LMFDB - Embedded newform 100.9.j.b.11.90

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(11,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.11"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [464] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			11.90
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.90

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(12.1877 - 10.3663i) q^{2} +(41.6337 + 13.5276i) q^{3} +(41.0777 - 252.683i) q^{4} +(617.041 - 99.4242i) q^{5} +(647.648 - 266.719i) q^{6} -2741.64i q^{7} +(-2118.76 - 3505.44i) q^{8} +(-3757.59 - 2730.05i) q^{9} +(6489.62 - 7608.21i) q^{10} +(3699.71 + 5092.22i) q^{11} +(5128.41 - 9964.43i) q^{12} +(-9465.41 - 6877.02i) q^{13} +(-28420.8 - 33414.2i) q^{14} +(27034.7 + 4207.69i) q^{15} +(-62161.2 - 20759.3i) q^{16} +(-13747.2 - 42309.4i) q^{17} +(-74096.9 + 5679.60i) q^{18} +(-140541. + 45664.6i) q^{19} +(223.872 - 160000. i) q^{20} +(37087.8 - 114145. i) q^{21} +(97878.6 + 23709.7i) q^{22} +(257427. + 354318. i) q^{23} +(-40791.5 - 174606. i) q^{24} +(370855. - 122698. i) q^{25} +(-186651. + 14307.0i) q^{26} +(-288333. - 396856. i) q^{27} +(-692766. - 112620. i) q^{28} +(43560.4 - 134065. i) q^{29} +(373107. - 228969. i) q^{30} +(990432. - 321811. i) q^{31} +(-972797. + 391378. i) q^{32} +(85147.2 + 262056. i) q^{33} +(-606139. - 373144. i) q^{34} +(-272585. - 1.69171e6i) q^{35} +(-844191. + 837335. i) q^{36} +(-1.49296e6 - 1.08470e6i) q^{37} +(-1.23949e6 + 2.01344e6i) q^{38} +(-301050. - 414360. i) q^{39} +(-1.65589e6 - 1.95234e6i) q^{40} +(-1.89931e6 - 1.37993e6i) q^{41} +(-731249. - 1.77562e6i) q^{42} -251346. i q^{43} +(1.43869e6 - 725678. i) q^{44} +(-2.59002e6 - 1.31096e6i) q^{45} +(6.81041e6 + 1.64973e6i) q^{46} +(6.44607e6 + 2.09446e6i) q^{47} +(-2.30718e6 - 1.70518e6i) q^{48} -1.75180e6 q^{49} +(3.24792e6 - 5.33980e6i) q^{50} -1.94746e6i q^{51} +(-2.12652e6 + 2.10925e6i) q^{52} +(504486. - 1.55265e6i) q^{53} +(-7.62804e6 - 1.84778e6i) q^{54} +(2.78917e6 + 2.77427e6i) q^{55} +(-9.61065e6 + 5.80887e6i) q^{56} -6.46897e6 q^{57} +(-858866. - 2.08550e6i) q^{58} +(6.74188e6 - 9.27940e6i) q^{59} +(2.17373e6 - 6.65835e6i) q^{60} +(-887999. + 645169. i) q^{61} +(8.73504e6 - 1.41893e7i) q^{62} +(-7.48483e6 + 1.03020e7i) q^{63} +(-7.79896e6 + 1.48543e7i) q^{64} +(-6.52429e6 - 3.30232e6i) q^{65} +(3.75431e6 + 2.31118e6i) q^{66} +(-2.81977e7 + 9.16199e6i) q^{67} +(-1.12556e7 + 1.73570e6i) q^{68} +(5.92456e6 + 1.82339e7i) q^{69} +(-2.08590e7 - 1.77922e7i) q^{70} +(-266190. - 86490.3i) q^{71} +(-1.60860e6 + 1.89563e7i) q^{72} +(1.76827e7 - 1.28472e7i) q^{73} +(-2.94399e7 + 2.25660e6i) q^{74} +(1.70998e7 - 91578.6i) q^{75} +(5.76554e6 + 3.73881e7i) q^{76} +(1.39610e7 - 1.01433e7i) q^{77} +(-7.96449e6 - 1.92928e6i) q^{78} +(-5.77183e7 - 1.87538e7i) q^{79} +(-4.04200e7 - 6.62900e6i) q^{80} +(2.78099e6 + 8.55901e6i) q^{81} +(-3.74529e7 + 2.87080e6i) q^{82} +(8.08802e7 - 2.62796e7i) q^{83} +(-2.73189e7 - 1.40603e7i) q^{84} +(-1.26891e7 - 2.47398e7i) q^{85} +(-2.60554e6 - 3.06332e6i) q^{86} +(3.62715e6 - 4.99235e6i) q^{87} +(1.00117e7 - 2.37583e7i) q^{88} +(-1.42816e7 + 1.03762e7i) q^{89} +(-4.51562e7 + 1.08716e7i) q^{90} +(-1.88543e7 + 2.59508e7i) q^{91} +(1.00105e8 - 5.04928e7i) q^{92} +4.55886e7 q^{93} +(1.00274e8 - 4.12957e7i) q^{94} +(-8.21794e7 + 4.21501e7i) q^{95} +(-4.57955e7 + 3.13489e6i) q^{96} +(3.06739e7 - 9.44045e7i) q^{97} +(-2.13503e7 + 1.81598e7i) q^{98} -2.92349e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) $ 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	12.1877	−	10.3663i	0.761728	−	0.647897i
$2$	12.1877	−	10.3663i	0.761728	−	0.647897i
$3$	41.6337	+	13.5276i	0.513996	+	0.167007i	0.554519	−	0.832171i	$-0.312902\pi$
$3$	41.6337	+	13.5276i	0.513996	+	0.167007i	−0.0405229	+	0.999179i	$0.512902\pi$
$4$	41.0777	−	252.683i	0.160460	−	0.987042i
$5$	617.041	−	99.4242i	0.987266	−	0.159079i
$5$	617.041	−	99.4242i	0.987266	−	0.159079i
$6$	647.648	−	266.719i	0.499729	−	0.205802i
$7$		−	2741.64i		−	1.14188i	−0.820993	−	0.570938i	$-0.806580\pi$
$7$		−	2741.64i		−	1.14188i	0.820993	−	0.570938i	$-0.193420\pi$
$8$	−2118.76	−	3505.44i	−0.517275	−	0.855819i
$9$	−3757.59	−	2730.05i	−0.572717	−	0.416103i
$10$	6489.62	−	7608.21i	0.648962	−	0.760821i
$11$	3699.71	+	5092.22i	0.252695	+	0.347805i	0.916453	−	0.400142i	$-0.131039\pi$
$11$	3699.71	+	5092.22i	0.252695	+	0.347805i	−0.663758	+	0.747948i	$0.731039\pi$
$12$	5128.41	−	9964.43i	0.247319	−	0.480538i
$13$	−9465.41	−	6877.02i	−0.331410	−	0.240784i	0.409619	−	0.912257i	$-0.365662\pi$
$13$	−9465.41	−	6877.02i	−0.331410	−	0.240784i	−0.741029	+	0.671473i	$0.765662\pi$
$14$	−28420.8	−	33414.2i	−0.739817	−	0.869799i
$15$	27034.7	+	4207.69i	0.534018	+	0.0831149i
$16$	−62161.2	−	20759.3i	−0.948505	−	0.316761i
$17$	−13747.2	−	42309.4i	−0.164595	−	0.506572i	0.834411	−	0.551143i	$-0.185808\pi$
$17$	−13747.2	−	42309.4i	−0.164595	−	0.506572i	−0.999006	+	0.0445707i	$0.985808\pi$
$18$	−74096.9	+	5679.60i	−0.705846	+	0.0541038i
$19$	−140541.	+	45664.6i	−1.07842	+	0.350401i	−0.793762	−	0.608228i	$-0.791881\pi$
$19$	−140541.	+	45664.6i	−1.07842	+	0.350401i	−0.284660	+	0.958629i	$0.591881\pi$
$20$	223.872	−	160000.i	0.00139920	−	0.999999i
$21$	37087.8	−	114145.i	0.190702	−	0.586919i
$22$	97878.6	+	23709.7i	0.417827	+	0.101213i
$23$	257427.	+	354318.i	0.919905	+	1.26614i	0.963669	+	0.267098i	$0.0860648\pi$
$23$	257427.	+	354318.i	0.919905	+	1.26614i	−0.0437646	+	0.999042i	$0.513935\pi$
$24$	−40791.5	−	174606.i	−0.122949	−	0.526276i
$25$	370855.	−	122698.i	0.949388	−	0.314106i
$26$	−186651.	+	14307.0i	−0.408447	+	0.0313079i
$27$	−288333.	−	396856.i	−0.542549	−	0.746754i
$28$	−692766.	−	112620.i	−1.12708	−	0.183225i
$29$	43560.4	−	134065.i	0.0615885	−	0.189550i	−0.915528	−	0.402254i	$-0.868227\pi$
$29$	43560.4	−	134065.i	0.0615885	−	0.189550i	0.977117	+	0.212704i	$0.0682270\pi$
$30$	373107.	−	228969.i	0.460626	−	0.282677i
$31$	990432.	−	321811.i	1.07245	−	0.348461i	0.281010	−	0.959705i	$-0.409331\pi$
$31$	990432.	−	321811.i	1.07245	−	0.348461i	0.791442	+	0.611244i	$0.209331\pi$
$32$	−972797.	+	391378.i	−0.927732	+	0.373247i
$33$	85147.2	+	262056.i	0.0717983	+	0.220973i
$34$	−606139.	−	373144.i	−0.453583	−	0.279230i
$35$	−272585.	−	1.69171e6i	−0.181648	−	1.12733i
$36$	−844191.	+	837335.i	−0.502609	+	0.498528i
$37$	−1.49296e6	−	1.08470e6i	−0.796599	−	0.578763i	0.113315	−	0.993559i	$-0.463853\pi$
$37$	−1.49296e6	−	1.08470e6i	−0.796599	−	0.578763i	−0.909914	+	0.414796i	$0.863853\pi$
$38$	−1.23949e6	+	2.01344e6i	−0.594441	+	0.965616i
$39$	−301050.	−	414360.i	−0.130131	−	0.179110i
$40$	−1.65589e6	−	1.95234e6i	−0.646830	−	0.762634i
$41$	−1.89931e6	−	1.37993e6i	−0.672140	−	0.488338i	0.198601	−	0.980080i	$-0.436360\pi$
$41$	−1.89931e6	−	1.37993e6i	−0.672140	−	0.488338i	−0.870741	+	0.491742i	$0.836360\pi$
$42$	−731249.	−	1.77562e6i	−0.235000	−	0.570628i
$43$		−	251346.i		−	0.0735187i	−0.999324	−	0.0367594i	$-0.988296\pi$
$43$		−	251346.i		−	0.0735187i	0.999324	−	0.0367594i	$-0.0117035\pi$
$44$	1.43869e6	−	725678.i	0.383846	−	0.193612i
$45$	−2.59002e6	−	1.31096e6i	−0.631617	−	0.319697i
$46$	6.81041e6	+	1.64973e6i	1.52105	+	0.368452i
$47$	6.44607e6	+	2.09446e6i	1.32100	+	0.429220i	0.882839	−	0.469675i	$-0.155629\pi$
$47$	6.44607e6	+	2.09446e6i	1.32100	+	0.429220i	0.438164	+	0.898895i	$0.355629\pi$
$48$	−2.30718e6	−	1.70518e6i	−0.434626	−	0.321221i
$49$	−1.75180e6			−0.303879
$50$	3.24792e6	−	5.33980e6i	0.519667	−	0.854369i
$51$		−	1.94746e6i		−	0.287865i
$52$	−2.12652e6	+	2.10925e6i	−0.290842	+	0.288480i
$53$	504486.	−	1.55265e6i	0.0639360	−	0.196775i	−0.913986	−	0.405746i	$-0.867012\pi$
$53$	504486.	−	1.55265e6i	0.0639360	−	0.196775i	0.977922	+	0.208972i	$0.0670116\pi$
$54$	−7.62804e6	−	1.84778e6i	−0.897094	−	0.217308i
$55$	2.78917e6	+	2.77427e6i	0.304806	+	0.303178i
$56$	−9.61065e6	+	5.80887e6i	−0.977239	+	0.590663i
$57$	−6.46897e6			−0.612824
$58$	−858866.	−	2.08550e6i	−0.0758950	−	0.184288i
$59$	6.74188e6	−	9.27940e6i	0.556382	−	0.765794i	−0.434479	−	0.900682i	$-0.643068\pi$
$59$	6.74188e6	−	9.27940e6i	0.556382	−	0.765794i	0.990861	+	0.134888i	$0.0430675\pi$
$60$	2.17373e6	−	6.65835e6i	0.167726	−	0.513762i
$61$	−887999.	+	645169.i	−0.0641347	+	0.0465966i	−0.619391	−	0.785083i	$-0.712620\pi$
$61$	−887999.	+	645169.i	−0.0641347	+	0.0465966i	0.555256	+	0.831680i	$0.312620\pi$
$62$	8.73504e6	−	1.41893e7i	0.591150	−	0.960270i
$63$	−7.48483e6	+	1.03020e7i	−0.475138	+	0.653971i
$64$	−7.79896e6	+	1.48543e7i	−0.464854	+	0.885387i
$65$	−6.52429e6	−	3.30232e6i	−0.365494	−	0.184997i
$66$	3.75431e6	+	2.31118e6i	0.197858	+	0.121803i
$67$	−2.81977e7	+	9.16199e6i	−1.39931	+	0.454664i	−0.908968	−	0.416865i	$-0.863129\pi$
$67$	−2.81977e7	+	9.16199e6i	−1.39931	+	0.454664i	−0.490343	+	0.871529i	$0.663129\pi$
$68$	−1.12556e7	+	1.73570e6i	−0.526419	+	0.0811780i
$69$	5.92456e6	+	1.82339e7i	0.261372	+	0.804422i
$70$	−2.08590e7	−	1.77922e7i	−0.868763	−	0.741033i
$71$	−266190.	−	86490.3i	−0.0104751	−	0.00340356i	0.303775	−	0.952744i	$-0.401753\pi$
$71$	−266190.	−	86490.3i	−0.0104751	−	0.00340356i	−0.314250	+	0.949340i	$0.601753\pi$
$72$	−1.60860e6	+	1.89563e7i	−0.0598573	+	0.705382i
$73$	1.76827e7	−	1.28472e7i	0.622669	−	0.452396i	−0.231184	−	0.972910i	$-0.574260\pi$
$73$	1.76827e7	−	1.28472e7i	0.622669	−	0.452396i	0.853853	+	0.520514i	$0.174260\pi$
$74$	−2.94399e7	+	2.25660e6i	−0.981771	+	0.0752537i
$75$	1.70998e7	−	91578.6i	0.540439	−	0.00289434i
$76$	5.76554e6	+	3.73881e7i	0.172817	+	1.12067i
$77$	1.39610e7	−	1.01433e7i	0.397150	−	0.288547i
$78$	−7.96449e6	−	1.92928e6i	−0.215169	−	0.0521216i
$79$	−5.77183e7	−	1.87538e7i	−1.48185	−	0.481483i	−0.547187	−	0.837010i	$-0.684301\pi$
$79$	−5.77183e7	−	1.87538e7i	−1.48185	−	0.481483i	−0.934666	+	0.355527i	$0.884301\pi$
$80$	−4.04200e7	−	6.62900e6i	−0.986817	−	0.161841i
