LMFDB - Embedded newform 560.2.ch.c.437.56

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(117,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.117"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 3, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ch (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [360,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$90$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			437.56
Character	$\chi$	$=$	560.437
Dual form			560.2.ch.c.173.56

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.497965 + 1.32364i) q^{2} +(-0.360092 + 0.623698i) q^{3} +(-1.50406 + 1.31826i) q^{4} +(-0.305784 + 2.21506i) q^{5} +(-1.00487 - 0.166053i) q^{6} +(-0.529295 - 2.59227i) q^{7} +(-2.49387 - 1.33439i) q^{8} +(1.24067 + 2.14890i) q^{9} +(-3.08422 + 0.698274i) q^{10} +(-3.86774 + 1.03636i) q^{11} +(-0.280593 - 1.41277i) q^{12} -1.30220 q^{13} +(3.16767 - 1.99146i) q^{14} +(-1.27142 - 0.988343i) q^{15} +(0.524399 - 3.96548i) q^{16} +(0.797258 + 2.97541i) q^{17} +(-2.22657 + 2.71228i) q^{18} +(-3.10711 - 0.832549i) q^{19} +(-2.46010 - 3.73469i) q^{20} +(1.80739 + 0.603335i) q^{21} +(-3.29776 - 4.60343i) q^{22} +(0.421249 - 1.57212i) q^{23} +(1.73028 - 1.07492i) q^{24} +(-4.81299 - 1.35466i) q^{25} +(-0.648449 - 1.72364i) q^{26} -3.94757 q^{27} +(4.21336 + 3.20118i) q^{28} +(-1.22355 - 1.22355i) q^{29} +(0.675091 - 2.17506i) q^{30} +(4.67056 + 2.69655i) q^{31} +(5.51001 - 1.28055i) q^{32} +(0.746367 - 2.78548i) q^{33} +(-3.54137 + 2.53693i) q^{34} +(5.90388 - 0.379746i) q^{35} +(-4.69884 - 1.59656i) q^{36} +(-1.06154 + 0.612879i) q^{37} +(-0.445238 - 4.52729i) q^{38} +(0.468911 - 0.812178i) q^{39} +(3.71835 - 5.11604i) q^{40} +5.53618 q^{41} +(0.101416 + 2.69277i) q^{42} -6.24099 q^{43} +(4.45113 - 6.65741i) q^{44} +(-5.13932 + 2.09105i) q^{45} +(2.29070 - 0.225279i) q^{46} +(9.27457 + 2.48511i) q^{47} +(2.28443 + 1.75500i) q^{48} +(-6.43969 + 2.74415i) q^{49} +(-0.603615 - 7.04526i) q^{50} +(-2.14284 - 0.574172i) q^{51} +(1.95859 - 1.71663i) q^{52} +(-2.68216 + 4.64563i) q^{53} +(-1.96575 - 5.22517i) q^{54} +(-1.11290 - 8.88417i) q^{55} +(-2.13911 + 7.17107i) q^{56} +(1.63811 - 1.63811i) q^{57} +(1.01026 - 2.22883i) q^{58} +(-8.86473 + 2.37530i) q^{59} +(3.21518 - 0.189527i) q^{60} +(-1.26482 + 4.72039i) q^{61} +(-1.24349 + 7.52494i) q^{62} +(4.91384 - 4.35354i) q^{63} +(4.43879 + 6.65561i) q^{64} +(0.398192 - 2.88445i) q^{65} +(4.05865 - 0.399149i) q^{66} +(4.04552 - 7.00704i) q^{67} +(-5.12147 - 3.42420i) q^{68} +(0.828841 + 0.828841i) q^{69} +(3.44257 + 7.62553i) q^{70} +14.6273i q^{71} +(-0.226587 - 7.01462i) q^{72} +(1.68877 + 6.30257i) q^{73} +(-1.33984 - 1.09990i) q^{74} +(2.57802 - 2.51405i) q^{75} +(5.77080 - 2.84377i) q^{76} +(4.73368 + 9.47766i) q^{77} +(1.30853 + 0.216234i) q^{78} +(-10.0365 + 5.79459i) q^{79} +(8.62342 + 2.37416i) q^{80} +(-2.30051 + 3.98461i) q^{81} +(2.75682 + 7.32792i) q^{82} +9.57150 q^{83} +(-3.51377 + 1.47515i) q^{84} +(-6.83450 + 0.856142i) q^{85} +(-3.10779 - 8.26084i) q^{86} +(1.20372 - 0.322536i) q^{87} +(11.0285 + 2.57654i) q^{88} +(-14.0247 + 8.09717i) q^{89} +(-5.32701 - 5.76135i) q^{90} +(0.689246 + 3.37564i) q^{91} +(1.43888 + 2.91988i) q^{92} +(-3.36366 + 1.94201i) q^{93} +(1.32901 + 13.5137i) q^{94} +(2.79425 - 6.62787i) q^{95} +(-1.18543 + 3.89770i) q^{96} +(0.176114 - 0.176114i) q^{97} +(-6.83901 - 7.15737i) q^{98} +(-7.02560 - 7.02560i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + 2 q^{2} - 6 q^{5} + 8 q^{7} - 4 q^{8} - 164 q^{9} - 6 q^{10} - 2 q^{11} + 18 q^{12} + 4 q^{14} - 32 q^{15} - 20 q^{16} + 4 q^{18} + 30 q^{19} - 4 q^{21} - 16 q^{22} + 10 q^{23} + 12 q^{24} + 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) $ 360 * q + 2 * q^2 - 6 * q^5 + 8 * q^7 - 4 * q^8 - 164 * q^9 - 6 * q^10 - 2 * q^11 + 18 * q^12 + 4 * q^14 - 32 * q^15 - 20 * q^16 + 4 * q^18 + 30 * q^19 - 4 * q^21 - 16 * q^22 + 10 * q^23 + 12 * q^24 + 12 * q^25 + 10 * q^28 - 8 * q^29 + 58 * q^30 - 24 * q^31 - 38 * q^32 - 12 * q^35 + 16 * q^36 - 24 * q^38 - 28 * q^39 - 96 * q^40 - 6 * q^42 - 24 * q^43 + 20 * q^44 + 36 * q^45 - 4 * q^46 - 6 * q^47 - 64 * q^50 + 16 * q^51 - 108 * q^52 + 32 * q^53 - 24 * q^54 - 8 * q^56 + 80 * q^57 + 2 * q^58 + 84 * q^59 + 8 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 4 * q^67 + 84 * q^68 + 72 * q^70 + 36 * q^72 - 52 * q^74 - 54 * q^75 - 52 * q^77 + 96 * q^78 - 120 * q^80 - 124 * q^81 - 150 * q^82 + 28 * q^84 - 4 * q^85 + 8 * q^86 + 20 * q^88 + 48 * q^89 + 28 * q^91 + 84 * q^92 - 72 * q^94 - 26 * q^95 - 60 * q^96 + 26 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.497965	+	1.32364i	0.352115	+	0.935957i
$2$	0.497965	+	1.32364i	0.352115	+	0.935957i
$3$	−0.360092	+	0.623698i	−0.207899	+	0.360092i	−0.951053	−	0.309029i	$-0.899996\pi$
$3$	−0.360092	+	0.623698i	−0.207899	+	0.360092i	0.743153	+	0.669121i	$0.233329\pi$
$4$	−1.50406	+	1.31826i	−0.752031	+	0.659128i
$5$	−0.305784	+	2.21506i	−0.136751	+	0.990605i
$5$	−0.305784	+	2.21506i	−0.136751	+	0.990605i
$6$	−1.00487	−	0.166053i	−0.410235	−	0.0677910i
$7$	−0.529295	−	2.59227i	−0.200055	−	0.979785i
$7$	−0.529295	−	2.59227i	−0.200055	−	0.979785i
$8$	−2.49387	−	1.33439i	−0.881717	−	0.471779i
$9$	1.24067	+	2.14890i	0.413556	+	0.716300i
$10$	−3.08422	+	0.698274i	−0.975316	+	0.220814i
$11$	−3.86774	+	1.03636i	−1.16617	+	0.312473i	−0.789426	−	0.613846i	$-0.789622\pi$
$11$	−3.86774	+	1.03636i	−1.16617	+	0.312473i	−0.376740	+	0.926319i	$0.622955\pi$
$12$	−0.280593	−	1.41277i	−0.0810003	−	0.407832i
$13$	−1.30220			−0.361165			−0.180582	−	0.983560i	$-0.557798\pi$
$13$	−1.30220			−0.361165			−0.180582	+	0.983560i	$0.557798\pi$
$14$	3.16767	−	1.99146i	0.846594	−	0.532239i
$15$	−1.27142	−	0.988343i	−0.328279	−	0.255189i
$16$	0.524399	−	3.96548i	0.131100	−	0.991369i
$17$	0.797258	+	2.97541i	0.193363	+	0.721642i	0.992684	+	0.120738i	$0.0385261\pi$
$17$	0.797258	+	2.97541i	0.193363	+	0.721642i	−0.799321	+	0.600904i	$0.794807\pi$
$18$	−2.22657	+	2.71228i	−0.524807	+	0.639290i
$19$	−3.10711	−	0.832549i	−0.712821	−	0.191000i	−0.115855	−	0.993266i	$-0.536961\pi$
$19$	−3.10711	−	0.832549i	−0.712821	−	0.191000i	−0.596966	+	0.802266i	$0.703627\pi$
$20$	−2.46010	−	3.73469i	−0.550095	−	0.835102i
$21$	1.80739	+	0.603335i	0.394404	+	0.131658i
$22$	−3.29776	−	4.60343i	−0.703086	−	0.981455i
$23$	0.421249	−	1.57212i	0.0878365	−	0.327810i	−0.908000	−	0.418971i	$-0.862391\pi$
$23$	0.421249	−	1.57212i	0.0878365	−	0.327810i	0.995836	+	0.0911604i	$0.0290576\pi$
$24$	1.73028	−	1.07492i	0.353192	−	0.219417i
$25$	−4.81299	−	1.35466i	−0.962598	−	0.270932i
$26$	−0.648449	−	1.72364i	−0.127171	−	0.338035i
$27$	−3.94757			−0.759710
$28$	4.21336	+	3.20118i	0.796251	+	0.604966i
$29$	−1.22355	−	1.22355i	−0.227208	−	0.227208i	0.584317	−	0.811525i	$-0.301362\pi$
$29$	−1.22355	−	1.22355i	−0.227208	−	0.227208i	−0.811525	+	0.584317i	$0.801362\pi$
$30$	0.675091	−	2.17506i	0.123254	−	0.397111i
$31$	4.67056	+	2.69655i	0.838857	+	0.484314i	0.856876	−	0.515523i	$-0.172402\pi$
$31$	4.67056	+	2.69655i	0.838857	+	0.484314i	−0.0180184	+	0.999838i	$0.505736\pi$
$32$	5.51001	−	1.28055i	0.974041	−	0.226372i
$33$	0.746367	−	2.78548i	0.129926	−	0.484890i
$34$	−3.54137	+	2.53693i	−0.607340	+	0.435081i
$35$	5.90388	−	0.379746i	0.997938	−	0.0641887i
$36$	−4.69884	−	1.59656i	−0.783140	−	0.266093i
$37$	−1.06154	+	0.612879i	−0.174516	+	0.100757i	−0.584713	−	0.811240i	$-0.698793\pi$
$37$	−1.06154	+	0.612879i	−0.174516	+	0.100757i	0.410198	+	0.911997i	$0.365460\pi$
$38$	−0.445238	−	4.52729i	−0.0722271	−	0.734424i
$39$	0.468911	−	0.812178i	0.0750859	−	0.130053i
$40$	3.71835	−	5.11604i	0.587923	−	0.808917i
$41$	5.53618			0.864606			0.432303	−	0.901728i	$-0.357701\pi$
$41$	5.53618			0.864606			0.432303	+	0.901728i	$0.357701\pi$
$42$	0.101416	+	2.69277i	0.0156488	+	0.415504i
$43$	−6.24099			−0.951741			−0.475871	−	0.879515i	$-0.657867\pi$
$43$	−6.24099			−0.951741			−0.475871	+	0.879515i	$0.657867\pi$
$44$	4.45113	−	6.65741i	0.671033	−	1.00364i
$45$	−5.13932	+	2.09105i	−0.766125	+	0.311716i
$46$	2.29070	−	0.225279i	0.337745	−	0.0332156i
$47$	9.27457	+	2.48511i	1.35284	+	0.362491i	0.861181	−	0.508299i	$-0.169726\pi$
$47$	9.27457	+	2.48511i	1.35284	+	0.362491i	0.491655	+	0.870790i	$0.336392\pi$
$48$	2.28443	+	1.75500i	0.329729	+	0.253313i
$49$	−6.43969	+	2.74415i	−0.919956	+	0.392021i
$50$	−0.603615	−	7.04526i	−0.0853640	−	0.996350i
$51$	−2.14284	−	0.574172i	−0.300058	−	0.0804002i
$52$	1.95859	−	1.71663i	0.271607	−	0.238054i
$53$	−2.68216	+	4.64563i	−0.368423	+	0.638127i	−0.989319	−	0.145766i	$-0.953435\pi$
$53$	−2.68216	+	4.64563i	−0.368423	+	0.638127i	0.620896	+	0.783893i	$0.286769\pi$
$54$	−1.96575	−	5.22517i	−0.267505	−	0.711056i
$55$	−1.11290	−	8.88417i	−0.150063	−	1.19794i
$56$	−2.13911	+	7.17107i	−0.285851	+	0.958274i
$57$	1.63811	−	1.63811i	0.216972	−	0.216972i
$58$	1.01026	−	2.22883i	0.132654	−	0.292660i
$59$	−8.86473	+	2.37530i	−1.15409	+	0.309237i	−0.784603	−	0.619999i	$-0.787133\pi$
$59$	−8.86473	+	2.37530i	−1.15409	+	0.309237i	−0.369487	+	0.929236i	$0.620466\pi$
$60$	3.21518	−	0.189527i	0.415078	−	0.0244679i
$61$	−1.26482	+	4.72039i	−0.161944	+	0.604384i	0.836466	+	0.548019i	$0.184618\pi$
$61$	−1.26482	+	4.72039i	−0.161944	+	0.604384i	−0.998410	+	0.0563651i	$0.982049\pi$
$62$	−1.24349	+	7.52494i	−0.157923	+	0.955668i
$63$	4.91384	−	4.35354i	0.619086	−	0.548495i
$64$	4.43879	+	6.65561i	0.554848	+	0.831951i
$65$	0.398192	−	2.88445i	0.0493896	−	0.357772i
$66$	4.05865	−	0.399149i	0.499585	−	0.0491319i
