	2.18895e10i	−0.734165	+	0.0459021i
$832$	3.29181e11	−	2.76216e11i	0.686976	−	0.576441i
$833$	3.28596e11	−	9.02809e11i	0.682467	−	1.87506i
$834$	1.53737e10	+	1.61566e10i	0.0317772	+	0.0333954i
$835$	2.32881e10	−	1.32073e11i	0.0479057	−	0.271687i
$836$			2.50394e11i			0.512624i
$837$	−4.76833e9	−	1.25971e10i	−0.00971548	−	0.0256667i
$838$	−2.24619e10			−0.0455482
$839$	−2.48039e11	−	4.37360e10i	−0.500579	−	0.0882655i	−0.0823430	−	0.996604i	$-0.526240\pi$
$839$	−2.48039e11	−	4.37360e10i	−0.500579	−	0.0882655i	−0.418236	+	0.908339i	$0.637351\pi$
$840$	−7.42030e9	−	3.07243e10i	−0.0149040	−	0.0617113i
$841$	4.41809e11	+	1.60805e11i	0.883184	+	0.321453i
$842$	6.78539e10	+	8.08651e10i	0.134998	+	0.160884i
$843$	−6.47224e11	+	4.29650e11i	−1.28158	+	0.850756i
$844$	3.18960e11	−	1.16092e11i	0.628588	−	0.228787i
$845$	1.32419e9	+	7.64521e8i	0.00259731	+	0.00149956i
$846$	−1.38623e10	+	3.29051e10i	−0.0270615	+	0.0642365i
$847$	2.46628e11	+	4.27172e11i	0.479191	+	0.829983i
$848$	−1.91058e11	+	2.27694e11i	−0.369472	+	0.440320i
$849$	7.55339e10	−	6.71035e11i	0.145382	−	1.29156i
$850$	−1.77987e10	−	1.00942e11i	−0.0340968	−	0.193373i
$851$	4.43546e10	−	7.82091e9i	0.0845708	−	0.0149121i
$852$	2.31208e11	+	2.60255e10i	0.438778	+	0.0493902i
$853$	1.21481e11	+	1.01935e11i	0.229464	+	0.192543i	0.750269	−	0.661133i	$-0.229924\pi$
$853$	1.21481e11	+	1.01935e11i	0.229464	+	0.192543i	−0.520806	+	0.853675i	$0.674368\pi$
$854$	−7.07455e9	+	4.08450e9i	−0.0133005	+	0.00767904i
$855$	7.18142e10	+	3.02539e10i	0.134383	+	0.0566131i
$856$	2.72489e10	−	4.71966e10i	0.0507522	−	0.0879053i
$857$	4.47678e10	+	1.22999e11i	0.0829933	+	0.228022i	0.974247	−	0.225482i	$-0.0723958\pi$
$857$	4.47678e10	+	1.22999e11i	0.0829933	+	0.228022i	−0.891254	+	0.453505i	$0.850174\pi$
$858$	2.26323e10	+	3.40933e10i	0.0417619	+	0.0629100i
$859$	−3.75658e11	+	3.15214e11i	−0.689953	+	0.578940i	−0.918896	−	0.394500i	$-0.870918\pi$
$859$	−3.75658e11	+	3.15214e11i	−0.689953	+	0.578940i	0.228942	+	0.973440i	$0.426473\pi$
$860$	−4.58219e10	+	1.25895e11i	−0.0837682	+	0.230151i
$861$	−1.21042e12	+	2.92332e11i	−2.20254	+	0.531942i
$862$	9.27893e9	−	5.26234e10i	0.0168062	−	0.0953126i
$863$		−	5.93817e11i		−	1.07056i	−0.844676	−	0.535278i	$-0.820207\pi$
$863$		−	5.93817e11i		−	1.07056i	0.844676	−	0.535278i	$-0.179793\pi$
$864$	−3.33966e10	+	2.04678e11i	−0.0599304	+	0.367296i
$865$	4.61813e10			0.0824900
