LMFDB - Embedded newform 100.9.j.b.11.69

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			11.69
Character	$\chi$	$=$	100.11
Dual form			100.9.j.b.91.69

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.43566 + 15.3729i) q^{2} +(-32.9851 - 10.7175i) q^{3} +(-216.650 + 136.378i) q^{4} +(-397.575 + 482.244i) q^{5} +(18.4482 - 554.615i) q^{6} -2164.38i q^{7} +(-3057.50 - 2725.61i) q^{8} +(-4334.81 - 3149.42i) q^{9} +(-9176.98 - 3972.79i) q^{10} +(-7225.93 - 9945.64i) q^{11} +(8607.85 - 2176.48i) q^{12} +(34926.9 + 25375.9i) q^{13} +(33272.8 - 9600.47i) q^{14} +(18282.5 - 11645.9i) q^{15} +(28338.3 - 59092.3i) q^{16} +(13805.5 + 42489.0i) q^{17} +(29187.9 - 80608.2i) q^{18} +(-28835.1 + 9369.08i) q^{19} +(20367.2 - 158698. i) q^{20} +(-23196.8 + 71392.5i) q^{21} +(120841. - 155199. i) q^{22} +(-183511. - 252581. i) q^{23} +(71640.2 + 122673. i) q^{24} +(-74493.8 - 383456. i) q^{25} +(-235176. + 649485. i) q^{26} +(242982. + 334436. i) q^{27} +(295173. + 468914. i) q^{28} +(-125952. + 387641. i) q^{29} +(260125. + 229397. i) q^{30} +(111192. - 36128.4i) q^{31} +(1.03412e6 + 173528. i) q^{32} +(131756. + 405502. i) q^{33} +(-591941. + 400697. i) q^{34} +(1.04376e6 + 860504. i) q^{35} +(1.36865e6 + 91151.6i) q^{36} +(-72584.6 - 52735.8i) q^{37} +(-271932. - 401720. i) q^{38} +(-880101. - 1.21136e6i) q^{39} +(2.52999e6 - 390829. i) q^{40} +(-1.29320e6 - 939564. i) q^{41} +(-1.20040e6 - 39929.0i) q^{42} +4.77706e6i q^{43} +(2.92186e6 + 1.16927e6i) q^{44} +(3.24220e6 - 838305. i) q^{45} +(3.06890e6 - 3.94145e6i) q^{46} +(5.38094e6 + 1.74837e6i) q^{47} +(-1.56807e6 + 1.64545e6i) q^{48} +1.08024e6 q^{49} +(5.56439e6 - 2.84606e6i) q^{50} -1.54946e6i q^{51} +(-1.10276e7 - 734436. i) q^{52} +(-4.34058e6 + 1.33589e7i) q^{53} +(-4.06346e6 + 5.21878e6i) q^{54} +(7.66907e6 + 469472. i) q^{55} +(-5.89926e6 + 6.61760e6i) q^{56} +1.05154e6 q^{57} +(-6.51783e6 - 216803. i) q^{58} +(9.56164e6 - 1.31605e7i) q^{59} +(-2.37267e6 + 5.01640e6i) q^{60} +(-1.06657e7 + 7.74908e6i) q^{61} +(1.04861e6 + 1.54908e6i) q^{62} +(-6.81656e6 + 9.38219e6i) q^{63} +(1.91937e6 + 1.66671e7i) q^{64} +(-2.61234e7 + 6.75448e6i) q^{65} +(-5.64930e6 + 3.82413e6i) q^{66} +(3.15345e7 - 1.02462e7i) q^{67} +(-8.78550e6 - 7.32247e6i) q^{68} +(3.34609e6 + 1.02982e7i) q^{69} +(-8.59865e6 + 1.98625e7i) q^{70} +(8.44126e6 + 2.74273e6i) q^{71} +(4.66959e6 + 2.14443e7i) q^{72} +(1.94324e7 - 1.41185e7i) q^{73} +(488740. - 1.34975e6i) q^{74} +(-1.65251e6 + 1.34467e7i) q^{75} +(4.96938e6 - 5.96227e6i) q^{76} +(-2.15262e7 + 1.56397e7i) q^{77} +(1.47182e7 - 1.89028e7i) q^{78} +(-2.50099e7 - 8.12621e6i) q^{79} +(1.72303e7 + 3.71596e7i) q^{80} +(6.43290e6 + 1.97984e7i) q^{81} +(8.70760e6 - 2.40478e7i) q^{82} +(-7.40952e6 + 2.40750e6i) q^{83} +(-4.71074e6 - 1.86307e7i) q^{84} +(-2.59788e7 - 1.02349e7i) q^{85} +(-7.34370e7 + 2.11894e7i) q^{86} +(8.30908e6 - 1.14365e7i) q^{87} +(-5.01462e6 + 5.01038e7i) q^{88} +(5.64541e7 - 4.10163e7i) q^{89} +(2.72684e7 + 4.61235e7i) q^{90} +(5.49231e7 - 7.55952e7i) q^{91} +(7.42040e7 + 2.96949e7i) q^{92} -4.05488e6 q^{93} +(-3.00950e6 + 9.04757e7i) q^{94} +(6.94591e6 - 1.76305e7i) q^{95} +(-3.22507e7 - 1.68070e7i) q^{96} +(3.31148e7 - 1.01917e8i) q^{97} +(4.79157e6 + 1.66064e7i) q^{98} +6.58700e7i 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 $

$2$	4.43566	+	15.3729i	0.277229	+	0.960804i
$2$	4.43566	+	15.3729i	0.277229	+	0.960804i
$3$	−32.9851	−	10.7175i	−0.407224	−	0.132315i	0.0982403	−	0.995163i	$-0.468679\pi$
$3$	−32.9851	−	10.7175i	−0.407224	−	0.132315i	−0.505464	+	0.862848i	$0.668679\pi$
$4$	−216.650	+	136.378i	−0.846289	+	0.532725i
$5$	−397.575	+	482.244i	−0.636119	+	0.771591i
$5$	−397.575	+	482.244i	−0.636119	+	0.771591i
$6$	18.4482	−	554.615i	0.0142347	−	0.427944i
$7$		−	2164.38i		−	0.901451i	−0.892663	−	0.450726i	$-0.851165\pi$
$7$		−	2164.38i		−	0.901451i	0.892663	−	0.450726i	$-0.148835\pi$
$8$	−3057.50	−	2725.61i	−0.746459	−	0.665431i
$9$	−4334.81	−	3149.42i	−0.660693	−	0.480022i
$10$	−9176.98	−	3972.79i	−0.917698	−	0.397279i
$11$	−7225.93	−	9945.64i	−0.493541	−	0.679301i	0.487495	−	0.873126i	$-0.337911\pi$
$11$	−7225.93	−	9945.64i	−0.493541	−	0.679301i	−0.981036	+	0.193825i	$0.937911\pi$
$12$	8607.85	−	2176.48i	0.415116	−	0.104961i
$13$	34926.9	+	25375.9i	1.22289	+	0.888480i	0.996336	−	0.0855197i	$-0.0272551\pi$
$13$	34926.9	+	25375.9i	1.22289	+	0.888480i	0.226551	+	0.973999i	$0.427255\pi$
$14$	33272.8	−	9600.47i	0.866118	−	0.249908i
$15$	18282.5	−	11645.9i	0.361136	−	0.230042i
$16$	28338.3	−	59092.3i	0.432409	−	0.901678i
$17$	13805.5	+	42489.0i	0.165294	+	0.508722i	0.999058	−	0.0433989i	$-0.0138186\pi$
$17$	13805.5	+	42489.0i	0.165294	+	0.508722i	−0.833764	+	0.552121i	$0.813819\pi$
$18$	29187.9	−	80608.2i	0.278044	−	0.767872i
$19$	−28835.1	+	9369.08i	−0.221262	+	0.0718924i	−0.417550	−	0.908654i	$-0.637111\pi$
$19$	−28835.1	+	9369.08i	−0.221262	+	0.0718924i	0.196288	+	0.980546i	$0.437111\pi$
$20$	20367.2	−	158698.i	0.127295	−	0.991865i
$21$	−23196.8	+	71392.5i	−0.119275	+	0.367092i
$22$	120841.	−	155199.i	0.515851	−	0.662518i
$23$	−183511.	−	252581.i	−0.655769	−	0.902588i	0.343563	−	0.939129i	$-0.388366\pi$
$23$	−183511.	−	252581.i	−0.655769	−	0.902588i	−0.999332	+	0.0365412i	$0.988366\pi$
$24$	71640.2	+	122673.i	0.215929	+	0.369747i
$25$	−74493.8	−	383456.i	−0.190704	−	0.981648i
$26$	−235176.	+	649485.i	−0.514635	+	1.42127i
$27$	242982.	+	334436.i	0.457214	+	0.629301i
$28$	295173.	+	468914.i	0.480225	+	0.762888i
$29$	−125952.	+	387641.i	−0.178079	+	0.548071i	−0.999761	−	0.0218755i	$-0.993036\pi$
$29$	−125952.	+	387641.i	−0.178079	+	0.548071i	0.821681	+	0.569947i	$0.193036\pi$
$30$	260125.	+	229397.i	0.321142	+	0.283207i
$31$	111192.	−	36128.4i	0.120400	−	0.0391203i	−0.248197	−	0.968709i	$-0.579838\pi$
$31$	111192.	−	36128.4i	0.120400	−	0.0391203i	0.368597	+	0.929589i	$0.379838\pi$
$32$	1.03412e6	+	173528.i	0.986212	+	0.165489i
$33$	131756.	+	405502.i	0.111100	+	0.341930i
$34$	−591941.	+	400697.i	−0.442958	+	0.299847i
$35$	1.04376e6	+	860504.i	0.695551	+	0.573431i
$36$	1.36865e6	+	91151.6i	0.814857	+	0.0542693i
$37$	−72584.6	−	52735.8i	−0.0387291	−	0.0281384i	0.568252	−	0.822854i	$-0.307620\pi$
$37$	−72584.6	−	52735.8i	−0.0387291	−	0.0281384i	−0.606981	+	0.794716i	$0.707620\pi$
$38$	−271932.	−	401720.i	−0.130415	−	0.192659i
$39$	−880101.	−	1.21136e6i	−0.380429	−	0.523616i
$40$	2.52999e6	−	390829.i	0.988278	−	0.152668i
$41$	−1.29320e6	−	939564.i	−0.457646	−	0.332500i	0.334961	−	0.942232i	$-0.391277\pi$
$41$	−1.29320e6	−	939564.i	−0.457646	−	0.332500i	−0.792607	+	0.609732i	$0.791277\pi$
$42$	−1.20040e6	−	39929.0i	−0.385770	−	0.0128319i
$43$			4.77706e6i			1.39729i	0.715469	+	0.698645i	$0.246213\pi$
$43$			4.77706e6i			1.39729i	−0.715469	+	0.698645i	$0.753787\pi$
$44$	2.92186e6	+	1.16927e6i	0.779558	+	0.311963i
$45$	3.24220e6	−	838305.i	0.790660	−	0.204434i
$46$	3.06890e6	−	3.94145e6i	0.685413	−	0.880289i
$47$	5.38094e6	+	1.74837e6i	1.10272	+	0.358297i	0.803150	−	0.595776i	$-0.203156\pi$
$47$	5.38094e6	+	1.74837e6i	1.10272	+	0.358297i	0.299574	+	0.954073i	$0.403156\pi$
$48$	−1.56807e6	+	1.64545e6i	−0.295392	+	0.309970i
$49$	1.08024e6			0.187385
$50$	5.56439e6	−	2.84606e6i	0.890302	−	0.455370i
$51$		−	1.54946e6i		−	0.229034i
$52$	−1.10276e7	−	734436.i	−1.50823	−	0.100448i
$53$	−4.34058e6	+	1.33589e7i	−0.550104	+	1.69305i	0.158431	+	0.987370i	$0.449356\pi$
$53$	−4.34058e6	+	1.33589e7i	−0.550104	+	1.69305i	−0.708535	+	0.705676i	$0.750644\pi$
$54$	−4.06346e6	+	5.21878e6i	−0.477882	+	0.613753i
$55$	7.66907e6	+	469472.i	0.838093	+	0.0513049i
$56$	−5.89926e6	+	6.61760e6i	−0.599854	+	0.672897i
$57$	1.05154e6			0.0996155
$58$	−6.51783e6	−	216803.i	−0.575958	−	0.0191581i
$59$	9.56164e6	−	1.31605e7i	0.789086	−	1.08608i	−0.205135	−	0.978734i	$-0.565763\pi$
$59$	9.56164e6	−	1.31605e7i	0.789086	−	1.08608i	0.994221	−	0.107350i	$-0.0342366\pi$
$60$	−2.37267e6	+	5.01640e6i	−0.183076	+	0.387068i
$61$	−1.06657e7	+	7.74908e6i	−0.770318	+	0.559669i	−0.902058	−	0.431616i	$-0.857944\pi$
$61$	−1.06657e7	+	7.74908e6i	−0.770318	+	0.559669i	0.131740	+	0.991284i	$0.457944\pi$
$62$	1.04861e6	+	1.54908e6i	0.0709652	+	0.104835i
$63$	−6.81656e6	+	9.38219e6i	−0.432716	+	0.595583i
$64$	1.91937e6	+	1.66671e7i	0.114403	+	0.993434i
$65$	−2.61234e7	+	6.75448e6i	−1.46344	+	0.378389i
$66$	−5.64930e6	+	3.82413e6i	−0.297728	+	0.201538i
$67$	3.15345e7	−	1.02462e7i	1.56490	−	0.508467i	0.606790	−	0.794862i	$-0.292457\pi$
$67$	3.15345e7	−	1.02462e7i	1.56490	−	0.508467i	0.958112	+	0.286395i	$0.0924569\pi$
$68$	−8.78550e6	−	7.32247e6i	−0.410895	−	0.342470i
$69$	3.34609e6	+	1.02982e7i	0.147619	+	0.454323i
$70$	−8.59865e6	+	1.98625e7i	−0.358128	+	0.827260i
$71$	8.44126e6	+	2.74273e6i	0.332180	+	0.107932i	0.470358	−	0.882475i	$-0.344125\pi$
$71$	8.44126e6	+	2.74273e6i	0.332180	+	0.107932i	−0.138178	+	0.990407i	$0.544125\pi$
$72$	4.66959e6	+	2.14443e7i	0.173759	+	0.797962i
$73$	1.94324e7	−	1.41185e7i	0.684282	−	0.497160i	−0.190493	−	0.981689i	$-0.561009\pi$
$73$	1.94324e7	−	1.41185e7i	0.684282	−	0.497160i	0.874776	+	0.484528i	$0.161009\pi$
$74$	488740.	−	1.34975e6i	0.0162986	−	0.0450119i
$75$	−1.65251e6	+	1.34467e7i	−0.0522274	+	0.424983i
$76$	4.96938e6	−	5.96227e6i	0.148953	−	0.178713i
$77$	−2.15262e7	+	1.56397e7i	−0.612357	+	0.444903i
$78$	1.47182e7	−	1.89028e7i	0.397627	−	0.510679i
$79$	−2.50099e7	−	8.12621e6i	−0.642102	−	0.208631i	−0.0301733	−	0.999545i	$-0.509606\pi$
$79$	−2.50099e7	−	8.12621e6i	−0.642102	−	0.208631i	−0.611928	+	0.790913i	$0.709606\pi$
$80$	1.72303e7	+	3.71596e7i	0.420662	+	0.907217i
$81$	6.43290e6	+	1.97984e7i	0.149440	+	0.459929i
$82$	8.70760e6	−	2.40478e7i	0.192594	−	0.531887i
$83$	−7.40952e6	+	2.40750e6i	−0.156127	+	0.0507287i	−0.386038	−	0.922483i	$-0.626157\pi$
