LMFDB - Embedded newform 425.2.k.b.86.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] 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("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.13
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.589613 - 0.428379i) q^{2} +(0.387406 - 1.19231i) q^{3} +(-0.453899 + 1.39696i) q^{4} +(-2.22905 + 0.177058i) q^{5} +(-0.282342 - 0.868960i) q^{6} +2.48707 q^{7} +(0.781226 + 2.40437i) q^{8} +(1.15552 + 0.839535i) q^{9} +(-1.23843 + 1.05927i) q^{10} +(5.16963 - 3.75596i) q^{11} +(1.48977 + 1.08238i) q^{12} +(-1.27127 - 0.923630i) q^{13} +(1.46641 - 1.06541i) q^{14} +(-0.652438 + 2.72632i) q^{15} +(-0.886046 - 0.643750i) q^{16} +(0.309017 + 0.951057i) q^{17} +1.04095 q^{18} +(1.25923 + 3.87551i) q^{19} +(0.764420 - 3.19425i) q^{20} +(0.963506 - 2.96537i) q^{21} +(1.43911 - 4.42912i) q^{22} +(2.99048 - 2.17271i) q^{23} +3.16941 q^{24} +(4.93730 - 0.789340i) q^{25} -1.14522 q^{26} +(4.49138 - 3.26318i) q^{27} +(-1.12888 + 3.47433i) q^{28} +(0.0835365 - 0.257099i) q^{29} +(0.783211 + 1.88696i) q^{30} +(2.06091 + 6.34281i) q^{31} -5.85440 q^{32} +(-2.47553 - 7.61891i) q^{33} +(0.589613 + 0.428379i) q^{34} +(-5.54379 + 0.440355i) q^{35} +(-1.69729 + 1.23315i) q^{36} +(-7.98027 - 5.79801i) q^{37} +(2.40264 + 1.74562i) q^{38} +(-1.59376 + 1.15793i) q^{39} +(-2.16710 - 5.22113i) q^{40} +(-1.88236 - 1.36761i) q^{41} +(-0.702204 - 2.16116i) q^{42} -4.37239 q^{43} +(2.90042 + 8.92658i) q^{44} +(-2.72436 - 1.66677i) q^{45} +(0.832481 - 2.56211i) q^{46} +(-2.00268 + 6.16361i) q^{47} +(-1.11081 + 0.807052i) q^{48} -0.814496 q^{49} +(2.57296 - 2.58044i) q^{50} +1.25367 q^{51} +(1.86730 - 1.35667i) q^{52} +(0.412891 - 1.27075i) q^{53} +(1.25030 - 3.84802i) q^{54} +(-10.8583 + 9.28753i) q^{55} +(1.94296 + 5.97982i) q^{56} +5.10866 q^{57} +(-0.0608815 - 0.187374i) q^{58} +(5.41721 + 3.93583i) q^{59} +(-3.51241 - 2.14890i) q^{60} +(-9.15540 + 6.65179i) q^{61} +(3.93226 + 2.85696i) q^{62} +(2.87386 + 2.08798i) q^{63} +(-1.67974 + 1.22040i) q^{64} +(2.99725 + 1.83373i) q^{65} +(-4.72338 - 3.43174i) q^{66} +(-4.13628 - 12.7301i) q^{67} -1.46885 q^{68} +(-1.43202 - 4.40731i) q^{69} +(-3.08005 + 2.63448i) q^{70} +(4.19569 - 12.9130i) q^{71} +(-1.11583 + 3.43417i) q^{72} +(0.931900 - 0.677065i) q^{73} -7.18901 q^{74} +(0.971600 - 6.19261i) q^{75} -5.98548 q^{76} +(12.8572 - 9.34132i) q^{77} +(-0.443665 + 1.36546i) q^{78} +(-4.13757 + 12.7341i) q^{79} +(2.08902 + 1.27807i) q^{80} +(-0.826633 - 2.54412i) q^{81} -1.69572 q^{82} +(1.63914 + 5.04476i) q^{83} +(3.70516 + 2.69195i) q^{84} +(-0.857205 - 2.06524i) q^{85} +(-2.57802 + 1.87304i) q^{86} +(-0.274180 - 0.199203i) q^{87} +(13.0694 + 9.49544i) q^{88} +(-4.32861 + 3.14492i) q^{89} +(-2.32033 + 0.184308i) q^{90} +(-3.16173 - 2.29713i) q^{91} +(1.67781 + 5.16376i) q^{92} +8.36103 q^{93} +(1.45955 + 4.49205i) q^{94} +(-3.49307 - 8.41573i) q^{95} +(-2.26803 + 6.98028i) q^{96} +(-2.21581 + 6.81956i) q^{97} +(-0.480237 + 0.348913i) q^{98} +9.12688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.589613	−	0.428379i	0.416919	−	0.302910i	−0.359478	−	0.933154i	$-0.617045\pi$