$81$	2.78099e6	+	8.55901e6i	0.0646040	+	0.198831i
$82$	−3.74529e7	+	2.87080e6i	−0.828380	+	0.0634961i
$83$	8.08802e7	−	2.62796e7i	1.70424	−	0.553740i	0.714879	−	0.699248i	$-0.246482\pi$
$83$	8.08802e7	−	2.62796e7i	1.70424	−	0.553740i	0.989357	+	0.145508i	$0.0464815\pi$
$84$	−2.73189e7	−	1.40603e7i	−0.548714	−	0.282407i
$85$	−1.26891e7	−	2.47398e7i	−0.243084	−	0.473938i
$86$	−2.60554e6	−	3.06332e6i	−0.0476325	−	0.0560013i
$87$	3.62715e6	−	4.99235e6i	0.0633124	−	0.0871421i
$88$	1.00117e7	−	2.37583e7i	0.166946	−	0.396173i
$89$	−1.42816e7	+	1.03762e7i	−0.227623	+	0.165378i	−0.695751	−	0.718283i	$-0.744928\pi$
$89$	−1.42816e7	+	1.03762e7i	−0.227623	+	0.165378i	0.468128	+	0.883660i	$0.344928\pi$
$90$	−4.51562e7	+	1.08716e7i	−0.688251	+	0.165700i
$91$	−1.88543e7	+	2.59508e7i	−0.274945	+	0.378429i
$92$	1.00105e8	−	5.04928e7i	1.39734	−	0.704820i
$93$	4.55886e7			0.609431
$94$	1.00274e8	−	4.12957e7i	1.28434	−	0.528925i
$95$	−8.21794e7	+	4.21501e7i	−1.00895	+	0.517492i
$96$	−4.57955e7	+	3.13489e6i	−0.539185	+	0.0369094i
$97$	3.06739e7	−	9.44045e7i	0.346483	−	1.06636i	−0.614302	−	0.789071i	$-0.710562\pi$
$97$	3.06739e7	−	9.44045e7i	0.346483	−	1.06636i	0.960785	−	0.277294i	$-0.0894375\pi$
$98$	−2.13503e7	+	1.81598e7i	−0.231473	+	0.196882i
$99$		−	2.92349e7i		−	0.304341i
$100$	−1.57697e7	−	9.87488e7i	−0.157697	−	0.987488i
$101$	1.44473e8			1.38836			0.694178	−	0.719803i	$-0.255768\pi$
$101$	1.44473e8			1.38836			0.694178	+	0.719803i	$0.255768\pi$
$102$	−2.01881e7	−	2.37350e7i	−0.186506	−	0.219275i
$103$	8.99580e7	+	2.92291e7i	0.799265	+	0.259697i	0.680045	−	0.733171i	$-0.261960\pi$
$103$	8.99580e7	+	2.92291e7i	0.799265	+	0.259697i	0.119221	+	0.992868i	$0.461960\pi$
$104$	−4.05207e6	+	4.77511e7i	−0.0346372	+	0.408179i
$105$	1.15360e7	−	7.41193e7i	0.0949068	−	0.609782i
$106$	−9.94679e6	−	2.41528e7i	−0.0787879	−	0.191313i
$107$			3.12925e7i			0.238729i	0.992850	+	0.119365i	$0.0380858\pi$
$107$			3.12925e7i			0.238729i	−0.992850	+	0.119365i	$0.961914\pi$
$108$	−1.12123e8	+	5.65548e7i	−0.824135	+	0.415694i
$109$	−1.62826e7	−	1.18300e7i	−0.115350	−	0.0838066i	0.528615	−	0.848862i	$-0.322712\pi$
$109$	−1.62826e7	−	1.18300e7i	−0.115350	−	0.0838066i	−0.643965	+	0.765055i	$0.722712\pi$
$110$	6.27524e7	+	4.89836e6i	0.428607	+	0.0334565i
$111$	−4.74839e7	−	6.53559e7i	−0.312791	−	0.430520i
$112$	−5.69145e7	+	1.70424e8i	−0.361702	+	1.08307i
$113$	1.21376e8	+	8.81850e7i	0.744423	+	0.540855i	0.894093	−	0.447881i	$-0.147821\pi$
$113$	1.21376e8	+	8.81850e7i	0.744423	+	0.540855i	−0.149670	+	0.988736i	$0.547821\pi$
$114$	−7.88416e7	+	6.70596e7i	−0.466805	+	0.397047i
$115$	1.94071e8	+	1.93034e8i	1.10961	+	1.10368i
$116$	−3.20866e7	−	1.65140e7i	−0.177211	−	0.0912056i
$117$	1.67925e7	+	5.16821e7i	0.0896134	+	0.275802i
$118$	−1.40258e7	−	1.82983e8i	−0.0723435	−	0.943805i
$119$	−1.15997e8	+	3.76898e7i	−0.578442	+	0.187947i
$120$	−4.25301e7	−	1.03683e8i	−0.205103	−	0.500016i
$121$	5.39977e7	−	1.66188e8i	0.251903	−	0.775279i
$122$	−4.13458e6	+	1.70684e7i	−0.0186634	+	0.0770466i
$123$	−6.04080e7	−	8.31444e7i	−0.263921	−	0.363256i
$124$	−4.06314e7	−	2.63484e8i	−0.171860	−	1.11447i
$125$	2.16633e8	−	1.12581e8i	0.887331	−	0.461133i
$126$	1.55714e7	+	2.03147e8i	0.0617798	+	0.805988i
$127$	6.98848e7	+	9.61882e7i	0.268638	+	0.369749i	0.921929	−	0.387358i	$-0.126612\pi$
$127$	6.98848e7	+	9.61882e7i	0.268638	+	0.369749i	−0.653291	+	0.757107i	$0.726612\pi$
$128$	5.89342e7	+	2.61886e8i	0.219547	+	0.975602i
$129$	3.40011e6	−	1.04644e7i	0.0122782	−	0.0377883i
$130$	−1.13749e8	+	2.73856e7i	−0.398266	+	0.0958845i
$131$	1.71965e8	−	5.58749e7i	0.583923	−	0.189728i	−0.00213404	−	0.999998i	$-0.500679\pi$
$131$	1.71965e8	−	5.58749e7i	0.583923	−	0.189728i	0.586057	+	0.810270i	$0.300679\pi$
$132$	6.97147e7	−	1.07506e7i	0.229630	−	0.0354108i
$133$	1.25196e8	+	3.85313e8i	0.400114	+	1.23142i
$134$	−2.48687e8	+	4.03970e8i	−0.771320	+	1.25294i
$135$	−2.17370e8	−	2.16209e8i	−0.654432	−	0.650937i
$136$	−1.19186e8	+	1.37833e8i	−0.348393	+	0.402901i
$137$	4.78082e8	+	3.47347e8i	1.35713	+	0.986009i	0.998622	+	0.0524806i	$0.0167128\pi$
$137$	4.78082e8	+	3.47347e8i	1.35713	+	0.986009i	0.358503	+	0.933529i	$0.383287\pi$
$138$	2.61226e8	+	1.60813e8i	0.720277	+	0.443408i
$139$	−1.80137e8	−	2.47937e8i	−0.482552	−	0.664176i	0.496441	−	0.868070i	$-0.334640\pi$
$139$	−1.80137e8	−	2.47937e8i	−0.482552	−	0.664176i	−0.978993	+	0.203895i	$0.934640\pi$
$140$	−4.38662e8	−	613777.i	−1.14187	−	0.00159771i
$141$	2.40041e8	+	1.74400e8i	0.607307	+	0.441235i
$142$	−4.14081e6	+	1.70530e6i	−0.0101843	+	0.00419419i
$143$		−	7.36430e7i		−	0.176111i
$144$	1.76903e8	+	2.47708e8i	0.411419	+	0.576091i
$145$	1.35492e7	−	8.70546e7i	0.0306509	−	0.196933i
$146$	8.23318e7	−	3.39883e8i	0.181199	−	0.748028i
$147$	−7.29339e7	−	2.36977e7i	−0.156192	−	0.0507500i
$148$	−3.35411e8	+	3.32687e8i	−0.699086	+	0.693409i
$149$	8.30453e8			1.68488			0.842442	−	0.538787i	$-0.181117\pi$
$149$	8.30453e8			1.68488			0.842442	+	0.538787i	$0.181117\pi$
$150$	2.07458e8	−	1.78379e8i	0.409793	−	0.352354i
$151$			6.94035e8i			1.33498i	0.744621	+	0.667488i	$0.232630\pi$
$151$			6.94035e8i			1.33498i	−0.744621	+	0.667488i	$0.767370\pi$
$152$	4.57846e8	+	3.95906e8i	0.857720	+	0.741681i
$153$	−6.38506e7	+	1.96512e8i	−0.116520	+	0.358611i
$154$	6.50035e7	−	2.68348e8i	0.115572	−	0.477107i
$155$	5.79141e8	−	2.97043e8i	1.00336	−	0.514628i
$156$	−1.17068e8	+	5.90492e7i	−0.197670	+	0.0997047i
$157$	8.57861e8			1.41195			0.705973	−	0.708238i	$-0.250510\pi$
$157$	8.57861e8			1.41195			0.705973	+	0.708238i	$0.250510\pi$
$158$	−8.97859e8	+	3.69763e8i	−1.44072	+	0.593328i
$159$	4.20072e7	−	5.78179e7i	0.0657257	−	0.0904636i
$160$	−5.61344e8	+	3.38216e8i	−0.856542	+	0.516077i
$161$	9.71413e8	−	7.05773e8i	1.44577	−	1.05042i
$162$	1.22619e8	+	7.54856e7i	0.178033	+	0.109598i
$163$	−3.93157e8	+	5.41134e8i	−0.556949	+	0.766574i	−0.990935	−	0.134345i	$-0.957107\pi$
$163$	−3.93157e8	+	5.41134e8i	−0.556949	+	0.766574i	0.433986	+	0.900920i	$0.357107\pi$
$164$	−4.26703e8	+	4.23238e8i	−0.589862	+	0.585072i
$165$	7.85940e7	+	1.53234e8i	0.106036	+	0.206737i
$166$	7.13317e8	−	1.15872e9i	0.939399	−	1.52597i
$167$	2.17334e7	−	7.06160e6i	0.0279423	−	0.00907899i	−0.295013	−	0.955493i	$-0.595324\pi$
$167$	2.17334e7	−	7.06160e6i	0.0279423	−	0.00907899i	0.322955	+	0.946414i	$0.395324\pi$
$168$	−4.78707e8	+	1.11836e8i	−0.600942	+	0.140392i
$169$	−2.09774e8	−	6.45618e8i	−0.257161	−	0.791460i
$170$	−4.11113e8	−	1.69981e8i	−0.492227	−	0.203518i
$171$	6.52763e8	+	2.12096e8i	0.763433	+	0.248054i
$172$	−6.35108e7	−	1.03247e7i	−0.0725661	−	0.0117968i
$173$	−6.24166e8	+	4.53483e8i	−0.696812	+	0.506263i	−0.878892	−	0.477020i	$-0.841717\pi$
$173$	−6.24166e8	+	4.53483e8i	−0.696812	+	0.506263i	0.182081	+	0.983284i	$0.441717\pi$
$174$	−7.54593e6	−	9.84454e7i	−0.00823220	−	0.107398i
$175$	−3.36393e8	−	1.01675e9i	−0.358670	−	1.08408i
$176$	−1.24268e8	−	3.93342e8i	−0.129512	−	0.409940i
$177$	4.06217e8	−	2.95134e8i	0.413871	−	0.300695i
$178$	−6.64958e7	+	2.74509e8i	−0.0662391	+	0.273449i
$179$	5.83863e8	+	1.89708e8i	0.568720	+	0.184788i	0.579241	−	0.815156i	$-0.303349\pi$
$179$	5.83863e8	+	1.89708e8i	0.568720	+	0.184788i	−0.0105210	+	0.999945i	$0.503349\pi$
$180$	−4.37649e8	+	6.00603e8i	−0.416904	+	0.572134i
$181$	−6.64539e7	−	2.04524e8i	−0.0619165	−	0.190559i	0.915314	−	0.402742i	$-0.131943\pi$
$181$	−6.64539e7	−	2.04524e8i	−0.0619165	−	0.190559i	−0.977230	+	0.212183i	$0.931943\pi$
$182$	3.92245e7	+	5.11729e8i	0.0357497	+	0.466396i
$183$	−4.56982e7	+	1.48483e7i	−0.0407470	+	0.0132395i
$184$	6.96614e8	−	1.65311e9i	0.607744	−	1.44221i
$185$	−1.02906e9	−	5.20866e8i	−0.878524	−	0.444671i
$186$	5.55618e8	−	4.72587e8i	0.464221	−	0.394848i
$187$	1.64588e8	−	2.26536e8i	0.134596	−	0.185256i
$188$	7.94023e8	−	1.54278e9i	0.635626	−	1.23501i
$189$	−1.08804e9	+	7.90505e8i	−0.852700	+	0.619523i
$190$	−5.64632e8	+	1.36561e9i	−0.433263	+	1.04788i
$191$	−1.19890e9	+	1.65014e9i	−0.900842	+	1.23990i	0.0693561	+	0.997592i	$0.477906\pi$
$191$	−1.19890e9	+	1.65014e9i	−0.900842	+	1.23990i	−0.970199	+	0.242311i	$0.922094\pi$
$192$	−5.25643e8	+	5.12939e8i	−0.386799	+	0.377451i
$193$	−1.25512e9			−0.904602			−0.452301	−	0.891865i	$-0.649397\pi$
$193$	−1.25512e9			−0.904602			−0.452301	+	0.891865i	$0.649397\pi$
$194$	−6.04787e8	−	1.46854e9i	−0.426968	−	1.03676i
$195$	−2.26958e8	−	2.25745e8i	−0.156966	−	0.156128i
$196$	−7.19600e7	+	4.42650e8i	−0.0487604	+	0.299941i
$197$	7.78167e7	−	2.39495e8i	0.0516664	−	0.159013i	−0.921894	−	0.387442i	$-0.873359\pi$
$197$	7.78167e7	−	2.39495e8i	0.0516664	−	0.159013i	0.973561	+	0.228429i	$0.0733588\pi$
$198$	−3.03059e8	−	3.56305e8i	−0.197182	−	0.231825i
$199$			2.12185e9i			1.35301i	0.736437	+	0.676506i	$0.236507\pi$
$199$			2.12185e9i			1.35301i	−0.736437	+	0.676506i	$0.763493\pi$
$200$	−1.21586e9	−	1.04004e9i	−0.759912	−	0.650026i
$201$	−1.29791e9			−0.795173
$202$	1.76079e9	−	1.49766e9i	1.05755	−	0.899511i
$203$	−3.67558e8	−	1.19427e8i	−0.216442	−	0.0703263i
$204$	−4.92090e8	−	7.99973e7i	−0.284134	−	0.0461907i
$205$	−1.30915e9	−	6.62635e8i	−0.741265	−	0.375196i
$206$	1.39938e9	−	5.76302e8i	0.777080	−	0.320023i
$207$		−	2.03417e9i		−	1.10791i
$208$	4.45620e8	+	6.23979e8i	0.238073	+	0.333363i
$209$	−7.52496e8	−	5.46720e8i	−0.394384	−	0.286536i
$210$	−6.27750e8	−	1.02293e9i	−0.322782	−	0.525978i
$211$	−1.66330e9	−	2.28933e9i	−0.839150	−	1.15499i	−0.986150	−	0.165855i	$-0.946962\pi$
$211$	−1.66330e9	−	2.28933e9i	−0.839150	−	1.15499i	0.147000	−	0.989136i	$-0.453038\pi$
$212$	−3.71604e8	−	1.91254e8i	−0.183966	−	0.0946820i
$213$	−9.91244e6	−	7.20181e6i	−0.00481573	−	0.00349883i
$214$	3.24389e8	+	3.81383e8i	0.154672	+	0.181847i
$215$	−2.49899e7	−	1.55091e8i	−0.0116953	−	0.0725825i
$216$	−7.80246e8	+	1.85157e9i	−0.358440	+	0.850601i
$217$	−8.82290e8	−	2.71541e9i	−0.397899	−	1.22461i