$866$	7.38472e10	+	1.30212e10i	0.131299	+	0.0231516i
$867$	6.30997e11	−	6.00421e11i	1.11674	−	1.06262i
$868$	2.16136e10	+	7.86670e9i	0.0380757	+	0.0138584i
$869$	1.21530e11	+	1.44834e11i	0.213111	+	0.253976i
$870$	−1.06182e9	−	1.69829e10i	−0.00185342	−	0.0296439i
$871$	2.31828e11	−	8.43785e10i	0.402804	−	0.146609i
$872$	−1.43523e10	−	8.28631e9i	−0.0248231	−	0.0143316i
$873$	−1.35968e11	−	4.40458e11i	−0.234088	−	0.758311i
$874$	4.73471e10	+	8.20076e10i	0.0811424	+	0.140543i
$875$	1.87551e11	−	2.23515e11i	0.319954	−	0.381307i
$876$	−3.79446e11	+	1.65600e11i	−0.644368	+	0.281218i
$877$	1.12371e11	+	6.37288e11i	0.189957	+	1.07730i	0.919419	+	0.393280i	$0.128660\pi$
$877$	1.12371e11	+	6.37288e11i	0.189957	+	1.07730i	−0.729461	+	0.684022i	$0.760229\pi$
$878$	1.02631e11	−	1.80966e10i	0.172703	−	0.0304522i
$879$	−5.20074e11	+	7.04835e11i	−0.871183	+	1.18068i
$880$	4.42303e10	+	3.71136e10i	0.0737546	+	0.0618874i
$881$	9.64127e11	−	5.56639e11i	1.60041	−	0.923995i	0.609002	−	0.793169i	$-0.291570\pi$
$881$	9.64127e11	−	5.56639e11i	1.60041	−	0.923995i	0.991405	−	0.130827i	$-0.0417631\pi$
$882$	9.58936e10	+	4.76501e9i	0.158458	+	0.00787390i
$883$	1.81808e11	−	3.14901e11i	0.299068	−	0.518002i	−0.676855	−	0.736117i	$-0.736657\pi$
$883$	1.81808e11	−	3.14901e11i	0.299068	−	0.518002i	0.975923	+	0.218115i	$0.0699908\pi$
$884$	−3.24688e11	−	8.92074e11i	−0.531689	−	1.46080i
$885$	−6.24194e10	+	1.25620e11i	−0.101753	+	0.204779i
$886$	5.07613e10	−	4.25938e10i	0.0823754	−	0.0691212i
$887$	1.03973e10	−	2.85665e10i	0.0167968	−	0.0461490i	−0.931011	−	0.364991i	$-0.881072\pi$
$887$	1.03973e10	−	2.85665e10i	0.0167968	−	0.0461490i	0.947808	+	0.318843i	$0.103294\pi$
$888$	−2.57008e9	+	8.71981e9i	−0.00413328	+	0.0140235i
$889$	−2.85561e11	+	1.61950e12i	−0.457185	+	2.59282i
$890$		−	2.94412e9i		−	0.00469241i
$891$	3.64722e11	+	1.02446e11i	0.578697	+	0.162549i
$892$	−5.96101e11			−0.941588
$893$	2.98497e11	+	5.26331e10i	0.469390	+	0.0827662i
$894$	−9.37578e10	−	2.76342e10i	−0.146777	−	0.0432610i
$895$	−1.57928e11	−	5.74812e10i	−0.246132	−	0.0895847i
$896$	−3.02655e11	−	3.60690e11i	−0.469586	−	0.559631i
$897$	−8.48724e11	−	4.21723e11i	−1.31098	−	0.651415i
$898$	−1.09767e10	+	3.99520e9i	−0.0168798	+	0.00614374i
$899$	2.16223e10	+	1.24836e10i	0.0331026	+	0.0191118i
$900$	−5.58142e11	+	2.86296e11i	−0.850697	+	0.436360i
$901$	3.17151e11	+	5.49322e11i	0.481246	+	0.833543i
$902$	−4.89538e10	+	5.83409e10i	−0.0739538	+	0.0881347i