$2$	0.589613	−	0.428379i	0.416919	−	0.302910i	0.776397	+	0.630244i	$0.217045\pi$
$3$	0.387406	−	1.19231i	0.223669	−	0.688383i	−0.774755	−	0.632262i	$-0.782127\pi$
$3$	0.387406	−	1.19231i	0.223669	−	0.688383i	0.998424	−	0.0561211i	$-0.0178733\pi$
$4$	−0.453899	+	1.39696i	−0.226950	+	0.698479i
$5$	−2.22905	+	0.177058i	−0.996860	+	0.0791827i
$5$	−2.22905	+	0.177058i	−0.996860	+	0.0791827i
$6$	−0.282342	−	0.868960i	−0.115266	−	0.354752i
$7$	2.48707			0.940023			0.470012	−	0.882660i	$-0.344250\pi$
$7$	2.48707			0.940023			0.470012	+	0.882660i	$0.344250\pi$
$8$	0.781226	+	2.40437i	0.276205	+	0.850072i
$9$	1.15552	+	0.839535i	0.385174	+	0.279845i
$10$	−1.23843	+	1.05927i	−0.391625	+	0.334971i
$11$	5.16963	−	3.75596i	1.55870	−	1.13246i	0.621639	−	0.783304i	$-0.286467\pi$
$11$	5.16963	−	3.75596i	1.55870	−	1.13246i	0.937063	−	0.349159i	$-0.113533\pi$
$12$	1.48977	+	1.08238i	0.430059	+	0.312456i
$13$	−1.27127	−	0.923630i	−0.352586	−	0.256169i	0.397367	−	0.917660i	$-0.369924\pi$
$13$	−1.27127	−	0.923630i	−0.352586	−	0.256169i	−0.749953	+	0.661491i	$0.769924\pi$
$14$	1.46641	−	1.06541i	0.391914	−	0.284742i
$15$	−0.652438	+	2.72632i	−0.168459	+	0.703932i
$16$	−0.886046	−	0.643750i	−0.221511	−	0.160937i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	1.04095			0.245354
$19$	1.25923	+	3.87551i	0.288887	+	0.889103i	0.985207	+	0.171371i	$0.0548196\pi$
$19$	1.25923	+	3.87551i	0.288887	+	0.889103i	−0.696320	+	0.717732i	$0.745180\pi$
$20$	0.764420	−	3.19425i	0.170930	−	0.714256i
$21$	0.963506	−	2.96537i	0.210254	−	0.647096i
$22$	1.43911	−	4.42912i	0.306819	−	0.944291i
$23$	2.99048	−	2.17271i	0.623558	−	0.453041i	−0.230605	−	0.973048i	$-0.574070\pi$
$23$	2.99048	−	2.17271i	0.623558	−	0.453041i	0.854162	+	0.520006i	$0.174070\pi$
$24$	3.16941			0.646954
$25$	4.93730	−	0.789340i	0.987460	−	0.157868i
$26$	−1.14522			−0.224596
$27$	4.49138	−	3.26318i	0.864366	−	0.627998i
$28$	−1.12888	+	3.47433i	−0.213338	+	0.656586i
$29$	0.0835365	−	0.257099i	0.0155123	−	0.0477421i	−0.943001	−	0.332791i	$-0.892010\pi$
$29$	0.0835365	−	0.257099i	0.0155123	−	0.0477421i	0.958513	+	0.285049i	$0.0920097\pi$
$30$	0.783211	+	1.88696i	0.142994	+	0.344511i
$31$	2.06091	+	6.34281i	0.370149	+	1.13920i	0.946693	+	0.322137i	$0.104401\pi$
$31$	2.06091	+	6.34281i	0.370149	+	1.13920i	−0.576544	+	0.817066i	$0.695599\pi$
$32$	−5.85440			−1.03492
$33$	−2.47553	−	7.61891i	−0.430935	−	1.32628i
$34$	0.589613	+	0.428379i	0.101118	+	0.0734664i
$35$	−5.54379	+	0.440355i	−0.937072	+	0.0744335i
$36$	−1.69729	+	1.23315i	−0.282881	+	0.205525i
$37$	−7.98027	−	5.79801i	−1.31195	−	0.953186i	−0.999995	−	0.00308866i	$-0.999017\pi$
$37$	−7.98027	−	5.79801i	−1.31195	−	0.953186i	−0.311953	−	0.950098i	$-0.600983\pi$
$38$	2.40264	+	1.74562i	0.389760	+	0.283177i
$39$	−1.59376	+	1.15793i	−0.255205	+	0.185417i
$40$	−2.16710	−	5.22113i	−0.342649	−	0.825533i
$41$	−1.88236	−	1.36761i	−0.293975	−	0.213585i	0.431015	−	0.902345i	$-0.358156\pi$
$41$	−1.88236	−	1.36761i	−0.293975	−	0.213585i	−0.724990	+	0.688760i	$0.758156\pi$
$42$	−0.702204	−	2.16116i	−0.108352	−	0.333475i
$43$	−4.37239			−0.666784			−0.333392	−	0.942788i	$-0.608193\pi$
$43$	−4.37239			−0.666784			−0.333392	+	0.942788i	$0.608193\pi$
