LMFDB - Embedded newform 416.2.bd.a.83.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(83,416)] 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("416.83"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 7, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, degree $4$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.17
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.825979 - 1.14794i) q^{2} +(0.518989 + 0.214972i) q^{3} +(-0.635517 + 1.89634i) q^{4} +(1.14210 - 2.75727i) q^{5} +(-0.181899 - 0.773329i) q^{6} +2.29289i q^{7} +(2.70181 - 0.836807i) q^{8} +(-1.89818 - 1.89818i) q^{9} +(-4.10852 + 0.966391i) q^{10} +(-3.98985 - 1.65265i) q^{11} +(-0.737487 + 0.847562i) q^{12} +(2.07019 - 2.95200i) q^{13} +(2.63209 - 1.89388i) q^{14} +(1.18547 - 1.18547i) q^{15} +(-3.19224 - 2.41032i) q^{16} +7.59132 q^{17} +(-0.611134 + 3.74686i) q^{18} +(-1.82624 - 4.40893i) q^{19} +(4.50291 + 3.91810i) q^{20} +(-0.492907 + 1.18998i) q^{21} +(1.39840 + 5.94515i) q^{22} +(2.02063 + 2.02063i) q^{23} +(1.58210 + 0.146519i) q^{24} +(-2.76262 - 2.76262i) q^{25} +(-5.09864 + 0.0618532i) q^{26} +(-1.22200 - 2.95016i) q^{27} +(-4.34811 - 1.45717i) q^{28} +(1.06580 - 2.57307i) q^{29} +(-2.34002 - 0.381672i) q^{30} +(-4.58378 - 4.58378i) q^{31} +(-0.130169 + 5.65536i) q^{32} +(-1.71541 - 1.71541i) q^{33} +(-6.27027 - 8.71436i) q^{34} +(6.32212 + 2.61871i) q^{35} +(4.80594 - 2.39328i) q^{36} +(-7.67223 - 3.17794i) q^{37} +(-3.55273 + 5.73809i) q^{38} +(1.70900 - 1.08702i) q^{39} +(0.778425 - 8.40533i) q^{40} +2.38731 q^{41} +(1.77316 - 0.417075i) q^{42} +(2.58284 + 6.23554i) q^{43} +(5.66961 - 6.51584i) q^{44} +(-7.40172 + 3.06589i) q^{45} +(0.650558 - 3.98856i) q^{46} +(0.800438 + 0.800438i) q^{47} +(-1.13858 - 1.93717i) q^{48} +1.74266 q^{49} +(-0.889445 + 5.45317i) q^{50} +(3.93981 + 1.63192i) q^{51} +(4.28238 + 5.80183i) q^{52} +(-3.63540 - 8.77663i) q^{53} +(-2.37725 + 3.83954i) q^{54} +(-9.11361 + 9.11361i) q^{55} +(1.91871 + 6.19494i) q^{56} -2.68077i q^{57} +(-3.83404 + 0.901829i) q^{58} +(-2.35581 + 5.68744i) q^{59} +(1.49468 + 3.00145i) q^{60} +(-3.55120 + 8.57336i) q^{61} +(-1.47578 + 9.04799i) q^{62} +(4.35233 - 4.35233i) q^{63} +(6.59951 - 4.52178i) q^{64} +(-5.77512 - 9.07954i) q^{65} +(-0.552290 + 3.38608i) q^{66} +(10.1877 - 4.21989i) q^{67} +(-4.82441 + 14.3958i) q^{68} +(0.614306 + 1.48307i) q^{69} +(-2.21583 - 9.42038i) q^{70} +7.20444 q^{71} +(-6.71694 - 3.54011i) q^{72} +12.0231i q^{73} +(2.68903 + 11.4321i) q^{74} +(-0.839881 - 2.02765i) q^{75} +(9.52144 - 0.661226i) q^{76} +(3.78934 - 9.14829i) q^{77} +(-2.65944 - 1.06397i) q^{78} -1.01246 q^{79} +(-10.2917 + 6.04904i) q^{80} +6.25952i q^{81} +(-1.97187 - 2.74048i) q^{82} +(1.54226 + 3.72333i) q^{83} +(-1.94337 - 1.69098i) q^{84} +(8.67004 - 20.9313i) q^{85} +(5.02463 - 8.11537i) q^{86} +(1.10627 - 1.10627i) q^{87} +(-12.1628 - 1.12640i) q^{88} +4.18739 q^{89} +(9.63312 + 5.96434i) q^{90} +(6.76862 + 4.74671i) q^{91} +(-5.11596 + 2.54767i) q^{92} +(-1.39354 - 3.36431i) q^{93} +(0.257707 - 1.58000i) q^{94} -14.2423 q^{95} +(-1.28330 + 2.90708i) q^{96} +(1.07250 - 1.07250i) q^{97} +(-1.43940 - 2.00046i) q^{98} +(4.43644 + 10.7105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24}+ \cdots - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.825979	−	1.14794i	−0.584055	−	0.811714i
$2$	−0.825979	−	1.14794i	−0.584055	−	0.811714i
$3$	0.518989	+	0.214972i	0.299638	+	0.124114i	0.527437	−	0.849594i	$-0.323153\pi$
$3$	0.518989	+	0.214972i	0.299638	+	0.124114i	−0.227799	+	0.973708i	$0.573153\pi$
$4$	−0.635517	+	1.89634i	−0.317758	+	0.948172i
$5$	1.14210	−	2.75727i	0.510762	−	1.23309i	−0.432679	−	0.901548i	$-0.642432\pi$
$5$	1.14210	−	2.75727i	0.510762	−	1.23309i	0.943441	−	0.331541i	$-0.107568\pi$
$6$	−0.181899	−	0.773329i	−0.0742601	−	0.315710i
$7$			2.29289i			0.866631i	0.901242	+	0.433315i	$0.142656\pi$
$7$			2.29289i			0.866631i	−0.901242	+	0.433315i	$0.857344\pi$
$8$	2.70181	−	0.836807i	0.955233	−	0.295856i
$9$	−1.89818	−	1.89818i	−0.632728	−	0.632728i
$10$	−4.10852	+	0.966391i	−1.29923	+	0.305600i
$11$	−3.98985	−	1.65265i	−1.20299	−	0.498293i	−0.311023	−	0.950402i	$-0.600672\pi$
$11$	−3.98985	−	1.65265i	−1.20299	−	0.498293i	−0.891962	+	0.452109i	$0.850672\pi$
$12$	−0.737487	+	0.847562i	−0.212894	+	0.244670i
$13$	2.07019	−	2.95200i	0.574166	−	0.818739i
$13$	2.07019	−	2.95200i	0.574166	−	0.818739i
$14$	2.63209	−	1.89388i	0.703456	−	0.506160i
$15$	1.18547	−	1.18547i	0.306088	−	0.306088i
$16$	−3.19224	−	2.41032i	−0.798059	−	0.602579i
$17$	7.59132			1.84117			0.920583	−	0.390547i	$-0.127714\pi$
$17$	7.59132			1.84117			0.920583	+	0.390547i	$0.127714\pi$
$18$	−0.611134	+	3.74686i	−0.144046	+	0.883142i
$19$	−1.82624	−	4.40893i	−0.418967	−	1.01148i	−0.982647	−	0.185484i	$-0.940615\pi$
$19$	−1.82624	−	4.40893i	−0.418967	−	1.01148i	0.563680	−	0.825993i	$-0.309385\pi$
$20$	4.50291	+	3.91810i	1.00688	+	0.876115i
$21$	−0.492907	+	1.18998i	−0.107561	+	0.259676i
$22$	1.39840	+	5.94515i	0.298139	+	1.26751i
$23$	2.02063	+	2.02063i	0.421331	+	0.421331i	0.885662	−	0.464331i	$-0.153705\pi$
$23$	2.02063	+	2.02063i	0.421331	+	0.421331i	−0.464331	+	0.885662i	$0.653705\pi$
$24$	1.58210	+	0.146519i	0.322944	+	0.0299082i
$25$	−2.76262	−	2.76262i	−0.552523	−	0.552523i
$26$	−5.09864	+	0.0618532i	−0.999926	+	0.0121304i
$27$	−1.22200	−	2.95016i	−0.235173	−	0.567758i
$28$	−4.34811	−	1.45717i	−0.821715	−	0.275379i
$29$	1.06580	−	2.57307i	0.197914	−	0.477806i	−0.793500	−	0.608571i	$-0.791743\pi$
$29$	1.06580	−	2.57307i	0.197914	−	0.477806i	0.991413	+	0.130764i	$0.0417432\pi$
$30$	−2.34002	−	0.381672i	−0.427228	−	0.0696834i
$31$	−4.58378	−	4.58378i	−0.823271	−	0.823271i	0.163305	−	0.986576i	$-0.447785\pi$
$31$	−4.58378	−	4.58378i	−0.823271	−	0.823271i	−0.986576	+	0.163305i	$0.947785\pi$
$32$	−0.130169	+	5.65536i	−0.0230108	+	0.999735i
$33$	−1.71541	−	1.71541i	−0.298615	−	0.298615i
$34$	−6.27027	−	8.71436i	−1.07534	−	1.49450i
$35$	6.32212	+	2.61871i	1.06863	+	0.442642i
$36$	4.80594	−	2.39328i	0.800989	−	0.398880i
$37$	−7.67223	−	3.17794i	−1.26131	−	0.522450i	−0.350997	−	0.936377i	$-0.614157\pi$
$37$	−7.67223	−	3.17794i	−1.26131	−	0.522450i	−0.910310	+	0.413926i	$0.864157\pi$
$38$	−3.55273	+	5.73809i	−0.576330	+	0.930840i
$39$	1.70900	−	1.08702i	0.273659	−	0.174063i
$40$	0.778425	−	8.40533i	0.123080	−	1.32900i
$41$	2.38731			0.372836			0.186418	−	0.982471i	$-0.440312\pi$
$41$	2.38731			0.372836			0.186418	+	0.982471i	$0.440312\pi$
$42$	1.77316	−	0.417075i	0.273604	−	0.0643561i
$43$	2.58284	+	6.23554i	0.393880	+	0.950911i	0.989086	+	0.147338i	$0.0470704\pi$
$43$	2.58284	+	6.23554i	0.393880	+	0.950911i	−0.595206	+	0.803573i	$0.702930\pi$
$44$	5.66961	−	6.51584i	0.854726	−	0.982300i
$45$	−7.40172	+	3.06589i	−1.10338	+	0.457036i
$46$	0.650558	−	3.98856i	0.0959195	−	0.588081i
$47$	0.800438	+	0.800438i	0.116756	+	0.116756i	0.763071	−	0.646315i	$-0.223691\pi$
$47$	0.800438	+	0.800438i	0.116756	+	0.116756i	−0.646315	+	0.763071i	$0.723691\pi$
$48$	−1.13858	−	1.93717i	−0.164340	−	0.279606i
$49$	1.74266			0.248951
$50$	−0.889445	+	5.45317i	−0.125787	+	0.771195i
$51$	3.93981	+	1.63192i	0.551684	+	0.228515i
$52$	4.28238	+	5.80183i	0.593859	+	0.804569i
$53$	−3.63540	−	8.77663i	−0.499360	−	1.20556i	−0.949829	−	0.312770i	$-0.898743\pi$
$53$	−3.63540	−	8.77663i	−0.499360	−	1.20556i	0.450469	−	0.892792i	$-0.351257\pi$
$54$	−2.37725	+	3.83954i	−0.323503	+	0.522496i
$55$	−9.11361	+	9.11361i	−1.22888	+	1.22888i
$56$	1.91871	+	6.19494i	0.256398	+	0.827834i
$57$		−	2.68077i		−	0.355077i
$58$	−3.83404	+	0.901829i	−0.503435	+	0.118416i
$59$	−2.35581	+	5.68744i	−0.306701	+	0.740441i	0.693107	+	0.720835i	$0.256241\pi$
$59$	−2.35581	+	5.68744i	−0.306701	+	0.740441i	−0.999808	+	0.0196065i	$0.993759\pi$
$60$	1.49468	+	3.00145i	0.192962	+	0.387486i
$61$	−3.55120	+	8.57336i	−0.454685	+	1.09771i	0.515835	+	0.856688i	$0.327482\pi$
$61$	−3.55120	+	8.57336i	−0.454685	+	1.09771i	−0.970520	+	0.241019i	$0.922518\pi$
$62$	−1.47578	+	9.04799i	−0.187424	+	1.14910i
$63$	4.35233	−	4.35233i	0.548342	−	0.548342i
$64$	6.59951	−	4.52178i	0.824938	−	0.565223i
$65$	−5.77512	−	9.07954i	−0.716315	−	1.12618i
$66$	−0.552290	+	3.38608i	−0.0679822	+	0.416798i
$67$	10.1877	−	4.21989i	1.24463	−	0.515542i	0.339470	−	0.940617i	$-0.389752\pi$
$67$	10.1877	−	4.21989i	1.24463	−	0.515542i	0.905158	+	0.425075i	$0.139752\pi$
$68$	−4.82441	+	14.3958i	−0.585046	+	1.74574i
$69$	0.614306	+	1.48307i	0.0739537	+	0.178540i
$70$	−2.21583	−	9.42038i	−0.264842	−	1.12595i
$71$	7.20444			0.855010			0.427505	−	0.904013i	$-0.359393\pi$
$71$	7.20444			0.855010			0.427505	+	0.904013i	$0.359393\pi$
$72$	−6.71694	−	3.54011i	−0.791599	−	0.417206i
$73$			12.0231i			1.40720i	0.710595	+	0.703602i	$0.248426\pi$
$73$			12.0231i			1.40720i	−0.710595	+	0.703602i	$0.751574\pi$
$74$	2.68903	+	11.4321i	0.312593	+	1.32896i
$75$	−0.839881	−	2.02765i	−0.0969811	−	0.234133i
$76$	9.52144	−	0.661226i	1.09218	−	0.0758478i
