LMFDB - Embedded newform 558.2.q.a.185.5

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			185.5
Character	$\chi$	$=$	558.185
Dual form			558.2.q.a.371.5

$q$-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} +(3.95396 - 3.91998i) 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} +(-9.26170 - 2.68716i) 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 $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	0.945411	−	0.325879i	$-0.105660\pi$
$5$	2.53994	+	1.46644i	1.13590	+	0.655810i	0.190486	+	0.981690i	$0.438994\pi$
$6$	1.48571	+	0.890313i	0.606540	+	0.363469i
$7$	2.03804	+	3.52999i	0.770306	+	1.33421i	0.937395	+	0.348268i	$0.113230\pi$
$7$	2.03804	+	3.52999i	0.770306	+	1.33421i	−0.167089	+	0.985942i	$0.553437\pi$
$8$			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	$-0.0250295\pi$
$11$	1.42757	+	2.47262i	0.430428	+	0.745522i	−0.566483	+	0.824074i	$0.691696\pi$
$12$	−1.73182	−	0.0281775i	−0.499934	−	0.00813413i
$13$	−0.887117	−	0.512177i	−0.246042	−	0.142052i	0.371909	−	0.928269i	$-0.378703\pi$
$13$	−0.887117	−	0.512177i	−0.246042	−	0.142052i	−0.617951	+	0.786217i	$0.712037\pi$
$14$	−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	$-0.741465\pi$
$17$	−5.67253			−1.37579			−0.687896	+	0.725810i	$0.741465\pi$
$18$	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	−0.0897370	+	0.995965i	$0.528603\pi$
$23$	−4.35174	+	7.53743i	−0.907400	+	1.57166i	−0.817663	+	0.575697i	$0.804731\pi$
$24$	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	0.993769	+	0.111456i	$0.0355513\pi$
$29$	3.19560	+	5.53494i	0.593408	+	1.02781i	−0.400361	+	0.916357i	$0.631115\pi$
$30$	2.46804	+	4.44005i	0.450600	+	0.810638i
$31$	3.95396	−	3.91998i	0.710151	−	0.704049i
$31$	3.95396	−	3.91998i	0.710151	−	0.704049i
$32$	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	0.730070	−	0.683372i	$-0.239487\pi$
$41$	3.22261	+	1.86058i	0.503288	+	0.290573i	−0.226783	+	0.973945i	$0.572821\pi$
$42$	−0.114854	+	7.05904i	−0.0177223	+	1.08923i
$43$	−3.66962	+	2.11866i	−0.559612	+	0.323092i	−0.752990	−	0.658032i	$-0.771389\pi$
$43$	−3.66962	+	2.11866i	−0.559612	+	0.323092i	0.193378	+	0.981124i	$0.438056\pi$
$44$	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	−0.265773	−	0.964036i	$-0.585627\pi$
$47$	2.99058	−	1.72661i	0.436221	−	0.251852i	0.701993	+	0.712184i	$0.252294\pi$
$48$	−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	$-0.241279\pi$
$53$	10.5738			1.45242			0.726211	+	0.687472i	$0.241279\pi$
$54$	−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	0.152751	−	0.988265i	$-0.451187\pi$
$59$	−4.81405	−	2.77939i	−0.626736	−	0.361846i	−0.779487	+	0.626419i	$0.784520\pi$
$60$	−4.35741	−	2.61118i	−0.562539	−	0.337101i
$61$	10.8811	−	6.28219i	1.39318	−	0.804352i	0.399512	−	0.916728i	$-0.369179\pi$
$61$	10.8811	−	6.28219i	1.39318	−	0.804352i	0.993666	+	0.112376i	$0.0358461\pi$
$62$	−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	−0.885344	−	0.464937i	$-0.846077\pi$
$67$	−0.327613	+	0.567442i	−0.0400242	+	0.0693240i	0.845319	+	0.534261i	$0.179410\pi$
$68$	−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	$-0.973176\pi$
$71$		−	1.41846i		−	0.168340i	0.996451	−	0.0841701i	$-0.0268239\pi$
$72$	−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	$-0.735214\pi$
$79$	−3.28967	+	1.89929i	−0.370117	+	0.213687i	0.303393	+	0.952866i	$0.401881\pi$
$80$		−	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	$-0.0889015\pi$
$83$	2.20366	+	3.81685i	0.241883	+	0.418954i	−0.719367	+	0.694630i	$0.755568\pi$