$83$	−7.40952e6	+	2.40750e6i	−0.156127	+	0.0507287i	0.229911	+	0.973212i	$0.426157\pi$
$84$	−4.71074e6	−	1.86307e7i	−0.0946176	−	0.374207i
$85$	−2.59788e7	−	1.02349e7i	−0.497672	−	0.196069i
$86$	−7.34370e7	+	2.11894e7i	−1.34252	+	0.387369i
$87$	8.30908e6	−	1.14365e7i	0.145036	−	0.199625i
$88$	−5.01462e6	+	5.01038e7i	−0.0836195	+	0.835488i
$89$	5.64541e7	−	4.10163e7i	0.899778	−	0.653727i	−0.0386308	−	0.999254i	$-0.512300\pi$
$89$	5.64541e7	−	4.10163e7i	0.899778	−	0.653727i	0.938409	+	0.345526i	$0.112300\pi$
$90$	2.72684e7	+	4.61235e7i	0.415614	+	0.702994i
$91$	5.49231e7	−	7.55952e7i	0.800921	−	1.10237i
$92$	7.42040e7	+	2.96949e7i	1.03580	+	0.414506i
$93$	−4.05488e6			−0.0542058
$94$	−3.00950e6	+	9.04757e7i	−0.0385463	+	1.15883i
$95$	6.94591e6	−	1.76305e7i	0.0852775	−	0.216456i
$96$	−3.22507e7	−	1.68070e7i	−0.379712	−	0.197882i
$97$	3.31148e7	−	1.01917e8i	0.374055	−	1.15122i	−0.570060	−	0.821603i	$-0.693080\pi$
$97$	3.31148e7	−	1.01917e8i	0.374055	−	1.15122i	0.944114	−	0.329618i	$-0.106920\pi$
$98$	4.79157e6	+	1.66064e7i	0.0519486	+	0.180041i
$99$			6.58700e7i			0.685720i
$100$	6.84339e7	+	7.29164e7i	0.684339	+	0.729164i
$101$	7.57831e6			0.0728260			0.0364130	−	0.999337i	$-0.488407\pi$
$101$	7.57831e6			0.0728260			0.0364130	+	0.999337i	$0.488407\pi$
$102$	2.38197e7	−	6.87289e6i	0.220057	−	0.0634949i
$103$	1.96290e8	+	6.37786e7i	1.74401	+	0.566665i	0.995353	−	0.0962885i	$-0.0306971\pi$
$103$	1.96290e8	+	6.37786e7i	1.74401	+	0.566665i	0.748661	+	0.662953i	$0.230697\pi$
$104$	−3.76243e7	−	1.72784e8i	−0.321614	−	1.47696i
$105$	−2.52061e7	−	3.95704e7i	−0.207371	−	0.325546i
$106$	−2.24619e8	−	7.47150e6i	−1.77919	−	0.0591813i
$107$		−	9.55202e7i		−	0.728719i	−0.931258	−	0.364360i	$-0.881288\pi$
$107$		−	9.55202e7i		−	0.728719i	0.931258	−	0.364360i	$-0.118712\pi$
$108$	−9.82516e7	−	3.93183e7i	−0.722179	−	0.289001i
$109$	1.56453e8	+	1.13670e8i	1.10835	+	0.805264i	0.982403	−	0.186773i	$-0.0598028\pi$
$109$	1.56453e8	+	1.13670e8i	1.10835	+	0.805264i	0.125948	+	0.992037i	$0.459803\pi$
$110$	2.68003e7	+	1.19978e8i	0.183049	+	0.819466i
$111$	1.82901e6	+	2.51742e6i	0.0120483	+	0.0165830i
$112$	−1.27899e8	−	6.13351e7i	−0.812819	−	0.389795i
$113$	−1.15574e8	−	8.39692e7i	−0.708835	−	0.514999i	0.173963	−	0.984752i	$-0.444343\pi$
$113$	−1.15574e8	−	8.39692e7i	−0.708835	−	0.514999i	−0.882798	+	0.469754i	$0.844343\pi$
$114$	4.66428e6	+	1.61652e7i	0.0276163	+	0.0957110i
$115$	1.94765e8	+	1.19228e7i	1.11358	+	0.0681689i
$116$	−2.55780e7	−	1.01159e8i	−0.141265	−	0.558694i
$117$	−7.14820e7	−	2.19999e8i	−0.381464	−	1.17402i
$118$	2.44726e8	+	8.86145e7i	1.26227	+	0.457064i
$119$	9.19625e7	−	2.98804e7i	0.458588	−	0.149004i
$120$	−8.76407e7	−	1.42237e7i	−0.422650	−	0.0685941i
$121$	1.95388e7	−	6.01344e7i	0.0911502	−	0.280531i
$122$	−1.66435e8	−	1.29590e8i	−0.751286	−	0.584968i
$123$	3.25865e7	+	4.48515e7i	0.142370	+	0.195955i
$124$	−1.91626e7	+	2.29913e7i	−0.0810526	+	0.0972470i
$125$	2.14536e8	+	1.16528e8i	0.878741	+	0.477299i
$126$	−1.74467e8	−	6.31739e7i	−0.692200	−	0.250643i
$127$	−3.27014e7	−	4.50097e7i	−0.125705	−	0.173018i	0.741526	−	0.670924i	$-0.234102\pi$
$127$	−3.27014e7	−	4.50097e7i	−0.125705	−	0.173018i	−0.867231	+	0.497906i	$0.834102\pi$
$128$	−2.47707e8	+	1.03436e8i	−0.922780	+	0.385328i
$129$	5.11981e7	−	1.57572e8i	0.184882	−	0.569009i
$130$	−2.19710e8	−	3.71631e8i	−0.769267	−	1.30118i
$131$	2.25280e8	−	7.31978e7i	0.764957	−	0.248549i	0.0995520	−	0.995032i	$-0.468259\pi$
$131$	2.25280e8	−	7.31978e7i	0.764957	−	0.248549i	0.665405	+	0.746483i	$0.268259\pi$
$132$	−8.38462e7	−	6.98835e7i	−0.276177	−	0.230186i
$133$	2.02783e7	+	6.24102e7i	0.0648075	+	0.199457i
$134$	2.97390e8	+	4.39327e8i	0.922373	+	1.36260i
$135$	−2.57883e8	−	1.57866e7i	−0.776405	−	0.0475286i
$136$	7.35979e7	−	1.67538e8i	0.215134	−	0.489732i
$137$	−3.69839e8	−	2.68704e8i	−1.04986	−	0.762766i	−0.0776720	−	0.996979i	$-0.524749\pi$
$137$	−3.69839e8	−	2.68704e8i	−1.04986	−	0.762766i	−0.972185	+	0.234213i	$0.924749\pi$
$138$	−1.43471e8	+	9.71182e7i	−0.395591	+	0.267784i
$139$	7.39201e7	+	1.01742e8i	0.198017	+	0.272548i	0.896466	−	0.443113i	$-0.146126\pi$
$139$	7.39201e7	+	1.01742e8i	0.198017	+	0.272548i	−0.698448	+	0.715660i	$0.746126\pi$
$140$	−3.43484e8	−	4.40825e7i	−0.894118	−	0.114750i
$141$	−1.58753e8	−	1.15341e8i	−0.401647	−	0.291814i
$142$	−4.72110e6	+	1.41932e8i	−0.0116115	+	0.349082i
$143$		−	5.30735e8i		−	1.26921i
$144$	−3.08948e8	+	1.66905e8i	−0.718514	+	0.388167i
$145$	−1.36862e8	−	2.14856e8i	−0.309607	−	0.486043i
$146$	3.03237e8	+	2.36107e8i	0.667376	+	0.519634i
$147$	−3.56318e7	−	1.15775e7i	−0.0763078	−	0.0247939i
$148$	2.29174e7	+	1.52630e6i	0.0477660	+	0.00318121i
$149$	−3.81595e8			−0.774208			−0.387104	−	0.922036i	$-0.626525\pi$
$149$	−3.81595e8			−0.774208			−0.387104	+	0.922036i	$0.626525\pi$
$150$	−2.14045e8	+	3.42413e7i	−0.422804	+	0.0676372i
$151$		−	2.79520e8i		−	0.537657i	−0.963188	−	0.268829i	$-0.913363\pi$
$151$		−	2.79520e8i		−	0.537657i	0.963188	−	0.268829i	$-0.0866365\pi$
$152$	1.13700e8	+	4.99471e7i	0.213002	+	0.0935698i
$153$	7.39715e7	−	2.27661e8i	0.134989	−	0.415454i
$154$	−3.35910e8	−	2.61547e8i	−0.597227	−	0.465015i
$155$	−2.67843e7	+	6.79853e7i	−0.0464038	+	0.117784i
$156$	3.55875e8	+	1.42414e8i	0.600896	+	0.240466i
$157$	1.86478e8			0.306923			0.153462	−	0.988155i	$-0.450958\pi$
$157$	1.86478e8			0.306923			0.153462	+	0.988155i	$0.450958\pi$
$158$	1.39878e7	−	4.20519e8i	0.0224450	−	0.674772i
$159$	2.86349e8	−	3.94126e8i	0.448031	−	0.616661i
$160$	−4.94822e8	+	4.29707e8i	−0.755038	+	0.655681i
$161$	−5.46683e8	+	3.97188e8i	−0.813639	+	0.591144i
$162$	−2.75825e8	+	1.86711e8i	−0.400473	+	0.271088i
$163$	−1.84989e8	+	2.54615e8i	−0.262057	+	0.360690i	−0.919688	−	0.392650i	$-0.871558\pi$
$163$	−1.84989e8	+	2.54615e8i	−0.262057	+	0.360690i	0.657631	+	0.753340i	$0.271558\pi$
$164$	4.08307e8	+	2.71932e7i	0.564432	+	0.0375910i
$165$	−2.47934e8	−	9.76790e7i	−0.334503	−	0.131785i
$166$	−6.98763e7	−	1.03227e8i	−0.0920232	−	0.135944i
$167$	6.73238e8	−	2.18748e8i	0.865572	−	0.281241i	0.157618	−	0.987500i	$-0.449619\pi$
$167$	6.73238e8	−	2.18748e8i	0.865572	−	0.281241i	0.707954	+	0.706259i	$0.249619\pi$
$168$	2.65512e8	−	1.55057e8i	0.333309	−	0.194650i
$169$	3.23878e8	+	9.96794e8i	0.397040	+	1.22196i
$170$	4.21070e7	−	4.44767e8i	0.0504148	−	0.532521i
$171$	1.54502e8	+	5.02007e7i	0.180696	+	0.0587117i
$172$	−6.51483e8	−	1.03495e9i	−0.744371	−	1.18251i
$173$	1.33118e9	−	9.67160e8i	1.48612	−	1.07973i	0.510596	−	0.859821i	$-0.329425\pi$
$173$	1.33118e9	−	9.67160e8i	1.48612	−	1.07973i	0.975521	−	0.219907i	$-0.0705753\pi$
$174$	2.12668e8	+	7.70061e7i	0.232009	+	0.0840095i
$175$	−8.29946e8	+	1.61233e8i	−0.884908	+	0.171911i
$176$	−7.92482e8	+	1.45154e8i	−0.825922	+	0.151279i
$177$	−4.56439e8	+	3.31623e8i	−0.465040	+	0.337871i
$178$	8.80949e8	+	6.85927e8i	0.877548	+	0.683279i
$179$	7.45921e8	+	2.42364e8i	0.726576	+	0.236079i	0.648872	−	0.760898i	$-0.275241\pi$
$179$	7.45921e8	+	2.42364e8i	0.726576	+	0.236079i	0.0777038	+	0.996976i	$0.475241\pi$
$180$	−5.88096e8	+	6.23782e8i	−0.560220	+	0.594214i
$181$	2.57420e8	+	7.92259e8i	0.239844	+	0.738164i	0.996442	+	0.0842833i	$0.0268601\pi$
$181$	2.57420e8	+	7.92259e8i	0.239844	+	0.738164i	−0.756598	+	0.653880i	$0.773140\pi$
$182$	1.40574e9	+	5.09011e8i	1.28120	+	0.463919i
$183$	4.34860e8	−	1.41295e8i	0.387744	−	0.125986i
$184$	−1.27352e8	+	1.27244e9i	−0.111105	+	1.11011i
$185$	5.42893e7	−	1.40371e7i	0.0463476	−	0.0119837i
$186$	−1.79860e7	−	6.23351e7i	−0.0150274	−	0.0520812i
$187$	3.22822e8	−	4.44327e8i	0.263996	−	0.363359i
$188$	−1.40422e9	+	3.55054e8i	−1.12410	+	0.284226i
$189$	7.23849e8	−	5.25907e8i	0.567284	−	0.412156i
$190$	3.01840e8	+	2.85758e7i	0.231613	+	0.0219273i
$191$	3.32058e8	−	4.57039e8i	0.249506	−	0.343416i	−0.665832	−	0.746102i	$-0.731923\pi$
$191$	3.32058e8	−	4.57039e8i	0.249506	−	0.343416i	0.915338	+	0.402686i	$0.131923\pi$
$192$	1.15319e8	−	5.70336e8i	0.0848585	−	0.419687i
$193$	−1.17796e8			−0.0848988			−0.0424494	−	0.999099i	$-0.513516\pi$
$193$	−1.17796e8			−0.0848988			−0.0424494	+	0.999099i	$0.513516\pi$
$194$	1.71364e9	+	5.70009e7i	1.20980	+	0.0402416i
$195$	9.34075e8	+	5.71805e7i	0.646016	+	0.0395466i
$196$	−2.34034e8	+	1.47320e8i	−0.158582	+	0.0998248i
$197$	3.63521e8	−	1.11880e9i	0.241360	−	0.742828i	−0.754854	−	0.655893i	$-0.772292\pi$
$197$	3.63521e8	−	1.11880e9i	0.241360	−	0.742828i	0.996214	−	0.0869360i	$-0.0277076\pi$
$198$	−1.01261e9	+	2.92177e8i	−0.658842	+	0.190101i
$199$			1.98643e9i			1.26666i	0.773881	+	0.633331i	$0.218313\pi$
$199$			1.98643e9i			1.26666i	−0.773881	+	0.633331i	$0.781687\pi$
$200$	−8.17385e8	+	1.37546e9i	−0.510866	+	0.859661i
$201$	−1.14998e9			−0.704543
$202$	3.36148e7	+	1.16500e8i	0.0201895	+	0.0699715i
$203$	8.39003e8	+	2.72609e8i	0.494060	+	0.160530i
$204$	2.11312e8	+	3.35691e8i	0.122012	+	0.193829i
$205$	9.67243e8	−	2.50091e8i	0.547671	−	0.141606i
$206$	−1.09783e8	+	3.30044e9i	−0.0609629	+	1.83275i
$207$			1.67284e9i			0.911117i
$208$	2.48929e9	−	1.34480e9i	1.32991	−	0.718464i
$209$	3.01542e8	+	2.19083e8i	0.158038	+	0.114822i
$210$	4.96504e8	−	5.63011e8i	0.255297	−	0.289494i
$211$	1.12597e9	+	1.54976e9i	0.568062	+	0.781870i	0.992323	−	0.123670i	$-0.0394663\pi$
$211$	1.12597e9	+	1.54976e9i	0.568062	+	0.781870i	−0.424262	+	0.905540i	$0.639466\pi$
$212$	−8.81473e8	−	3.48617e9i	−0.436381	−	1.72586i
$213$	−2.49041e8	−	1.80939e8i	−0.120991	−	0.0879049i
$214$	1.46842e9	−	4.23695e8i	0.700156	−	0.202022i
$215$	−2.30371e9	−	1.89924e9i	−1.07814	−	0.888843i
$216$	1.68624e8	−	1.68481e9i	0.0774647	−	0.773992i
$217$	−7.81957e7	−	2.40662e8i	−0.0352650	−	0.108535i
$218$	−1.05346e9	+	2.90933e9i	−0.466434	+	1.28815i
$219$	−7.92295e8	+	2.57432e8i	−0.344438	+	0.111915i
$220$	−1.72553e9	+	9.44178e8i	−0.736600	+	0.403054i