$77$	3.78934	−	9.14829i	0.431836	−	1.04254i
$78$	−2.65944	−	1.06397i	−0.301122	−	0.120470i
$79$	−1.01246			−0.113911			−0.0569555	−	0.998377i	$-0.518139\pi$
$79$	−1.01246			−0.113911			−0.0569555	+	0.998377i	$0.518139\pi$
$80$	−10.2917	+	6.04904i	−1.15065	+	0.676303i
$81$			6.25952i			0.695502i
$82$	−1.97187	−	2.74048i	−0.217757	−	0.302636i
$83$	1.54226	+	3.72333i	0.169285	+	0.408689i	0.985640	−	0.168861i	$-0.0540089\pi$
$83$	1.54226	+	3.72333i	0.169285	+	0.408689i	−0.816355	+	0.577550i	$0.804009\pi$
$84$	−1.94337	−	1.69098i	−0.212039	−	0.184501i
$85$	8.67004	−	20.9313i	0.940398	−	2.27032i
$86$	5.02463	−	8.11537i	0.541819	−	0.875102i
$87$	1.10627	−	1.10627i	0.118605	−	0.118605i
$88$	−12.1628	−	1.12640i	−1.29655	−	0.120075i
$89$	4.18739			0.443863			0.221931	−	0.975062i	$-0.428764\pi$
$89$	4.18739			0.443863			0.221931	+	0.975062i	$0.428764\pi$
$90$	9.63312	+	5.96434i	1.01542	+	0.628697i
$91$	6.76862	+	4.74671i	0.709544	+	0.497590i
$92$	−5.11596	+	2.54767i	−0.533376	+	0.265613i
$93$	−1.39354	−	3.36431i	−0.144504	−	0.348863i
$94$	0.257707	−	1.58000i	0.0265804	−	0.162964i
$95$	−14.2423			−1.46123
$96$	−1.28330	+	2.90708i	−0.130976	+	0.296703i
$97$	1.07250	−	1.07250i	0.108896	−	0.108896i	−0.650559	−	0.759455i	$-0.725466\pi$
$97$	1.07250	−	1.07250i	0.108896	−	0.108896i	0.759455	+	0.650559i	$0.225466\pi$
$98$	−1.43940	−	2.00046i	−0.145401	−	0.202077i
$99$	4.43644	+	10.7105i	0.445879	+	1.07645i
$100$	6.99456	−	3.48318i	0.699456	−	0.348318i
$101$	5.55787	+	13.4179i	0.553028	+	1.33513i	0.915193	+	0.403015i	$0.132038\pi$
$101$	5.55787	+	13.4179i	0.553028	+	1.33513i	−0.362165	+	0.932114i	$0.617962\pi$
$102$	−1.38086	−	5.87059i	−0.136725	−	0.581275i
$103$	−5.76332	+	5.76332i	−0.567877	+	0.567877i	−0.931533	−	0.363656i	$-0.881528\pi$
$103$	−5.76332	+	5.76332i	−0.567877	+	0.567877i	0.363656	+	0.931533i	$0.381528\pi$
$104$	3.12298	−	9.70809i	0.306233	−	0.951956i
$105$	2.71816	+	2.71816i	0.265265	+	0.265265i
$106$	−7.07225	+	11.4225i	−0.686917	+	1.10945i
$107$	17.2386	−	7.14048i	1.66652	−	0.690296i	0.667975	−	0.744184i	$-0.267161\pi$
$107$	17.2386	−	7.14048i	1.66652	−	0.690296i	0.998547	+	0.0538875i	$0.0171612\pi$
$108$	6.37111	−	0.442448i	0.613061	−	0.0425746i
$109$	5.32763	−	2.20677i	0.510294	−	0.211371i	−0.112654	−	0.993634i	$-0.535935\pi$
$109$	5.32763	−	2.20677i	0.510294	−	0.211371i	0.622948	+	0.782264i	$0.285935\pi$
$110$	17.9895	+	2.93419i	1.71523	+	0.279764i
$111$	−3.29863	−	3.29863i	−0.313092	−	0.313092i
$112$	5.52659	−	7.31945i	0.522213	−	0.691623i
$113$			17.1590i			1.61418i	0.590429	+	0.807090i	$0.298959\pi$
$113$			17.1590i			1.61418i	−0.590429	+	0.807090i	$0.701041\pi$
$114$	−3.07736	+	2.21426i	−0.288221	+	0.207385i
$115$	7.87920	−	3.26367i	0.734739	−	0.304339i
$116$	4.20208	+	3.65635i	0.390154	+	0.339483i
$117$	−9.53304	+	1.67386i	−0.881330	+	0.154748i
$118$	8.47467	−	1.99338i	0.780157	−	0.183506i
$119$			17.4061i			1.59561i
$120$	2.21090	−	4.19493i	0.201827	−	0.382943i
$121$	5.40949	+	5.40949i	0.491772	+	0.491772i
$122$	12.7749	−	3.00486i	1.15659	−	0.272048i
$123$	1.23899	+	0.513206i	0.111716	+	0.0462742i
$124$	11.6055	−	5.77935i	1.04220	−	0.519001i
$125$	3.01389	−	1.24839i	0.269570	−	0.111660i
$126$	−8.59112	−	1.40126i	−0.765358	−	0.124834i
$127$	6.61325			0.586831			0.293416	−	0.955985i	$-0.405208\pi$
$127$	6.61325			0.586831			0.293416	+	0.955985i	$0.405208\pi$
$128$	−10.6418	−	3.84092i	−0.940609	−	0.339492i
$129$			3.79141i			0.333815i
$130$	−5.65261	+	14.1290i	−0.495767	+	1.23919i
$131$	−0.294690	−	0.122064i	−0.0257472	−	0.0106648i	0.369773	−	0.929122i	$-0.379436\pi$
$131$	−0.294690	−	0.122064i	−0.0257472	−	0.0106648i	−0.395520	+	0.918457i	$0.629436\pi$
$132$	4.34319	−	2.16284i	0.378026	−	0.188251i
$133$	10.1092	−	4.18736i	0.876577	−	0.363090i
$134$	−13.2590	−	8.20931i	−1.14540	−	0.709177i
$135$	−9.53003			−0.820214
$136$	20.5103	−	6.35247i	1.75874	−	0.544720i
$137$		−	7.09917i		−	0.606523i	−0.952907	−	0.303262i	$-0.901924\pi$
$137$		−	7.09917i		−	0.606523i	0.952907	−	0.303262i	$-0.0980756\pi$
$138$	1.19506	−	1.93017i	0.101730	−	0.164307i
$139$	−0.967035	+	0.400559i	−0.0820228	+	0.0339750i	−0.423318	−	0.905981i	$-0.639135\pi$
$139$	−0.967035	+	0.400559i	−0.0820228	+	0.0339750i	0.341295	+	0.939956i	$0.389135\pi$
$140$	−8.98378	+	10.3247i	−0.759268	+	0.872594i
$141$	0.243346	+	0.587490i	0.0204935	+	0.0494756i
$142$	−5.95072	−	8.27024i	−0.499373	−	0.694023i
$143$	−13.1384	+	8.35677i	−1.09869	+	0.698828i
$144$	1.48423	+	10.6347i	0.123686	+	0.886223i
$145$	−5.87739	−	5.87739i	−0.488091	−	0.488091i
$146$	13.8018	−	9.93087i	1.14225	−	0.821885i
$147$	0.904421	+	0.374623i	0.0745954	+	0.0308984i
$148$	10.9023	−	12.5295i	0.896164	−	1.02992i
$149$	−3.89568	−	1.61364i	−0.319146	−	0.132195i	0.217359	−	0.976092i	$-0.430256\pi$
$149$	−3.89568	−	1.61364i	−0.319146	−	0.132195i	−0.536505	+	0.843897i	$0.680256\pi$
$150$	−1.63389	+	2.63893i	−0.133407	+	0.215468i
$151$	−6.85278			−0.557671			−0.278836	−	0.960339i	$-0.589948\pi$
$151$	−6.85278			−0.557671			−0.278836	+	0.960339i	$0.589948\pi$
$152$	−8.62356	−	10.3839i	−0.699463	−	0.842242i
$153$	−14.4097	−	14.4097i	−1.16496	−	1.16496i
$154$	−13.6316	+	3.20637i	−1.09846	+	0.258376i
$155$	−17.8738	+	7.40359i	−1.43566	+	0.594671i
$156$	0.975273	+	3.93168i	0.0780844	+	0.314786i
$157$	2.93514	−	7.08604i	0.234249	−	0.565528i	−0.762419	−	0.647083i	$-0.775989\pi$
$157$	2.93514	−	7.08604i	0.234249	−	0.565528i	0.996669	+	0.0815552i	$0.0259887\pi$
$158$	0.836273	+	1.16224i	0.0665303	+	0.0924631i
$159$		−	5.33648i		−	0.423210i
$160$	15.4447	+	6.81789i	1.22101	+	0.539001i
$161$	−4.63309	+	4.63309i	−0.365138	+	0.365138i
$162$	7.18553	−	5.17023i	0.564549	−	0.406212i
$163$	8.23010	+	19.8692i	0.644631	+	1.55628i	0.820366	+	0.571839i	$0.193770\pi$
$163$	8.23010	+	19.8692i	0.644631	+	1.55628i	−0.175735	+	0.984438i	$0.556230\pi$
$164$	−1.51718	+	4.52716i	−0.118472	+	0.353512i
$165$	−6.68903	+	2.77069i	−0.520740	+	0.215698i
$166$	3.00028	−	4.84581i	0.232867	−	0.376108i
$167$		−	16.8492i		−	1.30383i	−0.758291	−	0.651917i	$-0.773965\pi$
$167$		−	16.8492i		−	1.30383i	0.758291	−	0.651917i	$-0.226035\pi$
$168$	−0.335953	+	3.62757i	−0.0259193	+	0.279873i
$169$	−4.42867	−	12.2224i	−0.340667	−	0.940184i
$170$	−31.1891	+	7.33618i	−2.39210	+	0.562660i
$171$	−4.90242	+	11.8355i	−0.374897	+	0.905082i
$172$	−13.4662	+	0.935171i	−1.02679	+	0.0713061i
$173$	3.34097	−	8.06582i	0.254010	−	0.613233i	−0.744511	−	0.667610i	$-0.767317\pi$
$173$	3.34097	−	8.06582i	0.254010	−	0.613233i	0.998520	+	0.0543770i	$0.0173173\pi$
$174$	−2.18369	−	0.356173i	−0.165545	−	0.0270014i
$175$	6.33438	−	6.33438i	0.478834	−	0.478834i
$176$	8.75314	+	14.8925i	0.659793	+	1.12256i
$177$	−2.44528	+	2.44528i	−0.183799	+	0.183799i
$178$	−3.45870	−	4.80686i	−0.259240	−	0.360289i
$179$	−8.30773	−	3.44118i	−0.620949	−	0.257206i	0.0499528	−	0.998752i	$-0.484093\pi$
$179$	−8.30773	−	3.44118i	−0.620949	−	0.257206i	−0.670902	+	0.741546i	$0.734093\pi$
$180$	−1.11007	−	15.9846i	−0.0827396	−	1.19142i
$181$	−10.8456	+	4.49239i	−0.806146	+	0.333917i	−0.747415	−	0.664357i	$-0.768705\pi$
$181$	−10.8456	+	4.49239i	−0.806146	+	0.333917i	−0.0587311	+	0.998274i	$0.518705\pi$
$182$	−0.141823	−	11.6906i	−0.0105126	−	0.866567i
$183$	−3.68607	+	3.68607i	−0.272482	+	0.272482i
$184$	7.15024	+	3.76848i	0.527123	+	0.277816i
$185$	−17.5249	+	17.5249i	−1.28846	+	1.28846i
$186$	−2.71098	+	4.37855i	−0.198779	+	0.321051i
$187$	−30.2882	−	12.5458i	−2.21490	−	0.917440i
$188$	−2.02660	+	1.00921i	−0.147805	+	0.0736045i
$189$	6.76439	−	2.80190i	0.492037	−	0.203808i
$190$	11.7639	+	16.3493i	0.853442	+	1.18610i
$191$			15.9188i			1.15185i	0.817503	+	0.575924i	$0.195357\pi$
$191$			15.9188i			1.15185i	−0.817503	+	0.575924i	$0.804643\pi$
$192$	4.39713	−	0.928043i	0.317335	−	0.0669757i
$193$	−0.0112421	−	0.0112421i	−0.000809224	−	0.000809224i	0.706702	−	0.707511i	$-0.250182\pi$
$193$	−0.0112421	−	0.0112421i	−0.000809224	−	0.000809224i	−0.707511	+	0.706702i	$0.750182\pi$
$194$	−2.11703	−	0.345300i	−0.151994	−	0.0247911i
$195$	−1.04537	−	5.95367i	−0.0748607	−	0.426351i
$196$	−1.10749	+	3.30468i	−0.0791064	+	0.236049i
$197$	−5.88508	+	14.2078i	−0.419294	+	1.01227i	0.563258	+	0.826281i	$0.309548\pi$
$197$	−5.88508	+	14.2078i	−0.419294	+	1.01227i	−0.982553	+	0.185985i	$0.940452\pi$
$198$	8.63058	−	13.9394i	0.613349	−	0.990630i
$199$	−15.5175	+	15.5175i	−1.10001	+	1.10001i	−0.105600	+	0.994409i	$0.533676\pi$
$199$	−15.5175	+	15.5175i	−1.10001	+	1.10001i	−0.994409	+	0.105600i	$0.966324\pi$
$200$	−9.77583	−	5.15228i	−0.691256	−	0.364321i
$201$	6.19447			0.436924
$202$	10.8122	−	17.4630i	0.760743	−	1.22869i
$203$	5.89975	+	2.44376i	0.414082	+	0.171518i
$204$	−5.59850	+	6.43412i	−0.391973	+	0.450478i
$205$	2.72655	−	6.58247i	0.190430	−	0.459739i
$206$	11.3763	+	1.85554i	0.792625	+	0.129282i
$207$		−	7.67107i		−	0.533176i
$208$	−13.7238	+	4.43370i	−0.951573	+	0.307422i
$209$			20.6091i			1.42556i
$210$	0.875131	−	5.36541i	0.0603898	−	0.370249i