$218$	−3.21080e8	+	2.46111e7i	−0.142163	+	0.0108970i
$219$	9.09988e8	−	2.95673e8i	0.395603	−	0.128539i
$220$	8.15583e8	−	5.90814e8i	0.348159	−	0.252209i
$221$	−1.60840e8	+	4.95015e8i	−0.0674257	+	0.207515i
$222$	−1.25622e9	−	3.04301e8i	−0.517194	−	0.125283i
$223$	5.66013e7	+	7.79050e7i	0.0228880	+	0.0315026i	0.820308	−	0.571923i	$-0.193802\pi$
$223$	5.66013e7	+	7.79050e7i	0.0228880	+	0.0315026i	−0.797420	+	0.603425i	$0.793802\pi$
$224$	1.07302e9	+	2.66706e9i	0.426202	+	1.05935i
$225$	−1.72849e9	−	5.51405e8i	−0.674431	−	0.215150i
$226$	2.39345e9	−	1.83460e8i	0.917466	−	0.0703246i
$227$	−1.04723e9	−	1.44138e9i	−0.394400	−	0.542845i	0.564928	−	0.825140i	$-0.308904\pi$
$227$	−1.04723e9	−	1.44138e9i	−0.394400	−	0.542845i	−0.959327	+	0.282296i	$0.908904\pi$
$228$	−2.65731e8	+	1.63460e9i	−0.0983337	+	0.604883i
$229$	−1.01286e8	+	3.11727e8i	−0.0368306	+	0.113353i	−0.967782	−	0.251791i	$-0.918980\pi$
$229$	−1.01286e8	+	3.11727e8i	−0.0368306	+	0.113353i	0.930951	+	0.365144i	$0.118980\pi$
$230$	4.36633e9	+	3.40829e8i	1.56029	+	0.121794i
$231$	7.18464e8	−	2.33443e8i	0.252323	−	0.0819847i
$232$	−5.62250e8	+	1.31353e8i	−0.194079	+	0.0453407i
$233$	1.13617e9	+	3.49676e9i	0.385494	+	1.18643i	0.936121	+	0.351678i	$0.114389\pi$
$233$	1.13617e9	+	3.49676e9i	0.385494	+	1.18643i	−0.550627	+	0.834752i	$0.685611\pi$
$234$	7.40416e8	+	4.55806e8i	0.246952	+	0.152026i
$235$	4.18573e9	+	6.51470e8i	1.37246	+	0.213611i
$236$	−2.06780e9	−	2.08473e9i	−0.666594	−	0.672051i
$237$	−2.14933e9	−	1.56158e9i	−0.681255	−	0.494961i
$238$	−1.02303e9	+	1.66182e9i	−0.318845	+	0.517935i
$239$	−1.98059e9	−	2.72605e9i	−0.607021	−	0.835493i	0.389307	−	0.921108i	$-0.372714\pi$
$239$	−1.98059e9	−	2.72605e9i	−0.607021	−	0.835493i	−0.996328	+	0.0856150i	$0.972714\pi$
$240$	−1.59316e9	−	8.22775e8i	−0.480191	−	0.247991i
$241$	9.78527e8	+	7.10941e8i	0.290071	+	0.210749i	0.723298	−	0.690536i	$-0.242625\pi$
$241$	9.78527e8	+	7.10941e8i	0.290071	+	0.210749i	−0.433227	+	0.901285i	$0.642625\pi$
$242$	−1.06466e9	−	2.58520e9i	−0.310419	−	0.753759i
$243$			3.61240e9i			1.03603i
$244$	1.26546e8	+	2.50884e8i	0.0357018	+	0.0707806i
$245$	−1.08093e9	+	1.74171e8i	−0.300009	+	0.0483406i
$246$	−1.59814e9	−	3.87126e8i	−0.436388	−	0.105709i
$247$	1.64431e9	+	5.34270e8i	0.441771	+	0.143540i
$248$	−3.22657e9	−	2.79006e9i	−0.852972	−	0.737575i
$249$	3.72284e9			0.968449
$250$	1.47320e9	−	3.61780e9i	0.377138	−	0.926157i
$251$			3.37653e9i			0.850698i	0.905029	+	0.425349i	$0.139849\pi$
$251$			3.37653e9i			0.850698i	−0.905029	+	0.425349i	$0.860151\pi$
$252$	2.29567e9	+	2.31447e9i	0.569257	+	0.573917i
$253$	−8.51858e8	+	2.62175e9i	−0.207915	+	0.639896i
$254$	1.84885e9	+	4.47858e8i	0.444189	+	0.107598i
$255$	−1.93625e8	−	1.20166e9i	−0.0457931	−	0.284199i
$256$	3.43307e9	+	2.58084e9i	0.799324	+	0.600900i
$257$	−6.10083e9			−1.39848			−0.699240	−	0.714887i	$-0.746478\pi$
$257$	−6.10083e9			−1.39848			−0.699240	+	0.714887i	$0.746478\pi$
$258$	−6.70388e7	−	1.62784e8i	−0.0151303	−	0.0367394i
$259$	−2.97385e9	+	4.09315e9i	−0.660875	+	0.909617i
$260$	−1.10244e9	+	1.51292e9i	−0.241247	+	0.331073i
$261$	−5.29687e8	+	3.84840e8i	−0.114145	+	0.0829312i
$262$	1.51664e9	−	2.46364e9i	0.321867	−	0.522843i
$263$	4.07474e9	−	5.60839e9i	0.851680	−	1.17224i	−0.131810	−	0.991275i	$-0.542079\pi$
$263$	4.07474e9	−	5.60839e9i	0.851680	−	1.17224i	0.983490	−	0.180962i	$-0.0579212\pi$
$264$	7.38215e8	−	8.53711e8i	0.151973	−	0.175750i
$265$	1.56918e8	−	1.00821e9i	0.0318192	−	0.204440i
$266$	5.52013e9	+	3.39824e9i	1.10261	+	0.678778i
$267$	−7.34959e8	+	2.38802e8i	−0.144616	+	0.0469887i
$268$	1.15678e9	+	7.50143e9i	0.224239	+	1.45414i
$269$	1.68879e9	+	5.19757e9i	0.322528	+	0.992638i	0.972544	+	0.232718i	$0.0747620\pi$
$269$	1.68879e9	+	5.19757e9i	0.322528	+	0.992638i	−0.650017	+	0.759920i	$0.725238\pi$
$270$	−4.89053e9	−	3.81748e8i	−0.920240	−	0.0718325i
$271$	3.37140e9	+	1.09543e9i	0.625076	+	0.203099i	0.604393	−	0.796687i	$-0.293416\pi$
$271$	3.37140e9	+	1.09543e9i	0.625076	+	0.203099i	0.0206832	+	0.999786i	$0.493416\pi$
$272$	−2.37722e7	+	2.91539e9i	−0.00434304	+	0.532624i
$273$	−1.13603e9	+	8.25371e8i	−0.204521	+	0.148593i
$274$	9.42741e9	−	7.22620e8i	1.67259	−	0.128206i
$275$	1.99686e9	+	1.43453e9i	0.349154	+	0.250829i
$276$	4.85077e9	−	7.48027e8i	0.835938	−	0.128908i
$277$	9.80812e7	−	7.12602e7i	0.0166597	−	0.0121040i	−0.579424	−	0.815026i	$-0.696723\pi$
$277$	9.80812e7	−	7.12602e7i	0.0166597	−	0.0121040i	0.596084	+	0.802922i	$0.296723\pi$
$278$	−4.76565e9	−	1.15441e9i	−0.797890	−	0.193278i
$279$	−4.60020e9	−	1.49470e9i	−0.759207	−	0.246681i
$280$	−5.35263e9	+	4.53984e9i	−0.870833	+	0.738599i
$281$	3.57127e9	+	1.09912e10i	0.572792	+	1.76287i	0.643577	+	0.765381i	$0.277450\pi$
$281$	3.57127e9	+	1.09912e10i	0.572792	+	1.76287i	−0.0707851	+	0.997492i	$0.522550\pi$
$282$	4.73342e9	−	3.62821e8i	0.748478	−	0.0573715i
$283$	−4.51985e9	+	1.46859e9i	−0.704658	+	0.228957i	−0.639359	−	0.768909i	$-0.720800\pi$
$283$	−4.51985e9	+	1.46859e9i	−0.704658	+	0.228957i	−0.0652991	+	0.997866i	$0.520800\pi$
$284$	−3.27891e7	+	6.37087e7i	−0.00504029	+	0.00979322i
$285$	−3.99162e9	+	6.43172e8i	−0.605020	+	0.0974872i
$286$	−7.63408e8	−	8.97535e8i	−0.114102	−	0.134149i
$287$	−3.78326e9	+	5.20722e9i	−0.557621	+	0.767500i
$288$	4.72386e9	+	1.18515e9i	0.686637	+	0.172267i
$289$	4.04241e9	−	2.93698e9i	0.579493	−	0.421027i
$290$	−7.37304e8	−	1.20145e9i	−0.104245	−	0.169868i
$291$	2.55413e9	−	3.51546e9i	0.356181	−	0.490242i
$292$	−2.51991e9	−	4.99585e9i	−0.346620	−	0.687192i
$293$	−6.68954e9			−0.907666			−0.453833	−	0.891087i	$-0.649944\pi$
$293$	−6.68954e9			−0.907666			−0.453833	+	0.891087i	$0.649944\pi$
$294$	−1.13455e9	+	4.67239e8i	−0.151857	+	0.0625388i
$295$	3.23742e9	−	6.39608e9i	0.427475	−	0.844550i
$296$	−6.39122e8	+	7.53167e9i	−0.0832563	+	0.981125i
$297$	9.54129e8	−	2.93651e9i	0.122626	−	0.377403i
$298$	1.01213e10	−	8.60877e9i	1.28342	−	1.09163i
$299$		−	5.12410e9i		−	0.641110i
$300$	6.79282e8	−	4.32460e9i	0.0838620	−	0.533901i
$301$	−6.89100e8			−0.0839492
$302$	7.19460e9	+	8.45865e9i	0.864926	+	1.01689i
$303$	6.01494e9	+	1.95437e9i	0.713609	+	0.231866i
$304$	9.68417e9	+	7.89653e7i	1.13388	+	0.00924574i
$305$	−4.83787e8	+	4.86385e8i	−0.0559055	+	0.0562057i
$306$	1.25892e9	+	3.05692e9i	0.143586	+	0.348657i
$307$		−	7.28378e9i		−	0.819980i	−0.912090	−	0.409990i	$-0.865532\pi$
$307$		−	7.28378e9i		−	0.819980i	0.912090	−	0.409990i	$-0.134468\pi$
$308$	−1.98955e9	−	3.94438e9i	−0.221081	−	0.438304i
$309$	3.34988e9	+	2.43383e9i	0.367448	+	0.266966i
$310$	3.97912e9	−	9.62384e9i	0.430864	−	1.04208i
$311$	−3.38578e9	−	4.66013e9i	−0.361924	−	0.498146i	0.588760	−	0.808308i	$-0.299616\pi$
$311$	−3.38578e9	−	4.66013e9i	−0.361924	−	0.498146i	−0.950683	+	0.310163i	$0.899616\pi$
$312$	−8.14660e8	+	1.93324e9i	−0.0859722	+	0.204017i
$313$	−1.13588e10	−	8.25268e9i	−1.18347	−	0.859840i	−0.190910	−	0.981608i	$-0.561144\pi$
$313$	−1.13588e10	−	8.25268e9i	−1.18347	−	0.859840i	−0.992559	+	0.121768i	$0.961144\pi$
$314$	1.04553e10	−	8.89288e9i	1.07552	−	0.914795i
$315$	−3.59418e9	+	7.10092e9i	−0.365054	+	0.721228i
$316$	−7.10970e9	+	1.38141e10i	−0.713022	+	1.38539i
$317$	−3.56134e9	−	1.09607e10i	−0.352677	−	1.08543i	−0.957344	−	0.288949i	$-0.906694\pi$
$317$	−3.56134e9	−	1.09607e10i	−0.352677	−	1.08543i	0.604668	−	0.796478i	$-0.293306\pi$
$318$	−8.73917e7	−	1.14013e9i	−0.00854598	−	0.111492i
$319$	8.43849e8	−	2.74183e8i	0.0814896	−	0.0264776i
$320$	−3.33540e9	+	9.94114e9i	−0.318088	+	0.948061i
$321$	−4.23313e8	+	1.30282e9i	−0.0398695	+	0.122706i
$322$	4.52296e9	−	1.86717e10i	0.420726	−	1.73684i
$323$	3.86408e9	+	5.31845e9i	0.355006	+	0.488624i
$324$	2.27695e9	−	3.51124e8i	0.206621	−	0.0318626i
$325$	−4.35408e9	−	1.38899e9i	−0.390268	−	0.124499i
$326$	8.17923e8	+	1.06708e10i	0.0724173	+	0.944767i
$327$	−5.17872e8	−	7.12790e8i	−0.0452931	−	0.0623406i
$328$	−8.13078e8	+	9.58163e9i	−0.0702485	+	0.827835i
$329$	5.74225e9	−	1.76728e10i	0.490116	−	1.50842i
$330$	2.54635e9	+	1.05283e9i	0.214715	+	0.0887771i
$331$	−1.23709e10	+	4.01955e9i	−1.03060	+	0.334862i	−0.775027	−	0.631928i	$-0.782264\pi$
$331$	−1.23709e10	+	4.01955e9i	−1.03060	+	0.334862i	−0.255572	+	0.966790i	$0.582264\pi$
$332$	−3.31802e9	−	2.15165e10i	−0.273103	−	1.77101i
$333$	2.64865e9	+	8.15169e9i	0.215401	+	0.662935i
$334$	1.91676e8	−	3.11360e8i	0.0154022	−	0.0250194i
$335$	−1.64882e10	+	8.45686e9i	−1.30917	+	0.671475i
$336$	−4.67498e9	+	6.32545e9i	−0.366795	+	0.496289i
$337$	−8.29223e9	−	6.02466e9i	−0.642913	−	0.467103i	0.217937	−	0.975963i	$-0.430067\pi$
$337$	−8.29223e9	−	6.02466e9i	−0.642913	−	0.467103i	−0.860850	+	0.508860i	$0.830067\pi$
$338$	−9.24936e9	−	5.69398e9i	−0.708671	−	0.436264i
$339$	3.86041e9	+	5.31339e9i	0.292304	+	0.402321i
$340$	−6.77257e9	+	2.19007e9i	−0.506802	+	0.163886i
$341$	5.30305e9	+	3.85289e9i	0.392200	+	0.284950i
$342$	1.01543e10	−	4.18182e9i	0.742242	−	0.305676i
$343$		−	1.10022e10i		−	0.794883i
$344$	−8.81077e8	+	5.32541e8i	−0.0629187	+	0.0380294i
$345$	5.46859e9	+	1.06620e10i	0.386010	+	0.752599i
$346$	−2.90615e9	+	1.19972e10i	−0.202775	+	0.837097i
$347$	2.01794e10	+	6.55667e9i	1.39184	+	0.452237i	0.906543	−	0.422112i	$-0.138711\pi$
$347$	2.01794e10	+	6.55667e9i	1.39184	+	0.452237i	0.485298	+	0.874349i	$0.338711\pi$
$348$	−1.11249e9	−	1.12159e9i	−0.0758538	−	0.0764749i
$349$	2.21241e10			1.49130			0.745650	−	0.666338i	$-0.232139\pi$
$349$	2.21241e10			1.49130			0.745650	+	0.666338i	$0.232139\pi$
$350$	−1.46398e10	−	8.90464e9i	−0.975582	−	0.593395i
$351$			5.73927e9i			0.378119i
$352$	−5.59206e9	−	3.50571e9i	−0.364251	−	0.228352i
$353$	−8.67057e9	+	2.66853e10i	−0.558404	+	1.71859i	0.128375	+	0.991726i	$0.459024\pi$
$353$	−8.67057e9	+	2.66853e10i	−0.558404	+	1.71859i	−0.686779	+	0.726866i	$0.740976\pi$
$354$	1.89137e9	−	7.80798e9i	0.120438	−	0.497193i