$67$	4.04552	−	7.00704i	0.494239	−	0.856046i	−0.505739	−	0.862686i	$-0.668780\pi$
$67$	4.04552	−	7.00704i	0.494239	−	0.856046i	0.999978	+	0.00664007i	$0.00211362\pi$
$68$	−5.12147	−	3.42420i	−0.621070	−	0.415246i
$69$	0.828841	+	0.828841i	0.0997808	+	0.0997808i
$70$	3.44257	+	7.62553i	0.411466	+	0.911425i
$71$			14.6273i			1.73594i	0.496619	+	0.867969i	$0.334575\pi$
$71$			14.6273i			1.73594i	−0.496619	+	0.867969i	$0.665425\pi$
$72$	−0.226587	−	7.01462i	−0.0267036	−	0.826680i
$73$	1.68877	+	6.30257i	0.197655	+	0.737660i	0.991563	+	0.129622i	$0.0413765\pi$
$73$	1.68877	+	6.30257i	0.197655	+	0.737660i	−0.793908	+	0.608038i	$0.791957\pi$
$74$	−1.33984	−	1.09990i	−0.155753	−	0.127861i
$75$	2.57802	−	2.51405i	0.297684	−	0.290297i
$76$	5.77080	−	2.84377i	0.661957	−	0.326203i
$77$	4.73368	+	9.47766i	0.539453	+	1.08008i
$78$	1.30853	+	0.216234i	0.148162	+	0.0244837i
$79$	−10.0365	+	5.79459i	−1.12920	+	0.651942i	−0.943733	−	0.330709i	$-0.892712\pi$
$79$	−10.0365	+	5.79459i	−1.12920	+	0.651942i	−0.185464	+	0.982651i	$0.559379\pi$
$80$	8.62342	+	2.37416i	0.964128	+	0.265439i
$81$	−2.30051	+	3.98461i	−0.255613	+	0.442734i
$82$	2.75682	+	7.32792i	0.304440	+	0.809234i
$83$	9.57150			1.05061			0.525305	−	0.850914i	$-0.323951\pi$
$83$	9.57150			1.05061			0.525305	+	0.850914i	$0.323951\pi$
$84$	−3.51377	+	1.47515i	−0.383384	+	0.160952i
$85$	−6.83450	+	0.856142i	−0.741305	+	0.0928617i
$86$	−3.10779	−	8.26084i	−0.335122	−	0.890789i
$87$	1.20372	−	0.322536i	0.129052	−	0.0345794i
$88$	11.0285	+	2.57654i	1.17565	+	0.274660i
$89$	−14.0247	+	8.09717i	−1.48662	+	0.858298i	−0.999884	−	0.0152534i	$-0.995145\pi$
$89$	−14.0247	+	8.09717i	−1.48662	+	0.858298i	−0.486732	+	0.873551i	$0.661811\pi$
$90$	−5.32701	−	5.76135i	−0.561516	−	0.607300i
$91$	0.689246	+	3.37564i	0.0722526	+	0.353864i
$92$	1.43888	+	2.91988i	0.150013	+	0.304419i
$93$	−3.36366	+	1.94201i	−0.348796	+	0.201377i
$94$	1.32901	+	13.5137i	0.137077	+	1.39383i
$95$	2.79425	−	6.62787i	0.286684	−	0.680005i
$96$	−1.18543	+	3.89770i	−0.120988	+	0.397807i
$97$	0.176114	−	0.176114i	0.0178817	−	0.0178817i	−0.698109	−	0.715991i	$-0.745975\pi$
$97$	0.176114	−	0.176114i	0.0178817	−	0.0178817i	0.715991	+	0.698109i	$0.245975\pi$
$98$	−6.83901	−	7.15737i	−0.690845	−	0.723003i
$99$	−7.02560	−	7.02560i	−0.706099	−	0.706099i
$100$	9.02483	−	4.30726i	0.902483	−	0.430726i
$101$	3.17949	+	11.8660i	0.316371	+	1.18071i	0.922706	+	0.385503i	$0.125972\pi$
$101$	3.17949	+	11.8660i	0.316371	+	1.18071i	−0.606335	+	0.795209i	$0.707361\pi$
$102$	−0.307061	−	3.12227i	−0.0304036	−	0.309151i
$103$	11.8809	+	3.18347i	1.17066	+	0.313676i	0.791214	−	0.611540i	$-0.209450\pi$
$103$	11.8809	+	3.18347i	1.17066	+	0.313676i	0.379441	+	0.925216i	$0.376116\pi$
$104$	3.24751	+	1.73764i	0.318445	+	0.170390i
$105$	−1.88909	+	3.81898i	−0.184357	+	0.372694i
$106$	−7.48478	−	1.23685i	−0.726986	−	0.120134i
$107$	3.50852	−	2.02564i	0.339181	−	0.195826i	−0.320729	−	0.947171i	$-0.603928\pi$
$107$	3.50852	−	2.02564i	0.339181	−	0.195826i	0.659910	+	0.751345i	$0.270594\pi$
$108$	5.93739	−	5.20391i	0.571325	−	0.500746i
$109$	1.17022	−	0.313558i	0.112086	−	0.0300334i	−0.202340	−	0.979315i	$-0.564855\pi$
$109$	1.17022	−	0.313558i	0.112086	−	0.0300334i	0.314426	+	0.949282i	$0.398188\pi$
$110$	11.2053	−	5.89709i	1.06838	−	0.562266i
$111$		−	0.882771i		−	0.0837889i
$112$	−10.5571	+	0.739523i	−0.997556	+	0.0698783i
$113$	12.8737	−	12.8737i	1.21106	−	1.21106i	0.240378	−	0.970679i	$-0.422729\pi$
$113$	12.8737	−	12.8737i	1.21106	−	1.21106i	0.970679	−	0.240378i	$-0.0772714\pi$
$114$	2.98399	+	1.35255i	0.279476	+	0.126678i
$115$	3.35354	+	1.41382i	0.312719	+	0.131840i
$116$	3.45326	+	0.227342i	0.320627	+	0.0211081i
$117$	−1.61559	−	2.79829i	−0.149362	−	0.258702i
$118$	−7.55837	−	10.5509i	−0.695805	−	0.971291i
$119$	7.29106	−	3.64157i	0.668371	−	0.333822i
$120$	1.85191	+	4.16137i	0.169056	+	0.379880i
$121$	4.35906	−	2.51671i	0.396278	−	0.228791i
$122$	−6.87795	+	0.676414i	−0.622700	+	0.0612397i
$123$	−1.99353	+	3.45290i	−0.179751	+	0.311338i
$124$	−10.5795	+	2.10122i	−0.950072	+	0.188695i
$125$	4.47240	−	10.2468i	0.400023	−	0.916505i
$126$	8.20946	+	4.33626i	0.731357	+	0.386305i
$127$	−13.9513	−	13.9513i	−1.23798	−	1.23798i	−0.960825	−	0.277154i	$-0.910609\pi$
$127$	−13.9513	−	13.9513i	−1.23798	−	1.23798i	−0.277154	−	0.960825i	$-0.589391\pi$
$128$	−6.59929	+	9.18963i	−0.583300	+	0.812256i
$129$	2.24733	−	3.89249i	0.197866	−	0.342715i
$130$	4.01626	−	0.909291i	0.352250	−	0.0797501i
$131$	0.366673	−	1.36844i	0.0320364	−	0.119561i	−0.948056	−	0.318104i	$-0.896954\pi$
$131$	0.366673	−	1.36844i	0.0320364	−	0.119561i	0.980092	+	0.198542i	$0.0636207\pi$
$132$	2.54940	+	5.17344i	0.221897	+	0.450290i
$133$	−0.513610	+	8.49513i	−0.0445356	+	0.736622i
$134$	11.2893	+	1.86556i	0.975251	+	0.161160i
$135$	1.20710	−	8.74411i	0.103891	−	0.752573i
$136$	1.98211	−	8.48414i	0.169964	−	0.727509i
$137$	1.73301	+	6.46769i	0.148061	+	0.552572i	0.999600	+	0.0282805i	$0.00900315\pi$
$137$	1.73301	+	6.46769i	0.148061	+	0.552572i	−0.851539	+	0.524292i	$0.824330\pi$
$138$	−0.684356	+	1.50982i	−0.0582562	+	0.128525i
$139$	4.62212	+	4.62212i	0.392043	+	0.392043i	0.875415	−	0.483372i	$-0.160588\pi$
$139$	4.62212	+	4.62212i	0.392043	+	0.392043i	−0.483372	+	0.875415i	$0.660588\pi$
$140$	−8.37919	+	8.35399i	−0.708171	+	0.706041i
$141$	−4.88966	+	4.88966i	−0.411784	+	0.411784i
$142$	−19.3613	+	7.28387i	−1.62476	+	0.611249i
$143$	5.03656	−	1.34954i	0.421178	−	0.112854i
$144$	9.17201	−	3.79296i	0.764335	−	0.316080i
$145$	3.08439	−	2.33610i	0.256144	−	0.194003i
$146$	−7.50141	+	5.37379i	−0.620821	+	0.444738i
$147$	0.607365	−	5.00457i	0.0500946	−	0.412770i
$148$	0.788685	−	2.32119i	0.0648295	−	0.190800i
$149$	6.33152	+	1.69653i	0.518699	+	0.138985i	0.508665	−	0.860965i	$-0.330139\pi$
$149$	6.33152	+	1.69653i	0.518699	+	0.138985i	0.0100340	+	0.999950i	$0.496806\pi$
$150$	4.61147	+	2.16047i	0.376525	+	0.176401i
$151$	7.43917	+	4.29501i	0.605391	+	0.349523i	0.771159	−	0.636642i	$-0.219677\pi$
$151$	7.43917	+	4.29501i	0.605391	+	0.349523i	−0.165768	+	0.986165i	$0.553010\pi$
$152$	6.63780	+	6.22238i	0.538396	+	0.504702i
$153$	−5.40472	+	5.40472i	−0.436946	+	0.436946i
$154$	−10.1878	+	10.9853i	−0.820959	+	0.885217i
$155$	−7.40120	+	9.52101i	−0.594479	+	0.764746i
$156$	0.365388	+	1.83971i	0.0292544	+	0.147295i
$157$	19.6143	+	11.3243i	1.56539	+	0.903780i	0.996695	+	0.0812343i	$0.0258862\pi$
$157$	19.6143	+	11.3243i	1.56539	+	0.903780i	0.568698	+	0.822546i	$0.307447\pi$
$158$	−12.6678	−	10.3993i	−1.00780	−	0.827321i
$159$	−1.93165	−	3.34571i	−0.153190	−	0.265332i
$160$	1.15163	+	12.5966i	0.0910442	+	0.995847i
$161$	−4.29833	−	0.259874i	−0.338756	−	0.0204809i
$162$	−6.41977	−	1.06086i	−0.504385	−	0.0833492i
$163$	−18.3864	+	10.6154i	−1.44014	+	0.831463i	−0.997858	−	0.0654148i	$-0.979163\pi$
$163$	−18.3864	+	10.6154i	−1.44014	+	0.831463i	−0.442278	+	0.896878i	$0.645830\pi$
$164$	−8.32675	+	7.29810i	−0.650210	+	0.569886i
$165$	5.94178	+	2.50501i	0.462567	+	0.195014i
$166$	4.76628	+	12.6693i	0.369935	+	0.983325i
$167$	−5.40470	−	5.40470i	−0.418228	−	0.418228i	0.466365	−	0.884593i	$-0.345563\pi$
$167$	−5.40470	−	5.40470i	−0.418228	−	0.418228i	−0.884593	+	0.466365i	$0.845563\pi$
$168$	−3.70230	−	3.91640i	−0.285639	−	0.302157i
$169$	−11.3043			−0.869560
$170$	−4.53657	−	8.62011i	−0.347939	−	0.661132i
$171$	−2.06583	−	7.70979i	−0.157978	−	0.589583i
$172$	9.38682	−	8.22722i	0.715739	−	0.627320i
$173$	12.9318	+	22.3986i	0.983187	+	1.70293i	0.649730	+	0.760165i	$0.274882\pi$
$173$	12.9318	+	22.3986i	0.983187	+	1.70293i	0.333457	+	0.942765i	$0.391785\pi$
$174$	1.02633	+	1.43268i	0.0778060	+	0.108611i
$175$	−0.964154	+	13.1936i	−0.0728832	+	0.997340i
$176$	2.08141	+	15.8809i	0.156892	+	1.19707i
$177$	1.71065	−	6.38424i	0.128580	−	0.479869i
$178$	−17.7016	−	14.5316i	−1.32679	−	1.08919i
$179$	3.94762	−	1.05776i	0.295059	−	0.0790608i	−0.108253	−	0.994123i	$-0.534526\pi$
$179$	3.94762	−	1.05776i	0.295059	−	0.0790608i	0.403312	+	0.915063i	$0.367859\pi$
$180$	4.97330	−	9.92002i	0.370688	−	0.739394i
$181$	9.97127	−	9.97127i	0.741159	−	0.741159i	−0.231642	−	0.972801i	$-0.574410\pi$
$181$	9.97127	−	9.97127i	0.741159	−	0.741159i	0.972801	+	0.231642i	$0.0744099\pi$
$182$	−4.12493	+	2.59327i	−0.305760	+	0.192226i
$183$	−2.48864	−	2.48864i	−0.183966	−	0.183966i
$184$	−3.14837	+	3.35856i	−0.232101	+	0.247596i
$185$	−1.03296	−	2.53878i	−0.0759449	−	0.186655i
$186$	−4.24552	−	3.48523i	−0.311296	−	0.255550i
$187$	−6.16717	−	10.6818i	−0.450988	−	0.781134i
$188$	−17.2255	+	8.48850i	−1.25630	+	0.619088i
$189$	2.08943	+	10.2332i	0.151984	+	0.744352i
$190$	10.1644	+	0.398145i	0.737401	+	0.0288845i
$191$	−8.80890	−	15.2575i	−0.637390	−	1.10399i	−0.986003	−	0.166725i	$-0.946681\pi$
$191$	−8.80890	−	15.2575i	−0.637390	−	1.10399i	0.348614	−	0.937266i	$-0.386653\pi$
$192$	−5.74946	+	0.371828i	−0.414932	+	0.0268344i
$193$	−6.62260	−	24.7159i	−0.476705	−	1.77909i	−0.614815	−	0.788672i	$-0.710769\pi$
$193$	−6.62260	−	24.7159i	−0.476705	−	1.77909i	0.138109	−	0.990417i	$-0.455898\pi$
$194$	0.320811	+	0.145413i	0.0230329	+	0.0104401i
$195$	1.65564	+	1.28702i	0.118563	+	0.0921653i
$196$	6.06821	−	12.6165i	0.433443	−	0.901181i
$197$		−	18.7829i		−	1.33822i	−0.743161	−	0.669112i	$-0.766674\pi$
$197$		−	18.7829i		−	1.33822i	0.743161	−	0.669112i	$-0.233326\pi$
$198$	5.80088	−	12.7979i	0.412251	−	0.909506i
$199$	7.71789	+	4.45592i	0.547106	+	0.315872i	0.747954	−	0.663750i	$-0.231036\pi$