$44$	2.90042	+	8.92658i	0.437255	+	1.34573i
$45$	−2.72436	−	1.66677i	−0.406123	−	0.248467i
$46$	0.832481	−	2.56211i	0.122743	−	0.377763i
$47$	−2.00268	+	6.16361i	−0.292120	+	0.899054i	0.692053	+	0.721847i	$0.256706\pi$
$47$	−2.00268	+	6.16361i	−0.292120	+	0.899054i	−0.984173	+	0.177208i	$0.943294\pi$
$48$	−1.11081	+	0.807052i	−0.160332	+	0.116488i
$49$	−0.814496			−0.116357
$50$	2.57296	−	2.58044i	0.363871	−	0.364929i
$51$	1.25367			0.175549
$52$	1.86730	−	1.35667i	0.258948	−	0.188137i
$53$	0.412891	−	1.27075i	0.0567150	−	0.174551i	−0.918686	−	0.394988i	$-0.870749\pi$
$53$	0.412891	−	1.27075i	0.0567150	−	0.174551i	0.975401	+	0.220438i	$0.0707486\pi$
$54$	1.25030	−	3.84802i	0.170144	−	0.523649i
$55$	−10.8583	+	9.28753i	−1.46414	+	1.25233i
$56$	1.94296	+	5.97982i	0.259639	+	0.799088i
$57$	5.10866			0.676658
$58$	−0.0608815	−	0.187374i	−0.00799413	−	0.0246034i
$59$	5.41721	+	3.93583i	0.705260	+	0.512402i	0.881641	−	0.471920i	$-0.156439\pi$
$59$	5.41721	+	3.93583i	0.705260	+	0.512402i	−0.176381	+	0.984322i	$0.556439\pi$
$60$	−3.51241	−	2.14890i	−0.453450	−	0.277422i
$61$	−9.15540	+	6.65179i	−1.17223	+	0.851674i	−0.991274	−	0.131817i	$-0.957919\pi$
$61$	−9.15540	+	6.65179i	−1.17223	+	0.851674i	−0.180955	+	0.983491i	$0.557919\pi$
$62$	3.93226	+	2.85696i	0.499398	+	0.362834i
$63$	2.87386	+	2.08798i	0.362072	+	0.263061i
$64$	−1.67974	+	1.22040i	−0.209967	+	0.152550i
$65$	2.99725	+	1.83373i	0.371763	+	0.227446i
$66$	−4.72338	−	3.43174i	−0.581408	−	0.422418i
$67$	−4.13628	−	12.7301i	−0.505327	−	1.55524i	−0.800221	−	0.599705i	$-0.795284\pi$
$67$	−4.13628	−	12.7301i	−0.505327	−	1.55524i	0.294894	−	0.955530i	$-0.404716\pi$
$68$	−1.46885			−0.178124
$69$	−1.43202	−	4.40731i	−0.172395	−	0.530578i
$70$	−3.08005	+	2.63448i	−0.368136	+	0.314881i
$71$	4.19569	−	12.9130i	0.497937	−	1.53249i	−0.314393	−	0.949293i	$-0.601801\pi$
$71$	4.19569	−	12.9130i	0.497937	−	1.53249i	0.812330	−	0.583198i	$-0.198199\pi$
$72$	−1.11583	+	3.43417i	−0.131502	+	0.404720i
$73$	0.931900	−	0.677065i	0.109071	−	0.0792445i	−0.531913	−	0.846799i	$-0.678527\pi$
$73$	0.931900	−	0.677065i	0.109071	−	0.0792445i	0.640984	+	0.767555i	$0.278527\pi$
$74$	−7.18901			−0.835706
$75$	0.971600	−	6.19261i	0.112191	−	0.715061i
$76$	−5.98548			−0.686582
$77$	12.8572	−	9.34132i	1.46522	−	1.06454i
$78$	−0.443665	+	1.36546i	−0.0502352	+	0.154608i
$79$	−4.13757	+	12.7341i	−0.465513	+	1.43270i	0.392823	+	0.919614i	$0.371498\pi$
$79$	−4.13757	+	12.7341i	−0.465513	+	1.43270i	−0.858336	+	0.513088i	$0.828502\pi$
$80$	2.08902	+	1.27807i	0.233559	+	0.142892i
$81$	−0.826633	−	2.54412i	−0.0918481	−	0.282679i
$82$	−1.69572			−0.187261
$83$	1.63914	+	5.04476i	0.179919	+	0.553735i	0.999824	−	0.0187654i	$-0.00597356\pi$
$83$	1.63914	+	5.04476i	0.179919	+	0.553735i	−0.819905	+	0.572500i	$0.805974\pi$
$84$	3.70516	+	2.69195i	0.404266	+	0.293716i
$85$	−0.857205	−	2.06524i	−0.0929770	−	0.224006i
$86$	−2.57802	+	1.87304i	−0.277995	+	0.201975i
$87$	−0.274180	−	0.199203i	−0.0293952	−	0.0213569i
$88$	13.0694	+	9.49544i	1.39320	+	1.01222i
$89$	−4.32861	+	3.14492i	−0.458832	+	0.333361i	−0.793073	−	0.609127i	$-0.791520\pi$
$89$	−4.32861	+	3.14492i	−0.458832	+	0.333361i	0.334241	+	0.942488i	$0.391520\pi$