$355$	−1.72849e8	−	2.69024e7i	−0.0108831	−	0.00169386i
$356$	2.03522e9	+	4.03494e9i	0.126710	+	0.251210i
$357$	−5.33924e9			−0.328705
$358$	9.08250e9	−	3.74042e9i	0.552934	−	0.227713i
$359$	4.74879e8	−	6.53615e8i	0.0285894	−	0.0393499i	−0.794483	−	0.607286i	$-0.792258\pi$
$359$	4.74879e8	−	6.53615e8i	0.0285894	−	0.0393499i	0.823072	+	0.567936i	$0.192258\pi$
$360$	8.92147e8	+	1.18568e10i	0.0531161	+	0.705921i
$361$	3.92654e9	−	2.85280e9i	0.231196	−	0.167974i
$362$	−2.93009e9	−	1.80378e9i	−0.170626	−	0.105039i
$363$	4.49625e9	−	6.18855e9i	0.258955	−	0.356420i
$364$	5.78282e9	+	5.83016e9i	0.329408	+	0.332105i
$365$	9.63364e9	−	9.68537e9i	0.542774	−	0.545688i
$366$	−4.03032e8	+	6.54689e8i	−0.0224603	+	0.0364847i
$367$	−1.09709e10	+	3.56466e9i	−0.604752	+	0.196496i	−0.595359	−	0.803460i	$-0.702990\pi$
$367$	−1.09709e10	+	3.56466e9i	−0.604752	+	0.196496i	−0.00939329	+	0.999956i	$0.502990\pi$
$368$	−8.64660e9	−	2.73688e10i	−0.471470	−	1.49233i
$369$	3.36955e9	+	1.03704e10i	0.181747	+	0.559359i
$370$	−1.79413e10	+	4.31946e9i	−0.957298	+	0.230474i
$371$	−4.25680e9	−	1.38312e9i	−0.224692	−	0.0730069i
$372$	1.87268e9	−	1.15195e10i	0.0977893	−	0.601534i
$373$	−2.11352e9	+	1.53556e9i	−0.109187	+	0.0793288i	−0.641039	−	0.767508i	$-0.721496\pi$
$373$	−2.11352e9	+	1.53556e9i	−0.109187	+	0.0793288i	0.531852	+	0.846837i	$0.321496\pi$
$374$	−3.42409e8	−	4.46712e9i	−0.0175008	−	0.228319i
$375$	1.05422e10	−	1.75665e9i	0.533097	−	0.0888299i
$376$	−6.31568e9	−	2.70340e10i	−0.315987	−	1.35257i
$377$	−1.33428e9	+	9.69414e8i	−0.0660515	+	0.0479893i
$378$	−5.06596e9	+	2.09134e10i	−0.248139	+	1.02437i
$379$	1.99411e10	+	6.47926e9i	0.966479	+	0.314028i	0.749394	−	0.662125i	$-0.230345\pi$
$379$	1.99411e10	+	6.47926e9i	0.966479	+	0.314028i	0.217085	+	0.976153i	$0.430345\pi$
$380$	7.27486e9	+	2.24968e10i	0.348891	+	1.07891i
$381$	1.60837e9	+	4.95004e9i	0.0763282	+	0.234914i
$382$	2.49419e9	+	3.25395e10i	0.117132	+	1.52812i
$383$	−1.31006e10	+	4.25666e9i	−0.608832	+	0.197821i	−0.597176	−	0.802111i	$-0.703710\pi$
$383$	−1.31006e10	+	4.25666e9i	−0.608832	+	0.197821i	−0.0116564	+	0.999932i	$0.503710\pi$
$384$	−1.08904e9	+	1.17005e10i	−0.0500864	+	0.538121i
$385$	7.60605e9	−	7.64690e9i	0.346191	−	0.348050i
$386$	−1.52970e10	+	1.30111e10i	−0.689061	+	0.586089i
$387$	−6.86187e8	+	9.44456e8i	−0.0305914	+	0.0421054i
$388$	−2.25944e10	−	1.16287e10i	−0.996950	−	0.513102i
$389$	1.99890e10	−	1.45228e10i	0.872955	−	0.634239i	−0.0584231	−	0.998292i	$-0.518607\pi$
$389$	1.99890e10	−	1.45228e10i	0.872955	−	0.634239i	0.931378	+	0.364053i	$0.118607\pi$
$390$	−5.10624e9	−	3.98585e8i	−0.220720	−	0.0172291i
$391$	1.14521e10	−	1.57624e10i	0.489979	−	0.674399i
$392$	3.71164e9	+	6.14083e9i	0.157189	+	0.260065i
$393$	7.91540e9			0.331820
$394$	−1.53429e9	−	3.72556e9i	−0.0636681	−	0.154599i
$395$	−3.74791e10	−	5.83328e9i	−1.53958	−	0.239621i
$396$	−7.38716e9	−	1.20090e9i	−0.300398	−	0.0488346i
$397$	5.50098e9	−	1.69303e10i	0.221451	−	0.681556i	−0.777181	−	0.629277i	$-0.783351\pi$
$397$	5.50098e9	−	1.69303e10i	0.221451	−	0.681556i	0.998632	−	0.0522796i	$-0.0166487\pi$
$398$	2.19958e10	+	2.58603e10i	0.876612	+	1.03063i
$399$			1.77356e10i			0.699768i
$400$	−2.55999e10	−	7.16390e7i	−0.999996	−	0.00279840i
$401$	−1.72707e10			−0.667931			−0.333965	−	0.942585i	$-0.608387\pi$
$401$	−1.72707e10			−0.667931			−0.333965	+	0.942585i	$0.608387\pi$
$402$	−1.58185e10	+	1.34546e10i	−0.605705	+	0.515190i
$403$	−1.15879e10	−	3.76515e9i	−0.439325	−	0.142745i
$404$	5.93462e9	−	3.65058e10i	0.222775	−	1.37037i
$405$	2.56696e9	+	5.00477e9i	0.0954111	+	0.186022i
$406$	−5.71769e9	+	2.35470e9i	−0.210434	+	0.0866626i
$407$		−	1.16155e10i		−	0.423312i
$408$	−6.82670e9	+	4.12620e9i	−0.246360	+	0.148905i
$409$	2.77012e10	+	2.01261e10i	0.989934	+	0.719229i	0.959907	−	0.280320i	$-0.0904407\pi$
$409$	2.77012e10	+	2.01261e10i	0.989934	+	0.719229i	0.0300270	+	0.999549i	$0.490441\pi$
$410$	−2.28245e10	+	5.49512e9i	−0.807731	+	0.194465i
$411$	1.52055e10	+	2.09286e10i	0.532886	+	0.733454i
$412$	1.10810e10	−	2.15302e10i	0.384582	−	0.747238i
$413$	−2.54408e10	−	1.84838e10i	−0.874441	−	0.635318i
$414$	−2.10869e10	−	2.47918e10i	−0.717814	−	0.843930i
$415$	4.72936e10	−	2.42570e10i	1.59445	−	0.817796i
$416$	1.18994e10	+	2.98540e9i	0.397332	+	0.0996847i
$417$	−4.14577e9	−	1.27594e10i	−0.137107	−	0.421973i
$418$	−1.48386e10	+	1.13740e9i	−0.486059	+	0.0372569i
$419$	1.71835e10	−	5.58325e9i	0.557513	−	0.181147i	−0.0166889	−	0.999861i	$-0.505312\pi$
$419$	1.71835e10	−	5.58325e9i	0.557513	−	0.181147i	0.574202	+	0.818714i	$0.305312\pi$
$420$	−1.82548e10	−	5.95960e9i	−0.586652	−	0.191523i
$421$	1.39266e10	−	4.28618e10i	0.443321	−	1.36440i	−0.440995	−	0.897510i	$-0.645374\pi$
$421$	1.39266e10	−	4.28618e10i	0.443321	−	1.36440i	0.884315	−	0.466891i	$-0.154626\pi$
$422$	−4.40037e10	−	1.06593e10i	−1.38752	−	0.336107i
$423$	−1.85038e10	−	2.54682e10i	−0.577961	−	0.795495i
$424$	−6.51159e9	+	1.52124e9i	−0.201476	+	0.0470689i
$425$	−1.02895e10	−	1.40039e10i	−0.315382	−	0.429233i
$426$	−1.95466e8	+	1.49826e7i	−0.00593516	+	0.000454936i
$427$	1.76882e9	+	2.43458e9i	0.0532075	+	0.0732338i
$428$	7.90709e9	+	1.28543e9i	0.235636	+	0.0383065i
$429$	9.96212e8	−	3.06603e9i	0.0294119	−	0.0905204i
$430$	−1.91229e9	−	1.63114e9i	−0.0559346	−	0.0477108i
$431$	−1.90514e10	+	6.19016e9i	−0.552099	+	0.179388i	−0.571763	−	0.820419i	$-0.693740\pi$
$431$	−1.90514e10	+	6.19016e9i	−0.552099	+	0.179388i	0.0196641	+	0.999807i	$0.493740\pi$
$432$	9.68467e9	+	3.06546e10i	0.278067	+	0.880159i
$433$	1.21172e10	+	3.72930e10i	0.344708	+	1.06090i	0.961740	+	0.273965i	$0.0883352\pi$
$433$	1.21172e10	+	3.72930e10i	0.344708	+	1.06090i	−0.617031	+	0.786939i	$0.711665\pi$
$434$	−3.89019e10	−	2.39483e10i	−1.09651	−	0.675020i
$435$	1.74174e9	−	3.44111e9i	0.0486438	−	0.0961041i
$436$	−3.65809e9	+	3.62838e9i	−0.101230	+	0.100408i
$437$	−5.23588e10	−	3.80409e10i	−1.43570	−	1.04310i
$438$	8.02557e9	−	1.30368e10i	0.218062	−	0.354222i
$439$	−1.99464e10	−	2.74539e10i	−0.537041	−	0.739173i	0.451142	−	0.892452i	$-0.351017\pi$
$439$	−1.99464e10	−	2.74539e10i	−0.537041	−	0.739173i	−0.988183	+	0.153279i	$0.951017\pi$
$440$	3.81546e9	−	1.56552e10i	0.101797	−	0.417685i
$441$	6.58256e9	+	4.78251e9i	0.174036	+	0.126445i
$442$	3.17123e9	+	7.70040e9i	0.0830882	+	0.201755i
$443$		−	6.68662e9i		−	0.173617i	−0.996225	−	0.0868084i	$-0.972333\pi$
$443$		−	6.68662e9i		−	0.173617i	0.996225	−	0.0868084i	$-0.0276668\pi$
$444$	−1.84649e10	+	9.31369e9i	−0.475132	+	0.239657i
$445$	−7.78067e9	+	7.82245e9i	−0.198416	+	0.199482i
$446$	1.49743e9	+	3.62730e8i	0.0378448	+	0.00916737i
$447$	3.45748e10	+	1.12340e10i	0.866024	+	0.281388i
$448$	4.07253e10	+	2.13819e10i	1.01100	+	0.530805i
$449$	1.17890e10			0.290062			0.145031	−	0.989427i	$-0.453672\pi$
$449$	1.17890e10			0.290062			0.145031	+	0.989427i	$0.453672\pi$
$450$	−2.67823e10	+	1.11978e10i	−0.653128	+	0.273076i
$451$		−	1.47770e10i		−	0.357175i
$452$	2.72687e10	−	2.70472e10i	0.653297	−	0.647991i
$453$	−9.38862e9	+	2.88952e10i	−0.222951	+	0.686172i
$454$	−2.77051e10	−	6.71116e9i	−0.652133	−	0.157970i
$455$	−9.05377e9	+	1.78873e10i	−0.211244	+	0.417348i
$456$	1.37062e10	+	2.26766e10i	0.316998	+	0.524467i
$457$	4.01401e10			0.920267			0.460133	−	0.887850i	$-0.347802\pi$
$457$	4.01401e10			0.920267			0.460133	+	0.887850i	$0.347802\pi$
$458$	1.99703e9	+	4.84919e9i	0.0453861	+	0.110207i
$459$	−1.28270e10	+	1.76548e10i	−0.288984	+	0.397752i
$460$	5.67484e10	−	4.11090e10i	1.26743	−	0.918132i
$461$	4.58040e10	−	3.32785e10i	1.01414	−	0.736818i	0.0490693	−	0.998795i	$-0.484374\pi$
$461$	4.58040e10	−	3.32785e10i	1.01414	−	0.736818i	0.965074	+	0.261977i	$0.0843745\pi$
$462$	6.33644e9	−	1.02930e10i	0.139084	−	0.225929i
$463$	−4.25500e10	+	5.85650e10i	−0.925923	+	1.27442i	0.0355051	+	0.999369i	$0.488696\pi$
$463$	−4.25500e10	+	5.85650e10i	−0.925923	+	1.27442i	−0.961429	+	0.275055i	$0.911304\pi$
$464$	−5.49086e9	+	7.42936e9i	−0.118459	+	0.160280i
$465$	2.81301e10	−	4.53261e9i	0.601671	−	0.0969475i
$466$	5.00958e10	+	3.08394e10i	1.06233	+	0.653976i
$467$	5.11376e10	−	1.66156e10i	1.07516	−	0.349340i	0.282664	−	0.959219i	$-0.408782\pi$
$467$	5.11376e10	−	1.66156e10i	1.07516	−	0.349340i	0.792495	+	0.609878i	$0.208782\pi$
$468$	1.37490e10	−	2.12020e9i	0.286607	−	0.0441971i
$469$	2.51189e10	+	7.73080e10i	0.519169	+	1.59784i
$470$	5.77676e10	−	3.54509e10i	1.18384	−	0.726500i
$471$	3.57159e10	+	1.16048e10i	0.725735	+	0.235805i
$472$	−4.68127e10	−	3.97244e9i	−0.943183	−	0.0800367i
$473$	1.27991e9	−	9.29908e8i	0.0255702	−	0.0185778i
$474$	−4.23832e10	+	3.24871e9i	−0.839615	+	0.0643572i
$475$	−4.65174e10	+	3.41790e10i	−0.913778	+	0.671405i
$476$	4.75866e9	+	3.08587e10i	0.0926951	+	0.601105i
$477$	−6.13446e9	+	4.45695e9i	−0.118496	+	0.0860922i
$478$	−5.23980e10	−	1.26927e10i	−1.00370	−	0.243132i
$479$	4.74353e10	+	1.54127e10i	0.901072	+	0.292776i	0.722680	−	0.691183i	$-0.242910\pi$
$479$	4.74353e10	+	1.54127e10i	0.901072	+	0.292776i	0.178393	+	0.983959i	$0.442910\pi$
$480$	−2.79460e10	+	6.48754e9i	−0.526448	+	0.122212i
$481$	6.67196e9	+	2.05342e10i	0.124644	+	0.383616i
$482$	1.92958e10	−	1.47904e9i	0.357499	−	0.0274026i
$483$	4.99909e10	−	1.62430e10i	0.918549	−	0.298455i
$484$	−3.97747e10	−	2.04709e10i	−0.724813	−	0.373040i
$485$	9.54096e9	−	6.13012e10i	0.172435	−	1.10790i
$486$	3.74474e10	+	4.40267e10i	0.671238	+	0.789171i
$487$	−5.43755e10	+	7.48414e10i	−0.966690	+	1.33054i	−0.0229891	+	0.999736i	$0.507318\pi$
$487$	−5.43755e10	+	7.48414e10i	−0.966690	+	1.33054i	−0.943701	+	0.330799i	$0.892682\pi$
$488$	4.14305e9	+	1.74587e9i	0.0730535	+	0.0307845i
$489$	−2.36888e10	+	1.72109e10i	−0.414293	+	0.301002i
$490$	−1.13685e10	+	1.33281e10i	−0.197206	+	0.231197i
$491$	2.66554e10	−	3.66880e10i	0.458627	−	0.631245i	−0.515597	−	0.856831i	$-0.672430\pi$
