LMFDB - Embedded newform 570.2.q.c.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(49,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("570.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 $ x^20 - 49x^16 - 8x^15 + 72x^13 + 2145x^12 - 648x^11 + 32x^10 - 7056x^9 - 11968x^8 + 10368x^7 + 9344x^6 + 18176x^5 + 56320x^4 + 28160x^3 + 8192x^2 + 4096*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.4
Root			$-2.56046 - 0.686074i$ of defining polynomial
Character	$\chi$	$=$	570.349
Dual form			570.2.q.c.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.99313 + 1.01362i) q^{5} +(-0.500000 + 0.866025i) q^{6} +2.79875i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.99313 + 1.01362i) q^{5} +(-0.500000 + 0.866025i) q^{6} +2.79875i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.23291 + 0.118742i) q^{10} +4.02666 q^{11} -1.00000i q^{12} +(-0.0960560 - 0.0554580i) q^{13} +(-1.39938 - 2.42379i) q^{14} +(2.23291 - 0.118742i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.68457 + 2.12729i) q^{17} +1.00000i q^{18} +(0.163933 + 4.35582i) q^{19} +(1.87439 - 1.21929i) q^{20} +(1.39938 + 2.42379i) q^{21} +(-3.48719 + 2.01333i) q^{22} +(-7.65779 - 4.42123i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.94514 + 4.04057i) q^{25} +0.110916 q^{26} -1.00000i q^{27} +(2.42379 + 1.39938i) q^{28} +(0.907996 - 1.57270i) q^{29} +(-1.87439 + 1.21929i) q^{30} +7.88104 q^{31} +(0.866025 + 0.500000i) q^{32} +(3.48719 - 2.01333i) q^{33} +(2.12729 - 3.68457i) q^{34} +(-2.83688 + 5.57828i) q^{35} +(-0.500000 - 0.866025i) q^{36} +1.68176i q^{37} +(-2.31988 - 3.69028i) q^{38} -0.110916 q^{39} +(-1.01362 + 1.99313i) q^{40} +(-3.88203 - 6.72386i) q^{41} +(-2.42379 - 1.39938i) q^{42} +(6.46509 - 3.73262i) q^{43} +(2.01333 - 3.48719i) q^{44} +(1.87439 - 1.21929i) q^{45} +8.84246 q^{46} +(4.17060 + 2.40790i) q^{47} +(-0.866025 - 0.500000i) q^{48} -0.833029 q^{49} +(-4.57085 - 2.02666i) q^{50} +(-2.12729 + 3.68457i) q^{51} +(-0.0960560 + 0.0554580i) q^{52} +(6.45034 + 3.72410i) q^{53} +(0.500000 + 0.866025i) q^{54} +(8.02567 + 4.08152i) q^{55} -2.79875 q^{56} +(2.31988 + 3.69028i) q^{57} +1.81599i q^{58} +(-0.188606 - 0.326675i) q^{59} +(1.01362 - 1.99313i) q^{60} +(-6.18078 + 10.7054i) q^{61} +(-6.82518 + 3.94052i) q^{62} +(2.42379 + 1.39938i) q^{63} -1.00000 q^{64} +(-0.135239 - 0.207900i) q^{65} +(-2.01333 + 3.48719i) q^{66} +(3.82862 + 2.21046i) q^{67} +4.25457i q^{68} -8.84246 q^{69} +(-0.332330 - 6.24938i) q^{70} +(-5.90675 - 10.2308i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-8.33460 + 4.81199i) q^{73} +(-0.840881 - 1.45645i) q^{74} +(4.57085 + 2.02666i) q^{75} +(3.85421 + 2.03594i) q^{76} +11.2696i q^{77} +(0.0960560 - 0.0554580i) q^{78} +(-2.11845 - 3.66927i) q^{79} +(-0.118742 - 2.23291i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.72386 + 3.88203i) q^{82} -8.25792i q^{83} +2.79875 q^{84} +(-9.50009 + 0.505196i) q^{85} +(-3.73262 + 6.46509i) q^{86} -1.81599i q^{87} +4.02666i q^{88} +(5.01501 - 8.68625i) q^{89} +(-1.01362 + 1.99313i) q^{90} +(0.155213 - 0.268837i) q^{91} +(-7.65779 + 4.42123i) q^{92} +(6.82518 - 3.94052i) q^{93} -4.81579 q^{94} +(-4.08842 + 8.84787i) q^{95} +1.00000 q^{96} +(4.52207 - 2.61082i) q^{97} +(0.721424 - 0.416515i) q^{98} +(2.01333 - 3.48719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9	$ 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9} - 2 q^{10} + 12 q^{11} + 10 q^{14} + 2 q^{15} - 10 q^{16} + 6 q^{19} - 10 q^{21} + 10 q^{24} + 14 q^{25} + 8 q^{29} + 40 q^{31} + 12 q^{34} + 2 q^{35} - 10 q^{36} + 2 q^{40} - 14 q^{41} + 6 q^{44} + 44 q^{46} - 8 q^{49} - 8 q^{50} - 12 q^{51} + 10 q^{54} + 20 q^{56} + 8 q^{59} - 2 q^{60} + 16 q^{61} - 20 q^{64} + 40 q^{65} - 6 q^{66} - 44 q^{69} + 8 q^{70} - 4 q^{71} + 26 q^{74} + 8 q^{75} + 8 q^{79} - 10 q^{81} - 20 q^{84} - 16 q^{85} - 20 q^{86} - 2 q^{89} + 2 q^{90} - 44 q^{91} - 32 q^{94} - 80 q^{95} + 20 q^{96} + 6 q^{99}+O(q^{100}) $ 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9 - 2 * q^10 + 12 * q^11 + 10 * q^14 + 2 * q^15 - 10 * q^16 + 6 * q^19 - 10 * q^21 + 10 * q^24 + 14 * q^25 + 8 * q^29 + 40 * q^31 + 12 * q^34 + 2 * q^35 - 10 * q^36 + 2 * q^40 - 14 * q^41 + 6 * q^44 + 44 * q^46 - 8 * q^49 - 8 * q^50 - 12 * q^51 + 10 * q^54 + 20 * q^56 + 8 * q^59 - 2 * q^60 + 16 * q^61 - 20 * q^64 + 40 * q^65 - 6 * q^66 - 44 * q^69 + 8 * q^70 - 4 * q^71 + 26 * q^74 + 8 * q^75 + 8 * q^79 - 10 * q^81 - 20 * q^84 - 16 * q^85 - 20 * q^86 - 2 * q^89 + 2 * q^90 - 44 * q^91 - 32 * q^94 - 80 * q^95 + 20 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.99313	+	1.01362i	0.891355	+	0.453306i
$5$	1.99313	+	1.01362i	0.891355	+	0.453306i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$			2.79875i			1.05783i	0.848675	+	0.528915i	$0.177401\pi$
$7$			2.79875i			1.05783i	−0.848675	+	0.528915i	$0.822599\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.23291	+	0.118742i	−0.706109	+	0.0375495i
$11$	4.02666			1.21408			0.607042	−	0.794669i	$-0.292356\pi$
$11$	4.02666			1.21408			0.607042	+	0.794669i	$0.292356\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−0.0960560	−	0.0554580i	−0.0266411	−	0.0153813i	0.486620	−	0.873614i	$-0.338230\pi$
$13$	−0.0960560	−	0.0554580i	−0.0266411	−	0.0153813i	−0.513261	+	0.858232i	$0.671563\pi$
$14$	−1.39938	−	2.42379i	−0.373999	−	0.647786i
$15$	2.23291	−	0.118742i	0.576536	−	0.0306590i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.68457	+	2.12729i	−0.893639	+	0.515943i	−0.875131	−	0.483886i	$-0.839225\pi$
$17$	−3.68457	+	2.12729i	−0.893639	+	0.515943i	−0.0185079	+	0.999829i	$0.505892\pi$
$18$			1.00000i			0.235702i
$19$	0.163933	+	4.35582i	0.0376087	+	0.999293i
$19$	0.163933	+	4.35582i	0.0376087	+	0.999293i
$20$	1.87439	−	1.21929i	0.419126	−	0.272642i
$21$	1.39938	+	2.42379i	0.305369	+	0.528915i
$22$	−3.48719	+	2.01333i	−0.743472	+	0.429244i
$23$	−7.65779	−	4.42123i	−1.59676	−	0.921890i	−0.992106	−	0.125401i	$-0.959978\pi$
$23$	−7.65779	−	4.42123i	−1.59676	−	0.921890i	−0.604654	−	0.796489i	$-0.706688\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.94514	+	4.04057i	0.589027	+	0.808113i
$26$	0.110916			0.0217524
$27$		−	1.00000i		−	0.192450i
$28$	2.42379	+	1.39938i	0.458054	+	0.264457i
$29$	0.907996	−	1.57270i	0.168611	−	0.292042i	−0.769321	−	0.638862i	$-0.779405\pi$
$29$	0.907996	−	1.57270i	0.168611	−	0.292042i	0.937932	+	0.346820i	$0.112739\pi$
$30$	−1.87439	+	1.21929i	−0.342215	+	0.222611i
$31$	7.88104			1.41548			0.707739	−	0.706474i	$-0.249715\pi$
$31$	7.88104			1.41548			0.707739	+	0.706474i	$0.249715\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	3.48719	−	2.01333i	0.607042	−	0.350476i
$34$	2.12729	−	3.68457i	0.364827	−	0.631898i
$35$	−2.83688	+	5.57828i	−0.479521	+	0.942902i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$			1.68176i			0.276480i	0.990399	+	0.138240i	$0.0441445\pi$
$37$			1.68176i			0.276480i	−0.990399	+	0.138240i	$0.955855\pi$
$38$	−2.31988	−	3.69028i	−0.376334	−	0.598643i
$39$	−0.110916			−0.0177608
$40$	−1.01362	+	1.99313i	−0.160268	+	0.315142i
$41$	−3.88203	−	6.72386i	−0.606270	−	1.05009i	−0.991849	−	0.127416i	$-0.959332\pi$
$41$	−3.88203	−	6.72386i	−0.606270	−	1.05009i	0.385579	−	0.922675i	$-0.374002\pi$
$42$	−2.42379	−	1.39938i	−0.373999	−	0.215929i
$43$	6.46509	−	3.73262i	0.985917	−	0.569219i	0.0818657	−	0.996643i	$-0.473912\pi$
$43$	6.46509	−	3.73262i	0.985917	−	0.569219i	0.904051	+	0.427424i	$0.140579\pi$
$44$	2.01333	−	3.48719i	0.303521	−	0.525714i
$45$	1.87439	−	1.21929i	0.279417	−	0.181761i
$46$	8.84246			1.30375
$47$	4.17060	+	2.40790i	0.608344	+	0.351228i	0.772317	−	0.635237i	$-0.219098\pi$
$47$	4.17060	+	2.40790i	0.608344	+	0.351228i	−0.163973	+	0.986465i	$0.552431\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−0.833029			−0.119004
$50$	−4.57085	−	2.02666i	−0.646415	−	0.286614i
$51$	−2.12729	+	3.68457i	−0.297880	+	0.515943i
$52$	−0.0960560	+	0.0554580i	−0.0133206	+	0.00769064i
$53$	6.45034	+	3.72410i	0.886022	+	0.511545i	0.872639	−	0.488365i	$-0.162407\pi$
$53$	6.45034	+	3.72410i	0.886022	+	0.511545i	0.0133827	+	0.999910i	$0.495740\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	8.02567	+	4.08152i	1.08218	+	0.550352i
$56$	−2.79875			−0.373999
$57$	2.31988	+	3.69028i	0.307275	+	0.488790i
$58$			1.81599i			0.238451i
$59$	−0.188606	−	0.326675i	−0.0245544	−	0.0425294i	0.853487	−	0.521114i	$-0.174483\pi$
$59$	−0.188606	−	0.326675i	−0.0245544	−	0.0425294i	−0.878041	+	0.478585i	$0.841150\pi$
$60$	1.01362	−	1.99313i	0.130858	−	0.257312i
$61$	−6.18078	+	10.7054i	−0.791368	+	1.37069i	0.133752	+	0.991015i	$0.457297\pi$
$61$	−6.18078	+	10.7054i	−0.791368	+	1.37069i	−0.925120	+	0.379674i	$0.876036\pi$
$62$	−6.82518	+	3.94052i	−0.866799	+	0.500447i
$63$	2.42379	+	1.39938i	0.305369	+	0.176305i
$64$	−1.00000			−0.125000
$65$	−0.135239	−	0.207900i	−0.0167743	−	0.0257868i
$66$	−2.01333	+	3.48719i	−0.247824	+	0.429244i