$903$	−1.18781e12	−	8.76445e11i	−1.78647	−	1.31818i
$904$	3.55915e10	+	2.01850e11i	0.0532933	+	0.302242i
$905$	1.88103e9	−	3.31676e8i	0.00280415	−	0.000494448i
$906$	−6.33471e10	−	1.45150e11i	−0.0940186	−	0.215429i
$907$	−5.34610e11	−	4.48591e11i	−0.789965	−	0.662860i	0.155772	−	0.987793i	$-0.450214\pi$
$907$	−5.34610e11	−	4.48591e11i	−0.789965	−	0.662860i	−0.945737	+	0.324933i	$0.894658\pi$
$908$	−3.39113e11	+	1.95787e11i	−0.498885	+	0.288032i
$909$	−1.32663e11	+	5.81817e11i	−0.194310	+	0.852179i
$910$	−1.08737e10	+	1.88338e10i	−0.0158567	+	0.0274646i
$911$	−4.82114e10	−	1.32460e11i	−0.0699965	−	0.192314i	0.899762	−	0.436382i	$-0.143740\pi$
$911$	−4.82114e10	−	1.32460e11i	−0.0699965	−	0.192314i	−0.969758	+	0.244068i	$0.921518\pi$
$912$	5.69754e11	−	3.56226e10i	0.823584	−	0.0514928i
$913$	5.91708e10	−	4.96502e10i	0.0851578	−	0.0714559i
$914$	−1.40433e10	+	3.85836e10i	−0.0201226	+	0.0552863i
$915$	−6.56395e9	−	6.89821e9i	−0.00936442	−	0.00984130i
$916$	8.56023e10	−	4.85475e11i	0.121592	−	0.689580i
$917$			1.58041e12i			2.23508i
$918$	1.25192e11	+	7.01597e10i	0.176281	+	0.0987909i
$919$	−1.09245e10			−0.0153158			−0.00765789	−	0.999971i	$-0.502438\pi$
$919$	−1.09245e10			−0.0153158			−0.00765789	+	0.999971i	$0.502438\pi$
$920$	4.40906e10	+	7.77436e9i	0.0615452	+	0.0108521i
$921$	−3.36443e11	−	1.39307e12i	−0.467598	−	1.93612i
$922$	1.18885e11	+	4.32706e10i	0.164514	+	0.0598782i
$923$	−2.07483e11	−	2.47268e11i	−0.285874	−	0.340692i
$924$	−5.38967e11	+	3.57786e11i	−0.739392	+	0.490835i
$925$	−3.88627e10	+	1.41449e10i	−0.0530843	+	0.0193211i
$926$	3.57736e10	+	2.06539e10i	0.0486541	+	0.0280904i
$927$	8.47751e11	−	1.06424e11i	1.14802	−	0.144118i
$928$	−1.92207e11	−	3.32912e11i	−0.259166	−	0.448888i
$929$	4.80764e11	−	5.72952e11i	0.645459	−	0.769229i	−0.339763	−	0.940511i	$-0.610347\pi$
$929$	4.80764e11	−	5.72952e11i	0.645459	−	0.769229i	0.985222	+	0.171283i	$0.0547911\pi$
$930$	4.89708e7	−	4.35052e8i	6.54644e−5	−	0.000581580i
$931$	−1.41529e11	−	8.02649e11i	−0.188385	−	1.06838i
$932$	−5.57756e11	+	9.83475e10i	−0.739232	+	0.130347i
$933$	9.88712e11	+	1.11293e11i	1.30480	+	0.146872i
$934$	9.80378e10	+	8.22635e10i	0.128827	+	0.108099i
$935$	1.06708e11	−	6.16077e10i	0.139620	−	0.0806099i
$936$	1.52458e11	−	1.15535e11i	0.198631	−	0.150525i
$937$	−7.09425e11	+	1.22876e12i	−0.920339	+	1.59407i	−0.121449	+	0.992598i	$0.538754\pi$