$90$	−2.32033	+	0.184308i	−0.244584	+	0.0194278i
$91$	−3.16173	−	2.29713i	−0.331439	−	0.240805i
$92$	1.67781	+	5.16376i	0.174924	+	0.538359i
$93$	8.36103			0.866999
$94$	1.45955	+	4.49205i	0.150541	+	0.463319i
$95$	−3.49307	−	8.41573i	−0.358381	−	0.863436i
$96$	−2.26803	+	6.98028i	−0.231480	+	0.712422i
$97$	−2.21581	+	6.81956i	−0.224981	+	0.692421i	0.773312	+	0.634025i	$0.218599\pi$
$97$	−2.21581	+	6.81956i	−0.224981	+	0.692421i	−0.998294	+	0.0583958i	$0.981401\pi$
$98$	−0.480237	+	0.348913i	−0.0485113	+	0.0352455i
$99$	9.12688			0.917286
$100$	−1.13836	+	7.25548i	−0.113836	+	0.725548i
$101$	−11.7785			−1.17201			−0.586003	−	0.810309i	$-0.699300\pi$
$101$	−11.7785			−1.17201			−0.586003	+	0.810309i	$0.699300\pi$
$102$	0.739182	−	0.537047i	0.0731899	−	0.0531756i
$103$	5.31511	−	16.3582i	0.523713	−	1.61182i	−0.243133	−	0.969993i	$-0.578175\pi$
$103$	5.31511	−	16.3582i	0.523713	−	1.61182i	0.766846	−	0.641831i	$-0.221825\pi$
$104$	1.22760	−	3.77816i	0.120376	−	0.370479i
$105$	−1.62266	+	6.78054i	−0.158355	+	0.661713i
$106$	−0.300916	−	0.926123i	−0.0292275	−	0.0899531i
$107$	6.26637			0.605793			0.302896	−	0.953024i	$-0.402046\pi$
$107$	6.26637			0.605793			0.302896	+	0.953024i	$0.402046\pi$
$108$	2.51989	+	7.75542i	0.242476	+	0.746265i
$109$	2.42123	+	1.75913i	0.231912	+	0.168494i	0.697672	−	0.716417i	$-0.254219\pi$
$109$	2.42123	+	1.75913i	0.231912	+	0.168494i	−0.465761	+	0.884911i	$0.654219\pi$
$110$	−2.42363	+	10.1275i	−0.231084	+	0.965621i
$111$	−10.0047	+	7.26880i	−0.949600	+	0.689924i
$112$	−2.20366	−	1.60105i	−0.208226	−	0.151285i
$113$	3.86394	+	2.80732i	0.363489	+	0.264090i	0.754506	−	0.656293i	$-0.227877\pi$
$113$	3.86394	+	2.80732i	0.363489	+	0.264090i	−0.391017	+	0.920384i	$0.627877\pi$
$114$	3.01213	−	2.18844i	0.282112	−	0.204966i
$115$	−6.28122	+	5.37256i	−0.585727	+	0.500994i
$116$	0.321239	+	0.233394i	0.0298263	+	0.0216701i
$117$	−0.693557	−	2.13455i	−0.0641194	−	0.197339i
$118$	4.88008			0.449248
$119$	0.768546	+	2.36534i	0.0704525	+	0.216831i
$120$	−7.06477	+	0.561169i	−0.644923	+	0.0512275i
$121$	9.21868	−	28.3722i	0.838062	−	2.57929i
$122$	−2.54866	+	7.84396i	−0.230744	+	0.710158i
$123$	−2.35986	+	1.71454i	−0.212781	+	0.154595i
$124$	−9.79609			−0.879715
$125$	−10.8657	+	2.63366i	−0.971859	+	0.235562i
$126$	2.58891			0.230639
$127$	−10.9311	+	7.94188i	−0.969975	+	0.704728i	−0.955446	−	0.295167i	$-0.904625\pi$
$127$	−10.9311	+	7.94188i	−0.969975	+	0.704728i	−0.0145290	+	0.999894i	$0.504625\pi$
$128$	3.15062	−	9.69660i	0.278478	−	0.857066i
$129$	−1.69389	+	5.21327i	−0.149139	+	0.459003i
$130$	2.55275	−	0.202770i	0.223891	−	0.0177841i
$131$	−6.16512	−	18.9743i	−0.538649	−	1.65779i	−0.735629	−	0.677385i	$-0.763113\pi$
$131$	−6.16512	−	18.9743i	−0.538649	−	1.65779i	0.196980	−	0.980408i	$-0.436887\pi$
$132$	11.7669			1.02418
$133$	3.13179	+	9.63865i	0.271560	+	0.835777i
$134$	−7.89213	−	5.73397i	−0.681776	−	0.495339i
$135$	−9.43372	+	8.06900i	−0.811925	+	0.694469i
$136$	−2.04528	+	1.48598i	−0.175381	+	0.127422i
$137$	0.319315	+	0.231996i	0.0272809	+	0.0198208i	0.601342	−	0.798992i	$-0.294633\pi$