$67$	3.82862	+	2.21046i	0.467741	+	0.270050i	0.715293	−	0.698824i	$-0.246293\pi$
$67$	3.82862	+	2.21046i	0.467741	+	0.270050i	−0.247553	+	0.968874i	$0.579626\pi$
$68$			4.25457i			0.515943i
$69$	−8.84246			−1.06451
$70$	−0.332330	−	6.24938i	−0.0397210	−	0.746943i
$71$	−5.90675	−	10.2308i	−0.701002	−	1.21417i	−0.968115	−	0.250506i	$-0.919403\pi$
$71$	−5.90675	−	10.2308i	−0.701002	−	1.21417i	0.267113	−	0.963665i	$-0.413930\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−8.33460	+	4.81199i	−0.975492	+	0.563200i	−0.900906	−	0.434014i	$-0.857097\pi$
$73$	−8.33460	+	4.81199i	−0.975492	+	0.563200i	−0.0745857	+	0.997215i	$0.523763\pi$
$74$	−0.840881	−	1.45645i	−0.0977504	−	0.169309i
$75$	4.57085	+	2.02666i	0.527796	+	0.234019i
$76$	3.85421	+	2.03594i	0.442109	+	0.233538i
$77$			11.2696i			1.28430i
$78$	0.0960560	−	0.0554580i	0.0108762	−	0.00627938i
$79$	−2.11845	−	3.66927i	−0.238344	−	0.412825i	0.721895	−	0.692003i	$-0.243271\pi$
$79$	−2.11845	−	3.66927i	−0.238344	−	0.412825i	−0.960239	+	0.279178i	$0.909938\pi$
$80$	−0.118742	−	2.23291i	−0.0132758	−	0.249647i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.72386	+	3.88203i	0.742527	+	0.428698i
$83$		−	8.25792i		−	0.906425i	−0.891403	−	0.453212i	$-0.850278\pi$
$83$		−	8.25792i		−	0.906425i	0.891403	−	0.453212i	$-0.149722\pi$
$84$	2.79875			0.305369
$85$	−9.50009	+	0.505196i	−1.03043	+	0.0547962i
$86$	−3.73262	+	6.46509i	−0.402499	+	0.697149i
$87$		−	1.81599i		−	0.194695i
$88$			4.02666i			0.429244i
$89$	5.01501	−	8.68625i	0.531590	−	0.920740i	−0.467730	−	0.883871i	$-0.654928\pi$
$89$	5.01501	−	8.68625i	0.531590	−	0.920740i	0.999320	−	0.0368691i	$-0.0117385\pi$
$90$	−1.01362	+	1.99313i	−0.106845	+	0.210094i
$91$	0.155213	−	0.268837i	0.0162708	−	0.0281818i
$92$	−7.65779	+	4.42123i	−0.798380	+	0.460945i
$93$	6.82518	−	3.94052i	0.707739	−	0.408613i
$94$	−4.81579			−0.496711
$95$	−4.08842	+	8.84787i	−0.419463	+	0.907773i
$96$	1.00000			0.102062
$97$	4.52207	−	2.61082i	0.459146	−	0.265088i	−0.252539	−	0.967587i	$-0.581266\pi$
$97$	4.52207	−	2.61082i	0.459146	−	0.265088i	0.711685	+	0.702499i	$0.247932\pi$
$98$	0.721424	−	0.416515i	0.0728749	−	0.0420743i
$99$	2.01333	−	3.48719i	0.202347	−	0.350476i
$100$	4.97180	−	0.530281i	0.497180	−	0.0530281i
$101$	−5.86577	+	10.1598i	−0.583666	+	1.01094i	0.411374	+	0.911466i	$0.365049\pi$
$101$	−5.86577	+	10.1598i	−0.583666	+	1.01094i	−0.995040	+	0.0994725i	$0.968284\pi$
$102$		−	4.25457i		−	0.421265i
$103$		−	17.9496i		−	1.76863i	−0.466890	−	0.884315i	$-0.654626\pi$
$103$		−	17.9496i		−	1.76863i	0.466890	−	0.884315i	$-0.345374\pi$
$104$	0.0554580	−	0.0960560i	0.00543810	−	0.00941907i
$105$	0.332330	+	6.24938i	0.0324320	+	0.609877i
$106$	−7.44821			−0.723434
$107$		−	15.1358i		−	1.46324i	−0.681714	−	0.731619i	$-0.738765\pi$
$107$		−	15.1358i		−	1.46324i	0.681714	−	0.731619i	$-0.261235\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	−4.29258	−	7.43496i	−0.411154	−	0.712140i	0.583862	−	0.811853i	$-0.301541\pi$
$109$	−4.29258	−	7.43496i	−0.411154	−	0.712140i	−0.995016	+	0.0997127i	$0.968208\pi$
$110$	−8.99119	+	0.478134i	−0.857276	+	0.0455883i
$111$	0.840881	+	1.45645i	0.0798129	+	0.138240i
$112$	2.42379	−	1.39938i	0.229027	−	0.132229i
$113$			1.24691i			0.117299i	0.998279	+	0.0586497i	$0.0186795\pi$
$113$			1.24691i			0.117299i	−0.998279	+	0.0586497i	$0.981321\pi$
$114$	−3.85421	−	2.03594i	−0.360980	−	0.190683i
$115$	−10.7815	−	16.5742i	−1.00538	−	1.54555i
$116$	−0.907996	−	1.57270i	−0.0843053	−	0.146021i
$117$	−0.0960560	+	0.0554580i	−0.00888038	+	0.00512709i
$118$	0.326675	+	0.188606i	0.0300728	+	0.0173626i
$119$	−5.95375	−	10.3122i	−0.545780	−	0.945318i
$120$	0.118742	+	2.23291i	0.0108396	+	0.203836i
$121$	5.21402			0.474002
$122$		−	12.3616i		−	1.11916i
$123$	−6.72386	−	3.88203i	−0.606270	−	0.350030i
$124$	3.94052	−	6.82518i	0.353869	−	0.612920i
$125$	1.77443	+	11.0386i	0.158710	+	0.987325i
$126$	−2.79875			−0.249333
$127$	11.9143	+	6.87872i	1.05722	+	0.610388i	0.924663	−	0.380787i	$-0.124347\pi$
$127$	11.9143	+	6.87872i	1.05722	+	0.610388i	0.132560	+	0.991175i	$0.457680\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	3.73262	−	6.46509i	0.328639	−	0.569219i
$130$	0.221070	+	0.112427i	0.0193891	+	0.00986050i
$131$	6.42860	+	11.1347i	0.561669	+	0.972840i	0.997351	+	0.0727388i	$0.0231739\pi$
$131$	6.42860	+	11.1347i	0.561669	+	0.972840i	−0.435682	+	0.900101i	$0.643493\pi$
$132$		−	4.02666i		−	0.350476i
$133$	−12.1909	+	0.458807i	−1.05708	+	0.0397836i
$134$	−4.42091			−0.381909
$135$	1.01362	−	1.99313i	0.0872388	−	0.171541i
$136$	−2.12729	−	3.68457i	−0.182413	−	0.315949i
$137$	−7.06060	−	4.07644i	−0.603228	−	0.348274i	0.167082	−	0.985943i	$-0.446565\pi$
$137$	−7.06060	−	4.07644i	−0.603228	−	0.348274i	−0.770310	+	0.637669i	$0.779899\pi$
$138$	7.65779	−	4.42123i	0.651874	−	0.376360i
$139$	1.14277	−	1.97934i	0.0969289	−	0.167886i	−0.813483	−	0.581589i	$-0.802431\pi$
$139$	1.14277	−	1.97934i	0.0969289	−	0.167886i	0.910412	+	0.413703i	$0.135765\pi$
$140$	3.41249	+	5.24595i	0.288408	+	0.443364i
$141$	4.81579			0.405563
$142$	10.2308	+	5.90675i	0.858549	+	0.495683i
$143$	−0.386785	−	0.223311i	−0.0323446	−	0.0186742i
$144$	−1.00000			−0.0833333
$145$	3.40388	−	2.21422i	0.282676	−	0.183881i
$146$	4.81199	−	8.33460i	0.398243	−	0.689777i
$147$	−0.721424	+	0.416515i	−0.0595021	+	0.0343535i
$148$	1.45645	+	0.840881i	0.119719	+	0.0691200i
$149$	−9.36462	−	16.2200i	−0.767180	−	1.32879i	−0.939086	−	0.343681i	$-0.888326\pi$
$149$	−9.36462	−	16.2200i	−0.767180	−	1.32879i	0.171907	−	0.985113i	$-0.445007\pi$
$150$	−4.97180	+	0.530281i	−0.405946	+	0.0432972i
$151$	−16.1394			−1.31341			−0.656703	−	0.754150i	$-0.728049\pi$
$151$	−16.1394			−1.31341			−0.656703	+	0.754150i	$0.728049\pi$
$152$	−4.35582	+	0.163933i	−0.353303	+	0.0132967i
$153$			4.25457i			0.343962i
$154$	−5.63482	−	9.75980i	−0.454067	−	0.786467i
$155$	15.7079	+	7.98841i	1.26169	+	0.641644i
$156$	−0.0554580	+	0.0960560i	−0.00444019	+	0.00769064i
$157$	6.73626	−	3.88918i	0.537612	−	0.310390i	−0.206499	−	0.978447i	$-0.566207\pi$
$157$	6.73626	−	3.88918i	0.537612	−	0.310390i	0.744110	+	0.668057i	$0.232874\pi$
$158$	3.66927	+	2.11845i	0.291911	+	0.168535i
$159$	7.44821			0.590681
$160$	1.21929	+	1.87439i	0.0963933	+	0.148183i
$161$	12.3739	−	21.4323i	0.975202	−	1.68910i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$		−	1.99824i		−	0.156514i	−0.996933	−	0.0782570i	$-0.975065\pi$
$163$		−	1.99824i		−	0.156514i	0.996933	−	0.0782570i	$-0.0249355\pi$
$164$	−7.76405			−0.606270
$165$	8.99119	−	0.478134i	0.699963	−	0.0372227i
$166$	4.12896	+	7.15157i	0.320470	+	0.555069i
$167$	−15.5791	−	8.99462i	−1.20555	−	0.696024i	−0.243766	−	0.969834i	$-0.578383\pi$
$167$	−15.5791	−	8.99462i	−1.20555	−	0.696024i	−0.961784	+	0.273810i	$0.911716\pi$
$168$	−2.42379	+	1.39938i	−0.187000	+	0.107964i
$169$	−6.49385	−	11.2477i	−0.499527	−	0.865206i
$170$	7.97472	−	5.18756i	0.611633	−	0.397868i
$171$	3.85421	+	2.03594i	0.294739	+	0.155692i
$172$		−	7.46524i		−	0.569219i
$173$	−13.2653	+	7.65871i	−1.00854	+	0.582281i	−0.910764	−	0.412927i	$-0.864506\pi$
$173$	−13.2653	+	7.65871i	−1.00854	+	0.582281i	−0.0977767	+	0.995208i	$0.531173\pi$
$174$	0.907996	+	1.57270i	0.0688350	+	0.119226i
$175$	−11.3086	+	8.24272i	−0.854846	+	0.623091i
$176$	−2.01333	−	3.48719i	−0.151761	−	0.262857i
$177$	−0.326675	−	0.188606i	−0.0245544	−	0.0141765i
$178$			10.0300i			0.751781i
$179$	10.8958			0.814389			0.407195	−	0.913341i	$-0.366507\pi$
$179$	10.8958			0.814389			0.407195	+	0.913341i	$0.366507\pi$
$180$	−0.118742	−	2.23291i	−0.00885050	−	0.166432i
$181$	−9.12604	+	15.8068i	−0.678333	+	1.17491i	0.297150	+	0.954831i	$0.403964\pi$
$181$	−9.12604	+	15.8068i	−0.678333	+	1.17491i	−0.975483	+	0.220076i	$0.929369\pi$
$182$			0.310427i			0.0230103i
$183$			12.3616i			0.913793i
$184$	4.42123	−	7.65779i	0.325937	−	0.564540i
$185$	−1.70467	+	3.35197i	−0.125330	+	0.246442i
$186$	−3.94052	+	6.82518i	−0.288933	+	0.500447i
$187$	−14.8365	+	8.56587i	−1.08495	+	0.626398i
$188$	4.17060	−	2.40790i	0.304172	−	0.175614i
$189$	2.79875			0.203579
$190$	−0.883265	−	9.70669i	−0.0640788	−	0.704197i
$191$	−17.2519			−1.24830			−0.624151	−	0.781304i	$-0.714555\pi$
$191$	−17.2519			−1.24830			−0.624151	+	0.781304i	$0.714555\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	5.47129	−	3.15885i	0.393832	−	0.227379i	−0.289987	−	0.957031i	$-0.593651\pi$
$193$	5.47129	−	3.15885i	0.393832	−	0.227379i	0.683819	+	0.729651i	$0.260318\pi$
$194$	−2.61082	+	4.52207i	−0.187446	+	0.324665i
$195$	−0.221070	−	0.112427i	−0.0158311	−	0.00805106i
$196$	−0.416515	+	0.721424i	−0.0297510	+	0.0515303i
$197$		−	8.79248i		−	0.626438i	−0.949681	−	0.313219i	$-0.898593\pi$
$197$		−	8.79248i		−	0.626438i	0.949681	−	0.313219i	$-0.101407\pi$
$198$			4.02666i			0.286163i
$199$	2.38605	−	4.13275i	0.169142	−	0.292963i	−0.768976	−	0.639277i	$-0.779234\pi$
$199$	2.38605	−	4.13275i	0.169142	−	0.292963i	0.938119	+	0.346314i	$0.112567\pi$