$84$	−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	$-0.460434\pi$
$89$	2.33927			0.247962			0.123981	+	0.992285i	$0.460434\pi$
$90$	4.64487	−	7.47268i	0.489612	−	0.787689i
$91$		−	4.17535i		−	0.437696i
$92$	4.35174	+	7.53743i	0.453700	+	0.785831i
$93$	−9.26170	−	2.68716i	−0.960394	−	0.278645i
$94$	−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	0.969769	−	0.244024i	$-0.0784675\pi$
$97$	2.69419	+	4.66648i	0.273554	+	0.473809i	−0.696215	+	0.717833i	$0.745134\pi$
$98$		−	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	0.612722	−	0.790298i	$-0.290074\pi$
$101$	16.1150	−	9.30400i	1.60350	−	0.925782i	0.990780	−	0.135484i	$-0.0432589\pi$
$102$	−8.42775	−	5.05033i	−0.834472	−	0.500057i
$103$	0.824711	−	1.42844i	0.0812612	−	0.140748i	−0.822531	−	0.568721i	$-0.807439\pi$
$103$	0.824711	−	1.42844i	0.0812612	−	0.140748i	0.903792	+	0.427972i	$0.140772\pi$
$104$	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	$0.159218\pi$
$107$			9.92203i			0.959199i	−0.877488	+	0.479599i	$0.840782\pi$
$108$	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	0.841084	−	0.540904i	$-0.181918\pi$
$113$	8.43172	+	4.86805i	0.793189	+	0.457948i	−0.0478950	+	0.998852i	$0.515251\pi$
$114$	−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
$124$	−1.41782	−	5.38422i	−0.127324	−	0.483517i
$125$		−	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	0.457402	−	0.889260i	$-0.348780\pi$
$131$	−0.961641	−	0.555203i	−0.0840189	−	0.0485084i	−0.541421	+	0.840752i	$0.682113\pi$
$132$	−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	$-0.134268\pi$
$137$	1.18927	+	2.05988i	0.101606	+	0.175987i	−0.810740	+	0.585406i	$0.800935\pi$
$138$	−13.1761	+	7.32405i	−1.12162	+	0.623464i
$139$	15.1170	+	8.72781i	1.28221	+	0.740283i	0.977252	−	0.212084i	$-0.0680249\pi$
$139$	15.1170	+	8.72781i	1.28221	+	0.740283i	0.304956	+	0.952366i	$0.401358\pi$
$140$	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	0.577646	−	0.816287i	$-0.303971\pi$
$149$	1.94748	+	1.12438i	0.159544	+	0.0921129i	−0.418102	+	0.908400i	$0.637305\pi$
$150$	−0.101488	+	6.23758i	−0.00828647	+	0.509297i
$151$	−0.945284	+	0.545760i	−0.0769261	+	0.0444133i	−0.537970	−	0.842964i	$-0.680809\pi$
$151$	−0.945284	+	0.545760i	−0.0769261	+	0.0444133i	0.461044	+	0.887378i	$0.347475\pi$
$152$		−	7.01983i		−	0.569383i
$153$	8.98374	−	14.4531i	0.726293	−	1.16846i
$154$		−	11.6377i		−	0.937796i
$155$	15.7912	−	4.15830i	1.26838	−	0.334002i
$156$	1.52190	+	0.911996i	0.121849	+	0.0730182i
$157$	−3.28221	+	5.68495i	−0.261949	+	0.453708i	−0.966760	−	0.255687i	$-0.917698\pi$
$157$	−3.28221	+	5.68495i	−0.261949	+	0.453708i	0.704811	+	0.709395i	$0.251032\pi$
$158$	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	$-0.825616\pi$
$167$	0.313267	−	0.542595i	0.0242414	−	0.0419873i	0.877892	+	0.478859i	$0.158950\pi$
$168$	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	−0.561181	+	0.827693i	$0.689653\pi$
$173$	−20.4999	+	11.8356i	−1.55857	+	0.899844i	−0.997394	+	0.0721506i	$0.977014\pi$
$174$	−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	$-0.518469\pi$
$179$	−1.55169			−0.115979			−0.0579894	+	0.998317i	$0.518469\pi$
$180$	−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
$186$	9.36445	−	2.30370i	0.686635	−	0.168916i
$187$	−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	−0.392459	−	0.919770i	$-0.628375\pi$
$191$	2.87262	−	1.65851i	0.207855	−	0.120005i	0.600314	+	0.799764i	$0.295042\pi$
$192$	0.841508	+	1.51389i	0.0607306	+	0.109256i
$193$	0.0584452	−	0.101230i	0.00420698	−	0.00728670i	−0.863914	−	0.503639i	$-0.831994\pi$