$211$	6.09460	−	14.7137i	0.419570	−	1.01293i	−0.562903	−	0.826523i	$-0.690315\pi$
$211$	6.09460	−	14.7137i	0.419570	−	1.01293i	0.982472	−	0.186408i	$-0.0596845\pi$
$212$	18.9539	−	1.31627i	1.30176	−	0.0904017i
$213$	3.73902	+	1.54875i	0.256194	+	0.106119i
$214$	−22.4356	−	13.8910i	−1.53366	−	0.949568i
$215$	20.1429			1.37374
$216$	−5.77031	−	6.94818i	−0.392620	−	0.472764i
$217$	10.5101	−	10.5101i	0.713472	−	0.713472i
$218$	−6.93375	−	4.29303i	−0.469612	−	0.290760i
$219$	−2.58464	+	6.23988i	−0.174654	+	0.421652i
$220$	−11.4907	−	23.0744i	−0.774702	−	1.55567i
$221$	15.7154	−	22.4096i	1.05713	−	1.50743i
$222$	−1.06202	+	6.51122i	−0.0712780	+	0.437004i
$223$	−5.30433	−	5.30433i	−0.355204	−	0.355204i	0.506837	−	0.862042i	$-0.330814\pi$
$223$	−5.30433	−	5.30433i	−0.355204	−	0.355204i	−0.862042	+	0.506837i	$0.830814\pi$
$224$	−12.9671	−	0.298463i	−0.866401	−	0.0199419i
$225$			10.4879i			0.699194i
$226$	19.6974	−	14.1729i	1.31025	−	0.942770i
$227$	0.0178168	−	0.00737995i	0.00118254	−	0.000489824i	−0.382092	−	0.924124i	$-0.624796\pi$
$227$	0.0178168	−	0.00737995i	0.00118254	−	0.000489824i	0.383275	+	0.923634i	$0.374796\pi$
$228$	5.08367	+	1.70368i	0.336674	+	0.112829i
$229$	7.74380	+	3.20759i	0.511725	+	0.211963i	0.623578	−	0.781762i	$-0.285679\pi$
$229$	7.74380	+	3.20759i	0.511725	+	0.211963i	−0.111853	+	0.993725i	$0.535679\pi$
$230$	−10.2545	−	6.34909i	−0.676164	−	0.418647i
$231$	3.93325	−	3.93325i	0.258789	−	0.258789i
$232$	0.726421	−	7.84379i	0.0476919	−	0.514970i
$233$	−8.53569	+	8.53569i	−0.559192	+	0.559192i	−0.929077	−	0.369886i	$-0.879397\pi$
$233$	−8.53569	+	8.53569i	−0.559192	+	0.559192i	0.369886	+	0.929077i	$0.379397\pi$
$234$	9.79557	+	9.56076i	0.640357	+	0.625006i
$235$	3.12120	−	1.29284i	0.203605	−	0.0843359i
$236$	−9.28817	−	8.08189i	−0.604609	−	0.526086i
$237$	−0.525456	−	0.217651i	−0.0341321	−	0.0141380i
$238$	19.9811	−	14.3770i	1.29518	−	0.931925i
$239$	18.4356	−	18.4356i	1.19250	−	1.19250i	0.216136	−	0.976363i	$-0.430655\pi$
$239$	18.4356	−	18.4356i	1.19250	−	1.19250i	0.976363	−	0.216136i	$-0.0693453\pi$
$240$	−6.64167	+	0.926946i	−0.428718	+	0.0598341i
$241$	−2.31674	+	2.31674i	−0.149234	+	0.149234i	−0.777776	−	0.628542i	$-0.783652\pi$
$241$	−2.31674	+	2.31674i	−0.149234	+	0.149234i	0.628542	+	0.777776i	$0.283652\pi$
$242$	1.74162	−	10.6779i	0.111956	−	0.686400i
$243$	−5.01161	+	12.0991i	−0.321495	+	0.776157i
$244$	−14.0012	−	12.1828i	−0.896335	−	0.779925i
$245$	1.99029	−	4.80498i	0.127155	−	0.306979i
$246$	−0.434251	−	1.84618i	−0.0276868	−	0.117708i
$247$	−16.7958	−	3.73623i	−1.06869	−	0.237731i
$248$	−16.2202	−	8.54874i	−1.02999	−	0.542846i
$249$			2.26391i			0.143469i
$250$	−3.92248	−	2.42860i	−0.248080	−	0.153598i
$251$	19.8162	−	8.20813i	1.25079	−	0.518092i	0.343716	−	0.939074i	$-0.388314\pi$
$251$	19.8162	−	8.20813i	1.25079	−	0.518092i	0.907069	+	0.420981i	$0.138314\pi$
$252$	5.48753	+	11.0195i	0.345682	+	0.694162i
$253$	−4.72263	−	11.4014i	−0.296909	−	0.716802i
$254$	−5.46241	−	7.59159i	−0.342742	−	0.476339i
$255$	8.99930	−	8.99930i	0.563558	−	0.563558i
$256$	4.38075	+	15.3886i	0.273797	+	0.961787i
$257$			11.1031i			0.692595i	0.938125	+	0.346297i	$0.112561\pi$
$257$			11.1031i			0.692595i	−0.938125	+	0.346297i	$0.887439\pi$
$258$	4.35230	−	3.13163i	0.270962	−	0.194967i
$259$	7.28667	−	17.5916i	0.452772	−	1.09309i
$260$	20.8881	−	5.18141i	1.29543	−	0.321337i
$261$	−6.90724	+	2.86107i	−0.427547	+	0.177096i
$262$	0.103285	+	0.439108i	0.00638099	+	0.0271282i
$263$	−21.5902	−	21.5902i	−1.33131	−	1.33131i	−0.904199	−	0.427111i	$-0.859531\pi$
$263$	−21.5902	−	21.5902i	−1.33131	−	1.33131i	−0.427111	−	0.904199i	$-0.640469\pi$
$264$	−6.07019	−	3.19924i	−0.373594	−	0.196900i
$265$	−28.3515			−1.74162
$266$	−13.1568	−	8.14602i	−0.806695	−	0.499465i
$267$	2.17321	+	0.900172i	0.132998	+	0.0550896i
$268$	1.52790	+	22.0012i	0.0933312	+	1.34394i
$269$	18.3561	+	7.60334i	1.11919	+	0.463584i	0.864093	−	0.503332i	$-0.167893\pi$
$269$	18.3561	+	7.60334i	1.11919	+	0.463584i	0.255097	+	0.966915i	$0.417893\pi$
$270$	7.87160	+	10.9399i	0.479050	+	0.665779i
$271$	6.51693	+	6.51693i	0.395875	+	0.395875i	0.876775	−	0.480900i	$-0.159690\pi$
$271$	6.51693	+	6.51693i	0.395875	+	0.395875i	−0.480900	+	0.876775i	$0.659690\pi$
$272$	−24.2333	−	18.2975i	−1.46936	−	1.10945i
$273$	2.49243	+	3.91855i	0.150849	+	0.237161i
$274$	−8.14940	+	5.86377i	−0.492323	+	0.354243i
$275$	6.45679	+	15.5881i	0.389359	+	0.939996i
$276$	−3.20280	+	0.222422i	−0.192786	+	0.0133882i
$277$	−25.3091	+	10.4834i	−1.52068	+	0.629885i	−0.977727	−	0.209879i	$-0.932693\pi$
$277$	−25.3091	+	10.4834i	−1.52068	+	0.629885i	−0.542951	+	0.839765i	$0.682693\pi$
$278$	1.25857	+	0.779241i	0.0754838	+	0.0467358i
$279$			17.4017i			1.04181i
$280$	19.2725	+	1.78484i	1.15175	+	0.106665i
$281$	10.6480			0.635204			0.317602	−	0.948224i	$-0.397122\pi$
$281$	10.6480			0.635204			0.317602	+	0.948224i	$0.397122\pi$
$282$	0.473402	−	0.764601i	0.0281907	−	0.0455313i
$283$	26.4623	−	10.9610i	1.57302	−	0.651566i	0.585732	−	0.810505i	$-0.300807\pi$
$283$	26.4623	−	10.9610i	1.57302	−	0.651566i	0.987288	+	0.158938i	$0.0508071\pi$
$284$	−4.57854	+	13.6621i	−0.271686	+	0.810696i
$285$	−7.39162	−	3.06171i	−0.437842	−	0.181360i
$286$	20.4451	+	8.17949i	1.20894	+	0.483664i
$287$			5.47384i			0.323111i
$288$	10.9820	−	10.4878i	0.647120	−	0.618001i
$289$	40.6282			2.38989
$290$	−1.89227	+	11.6015i	−0.111118	+	0.681262i
$291$	0.787174	−	0.326058i	0.0461449	−	0.0191139i
$292$	−22.8000	−	7.64091i	−1.33427	−	0.447151i
$293$	−3.38161	−	1.40071i	−0.197556	−	0.0818304i	0.281712	−	0.959499i	$-0.409098\pi$
$293$	−3.38161	−	1.40071i	−0.197556	−	0.0818304i	−0.479268	+	0.877669i	$0.659098\pi$
$294$	−0.316989	−	1.34765i	−0.0184872	−	0.0785965i
$295$	12.9912	+	12.9912i	0.756379	+	0.756379i
$296$	−23.3882	−	2.16600i	−1.35941	−	0.125896i
$297$			13.7902i			0.800190i
$298$	1.36539	+	5.80482i	0.0790949	+	0.336264i
$299$	10.1480	−	1.78183i	0.586874	−	0.103046i
$300$	4.37888	−	0.304096i	0.252815	−	0.0175570i
$301$	−14.2974	+	5.92218i	−0.824088	+	0.341349i
$302$	5.66025	+	7.86656i	0.325711	+	0.452669i
$303$			8.15851i			0.468694i
$304$	−4.79712	+	18.4761i	−0.275134	+	1.05968i
$305$	19.5833	+	19.5833i	1.12133	+	1.12133i
$306$	−4.63932	+	28.4436i	−0.265212	+	1.62601i
$307$	−23.7893	+	9.85386i	−1.35773	+	0.562389i	−0.938433	−	0.345461i	$-0.887723\pi$
$307$	−23.7893	+	9.85386i	−1.35773	+	0.562389i	−0.419295	+	0.907850i	$0.637723\pi$
$308$	14.9401	+	12.9998i	0.851291	+	0.740732i
$309$	−4.23005	+	1.75214i	−0.240639	+	0.0996760i
$310$	23.2623	+	14.4028i	1.32121	+	0.818026i
$311$	−10.4507	−	10.4507i	−0.592602	−	0.592602i	0.345731	−	0.938334i	$-0.387631\pi$
$311$	−10.4507	−	10.4507i	−0.592602	−	0.592602i	−0.938334	+	0.345731i	$0.887631\pi$
$312$	3.70776	−	4.36703i	0.209911	−	0.247235i
$313$	−1.65921	+	1.65921i	−0.0937843	+	0.0937843i	−0.752442	−	0.658658i	$-0.771124\pi$
$313$	−1.65921	+	1.65921i	−0.0937843	+	0.0937843i	0.658658	+	0.752442i	$0.271124\pi$
$314$	−10.5587	+	2.48358i	−0.595861	+	0.140156i
$315$	−7.02975	−	16.9713i	−0.396082	−	0.956226i
$316$	0.643437	−	1.91998i	0.0361961	−	0.108007i
$317$	−1.12313	−	2.71146i	−0.0630810	−	0.152291i	0.889196	−	0.457527i	$-0.151265\pi$
$317$	−1.12313	−	2.71146i	−0.0630810	−	0.152291i	−0.952277	+	0.305236i	$0.901265\pi$
$318$	−6.12594	+	4.40782i	−0.343526	+	0.247178i
$319$	−8.50476	+	8.50476i	−0.476175	+	0.476175i
$320$	−4.93048	−	23.3609i	−0.275622	−	1.30592i
$321$	10.4817			0.585029
$322$	9.14533	+	1.49166i	0.509649	+	0.0831268i
$323$	−13.8636	−	33.4696i	−0.771389	−	1.86230i
$324$	−11.8702	−	3.97803i	−0.659455	−	0.221002i
$325$	−13.8744	+	2.43613i	−0.769613	+	0.135132i
$326$	16.0107	−	25.8592i	0.886751	−	1.43221i
$327$	3.23937			0.179138
$328$	6.45005	−	1.99772i	0.356145	−	0.110306i
$329$	−1.83532	+	1.83532i	−0.101184	+	0.101184i
$330$	8.70558	+	5.39005i	0.479226	+	0.296713i
$331$	−1.47260	+	3.55517i	−0.0809415	+	0.195410i	−0.959169	−	0.282832i	$-0.908726\pi$
$331$	−1.47260	+	3.55517i	−0.0809415	+	0.195410i	0.878228	+	0.478242i	$0.158726\pi$
$332$	−8.04085	+	0.558405i	−0.441299	+	0.0306464i
$333$	8.53099	+	20.5956i	0.467495	+	1.12863i
$334$	−19.3419	+	13.9171i	−1.05834	+	0.761511i
$335$		−	32.9098i		−	1.79806i
$336$	4.44171	−	2.61065i	0.242315	−	0.142422i
$337$	19.0403			1.03719			0.518595	−	0.855020i	$-0.326455\pi$
$337$	19.0403			1.03719			0.518595	+	0.855020i	$0.326455\pi$
$338$	−10.3725	+	15.1793i	−0.564192	+	0.825643i
$339$	−3.68870	+	8.90531i	−0.200343	+	0.483670i
$340$	34.1830	+	29.7436i	1.85384	+	1.61307i
$341$	10.7132	+	25.8640i	0.580153	+	1.40061i
$342$	17.6357	−	4.14820i	0.953629	−	0.224309i
$343$			20.0459i			1.08238i
$344$	12.1963	+	14.6859i	0.657580	+	0.791809i
$345$	4.79081			0.257929
$346$	−12.0186	+	2.82698i	−0.646126	+	0.151979i
$347$	−8.78988	−	21.2206i	−0.471865	−	1.13918i	−0.963338	−	0.268291i	$-0.913541\pi$
$347$	−8.78988	−	21.2206i	−0.471865	−	1.13918i	0.491472	−	0.870893i	$-0.336459\pi$
$348$	1.39482	+	2.80093i	0.0747702	+	0.150146i