$200$	−4.04057	+	2.94514i	−0.285711	+	0.208253i
$201$	4.42091			0.311827
$202$		−	11.7315i		−	0.825428i
$203$	4.40159	+	2.54126i	0.308931	+	0.178361i
$204$	2.12729	+	3.68457i	0.148940	+	0.257971i
$205$	−0.921918	−	17.3364i	−0.0643896	−	1.21083i
$206$	8.97482	+	15.5448i	0.625305	+	1.08306i
$207$	−7.65779	+	4.42123i	−0.532253	+	0.307297i
$208$			0.110916i			0.00769064i
$209$	0.660101	+	17.5394i	0.0456601	+	1.21323i
$210$	−3.41249	−	5.24595i	−0.235484	−	0.362005i
$211$	−10.6837	−	18.5047i	−0.735497	−	1.27392i	−0.954505	−	0.298196i	$-0.903615\pi$
$211$	−10.6837	−	18.5047i	−0.735497	−	1.27392i	0.219007	−	0.975723i	$-0.429718\pi$
$212$	6.45034	−	3.72410i	0.443011	−	0.255772i
$213$	−10.2308	−	5.90675i	−0.701002	−	0.404724i
$214$	7.56792	+	13.1080i	0.517333	+	0.896046i
$215$	16.6692	−	0.886437i	1.13683	−	0.0604545i
$216$	1.00000			0.0680414
$217$			22.0571i			1.49733i
$218$	7.43496	+	4.29258i	0.503559	+	0.290730i
$219$	−4.81199	+	8.33460i	−0.325164	+	0.563200i
$220$	7.54753	−	4.90967i	0.508854	−	0.331010i
$221$	0.471900			0.0317434
$222$	−1.45645	−	0.840881i	−0.0977504	−	0.0564362i
$223$	−0.769596	+	0.444327i	−0.0515360	+	0.0297543i	−0.525547	−	0.850765i	$-0.676139\pi$
$223$	−0.769596	+	0.444327i	−0.0515360	+	0.0297543i	0.474011	+	0.880519i	$0.342806\pi$
$224$	−1.39938	+	2.42379i	−0.0934998	+	0.161946i
$225$	4.97180	−	0.530281i	0.331453	−	0.0353521i
$226$	−0.623455	−	1.07986i	−0.0414716	−	0.0718309i
$227$		−	0.227679i		−	0.0151116i	−0.999971	−	0.00755579i	$-0.997595\pi$
$227$		−	0.227679i		−	0.0151116i	0.999971	−	0.00755579i	$-0.00240511\pi$
$228$	4.35582	−	0.163933i	0.288471	−	0.0108567i
$229$	−16.2385			−1.07307			−0.536536	−	0.843878i	$-0.680267\pi$
$229$	−16.2385			−1.07307			−0.536536	+	0.843878i	$0.680267\pi$
$230$	17.6242	+	8.96292i	1.16210	+	0.590997i
$231$	5.63482	+	9.75980i	0.370744	+	0.642148i
$232$	1.57270	+	0.907996i	0.103253	+	0.0596129i
$233$	2.89217	−	1.66979i	0.189472	−	0.109392i	−0.402263	−	0.915524i	$-0.631776\pi$
$233$	2.89217	−	1.66979i	0.189472	−	0.109392i	0.591735	+	0.806132i	$0.298443\pi$
$234$	0.0554580	−	0.0960560i	0.00362540	−	0.00627938i
$235$	5.87185	+	9.02666i	0.383037	+	0.588835i
$236$	−0.377211			−0.0245544
$237$	−3.66927	−	2.11845i	−0.238344	−	0.137608i
$238$	10.3122	+	5.95375i	0.668441	+	0.385924i
$239$	28.3414			1.83325			0.916626	−	0.399745i	$-0.130901\pi$
$239$	28.3414			1.83325			0.916626	+	0.399745i	$0.130901\pi$
$240$	−1.21929	−	1.87439i	−0.0787048	−	0.120991i
$241$	−7.12956	+	12.3488i	−0.459255	+	0.795453i	−0.998922	−	0.0464255i	$-0.985217\pi$
$241$	−7.12956	+	12.3488i	−0.459255	+	0.795453i	0.539667	+	0.841879i	$0.318550\pi$
$242$	−4.51547	+	2.60701i	−0.290266	+	0.167585i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	6.18078	+	10.7054i	0.395684	+	0.685345i
$245$	−1.66034	−	0.844377i	−0.106075	−	0.0539453i
$246$	7.76405			0.495018
$247$	0.225818	−	0.427494i	0.0143685	−	0.0272008i
$248$			7.88104i			0.500447i
$249$	−4.12896	−	7.15157i	−0.261662	−	0.453212i
$250$	−7.05602	−	8.67252i	−0.446262	−	0.548498i
$251$	12.1437	−	21.0334i	0.766501	−	1.32762i	−0.172949	−	0.984931i	$-0.555329\pi$
$251$	12.1437	−	21.0334i	0.766501	−	1.32762i	0.939449	−	0.342687i	$-0.111337\pi$
$252$	2.42379	−	1.39938i	0.152685	−	0.0881525i
$253$	−30.8353	−	17.8028i	−1.93860	−	1.11925i
$254$	−13.7574			−0.863219
$255$	−7.97472	+	5.18756i	−0.499396	+	0.324857i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.06264	+	1.19086i	0.128664	+	0.0742840i	0.562950	−	0.826491i	$-0.309666\pi$
$257$	2.06264	+	1.19086i	0.128664	+	0.0742840i	−0.434287	+	0.900775i	$0.643000\pi$
$258$			7.46524i			0.464766i
$259$	−4.70684			−0.292469
$260$	−0.247666	+	0.0131704i	−0.0153596	+	0.000816792i
$261$	−0.907996	−	1.57270i	−0.0562036	−	0.0973474i
$262$	−11.1347	−	6.42860i	−0.687901	−	0.397160i
$263$	−6.92724	+	3.99944i	−0.427152	+	0.246616i	−0.698133	−	0.715969i	$-0.745985\pi$
$263$	−6.92724	+	3.99944i	−0.427152	+	0.246616i	0.270981	+	0.962585i	$0.412652\pi$
$264$	2.01333	+	3.48719i	0.123912	+	0.214622i
$265$	9.08152	+	13.9608i	0.557874	+	0.857607i
$266$	10.3282	−	6.49277i	0.633262	−	0.398097i
$267$		−	10.0300i		−	0.613827i
$268$	3.82862	−	2.21046i	0.233870	−	0.135025i
$269$	5.32072	+	9.21576i	0.324410	+	0.561895i	0.981393	−	0.192011i	$-0.0615009\pi$
$269$	5.32072	+	9.21576i	0.324410	+	0.561895i	−0.656983	+	0.753906i	$0.728168\pi$
$270$	0.118742	+	2.23291i	0.00722640	+	0.135891i
$271$	8.07644	+	13.9888i	0.490609	+	0.849759i	0.999942	−	0.0108102i	$-0.00344107\pi$
$271$	8.07644	+	13.9888i	0.490609	+	0.849759i	−0.509333	+	0.860570i	$0.670108\pi$
$272$	3.68457	+	2.12729i	0.223410	+	0.128986i
$273$		−	0.310427i		−	0.0187879i
$274$	8.15288			0.492534
$275$	11.8591	+	16.2700i	0.715129	+	0.981118i
$276$	−4.42123	+	7.65779i	−0.266127	+	0.460945i
$277$			21.6950i			1.30352i	0.758423	+	0.651762i	$0.225970\pi$
$277$			21.6950i			1.30352i	−0.758423	+	0.651762i	$0.774030\pi$
$278$			2.28555i			0.137078i
$279$	3.94052	−	6.82518i	0.235913	−	0.408613i
$280$	−5.57828	−	2.83688i	−0.333366	−	0.169536i
$281$	−0.595143	+	1.03082i	−0.0355032	+	0.0614934i	−0.883231	−	0.468938i	$-0.844637\pi$
$281$	−0.595143	+	1.03082i	−0.0355032	+	0.0614934i	0.847728	+	0.530431i	$0.177970\pi$
$282$	−4.17060	+	2.40790i	−0.248355	+	0.143388i
$283$	−0.262002	+	0.151267i	−0.0155744	+	0.00899189i	−0.507767	−	0.861494i	$-0.669529\pi$
$283$	−0.262002	+	0.151267i	−0.0155744	+	0.00899189i	0.492193	+	0.870486i	$0.336196\pi$
$284$	−11.8135			−0.701002
$285$	0.883265	+	9.70669i	0.0523201	+	0.574975i
$286$	0.446621			0.0264093
$287$	18.8184	−	10.8648i	1.11082	−	0.641331i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	0.550694	−	0.953829i	0.0323937	−	0.0561076i
$290$	−1.84073	+	3.61951i	−0.108091	+	0.212545i
$291$	2.61082	−	4.52207i	0.153049	−	0.265088i
$292$			9.62397i			0.563200i
$293$			25.2078i			1.47266i	0.676625	+	0.736328i	$0.263442\pi$
$293$			25.2078i			1.47266i	−0.676625	+	0.736328i	$0.736558\pi$
$294$	0.416515	−	0.721424i	0.0242916	−	0.0420743i
$295$	−0.0447908	−	0.842280i	−0.00260782	−	0.0490395i
$296$	−1.68176			−0.0977504
$297$		−	4.02666i		−	0.233651i
$298$	16.2200	+	9.36462i	0.939599	+	0.542478i
$299$	0.490385	+	0.849371i	0.0283597	+	0.0491204i
$300$	4.04057	−	2.94514i	0.233282	−	0.170038i
$301$	10.4467	+	18.0942i	0.602137	+	1.04293i
$302$	13.9771	−	8.06970i	0.804293	−	0.464359i
$303$			11.7315i			0.673959i
$304$	3.69028	−	2.31988i	0.211652	−	0.133054i
$305$	−23.1704	+	15.0723i	−1.32673	+	0.863039i
$306$	−2.12729	−	3.68457i	−0.121609	−	0.210633i
$307$	19.7299	−	11.3911i	1.12605	−	0.650123i	0.183109	−	0.983093i	$-0.441384\pi$
$307$	19.7299	−	11.3911i	1.12605	−	0.650123i	0.942938	+	0.332969i	$0.108050\pi$
$308$	9.75980	+	5.63482i	0.556116	+	0.321074i
$309$	−8.97482	−	15.5448i	−0.510560	−	0.884315i
$310$	−17.5977	+	0.935810i	−0.999481	+	0.0531505i
$311$	−12.0752			−0.684724			−0.342362	−	0.939568i	$-0.611227\pi$
$311$	−12.0752			−0.684724			−0.342362	+	0.939568i	$0.611227\pi$
$312$		−	0.110916i		−	0.00627938i
$313$	−9.22306	−	5.32494i	−0.521318	−	0.300983i	0.216156	−	0.976359i	$-0.430648\pi$
$313$	−9.22306	−	5.32494i	−0.521318	−	0.300983i	−0.737474	+	0.675376i	$0.763981\pi$
$314$	−3.88918	+	6.73626i	−0.219479	+	0.380149i
$315$	3.41249	+	5.24595i	0.192272	+	0.295576i
$316$	−4.23690			−0.238344
$317$	14.3154	+	8.26498i	0.804031	+	0.464208i	0.844879	−	0.534958i	$-0.179673\pi$
$317$	14.3154	+	8.26498i	0.804031	+	0.464208i	−0.0408477	+	0.999165i	$0.513006\pi$
$318$	−6.45034	+	3.72410i	−0.361717	+	0.208837i
$319$	3.65620	−	6.33272i	0.204708	−	0.354564i
$320$	−1.99313	−	1.01362i	−0.111419	−	0.0566632i
$321$	−7.56792	−	13.1080i	−0.422400	−	0.731619i
$322$			24.7479i			1.37914i
$323$	−9.87009	−	15.7006i	−0.549186	−	0.873603i
$324$	−1.00000			−0.0555556
$325$	−0.0588166	−	0.551452i	−0.00326256	−	0.0305891i
$326$	0.999118	+	1.73052i	0.0553360	+	0.0958448i
$327$	−7.43496	−	4.29258i	−0.411154	−	0.237380i
$328$	6.72386	−	3.88203i	0.371263	−	0.214349i
$329$	−6.73911	+	11.6725i	−0.371539	+	0.643525i
$330$	−7.54753	+	4.90967i	−0.415478	+	0.270268i
$331$	33.3848			1.83499			0.917496	−	0.397744i	$-0.130207\pi$
$331$	33.3848			1.83499			0.917496	+	0.397744i	$0.130207\pi$
$332$	−7.15157	−	4.12896i	−0.392493	−	0.226606i
$333$	1.45645	+	0.840881i	0.0798129	+	0.0460800i
$334$	17.9892			0.984327
$335$	5.39037	+	8.28651i	0.294508	+	0.452740i
$336$	1.39938	−	2.42379i	0.0763423	−	0.132229i
$337$	19.2072	−	11.0893i	1.04628	−	0.604072i	0.124677	−	0.992197i	$-0.460211\pi$
$337$	19.2072	−	11.0893i	1.04628	−	0.604072i	0.921607	+	0.388125i	$0.126877\pi$
$338$	11.2477	+	6.49385i	0.611793	+	0.353219i
$339$	0.623455	+	1.07986i	0.0338614	+	0.0586497i
$340$	−4.31253	+	8.47992i	−0.233880	+	0.459888i
$341$	31.7343			1.71851
$342$	−4.35582	+	0.163933i	−0.235536	+	0.00886446i
$343$			17.2598i			0.931944i
$344$	3.73262	+	6.46509i	0.201249	+	0.348574i
$345$	−17.6242	−	8.96292i	−0.948853	−	0.482547i
$346$	7.65871	−	13.2653i	0.411735	−	0.713146i