$193$	0.0584452	−	0.101230i	0.00420698	−	0.00728670i	0.868121	+	0.496352i	$0.165328\pi$
$194$	−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	$-0.681286\pi$
$197$	−15.1370			−1.07847			−0.539233	+	0.842157i	$0.681286\pi$
$198$	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	−0.949668	−	0.313258i	$-0.898580\pi$
$211$	−2.95666	+	5.12109i	−0.203545	+	0.352550i	0.746123	+	0.665808i	$0.231913\pi$
$212$	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	$-0.373868\pi$
$223$	20.5760	−	11.8796i	1.37787	−	0.795514i	0.991903	+	0.126999i	$0.0405345\pi$
$224$			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	−0.690123	−	0.723692i	$-0.742443\pi$
$227$	−6.15389	+	3.55295i	−0.408448	+	0.235818i	0.281675	+	0.959510i	$0.409110\pi$
$228$	12.1571	+	0.197801i	0.805123	+	0.0130997i
$229$	11.7189	+	6.76589i	0.774405	+	0.447103i	0.834444	−	0.551093i	$-0.185789\pi$
$229$	11.7189	+	6.76589i	0.774405	+	0.447103i	−0.0600390	+	0.998196i	$0.519123\pi$
$230$	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	$0.0463682\pi$
$233$			4.43140i			0.290311i	−0.989409	+	0.145155i	$0.953632\pi$
$234$	−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	0.327562	−	0.944830i	$-0.393773\pi$
$239$	15.1818	−	26.2956i	0.982028	−	1.70092i	0.654465	−	0.756092i	$-0.272894\pi$
$240$	−4.44005	+	2.46804i	−0.286604	+	0.159311i
$241$	−6.71197	+	3.87516i	−0.432356	+	0.249621i	−0.700350	−	0.713800i	$-0.746973\pi$
$241$	−6.71197	+	3.87516i	−0.432356	+	0.249621i	0.267994	+	0.963421i	$0.413639\pi$
$242$			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
$248$	3.91998	+	3.95396i	0.248919	+	0.251076i
$249$	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	$-0.590291\pi$
$251$	−8.86796			−0.559740			−0.279870	+	0.960038i	$0.590291\pi$
$252$	−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	−0.475679	−	0.879619i	$-0.657797\pi$
$257$	−23.6507	−	13.6547i	−1.47529	−	0.851759i	−0.999612	+	0.0278599i	$0.991131\pi$
$258$	−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	$-0.307908\pi$
$263$	−6.96217	−	12.0588i	−0.429306	−	0.743580i	−0.996812	+	0.0797897i	$0.974575\pi$
$264$	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	$-0.386969\pi$
$269$	11.4048			0.695365			0.347683	+	0.937612i	$0.386969\pi$
$270$	−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	−0.602599	+	0.798044i	$0.705868\pi$
$277$	−26.5465	+	15.3266i	−1.59502	+	0.920888i	−0.992426	+	0.122844i	$0.960799\pi$
$278$	−17.4556			−1.04692
$279$	3.72574	+	16.2825i	0.223054	+	0.974806i
$280$	−11.9546			−0.714425
$281$	11.1689	−	6.44836i	0.666279	−	0.384677i	−0.128386	−	0.991724i	$-0.540980\pi$
$281$	11.1689	−	6.44836i	0.666279	−	0.384677i	0.794665	+	0.607048i	$0.207646\pi$
$282$	5.98036	+	0.0973030i	0.356125	+	0.00579431i
$283$	1.29250	−	2.23868i	0.0768312	−	0.133076i	−0.825050	−	0.565060i	$-0.808853\pi$
$283$	1.29250	−	2.23868i	0.0768312	−	0.133076i	0.901881	+	0.431984i	$0.142186\pi$
$284$	−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	0.532504	−	0.846428i	$-0.321251\pi$
$293$	1.12509	+	0.649569i	0.0657282	+	0.0379482i	−0.466776	+	0.884376i	$0.654584\pi$
$294$	−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
$310$	−11.5965	+	11.4968i	−0.658634	+	0.652975i
$311$	−11.9653	−	6.90814i	−0.678487	−	0.391725i	0.120798	−	0.992677i	$-0.461455\pi$
$311$	−11.9653	−	6.90814i	−0.678487	−	0.391725i	−0.799285	+	0.600952i	$0.794788\pi$
$312$	−1.77400	−	0.0288637i	−0.100433	−	0.00163409i
$313$	−15.1750	+	8.76129i	−0.857741	+	0.495217i	−0.863255	−	0.504768i	$-0.831578\pi$