$199$	7.71789	+	4.45592i	0.547106	+	0.315872i	−0.200848	+	0.979622i	$0.564370\pi$
$200$	10.1953	+	9.80078i	0.720919	+	0.693020i
$201$	2.91352	+	5.04636i	0.205504	+	0.355943i
$202$	−14.1231	+	10.1174i	−0.993697	+	0.711856i
$203$	−2.52416	+	3.81940i	−0.177161	+	0.268069i
$204$	3.97987	−	1.96122i	0.278647	−	0.137313i
$205$	−1.69288	+	12.2630i	−0.118236	+	0.856483i
$206$	1.70248	+	17.3113i	0.118618	+	1.20613i
$207$	3.90097	−	1.04526i	0.271136	−	0.0726506i
$208$	−0.682872	+	5.16384i	−0.0473486	+	0.358048i
$209$	12.8803			0.890950
$210$	−5.99567	−	0.598766i	−0.413740	−	0.0413188i
$211$	−6.90757	+	6.90757i	−0.475537	+	0.475537i	−0.903701	−	0.428164i	$-0.859161\pi$
$211$	−6.90757	+	6.90757i	−0.475537	+	0.475537i	0.428164	+	0.903701i	$0.359161\pi$
$212$	−2.09001	−	10.5231i	−0.143542	−	0.722729i
$213$	−9.12299	−	5.26716i	−0.625097	−	0.360900i
$214$	4.42835	+	3.63532i	0.302716	+	0.248505i
$215$	1.90840	−	13.8242i	0.130151	−	0.942800i
$216$	9.84473	+	5.26761i	0.669849	+	0.358416i
$217$	4.51807	−	13.5346i	0.306707	−	0.918789i
$218$	0.997766	+	1.39281i	0.0675772	+	0.0943327i
$219$	−4.53901	−	1.21622i	−0.306718	−	0.0821848i
$220$	13.3855	+	11.8952i	0.902449	+	0.801977i
$221$	−1.03819	−	3.87457i	−0.0698361	−	0.260632i
$222$	1.16847	−	0.439589i	0.0784228	−	0.0295033i
$223$	4.16871	+	4.16871i	0.279157	+	0.279157i	0.832773	−	0.553615i	$-0.186752\pi$
$223$	4.16871	+	4.16871i	0.279157	+	0.279157i	−0.553615	+	0.832773i	$0.686752\pi$
$224$	−6.23595	−	13.6056i	−0.416657	−	0.909064i
$225$	−3.06029	−	12.0233i	−0.204019	−	0.801555i
$226$	23.4509	+	10.6295i	1.55993	+	0.707066i
$227$	12.4490	+	7.18744i	0.826270	+	0.477047i	0.852574	−	0.522607i	$-0.175040\pi$
$227$	12.4490	+	7.18744i	0.826270	+	0.477047i	−0.0263039	+	0.999654i	$0.508374\pi$
$228$	−0.304367	+	4.62326i	−0.0201572	+	0.306183i
$229$	1.03029	−	3.84511i	0.0680838	−	0.254092i	−0.923492	−	0.383617i	$-0.874678\pi$
$229$	1.03029	−	3.84511i	0.0680838	−	0.254092i	0.991576	+	0.129524i	$0.0413451\pi$
$230$	−0.201452	+	5.14292i	−0.0132833	+	0.339114i
$231$	−7.61576	−	0.460443i	−0.501080	−	0.0302949i
$232$	1.41868	+	4.68408i	0.0931410	+	0.307525i
$233$	0.145597	−	0.543375i	0.00953837	−	0.0355977i	−0.960993	−	0.276574i	$-0.910801\pi$
$233$	0.145597	−	0.543375i	0.00953837	−	0.0355977i	0.970531	+	0.240976i	$0.0774676\pi$
$234$	2.89943	−	3.53192i	0.189542	−	0.230889i
$235$	−8.34070	+	19.7838i	−0.544087	+	1.29056i
$236$	10.2018	−	15.2586i	0.664083	−	0.993249i
$237$		−	8.34634i		−	0.542153i
$238$	8.45084	+	7.83739i	0.547787	+	0.508022i
$239$		−	16.8638i		−	1.09083i	−0.838167	−	0.545414i	$-0.816372\pi$
$239$		−	16.8638i		−	1.09083i	0.838167	−	0.545414i	$-0.183628\pi$
$240$	−4.58598	+	4.52349i	−0.296024	+	0.291990i
$241$	5.17220	+	2.98617i	0.333170	+	0.192356i	0.657248	−	0.753675i	$-0.271720\pi$
$241$	5.17220	+	2.98617i	0.333170	+	0.192356i	−0.324077	+	0.946031i	$0.605054\pi$
$242$	5.50188	+	4.51661i	0.353674	+	0.290339i
$243$	−7.57815	−	13.1257i	−0.486138	−	0.842017i
$244$	−4.32031	−	8.76712i	−0.276580	−	0.561257i
$245$	−4.10929	−	15.1034i	−0.262533	−	0.964923i
$246$	−5.56312	−	0.919301i	−0.354692	−	0.0586125i
$247$	4.04608	+	1.08414i	0.257446	+	0.0689824i
$248$	−8.04952	−	12.9572i	−0.511145	−	0.822784i
$249$	−3.44662	+	5.96973i	−0.218421	+	0.378316i
$250$	15.7903	+	0.817286i	0.998663	+	0.0516897i
$251$	0.424636	−	0.424636i	0.0268028	−	0.0268028i	−0.693578	−	0.720381i	$-0.743967\pi$
$251$	0.424636	−	0.424636i	0.0268028	−	0.0268028i	0.720381	+	0.693578i	$0.243967\pi$
$252$	−1.65163	+	13.0257i	−0.104043	+	0.820542i
$253$			6.51712i			0.409728i
$254$	11.5193	−	25.4138i	0.722785	−	1.59461i
$255$	1.92707	−	4.57095i	0.120678	−	0.286244i
$256$	−15.4500	−	4.15899i	−0.965626	−	0.259937i
$257$	−10.0026	−	2.68019i	−0.623945	−	0.167185i	−0.0670243	−	0.997751i	$-0.521350\pi$
$257$	−10.0026	−	2.68019i	−0.623945	−	0.167185i	−0.556920	+	0.830566i	$0.688017\pi$
$258$	6.27136	+	1.03634i	0.390438	+	0.0645195i
$259$	2.15061	+	2.42739i	0.133632	+	0.150831i
$260$	3.20354	+	4.86330i	0.198675	+	0.301609i
$261$	1.11127	−	4.14731i	0.0687859	−	0.256712i
$262$	1.99392	−	0.196093i	0.123185	−	0.0121146i
$263$	20.1291	−	5.39358i	1.24121	−	0.332582i	0.422278	−	0.906466i	$-0.361231\pi$
$263$	20.1291	−	5.39358i	1.24121	−	0.332582i	0.818937	+	0.573884i	$0.194564\pi$
$264$	−5.57827	+	5.95068i	−0.343319	+	0.366239i
$265$	−9.47020	−	7.36170i	−0.581750	−	0.452226i
$266$	−11.5003	+	3.55045i	−0.705128	+	0.217692i
$267$		−	11.6629i		−	0.713758i
$268$	3.15237	+	15.8720i	0.192562	+	0.969539i
$269$	−7.70811	−	28.7671i	−0.469972	−	1.75396i	−0.639856	−	0.768495i	$-0.721006\pi$
$269$	−7.70811	−	28.7671i	−0.469972	−	1.75396i	0.169884	−	0.985464i	$-0.445661\pi$
$270$	12.1752	−	2.75649i	0.740958	−	0.167754i
$271$	−3.82804	+	2.21012i	−0.232537	+	0.134255i	−0.611742	−	0.791058i	$-0.709531\pi$
$271$	−3.82804	+	2.21012i	−0.232537	+	0.134255i	0.379205	+	0.925313i	$0.376197\pi$
$272$	12.2170	−	1.60121i	0.740764	−	0.0970874i
$273$	−2.35357	−	0.785661i	−0.142445	−	0.0475504i
$274$	−7.69793	+	5.51457i	−0.465049	+	0.333148i
$275$	20.0193	+	0.251498i	1.20721	+	0.0151659i
$276$	−2.33925	−	0.154002i	−0.140807	−	0.00926986i
$277$	7.35664	+	4.24736i	0.442018	+	0.255199i	0.704453	−	0.709751i	$-0.251192\pi$
$277$	7.35664	+	4.24736i	0.442018	+	0.255199i	−0.262435	+	0.964950i	$0.584526\pi$
$278$	−3.81638	+	8.41969i	−0.228891	+	0.504979i
$279$			13.3821i			0.801164i
$280$	−15.2302	−	6.93106i	−0.910181	−	0.414210i
$281$		−	1.51577i		−	0.0904234i	−0.998977	−	0.0452117i	$-0.985604\pi$
$281$		−	1.51577i		−	0.0904234i	0.998977	−	0.0452117i	$-0.0143962\pi$
$282$	−8.90704	−	4.03728i	−0.530407	−	0.240417i
$283$	−10.6212	−	6.13216i	−0.631365	−	0.364519i	0.149915	−	0.988699i	$-0.452100\pi$
$283$	−10.6212	−	6.13216i	−0.631365	−	0.364519i	−0.781281	+	0.624180i	$0.785433\pi$
$284$	−19.2825	−	22.0003i	−1.14421	−	1.30548i
$285$	3.12760	+	4.12941i	0.185263	+	0.244605i
$286$	4.29434	+	5.99458i	0.253930	+	0.354467i
$287$	−2.93027	−	14.3512i	−0.172968	−	0.847128i
$288$	9.58787	+	10.2517i	0.564970	+	0.604088i
$289$	6.50500	−	3.75567i	0.382647	−	0.220922i
$290$	4.62808	+	2.91933i	0.271770	+	0.171429i
$291$	0.0464247	+	0.173259i	0.00272146	+	0.0101566i
$292$	−10.8484	−	7.25322i	−0.634856	−	0.424463i
$293$			0.845374i			0.0493873i	0.999695	+	0.0246936i	$0.00786103\pi$
$293$			0.845374i			0.0493873i	−0.999695	+	0.0246936i	$0.992139\pi$
$294$	6.92671	−	1.68817i	0.403974	−	0.0984559i
$295$	−2.55073	−	20.3622i	−0.148509	−	1.18554i
$296$	3.46516	−	0.111932i	0.201408	−	0.00650593i
$297$	15.2682	−	4.09109i	0.885948	−	0.237389i
$298$	0.907284	+	9.22549i	0.0525575	+	0.534418i
$299$	−0.548550	+	2.04722i	−0.0317235	+	0.118394i
$300$	−0.563337	+	7.17977i	−0.0325243	+	0.414524i
$301$	3.30332	+	16.1783i	0.190400	+	0.932502i
$302$	−1.98061	+	11.9856i	−0.113971	+	0.689692i
$303$	−8.54571	−	2.28982i	−0.490938	−	0.131547i
$304$	−4.93082	+	11.8846i	−0.282802	+	0.681629i
$305$	−10.0692	−	4.24508i	−0.576560	−	0.243073i
$306$	−9.84528	−	4.46255i	−0.562817	−	0.255107i
$307$		−	16.2854i		−	0.929459i	−0.885453	−	0.464730i	$-0.846152\pi$
$307$		−	16.2854i		−	0.929459i	0.885453	−	0.464730i	$-0.153848\pi$
$308$	−19.6137	−	8.01477i	−1.11760	−	0.456684i
$309$	−6.26372	+	6.26372i	−0.356331	+	0.356331i
$310$	−16.2880	−	5.05542i	−0.925094	−	0.287128i
$311$	−1.90495	+	3.29948i	−0.108020	+	0.187096i	−0.914968	−	0.403526i	$-0.867784\pi$
$311$	−1.90495	+	3.29948i	−0.108020	+	0.187096i	0.806948	+	0.590622i	$0.201118\pi$
$312$	−2.25317	+	1.39975i	−0.127561	+	0.0792455i
$313$	−22.7040	−	6.08353i	−1.28331	−	0.343861i	−0.448193	−	0.893937i	$-0.647932\pi$
$313$	−22.7040	−	6.08353i	−1.28331	−	0.343861i	−0.835115	+	0.550075i	$0.814599\pi$
$314$	−5.22212	+	31.6015i	−0.294701	+	1.78338i
$315$	8.14079	+	12.2157i	0.458681	+	0.688277i
$316$	7.45678	−	21.9461i	0.419477	−	1.23457i
$317$	0.0142434	+	0.0246702i	0.000799987	+	0.00138562i	0.866425	−	0.499307i	$-0.166412\pi$
$317$	0.0142434	+	0.0246702i	0.000799987	+	0.00138562i	−0.865625	+	0.500693i	$0.833079\pi$
$318$	3.46663	−	4.22286i	0.194399	−	0.236806i
$319$	6.00042	+	3.46434i	0.335959	+	0.193966i
$320$	−16.0999	+	7.79700i	−0.900012	+	0.435866i
$321$			2.91767i			0.162849i
$322$	−1.79644	−	5.81886i	−0.100112	−	0.324272i
$323$		−	9.90869i		−	0.551334i
$324$	−1.79262	−	9.02576i	−0.0995900	−	0.501431i
$325$	6.26747	+	1.76404i	0.347657	+	0.0978512i
$326$	−23.2068	−	19.0510i	−1.28531	−	1.05514i
$327$	−0.225820	+	0.842770i	−0.0124879	+	0.0466053i
$328$	−13.8065	−	7.38744i	−0.762337	−	0.407903i
$329$	1.53310	−	25.3575i	0.0845224	−	1.39801i
$330$	−0.356931	+	9.11221i	−0.0196484	+	0.501610i
$331$	0.342677	−	1.27889i	0.0188352	−	0.0702941i	−0.955869	−	0.293795i	$-0.905082\pi$
$331$	0.342677	−	1.27889i	0.0188352	−	0.0702941i	0.974704	+	0.223501i	$0.0717485\pi$
$332$	−14.3961	+	12.6177i	−0.790090	+	0.692486i
$333$	−2.63403	−	1.52076i	−0.144344	−	0.0833370i
$334$	4.46254	−	9.84524i	0.244179	−	0.538708i
$335$	14.2840	+	11.1037i	0.780416	+	0.606660i
$336$	3.34030	−	6.85076i	0.182228	−	0.373739i
$337$	9.95073	+	9.95073i	0.542051	+	0.542051i	0.924130	−	0.382079i	$-0.124792\pi$
$337$	9.95073	+	9.95073i	0.542051	+	0.542051i	−0.382079	+	0.924130i	$0.624792\pi$
$338$	−5.62914	−	14.9628i	−0.306185	−	0.813871i
$339$	3.39358	+	12.6650i	0.184314	+	0.687870i
$340$	9.15089	−	10.2973i	0.496277	−	0.558450i
$341$	−20.8591	−	5.58917i	−1.12958	−	0.302671i
$342$	9.17630	−	6.57363i	0.496197	−	0.355461i
$343$	10.5221	+	15.2409i	0.568138	+	0.822934i
$344$	15.5642	+	8.32793i	0.839166	+	0.449012i