$349$	−11.1763	+	4.62938i	−0.598254	+	0.247805i	−0.661197	−	0.750212i	$-0.729951\pi$
$349$	−11.1763	+	4.62938i	−0.598254	+	0.247805i	0.0629430	+	0.998017i	$0.479951\pi$
$350$	−12.5035	−	2.03940i	−0.668341	−	0.109010i
$351$	−11.2386	−	2.50004i	−0.599874	−	0.133442i
$352$	9.86568	−	22.3489i	0.525843	−	1.19120i
$353$	6.47553	−	6.47553i	0.344658	−	0.344658i	−0.513457	−	0.858115i	$-0.671636\pi$
$353$	6.47553	−	6.47553i	0.344658	−	0.344658i	0.858115	+	0.513457i	$0.171636\pi$
$354$	4.82678	+	0.787276i	0.256540	+	0.0418433i
$355$	8.22818	−	19.8646i	0.436707	−	1.05430i
$356$	−2.66116	+	7.94073i	−0.141041	+	0.420858i
$357$	−3.74182	+	9.03355i	−0.198038	+	0.478106i
$358$	2.91176	+	12.3791i	0.153891	+	0.654255i
$359$		−	29.7972i		−	1.57264i	−0.617820	−	0.786319i	$-0.711984\pi$
$359$		−	29.7972i		−	1.57264i	0.617820	−	0.786319i	$-0.288016\pi$
$360$	−17.4325	+	14.4773i	−0.918771	+	0.763019i
$361$	−2.66846	+	2.66846i	−0.140445	+	0.140445i
$362$	14.1152	+	8.73943i	0.741879	+	0.459334i
$363$	1.64457	+	3.97035i	0.0863177	+	0.208389i
$364$	−13.3030	+	9.81902i	−0.697264	+	0.514656i
$365$	33.1511	+	13.7316i	1.73521	+	0.718746i
$366$	7.27599	+	1.18676i	0.380322	+	0.0620328i
$367$	−8.76959			−0.457769			−0.228884	−	0.973454i	$-0.573508\pi$
$367$	−8.76959			−0.457769			−0.228884	+	0.973454i	$0.573508\pi$
$368$	−1.57998	−	11.3207i	−0.0823619	−	0.590133i
$369$	−4.53156	−	4.53156i	−0.235904	−	0.235904i
$370$	34.5927	+	5.64227i	1.79839	+	0.293328i
$371$	20.1238	−	8.33556i	1.04478	−	0.432761i
$372$	7.26552	−	0.504561i	0.376699	−	0.0261603i
$373$	−6.66474	−	16.0901i	−0.345087	−	0.833114i	−0.997185	−	0.0749793i	$-0.976111\pi$
$373$	−6.66474	−	16.0901i	−0.345087	−	0.833114i	0.652098	−	0.758135i	$-0.273889\pi$
$374$	10.6157	+	45.1316i	0.548923	+	2.33370i
$375$	1.83254			0.0946321
$376$	2.83244	+	1.49282i	0.146072	+	0.0769861i
$377$	−5.38930	−	8.47297i	−0.277563	−	0.436380i
$378$	−8.80365	−	5.45077i	−0.452811	−	0.280358i
$379$	−24.4128	−	10.1121i	−1.25400	−	0.519424i	−0.345938	−	0.938258i	$-0.612439\pi$
$379$	−24.4128	−	10.1121i	−1.25400	−	0.519424i	−0.908063	+	0.418833i	$0.862439\pi$
$380$	9.05125	−	27.0084i	0.464319	−	1.38550i
$381$	3.43220	+	1.42166i	0.175837	+	0.0728341i
$382$	18.2738	−	13.1486i	0.934970	−	0.672743i
$383$	−5.86845	−	5.86845i	−0.299864	−	0.299864i	0.541097	−	0.840960i	$-0.318009\pi$
$383$	−5.86845	−	5.86845i	−0.299864	−	0.299864i	−0.840960	+	0.541097i	$0.818009\pi$
$384$	−4.69727	−	4.28108i	−0.239707	−	0.218468i
$385$	−20.8965	−	20.8965i	−1.06498	−	1.06498i
$386$	−0.00361948	+	0.0221910i	−0.000184227	+	0.00112949i
$387$	6.93349	−	16.7389i	0.352449	−	0.850887i
$388$	1.35224	+	2.71542i	0.0686495	+	0.137855i
$389$	−0.619840	−	1.49643i	−0.0314272	−	0.0758719i	0.907387	−	0.420297i	$-0.138074\pi$
$389$	−0.619840	−	1.49643i	−0.0314272	−	0.0758719i	−0.938814	+	0.344425i	$0.888074\pi$
$390$	−5.97098	+	6.11763i	−0.302352	+	0.309778i
$391$	15.3393	+	15.3393i	0.775741	+	0.775741i
$392$	4.70833	−	1.45827i	0.237806	−	0.0736538i
$393$	−0.126700	−	0.126700i	−0.00639118	−	0.00639118i
$394$	21.1706	−	4.97968i	1.06656	−	0.250873i
$395$	−1.15633	+	2.79163i	−0.0581814	+	0.140462i
$396$	−23.1302	+	1.60630i	−1.16234	+	0.0807197i
$397$	−7.65475	−	18.4802i	−0.384181	−	0.927495i	−0.991147	−	0.132768i	$-0.957614\pi$
$397$	−7.65475	−	18.4802i	−0.384181	−	0.927495i	0.606966	−	0.794728i	$-0.292386\pi$
$398$	30.6303	+	4.99599i	1.53536	+	0.250426i
$399$	6.14671			0.307721
$400$	2.16015	+	15.4777i	0.108007	+	0.773886i
$401$	2.54345	−	2.54345i	0.127014	−	0.127014i	−0.640742	−	0.767756i	$-0.721373\pi$
$401$	2.54345	−	2.54345i	0.127014	−	0.127014i	0.767756	+	0.640742i	$0.221373\pi$
$402$	−5.11650	−	7.11086i	−0.255188	−	0.354657i
$403$	−23.0206	+	4.04207i	−1.14674	+	0.201350i
$404$	−28.9770	+	2.01234i	−1.44166	+	0.100118i
$405$	17.2592	+	7.14899i	0.857616	+	0.355236i
$406$	−2.06779	−	8.79104i	−0.102623	−	0.436292i
$407$	25.3590	+	25.3590i	1.25700	+	1.25700i
$408$	12.0102	+	1.11228i	0.594594	+	0.0550659i
$409$		−	17.7108i		−	0.875742i	−0.899038	−	0.437871i	$-0.855733\pi$
$409$		−	17.7108i		−	0.875742i	0.899038	−	0.437871i	$-0.144267\pi$
$410$	−9.80832	+	2.30708i	−0.484399	+	0.113938i
$411$	1.52612	−	3.68439i	0.0752781	−	0.181738i
$412$	−7.26655	−	14.5919i	−0.357997	−	0.718892i
$413$	−13.0407	−	5.40162i	−0.641689	−	0.265796i
$414$	−8.80590	+	6.33614i	−0.432786	+	0.311404i
$415$	12.0276			0.590414
$416$	16.4252	+	12.0919i	0.805310	+	0.592854i
$417$	−0.587989			−0.0287939
$418$	23.6579	−	17.0227i	1.15715	−	0.832607i
$419$	20.5866	+	8.52723i	1.00572	+	0.416582i	0.823891	−	0.566748i	$-0.191799\pi$
$419$	20.5866	+	8.52723i	1.00572	+	0.416582i	0.181828	+	0.983330i	$0.441799\pi$
$420$	−6.88199	+	3.42713i	−0.335807	+	0.167227i
$421$	−11.7353	+	28.3316i	−0.571946	+	1.38080i	0.327950	+	0.944695i	$0.393642\pi$
$421$	−11.7353	+	28.3316i	−0.571946	+	1.38080i	−0.899896	+	0.436104i	$0.856358\pi$
$422$	−21.9244	+	5.15697i	−1.06726	+	0.251037i
$423$		−	3.03876i		−	0.147749i
$424$	−17.1665	−	20.6706i	−0.833678	−	1.00385i
$425$	−20.9719	−	20.9719i	−1.01729	−	1.01729i
$426$	−1.31048	−	5.57140i	−0.0634931	−	0.269935i
$427$	−19.6578	−	8.14252i	−0.951306	−	0.394044i
$428$	2.58535	+	37.2283i	0.124968	+	1.79950i
$429$	−8.61513	+	1.51269i	−0.415943	+	0.0730331i
$430$	−16.6376	−	23.1228i	−0.802338	−	1.11508i
$431$	−19.1335	+	19.1335i	−0.921629	+	0.921629i	−0.997145	−	0.0755159i	$-0.975940\pi$
$431$	−19.1335	+	19.1335i	−0.921629	+	0.921629i	0.0755159	+	0.997145i	$0.475940\pi$
$432$	−3.20992	+	12.3630i	−0.154437	+	0.594815i
$433$	26.0534			1.25205			0.626023	−	0.779804i	$-0.284681\pi$
$433$	26.0534			1.25205			0.626023	+	0.779804i	$0.284681\pi$
$434$	−20.7460	−	3.38380i	−0.995842	−	0.162428i
$435$	−1.78682	−	4.31377i	−0.0856716	−	0.206830i
$436$	0.799007	+	11.5055i	0.0382655	+	0.551011i
$437$	5.21867	−	12.5990i	0.249643	−	0.602691i
$438$	9.29784	−	2.18700i	0.444268	−	0.104499i
$439$	−0.195559	−	0.195559i	−0.00933350	−	0.00933350i	0.702425	−	0.711758i	$-0.252101\pi$
$439$	−0.195559	−	0.195559i	−0.00933350	−	0.00933350i	−0.711758	+	0.702425i	$0.752101\pi$
$440$	−16.9969	+	32.2495i	−0.810294	+	1.53744i
$441$	−3.30789	−	3.30789i	−0.157519	−	0.157519i
$442$	−38.7054	+	0.469548i	−1.84103	+	0.0223341i
$443$	11.9944	+	28.9570i	0.569871	+	1.37579i	0.901664	+	0.432438i	$0.142347\pi$
$443$	11.9944	+	28.9570i	0.569871	+	1.37579i	−0.331792	+	0.943352i	$0.607653\pi$
$444$	8.35167	−	4.15900i	0.396353	−	0.197378i
$445$	4.78241	−	11.5458i	0.226708	−	0.547322i
$446$	−1.70777	+	10.4703i	−0.0808652	+	0.495783i
$447$	−1.67492	−	1.67492i	−0.0792212	−	0.0792212i
$448$	10.3679	+	15.1319i	0.489839	+	0.714917i
$449$	0.639812	+	0.639812i	0.0301946	+	0.0301946i	0.722043	−	0.691848i	$-0.243203\pi$
$449$	0.639812	+	0.639812i	0.0301946	+	0.0301946i	−0.691848	+	0.722043i	$0.743203\pi$
$450$	12.0395	−	8.66280i	0.567546	−	0.408368i
$451$	−9.52502	−	3.94539i	−0.448516	−	0.185781i
$452$	−32.5393	−	10.9048i	−1.53052	−	0.512919i
$453$	−3.55651	−	1.47316i	−0.167100	−	0.0692149i
$454$	−0.0231880	−	0.0143568i	−0.00108827	−	0.000673800i
$455$	20.8184	−	13.2417i	0.975981	−	0.620781i
$456$	−2.24329	−	7.24293i	−0.105052	−	0.339181i
$457$	31.2843			1.46342			0.731709	−	0.681617i	$-0.238723\pi$
$457$	31.2843			1.46342			0.731709	+	0.681617i	$0.238723\pi$
$458$	−2.71411	−	11.5388i	−0.126822	−	0.539172i
$459$	−9.27656	−	22.3956i	−0.432993	−	1.04534i
$460$	1.18168	+	17.0158i	0.0550960	+	0.793365i
$461$	20.3607	−	8.43368i	0.948292	−	0.392796i	0.145704	−	0.989328i	$-0.453455\pi$
$461$	20.3607	−	8.43368i	0.948292	−	0.392796i	0.802589	+	0.596533i	$0.203455\pi$
$462$	−7.76391	−	1.26634i	−0.361210	−	0.0589155i
$463$	11.9587	+	11.9587i	0.555768	+	0.555768i	0.928100	−	0.372332i	$-0.121442\pi$
$463$	11.9587	+	11.9587i	0.555768	+	0.555768i	−0.372332	+	0.928100i	$0.621442\pi$
$464$	−9.60418	+	5.64492i	−0.445863	+	0.262059i
$465$	−10.8679			−0.503986
$466$	16.8487	+	2.74813i	0.780502	+	0.127305i
$467$	30.2851	+	12.5445i	1.40143	+	0.580490i	0.950121	−	0.311880i	$-0.100959\pi$
$467$	30.2851	+	12.5445i	1.40143	+	0.580490i	0.451305	+	0.892370i	$0.350959\pi$
$468$	2.88420	−	19.1417i	0.133322	−	0.884825i
$469$	9.67574	+	23.3593i	0.446784	+	1.07863i
$470$	−4.06215	−	2.51508i	−0.187373	−	0.116012i
$471$	3.04660	−	3.04660i	0.140380	−	0.140380i
$472$	−1.60566	+	17.3377i	−0.0739066	+	0.798033i
$473$		−	29.1474i		−	1.34020i
$474$	0.184166	+	0.782966i	0.00845904	+	0.0359628i
$475$	−7.13498	+	17.2254i	−0.327375	+	0.790354i
$476$	−33.0079	−	11.0618i	−1.51291	−	0.507019i
$477$	−9.75900	+	23.5603i	−0.446834	+	1.07875i
$478$	−36.3903	−	5.93547i	−1.66445	−	0.271482i
$479$	17.8581	−	17.8581i	0.815958	−	0.815958i	−0.169562	−	0.985520i	$-0.554235\pi$
$479$	17.8581	−	17.8581i	0.815958	−	0.815958i	0.985520	+	0.169562i	$0.0542352\pi$
$480$	6.54996	+	6.85858i	0.298963	+	0.313050i
$481$	−25.2642	+	16.0695i	−1.15195	+	0.732708i
$482$	4.57304	+	0.745890i	0.208296	+	0.0339744i
$483$	−3.40050	+	1.40854i	−0.154728	+	0.0640906i