$313$	−15.1750	+	8.76129i	−0.857741	+	0.495217i	0.00551388	+	0.999985i	$0.498245\pi$
$314$		−	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	−0.0573812	−	0.998352i	$-0.518275\pi$
$317$	13.8613	−	8.00281i	0.778527	−	0.449483i	0.835908	+	0.548870i	$0.184942\pi$
$318$	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	0.724559	−	0.689213i	$-0.242043\pi$
$331$	30.6325	−	17.6857i	1.68371	−	0.972093i	0.959155	−	0.282880i	$-0.0912899\pi$
$332$	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	$-0.471593\pi$
$337$	−13.3807	−	7.72535i	−0.728893	−	0.420827i	−0.818017	+	0.575194i	$0.804927\pi$
$338$	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	0.139348	+	0.990244i	$0.455499\pi$
$347$	−14.6770	+	25.4213i	−0.787902	+	1.36469i	−0.927250	+	0.374443i	$0.877834\pi$
$348$	−5.37825	−	9.67558i	−0.288304	−	0.518665i
$349$	5.36076	+	9.28512i	0.286955	+	0.497021i	0.973081	−	0.230462i	$-0.0740236\pi$
$349$	5.36076	+	9.28512i	0.286955	+	0.497021i	−0.686126	+	0.727482i	$0.740690\pi$
$350$		−	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	$-0.194691\pi$
$353$	−1.65198	−	2.86131i	−0.0879258	−	0.152292i	−0.906634	+	0.421918i	$0.861357\pi$
$354$	−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	$0.132831\pi$
$359$			15.3585i			0.810589i	−0.914186	+	0.405295i	$0.867169\pi$
$360$	−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	$-0.578011\pi$
$367$	9.12269	−	5.26699i	0.476200	−	0.274934i	0.718832	+	0.695184i	$0.244677\pi$
$368$	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
$372$	−6.95800	+	6.67729i	−0.360756	+	0.346201i
$373$	−14.7654	+	25.5743i	−0.764521	+	1.32419i	0.175978	+	0.984394i	$0.443691\pi$
$373$	−14.7654	+	25.5743i	−0.764521	+	1.32419i	−0.940499	+	0.339796i	$0.889642\pi$
$374$	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	$-0.823513\pi$
$383$	0.603701	−	1.04564i	0.0308477	−	0.0534297i	0.881037	+	0.473047i	$0.156846\pi$
$384$	−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	$-0.0725711\pi$
$389$	5.74579	+	9.95201i	0.291323	+	0.504587i	−0.682800	+	0.730606i	$0.739238\pi$
$390$	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	$-0.988486\pi$
$401$	−9.37877	+	16.2445i	−0.468354	+	0.811212i	0.530992	+	0.847377i	$0.321819\pi$
$402$	−0.991939	+	0.551377i	−0.0494734	+	0.0275002i
$403$	−5.51535	+	1.45235i	−0.274739	+	0.0723469i
$404$		−	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	$-0.216750\pi$
$409$	12.5445	+	7.24259i	0.620287	+	0.358123i	−0.156693	+	0.987647i	$0.550083\pi$
$410$	−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	−0.152101	−	0.988365i	$-0.548604\pi$
$419$	−22.1910	−	12.8120i	−1.08410	−	0.625906i	−0.932000	+	0.362459i	$0.881937\pi$
$420$	0.336851	−	20.7033i	0.0164366	−	1.01022i
$421$	15.0985	+	26.1513i	0.735854	+	1.27454i	0.954348	+	0.298698i	$0.0965522\pi$
$421$	15.0985	+	26.1513i	0.735854	+	1.27454i	−0.218494	+	0.975838i	$0.570114\pi$
$422$		−	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	$-0.813544\pi$
$431$		−	22.9545i		−	1.10568i	0.833287	−	0.552840i	$-0.186456\pi$
$432$	−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	$-0.121715\pi$
$434$	−21.9465	+	5.77916i	−1.05346	+	0.277409i
$435$	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	0.738074	−	0.674720i	$-0.235736\pi$
$439$	−4.51078	−	7.81290i	−0.215288	−	0.372889i	−0.953362	+	0.301831i	$0.902402\pi$
$440$	−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	0.298194	−	0.954505i	$-0.403616\pi$
$443$	26.8128	−	15.4804i	1.27392	−	0.735496i	0.975723	+	0.219009i	$0.0702824\pi$