$345$	−2.08938	+	1.58249i	−0.112488	+	0.0851983i
$346$	−23.2081	+	28.2708i	−1.24767	+	1.51985i
$347$	7.36834	+	4.25411i	0.395553	+	0.228373i	0.684563	−	0.728953i	$-0.259993\pi$
$347$	7.36834	+	4.25411i	0.395553	+	0.228373i	−0.289010	+	0.957326i	$0.593326\pi$
$348$	−1.38528	+	2.07192i	−0.0742589	+	0.111067i
$349$	21.0228	−	21.0228i	1.12532	−	1.12532i	0.134397	−	0.990928i	$-0.457090\pi$
$349$	21.0228	−	21.0228i	1.12532	−	1.12532i	0.990928	−	0.134397i	$-0.0429099\pi$
$350$	−17.9437	+	5.29375i	−0.959131	+	0.282963i
$351$	5.14052			0.274381
$352$	−19.9841	+	10.6632i	−1.06516	+	0.568349i
$353$	−13.5031	+	3.61815i	−0.718698	+	0.192574i	−0.599591	−	0.800307i	$-0.704670\pi$
$353$	−13.5031	+	3.61815i	−0.718698	+	0.192574i	−0.119107	+	0.992881i	$0.538003\pi$
$354$	9.30230	−	0.914837i	0.494411	−	0.0486231i
$355$	−32.4003	−	4.47279i	−1.71963	−	0.237391i
$356$	10.4199	−	30.6668i	0.552252	−	1.62534i
$357$	−0.354214	+	5.85872i	−0.0187470	+	0.310076i
$358$	3.36588	+	4.69851i	0.177892	+	0.248324i
$359$	11.6770	+	20.2251i	0.616287	+	1.06744i	0.990157	+	0.139959i	$0.0446972\pi$
$359$	11.6770	+	20.2251i	0.616287	+	1.06744i	−0.373870	+	0.927481i	$0.621970\pi$
$360$	15.6071	+	1.64305i	0.822566	+	0.0865966i
$361$	−7.49346	−	4.32635i	−0.394393	−	0.227703i
$362$	18.1637	+	8.23305i	0.954665	+	0.432720i
$363$			3.62498i			0.190262i
$364$	−5.48663	−	4.16857i	−0.287578	−	0.218493i
$365$	−14.4770	+	1.81350i	−0.757760	+	0.0949229i
$366$	2.05482	−	4.53333i	0.107407	−	0.236961i
$367$	1.82038	+	6.79376i	0.0950232	+	0.354631i	0.997023	−	0.0771051i	$-0.0245677\pi$
$367$	1.82038	+	6.79376i	0.0950232	+	0.354631i	−0.902000	+	0.431736i	$0.857901\pi$
$368$	−6.01332	−	2.49487i	−0.313466	−	0.130054i
$369$	6.86856	+	11.8967i	0.357563	+	0.619317i
$370$	2.84606	−	2.63150i	0.147959	−	0.136805i
$371$	13.4624	+	4.49396i	0.698932	+	0.233315i
$372$	2.49908	−	7.35507i	0.129571	−	0.381343i
$373$	14.3654	+	24.8817i	0.743814	+	1.28832i	0.950747	+	0.309969i	$0.100319\pi$
$373$	14.3654	+	24.8817i	0.743814	+	1.28832i	−0.206932	+	0.978355i	$0.566348\pi$
$374$	11.0679	−	13.4823i	0.572308	−	0.697154i
$375$	4.78045	+	6.47923i	0.246862	+	0.334586i
$376$	−19.8135	−	18.5735i	−1.02180	−	0.957854i
$377$	1.59331	+	1.59331i	0.0820595	+	0.0820595i
$378$	−12.5046	+	7.86141i	−0.643166	+	0.404347i
$379$	−12.2721	+	12.2721i	−0.630375	+	0.630375i	−0.948162	−	0.317787i	$-0.897060\pi$
$379$	−12.2721	+	12.2721i	−0.630375	+	0.630375i	0.317787	+	0.948162i	$0.397060\pi$
$380$	4.53450	+	13.6523i	0.232615	+	0.700346i
$381$	13.7252	−	3.67765i	0.703162	−	0.188412i
$382$	15.8089	−	19.2575i	0.808854	−	0.985301i
$383$	3.88593	−	14.5025i	0.198562	−	0.741042i	−0.792754	−	0.609541i	$-0.791354\pi$
$383$	3.88593	−	14.5025i	0.198562	−	0.741042i	0.991316	−	0.131501i	$-0.0419796\pi$
$384$	−3.35520	−	7.42508i	−0.171219	−	0.378909i
$385$	−22.4411	+	7.58728i	−1.14370	+	0.386684i
$386$	29.4172	−	21.0736i	1.49730	−	1.07262i
$387$	−7.74299	−	13.4112i	−0.393598	−	0.681732i
$388$	−0.0327228	+	0.497050i	−0.00166125	+	0.0252339i
$389$	−6.53876	−	24.4030i	−0.331528	−	1.23728i	−0.907584	−	0.419870i	$-0.862076\pi$
$389$	−6.53876	−	24.4030i	−0.331528	−	1.23728i	0.576056	−	0.817410i	$-0.304591\pi$
$390$	−0.879102	+	2.83236i	−0.0445151	+	0.143422i
$391$	5.01355			0.253546
$392$	19.7215	+	1.74954i	0.996088	+	0.0883652i
$393$	0.721458	+	0.721458i	0.0363928	+	0.0363928i
$394$	24.8618	−	9.35322i	1.25252	−	0.471209i
$395$	−9.76635	−	24.0034i	−0.491399	−	1.20774i
$396$	19.8285	+	1.30539i	0.996418	+	0.0655982i
$397$	−10.5564	+	6.09474i	−0.529811	+	0.305886i	−0.740939	−	0.671572i	$-0.765619\pi$
$397$	−10.5564	+	6.09474i	−0.529811	+	0.305886i	0.211129	+	0.977458i	$0.432286\pi$
$398$	−2.05481	+	12.4346i	−0.102998	+	0.623291i
$399$	−5.11345	−	3.37937i	−0.255993	−	0.169180i
$400$	−7.89581	+	18.3754i	−0.394790	+	0.918771i
$401$	17.8560	+	30.9276i	0.891688	+	1.54445i	0.837851	+	0.545899i	$0.183812\pi$
$401$	17.8560	+	30.9276i	0.891688	+	1.54445i	0.0538373	+	0.998550i	$0.482855\pi$
$402$	−5.22875	+	6.36937i	−0.260786	+	0.317675i
$403$	−6.08199	−	3.51144i	−0.302966	−	0.174917i
$404$	−20.4246	−	13.6558i	−1.01616	−	0.679403i
$405$	−8.12269	−	6.31421i	−0.403620	−	0.313756i
$406$	−6.31246	−	1.43915i	−0.313282	−	0.0714240i
$407$	3.47058	−	3.47058i	0.172030	−	0.172030i
$408$	4.57780	+	4.29131i	0.226635	+	0.212451i
$409$	13.5323	+	7.81290i	0.669131	+	0.386323i	0.795747	−	0.605629i	$-0.207078\pi$
$409$	13.5323	+	7.81290i	0.669131	+	0.386323i	−0.126616	+	0.991952i	$0.540412\pi$
$410$	−17.0748	+	3.86577i	−0.843264	+	0.190917i
$411$	−4.65793	−	1.24809i	−0.229759	−	0.0615636i
$412$	−22.0662	+	10.8739i	−1.08712	+	0.535718i
$413$	10.8495	+	21.7225i	0.533867	+	1.06889i
$414$	3.32610	+	4.64298i	0.163469	+	0.228190i
$415$	−2.92682	+	21.2015i	−0.143672	+	1.04074i
$416$	−7.17512	+	1.66753i	−0.351789	+	0.0817575i
$417$	−4.54719	+	1.21842i	−0.222677	+	0.0596661i
$418$	6.41395	+	17.0489i	0.313717	+	0.833891i
$419$	3.05027	−	3.05027i	0.149016	−	0.149016i	−0.628663	−	0.777678i	$-0.716397\pi$
$419$	3.05027	−	3.05027i	0.149016	−	0.149016i	0.777678	+	0.628663i	$0.216397\pi$
$420$	−2.19308	−	8.23429i	−0.107011	−	0.401792i
$421$	21.6422	+	21.6422i	1.05478	+	1.05478i	0.998410	+	0.0563674i	$0.0179518\pi$
$421$	21.6422	+	21.6422i	1.05478	+	1.05478i	0.0563674	+	0.998410i	$0.482048\pi$
$422$	−12.5829	−	5.70343i	−0.612525	−	0.277638i
$423$	6.16640	+	23.0133i	0.299821	+	1.11895i
$424$	12.8881	−	8.00656i	0.625899	−	0.388833i
$425$	0.193474	−	15.4006i	0.00938489	−	0.747040i
$426$	2.42891	−	14.6984i	0.117681	−	0.712142i
$427$	12.9060	+	0.780286i	0.624564	+	0.0377607i
$428$	−2.60671	+	7.67181i	−0.126000	+	0.370831i
$429$	−0.971918	+	3.62725i	−0.0469246	+	0.175125i
$430$	19.2486	−	4.35792i	0.928249	−	0.210158i
$431$	2.56467	−	4.44214i	0.123536	−	0.213970i	−0.797624	−	0.603155i	$-0.793910\pi$
$431$	2.56467	−	4.44214i	0.123536	−	0.213970i	0.921160	+	0.389185i	$0.127243\pi$
$432$	−2.07010	+	15.6540i	−0.0995979	+	0.753153i
$433$	−29.1874	−	29.1874i	−1.40266	−	1.40266i	−0.791540	−	0.611117i	$-0.790720\pi$
$433$	−29.1874	−	29.1874i	−1.40266	−	1.40266i	−0.611117	−	0.791540i	$-0.709280\pi$
$434$	20.1648	−	0.759451i	0.967943	−	0.0364548i
$435$	0.346358	+	2.76494i	0.0166066	+	0.132569i
$436$	−1.34672	+	2.01425i	−0.0644964	+	0.0964653i
$437$	−2.61774	+	4.53406i	−0.125223	+	0.216893i
$438$	−0.650423	−	6.61367i	−0.0310784	−	0.316013i
$439$	−27.2269	+	15.7195i	−1.29947	+	0.750250i	−0.980313	−	0.197452i	$-0.936733\pi$
$439$	−27.2269	+	15.7195i	−1.29947	+	0.750250i	−0.319158	+	0.947701i	$0.603400\pi$
$440$	−9.07955	+	23.6410i	−0.432851	+	1.12704i
$441$	−13.8864	−	10.4337i	−0.661258	−	0.496842i
$442$	4.61156	−	3.30359i	0.219350	−	0.157136i
$443$	7.19894	+	12.4689i	0.342032	+	0.592417i	0.984810	−	0.173636i	$-0.0555515\pi$
$443$	7.19894	+	12.4689i	0.342032	+	0.592417i	−0.642778	+	0.766053i	$0.722218\pi$
$444$	1.16372	+	1.32774i	0.0552276	+	0.0630118i
$445$	−13.6472	−	33.5416i	−0.646939	−	1.59002i
$446$	−3.44201	+	7.59375i	−0.162984	+	0.359575i
$447$	−3.33805	+	3.33805i	−0.157884	+	0.157884i
$448$	14.9037	−	15.0293i	0.704133	−	0.710068i
$449$		−	24.3063i		−	1.14709i	−0.819175	−	0.573544i	$-0.805568\pi$
$449$		−	24.3063i		−	1.14709i	0.819175	−	0.573544i	$-0.194432\pi$
$450$	14.3907	−	10.0379i	0.678382	−	0.473192i
$451$	−21.4125	+	5.73745i	−1.00827	+	0.270166i
$452$	−2.39199	+	36.3337i	−0.112510	+	1.70899i
$453$	−5.35757	+	3.09319i	−0.251721	+	0.145331i
$454$	−3.31443	+	20.0571i	−0.155554	+	0.941328i
$455$	−7.68802	+	0.494504i	−0.360420	+	0.0231827i
$456$	−6.27110	+	1.89935i	−0.293671	+	0.0889451i
$457$	10.4424	+	2.79803i	0.488474	+	0.130886i	0.494646	−	0.869095i	$-0.335298\pi$
$457$	10.4424	+	2.79803i	0.488474	+	0.130886i	−0.00617169	+	0.999981i	$0.501965\pi$
$458$	5.60261	−	0.550990i	0.261793	−	0.0257461i
$459$	−3.14723	−	11.7456i	−0.146900	−	0.548239i
$460$	−6.90771	+	2.29435i	−0.322074	+	0.106974i
$461$	−9.72905	−	9.72905i	−0.453127	−	0.453127i	0.443264	−	0.896391i	$-0.353820\pi$
$461$	−9.72905	−	9.72905i	−0.453127	−	0.453127i	−0.896391	+	0.443264i	$0.853820\pi$
$462$	−3.18292	−	10.3098i	−0.148083	−	0.479657i
$463$	−17.8524	+	17.8524i	−0.829671	+	0.829671i	−0.987471	−	0.157800i	$-0.949560\pi$
$463$	−17.8524	+	17.8524i	−0.829671	+	0.829671i	0.157800	+	0.987471i	$0.449560\pi$
$464$	−5.49360	+	4.21034i	−0.255034	+	0.195460i
$465$	−3.27312	−	8.04455i	−0.151787	−	0.373057i
$466$	0.791736	−	0.0778636i	0.0366765	−	0.00360696i
$467$	−0.285082	+	0.164592i	−0.0131920	+	0.00761641i	−0.506582	−	0.862192i	$-0.669091\pi$
$467$	−0.285082	+	0.164592i	−0.0131920	+	0.00761641i	0.493389	+	0.869808i	$0.335758\pi$
$468$	6.11882	+	2.07903i	0.282843	+	0.0961034i
$469$	−20.3054	−	6.77827i	−0.937616	−	0.312991i
$470$	−30.3401	−	1.18844i	−1.39949	−	0.0548187i
$471$	−14.1259	+	8.15561i	−0.650888	+	0.375790i
$472$	25.2771	+	5.90535i	1.16347	+	0.271816i
$473$	24.1385	−	6.46789i	1.10989	−	0.297394i
$474$	11.0476	−	4.15619i	0.507432	−	0.190900i
$475$	13.8267	+	8.21614i	0.634412	+	0.376982i
$476$	−6.16568	+	15.0886i	−0.282603	+	0.691587i
$477$	−13.3107			−0.609453
$478$	22.3216	−	8.39759i	1.02097	−	0.384097i
$479$	−8.80324	+	15.2477i	−0.402230	+	0.696683i	−0.993995	−	0.109428i	$-0.965098\pi$
$479$	−8.80324	+	15.2477i	−0.402230	+	0.696683i	0.591764	+	0.806111i	$0.298432\pi$
$480$	−8.27115	−	3.81766i	−0.377525	−	0.174252i
$481$	1.38233	−	0.798089i	0.0630289	−	0.0363897i
$482$	−1.37705	+	8.33315i	−0.0627228	+	0.379565i
$483$	1.70988	−	2.58728i	0.0778021	−	0.117725i
$484$	−3.23863	+	9.53164i	−0.147211	+	0.433256i