$347$	−15.7368	+	9.08564i	−0.844795	+	0.487743i	−0.858891	−	0.512158i	$-0.828846\pi$
$347$	−15.7368	+	9.08564i	−0.844795	+	0.487743i	0.0140963	+	0.999901i	$0.495513\pi$
$348$	−1.57270	−	0.907996i	−0.0843053	−	0.0486737i
$349$	−5.54988			−0.297078			−0.148539	−	0.988907i	$-0.547457\pi$
$349$	−5.54988			−0.297078			−0.148539	+	0.988907i	$0.547457\pi$
$350$	5.67213	−	12.7927i	0.303188	−	0.683797i
$351$	−0.0554580	+	0.0960560i	−0.00296013	+	0.00512709i
$352$	3.48719	+	2.01333i	0.185868	+	0.107311i
$353$		−	11.9998i		−	0.638686i	−0.947639	−	0.319343i	$-0.896538\pi$
$353$		−	11.9998i		−	0.638686i	0.947639	−	0.319343i	$-0.103462\pi$
$354$	0.377211			0.0200486
$355$	−1.40276	−	26.3785i	−0.0744506	−	1.40003i
$356$	−5.01501	−	8.68625i	−0.265795	−	0.460370i
$357$	−10.3122	−	5.95375i	−0.545780	−	0.315106i
$358$	−9.43602	+	5.44789i	−0.498709	+	0.287930i
$359$	15.8492	+	27.4515i	0.836487	+	1.44884i	0.892814	+	0.450425i	$0.148728\pi$
$359$	15.8492	+	27.4515i	0.836487	+	1.44884i	−0.0563277	+	0.998412i	$0.517939\pi$
$360$	1.21929	+	1.87439i	0.0642622	+	0.0987889i
$361$	−18.9463	+	1.42812i	−0.997171	+	0.0751642i
$362$		−	18.2521i		−	0.959308i
$363$	4.51547	−	2.60701i	0.237001	−	0.136833i
$364$	−0.155213	−	0.268837i	−0.00813539	−	0.0140909i
$365$	−21.4895	+	1.14277i	−1.12481	+	0.0598153i
$366$	−6.18078	−	10.7054i	−0.323075	−	0.559582i
$367$	3.14212	+	1.81410i	0.164017	+	0.0946954i	0.579762	−	0.814786i	$-0.303146\pi$
$367$	3.14212	+	1.81410i	0.164017	+	0.0946954i	−0.415745	+	0.909481i	$0.636479\pi$
$368$			8.84246i			0.460945i
$369$	−7.76405			−0.404180
$370$	−0.199696	−	3.75523i	−0.0103817	−	0.195225i
$371$	−10.4229	+	18.0529i	−0.541128	+	0.937260i
$372$		−	7.88104i		−	0.408613i
$373$			7.74901i			0.401228i	0.979670	+	0.200614i	$0.0642938\pi$
$373$			7.74901i			0.401228i	−0.979670	+	0.200614i	$0.935706\pi$
$374$	8.56587	−	14.8365i	0.442930	−	0.767178i
$375$	7.05602	+	8.67252i	0.364371	+	0.447847i
$376$	−2.40790	+	4.17060i	−0.124178	+	0.215082i
$377$	−0.174437	+	0.100711i	−0.00898396	+	0.00518689i
$378$	−2.42379	+	1.39938i	−0.124666	+	0.0719762i
$379$	6.68218			0.343241			0.171620	−	0.985163i	$-0.445100\pi$
$379$	6.68218			0.343241			0.171620	+	0.985163i	$0.445100\pi$
$380$	5.61828	+	7.96461i	0.288211	+	0.408576i
$381$	13.7574			0.704815
$382$	14.9406	−	8.62594i	0.764426	−	0.441341i
$383$	17.5053	−	10.1067i	0.894479	−	0.516428i	0.0190744	−	0.999818i	$-0.493928\pi$
$383$	17.5053	−	10.1067i	0.894479	−	0.516428i	0.875405	+	0.483390i	$0.160595\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−11.4232	+	22.4619i	−0.582179	+	1.14476i
$386$	−3.15885	+	5.47129i	−0.160781	+	0.278481i
$387$		−	7.46524i		−	0.379480i
$388$		−	5.22163i		−	0.265088i
$389$	0.559544	−	0.969159i	0.0283700	−	0.0491383i	−0.851492	−	0.524368i	$-0.824302\pi$
$389$	0.559544	−	0.969159i	0.0283700	−	0.0491383i	0.879862	+	0.475230i	$0.157635\pi$
$390$	0.247666	−	0.0131704i	0.0125410	−	0.000666908i
$391$	37.6209			1.90257
$392$		−	0.833029i		−	0.0420743i
$393$	11.1347	+	6.42860i	0.561669	+	0.324280i
$394$	4.39624	+	7.61451i	0.221479	+	0.383613i
$395$	−0.503098	−	9.46064i	−0.0253136	−	0.476016i
$396$	−2.01333	−	3.48719i	−0.101174	−	0.175238i
$397$	8.44367	−	4.87495i	0.423776	−	0.244667i	−0.272916	−	0.962038i	$-0.587988\pi$
$397$	8.44367	−	4.87495i	0.423776	−	0.244667i	0.696691	+	0.717371i	$0.254655\pi$
$398$			4.77209i			0.239203i
$399$	−10.3282	+	6.49277i	−0.517056	+	0.325045i
$400$	2.02666	−	4.57085i	0.101333	−	0.228542i
$401$	−4.85007	−	8.40056i	−0.242201	−	0.419504i	0.719140	−	0.694865i	$-0.244536\pi$
$401$	−4.85007	−	8.40056i	−0.242201	−	0.419504i	−0.961341	+	0.275361i	$0.911203\pi$
$402$	−3.82862	+	2.21046i	−0.190954	+	0.110248i
$403$	−0.757022	−	0.437067i	−0.0377099	−	0.0217718i
$404$	5.86577	+	10.1598i	0.291833	+	0.505469i
$405$	−0.118742	−	2.23291i	−0.00590033	−	0.110954i
$406$	−5.08252			−0.252241
$407$			6.77189i			0.335670i
$408$	−3.68457	−	2.12729i	−0.182413	−	0.105316i
$409$	1.03028	−	1.78451i	0.0509443	−	0.0882381i	−0.839429	−	0.543470i	$-0.817110\pi$
$409$	1.03028	−	1.78451i	0.0509443	−	0.0882381i	0.890373	+	0.455232i	$0.150444\pi$
$410$	9.46663	+	14.5528i	0.467523	+	0.718714i
$411$	−8.15288			−0.402152
$412$	−15.5448	−	8.97482i	−0.765840	−	0.442158i
$413$	0.914282	−	0.527861i	0.0449889	−	0.0259744i
$414$	4.42123	−	7.65779i	0.217291	−	0.376360i
$415$	8.37042	−	16.4591i	0.410888	−	0.807946i
$416$	−0.0554580	−	0.0960560i	−0.00271905	−	0.00470953i
$417$		−	2.28555i		−	0.111924i
$418$	−9.34137	−	14.8595i	−0.456901	−	0.726803i
$419$	17.5492			0.857336			0.428668	−	0.903462i	$-0.358983\pi$
$419$	17.5492			0.857336			0.428668	+	0.903462i	$0.358983\pi$
$420$	5.57828	+	2.83688i	0.272192	+	0.138426i
$421$	−5.86950	−	10.1663i	−0.286062	−	0.495474i	0.686804	−	0.726842i	$-0.259013\pi$
$421$	−5.86950	−	10.1663i	−0.286062	−	0.495474i	−0.972866	+	0.231369i	$0.925680\pi$
$422$	18.5047	+	10.6837i	0.900797	+	0.520075i
$423$	4.17060	−	2.40790i	0.202781	−	0.117076i
$424$	−3.72410	+	6.45034i	−0.180858	+	0.313256i
$425$	−19.4470	−	8.62259i	−0.943318	−	0.418257i
$426$	11.8135			0.572366
$427$	−29.9619	−	17.2985i	−1.44996	−	0.837133i
$428$	−13.1080	−	7.56792i	−0.633600	−	0.365809i
$429$	−0.446621			−0.0215631
$430$	−13.9928	+	9.10230i	−0.674791	+	0.438952i
$431$	−9.77272	+	16.9268i	−0.470735	+	0.815337i	−0.999440	−	0.0334686i	$-0.989345\pi$
$431$	−9.77272	+	16.9268i	−0.470735	+	0.815337i	0.528705	+	0.848806i	$0.322678\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−30.9164	−	17.8496i	−1.48575	−	0.857797i	−0.485881	−	0.874025i	$-0.661501\pi$
$433$	−30.9164	−	17.8496i	−1.48575	−	0.857797i	−0.999868	+	0.0162277i	$0.994834\pi$
$434$	−11.0286	−	19.1020i	−0.529388	−	0.916926i
$435$	1.84073	−	3.61951i	0.0882563	−	0.173542i
$436$	−8.58516			−0.411154
$437$	18.0027	−	34.0807i	0.861185	−	1.63030i
$438$		−	9.62397i		−	0.459851i
$439$	−19.4194	−	33.6354i	−0.926838	−	1.60533i	−0.788579	−	0.614934i	$-0.789183\pi$
$439$	−19.4194	−	33.6354i	−0.926838	−	1.60533i	−0.138259	−	0.990396i	$-0.544151\pi$
$440$	−4.08152	+	8.02567i	−0.194579	+	0.382609i
$441$	−0.416515	+	0.721424i	−0.0198340	+	0.0343535i
$442$	−0.408677	+	0.235950i	−0.0194388	+	0.0112230i
$443$	−25.1014	−	14.4923i	−1.19260	−	0.688549i	−0.233707	−	0.972307i	$-0.575086\pi$
$443$	−25.1014	−	14.4923i	−1.19260	−	0.688549i	−0.958896	+	0.283758i	$0.908419\pi$
$444$	1.68176			0.0798129
$445$	18.8001	−	12.2295i	0.891212	−	0.579734i
$446$	0.444327	−	0.769596i	0.0210395	−	0.0364414i
$447$	−16.2200	−	9.36462i	−0.767180	−	0.442931i
$448$		−	2.79875i		−	0.132229i
$449$	−11.5314			−0.544201			−0.272100	−	0.962269i	$-0.587718\pi$
$449$	−11.5314			−0.544201			−0.272100	+	0.962269i	$0.587718\pi$
$450$	−4.04057	+	2.94514i	−0.190474	+	0.138835i
$451$	−15.6316	−	27.0747i	−0.736064	−	1.27490i
$452$	1.07986	+	0.623455i	0.0507921	+	0.0293248i
$453$	−13.9771	+	8.06970i	−0.656703	+	0.379147i
$454$	0.113839	+	0.197176i	0.00534275	+	0.00925392i
$455$	0.581860	−	0.378500i	0.0272780	−	0.0177444i
$456$	−3.69028	+	2.31988i	−0.172813	+	0.108638i
$457$			22.1107i			1.03430i	0.855896	+	0.517148i	$0.173006\pi$
$457$			22.1107i			1.03430i	−0.855896	+	0.517148i	$0.826994\pi$
$458$	14.0630	−	8.11926i	0.657119	−	0.379388i
$459$	2.12729	+	3.68457i	0.0992932	+	0.171981i
$460$	−19.7444	+	1.04997i	−0.920589	+	0.0489551i
$461$	−9.08841	−	15.7416i	−0.423289	−	0.733159i	0.572970	−	0.819577i	$-0.305791\pi$
$461$	−9.08841	−	15.7416i	−0.423289	−	0.733159i	−0.996259	+	0.0864179i	$0.972458\pi$
$462$	−9.75980	−	5.63482i	−0.454067	−	0.262156i
$463$		−	34.9548i		−	1.62449i	−0.583318	−	0.812244i	$-0.698246\pi$
$463$		−	34.9548i		−	1.62449i	0.583318	−	0.812244i	$-0.301754\pi$
$464$	−1.81599			−0.0843053
$465$	17.5977	−	0.935810i	0.816073	−	0.0433972i
$466$	−1.66979	+	2.89217i	−0.0773517	+	0.133977i
$467$			13.0120i			0.602125i	0.953604	+	0.301063i	$0.0973414\pi$
$467$			13.0120i			0.602125i	−0.953604	+	0.301063i	$0.902659\pi$
$468$			0.110916i			0.00512709i
$469$	−6.18652	+	10.7154i	−0.285667	+	0.494790i
$470$	−9.59850	−	4.88140i	−0.442746	−	0.225162i
$471$	3.88918	−	6.73626i	0.179204	−	0.310390i
$472$	0.326675	−	0.188606i	0.0150364	−	0.00868128i
$473$	26.0327	−	15.0300i	1.19699	−	0.691081i
$474$	4.23690			0.194607
$475$	−17.1172	+	13.4909i	−0.785389	+	0.619003i
$476$	−11.9075			−0.545780
$477$	6.45034	−	3.72410i	0.295341	−	0.170515i
$478$	−24.5444	+	14.1707i	−1.12263	+	0.648153i
$479$	−15.1415	+	26.2259i	−0.691833	+	1.19829i	0.279403	+	0.960174i	$0.409863\pi$
$479$	−15.1415	+	26.2259i	−0.691833	+	1.19829i	−0.971237	+	0.238117i	$0.923470\pi$
$480$	1.99313	+	1.01362i	0.0909735	+	0.0462653i
$481$	0.0932671	−	0.161543i	0.00425261	−	0.00736574i
$482$		−	14.2591i		−	0.649485i
$483$		−	24.7479i		−	1.12607i
$484$	2.60701	−	4.51547i	0.118500	−	0.205249i
$485$	11.6594	−	0.620027i	0.529428	−	0.0281540i
$486$	1.00000			0.0453609
$487$			35.5166i			1.60941i	0.593674	+	0.804706i	$0.297677\pi$