$221$	−5.96011e8	+	1.83433e9i	−0.249853	+	0.768970i
$222$	−3.05871e7	+	3.92836e7i	−0.0125929	+	0.0161733i
$223$	1.80372e9	+	2.48261e9i	0.729375	+	1.00390i	0.999160	+	0.0409779i	$0.0130473\pi$
$223$	1.80372e9	+	2.48261e9i	0.729375	+	1.00390i	−0.269785	+	0.962921i	$0.586953\pi$
$224$	3.75581e8	−	2.23823e9i	0.149180	−	0.889022i
$225$	−8.84749e8	+	1.89682e9i	−0.345215	+	0.740110i
$226$	7.78201e8	−	2.14916e9i	0.298303	−	0.823824i
$227$	−1.30079e9	−	1.79038e9i	−0.489895	−	0.674282i	0.490474	−	0.871456i	$-0.336824\pi$
$227$	−1.30079e9	−	1.79038e9i	−0.489895	−	0.674282i	−0.980369	+	0.197174i	$0.936824\pi$
$228$	−2.27816e8	+	1.43407e8i	−0.0843035	+	0.0530676i
$229$	−6.40588e8	+	1.97153e9i	−0.232936	+	0.716903i	0.764452	+	0.644680i	$0.223009\pi$
$229$	−6.40588e8	+	1.97153e9i	−0.232936	+	0.716903i	−0.997388	+	0.0722233i	$0.976991\pi$
$230$	6.80624e8	+	3.04698e9i	0.243218	+	1.08883i
$231$	8.77662e8	−	2.85170e8i	0.308233	−	0.100151i
$232$	1.44165e9	−	8.41915e8i	0.497633	−	0.290614i
$233$	−2.09740e8	−	6.45513e8i	−0.0711635	−	0.219019i	0.909149	−	0.416471i	$-0.136733\pi$
$233$	−2.09740e8	−	6.45513e8i	−0.0711635	−	0.219019i	−0.980313	+	0.197452i	$0.936733\pi$
$234$	3.06495e9	−	2.07472e9i	1.02226	−	0.691985i
$235$	−2.98247e9	+	1.89982e9i	−0.977922	+	0.622932i
$236$	−2.76736e8	+	4.15521e9i	−0.0892109	+	1.33951i
$237$	7.37862e8	+	5.36088e8i	0.233874	+	0.169919i
$238$	8.67262e8	+	1.28119e9i	0.270298	+	0.399305i
$239$	−3.76381e9	−	5.18045e9i	−1.15355	−	1.58773i	−0.732628	−	0.680629i	$-0.761706\pi$
$239$	−3.76381e9	−	5.18045e9i	−1.15355	−	1.58773i	−0.420923	−	0.907097i	$-0.638294\pi$
$240$	−1.70086e8	−	1.41038e9i	−0.0512653	−	0.425100i
$241$	1.45172e9	+	1.05473e9i	0.430342	+	0.312662i	0.781786	−	0.623547i	$-0.214309\pi$
$241$	1.45172e9	+	1.05473e9i	0.430342	+	0.312662i	−0.351444	+	0.936209i	$0.614309\pi$
$242$	1.01111e9	+	3.36325e7i	0.294805	+	0.00980612i
$243$		−	3.43422e9i		−	0.984926i
$244$	1.25392e9	−	3.13340e9i	0.353762	−	0.884009i
$245$	−4.29476e8	+	5.20939e8i	−0.119200	+	0.144585i
$246$	−5.44953e8	+	6.99894e8i	−0.148806	+	0.191114i
$247$	−1.24487e9	−	4.04482e8i	−0.334453	−	0.108670i
$248$	−4.38440e8	−	1.92602e8i	−0.115905	−	0.0509160i
$249$	2.70206e8			0.0702908
$250$	−8.39762e8	+	3.81492e9i	−0.214979	+	0.976619i
$251$		−	5.85830e8i		−	0.147597i	−0.997273	−	0.0737983i	$-0.976488\pi$
$251$		−	5.85830e8i		−	0.147597i	0.997273	−	0.0737983i	$-0.0235121\pi$
$252$	1.97287e8	−	2.96228e9i	0.0489211	−	0.734554i
$253$	−1.18604e9	+	3.65027e9i	−0.289480	+	0.890928i
$254$	5.46875e8	−	7.02362e8i	0.131387	−	0.168743i
$255$	7.47220e8	+	6.16028e8i	0.176721	+	0.145693i
$256$	−2.68884e9	−	3.34916e9i	−0.626045	−	0.779787i
$257$	−4.52573e9			−1.03742			−0.518712	−	0.854949i	$-0.673588\pi$
$257$	−4.52573e9			−1.03742			−0.518712	+	0.854949i	$0.673588\pi$
$258$	2.64943e9	+	8.81280e7i	0.597961	+	0.0198900i
$259$	−1.14141e8	+	1.57101e8i	−0.0253654	+	0.0349124i
$260$	4.73847e9	−	5.02600e9i	1.03692	−	1.09984i
$261$	1.76682e9	−	1.28367e9i	0.380742	−	0.276625i
$262$	2.12452e9	+	3.13851e9i	0.450875	+	0.666068i
$263$	−5.06129e9	+	6.96627e9i	−1.05789	+	1.45605i	−0.176118	+	0.984369i	$0.556354\pi$
$263$	−5.06129e9	+	6.96627e9i	−1.05789	+	1.45605i	−0.881767	+	0.471685i	$0.843646\pi$
$264$	7.02396e8	−	1.59894e9i	0.144599	−	0.329166i
$265$	−4.71657e9	−	7.40440e9i	−0.956406	−	1.50143i
$266$	−8.69476e8	+	5.88566e8i	−0.173672	+	0.117562i
$267$	−2.30174e9	+	7.47880e8i	−0.452909	+	0.147159i
$268$	−5.43460e9	+	6.52044e9i	−1.05349	+	1.26397i
$269$	2.93342e9	+	9.02813e9i	0.560228	+	1.72420i	0.681721	+	0.731612i	$0.261232\pi$
$269$	2.93342e9	+	9.02813e9i	0.560228	+	1.72420i	−0.121493	+	0.992592i	$0.538768\pi$
$270$	−9.01197e8	−	4.03443e9i	−0.169576	−	0.759149i
$271$	−2.64408e9	−	8.59113e8i	−0.490227	−	0.159284i	0.0534644	−	0.998570i	$-0.482974\pi$
$271$	−2.64408e9	−	8.59113e8i	−0.490227	−	0.159284i	−0.543691	+	0.839285i	$0.682974\pi$
$272$	2.90200e9	+	3.88267e8i	0.530178	+	0.0709341i
$273$	−2.62184e9	+	1.90488e9i	−0.472014	+	0.342939i
$274$	2.49027e9	−	6.87736e9i	0.441818	−	1.22017i
$275$	−3.27543e9	+	3.51172e9i	−0.572714	+	0.614029i
$276$	−2.12937e9	−	1.77477e9i	−0.366957	−	0.305849i
$277$	8.74380e9	−	6.35275e9i	1.48519	−	1.07905i	0.509349	−	0.860560i	$-0.329886\pi$
$277$	8.74380e9	−	6.35275e9i	1.48519	−	1.07905i	0.975839	−	0.218492i	$-0.0701137\pi$
$278$	−1.23619e9	+	1.58766e9i	−0.206969	+	0.265814i
$279$	−5.95778e8	−	1.93580e8i	−0.0983259	−	0.0319480i
$280$	−8.45904e8	−	5.47587e9i	−0.137622	−	0.890884i
$281$	2.59994e9	+	8.00180e9i	0.417002	+	1.28340i	0.910448	+	0.413624i	$0.135737\pi$
$281$	2.59994e9	+	8.00180e9i	0.417002	+	1.28340i	−0.493445	+	0.869777i	$0.664263\pi$
$282$	1.06894e9	−	2.95210e9i	0.169028	−	0.466803i
$283$	−7.42458e9	+	2.41239e9i	−1.15751	+	0.376099i	−0.823969	−	0.566635i	$-0.808245\pi$
$283$	−7.42458e9	+	2.41239e9i	−1.15751	+	0.376099i	−0.333545	+	0.942734i	$0.608245\pi$
$284$	−2.20285e9	+	5.56986e8i	−0.338619	+	0.0856191i
$285$	−4.18066e8	+	5.07100e8i	−0.0633674	+	0.0768624i
$286$	8.15891e9	−	2.35416e9i	1.21946	−	0.351861i
$287$	−2.03358e9	+	2.79898e9i	−0.299732	+	0.412546i
$288$	−3.93619e9	−	4.00908e9i	−0.572145	−	0.582741i
$289$	4.02879e9	−	2.92708e9i	0.577541	−	0.419608i
$290$	2.69587e9	−	3.05699e9i	0.381160	−	0.432217i
$291$	−2.18459e9	+	3.00683e9i	−0.304648	+	0.419312i
$292$	−2.28459e9	+	5.70891e9i	−0.314251	+	0.785275i
$293$	−1.32130e10			−1.79279			−0.896396	−	0.443254i	$-0.853824\pi$
$293$	−1.32130e10			−1.79279			−0.896396	+	0.443254i	$0.853824\pi$
$294$	1.99285e7	−	5.99117e8i	0.00266738	−	0.0801904i
$295$	2.54509e9	+	9.84332e9i	0.336059	+	1.29973i
$296$	7.81903e7	+	3.59077e8i	0.0101856	+	0.0467757i
$297$	1.57041e9	−	4.83323e9i	0.201831	−	0.621171i
$298$	−1.69263e9	−	5.86621e9i	−0.214633	−	0.743862i
$299$		−	1.34786e10i		−	1.68640i
$300$	−1.47582e9	−	3.13860e9i	−0.182200	−	0.387481i
$301$	1.03394e10			1.25959
$302$	4.29703e9	−	1.23986e9i	0.516583	−	0.149054i
$303$	−2.49971e8	−	8.12206e7i	−0.0296565	−	0.00963597i
$304$	−2.63497e8	+	1.96944e9i	−0.0308519	+	0.230594i
$305$	5.03461e8	−	8.22431e9i	0.0581790	−	0.950386i
$306$	3.82791e9	+	1.27328e8i	0.436593	+	0.0145224i
$307$		−	8.02141e9i		−	0.903020i	−0.892266	−	0.451510i	$-0.850886\pi$
$307$		−	8.02141e9i		−	0.903020i	0.892266	−	0.451510i	$-0.149114\pi$
$308$	2.53074e9	−	6.32403e9i	0.281219	−	0.702734i
$309$	−5.79111e9	−	4.20749e9i	−0.635226	−	0.461518i
$310$	−1.16393e9	−	1.10192e8i	−0.126032	−	0.0119317i
$311$	2.96150e9	+	4.07616e9i	0.316571	+	0.435722i	0.937416	−	0.348211i	$-0.113211\pi$
$311$	2.96150e9	+	4.07616e9i	0.316571	+	0.435722i	−0.620846	+	0.783933i	$0.713211\pi$
$312$	−6.10769e8	+	6.10252e9i	−0.0644552	+	0.644008i
$313$	3.79488e9	+	2.75714e9i	0.395386	+	0.287265i	0.767659	−	0.640859i	$-0.221422\pi$
$313$	3.79488e9	+	2.75714e9i	0.395386	+	0.287265i	−0.372273	+	0.928123i	$0.621422\pi$
$314$	8.27154e8	+	2.86671e9i	0.0850879	+	0.294893i
$315$	−1.81442e9	−	7.01737e9i	−0.184287	−	0.712742i
$316$	6.52663e9	−	1.65025e9i	0.654546	−	0.165501i
$317$	−1.80441e9	−	5.55339e9i	−0.178689	−	0.549947i	0.821094	−	0.570793i	$-0.193364\pi$
$317$	−1.80441e9	−	5.55339e9i	−0.178689	−	0.549947i	−0.999783	+	0.0208456i	$0.993364\pi$
$318$	7.32899e9	+	2.65380e9i	0.716697	+	0.259513i
$319$	4.76545e9	−	1.54839e9i	0.460195	−	0.149526i
$320$	−8.80069e9	−	5.70080e9i	−0.839299	−	0.543670i
$321$	−1.02374e9	+	3.15075e9i	−0.0964205	+	0.296752i
$322$	−8.53082e9	−	6.64229e9i	−0.793537	−	0.617866i
$323$	−7.96166e8	−	1.09583e9i	−0.0731465	−	0.100677i
$324$	−4.09375e9	−	3.41203e9i	−0.371485	−	0.309622i
$325$	7.12869e9	−	1.52833e10i	0.638964	−	1.36988i
$326$	−4.73471e9	−	1.71442e9i	−0.419202	−	0.151791i
$327$	−3.94236e9	−	5.42619e9i	−0.344798	−	0.474574i
$328$	1.39307e9	+	6.39747e9i	0.120359	+	0.552730i
$329$	3.78415e9	−	1.16464e10i	0.322987	−	0.994052i
$330$	4.01856e8	−	4.24472e9i	0.0338856	−	0.357926i
$331$	1.45069e10	−	4.71359e9i	1.20855	−	0.392681i	0.365649	−	0.930753i	$-0.380847\pi$
$331$	1.45069e10	−	4.71359e9i	1.20855	−	0.392681i	0.842899	+	0.538072i	$0.180847\pi$
$332$	1.27694e9	−	1.53208e9i	0.105104	−	0.126104i
$333$	1.48553e8	+	4.57199e8i	0.0120810	+	0.0371816i
$334$	6.34904e9	+	9.37931e9i	0.510179	+	0.753676i
$335$	−7.59616e9	+	1.92810e10i	−0.603136	+	1.53091i
$336$	3.56139e9	+	3.39390e9i	0.279423	+	0.266282i
$337$	1.71013e10	+	1.24248e10i	1.32590	+	0.963319i	0.999839	+	0.0179690i	$0.00572002\pi$
$337$	1.71013e10	+	1.24248e10i	1.32590	+	0.963319i	0.326057	+	0.945350i	$0.394280\pi$
$338$	−1.38870e10	+	9.40037e9i	−1.06400	+	0.720241i
$339$	2.91227e9	+	4.00839e9i	0.220512	+	0.303509i
$340$	7.02411e9	−	1.32553e9i	0.525625	−	0.0991913i
$341$	−1.16278e9	−	8.44812e8i	−0.0859966	−	0.0624802i
$342$	−8.64110e7	+	2.59781e9i	−0.00631633	+	0.189890i
$343$		−	1.48153e10i		−	1.07037i
$344$	1.30204e10	−	1.46058e10i	0.929800	−	1.04302i
$345$	−6.29657e9	−	2.48067e9i	−0.444455	−	0.175103i
$346$	2.07727e10	+	1.61741e10i	1.44940	+	1.12854i
$347$	−1.24284e10	−	4.03823e9i	−0.857230	−	0.278531i	−0.152759	−	0.988264i	$-0.548816\pi$
$347$	−1.24284e10	−	4.03823e9i	−0.857230	−	0.278531i	−0.704471	+	0.709733i	$0.748816\pi$
$348$	−2.40484e8	+	3.61088e9i	−0.0163972	+	0.246205i
$349$	1.26473e10			0.852503			0.426252	−	0.904605i	$-0.359834\pi$
$349$	1.26473e10			0.852503			0.426252	+	0.904605i	$0.359834\pi$
$350$	−6.15998e9	−	1.20435e10i	−0.410494	−	0.802564i
$351$			1.78467e10i			1.17579i
$352$	−5.74662e9	−	1.15389e10i	−0.374319	−	0.751610i
$353$	−3.08579e9	+	9.49708e9i	−0.198732	+	0.611633i	0.801181	+	0.598422i	$0.204205\pi$
$353$	−3.08579e9	+	9.49708e9i	−0.198732	+	0.611633i	−0.999913	+	0.0132113i	$0.995795\pi$
$354$	−7.12260e9	−	5.54582e9i	−0.453550	−	0.353144i
$355$	−4.67870e9	+	2.98031e9i	−0.294586	+	0.187650i
$356$	−6.63707e9	+	1.65852e10i	−0.413215	+	1.03258i
$357$	−3.35364e9			−0.206463
