LMFDB - Embedded newform 558.2.q.a.371.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(185,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.185"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			371.12
Character	$\chi$	$=$	558.371
Dual form			558.2.q.a.185.12

$q$-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} +(0.841508 - 1.51389i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.53994 - 1.46644i) q^{5} +(-1.48571 + 0.890313i) q^{6} +(2.03804 - 3.52999i) q^{7} -1.00000i q^{8} +(-1.58373 - 2.54790i) q^{9} -2.93287 q^{10} +(-1.42757 + 2.47262i) q^{11} +(1.73182 - 0.0281775i) q^{12} +(0.887117 - 0.512177i) q^{13} +(-3.52999 + 2.03804i) q^{14} +(-0.0826409 - 5.07921i) q^{15} +(-0.500000 + 0.866025i) q^{16} +5.67253 q^{17} +(0.0975967 + 2.99841i) q^{18} -7.01983 q^{19} +(2.53994 + 1.46644i) q^{20} +(-3.62899 - 6.05588i) q^{21} +(2.47262 - 1.42757i) q^{22} +(4.35174 + 7.53743i) q^{23} +(-1.51389 - 0.841508i) q^{24} +(1.80087 - 3.11920i) q^{25} -1.02435 q^{26} +(-5.18996 + 0.253508i) q^{27} +4.07608 q^{28} +(-3.19560 + 5.53494i) q^{29} +(-2.46804 + 4.44005i) q^{30} +(1.41782 + 5.38422i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.54196 + 4.24191i) q^{33} +(-4.91256 - 2.83627i) q^{34} -11.9546i q^{35} +(1.41468 - 2.64550i) q^{36} -5.63967i q^{37} +(6.07935 + 3.50991i) q^{38} +(-0.0288637 - 1.77400i) q^{39} +(-1.46644 - 2.53994i) q^{40} +(3.22261 - 1.86058i) q^{41} +(0.114854 + 7.05904i) q^{42} +(3.66962 + 2.11866i) q^{43} -2.85513 q^{44} +(-7.75892 - 4.14909i) q^{45} -8.70347i q^{46} +(2.99058 + 1.72661i) q^{47} +(0.890313 + 1.48571i) q^{48} +(-4.80721 - 8.32632i) q^{49} +(-3.11920 + 1.80087i) q^{50} +(4.77348 - 8.58759i) q^{51} +(0.887117 + 0.512177i) q^{52} -10.5738 q^{53} +(4.62140 + 2.37544i) q^{54} +8.37374i q^{55} +(-3.52999 - 2.03804i) q^{56} +(-5.90724 + 10.6272i) q^{57} +(5.53494 - 3.19560i) q^{58} +(-4.81405 + 2.77939i) q^{59} +(4.35741 - 2.61118i) q^{60} +(-10.8811 - 6.28219i) q^{61} +(1.46424 - 5.37178i) q^{62} +(-12.2218 + 0.397812i) q^{63} -1.00000 q^{64} +(1.50215 - 2.60180i) q^{65} +(-0.0804504 - 4.94458i) q^{66} +(-0.327613 - 0.567442i) q^{67} +(2.83627 + 4.91256i) q^{68} +(15.0729 - 0.245242i) q^{69} +(-5.97731 + 10.3530i) q^{70} +1.41846i q^{71} +(-2.54790 + 1.58373i) q^{72} -12.9850i q^{73} +(-2.81984 + 4.88410i) q^{74} +(-3.20668 - 5.35116i) q^{75} +(-3.50991 - 6.07935i) q^{76} +(5.81887 + 10.0786i) q^{77} +(-0.862003 + 1.55076i) q^{78} +(3.28967 + 1.89929i) q^{79} +2.93287i q^{80} +(-3.98362 + 8.07037i) q^{81} -3.72115 q^{82} +(-2.20366 + 3.81685i) q^{83} +(3.43005 - 6.17073i) q^{84} +(14.4079 - 8.31841i) q^{85} +(-2.11866 - 3.66962i) q^{86} +(5.69017 + 9.49549i) q^{87} +(2.47262 + 1.42757i) q^{88} -2.33927 q^{89} +(4.64487 + 7.47268i) q^{90} -4.17535i q^{91} +(-4.35174 + 7.53743i) q^{92} +(9.34422 + 2.38443i) q^{93} +(-1.72661 - 2.99058i) q^{94} +(-17.8300 + 10.2941i) q^{95} +(-0.0281775 - 1.73182i) q^{96} +(2.69419 - 4.66648i) q^{97} +9.61441i q^{98} +(8.56087 - 0.278652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) $ 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.841508	−	1.51389i	0.485845	−	0.874045i
$3$	0.841508	−	1.51389i	0.485845	−	0.874045i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.53994	−	1.46644i	1.13590	−	0.655810i	0.190486	−	0.981690i	$-0.438994\pi$
$5$	2.53994	−	1.46644i	1.13590	−	0.655810i	0.945411	+	0.325879i	$0.105660\pi$
$6$	−1.48571	+	0.890313i	−0.606540	+	0.363469i
$7$	2.03804	−	3.52999i	0.770306	−	1.33421i	−0.167089	−	0.985942i	$-0.553437\pi$
$7$	2.03804	−	3.52999i	0.770306	−	1.33421i	0.937395	−	0.348268i	$-0.113230\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.58373	−	2.54790i	−0.527909	−	0.849301i
$10$	−2.93287			−0.927456
$11$	−1.42757	+	2.47262i	−0.430428	+	0.745522i	−0.996910	−	0.0785514i	$-0.974971\pi$
$11$	−1.42757	+	2.47262i	−0.430428	+	0.745522i	0.566483	+	0.824074i	$0.308304\pi$
$12$	1.73182	−	0.0281775i	0.499934	−	0.00813413i
$13$	0.887117	−	0.512177i	0.246042	−	0.142052i	−0.371909	−	0.928269i	$-0.621297\pi$
$13$	0.887117	−	0.512177i	0.246042	−	0.142052i	0.617951	+	0.786217i	$0.287963\pi$
$14$	−3.52999	+	2.03804i	−0.943429	+	0.544689i
$15$	−0.0826409	−	5.07921i	−0.0213378	−	1.31145i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.67253			1.37579			0.687896	−	0.725810i	$-0.258535\pi$
$17$	5.67253			1.37579			0.687896	+	0.725810i	$0.258535\pi$
$18$	0.0975967	+	2.99841i	0.0230038	+	0.706733i
$19$	−7.01983			−1.61046			−0.805229	−	0.592964i	$-0.797958\pi$
$19$	−7.01983			−1.61046			−0.805229	+	0.592964i	$0.797958\pi$
$20$	2.53994	+	1.46644i	0.567949	+	0.327905i
$21$	−3.62899	−	6.05588i	−0.791910	−	1.32150i
$22$	2.47262	−	1.42757i	0.527164	−	0.304358i
$23$	4.35174	+	7.53743i	0.907400	+	1.57166i	0.817663	+	0.575697i	$0.195269\pi$
$23$	4.35174	+	7.53743i	0.907400	+	1.57166i	0.0897370	+	0.995965i	$0.471397\pi$
$24$	−1.51389	−	0.841508i	−0.309022	−	0.171772i
$25$	1.80087	−	3.11920i	0.360175	−	0.623841i
$26$	−1.02435			−0.200892
$27$	−5.18996	+	0.253508i	−0.998809	+	0.0487876i
$28$	4.07608			0.770306
$29$	−3.19560	+	5.53494i	−0.593408	+	1.02781i	0.400361	+	0.916357i	$0.368885\pi$
$29$	−3.19560	+	5.53494i	−0.593408	+	1.02781i	−0.993769	+	0.111456i	$0.964449\pi$
$30$	−2.46804	+	4.44005i	−0.450600	+	0.810638i
$31$	1.41782	+	5.38422i	0.254649	+	0.967034i
$31$	1.41782	+	5.38422i	0.254649	+	0.967034i
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.54196	+	4.24191i	0.442499	+	0.738421i
$34$	−4.91256	−	2.83627i	−0.842497	−	0.486416i
$35$		−	11.9546i		−	2.02070i
$36$	1.41468	−	2.64550i	0.235781	−	0.440917i
$37$		−	5.63967i		−	0.927157i	−0.886056	−	0.463578i	$-0.846565\pi$
$37$		−	5.63967i		−	0.927157i	0.886056	−	0.463578i	$-0.153435\pi$
$38$	6.07935	+	3.50991i	0.986200	+	0.569383i
$39$	−0.0288637	−	1.77400i	−0.00462189	−	0.284067i
$40$	−1.46644	−	2.53994i	−0.231864	−	0.401600i
$41$	3.22261	−	1.86058i	0.503288	−	0.290573i	−0.226783	−	0.973945i	$-0.572821\pi$
$41$	3.22261	−	1.86058i	0.503288	−	0.290573i	0.730070	+	0.683372i	$0.239487\pi$
$42$	0.114854	+	7.05904i	0.0177223	+	1.08923i
$43$	3.66962	+	2.11866i	0.559612	+	0.323092i	0.752990	−	0.658032i	$-0.228611\pi$
$43$	3.66962	+	2.11866i	0.559612	+	0.323092i	−0.193378	+	0.981124i	$0.561944\pi$
$44$	−2.85513			−0.430428
$45$	−7.75892	−	4.14909i	−1.15663	−	0.618510i
$46$		−	8.70347i		−	1.28326i
$47$	2.99058	+	1.72661i	0.436221	+	0.251852i	0.701993	−	0.712184i	$-0.252294\pi$
$47$	2.99058	+	1.72661i	0.436221	+	0.251852i	−0.265773	+	0.964036i	$0.585627\pi$
$48$	0.890313	+	1.48571i	0.128506	+	0.214444i
$49$	−4.80721	−	8.32632i	−0.686744	−	1.18947i
$50$	−3.11920	+	1.80087i	−0.441122	+	0.254682i
$51$	4.77348	−	8.58759i	0.668421	−	1.20250i
$52$	0.887117	+	0.512177i	0.123021	+	0.0710262i
$53$	−10.5738			−1.45242			−0.726211	−	0.687472i	$-0.758721\pi$
$53$	−10.5738			−1.45242			−0.726211	+	0.687472i	$0.758721\pi$
$54$	4.62140	+	2.37544i	0.628892	+	0.323256i
$55$			8.37374i			1.12912i
$56$	−3.52999	−	2.03804i	−0.471714	−	0.272344i
$57$	−5.90724	+	10.6272i	−0.782433	+	1.40761i
$58$	5.53494	−	3.19560i	0.726773	−	0.419603i
$59$	−4.81405	+	2.77939i	−0.626736	+	0.361846i	−0.779487	−	0.626419i	$-0.784520\pi$
$59$	−4.81405	+	2.77939i	−0.626736	+	0.361846i	0.152751	+	0.988265i	$0.451187\pi$
$60$	4.35741	−	2.61118i	0.562539	−	0.337101i
$61$	−10.8811	−	6.28219i	−1.39318	−	0.804352i	−0.399512	−	0.916728i	$-0.630821\pi$
$61$	−10.8811	−	6.28219i	−1.39318	−	0.804352i	−0.993666	+	0.112376i	$0.964154\pi$
$62$	1.46424	−	5.37178i	0.185958	−	0.682217i
$63$	−12.2218	+	0.397812i	−1.53980	+	0.0501196i
$64$	−1.00000			−0.125000
$65$	1.50215	−	2.60180i	0.186319	−	0.322714i
$66$	−0.0804504	−	4.94458i	−0.00990276	−	0.608636i
$67$	−0.327613	−	0.567442i	−0.0400242	−	0.0693240i	0.845319	−	0.534261i	$-0.179410\pi$
$67$	−0.327613	−	0.567442i	−0.0400242	−	0.0693240i	−0.885344	+	0.464937i	$0.846077\pi$
$68$	2.83627	+	4.91256i	0.343948	+	0.595735i
$69$	15.0729	−	0.245242i	1.81456	−	0.0295236i
$70$	−5.97731	+	10.3530i	−0.714425	+	1.23742i
$71$			1.41846i			0.168340i	0.996451	+	0.0841701i	$0.0268239\pi$
$71$			1.41846i			0.168340i	−0.996451	+	0.0841701i	$0.973176\pi$
$72$	−2.54790	+	1.58373i	−0.300273	+	0.186644i
$73$		−	12.9850i		−	1.51978i	−0.650052	−	0.759890i	$-0.725253\pi$
$73$		−	12.9850i		−	1.51978i	0.650052	−	0.759890i	$-0.274747\pi$
$74$	−2.81984	+	4.88410i	−0.327799	+	0.567765i
$75$	−3.20668	−	5.35116i	−0.370276	−	0.617899i
$76$	−3.50991	−	6.07935i	−0.402615	−	0.697349i
$77$	5.81887	+	10.0786i	0.663122	+	1.14856i
$78$	−0.862003	+	1.55076i	−0.0976026	+	0.175589i
$79$	3.28967	+	1.89929i	0.370117	+	0.213687i	0.673510	−	0.739178i	$-0.264786\pi$