$485$	0.336251	+	0.443956i	0.0152684	+	0.0201590i
$486$	13.6001	−	16.5669i	0.616915	−	0.751491i
$487$	4.22342	+	15.7620i	0.191381	+	0.714245i	0.993174	+	0.116643i	$0.0372132\pi$
$487$	4.22342	+	15.7620i	0.191381	+	0.714245i	−0.801793	+	0.597603i	$0.796120\pi$
$488$	9.45317	−	10.0843i	0.427925	−	0.456493i
$489$		−	15.2901i		−	0.691442i
$490$	17.9453	−	12.9602i	0.810685	−	0.585483i
$491$	26.7226	+	26.7226i	1.20597	+	1.20597i	0.972320	+	0.233652i	$0.0750676\pi$
$491$	26.7226	+	26.7226i	1.20597	+	1.20597i	0.233652	+	0.972320i	$0.424932\pi$
$492$	−1.55341	−	7.82136i	−0.0700333	−	0.352614i
$493$	2.66508	−	4.61606i	0.120029	−	0.207897i
$494$	0.579788	+	5.89543i	0.0260859	+	0.265248i
$495$	17.7104	−	13.4138i	0.796025	−	0.602906i
$496$	13.1423	−	17.1069i	0.590108	−	0.768124i
$497$	37.9178	−	7.74213i	1.70084	−	0.347282i
$498$	−9.61808	−	1.58938i	−0.430997	−	0.0712219i
$499$	−10.3634	+	38.6769i	−0.463931	+	1.73142i	0.196476	+	0.980509i	$0.437050\pi$
$499$	−10.3634	+	38.6769i	−0.463931	+	1.73142i	−0.660408	+	0.750907i	$0.729617\pi$
$500$	6.78120	+	21.3076i	0.303265	+	0.952906i
$501$	5.31709	−	1.42471i	0.237550	−	0.0636513i
$502$	0.773521	+	0.350613i	0.0345239	+	0.0156486i
$503$	16.4835	−	16.4835i	0.734965	−	0.734965i	−0.236634	−	0.971599i	$-0.576044\pi$
$503$	16.4835	−	16.4835i	0.734965	−	0.734965i	0.971599	+	0.236634i	$0.0760443\pi$
$504$	−18.0638	+	4.30017i	−0.804627	+	0.191545i
$505$	−27.2562	+	3.41432i	−1.21288	+	0.151935i
$506$	−8.62634	+	3.24530i	−0.383488	+	0.144271i
$507$	4.07058	−	7.05045i	0.180781	−	0.313122i
$508$	39.3751	+	2.59222i	1.74699	+	0.115011i
$509$	28.8827	+	7.73911i	1.28020	+	0.343030i	0.833932	−	0.551867i	$-0.186084\pi$
$509$	28.8827	+	7.73911i	1.28020	+	0.343030i	0.446273	+	0.894897i	$0.352751\pi$
$510$	7.00992	+	0.274583i	0.310405	+	0.0121587i
$511$	15.4441	−	7.71366i	0.683206	−	0.341232i
$512$	−2.18856	−	22.5213i	−0.0967215	−	0.995311i
$513$	12.2656	+	3.28654i	0.541537	+	0.145105i
$514$	−1.43333	−	14.5745i	−0.0632217	−	0.642854i
$515$	−10.6845	+	25.3434i	−0.470817	+	1.11676i
$516$	1.75118	+	8.81710i	0.0770913	+	0.388151i
$517$	−38.4471			−1.69090
$518$	−2.14207	+	4.05540i	−0.0941173	+	0.178184i
$519$	−18.6266			−0.817616
$520$	−4.84203	+	6.66210i	−0.212337	+	0.292152i
$521$	−15.0914	+	26.1390i	−0.661165	+	1.14517i	0.319145	+	0.947706i	$0.396604\pi$
$521$	−15.0914	+	26.1390i	−0.661165	+	1.14517i	−0.980310	+	0.197465i	$0.936729\pi$
$522$	6.04294	−	0.594295i	0.264492	−	0.0260116i
$523$	7.76736	−	4.48449i	0.339643	−	0.196093i	−0.320471	−	0.947258i	$-0.603841\pi$
$523$	7.76736	−	4.48449i	0.339643	−	0.196093i	0.660114	+	0.751165i	$0.270508\pi$
$524$	1.25246	+	2.54159i	0.0547139	+	0.111030i
$525$	−7.88162	−	5.35224i	−0.343982	−	0.233591i
$526$	17.1628	+	23.9580i	0.748333	+	1.04462i
$527$	−4.29969	+	16.0467i	−0.187297	+	0.699003i
$528$	−10.6544	−	4.42041i	−0.463672	−	0.192374i
$529$	17.6245	+	10.1755i	0.766281	+	0.442413i
$530$	5.02844	−	16.2010i	0.218421	−	0.703728i
$531$	−16.1025	−	16.1025i	−0.698787	−	0.698787i
$532$	−10.4263	−	13.4543i	−0.452036	−	0.583317i
$533$	−7.20920			−0.312265
$534$	15.4375	−	5.80772i	0.668047	−	0.251325i
$535$	3.41407	+	8.39099i	0.147603	+	0.362774i
$536$	−19.4391	+	12.0763i	−0.839643	+	0.521619i
$537$	−0.761783	+	2.84301i	−0.0328734	+	0.122685i
$538$	34.2389	−	24.5278i	1.47615	−	1.05747i
$539$	22.0631	−	17.2874i	0.950326	−	0.744623i
$540$	9.71142	+	14.7429i	0.417913	+	0.634435i
$541$	2.57671	+	0.690427i	0.110781	+	0.0296838i	0.313784	−	0.949494i	$-0.398403\pi$
$541$	2.57671	+	0.690427i	0.110781	+	0.0296838i	−0.203003	+	0.979178i	$0.565070\pi$
$542$	−4.83164	−	3.96639i	−0.207537	−	0.170371i
$543$	2.62848	+	9.80963i	0.112799	+	0.420972i
$544$	8.20306	+	15.3736i	0.351703	+	0.659137i
$545$	0.336717	+	2.68798i	0.0144234	+	0.115140i
$546$	−0.132063	−	3.50652i	−0.00565178	−	0.150065i
$547$	−9.41386			−0.402508			−0.201254	−	0.979539i	$-0.564502\pi$
$547$	−9.41386			−0.402508			−0.201254	+	0.979539i	$0.564502\pi$
$548$	−11.1326	−	7.44325i	−0.475562	−	0.317960i
$549$	−11.7129	+	3.13845i	−0.499893	+	0.133946i
$550$	9.63602	+	26.6236i	0.410881	+	1.13524i
$551$	2.78305	+	4.82039i	0.118562	+	0.205355i
$552$	−0.961023	−	3.17302i	−0.0409039	−	0.135053i
$553$	20.3334	+	22.9503i	0.864664	+	0.975945i
$554$	−1.95863	+	11.8526i	−0.0832144	+	0.503569i
$555$	1.95539	+	0.269938i	0.0830018	+	0.0114582i
$556$	−13.0451	−	0.858810i	−0.553235	−	0.0364217i
$557$	−11.9097	+	20.6283i	−0.504632	+	0.874048i	0.495354	+	0.868691i	$0.335038\pi$
$557$	−11.9097	+	20.6283i	−0.504632	+	0.874048i	−0.999986	+	0.00535649i	$0.998295\pi$
$558$	−17.7131	+	6.66381i	−0.749855	+	0.282102i
$559$	8.12700			0.343735
$560$	1.59012	−	23.6108i	0.0671948	−	0.997740i
$561$	8.88299			0.375040
$562$	2.00634	−	0.754802i	0.0846324	−	0.0318394i
$563$	13.6305	−	23.6088i	0.574459	−	0.994992i	−0.421641	−	0.906763i	$-0.638546\pi$
$563$	13.6305	−	23.6088i	0.574459	−	0.994992i	0.996100	−	0.0882292i	$-0.0281208\pi$
$564$	0.908521	−	13.8002i	0.0382556	−	0.581092i
$565$	24.5795	+	32.4526i	1.03407	+	1.36529i
$566$	2.82779	−	17.1123i	0.118861	−	0.719283i
$567$	11.5468	+	3.85451i	0.484921	+	0.161874i
$568$	19.5185	−	36.4785i	0.818979	−	1.53060i
$569$	−18.6660	−	32.3304i	−0.782519	−	1.35536i	−0.930470	−	0.366368i	$-0.880601\pi$
$569$	−18.6660	−	32.3304i	−0.782519	−	1.35536i	0.147951	−	0.988995i	$-0.452732\pi$
$570$	−3.90843	+	6.19613i	−0.163706	+	0.259527i
$571$	−21.9928	+	5.89295i	−0.920369	+	0.246612i	−0.687743	−	0.725954i	$-0.741398\pi$
$571$	−21.9928	+	5.89295i	−0.920369	+	0.246612i	−0.232626	+	0.972566i	$0.574732\pi$
$572$	−5.79625	+	8.66927i	−0.242353	+	0.362480i
$573$	12.6881			0.530051
$574$	17.5368	−	11.0251i	0.731970	−	0.460177i
$575$	−4.15716	+	6.99597i	−0.173366	+	0.291752i
$576$	−8.79518	+	17.7959i	−0.366466	+	0.741496i
$577$	0.792593	+	2.95800i	0.0329961	+	0.123143i	0.980459	−	0.196721i	$-0.0630294\pi$
$577$	0.792593	+	2.95800i	0.0329961	+	0.123143i	−0.947463	+	0.319864i	$0.896363\pi$
$578$	8.21043	+	6.74011i	0.341509	+	0.280352i
$579$	17.8000	+	4.76949i	0.739742	+	0.198213i
$580$	−1.55953	+	7.57965i	−0.0647558	+	0.314728i
$581$	−5.06615	−	24.8119i	−0.210179	−	1.02937i
$582$	−0.206215	+	0.147727i	−0.00854791	+	0.00612347i
$583$	5.55934	−	20.7478i	0.230244	−	0.859284i
$584$	4.19854	−	17.9713i	0.173737	−	0.743657i
$585$	6.69241	−	2.72297i	0.276697	−	0.112581i
$586$	−1.11897	+	0.420967i	−0.0462243	+	0.0173900i
$587$	−16.5240			−0.682019			−0.341010	−	0.940060i	$-0.610769\pi$
$587$	−16.5240			−0.682019			−0.341010	+	0.940060i	$0.610769\pi$
$588$	5.68379	+	8.32784i	0.234396	+	0.343434i
$589$	−12.2670	−	12.2670i	−0.505451	−	0.505451i
$590$	25.6822	−	13.5160i	1.05732	−	0.556443i
$591$	11.7148	+	6.76357i	0.481884	+	0.278216i
$592$	1.87369	+	4.53089i	0.0770081	+	0.186219i
$593$	−9.26597	+	34.5811i	−0.380508	+	1.42007i	0.464620	+	0.885510i	$0.346191\pi$
$593$	−9.26597	+	34.5811i	−0.380508	+	1.42007i	−0.845128	+	0.534564i	$0.820476\pi$
$594$	13.0182	+	18.1724i	0.534141	+	0.745621i
$595$	5.83681	+	17.2637i	0.239286	+	0.707742i
$596$	−11.7595	+	5.79489i	−0.481686	+	0.237368i
$597$	−5.55830	+	3.20909i	−0.227486	+	0.131339i
$598$	−2.98294	+	0.293358i	−0.121982	+	0.0119963i
$599$	−15.7308	+	27.2465i	−0.642742	+	1.11326i	0.342077	+	0.939672i	$0.388870\pi$
$599$	−15.7308	+	27.2465i	−0.642742	+	1.11326i	−0.984818	+	0.173589i	$0.944464\pi$
$600$	−9.78398	+	2.82962i	−0.399429	+	0.115519i
$601$	42.9833			1.75333			0.876663	−	0.481104i	$-0.159764\pi$
$601$	42.9833			1.75333			0.876663	+	0.481104i	$0.159764\pi$
$602$	−19.7694	+	12.4287i	−0.805739	+	0.506554i
$603$	20.0766			0.817581
$604$	−16.8509	+	3.34678i	−0.685653	+	0.136179i
$605$	4.24172	+	10.4252i	0.172451	+	0.423843i
$606$	−1.22457	−	12.4517i	−0.0497447	−	0.505817i
$607$	−12.6219	−	3.38204i	−0.512308	−	0.137273i	−0.00660186	−	0.999978i	$-0.502101\pi$
$607$	−12.6219	−	3.38204i	−0.512308	−	0.137273i	−0.505706	+	0.862706i	$0.668768\pi$
$608$	−18.1863	−	0.608527i	−0.737554	−	0.0246790i
$609$	−1.47322	−	2.94964i	−0.0596979	−	0.119526i
$610$	0.604870	−	15.4419i	0.0244905	−	0.625225i
$611$	−12.0773	−	3.23611i	−0.488596	−	0.130919i
$612$	1.00422	−	15.2538i	0.0405932	−	0.616600i
$613$	18.6071	−	32.2284i	0.751534	−	1.30169i	−0.195546	−	0.980695i	$-0.562648\pi$
$613$	18.6071	−	32.2284i	0.751534	−	1.30169i	0.947079	−	0.321000i	$-0.104019\pi$
$614$	21.5561	−	8.10958i	0.869934	−	0.327276i
$615$	−7.03880	−	5.47164i	−0.283832	−	0.220638i
$616$	0.841736	−	29.9527i	0.0339145	−	1.20683i
$617$	−0.636726	+	0.636726i	−0.0256336	+	0.0256336i	−0.719807	−	0.694174i	$-0.755770\pi$
$617$	−0.636726	+	0.636726i	−0.0256336	+	0.0256336i	0.694174	+	0.719807i	$0.255770\pi$
$618$	−11.4100	−	5.17181i	−0.458979	−	0.208041i
$619$	−5.48706	+	1.47025i	−0.220544	+	0.0590945i	−0.367399	−	0.930064i	$-0.619752\pi$
$619$	−5.48706	+	1.47025i	−0.220544	+	0.0590945i	0.146855	+	0.989158i	$0.453085\pi$
$620$	−1.41927	−	24.0769i	−0.0569994	−	0.966950i
$621$	−1.66291	+	6.20607i	−0.0667303	+	0.249041i
$622$	−5.31593	−	0.878454i	−0.213149	−	0.0352228i
$623$	28.4132	+	32.0700i	1.13835	+	1.28486i
$624$	−2.97478	−	2.28536i	−0.119086	−	0.0914877i
$625$	21.3298	+	13.0400i	0.853191	+	0.521598i
$626$	−3.25340	−	33.0814i	−0.130032	−	1.32220i
$627$	−4.63810	+	8.03342i	−0.185228	+	0.320824i
$628$	−44.4295	+	8.82422i	−1.77293	+	0.352125i
$629$	−2.66988	−	2.66988i	−0.106455	−	0.106455i
$630$	−12.1154	+	16.8585i	−0.482689	+	0.671658i
$631$		−	32.0044i		−	1.27408i	−0.770832	−	0.637038i	$-0.780159\pi$
$631$		−	32.0044i		−	1.27408i	0.770832	−	0.637038i	$-0.219841\pi$