$484$	−13.6961	+	6.82043i	−0.622548	+	0.310019i
$485$	−1.73227	−	4.18208i	−0.0786585	−	0.189898i
$486$	18.0285	−	4.24059i	0.817788	−	0.192357i
$487$	3.48947			0.158123			0.0790614	−	0.996870i	$-0.474808\pi$
$487$	3.48947			0.158123			0.0790614	+	0.996870i	$0.474808\pi$
$488$	−2.42041	+	26.1352i	−0.109567	+	1.18309i
$489$			12.0811i			0.546328i
$490$	−7.15976	+	1.68409i	−0.323445	+	0.0760795i
$491$	−4.81645	−	11.6279i	−0.217363	−	0.524762i	0.777157	−	0.629307i	$-0.216661\pi$
$491$	−4.81645	−	11.6279i	−0.217363	−	0.524762i	−0.994520	+	0.104545i	$0.966661\pi$
$492$	−1.76061	+	2.02340i	−0.0793745	+	0.0912217i
$493$	8.09082	−	19.5330i	0.364392	−	0.879721i
$494$	9.58404	+	22.3666i	0.431206	+	1.00632i
$495$	34.5986			1.55509
$496$	3.58415	+	25.6809i	0.160933	+	1.15310i
$497$			16.5190i			0.740977i
$498$	2.59882	−	1.86994i	0.116456	−	0.0837941i
$499$	−0.196016	−	0.473223i	−0.00877486	−	0.0211844i	0.919431	−	0.393250i	$-0.128649\pi$
$499$	−0.196016	−	0.473223i	−0.00877486	−	0.0211844i	−0.928206	+	0.372066i	$0.878649\pi$
$500$	0.452006	+	6.50874i	0.0202143	+	0.291080i
$501$	3.62212	−	8.74456i	0.161824	−	0.390678i
$502$	−25.7901	−	15.9680i	−1.15107	−	0.712685i
$503$	−16.1899	+	16.1899i	−0.721872	+	0.721872i	−0.968986	−	0.247114i	$-0.920518\pi$
$503$	−16.1899	+	16.1899i	−0.721872	+	0.721872i	0.247114	+	0.968986i	$0.420518\pi$
$504$	8.11708	−	15.4012i	0.361563	−	0.686024i
$505$	43.3444			1.92880
$506$	−9.18733	+	14.8386i	−0.408426	+	0.659657i
$507$	0.329047	−	7.29532i	0.0146135	−	0.323997i
$508$	−4.20283	+	12.5410i	−0.186471	+	0.556417i
$509$	5.91082	+	14.2700i	0.261992	+	0.632505i	0.999062	−	0.0433118i	$-0.0137909\pi$
$509$	5.91082	+	14.2700i	0.261992	+	0.632505i	−0.737069	+	0.675817i	$0.763791\pi$
$510$	−17.7639	−	2.89739i	−0.786597	−	0.128299i
$511$	−27.5677			−1.21953
$512$	14.0467	−	17.7395i	0.620783	−	0.783982i
$513$	−10.7754	+	10.7754i	−0.475745	+	0.475745i
$514$	12.7457	−	9.17096i	0.562189	−	0.404514i
$515$	9.30875	+	22.4733i	0.410193	+	0.990293i
$516$	−7.18982	−	2.40951i	−0.316514	−	0.106073i
$517$	−1.87078	−	4.51647i	−0.0822770	−	0.198634i
$518$	−26.2126	+	6.16564i	−1.15172	+	0.270903i
$519$	3.46785	−	3.46785i	0.152222	−	0.152222i
$520$	−23.2011	−	19.6985i	−1.01743	−	0.863836i
$521$	−20.3087	−	20.3087i	−0.889739	−	0.889739i	0.104759	−	0.994498i	$-0.466593\pi$
$521$	−20.3087	−	20.3087i	−0.889739	−	0.889739i	−0.994498	+	0.104759i	$0.966593\pi$
$522$	8.98956	+	5.56588i	0.393462	+	0.243612i
$523$	−34.3338	+	14.2215i	−1.50131	+	0.621865i	−0.973744	−	0.227647i	$-0.926897\pi$
$523$	−34.3338	+	14.2215i	−1.50131	+	0.621865i	−0.527570	+	0.849512i	$0.676897\pi$
$524$	0.418756	−	0.481259i	0.0182935	−	0.0210239i
$525$	4.64918	−	1.92575i	0.202907	−	0.0840468i
$526$	−6.95113	+	42.6173i	−0.303084	+	1.85820i
$527$	−34.7969	−	34.7969i	−1.51578	−	1.51578i
$528$	1.34132	+	9.61070i	0.0583734	+	0.418252i
$529$		−	14.8341i		−	0.644960i
$530$	23.4178	+	32.5457i	1.01720	+	1.41370i
$531$	15.2676	−	6.32403i	0.662556	−	0.274440i
$532$	1.51612	+	21.8316i	0.0657321	+	0.946520i
$533$	4.94218	−	7.04736i	0.214070	−	0.305255i
$534$	−0.761684	−	3.23823i	−0.0329613	−	0.140132i
$535$		−	55.6867i		−	2.40755i
$536$	23.9940	−	19.9265i	1.03638	−	0.860693i
$537$	−3.57186	−	3.57186i	−0.154137	−	0.154137i
$538$	−6.43359	−	27.3518i	−0.277372	−	1.17922i
$539$	−6.95295	−	2.88001i	−0.299485	−	0.124051i
$540$	6.05649	−	18.0722i	0.260630	−	0.777704i
$541$	−14.8442	+	6.14866i	−0.638201	+	0.264351i	−0.678233	−	0.734847i	$-0.737254\pi$
$541$	−14.8442	+	6.14866i	−0.638201	+	0.264351i	0.0400322	+	0.999198i	$0.487254\pi$
$542$	2.09817	−	12.8639i	0.0901242	−	0.552550i
$543$	−6.59448			−0.282996
$544$	−0.988153	+	42.9316i	−0.0423667	+	1.84068i
$545$		−	17.2101i		−	0.737198i
$546$	2.43955	−	6.09779i	0.104403	−	0.260961i
$547$	21.1875	+	8.77613i	0.905910	+	0.375240i	0.786490	−	0.617604i	$-0.211896\pi$
$547$	21.1875	+	8.77613i	0.905910	+	0.375240i	0.119420	+	0.992844i	$0.461896\pi$
$548$	13.4625	+	4.51164i	0.575088	+	0.192728i
$549$	23.0147	−	9.53299i	0.982242	−	0.406858i
$550$	12.5609	−	20.2874i	0.535601	−	0.865058i
$551$	−13.2909			−0.566210
$552$	2.90078	+	3.49290i	0.123465	+	0.148668i
$553$		−	2.32146i		−	0.0987187i
$554$	32.9391	+	20.3942i	1.39945	+	0.866467i
$555$	−12.8626	+	5.32786i	−0.545986	+	0.226155i
$556$	−0.145030	−	2.08839i	−0.00615066	−	0.0885676i
$557$	−1.56000	−	3.76617i	−0.0660992	−	0.159578i	0.887378	−	0.461042i	$-0.152524\pi$
$557$	−1.56000	−	3.76617i	−0.0660992	−	0.159578i	−0.953477	+	0.301465i	$0.902524\pi$
$558$	19.9761	−	14.3735i	0.845654	−	0.608477i
$559$	23.7543	+	5.28415i	1.00470	+	0.223496i
$560$	−13.8698	−	23.5978i	−0.586105	−	0.997190i
$561$	−13.0223	−	13.0223i	−0.549800	−	0.549800i
$562$	−8.79499	−	12.2232i	−0.370994	−	0.515604i
$563$	−9.94373	−	4.11883i	−0.419078	−	0.173588i	0.163172	−	0.986598i	$-0.447828\pi$
$563$	−9.94373	−	4.11883i	−0.419078	−	0.173588i	−0.582250	+	0.813010i	$0.697828\pi$
$564$	−1.26873	+	0.0881085i	−0.0534233	+	0.00371004i
$565$	47.3119	+	19.5972i	1.99043	+	0.824462i
$566$	−34.4399	−	21.3234i	−1.44762	−	0.896291i
$567$	−14.3524			−0.602743
$568$	19.4650	−	6.02873i	0.816733	−	0.252960i
$569$	−6.47792	−	6.47792i	−0.271569	−	0.271569i	0.558163	−	0.829731i	$-0.311506\pi$
$569$	−6.47792	−	6.47792i	−0.271569	−	0.271569i	−0.829731	+	0.558163i	$0.811506\pi$
$570$	2.59067	+	11.0140i	0.108511	+	0.461326i
$571$	−19.9626	+	8.26880i	−0.835411	+	0.346038i	−0.759042	−	0.651041i	$-0.774332\pi$
$571$	−19.9626	+	8.26880i	−0.835411	+	0.346038i	−0.0763683	+	0.997080i	$0.524332\pi$
$572$	−7.49765	−	30.2257i	−0.313493	−	1.26380i
$573$	−3.42211	+	8.26170i	−0.142961	+	0.345137i
$574$	6.28362	−	4.52128i	0.262273	−	0.188715i
$575$		−	11.1645i		−	0.465591i
$576$	−21.1103	−	3.94391i	−0.879594	−	0.164329i
$577$	9.29739	−	9.29739i	0.387056	−	0.387056i	−0.486580	−	0.873636i	$-0.661756\pi$
$577$	9.29739	−	9.29739i	0.387056	−	0.387056i	0.873636	+	0.486580i	$0.161756\pi$
$578$	−33.5580	−	46.6385i	−1.39583	−	1.93991i
$579$	−0.00341778	−	0.00825126i	−0.000142038	−	0.000342911i
$580$	14.8807	−	7.41037i	0.617889	−	0.307699i
$581$	−8.53719	+	3.53622i	−0.354182	+	0.146707i
$582$	−1.02448	−	0.634308i	−0.0424662	−	0.0262929i
$583$			41.0255i			1.69910i
$584$	10.0611	+	32.4842i	0.416330	+	1.34421i
$585$	−6.27240	+	28.1969i	−0.259332	+	1.16580i
$586$	1.18522	+	5.03884i	0.0489608	+	0.208152i
$587$	−3.40778	+	8.22711i	−0.140654	+	0.339569i	−0.978472	−	0.206381i	$-0.933831\pi$
$587$	−3.40778	+	8.22711i	−0.140654	+	0.339569i	0.837818	+	0.545950i	$0.183831\pi$
$588$	−1.28519	+	1.47701i	−0.0530003	+	0.0609110i
$589$	−11.8385	+	28.5806i	−0.487796	+	1.17764i
$590$	4.18262	−	25.6436i	0.172196	−	1.05573i
$591$	−6.10858	+	6.10858i	−0.251273	+	0.251273i
$592$	16.8317	+	28.6372i	0.691780	+	1.17698i
$593$	−19.2190	+	19.2190i	−0.789232	+	0.789232i	−0.981368	−	0.192137i	$-0.938458\pi$
$593$	−19.2190	+	19.2190i	−0.789232	+	0.789232i	0.192137	+	0.981368i	$0.438458\pi$
$594$	15.8303	−	11.3904i	0.649525	−	0.467355i
$595$	47.9932	+	19.8794i	1.96753	+	0.814978i
$596$	5.53579	−	6.36204i	0.226755	−	0.260599i
$597$	−11.3893	+	4.71759i	−0.466132	+	0.193078i
$598$	−10.4275	−	10.1775i	−0.426411	−	0.416189i
$599$	21.1752	−	21.1752i	0.865196	−	0.865196i	−0.126740	−	0.991936i	$-0.540451\pi$
$599$	21.1752	−	21.1752i	0.865196	−	0.865196i	0.991936	+	0.126740i	$0.0404513\pi$
$600$	−3.96595	−	4.77550i	−0.161909	−	0.194959i
$601$	−32.0385	+	32.0385i	−1.30688	+	1.30688i	−0.383219	+	0.923658i	$0.625185\pi$
$601$	−32.0385	+	32.0385i	−1.30688	+	1.30688i	−0.923658	+	0.383219i	$0.874815\pi$
$602$	18.6076	+	11.5209i	0.758391	+	0.469557i
$603$	−27.3483	−	11.3280i	−1.11371	−	0.461313i
$604$	4.35506	−	12.9952i	0.177205	−	0.528768i
$605$	21.0936	−	8.73725i	0.857576	−	0.355220i
$606$	9.36546	−	6.73876i	0.380446	−	0.273743i
$607$		−	21.6218i		−	0.877601i	−0.898584	−	0.438801i	$-0.855403\pi$
$607$		−	21.6218i		−	0.877601i	0.898584	−	0.438801i	$-0.144597\pi$
$608$	25.1718	−	9.75412i	1.02085	−	0.395582i
$609$	2.53657	+	2.53657i	0.102787	+	0.102787i
$610$	6.30498	−	38.6557i	0.255281	−	1.56512i
$611$	4.01995	−	0.705842i	0.162630	−	0.0285553i
$612$	36.4834	−	18.1682i	1.47475	−	0.734405i
$613$	3.28278	−	7.92533i	0.132590	−	0.320101i	−0.843615	−	0.536948i	$-0.819577\pi$
$613$	3.28278	−	7.92533i	0.132590	−	0.320101i	0.976206	+	0.216847i	$0.0695772\pi$
$614$	30.9611	+	19.1695i	1.24949	+	0.773620i
$615$	2.83009	−	2.83009i	0.114120	−	0.114120i
$616$	2.58272	−	27.8878i	0.104061	−	1.12363i
$617$	10.6098			0.427136			0.213568	−	0.976928i	$-0.431492\pi$
$617$	10.6098			0.427136			0.213568	+	0.976928i	$0.431492\pi$
$618$	5.50529	+	3.40860i	0.221455	+	0.137114i
$619$	2.82937	+	1.17196i	0.113722	+	0.0471052i	0.438819	−	0.898575i	$-0.355397\pi$
$619$	2.82937	+	1.17196i	0.113722	+	0.0471052i	−0.325097	+	0.945681i	$0.605397\pi$
$620$	−2.68062	−	38.6001i	−0.107656	−	1.55022i
$621$	3.49198	−	8.43039i	0.140128	−	0.338300i
$622$	−3.36466	+	20.6287i	−0.134911	+	0.827136i