$358$	−4.17185e8	+	1.25420e10i	−0.0253978	+	0.763545i
$359$	−5.06603e9	+	6.97280e9i	−0.304993	+	0.419787i	−0.933812	−	0.357765i	$-0.883539\pi$
$359$	−5.06603e9	+	6.97280e9i	−0.304993	+	0.419787i	0.628818	+	0.777552i	$0.283539\pi$
$360$	−1.21979e10	−	6.27384e9i	−0.726232	−	0.373528i
$361$	−1.29963e10	+	9.44237e9i	−0.765229	+	0.555971i
$362$	−1.10375e10	+	7.47148e9i	−0.642739	+	0.435083i
$363$	−1.28898e9	+	1.77413e9i	−0.0742370	+	0.102178i
$364$	−1.58960e9	+	2.38680e10i	−0.0905489	+	1.35960i
$365$	−9.17283e8	+	1.49843e10i	−0.0516811	+	0.844239i
$366$	4.10099e9	+	6.05831e9i	0.228541	+	0.337619i
$367$	1.86104e9	−	6.04690e8i	0.102587	−	0.0333326i	−0.257274	−	0.966339i	$-0.582824\pi$
$367$	1.86104e9	−	6.04690e8i	0.102587	−	0.0333326i	0.359861	+	0.933006i	$0.382824\pi$
$368$	−2.01260e10	+	3.68636e9i	−1.09740	+	0.201005i
$369$	2.64669e9	+	8.14566e9i	0.142757	+	0.439360i
$370$	4.56599e8	+	7.72319e8i	0.0243629	+	0.0412088i
$371$	2.89139e10	+	9.39469e9i	1.52620	+	0.495892i
$372$	8.78489e8	−	5.52994e8i	0.0458738	−	0.0288768i
$373$	−2.03469e10	+	1.47829e10i	−1.05114	+	0.763701i	−0.972430	−	0.233197i	$-0.925081\pi$
$373$	−2.03469e10	+	1.47829e10i	−1.05114	+	0.763701i	−0.0787141	+	0.996897i	$0.525081\pi$
$374$	8.26251e9	+	2.99182e9i	0.422304	+	0.152915i
$375$	−5.82761e9	−	6.14299e9i	−0.294690	−	0.310638i
$376$	−1.16868e10	−	2.00120e10i	−0.584717	−	1.00124i
$377$	−1.42358e10	+	1.03429e10i	−0.704721	+	0.512010i
$378$	1.12954e10	+	8.79488e9i	0.553269	+	0.430787i
$379$	−1.29258e10	−	4.19983e9i	−0.626469	−	0.203552i	−0.0214584	−	0.999770i	$-0.506831\pi$
$379$	−1.29258e10	−	4.19983e9i	−0.626469	−	0.203552i	−0.605010	+	0.796218i	$0.706831\pi$
$380$	8.99568e8	+	4.76690e9i	0.0431419	+	0.228613i
$381$	5.96269e8	+	1.83513e9i	0.0282971	+	0.0870896i
$382$	8.49890e9	+	3.07742e9i	0.399125	+	0.144522i
$383$	3.88193e10	−	1.26132e10i	1.80407	−	0.586177i	0.804101	−	0.594493i	$-0.202647\pi$
$383$	3.88193e10	−	1.26132e10i	1.80407	−	0.586177i	0.999965	+	0.00831576i	$0.00264702\pi$
$384$	9.27921e9	−	7.57034e8i	0.426762	−	0.0348169i
$385$	1.01612e9	−	1.65988e10i	0.0462488	−	0.755500i
$386$	−5.22503e8	−	1.81086e9i	−0.0235364	−	0.0815711i
$387$	1.50450e10	−	2.07076e10i	0.670729	−	0.923180i
$388$	6.72485e9	+	2.65964e10i	0.296726	+	1.17353i
$389$	−1.93848e10	+	1.40839e10i	−0.846570	+	0.615069i	−0.924198	−	0.381914i	$-0.875265\pi$
$389$	−1.93848e10	+	1.40839e10i	−0.846570	+	0.615069i	0.0776285	+	0.996982i	$0.475265\pi$
$390$	3.26421e9	+	1.46130e10i	0.141098	+	0.631658i
$391$	8.19845e9	−	1.12842e10i	0.350772	−	0.482796i
$392$	−3.30283e9	−	2.94431e9i	−0.139876	−	0.124692i
$393$	−8.21537e9			−0.344395
$394$	1.88117e10	+	6.25733e8i	0.780624	+	0.0259660i
$395$	1.38621e10	−	8.83011e9i	0.569431	−	0.362725i
$396$	−8.98318e9	−	1.42707e10i	−0.365300	−	0.580317i
$397$	6.44160e9	−	1.98252e10i	0.259317	−	0.798097i	−0.733631	−	0.679548i	$-0.762176\pi$
$397$	6.44160e9	−	1.98252e10i	0.259317	−	0.798097i	0.992948	−	0.118549i	$-0.0378241\pi$
$398$	−3.05371e10	+	8.81112e9i	−1.21701	+	0.351155i
$399$		−	2.27594e9i		−	0.0897985i
$400$	−2.47704e10	−	6.46449e9i	−0.967592	−	0.252519i
$401$	2.48015e9			0.0959180			0.0479590	−	0.998849i	$-0.484728\pi$
$401$	2.48015e9			0.0959180			0.0479590	+	0.998849i	$0.484728\pi$
$402$	−5.10093e9	−	1.76785e10i	−0.195319	−	0.676927i
$403$	4.80037e9	+	1.55973e9i	0.181993	+	0.0591331i
$404$	−1.64184e9	+	1.03351e9i	−0.0616318	+	0.0387962i
$405$	−1.21052e10	−	4.76913e9i	−0.449939	−	0.177263i
$406$	−4.69245e8	+	1.41071e10i	−0.0172701	+	0.519198i
$407$			1.10297e9i			0.0401961i
$408$	−4.22323e9	+	4.73748e9i	−0.152407	+	0.170965i
$409$	2.59669e10	+	1.88660e10i	0.927954	+	0.674198i	0.945491	−	0.325648i	$-0.105582\pi$
$409$	2.59669e10	+	1.88660e10i	0.927954	+	0.674198i	−0.0175367	+	0.999846i	$0.505582\pi$
$410$	8.13497e9	+	1.37600e10i	0.287886	+	0.486947i
$411$	9.31934e9	+	1.28270e10i	0.326601	+	0.449528i
$412$	−5.12243e10	+	1.29520e10i	−1.77782	+	0.449518i
$413$	−2.84843e10	−	2.06951e10i	−0.979052	−	0.711323i
$414$	−2.57164e10	+	7.42017e9i	−0.875405	+	0.252588i
$415$	1.78484e9	−	4.53036e9i	0.0601736	−	0.152736i
$416$	3.17151e10	+	3.23024e10i	1.05899	+	1.07860i
$417$	−1.34784e9	−	4.14822e9i	−0.0445752	−	0.137188i
$418$	−2.03040e9	+	5.60734e9i	−0.0665083	+	0.183676i
$419$	2.84517e10	−	9.24452e9i	0.923107	−	0.299936i	0.191367	−	0.981519i	$-0.438708\pi$
$419$	2.84517e10	−	9.24452e9i	0.923107	−	0.299936i	0.731741	+	0.681583i	$0.238708\pi$
$420$	1.08574e10	+	5.13536e9i	0.348923	+	0.165034i
$421$	1.42740e10	−	4.39310e10i	0.454379	−	1.39844i	−0.417483	−	0.908685i	$-0.637088\pi$
$421$	1.42740e10	−	4.39310e10i	0.454379	−	1.39844i	0.871863	−	0.489751i	$-0.162912\pi$
$422$	−1.88298e10	+	2.41835e10i	−0.593741	+	0.762553i
$423$	−1.78190e10	−	2.45257e10i	−0.556572	−	0.766056i
$424$	4.96825e10	−	2.90142e10i	1.53724	−	0.897734i
$425$	1.52642e10	−	8.45897e9i	0.467864	−	0.259276i
$426$	1.67689e9	−	4.63105e9i	0.0509173	−	0.140618i
$427$	1.67720e10	+	2.30847e10i	0.504514	+	0.694404i
$428$	1.30268e10	+	2.06944e10i	0.388207	+	0.616707i
$429$	−5.68815e9	+	1.75063e10i	−0.167935	+	0.516852i
$430$	1.89782e10	−	4.38389e10i	0.555114	−	1.28229i
$431$	5.80837e10	−	1.88725e10i	1.68324	−	0.546917i	0.697702	−	0.716388i	$-0.254206\pi$
$431$	5.80837e10	−	1.88725e10i	1.68324	−	0.546917i	0.985535	+	0.169471i	$0.0542058\pi$
$432$	2.66483e10	−	4.88102e9i	0.765130	−	0.140144i
$433$	−3.50926e8	−	1.08004e9i	−0.00998308	−	0.0307248i	0.945941	−	0.324339i	$-0.105142\pi$
$433$	−3.50926e8	−	1.08004e9i	−0.00998308	−	0.0307248i	−0.955924	+	0.293614i	$0.905142\pi$
$434$	3.35281e9	−	2.26958e9i	0.0945039	−	0.0639716i
$435$	2.21169e9	+	8.55386e9i	0.0617686	+	0.238894i
$436$	−4.93975e10	−	3.28986e9i	−1.36697	−	0.0910399i
$437$	7.65801e9	+	5.56387e9i	0.209986	+	0.152564i
$438$	−7.47182e9	−	1.10380e10i	−0.203016	−	0.299911i
$439$	−7.70843e9	−	1.06097e10i	−0.207543	−	0.285658i	0.692538	−	0.721382i	$-0.256493\pi$
$439$	−7.70843e9	−	1.06097e10i	−0.207543	−	0.285658i	−0.900081	+	0.435723i	$0.856493\pi$
$440$	−2.21686e10	−	2.23383e10i	−0.591463	−	0.595990i
$441$	−4.68263e9	−	3.40213e9i	−0.123804	−	0.0899491i
$442$	−3.08427e10	−	1.02592e9i	−0.808096	−	0.0268797i
$443$			1.92370e10i			0.499485i	0.968312	+	0.249743i	$0.0803460\pi$
$443$			1.92370e10i			0.499485i	−0.968312	+	0.249743i	$0.919654\pi$
$444$	−7.39576e8	−	2.95963e8i	−0.0190305	−	0.00761562i
$445$	−2.66485e9	+	4.35317e10i	−0.0679567	+	1.11011i
$446$	−3.01642e10	+	3.87404e10i	−0.762346	+	0.979096i
$447$	1.25870e10	+	4.08975e9i	0.315276	+	0.102439i
$448$	3.60739e10	−	4.15426e9i	0.895533	−	0.103129i
$449$	−1.13811e9			−0.0280026			−0.0140013	−	0.999902i	$-0.504457\pi$
$449$	−1.13811e9			−0.0280026			−0.0140013	+	0.999902i	$0.504457\pi$
$450$	−3.30840e10	−	5.18747e9i	−0.806804	−	0.126504i
$451$			1.96509e10i			0.474982i
$452$	3.64905e10	+	2.43026e9i	0.874231	+	0.0582236i
$453$	−2.99576e9	+	9.22001e9i	−0.0711401	+	0.218947i
$454$	2.17534e10	−	2.79383e10i	0.512040	−	0.657623i
$455$	1.46193e10	+	5.65411e10i	0.341100	+	1.31922i
$456$	−3.21509e9	−	2.86609e9i	−0.0743589	−	0.0662872i
$457$	−1.07732e10			−0.246990			−0.123495	−	0.992345i	$-0.539410\pi$
$457$	−1.07732e10			−0.246990			−0.123495	+	0.992345i	$0.539410\pi$
$458$	−3.31494e10	−	1.10265e9i	−0.753380	−	0.0250597i
$459$	−1.08554e10	+	1.49411e10i	−0.244565	+	0.336614i
$460$	−4.38218e10	+	2.39785e10i	−0.978722	+	0.535539i
$461$	−1.38782e10	+	1.00831e10i	−0.307276	+	0.223249i	−0.730727	−	0.682670i	$-0.760819\pi$
$461$	−1.38782e10	+	1.00831e10i	−0.307276	+	0.223249i	0.423451	+	0.905919i	$0.360819\pi$
$462$	8.27689e9	+	1.22273e10i	0.181677	+	0.268387i
$463$	−2.91554e10	+	4.01290e10i	−0.634447	+	0.873242i	−0.998304	−	0.0582130i	$-0.981460\pi$
$463$	−2.91554e10	+	4.01290e10i	−0.634447	+	0.873242i	0.363857	+	0.931455i	$0.381460\pi$
$464$	1.93373e10	+	1.84279e10i	0.417181	+	0.397561i
$465$	1.61212e9	−	1.95544e9i	0.0344814	−	0.0418247i
$466$	8.99305e9	−	6.08758e9i	0.190706	−	0.129092i
$467$	7.44356e10	−	2.41856e10i	1.56500	−	0.508498i	0.606859	−	0.794810i	$-0.292429\pi$
$467$	7.44356e10	−	2.41856e10i	1.56500	−	0.508498i	0.958136	+	0.286312i	$0.0924294\pi$
$468$	4.54895e10	+	3.79142e10i	0.948261	+	0.790349i
$469$	−2.21767e10	−	6.82528e10i	−0.458359	−	1.41068i
$470$	−4.24349e10	−	3.74221e10i	−0.869624	−	0.766897i
$471$	−6.15101e9	−	1.99858e9i	−0.124986	−	0.0406106i
$472$	−6.51049e10	+	1.41769e10i	−1.31173	+	0.285635i
$473$	4.75109e10	−	3.45187e10i	0.949180	−	0.689619i
$474$	−4.96831e9	+	1.37210e10i	−0.0984226	+	0.271813i
$475$	5.74067e9	+	1.03590e10i	0.112769	+	0.203491i
$476$	−1.58486e10	+	1.90152e10i	−0.308720	+	0.370402i
$477$	6.08886e10	−	4.42381e10i	1.17615	−	0.854522i
$478$	6.29433e10	−	8.08393e10i	1.20570	−	1.54850i
$479$	−8.64664e10	−	2.80946e10i	−1.64250	−	0.533680i	−0.665404	−	0.746483i	$-0.731741\pi$
$479$	−8.64664e10	−	2.80946e10i	−1.64250	−	0.533680i	−0.977095	+	0.212803i	$0.931741\pi$
$480$	2.09271e10	−	8.87067e9i	0.394226	−	0.167106i
$481$	−1.19694e9	−	3.68380e9i	−0.0223610	−	0.0688201i
$482$	−9.77497e9	+	2.69955e10i	−0.181104	+	0.500153i
$483$	2.22893e10	−	7.24222e9i	0.409550	−	0.133071i
$484$	3.96789e9	+	1.56928e10i	0.0723066	+	0.285968i
$485$	3.59832e10	+	5.64890e10i	0.650328	+	1.02093i
$486$	5.27939e10	−	1.52330e10i	0.946321	−	0.273050i
$487$	5.41674e10	−	7.45550e10i	0.962990	−	1.32544i	0.0174812	−	0.999847i	$-0.494435\pi$
$487$	5.41674e10	−	7.45550e10i	0.962990	−	1.32544i	0.945509	−	0.325595i	$-0.105565\pi$
$488$	5.37313e10	+	5.37768e9i	0.947432	+	0.0948233i
$489$	8.83072e9	−	6.41590e9i	0.154440	−	0.112207i
$490$	−9.91334e9	−	4.29157e9i	−0.171963	−	0.0744443i
$491$	−3.33606e10	+	4.59169e10i	−0.573994	+	0.790035i	−0.993021	−	0.117939i	$-0.962371\pi$
$491$	−3.33606e10	+	4.59169e10i	−0.573994	+	0.790035i	0.419027	+	0.907974i	$0.362371\pi$