$487$			35.5166i			1.60941i	−0.593674	+	0.804706i	$0.702323\pi$
$488$	−10.7054	−	6.18078i	−0.484612	−	0.279791i
$489$	−0.999118	−	1.73052i	−0.0451817	−	0.0782570i
$490$	1.86008	−	0.0989155i	0.0840299	−	0.00446855i
$491$	5.36057	+	9.28479i	0.241919	+	0.419017i	0.961261	−	0.275640i	$-0.0888897\pi$
$491$	5.36057	+	9.28479i	0.241919	+	0.419017i	−0.719342	+	0.694656i	$0.755556\pi$
$492$	−6.72386	+	3.88203i	−0.303135	+	0.175015i
$493$			7.72627i			0.347974i
$494$	0.0181827	+	0.483129i	0.000818080	+	0.0217370i
$495$	7.54753	−	4.90967i	0.339236	−	0.220673i
$496$	−3.94052	−	6.82518i	−0.176935	−	0.306460i
$497$	28.6335	−	16.5315i	1.28439	−	0.741541i
$498$	7.15157	+	4.12896i	0.320470	+	0.185023i
$499$	12.0259	+	20.8295i	0.538353	+	0.932455i	0.998993	+	0.0448675i	$0.0142866\pi$
$499$	12.0259	+	20.8295i	0.538353	+	0.932455i	−0.460640	+	0.887587i	$0.652380\pi$
$500$	10.4470	+	3.98261i	0.467202	+	0.178108i
$501$	−17.9892			−0.803700
$502$			24.2873i			1.08400i
$503$	34.4057	+	19.8642i	1.53408	+	0.885699i	0.999168	+	0.0407894i	$0.0129873\pi$
$503$	34.4057	+	19.8642i	1.53408	+	0.885699i	0.534909	+	0.844910i	$0.320346\pi$
$504$	−1.39938	+	2.42379i	−0.0623332	+	0.107964i
$505$	−21.9895	+	14.3041i	−0.978518	+	0.636526i
$506$	35.6056			1.58286
$507$	−11.2477	−	6.49385i	−0.499527	−	0.288402i
$508$	11.9143	−	6.87872i	0.528611	−	0.305194i
$509$	−2.51441	+	4.35509i	−0.111449	+	0.193036i	−0.916355	−	0.400367i	$-0.868883\pi$
$509$	−2.51441	+	4.35509i	−0.111449	+	0.193036i	0.804905	+	0.593403i	$0.202216\pi$
$510$	4.31253	−	8.47992i	0.190962	−	0.375497i
$511$	−13.4676	−	23.3265i	−0.595770	−	1.03190i
$512$		−	1.00000i		−	0.0441942i
$513$	4.35582	−	0.163933i	0.192314	−	0.00723780i
$514$	−2.38173			−0.105053
$515$	18.1942	−	35.7760i	0.801731	−	1.57648i
$516$	−3.73262	−	6.46509i	−0.164320	−	0.284610i
$517$	16.7936	+	9.69579i	0.738581	+	0.426420i
$518$	4.07624	−	2.35342i	0.179100	−	0.103403i
$519$	−7.65871	+	13.2653i	−0.336180	+	0.582281i
$520$	0.207900	−	0.135239i	0.00911700	−	0.00593061i
$521$	−43.2225			−1.89361			−0.946806	−	0.321806i	$-0.895710\pi$
$521$	−43.2225			−1.89361			−0.946806	+	0.321806i	$0.895710\pi$
$522$	1.57270	+	0.907996i	0.0688350	+	0.0397419i
$523$	−0.0430629	−	0.0248624i	−0.00188301	−	0.00108716i	0.499058	−	0.866568i	$-0.333679\pi$
$523$	−0.0430629	−	0.0248624i	−0.00188301	−	0.00108716i	−0.500941	+	0.865481i	$0.667013\pi$
$524$	12.8572			0.561669
$525$	−5.67213	+	12.7927i	−0.247552	+	0.558318i
$526$	3.99944	−	6.92724i	0.174384	−	0.302042i
$527$	−29.0382	+	16.7652i	−1.26493	+	0.730305i
$528$	−3.48719	−	2.01333i	−0.151761	−	0.0876190i
$529$	27.5945	+	47.7951i	1.19976	+	2.07805i
$530$	−14.8452	−	7.54967i	−0.644836	−	0.327937i
$531$	−0.377211			−0.0163696
$532$	−5.69809	+	10.7870i	−0.247044	+	0.467676i
$533$			0.861157i			0.0373008i
$534$	5.01501	+	8.68625i	0.217021	+	0.375891i
$535$	15.3420	−	30.1677i	0.663294	−	1.30426i
$536$	−2.21046	+	3.82862i	−0.0954772	+	0.165371i
$537$	9.43602	−	5.44789i	0.407195	−	0.235094i
$538$	−9.21576	−	5.32072i	−0.397320	−	0.229393i
$539$	−3.35433			−0.144481
$540$	−1.21929	−	1.87439i	−0.0524699	−	0.0806608i
$541$	3.67092	−	6.35822i	0.157825	−	0.273361i	−0.776259	−	0.630414i	$-0.782885\pi$
$541$	3.67092	−	6.35822i	0.157825	−	0.273361i	0.934084	+	0.357053i	$0.116218\pi$
$542$	−13.9888	−	8.07644i	−0.600871	−	0.346913i
$543$			18.2521i			0.783271i
$544$	−4.25457			−0.182413
$545$	−1.01942	−	19.1699i	−0.0436671	−	0.821148i
$546$	0.155213	+	0.268837i	0.00664252	+	0.0115052i
$547$	20.7675	+	11.9901i	0.887954	+	0.512660i	0.873273	−	0.487232i	$-0.161993\pi$
$547$	20.7675	+	11.9901i	0.887954	+	0.512660i	0.0146810	+	0.999892i	$0.495327\pi$
$548$	−7.06060	+	4.07644i	−0.301614	+	0.174137i
$549$	6.18078	+	10.7054i	0.263789	+	0.456896i
$550$	−18.4053	−	8.16069i	−0.784803	−	0.347973i
$551$	6.99922	+	3.69725i	0.298177	+	0.157508i
$552$		−	8.84246i		−	0.376360i
$553$	10.2694	−	5.92903i	0.436698	−	0.252128i
$554$	−10.8475	−	18.7884i	−0.460865	−	0.798242i
$555$	0.199696	+	3.75523i	0.00847661	+	0.159401i
$556$	−1.14277	−	1.97934i	−0.0484644	−	0.0839429i
$557$	21.6447	+	12.4966i	0.917115	+	0.529497i	0.882714	−	0.469911i	$-0.155714\pi$
$557$	21.6447	+	12.4966i	0.917115	+	0.529497i	0.0344016	+	0.999408i	$0.489047\pi$
$558$			7.88104i			0.333631i
$559$	−0.828015			−0.0350213
$560$	6.24938	−	0.332330i	0.264084	−	0.0140435i
$561$	−8.56587	+	14.8365i	−0.361651	+	0.626398i
$562$		−	1.19029i		−	0.0502092i
$563$		−	23.2863i		−	0.981403i	−0.871328	−	0.490701i	$-0.836741\pi$
$563$		−	23.2863i		−	0.981403i	0.871328	−	0.490701i	$-0.163259\pi$
$564$	2.40790	−	4.17060i	0.101391	−	0.175614i
$565$	−1.26390	+	2.48525i	−0.0531725	+	0.104555i
$566$	0.151267	−	0.262002i	0.00635822	−	0.0110128i
$567$	2.42379	−	1.39938i	0.101790	−	0.0587683i
$568$	10.2308	−	5.90675i	0.429274	−	0.247842i
$569$	16.8454			0.706196			0.353098	−	0.935586i	$-0.385128\pi$
$569$	16.8454			0.706196			0.353098	+	0.935586i	$0.385128\pi$
$570$	−5.61828	−	7.96461i	−0.235324	−	0.333601i
$571$	−16.1395			−0.675418			−0.337709	−	0.941250i	$-0.609652\pi$
$571$	−16.1395			−0.675418			−0.337709	+	0.941250i	$0.609652\pi$
$572$	−0.386785	+	0.223311i	−0.0161723	+	0.00933709i
$573$	−14.9406	+	8.62594i	−0.624151	+	0.360354i
$574$	−10.8648	+	18.8184i	−0.453490	+	0.785467i
$575$	−4.68898	−	43.9629i	−0.195544	−	1.83338i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$		−	3.05772i		−	0.127295i	−0.997972	−	0.0636473i	$-0.979727\pi$
$577$		−	3.05772i		−	0.127295i	0.997972	−	0.0636473i	$-0.0202733\pi$
$578$			1.10139i			0.0458117i
$579$	3.15885	−	5.47129i	0.131277	−	0.227379i
$580$	−0.215634	−	4.05495i	−0.00895373	−	0.168373i
$581$	23.1119			0.958843
$582$			5.22163i			0.216444i
$583$	25.9733	+	14.9957i	1.07571	+	0.621059i
$584$	−4.81199	−	8.33460i	−0.199121	−	0.344888i
$585$	−0.247666	+	0.0131704i	−0.0102397	+	0.000544528i
$586$	−12.6039	−	21.8306i	−0.520662	−	0.901813i
$587$	−26.8130	+	15.4805i	−1.10669	+	0.638949i	−0.937971	−	0.346714i	$-0.887297\pi$
$587$	−26.8130	+	15.4805i	−1.10669	+	0.638949i	−0.168722	+	0.985664i	$0.553964\pi$
$588$			0.833029i			0.0343535i
$589$	1.29196	+	34.3284i	0.0532343	+	1.41448i
$590$	0.459930	+	0.707041i	0.0189350	+	0.0291084i
$591$	−4.39624	−	7.61451i	−0.180837	−	0.313219i
$592$	1.45645	−	0.840881i	0.0598597	−	0.0345600i
$593$	21.9486	+	12.6720i	0.901322	+	0.520379i	0.877629	−	0.479341i	$-0.159124\pi$
$593$	21.9486	+	12.6720i	0.901322	+	0.520379i	0.0236932	+	0.999719i	$0.492458\pi$
$594$	2.01333	+	3.48719i	0.0826080	+	0.143081i
$595$	−1.41392	−	26.5884i	−0.0579651	−	1.09002i
$596$	−18.7292			−0.767180
$597$		−	4.77209i		−	0.195309i
$598$	−0.849371	−	0.490385i	−0.0347334	−	0.0200533i
$599$	−11.1523	+	19.3163i	−0.455670	+	0.789243i	−0.998726	−	0.0504529i	$-0.983934\pi$
$599$	−11.1523	+	19.3163i	−0.455670	+	0.789243i	0.543057	+	0.839696i	$0.317267\pi$
$600$	−2.02666	+	4.57085i	−0.0827382	+	0.186604i
$601$	27.6758			1.12892			0.564460	−	0.825460i	$-0.309084\pi$
$601$	27.6758			1.12892			0.564460	+	0.825460i	$0.309084\pi$
$602$	−18.0942	−	10.4467i	−0.737465	−	0.425775i
$603$	3.82862	−	2.21046i	0.155914	−	0.0900167i
$604$	−8.06970	+	13.9771i	−0.328351	+	0.568721i
$605$	10.3922	+	5.28505i	0.422504	+	0.214868i
$606$	−5.86577	−	10.1598i	−0.238281	−	0.412714i
$607$		−	16.7201i		−	0.678650i	−0.940669	−	0.339325i	$-0.889801\pi$
$607$		−	16.7201i		−	0.678650i	0.940669	−	0.339325i	$-0.110199\pi$
$608$	−2.03594	+	3.85421i	−0.0825682	+	0.156309i
$609$	5.08252			0.205954
$610$	12.5300	−	24.6382i	0.507323	−	0.997572i
$611$	−0.267074	−	0.462586i	−0.0108047	−	0.0187142i
$612$	3.68457	+	2.12729i	0.148940	+	0.0859904i
$613$	25.3849	−	14.6560i	1.02529	−	0.591950i	0.109656	−	0.993970i	$-0.465025\pi$
$613$	25.3849	−	14.6560i	1.02529	−	0.591950i	0.915631	+	0.402020i	$0.131692\pi$
$614$	−11.3911	+	19.7299i	−0.459707	+	0.796235i
$615$	−9.46663	−	14.5528i	−0.381731	−	0.586827i
$616$	−11.2696			−0.454067
$617$	−32.4820	−	18.7535i	−1.30767	−	0.754986i	−0.325967	−	0.945381i	$-0.605690\pi$
$617$	−32.4820	−	18.7535i	−1.30767	−	0.754986i	−0.981708	+	0.190395i	$0.939023\pi$
$618$	15.5448	+	8.97482i	0.625305	+	0.361020i
$619$	−39.0394			−1.56912			−0.784562	−	0.620050i	$-0.787112\pi$
$619$	−39.0394			−1.56912			−0.784562	+	0.620050i	$0.787112\pi$
$620$	14.7721	−	9.60928i	0.593263	−	0.385918i
$621$	−4.42123	+	7.65779i	−0.177418	+	0.307297i
$622$	10.4575	−	6.03762i	0.419306	−	0.242087i
$623$	24.3107	+	14.0358i	0.973987	+	0.562331i
$624$	0.0554580	+	0.0960560i	0.00222010	+	0.00384532i
$625$	−7.65234	+	23.8000i	−0.306093	+	0.952001i
$626$	10.6499			0.425655
$627$	9.34137	+	14.8595i	0.373058	+	0.593432i
$628$		−	7.77836i		−	0.310390i
$629$	−3.57759	−	6.19657i	−0.142648	−	0.247073i
$630$	−5.57828	−	2.83688i	−0.222244	−	0.113024i
$631$	13.0406	−	22.5870i	0.519139	−	0.899174i	−0.480614	−	0.876932i	$-0.659586\pi$
$631$	13.0406	−	22.5870i	0.519139	−	0.899174i	0.999753	−	0.0222421i	$-0.00708045\pi$
$632$	3.66927	−	2.11845i	0.145956	−	0.0842675i