$623$			9.60122i			0.384665i
$624$	−8.07561	−	0.649193i	−0.323283	−	0.0259885i
$625$		−	29.2705i		−	1.17082i
$626$	3.27515	+	0.534196i	0.130901	+	0.0213508i
$627$	−4.43038	+	10.6959i	−0.176932	+	0.427152i
$628$	11.5722	+	10.0693i	0.461783	+	0.401810i
$629$	−58.2424	−	24.1248i	−2.32228	−	0.961918i
$630$	−13.6756	+	22.0877i	−0.544848	+	0.879994i
$631$	−10.8706			−0.432750			−0.216375	−	0.976310i	$-0.569423\pi$
$631$	−10.8706			−0.432750			−0.216375	+	0.976310i	$0.569423\pi$
$632$	−2.73548	+	0.847236i	−0.108811	+	0.0337012i
$633$	6.32606	−	6.32606i	0.251438	−	0.251438i
$634$	−2.18491	+	3.52889i	−0.0867739	+	0.140150i
$635$	7.55299	−	18.2345i	0.299731	−	0.723615i
$636$	10.1198	+	3.39142i	0.401276	+	0.134479i
$637$	3.60763	−	5.14434i	0.142939	−	0.203826i
$638$	16.7877	+	2.73817i	0.664630	+	0.108405i
$639$	−13.6754	−	13.6754i	−0.540989	−	0.540989i
$640$	−22.7444	+	24.9555i	−0.899052	+	0.986454i
$641$			32.4069i			1.28000i	0.768376	+	0.639999i	$0.221065\pi$
$641$			32.4069i			1.28000i	−0.768376	+	0.639999i	$0.778935\pi$
$642$	−8.65763	−	12.0323i	−0.341690	−	0.474876i
$643$	−25.3392	+	10.4958i	−0.999281	+	0.413916i	−0.821533	−	0.570160i	$-0.806881\pi$
$643$	−25.3392	+	10.4958i	−0.999281	+	0.413916i	−0.177748	+	0.984076i	$0.556881\pi$
$644$	−5.84152	−	11.7303i	−0.230188	−	0.462240i
$645$	10.4540	+	4.33017i	0.411624	+	0.170500i
$646$	−26.9699	+	43.5596i	−1.06112	+	1.71383i
$647$	5.92860	−	5.92860i	0.233077	−	0.233077i	−0.580899	−	0.813976i	$-0.697299\pi$
$647$	5.92860	−	5.92860i	0.233077	−	0.233077i	0.813976	+	0.580899i	$0.197299\pi$
$648$	5.23801	+	16.9120i	0.205769	+	0.664366i
$649$	18.7987	−	18.7987i	0.737913	−	0.737913i
$650$	14.2565	+	13.9147i	0.559185	+	0.545780i
$651$	7.71400	−	3.19524i	0.302335	−	0.125231i
$652$	−42.9092	+	2.97987i	−1.68045	+	0.116701i
$653$	1.93017	+	0.799504i	0.0755335	+	0.0312870i	0.420130	−	0.907464i	$-0.361984\pi$
$653$	1.93017	+	0.799504i	0.0755335	+	0.0312870i	−0.344597	+	0.938751i	$0.611984\pi$
$654$	−2.67565	−	3.71859i	−0.104626	−	0.145409i
$655$	−0.673129	+	0.673129i	−0.0263013	+	0.0263013i
$656$	−7.62087	−	5.75418i	−0.297545	−	0.224663i
$657$	22.8222	−	22.8222i	0.890377	−	0.890377i
$658$	3.62276	+	0.590893i	0.141230	+	0.0230354i
$659$	−6.07211	+	14.6594i	−0.236536	+	0.571048i	−0.996920	−	0.0784254i	$-0.975011\pi$
$659$	−6.07211	+	14.6594i	−0.236536	+	0.571048i	0.760384	+	0.649474i	$0.225011\pi$
$660$	−1.00318	−	14.4455i	−0.0390489	−	0.562291i
$661$	3.44087	−	8.30699i	0.133834	−	0.323104i	−0.842728	−	0.538340i	$-0.819052\pi$
$661$	3.44087	−	8.30699i	0.133834	−	0.323104i	0.976562	+	0.215235i	$0.0690518\pi$
$662$	5.29745	−	1.24605i	0.205891	−	0.0484290i
$663$	12.9736	−	8.25195i	0.503852	−	0.320479i
$664$	7.28259	+	8.76915i	0.282619	+	0.340309i
$665$		−	32.6561i		−	1.26635i
$666$	16.5961	−	26.8046i	0.643084	−	1.03866i
$667$	7.35281	−	3.04563i	0.284702	−	0.117927i
$668$	31.9519	+	10.7080i	1.23626	+	0.414304i
$669$	−1.61261	−	3.89317i	−0.0623469	−	0.150519i
$670$	−37.7784	+	27.1828i	−1.45951	+	1.05016i
$671$	28.3376	−	28.3376i	1.09396	−	1.09396i
$672$	−6.66562	−	2.94246i	−0.257132	−	0.113508i
$673$		−	4.73644i		−	0.182576i	−0.995825	−	0.0912881i	$-0.970902\pi$
$673$		−	4.73644i		−	0.182576i	0.995825	−	0.0912881i	$-0.0290984\pi$
$674$	−15.7269	−	21.8570i	−0.605776	−	0.841901i
$675$	−4.77425	+	11.5261i	−0.183761	+	0.443638i
$676$	25.9923	−	0.630735i	0.999706	−	0.0242590i
$677$	−5.58760	+	2.31446i	−0.214749	+	0.0889519i	−0.487465	−	0.873143i	$-0.662078\pi$
$677$	−5.58760	+	2.31446i	−0.214749	+	0.0889519i	0.272716	+	0.962095i	$0.412078\pi$
$678$	13.2695	−	3.12121i	0.509613	−	0.119869i
$679$	2.45913	+	2.45913i	0.0943726	+	0.0943726i
$680$	5.90927	−	63.8075i	0.226610	−	2.44691i
$681$	0.0108332			0.000415128
$682$	20.8413	−	33.6612i	0.798056	−	1.28895i
$683$	−8.51011	−	3.52500i	−0.325630	−	0.134880i	0.213879	−	0.976860i	$-0.431390\pi$
$683$	−8.51011	−	3.52500i	−0.325630	−	0.134880i	−0.539509	+	0.841980i	$0.681390\pi$
$684$	−19.3286	−	16.8183i	−0.739047	−	0.643065i
$685$	−19.5743	−	8.10796i	−0.747897	−	0.309789i
$686$	23.0115	−	16.5575i	0.878582	−	0.632170i
$687$	3.32940	+	3.32940i	0.127025	+	0.127025i
$688$	6.78457	−	26.1308i	0.258659	−	0.996227i
$689$	−33.4346	−	7.43753i	−1.27376	−	0.283347i
$690$	−3.95711	−	5.49955i	−0.150645	−	0.209364i
$691$	−15.3202	−	36.9863i	−0.582809	−	1.40703i	−0.890256	−	0.455460i	$-0.849475\pi$
$691$	−15.3202	−	36.9863i	−0.582809	−	1.40703i	0.307447	−	0.951565i	$-0.400525\pi$
$692$	13.1723	+	11.4616i	0.500737	+	0.435705i
$693$	−24.5580	+	10.1723i	−0.932882	+	0.386412i
$694$	−17.0997	+	27.6180i	−0.649096	+	1.04837i
$695$			3.12385i			0.118495i
$696$	2.06320	−	3.91468i	0.0782054	−	0.148386i
$697$	18.1229			0.686452
$698$	14.5456	+	9.00593i	0.550560	+	0.340879i
$699$	−6.26486	+	2.59499i	−0.236959	+	0.0981515i
$700$	7.98655	+	16.0378i	0.301863	+	0.606170i
$701$	5.56687	+	2.30587i	0.210258	+	0.0870916i	0.485327	−	0.874333i	$-0.338701\pi$
$701$	5.56687	+	2.30587i	0.210258	+	0.0870916i	−0.275069	+	0.961425i	$0.588701\pi$
$702$	6.41300	+	14.9662i	0.242043	+	0.564864i
$703$			39.6300i			1.49467i
$704$	−33.8040	+	7.13456i	−1.27404	+	0.268894i
$705$	1.89779			0.0714751
$706$	−12.7821	−	2.08484i	−0.481062	−	0.0784641i
$707$	−30.7657	+	12.7436i	−1.15706	+	0.479271i
$708$	−3.08308	−	6.19111i	−0.115869	−	0.232676i
$709$	17.6647	+	7.31694i	0.663410	+	0.274794i	0.688873	−	0.724882i	$-0.258106\pi$
$709$	17.6647	+	7.31694i	0.663410	+	0.274794i	−0.0254625	+	0.999676i	$0.508106\pi$
$710$	−29.5996	+	6.96231i	−1.11085	+	0.261291i
$711$	1.92184	+	1.92184i	0.0720746	+	0.0720746i
$712$	11.3135	−	3.50404i	0.423992	−	0.131319i
$713$		−	18.5243i		−	0.693740i
$714$	13.4606	−	3.16615i	0.503750	−	0.118490i
$715$	8.03656	+	45.7703i	0.300550	+	1.71171i
$716$	11.8054	−	13.5674i	0.441187	−	0.507037i
$717$	13.5310	−	5.60472i	0.505324	−	0.209312i
$718$	−34.2053	+	24.6119i	−1.27653	+	0.918508i
$719$			19.3072i			0.720039i	0.932945	+	0.360019i	$0.117230\pi$
$719$			19.3072i			0.720039i	−0.932945	+	0.360019i	$0.882770\pi$
$720$	31.0178	+	8.05343i	1.15597	+	0.300134i
$721$	−13.2147	−	13.2147i	−0.492140	−	0.492140i
$722$	5.26731	+	0.859130i	0.196029	+	0.0319735i
$723$	−1.70039	+	0.704326i	−0.0632383	+	0.0261942i
$724$	−1.62656	−	23.4220i	−0.0604507	−	0.870470i
$725$	−10.0528	+	4.16400i	−0.373351	+	0.154647i
$726$	3.19933	−	5.16729i	0.118738	−	0.191776i
$727$	22.1623	+	22.1623i	0.821956	+	0.821956i	0.986388	−	0.164432i	$-0.0525792\pi$
$727$	22.1623	+	22.1623i	0.821956	+	0.821956i	−0.164432	+	0.986388i	$0.552579\pi$
$728$	22.2596	+	7.16064i	0.824995	+	0.265391i
$729$	8.07651	−	8.07651i	0.299130	−	0.299130i
$730$	−11.6191	−	49.3974i	−0.430041	−	1.82828i
$731$	19.6072	+	47.3360i	0.725199	+	1.75078i
$732$	−4.64749	−	9.33261i	−0.171776	−	0.344943i
$733$	16.1404	+	38.9665i	0.596161	+	1.43926i	0.877465	+	0.479641i	$0.159233\pi$
$733$	16.1404	+	38.9665i	0.596161	+	1.43926i	−0.281304	+	0.959619i	$0.590767\pi$
$734$	7.24350	+	10.0669i	0.267362	+	0.371577i
$735$	2.06588	−	2.06588i	0.0762010	−	0.0762010i
$736$	−11.6904	+	11.1644i	−0.430915	+	0.411524i
$737$	−47.6215			−1.75416
$738$	−1.45897	+	8.94491i	−0.0537054	+	0.329267i
$739$	12.9292	+	31.2138i	0.475607	+	1.14822i	0.961649	+	0.274282i	$0.0884401\pi$
$739$	12.9292	+	31.2138i	0.475607	+	1.14822i	−0.486042	+	0.873935i	$0.661560\pi$
$740$	−22.0959	−	44.3706i	−0.812260	−	1.63109i
$741$	−7.91365	−	5.54970i	−0.290715	−	0.203873i
$742$	−26.1906	−	16.2159i	−0.961486	−	0.595304i
$743$	20.3591			0.746904			0.373452	−	0.927649i	$-0.378174\pi$
$743$	20.3591			0.746904			0.373452	+	0.927649i	$0.378174\pi$
$744$	−6.58037	−	7.92359i	−0.241248	−	0.290493i
$745$	−8.89850	+	8.89850i	−0.326016	+	0.326016i
$746$	−12.9655	+	20.9408i	−0.474700	+	0.766697i
$747$	4.14009	−	9.99506i	0.151478	−	0.365700i
$748$	43.0398	−	49.4638i	1.57369	−	1.80858i
$749$	16.3723	+	39.5263i	0.598232	+	1.44426i
$750$	−1.51364	−	2.10364i	−0.0552704	−	0.0768142i
$751$		−	9.18065i		−	0.335007i	−0.985872	−	0.167503i	$-0.946430\pi$
$751$		−	9.18065i		−	0.335007i	0.985872	−	0.167503i	$-0.0535705\pi$
$752$	−0.625879	−	4.48450i	−0.0228235	−	0.163533i
$753$	12.0489			0.439086
$754$	−5.27498	+	13.1851i	−0.192103	+	0.480172i
$755$	−7.82655	+	18.8950i	−0.284837	+	0.687658i
$756$	1.01448	+	14.6083i	0.0368965	+	0.531297i
$757$	−3.31231	−	7.99661i	−0.120388	−	0.290642i	0.852185	−	0.523241i	$-0.175277\pi$
$757$	−3.31231	−	7.99661i	−0.120388	−	0.290642i	−0.972573	+	0.232599i	$0.925277\pi$
$758$	8.55640	+	36.3767i	0.310782	+	1.32126i
$759$		−	6.93244i		−	0.251632i
$760$	−38.4800	+	11.9181i	−1.39582	+	0.432315i
$761$	−35.1003			−1.27238			−0.636192	−	0.771531i	$-0.719491\pi$
$761$	−35.1003			−1.27238			−0.636192	+	0.771531i	$0.719491\pi$
$762$	−1.20295	−	5.11422i	−0.0435782	−	0.185269i
$763$	5.05989	+	12.2157i	0.183180	+	0.442236i
$764$	−30.1876	−	10.1167i	−1.09215	−	0.366009i
$765$	−56.1888	+	23.2742i	−2.03151	+	0.841480i
$766$	−1.88939	+	11.5838i	−0.0682665	+	0.418541i