$491$	2.66554e10	−	3.66880e10i	0.458627	−	0.631245i	0.974223	+	0.225586i	$0.0724297\pi$
$492$	−2.34906e10	+	1.18487e10i	−0.400898	+	0.202213i
$493$	−6.27104e9			−0.106158
$494$	2.55788e10	−	1.05340e10i	0.429508	−	0.176883i
$495$	−2.90666e9	−	1.80391e10i	−0.0484142	−	0.300466i
$496$	−6.82470e10	−	5.56490e8i	−1.12761	−	0.00919456i
$497$	−2.37125e8	+	7.29797e8i	−0.00388644	+	0.0119612i
$498$	4.53727e10	−	3.85922e10i	0.737695	−	0.627455i
$499$			3.80992e9i			0.0614488i	0.999528	+	0.0307244i	$0.00978142\pi$
$499$			3.80992e9i			0.0614488i	−0.999528	+	0.0307244i	$0.990219\pi$
$500$	−1.95486e10	−	5.93642e10i	−0.312777	−	0.949827i
$501$	1.00037e9			0.0158785
$502$	3.50022e10	+	4.11519e10i	0.551164	+	0.648000i
$503$	−9.46953e10	−	3.07684e10i	−1.47930	−	0.480654i	−0.545397	−	0.838178i	$-0.683621\pi$
$503$	−9.46953e10	−	3.07684e10i	−1.47930	−	0.480654i	−0.933904	+	0.357524i	$0.883621\pi$
$504$	5.19715e10	+	4.41020e9i	0.805458	+	0.0683496i
$505$	8.91457e10	−	1.43641e10i	1.37068	−	0.220858i
$506$	1.67958e10	+	4.07836e10i	0.256212	+	0.622134i
$507$		−	2.97172e10i		−	0.449755i
$508$	2.71758e10	−	1.37075e10i	0.408064	−	0.205828i
$509$	−2.21720e10	−	1.61089e10i	−0.330319	−	0.239991i	0.410247	−	0.911974i	$-0.365442\pi$
$509$	−2.21720e10	−	1.61089e10i	−0.330319	−	0.239991i	−0.740566	+	0.671984i	$0.765442\pi$
$510$	−1.48167e10	−	1.26383e10i	−0.219013	−	0.186813i
$511$	−3.52225e10	−	4.84797e10i	−0.516579	−	0.711011i
$512$	6.85950e10	−	4.13397e9i	0.998189	−	0.0601572i
$513$	5.86448e10	+	4.26079e10i	0.846759	+	0.615207i
$514$	−7.43548e10	+	6.32433e10i	−1.06526	+	0.906070i
$515$	5.84139e10	+	9.09158e9i	0.830400	+	0.129244i
$516$	−2.50452e9	−	1.28900e9i	−0.0353285	−	0.0181826i
$517$	1.31832e10	+	4.05737e10i	0.184527	+	0.567914i
$518$	6.18679e9	+	8.07138e10i	0.0859303	+	1.12106i
$519$	−3.21208e10	+	1.04367e10i	−0.442708	+	0.143845i
$520$	2.24732e9	+	2.98673e10i	0.0307364	+	0.408491i
$521$	3.75909e10	−	1.15693e11i	0.510189	−	1.57020i	−0.281679	−	0.959509i	$-0.590891\pi$
$521$	3.75909e10	−	1.15693e11i	0.510189	−	1.57020i	0.791868	−	0.610692i	$-0.209109\pi$
$522$	−2.46625e9	+	1.01812e10i	−0.0332166	+	0.137125i
$523$	4.14047e10	+	5.69886e10i	0.553404	+	0.761696i	0.990469	−	0.137734i	$-0.0439820\pi$
$523$	4.14047e10	+	5.69886e10i	0.553404	+	0.761696i	−0.437065	+	0.899430i	$0.643982\pi$
$524$	−7.05469e9	−	4.57479e10i	−0.0935735	−	0.606801i
$525$	−2.51076e8	−	4.68816e10i	−0.00330497	−	0.617114i
$526$	−8.47708e9	−	1.10593e11i	−0.110740	−	1.44473i
$527$	−2.72312e10	−	3.74806e10i	−0.353041	−	0.485919i
$528$	1.47240e8	−	1.80573e10i	0.00189449	−	0.232337i
$529$	−3.50731e10	+	1.07944e11i	−0.447869	+	1.37840i
$530$	−8.53895e9	−	1.39143e10i	−0.108218	−	0.176343i
$531$	−5.06665e10	+	1.64625e10i	−0.637298	+	0.207071i
$532$	1.02505e11	−	1.58071e10i	1.27967	−	0.197335i
$533$	8.48792e9	+	2.61231e10i	0.105170	+	0.323680i
$534$	−6.48191e9	+	1.05293e10i	−0.0797146	+	0.129489i
$535$	3.11123e9	+	1.93088e10i	0.0379767	+	0.235689i
$536$	9.18608e10	+	7.94332e10i	1.11294	+	0.962372i
$537$	2.17420e10	+	1.57965e10i	0.261459	+	0.189961i
$538$	7.44622e10	+	4.58395e10i	0.888805	+	0.547156i
$539$	−6.48116e9	−	8.92056e9i	−0.0767888	−	0.105691i
$540$	−6.35614e10	+	4.60443e10i	−0.747513	+	0.541503i
$541$	−1.54765e10	−	1.12444e10i	−0.180669	−	0.131264i	0.493775	−	0.869590i	$-0.335617\pi$
$541$	−1.54765e10	−	1.12444e10i	−0.180669	−	0.131264i	−0.674444	+	0.738326i	$0.735617\pi$
$542$	5.24450e10	−	2.15983e10i	0.607725	−	0.250278i
$543$		−	9.41405e9i		−	0.108287i
$544$	2.99322e10	+	3.57781e10i	0.341777	+	0.408528i
$545$	−1.12232e10	−	5.68071e9i	−0.127213	−	0.0643897i
$546$	−5.28941e9	+	2.18358e10i	−0.0595164	+	0.245696i
$547$	−1.02044e11	−	3.31560e10i	−1.13982	−	0.370350i	−0.322520	−	0.946563i	$-0.604530\pi$
$547$	−1.02044e11	−	3.31560e10i	−1.13982	−	0.370350i	−0.817300	+	0.576213i	$0.804530\pi$
$548$	1.07407e11	−	1.06535e11i	1.19100	−	1.18133i
$549$	5.09809e9			0.0561200
$550$	3.92078e10	−	3.21662e9i	0.428472	−	0.0351519i
$551$			2.08308e10i			0.225995i
$552$	5.13652e10	−	5.94014e10i	0.553238	−	0.639794i
$553$	−5.14162e10	+	1.58243e11i	−0.549794	+	1.69209i
$554$	4.56672e8	−	1.88524e9i	0.00484803	−	0.0200137i
$555$	−3.57975e10	−	3.56063e10i	−0.377294	−	0.375279i
$556$	−7.00492e10	+	3.53328e10i	−0.733000	+	0.369726i
$557$	−1.87201e11			−1.94485			−0.972427	−	0.233206i	$-0.925078\pi$
$557$	−1.87201e11			−1.94485			−0.972427	+	0.233206i	$0.925078\pi$
$558$	−7.15602e10	+	2.94704e10i	−0.738133	+	0.303983i
$559$	−1.72851e9	+	2.37909e9i	−0.0177021	+	0.0243649i
$560$	−1.81743e10	+	1.10817e11i	−0.184802	+	1.12682i
$561$	9.91690e9	−	7.20505e9i	0.100121	−	0.0727421i
$562$	1.57464e11	+	9.69363e10i	1.57847	+	0.971720i
$563$	3.88942e10	−	5.35332e10i	0.387125	−	0.532831i	−0.570330	−	0.821416i	$-0.693185\pi$
$563$	3.88942e10	−	5.35332e10i	0.387125	−	0.532831i	0.957454	+	0.288584i	$0.0931846\pi$
$564$	5.39282e10	−	5.34902e10i	0.532966	−	0.528638i
$565$	8.36618e10	+	4.23460e10i	0.820982	+	0.415546i
$566$	−3.98625e10	+	6.47530e10i	−0.388417	+	0.630949i
$567$	2.34658e10	−	7.62448e9i	0.227040	−	0.0737697i
$568$	2.60805e8	+	1.11636e9i	0.00250566	+	0.0107254i
$569$	7.76089e9	+	2.38856e10i	0.0740393	+	0.227869i	0.981227	−	0.192857i	$-0.0617753\pi$
$569$	7.76089e9	+	2.38856e10i	0.0740393	+	0.227869i	−0.907188	+	0.420726i	$0.861775\pi$
$570$	−4.19811e10	+	4.92173e10i	−0.397699	+	0.466249i
$571$	1.10037e11	+	3.57533e10i	1.03513	+	0.336335i	0.776817	−	0.629726i	$-0.216833\pi$
$571$	1.10037e11	+	3.57533e10i	1.03513	+	0.336335i	0.258315	+	0.966061i	$0.416833\pi$
$572$	−1.86083e10	−	3.02509e9i	−0.173829	−	0.0282588i
$573$	−7.22370e10	+	5.24832e10i	−0.670102	+	0.486858i
$574$	7.87070e9	+	1.02682e11i	0.0725046	+	0.945907i
$575$	1.38942e11	+	9.98148e10i	1.27105	+	0.913111i
$576$	6.98584e10	−	3.45250e10i	0.634642	−	0.313649i
$577$	−1.09128e11	+	7.92864e10i	−0.984543	+	0.715312i	−0.958719	−	0.284354i	$-0.908221\pi$
$577$	−1.09128e11	+	7.92864e10i	−0.984543	+	0.715312i	−0.0258234	+	0.999667i	$0.508221\pi$
$578$	1.88217e10	−	7.76999e10i	0.168635	−	0.696160i
$579$	−5.22554e10	−	1.69788e10i	−0.464962	−	0.151075i
$580$	−2.14406e10	−	6.99966e9i	−0.189463	−	0.0618536i
$581$	−7.20492e10	−	2.21745e11i	−0.632302	−	1.94603i
$582$	−5.31361e9	−	6.93222e10i	−0.0463125	−	0.604200i
$583$	9.77288e9	−	3.17540e9i	0.0845957	−	0.0274868i
$584$	−8.25006e10	−	3.47654e10i	−0.709260	−	0.298880i
$585$	1.55001e10	+	3.02204e10i	0.132346	+	0.258034i
$586$	−8.15298e10	+	6.93461e10i	−0.691395	+	0.588073i
$587$	−6.62406e10	+	9.11724e10i	−0.557920	+	0.767911i	−0.991060	−	0.133416i	$-0.957405\pi$
$587$	−6.62406e10	+	9.11724e10i	−0.557920	+	0.767911i	0.433140	+	0.901327i	$0.357405\pi$
$588$	−8.98395e9	+	1.74557e10i	−0.0751550	+	0.146025i
$589$	−1.24501e11	+	9.04552e10i	−1.03445	+	0.751575i
$590$	−2.68474e10	−	1.11513e11i	−0.221561	−	0.920278i
$591$	6.47959e9	−	8.91839e9i	0.0531126	−	0.0731032i
$592$	7.02865e10	+	9.84187e10i	0.572249	+	0.801292i
$593$	−2.11876e11			−1.71341			−0.856706	−	0.515804i	$-0.827493\pi$
$593$	−2.11876e11			−1.71341			−0.856706	+	0.515804i	$0.827493\pi$
$594$	−1.88123e10	−	4.56799e10i	−0.151111	−	0.366927i
$595$	−6.78278e10	+	3.47891e10i	−0.541178	+	0.277572i
$596$	3.41131e10	−	2.09841e11i	0.270356	−	1.66305i
$597$	−2.87035e10	+	8.83402e10i	−0.225963	+	0.695442i
$598$	−5.31181e10	−	6.24507e10i	−0.415373	−	0.488351i
$599$		−	1.46156e11i		−	1.13530i	−0.823271	−	0.567649i	$-0.807853\pi$
$599$		−	1.46156e11i		−	1.13530i	0.823271	−	0.567649i	$-0.192147\pi$
$600$	−3.65514e10	−	5.97484e10i	−0.282033	−	0.461021i
$601$	−1.67650e11			−1.28501			−0.642504	−	0.766282i	$-0.722104\pi$
$601$	−1.67650e11			−1.28501			−0.642504	+	0.766282i	$0.722104\pi$
$602$	−8.39852e9	+	7.14345e9i	−0.0639465	+	0.0543904i
$603$	1.30968e11	+	4.25542e10i	0.990596	+	0.321864i
$604$	1.75371e11	+	2.85094e10i	1.31768	+	0.214210i
$605$	1.67957e10	−	1.07913e11i	0.125365	−	0.805479i
$606$	9.35676e10	−	3.85337e10i	0.693801	−	0.285726i
$607$			6.14673e9i			0.0452782i	0.999744	+	0.0226391i	$0.00720687\pi$
$607$			6.14673e9i			0.0452782i	−0.999744	+	0.0226391i	$0.992793\pi$
$608$	1.18846e11	−	9.94270e10i	0.869700	−	0.727596i
$609$	−1.36872e10	−	9.94436e9i	−0.0995054	−	0.0722949i
$610$	−8.54193e8	+	1.09430e10i	−0.00616931	+	0.0790345i
$611$	−4.66111e10	−	6.41547e10i	−0.334445	−	0.460324i
$612$	4.70324e10	+	2.42062e10i	0.335267	+	0.172553i
$613$	−4.39431e10	−	3.19266e10i	−0.311207	−	0.226105i	0.421207	−	0.906964i	$-0.361606\pi$
$613$	−4.39431e10	−	3.19266e10i	−0.311207	−	0.226105i	−0.732414	+	0.680859i	$0.761606\pi$
$614$	−7.55061e10	−	8.87721e10i	−0.531262	−	0.624602i
$615$	−4.55408e10	−	4.52975e10i	−0.318346	−	0.316646i
$616$	−6.51367e10	−	2.74484e10i	−0.452380	−	0.190631i
$617$	−4.55874e10	−	1.40304e11i	−0.314560	−	0.968117i	−0.975935	−	0.218061i	$-0.930027\pi$
$617$	−4.55874e10	−	1.40304e11i	−0.314560	−	0.968117i	0.661375	−	0.750056i	$-0.269973\pi$
$618$	6.60571e10	−	5.06334e9i	0.452862	−	0.0347123i
$619$	4.45778e10	−	1.44842e10i	0.303638	−	0.0986579i	−0.153235	−	0.988190i	$-0.548969\pi$
$619$	4.45778e10	−	1.44842e10i	0.303638	−	0.0986579i	0.456873	+	0.889532i	$0.348969\pi$
$620$	−5.12679e10	−	1.58541e11i	−0.346960	−	1.07294i
$621$	6.63885e10	−	2.04323e11i	0.446402	−	1.37389i
$622$	−8.95732e10	−	2.16978e10i	−0.598434	−	0.144962i
$623$	2.84477e10	+	3.91549e10i	0.188841	+	0.259917i
$624$	1.01118e10	+	3.20067e10i	0.0666947	+	0.211107i
$625$	1.22478e11	−	9.10060e10i	0.802675	−	0.596417i
$626$	−2.23988e11	+	1.71689e10i	−1.45857	+	0.111801i
$627$	−2.39333e10	−	3.29414e10i	−0.154858	−	0.213144i
$628$	3.52390e10	−	2.16767e11i	0.226561	−	1.39365i
$629$	−2.53689e10	+	7.80775e10i	−0.162069	+	0.498797i
$630$	2.98060e10	+	1.23802e11i	0.189209	+	0.785897i
$631$	1.02133e11	−	3.31851e10i	0.644242	−	0.209327i	0.0313687	−	0.999508i	$-0.490013\pi$