$137$	0.319315	+	0.231996i	0.0272809	+	0.0198208i	−0.574061	+	0.818812i	$0.694633\pi$
$138$	−2.73234	−	1.98516i	−0.232592	−	0.168988i
$139$	−10.4523	+	7.59401i	−0.886550	+	0.644116i	−0.934976	−	0.354711i	$-0.884579\pi$
$139$	−10.4523	+	7.59401i	−0.886550	+	0.644116i	0.0484265	+	0.998827i	$0.484579\pi$
$140$	1.90116	−	7.94432i	0.160678	−	0.671417i
$141$	6.57311	+	4.77564i	0.553555	+	0.402181i
$142$	−3.05782	−	9.41101i	−0.256607	−	0.789755i
$143$	−10.0411			−0.839679
$144$	−0.483394	−	1.48773i	−0.0402828	−	0.123978i
$145$	−0.140685	+	0.587876i	−0.0116833	+	0.0488205i
$146$	0.259420	−	0.798413i	0.0214698	−	0.0660771i
$147$	−0.315541	+	0.971135i	−0.0260254	+	0.0800978i
$148$	11.7218	−	8.51639i	0.963527	−	0.700043i
$149$	−7.77427			−0.636893			−0.318447	−	0.947941i	$-0.603161\pi$
$149$	−7.77427			−0.636893			−0.318447	+	0.947941i	$0.603161\pi$
$150$	−2.07991	−	4.06745i	−0.169824	−	0.332106i
$151$	8.64459			0.703487			0.351743	−	0.936096i	$-0.385589\pi$
$151$	8.64459			0.703487			0.351743	+	0.936096i	$0.385589\pi$
$152$	−8.33440	+	6.05530i	−0.676009	+	0.491150i
$153$	−0.441370	+	1.35840i	−0.0356826	+	0.109820i
$154$	3.57916	−	11.0155i	0.288417	−	0.887656i
$155$	−5.71690	−	13.7735i	−0.459192	−	1.10632i
$156$	−0.894177	−	2.75199i	−0.0715914	−	0.220336i
$157$	−3.75636			−0.299790			−0.149895	−	0.988702i	$-0.547894\pi$
$157$	−3.75636			−0.299790			−0.149895	+	0.988702i	$0.547894\pi$
$158$	3.01547	+	9.28065i	0.239898	+	0.738329i
$159$	−1.35517	−	0.984592i	−0.107472	−	0.0780832i
$160$	13.0497	−	1.03657i	1.03167	−	0.0819478i
$161$	7.43752	−	5.40367i	0.586159	−	0.425869i
$162$	−1.57724	−	1.14593i	−0.123920	−	0.0900328i
$163$	−15.6764	−	11.3896i	−1.22787	−	0.892102i	−0.231144	−	0.972920i	$-0.574247\pi$
$163$	−15.6764	−	11.3896i	−1.22787	−	0.892102i	−0.996729	+	0.0808178i	$0.974247\pi$
$164$	2.76490	−	2.00881i	0.215902	−	0.156862i
$165$	6.86706	+	16.5446i	0.534600	+	1.28799i
$166$	3.12753	+	2.27228i	0.242743	+	0.176363i
$167$	−2.39301	−	7.36492i	−0.185177	−	0.569915i	0.814775	−	0.579778i	$-0.196861\pi$
$167$	−2.39301	−	7.36492i	−0.185177	−	0.569915i	−0.999951	+	0.00986271i	$0.996861\pi$
$168$	7.88255			0.608152
$169$	−3.25419	−	10.0154i	−0.250322	−	0.770413i
$170$	−1.39012	−	0.850481i	−0.106618	−	0.0652289i
$171$	−1.79856	+	5.53540i	−0.137539	+	0.423303i
$172$	1.98463	−	6.10805i	0.151326	−	0.465734i
$173$	10.1527	−	7.37636i	0.771894	−	0.560814i	−0.130641	−	0.991430i	$-0.541704\pi$
$173$	10.1527	−	7.37636i	0.771894	−	0.560814i	0.902535	+	0.430616i	$0.141704\pi$
$174$	−0.246995			−0.0187246
$175$	12.2794	−	1.96314i	0.928235	−	0.148400i
$176$	−6.99842			−0.527526
$177$	6.79141	−	4.93425i	0.510474	−	0.370881i
$178$	−1.20499	+	3.70857i	−0.0903176	+	0.277969i
$179$	3.28369	−	10.1061i	0.245434	−	0.755369i	−0.750131	−	0.661290i	$-0.770009\pi$
$179$	3.28369	−	10.1061i	0.245434	−	0.755369i	0.995565	−	0.0940790i	$-0.0299906\pi$
$180$	3.56499	−	3.04927i	0.265719	−	0.227279i
$181$	3.13079	+	9.63558i	0.232710	+	0.716207i	0.997417	+	0.0718292i	$0.0228837\pi$
$181$	3.13079	+	9.63558i	0.232710	+	0.716207i	−0.764707	+	0.644378i	$0.777116\pi$
$182$	−2.84824			−0.211125
$183$	4.38416	+	13.4931i	0.324086	+	0.997435i
$184$	7.56023	+	5.49283i	0.557348	+	0.404937i