$492$	−1.31766e10	−	5.27300e9i	−0.224876	−	0.0899907i
$493$	−1.82093e10			−0.308251
$494$	6.96240e8	−	2.09313e10i	0.0116910	−	0.351471i
$495$	−3.17654e10	−	2.61882e10i	−0.529095	−	0.436200i
$496$	1.01608e9	−	7.59440e9i	0.0167881	−	0.125478i
$497$	5.93633e9	−	1.82701e10i	0.0972954	−	0.299445i
$498$	1.19854e9	+	4.15385e9i	0.0194866	+	0.0675356i
$499$		−	7.68992e10i		−	1.24028i	−0.784491	−	0.620140i	$-0.787076\pi$
$499$		−	7.68992e10i		−	1.24028i	0.784491	−	0.620140i	$-0.212924\pi$
$500$	−6.23711e10	+	4.01211e9i	−0.997937	+	0.0641938i
$501$	−2.45513e10			−0.389694
$502$	9.00588e9	−	2.59854e9i	0.141811	−	0.0409180i
$503$	−1.09671e10	−	3.56342e9i	−0.171324	−	0.0556666i	0.222099	−	0.975024i	$-0.428709\pi$
$503$	−1.09671e10	−	3.56342e9i	−0.171324	−	0.0556666i	−0.393423	+	0.919358i	$0.628709\pi$
$504$	4.64138e10	−	1.01068e10i	0.719324	−	0.156636i
$505$	−3.01294e9	+	3.65459e9i	−0.0463261	+	0.0561919i
$506$	−6.13760e10	−	2.04155e9i	−0.936260	−	0.0311429i
$507$		−	3.63505e10i		−	0.550147i
$508$	1.32231e10	+	5.29160e9i	0.198553	+	0.0794570i
$509$	3.70266e10	+	2.69014e10i	0.551623	+	0.400778i	0.828384	−	0.560161i	$-0.189261\pi$
$509$	3.70266e10	+	2.69014e10i	0.551623	+	0.400778i	−0.276760	+	0.960939i	$0.589261\pi$
$510$	−6.15570e9	+	1.42194e10i	−0.0909906	+	0.210184i
$511$	−3.05578e10	−	4.20592e10i	−0.448166	−	0.616847i
$512$	3.95594e10	−	5.61910e10i	0.575664	−	0.817686i
$513$	−1.01398e10	−	7.36697e9i	−0.146406	−	0.106370i
$514$	−2.00746e10	−	6.95735e10i	−0.287604	−	0.996761i
$515$	−1.08797e11	+	6.93031e10i	−1.54663	+	0.985199i
$516$	1.03972e10	+	4.11202e10i	0.146662	+	0.580037i
$517$	−2.14936e10	−	6.61505e10i	−0.300848	−	0.925915i
$518$	−2.92138e9	−	1.05782e9i	−0.0405760	−	0.0146924i
$519$	−5.42747e10	+	1.76349e10i	−0.748046	+	0.243055i
$520$	9.82823e10	+	5.05503e10i	1.34419	+	0.691369i
$521$	1.15208e10	−	3.54573e10i	0.156362	−	0.481232i	−0.841935	−	0.539580i	$-0.818583\pi$
$521$	1.15208e10	−	3.54573e10i	0.156362	−	0.481232i	0.998296	+	0.0583477i	$0.0185832\pi$
$522$	2.75707e10	+	2.14672e10i	0.371335	+	0.289130i
$523$	−6.77609e10	−	9.32648e10i	−0.905675	−	1.24655i	−0.968622	−	0.248537i	$-0.920050\pi$
$523$	−6.77609e10	−	9.32648e10i	−0.905675	−	1.24655i	0.0629477	−	0.998017i	$-0.479950\pi$
$524$	−3.88243e10	+	4.65814e10i	−0.514966	+	0.617856i
$525$	2.91039e10	+	3.57666e9i	0.383102	+	0.0470805i
$526$	−1.29542e11	−	4.69066e10i	−1.69226	−	0.612760i
$527$	3.07012e9	+	4.22565e9i	0.0398027	+	0.0547837i
$528$	2.76958e10	+	3.70551e9i	0.356351	+	0.0476773i
$529$	−5.92156e9	+	1.82247e10i	−0.0756159	+	0.232722i
$530$	9.29057e10	−	1.05351e11i	1.17744	−	1.33516i
$531$	−8.28958e10	+	2.69345e10i	−1.04269	+	0.338790i
$532$	−1.29046e10	−	1.07557e10i	−0.161101	−	0.134274i
$533$	−2.13252e10	−	6.56321e10i	−0.264231	−	0.813219i
$534$	−2.17068e10	−	3.20670e10i	−0.266950	−	0.394360i
$535$	4.60641e10	+	3.79764e10i	0.562273	+	0.463552i
$536$	−1.24344e11	−	5.46230e10i	−1.50649	−	0.661784i
$537$	−2.20067e10	−	1.59888e10i	−0.264642	−	0.192274i
$538$	−1.25777e11	+	8.51407e10i	−1.50131	+	1.01627i
$539$	−7.80574e9	−	1.07437e10i	−0.0924824	−	0.127291i
$540$	5.80234e10	−	3.17493e10i	0.682382	−	0.373387i
$541$	1.41853e10	+	1.03062e10i	0.165596	+	0.120312i	0.667497	−	0.744613i	$-0.267366\pi$
$541$	1.41853e10	+	1.03062e10i	0.165596	+	0.120312i	−0.501901	+	0.864925i	$0.667366\pi$
$542$	1.47880e9	−	4.44578e10i	0.0171361	−	0.515170i
$543$		−	2.88916e10i		−	0.332333i
$544$	6.90349e9	+	4.63342e10i	0.0788267	+	0.529062i
$545$	−1.17018e11	+	3.02563e10i	−1.32638	+	0.342949i
$546$	−4.09130e10	−	3.18558e10i	−0.460353	−	0.358441i
$547$	1.67032e9	+	5.42719e8i	0.0186573	+	0.00606214i	0.318331	−	0.947980i	$-0.396878\pi$
$547$	1.67032e9	+	5.42719e8i	0.0186573	+	0.00606214i	−0.299673	+	0.954042i	$0.596878\pi$
$548$	1.16771e11	+	7.77691e9i	1.29483	+	0.0862352i
$549$	7.06389e10			0.777597
$550$	−6.85138e10	−	3.47760e10i	−0.748734	−	0.380039i
$551$		−	1.23577e10i		−	0.134070i
$552$	1.78382e10	−	4.06068e10i	0.192129	−	0.437364i
$553$	−1.75882e10	+	5.41311e10i	−0.188071	+	0.578823i
$554$	1.36444e11	+	1.06239e11i	1.44849	+	1.12783i
$555$	−1.94118e9	−	1.18832e8i	−0.0204595	−	0.00125245i
$556$	−2.98901e10	−	1.19614e10i	−0.312773	−	0.125165i
$557$	−7.98064e10			−0.829119			−0.414560	−	0.910022i	$-0.636064\pi$
$557$	−7.98064e10			−0.829119			−0.414560	+	0.910022i	$0.636064\pi$
$558$	3.33212e8	−	1.00175e10i	0.00343703	−	0.103329i
$559$	−1.21222e11	+	1.66848e11i	−1.24146	+	1.70873i
$560$	8.04277e10	−	3.72931e10i	0.817812	−	0.379207i
$561$	−1.54104e10	+	1.11963e10i	−0.155583	+	0.113038i
$562$	−1.11478e11	+	7.54618e10i	−1.11749	+	0.756453i
$563$	4.50478e10	−	6.20030e10i	0.448374	−	0.617134i	−0.523673	−	0.851919i	$-0.675439\pi$
$563$	4.50478e10	−	6.20030e10i	0.448374	−	0.617134i	0.972047	+	0.234785i	$0.0754387\pi$
$564$	5.01236e10	+	3.33822e9i	0.495366	+	0.0329913i
$565$	8.64428e10	−	2.23507e10i	0.848272	−	0.219330i
$566$	−7.00183e10	−	1.03436e11i	−0.682253	−	1.00788i
$567$	4.28514e10	−	1.39233e10i	0.414604	−	0.134713i
$568$	−1.83335e10	−	3.13935e10i	−0.176138	−	0.301610i
$569$	3.93667e10	+	1.21158e11i	0.375560	+	1.15586i	0.943100	+	0.332510i	$0.107895\pi$
$569$	3.93667e10	+	1.21158e11i	0.375560	+	1.15586i	−0.567539	+	0.823346i	$0.692105\pi$
$570$	−9.64997e9	−	4.17755e9i	−0.0914169	−	0.0395752i
$571$	1.31196e11	+	4.26283e10i	1.23418	+	0.401009i	0.852226	−	0.523174i	$-0.175252\pi$
$571$	1.31196e11	+	4.26283e10i	1.23418	+	0.401009i	0.381952	+	0.924182i	$0.375252\pi$
$572$	7.23803e10	+	1.14984e11i	0.676139	+	1.07412i
$573$	−1.58513e10	+	1.15166e10i	−0.147044	+	0.106834i
$574$	−5.20486e10	−	1.88466e10i	−0.479470	−	0.173614i
$575$	−8.31834e10	+	8.91841e10i	−0.760966	+	0.815861i
$576$	4.41715e10	−	7.82934e10i	0.401285	−	0.711271i
$577$	−1.59644e11	+	1.15988e11i	−1.44029	+	1.04643i	−0.452303	+	0.891864i	$0.649397\pi$
$577$	−1.59644e11	+	1.15988e11i	−1.44029	+	1.04643i	−0.987983	+	0.154564i	$0.950603\pi$
$578$	6.28680e10	+	4.89504e10i	0.563272	+	0.438576i
$579$	3.88551e9	+	1.26248e9i	0.0345728	+	0.0112334i
$580$	5.89526e10	+	2.78835e10i	0.520944	+	0.246397i
$581$	5.21076e9	+	1.60371e10i	0.0457295	+	0.140741i
$582$	−5.59137e10	−	2.02461e10i	−0.487333	−	0.176462i
$583$	1.64228e11	−	5.33609e10i	1.42159	−	0.461901i
$584$	−9.78960e10	−	9.79788e9i	−0.841615	−	0.0842327i
$585$	1.34513e11	+	5.29942e10i	1.14852	+	0.452486i
$586$	−5.86082e10	−	2.03121e11i	−0.497013	−	1.72252i
$587$	−5.48269e10	+	7.54627e10i	−0.461786	+	0.635594i	−0.974878	−	0.222740i	$-0.928500\pi$
$587$	−5.48269e10	+	7.54627e10i	−0.461786	+	0.635594i	0.513092	+	0.858334i	$0.328500\pi$
$588$	9.29854e9	−	2.35112e9i	0.0777867	−	0.0196682i
$589$	−2.86773e9	+	2.08353e9i	−0.0238274	+	0.0173116i
$590$	−1.40031e11	+	8.27870e10i	−1.15562	+	0.683209i
$591$	−2.39816e10	+	3.30078e10i	−0.196575	+	0.270562i
$592$	−5.17321e9	+	2.79475e9i	−0.0421185	+	0.0227539i
$593$	5.25507e10			0.424972			0.212486	−	0.977164i	$-0.431844\pi$
$593$	5.25507e10			0.424972			0.212486	+	0.977164i	$0.431844\pi$
$594$	8.12663e10	+	2.70317e9i	0.652777	+	0.0217134i
$595$	−2.21523e10	+	5.62281e10i	−0.176746	+	0.448627i
$596$	8.26725e10	−	5.20410e10i	0.655203	−	0.412440i
$597$	2.12896e10	−	6.55226e10i	0.167598	−	0.515814i
$598$	2.07205e11	−	5.97866e10i	1.62030	−	0.467519i
$599$			1.09949e11i			0.854054i	0.904239	+	0.427027i	$0.140439\pi$
$599$			1.09949e11i			0.854054i	−0.904239	+	0.427027i	$0.859561\pi$
$600$	4.17030e10	−	3.66093e10i	0.321782	−	0.282479i
$601$	−2.02215e10			−0.154994			−0.0774970	−	0.996993i	$-0.524693\pi$
$601$	−2.02215e10			−0.154994			−0.0774970	+	0.996993i	$0.524693\pi$
$602$	4.58620e10	+	1.58946e11i	0.349194	+	1.21022i
$603$	−1.68966e11	−	5.49003e10i	−1.27800	−	0.415246i
$604$	3.81203e10	+	6.05580e10i	0.286423	+	0.455013i
$605$	2.12313e10	+	3.33304e10i	0.158473	+	0.248782i
$606$	1.39806e8	−	4.20304e9i	0.00103666	−	0.0311654i
$607$		−	6.20157e10i		−	0.456822i	−0.973565	−	0.228411i	$-0.926647\pi$
$607$		−	6.20157e10i		−	0.456822i	0.973565	−	0.228411i	$-0.0733530\pi$
$608$	−3.14447e10	+	4.68504e9i	−0.230108	+	0.0342846i
$609$	−2.47529e10	−	1.79841e10i	−0.179952	−	0.130743i
$610$	1.28664e11	−	2.87406e10i	0.929264	−	0.207576i
$611$	1.43573e11	+	1.97611e11i	1.03017	+	1.41790i
$612$	1.50219e10	+	5.94108e10i	0.107083	+	0.423506i
$613$	1.34284e11	+	9.75627e10i	0.951001	+	0.690943i	0.951043	−	0.309057i	$-0.100013\pi$
$613$	1.34284e11	+	9.75627e10i	0.951001	+	0.690943i	−4.23153e−5		1.00000i	$0.500013\pi$
$614$	1.23312e11	−	3.55802e10i	0.867625	−	0.250343i
$615$	−3.45850e10	−	2.11716e9i	−0.241761	−	0.0147997i
$616$	1.08444e11	+	1.08536e10i	0.753152	+	0.0753789i
$617$	2.78328e10	+	8.56605e10i	0.192051	+	0.591072i	0.999998	+	0.00181721i	$0.000578438\pi$
$617$	2.78328e10	+	8.56605e10i	0.192051	+	0.591072i	−0.807948	+	0.589254i	$0.799422\pi$
$618$	3.89938e10	−	1.07689e11i	0.267326	−	0.738273i
$619$	−1.96079e11	+	6.37099e10i	−1.33557	+	0.433955i	−0.887816	−	0.460200i	$-0.847778\pi$
$619$	−1.96079e11	+	6.37099e10i	−1.33557	+	0.433955i	−0.447759	+	0.894154i	$0.647778\pi$
$620$	−3.46885e9	−	1.83818e10i	−0.0234757	−	0.124400i
$621$	3.98824e10	−	1.22745e11i	0.268173	−	0.825352i
$622$	−4.95261e10	+	6.36073e10i	−0.330881	+	0.424957i
$623$	−8.87751e10	−	1.22188e11i	−0.589303	−	0.811106i
$624$	−9.65224e10	+	1.76794e10i	−0.636634	+	0.116608i
$625$	−1.41489e11	+	5.71302e10i	−0.927264	+	0.374409i
$626$	−2.55524e10	+	7.05680e10i	−0.166393	+	0.459526i
$627$	−7.59837e9	−	1.04583e10i	−0.0491643	−	0.0676689i
$628$	−4.04005e10	+	2.54315e10i	−0.259746	+	0.163506i
$629$	1.23862e9	−	3.81209e9i	0.00791292	−	0.0243535i
$630$	9.98289e10	−	5.90194e10i	0.633715	−	0.374656i
$631$	1.46138e10	−	4.74833e9i	0.0921822	−	0.0299518i	−0.262563	−	0.964915i	$-0.584568\pi$
$631$	1.46138e10	−	4.74833e9i	0.0921822	−	0.0299518i	0.354745	+	0.934963i	$0.384568\pi$