$631$	1.02133e11	−	3.31851e10i	0.644242	−	0.209327i	0.612874	+	0.790181i	$0.290013\pi$
$632$	5.65507e10	+	2.42063e11i	0.354462	+	1.51726i
$633$	−3.82800e10	−	1.17814e11i	−0.238428	−	0.733805i
$634$	−1.57027e11	−	9.66669e10i	−0.971888	−	0.598303i
$635$	5.26853e10	+	5.24039e10i	0.324037	+	0.322306i
$636$	−1.28840e10	−	1.29895e10i	−0.0787451	−	0.0793898i
$637$	1.65815e10	+	1.20472e10i	0.100709	+	0.0731690i
$638$	7.44226e9	−	1.20893e10i	0.0449182	−	0.0729655i
$639$	7.64110e8	+	1.05171e9i	0.00458303	+	0.00630799i
$640$	6.24026e10	+	1.55735e11i	0.371949	+	0.928253i
$641$	−2.37380e11	−	1.72467e11i	−1.40609	−	1.02158i	−0.993877	−	0.110496i	$-0.964756\pi$
$641$	−2.37380e11	−	1.72467e11i	−1.40609	−	1.02158i	−0.412213	−	0.911088i	$-0.635244\pi$
$642$	8.34632e9	+	2.02666e10i	0.0491309	+	0.119300i
$643$		−	1.74057e11i		−	1.01823i	−0.860698	−	0.509116i	$-0.829972\pi$
$643$		−	1.74057e11i		−	1.01823i	0.860698	−	0.509116i	$-0.170028\pi$
$644$	−1.38433e11	−	2.74451e11i	−0.804817	−	1.59559i
$645$	1.05759e9	−	6.79505e9i	0.00611050	−	0.0392603i
$646$	1.02227e11	+	2.47630e10i	0.586996	+	0.142191i
$647$	2.40753e11	+	7.82253e10i	1.37390	+	0.446406i	0.900658	−	0.434528i	$-0.143085\pi$
$647$	2.40753e11	+	7.82253e10i	1.37390	+	0.446406i	0.473238	+	0.880934i	$0.343085\pi$
$648$	2.41108e10	−	2.78831e10i	0.136745	−	0.158140i
$649$	7.21958e10			0.406942
$650$	−6.74649e10	+	2.82074e10i	−0.377941	+	0.158019i
$651$		−	1.24988e11i		−	0.695894i
$652$	1.20585e11	+	1.21573e11i	0.667274	+	0.672737i
$653$	9.16271e8	−	2.81999e9i	0.00503931	−	0.0155094i	−0.948505	−	0.316761i	$-0.897405\pi$
$653$	9.16271e8	−	2.81999e9i	0.00503931	−	0.0155094i	0.953545	+	0.301252i	$0.0974045\pi$
$654$	−1.37007e10	−	3.31879e9i	−0.0748912	−	0.0181413i
$655$	1.00554e11	−	5.15747e10i	0.546306	−	0.280202i
$656$	8.94169e10	+	1.25206e11i	0.482841	+	0.676099i
$657$	−1.01518e11			−0.544856
$658$	−1.13218e11	−	2.74916e11i	−0.603966	−	1.46655i
$659$	−8.31402e10	+	1.14433e11i	−0.440828	+	0.606748i	−0.970396	−	0.241519i	$-0.922354\pi$
$659$	−8.31402e10	+	1.14433e11i	−0.440828	+	0.606748i	0.529567	+	0.848268i	$0.322354\pi$
$660$	4.19480e10	−	1.35649e10i	0.221073	−	0.0714891i
$661$	−3.18497e10	+	2.31401e10i	−0.166840	+	0.121216i	−0.668072	−	0.744097i	$-0.732880\pi$
$661$	−3.18497e10	+	2.31401e10i	−0.166840	+	0.121216i	0.501232	+	0.865313i	$0.332880\pi$
$662$	−1.09104e11	+	1.77230e11i	−0.568081	+	0.922796i
$663$	−1.33927e10	+	1.84335e10i	−0.0693131	+	0.0954012i
$664$	−2.63487e11	−	2.27840e11i	−1.35546	−	1.17208i
$665$	1.15560e11	+	2.25307e11i	0.590912	+	1.15209i
$666$	1.16784e11	+	7.18932e10i	0.593590	+	0.365419i
$667$	5.87152e10	−	1.90777e10i	0.296652	−	0.0963881i
$668$	−8.91588e8	−	5.78173e9i	−0.00447773	−	0.0290370i
$669$	1.30265e9	+	4.00915e9i	0.00650315	+	0.0200146i
$670$	−1.13286e11	+	2.73992e11i	−0.562182	+	1.35969i
$671$	−6.57069e9	−	2.13495e9i	−0.0324131	−	0.0105317i
$672$	8.59475e9	+	1.25555e11i	0.0421460	+	0.615682i
$673$	3.95078e10	−	2.87041e10i	0.192585	−	0.139921i	−0.487314	−	0.873227i	$-0.662023\pi$
$673$	3.95078e10	−	2.87041e10i	0.192585	−	0.139921i	0.679899	+	0.733305i	$0.262023\pi$
$674$	−1.63517e11	+	1.25337e10i	−0.792359	+	0.0607351i
$675$	−1.55623e11	−	1.11798e11i	−0.749649	−	0.538542i
$676$	−1.71754e11	+	2.64858e10i	−0.822469	+	0.126831i
$677$	−1.92745e11	+	1.40037e11i	−0.917545	+	0.666636i	−0.942912	−	0.333042i	$-0.891925\pi$
$677$	−1.92745e11	+	1.40037e11i	−0.917545	+	0.666636i	0.0253665	+	0.999678i	$0.491925\pi$
$678$	1.02130e11	+	2.47395e10i	0.483319	+	0.117077i
$679$	−2.58823e11	−	8.40968e10i	−1.21765	−	0.395640i
$680$	−5.98388e10	+	9.68987e10i	−0.279864	+	0.453192i
$681$	−2.41014e10	−	7.41764e10i	−0.112061	−	0.344888i
$682$	1.04572e11	−	8.01555e9i	0.483368	−	0.0370506i
$683$	−2.75201e11	+	8.94184e10i	−1.26464	+	0.410907i	−0.863147	−	0.504953i	$-0.831510\pi$
$683$	−2.75201e11	+	8.94184e10i	−1.26464	+	0.410907i	−0.401496	+	0.915861i	$0.631510\pi$
$684$	8.04069e10	−	1.56230e11i	0.367341	−	0.713738i
$685$	3.29531e11	+	1.66794e11i	1.49670	+	0.757564i
$686$	−1.14053e11	−	1.34091e11i	−0.515002	−	0.605485i
$687$	−8.43385e9	+	1.16082e10i	−0.0378616	+	0.0521120i
$688$	−5.21776e9	+	1.56240e10i	−0.0232879	+	0.0697329i
$689$	−1.54528e10	+	1.12271e10i	−0.0685692	+	0.0498184i
$690$	1.77176e11	+	7.32559e10i	0.781642	+	0.323181i
$691$	−2.31558e11	+	3.18712e11i	−1.01566	+	1.39793i	−0.100453	+	0.994942i	$0.532029\pi$
$691$	−2.31558e11	+	3.18712e11i	−1.01566	+	1.39793i	−0.915204	+	0.402990i	$0.867971\pi$
$692$	8.89480e10	+	1.76344e11i	0.387893	+	0.769018i
$693$	−8.01517e10			−0.347520
$694$	3.13908e11	−	1.29276e11i	1.35321	−	0.557288i
$695$	−1.35803e11	−	1.35078e11i	−0.582063	−	0.578954i
$696$	−2.51854e10	−	2.13719e9i	−0.107328	−	0.00910763i
$697$	−3.22738e10	+	9.93286e10i	−0.136747	+	0.420865i
$698$	2.69641e11	−	2.29347e11i	1.13596	−	0.966208i
$699$			1.60952e11i			0.674200i
$700$	−2.70734e11	+	4.32349e10i	−1.12759	+	0.180070i
$701$	−2.26921e11			−0.939730			−0.469865	−	0.882738i	$-0.655697\pi$
$701$	−2.26921e11			−0.939730			−0.469865	+	0.882738i	$0.655697\pi$
$702$	5.94953e10	+	6.99482e10i	0.244982	+	0.288024i
$703$	2.59354e11	+	8.42691e10i	1.06187	+	0.345022i
$704$	−1.04495e11	+	1.52428e10i	−0.425409	+	0.0620546i
$705$	1.65455e11	+	8.37460e10i	0.669765	+	0.339006i
$706$	1.70955e11	+	4.15113e11i	0.688118	+	1.67089i
$707$		−	3.96093e11i		−	1.58533i
$708$	−5.78888e10	−	1.14768e11i	−0.230389	−	0.456758i
$709$	3.45011e11	+	2.50665e11i	1.36536	+	0.991994i	0.998083	+	0.0618839i	$0.0197109\pi$
$709$	3.45011e11	+	2.50665e11i	1.36536	+	0.991994i	0.367280	+	0.930110i	$0.380289\pi$
$710$	−2.38551e9	+	1.46394e9i	−0.00938744	+	0.00576089i
$711$	1.65683e11	+	2.28043e11i	0.648335	+	0.892357i
$712$	6.66322e10	+	2.80786e10i	0.259277	+	0.109258i
$713$	3.68987e11	+	2.68085e11i	1.42775	+	1.03732i
$714$	−6.50728e10	+	5.53484e10i	−0.250384	+	0.212967i
$715$	−7.32189e9	−	4.54407e10i	−0.0280155	−	0.173869i
$716$	7.19198e10	−	1.39739e11i	0.273651	−	0.531700i
$717$	−4.55824e10	−	1.40288e11i	−0.172473	−	0.530817i
$718$	−9.87938e8	−	1.28888e10i	−0.00371734	−	0.0484969i
$719$	1.03865e11	−	3.37478e10i	0.388645	−	0.126279i	−0.108175	−	0.994132i	$-0.534501\pi$
$719$	1.03865e11	−	3.37478e10i	0.388645	−	0.126279i	0.496821	+	0.867853i	$0.334501\pi$
$720$	1.33785e11	+	1.35258e11i	0.497824	+	0.503306i
$721$	8.01358e10	−	2.46633e11i	0.296542	−	0.912661i
$722$	1.82822e10	−	7.54728e10i	0.0672791	−	0.277742i
$723$	3.11223e10	+	4.28362e10i	0.113899	+	0.156768i
$724$	−5.44095e10	+	8.39038e9i	−0.198025	+	0.0305371i
$725$	−2.94893e8	−	5.50634e10i	−0.00106736	−	0.199302i
$726$	−9.35399e9	−	1.22034e11i	−0.0336706	−	0.439271i
$727$	3.78280e10	+	5.20658e10i	0.135418	+	0.186387i	0.871340	−	0.490679i	$-0.163251\pi$
$727$	3.78280e10	+	5.20658e10i	0.135418	+	0.186387i	−0.735922	+	0.677066i	$0.763251\pi$
$728$	1.30916e11	+	1.11093e10i	0.466089	+	0.0395514i
$729$	−3.06210e10	+	9.42418e10i	−0.108420	+	0.333682i
$730$	1.70095e10	−	2.17907e11i	0.0598964	−	0.767327i
$731$	−1.06343e10	+	3.45529e9i	−0.0372425	+	0.0121008i
$732$	1.87472e9	+	1.21571e10i	0.00652968	+	0.0423434i
$733$	−1.00739e11	−	3.10044e11i	−0.348966	−	1.07401i	−0.959426	−	0.281960i	$-0.909015\pi$
$733$	−1.00739e11	−	3.10044e11i	−0.348966	−	1.07401i	0.610460	−	0.792047i	$-0.290985\pi$
$734$	−9.67568e10	+	1.57173e11i	−0.333348	+	0.541493i
$735$	−4.73593e10	−	7.37104e9i	−0.162277	−	0.0252569i
$736$	−3.89097e11	−	2.43928e11i	−1.32601	−	0.831287i
$737$	−1.50978e11	−	1.09692e11i	−0.511734	−	0.371797i
$738$	1.48570e11	+	9.14610e10i	0.500848	+	0.308326i
$739$	4.50459e10	+	6.20004e10i	0.151035	+	0.207882i	0.877830	−	0.478973i	$-0.158991\pi$
$739$	4.50459e10	+	6.20004e10i	0.151035	+	0.207882i	−0.726795	+	0.686855i	$0.758991\pi$
$740$	−1.73885e11	+	2.38630e11i	−0.579877	+	0.795789i
$741$	6.12314e10	+	4.44872e10i	0.203096	+	0.147558i
$742$	−6.62183e10	+	2.72705e10i	−0.218455	+	0.0899659i
$743$		−	4.53101e10i		−	0.148675i	−0.997233	−	0.0743377i	$-0.976316\pi$
$743$		−	4.53101e10i		−	0.148675i	0.997233	−	0.0743377i	$-0.0236843\pi$
$744$	−9.65912e10	−	1.59808e11i	−0.315243	−	0.521563i
$745$	5.12424e11	−	8.25671e10i	1.66343	−	0.268029i
$746$	−9.84066e9	+	4.06243e10i	−0.0317738	+	0.131169i
$747$	−3.75660e11	−	1.22059e11i	−1.20646	−	0.392002i
$748$	−5.04809e10	−	5.08942e10i	−0.161258	−	0.162578i
$749$	8.57929e10			0.272599
$750$	1.10275e11	−	1.30693e11i	0.348522	−	0.413056i
$751$			5.14865e11i			1.61858i	0.587411	+	0.809288i	$0.300147\pi$
$751$			5.14865e11i			1.61858i	−0.587411	+	0.809288i	$0.699853\pi$
$752$	−3.57217e11	−	2.64010e11i	−1.11702	−	0.825560i
$753$	−4.56763e10	+	1.40577e11i	−0.142073	+	0.437255i
$754$	−6.21251e9	+	2.56465e10i	−0.0192213	+	0.0793493i
$755$	6.90038e10	+	4.28248e11i	0.212366	+	1.31798i
$756$	1.55053e11	+	3.07400e11i	0.474671	+	0.941060i
$757$	−8.93707e10			−0.272152			−0.136076	−	0.990698i	$-0.543449\pi$
$757$	−8.93707e10			−0.272152			−0.136076	+	0.990698i	$0.543449\pi$
$758$	3.10201e11	−	1.27749e11i	0.939652	−	0.386974i
$759$	−7.09320e10	+	9.76295e10i	−0.213735	+	0.294180i
$760$	3.21873e11	+	1.98769e11i	0.964783	+	0.595792i
$761$	1.18035e11	−	8.57574e10i	0.351943	−	0.255701i	−0.397741	−	0.917498i	$-0.630206\pi$
$761$	1.18035e11	−	8.57574e10i	0.351943	−	0.255701i	0.749684	+	0.661796i	$0.230206\pi$
$762$	7.09161e10	+	4.36565e10i	0.210341	+	0.129488i
$763$	−3.24336e10	+	4.46410e10i	−0.0956967	+	0.131715i
$764$	3.67715e11	+	3.70725e11i	1.07929	+	1.08812i
$765$	−1.98604e10	+	1.27604e11i	−0.0579886	+	0.372580i
$766$	−1.15540e11	+	1.87684e11i	−0.335597	+	0.545146i
$767$	−1.27629e11	+	4.14693e10i	−0.368781	+	0.119824i
$768$	1.08019e11	+	1.53891e11i	0.310495	+	0.442353i
$769$	1.48126e11	+	4.55884e11i	0.423570	+	1.30361i	0.904357	+	0.426776i	$0.140351\pi$
$769$	1.48126e11	+	4.55884e11i	0.423570	+	1.30361i	−0.480788	+	0.876837i	$0.659649\pi$