$79$	3.28967	+	1.89929i	0.370117	+	0.213687i	−0.303393	+	0.952866i	$0.598119\pi$
$80$			2.93287i			0.327905i
$81$	−3.98362	+	8.07037i	−0.442624	+	0.896707i
$82$	−3.72115			−0.410933
$83$	−2.20366	+	3.81685i	−0.241883	+	0.418954i	−0.961251	−	0.275676i	$-0.911098\pi$
$83$	−2.20366	+	3.81685i	−0.241883	+	0.418954i	0.719367	+	0.694630i	$0.244432\pi$
$84$	3.43005	−	6.17073i	0.374250	−	0.673282i
$85$	14.4079	−	8.31841i	1.56276	−	0.902258i
$86$	−2.11866	−	3.66962i	−0.228460	−	0.395705i
$87$	5.69017	+	9.49549i	0.610050	+	1.01802i
$88$	2.47262	+	1.42757i	0.263582	+	0.152179i
$89$	−2.33927			−0.247962			−0.123981	−	0.992285i	$-0.539566\pi$
$89$	−2.33927			−0.247962			−0.123981	+	0.992285i	$0.539566\pi$
$90$	4.64487	+	7.47268i	0.489612	+	0.787689i
$91$		−	4.17535i		−	0.437696i
$92$	−4.35174	+	7.53743i	−0.453700	+	0.785831i
$93$	9.34422	+	2.38443i	0.968951	+	0.247254i
$94$	−1.72661	−	2.99058i	−0.178086	−	0.308455i
$95$	−17.8300	+	10.2941i	−1.82932	+	1.05616i
$96$	−0.0281775	−	1.73182i	−0.00287585	−	0.176753i
$97$	2.69419	−	4.66648i	0.273554	−	0.473809i	−0.696215	−	0.717833i	$-0.745134\pi$
$97$	2.69419	−	4.66648i	0.273554	−	0.473809i	0.969769	+	0.244024i	$0.0784675\pi$
$98$			9.61441i			0.971202i
$99$	8.56087	−	0.278652i	0.860399	−	0.0280055i
$100$	3.60175			0.360175
$101$	16.1150	+	9.30400i	1.60350	+	0.925782i	0.990780	+	0.135484i	$0.0432589\pi$
$101$	16.1150	+	9.30400i	1.60350	+	0.925782i	0.612722	+	0.790298i	$0.290074\pi$
$102$	−8.42775	+	5.05033i	−0.834472	+	0.500057i
$103$	0.824711	+	1.42844i	0.0812612	+	0.140748i	0.903792	−	0.427972i	$-0.140772\pi$
$103$	0.824711	+	1.42844i	0.0812612	+	0.140748i	−0.822531	+	0.568721i	$0.807439\pi$
$104$	−0.512177	−	0.887117i	−0.0502231	−	0.0869890i
$105$	−18.0980	−	10.0599i	−1.76618	−	0.981747i
$106$	9.15718	+	5.28690i	0.889423	+	0.513509i
$107$		−	9.92203i		−	0.959199i	−0.877488	−	0.479599i	$-0.840782\pi$
$107$		−	9.92203i		−	0.959199i	0.877488	−	0.479599i	$-0.159218\pi$
$108$	−2.81453	−	4.36789i	−0.270828	−	0.420300i
$109$	18.8530			1.80579			0.902897	−	0.429857i	$-0.141436\pi$
$109$	18.8530			1.80579			0.902897	+	0.429857i	$0.141436\pi$
$110$	4.18687	−	7.25188i	0.399203	−	0.691439i
$111$	−8.53785	−	4.74583i	−0.810377	−	0.450454i
$112$	2.03804	+	3.52999i	0.192577	+	0.333552i
$113$	8.43172	−	4.86805i	0.793189	−	0.457948i	−0.0478950	−	0.998852i	$-0.515251\pi$
$113$	8.43172	−	4.86805i	0.793189	−	0.457948i	0.841084	+	0.540904i	$0.181918\pi$
$114$	10.4294	−	6.24984i	0.976807	−	0.585351i
$115$	22.1063	+	12.7631i	2.06143	+	1.19016i
$116$	−6.39120			−0.593408
$117$	−2.70993	−	1.44914i	−0.250533	−	0.133973i
$118$	5.55879			0.511728
$119$	11.5608	−	20.0240i	1.05978	−	1.83559i
$120$	−5.07921	+	0.0826409i	−0.463667	+	0.00754405i
$121$	1.42411	+	2.46663i	0.129464	+	0.224239i
$122$	6.28219	+	10.8811i	0.568763	+	0.985126i
$123$	−0.104853	−	6.44437i	−0.00945425	−	0.581070i
$124$	−3.95396	+	3.91998i	−0.355076	+	0.352025i
$125$			4.10090i			0.366795i
$126$	10.7833	+	5.76637i	0.960649	+	0.513709i
$127$			9.65404i			0.856657i	0.903623	+	0.428329i	$0.140897\pi$
$127$			9.65404i			0.856657i	−0.903623	+	0.428329i	$0.859103\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	6.29543	−	3.77253i	0.554281	−	0.332153i
$130$	−2.60180	+	1.50215i	−0.228193	+	0.131747i
$131$	−0.961641	+	0.555203i	−0.0840189	+	0.0485084i	−0.541421	−	0.840752i	$-0.682113\pi$
$131$	−0.961641	+	0.555203i	−0.0840189	+	0.0485084i	0.457402	+	0.889260i	$0.348780\pi$
$132$	−2.40262	+	4.32236i	−0.209121	+	0.376213i
$133$	−14.3067	+	24.7799i	−1.24055	+	2.14869i
$134$			0.655225i			0.0566028i
$135$	−12.8105	+	8.25465i	−1.10255	+	0.710447i
$136$		−	5.67253i		−	0.486416i
$137$	−1.18927	+	2.05988i	−0.101606	+	0.175987i	−0.912347	−	0.409419i	$-0.865732\pi$
$137$	−1.18927	+	2.05988i	−0.101606	+	0.175987i	0.810740	+	0.585406i	$0.199065\pi$
$138$	−13.1761	−	7.32405i	−1.12162	−	0.623464i
$139$	−15.1170	+	8.72781i	−1.28221	+	0.740283i	−0.977252	−	0.212084i	$-0.931975\pi$
$139$	−15.1170	+	8.72781i	−1.28221	+	0.740283i	−0.304956	+	0.952366i	$0.598642\pi$
$140$	10.3530	−	5.97731i	0.874989	−	0.505175i
$141$	5.13050	−	3.07445i	0.432066	−	0.258915i
$142$	0.709229	−	1.22842i	0.0595172	−	0.103087i
$143$			2.92467i			0.244573i
$144$	2.99841	−	0.0975967i	0.249868	−	0.00813306i
$145$			18.7446i			1.55665i
$146$	−6.49250	+	11.2453i	−0.537323	+	0.930671i
$147$	−16.6504	+	0.270910i	−1.37331	+	0.0223443i
$148$	4.88410	−	2.81984i	0.401471	−	0.231789i
$149$	1.94748	−	1.12438i	0.159544	−	0.0921129i	−0.418102	−	0.908400i	$-0.637305\pi$
$149$	1.94748	−	1.12438i	0.159544	−	0.0921129i	0.577646	+	0.816287i	$0.303971\pi$
$150$	0.101488	+	6.23758i	0.00828647	+	0.509297i
$151$	0.945284	+	0.545760i	0.0769261	+	0.0444133i	0.537970	−	0.842964i	$-0.319191\pi$
$151$	0.945284	+	0.545760i	0.0769261	+	0.0444133i	−0.461044	+	0.887378i	$0.652525\pi$
$152$			7.01983i			0.569383i
$153$	−8.98374	−	14.4531i	−0.726293	−	1.16846i
$154$		−	11.6377i		−	0.937796i
$155$	11.4968	+	11.5965i	0.923445	+	0.931449i
$156$	1.52190	−	0.911996i	0.121849	−	0.0730182i
$157$	−3.28221	−	5.68495i	−0.261949	−	0.453708i	0.704811	−	0.709395i	$-0.251032\pi$
$157$	−3.28221	−	5.68495i	−0.261949	−	0.453708i	−0.966760	+	0.255687i	$0.917698\pi$
$158$	−1.89929	−	3.28967i	−0.151100	−	0.261712i
$159$	−8.89794	+	16.0076i	−0.705652	+	1.26948i
$160$	1.46644	−	2.53994i	0.115932	−	0.200800i
$161$	35.4760			2.79590
$162$	7.48510	−	4.99733i	0.588085	−	0.392628i
$163$	9.26680			0.725832			0.362916	−	0.931822i	$-0.381781\pi$
$163$	9.26680			0.725832			0.362916	+	0.931822i	$0.381781\pi$
$164$	3.22261	+	1.86058i	0.251644	+	0.145287i
$165$	12.6769	+	7.04658i	0.986898	+	0.548575i
$166$	3.81685	−	2.20366i	0.296245	−	0.171037i
$167$	−0.313267	−	0.542595i	−0.0242414	−	0.0419873i	0.853650	−	0.520847i	$-0.174384\pi$
$167$	−0.313267	−	0.542595i	−0.0242414	−	0.0419873i	−0.877892	+	0.478859i	$0.841050\pi$
$168$	−6.05588	+	3.62899i	−0.467221	+	0.279982i
$169$	−5.97535	+	10.3496i	−0.459642	+	0.796124i
$170$	−16.6368			−1.27599
$171$	11.1175	+	17.8858i	0.850176	+	1.36776i
$172$			4.23731i			0.323092i
$173$	−20.4999	−	11.8356i	−1.55857	−	0.899844i	−0.997394	−	0.0721506i	$-0.977014\pi$
$173$	−20.4999	−	11.8356i	−1.55857	−	0.899844i	−0.561181	−	0.827693i	$-0.689653\pi$
$174$	−0.180088	−	11.0684i	−0.0136524	−	0.839095i
$175$	−7.34050	−	12.7141i	−0.554890	−	0.961097i
$176$	−1.42757	−	2.47262i	−0.107607	−	0.186381i
$177$	0.156632	+	9.62682i	0.0117732	+	0.723596i
$178$	2.02587	+	1.16963i	0.151845	+	0.0876678i
$179$	1.55169			0.115979			0.0579894	−	0.998317i	$-0.481531\pi$
$179$	1.55169			0.115979			0.0579894	+	0.998317i	$0.481531\pi$
$180$	−0.286239	−	8.79396i	−0.0213350	−	0.655463i
$181$		−	12.3884i		−	0.920822i	−0.887706	−	0.460411i	$-0.847702\pi$
$181$		−	12.3884i		−	0.920822i	0.887706	−	0.460411i	$-0.152298\pi$
$182$	−2.08767	+	3.61596i	−0.154749	+	0.268033i
$183$	−18.6671	+	11.1862i	−1.37991	+	0.826910i
$184$	7.53743	−	4.35174i	0.555667	−	0.320814i
$185$	−8.27022	−	14.3244i	−0.608039	−	1.05315i
$186$	−6.90012	−	6.73709i	−0.505941	−	0.493987i
$187$	−8.09792	+	14.0260i	−0.592178	+	1.02568i
$188$			3.45322i			0.251852i
$189$	−9.68247	+	18.8372i	−0.704296	+	1.37020i
$190$	20.5883			1.49363
$191$	2.87262	+	1.65851i	0.207855	+	0.120005i	0.600314	−	0.799764i	$-0.295042\pi$
$191$	2.87262	+	1.65851i	0.207855	+	0.120005i	−0.392459	+	0.919770i	$0.628375\pi$
$192$	−0.841508	+	1.51389i	−0.0607306	+	0.109256i
$193$	0.0584452	+	0.101230i	0.00420698	+	0.00728670i	0.868121	−	0.496352i	$-0.165328\pi$
$193$	0.0584452	+	0.101230i	0.00420698	+	0.00728670i	−0.863914	+	0.503639i	$0.831994\pi$
$194$	−4.66648	+	2.69419i	−0.335034	+	0.193432i
$195$	−2.67477	−	4.46353i	−0.191544	−	0.319640i
$196$	4.80721	−	8.32632i	0.343372	−	0.594737i
$197$	15.1370			1.07847			0.539233	−	0.842157i	$-0.318714\pi$
$197$	15.1370			1.07847			0.539233	+	0.842157i	$0.318714\pi$
$198$	−7.55325	−	4.03911i	−0.536786	−	0.287047i
$199$			11.8299i			0.838598i	0.907848	+	0.419299i	$0.137724\pi$
$199$			11.8299i			0.838598i	−0.907848	+	0.419299i	$0.862276\pi$
$200$	−3.11920	−	1.80087i	−0.220561	−	0.127341i
$201$	−1.13473	+	0.0184626i	−0.0800379	+	0.00130225i
$202$	−9.30400	−	16.1150i	−0.654627	−	1.13385i
$203$	13.0255	+	22.5609i	0.914212	+	1.58346i
$204$	9.82381	−	0.159838i	0.687805	−	0.0111909i
$205$	5.45684	−	9.45152i	0.381122	−	0.660123i
$206$		−	1.64942i		−	0.114921i
$207$	12.3127	−	23.0250i	0.855790	−	1.60035i
$208$			1.02435i			0.0710262i
$209$	10.0213	−	17.3573i	0.693186	−	1.20063i
$210$	10.6434	+	17.7611i	0.734461	+	1.22563i
$211$	−2.95666	−	5.12109i	−0.203545	−	0.352550i	0.746123	−	0.665808i	$-0.231913\pi$
$211$	−2.95666	−	5.12109i	−0.203545	−	0.352550i	−0.949668	+	0.313258i	$0.898580\pi$