$632$	5.43189e10	+	9.30130e10i	0.340473	+	0.583009i
$633$	−2.05306e10	−	6.31865e10i	−0.127875	−	0.393559i
$634$	7.73678e10	−	5.23718e10i	0.478854	−	0.324146i
$635$	3.47069e10	+	2.12462e9i	0.213462	+	0.0130673i
$636$	−8.28761e9	+	1.24439e11i	−0.0506525	+	0.760550i
$637$	3.77294e10	+	2.74120e10i	0.229151	+	0.166488i
$638$	4.49411e10	+	6.63906e10i	0.271245	+	0.400704i
$639$	−2.79532e10	−	3.84743e10i	−0.167660	−	0.230764i
$640$	4.86007e10	−	1.60579e11i	0.289683	−	0.957123i
$641$	5.29232e10	+	3.84510e10i	0.313483	+	0.227759i	0.733390	−	0.679809i	$-0.237937\pi$
$641$	5.29232e10	+	3.84510e10i	0.313483	+	0.227759i	−0.419907	+	0.907567i	$0.637937\pi$
$642$	−5.29769e10	−	1.76218e9i	−0.311851	−	0.0103731i
$643$		−	2.95426e11i		−	1.72824i	−0.503285	−	0.864120i	$-0.667875\pi$
$643$		−	2.95426e11i		−	1.72824i	0.503285	−	0.864120i	$-0.332125\pi$
$644$	6.42712e10	−	1.60606e11i	0.373657	−	0.933724i
$645$	5.56329e10	+	8.73365e10i	0.321435	+	0.504611i
$646$	1.33145e10	−	1.71001e10i	0.0764530	−	0.0981901i
$647$	2.35213e11	+	7.64254e10i	1.34228	+	0.436135i	0.890090	−	0.455785i	$-0.150641\pi$
$647$	2.35213e11	+	7.64254e10i	1.34228	+	0.436135i	0.452195	+	0.891919i	$0.350641\pi$
$648$	3.42941e10	−	7.80672e10i	0.194500	−	0.442760i
$649$	−1.99981e11			−1.12722
$650$	2.66568e11	+	4.17971e10i	1.49333	+	0.234149i
$651$			8.77631e9i			0.0488639i
$652$	5.35401e9	−	8.03907e10i	0.0296271	−	0.444852i
$653$	−4.93631e10	+	1.51924e11i	−0.271487	+	0.835552i	0.718640	+	0.695382i	$0.244765\pi$
$653$	−4.93631e10	+	1.51924e11i	−0.271487	+	0.835552i	−0.990128	+	0.140170i	$0.955235\pi$
$654$	6.59291e10	−	8.46740e10i	0.360385	−	0.462849i
$655$	−5.42663e10	+	1.37741e11i	−0.294825	+	0.748340i
$656$	−9.21682e10	+	4.97925e10i	−0.497698	+	0.268874i
$657$	−1.28701e11			−0.690748
$658$	1.95824e11	+	6.51371e9i	1.04463	+	0.0347476i
$659$	−6.07474e10	+	8.36116e10i	−0.322097	+	0.443328i	−0.939106	−	0.343628i	$-0.888344\pi$
$659$	−6.07474e10	+	8.36116e10i	−0.322097	+	0.443328i	0.617009	+	0.786956i	$0.288344\pi$
$660$	6.70360e10	−	1.26504e10i	0.353291	−	0.0666699i
$661$	2.17580e11	−	1.58081e11i	1.13976	−	0.828084i	0.152675	−	0.988277i	$-0.451211\pi$
$661$	2.17580e11	−	1.58081e11i	1.13976	−	0.828084i	0.987086	+	0.160192i	$0.0512114\pi$
$662$	1.36809e11	+	2.02105e11i	0.712334	+	1.05232i
$663$	3.93190e10	−	5.41180e10i	0.203492	−	0.280083i
$664$	2.92165e10	+	1.28345e10i	0.150299	+	0.0660248i
$665$	−3.81591e10	−	1.50336e10i	−0.195124	−	0.0768736i
$666$	−6.36953e9	+	4.31167e9i	−0.0323751	+	0.0219153i
$667$	1.21024e11	−	3.93232e10i	0.611462	−	0.198676i
$668$	−1.16025e11	+	1.39206e11i	−0.582699	+	0.699123i
$669$	−3.28886e10	−	1.01221e11i	−0.164188	−	0.505318i
$670$	−3.30098e11	−	3.12510e10i	−1.63811	−	0.155083i
$671$	1.54139e11	+	5.00829e10i	0.760367	+	0.247058i
$672$	−3.63768e10	+	6.98029e10i	−0.178381	+	0.342292i
$673$	−1.00394e10	+	7.29404e9i	−0.0489381	+	0.0355556i	−0.611985	−	0.790869i	$-0.709629\pi$
$673$	−1.00394e10	+	7.29404e9i	−0.0489381	+	0.0355556i	0.563047	+	0.826425i	$0.309629\pi$
$674$	−1.15149e11	+	3.18008e11i	−0.557985	+	1.54099i
$675$	1.10141e11	−	1.18086e11i	0.530559	−	0.568833i
$676$	−2.06108e11	−	1.71786e11i	−0.986981	−	0.822621i
$677$	−5.52815e10	+	4.01644e10i	−0.263163	+	0.191199i	−0.711540	−	0.702645i	$-0.752002\pi$
$677$	−5.52815e10	+	4.01644e10i	−0.263163	+	0.191199i	0.448377	+	0.893844i	$0.352002\pi$
$678$	−4.87027e10	+	6.25498e10i	−0.230480	+	0.296010i
$679$	−2.20587e11	−	7.16731e10i	−1.03777	−	0.337192i
$680$	5.15337e10	+	1.02101e11i	0.241022	+	0.477524i
$681$	2.37182e10	+	7.29971e10i	0.110279	+	0.339404i
$682$	7.82947e9	−	2.16226e10i	0.0361905	−	0.0999472i
$683$	−4.04100e11	+	1.31300e11i	−1.85698	+	0.603368i	−0.861569	+	0.507641i	$0.830518\pi$
$683$	−4.04100e11	+	1.31300e11i	−1.85698	+	0.603368i	−0.995408	+	0.0957269i	$0.969482\pi$
$684$	−4.03190e10	+	1.01946e10i	−0.184198	+	0.0465742i
$685$	2.76619e11	−	7.15229e10i	1.25638	−	0.324850i
$686$	2.27754e11	−	6.57156e10i	1.02842	−	0.296737i
$687$	4.22597e10	−	5.81655e10i	0.189714	−	0.261119i
$688$	2.82287e11	+	1.35374e11i	1.25990	+	0.604200i
$689$	−4.90598e11	+	3.56440e11i	−2.17695	+	1.58165i
$690$	1.02056e10	−	1.07800e11i	0.0450239	−	0.475577i
$691$	4.68815e10	−	6.45268e10i	0.205631	−	0.283027i	−0.693728	−	0.720237i	$-0.744033\pi$
$691$	4.68815e10	−	6.45268e10i	0.205631	−	0.283027i	0.899360	+	0.437210i	$0.144033\pi$
$692$	−1.56501e11	+	3.91078e11i	−0.682487	+	1.70545i
$693$	1.42568e11			0.618143
$694$	6.95106e9	−	2.08972e11i	0.0299649	−	0.900847i
$695$	−7.84534e10	−	4.80262e9i	−0.336258	−	0.0205844i
$696$	−5.65763e10	+	1.23197e10i	−0.241100	+	0.0525005i
$697$	2.20679e10	−	6.79179e10i	0.0935037	−	0.287775i
$698$	5.60991e10	+	1.94425e11i	0.236338	+	0.819089i
$699$			2.35402e10i			0.0986056i
$700$	1.57819e11	−	1.48117e11i	0.657306	−	0.616898i
$701$	−1.89546e11			−0.784951			−0.392475	−	0.919763i	$-0.628381\pi$
$701$	−1.89546e11			−0.784951			−0.392475	+	0.919763i	$0.628381\pi$
$702$	−2.74355e11	+	7.91618e10i	−1.12970	+	0.325962i
$703$	2.58707e9	+	8.40590e8i	0.0105922	+	0.00344162i
$704$	1.51895e11	−	1.39524e11i	0.618378	−	0.568015i
$705$	1.18738e11	−	3.07011e10i	0.480656	−	0.124279i
$706$	−1.59685e11	−	5.31161e9i	−0.642754	−	0.0213800i
$707$		−	1.64024e10i		−	0.0656491i
$708$	5.36617e10	−	1.34094e11i	0.213565	−	0.533675i
$709$	−4.38775e10	−	3.18788e10i	−0.173643	−	0.126159i	0.497569	−	0.867424i	$-0.334226\pi$
$709$	−4.38775e10	−	3.18788e10i	−0.173643	−	0.126159i	−0.671212	+	0.741265i	$0.734226\pi$
$710$	−6.65690e10	−	5.87054e10i	−0.261962	−	0.231017i
$711$	8.28203e10	+	1.13992e11i	0.324085	+	0.446064i
$712$	−2.84403e11	−	2.84643e10i	−1.10666	−	0.110759i
$713$	−2.95303e10	−	2.14550e10i	−0.114264	−	0.0830176i
$714$	−1.48756e10	−	5.15550e10i	−0.0572376	−	0.198371i
$715$	2.55944e11	+	2.11007e11i	0.979310	+	0.807369i
$716$	−1.94657e11	+	4.92187e10i	−0.740658	+	0.187274i
$717$	6.86283e10	+	2.11216e11i	0.259673	+	0.799191i
$718$	−1.29663e11	−	4.69505e10i	−0.487886	−	0.176662i
$719$	−3.15788e10	+	1.02606e10i	−0.118163	+	0.0383934i	−0.367501	−	0.930023i	$-0.619787\pi$
$719$	−3.15788e10	+	1.02606e10i	−0.118163	+	0.0383934i	0.249339	+	0.968416i	$0.419787\pi$
$720$	4.23411e10	−	2.15345e11i	0.157555	−	0.801319i
$721$	1.38041e11	−	4.24848e11i	0.510821	−	1.57214i
$722$	−2.02803e11	−	1.57907e11i	−0.746323	−	0.581104i
$723$	−3.65809e10	−	5.03493e10i	−0.133876	−	0.184264i
$724$	−1.63816e11	−	1.36536e11i	−0.596215	−	0.496929i
$725$	1.58026e11	+	1.94202e10i	0.571973	+	0.0702915i
$726$	−3.29910e10	−	1.19459e10i	−0.118754	−	0.0430004i
$727$	1.78369e11	+	2.45504e11i	0.638532	+	0.878864i	0.998536	−	0.0540866i	$-0.0172247\pi$
$727$	1.78369e11	+	2.45504e11i	0.638532	+	0.878864i	−0.360004	+	0.932951i	$0.617225\pi$
$728$	−3.73970e11	+	8.14334e10i	−1.33141	+	0.289919i
$729$	5.39995e9	−	1.66193e10i	0.0191196	−	0.0588442i
$730$	−2.34421e11	+	5.23640e10i	−0.825476	+	0.184392i
$731$	−2.02972e11	+	6.59497e10i	−0.710832	+	0.230963i
$732$	−7.49430e10	+	8.99166e10i	−0.261028	+	0.313181i
$733$	−5.21590e10	−	1.60529e11i	−0.180681	−	0.556080i	0.819166	−	0.573557i	$-0.194437\pi$
$733$	−5.21590e10	−	1.60529e11i	−0.180681	−	0.556080i	−0.999847	+	0.0174766i	$0.994437\pi$
$734$	1.75508e10	+	2.59274e10i	0.0604661	+	0.0893253i
$735$	1.97495e10	−	1.25803e10i	0.0676716	−	0.0431065i
$736$	−1.45942e11	−	2.93043e11i	−0.497358	−	0.998666i
$737$	−3.29771e11	−	2.39593e11i	−1.11775	−	0.812089i
$738$	−1.13482e11	+	7.68185e10i	−0.382563	+	0.258965i
$739$	−1.15173e11	−	1.58523e11i	−0.386167	−	0.531513i	0.571038	−	0.820923i	$-0.306541\pi$
$739$	−1.15173e11	−	1.58523e11i	−0.386167	−	0.531513i	−0.957205	+	0.289411i	$0.906541\pi$
$740$	−9.84744e9	+	1.04450e10i	−0.0328395	+	0.0348322i
$741$	3.67271e10	+	2.66838e10i	0.121819	+	0.0885063i
$742$	−1.61712e10	+	4.86161e11i	−0.0533491	+	1.60385i
$743$		−	5.93062e11i		−	1.94601i	−0.230783	−	0.973005i	$-0.574129\pi$
$743$		−	5.93062e11i		−	1.94601i	0.230783	−	0.973005i	$-0.425871\pi$
$744$	1.23978e10	+	1.10520e10i	0.0404624	+	0.0360702i
$745$	1.51713e11	−	1.84022e11i	0.492489	−	0.597372i
$746$	−3.17507e11	−	2.47218e11i	−1.02517	−	0.798223i
$747$	3.97011e10	+	1.28997e10i	0.127503	+	0.0414282i
$748$	−9.34323e9	+	1.40289e11i	−0.0298463	+	0.448144i
$749$	−2.06743e11			−0.656905
$750$	6.85861e10	−	1.16835e11i	0.216766	−	0.369257i
$751$		−	2.87605e11i		−	0.904141i	−0.891982	−	0.452071i	$-0.850685\pi$
$751$		−	2.87605e11i		−	0.904141i	0.891982	−	0.452071i	$-0.149315\pi$
$752$	2.55802e11	−	2.68426e11i	0.799896	−	0.839371i
$753$	−6.27863e9	+	1.93237e10i	−0.0195292	+	0.0601048i
$754$	−2.22146e11	−	1.72968e11i	−0.687310	−	0.535155i
$755$	1.34797e11	+	1.11130e11i	0.414851	+	0.342014i
$756$	−8.50999e10	+	2.12654e11i	−0.260520	+	0.651009i
$757$	1.33933e11			0.407853			0.203926	−	0.978986i	$-0.434630\pi$
$757$	1.33933e11			0.407853			0.203926	+	0.978986i	$0.434630\pi$
$758$	7.22923e9	−	2.17335e11i	0.0218985	−	0.658344i
$759$	7.82436e10	−	1.07693e11i	0.235766	−	0.324504i
$760$	−6.92908e10	+	3.49733e10i	−0.207693	+	0.104829i
$761$	3.71105e11	−	2.69624e11i	1.10652	−	0.803932i	0.124406	−	0.992231i	$-0.460298\pi$
$761$	3.71105e11	−	2.69624e11i	1.10652	−	0.803932i	0.982112	+	0.188299i	$0.0602975\pi$
$762$	−2.55663e10	+	1.73064e10i	−0.0758312	+	0.0513317i
$763$	2.46025e11	−	3.38624e11i	0.725906	−	0.999124i
$764$	−9.61054e9	+	1.44303e11i	−0.0282081	+	0.423547i
$765$	8.03789e10	+	1.26185e11i	0.234691	+	0.368435i
$766$	3.66089e11	+	5.40816e11i	1.06334	+	1.57085i
$767$	6.67917e11	−	2.17019e11i	1.92993	−	0.627071i
$768$	5.27972e10	+	1.39290e11i	0.151763	+	0.400383i
$769$	3.50294e10	+	1.07809e11i	0.100168	+	0.308284i	0.988566	−	0.150789i	$-0.0481815\pi$
$769$	3.50294e10	+	1.07809e11i	0.100168	+	0.308284i	−0.888398	+	0.459073i	$0.848181\pi$
$770$	2.59679e11	−	5.80061e10i	0.738709	−	0.165010i
$771$	1.49282e11	+	4.85046e10i	0.422463	+	0.137267i