$444$	−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	$-0.500858\pi$
$449$	−0.114241			−0.00539135			−0.00269568	+	0.999996i	$0.500858\pi$
$450$	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	$-0.790739\pi$
$457$	−14.0698	+	8.12321i	−0.658158	+	0.379988i	0.133417	+	0.991060i	$0.457405\pi$
$458$	−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	−0.997340	−	0.0728965i	$-0.976776\pi$
$461$	−12.0624	−	20.8926i	−0.561800	−	0.973066i	0.435540	−	0.900170i	$-0.356558\pi$
$462$	−17.6183	+	9.79326i	−0.819676	+	0.455624i
$463$	−2.07227	−	1.19642i	−0.0963065	−	0.0556026i	0.451073	−	0.892487i	$-0.351041\pi$
$463$	−2.07227	−	1.19642i	−0.0963065	−	0.0556026i	−0.547380	+	0.836884i	$0.684375\pi$
$464$	3.19560	−	5.53494i	0.148352	−	0.256953i
$465$	−19.5837	−	20.4069i	−0.908170	−	0.946349i
$466$	−2.21570	−	3.83770i	−0.102640	−	0.177778i
$467$			13.5383i			0.626476i	0.949675	+	0.313238i	$0.101414\pi$
$467$			13.5383i			0.626476i	−0.949675	+	0.313238i	$0.898586\pi$
$468$	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	−0.905682	−	0.423958i	$-0.860640\pi$
$479$	−21.6971	+	12.5268i	−0.991364	+	0.572364i	−0.0856824	+	0.996323i	$0.527307\pi$
$480$	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	$-0.991422\pi$
$491$	−10.5582	+	18.2873i	−0.476484	+	0.825294i	0.523153	+	0.852239i	$0.324756\pi$
$492$	−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	$-0.416298\pi$
$499$	−9.97074	−	5.75661i	−0.446352	−	0.257701i	−0.706288	+	0.707925i	$0.749632\pi$
$500$	−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	$0.345079\pi$
$503$			39.6468i			1.76776i	−0.467710	+	0.883882i	$0.654921\pi$
$504$	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	$-0.667671\pi$
$509$	11.2188	−	19.4315i	0.497265	−	0.861288i	0.999995	+	0.00315565i	$0.00100448\pi$
$510$	−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	$-0.852043\pi$
$521$		−	20.4636i		−	0.896526i	0.893902	−	0.448263i	$-0.147957\pi$
$522$	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
$527$	−22.4289	+	22.2362i	−0.977020	+	0.968624i
$528$	−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	0.998999	−	0.0447319i	$-0.0142434\pi$
$547$	10.7763	+	18.6651i	0.460761	+	0.798061i	−0.538238	+	0.842793i	$0.680910\pi$
$548$	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	$-0.284203\pi$
$557$	29.6046			1.25439			0.627194	+	0.778863i	$0.284203\pi$
$558$	−11.3678	−	12.2382i	−0.481238	−	0.518083i
$559$	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	−0.482963	−	0.875641i	$-0.660440\pi$
$563$	−35.1826	−	20.3127i	−1.48277	−	0.856079i	−0.999809	+	0.0195620i	$0.993773\pi$
$564$	−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	$-0.170121\pi$
$569$	−0.258866	−	0.448369i	−0.0108522	−	0.0187966i	−0.871401	+	0.490572i	$0.836788\pi$
$570$	−17.3252	−	31.1684i	−0.725673	−	1.30550i
$571$	−37.4562	−	21.6254i	−1.56749	−	0.904993i	−0.996460	−	0.0840671i	$-0.973209\pi$
$571$	−37.4562	−	21.6254i	−1.56749	−	0.904993i	−0.571034	−	0.820926i	$-0.693458\pi$
$572$	−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	$-0.0890568\pi$
$587$	5.84891	+	10.1306i	0.241410	+	0.418135i	−0.719706	+	0.694279i	$0.755723\pi$
$588$	8.55984	−	14.2843i	0.353002	−	0.589073i
$589$	−27.7561	+	27.5176i	−1.14367	+	1.13384i
$590$	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	$0.0900094\pi$
$593$			13.5891i			0.558039i	−0.960285	+	0.279020i	$0.909991\pi$
$594$	−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	0.693616	−	0.720345i	$-0.256017\pi$
$599$	10.1957	+	5.88651i	0.416587	+	0.240516i	−0.277029	+	0.960861i	$0.589350\pi$