$633$	−18.5047	−	10.6837i	−0.735497	−	0.424640i
$634$	−16.5300			−0.656489
$635$	16.7743	+	25.7868i	0.665668	+	1.02332i
$636$	3.72410	−	6.45034i	0.147670	−	0.255772i
$637$	0.0800175	+	0.0461981i	0.00317041	+	0.00183044i
$638$			7.31239i			0.289500i
$639$	−11.8135			−0.467335
$640$	2.23291	−	0.118742i	0.0882636	−	0.00469369i
$641$	1.56243	+	2.70621i	0.0617122	+	0.106889i	0.895231	−	0.445603i	$-0.147011\pi$
$641$	1.56243	+	2.70621i	0.0617122	+	0.106889i	−0.833519	+	0.552491i	$0.813677\pi$
$642$	13.1080	+	7.56792i	0.517333	+	0.298682i
$643$	17.9701	−	10.3750i	0.708671	−	0.409151i	−0.101898	−	0.994795i	$-0.532491\pi$
$643$	17.9701	−	10.3750i	0.708671	−	0.409151i	0.810569	+	0.585644i	$0.199158\pi$
$644$	−12.3739	−	21.4323i	−0.487601	−	0.844550i
$645$	13.9928	−	9.10230i	0.550965	−	0.358403i
$646$	16.3980	+	8.66205i	0.645172	+	0.340804i
$647$			16.4405i			0.646344i	0.946340	+	0.323172i	$0.104749\pi$
$647$			16.4405i			0.646344i	−0.946340	+	0.323172i	$0.895251\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−0.759452	−	1.31541i	−0.0298111	−	0.0516343i
$650$	0.326663	+	0.448163i	0.0128128	+	0.0175784i
$651$	11.0286	+	19.1020i	0.432243	+	0.748667i
$652$	−1.73052	−	0.999118i	−0.0677725	−	0.0391285i
$653$			6.77814i			0.265249i	0.991166	+	0.132625i	$0.0423405\pi$
$653$			6.77814i			0.265249i	−0.991166	+	0.132625i	$0.957660\pi$
$654$	8.58516			0.335706
$655$	1.52669	+	28.7090i	0.0596526	+	1.12175i
$656$	−3.88203	+	6.72386i	−0.151568	+	0.262523i
$657$			9.62397i			0.375467i
$658$		−	13.4782i		−	0.525436i
$659$	12.0863	−	20.9341i	0.470817	−	0.815478i	−0.528626	−	0.848855i	$-0.677293\pi$
$659$	12.0863	−	20.9341i	0.470817	−	0.815478i	0.999443	+	0.0333765i	$0.0106260\pi$
$660$	4.08152	−	8.02567i	0.158873	−	0.312399i
$661$	−13.5085	+	23.3974i	−0.525420	+	0.910055i	0.474141	+	0.880449i	$0.342759\pi$
$661$	−13.5085	+	23.3974i	−0.525420	+	0.910055i	−0.999562	+	0.0296059i	$0.990575\pi$
$662$	−28.9121	+	16.6924i	−1.12370	+	0.648768i
$663$	0.408677	−	0.235950i	0.0158717	−	0.00916354i
$664$	8.25792			0.320470
$665$	−24.7630	−	11.4425i	−0.960269	−	0.443720i
$666$	−1.68176			−0.0651670
$667$	−13.9065	+	8.02892i	−0.538461	+	0.310881i
$668$	−15.5791	+	8.99462i	−0.602775	+	0.348012i
$669$	−0.444327	+	0.769596i	−0.0171787	+	0.0297543i
$670$	−8.81145	−	4.48114i	−0.340416	−	0.173121i
$671$	−24.8879	+	43.1071i	−0.960788	+	1.66413i
$672$			2.79875i			0.107964i
$673$			21.9407i			0.845751i	0.906188	+	0.422875i	$0.138979\pi$
$673$			21.9407i			0.845751i	−0.906188	+	0.422875i	$0.861021\pi$
$674$	−11.0893	+	19.2072i	−0.427144	+	0.739834i
$675$	4.04057	−	2.94514i	0.155521	−	0.113358i
$676$	−12.9877			−0.499527
$677$		−	18.8185i		−	0.723254i	−0.932323	−	0.361627i	$-0.882221\pi$
$677$		−	18.8185i		−	0.723254i	0.932323	−	0.361627i	$-0.117779\pi$
$678$	−1.07986	−	0.623455i	−0.0414716	−	0.0239436i
$679$	7.30703	+	12.6562i	0.280418	+	0.485699i
$680$	−0.505196	−	9.50009i	−0.0193734	−	0.364312i
$681$	−0.113839	−	0.197176i	−0.00436234	−	0.00755579i
$682$	−27.4827	+	15.8672i	−1.05237	+	0.607585i
$683$		−	19.3651i		−	0.740986i	−0.928835	−	0.370493i	$-0.879189\pi$
$683$		−	19.3651i		−	0.740986i	0.928835	−	0.370493i	$-0.120811\pi$
$684$	3.69028	−	2.31988i	0.141101	−	0.0887027i
$685$	−9.94073	−	15.2817i	−0.379816	−	0.583882i
$686$	−8.62992	−	14.9475i	−0.329492	−	0.570697i
$687$	−14.0630	+	8.11926i	−0.536536	+	0.309769i
$688$	−6.46509	−	3.73262i	−0.246479	−	0.142305i
$689$	−0.413062	−	0.715445i	−0.0157364	−	0.0272563i
$690$	19.7444	−	1.04997i	0.751658	−	0.0399717i
$691$	0.642365			0.0244367			0.0122184	−	0.999925i	$-0.496111\pi$
$691$	0.642365			0.0244367			0.0122184	+	0.999925i	$0.496111\pi$
$692$			15.3174i			0.582281i
$693$	9.75980	+	5.63482i	0.370744	+	0.214049i
$694$	9.08564	−	15.7368i	0.344886	−	0.597360i
$695$	4.28401	−	2.78675i	0.162502	−	0.105707i
$696$	1.81599			0.0688350
$697$	28.6072	+	16.5164i	1.08357	+	0.625602i
$698$	4.80634	−	2.77494i	0.181923	−	0.105033i
$699$	1.66979	−	2.89217i	0.0631574	−	0.109392i
$700$	1.48413	+	13.9149i	0.0560947	+	0.525932i
$701$	−22.4846	−	38.9445i	−0.849233	−	1.47091i	−0.881894	−	0.471448i	$-0.843732\pi$
$701$	−22.4846	−	38.9445i	−0.849233	−	1.47091i	0.0326612	−	0.999466i	$-0.489602\pi$
$702$		−	0.110916i		−	0.00418625i
$703$	−7.32544	+	0.275695i	−0.276284	+	0.0103981i
$704$	−4.02666			−0.151761
$705$	9.59850	+	4.88140i	0.361500	+	0.183844i
$706$	5.99991	+	10.3922i	0.225810	+	0.391114i
$707$	−28.4348	−	16.4169i	−1.06940	−	0.617419i
$708$	−0.326675	+	0.188606i	−0.0122772	+	0.00708824i
$709$	4.09461	−	7.09207i	0.153776	−	0.266348i	−0.778836	−	0.627227i	$-0.784190\pi$
$709$	4.09461	−	7.09207i	0.153776	−	0.266348i	0.932613	+	0.360879i	$0.117523\pi$
$710$	14.4041	+	22.1431i	0.540575	+	0.831015i
$711$	−4.23690			−0.158896
$712$	8.68625	+	5.01501i	0.325531	+	0.187945i
$713$	−60.3514	−	34.8439i	−2.26018	−	1.30491i
$714$	11.9075			0.445627
$715$	−0.544561	−	0.837142i	−0.0203654	−	0.0313073i
$716$	5.44789	−	9.43602i	0.203597	−	0.352641i
$717$	24.5444	−	14.1707i	0.916626	−	0.529214i
$718$	−27.4515	−	15.8492i	−1.02448	−	0.591485i
$719$	25.2772	+	43.7813i	0.942679	+	1.63277i	0.760334	+	0.649533i	$0.225035\pi$
$719$	25.2772	+	43.7813i	0.942679	+	1.63277i	0.182345	+	0.983235i	$0.441631\pi$
$720$	−1.99313	−	1.01362i	−0.0742796	−	0.0377755i
$721$	50.2367			1.87091
$722$	15.6939	−	10.7099i	0.584066	−	0.398582i
$723$			14.2591i			0.530302i
$724$	9.12604	+	15.8068i	0.339167	+	0.587454i
$725$	9.02875	−	0.962986i	0.335319	−	0.0357644i
$726$	−2.60701	+	4.51547i	−0.0967552	+	0.167585i
$727$	−2.96717	+	1.71310i	−0.110046	+	0.0635353i	−0.554013	−	0.832508i	$-0.686904\pi$
$727$	−2.96717	+	1.71310i	−0.110046	+	0.0635353i	0.443967	+	0.896043i	$0.353571\pi$
$728$	0.268837	+	0.155213i	0.00996377	+	0.00575259i
$729$	−1.00000			−0.0370370
$730$	18.0391	−	11.7344i	0.667656	−	0.434310i
$731$	−15.8807	+	27.5062i	−0.587369	+	1.01735i
$732$	10.7054	+	6.18078i	0.395684	+	0.228448i
$733$			0.420632i			0.0155364i	0.999970	+	0.00776819i	$0.00247272\pi$
$733$			0.420632i			0.0155364i	−0.999970	+	0.00776819i	$0.997527\pi$
$734$	−3.62820			−0.133919
$735$	−1.86008	+	0.0989155i	−0.0686101	+	0.00364855i
$736$	−4.42123	−	7.65779i	−0.162969	−	0.282270i
$737$	15.4166	+	8.90076i	0.567877	+	0.327864i
$738$	6.72386	−	3.88203i	0.247509	−	0.142899i
$739$	6.70752	+	11.6178i	0.246740	+	0.427366i	0.962619	−	0.270858i	$-0.0873073\pi$
$739$	6.70752	+	11.6178i	0.246740	+	0.427366i	−0.715879	+	0.698224i	$0.753974\pi$
$740$	2.05056	+	3.15228i	0.0753799	+	0.115880i
$741$	−0.0181827	−	0.483129i	−0.000667959	−	0.0177482i
$742$		−	20.8457i		−	0.765270i
$743$	−29.4635	+	17.0108i	−1.08091	+	0.624064i	−0.931142	−	0.364657i	$-0.881186\pi$
$743$	−29.4635	+	17.0108i	−1.08091	+	0.624064i	−0.149769	+	0.988721i	$0.547853\pi$
$744$	3.94052	+	6.82518i	0.144467	+	0.250223i
$745$	−2.22395	−	41.8208i	−0.0814791	−	1.53219i
$746$	−3.87450	−	6.71084i	−0.141856	−	0.245701i
$747$	−7.15157	−	4.12896i	−0.261662	−	0.151071i
$748$			17.1317i			0.626398i
$749$	42.3615			1.54786
$750$	−10.4470	−	3.98261i	−0.381469	−	0.145424i
$751$	−11.0748	+	19.1820i	−0.404123	+	0.699962i	−0.994219	−	0.107371i	$-0.965757\pi$
$751$	−11.0748	+	19.1820i	−0.404123	+	0.699962i	0.590096	+	0.807333i	$0.299090\pi$
$752$		−	4.81579i		−	0.175614i
$753$		−	24.2873i		−	0.885079i
$754$	0.100711	−	0.174437i	0.00366769	−	0.00635262i
$755$	−32.1679	−	16.3593i	−1.17071	−	0.595374i
$756$	1.39938	−	2.42379i	0.0508949	−	0.0881525i
$757$	5.58767	−	3.22604i	0.203087	−	0.117252i	−0.395008	−	0.918678i	$-0.629258\pi$
$757$	5.58767	−	3.22604i	0.203087	−	0.117252i	0.598095	+	0.801425i	$0.295925\pi$
$758$	−5.78694	+	3.34109i	−0.210191	+	0.121354i
$759$	−35.6056			−1.29240
$760$	−8.84787	−	4.08842i	−0.320946	−	0.148302i
$761$	25.4438			0.922338			0.461169	−	0.887312i	$-0.347430\pi$
$761$	25.4438			0.922338			0.461169	+	0.887312i	$0.347430\pi$
$762$	−11.9143	+	6.87872i	−0.431609	+	0.249190i
$763$	20.8086	−	12.0139i	0.753323	−	0.434931i
$764$	−8.62594	+	14.9406i	−0.312075	+	0.540531i
$765$	−4.31253	+	8.47992i	−0.155920	+	0.306592i
$766$	−10.1067	+	17.5053i	−0.365170	+	0.632492i
$767$			0.0418388i			0.00151071i
$768$			1.00000i			0.0360844i
$769$	22.8321	−	39.5464i	0.823348	−	1.42608i	−0.0798275	−	0.996809i	$-0.525437\pi$
$769$	22.8321	−	39.5464i	0.823348	−	1.42608i	0.903175	−	0.429272i	$-0.141230\pi$
$770$	−1.33818	−	25.1641i	−0.0482246	−	0.906853i
$771$	2.38173			0.0857758
$772$		−	6.31770i		−	0.227379i
$773$	23.3288	+	13.4689i	0.839080	+	0.484443i	0.856951	−	0.515397i	$-0.172356\pi$
$773$	23.3288	+	13.4689i	0.839080	+	0.484443i	−0.0178717	+	0.999840i	$0.505689\pi$
$774$	3.73262	+	6.46509i	0.134166	+	0.232383i
$775$	23.2108	+	31.8439i	0.833755	+	1.14387i
$776$	2.61082	+	4.52207i	0.0937228	+	0.162333i
$777$	−4.07624	+	2.35342i	−0.146234	+	0.0844285i
$778$			1.11909i			0.0401213i
$779$	28.6515	−	18.0116i	1.02655	−	0.645334i
$780$	−0.207900	+	0.135239i	−0.00744400	+	0.00484232i