$632$	32.7620	−	1.05829i	1.30320	−	0.0420963i
$633$	−1.82087	−	6.79560i	−0.0723733	−	0.270101i
$634$	−0.0255619	+	0.0311380i	−0.00101519	+	0.00123665i
$635$	35.1691	−	26.6369i	1.39564	−	1.05705i
$636$	7.31582	+	2.48575i	0.290091	+	0.0985663i
$637$	8.38576	−	3.57342i	0.332256	−	0.141584i
$638$	−1.59755	+	9.66753i	−0.0632477	+	0.382741i
$639$	−31.4325	+	18.1476i	−1.24345	+	0.717907i
$640$	−18.3376	−	17.4279i	−0.724859	−	0.688897i
$641$	−16.6572	+	28.8512i	−0.657921	+	1.13955i	0.323231	+	0.946320i	$0.395231\pi$
$641$	−16.6572	+	28.8512i	−0.657921	+	1.13955i	−0.981153	+	0.193233i	$0.938103\pi$
$642$	−3.86195	+	1.45290i	−0.152419	+	0.0573413i
$643$	5.26026			0.207444			0.103722	−	0.994606i	$-0.466925\pi$
$643$	5.26026			0.207444			0.103722	+	0.994606i	$0.466925\pi$
$644$	6.80753	−	5.27543i	0.268254	−	0.207881i
$645$	7.93490	+	6.16823i	0.312436	+	0.242874i
$646$	13.1156	−	4.93418i	0.516025	−	0.194133i
$647$	−41.4921	+	11.1178i	−1.63122	+	0.437085i	−0.954271	−	0.298942i	$-0.903366\pi$
$647$	−41.4921	+	11.1178i	−1.63122	+	0.437085i	−0.676952	+	0.736027i	$0.736699\pi$
$648$	11.0542	−	6.86731i	0.434251	−	0.269773i
$649$	31.8248	−	18.3740i	1.24923	−	0.721244i
$650$	0.786026	+	9.17432i	0.0308305	+	0.359846i
$651$	6.81458	+	7.69161i	0.267084	+	0.301458i
$652$	13.6605	−	40.2043i	0.534986	−	1.57452i
$653$	17.2860	−	9.98010i	0.676455	−	0.390552i	−0.122063	−	0.992522i	$-0.538951\pi$
$653$	17.2860	−	9.98010i	0.676455	−	0.390552i	0.798518	+	0.601971i	$0.205618\pi$
$654$	−1.22798	+	0.120766i	−0.0480177	+	0.00472232i
$655$	2.91906	+	1.23065i	0.114057	+	0.0480855i
$656$	2.90317	−	21.9536i	0.113350	−	0.857143i
$657$	−11.4484	+	11.4484i	−0.446644	+	0.446644i
$658$	34.3277	−	10.5979i	1.33823	−	0.413149i
$659$	29.6719	+	29.6719i	1.15585	+	1.15585i	0.985359	+	0.170494i	$0.0545363\pi$
$659$	29.6719	+	29.6719i	1.15585	+	1.15585i	0.170494	+	0.985359i	$0.445464\pi$
$660$	−12.2390	+	4.06511i	−0.476404	+	0.158234i
$661$	3.17323	+	11.8427i	0.123424	+	0.460626i	0.999779	−	0.0210412i	$-0.00669813\pi$
$661$	3.17323	+	11.8427i	0.123424	+	0.460626i	−0.876354	+	0.481667i	$0.840031\pi$
$662$	1.86343	−	0.183260i	0.0724244	−	0.00712260i
$663$	2.79040	+	0.747686i	0.108370	+	0.0290377i
$664$	−23.8701	−	12.7722i	−0.926339	−	0.495656i
$665$	−18.6602	−	3.73535i	−0.723611	−	0.144851i
$666$	0.701285	−	4.24380i	0.0271742	−	0.164444i
$667$	−2.43900	+	1.40816i	−0.0944384	+	0.0545240i
$668$	15.2538	+	1.00422i	0.590186	+	0.0388543i
$669$	−4.10113	+	1.09889i	−0.158559	+	0.0424857i
$670$	−7.58443	+	24.4361i	−0.293012	+	0.944050i
$671$		−	19.5680i		−	0.755415i
$672$	10.7313	+	1.00993i	0.413969	+	0.0389588i
$673$	20.2676	−	20.2676i	0.781258	−	0.781258i	−0.198785	−	0.980043i	$-0.563700\pi$
$673$	20.2676	−	20.2676i	0.781258	−	0.781258i	0.980043	+	0.198785i	$0.0636996\pi$
$674$	−8.21609	+	18.1263i	−0.316472	+	0.698200i
$675$	18.9996	+	5.34762i	0.731296	+	0.205830i
$676$	17.0023	−	14.9019i	0.653936	−	0.573152i
$677$	−3.51471	−	6.08766i	−0.135081	−	0.233968i	0.790547	−	0.612401i	$-0.209796\pi$
$677$	−3.51471	−	6.08766i	−0.135081	−	0.233968i	−0.925629	+	0.378433i	$0.876463\pi$
$678$	−15.0741	+	10.7986i	−0.578917	+	0.414719i
$679$	−0.549751	−	0.363318i	−0.0210975	−	0.0139429i
$680$	18.1868	+	6.98480i	0.697431	+	0.267855i
$681$	−8.96558	+	5.17628i	−0.343562	+	0.198355i
$682$	−2.98903	−	30.3932i	−0.114456	−	1.16381i
$683$	−23.8074	+	41.2356i	−0.910965	+	1.57784i	−0.0982608	+	0.995161i	$0.531328\pi$
$683$	−23.8074	+	41.2356i	−0.910965	+	1.57784i	−0.812704	+	0.582677i	$0.802005\pi$
$684$	13.2706	+	8.87270i	0.507415	+	0.339256i
$685$	−14.8563	+	1.86101i	−0.567628	+	0.0711055i
$686$	−14.9339	+	21.5169i	−0.570181	+	0.821519i
$687$	2.02719	+	2.02719i	0.0773420	+	0.0773420i
$688$	−3.27277	+	24.7485i	−0.124773	+	0.943527i
$689$	3.49270	−	6.04953i	0.133061	−	0.230469i
$690$	−3.13509	−	1.97757i	−0.119351	−	0.0752848i
$691$	−5.92635	+	22.1174i	−0.225449	+	0.841387i	0.756775	+	0.653675i	$0.226774\pi$
$691$	−5.92635	+	22.1174i	−0.225449	+	0.841387i	−0.982224	+	0.187712i	$0.939893\pi$
$692$	−48.9773	−	16.6413i	−1.86184	−	0.632609i
$693$	−14.4936	+	21.9308i	−0.550567	+	0.833084i
$694$	−1.96175	+	11.8715i	−0.0744670	+	0.450634i
$695$	−11.6516	+	8.82490i	−0.441972	+	0.334748i
$696$	−3.43231	−	0.801873i	−0.130101	−	0.0303949i
$697$	4.41376	+	16.4724i	0.167183	+	0.623936i
$698$	38.2953	+	17.3581i	1.44950	+	0.657012i
$699$	0.286473	+	0.286473i	0.0108354	+	0.0108354i
$700$	−15.9424	−	21.1149i	−0.602565	−	0.798070i
$701$	18.7237	−	18.7237i	0.707185	−	0.707185i	−0.258757	−	0.965942i	$-0.583313\pi$
$701$	18.7237	−	18.7237i	0.707185	−	0.707185i	0.965942	+	0.258757i	$0.0833130\pi$
$702$	2.55980	+	6.80421i	0.0966134	+	0.256808i
$703$	3.80857	−	1.02050i	0.143643	−	0.0384890i
$704$	−24.0656	−	21.1420i	−0.907008	−	0.796818i
$705$	−9.33571	−	12.3261i	−0.351603	−	0.464227i
$706$	−11.5132	−	16.0716i	−0.433305	−	0.604862i
$707$	29.0770	−	14.5227i	1.09355	−	0.546182i
$708$	5.84314	+	11.8574i	0.219599	+	0.445627i
$709$	18.4310	+	4.93857i	0.692190	+	0.185472i	0.587730	−	0.809057i	$-0.300022\pi$
$709$	18.4310	+	4.93857i	0.692190	+	0.185472i	0.104460	+	0.994529i	$0.466688\pi$
$710$	−10.2138	−	45.1137i	−0.383319	−	1.69309i
$711$	−24.9040	−	14.3783i	−0.933971	−	0.539229i
$712$	45.7806	−	1.47881i	1.71570	−	0.0554209i
$713$	6.20678	−	6.20678i	0.232446	−	0.232446i
$714$	−7.93124	+	2.44859i	−0.296819	+	0.0916361i
$715$	1.44922	+	11.5689i	0.0541976	+	0.432654i
$716$	−4.54306	+	6.79492i	−0.169782	+	0.253938i
$717$	10.5179	+	6.07252i	0.392799	+	0.226782i
$718$	−20.9561	+	25.5275i	−0.782074	+	0.952679i
$719$	−7.09781	−	12.2938i	−0.264704	−	0.458480i	0.702782	−	0.711405i	$-0.251941\pi$
$719$	−7.09781	−	12.2938i	−0.264704	−	0.458480i	−0.967486	+	0.252925i	$0.918607\pi$
$720$	5.59697	+	21.4764i	0.208587	+	0.800378i
$721$	1.96392	−	32.4833i	0.0731401	−	1.20974i
$722$	1.99506	−	12.0730i	0.0742485	−	0.449312i
$723$	−3.72493	+	2.15059i	−0.138532	+	0.0799814i
$724$	−1.85271	+	28.1421i	−0.0688553	+	1.04589i
$725$	4.23145	+	7.54645i	0.157152	+	0.280268i
$726$	−4.79818	+	1.80512i	−0.178077	+	0.0669941i
$727$	5.68905	+	5.68905i	0.210995	+	0.210995i	0.804690	−	0.593695i	$-0.202331\pi$
$727$	5.68905	+	5.68905i	0.210995	+	0.210995i	−0.593695	+	0.804690i	$0.702331\pi$
$728$	2.78555	−	9.33815i	0.103239	−	0.346095i
$729$	−2.88776			−0.106954
$730$	−9.60946	−	18.2593i	−0.355662	−	0.675807i
$731$	−4.97568	−	18.5695i	−0.184032	−	0.686817i
$732$	7.02374	+	0.462401i	0.259605	+	0.0170908i
$733$	−6.37528	−	11.0423i	−0.235476	−	0.407857i	0.723935	−	0.689869i	$-0.242332\pi$
$733$	−6.37528	−	11.0423i	−0.235476	−	0.407857i	−0.959411	+	0.282012i	$0.908998\pi$
$734$	−8.08602	+	5.79259i	−0.298461	+	0.213808i
$735$	10.8997	+	2.87567i	0.402042	+	0.106071i
$736$	0.307900	−	9.20184i	0.0113493	−	0.339185i
$737$	−8.38520	+	31.2940i	−0.308873	+	1.15273i
$738$	−12.3267	+	15.0157i	−0.453751	+	0.552734i
$739$	−10.4001	+	2.78670i	−0.382574	+	0.102510i	−0.444980	−	0.895540i	$-0.646789\pi$
$739$	−10.4001	+	2.78670i	−0.382574	+	0.102510i	0.0624060	+	0.998051i	$0.480123\pi$
$740$	4.90040	+	2.45677i	0.180142	+	0.0903126i
$741$	−2.13314	+	2.13314i	−0.0783628	+	0.0783628i
$742$	0.755398	+	20.0572i	0.0277315	+	0.736323i
$743$	−12.8147	−	12.8147i	−0.470126	−	0.470126i	0.431829	−	0.901955i	$-0.357868\pi$
$743$	−12.8147	−	12.8147i	−0.470126	−	0.470126i	−0.901955	+	0.431829i	$0.857868\pi$
$744$	10.9799	−	0.354676i	0.402544	−	0.0130031i
$745$	−5.69399	+	13.5059i	−0.208612	+	0.494819i
$746$	−25.7810	+	31.4049i	−0.943908	+	1.14982i
$747$	11.8751	+	20.5682i	0.434485	+	0.752551i
$748$	23.3572	+	7.93624i	0.854024	+	0.290178i
$749$	−7.10804	−	8.02285i	−0.259722	−	0.293148i
$750$	−6.19568	+	9.55405i	−0.226234	+	0.348864i
$751$	−25.4233	−	44.0345i	−0.927711	−	1.60684i	−0.787142	−	0.616772i	$-0.788440\pi$
$751$	−25.4233	−	44.0345i	−0.927711	−	1.60684i	−0.140569	−	0.990071i	$-0.544893\pi$
$752$	14.7182	−	35.4749i	0.536719	−	1.29364i
$753$	0.111937	+	0.417753i	0.00407919	+	0.0152238i
$754$	−1.31556	+	2.90238i	−0.0479098	+	0.105699i
$755$	−11.7885	+	15.1649i	−0.429027	+	0.551906i
$756$	−16.6326	−	12.6369i	−0.604920	−	0.459599i
$757$		−	16.7501i		−	0.608791i	−0.952546	−	0.304396i	$-0.901546\pi$
$757$		−	16.7501i		−	0.608791i	0.952546	−	0.304396i	$-0.0984545\pi$
$758$	−22.3550	−	10.1328i	−0.811968	−	0.368040i
$759$	−4.06471	−	2.34676i	−0.147540	−	0.0851821i
$760$	−15.8127	+	12.8004i	−0.573587	+	0.464320i
$761$	−3.95436	−	6.84916i	−0.143346	−	0.248282i	0.785409	−	0.618977i	$-0.212453\pi$
$761$	−3.95436	−	6.84916i	−0.143346	−	0.248282i	−0.928754	+	0.370695i	$0.879119\pi$
$762$	11.7025	+	16.3359i	0.423939	+	0.591786i
$763$	−1.43222	−	2.86755i	−0.0518497	−	0.103812i
$764$	33.3624	+	11.3358i	1.20701	+	0.410114i
$765$	−10.3191	−	13.6245i	−0.373088	−	0.492593i
$766$	21.1312	−	2.07815i	0.763500	−	0.0750867i
$767$	11.5436	−	3.09311i	0.416816	−	0.111686i
$768$	8.15738	−	8.13852i	0.294354	−	0.293673i
$769$	32.4594			1.17052			0.585258	−	0.810847i	$-0.300993\pi$
$769$	32.4594			1.17052			0.585258	+	0.810847i	$0.300993\pi$
$770$	−21.2177	−	25.9258i	−0.764634	−	0.934301i
$771$	5.27348	−	5.27348i	0.189920	−	0.189920i
$772$	42.5427	+	28.4439i	1.53114	+	1.02372i
$773$	−1.57871	−	0.911466i	−0.0567821	−	0.0327832i	0.471340	−	0.881951i	$-0.343770\pi$
$773$	−1.57871	−	0.911466i	−0.0567821	−	0.0327832i	−0.528122	+	0.849168i	$0.677104\pi$
$774$	13.8960	−	16.9273i	0.499480	−	0.608439i
$775$	−18.8265	−	19.3055i	−0.676266	−	0.693474i