$185$	18.8150	+	11.5111i	1.38330	+	0.846310i
$186$	4.92977	−	3.58169i	0.361468	−	0.262622i
$187$	5.16963	+	3.75596i	0.378041	+	0.274663i
$188$	−7.70128	−	5.59531i	−0.561674	−	0.408080i
$189$	11.1704	−	8.11574i	0.812524	−	0.590333i
$190$	−5.66468	−	3.46567i	−0.410959	−	0.251426i
$191$	7.44872	+	5.41181i	0.538970	+	0.391585i	0.823702	−	0.567022i	$-0.191905\pi$
$191$	7.44872	+	5.41181i	0.538970	+	0.391585i	−0.284732	+	0.958607i	$0.591905\pi$
$192$	0.804359	+	2.47556i	0.0580496	+	0.178658i
$193$	11.0254			0.793628			0.396814	−	0.917899i	$-0.370116\pi$
$193$	11.0254			0.793628			0.396814	+	0.917899i	$0.370116\pi$
$194$	1.61488	+	4.97010i	0.115942	+	0.356833i
$195$	3.34753	−	2.86327i	0.239722	−	0.205043i
$196$	0.369699	−	1.13782i	0.0264071	−	0.0812726i
$197$	2.08934	−	6.43034i	0.148860	−	0.458143i	−0.848628	−	0.528991i	$-0.822571\pi$
$197$	2.08934	−	6.43034i	0.148860	−	0.458143i	0.997487	+	0.0708483i	$0.0225706\pi$
$198$	5.38132	−	3.90976i	0.382434	−	0.277855i
$199$	−4.83766			−0.342933			−0.171466	−	0.985190i	$-0.554850\pi$
$199$	−4.83766			−0.342933			−0.171466	+	0.985190i	$0.554850\pi$
$200$	5.75501	+	11.2544i	0.406941	+	0.795809i
$201$	−16.7808			−1.18362
$202$	−6.94477	+	5.04567i	−0.488632	+	0.355012i
$203$	0.207761	−	0.639422i	0.0145820	−	0.0448786i
$204$	−0.569041	+	1.75133i	−0.0398409	+	0.122618i
$205$	4.43801	+	2.71518i	0.309964	+	0.189637i
$206$	−3.87366	−	11.9219i	−0.269891	−	0.830638i
$207$	5.27963			0.366960
$208$	0.531815	+	1.63676i	0.0368747	+	0.113489i
$209$	21.0660	+	15.3053i	1.45716	+	1.05869i
$210$	1.94790	+	4.69300i	0.134418	+	0.323848i
$211$	−19.7927	+	14.3802i	−1.36259	+	0.989976i	−0.364309	+	0.931278i	$0.618695\pi$
$211$	−19.7927	+	14.3802i	−1.36259	+	0.989976i	−0.998276	+	0.0586980i	$0.981305\pi$
$212$	1.58777	+	1.15358i	0.109049	+	0.0792284i
$213$	−13.7709	−	10.0052i	−0.943568	−	0.685542i
$214$	3.69473	−	2.68438i	0.252567	−	0.183500i
$215$	9.74627	−	0.774167i	0.664690	−	0.0527977i
$216$	11.3547	+	8.24964i	0.772586	+	0.561317i
$217$	5.12561	+	15.7750i	0.347949	+	1.07088i
$218$	2.18116			0.147727
$219$	−0.446250	−	1.37342i	−0.0301548	−	0.0928070i
$220$	−8.04570	−	19.3842i	−0.542441	−	1.30688i
$221$	0.485581	−	1.49447i	0.0326637	−	0.100529i
$222$	−2.78507	+	8.57156i	−0.186922	+	0.575285i
$223$	−17.6308	+	12.8096i	−1.18065	+	0.857791i	−0.992245	−	0.124300i	$-0.960331\pi$
$223$	−17.6308	+	12.8096i	−1.18065	+	0.857791i	−0.188404	+	0.982092i	$0.560331\pi$
$224$	−14.5603			−0.972849
$225$	6.36784	+	3.23294i	0.424522	+	0.215529i
$226$	3.48082			0.231541
$227$	13.0959	−	9.51471i	0.869204	−	0.631514i	−0.0611691	−	0.998127i	$-0.519483\pi$
$227$	13.0959	−	9.51471i	0.869204	−	0.631514i	0.930373	+	0.366614i	$0.119483\pi$
$228$	−2.31881	+	7.13658i	−0.153567	+	0.472631i
$229$	0.761319	−	2.34310i	0.0503094	−	0.154836i	−0.922746	−	0.385410i	$-0.874060\pi$
$229$	0.761319	−	2.34310i	0.0503094	−	0.154836i	0.973055	+	0.230573i	$0.0740602\pi$
$230$	−1.40200	+	5.85847i	−0.0924450	+	0.386296i
$231$	−6.15682	−	18.9487i	−0.405089	−	1.24673i
$232$	0.683421			0.0448688
$233$	3.40962	+	10.4937i	0.223371	+	0.687467i	0.998453	+	0.0556053i	$0.0177088\pi$