$781$	−23.7845	−	41.1959i	−0.851076	−	1.47411i
$782$	−32.5806	+	18.8104i	−1.16508	+	0.672660i
$783$	−1.57270	−	0.907996i	−0.0562036	−	0.0324491i
$784$	0.416515	+	0.721424i	0.0148755	+	0.0257652i
$785$	17.3684	−	0.923617i	0.619905	−	0.0329653i
$786$	−12.8572			−0.458601
$787$			13.7880i			0.491488i	0.969335	+	0.245744i	$0.0790322\pi$
$787$			13.7880i			0.491488i	−0.969335	+	0.245744i	$0.920968\pi$
$788$	−7.61451	−	4.39624i	−0.271256	−	0.156610i
$789$	−3.99944	+	6.92724i	−0.142384	+	0.246616i
$790$	5.16602	+	7.94160i	0.183799	+	0.282550i
$791$	−3.48979			−0.124083
$792$	3.48719	+	2.01333i	0.123912	+	0.0715406i
$793$	1.18740	−	0.685547i	0.0421659	−	0.0243445i
$794$	−4.87495	+	8.44367i	−0.173006	+	0.299655i
$795$	14.8452	+	7.54967i	0.526507	+	0.267759i
$796$	−2.38605	−	4.13275i	−0.0845711	−	0.146482i
$797$			18.6991i			0.662354i	0.943569	+	0.331177i	$0.107446\pi$
$797$			18.6991i			0.662354i	−0.943569	+	0.331177i	$0.892554\pi$
$798$	5.69809	−	10.7870i	0.201710	−	0.381856i
$799$	−20.4891			−0.724853
$800$	0.530281	+	4.97180i	0.0187483	+	0.175780i
$801$	−5.01501	−	8.68625i	−0.177197	−	0.306913i
$802$	8.40056	+	4.85007i	0.296634	+	0.171262i
$803$	−33.5607	+	19.3763i	−1.18433	+	0.683773i
$804$	2.21046	−	3.82862i	0.0779568	−	0.135025i
$805$	46.3871	−	30.1748i	1.63493	−	1.06352i
$806$	0.874133			0.0307900
$807$	9.21576	+	5.32072i	0.324410	+	0.187298i
$808$	−10.1598	−	5.86577i	−0.357421	−	0.206357i
$809$	1.32846			0.0467063			0.0233531	−	0.999727i	$-0.492566\pi$
$809$	1.32846			0.0467063			0.0233531	+	0.999727i	$0.492566\pi$
$810$	1.21929	+	1.87439i	0.0428415	+	0.0658593i
$811$	13.6087	−	23.5710i	0.477866	−	0.827688i	−0.521812	−	0.853060i	$-0.674744\pi$
$811$	13.6087	−	23.5710i	0.477866	−	0.827688i	0.999678	+	0.0253723i	$0.00807712\pi$
$812$	4.40159	−	2.54126i	0.154466	−	0.0891807i
$813$	13.9888	+	8.07644i	0.490609	+	0.283253i
$814$	−3.38595	−	5.86463i	−0.118677	−	0.205555i
$815$	2.02546	−	3.98275i	0.0709487	−	0.139510i
$816$	4.25457			0.148940
$817$	17.3184	+	27.5488i	0.605896	+	0.963812i
$818$			2.06057i			0.0720461i
$819$	−0.155213	−	0.268837i	−0.00542359	−	0.00939393i
$820$	−15.4748	−	7.86982i	−0.540402	−	0.274826i
$821$	8.87124	−	15.3654i	0.309608	−	0.536258i	−0.668668	−	0.743561i	$-0.733135\pi$
$821$	8.87124	−	15.3654i	0.309608	−	0.536258i	0.978277	+	0.207303i	$0.0664687\pi$
$822$	7.06060	−	4.07644i	0.246267	−	0.142182i
$823$	0.288501	+	0.166566i	0.0100565	+	0.00580614i	0.505020	−	0.863108i	$-0.331485\pi$
$823$	0.288501	+	0.166566i	0.0100565	+	0.00580614i	−0.494963	+	0.868914i	$0.664819\pi$
$824$	17.9496			0.625305
$825$	18.4053	+	8.16069i	0.640789	+	0.284119i
$826$	−0.527861	+	0.914282i	−0.0183666	+	0.0318120i
$827$	−45.8579	−	26.4760i	−1.59463	−	0.920662i	−0.992497	−	0.122270i	$-0.960983\pi$
$827$	−45.8579	−	26.4760i	−1.59463	−	0.920662i	−0.602137	−	0.798393i	$-0.705684\pi$
$828$			8.84246i			0.307297i
$829$	15.5012			0.538380			0.269190	−	0.963087i	$-0.413244\pi$
$829$	15.5012			0.538380			0.269190	+	0.963087i	$0.413244\pi$
$830$	0.980562	+	18.4392i	0.0340358	+	0.640035i
$831$	10.8475	+	18.7884i	0.376295	+	0.651762i
$832$	0.0960560	+	0.0554580i	0.00333014	+	0.00192266i
$833$	3.06935	−	1.77209i	0.106347	−	0.0613993i
$834$	1.14277	+	1.97934i	0.0395711	+	0.0685391i
$835$	−21.9341	−	33.7188i	−0.759060	−	1.16689i
$836$	15.5196	+	8.19804i	0.536757	+	0.283535i
$837$		−	7.88104i		−	0.272409i
$838$	−15.1981	+	8.77461i	−0.525009	+	0.303114i
$839$	1.03450	+	1.79181i	0.0357150	+	0.0618603i	0.883330	−	0.468751i	$-0.155296\pi$
$839$	1.03450	+	1.79181i	0.0357150	+	0.0618603i	−0.847615	+	0.530611i	$0.821962\pi$
$840$	−6.24938	+	0.332330i	−0.215624	+	0.0114665i
$841$	12.8511	+	22.2587i	0.443141	+	0.767543i
$842$	10.1663	+	5.86950i	0.350353	+	0.202276i
$843$			1.19029i			0.0409956i
$844$	−21.3674			−0.735497
$845$	−1.54218	−	29.0004i	−0.0530528	−	0.997644i
$846$	−2.40790	+	4.17060i	−0.0827852	+	0.143388i
$847$			14.5928i			0.501413i
$848$		−	7.44821i		−	0.255772i
$849$	−0.151267	+	0.262002i	−0.00519147	+	0.00899189i
$850$	21.1529	−	2.25612i	0.725538	−	0.0773842i
$851$	7.43545	−	12.8786i	0.254884	−	0.441472i
$852$	−10.2308	+	5.90675i	−0.350501	+	0.202362i
$853$	−8.36952	+	4.83215i	−0.286567	+	0.165450i	−0.636393	−	0.771365i	$-0.719574\pi$
$853$	−8.36952	+	4.83215i	−0.286567	+	0.165450i	0.349826	+	0.936815i	$0.386241\pi$
$854$	34.5970			1.18388
$855$	5.61828	+	7.96461i	0.192141	+	0.272384i
$856$	15.1358			0.517333
$857$	15.4663	−	8.92948i	0.528319	−	0.305025i	−0.212013	−	0.977267i	$-0.568002\pi$
$857$	15.4663	−	8.92948i	0.528319	−	0.305025i	0.740332	+	0.672242i	$0.234668\pi$
$858$	0.386785	−	0.223311i	0.0132046	−	0.00762370i
$859$	11.9479	−	20.6944i	0.407658	−	0.706084i	−0.586969	−	0.809609i	$-0.699679\pi$
$859$	11.9479	−	20.6944i	0.407658	−	0.706084i	0.994627	+	0.103526i	$0.0330123\pi$
$860$	7.56694	−	14.8792i	0.258031	−	0.507377i
$861$	10.8648	−	18.8184i	0.370273	−	0.641331i
$862$		−	19.5454i		−	0.665720i
$863$			25.3969i			0.864520i	0.901749	+	0.432260i	$0.142284\pi$
$863$			25.3969i			0.864520i	−0.901749	+	0.432260i	$0.857716\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−34.2025	+	1.81882i	−1.16292	+	0.0618418i
$866$	35.6992			1.21311
$867$		−	1.10139i		−	0.0374051i
$868$	19.1020	+	11.0286i	0.648365	+	0.374334i
$869$	−8.53029	−	14.7749i	−0.289370	−	0.501204i
$870$	0.215634	+	4.05495i	0.00731069	+	0.137476i
$871$	−0.245175	−	0.424655i	−0.00830743	−	0.0143889i
$872$	7.43496	−	4.29258i	0.251780	−	0.145365i
$873$		−	5.22163i		−	0.176725i
$874$	1.44957	+	38.5161i	0.0490323	+	1.30283i
$875$	−30.8944	+	4.96620i	−1.04442	+	0.167888i
$876$	4.81199	+	8.33460i	0.162582	+	0.281600i
$877$	−10.4421	+	6.02877i	−0.352606	+	0.203577i	−0.665832	−	0.746101i	$-0.731923\pi$
$877$	−10.4421	+	6.02877i	−0.352606	+	0.203577i	0.313226	+	0.949678i	$0.398590\pi$
$878$	33.6354	+	19.4194i	1.13514	+	0.655373i
$879$	12.6039	+	21.8306i	0.425119	+	0.736328i
$880$	−0.478134	−	8.99119i	−0.0161179	−	0.303093i
$881$	−1.15688			−0.0389762			−0.0194881	−	0.999810i	$-0.506204\pi$
$881$	−1.15688			−0.0389762			−0.0194881	+	0.999810i	$0.506204\pi$
$882$		−	0.833029i		−	0.0280495i
$883$	1.74123	+	1.00530i	0.0585970	+	0.0338310i	0.529012	−	0.848614i	$-0.322563\pi$
$883$	1.74123	+	1.00530i	0.0585970	+	0.0338310i	−0.470415	+	0.882445i	$0.655896\pi$
$884$	0.235950	−	0.408677i	0.00793586	−	0.0137453i
$885$	−0.459930	−	0.707041i	−0.0154604	−	0.0237669i
$886$	28.9846			0.973756
$887$	27.5504	+	15.9062i	0.925051	+	0.534078i	0.885243	−	0.465129i	$-0.153992\pi$
$887$	27.5504	+	15.9062i	0.925051	+	0.534078i	0.0398079	+	0.999207i	$0.487325\pi$
$888$	−1.45645	+	0.840881i	−0.0488752	+	0.0282181i
$889$	−19.2519	+	33.3452i	−0.645686	+	1.11836i
$890$	−10.1667	+	19.9911i	−0.340787	+	0.670104i
$891$	−2.01333	−	3.48719i	−0.0674492	−	0.116825i
$892$			0.888653i			0.0297543i
$893$	−9.80465	+	18.5611i	−0.328100	+	0.621123i
$894$	18.7292			0.626400
$895$	21.7167	+	11.0442i	0.725910	+	0.369167i
$896$	1.39938	+	2.42379i	0.0467499	+	0.0809732i
$897$	0.849371	+	0.490385i	0.0283597	+	0.0163735i
$898$	9.98649	−	5.76570i	0.333254	−	0.192404i
$899$	7.15596	−	12.3945i	0.238665	−	0.413379i
$900$	2.02666	−	4.57085i	0.0675555	−	0.152362i
$901$	−31.6889			−1.05571
$902$	27.0747	+	15.6316i	0.901490	+	0.520476i
$903$	18.0942	+	10.4467i	0.602137	+	0.347644i
$904$	−1.24691			−0.0414716
$905$	−34.2115	+	22.2546i	−1.13723	+	0.739767i
$906$	8.06970	−	13.9771i	0.268098	−	0.464359i
$907$	16.4814	−	9.51555i	0.547257	−	0.315959i	−0.200758	−	0.979641i	$-0.564341\pi$
$907$	16.4814	−	9.51555i	0.547257	−	0.315959i	0.748015	+	0.663682i	$0.231007\pi$
$908$	−0.197176	−	0.113839i	−0.00654351	−	0.00377790i
$909$	5.86577	+	10.1598i	0.194555	+	0.336980i
$910$	−0.314655	+	0.618721i	−0.0104307	+	0.0205104i
$911$	−28.9516			−0.959208			−0.479604	−	0.877485i	$-0.659220\pi$
$911$	−28.9516			−0.959208			−0.479604	+	0.877485i	$0.659220\pi$
$912$	2.03594	−	3.85421i	0.0674166	−	0.127626i
$913$		−	33.2519i		−	1.10048i
$914$	−11.0554	−	19.1485i	−0.365679	−	0.633375i
$915$	−12.5300	+	24.6382i	−0.414228	+	0.814514i
$916$	−8.11926	+	14.0630i	−0.268268	+	0.464654i
$917$	−31.1632	+	17.9921i	−1.02910	+	0.594150i
$918$	−3.68457	−	2.12729i	−0.121609	−	0.0702109i
$919$	21.7479			0.717398			0.358699	−	0.933453i	$-0.383220\pi$
$919$	21.7479			0.717398			0.358699	+	0.933453i	$0.383220\pi$
$920$	16.5742	−	10.7815i	0.546435	−	0.355456i
$921$	11.3911	−	19.7299i	0.375349	−	0.650123i
$922$	15.7416	+	9.08841i	0.518422	+	0.299311i
$923$			1.31030i			0.0431292i
$924$	11.2696			0.370744
$925$	−6.79527	+	4.95302i	−0.223427	+	0.162854i
$926$	17.4774	+	30.2718i	0.574343	+	0.994791i
$927$	−15.5448	−	8.97482i	−0.510560	−	0.294772i
$928$	1.57270	−	0.907996i	0.0516263	−	0.0298064i
$929$	20.2037	+	34.9938i	0.662862	+	1.14811i	0.979860	+	0.199685i	$0.0639917\pi$
$929$	20.2037	+	34.9938i	0.662862	+	1.14811i	−0.316998	+	0.948426i	$0.602675\pi$
$930$	−14.7721	+	9.60928i	−0.484397	+	0.315101i