$937$	−7.09425e11	+	1.22876e12i	−0.920339	+	1.59407i	−0.798890	+	0.601477i	$0.794579\pi$
$938$	−2.17818e10	−	5.98451e10i	−0.0281373	−	0.0773067i
$939$	6.73610e11	+	1.01472e12i	0.866455	+	1.30523i
$940$	5.44442e10	−	4.56841e10i	0.0697333	−	0.0585132i
$941$	4.20534e10	−	1.15541e11i	0.0536342	−	0.147359i	−0.909983	−	0.414647i	$-0.863905\pi$
$941$	4.20534e10	−	1.15541e11i	0.0536342	−	0.147359i	0.963617	+	0.267288i	$0.0861274\pi$
$942$	1.28388e11	−	3.10073e10i	0.163050	−	0.0393786i
$943$	3.06281e11	−	1.73701e12i	0.387323	−	2.19662i
$944$			1.02760e12i			1.29400i
$945$	3.74939e10	+	1.97808e11i	0.0470146	+	0.248037i
$946$	−9.02829e10			−0.112730
$947$	6.20520e11	+	1.09414e11i	0.771535	+	0.136042i	0.545539	−	0.838086i	$-0.316325\pi$
$947$	6.20520e11	+	1.09414e11i	0.771535	+	0.136042i	0.225996	+	0.974128i	$0.427436\pi$
$948$	3.17540e11	−	3.02153e11i	0.393156	−	0.374105i
$949$	5.39724e11	+	1.96443e11i	0.665437	+	0.242199i
$950$	−5.58922e10	−	6.66097e10i	−0.0686209	−	0.0817792i
$951$	5.68967e10	+	9.10014e11i	0.0695609	+	1.11257i
$952$	−4.64328e11	+	1.69002e11i	−0.565297	+	0.205751i
$953$	−9.29664e11	−	5.36742e11i	−1.12708	−	0.650719i	−0.183880	−	0.982949i	$-0.558866\pi$
$953$	−9.29664e11	−	5.36742e11i	−1.12708	−	0.650719i	−0.943199	+	0.332229i	$0.892199\pi$
$954$	−4.31052e10	+	4.64765e10i	−0.0520398	+	0.0561100i
$955$	1.56396e10	+	2.70886e10i	0.0188024	+	0.0325667i
$956$	−2.86992e11	+	3.42024e11i	−0.343588	+	0.409472i
$957$	−6.43601e11	+	2.80883e11i	−0.767307	+	0.334871i
$958$	−7.57215e9	−	4.29438e10i	−0.00898995	−	0.0509845i
$959$	−1.81649e12	+	3.20296e11i	−2.14762	+	0.378684i
$960$	7.67714e10	−	1.04045e11i	0.0903888	−	0.122500i
$961$	−6.52860e11	−	5.47815e11i	−0.765467	−	0.642303i
$962$	5.41680e9	−	3.12739e9i	0.00632473	−	0.00365159i
$963$	−1.88272e11	+	2.91641e11i	−0.218918	+	0.339113i
$964$	1.17695e11	−	2.03853e11i	0.136285	−	0.236053i
$965$	4.72859e10	+	1.29917e11i	0.0545284	+	0.149815i
$966$	−1.08865e11	+	2.19093e11i	−0.125021	+	0.251606i
$967$	1.04835e12	−	8.79666e11i	1.19894	−	1.00603i	0.199283	−	0.979942i	$-0.436139\pi$
$967$	1.04835e12	−	8.79666e11i	1.19894	−	1.00603i	0.999660	−	0.0260903i	$-0.00830575\pi$
$968$	4.82320e10	−	1.32516e11i	0.0549331	−	0.150927i
$969$	3.44416e11	−	1.16854e12i	0.390651	−	1.32541i
$970$	2.60176e9	−	1.47553e10i	0.00293887	−	0.0166671i
$971$			9.79743e11i			1.10214i	0.834460	+	0.551068i	$0.185780\pi$
$971$			9.79743e11i			1.10214i	−0.834460	+	0.551068i	$0.814220\pi$