$212$	−5.28690	−	9.15718i	−0.363106	−	0.628917i
$213$	2.14739	+	1.19365i	0.147137	+	0.0817872i
$214$	−4.96101	+	8.59273i	−0.339128	+	0.587387i
$215$	12.4275			0.847548
$216$	0.253508	+	5.18996i	0.0172490	+	0.353132i
$217$	21.8958	+	5.96834i	1.48638	+	0.405157i
$218$	−16.3272	−	9.42652i	−1.10582	−	0.638445i
$219$	−19.6579	−	10.9270i	−1.32836	−	0.738377i
$220$	−7.25188	+	4.18687i	−0.488921	+	0.282279i
$221$	5.03220	−	2.90534i	0.338502	−	0.195434i
$222$	5.02108	+	8.37893i	0.336993	+	0.562357i
$223$	−20.5760	−	11.8796i	−1.37787	−	0.795514i	−0.385967	−	0.922513i	$-0.626132\pi$
$223$	−20.5760	−	11.8796i	−1.37787	−	0.795514i	−0.991903	+	0.126999i	$0.959465\pi$
$224$		−	4.07608i		−	0.272344i
$225$	−10.7995	+	0.351519i	−0.719968	+	0.0234346i
$226$	−9.73611			−0.647636
$227$	−6.15389	−	3.55295i	−0.408448	−	0.235818i	0.281675	−	0.959510i	$-0.409110\pi$
$227$	−6.15389	−	3.55295i	−0.408448	−	0.235818i	−0.690123	+	0.723692i	$0.742443\pi$
$228$	−12.1571	+	0.197801i	−0.805123	+	0.0130997i
$229$	−11.7189	+	6.76589i	−0.774405	+	0.447103i	−0.834444	−	0.551093i	$-0.814211\pi$
$229$	−11.7189	+	6.76589i	−0.774405	+	0.447103i	0.0600390	+	0.998196i	$0.480877\pi$
$230$	−12.7631	−	22.1063i	−0.841574	−	1.45765i
$231$	20.1545	−	0.327922i	1.32607	−	0.0215757i
$232$	5.53494	+	3.19560i	0.363387	+	0.209801i
$233$		−	4.43140i		−	0.290311i	−0.989409	−	0.145155i	$-0.953632\pi$
$233$		−	4.43140i		−	0.290311i	0.989409	−	0.145155i	$-0.0463682\pi$
$234$	1.62230	+	2.60996i	0.106053	+	0.170618i
$235$	10.1279			0.660669
$236$	−4.81405	−	2.77939i	−0.313368	−	0.180923i
$237$	5.64361	−	3.38193i	0.366592	−	0.219680i
$238$	−20.0240	+	11.5608i	−1.29796	+	0.749378i
$239$	−15.1818	−	26.2956i	−0.982028	−	1.70092i	−0.654465	−	0.756092i	$-0.727106\pi$
$239$	−15.1818	−	26.2956i	−0.982028	−	1.70092i	−0.327562	−	0.944830i	$-0.606227\pi$
$240$	4.44005	+	2.46804i	0.286604	+	0.159311i
$241$	6.71197	+	3.87516i	0.432356	+	0.249621i	0.700350	−	0.713800i	$-0.253027\pi$
$241$	6.71197	+	3.87516i	0.432356	+	0.249621i	−0.267994	+	0.963421i	$0.586361\pi$
$242$		−	2.84821i		−	0.183090i
$243$	8.86540	+	12.8220i	0.568716	+	0.822534i
$244$		−	12.5644i		−	0.804352i
$245$	−24.4201	−	14.0989i	−1.56014	−	0.900747i
$246$	−3.13138	+	5.63342i	−0.199650	+	0.359174i
$247$	−6.22741	+	3.59540i	−0.396240	+	0.228770i
$248$	5.38422	−	1.41782i	0.341898	−	0.0900319i
$249$	3.92390	+	6.54802i	0.248667	+	0.414964i
$250$	2.05045	−	3.55148i	0.129682	−	0.224615i
$251$	8.86796			0.559740			0.279870	−	0.960038i	$-0.409709\pi$
$251$	8.86796			0.559740			0.279870	+	0.960038i	$0.409709\pi$
$252$	−6.45540	−	10.3854i	−0.406652	−	0.654222i
$253$	−24.8496			−1.56228
$254$	4.82702	−	8.36064i	0.302874	−	0.524593i
$255$	−0.468783	−	28.8120i	−0.0293564	−	1.80428i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−23.6507	+	13.6547i	−1.47529	+	0.851759i	−0.999612	−	0.0278599i	$-0.991131\pi$
$257$	−23.6507	+	13.6547i	−1.47529	+	0.851759i	−0.475679	+	0.879619i	$0.657797\pi$
$258$	−7.33827	+	0.119397i	−0.456860	+	0.00743331i
$259$	−19.9080	−	11.4939i	−1.23702	−	0.714195i
$260$	3.00430			0.186319
$261$	19.1635	−	0.623760i	1.18619	−	0.0386098i
$262$	1.11041			0.0686012
$263$	6.96217	−	12.0588i	0.429306	−	0.743580i	−0.567506	−	0.823369i	$-0.692092\pi$
$263$	6.96217	−	12.0588i	0.429306	−	0.743580i	0.996812	+	0.0797897i	$0.0254249\pi$
$264$	4.24191	−	2.54196i	0.261071	−	0.156447i
$265$	−26.8568	+	15.5058i	−1.64980	+	0.952514i
$266$	24.7799	−	14.3067i	1.51935	−	0.877199i
$267$	−1.96851	+	3.54140i	−0.120471	+	0.216730i
$268$	0.327613	−	0.567442i	0.0200121	−	0.0346620i
$269$	−11.4048			−0.695365			−0.347683	−	0.937612i	$-0.613031\pi$
$269$	−11.4048			−0.695365			−0.347683	+	0.937612i	$0.613031\pi$
$270$	15.2215	−	0.743506i	0.926352	−	0.0452483i
$271$			2.56098i			0.155568i	0.996970	+	0.0777842i	$0.0247845\pi$
$271$			2.56098i			0.155568i	−0.996970	+	0.0777842i	$0.975215\pi$
$272$	−2.83627	+	4.91256i	−0.171974	+	0.297868i
$273$	−6.32102	−	3.51359i	−0.382566	−	0.212652i
$274$	2.05988	−	1.18927i	0.124442	−	0.0718466i
$275$	5.14173	+	8.90575i	0.310058	+	0.537037i
$276$	7.74882	+	12.9309i	0.466424	+	0.778346i
$277$	26.5465	+	15.3266i	1.59502	+	0.920888i	0.992426	+	0.122844i	$0.0392014\pi$
$277$	26.5465	+	15.3266i	1.59502	+	0.920888i	0.602599	+	0.798044i	$0.294132\pi$
$278$	17.4556			1.04692
$279$	11.4730	−	12.1396i	0.686871	−	0.726779i
$280$	−11.9546			−0.714425
$281$	11.1689	+	6.44836i	0.666279	+	0.384677i	0.794665	−	0.607048i	$-0.207646\pi$
$281$	11.1689	+	6.44836i	0.666279	+	0.384677i	−0.128386	+	0.991724i	$0.540980\pi$
$282$	−5.98036	+	0.0973030i	−0.356125	+	0.00579431i
$283$	1.29250	+	2.23868i	0.0768312	+	0.133076i	0.901881	−	0.431984i	$-0.142186\pi$
$283$	1.29250	+	2.23868i	0.0768312	+	0.133076i	−0.825050	+	0.565060i	$0.808853\pi$
$284$	−1.22842	+	0.709229i	−0.0728934	+	0.0420850i
$285$	0.580125	+	35.6552i	0.0343636	+	2.11203i
$286$	1.46233	−	2.53284i	0.0864697	−	0.149770i
$287$		−	15.1677i		−	0.895322i
$288$	−2.64550	−	1.41468i	−0.155888	−	0.0833611i
$289$	15.1776			0.892801
$290$	9.37229	−	16.2333i	0.550360	−	0.953251i
$291$	−4.79735	−	8.00559i	−0.281226	−	0.469296i
$292$	11.2453	−	6.49250i	0.658084	−	0.379945i
$293$	1.12509	−	0.649569i	0.0657282	−	0.0379482i	−0.466776	−	0.884376i	$-0.654584\pi$
$293$	1.12509	−	0.649569i	0.0657282	−	0.0379482i	0.532504	+	0.846428i	$0.321251\pi$
$294$	14.5552	+	8.09061i	0.848874	+	0.471854i
$295$	−8.15161	+	14.1190i	−0.474605	+	0.822040i
$296$	−5.63967			−0.327799
$297$	6.78219	−	13.1947i	0.393543	−	0.765634i
$298$	−2.24876			−0.130267
$299$	7.72100	+	4.45772i	0.446517	+	0.257797i
$300$	3.03090	−	5.45265i	0.174989	−	0.314809i
$301$	14.9577	−	8.63580i	0.862145	−	0.497759i
$302$	−0.545760	−	0.945284i	−0.0314050	−	0.0543950i
$303$	27.6461	−	16.5669i	1.58823	−	0.951746i
$304$	3.50991	−	6.07935i	0.201307	−	0.348674i
$305$	−36.8497			−2.11001
$306$	0.553620	+	17.0086i	0.0316484	+	0.972316i
$307$	−2.15765			−0.123144			−0.0615718	−	0.998103i	$-0.519611\pi$
$307$	−2.15765			−0.123144			−0.0615718	+	0.998103i	$0.519611\pi$
$308$	−5.81887	+	10.0786i	−0.331561	+	0.574281i
$309$	2.85650	−	0.0464765i	0.162501	−	0.00264396i
$310$	−4.15830	−	15.7912i	−0.236175	−	0.896881i
$311$	−11.9653	+	6.90814i	−0.678487	+	0.391725i	−0.799285	−	0.600952i	$-0.794788\pi$
$311$	−11.9653	+	6.90814i	−0.678487	+	0.391725i	0.120798	+	0.992677i	$0.461455\pi$
$312$	−1.77400	+	0.0288637i	−0.100433	+	0.00163409i
$313$	15.1750	+	8.76129i	0.857741	+	0.495217i	0.863255	−	0.504768i	$-0.168422\pi$
$313$	15.1750	+	8.76129i	0.857741	+	0.495217i	−0.00551388	+	0.999985i	$0.501755\pi$
$314$			6.56441i			0.370451i
$315$	−30.4592	+	18.9329i	−1.71618	+	1.06675i
$316$			3.79859i			0.213687i
$317$	13.8613	+	8.00281i	0.778527	+	0.449483i	0.835908	−	0.548870i	$-0.184942\pi$
$317$	13.8613	+	8.00281i	0.778527	+	0.449483i	−0.0573812	+	0.998352i	$0.518275\pi$
$318$	15.7096	−	9.41399i	0.880952	−	0.527910i
$319$	−9.12386	−	15.8030i	−0.510838	−	0.884798i
$320$	−2.53994	+	1.46644i	−0.141987	+	0.0819763i
$321$	−15.0209	−	8.34947i	−0.838383	−	0.466022i
$322$	−30.7232	−	17.7380i	−1.71213	−	0.988501i
$323$	−39.8202			−2.21565
$324$	−8.98095	+	0.585270i	−0.498942	+	0.0325150i
$325$		−	3.68947i		−	0.204655i
$326$	−8.02529	−	4.63340i	−0.444479	−	0.256620i
$327$	15.8650	−	28.5414i	0.877336	−	1.57835i
$328$	−1.86058	−	3.22261i	−0.102733	−	0.177939i
$329$	12.1898	−	7.03780i	0.672047	−	0.388006i
$330$	−7.45526	−	12.4410i	−0.410398	−	0.684853i
$331$	−30.6325	−	17.6857i	−1.68371	−	0.972093i	−0.959155	−	0.282880i	$-0.908710\pi$
$331$	−30.6325	−	17.6857i	−1.68371	−	0.972093i	−0.724559	−	0.689213i	$-0.757957\pi$
$332$	−4.40732			−0.241883
$333$	−14.3693	+	8.93170i	−0.787435	+	0.489454i
$334$			0.626535i			0.0342824i
$335$	−1.66423	−	0.960846i	−0.0909268	−	0.0524966i
$336$	7.05904	−	0.114854i	0.385102	−	0.00626577i
$337$	13.3807	−	7.72535i	0.728893	−	0.420827i	−0.0891240	−	0.996021i	$-0.528407\pi$
$337$	13.3807	−	7.72535i	0.728893	−	0.420827i	0.818017	+	0.575194i	$0.195073\pi$
$338$	10.3496	−	5.97535i	0.562944	−	0.325016i
$339$	−0.274339	−	16.8612i	−0.0149000	−	0.915775i
$340$	14.4079	+	8.31841i	0.781379	+	0.451129i
$341$	−15.3371	−	4.18059i	−0.830553	−	0.226392i
$342$	−0.685112	−	21.0483i	−0.0370466	−	1.13816i
$343$	−10.6565			−0.575399
$344$	2.11866	−	3.66962i	0.114230	−	0.197853i
$345$	37.9246	−	22.7263i	2.04179	−	1.22354i
$346$	11.8356	+	20.4999i	0.636286	+	1.10208i
$347$	14.6770	+	25.4213i	0.787902	+	1.36469i	0.927250	+	0.374443i	$0.122166\pi$
$347$	14.6770	+	25.4213i	0.787902	+	1.36469i	−0.139348	+	0.990244i	$0.544501\pi$
$348$	−5.37825	+	9.67558i	−0.288304	+	0.518665i
$349$	5.36076	−	9.28512i	0.286955	−	0.497021i	−0.686126	−	0.727482i	$-0.740690\pi$