$770$	1.34296e10	−	1.72045e11i	0.0382031	−	0.489416i
$771$	−2.54000e11	−	8.25295e10i	−0.718813	−	0.233556i
$772$	−5.15577e10	+	3.17149e11i	−0.145152	+	0.892881i
$773$	2.83835e11	−	2.06218e11i	0.794966	−	0.577576i	−0.114467	−	0.993427i	$-0.536516\pi$
$773$	2.83835e11	−	2.06218e11i	0.794966	−	0.577576i	0.909433	+	0.415851i	$0.136516\pi$
$774$	1.42754e9	+	1.86240e10i	0.00397764	+	0.0518929i
$775$	3.27821e11	−	2.40869e11i	0.908719	−	0.667688i
$776$	−3.95919e11	+	9.24948e10i	−1.09184	+	0.255076i
$777$	−1.79183e11	+	1.30184e11i	−0.491600	+	0.357168i
$778$	9.30698e10	−	3.84212e11i	0.254033	−	1.04870i
$779$	3.29944e11	+	1.07205e11i	0.895964	+	0.291116i
$780$	−6.63649e10	+	4.80752e10i	−0.179292	+	0.129880i
$781$	−5.44398e8	−	1.67549e9i	−0.00146323	−	0.00450336i
$782$	−2.38249e10	−	3.10824e11i	−0.0637095	−	0.831164i
$783$	−6.57643e10	+	2.13681e10i	−0.174962	+	0.0568485i
$784$	1.08894e11	+	3.63661e10i	0.288231	+	0.0962571i
$785$	5.29335e11	−	8.52921e10i	1.39397	−	0.224611i
$786$	9.64702e10	−	8.20538e10i	0.252757	−	0.214985i
$787$	4.10817e11	−	5.65441e11i	1.07090	−	1.47397i	0.201739	−	0.979439i	$-0.435341\pi$
$787$	4.10817e11	−	5.65441e11i	1.07090	−	1.47397i	0.869161	−	0.494529i	$-0.164659\pi$
$788$	−5.73198e10	−	2.95009e10i	−0.148662	−	0.0765121i
$789$	2.45514e11	−	1.78377e11i	0.633532	−	0.460288i
$790$	−5.17253e11	+	3.17428e11i	−1.32799	+	0.814961i
$791$	2.41772e11	−	3.32770e11i	0.617589	−	0.850038i
$792$	−1.02481e11	+	6.19417e10i	−0.260461	+	0.157428i
$793$	1.28421e10			0.0324746
$794$	−1.08461e11	−	2.63365e11i	−0.272892	−	0.662638i
$795$	2.01717e10	−	3.98526e10i	0.0504979	−	0.0997672i
$796$	5.36154e11	+	8.71606e10i	1.33548	+	0.217104i
$797$	−1.42378e10	+	4.38196e10i	−0.0352867	+	0.108601i	−0.967148	−	0.254212i	$-0.918184\pi$
$797$	−1.42378e10	+	4.38196e10i	−0.0352867	+	0.108601i	0.931862	+	0.362814i	$0.118184\pi$
$798$	1.83853e11	+	2.16155e11i	0.453378	+	0.533033i
$799$		−	3.01522e11i		−	0.739831i
$800$	−3.12745e11	+	2.64504e11i	−0.763538	+	0.645762i
$801$	8.19918e10			0.199178
$802$	−2.10489e11	+	1.79034e11i	−0.508782	+	0.432750i
$803$	1.30842e11	+	4.25131e10i	0.314691	+	0.102249i
$804$	−5.33153e10	+	3.27960e11i	−0.127593	+	0.784869i
$805$	5.29231e11	−	5.32073e11i	1.26026	−	1.26703i
$806$	−1.80261e11	+	7.42363e10i	−0.427131	+	0.175904i
$807$			2.39239e11i			0.564076i
$808$	−3.06103e11	−	5.06441e11i	−0.718161	−	1.18818i
$809$	4.30208e11	+	3.12564e11i	1.00435	+	0.729701i	0.963016	−	0.269444i	$-0.0868400\pi$
$809$	4.30208e11	+	3.12564e11i	1.00435	+	0.729701i	0.0413317	+	0.999145i	$0.486840\pi$
$810$	8.31663e10	+	3.43864e10i	0.193200	+	0.0798815i
$811$	−2.24102e11	−	3.08450e11i	−0.518040	−	0.713020i	0.467210	−	0.884147i	$-0.345259\pi$
$811$	−2.24102e11	−	3.08450e11i	−0.518040	−	0.713020i	−0.985249	+	0.171126i	$0.945259\pi$
$812$	−4.52756e10	+	8.79699e10i	−0.104145	+	0.202353i
$813$	1.25545e11	+	9.12138e10i	0.287367	+	0.208785i
$814$	−1.20411e11	−	1.41566e11i	−0.274263	−	0.322449i
$815$	−1.88792e11	+	3.72991e11i	−0.427911	+	0.845412i
$816$	−4.04279e10	+	1.21057e11i	−0.0911844	+	0.273041i
$817$	1.14776e10	+	3.53244e10i	0.0257610	+	0.0792842i
$818$	5.46248e11	−	4.18704e10i	1.22005	−	0.0935177i
$819$	1.41694e11	−	4.60391e10i	0.314931	−	0.102327i
$820$	−2.21213e11	+	3.03580e11i	−0.489278	+	0.671456i
$821$	2.47944e11	−	7.63094e11i	0.545735	−	1.67960i	−0.173502	−	0.984833i	$-0.555508\pi$
$821$	2.47944e11	−	7.63094e11i	0.545735	−	1.67960i	0.719237	−	0.694765i	$-0.244492\pi$
$822$	4.02273e11	+	9.74449e10i	0.881117	+	0.213438i
$823$	−3.10045e11	−	4.26741e11i	−0.675812	−	0.930175i	0.324062	−	0.946036i	$-0.394951\pi$
$823$	−3.10045e11	−	4.26741e11i	−0.675812	−	0.930175i	−0.999874	+	0.0158605i	$0.994951\pi$
$824$	−8.81383e10	−	3.77272e11i	−0.191186	−	0.818362i
$825$	6.37309e10	+	8.67373e10i	0.137573	+	0.187236i
$826$	−5.01673e11	+	3.84537e10i	−1.07771	+	0.0826072i
$827$	1.89776e11	+	2.61204e11i	0.405713	+	0.558416i	0.962166	−	0.272463i	$-0.0878382\pi$
$827$	1.89776e11	+	2.61204e11i	0.405713	+	0.558416i	−0.556453	+	0.830879i	$0.687838\pi$
$828$	−5.14000e11	−	8.35592e10i	−1.09356	−	0.177776i
$829$	−4.35835e10	+	1.34136e11i	−0.0922791	+	0.284006i	−0.986535	−	0.163550i	$-0.947705\pi$
$829$	−4.35835e10	+	1.34136e11i	−0.0922791	+	0.284006i	0.894256	+	0.447556i	$0.147705\pi$
$830$	3.24941e11	−	7.85898e11i	0.684687	−	1.65598i
$831$	5.04746e9	−	1.64002e9i	0.0105845	−	0.00343910i
$832$	1.75974e11	−	8.69688e10i	0.367244	−	0.181497i
$833$	2.40823e10	+	7.41176e10i	0.0500170	+	0.153936i
$834$	−1.82795e11	−	1.12530e11i	−0.377834	−	0.232597i
$835$	1.27083e10	−	6.51812e9i	0.0261422	−	0.0134084i
$836$	−1.69058e11	+	1.67685e11i	−0.346106	+	0.343296i
$837$	−4.13286e11	−	3.00270e11i	−0.842072	−	0.611801i
$838$	1.51548e11	−	2.46177e11i	0.307309	−	0.499195i
$839$	8.73382e10	+	1.20211e11i	0.176261	+	0.242603i	0.888002	−	0.459839i	$-0.152093\pi$
$839$	8.73382e10	+	1.20211e11i	0.176261	+	0.242603i	−0.711741	+	0.702442i	$0.752093\pi$
$840$	−2.84263e11	+	1.16602e11i	−0.570956	+	0.234201i
$841$	3.88632e11	+	2.82358e11i	0.776881	+	0.564437i
$842$	−2.74587e11	−	6.66753e11i	−0.546301	−	1.32653i
$843$			5.05916e11i			1.00177i
$844$	−6.46799e11	+	3.26246e11i	−1.27467	+	0.642947i
$845$	−1.93629e11	−	3.77517e11i	−0.379791	−	0.740473i
$846$	−4.89530e11	−	1.18582e11i	−0.955648	−	0.231492i
$847$	−4.55628e11	−	1.48042e11i	−0.885272	−	0.287642i
$848$	−6.35913e10	+	8.60417e10i	−0.122974	+	0.166389i
$849$	−2.08044e11			−0.400429
$850$	−2.70574e11	−	6.40105e10i	−0.518334	−	0.122624i
$851$		−	8.08211e11i		−	1.54101i
$852$	−2.22696e9	+	2.20887e9i	−0.00422623	+	0.00419191i
$853$	−5.12651e10	+	1.57778e11i	−0.0968334	+	0.298023i	−0.987727	−	0.156189i	$-0.950079\pi$
$853$	−5.12651e10	+	1.57778e11i	−0.0968334	+	0.298023i	0.890894	+	0.454212i	$0.150079\pi$
$854$	4.67955e10	+	1.13355e10i	0.0879776	+	0.0213113i
$855$	4.23869e11	+	6.59713e10i	0.793172	+	0.123450i
$856$	1.09694e11	−	6.63013e10i	0.204309	−	0.123489i
$857$	1.15095e11			0.213370			0.106685	−	0.994293i	$-0.465976\pi$
$857$	1.15095e11			0.213370			0.106685	+	0.994293i	$0.465976\pi$
$858$	−1.96420e10	−	4.76947e10i	−0.0362440	−	0.0880078i
$859$	−3.65994e11	+	5.03747e11i	−0.672204	+	0.925210i	−0.999808	−	0.0196056i	$-0.993759\pi$
$859$	−3.65994e11	+	5.03747e11i	−0.672204	+	0.925210i	0.327604	+	0.944815i	$0.393759\pi$
$860$	−4.02153e10	−	5.62693e7i	−0.0735186	−	0.000102867i
$861$	−2.27952e11	+	1.65617e11i	−0.414793	+	0.301365i
$862$	−1.68022e11	+	2.72937e11i	−0.304325	+	0.494348i
$863$	−3.48237e11	+	4.79307e11i	−0.627815	+	0.864114i	−0.997893	−	0.0648873i	$-0.979331\pi$
$863$	−3.48237e11	+	4.79307e11i	−0.627815	+	0.864114i	0.370077	+	0.929001i	$0.379331\pi$
$864$	4.35810e11	+	2.73213e11i	0.782064	+	0.490283i
$865$	−3.40049e11	+	3.41875e11i	−0.607403	+	0.610664i
$866$	5.34273e11	+	3.28903e11i	0.949930	+	0.584785i
$867$	2.08030e11	−	6.75932e10i	0.368172	−	0.119626i
$868$	−7.22380e11	+	1.11397e11i	−1.27258	+	0.196243i
$869$	−1.18043e11	−	3.63298e11i	−0.206995	−	0.637065i
$870$	−1.44440e10	−	5.99946e10i	−0.0252122	−	0.104721i
$871$	3.29910e11	+	1.07194e11i	0.573222	+	0.186251i
$872$	−6.97045e9	+	8.21424e10i	−0.0120558	+	0.142070i
$873$	−3.72989e11	+	2.70992e11i	−0.642154	+	0.466552i
$874$	−1.03248e12	+	7.91403e10i	−1.76943	+	0.135629i
$875$	−3.08658e11	−	5.93932e11i	−0.526557	−	1.01322i
$876$	−3.73313e10	−	2.42084e11i	−0.0633952	−	0.411102i
$877$	8.24198e10	−	5.98815e10i	0.139326	−	0.101226i	−0.515939	−	0.856625i	$-0.672557\pi$
$877$	8.24198e10	−	5.98815e10i	0.139326	−	0.101226i	0.655265	+	0.755399i	$0.272557\pi$
$878$	−5.27697e11	−	1.27827e11i	−0.887987	−	0.215102i
$879$	−2.78510e11	−	9.04934e10i	−0.466536	−	0.151587i
$880$	−1.15786e11	−	2.30353e11i	−0.193075	−	0.384117i
$881$	1.70447e11	+	5.24581e11i	0.282934	+	0.870781i	0.987010	+	0.160657i	$0.0513613\pi$
$881$	1.70447e11	+	5.24581e11i	0.282934	+	0.870781i	−0.704076	+	0.710124i	$0.748639\pi$
$882$	1.29803e11	−	9.94952e9i	0.214492	−	0.0164410i
$883$	1.06207e12	−	3.45087e11i	1.74707	−	0.567657i	0.751333	−	0.659923i	$-0.229411\pi$
$883$	1.06207e12	−	3.45087e11i	1.74707	−	0.567657i	0.995734	+	0.0922666i	$0.0294112\pi$
$884$	1.18475e11	+	6.09757e10i	0.194007	+	0.0998499i
$885$	2.21309e11	−	2.22498e11i	0.360767	−	0.362704i
$886$	−6.93158e10	−	8.14942e10i	−0.112486	−	0.132249i
$887$	−3.15377e11	+	4.34079e11i	−0.509490	+	0.701252i	−0.983833	−	0.179087i	$-0.942685\pi$
$887$	−3.15377e11	+	4.34079e11i	−0.509490	+	0.701252i	0.474343	+	0.880340i	$0.342685\pi$
$888$	−1.28494e11	+	3.04925e11i	−0.206648	+	0.490390i
$889$	2.63714e11	−	1.91599e11i	0.422207	−	0.306751i
$890$	−1.37379e10	+	1.75995e11i	−0.0218957	+	0.280504i
$891$	−3.32955e10	+	4.58273e10i	−0.0528293	+	0.0727133i
$892$	2.20103e10	−	1.11020e10i	0.0347670	−	0.0175365i
$893$	−1.00158e12			−1.57500
$894$	5.37842e11	−	2.21498e11i	0.841985	−	0.346752i
$895$	3.79129e11	+	5.90079e10i	0.590874	+	0.0919640i
$896$	7.17998e11	−	1.61577e11i	1.11402	−	0.250695i
$897$	6.93167e10	−	2.13335e11i	0.107070	−	0.329528i
$898$	1.43680e11	−	1.22208e11i	0.220948	−	0.187930i
$899$		−	1.46800e11i		−	0.224744i
$900$	−2.10333e11	+	4.14110e11i	−0.320581	+	0.631169i
$901$	−7.26268e10			−0.110204
$902$	−1.53184e11	−	1.80097e11i	−0.231412	−	0.272070i
$903$	−2.86898e10	−	9.32187e9i	−0.0431495	−	0.0140201i
$904$	5.19602e10	−	6.12319e11i	0.0778031	−	0.916862i
$905$	−6.13395e10	−	1.19593e11i	−0.0914420	−	0.178283i
$906$	1.85112e11	+	4.49490e11i	0.274741	+	0.667126i
$907$			1.01891e12i			1.50559i	0.658255	+	0.752795i	$0.271295\pi$
$907$			1.01891e12i			1.50559i	−0.658255	+	0.752795i	$0.728705\pi$
$908$	−4.07230e11	+	2.05407e11i	−0.599096	+	0.302184i
$909$	−5.42871e11	−	3.94419e11i	−0.795135	−	0.577699i
$910$	7.50814e10	+	3.11858e11i	0.109488	+	0.454770i
$911$	3.14232e11	+	4.32503e11i	0.456223	+	0.627937i	0.973720	−	0.227748i	$-0.0731363\pi$