$972$	1.84280e11	−	8.58725e11i	0.206449	−	0.962031i
$973$	4.89124e11			0.545717
$974$	−5.27269e10	−	9.29718e9i	−0.0585864	−	0.0103304i
$975$	8.34744e11	+	2.46033e11i	0.923709	+	0.272254i
$976$	−6.55492e10	−	2.38580e10i	−0.0722384	−	0.0262926i
$977$	5.47974e11	+	6.53049e11i	0.601425	+	0.716750i	0.977758	−	0.209734i	$-0.0672598\pi$
$977$	5.47974e11	+	6.53049e11i	0.601425	+	0.716750i	−0.376334	+	0.926484i	$0.622815\pi$
$978$	−5.63517e10	−	2.80006e10i	−0.0615959	−	0.0306064i
$979$	−1.14171e11	+	4.15549e10i	−0.124287	+	0.0452368i
$980$	−1.65506e11	−	9.55551e10i	−0.179436	−	0.103598i
$981$	8.86872e10	+	5.72530e10i	0.0957601	+	0.0618190i
$982$	−8.13112e10	−	1.40835e11i	−0.0874388	−	0.151448i
$983$	3.08149e10	−	3.67237e10i	0.0330025	−	0.0393308i	−0.749291	−	0.662241i	$-0.769605\pi$
$983$	3.08149e10	−	3.67237e10i	0.0330025	−	0.0393308i	0.782293	+	0.622910i	$0.214050\pi$
$984$	2.86465e11	+	2.11373e11i	0.305557	+	0.225460i
$985$	2.38089e10	+	1.35027e11i	0.0252927	+	0.143442i
$986$	−2.61974e11	+	4.61931e10i	−0.277173	+	0.0488730i
$987$	3.13228e11	+	7.17714e11i	0.330059	+	0.756280i
$988$	−6.16926e11	−	5.17663e11i	−0.647449	−	0.543274i
$989$	1.81078e12	−	1.04546e12i	1.89270	−	1.09275i
$990$	9.02822e9	+	8.37332e9i	0.00939856	+	0.00871680i
$991$	−6.84665e11	+	1.18587e12i	−0.709878	+	1.22954i	0.255025	+	0.966935i	$0.417916\pi$
$991$	−6.84665e11	+	1.18587e12i	−0.709878	+	1.22954i	−0.964902	+	0.262609i	$0.915417\pi$
$992$	−3.38272e9	−	9.29395e9i	−0.00349317	−	0.00959740i
$993$	5.70540e11	−	3.56718e10i	0.586799	−	0.0366883i
$994$	−6.38309e10	+	5.35604e10i	−0.0653860	+	0.0548654i
$995$	2.87249e10	−	7.89209e10i	0.0293066	−	0.0805193i
$996$	−1.23442e11	−	1.29728e11i	−0.125437	−	0.131825i
$997$	3.84888e10	−	2.18281e11i	0.0389542	−	0.220920i	−0.959116	−	0.283012i	$-0.908666\pi$
$997$	3.84888e10	−	2.18281e11i	0.0389542	−	0.220920i	0.998070	+	0.0620923i	$0.0197773\pi$
$998$		−	9.97200e10i		−	0.100522i
$999$	1.91069e10	−	5.46613e10i	0.0191835	−	0.0548805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.9.f.a.2.13	✓	138
3.2	odd	2		81.9.f.a.8.11		138
27.13	even	9		81.9.f.a.71.11		138
27.14	odd	18	inner	27.9.f.a.14.13	yes	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.13	✓	138	1.1	even	1	trivial
27.9.f.a.14.13	yes	138	27.14	odd	18	inner
81.9.f.a.8.11		138	3.2	odd	2
81.9.f.a.71.11		138	27.13	even	9