$776$	−0.674211	+	0.204200i	−0.0242028	+	0.00733037i
$777$	−2.28838	+	0.467246i	−0.0820951	+	0.0167624i
$778$	29.0448	−	20.8068i	1.04131	−	0.745961i
$779$	−17.2015	−	4.60914i	−0.616309	−	0.165140i
$780$	−4.18680	+	0.246802i	−0.149911	+	0.00883693i
$781$	−15.1591	−	56.5744i	−0.542434	−	2.02439i
$782$	2.49658	+	6.63615i	0.0892773	+	0.237308i
$783$	4.83006	+	4.83006i	0.172612	+	0.172612i
$784$	7.50488	+	26.9755i	0.268031	+	0.963410i
$785$	−31.0818	+	39.9841i	−1.10936	+	1.42709i
$786$	−0.595692	+	1.31421i	−0.0212476	+	0.0468765i
$787$	−28.6835	−	16.5605i	−1.02246	−	0.590316i	−0.107643	−	0.994190i	$-0.534330\pi$
$787$	−28.6835	−	16.5605i	−1.02246	−	0.590316i	−0.914815	+	0.403873i	$0.867664\pi$
$788$	24.7607	+	28.2506i	0.882062	+	1.00639i
$789$	−3.88437	+	14.4967i	−0.138287	+	0.516095i
$790$	26.9086	−	24.8800i	0.957366	−	0.885191i
$791$	−40.1861	−	26.5581i	−1.42885	−	0.944298i
$792$	8.14602	+	26.8959i	0.289456	+	0.955703i
$793$	1.64705	−	6.14688i	0.0584885	−	0.218282i
$794$	−13.3240	−	10.9379i	−0.472851	−	0.388173i
$795$	8.00162	−	3.25565i	0.283788	−	0.115466i
$796$	−17.4822	+	3.47217i	−0.619641	+	0.123068i
$797$			37.6739i			1.33448i	0.744844	+	0.667238i	$0.232524\pi$
$797$			37.6739i			1.33448i	−0.744844	+	0.667238i	$0.767476\pi$
$798$	1.92676	−	8.45119i	0.0682064	−	0.299169i
$799$			29.5769i			1.04636i
$800$	−28.2543	−	1.30091i	−0.998942	−	0.0459941i
$801$	−34.8000	−	20.0918i	−1.22960	−	0.709908i
$802$	−32.0454	+	39.0359i	−1.13156	+	1.37840i
$803$	−13.0634	−	22.6265i	−0.460998	−	0.798472i
$804$	−11.0345	−	3.74927i	−0.389157	−	0.132227i
$805$	1.89000	−	9.44160i	0.0666137	−	0.332773i
$806$	1.61927	−	9.79896i	0.0570364	−	0.345154i
$807$	20.7176	+	5.55126i	0.729293	+	0.195414i
$808$	7.90470	−	33.8350i	0.278086	−	1.19031i
$809$	0.337958	−	0.585360i	0.0118820	−	0.0205802i	−0.860023	−	0.510255i	$-0.829551\pi$
$809$	0.337958	−	0.585360i	0.0118820	−	0.0205802i	0.871905	+	0.489675i	$0.162884\pi$
$810$	4.31294	−	13.8958i	0.151541	−	0.488248i
$811$	−8.03712	+	8.03712i	−0.282222	+	0.282222i	−0.833994	−	0.551773i	$-0.813952\pi$
$811$	−8.03712	+	8.03712i	−0.282222	+	0.282222i	0.551773	+	0.833994i	$0.313952\pi$
$812$	−1.23846	−	9.07209i	−0.0434614	−	0.318368i
$813$		−	3.18338i		−	0.111646i
$814$	6.32204	+	2.86558i	0.221588	+	0.100439i
$815$	−17.8915	−	43.9731i	−0.626712	−	1.54031i
$816$	−3.40057	+	8.19629i	−0.119044	+	0.286928i
$817$	19.3915	+	5.19593i	0.678421	+	0.181782i
$818$	−3.60285	+	21.8025i	−0.125971	+	0.762308i
$819$	−6.39879	+	5.66917i	−0.223592	+	0.198097i
$820$	−13.6196	−	20.6759i	−0.475615	−	0.722034i
$821$	6.62898	−	24.7397i	0.231353	−	0.863421i	−0.748406	−	0.663241i	$-0.769181\pi$
$821$	6.62898	−	24.7397i	0.231353	−	0.863421i	0.979759	−	0.200180i	$-0.0641528\pi$
$822$	−0.667464	−	6.78694i	−0.0232805	−	0.236722i
$823$	7.86830	−	2.10830i	0.274272	−	0.0734909i	−0.119062	−	0.992887i	$-0.537989\pi$
$823$	7.86830	−	2.10830i	0.274272	−	0.0734909i	0.393333	+	0.919396i	$0.371322\pi$
$824$	−25.3813	−	23.7929i	−0.884200	−	0.828864i
$825$	−7.36565	+	12.3954i	−0.256439	+	0.431553i
$826$	−23.3502	+	25.1779i	−0.812457	+	0.876050i
$827$			24.7546i			0.860801i	0.902638	+	0.430400i	$0.141628\pi$
$827$			24.7546i			0.860801i	−0.902638	+	0.430400i	$0.858372\pi$
$828$	−4.48937	+	6.71461i	−0.156016	+	0.233349i
$829$	−5.97792	−	22.3099i	−0.207622	−	0.774854i	−0.988634	−	0.150339i	$-0.951963\pi$
$829$	−5.97792	−	22.3099i	−0.207622	−	0.774854i	0.781013	−	0.624515i	$-0.214703\pi$
$830$	−29.5206	+	6.68354i	−1.02468	+	0.231989i
$831$	−5.29813	+	3.05888i	−0.183790	+	0.106111i
$832$	−5.78018	−	8.66692i	−0.200392	−	0.300472i
$833$	−13.2990	−	16.9729i	−0.460785	−	0.588077i
$834$	−3.87709	−	5.41213i	−0.134253	−	0.187407i
$835$	13.6244	−	10.3191i	0.471492	−	0.357106i
$836$	−19.3728	+	16.9796i	−0.670022	+	0.587250i
$837$	−18.4374	−	10.6448i	−0.637288	−	0.367939i
$838$	5.55640	+	2.51854i	0.191943	+	0.0870016i
$839$			9.36329i			0.323257i	0.986852	+	0.161628i	$0.0516746\pi$
$839$			9.36329i			0.323257i	−0.986852	+	0.161628i	$0.948325\pi$
$840$	9.80718	−	7.00325i	0.338380	−	0.241635i
$841$		−	26.0058i		−	0.896753i
$842$	−17.8695	+	39.4237i	−0.615824	+	1.35863i
$843$	0.945384	+	0.545817i	0.0325607	+	0.0187990i
$844$	1.28346	−	19.4954i	0.0441784	−	0.671058i
$845$	3.45667	−	25.0397i	0.118913	−	0.861391i
$846$	−27.3908	+	19.6219i	−0.941714	+	0.674616i
$847$	−8.83120	−	9.96777i	−0.303444	−	0.342497i
$848$	17.0156	+	13.0722i	0.584319	+	0.448901i
$849$	7.64923	−	4.41628i	0.262521	−	0.151566i
$850$	20.4813	−	7.41289i	0.702502	−	0.254260i
$851$	0.516349	+	1.92704i	0.0177002	+	0.0660582i
$852$	20.6650	−	4.10431i	0.707972	−	0.140611i
$853$			14.6246i			0.500735i	0.968151	+	0.250368i	$0.0805515\pi$
$853$			14.6246i			0.500735i	−0.968151	+	0.250368i	$0.919449\pi$
$854$	5.39391	+	17.4715i	0.184576	+	0.597861i
$855$	17.7094	−	2.21841i	0.605647	−	0.0758681i
$856$	−11.4528	+	0.369950i	−0.391448	+	0.0126446i
$857$	−37.9291	+	10.1631i	−1.29563	+	0.347164i	−0.839798	−	0.542900i	$-0.817326\pi$
$857$	−37.9291	+	10.1631i	−1.29563	+	0.347164i	−0.455836	+	0.890064i	$0.650660\pi$
$858$	−5.28516	+	0.519771i	−0.180432	+	0.0177447i
$859$	7.70414	−	28.7522i	0.262862	−	0.981013i	−0.700684	−	0.713471i	$-0.747122\pi$
$859$	7.70414	−	28.7522i	0.262862	−	0.981013i	0.963546	−	0.267542i	$-0.0862114\pi$
$860$	15.3535	+	23.3081i	0.523548	+	0.794801i
$861$	10.0060	+	3.34017i	0.341004	+	0.113833i
$862$	7.15692	+	1.18268i	0.243766	+	0.0402821i
$863$	−9.74854	−	2.61211i	−0.331844	−	0.0889174i	0.0890498	−	0.996027i	$-0.471617\pi$
$863$	−9.74854	−	2.61211i	−0.331844	−	0.0889174i	−0.420894	+	0.907110i	$0.638284\pi$
$864$	−21.7511	+	5.05507i	−0.739989	+	0.171977i
$865$	−53.5685	+	21.7956i	−1.82138	+	0.741073i
$866$	24.0994	−	53.1680i	0.818931	−	1.80672i
$867$			5.40954i			0.183718i
$868$	11.0466	+	26.3128i	0.374947	+	0.893116i
$869$	32.8133	−	32.8133i	1.11312	−	1.11312i
$870$	−3.48732	+	1.83530i	−0.118231	+	0.0622224i
$871$	−5.26806	+	9.12455i	−0.178501	+	0.309174i
$872$	−3.33678	−	0.779554i	−0.112997	−	0.0263990i
$873$	0.596950	+	0.159952i	0.0202037	+	0.00541357i
$874$	−7.30502	−	1.20715i	−0.247096	−	0.0408324i
$875$	−28.9298	−	6.17005i	−0.978004	−	0.208586i
$876$	8.43025	−	4.15431i	0.284832	−	0.140361i
$877$	−12.3785	−	21.4403i	−0.417994	−	0.723986i	0.577744	−	0.816218i	$-0.303933\pi$
$877$	−12.3785	−	21.4403i	−0.417994	−	0.723986i	−0.995738	+	0.0922319i	$0.970600\pi$
$878$	−34.3650	−	28.2110i	−1.15976	−	0.952075i
$879$	−0.527258	−	0.304412i	−0.0177840	−	0.0102676i
$880$	−35.8136	−	0.245673i	−1.20728	−	0.00828163i
$881$			32.4793i			1.09426i	0.837049	+	0.547128i	$0.184279\pi$
$881$			32.4793i			1.09426i	−0.837049	+	0.547128i	$0.815721\pi$
$882$	6.89552	−	23.5763i	0.232184	−	0.793854i
$883$			5.96843i			0.200854i	0.994944	+	0.100427i	$0.0320209\pi$
$883$			5.96843i			0.200854i	−0.994944	+	0.100427i	$0.967979\pi$
$884$	6.66917	+	4.45899i	0.224309	+	0.149972i
$885$	13.6184	+	5.74140i	0.457777	+	0.192995i
$886$	−12.9196	+	15.7379i	−0.434042	+	0.528726i
$887$	−6.40678	+	23.9104i	−0.215118	+	0.802833i	0.771006	+	0.636827i	$0.219754\pi$
$887$	−6.40678	+	23.9104i	−0.215118	+	0.802833i	−0.986125	+	0.166006i	$0.946913\pi$
$888$	−1.17796	+	2.20152i	−0.0395299	+	0.0738781i
$889$	−28.7812	+	43.5499i	−0.965290	+	1.46062i
$890$	37.6012	−	34.7665i	1.26040	−	1.16538i
$891$	4.76831	−	17.7956i	0.159744	−	0.596174i
$892$	−11.7654	−	0.774565i	−0.393935	−	0.0259343i
$893$	−26.7482	−	15.4431i	−0.895094	−	0.516783i
$894$	−6.08062	−	2.75615i	−0.203366	−	0.0921796i
$895$	1.13589	+	9.06767i	0.0379685	+	0.303099i
$896$	27.3150	+	12.2431i	0.912528	+	0.409013i
$897$	−1.07932	−	1.07932i	−0.0360373	−	0.0360373i
$898$	32.1729	−	12.1037i	1.07362	−	0.403906i
$899$	−2.41531	−	9.01405i	−0.0805550	−	0.300635i
$900$	20.4527	+	14.0496i	0.681756	+	0.468319i
$901$	−15.9610	−	4.27674i	−0.531739	−	0.142479i
$902$	−18.2570	−	25.4854i	−0.607892	−	0.848571i
$903$	−11.2799	−	3.76540i	−0.375371	−	0.125305i
$904$	−49.2840	+	14.9268i	−1.63916	+	0.496457i
$905$	19.0379	+	25.1360i	0.632842	+	0.835550i
$906$	−6.76217	−	5.55121i	−0.224658	−	0.184426i
$907$	−43.7978	−	25.2867i	−1.45428	−	0.839630i	−0.455561	−	0.890204i	$-0.650561\pi$
$907$	−43.7978	−	25.2867i	−1.45428	−	0.839630i	−0.998720	+	0.0505746i	$0.983895\pi$
$908$	−28.1990	+	5.60064i	−0.935815	+	0.185864i
$909$	−21.5542	+	21.5542i	−0.714907	+	0.714907i
$910$	−4.48291	−	9.92995i	−0.148607	−	0.329175i
$911$	−29.4944			−0.977193			−0.488597	−	0.872510i	$-0.662491\pi$
$911$	−29.4944			−0.977193			−0.488597	+	0.872510i	$0.662491\pi$
$912$	−5.63685	−	7.35489i	−0.186655	−	0.243545i
$913$	−37.0200	+	9.91949i	−1.22518	+	0.328287i
$914$	1.49635	+	15.2153i	0.0494950	+	0.503277i
$915$	6.27348	−	4.75151i	0.207395	−	0.157080i
$916$	3.51922	+	7.14148i	0.116278	+	0.235961i
$917$	−3.74145	−	0.226205i	−0.123553	−	0.00746995i
$918$	13.9798	−	10.0147i	0.461402	−	0.330535i
$919$	6.17836	+	10.7012i	0.203805	+	0.353001i	0.949751	−	0.313005i	$-0.101336\pi$
$919$	6.17836	+	10.7012i	0.203805	+	0.353001i	−0.745946	+	0.666006i	$0.768002\pi$
$920$	−6.47670	−	8.00083i	−0.213530	−	0.263780i
$921$	10.1572	+	5.86426i	0.334691	+	0.193234i
$922$	8.03306	−	17.7225i	0.264555	−	0.583660i
$923$		−	19.0476i		−	0.626959i
$924$	12.0615	−	9.34699i	0.396796	−	0.307493i
$925$	5.93941	−	1.51176i	0.195287	−	0.0497063i
$926$	−32.5201	−	14.7403i	−1.06868	−	0.484397i
$927$	7.89924	+	29.4804i	0.259445	+	0.968263i
$928$	−8.30861	−	5.17496i	−0.272743	−	0.169876i
$929$	29.2360	+	50.6382i	0.959201	+	1.66138i	0.724448	+	0.689330i	$0.242095\pi$