$772$	2.55205e10	−	1.60647e10i	0.0718488	−	0.0452277i
$773$	4.00528e11	−	2.91001e11i	1.12180	−	0.815035i	0.137318	−	0.990527i	$-0.456152\pi$
$773$	4.00528e11	−	2.91001e11i	1.12180	−	0.815035i	0.984481	+	0.175492i	$0.0561517\pi$
$774$	3.85070e11	+	1.39432e11i	1.07294	+	0.388508i
$775$	−2.21367e10	−	3.99458e10i	−0.0613630	−	0.110730i
$776$	−3.79033e11	+	2.21353e11i	−1.04528	+	0.610433i
$777$	5.44867e9	−	3.95869e9i	0.0149488	−	0.0108609i
$778$	−3.02494e11	−	2.35528e11i	−0.825654	−	0.642873i
$779$	4.60924e10	+	1.49763e10i	0.125164	+	0.0406682i
$780$	−2.10165e11	+	1.14999e11i	−0.567783	+	0.310681i
$781$	−3.37178e10	−	1.03773e11i	−0.0906264	−	0.278919i
$782$	2.09836e11	+	7.59809e10i	0.561117	+	0.203178i
$783$	−1.60245e11	+	5.20668e10i	−0.426322	+	0.138520i
$784$	3.06122e10	−	6.38339e10i	0.0810271	−	0.168961i
$785$	−7.41391e10	+	8.99281e10i	−0.195240	+	0.236819i
$786$	−3.64406e10	−	1.26294e11i	−0.0954762	−	0.330896i
$787$	1.44703e11	−	1.99167e11i	0.377206	−	0.519179i	−0.577636	−	0.816295i	$-0.696025\pi$
$787$	1.44703e11	−	1.99167e11i	0.377206	−	0.519179i	0.954842	+	0.297115i	$0.0960246\pi$
$788$	7.38227e10	+	2.91965e11i	0.191463	+	0.757225i
$789$	2.41608e11	−	1.75539e11i	0.623453	−	0.452965i
$790$	1.97232e11	+	1.73933e11i	0.506370	+	0.446554i
$791$	−1.81742e11	+	2.50146e11i	−0.464246	+	0.638980i
$792$	1.79535e11	−	2.01397e11i	0.456299	−	0.511862i
$793$	−5.69159e11			−1.43927
$794$	3.33343e11	+	1.10880e10i	0.838705	+	0.0278979i
$795$	7.62197e10	+	2.94785e11i	0.190809	+	0.737966i
$796$	−2.70904e11	−	4.30359e11i	−0.674782	−	1.07196i
$797$	−1.37476e11	+	4.23106e11i	−0.340716	+	1.04862i	0.623122	+	0.782125i	$0.285864\pi$
$797$	−1.37476e11	+	4.23106e11i	−0.340716	+	1.04862i	−0.963838	+	0.266490i	$0.914136\pi$
$798$	3.49877e10	−	1.00953e10i	0.0862788	−	0.0248947i
$799$			2.52768e11i			0.620204i
$800$	−1.04950e10	−	4.09466e11i	−0.0256226	−	0.999672i
$801$	−3.73895e11			−0.908281
$802$	1.10011e10	+	3.81270e10i	0.0265912	+	0.0921584i
$803$	−2.80835e11	−	9.12487e10i	−0.675443	−	0.219465i
$804$	2.49144e11	−	1.56832e11i	0.596246	−	0.375327i
$805$	2.58055e10	−	4.21547e11i	0.0614509	−	1.00383i
$806$	−2.68479e9	+	8.07139e10i	−0.00636166	+	0.191253i
$807$		−	3.29233e11i		−	0.776263i
$808$	−2.31707e10	−	2.06555e10i	−0.0543617	−	0.0484607i
$809$	−2.02590e11	−	1.47190e11i	−0.472960	−	0.343625i	0.325634	−	0.945496i	$-0.394422\pi$
$809$	−2.02590e11	−	1.47190e11i	−0.472960	−	0.343625i	−0.798594	+	0.601871i	$0.794422\pi$
$810$	1.96204e10	−	2.07246e11i	0.0455794	−	0.481445i
$811$	3.72153e11	+	5.12225e11i	0.860278	+	1.18407i	0.981503	+	0.191445i	$0.0613175\pi$
$811$	3.72153e11	+	5.12225e11i	0.860278	+	1.18407i	−0.121226	+	0.992625i	$0.538682\pi$
$812$	−2.18948e11	+	5.53606e10i	−0.503635	+	0.127343i
$813$	7.80076e10	+	5.66758e10i	0.178556	+	0.129729i
$814$	−1.69557e10	+	4.89238e9i	−0.0386206	+	0.0111435i
$815$	−4.92399e10	−	1.90438e11i	−0.111606	−	0.431642i
$816$	−9.15615e10	−	4.39092e10i	−0.206515	−	0.0990365i
$817$	−4.47566e10	−	1.37747e11i	−0.100454	−	0.309167i
$818$	−1.74845e11	+	4.82869e11i	−0.390517	+	1.07849i
$819$	−4.76163e11	+	1.54715e11i	−1.05833	+	0.343871i
$820$	−1.75446e11	+	1.86092e11i	−0.388051	+	0.411598i
$821$	9.04032e10	−	2.78233e11i	0.198981	−	0.612400i	−0.800926	−	0.598763i	$-0.795659\pi$
$821$	9.04032e10	−	2.78233e11i	0.198981	−	0.612400i	0.999907	−	0.0136370i	$-0.00434093\pi$
$822$	−1.55850e11	+	2.00161e11i	−0.341365	+	0.438422i
$823$	3.79110e11	+	5.21800e11i	0.826353	+	1.13738i	0.988591	+	0.150626i	$0.0481290\pi$
$823$	3.79110e11	+	5.21800e11i	0.826353	+	1.13738i	−0.162237	+	0.986752i	$0.551871\pi$
$824$	−4.26322e11	−	7.30013e11i	−0.924760	−	1.58351i
$825$	1.45677e11	−	8.07299e10i	0.314468	−	0.174268i
$826$	1.91796e11	−	5.29682e11i	0.412021	−	1.13788i
$827$	−7.56873e10	−	1.04175e11i	−0.161808	−	0.222710i	0.720413	−	0.693546i	$-0.243952\pi$
$827$	−7.56873e10	−	1.04175e11i	−0.161808	−	0.222710i	−0.882221	+	0.470836i	$0.843952\pi$
$828$	−2.28138e11	−	3.62422e11i	−0.485375	−	0.771068i
$829$	1.35050e11	−	4.15642e11i	0.285941	−	0.880037i	−0.700173	−	0.713973i	$-0.746894\pi$
$829$	1.35050e11	−	4.15642e11i	0.285941	−	0.880037i	0.986115	−	0.166065i	$-0.0531060\pi$
$830$	7.75615e10	+	7.34291e9i	0.163431	+	0.0154723i
$831$	−3.56501e11	+	1.15834e11i	−0.747578	+	0.242903i
$832$	−3.55904e11	+	6.30834e11i	−0.742744	+	1.31650i
$833$	1.49133e10	+	4.58983e10i	0.0309737	+	0.0953271i
$834$	5.77915e10	−	3.91202e10i	0.119454	−	0.0808606i
$835$	−1.62172e11	+	4.11634e11i	−0.333604	+	0.846770i
$836$	−9.52070e10	−	6.34077e9i	−0.194914	−	0.0129813i
$837$	3.91002e10	+	2.84080e10i	0.0796668	+	0.0578814i
$838$	2.68317e11	+	3.96379e11i	0.544091	+	0.803775i
$839$	−2.60468e11	−	3.58503e11i	−0.525661	−	0.723510i	0.460800	−	0.887504i	$-0.347562\pi$
$839$	−2.60468e11	−	3.58503e11i	−0.525661	−	0.723510i	−0.986461	+	0.163993i	$0.947562\pi$
$840$	−3.07855e10	+	1.89688e11i	−0.0618342	+	0.380999i
$841$	2.70307e11	+	1.96389e11i	0.540347	+	0.392585i
$842$	7.38659e11	+	2.45701e10i	1.46959	+	0.0488830i
$843$		−	2.91805e11i		−	0.577807i
$844$	−4.55293e11	−	1.82199e11i	−0.897266	−	0.359067i
$845$	−6.09464e11	−	2.40112e11i	−1.19542	−	0.470963i
$846$	2.97992e11	−	3.82716e11i	0.581732	−	0.747129i
$847$	−1.30154e11	−	4.22896e10i	−0.252885	−	0.0821674i
$848$	6.66407e11	+	6.35066e11i	1.28871	+	1.22810i
$849$	2.70755e11			0.521130
$850$	1.97746e11	+	1.97134e11i	0.378818	+	0.377647i
$851$			2.80111e10i			0.0534087i
$852$	7.86306e10	+	5.23678e9i	0.149222	+	0.00993817i
$853$	−4.97020e10	+	1.52967e11i	−0.0938810	+	0.288936i	−0.986960	−	0.160963i	$-0.948540\pi$
$853$	−4.97020e10	+	1.52967e11i	−0.0938810	+	0.288936i	0.893079	+	0.449899i	$0.148540\pi$
$854$	−2.80483e11	+	3.60229e11i	−0.527320	+	0.677248i
$855$	−8.56349e10	+	5.45490e10i	−0.160246	+	0.102076i
$856$	−2.60350e11	+	2.92053e11i	−0.484912	+	0.543959i
$857$	−1.20876e11			−0.224086			−0.112043	−	0.993703i	$-0.535739\pi$
$857$	−1.20876e11			−0.224086			−0.112043	+	0.993703i	$0.535739\pi$
$858$	−2.94353e11	−	9.79109e9i	−0.543150	−	0.0180668i
$859$	4.87013e11	−	6.70316e11i	0.894475	−	1.23114i	−0.0777227	−	0.996975i	$-0.524765\pi$
$859$	4.87013e11	−	6.70316e11i	0.894475	−	1.23114i	0.972197	−	0.234164i	$-0.0752351\pi$
$860$	7.58111e11	+	9.72954e10i	1.38592	+	0.177868i
$861$	9.70759e10	−	7.05298e10i	0.176644	−	0.128339i
$862$	5.47765e11	+	8.09201e11i	0.992122	+	1.46564i
$863$	3.05841e11	−	4.20954e11i	0.551382	−	0.758912i	−0.438817	−	0.898576i	$-0.644602\pi$
$863$	3.05841e11	−	4.20954e11i	0.551382	−	0.758912i	0.990199	+	0.139665i	$0.0446025\pi$
$864$	1.93238e11	+	3.88011e11i	0.346767	+	0.696288i
$865$	−6.28368e10	+	1.02647e12i	−0.112240	+	1.83351i
$866$	1.50467e10	−	1.01854e10i	0.0267529	−	0.0181096i
$867$	−1.64261e11	+	5.33716e10i	−0.290709	+	0.0944570i
$868$	4.97619e10	+	4.14752e10i	0.0876634	+	0.0730650i
$869$	9.98995e10	+	3.07459e11i	0.175180	+	0.539148i
$870$	−1.21687e11	+	7.19420e10i	−0.212406	+	0.125576i
$871$	1.36141e12	+	4.42348e11i	2.36546	+	0.768585i
$872$	−1.68536e11	−	7.73973e11i	−0.291491	−	1.33863i
$873$	−4.64525e11	+	3.37497e11i	−0.799747	+	0.581050i
$874$	−5.15643e10	+	1.42405e11i	−0.0883697	+	0.244050i
$875$	2.52212e11	−	4.64339e11i	0.430262	−	0.792142i
$876$	1.36543e11	−	1.63824e11i	0.231874	−	0.278203i
$877$	8.15751e11	−	5.92678e11i	1.37898	−	1.00189i	0.382009	−	0.924158i	$-0.375232\pi$
$877$	8.15751e11	−	5.92678e11i	1.37898	−	1.00189i	0.996974	−	0.0777318i	$-0.0247678\pi$
$878$	1.28910e11	−	1.65562e11i	0.216925	−	0.278601i
$879$	4.35831e11	+	1.41610e11i	0.730067	+	0.237213i
$880$	2.45071e11	−	4.39880e11i	0.408659	−	0.733505i
$881$	3.02322e11	+	9.30451e11i	0.501841	+	1.54451i	0.806017	+	0.591892i	$0.201619\pi$
$881$	3.02322e11	+	9.30451e11i	0.501841	+	1.54451i	−0.304176	+	0.952616i	$0.598381\pi$
$882$	3.15299e10	−	8.70761e10i	0.0521013	−	0.143888i
$883$	6.10556e11	−	1.98382e11i	1.00434	−	0.326331i	0.239745	−	0.970836i	$-0.422936\pi$
$883$	6.10556e11	−	1.98382e11i	1.00434	−	0.326331i	0.764600	+	0.644505i	$0.222936\pi$
$884$	−1.21036e11	−	4.78691e11i	−0.198201	−	0.783874i
$885$	2.15456e10	−	3.51960e11i	0.0351226	−	0.573747i
$886$	−2.95728e11	+	8.53288e10i	−0.479907	+	0.138472i
$887$	7.89014e10	−	1.08598e11i	0.127465	−	0.175440i	−0.740515	−	0.672040i	$-0.765418\pi$
$887$	7.89014e10	−	1.08598e11i	0.127465	−	0.175440i	0.867980	+	0.496600i	$0.165418\pi$
$888$	1.26929e9	−	1.26822e10i	0.00204131	−	0.0203959i
$889$	−9.74182e10	+	7.07785e10i	−0.155967	+	0.113317i
$890$	−6.81027e11	+	1.52125e11i	−1.08544	+	0.242461i
$891$	1.50424e11	−	2.07042e11i	0.238675	−	0.328508i
$892$	−7.29350e11	−	2.91871e11i	−1.15206	−	0.461032i
$893$	−1.71540e11			−0.269750
$894$	−7.03974e9	+	2.11638e11i	−0.0110206	+	0.331317i
$895$	−4.13438e11	+	2.63358e11i	−0.644345	+	0.410445i
$896$	2.23874e11	+	5.36133e11i	0.347354	+	0.831841i
$897$	−1.44457e11	+	4.44594e11i	−0.223136	+	0.686742i
$898$	−5.04825e9	−	1.74960e10i	−0.00776311	−	0.0269050i
$899$			4.76529e10i			0.0729542i
$900$	−6.70031e10	−	5.31606e11i	−0.102123	−	0.810251i
$901$	−6.27532e11			−0.952218
$902$	−3.02091e11	+	8.71648e10i	−0.456364	+	0.131678i
$903$	−3.41046e11	−	1.10812e11i	−0.512934	−	0.166662i
$904$	1.24499e11	+	5.71744e11i	0.186420	+	0.856106i
$905$	−4.84406e11	−	1.90842e11i	−0.722130	−	0.284499i
$906$	−1.55026e11	−	5.15664e9i	−0.230087	−	0.00765340i
$907$			1.03978e12i			1.53643i	0.640192	+	0.768215i	$0.278855\pi$
$907$			1.03978e12i			1.53643i	−0.640192	+	0.768215i	$0.721145\pi$
$908$	5.25983e11	+	2.10487e11i	0.773799	+	0.309658i
$909$	−3.28505e10	−	2.38673e10i	−0.0481157	−	0.0349581i
$910$	−8.04352e11	+	4.75538e11i	−1.17295	+	0.693457i
$911$	−4.71848e11	−	6.49444e11i	−0.685061	−	0.942905i	0.314920	−	0.949118i	$-0.398022\pi$
$911$	−4.71848e11	−	6.49444e11i	−0.685061	−	0.942905i	−0.999981	+	0.00621310i	$0.998022\pi$