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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99728 + 0.352174i) q^{2} +(77.6955 + 22.9000i) q^{3} +(-236.696 - 86.1504i) q^{4} +(67.5893 + 80.5497i) q^{5} +(147.115 + 73.1000i) q^{6} +(3385.55 - 1232.24i) q^{7} +(-892.041 - 515.020i) q^{8} +(5512.18 + 3558.45i) q^{9} +(106.627 + 184.683i) q^{10} +(5656.92 - 6741.66i) q^{11} +(-16417.4 - 12113.8i) q^{12} +(4915.16 + 27875.3i) q^{13} +(7195.84 - 1268.82i) q^{14} +(3406.79 + 7806.14i) q^{15} +(47796.6 + 40106.1i) q^{16} +(115312. - 66575.1i) q^{17} +(9756.17 + 9048.46i) q^{18} +(56477.6 - 97822.1i) q^{19} +(-9058.73 - 24888.7i) q^{20} +(291260. - 18210.4i) q^{21} +(13672.7 - 11472.7i) q^{22} +(-141378. + 388433. i) q^{23} +(-57513.6 - 60442.5i) q^{24} +(65911.4 - 373802. i) q^{25} +57405.7i q^{26} +(346783. + 402705. i) q^{27} -907504. q^{28} +(-970128. - 171060. i) q^{29} +(4055.19 + 16790.8i) q^{30} +(-23816.5 - 8668.51i) q^{31} +(250836. + 298934. i) q^{32} +(593901. - 394253. i) q^{33} +(253755. - 92359.3i) q^{34} +(328083. + 189419. i) q^{35} +(-998151. - 1.31715e6i) q^{36} +(-54478.7 - 94360.0i) q^{37} +(147252. - 175488. i) q^{38} +(-256457. + 2.27834e6i) q^{39} +(-18807.6 - 106663. i) q^{40} +(-4.20215e6 + 740952. i) q^{41} +(588140. + 66202.9i) q^{42} +(-3.87489e6 - 3.25142e6i) q^{43} +(-1.91977e6 + 1.10838e6i) q^{44} +(85931.9 + 684518. i) q^{45} +(-419167. + 726019. i) q^{46} +(917770. + 2.52155e6i) q^{47} +(2.79515e6 + 4.21060e6i) q^{48} +(5.52741e6 - 4.63805e6i) q^{49} +(263287. - 723374. i) q^{50} +(1.04838e7 - 2.53196e6i) q^{51} +(1.23806e6 - 7.02141e6i) q^{52} +4.76381e6i q^{53} +(550801. + 926441. i) q^{54} +925386. q^{55} +(-3.65467e6 - 644417. i) q^{56} +(6.62818e6 - 6.30700e6i) q^{57} +(-1.87737e6 - 683308. i) q^{58} +(1.05864e7 + 1.26163e7i) q^{59} +(-133873. - 2.14118e6i) q^{60} +(-1.05057e6 + 382376. i) q^{61} +(-44515.4 - 25701.0i) q^{62} +(2.30466e7 + 5.25498e6i) q^{63} +(-7.59072e6 - 1.31475e7i) q^{64} +(-1.91313e6 + 2.27998e6i) q^{65} +(1.32503e6 - 578276. i) q^{66} +(-1.51350e6 - 8.58350e6i) q^{67} +(-3.30293e7 + 5.82395e6i) q^{68} +(-1.98795e7 + 2.69419e7i) q^{69} +(588565. + 493864. i) q^{70} +(-9.87592e6 + 5.70186e6i) q^{71} +(-3.08442e6 - 6.01317e6i) q^{72} +(1.01458e7 - 1.75731e7i) q^{73} +(-75578.1 - 207649. i) q^{74} +(1.36811e7 - 2.75334e7i) q^{75} +(-2.17954e7 + 1.82886e7i) q^{76} +(1.08444e7 - 2.97949e7i) q^{77} +(-1.31459e6 + 4.46016e6i) q^{78} +(-3.73057e6 + 