$600$	5.35116	+	3.20668i	0.218460	+	0.130912i
$601$	4.87209	−	2.81290i	0.198737	−	0.114741i	−0.397329	−	0.917676i	$-0.630063\pi$
$601$	4.87209	−	2.81290i	0.198737	−	0.114741i	0.596066	+	0.802935i	$0.296730\pi$
$602$	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	−0.253734	−	0.967274i	$-0.581659\pi$
$607$	17.5127	−	30.3328i	0.710817	−	1.23117i	0.964551	−	0.263897i	$-0.0850079\pi$
$608$	−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	−0.0727809	−	0.997348i	$-0.523187\pi$
$617$	−24.1663	−	13.9524i	−0.972900	−	0.561704i	−0.900119	+	0.435644i	$0.856521\pi$
$618$	2.49704	−	1.38800i	0.100446	−	0.0558336i
$619$	−11.3385	+	6.54630i	−0.455734	+	0.263118i	−0.710249	−	0.703951i	$-0.751418\pi$
$619$	−11.3385	+	6.54630i	−0.455734	+	0.263118i	0.254515	+	0.967069i	$0.418084\pi$
$620$	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	$-0.332891\pi$
$641$	−12.6285	−	21.8732i	−0.498796	−	0.863939i	−0.999999	+	0.00139021i	$0.999557\pi$
$642$	−8.83371	+	14.7413i	−0.348639	+	0.581792i
$643$	5.65600	+	3.26550i	0.223051	+	0.128779i	0.607362	−	0.794425i	$-0.292228\pi$
$643$	5.65600	+	3.26550i	0.223051	+	0.128779i	−0.384311	+	0.923204i	$0.625561\pi$
$644$	−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	$-0.292562\pi$
$647$	30.8555			1.21306			0.606528	+	0.795062i	$0.292562\pi$
$648$	8.07037	−	3.98362i	0.317034	−	0.156491i
$649$		−	15.8711i		−	0.622994i
$650$	1.84473	+	3.19517i	0.0723564	+	0.125325i
$651$	−9.39008	−	38.1702i	−0.368026	−	1.49601i
$652$	4.63340	−	8.02529i	0.181458	−	0.314294i
$653$	−21.0077	−	12.1288i	−0.822095	−	0.474637i	0.0290431	−	0.999578i	$-0.490754\pi$
$653$	−21.0077	−	12.1288i	−0.822095	−	0.474637i	−0.851139	+	0.524941i	$0.824087\pi$
$654$	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	−0.729962	−	0.683488i	$-0.760462\pi$
$659$	−12.9132	+	7.45542i	−0.503026	+	0.290422i	0.226937	+	0.973910i	$0.427129\pi$
$660$	0.235951	−	14.5018i	0.00918438	−	0.564483i
$661$	−5.59524	+	9.69123i	−0.217629	+	0.376945i	−0.954083	−	0.299543i	$-0.903166\pi$
$661$	−5.59524	+	9.69123i	−0.217629	+	0.376945i	0.736453	+	0.676488i	$0.236499\pi$
$662$	−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	$-0.412184\pi$
$673$	32.2169	−	18.6004i	1.24187	−	0.716993i	0.969474	+	0.245192i	$0.0788511\pi$
$674$	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	0.992690	+	0.120692i	$0.0385112\pi$
$677$	15.6341	+	27.0790i	0.600867	+	1.04073i	−0.391823	+	0.920041i	$0.628155\pi$
$678$	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
$682$	−15.3727	+	4.04808i	−0.588649	+	0.155009i
$683$		−	13.5166i		−	0.517199i	−0.965985	−	0.258600i	$-0.916739\pi$
$683$		−	13.5166i		−	0.517199i	0.965985	−	0.258600i	$-0.0832610\pi$
$684$	−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	0.848038	−	0.529935i	$-0.177784\pi$
$691$	−0.917897	−	1.58984i	−0.0349185	−	0.0604805i	−0.882956	+	0.469455i	$0.844450\pi$
$692$			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	$0.211893\pi$
$701$			32.7034i			1.23519i	−0.786496	+	0.617595i	$0.788107\pi$
$702$	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	$-0.910304\pi$
$709$	−31.9531	+	18.4481i	−1.20002	+	0.692833i	−0.239462	+	0.970906i	$0.576971\pi$
$710$			4.16016i			0.156128i
$711$	0.370729	−	11.3897i	0.0139034	−	0.427148i
$712$			2.33927i			0.0876678i
$713$	12.3400	+	46.8614i	0.462136	+	1.75497i
$714$	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	$-0.402952\pi$
$719$	16.0983			0.600367			0.300183	+	0.953881i	$0.402952\pi$