$767$	11.9124	+	18.7284i	0.430131	+	0.676244i
$768$	−1.03456	+	8.92825i	−0.0373314	+	0.322170i
$769$	−4.27039	+	4.27039i	−0.153994	+	0.153994i	−0.779899	−	0.625905i	$-0.784730\pi$
$769$	−4.27039	+	4.27039i	−0.153994	+	0.153994i	0.625905	+	0.779899i	$0.284730\pi$
$770$	−6.72778	+	41.2479i	−0.242452	+	1.48647i
$771$	−2.38687	+	5.76240i	−0.0859609	+	0.207528i
$772$	0.0284634	−	0.0141743i	0.00102442	−	0.000510146i
$773$	3.42003	−	8.25667i	0.123010	−	0.296972i	−0.850364	−	0.526195i	$-0.823618\pi$
$773$	3.42003	−	8.25667i	0.123010	−	0.296972i	0.973374	+	0.229223i	$0.0736184\pi$
$774$	−24.9421	+	5.86679i	−0.896526	+	0.210878i
$775$			25.3265i			0.909753i
$776$	2.00021	−	3.79517i	0.0718034	−	0.136239i
$777$	7.56340	−	7.56340i	0.271335	−	0.271335i
$778$	−1.20583	+	1.94756i	−0.0432310	+	0.0698232i
$779$	−4.35980	−	10.5255i	−0.156206	−	0.377115i
$780$	11.9546	+	1.80127i	0.428042	+	0.0644958i
$781$	−28.7446	−	11.9064i	−1.02856	−	0.426045i
$782$	4.93859	−	30.2784i	0.176604	−	1.08275i
$783$	−8.89335			−0.317823
$784$	−5.56298	−	4.20036i	−0.198678	−	0.150013i
$785$	−16.1859	−	16.1859i	−0.577701	−	0.577701i
$786$	−0.0407920	+	0.250095i	−0.00145500	+	0.00892061i
$787$	−26.4258	+	10.9459i	−0.941977	+	0.390180i	−0.800210	−	0.599720i	$-0.795278\pi$
$787$	−26.4258	+	10.9459i	−0.941977	+	0.390180i	−0.141767	+	0.989900i	$0.545278\pi$
$788$	−23.2029	−	20.1894i	−0.826568	−	0.719219i
$789$	−6.56378	−	15.8464i	−0.233677	−	0.564146i
$790$	4.15972	−	0.978435i	0.147996	−	0.0348111i
$791$	−39.3436			−1.39890
$792$	20.9490	+	25.2253i	0.744391	+	0.896341i
$793$	17.9570	+	28.2316i	0.637671	+	1.00253i
$794$	−14.8914	+	24.0514i	−0.528478	+	0.853554i
$795$	−14.7141	−	6.09479i	−0.521856	−	0.216160i
$796$	−19.5649	−	39.2882i	−0.693460	−	1.39253i
$797$	−21.7208	−	8.99705i	−0.769390	−	0.318692i	−0.0367647	−	0.999324i	$-0.511705\pi$
$797$	−21.7208	−	8.99705i	−0.769390	−	0.318692i	−0.732625	+	0.680632i	$0.761705\pi$
$798$	−5.07706	−	7.05604i	−0.179726	−	0.249781i
$799$	6.07638	+	6.07638i	0.214967	+	0.214967i
$800$	15.9832	−	15.2640i	0.565091	−	0.539663i
$801$	−7.94844	−	7.94844i	−0.280844	−	0.280844i
$802$	−5.02056	−	0.818884i	−0.177282	−	0.0289158i
$803$	19.8701	−	47.9706i	0.701199	−	1.69285i
$804$	−3.93669	+	11.7468i	−0.138836	+	0.414279i
$805$	7.48323	+	18.0661i	0.263749	+	0.636747i
$806$	23.6546	+	23.0875i	0.833197	+	0.813224i
$807$	7.89209	+	7.89209i	0.277815	+	0.277815i
$808$	26.2445	+	31.6016i	0.923277	+	1.11174i
$809$	11.4342	+	11.4342i	0.402005	+	0.402005i	0.878939	−	0.476934i	$-0.158252\pi$
$809$	11.4342	+	11.4342i	0.402005	+	0.402005i	−0.476934	+	0.878939i	$0.658252\pi$
$810$	−6.04914	−	25.7174i	−0.212545	−	0.903616i
$811$	−5.97638	+	14.4282i	−0.209859	+	0.506644i	−0.993401	−	0.114695i	$-0.963411\pi$
$811$	−5.97638	+	14.4282i	−0.209859	+	0.506644i	0.783542	+	0.621339i	$0.213411\pi$
$812$	−8.38360	+	9.63491i	−0.294207	+	0.338119i
$813$	1.98125	+	4.78317i	0.0694856	+	0.167753i
$814$	8.16453	−	50.0566i	0.286167	−	1.75448i
$815$	64.1844			2.24828
$816$	−8.64336	−	14.7057i	−0.302578	−	0.514801i
$817$	22.7751	−	22.7751i	0.796801	−	0.796801i
$818$	−20.3309	+	14.6287i	−0.710852	+	0.511482i
$819$	−3.83797	−	21.8582i	−0.134109	−	0.763788i
$820$	10.7498	+	9.35374i	0.375401	+	0.326647i
$821$	44.1761	+	18.2983i	1.54176	+	0.638616i	0.981802	−	0.189908i	$-0.0608190\pi$
$821$	44.1761	+	18.2983i	1.54176	+	0.638616i	0.559953	+	0.828524i	$0.310819\pi$
$822$	−5.48999	+	1.29134i	−0.191485	+	0.0450405i
$823$	5.00957	+	5.00957i	0.174623	+	0.174623i	0.789007	−	0.614384i	$-0.210596\pi$
$823$	5.00957	+	5.00957i	0.174623	+	0.174623i	−0.614384	+	0.789007i	$0.710596\pi$
$824$	−10.7486	+	20.3942i	−0.374445	+	0.710464i
$825$			9.47806i			0.329984i
$826$	4.57060	+	19.4315i	0.159031	+	0.676108i
$827$	3.48906	−	8.42334i	0.121327	−	0.292908i	−0.851534	−	0.524299i	$-0.824328\pi$
$827$	3.48906	−	8.42334i	0.121327	−	0.292908i	0.972861	+	0.231391i	$0.0743275\pi$
$828$	14.5470	+	4.87509i	0.505543	+	0.169421i
$829$	19.9137	+	8.24852i	0.691631	+	0.286483i	0.700680	−	0.713476i	$-0.252880\pi$
$829$	19.9137	+	8.24852i	0.691631	+	0.286483i	−0.00904854	+	0.999959i	$0.502880\pi$
$830$	−9.93459	−	13.8070i	−0.344835	−	0.479247i
$831$	−15.3888			−0.533831
$832$	0.313882	−	28.8427i	0.0108819	−	0.999941i
$833$	13.2291			0.458361
$834$	0.485667	+	0.674974i	0.0168173	+	0.0233724i
$835$	−46.4579	−	19.2435i	−1.60774	−	0.665949i
$836$	−39.0819	−	13.0974i	−1.35168	−	0.452984i
$837$	−7.92152	+	19.1242i	−0.273808	+	0.661030i
$838$	−7.21535	−	30.6754i	−0.249250	−	1.05966i
$839$			33.5673i			1.15887i	0.815017	+	0.579437i	$0.196727\pi$
$839$			33.5673i			1.15887i	−0.815017	+	0.579437i	$0.803273\pi$
$840$	9.61851	+	5.06936i	0.331870	+	0.174909i
$841$	15.0214	+	15.0214i	0.517978	+	0.517978i
$842$	42.2161	−	9.92991i	1.45486	−	0.342207i
$843$	5.52617	+	2.28901i	0.190331	+	0.0788379i
$844$	24.0290	+	20.9082i	0.827111	+	0.719691i
$845$	−38.7584	−	1.74815i	−1.33333	−	0.0601383i
$846$	−3.48830	+	2.50995i	−0.119930	+	0.0862939i
$847$	−12.4034	+	12.4034i	−0.426184	+	0.426184i
$848$	−9.54939	+	36.7795i	−0.327927	+	1.26301i
$849$	16.0900			0.552206
$850$	−6.75206	+	41.3968i	−0.231594	+	1.41990i
$851$	−9.08131	−	21.9242i	−0.311303	−	0.751553i
$852$	−5.31318	+	6.10621i	−0.182027	+	0.209195i
$853$	2.75027	−	6.63974i	0.0941674	−	0.227340i	−0.869776	−	0.493446i	$-0.835737\pi$
$853$	2.75027	−	6.63974i	0.0941674	−	0.227340i	0.963944	+	0.266106i	$0.0857370\pi$
$854$	6.88982	+	29.2914i	0.235765	+	1.00233i
$855$	27.0346	+	27.0346i	0.924564	+	0.924564i
$856$	40.6002	−	33.7176i	1.38769	−	1.15244i
$857$	21.8315	+	21.8315i	0.745748	+	0.745748i	0.973678	−	0.227929i	$-0.0731956\pi$
$857$	21.8315	+	21.8315i	0.745748	+	0.745748i	−0.227929	+	0.973678i	$0.573196\pi$
$858$	8.85239	+	8.64018i	0.302216	+	0.294971i
$859$	−5.44024	−	13.1339i	−0.185619	−	0.448123i	0.803489	−	0.595320i	$-0.202975\pi$
$859$	−5.44024	−	13.1339i	−0.185619	−	0.448123i	−0.989107	+	0.147197i	$0.952975\pi$
$860$	−12.8012	+	38.1979i	−0.436516	+	1.30254i
$861$	−1.17672	+	2.84086i	−0.0401026	+	0.0968163i
$862$	37.7679	+	6.16017i	1.28638	+	0.209816i
$863$	10.4855	+	10.4855i	0.356931	+	0.356931i	0.862681	−	0.505749i	$-0.168784\pi$
$863$	10.4855	+	10.4855i	0.356931	+	0.356931i	−0.505749	+	0.862681i	$0.668784\pi$
$864$	16.8433	−	6.52680i	0.573019	−	0.222046i
$865$	−18.4239	−	18.4239i	−0.626433	−	0.626433i
$866$	−21.5196	−	29.9077i	−0.731265	−	1.01630i
$867$	21.0856	+	8.73392i	0.716103	+	0.296620i
$868$	13.2514	+	26.6101i	0.449782	+	0.903206i
$869$	4.03957	+	1.67325i	0.137033	+	0.0567610i
$870$	−3.47606	+	5.61425i	−0.117849	+	0.190341i
$871$	8.63333	−	38.8102i	0.292529	−	1.31503i
$872$	12.5476	−	10.4205i	0.424914	−	0.352882i
$873$	−4.07161			−0.137803
$874$	−18.7733	+	4.41579i	−0.635018	+	0.149366i
$875$	2.86243	+	6.91051i	0.0967677	+	0.233618i
$876$	−10.1904	−	8.86692i	−0.344301	−	0.299585i
$877$	13.6474	−	5.65292i	0.460839	−	0.190886i	−0.140171	−	0.990127i	$-0.544765\pi$
$877$	13.6474	−	5.65292i	0.460839	−	0.190886i	0.601010	+	0.799242i	$0.294765\pi$
$878$	−0.0629615	+	0.386016i	−0.00212485	+	0.0130274i
$879$	−1.45391	−	1.45391i	−0.0490390	−	0.0490390i
$880$	51.0595	−	7.12612i	1.72121	−	0.240221i
$881$	10.2987			0.346973			0.173487	−	0.984836i	$-0.444497\pi$
$881$	10.2987			0.346973			0.173487	+	0.984836i	$0.444497\pi$
$882$	−1.06500	+	6.52949i	−0.0358604	+	0.219860i
$883$	−26.0338	−	10.7836i	−0.876108	−	0.362896i	−0.101122	−	0.994874i	$-0.532243\pi$
$883$	−26.0338	−	10.7836i	−0.876108	−	0.362896i	−0.774986	+	0.631978i	$0.782243\pi$
$884$	32.5089	+	44.0436i	1.09339	+	1.48135i
$885$	3.94955	+	9.53505i	0.132763	+	0.320517i
$886$	23.3337	−	37.6867i	0.783912	−	1.26611i
$887$	38.3160	−	38.3160i	1.28652	−	1.28652i	0.349639	−	0.936884i	$-0.386304\pi$
$887$	38.3160	−	38.3160i	1.28652	−	1.28652i	0.936884	−	0.349639i	$-0.113696\pi$
$888$	−11.6726	−	6.15194i	−0.391706	−	0.206446i
$889$			15.1635i			0.508566i
$890$	−17.2040	+	4.04666i	−0.576679	+	0.135644i
$891$	10.3448	−	24.9746i	0.346564	−	0.836679i
$892$	13.4298	−	6.68785i	0.449664	−	0.223926i
$893$	2.06728	−	4.99086i	0.0691790	−	0.167013i
$894$	−0.539254	+	3.30616i	−0.0180354	+	0.110574i
$895$	−18.9765	+	18.9765i	−0.634315	+	0.634315i
$896$	8.80680	−	24.4004i	0.294215	−	0.815160i
$897$	5.64974	+	1.25679i	0.188639	+	0.0419629i
$898$	0.205992	−	1.26293i	0.00687405	−	0.0421447i
$899$	−16.6798	+	6.90898i	−0.556301	+	0.230427i
$900$	−19.8887	−	6.66524i	−0.662956	−	0.222175i
$901$	−27.5975	−	66.6262i	−0.919405	−	2.21964i
$902$	3.33841	+	14.1929i	0.111157	+	0.472573i
$903$	−8.69329			−0.289295
$904$	14.3587	+	46.3602i	0.477565	+	1.54192i
$905$			35.0350i			1.16460i
$906$	1.24652	+	5.29945i	0.0414127	+	0.176062i
$907$	6.54445	+	15.7997i	0.217305	+	0.524621i	0.994512	−	0.104625i	$-0.0333641\pi$
$907$	6.54445	+	15.7997i	0.217305	+	0.524621i	−0.777207	+	0.629245i	$0.783364\pi$
$908$	0.00267206	+	0.0384768i	8.86754e−5	+	0.00127690i
$909$	14.9197	−	36.0195i	0.494857	−	1.19469i
$910$	−32.3962	−	12.9608i	−1.07392	−	0.429647i