$911$	3.14232e11	+	4.32503e11i	0.456223	+	0.627937i	−0.517497	+	0.855685i	$0.673136\pi$
$912$	4.02119e11	+	1.34291e11i	0.581267	+	0.194119i
$913$	4.33055e11	+	3.14633e11i	0.623247	+	0.452815i
$914$	4.89214e11	−	4.16106e11i	0.700993	−	0.596238i
$915$	−2.67214e10	+	1.37055e10i	−0.0381220	+	0.0195529i
$916$	7.46076e10	+	3.83984e10i	0.105974	+	0.0545420i
$917$	−1.53189e11	−	4.71468e11i	−0.216646	−	0.666768i
$918$	2.66852e10	+	3.48140e11i	0.0375751	+	0.490211i
$919$	−5.59725e11	+	1.81866e11i	−0.784716	+	0.254970i	−0.673852	−	0.738866i	$-0.735362\pi$
$919$	−5.59725e11	+	1.81866e11i	−0.784716	+	0.254970i	−0.110864	+	0.993836i	$0.535362\pi$
$920$	2.65481e11	−	1.08930e12i	0.370579	−	1.52053i
$921$	9.85320e10	−	3.03250e11i	0.136943	−	0.421466i
$922$	2.13266e11	−	8.80407e11i	0.295120	−	1.21832i
$923$	1.92480e9	+	2.64926e9i	0.00265203	+	0.00365021i
$924$	−2.94742e10	−	1.91133e11i	−0.0404347	−	0.262209i
$925$	−6.86759e11	−	2.19082e11i	−0.938075	−	0.299254i
$926$	8.85209e10	+	1.15486e12i	0.120393	+	1.57067i
$927$	−2.58229e11	−	3.55421e11i	−0.349692	−	0.481310i
$928$	1.00947e10	+	1.47467e11i	0.0136114	+	0.198839i
$929$	−4.91487e10	+	1.51264e11i	−0.0659856	+	0.203083i	−0.978613	−	0.205709i	$-0.934050\pi$
$929$	−4.91487e10	+	1.51264e11i	−0.0659856	+	0.203083i	0.912628	+	0.408792i	$0.134050\pi$
$930$	2.95853e11	−	3.46848e11i	0.395498	−	0.463668i
$931$	2.46200e11	−	7.99952e10i	0.327710	−	0.106479i
$932$	9.30242e11	−	1.43451e11i	1.23291	−	0.190125i
$933$	−7.79221e10	−	2.39820e11i	−0.102833	−	0.316489i
$934$	4.51004e11	−	7.32615e11i	0.592643	−	0.962695i
$935$	7.90345e10	−	1.56146e11i	0.103412	−	0.204308i
$936$	1.45589e11	−	1.68367e11i	0.189682	−	0.219358i
$937$	6.68159e11	+	4.85446e11i	0.866806	+	0.629771i	0.929728	−	0.368247i	$-0.120042\pi$
$937$	6.68159e11	+	4.85446e11i	0.866806	+	0.629771i	−0.0629223	+	0.998018i	$0.520042\pi$
$938$	1.10754e12	+	6.81812e11i	1.43070	+	0.880751i
$939$	−3.61271e11	−	4.97247e11i	−0.464698	−	0.639602i
$940$	3.36556e11	−	1.03090e12i	0.431068	−	1.32040i
$941$	−7.01827e11	−	5.09907e11i	−0.895100	−	0.650328i	0.0421031	−	0.999113i	$-0.486594\pi$
$941$	−7.01827e11	−	5.09907e11i	−0.895100	−	0.650328i	−0.937203	+	0.348785i	$0.886594\pi$
$942$	5.55592e11	−	2.28808e11i	0.705590	−	0.290581i
$943$		−	1.02819e12i		−	1.30025i
$944$	−6.11717e11	+	4.36862e11i	−0.770305	+	0.550119i
$945$	−5.92768e11	+	5.95951e11i	−0.743289	+	0.747280i
$946$	5.95933e9	−	2.46014e10i	0.00744103	−	0.0307181i
$947$	3.98670e11	+	1.29536e11i	0.495694	+	0.161061i	0.546186	−	0.837664i	$-0.316079\pi$
$947$	3.98670e11	+	1.29536e11i	0.495694	+	0.161061i	−0.0504925	+	0.998724i	$0.516079\pi$
$948$	−4.82874e11	+	4.78953e11i	−0.597861	+	0.593006i
$949$	−2.55725e11			−0.315288
$950$	−2.12627e11	+	8.98776e11i	−0.261050	+	1.10346i
$951$		−	5.04510e11i		−	0.616805i
$952$	3.77889e11	+	3.26765e11i	0.460062	+	0.397822i
$953$	−4.23353e11	+	1.30295e12i	−0.513252	+	1.57963i	0.273187	+	0.961961i	$0.411922\pi$
$953$	−4.23353e11	+	1.30295e12i	−0.513252	+	1.57963i	−0.786440	+	0.617667i	$0.788078\pi$
$954$	−2.85624e10	+	1.17912e11i	−0.0344827	+	0.142352i
$955$	−5.75706e11	+	1.13740e12i	−0.692129	+	1.36742i
$956$	−7.70185e11	+	3.88482e11i	−0.922070	+	0.465093i
$957$	3.88416e10			0.0463073
$958$	7.37898e11	−	3.03887e11i	0.876061	−	0.360786i
$959$	9.52300e11	−	1.31073e12i	1.12590	−	1.54967i
$960$	−2.73345e11	+	3.68766e11i	−0.321829	+	0.434176i
$961$	1.87390e11	−	1.36146e11i	0.219711	−	0.159629i
$962$	2.94180e11	+	1.81100e11i	0.343489	+	0.211455i
$963$	8.54303e10	−	1.17585e11i	0.0993360	−	0.136724i
$964$	2.19838e11	−	2.18053e11i	0.254563	−	0.252496i
$965$	−7.74464e11	+	1.24790e11i	−0.893083	+	0.143903i
$966$	4.40891e11	−	7.16187e11i	0.506317	−	0.822466i
$967$	−8.53587e11	+	2.77347e11i	−0.976207	+	0.317189i	−0.753319	−	0.657655i	$-0.771548\pi$
$967$	−8.53587e11	+	2.77347e11i	−0.976207	+	0.317189i	−0.222888	+	0.974844i	$0.571548\pi$
$968$	−6.96969e11	+	1.62826e11i	−0.793802	+	0.185448i
$969$	8.89299e10	+	2.73698e11i	0.100868	+	0.310439i
$970$	−5.19187e11	−	8.46022e11i	−0.586458	−	0.955641i
$971$	−1.02584e11	−	3.33317e10i	−0.115400	−	0.0374956i	0.250748	−	0.968052i	$-0.419323\pi$
$971$	−1.02584e11	−	3.33317e10i	−0.115400	−	0.0374956i	−0.366148	+	0.930557i	$0.619323\pi$
$972$	9.12792e11	+	1.48389e11i	1.02260	+	0.166241i
$973$	−6.79756e11	+	4.93871e11i	−0.758406	+	0.551014i
$974$	1.13123e11	+	1.47582e12i	0.125694	+	1.63982i
$975$	−1.62487e11	−	1.16729e11i	−0.179804	−	0.129170i
$976$	6.85924e10	−	2.16703e10i	0.0755921	−	0.0238817i
$977$	−9.25946e11	+	6.72739e11i	−1.01627	+	0.738361i	−0.965514	−	0.260350i	$-0.916162\pi$
$977$	−9.25946e11	+	6.72739e11i	−1.01627	+	0.738361i	−0.0507523	+	0.998711i	$0.516162\pi$
$978$	−1.10296e11	+	4.55327e11i	−0.120561	+	0.497700i
$979$	−1.05675e11	−	3.43360e10i	−0.115039	−	0.0373783i
$980$	−3.92179e8	+	2.80288e11i	−0.000425188	+	0.303878i
$981$	2.88869e10	+	8.89046e10i	0.0311906	+	0.0959949i
$982$	−5.54539e10	−	7.23460e11i	−0.0596329	−	0.777980i
$983$	−1.64894e12	+	5.35772e11i	−1.76600	+	0.573807i	−0.997793	−	0.0663995i	$-0.978849\pi$
$983$	−1.64894e12	+	5.35772e11i	−1.76600	+	0.573807i	−0.768203	+	0.640206i	$0.778849\pi$
$984$	−1.63468e11	+	3.87919e11i	−0.174362	+	0.413772i
$985$	2.42045e10	−	1.55515e11i	0.0257129	−	0.165207i
$986$	−7.64293e10	+	6.50078e10i	−0.0808634	+	0.0687793i
$987$	4.78142e11	−	6.58106e11i	0.503835	−	0.693469i
$988$	2.02546e11	−	3.93543e11i	0.212567	−	0.413014i
$989$	8.90563e10	−	6.47032e10i	0.0930850	−	0.0676302i
$990$	−2.22425e11	−	1.89723e11i	−0.231549	−	0.197506i
$991$	1.37363e11	−	1.89064e11i	0.142422	−	0.196027i	−0.731847	−	0.681469i	$-0.761341\pi$
$991$	1.37363e11	−	1.89064e11i	0.142422	−	0.196027i	0.874269	+	0.485442i	$0.161341\pi$
$992$	−8.37540e11	+	7.00690e11i	−0.864886	+	0.723568i
$993$	−5.69421e11			−0.585648
$994$	4.67532e9	+	1.13526e10i	0.00478924	+	0.0116292i
$995$	2.10963e11	+	1.30927e12i	0.215235	+	1.33578i
$996$	1.52926e11	−	9.40697e11i	0.155397	−	0.955900i
$997$	4.46071e11	−	1.37287e12i	0.451464	−	1.38946i	−0.423772	−	0.905769i	$-0.639294\pi$
$997$	4.46071e11	−	1.37287e12i	0.451464	−	1.38946i	0.875236	−	0.483696i	$-0.160706\pi$
$998$	3.94949e10	+	4.64340e10i	0.0398125	+	0.0468073i
$999$			9.05241e11i			0.908871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.90	✓	464
4.3	odd	2	inner	100.9.j.b.11.97	yes	464
25.16	even	5	inner	100.9.j.b.91.97	yes	464
100.91	odd	10	inner	100.9.j.b.91.90	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.90	✓	464	1.1	even	1	trivial
100.9.j.b.11.97	yes	464	4.3	odd	2	inner
100.9.j.b.91.90	yes	464	100.91	odd	10	inner
100.9.j.b.91.97	yes	464	25.16	even	5	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(12.1877 - 10.3663i) q^{2} +(41.6337 + 13.5276i) q^{3} +(41.0777 - 252.683i) q^{4} +(617.041 - 99.4242i) q^{5} +(647.648 - 266.719i) q^{6} -2741.64i q^{7} +(-2118.76 - 3505.44i) q^{8} +(-3757.59 - 2730.05i) q^{9} +(6489.62 - 7608.21i) q^{10} +(3699.71 + 5092.22i) q^{11} +(5128.41 - 9964.43i) q^{12} +(-9465.41 - 6877.02i) q^{13} +(-28420.8 - 33414.2i) q^{14} +(27034.7 + 4207.69i) q^{15} +(-62161.2 - 20759.3i) q^{16} +(-13747.2 - 42309.4i) q^{17} +(-74096.9 + 5679.60i) q^{18} +(-140541. + 45664.6i) q^{19} +(223.872 - 160000. i) q^{20} +(37087.8 - 114145. i) q^{21} +(97878.6 + 23709.7i) q^{22} +(257427. + 354318. i) q^{23} +(-40791.5 - 174606. i) q^{24} +(370855. - 122698. i) q^{25} +(-186651. + 14307.0i) q^{26} +(-288333. - 396856. i) q^{27} +(-692766. - 112620. i) q^{28} +(43560.4 - 134065. i) q^{29} +(373107. - 228969. i) q^{30} +(990432. - 321811. i) q^{31} +(-972797. + 391378. i) q^{32} +(85147.2 + 262056. i) q^{33} +(-606139. - 373144. i) q^{34} +(-272585. - 1.69171e6i) q^{35} +(-844191. + 837335. i) q^{36} +(-1.49296e6 - 1.08470e6i) q^{37} +(-1.23949e6 + 2.01344e6i) q^{38} +(-301050. - 414360. i) q^{39} +(-1.65589e6 - 1.95234e6i) q^{40} +(-1.89931e6 - 1.37993e6i) q^{41} +(-731249. - 1.77562e6i) q^{42} -251346. i q^{43} +(1.43869e6 - 725678. i) q^{44} +(-2.59002e6 - 1.31096e6i) q^{45} +(6.81041e6 + 1.64973e6i) q^{46} +(6.44607e6 + 2.09446e6i) q^{47} +(-2.30718e6 - 1.70518e6i) q^{48} -1.75180e6 q^{49} +(3.24792e6 - 5.33980e6i) q^{50} -1.94746e6i q^{51} +(-2.12652e6 + 2.10925e6i) q^{52} +(504486. - 1.55265e6i) q^{53} +(-7.62804e6 - 1.84778e6i) q^{54} +(2.78917e6 + 2.77427e6i) q^{55} +(-9.61065e6 + 5.80887e6i) q^{56} -6.46897e6 q^{57} +(-858866. - 2.08550e6i) q^{58} +(6.74188e6 - 9.27940e6i) q^{59} +(2.17373e6 - 6.65835e6i) q^{60} +(-887999. + 645169. i) q^{61} +(8.73504e6 - 1.41893e7i) q^{62} +(-7.48483e6 + 1.03020e7i) q^{63} +(-7.79896e6 + 1.48543e7i) q^{64} +(-6.52429e6 - 3.30232e6i) q^{65} +(3.75431e6 + 2.31118e6i) q^{66} +(-2.81977e7 + 9.16199e6i) q^{67} +(-1.12556e7 + 1.73570e6i) q^{68} +(5.92456e6 + 1.82339e7i) q^{69} +(-2.08590e7 - 1.77922e7i) q^{70} +(-266190. - 86490.3i) q^{71} +(-1.60860e6 + 1.89563e7i) q^{72} +(1.76827e7 - 1.28472e7i) q^{73} +(-2.94399e7 + 2.25660e6i) q^{74} +(1.70998e7 - 91578.6i) q^{75} +(5.76554e6 + 3.73881e7i) q^{76} +(1.39610e7 - 1.01433e7i) q^{77} +(-7.96449e6 - 1.92928e6i) q^{78} +(-5.77183e7 - 1.87538e7i) q^{79} +(-4.04200e7 - 6.62900e6i) q^{80} +(2.78099e6 + 8.55901e6i) q^{81} +(-3.74529e7 + 2.87080e6i) q^{82} +(8.08802e7 - 2.62796e7i) q^{83} +(-2.73189e7 - 1.40603e7i) q^{84} +(-1.26891e7 - 2.47398e7i) q^{85} +(-2.60554e6 - 3.06332e6i) q^{86} +(3.62715e6 - 4.99235e6i) q^{87} +(1.00117e7 - 2.37583e7i) q^{88} +(-1.42816e7 + 1.03762e7i) q^{89} +(-4.51562e7 + 1.08716e7i) q^{90} +(-1.88543e7 + 2.59508e7i) q^{91} +(1.00105e8 - 5.04928e7i) q^{92} +4.55886e7 q^{93} +(1.00274e8 - 4.12957e7i) q^{94} +(-8.21794e7 + 4.21501e7i) q^{95} +(-4.57955e7 + 3.13489e6i) q^{96} +(3.06739e7 - 9.44045e7i) q^{97} +(-2.13503e7 + 1.81598e7i) q^{98} -2.92349e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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