$929$	29.2360	+	50.6382i	0.959201	+	1.66138i	0.234753	+	0.972055i	$0.424572\pi$
$930$	9.01822	−	8.33835i	0.295719	−	0.273425i
$931$	22.2935	−	3.16502i	0.730640	−	0.103729i
$932$	0.497321	+	1.00920i	0.0162903	+	0.0330575i
$933$	−1.37192	−	2.37623i	−0.0449146	−	0.0777943i
$934$	−0.359822	−	0.295385i	−0.0117737	−	0.00966531i
$935$	25.5468	−	10.3943i	0.835468	−	0.339930i
$936$	0.295062	+	9.13442i	0.00964439	+	0.298568i
$937$	−3.44627	−	3.44627i	−0.112585	−	0.112585i	0.648570	−	0.761155i	$-0.275367\pi$
$937$	−3.44627	−	3.44627i	−0.112585	−	0.112585i	−0.761155	+	0.648570i	$0.775367\pi$
$938$	−1.13937	−	30.2524i	−0.0372018	−	0.987777i
$939$	11.9698	−	11.9698i	0.390621	−	0.390621i
$940$	−13.5353	−	40.7513i	−0.441471	−	1.32916i
$941$	37.3071	−	9.99642i	1.21618	−	0.325874i	0.406995	−	0.913430i	$-0.366577\pi$
$941$	37.3071	−	9.99642i	1.21618	−	0.325874i	0.809183	+	0.587557i	$0.199910\pi$
$942$	−17.8293	−	14.6365i	−0.580911	−	0.476882i
$943$	2.33211	−	8.70356i	0.0759440	−	0.283427i
$944$	4.77053	+	36.3985i	0.155267	+	1.18467i
$945$	−23.3060	+	1.49907i	−0.758144	+	0.0487648i
$946$	20.5813	+	28.7299i	0.669156	+	0.934091i
$947$	−1.29120	−	2.23642i	−0.0419582	−	0.0726737i	0.844284	−	0.535897i	$-0.180026\pi$
$947$	−1.29120	−	2.23642i	−0.0419582	−	0.0726737i	−0.886242	+	0.463223i	$0.846693\pi$
$948$	11.0026	+	12.5534i	0.357348	+	0.407715i
$949$	−2.19911	−	8.20719i	−0.0713862	−	0.266417i
$950$	−3.99002	+	22.3930i	−0.129453	+	0.726524i
$951$	−0.0205157			−0.000665267
$952$	−23.0423	−	0.647538i	−0.746804	−	0.0209868i
$953$	19.3433	+	19.3433i	0.626592	+	0.626592i	0.947209	−	0.320617i	$-0.103890\pi$
$953$	19.3433	+	19.3433i	0.626592	+	0.626592i	−0.320617	+	0.947209i	$0.603890\pi$
$954$	−6.62825	−	17.6186i	−0.214597	−	0.570422i
$955$	36.4898	−	14.8468i	1.18078	−	0.480430i
$956$	22.2308	+	25.3642i	0.718996	+	0.820336i
$957$	−4.32140	+	2.49496i	−0.139691	+	0.0806507i
$958$	−24.5662	−	4.05954i	−0.793697	−	0.131158i
$959$	15.8487	−	7.91574i	0.511781	−	0.255613i
$960$	0.934472	−	12.8491i	0.0301600	−	0.414703i
$961$	−0.957251	−	1.65801i	−0.0308791	−	0.0534841i
$962$	1.74474	+	1.43229i	0.0562526	+	0.0461790i
$963$	8.70580	+	5.02630i	0.280541	+	0.161970i
$964$	−11.7158	+	2.32690i	−0.377342	+	0.0749445i
$965$	56.7723	−	7.11174i	1.82756	−	0.228935i
$966$	4.27609	+	0.974891i	0.137581	+	0.0313666i
$967$	17.8010	−	17.8010i	0.572442	−	0.572442i	−0.360368	−	0.932810i	$-0.617349\pi$
$967$	17.8010	−	17.8010i	0.572442	−	0.572442i	0.932810	+	0.360368i	$0.117349\pi$
$968$	−14.2292	+	0.459635i	−0.457344	+	0.0147732i
$969$	6.18003	+	3.56804i	0.198531	+	0.114622i
$970$	−0.420199	+	0.666151i	−0.0134918	+	0.0213888i
$971$	44.9534	+	12.0452i	1.44262	+	0.386550i	0.893451	−	0.449160i	$-0.148277\pi$
$971$	44.9534	+	12.0452i	1.44262	+	0.386550i	0.549171	+	0.835710i	$0.314943\pi$
$972$	28.7011	+	9.75197i	0.920588	+	0.312795i
$973$	9.53530	−	14.4282i	0.305688	−	0.462548i
$974$	−18.7602	+	13.4392i	−0.601114	+	0.430621i
$975$	−3.35709	+	3.27379i	−0.107513	+	0.104845i
$976$	18.0553	+	7.49100i	0.577937	+	0.239781i
$977$	28.8578	−	7.73241i	0.923241	−	0.247382i	0.234271	−	0.972171i	$-0.424730\pi$
$977$	28.8578	−	7.73241i	0.923241	−	0.247382i	0.688970	+	0.724790i	$0.258063\pi$
$978$	20.2386	−	7.61394i	0.647160	−	0.243467i
$979$	45.8523	−	45.8523i	1.46545	−	1.46545i
$980$	26.0908	+	17.2994i	0.833441	+	0.552609i
$981$	2.12565	+	2.12565i	0.0678669	+	0.0678669i
$982$	−22.0642	+	48.6780i	−0.704097	+	1.55338i
$983$	1.76711	+	6.59494i	0.0563620	+	0.210346i	0.988364	−	0.152107i	$-0.0486059\pi$
$983$	1.76711	+	6.59494i	0.0563620	+	0.210346i	−0.932002	+	0.362453i	$0.881939\pi$
$984$	9.57915	−	5.95093i	0.305372	−	0.189709i
$985$	41.6052	+	5.74351i	1.32565	+	0.183003i
$986$	7.43713	+	1.22898i	0.236846	+	0.0391387i
$987$	15.2634	+	10.0872i	0.485839	+	0.321080i
$988$	−7.51473	+	3.70315i	−0.239075	+	0.117813i
$989$	−2.62901	+	9.81160i	−0.0835977	+	0.311991i
$990$	26.5743	+	16.7627i	0.844586	+	0.532753i
$991$	−22.3880	+	38.7772i	−0.711179	+	1.23180i	0.253236	+	0.967405i	$0.418505\pi$
$991$	−22.3880	+	38.7772i	−0.711179	+	1.23180i	−0.964415	+	0.264394i	$0.914828\pi$
$992$	29.1879	+	8.87711i	0.926716	+	0.281848i
$993$	0.674245	+	0.674245i	0.0213965	+	0.0213965i
$994$	29.1296	+	46.3343i	0.923934	+	1.46963i
$995$	−12.2302	+	15.7330i	−0.387722	+	0.498771i
$996$	−2.68570	−	13.5224i	−0.0850996	−	0.428472i
$997$	17.2135	−	29.8147i	0.545159	−	0.944242i	−0.453438	−	0.891288i	$-0.649803\pi$
$997$	17.2135	−	29.8147i	0.545159	−	0.944242i	0.998597	−	0.0529547i	$-0.0168639\pi$
$998$	−56.3550	+	5.54226i	−1.78389	+	0.175437i
$999$	4.19049	−	2.41938i	0.132581	−	0.0765459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ch.c.437.56	yes	360
5.3	odd	4		560.2.cz.c.213.79	yes	360
7.5	odd	6	inner	560.2.ch.c.117.64	✓	360
16.13	even	4		560.2.cz.c.157.20	yes	360
35.33	even	12		560.2.cz.c.453.20	yes	360
80.13	odd	4	inner	560.2.ch.c.493.64	yes	360
112.61	odd	12		560.2.cz.c.397.79	yes	360
560.173	even	12	inner	560.2.ch.c.173.56	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.ch.c.117.64	✓	360	7.5	odd	6	inner
560.2.ch.c.173.56	yes	360	560.173	even	12	inner
560.2.ch.c.437.56	yes	360	1.1	even	1	trivial
560.2.ch.c.493.64	yes	360	80.13	odd	4	inner
560.2.cz.c.157.20	yes	360	16.13	even	4
560.2.cz.c.213.79	yes	360	5.3	odd	4
560.2.cz.c.397.79	yes	360	112.61	odd	12
560.2.cz.c.453.20	yes	360	35.33	even	12

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.497965 + 1.32364i) q^{2} +(-0.360092 + 0.623698i) q^{3} +(-1.50406 + 1.31826i) q^{4} +(-0.305784 + 2.21506i) q^{5} +(-1.00487 - 0.166053i) q^{6} +(-0.529295 - 2.59227i) q^{7} +(-2.49387 - 1.33439i) q^{8} +(1.24067 + 2.14890i) q^{9} +(-3.08422 + 0.698274i) q^{10} +(-3.86774 + 1.03636i) q^{11} +(-0.280593 - 1.41277i) q^{12} -1.30220 q^{13} +(3.16767 - 1.99146i) q^{14} +(-1.27142 - 0.988343i) q^{15} +(0.524399 - 3.96548i) q^{16} +(0.797258 + 2.97541i) q^{17} +(-2.22657 + 2.71228i) q^{18} +(-3.10711 - 0.832549i) q^{19} +(-2.46010 - 3.73469i) q^{20} +(1.80739 + 0.603335i) q^{21} +(-3.29776 - 4.60343i) q^{22} +(0.421249 - 1.57212i) q^{23} +(1.73028 - 1.07492i) q^{24} +(-4.81299 - 1.35466i) q^{25} +(-0.648449 - 1.72364i) q^{26} -3.94757 q^{27} +(4.21336 + 3.20118i) q^{28} +(-1.22355 - 1.22355i) q^{29} +(0.675091 - 2.17506i) q^{30} +(4.67056 + 2.69655i) q^{31} +(5.51001 - 1.28055i) q^{32} +(0.746367 - 2.78548i) q^{33} +(-3.54137 + 2.53693i) q^{34} +(5.90388 - 0.379746i) q^{35} +(-4.69884 - 1.59656i) q^{36} +(-1.06154 + 0.612879i) q^{37} +(-0.445238 - 4.52729i) q^{38} +(0.468911 - 0.812178i) q^{39} +(3.71835 - 5.11604i) q^{40} +5.53618 q^{41} +(0.101416 + 2.69277i) q^{42} -6.24099 q^{43} +(4.45113 - 6.65741i) q^{44} +(-5.13932 + 2.09105i) q^{45} +(2.29070 - 0.225279i) q^{46} +(9.27457 + 2.48511i) q^{47} +(2.28443 + 1.75500i) q^{48} +(-6.43969 + 2.74415i) q^{49} +(-0.603615 - 7.04526i) q^{50} +(-2.14284 - 0.574172i) q^{51} +(1.95859 - 1.71663i) q^{52} +(-2.68216 + 4.64563i) q^{53} +(-1.96575 - 5.22517i) q^{54} +(-1.11290 - 8.88417i) q^{55} +(-2.13911 + 7.17107i) q^{56} +(1.63811 - 1.63811i) q^{57} +(1.01026 - 2.22883i) q^{58} +(-8.86473 + 2.37530i) q^{59} +(3.21518 - 0.189527i) q^{60} +(-1.26482 + 4.72039i) q^{61} +(-1.24349 + 7.52494i) q^{62} +(4.91384 - 4.35354i) q^{63} +(4.43879 + 6.65561i) q^{64} +(0.398192 - 2.88445i) q^{65} +(4.05865 - 0.399149i) q^{66} +(4.04552 - 7.00704i) q^{67} +(-5.12147 - 3.42420i) q^{68} +(0.828841 + 0.828841i) q^{69} +(3.44257 + 7.62553i) q^{70} +14.6273i q^{71} +(-0.226587 - 7.01462i) q^{72} +(1.68877 + 6.30257i) q^{73} +(-1.33984 - 1.09990i) q^{74} +(2.57802 - 2.51405i) q^{75} +(5.77080 - 2.84377i) q^{76} +(4.73368 + 9.47766i) q^{77} +(1.30853 + 0.216234i) q^{78} +(-10.0365 + 5.79459i) q^{79} +(8.62342 + 2.37416i) q^{80} +(-2.30051 + 3.98461i) q^{81} +(2.75682 + 7.32792i) q^{82} +9.57150 q^{83} +(-3.51377 + 1.47515i) q^{84} +(-6.83450 + 0.856142i) q^{85} +(-3.10779 - 8.26084i) q^{86} +(1.20372 - 0.322536i) q^{87} +(11.0285 + 2.57654i) q^{88} +(-14.0247 + 8.09717i) q^{89} +(-5.32701 - 5.76135i) q^{90} +(0.689246 + 3.37564i) q^{91} +(1.43888 + 2.91988i) q^{92} +(-3.36366 + 1.94201i) q^{93} +(1.32901 + 13.5137i) q^{94} +(2.79425 - 6.62787i) q^{95} +(-1.18543 + 3.89770i) q^{96} +(0.176114 - 0.176114i) q^{97} +(-6.83901 - 7.15737i) q^{98} +(-7.02560 - 7.02560i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + 2 q^{2} - 6 q^{5} + 8 q^{7} - 4 q^{8} - 164 q^{9} - 6 q^{10} - 2 q^{11} + 18 q^{12} + 4 q^{14} - 32 q^{15} - 20 q^{16} + 4 q^{18} + 30 q^{19} - 4 q^{21} - 16 q^{22} + 10 q^{23} + 12 q^{24} + 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) \) 360 * q + 2 * q^2 - 6 * q^5 + 8 * q^7 - 4 * q^8 - 164 * q^9 - 6 * q^10 - 2 * q^11 + 18 * q^12 + 4 * q^14 - 32 * q^15 - 20 * q^16 + 4 * q^18 + 30 * q^19 - 4 * q^21 - 16 * q^22 + 10 * q^23 + 12 * q^24 + 12 * q^25 + 10 * q^28 - 8 * q^29 + 58 * q^30 - 24 * q^31 - 38 * q^32 - 12 * q^35 + 16 * q^36 - 24 * q^38 - 28 * q^39 - 96 * q^40 - 6 * q^42 - 24 * q^43 + 20 * q^44 + 36 * q^45 - 4 * q^46 - 6 * q^47 - 64 * q^50 + 16 * q^51 - 108 * q^52 + 32 * q^53 - 24 * q^54 - 8 * q^56 + 80 * q^57 + 2 * q^58 + 84 * q^59 + 8 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 4 * q^67 + 84 * q^68 + 72 * q^70 + 36 * q^72 - 52 * q^74 - 54 * q^75 - 52 * q^77 + 96 * q^78 - 120 * q^80 - 124 * q^81 - 150 * q^82 + 28 * q^84 - 4 * q^85 + 8 * q^86 + 20 * q^88 + 48 * q^89 + 28 * q^91 + 84 * q^92 - 72 * q^94 - 26 * q^95 - 60 * q^96 + 26 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more