$233$	3.40962	+	10.4937i	0.223371	+	0.687467i	−0.775081	+	0.631861i	$0.782291\pi$
$234$	−1.32333	−	0.961452i	−0.0865085	−	0.0628521i
$235$	3.37275	−	14.0936i	0.220014	−	0.919362i
$236$	−7.95706	+	5.78114i	−0.517960	+	0.376320i
$237$	13.5802	+	9.86657i	0.882127	+	0.640902i
$238$	1.46641	+	1.06541i	0.0950530	+	0.0690601i
$239$	−13.0353	+	9.47072i	−0.843185	+	0.612610i	−0.923259	−	0.384179i	$-0.874485\pi$
$239$	−13.0353	+	9.47072i	−0.843185	+	0.612610i	0.0800732	+	0.996789i	$0.474485\pi$
$240$	2.33316	−	1.99563i	0.150605	−	0.128818i
$241$	1.63634	+	1.18887i	0.105406	+	0.0765820i	0.639240	−	0.769008i	$-0.279249\pi$
$241$	1.63634	+	1.18887i	0.105406	+	0.0765820i	−0.533834	+	0.845590i	$0.679249\pi$
$242$	−6.71859	−	20.6777i	−0.431887	−	1.32921i
$243$	13.3013			0.853279
$244$	−5.13664	−	15.8089i	−0.328840	−	1.01206i
$245$	1.81555	−	0.144213i	0.115991	−	0.00921342i
$246$	−0.656931	+	2.02183i	−0.0418844	+	0.128907i
$247$	1.97872	−	6.08987i	0.125903	−	0.387489i
$248$	−13.6404	+	9.91035i	−0.866168	+	0.629308i
$249$	6.64996			0.421424
$250$	−5.27836	+	6.20748i	−0.333833	+	0.392596i
$251$	21.0072			1.32596			0.662980	−	0.748637i	$-0.269291\pi$
$251$	21.0072			1.32596			0.662980	+	0.748637i	$0.269291\pi$
$252$	−4.22126	+	3.06693i	−0.265915	+	0.193198i
$253$	7.29906	−	22.4642i	0.458888	−	1.41231i
$254$	−3.04296	+	9.36527i	−0.190932	+	0.587629i
$255$	−2.79450	+	0.221973i	−0.174998	+	0.0139005i
$256$	−3.57938	−	11.0162i	−0.223711	−	0.688512i
$257$	0.236987			0.0147828			0.00739142	−	0.999973i	$-0.497647\pi$
$257$	0.236987			0.0147828			0.00739142	+	0.999973i	$0.497647\pi$
$258$	1.23451	+	3.79944i	0.0768574	+	0.236543i
$259$	−19.8475	−	14.4200i	−1.23326	−	0.896017i
$260$	−3.92209	+	3.35471i	−0.243238	+	0.208050i
$261$	0.312372	−	0.226951i	0.0193353	−	0.0140479i
$262$	−11.7632	−	8.54648i	−0.726734	−	0.528003i
$263$	−18.2932	−	13.2908i	−1.12801	−	0.819546i	−0.142605	−	0.989780i	$-0.545548\pi$
$263$	−18.2932	−	13.2908i	−1.12801	−	0.819546i	−0.985404	+	0.170233i	$0.945548\pi$
$264$	16.3847	−	11.9042i	1.00841	−	0.732652i
$265$	−0.695358	+	2.90566i	−0.0427155	+	0.178494i
$266$	5.97553	+	4.34148i	0.366384	+	0.266193i
$267$	2.07280	+	6.37942i	0.126853	+	0.390414i
$268$	19.6609			1.20098
$269$	7.23560	+	22.2689i	0.441162	+	1.35776i	0.886638	+	0.462464i	$0.153035\pi$
$269$	7.23560	+	22.2689i	0.441162	+	1.35776i	−0.445475	+	0.895294i	$0.646965\pi$
$270$	−2.10565	+	8.79879i	−0.128146	+	0.535477i
$271$	−1.96977	+	6.06232i	−0.119655	+	0.368260i	−0.992889	−	0.119040i	$-0.962018\pi$
$271$	−1.96977	+	6.06232i	−0.119655	+	0.368260i	0.873235	+	0.487300i	$0.162018\pi$
$272$	0.338439	−	1.04161i	0.0205209	−	0.0631568i
$273$	−3.96378	+	2.87985i	−0.239899	+	0.174297i
$274$	0.287655			0.0173778
$275$	22.5593	−	22.6249i	1.36038	−	1.36433i
$276$	6.80682			0.409722
$277$	6.26009	−	4.54822i	0.376132	−	0.273276i	−0.383617	−	0.923492i	$-0.625322\pi$
$277$	6.26009	−	4.54822i	0.376132	−	0.273276i	0.759749	+	0.650216i	$0.225322\pi$
$278$	−2.90967	+	8.95506i	−0.174511	+	0.537089i
$279$	−2.94360	+	9.05946i	−0.176229	+	0.542376i
$280$	−5.38973	−	12.9853i	−0.322098	−	0.776020i
$281$	9.14310	+	28.1396i	0.545431	+	1.67867i	0.719962	+	0.694014i	$0.244159\pi$