$720$	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	0.853795	−	0.520610i	$-0.174295\pi$
$727$	−0.646145	−	1.11916i	−0.0239642	−	0.0415072i	−0.877759	+	0.479103i	$0.840962\pi$
$728$	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	−0.717590	−	0.696466i	$-0.754755\pi$
$733$	6.61585	−	11.4590i	0.244362	−	0.423247i	0.961952	+	0.273218i	$0.0880882\pi$
$734$	−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	$-0.683113\pi$
$743$	12.3917	−	21.4630i	0.454606	−	0.787401i	0.998665	+	0.0516459i	$0.0164467\pi$
$744$	2.68716	−	9.26170i	0.0985160	−	0.339551i
$745$	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	−0.888569	−	0.458744i	$-0.848300\pi$
$751$	−1.28802	+	2.23091i	−0.0470004	+	0.0814071i	0.841568	+	0.540151i	$0.181633\pi$
$752$	−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	$-0.836200\pi$
$761$	−0.248473	+	0.430368i	−0.00900715	+	0.0156008i	0.861487	+	0.507780i	$0.169534\pi$
$762$	−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	−0.694827	−	0.719177i	$-0.744519\pi$
$769$	7.63741	−	13.2284i	0.275412	−	0.477028i	0.970239	+	0.242149i	$0.0778524\pi$
$770$	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	$-0.244123\pi$
$773$	40.0384			1.44008			0.720040	+	0.693932i	$0.244123\pi$
$774$	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	$-0.439376\pi$
$787$	−15.8897	−	9.17391i	−0.566406	−	0.327015i	−0.755713	+	0.654903i	$0.772709\pi$
$788$	−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	$-0.794425\pi$
$797$	3.44226	−	5.96217i	0.121931	−	0.211191i	0.920529	+	0.390674i	$0.127758\pi$
$798$	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
$806$	4.05025	−	4.01545i	0.142664	−	0.141438i
$807$	−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	$-0.523678\pi$
$809$	−4.22765			−0.148636			−0.0743182	+	0.997235i	$0.523678\pi$
$810$	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	$-0.0772385\pi$
$821$	7.94452	+	13.7603i	0.277266	+	0.480238i	−0.693439	+	0.720516i	$0.743905\pi$
$822$	−0.0670213	+	4.11921i	−0.00233764	+	0.143674i
$823$	30.1165	+	17.3878i	1.04979	+	0.606099i	0.922592	−	0.385778i	$-0.126067\pi$
$823$	30.1165	+	17.3878i	1.04979	+	0.606099i	0.127203	+	0.991877i	$0.459400\pi$
$824$	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	$-0.759542\pi$
$827$	−41.8701			−1.45597			−0.727983	+	0.685595i	$0.759542\pi$
$828$	−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
$837$	21.5146	−	19.3422i	0.743655	−	0.668564i
$838$	25.6239			0.885165
$839$	−9.44010	+	5.45024i	−0.325908	+	0.188163i	−0.654023	−	0.756475i	$-0.726920\pi$
$839$	−9.44010	+	5.45024i	−0.325908	+	0.188163i	0.328115	+	0.944638i	$0.393587\pi$
$840$	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	0.836417	+	0.548094i	$0.184646\pi$
$853$	26.0774	+	45.1673i	0.892872	+	1.54650i	0.0564553	+	0.998405i	$0.482020\pi$
$854$	−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	−0.369774	−	0.929122i	$-0.620565\pi$
$857$	7.31813	−	4.22512i	0.249982	−	0.144327i	0.619756	+	0.784794i	$0.287231\pi$
$858$	2.60387	−	4.34522i	0.0888947	−	0.148343i
$859$	2.65979	+	1.53563i	0.0907510	+	0.0523951i	0.544689	−	0.838638i	$-0.316648\pi$
$859$	2.65979	+	1.53563i	0.0907510	+	0.0523951i	−0.453938	+	0.891033i	$0.649981\pi$
$860$	−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	$-0.554853\pi$
$863$	−10.0748			−0.342949			−0.171475	+	0.985189i	$0.554853\pi$
$864$	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
$868$	16.1166	−	15.9781i	0.547034	−	0.542333i
$869$	−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	−0.916048	−	0.401068i	$-0.868639\pi$