$349$	5.36076	−	9.28512i	0.286955	−	0.497021i	0.973081	+	0.230462i	$0.0740236\pi$
$350$			14.6810i			0.784733i
$351$	−4.47427	+	2.88307i	−0.238819	+	0.153887i
$352$			2.85513i			0.152179i
$353$	1.65198	−	2.86131i	0.0879258	−	0.152292i	−0.818708	−	0.574210i	$-0.805309\pi$
$353$	1.65198	−	2.86131i	0.0879258	−	0.152292i	0.906634	+	0.421918i	$0.138643\pi$
$354$	4.67776	−	8.41539i	0.248620	−	0.447273i
$355$	2.08008	+	3.60280i	0.110399	+	0.191217i
$356$	−1.16963	−	2.02587i	−0.0619905	−	0.107371i
$357$	−20.5855	−	34.3522i	−1.08950	−	1.81811i
$358$	−1.34380	−	0.775846i	−0.0710223	−	0.0410047i
$359$		−	15.3585i		−	0.810589i	−0.914186	−	0.405295i	$-0.867169\pi$
$359$		−	15.3585i		−	0.810589i	0.914186	−	0.405295i	$-0.132831\pi$
$360$	−4.14909	+	7.75892i	−0.218676	+	0.408931i
$361$	30.2780			1.59358
$362$	−6.19420	+	10.7287i	−0.325560	+	0.563886i
$363$	4.93260	−	0.0802555i	0.258894	−	0.00421232i
$364$	3.61596	−	2.08767i	0.189528	−	0.109424i
$365$	−19.0417	−	32.9812i	−0.996687	−	1.72631i
$366$	21.7593	−	0.354032i	1.13737	−	0.0185056i
$367$	−9.12269	−	5.26699i	−0.476200	−	0.274934i	0.242631	−	0.970119i	$-0.421989\pi$
$367$	−9.12269	−	5.26699i	−0.476200	−	0.274934i	−0.718832	+	0.695184i	$0.755323\pi$
$368$	−8.70347			−0.453700
$369$	−9.84431	−	5.26426i	−0.512474	−	0.274046i
$370$			16.5404i			0.859897i
$371$	−21.5498	+	37.3254i	−1.11881	+	1.93784i
$372$	2.60713	+	9.28455i	0.135173	+	0.481381i
$373$	−14.7654	−	25.5743i	−0.764521	−	1.32419i	−0.940499	−	0.339796i	$-0.889642\pi$
$373$	−14.7654	−	25.5743i	−0.764521	−	1.32419i	0.175978	−	0.984394i	$-0.443691\pi$
$374$	14.0260	−	8.09792i	0.725267	−	0.418733i
$375$	6.20831	+	3.45094i	0.320596	+	0.178206i
$376$	1.72661	−	2.99058i	0.0890432	−	0.154227i
$377$			6.54686i			0.337180i
$378$	17.8038	−	11.4722i	0.915731	−	0.590068i
$379$	−7.54595			−0.387609			−0.193805	−	0.981040i	$-0.562083\pi$
$379$	−7.54595			−0.387609			−0.193805	+	0.981040i	$0.562083\pi$
$380$	−17.8300	−	10.2941i	−0.914658	−	0.528078i
$381$	14.6152	+	8.12396i	0.748757	+	0.416203i
$382$	−1.65851	−	2.87262i	−0.0848566	−	0.146976i
$383$	−0.603701	−	1.04564i	−0.0308477	−	0.0534297i	0.850189	−	0.526477i	$-0.176487\pi$
$383$	−0.603701	−	1.04564i	−0.0308477	−	0.0534297i	−0.881037	+	0.473047i	$0.843154\pi$
$384$	1.48571	−	0.890313i	0.0758175	−	0.0454336i
$385$	29.5592	+	17.0660i	1.50648	+	0.869765i
$386$		−	0.116890i		−	0.00594957i
$387$	−0.413547	−	12.7052i	−0.0210218	−	0.645842i
$388$	5.38838			0.273554
$389$	−5.74579	+	9.95201i	−0.291323	+	0.504587i	−0.974123	−	0.226019i	$-0.927429\pi$
$389$	−5.74579	+	9.95201i	−0.291323	+	0.504587i	0.682800	+	0.730606i	$0.260762\pi$
$390$	0.0846536	+	5.20292i	0.00428660	+	0.263460i
$391$	24.6854	+	42.7563i	1.24839	+	2.16228i
$392$	−8.32632	+	4.80721i	−0.420543	+	0.242801i
$393$	0.0312885	+	1.92303i	0.00157829	+	0.0970039i
$394$	−13.1090	−	7.56850i	−0.660423	−	0.381295i
$395$	11.1408			0.560553
$396$	4.52175	+	7.27460i	0.227227	+	0.365562i
$397$	−17.4608			−0.876333			−0.438167	−	0.898894i	$-0.644372\pi$
$397$	−17.4608			−0.876333			−0.438167	+	0.898894i	$0.644372\pi$
$398$	5.91494	−	10.2450i	0.296489	−	0.513534i
$399$	25.4748	+	42.5112i	1.27534	+	2.12822i
$400$	1.80087	+	3.11920i	0.0900437	+	0.155960i
$401$	9.37877	+	16.2445i	0.468354	+	0.811212i	0.999346	−	0.0361645i	$-0.0115140\pi$
$401$	9.37877	+	16.2445i	0.468354	+	0.811212i	−0.530992	+	0.847377i	$0.678181\pi$
$402$	0.991939	+	0.551377i	0.0494734	+	0.0275002i
$403$	4.01545	+	4.05025i	0.200024	+	0.201757i
$404$			18.6080i			0.925782i
$405$	1.71652	+	26.3400i	0.0852947	+	1.30884i
$406$		−	26.0510i		−	1.29289i
$407$	13.9448	+	8.05101i	0.691216	+	0.399074i
$408$	−8.58759	−	4.77348i	−0.425149	−	0.236323i
$409$	−12.5445	+	7.24259i	−0.620287	+	0.358123i	−0.776981	−	0.629524i	$-0.783250\pi$
$409$	−12.5445	+	7.24259i	−0.620287	+	0.358123i	0.156693	+	0.987647i	$0.449917\pi$
$410$	−9.45152	+	5.45684i	−0.466777	+	0.269494i
$411$	2.11765	+	3.53383i	0.104456	+	0.174311i
$412$	−0.824711	+	1.42844i	−0.0406306	+	0.0703742i
$413$			22.6580i			1.11493i
$414$	−22.1756	+	13.7839i	−1.08987	+	0.677443i
$415$			12.9261i			0.634518i
$416$	0.512177	−	0.887117i	0.0251116	−	0.0434945i
$417$	0.491855	+	30.2300i	0.0240862	+	1.48037i
$418$	−17.3573	+	10.0213i	−0.848976	+	0.490156i
$419$	−22.1910	+	12.8120i	−1.08410	+	0.625906i	−0.932000	−	0.362459i	$-0.881937\pi$
$419$	−22.1910	+	12.8120i	−1.08410	+	0.625906i	−0.152101	+	0.988365i	$0.548604\pi$
$420$	−0.336851	−	20.7033i	−0.0164366	−	1.01022i
$421$	15.0985	−	26.1513i	0.735854	−	1.27454i	−0.218494	−	0.975838i	$-0.570114\pi$
$421$	15.0985	−	26.1513i	0.735854	−	1.27454i	0.954348	−	0.298698i	$-0.0965522\pi$
$422$			5.91332i			0.287856i
$423$	−0.337023	−	10.3542i	−0.0163866	−	0.503438i
$424$			10.5738i			0.513509i
$425$	10.2155	−	17.6938i	0.495525	−	0.858275i
$426$	−1.26287	−	2.10742i	−0.0611864	−	0.102105i
$427$	−44.3521	+	25.6067i	−2.14635	+	1.23919i
$428$	8.59273	−	4.96101i	0.415345	−	0.239800i
$429$	4.42763	+	2.46113i	0.213768	+	0.118825i
$430$	−10.7625	−	6.21375i	−0.519015	−	0.299654i
$431$			22.9545i			1.10568i	0.833287	+	0.552840i	$0.186456\pi$
$431$			22.9545i			1.10568i	−0.833287	+	0.552840i	$0.813544\pi$
$432$	2.37544	−	4.62140i	0.114288	−	0.222347i
$433$		−	15.5286i		−	0.746257i	−0.927780	−	0.373129i	$-0.878285\pi$
$433$		−	15.5286i		−	0.746257i	0.927780	−	0.373129i	$-0.121715\pi$
$434$	−15.9781	−	16.1166i	−0.766975	−	0.773623i
$435$	28.3772	+	15.7737i	1.36058	+	0.756292i
$436$	9.42652	+	16.3272i	0.451449	+	0.781932i
$437$	−30.5484	−	52.9114i	−1.46133	−	2.53110i
$438$	11.5607	+	19.2920i	0.552392	+	0.921807i
$439$	−4.51078	+	7.81290i	−0.215288	+	0.372889i	−0.953362	−	0.301831i	$-0.902402\pi$
$439$	−4.51078	+	7.81290i	−0.215288	+	0.372889i	0.738074	+	0.674720i	$0.235736\pi$
$440$	8.37374			0.399203
$441$	−13.6014	+	25.4349i	−0.647684	+	1.21119i
$442$	−5.81068			−0.276386
$443$	26.8128	+	15.4804i	1.27392	+	0.735496i	0.975723	−	0.219009i	$-0.0702824\pi$
$443$	26.8128	+	15.4804i	1.27392	+	0.735496i	0.298194	+	0.954505i	$0.403616\pi$
$444$	−0.158912	−	9.76691i	−0.00754162	−	0.463517i
$445$	−5.94161	+	3.43039i	−0.281659	+	0.162616i
$446$	11.8796	+	20.5760i	0.562513	+	0.974301i
$447$	−0.0633644	−	3.89445i	−0.00299703	−	0.184201i
$448$	−2.03804	+	3.52999i	−0.0962883	+	0.166776i
$449$	0.114241			0.00539135			0.00269568	−	0.999996i	$-0.499142\pi$
$449$	0.114241			0.00539135			0.00269568	+	0.999996i	$0.499142\pi$
$450$	9.52842	+	5.09534i	0.449174	+	0.240197i
$451$			10.6244i			0.500283i
$452$	8.43172	+	4.86805i	0.396595	+	0.228974i
$453$	1.62169	−	0.971795i	0.0761934	−	0.0456589i
$454$	3.55295	+	6.15389i	0.166748	+	0.288816i
$455$	−6.12289	−	10.6051i	−0.287045	−	0.497177i
$456$	10.6272	+	5.90724i	0.497666	+	0.276632i
$457$	14.0698	+	8.12321i	0.658158	+	0.379988i	0.791575	−	0.611072i	$-0.209261\pi$
$457$	14.0698	+	8.12321i	0.658158	+	0.379988i	−0.133417	+	0.991060i	$0.542595\pi$
$458$	13.5318			0.632299
$459$	−29.4402	+	1.43803i	−1.37415	+	0.0671215i
$460$			25.5262i			1.19016i
$461$	12.0624	−	20.8926i	0.561800	−	0.973066i	−0.435540	−	0.900170i	$-0.643442\pi$
$461$	12.0624	−	20.8926i	0.561800	−	0.973066i	0.997340	−	0.0728965i	$-0.0232243\pi$
$462$	−17.6183	−	9.79326i	−0.819676	−	0.455624i
$463$	2.07227	−	1.19642i	0.0963065	−	0.0556026i	−0.451073	−	0.892487i	$-0.648959\pi$
$463$	2.07227	−	1.19642i	0.0963065	−	0.0556026i	0.547380	+	0.836884i	$0.315625\pi$
$464$	−3.19560	−	5.53494i	−0.148352	−	0.256953i
$465$	27.2304	−	7.64639i	1.26278	−	0.354593i
$466$	−2.21570	+	3.83770i	−0.102640	+	0.177778i
$467$		−	13.5383i		−	0.626476i	−0.949675	−	0.313238i	$-0.898586\pi$
$467$		−	13.5383i		−	0.626476i	0.949675	−	0.313238i	$-0.101414\pi$
$468$	−0.0999736	−	3.07144i	−0.00462128	−	0.141977i
$469$	−2.67075			−0.123324
$470$	−8.77099	−	5.06393i	−0.404575	−	0.233582i
$471$	−11.3684	+	0.184968i	−0.523828	+	0.00852290i
$472$	2.77939	+	4.81405i	0.127932	+	0.221585i
$473$	−10.4772	+	6.04904i	−0.481744	+	0.278135i
$474$	−6.57847	+	0.107035i	−0.302159	+	0.00491626i
$475$	−12.6418	+	21.8963i	−0.580046	+	1.00467i
$476$	23.1217			1.05978
$477$	16.7460	+	26.9410i	0.766747	+	1.23354i
$478$			30.3636i			1.38880i
$479$	−21.6971	−	12.5268i	−0.991364	−	0.572364i	−0.0856824	−	0.996323i	$-0.527307\pi$
$479$	−21.6971	−	12.5268i	−0.991364	−	0.572364i	−0.905682	+	0.423958i	$0.860640\pi$
$480$	−2.61118	−	4.35741i	−0.119183	−	0.198888i
$481$	−2.88851	−	5.00305i	−0.131705	−	0.228119i
$482$	−3.87516	−	6.71197i	−0.176509	−	0.305722i
$483$	29.8534	−	53.7068i	1.35838	−	2.44375i
$484$	−1.42411	+	2.46663i	−0.0647321	+	0.112119i
$485$		−	15.8035i		−	0.717598i
$486$	−1.26664	−	15.5369i	−0.0574561	−	0.704769i
$487$		−	2.48634i		−	0.112667i	−0.998412	−	0.0563335i	$-0.982059\pi$