$911$	29.2848			0.970250			0.485125	−	0.874445i	$-0.338774\pi$
$911$	29.2848			0.970250			0.485125	+	0.874445i	$0.338774\pi$
$912$	−6.46151	+	8.55766i	−0.213962	+	0.283372i
$913$		−	17.4044i		−	0.576000i
$914$	−25.8402	−	35.9124i	−0.854718	−	1.18788i
$915$	5.95363	+	14.3733i	0.196821	+	0.475168i
$916$	−11.0040	+	12.6464i	−0.363582	+	0.417850i
$917$	0.279880	−	0.675691i	0.00924246	−	0.0223133i
$918$	−18.0465	+	29.1472i	−0.595623	+	0.962001i
$919$	−14.6021	+	14.6021i	−0.481679	+	0.481679i	−0.905668	−	0.423988i	$-0.860630\pi$
$919$	−14.6021	+	14.6021i	−0.481679	+	0.481679i	0.423988	+	0.905668i	$0.360630\pi$
$920$	18.5570	−	15.4112i	0.611806	−	0.508091i
$921$	−14.4647			−0.476628
$922$	−26.4988	−	16.4068i	−0.872693	−	0.540328i
$923$	14.9145	−	21.2675i	0.490918	−	0.700030i
$924$	4.95915	+	9.95845i	0.163144	+	0.327609i
$925$	12.4160	+	29.9749i	0.408236	+	0.985568i
$926$	3.85019	−	23.6055i	0.126525	−	0.775724i
$927$	21.8797			0.718623
$928$	14.4129	+	6.36240i	0.473126	+	0.208856i
$929$	12.0905	−	12.0905i	0.396678	−	0.396678i	−0.480382	−	0.877059i	$-0.659502\pi$
$929$	12.0905	−	12.0905i	0.396678	−	0.396678i	0.877059	+	0.480382i	$0.159502\pi$
$930$	8.97665	+	12.4756i	0.294356	+	0.409093i
$931$	−3.18251	−	7.68326i	−0.104303	−	0.251809i
$932$	−10.7620	−	21.6112i	−0.352522	−	0.707897i
$933$	−3.17717	−	7.67037i	−0.104016	−	0.251117i
$934$	−10.6146	−	45.1268i	−0.347319	−	1.47660i
$935$	−69.1843	+	69.1843i	−2.26257	+	2.26257i
$936$	−24.3557	+	12.4998i	−0.796092	+	0.408567i
$937$	−37.9446	−	37.9446i	−1.23960	−	1.23960i	−0.960166	−	0.279432i	$-0.909854\pi$
$937$	−37.9446	−	37.9446i	−1.23960	−	1.23960i	−0.279432	−	0.960166i	$-0.590146\pi$
$938$	18.8230	−	30.4014i	0.614594	−	0.992642i
$939$	−1.21780	+	0.504429i	−0.0397413	+	0.0164614i
$940$	0.468101	+	6.74050i	0.0152678	+	0.219851i
$941$	14.2001	−	5.88186i	0.462909	−	0.191743i	−0.139025	−	0.990289i	$-0.544397\pi$
$941$	14.2001	−	5.88186i	0.462909	−	0.191743i	0.601934	+	0.798546i	$0.294397\pi$
$942$	−6.01374	−	0.980877i	−0.195938	−	0.0319587i
$943$	4.82388	+	4.82388i	0.157087	+	0.157087i
$944$	21.2288	−	12.4774i	0.690940	−	0.406104i
$945$		−	21.8513i		−	0.710823i
$946$	−33.4594	+	24.0752i	−1.08786	+	0.782751i
$947$	−25.5360	+	10.5774i	−0.829809	+	0.343718i	−0.756827	−	0.653615i	$-0.773252\pi$
$947$	−25.5360	+	10.5774i	−0.829809	+	0.343718i	−0.0729818	+	0.997333i	$0.523252\pi$
$948$	0.746678	−	0.858125i	0.0242510	−	0.0278706i
$949$	35.4924	+	24.8901i	1.15213	+	0.807968i
$950$	25.6670	−	6.03729i	0.832747	−	0.195876i
$951$		−	1.64866i		−	0.0534615i
$952$	14.5655	+	47.0278i	0.472071	+	1.52418i
$953$	−11.0742	−	11.0742i	−0.358729	−	0.358729i	0.504615	−	0.863344i	$-0.331634\pi$
$953$	−11.0742	−	11.0742i	−0.358729	−	0.358729i	−0.863344	+	0.504615i	$0.831634\pi$
$954$	35.1065	−	8.25761i	1.13661	−	0.267350i
$955$	43.8926	+	18.1809i	1.42033	+	0.588320i
$956$	23.2441	+	46.6763i	0.751767	+	1.50962i
$957$	−6.24216	+	2.58559i	−0.201780	+	0.0835801i
$958$	−35.2504	−	5.74955i	−1.13889	−	0.185760i
$959$	16.2776			0.525632
$960$	2.46309	−	13.1840i	0.0794958	−	0.425511i
$961$			11.0221i			0.355551i
$962$	39.3145	+	15.7286i	1.26755	+	0.507112i
$963$	−46.2761	−	19.1682i	−1.49122	−	0.617686i
$964$	−2.92100	−	5.86565i	−0.0940791	−	0.188920i
$965$	−0.0438371	+	0.0181579i	−0.00141117	+	0.000584524i
$966$	4.42566	+	2.74014i	0.142393	+	0.0881627i
$967$	−13.2089			−0.424771			−0.212386	−	0.977186i	$-0.568123\pi$
$967$	−13.2089			−0.424771			−0.212386	+	0.977186i	$0.568123\pi$
$968$	19.1421	+	10.0887i	0.615250	+	0.324263i
$969$		−	20.3506i		−	0.653756i
$970$	−3.36994	+	5.44285i	−0.108202	+	0.174759i
$971$	26.8469	−	11.1203i	0.861558	−	0.356869i	0.0922411	−	0.995737i	$-0.470597\pi$
$971$	26.8469	−	11.1203i	0.861558	−	0.356869i	0.769316	+	0.638868i	$0.220597\pi$
$972$	−19.7591	−	17.1929i	−0.633773	−	0.551463i
$973$	−0.918437	−	2.21730i	−0.0294437	−	0.0710835i
$974$	−2.88223	−	4.00569i	−0.0923525	−	0.128350i
$975$	−7.72435	−	1.71828i	−0.247377	−	0.0550291i
$976$	32.0008	−	18.8087i	1.02432	−	0.602051i
$977$	34.4052	+	34.4052i	1.10072	+	1.10072i	0.994324	+	0.106395i	$0.0339310\pi$
$977$	34.4052	+	34.4052i	1.10072	+	1.10072i	0.106395	+	0.994324i	$0.466069\pi$
$978$	13.8684	−	9.97877i	0.443462	−	0.319086i
$979$	−16.7071	−	6.92029i	−0.533960	−	0.221174i
$980$	7.84704	+	6.82792i	0.250664	+	0.218110i
$981$	−14.3017	−	5.92395i	−0.456617	−	0.189137i
$982$	−9.36985	+	15.1334i	−0.299004	+	0.482927i
$983$	−11.6411			−0.371294			−0.185647	−	0.982616i	$-0.559438\pi$
$983$	−11.6411			−0.371294			−0.185647	+	0.982616i	$0.559438\pi$
$984$	3.77696	+	0.349788i	0.120405	+	0.0111508i
$985$	32.4535	+	32.4535i	1.03405	+	1.03405i
$986$	−29.1055	+	6.84608i	−0.926907	+	0.218024i
$987$	−1.34705	+	0.557966i	−0.0428771	+	0.0177603i
$988$	17.7592	−	29.4762i	0.564996	−	0.937763i
$989$	−7.38075	+	17.8187i	−0.234694	+	0.566602i
$990$	−28.5777	−	39.7170i	−0.908260	−	1.26229i
$991$			2.85627i			0.0907325i	0.998970	+	0.0453662i	$0.0144455\pi$
$991$			2.85627i			0.0907325i	−0.998970	+	0.0453662i	$0.985555\pi$
$992$	26.5196	−	25.3262i	0.841997	−	0.804109i
$993$	−1.52853	+	1.52853i	−0.0485063	+	0.0485063i
$994$	18.9627	−	13.6443i	0.601462	−	0.432772i
$995$	25.0635	+	60.5086i	0.794566	+	1.91825i
$996$	−4.29315	−	1.43875i	−0.136034	−	0.0455886i
$997$	47.7637	−	19.7844i	1.51269	−	0.626578i	0.536581	−	0.843849i	$-0.319715\pi$
$997$	47.7637	−	19.7844i	1.51269	−	0.626578i	0.976111	+	0.217271i	$0.0697155\pi$
$998$	−0.381326	+	0.615886i	−0.0120707	+	0.0194955i
$999$			26.5177i			0.838984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bd.a.83.17	✓	216
13.8	odd	4		416.2.bi.a.307.44	yes	216
32.27	odd	8		416.2.bi.a.187.44	yes	216
416.411	even	8	inner	416.2.bd.a.411.17	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bd.a.83.17	✓	216	1.1	even	1	trivial
416.2.bd.a.411.17	yes	216	416.411	even	8	inner
416.2.bi.a.187.44	yes	216	32.27	odd	8
416.2.bi.a.307.44	yes	216	13.8	odd	4

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.825979 - 1.14794i) q^{2} +(0.518989 + 0.214972i) q^{3} +(-0.635517 + 1.89634i) q^{4} +(1.14210 - 2.75727i) q^{5} +(-0.181899 - 0.773329i) q^{6} +2.29289i q^{7} +(2.70181 - 0.836807i) q^{8} +(-1.89818 - 1.89818i) q^{9} +(-4.10852 + 0.966391i) q^{10} +(-3.98985 - 1.65265i) q^{11} +(-0.737487 + 0.847562i) q^{12} +(2.07019 - 2.95200i) q^{13} +(2.63209 - 1.89388i) q^{14} +(1.18547 - 1.18547i) q^{15} +(-3.19224 - 2.41032i) q^{16} +7.59132 q^{17} +(-0.611134 + 3.74686i) q^{18} +(-1.82624 - 4.40893i) q^{19} +(4.50291 + 3.91810i) q^{20} +(-0.492907 + 1.18998i) q^{21} +(1.39840 + 5.94515i) q^{22} +(2.02063 + 2.02063i) q^{23} +(1.58210 + 0.146519i) q^{24} +(-2.76262 - 2.76262i) q^{25} +(-5.09864 + 0.0618532i) q^{26} +(-1.22200 - 2.95016i) q^{27} +(-4.34811 - 1.45717i) q^{28} +(1.06580 - 2.57307i) q^{29} +(-2.34002 - 0.381672i) q^{30} +(-4.58378 - 4.58378i) q^{31} +(-0.130169 + 5.65536i) q^{32} +(-1.71541 - 1.71541i) q^{33} +(-6.27027 - 8.71436i) q^{34} +(6.32212 + 2.61871i) q^{35} +(4.80594 - 2.39328i) q^{36} +(-7.67223 - 3.17794i) q^{37} +(-3.55273 + 5.73809i) q^{38} +(1.70900 - 1.08702i) q^{39} +(0.778425 - 8.40533i) q^{40} +2.38731 q^{41} +(1.77316 - 0.417075i) q^{42} +(2.58284 + 6.23554i) q^{43} +(5.66961 - 6.51584i) q^{44} +(-7.40172 + 3.06589i) q^{45} +(0.650558 - 3.98856i) q^{46} +(0.800438 + 0.800438i) q^{47} +(-1.13858 - 1.93717i) q^{48} +1.74266 q^{49} +(-0.889445 + 5.45317i) q^{50} +(3.93981 + 1.63192i) q^{51} +(4.28238 + 5.80183i) q^{52} +(-3.63540 - 8.77663i) q^{53} +(-2.37725 + 3.83954i) q^{54} +(-9.11361 + 9.11361i) q^{55} +(1.91871 + 6.19494i) q^{56} -2.68077i q^{57} +(-3.83404 + 0.901829i) q^{58} +(-2.35581 + 5.68744i) q^{59} +(1.49468 + 3.00145i) q^{60} +(-3.55120 + 8.57336i) q^{61} +(-1.47578 + 9.04799i) q^{62} +(4.35233 - 4.35233i) q^{63} +(6.59951 - 4.52178i) q^{64} +(-5.77512 - 9.07954i) q^{65} +(-0.552290 + 3.38608i) q^{66} +(10.1877 - 4.21989i) q^{67} +(-4.82441 + 14.3958i) q^{68} +(0.614306 + 1.48307i) q^{69} +(-2.21583 - 9.42038i) q^{70} +7.20444 q^{71} +(-6.71694 - 3.54011i) q^{72} +12.0231i q^{73} +(2.68903 + 11.4321i) q^{74} +(-0.839881 - 2.02765i) q^{75} +(9.52144 - 0.661226i) q^{76} +(3.78934 - 9.14829i) q^{77} +(-2.65944 - 1.06397i) q^{78} -1.01246 q^{79} +(-10.2917 + 6.04904i) q^{80} +6.25952i q^{81} +(-1.97187 - 2.74048i) q^{82} +(1.54226 + 3.72333i) q^{83} +(-1.94337 - 1.69098i) q^{84} +(8.67004 - 20.9313i) q^{85} +(5.02463 - 8.11537i) q^{86} +(1.10627 - 1.10627i) q^{87} +(-12.1628 - 1.12640i) q^{88} +4.18739 q^{89} +(9.63312 + 5.96434i) q^{90} +(6.76862 + 4.74671i) q^{91} +(-5.11596 + 2.54767i) q^{92} +(-1.39354 - 3.36431i) q^{93} +(0.257707 - 1.58000i) q^{94} -14.2423 q^{95} +(-1.28330 + 2.90708i) q^{96} +(1.07250 - 1.07250i) q^{97} +(-1.43940 - 2.00046i) q^{98} +(4.43644 + 10.7105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24}+ \cdots - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

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