$931$	−0.136561	−	3.62852i	−0.00447559	−	0.118920i
$932$		−	3.33959i		−	0.109392i
$933$	−10.4575	+	6.03762i	−0.342362	+	0.197663i
$934$	−6.50602	−	11.2688i	−0.212883	−	0.368725i
$935$	−38.2537	+	2.03426i	−1.25103	+	0.0665273i
$936$	−0.0554580	−	0.0960560i	−0.00181270	−	0.00313969i
$937$	−17.2215	−	9.94286i	−0.562603	−	0.324819i	0.191587	−	0.981476i	$-0.438637\pi$
$937$	−17.2215	−	9.94286i	−0.562603	−	0.324819i	−0.754190	+	0.656657i	$0.771970\pi$
$938$		−	12.3730i		−	0.403994i
$939$	−10.6499			−0.347545
$940$	10.7532	−	0.571836i	0.350732	−	0.0186512i
$941$	11.7807	−	20.4048i	0.384040	−	0.665176i	−0.607596	−	0.794246i	$-0.707866\pi$
$941$	11.7807	−	20.4048i	0.384040	−	0.665176i	0.991635	+	0.129070i	$0.0411993\pi$
$942$			7.77836i			0.253433i
$943$			68.6533i			2.23566i
$944$	−0.188606	+	0.326675i	−0.00613859	+	0.0106324i
$945$	5.57828	+	2.83688i	0.181462	+	0.0922838i
$946$	−15.0300	+	26.0327i	−0.488668	+	0.846398i
$947$	−37.0234	+	21.3755i	−1.20310	+	0.694610i	−0.961243	−	0.275702i	$-0.911090\pi$
$947$	−37.0234	+	21.3755i	−1.20310	+	0.694610i	−0.241857	+	0.970312i	$0.577757\pi$
$948$	−3.66927	+	2.11845i	−0.119172	+	0.0688041i
$949$	1.06745			0.0346510
$950$	8.07846	−	20.2420i	0.262100	−	0.656737i
$951$	16.5300			0.536021
$952$	10.3122	−	5.95375i	0.334220	−	0.192962i
$953$	−20.0662	+	11.5852i	−0.650007	+	0.375282i	−0.788459	−	0.615087i	$-0.789121\pi$
$953$	−20.0662	+	11.5852i	−0.650007	+	0.375282i	0.138452	+	0.990369i	$0.455787\pi$
$954$	−3.72410	+	6.45034i	−0.120572	+	0.208837i
$955$	−34.3852	−	17.4869i	−1.11268	−	0.565863i
$956$	14.1707	−	24.5444i	0.458313	−	0.793822i
$957$		−	7.31239i		−	0.236376i
$958$		−	30.2830i		−	0.978400i
$959$	11.4090	−	19.7609i	0.368414	−	0.638113i
$960$	−2.23291	+	0.118742i	−0.0720670	+	0.00383238i
$961$	31.1108			1.00358
$962$			0.186534i			0.00601411i
$963$	−13.1080	−	7.56792i	−0.422400	−	0.243873i
$964$	7.12956	+	12.3488i	0.229628	+	0.397727i
$965$	14.1069	−	0.750176i	0.454117	−	0.0241490i
$966$	12.3739	+	21.4323i	0.398125	+	0.689572i
$967$	29.3348	−	16.9365i	0.943344	−	0.544640i	0.0523370	−	0.998629i	$-0.483333\pi$
$967$	29.3348	−	16.9365i	0.943344	−	0.544640i	0.891007	+	0.453990i	$0.150000\pi$
$968$			5.21402i			0.167585i
$969$	−16.3980	−	8.66205i	−0.526781	−	0.278265i
$970$	−9.78736	+	6.36668i	−0.314253	+	0.204422i
$971$	−3.13260	−	5.42583i	−0.100530	−	0.174123i	0.811373	−	0.584529i	$-0.198721\pi$
$971$	−3.13260	−	5.42583i	−0.100530	−	0.174123i	−0.911903	+	0.410405i	$0.865387\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	5.53970	+	3.19835i	0.177595	+	0.102534i
$974$	−17.7583	−	30.7583i	−0.569013	−	0.985560i
$975$	−0.326663	−	0.448163i	−0.0104616	−	0.0143527i
$976$	12.3616			0.395684
$977$		−	10.4850i		−	0.335446i	−0.985834	−	0.167723i	$-0.946359\pi$
$977$		−	10.4850i		−	0.335446i	0.985834	−	0.167723i	$-0.0536414\pi$
$978$	1.73052	+	0.999118i	0.0553360	+	0.0319483i
$979$	20.1937	−	34.9766i	0.645395	−	1.11786i
$980$	−1.56142	+	1.01570i	−0.0498777	+	0.0324455i
$981$	−8.58516			−0.274103
$982$	−9.28479	−	5.36057i	−0.296289	−	0.171063i
$983$	−46.9978	+	27.1342i	−1.49900	+	0.865446i	−0.999999	−	0.00115735i	$-0.999632\pi$
$983$	−46.9978	+	27.1342i	−1.49900	+	0.865446i	−0.498997	+	0.866603i	$0.666298\pi$
$984$	3.88203	−	6.72386i	0.123754	−	0.214349i
$985$	8.91226	−	17.5246i	0.283968	−	0.558379i
$986$	−3.86314	−	6.69115i	−0.123027	−	0.213090i
$987$			13.4782i			0.429016i
$988$	−0.257311	−	0.409311i	−0.00818617	−	0.0130219i
$989$	−66.0111			−2.09903
$990$	−4.08152	+	8.02567i	−0.129719	+	0.255072i
$991$	−11.8865	−	20.5881i	−0.377588	−	0.654001i	0.613123	−	0.789987i	$-0.289913\pi$
$991$	−11.8865	−	20.5881i	−0.377588	−	0.654001i	−0.990711	+	0.135986i	$0.956580\pi$
$992$	6.82518	+	3.94052i	0.216700	+	0.125112i
$993$	28.9121	−	16.6924i	0.917496	−	0.529717i
$994$	−16.5315	+	28.6335i	−0.524349	+	0.908198i
$995$	8.94475	−	5.81856i	0.283568	−	0.184461i
$996$	−8.25792			−0.261662
$997$	2.37529	+	1.37138i	0.0752263	+	0.0434319i	0.537141	−	0.843492i	$-0.319504\pi$
$997$	2.37529	+	1.37138i	0.0752263	+	0.0434319i	−0.461915	+	0.886924i	$0.652838\pi$
$998$	−20.8295	−	12.0259i	−0.659345	−	0.380673i
$999$	1.68176			0.0532086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.q.c.349.4	yes	20
3.2	odd	2		1710.2.t.c.919.7		20
5.4	even	2	inner	570.2.q.c.349.8	yes	20
15.14	odd	2		1710.2.t.c.919.3		20
19.11	even	3	inner	570.2.q.c.49.8	yes	20
57.11	odd	6		1710.2.t.c.1189.3		20
95.49	even	6	inner	570.2.q.c.49.4	✓	20
285.239	odd	6		1710.2.t.c.1189.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.c.49.4	✓	20	95.49	even	6	inner
570.2.q.c.49.8	yes	20	19.11	even	3	inner
570.2.q.c.349.4	yes	20	1.1	even	1	trivial
570.2.q.c.349.8	yes	20	5.4	even	2	inner
1710.2.t.c.919.3		20	15.14	odd	2
1710.2.t.c.919.7		20	3.2	odd	2
1710.2.t.c.1189.3		20	57.11	odd	6
1710.2.t.c.1189.7		20	285.239	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.99313 + 1.01362i) q^{5} +(-0.500000 + 0.866025i) q^{6} +2.79875i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.99313 + 1.01362i) q^{5} +(-0.500000 + 0.866025i) q^{6} +2.79875i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.23291 + 0.118742i) q^{10} +4.02666 q^{11} -1.00000i q^{12} +(-0.0960560 - 0.0554580i) q^{13} +(-1.39938 - 2.42379i) q^{14} +(2.23291 - 0.118742i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.68457 + 2.12729i) q^{17} +1.00000i q^{18} +(0.163933 + 4.35582i) q^{19} +(1.87439 - 1.21929i) q^{20} +(1.39938 + 2.42379i) q^{21} +(-3.48719 + 2.01333i) q^{22} +(-7.65779 - 4.42123i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.94514 + 4.04057i) q^{25} +0.110916 q^{26} -1.00000i q^{27} +(2.42379 + 1.39938i) q^{28} +(0.907996 - 1.57270i) q^{29} +(-1.87439 + 1.21929i) q^{30} +7.88104 q^{31} +(0.866025 + 0.500000i) q^{32} +(3.48719 - 2.01333i) q^{33} +(2.12729 - 3.68457i) q^{34} +(-2.83688 + 5.57828i) q^{35} +(-0.500000 - 0.866025i) q^{36} +1.68176i q^{37} +(-2.31988 - 3.69028i) q^{38} -0.110916 q^{39} +(-1.01362 + 1.99313i) q^{40} +(-3.88203 - 6.72386i) q^{41} +(-2.42379 - 1.39938i) q^{42} +(6.46509 - 3.73262i) q^{43} +(2.01333 - 3.48719i) q^{44} +(1.87439 - 1.21929i) q^{45} +8.84246 q^{46} +(4.17060 + 2.40790i) q^{47} +(-0.866025 - 0.500000i) q^{48} -0.833029 q^{49} +(-4.57085 - 2.02666i) q^{50} +(-2.12729 + 3.68457i) q^{51} +(-0.0960560 + 0.0554580i) q^{52} +(6.45034 + 3.72410i) q^{53} +(0.500000 + 0.866025i) q^{54} +(8.02567 + 4.08152i) q^{55} -2.79875 q^{56} +(2.31988 + 3.69028i) q^{57} +1.81599i q^{58} +(-0.188606 - 0.326675i) q^{59} +(1.01362 - 1.99313i) q^{60} +(-6.18078 + 10.7054i) q^{61} +(-6.82518 + 3.94052i) q^{62} +(2.42379 + 1.39938i) q^{63} -1.00000 q^{64} +(-0.135239 - 0.207900i) q^{65} +(-2.01333 + 3.48719i) q^{66} +(3.82862 + 2.21046i) q^{67} +4.25457i q^{68} -8.84246 q^{69} +(-0.332330 - 6.24938i) q^{70} +(-5.90675 - 10.2308i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-8.33460 + 4.81199i) q^{73} +(-0.840881 - 1.45645i) q^{74} +(4.57085 + 2.02666i) q^{75} +(3.85421 + 2.03594i) q^{76} +11.2696i q^{77} +(0.0960560 - 0.0554580i) q^{78} +(-2.11845 - 3.66927i) q^{79} +(-0.118742 - 2.23291i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.72386 + 3.88203i) q^{82} -8.25792i q^{83} +2.79875 q^{84} +(-9.50009 + 0.505196i) q^{85} +(-3.73262 + 6.46509i) q^{86} -1.81599i q^{87} +4.02666i q^{88} +(5.01501 - 8.68625i) q^{89} +(-1.01362 + 1.99313i) q^{90} +(0.155213 - 0.268837i) q^{91} +(-7.65779 + 4.42123i) q^{92} +(6.82518 - 3.94052i) q^{93} -4.81579 q^{94} +(-4.08842 + 8.84787i) q^{95} +1.00000 q^{96} +(4.52207 - 2.61082i) q^{97} +(0.721424 - 0.416515i) q^{98} +(2.01333 - 3.48719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9	\( 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9} - 2 q^{10} + 12 q^{11} + 10 q^{14} + 2 q^{15} - 10 q^{16} + 6 q^{19} - 10 q^{21} + 10 q^{24} + 14 q^{25} + 8 q^{29} + 40 q^{31} + 12 q^{34} + 2 q^{35} - 10 q^{36} + 2 q^{40} - 14 q^{41} + 6 q^{44} + 44 q^{46} - 8 q^{49} - 8 q^{50} - 12 q^{51} + 10 q^{54} + 20 q^{56} + 8 q^{59} - 2 q^{60} + 16 q^{61} - 20 q^{64} + 40 q^{65} - 6 q^{66} - 44 q^{69} + 8 q^{70} - 4 q^{71} + 26 q^{74} + 8 q^{75} + 8 q^{79} - 10 q^{81} - 20 q^{84} - 16 q^{85} - 20 q^{86} - 2 q^{89} + 2 q^{90} - 44 q^{91} - 32 q^{94} - 80 q^{95} + 20 q^{96} + 6 q^{99}+O(q^{100}) \) 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9 - 2 * q^10 + 12 * q^11 + 10 * q^14 + 2 * q^15 - 10 * q^16 + 6 * q^19 - 10 * q^21 + 10 * q^24 + 14 * q^25 + 8 * q^29 + 40 * q^31 + 12 * q^34 + 2 * q^35 - 10 * q^36 + 2 * q^40 - 14 * q^41 + 6 * q^44 + 44 * q^46 - 8 * q^49 - 8 * q^50 - 12 * q^51 + 10 * q^54 + 20 * q^56 + 8 * q^59 - 2 * q^60 + 16 * q^61 - 20 * q^64 + 40 * q^65 - 6 * q^66 - 44 * q^69 + 8 * q^70 - 4 * q^71 + 26 * q^74 + 8 * q^75 + 8 * q^79 - 10 * q^81 - 20 * q^84 - 16 * q^85 - 20 * q^86 - 2 * q^89 + 2 * q^90 - 44 * q^91 - 32 * q^94 - 80 * q^95 + 20 * q^96 + 6 * q^99

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