$487$		−	2.48634i		−	0.112667i	0.998412	−	0.0563335i	$-0.0179410\pi$
$488$	−6.28219	+	10.8811i	−0.284381	+	0.492563i
$489$	7.79809	−	14.0289i	0.352642	−	0.634410i
$490$	14.0989	+	24.4201i	0.636925	+	1.10319i
$491$	10.5582	+	18.2873i	0.476484	+	0.825294i	0.999637	−	0.0269445i	$-0.00857774\pi$
$491$	10.5582	+	18.2873i	0.476484	+	0.825294i	−0.523153	+	0.852239i	$0.675244\pi$
$492$	5.52857	−	3.31299i	0.249247	−	0.149361i
$493$	−18.1271	+	31.3971i	−0.816406	+	1.41406i
$494$	7.19079			0.323529
$495$	21.3355	−	13.2617i	0.958959	−	0.596070i
$496$	−5.37178	−	1.46424i	−0.241200	−	0.0657462i
$497$	5.00714	+	2.89087i	0.224601	+	0.129673i
$498$	−0.124187	−	7.63270i	−0.00556496	−	0.342029i
$499$	9.97074	−	5.75661i	0.446352	−	0.257701i	−0.259937	−	0.965626i	$-0.583702\pi$
$499$	9.97074	−	5.75661i	0.446352	−	0.257701i	0.706288	+	0.707925i	$0.250368\pi$
$500$	−3.55148	+	2.05045i	−0.158827	+	0.0916989i
$501$	−1.08505	+	0.0176542i	−0.0484763	+	0.000788730i
$502$	−7.67988	−	4.43398i	−0.342770	−	0.197898i
$503$		−	39.6468i		−	1.76776i	−0.467710	−	0.883882i	$-0.654921\pi$
$503$		−	39.6468i		−	1.76776i	0.467710	−	0.883882i	$-0.345079\pi$
$504$	0.397812	+	12.2218i	0.0177199	+	0.544401i
$505$	54.5749			2.42855
$506$	21.5204	+	12.4248i	0.956697	+	0.552349i
$507$	10.6399	+	17.7553i	0.472533	+	0.788541i
$508$	−8.36064	+	4.82702i	−0.370944	+	0.214164i
$509$	−11.2188	−	19.4315i	−0.497265	−	0.861288i	0.502730	−	0.864443i	$-0.332329\pi$
$509$	−11.2188	−	19.4315i	−0.497265	−	0.861288i	−0.999995	+	0.00315565i	$0.998996\pi$
$510$	−14.0000	+	25.1863i	−0.619931	+	1.11527i
$511$	−45.8369	−	26.4639i	−2.02770	−	1.17070i
$512$			1.00000i			0.0441942i
$513$	36.4326	−	1.77958i	1.60854	−	0.0785704i
$514$	27.3095			1.20457
$515$	4.18944	+	2.41877i	0.184609	+	0.106584i
$516$	6.41482	+	3.56573i	0.282397	+	0.156973i
$517$	−8.53850	+	4.92970i	−0.375523	+	0.216808i
$518$	11.4939	+	19.9080i	0.505012	+	0.874706i
$519$	−35.1686	+	21.0748i	−1.54373	+	0.925080i
$520$	−2.60180	−	1.50215i	−0.114097	−	0.0658737i
$521$			20.4636i			0.896526i	0.893902	+	0.448263i	$0.147957\pi$
$521$			20.4636i			0.896526i	−0.893902	+	0.448263i	$0.852043\pi$
$522$	−16.9079	−	9.04153i	−0.740039	−	0.395737i
$523$		−	24.0253i		−	1.05055i	−0.850931	−	0.525277i	$-0.823962\pi$
$523$		−	24.0253i		−	1.05055i	0.850931	−	0.525277i	$-0.176038\pi$
$524$	−0.961641	−	0.555203i	−0.0420095	−	0.0242542i
$525$	−25.4249	+	0.413673i	−1.10963	+	0.0180542i
$526$	−12.0588	+	6.96217i	−0.525790	+	0.303565i
$527$	8.04265	+	30.5421i	0.350343	+	1.33044i
$528$	−4.94458	+	0.0804504i	−0.215185	+	0.00350116i
$529$	−26.3752	+	45.6832i	−1.14675	+	1.98623i
$530$	31.0116			1.34706
$531$	14.7058	+	7.86393i	0.638176	+	0.341265i
$532$	−28.6134			−1.24055
$533$	1.90589	−	3.30110i	0.0825533	−	0.142986i
$534$	3.47548	−	2.08268i	0.150399	−	0.0901265i
$535$	−14.5500	−	25.2014i	−0.629052	−	1.08955i
$536$	−0.567442	+	0.327613i	−0.0245097	+	0.0141507i
$537$	1.30576	−	2.34909i	0.0563478	−	0.101371i
$538$	9.87688	+	5.70242i	0.425822	+	0.245849i
$539$	27.4504			1.18237
$540$	−13.5540	−	6.96686i	−0.583270	−	0.299806i
$541$	4.82179			0.207305			0.103653	−	0.994614i	$-0.466947\pi$
$541$	4.82179			0.207305			0.103653	+	0.994614i	$0.466947\pi$
$542$	1.28049	−	2.21787i	0.0550018	−	0.0952658i
$543$	−18.7547	−	10.4249i	−0.804840	−	0.447377i
$544$	4.91256	−	2.83627i	0.210624	−	0.121604i
$545$	47.8857	−	27.6468i	2.05120	−	1.18426i
$546$	3.71737	+	6.20337i	0.159089	+	0.265480i
$547$	10.7763	−	18.6651i	0.460761	−	0.798061i	−0.538238	−	0.842793i	$-0.680910\pi$
$547$	10.7763	−	18.6651i	0.460761	−	0.798061i	0.998999	+	0.0447319i	$0.0142434\pi$
$548$	−2.37854			−0.101606
$549$	1.22624	+	37.6732i	0.0523347	+	1.60785i
$550$		−	10.2835i		−	0.438489i
$551$	22.4326	−	38.8543i	0.955659	−	1.65525i
$552$	−0.245242	−	15.0729i	−0.0104382	−	0.641544i
$553$	13.4090	−	7.74167i	0.570207	−	0.329209i
$554$	−15.3266	−	26.5465i	−0.651166	−	1.12785i
$555$	−28.6451	+	0.466068i	−1.21592	+	0.0197835i
$556$	−15.1170	−	8.72781i	−0.641104	−	0.370141i
$557$	−29.6046			−1.25439			−0.627194	−	0.778863i	$-0.715797\pi$
$557$	−29.6046			−1.25439			−0.627194	+	0.778863i	$0.715797\pi$
$558$	−16.0057	+	4.77670i	−0.677576	+	0.202214i
$559$	4.34051			0.183584
$560$	10.3530	+	5.97731i	0.437494	+	0.252587i
$561$	14.4194	+	24.0624i	0.608786	+	1.01591i
$562$	−6.44836	−	11.1689i	−0.272007	−	0.471131i
$563$	−35.1826	+	20.3127i	−1.48277	+	0.856079i	−0.999809	−	0.0195620i	$-0.993773\pi$
$563$	−35.1826	+	20.3127i	−1.48277	+	0.856079i	−0.482963	+	0.875641i	$0.660440\pi$
$564$	5.22780	+	2.90591i	0.220130	+	0.122361i
$565$	14.2774	−	24.7292i	0.600654	−	1.04036i
$566$		−	2.58500i		−	0.108656i
$567$	20.3695	+	30.5098i	0.855439	+	1.28129i
$568$	1.41846			0.0595172
$569$	0.258866	−	0.448369i	0.0108522	−	0.0187966i	−0.860548	−	0.509369i	$-0.829879\pi$
$569$	0.258866	−	0.448369i	0.0108522	−	0.0187966i	0.871401	+	0.490572i	$0.163212\pi$
$570$	17.3252	−	31.1684i	0.725673	−	1.30550i
$571$	37.4562	−	21.6254i	1.56749	−	0.904993i	0.571034	−	0.820926i	$-0.306542\pi$
$571$	37.4562	−	21.6254i	1.56749	−	0.904993i	0.996460	−	0.0840671i	$-0.0267910\pi$
$572$	−2.53284	+	1.46233i	−0.105903	+	0.0611433i
$573$	4.92813	−	2.95318i	0.205876	−	0.123371i
$574$	−7.58386	+	13.1356i	−0.316544	+	0.548270i
$575$	31.3477			1.30729
$576$	1.58373	+	2.54790i	0.0659886	+	0.106163i
$577$	−24.4727			−1.01881			−0.509405	−	0.860527i	$-0.670135\pi$
$577$	−24.4727			−1.01881			−0.509405	+	0.860527i	$0.670135\pi$
$578$	−13.1442	−	7.58881i	−0.546727	−	0.315653i
$579$	0.202433	−	0.00329368i	0.00841284	−	0.000136880i
$580$	−16.2333	+	9.37229i	−0.674050	+	0.389163i
$581$	8.98230	+	15.5578i	0.372648	+	0.645446i
$582$	0.151831	+	9.33172i	0.00629360	+	0.386812i
$583$	15.0948	−	26.1450i	0.625163	−	1.08281i
$584$	−12.9850			−0.537323
$585$	−9.00814	+	0.293210i	−0.372441	+	0.0121227i
$586$	−1.29914			−0.0536669
$587$	−5.84891	+	10.1306i	−0.241410	+	0.418135i	−0.961116	−	0.276144i	$-0.910943\pi$
$587$	−5.84891	+	10.1306i	−0.241410	+	0.418135i	0.719706	+	0.694279i	$0.244277\pi$
$588$	−8.55984	−	14.2843i	−0.353002	−	0.589073i
$589$	−9.95287	−	37.7963i	−0.410101	−	1.55737i
$590$	14.1190	−	8.15161i	0.581270	−	0.335596i
$591$	12.7379	−	22.9157i	0.523967	−	0.942628i
$592$	4.88410	+	2.81984i	0.200735	+	0.115895i
$593$		−	13.5891i		−	0.558039i	−0.960285	−	0.279020i	$-0.909991\pi$
$593$		−	13.5891i		−	0.558039i	0.960285	−	0.279020i	$-0.0900094\pi$
$594$	−12.4709	+	8.03585i	−0.511687	+	0.329715i
$595$		−	67.8130i		−	2.78006i
$596$	1.94748	+	1.12438i	0.0797721	+	0.0460564i
$597$	17.9091	+	9.95494i	0.732972	+	0.407429i
$598$	−4.45772	−	7.72100i	−0.182290	−	0.315735i
$599$	10.1957	−	5.88651i	0.416587	−	0.240516i	−0.277029	−	0.960861i	$-0.589350\pi$
$599$	10.1957	−	5.88651i	0.416587	−	0.240516i	0.693616	+	0.720345i	$0.256017\pi$
$600$	−5.35116	+	3.20668i	−0.218460	+	0.130912i
$601$	−4.87209	−	2.81290i	−0.198737	−	0.114741i	0.397329	−	0.917676i	$-0.369937\pi$
$601$	−4.87209	−	2.81290i	−0.198737	−	0.114741i	−0.596066	+	0.802935i	$0.703270\pi$
$602$	−17.2716			−0.703938
$603$	−0.926937	+	1.73340i	−0.0377478	+	0.0705894i
$604$			1.09152i			0.0444133i
$605$	7.23430	+	4.17673i	0.294116	+	0.169808i
$606$	−32.2257	+	0.524326i	−1.30908	+	0.0212993i
$607$	17.5127	+	30.3328i	0.710817	+	1.23117i	0.964551	+	0.263897i	$0.0850079\pi$
$607$	17.5127	+	30.3328i	0.710817	+	1.23117i	−0.253734	+	0.967274i	$0.581659\pi$
$608$	−6.07935	+	3.50991i	−0.246550	+	0.142346i
$609$	45.1157	−	0.734052i	1.82818	−	0.0297453i
$610$	31.9128	+	18.4249i	1.29211	+	0.746001i
$611$	3.53732			0.143105
$612$	8.02485	−	15.0067i	0.324385	−	0.606609i
$613$			41.6914i			1.68390i	0.539555	+	0.841950i	$0.318592\pi$
$613$			41.6914i			1.68390i	−0.539555	+	0.841950i	$0.681408\pi$
$614$	1.86858	+	1.07883i	0.0754098	+	0.0435379i
$615$	−9.71659	−	16.2146i	−0.391811	−	0.653835i
$616$	10.0786	−	5.81887i	0.406078	−	0.234449i
$617$	−24.1663	+	13.9524i	−0.972900	+	0.561704i	−0.900119	−	0.435644i	$-0.856521\pi$
$617$	−24.1663	+	13.9524i	−0.972900	+	0.561704i	−0.0727809	+	0.997348i	$0.523187\pi$
$618$	−2.49704	−	1.38800i	−0.100446	−	0.0558336i
$619$	11.3385	+	6.54630i	0.455734	+	0.263118i	0.710249	−	0.703951i	$-0.248582\pi$
$619$	11.3385	+	6.54630i	0.455734	+	0.263118i	−0.254515	+	0.967069i	$0.581916\pi$
$620$	−4.29442	+	15.7547i	−0.172468	+	0.632726i
$621$	−24.4962	−	38.0158i	−0.982997	−	1.52552i
$622$	13.8163			0.553982
$623$	−4.76752	+	8.25759i	−0.191007	+	0.330833i
$624$	1.55076	+	0.862003i	0.0620801	+	0.0345077i
$625$	15.0181	+	26.0121i	0.600723	+	1.04048i
$626$	−8.76129	−	15.1750i	−0.350171	−	0.606515i
$627$	−17.8441	−	29.7775i	−0.712626	−	1.18920i
$628$	3.28221	−	5.68495i	0.130974	−	0.226854i