$912$	2.97989e10	−	6.21381e10i	0.0430746	−	0.0898211i
$913$	7.74849e10	+	5.62960e10i	0.111515	+	0.0810205i
$914$	−4.77862e10	−	1.65615e11i	−0.0684728	−	0.237309i
$915$	−1.04751e11	+	2.65884e11i	−0.149442	+	0.379322i
$916$	−1.30089e11	−	5.14493e11i	−0.184781	−	0.730798i
$917$	−1.58428e11	−	4.87592e11i	−0.224055	−	0.689571i
$918$	−2.77839e11	−	1.00604e11i	−0.391221	−	0.141660i
$919$	−1.31088e11	+	4.25931e10i	−0.183781	+	0.0597142i	−0.399462	−	0.916750i	$-0.630803\pi$
$919$	−1.31088e11	+	4.25931e10i	−0.183781	+	0.0597142i	0.215681	+	0.976464i	$0.430803\pi$
$920$	−5.62997e11	−	5.67307e11i	−0.785878	−	0.791893i
$921$	−8.59696e10	+	2.64587e11i	−0.119483	+	0.367731i
$922$	−2.16565e11	−	1.68622e11i	−0.299684	−	0.233341i
$923$	2.25228e11	+	3.09999e11i	0.310324	+	0.427124i
$924$	−1.51255e11	+	1.81475e11i	−0.207501	+	0.248960i
$925$	−1.48148e10	+	3.17615e10i	−0.0202361	+	0.0433845i
$926$	−7.46221e11	−	2.70204e11i	−1.01490	−	0.367492i
$927$	−6.50015e11	−	8.94669e11i	−0.880247	−	1.21156i
$928$	−1.97516e11	+	3.79010e11i	−0.266324	+	0.511044i
$929$	−2.99636e11	+	9.22184e11i	−0.402282	+	1.23810i	0.520861	+	0.853641i	$0.325611\pi$
$929$	−2.99636e11	+	9.22184e11i	−0.402282	+	1.23810i	−0.923143	+	0.384456i	$0.874389\pi$
$930$	3.72115e10	+	1.61092e10i	0.0497446	+	0.0215348i
$931$	−3.11488e10	+	1.01209e10i	−0.0414613	+	0.0134716i
$932$	1.33474e11	+	1.11246e11i	0.176902	+	0.147442i
$933$	−5.39992e10	−	1.66193e11i	−0.0712625	−	0.219323i
$934$	7.01972e11	+	1.03701e12i	0.922428	+	1.36268i
$935$	8.59281e10	+	3.32332e11i	0.112432	+	0.434837i
$936$	−3.81074e11	+	8.67478e11i	−0.496485	+	1.13020i
$937$	−4.83923e11	−	3.51591e11i	−0.627795	−	0.456120i	0.227841	−	0.973698i	$-0.426833\pi$
$937$	−4.83923e11	−	3.51591e11i	−0.627795	−	0.456120i	−0.855636	+	0.517579i	$0.826833\pi$
$938$	9.50873e11	−	6.43666e11i	1.22832	−	0.831474i
$939$	−9.56249e10	−	1.31616e11i	−0.123001	−	0.169296i
$940$	3.87059e11	−	8.18337e11i	0.495753	−	1.04814i
$941$	7.12425e11	+	5.17607e11i	0.908617	+	0.660149i	0.940665	−	0.339338i	$-0.110203\pi$
$941$	7.12425e11	+	5.17607e11i	0.908617	+	0.660149i	−0.0320479	+	0.999486i	$0.510203\pi$
$942$	3.44019e9	−	1.03424e11i	0.00436897	−	0.131346i
$943$			4.99058e11i			0.631109i
$944$	−5.06722e11	−	9.37966e11i	−0.638090	−	1.18113i
$945$	−3.41684e10	+	5.58159e11i	−0.0428447	+	0.699892i
$946$	7.41393e11	+	5.77265e11i	0.925729	+	0.720793i
$947$	4.55815e11	+	1.48103e11i	0.566747	+	0.184147i	0.578355	−	0.815785i	$-0.303695\pi$
$947$	4.55815e11	+	1.48103e11i	0.566747	+	0.184147i	−0.0116079	+	0.999933i	$0.503695\pi$
$948$	−2.32968e11	−	1.55156e10i	−0.288445	−	0.0192104i
$949$	1.03698e12			1.27852
$950$	−1.33785e11	+	1.34200e11i	−0.164252	+	0.164762i
$951$			2.02518e11i			0.247595i
$952$	−3.62617e11	−	1.59294e11i	−0.441470	−	0.193933i
$953$	−1.73925e11	+	5.35287e11i	−0.210859	+	0.648956i	0.788563	+	0.614954i	$0.210825\pi$
$953$	−1.73925e11	+	5.35287e11i	−0.210859	+	0.648956i	−0.999422	+	0.0340022i	$0.989175\pi$
$954$	9.50148e11	+	7.39806e11i	1.14709	+	0.893150i
$955$	8.83865e10	+	3.41840e11i	0.106261	+	0.410970i
$956$	1.52193e12	+	6.09043e11i	1.82206	+	0.729150i
$957$	−1.73784e11			−0.207187
$958$	4.83596e10	−	1.45385e12i	0.0574144	−	1.72607i
$959$	−5.81578e11	+	8.00474e11i	−0.687596	+	0.946395i
$960$	2.29193e11	+	2.82363e11i	0.269847	+	0.332447i
$961$	−6.78945e11	+	4.93282e11i	−0.796051	+	0.578365i
$962$	5.13213e10	−	3.47404e10i	0.0599235	−	0.0405634i
$963$	−3.00834e11	+	4.14062e11i	−0.349801	+	0.481460i
$964$	−4.58356e11	−	3.05265e10i	−0.530756	−	0.0353483i
$965$	4.68327e10	−	5.68064e10i	0.0540057	−	0.0655071i
$966$	2.10201e11	+	3.10526e11i	0.241394	+	0.356606i
$967$	3.56536e11	−	1.15846e11i	0.407753	−	0.132487i	−0.0979567	−	0.995191i	$-0.531231\pi$
$967$	3.56536e11	−	1.15846e11i	0.407753	−	0.132487i	0.505710	+	0.862704i	$0.331231\pi$
$968$	−2.23643e11	+	1.30606e11i	−0.254714	+	0.148751i
$969$	1.45171e10	+	4.46789e10i	0.0164658	+	0.0506766i
$970$	−7.08788e11	+	8.03730e11i	−0.800625	+	0.907870i
$971$	−1.67966e11	−	5.45756e10i	−0.188949	−	0.0613934i	0.213014	−	0.977049i	$-0.431672\pi$
$971$	−1.67966e11	−	5.45756e10i	−0.188949	−	0.0613934i	−0.401963	+	0.915656i	$0.631672\pi$
$972$	4.68351e11	+	7.44024e11i	0.524694	+	0.833531i
$973$	2.20209e11	−	1.59992e11i	0.245688	−	0.178503i
$974$	1.38639e12	+	5.02007e11i	1.54046	+	0.557794i
$975$	−3.98939e11	+	4.27719e11i	−0.441457	+	0.473303i
$976$	1.55663e11	+	8.49857e11i	0.171549	+	0.936584i
$977$	1.39385e12	−	1.01269e12i	1.52981	−	1.11148i	0.573473	−	0.819224i	$-0.305596\pi$
$977$	1.39385e12	−	1.01269e12i	1.52981	−	1.11148i	0.956342	−	0.292251i	$-0.0944043\pi$
$978$	1.37801e11	+	1.07295e11i	0.150625	+	0.117280i
$979$	−8.15867e11	−	2.65091e11i	−0.888155	−	0.288579i
$980$	2.20015e10	−	1.71432e11i	0.0238533	−	0.185861i
$981$	−3.20199e11	−	9.85472e11i	−0.345736	−	1.06406i
$982$	−8.53850e11	−	3.09176e11i	−0.918196	−	0.332475i
$983$	−1.08372e12	+	3.52122e11i	−1.16065	+	0.377119i	−0.825147	−	0.564919i	$-0.808908\pi$
$983$	−1.08372e12	+	3.52122e11i	−1.16065	+	0.377119i	−0.335507	+	0.942038i	$0.608908\pi$
$984$	2.26143e10	−	2.25951e11i	0.0241214	−	0.241010i
$985$	3.95009e11	+	6.20113e11i	0.419626	+	0.658758i
$986$	−8.07701e10	−	2.79929e11i	−0.0854561	−	0.296169i
$987$	−2.49641e11	+	3.43602e11i	−0.263056	+	0.362065i
$988$	3.24863e11	−	8.21410e10i	0.340935	−	0.0862050i
$989$	1.20659e12	−	8.76642e11i	1.26118	−	0.916299i
$990$	2.61688e11	−	6.04487e11i	0.272422	−	0.629283i
$991$	4.59305e11	−	6.32179e11i	0.476219	−	0.655459i	−0.501554	−	0.865126i	$-0.667238\pi$
$991$	4.59305e11	−	6.32179e11i	0.476219	−	0.655459i	0.977773	+	0.209667i	$0.0672381\pi$
$992$	1.21255e11	−	1.80661e10i	0.125214	−	0.0186560i
$993$	−5.29031e11			−0.544107
$994$	3.07196e11	+	1.02183e10i	0.314681	+	0.0104672i
$995$	−9.57943e11	−	7.89753e11i	−0.977344	−	0.805748i
$996$	−5.85402e10	+	3.68501e10i	−0.0594863	+	0.0374456i
$997$	1.97370e11	−	6.07444e11i	0.199757	−	0.614788i	−0.800131	−	0.599825i	$-0.795237\pi$
$997$	1.97370e11	−	6.07444e11i	0.199757	−	0.614788i	0.999888	−	0.0149632i	$-0.00476312\pi$
$998$	1.18216e12	−	3.41098e11i	1.19167	−	0.343841i
$999$		−	3.70888e10i		−	0.0372375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.11.69	yes	464
4.3	odd	2	inner	100.9.j.b.11.22	✓	464
25.16	even	5	inner	100.9.j.b.91.22	yes	464
100.91	odd	10	inner	100.9.j.b.91.69	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.22	✓	464	4.3	odd	2	inner
100.9.j.b.11.69	yes	464	1.1	even	1	trivial
100.9.j.b.91.22	yes	464	25.16	even	5	inner
100.9.j.b.91.69	yes	464	100.91	odd	10	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+(4.43566 + 15.3729i) q^{2} +(-32.9851 - 10.7175i) q^{3} +(-216.650 + 136.378i) q^{4} +(-397.575 + 482.244i) q^{5} +(18.4482 - 554.615i) q^{6} -2164.38i q^{7} +(-3057.50 - 2725.61i) q^{8} +(-4334.81 - 3149.42i) q^{9} +(-9176.98 - 3972.79i) q^{10} +(-7225.93 - 9945.64i) q^{11} +(8607.85 - 2176.48i) q^{12} +(34926.9 + 25375.9i) q^{13} +(33272.8 - 9600.47i) q^{14} +(18282.5 - 11645.9i) q^{15} +(28338.3 - 59092.3i) q^{16} +(13805.5 + 42489.0i) q^{17} +(29187.9 - 80608.2i) q^{18} +(-28835.1 + 9369.08i) q^{19} +(20367.2 - 158698. i) q^{20} +(-23196.8 + 71392.5i) q^{21} +(120841. - 155199. i) q^{22} +(-183511. - 252581. i) q^{23} +(71640.2 + 122673. i) q^{24} +(-74493.8 - 383456. i) q^{25} +(-235176. + 649485. i) q^{26} +(242982. + 334436. i) q^{27} +(295173. + 468914. i) q^{28} +(-125952. + 387641. i) q^{29} +(260125. + 229397. i) q^{30} +(111192. - 36128.4i) q^{31} +(1.03412e6 + 173528. i) q^{32} +(131756. + 405502. i) q^{33} +(-591941. + 400697. i) q^{34} +(1.04376e6 + 860504. i) q^{35} +(1.36865e6 + 91151.6i) q^{36} +(-72584.6 - 52735.8i) q^{37} +(-271932. - 401720. i) q^{38} +(-880101. - 1.21136e6i) q^{39} +(2.52999e6 - 390829. i) q^{40} +(-1.29320e6 - 939564. i) q^{41} +(-1.20040e6 - 39929.0i) q^{42} +4.77706e6i q^{43} +(2.92186e6 + 1.16927e6i) q^{44} +(3.24220e6 - 838305. i) q^{45} +(3.06890e6 - 3.94145e6i) q^{46} +(5.38094e6 + 1.74837e6i) q^{47} +(-1.56807e6 + 1.64545e6i) q^{48} +1.08024e6 q^{49} +(5.56439e6 - 2.84606e6i) q^{50} -1.54946e6i q^{51} +(-1.10276e7 - 734436. i) q^{52} +(-4.34058e6 + 1.33589e7i) q^{53} +(-4.06346e6 + 5.21878e6i) q^{54} +(7.66907e6 + 469472. i) q^{55} +(-5.89926e6 + 6.61760e6i) q^{56} +1.05154e6 q^{57} +(-6.51783e6 - 216803. i) q^{58} +(9.56164e6 - 1.31605e7i) q^{59} +(-2.37267e6 + 5.01640e6i) q^{60} +(-1.06657e7 + 7.74908e6i) q^{61} +(1.04861e6 + 1.54908e6i) q^{62} +(-6.81656e6 + 9.38219e6i) q^{63} +(1.91937e6 + 1.66671e7i) q^{64} +(-2.61234e7 + 6.75448e6i) q^{65} +(-5.64930e6 + 3.82413e6i) q^{66} +(3.15345e7 - 1.02462e7i) q^{67} +(-8.78550e6 - 7.32247e6i) q^{68} +(3.34609e6 + 1.02982e7i) q^{69} +(-8.59865e6 + 1.98625e7i) q^{70} +(8.44126e6 + 2.74273e6i) q^{71} +(4.66959e6 + 2.14443e7i) q^{72} +(1.94324e7 - 1.41185e7i) q^{73} +(488740. - 1.34975e6i) q^{74} +(-1.65251e6 + 1.34467e7i) q^{75} +(4.96938e6 - 5.96227e6i) q^{76} +(-2.15262e7 + 1.56397e7i) q^{77} +(1.47182e7 - 1.89028e7i) q^{78} +(-2.50099e7 - 8.12621e6i) q^{79} +(1.72303e7 + 3.71596e7i) q^{80} +(6.43290e6 + 1.97984e7i) q^{81} +(8.70760e6 - 2.40478e7i) q^{82} +(-7.40952e6 + 2.40750e6i) q^{83} +(-4.71074e6 - 1.86307e7i) q^{84} +(-2.59788e7 - 1.02349e7i) q^{85} +(-7.34370e7 + 2.11894e7i) q^{86} +(8.30908e6 - 1.14365e7i) q^{87} +(-5.01462e6 + 5.01038e7i) q^{88} +(5.64541e7 - 4.10163e7i) q^{89} +(2.72684e7 + 4.61235e7i) q^{90} +(5.49231e7 - 7.55952e7i) q^{91} +(7.42040e7 + 2.96949e7i) q^{92} -4.05488e6 q^{93} +(-3.00950e6 + 9.04757e7i) q^{94} +(6.94591e6 - 1.76305e7i) q^{95} +(-3.22507e7 - 1.68070e7i) q^{96} +(3.31148e7 - 1.01917e8i) q^{97} +(4.79157e6 + 1.66064e7i) q^{98} +6.58700e7i 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

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