$877$	−3.27797	+	5.67761i	−0.110689	+	0.191719i	0.805359	+	0.592787i	$0.201972\pi$
$878$	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	$-0.516218\pi$
$881$	−3.02318			−0.101854			−0.0509268	+	0.998702i	$0.516218\pi$
$882$	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	−0.0646591	−	0.997907i	$-0.520596\pi$
$887$	−28.6270	−	16.5278i	−0.961202	−	0.554950i	−0.896543	+	0.442957i	$0.853929\pi$
$888$	−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	−0.989333	−	0.145669i	$-0.953467\pi$
$907$	−18.6969	−	32.3839i	−0.620820	−	1.07529i	0.368514	−	0.929622i	$-0.379867\pi$
$908$			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	$-0.150788\pi$
$911$	1.50507	+	2.60685i	0.0498651	+	0.0863689i	−0.840015	+	0.542562i	$0.817454\pi$
$912$	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	$-0.0254520\pi$
$929$	13.0827	+	22.6599i	0.429229	+	0.743447i	−0.567576	+	0.823321i	$0.692119\pi$
$930$	27.1634	+	7.88110i	0.890723	+	0.258431i
$931$	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	0.178295	+	0.983977i	$0.442942\pi$
$941$	−23.4056	+	40.5397i	−0.763002	+	1.32156i	−0.941297	+	0.337580i	$0.890392\pi$
$942$	−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	−0.997842	−	0.0656618i	$-0.979084\pi$
$947$	−17.1034	−	29.6240i	−0.555786	−	0.962649i	0.442056	−	0.896987i	$-0.354249\pi$
$948$	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	$-0.450845\pi$
$953$	9.49649			0.307621			0.153811	+	0.988100i	$0.450845\pi$
$954$	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
$961$	0.267530	−	30.9988i	0.00862999	−	0.999963i
$962$		−	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	$-0.495492\pi$
$967$	−26.2672	−	15.1654i	−0.844696	−	0.487686i	−0.858858	+	0.512214i	$0.828825\pi$
$968$	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	$0.0728397\pi$
$971$			14.1371i			0.453682i	−0.973932	+	0.226841i	$0.927160\pi$
$972$	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	−0.0934521	−	0.995624i	$-0.529790\pi$
$977$	−31.3324	−	18.0898i	−1.00241	−	0.578744i	−0.908962	+	0.416880i	$0.863124\pi$
$978$	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	−0.987962	−	0.154699i	$-0.950559\pi$
$983$	−19.6881	−	34.1009i	−0.627954	−	1.08765i	0.360008	−	0.932949i	$-0.382774\pi$
$984$	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	$0.914786\pi$
$992$	5.38422	−	1.41782i	0.170949	−	0.0450159i
$993$	−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	0.927753	+	0.373195i	$0.121738\pi$
$997$	24.8521	+	43.0450i	0.787073	+	1.36325i	−0.140680	+	0.990055i	$0.544929\pi$
$998$	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.185.5	✓	64
3.2	odd	2		1674.2.q.a.557.25		64
9.2	odd	6	inner	558.2.q.a.371.12	yes	64
9.7	even	3		1674.2.q.a.1115.20		64
31.30	odd	2	inner	558.2.q.a.185.12	yes	64
93.92	even	2		1674.2.q.a.557.20		64
279.61	odd	6		1674.2.q.a.1115.25		64
279.92	even	6	inner	558.2.q.a.371.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.5	✓	64	1.1	even	1	trivial
558.2.q.a.185.12	yes	64	31.30	odd	2	inner
558.2.q.a.371.5	yes	64	279.92	even	6	inner
558.2.q.a.371.12	yes	64	9.2	odd	6	inner
1674.2.q.a.557.20		64	93.92	even	2
1674.2.q.a.557.25		64	3.2	odd	2
1674.2.q.a.1115.20		64	9.7	even	3
1674.2.q.a.1115.25		64	279.61	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 $\F_{q}$
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} +(3.95396 - 3.91998i) 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} +(-9.26170 - 2.68716i) 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

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