$629$		−	31.9912i		−	1.27557i
$630$	35.8449	−	1.16673i	1.42809	−	0.0464837i
$631$		−	10.9471i		−	0.435796i	−0.975972	−	0.217898i	$-0.930080\pi$
$631$		−	10.9471i		−	0.435796i	0.975972	−	0.217898i	$-0.0699200\pi$
$632$	1.89929	−	3.28967i	0.0755498	−	0.130856i
$633$	−10.2408	+	0.166622i	−0.407036	+	0.00662265i
$634$	−8.00281	−	13.8613i	−0.317832	−	0.550502i
$635$	14.1570	+	24.5207i	0.561805	+	0.973075i
$636$	−18.3119	+	0.297943i	−0.726115	+	0.0118142i
$637$	−8.52911	−	4.92428i	−0.337936	−	0.195107i
$638$			18.2477i			0.722434i
$639$	3.61410	−	2.24645i	0.142971	−	0.0888683i
$640$	2.93287			0.115932
$641$	12.6285	−	21.8732i	0.498796	−	0.863939i	−0.501203	−	0.865329i	$-0.667109\pi$
$641$	12.6285	−	21.8732i	0.498796	−	0.863939i	0.999999	+	0.00139021i	$0.000442517\pi$
$642$	8.83371	+	14.7413i	0.348639	+	0.581792i
$643$	−5.65600	+	3.26550i	−0.223051	+	0.128779i	−0.607362	−	0.794425i	$-0.707772\pi$
$643$	−5.65600	+	3.26550i	−0.223051	+	0.128779i	0.384311	+	0.923204i	$0.374439\pi$
$644$	17.7380	+	30.7232i	0.698976	+	1.21066i
$645$	10.4578	−	18.8139i	0.411777	−	0.740795i
$646$	34.4853	+	19.9101i	1.35681	+	0.783352i
$647$	−30.8555			−1.21306			−0.606528	−	0.795062i	$-0.707438\pi$
$647$	−30.8555			−1.21306			−0.606528	+	0.795062i	$0.707438\pi$
$648$	8.07037	+	3.98362i	0.317034	+	0.156491i
$649$		−	15.8711i		−	0.622994i
$650$	−1.84473	+	3.19517i	−0.0723564	+	0.125325i
$651$	27.4609	−	28.1254i	1.07628	−	1.10232i
$652$	4.63340	+	8.02529i	0.181458	+	0.314294i
$653$	−21.0077	+	12.1288i	−0.822095	+	0.474637i	−0.851139	−	0.524941i	$-0.824087\pi$
$653$	−21.0077	+	12.1288i	−0.822095	+	0.474637i	0.0290431	+	0.999578i	$0.490754\pi$
$654$	−28.0102	+	16.7851i	−1.09529	+	0.656350i
$655$	−1.62834	+	2.82037i	−0.0636246	+	0.110201i
$656$			3.72115i			0.145287i
$657$	−33.0845	+	20.5647i	−1.29075	+	0.802305i
$658$	−14.0756			−0.548724
$659$	−12.9132	−	7.45542i	−0.503026	−	0.290422i	0.226937	−	0.973910i	$-0.427129\pi$
$659$	−12.9132	−	7.45542i	−0.503026	−	0.290422i	−0.729962	+	0.683488i	$0.760462\pi$
$660$	0.235951	+	14.5018i	0.00918438	+	0.564483i
$661$	−5.59524	−	9.69123i	−0.217629	−	0.376945i	0.736453	−	0.676488i	$-0.236499\pi$
$661$	−5.59524	−	9.69123i	−0.217629	−	0.376945i	−0.954083	+	0.299543i	$0.903166\pi$
$662$	17.6857	+	30.6325i	0.687373	+	1.19057i
$663$	−0.163730	−	10.0631i	−0.00635876	−	0.390817i
$664$	3.81685	+	2.20366i	0.148123	+	0.0855187i
$665$			83.9194i			3.25425i
$666$	16.9101	−	0.550413i	0.655252	−	0.0213281i
$667$	−55.6256			−2.15383
$668$	0.313267	−	0.542595i	0.0121207	−	0.0209936i
$669$	−35.2992	+	21.1530i	−1.36475	+	0.817824i
$670$	0.960846	+	1.66423i	0.0371207	+	0.0642950i
$671$	31.0669	−	17.9365i	1.19932	−	0.692430i
$672$	−6.17073	−	3.43005i	−0.238041	−	0.132317i
$673$	−32.2169	−	18.6004i	−1.24187	−	0.716993i	−0.272395	−	0.962186i	$-0.587816\pi$
$673$	−32.2169	−	18.6004i	−1.24187	−	0.716993i	−0.969474	+	0.245192i	$0.921149\pi$
$674$	−15.4507			−0.595139
$675$	−8.55573	+	16.6451i	−0.329310	+	0.640670i
$676$	−11.9507			−0.459642
$677$	−15.6341	+	27.0790i	−0.600867	+	1.04073i	0.391823	+	0.920041i	$0.371845\pi$
$677$	−15.6341	+	27.0790i	−0.600867	+	1.04073i	−0.992690	+	0.120692i	$0.961489\pi$
$678$	−8.19302	+	14.7394i	−0.314651	+	0.566063i
$679$	−10.9817	−	19.0209i	−0.421440	−	0.729956i
$680$	−8.31841	−	14.4079i	−0.318996	−	0.552518i
$681$	−10.5573	+	6.32647i	−0.404557	+	0.242431i
$682$	11.1921	+	11.2891i	0.428566	+	0.432281i
$683$			13.5166i			0.517199i	0.965985	+	0.258600i	$0.0832610\pi$
$683$			13.5166i			0.517199i	−0.965985	+	0.258600i	$0.916739\pi$
$684$	−9.93084	+	18.5709i	−0.379715	+	0.710078i
$685$			6.97597i			0.266538i
$686$	9.22884	+	5.32827i	0.352359	+	0.203434i
$687$	0.381291	+	23.4346i	0.0145472	+	0.894087i
$688$	−3.66962	+	2.11866i	−0.139903	+	0.0807730i
$689$	−9.38019	+	5.41566i	−0.357357	+	0.206320i
$690$	−44.2068	+	0.719263i	−1.68292	+	0.0273819i
$691$	−0.917897	+	1.58984i	−0.0349185	+	0.0604805i	−0.882956	−	0.469455i	$-0.844450\pi$
$691$	−0.917897	+	1.58984i	−0.0349185	+	0.0604805i	0.848038	+	0.529935i	$0.177784\pi$
$692$		−	23.6712i		−	0.899844i
$693$	16.4637	−	30.7876i	0.625406	−	1.16953i
$694$		−	29.3540i		−	1.11426i
$695$	−25.5976	+	44.3363i	−0.970970	+	1.68177i
$696$	9.49549	−	5.69017i	0.359926	−	0.215685i
$697$	18.2804	−	10.5542i	0.692419	−	0.399768i
$698$	−9.28512	+	5.36076i	−0.351447	+	0.202908i
$699$	−6.70865	−	3.72906i	−0.253745	−	0.141046i
$700$	7.34050	−	12.7141i	0.277445	−	0.480549i
$701$		−	32.7034i		−	1.23519i	−0.786496	−	0.617595i	$-0.788107\pi$
$701$		−	32.7034i		−	1.23519i	0.786496	−	0.617595i	$-0.211893\pi$
$702$	5.31636	−	0.259682i	0.200653	−	0.00980106i
$703$			39.5895i			1.49315i
$704$	1.42757	−	2.47262i	0.0538034	−	0.0931903i
$705$	8.52268	−	15.3325i	0.320983	−	0.577454i
$706$	−2.86131	+	1.65198i	−0.107687	+	0.0621729i
$707$	65.6860	−	37.9238i	2.47038	−	1.42627i
$708$	−8.25876	+	4.94906i	−0.310383	+	0.185997i
$709$	31.9531	+	18.4481i	1.20002	+	0.692833i	0.960560	−	0.278073i	$-0.0896956\pi$
$709$	31.9531	+	18.4481i	1.20002	+	0.692833i	0.239462	+	0.970906i	$0.423029\pi$
$710$		−	4.16016i		−	0.156128i
$711$	−0.370729	−	11.3897i	−0.0139034	−	0.427148i
$712$			2.33927i			0.0876678i
$713$	−34.4132	+	34.1174i	−1.28878	+	1.27771i
$714$	0.651510	+	40.0426i	0.0243822	+	1.49856i
$715$	4.28884	+	7.42849i	0.160394	+	0.277810i
$716$	0.775846	+	1.34380i	0.0289947	+	0.0502203i
$717$	−52.5843	+	0.855568i	−1.96380	+	0.0319518i
$718$	−7.67923	+	13.3008i	−0.286587	+	0.496382i
$719$	−16.0983			−0.600367			−0.300183	−	0.953881i	$-0.597048\pi$
$719$	−16.0983			−0.600367			−0.300183	+	0.953881i	$0.597048\pi$
$720$	7.47268	−	4.64487i	0.278490	−	0.173104i
$721$	6.72317			0.250384
$722$	−26.2215	−	15.1390i	−0.975862	−	0.563414i
$723$	11.5148	−	6.90021i	0.428238	−	0.256622i
$724$	10.7287	−	6.19420i	0.398728	−	0.230206i
$725$	11.5097	+	19.9355i	0.427461	+	0.740384i
$726$	−4.31188	−	2.39680i	−0.160029	−	0.0889534i
$727$	−0.646145	+	1.11916i	−0.0239642	+	0.0415072i	−0.877759	−	0.479103i	$-0.840962\pi$
$727$	−0.646145	+	1.11916i	−0.0239642	+	0.0415072i	0.853795	+	0.520610i	$0.174295\pi$
$728$	−4.17535			−0.154749
$729$	26.8715	−	2.63139i	0.995240	−	0.0974590i
$730$			38.0834i			1.40953i
$731$	20.8160	+	12.0181i	0.769909	+	0.444507i
$732$	−19.0211	−	10.5730i	−0.703040	−	0.390790i
$733$	6.61585	+	11.4590i	0.244362	+	0.423247i	0.961952	−	0.273218i	$-0.0880882\pi$
$733$	6.61585	+	11.4590i	0.244362	+	0.423247i	−0.717590	+	0.696466i	$0.754755\pi$
$734$	5.26699	+	9.12269i	0.194408	+	0.336725i
$735$	−41.8939	+	25.1049i	−1.54528	+	0.926009i
$736$	7.53743	+	4.35174i	0.277833	+	0.160407i
$737$	1.87075			0.0689101
$738$	5.89329	+	9.48114i	0.216935	+	0.349005i
$739$		−	14.0404i		−	0.516483i	−0.966080	−	0.258242i	$-0.916857\pi$
$739$		−	14.0404i		−	0.516483i	0.966080	−	0.258242i	$-0.0831431\pi$
$740$	8.27022	−	14.3244i	0.304020	−	0.526577i
$741$	0.202618	+	12.4532i	0.00744337	+	0.457479i
$742$	37.3254	−	21.5498i	1.37026	−	0.791118i
$743$	−12.3917	−	21.4630i	−0.454606	−	0.787401i	0.544059	−	0.839047i	$-0.316887\pi$
$743$	−12.3917	−	21.4630i	−0.454606	−	0.787401i	−0.998665	+	0.0516459i	$0.983553\pi$
$744$	2.38443	−	9.34422i	0.0874176	−	0.342576i
$745$	3.29767	−	5.71173i	0.120817	−	0.209261i
$746$			29.5307i			1.08120i
$747$	13.2150	−	0.430140i	0.483511	−	0.0157380i
$748$	−16.1958			−0.592178
$749$	−35.0246	−	20.2215i	−1.27977	−	0.738877i
$750$	−3.65108	−	6.09276i	−0.133319	−	0.222476i
$751$	−1.28802	−	2.23091i	−0.0470004	−	0.0814071i	0.841568	−	0.540151i	$-0.181633\pi$
$751$	−1.28802	−	2.23091i	−0.0470004	−	0.0814071i	−0.888569	+	0.458744i	$0.848300\pi$
$752$	−2.99058	+	1.72661i	−0.109055	+	0.0629630i
$753$	7.46246	−	13.4251i	0.271947	−	0.489238i
$754$	3.27343	−	5.66974i	0.119211	−	0.206480i
$755$	3.20129			0.116507
$756$	−21.1547	+	1.03332i	−0.769389	+	0.0375814i
$757$		−	29.0801i		−	1.05693i	−0.848954	−	0.528466i	$-0.822767\pi$
$757$		−	29.0801i		−	1.05693i	0.848954	−	0.528466i	$-0.177233\pi$
$758$	6.53498	+	3.77297i	0.237361	+	0.137041i
$759$	−20.9111	+	37.6195i	−0.759026	+	1.36550i
$760$	10.2941	+	17.8300i	0.373407	+	0.646761i
$761$	0.248473	+	0.430368i	0.00900715	+	0.0156008i	0.870494	−	0.492179i	$-0.163800\pi$
$761$	0.248473	+	0.430368i	0.00900715	+	0.0156008i	−0.861487	+	0.507780i	$0.830466\pi$
$762$	−8.59512	−	14.3431i	−0.311368	−	0.519597i
$763$	38.4232	−	66.5510i	1.39101	−	2.40931i
$764$			3.31701i			0.120005i
$765$	−44.0127	−	23.5359i	−1.59128	−	0.850941i
$766$			1.20740i			0.0436252i
$767$	−2.84708	+	4.93129i	−0.102802	+	0.178059i
$768$	−1.73182	+	0.0281775i	−0.0624917	+	0.00101677i
$769$	7.63741	+	13.2284i	0.275412	+	0.477028i	0.970239	−	0.242149i	$-0.0778524\pi$