2.11571e7i) q^{79} +6.56074e6i q^{80} +(1.77216e7 + 3.92297e7i) q^{81} -8.65380e6 q^{82} +(8.64355e6 + 1.52409e6i) q^{83} +(-7.05089e7 - 2.07818e7i) q^{84} +(1.31564e7 + 4.78855e6i) q^{85} +(-6.59417e6 - 7.85863e6i) q^{86} +(-7.14573e7 - 3.55065e7i) q^{87} +(-8.51829e6 + 3.10040e6i) q^{88} +(-1.19561e7 - 6.90285e6i) q^{89} +(-69439.4 + 1.39744e6i) q^{90} +(5.09895e7 + 8.83163e7i) q^{91} +(6.69273e7 - 7.97608e7i) q^{92} +(-1.65193e6 - 1.21890e6i) q^{93} +(945017. + 5.35946e6i) q^{94} +(1.16968e7 - 2.06247e6i) q^{95} +(1.26432e7 + 2.89700e7i) q^{96} +(-5.38212e7 - 4.51614e7i) q^{97} +(1.26732e7 - 7.31687e6i) q^{98} +(5.51718e7 - 1.70314e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17}+ \cdots + 228876057 q^{99}+O(q^{100}) \) 138 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 447 * q^5 - 774 * q^6 - 6 * q^7 - 9 * q^8 - 12960 * q^9 - 3 * q^10 + 28668 * q^11 + 77421 * q^12 - 6 * q^13 - 120975 * q^14 + 105507 * q^15 - 774 * q^16 - 9 * q^17 - 241317 * q^18 - 3 * q^19 + 137913 * q^20 + 1164372 * q^21 - 185478 * q^22 + 68376 * q^23 - 2624256 * q^24 + 507585 * q^25 + 3500568 * q^27 - 12 * q^28 - 943980 * q^29 - 1533627 * q^30 + 920739 * q^31 - 3005136 * q^32 - 1245285 * q^33 + 660474 * q^34 + 6225408 * q^35 + 4021128 * q^36 - 3 * q^37 - 23716884 * q^38 - 5699685 * q^39 - 975273 * q^40 + 16694382 * q^41 + 1594134 * q^42 + 4412514 * q^43 + 17341119 * q^44 + 12986721 * q^45 - 3 * q^46 - 11341869 * q^47 - 26229183 * q^48 + 11347482 * q^49 - 40948977 * q^50 - 16497396 * q^51 + 14465511 * q^52 + 34106454 * q^54 - 12 * q^55 + 52215771 * q^56 + 26766582 * q^57 - 19078611 * q^58 + 76116738 * q^59 - 24031170 * q^60 + 34059450 * q^61 - 223709616 * q^62 - 149069421 * q^63 + 100663293 * q^64 + 20396037 * q^65 + 83336805 * q^66 - 103603884 * q^67 + 101921427 * q^68 + 38038563 * q^69 + 135373629 * q^70 + 125718795 * q^71 + 183269700 * q^72 - 7632642 * q^73 - 66643887 * q^74 - 167459145 * q^75 - 203790342 * q^76 - 343269159 * q^77 - 344470788 * q^78 - 68767890 * q^79 + 151392924 * q^81 - 12 * q^82 + 383244663 * q^83 + 836800692 * q^84 + 170435619 * q^85 + 71426730 * q^86 - 145695735 * q^87 - 192774918 * q^88 + 135692730 * q^89 - 821329020 * q^90 + 77546796 * q^91 - 1343159175 * q^92 - 414573177 * q^93 - 44451609 * q^94 + 881099997 * q^95 + 1578184830 * q^96 + 31339344 * q^97 + 1293135102 * q^98 + 228876057 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more