$769$	7.63741	+	13.2284i	0.275412	+	0.477028i	−0.694827	+	0.719177i	$0.744519\pi$
$770$	−17.0660	−	29.5592i	−0.615017	−	1.06524i
$771$	0.769512	+	47.2951i	0.0277133	+	1.70329i
$772$	−0.0584452	+	0.101230i	−0.00210349	+	0.00364335i
$773$	−40.0384			−1.44008			−0.720040	−	0.693932i	$-0.755877\pi$
$773$	−40.0384			−1.44008			−0.720040	+	0.693932i	$0.755877\pi$
$774$	−5.99446	+	11.2098i	−0.215466	+	0.402928i
$775$	19.3478	+	5.27381i	0.694993	+	0.189441i
$776$	−4.66648	−	2.69419i	−0.167517	−	0.0967159i
$777$	−34.1532	+	20.4663i	−1.22524	+	0.734224i
$778$	9.95201	−	5.74579i	0.356797	−	0.205997i
$779$	−22.6222	+	13.0609i	−0.810524	+	0.467956i
$780$	2.52815	−	4.54818i	0.0905221	−	0.162851i
$781$	−3.50731	−	2.02494i	−0.125501	−	0.0724582i
$782$		−	49.3707i		−	1.76549i
$783$	15.1819	−	29.5363i	0.542557	−	1.05554i
$784$	9.61441			0.343372
$785$	−16.6732	−	9.62629i	−0.595093	−	0.343577i
$786$	0.934417	−	1.68103i	0.0333295	−	0.0599605i
$787$	15.8897	−	9.17391i	0.566406	−	0.327015i	−0.189307	−	0.981918i	$-0.560624\pi$
$787$	15.8897	−	9.17391i	0.566406	−	0.327015i	0.755713	+	0.654903i	$0.227291\pi$
$788$	7.56850	+	13.1090i	0.269616	+	0.466989i
$789$	−12.3970	−	20.6876i	−0.441346	−	0.736497i
$790$	−9.64819	−	5.57039i	−0.343267	−	0.198185i
$791$		−	39.6851i		−	1.41104i
$792$	−0.278652	−	8.56087i	−0.00990145	−	0.304197i
$793$	−12.8704			−0.457040
$794$	15.1215	+	8.73041i	0.536642	+	0.309831i
$795$	0.873828	+	53.7066i	0.0309915	+	1.90478i
$796$	−10.2450	+	5.91494i	−0.363123	+	0.209649i
$797$	−3.44226	−	5.96217i	−0.121931	−	0.211191i	0.798598	−	0.601865i	$-0.205575\pi$
$797$	−3.44226	−	5.96217i	−0.121931	−	0.211191i	−0.920529	+	0.390674i	$0.872242\pi$
$798$	−0.806252	−	49.5532i	−0.0285410	−	1.75417i
$799$	16.9641	+	9.79426i	0.600148	+	0.346496i
$800$		−	3.60175i		−	0.127341i
$801$	3.70476	+	5.96023i	0.130901	+	0.210594i
$802$		−	18.7575i		−	0.662352i
$803$	32.1069	+	18.5370i	1.13303	+	0.654155i
$804$	−0.583355	−	0.973476i	−0.0205734	−	0.0343319i
$805$	90.1071	−	52.0234i	3.17586	−	1.83358i
$806$	−1.45235	−	5.51535i	−0.0511570	−	0.194270i
$807$	−9.59727	+	17.2657i	−0.337840	+	0.607780i
$808$	9.30400	−	16.1150i	0.327313	−	0.566924i
$809$	4.22765			0.148636			0.0743182	−	0.997235i	$-0.476322\pi$
$809$	4.22765			0.148636			0.0743182	+	0.997235i	$0.476322\pi$
$810$	11.6834	−	23.6694i	0.410514	−	0.831657i
$811$	−5.17461			−0.181705			−0.0908525	−	0.995864i	$-0.528959\pi$
$811$	−5.17461			−0.181705			−0.0908525	+	0.995864i	$0.528959\pi$
$812$	−13.0255	+	22.5609i	−0.457106	+	0.791731i
$813$	3.87704	+	2.15509i	0.135974	+	0.0755822i
$814$	−8.05101	−	13.9448i	−0.282188	−	0.488763i
$815$	23.5371	−	13.5892i	0.824470	−	0.476008i
$816$	5.05033	+	8.42775i	0.176797	+	0.295030i
$817$	−25.7601	−	14.8726i	−0.901231	−	0.520326i
$818$	14.4852			0.506463
$819$	−10.6384	+	6.61261i	−0.371735	+	0.231063i
$820$	10.9137			0.381122
$821$	−7.94452	+	13.7603i	−0.277266	+	0.480238i	−0.970704	−	0.240278i	$-0.922762\pi$
$821$	−7.94452	+	13.7603i	−0.277266	+	0.480238i	0.693439	+	0.720516i	$0.256095\pi$
$822$	−0.0670213	−	4.11921i	−0.00233764	−	0.143674i
$823$	−30.1165	+	17.3878i	−1.04979	+	0.606099i	−0.922592	−	0.385778i	$-0.873933\pi$
$823$	−30.1165	+	17.3878i	−1.04979	+	0.606099i	−0.127203	+	0.991877i	$0.540600\pi$
$824$	1.42844	−	0.824711i	0.0497621	−	0.0287302i
$825$	17.8091	−	0.289762i	0.620034	−	0.0100882i
$826$	11.3290	−	19.6224i	0.394187	−	0.682752i
$827$	41.8701			1.45597			0.727983	−	0.685595i	$-0.240458\pi$
$827$	41.8701			1.45597			0.727983	+	0.685595i	$0.240458\pi$
$828$	26.0966	−	0.849430i	0.906920	−	0.0295197i
$829$		−	8.11598i		−	0.281880i	−0.990018	−	0.140940i	$-0.954988\pi$
$829$		−	8.11598i		−	0.281880i	0.990018	−	0.140940i	$-0.0450124\pi$
$830$	6.46306	−	11.1944i	0.224336	−	0.388562i
$831$	45.5419	−	27.2910i	1.57983	−	0.946714i
$832$	−0.887117	+	0.512177i	−0.0307553	+	0.0177566i
$833$	−27.2690	−	47.2313i	−0.944816	−	1.63647i
$834$	14.6890	−	26.4259i	0.508640	−	0.915053i
$835$	−1.59136	−	0.918773i	−0.0550714	−	0.0317955i
$836$	20.0425			0.693186
$837$	−8.72339	−	27.5845i	−0.301525	−	0.953458i
$838$	25.6239			0.885165
$839$	−9.44010	−	5.45024i	−0.325908	−	0.188163i	0.328115	−	0.944638i	$-0.393587\pi$
$839$	−9.44010	−	5.45024i	−0.325908	−	0.188163i	−0.654023	+	0.756475i	$0.726920\pi$
$840$	−10.0599	+	18.0980i	−0.347100	+	0.624440i
$841$	−5.92372	−	10.2602i	−0.204266	−	0.353800i
$842$	−26.1513	+	15.0985i	−0.901233	+	0.520327i
$843$	19.1608	−	11.4821i	0.659933	−	0.395465i
$844$	2.95666	−	5.12109i	0.101772	−	0.176275i
$845$			35.0499i			1.20575i
$846$	−4.88522	+	9.13550i	−0.167957	+	0.314085i
$847$	11.6095			0.398909
$848$	5.28690	−	9.15718i	0.181553	−	0.314459i
$849$	4.47676	−	0.0728388i	0.153642	−	0.00249982i
$850$	−17.6938	+	10.2155i	−0.606892	+	0.350389i
$851$	42.5086	−	24.5424i	1.45718	−	0.841302i
$852$	0.0399686	+	2.45652i	0.00136930	+	0.0841589i
$853$	26.0774	−	45.1673i	0.892872	−	1.54650i	0.0564553	−	0.998405i	$-0.482020\pi$
$853$	26.0774	−	45.1673i	0.892872	−	1.54650i	0.836417	−	0.548094i	$-0.184646\pi$
$854$	51.2134			1.75249
$855$	54.4662	+	29.1259i	1.86271	+	0.996085i
$856$	−9.92203			−0.339128
$857$	7.31813	+	4.22512i	0.249982	+	0.144327i	0.619756	−	0.784794i	$-0.287231\pi$
$857$	7.31813	+	4.22512i	0.249982	+	0.144327i	−0.369774	+	0.929122i	$0.620565\pi$
$858$	−2.60387	−	4.34522i	−0.0888947	−	0.148343i
$859$	−2.65979	+	1.53563i	−0.0907510	+	0.0523951i	−0.544689	−	0.838638i	$-0.683352\pi$
$859$	−2.65979	+	1.53563i	−0.0907510	+	0.0523951i	0.453938	+	0.891033i	$0.350019\pi$
$860$	6.21375	+	10.7625i	0.211887	+	0.366999i
$861$	−22.9623	−	12.7638i	−0.782551	−	0.434988i
$862$	11.4773	−	19.8792i	0.390917	−	0.677088i
$863$	10.0748			0.342949			0.171475	−	0.985189i	$-0.445147\pi$
$863$	10.0748			0.342949			0.171475	+	0.985189i	$0.445147\pi$
$864$	−4.36789	+	2.81453i	−0.148599	+	0.0957521i
$865$	−69.4246			−2.36051
$866$	−7.76430	+	13.4482i	−0.263842	+	0.456987i
$867$	12.7721	−	22.9773i	0.433763	−	0.780348i
$868$	5.77916	+	21.9465i	0.196157	+	0.744912i
$869$	−9.39245	+	5.42273i	−0.318617	+	0.183954i
$870$	−16.6885	−	27.8491i	−0.565795	−	0.944172i
$871$	−0.581261	−	0.335591i	−0.0196953	−	0.0113711i
$872$		−	18.8530i		−	0.638445i
$873$	−16.1566	+	0.525888i	−0.546818	+	0.0177986i
$874$			61.0969i			2.06663i
$875$	14.4761	+	8.35779i	0.489382	+	0.282545i
$876$	−0.365884	−	22.4877i	−0.0123621	−	0.759789i
$877$	−3.27797	−	5.67761i	−0.110689	−	0.191719i	0.805359	−	0.592787i	$-0.201972\pi$
$877$	−3.27797	−	5.67761i	−0.110689	−	0.191719i	−0.916048	+	0.401068i	$0.868639\pi$
$878$	7.81290	−	4.51078i	0.263673	−	0.152231i
$879$	−0.0366064	−	2.24987i	−0.00123470	−	0.0758864i
$880$	−7.25188	−	4.18687i	−0.244461	−	0.141139i
$881$	3.02318			0.101854			0.0509268	−	0.998702i	$-0.483782\pi$
$881$	3.02318			0.101854			0.0509268	+	0.998702i	$0.483782\pi$
$882$	24.4966	−	15.2266i	0.824843	−	0.512706i
$883$		−	20.0772i		−	0.675653i	−0.941208	−	0.337826i	$-0.890308\pi$
$883$		−	20.0772i		−	0.675653i	0.941208	−	0.337826i	$-0.109692\pi$
$884$	5.03220	+	2.90534i	0.169251	+	0.0977172i
$885$	14.5150	+	24.2219i	0.487915	+	0.814210i
$886$	−15.4804	−	26.8128i	−0.520074	−	0.900795i
$887$	−28.6270	+	16.5278i	−0.961202	+	0.554950i	−0.896543	−	0.442957i	$-0.853929\pi$
$887$	−28.6270	+	16.5278i	−0.961202	+	0.554950i	−0.0646591	+	0.997907i	$0.520596\pi$
$888$	−4.74583	+	8.53785i	−0.159260	+	0.286511i
$889$	34.0786	+	19.6753i	1.14296	+	0.659889i
$890$	6.86078			0.229974
$891$	−14.2681	−	21.3709i	−0.477998	−	0.715954i
$892$		−	23.7591i		−	0.795514i
$893$	−20.9933	−	12.1205i	−0.702515	−	0.405597i
$894$	−1.89235	+	3.40438i	−0.0632897	+	0.113859i
$895$	3.94121	−	2.27546i	0.131740	−	0.0760602i
$896$	3.52999	−	2.03804i	0.117929	−	0.0680861i
$897$	13.2458	−	7.93754i	0.442264	−	0.265027i
$898$	−0.0989353	−	0.0571203i	−0.00330151	−	0.00190613i
$899$	−34.3321	−	9.35823i	−1.14504	−	0.312114i
$900$	−5.70419	−	9.17690i	−0.190140	−	0.305897i
$901$	−59.9802			−1.99823
$902$	5.31219	−	9.20099i	0.176877	−	0.306359i
$903$	−0.486670	−	29.9113i	−0.0161954	−	0.995387i
$904$	−4.86805	−	8.43172i	−0.161909	−	0.280435i
$905$	−18.1668	−	31.4658i	−0.603885	−	1.04596i
$906$	−1.89032	+	0.0307563i	−0.0628016	+	0.00102181i
$907$	−18.6969	+	32.3839i	−0.620820	+	1.07529i	0.368514	+	0.929622i	$0.379867\pi$
$907$	−18.6969	+	32.3839i	−0.620820	+	1.07529i	−0.989333	+	0.145669i	$0.953467\pi$
$908$		−	7.10590i		−	0.235818i
$909$	−1.81608	−	55.7944i	−0.0602355	−	1.85058i
$910$			12.2458i			0.405943i
$911$	−1.50507	+	2.60685i	−0.0498651	+	0.0863689i	−0.889881	−	0.456194i	$-0.849212\pi$
$911$	−1.50507	+	2.60685i	−0.0498651	+	0.0863689i	0.840015	+	0.542562i	$0.182546\pi$
$912$	−6.24984	−	10.4294i	−0.206953	−	0.345353i
$913$	−6.29175	−	10.8976i	−0.208226	−	0.360659i
$914$	−8.12321	−	14.0698i	−0.268692	−	0.465388i
$915$	−31.0094	+	55.7864i	−1.02514	+	1.84424i
$916$	−11.7189	−	6.76589i	−0.387202	−	0.223551i
$917$			4.52611i			0.149465i
$918$	26.2150	+	13.4748i	0.865224	+	0.444733i
$919$	3.34394			0.110306			0.0551532	−	0.998478i	$-0.482435\pi$
$919$	3.34394			0.110306			0.0551532	+	0.998478i	$0.482435\pi$
$920$	12.7631	−	22.1063i	0.420787	−	0.728824i
$921$	−1.81568	+	3.26645i	−0.0598287	+	0.107633i
$922$	−20.8926	+	12.0624i	−0.688062	+	0.397253i
$923$	0.726503	+	1.25834i	0.0239131	+	0.0414187i
$924$	10.3612	+	17.2903i	0.340860	+	0.568811i
$925$	−17.5913	−	10.1563i	−0.578398	−	0.333938i
$926$	−2.39285			−0.0786339
$927$	2.33341	−	4.36354i	0.0766393	−	0.143318i
$928$			6.39120i			0.209801i
$929$	−13.0827	+	22.6599i	−0.429229	+	0.743447i	−0.996805	−	0.0798745i	$-0.974548\pi$
$929$	−13.0827	+	22.6599i	−0.429229	+	0.743447i	0.567576	+	0.823321i	$0.307881\pi$
$930$	−27.4054	−	6.99324i	−0.898659	−	0.229317i
$931$	33.7457	+	58.4493i	1.10597	+	1.91560i
$932$	3.83770	−	2.21570i	0.125708	−	0.0725777i
$933$	0.389308	+	23.9273i	0.0127454	+	0.783346i
$934$	−6.76913	+	11.7245i	−0.221493	+	0.383637i
$935$			47.5003i			1.55343i
$936$	−1.44914	+	2.70993i	−0.0473666	+	0.0885768i
$937$	−6.83244			−0.223206			−0.111603	−	0.993753i	$-0.535599\pi$
$937$	−6.83244			−0.223206			−0.111603	+	0.993753i	$0.535599\pi$
$938$	2.31294	+	1.33537i	0.0755200	+	0.0436015i
$939$	26.0335	−	15.6006i	0.849572	−	0.509106i
$940$	5.06393	+	8.77099i	0.165167	+	0.286078i
$941$	23.4056	+	40.5397i	0.763002	+	1.32156i	0.941297	+	0.337580i	$0.109608\pi$
$941$	23.4056	+	40.5397i	0.763002	+	1.32156i	−0.178295	+	0.983977i	$0.557058\pi$
$942$	9.93780	+	5.52401i	0.323791	+	0.179982i
$943$	28.0479	+	16.1935i	0.913366	+	0.527332i
$944$		−	5.55879i		−	0.180923i
$945$	3.03059	+	62.0441i	0.0985851	+	2.01829i
$946$	12.0981			0.393343
$947$	17.1034	−	29.6240i	0.555786	−	0.962649i	−0.442056	−	0.896987i	$-0.645751\pi$
$947$	17.1034	−	29.6240i	0.555786	−	0.962649i	0.997842	−	0.0656618i	$-0.0209159\pi$
$948$	5.75064	+	3.19654i	0.186772	+	0.103819i
$949$	−6.65062	−	11.5192i	−0.215888	−	0.373930i
$950$	21.8963	−	12.6418i	0.710409	−	0.410155i
$951$	23.7798	−	14.2500i	0.771111	−	0.462088i
$952$	−20.0240	−	11.5608i	−0.648980	−	0.374689i
$953$	−9.49649			−0.307621			−0.153811	−	0.988100i	$-0.549155\pi$
$953$	−9.49649			−0.307621			−0.153811	+	0.988100i	$0.549155\pi$
$954$	−1.03197	−	31.7046i	−0.0334112	−	1.02647i
$955$	9.72838			0.314803
$956$	15.1818	−	26.2956i	0.491014	−	0.850461i
$957$	−31.6018	+	0.514175i	−1.02154	+	0.0166209i
$958$	12.5268	+	21.6971i	0.404723	+	0.701000i
$959$	4.84757	+	8.39623i	0.156536	+	0.271128i
$960$	0.0826409	+	5.07921i	0.00266723	+	0.163931i
$961$	−26.9796	+	15.2677i	−0.870308	+	0.492508i
$962$			5.77703i			0.186259i
$963$	−25.2804	+	15.7138i	−0.814648	+	0.506370i
$964$			7.75032i			0.249621i
$965$	0.296895	+	0.171412i	0.00955739	+	0.00551796i
$966$	−52.7072	+	31.5848i	−1.69583	+	1.01622i
$967$	26.2672	−	15.1654i	0.844696	−	0.487686i	−0.0141616	−	0.999900i	$-0.504508\pi$
$967$	26.2672	−	15.1654i	0.844696	−	0.487686i	0.858858	+	0.512214i	$0.171175\pi$
$968$	2.46663	−	1.42411i	0.0792804	−	0.0457725i
$969$	−33.5090	+	60.2834i	−1.07646	+	1.93658i
$970$	−7.90173	+	13.6862i	−0.253709	+	0.439437i
$971$		−	14.1371i		−	0.453682i	−0.973932	−	0.226841i	$-0.927160\pi$
$971$		−	14.1371i		−	0.453682i	0.973932	−	0.226841i	$-0.0728397\pi$
$972$	−6.67151	+	14.0887i	−0.213989	+	0.451895i
$973$			71.1504i			2.28098i
$974$	−1.24317	+	2.15324i	−0.0398338	+	0.0689942i
$975$	−5.58545	−	3.10472i	−0.178877	−	0.0994305i
$976$	10.8811	−	6.28219i	0.348295	−	0.201088i
$977$	−31.3324	+	18.0898i	−1.00241	+	0.578744i	−0.908962	−	0.416880i	$-0.863124\pi$
$977$	−31.3324	+	18.0898i	−1.00241	+	0.578744i	−0.0934521	+	0.995624i	$0.529790\pi$
$978$	−13.7678	+	8.25036i	−0.440246	+	0.263817i
$979$	3.33946	−	5.78412i	0.106730	−	0.184861i
$980$		−	28.1979i		−	0.900747i
$981$	−29.8581	−	48.0357i	−0.953295	−	1.53366i
$982$		−	21.1164i		−	0.673850i
$983$	19.6881	−	34.1009i	0.627954	−	1.08765i	−0.360008	−	0.932949i	$-0.617226\pi$
$983$	19.6881	−	34.1009i	0.627954	−	1.08765i	0.987962	−	0.154699i	$-0.0494408\pi$
$984$	−6.44437	+	0.104853i	−0.205439	+	0.00334258i
$985$	38.4471	−	22.1974i	1.22503	−	0.707269i
$986$	31.3971	−	18.1271i	0.999889	−	0.577286i
$987$	−0.396615	−	24.3764i	−0.0126244	−	0.775910i
$988$	−6.22741	−	3.59540i	−0.198120	−	0.114385i
$989$			36.8793i			1.17269i
$990$	−25.1079	+	0.817250i	−0.797983	+	0.0259739i
$991$			16.6544i			0.529045i	0.964379	+	0.264523i	$0.0852144\pi$
$991$			16.6544i			0.529045i	−0.964379	+	0.264523i	$0.914786\pi$
$992$	3.91998	+	3.95396i	0.124459	+	0.125538i
$993$	−52.5517	+	31.4916i	−1.66768	+	0.999355i
$994$	−2.89087	−	5.00714i	−0.0916930	−	0.158817i
$995$	17.3478	+	30.0472i	0.549961	+	0.952560i
$996$	−3.70880	+	6.67220i	−0.117518	+	0.211417i
$997$	24.8521	−	43.0450i	0.787073	−	1.36325i	−0.140680	−	0.990055i	$-0.544929\pi$
$997$	24.8521	−	43.0450i	0.787073	−	1.36325i	0.927753	−	0.373195i	$-0.121738\pi$
$998$	−11.5132			−0.364445
$999$	1.42970	+	29.2697i	0.0452337	+	0.926053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.q.a.371.12	yes	64
3.2	odd	2		1674.2.q.a.1115.20		64
9.4	even	3		1674.2.q.a.557.25		64
9.5	odd	6	inner	558.2.q.a.185.5	✓	64
31.30	odd	2	inner	558.2.q.a.371.5	yes	64
93.92	even	2		1674.2.q.a.1115.25		64
279.185	even	6	inner	558.2.q.a.185.12	yes	64
279.247	odd	6		1674.2.q.a.557.20		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.5	✓	64	9.5	odd	6	inner
558.2.q.a.185.12	yes	64	279.185	even	6	inner
558.2.q.a.371.5	yes	64	31.30	odd	2	inner
558.2.q.a.371.12	yes	64	1.1	even	1	trivial
1674.2.q.a.557.20		64	279.247	odd	6
1674.2.q.a.557.25		64	9.4	even	3
1674.2.q.a.1115.20		64	3.2	odd	2
1674.2.q.a.1115.25		64	93.92	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.841508 - 1.51389i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.53994 - 1.46644i) q^{5} +(-1.48571 + 0.890313i) q^{6} +(2.03804 - 3.52999i) q^{7} -1.00000i q^{8} +(-1.58373 - 2.54790i) q^{9} -2.93287 q^{10} +(-1.42757 + 2.47262i) q^{11} +(1.73182 - 0.0281775i) q^{12} +(0.887117 - 0.512177i) q^{13} +(-3.52999 + 2.03804i) q^{14} +(-0.0826409 - 5.07921i) q^{15} +(-0.500000 + 0.866025i) q^{16} +5.67253 q^{17} +(0.0975967 + 2.99841i) q^{18} -7.01983 q^{19} +(2.53994 + 1.46644i) q^{20} +(-3.62899 - 6.05588i) q^{21} +(2.47262 - 1.42757i) q^{22} +(4.35174 + 7.53743i) q^{23} +(-1.51389 - 0.841508i) q^{24} +(1.80087 - 3.11920i) q^{25} -1.02435 q^{26} +(-5.18996 + 0.253508i) q^{27} +4.07608 q^{28} +(-3.19560 + 5.53494i) q^{29} +(-2.46804 + 4.44005i) q^{30} +(1.41782 + 5.38422i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.54196 + 4.24191i) q^{33} +(-4.91256 - 2.83627i) q^{34} -11.9546i q^{35} +(1.41468 - 2.64550i) q^{36} -5.63967i q^{37} +(6.07935 + 3.50991i) q^{38} +(-0.0288637 - 1.77400i) q^{39} +(-1.46644 - 2.53994i) q^{40} +(3.22261 - 1.86058i) q^{41} +(0.114854 + 7.05904i) q^{42} +(3.66962 + 2.11866i) q^{43} -2.85513 q^{44} +(-7.75892 - 4.14909i) q^{45} -8.70347i q^{46} +(2.99058 + 1.72661i) q^{47} +(0.890313 + 1.48571i) q^{48} +(-4.80721 - 8.32632i) q^{49} +(-3.11920 + 1.80087i) q^{50} +(4.77348 - 8.58759i) q^{51} +(0.887117 + 0.512177i) q^{52} -10.5738 q^{53} +(4.62140 + 2.37544i) q^{54} +8.37374i q^{55} +(-3.52999 - 2.03804i) q^{56} +(-5.90724 + 10.6272i) q^{57} +(5.53494 - 3.19560i) q^{58} +(-4.81405 + 2.77939i) q^{59} +(4.35741 - 2.61118i) q^{60} +(-10.8811 - 6.28219i) q^{61} +(1.46424 - 5.37178i) q^{62} +(-12.2218 + 0.397812i) q^{63} -1.00000 q^{64} +(1.50215 - 2.60180i) q^{65} +(-0.0804504 - 4.94458i) q^{66} +(-0.327613 - 0.567442i) q^{67} +(2.83627 + 4.91256i) q^{68} +(15.0729 - 0.245242i) q^{69} +(-5.97731 + 10.3530i) q^{70} +1.41846i q^{71} +(-2.54790 + 1.58373i) q^{72} -12.9850i q^{73} +(-2.81984 + 4.88410i) q^{74} +(-3.20668 - 5.35116i) q^{75} +(-3.50991 - 6.07935i) q^{76} +(5.81887 + 10.0786i) q^{77} +(-0.862003 + 1.55076i) q^{78} +(3.28967 + 1.89929i) q^{79} +2.93287i q^{80} +(-3.98362 + 8.07037i) q^{81} -3.72115 q^{82} +(-2.20366 + 3.81685i) q^{83} +(3.43005 - 6.17073i) q^{84} +(14.4079 - 8.31841i) q^{85} +(-2.11866 - 3.66962i) q^{86} +(5.69017 + 9.49549i) q^{87} +(2.47262 + 1.42757i) q^{88} -2.33927 q^{89} +(4.64487 + 7.47268i) q^{90} -4.17535i q^{91} +(-4.35174 + 7.53743i) q^{92} +(9.34422 + 2.38443i) q^{93} +(-1.72661 - 2.99058i) q^{94} +(-17.8300 + 10.2941i) q^{95} +(-0.0281775 - 1.73182i) q^{96} +(2.69419 - 4.66648i) q^{97} +9.61441i q^{98} +(8.56087 - 0.278652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) \) 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more