$281$	9.14310	+	28.1396i	0.545431	+	1.67867i	−0.174530	+	0.984652i	$0.555841\pi$
$282$	5.92137			0.352612
$283$	−0.899846	−	2.76944i	−0.0534903	−	0.164626i	0.920743	−	0.390171i	$-0.127584\pi$
$283$	−0.899846	−	2.76944i	−0.0534903	−	0.164626i	−0.974233	+	0.225544i	$0.927584\pi$
$284$	16.1345	+	11.7224i	0.957406	+	0.695596i
$285$	−11.3874	+	0.904528i	−0.674534	+	0.0535796i
$286$	−5.92036	+	4.30139i	−0.350078	+	0.254347i
$287$	−4.68155	−	3.40134i	−0.276343	−	0.200775i
$288$	−6.76488	−	4.91497i	−0.398624	−	0.289618i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	0.168884	+	0.406886i	0.00991720	+	0.0238932i
$291$	7.27264	+	5.28388i	0.426330	+	0.309747i
$292$	0.522843	+	1.60914i	0.0305971	+	0.0941681i
$293$	−3.08856			−0.180436			−0.0902178	−	0.995922i	$-0.528756\pi$
$293$	−3.08856			−0.180436			−0.0902178	+	0.995922i	$0.528756\pi$
$294$	0.229967	+	0.707764i	0.0134119	+	0.0412777i
$295$	−12.7721	−	7.81400i	−0.743619	−	0.454948i
$296$	7.70614	−	23.7171i	0.447910	−	1.37853i
$297$	10.9624	−	33.7388i	0.636103	−	1.95772i
$298$	−4.58381	+	3.33033i	−0.265533	+	0.192921i
$299$	−5.80848			−0.335913
$300$	8.20981	+	4.16810i	0.473993	+	0.240646i
$301$	−10.8744			−0.626792
$302$	5.09696	−	3.70316i	0.293297	−	0.213093i
$303$	−4.56308	+	14.0437i	−0.262142	+	0.806790i
$304$	1.37912	−	4.24451i	0.0790981	−	0.243439i
$305$	19.2301	−	16.4482i	1.10111	−	0.941820i
$306$	0.321671	+	0.990002i	0.0183887	+	0.0565946i
$307$	23.8832			1.36309			0.681544	−	0.731778i	$-0.261309\pi$
$307$	23.8832			1.36309			0.681544	+	0.731778i	$0.261309\pi$
$308$	7.21354	+	22.2010i	0.411030	+	1.26502i
$309$	−17.4450	−	12.6746i	−0.992413	−	0.721031i
$310$	−9.27104	−	5.67205i	−0.526560	−	0.322151i
$311$	−5.29834	+	3.84947i	−0.300441	+	0.218283i	−0.727784	−	0.685806i	$-0.759450\pi$
$311$	−5.29834	+	3.84947i	−0.300441	+	0.218283i	0.427343	+	0.904090i	$0.359450\pi$
$312$	−4.02918	−	2.92737i	−0.228107	−	0.165730i
$313$	12.1858	+	8.85350i	0.688782	+	0.500429i	0.876259	−	0.481840i	$-0.160031\pi$
$313$	12.1858	+	8.85350i	0.688782	+	0.500429i	−0.187478	+	0.982269i	$0.560031\pi$
$314$	−2.21480	+	1.60915i	−0.124988	+	0.0908093i
$315$	−6.77566	−	4.14537i	−0.381765	−	0.233565i
$316$	−15.9110	−	11.5600i	−0.895064	−	0.650302i
$317$	−5.21687	−	16.0559i	−0.293009	−	0.901788i	−0.983883	−	0.178813i	$-0.942774\pi$
$317$	−5.21687	−	16.0559i	−0.293009	−	0.901788i	0.690874	−	0.722975i	$-0.257226\pi$
$318$	−1.22081			−0.0684594
$319$	−0.533799	−	1.64287i	−0.0298870	−	0.0919828i
$320$	3.52813	−	3.01774i	0.197228	−	0.168697i
$321$	2.42763	−	7.47148i	0.135497	−	0.417017i
$322$	2.07044	−	6.37215i	0.115381	−	0.355106i
$323$	−3.29670	+	2.39520i	−0.183434	+	0.133272i
$324$	3.92923			0.218291
$325$	−7.00569	−	3.55678i	−0.388606	−	0.197295i
$326$	−14.1221			−0.782150
$327$	3.03543	−	2.20537i	0.167860	−	0.121957i
$328$	1.81769	−	5.59429i	0.100365	−	0.308893i
$329$	−4.98079	+	15.3293i	−0.274600	+	0.845132i
$330$	11.1363	+	6.81319i	0.613031	+	0.375054i
$331$	8.72545	+	26.8542i	0.479594	+	1.47604i	0.839660	+	0.543112i	$0.182754\pi$
$331$	8.72545	+	26.8542i	0.479594	+	1.47604i	−0.360066	+	0.932927i	$0.617246\pi$
$332$	−7.79133			−0.427605
$333$	−4.35374	−	13.3994i	−0.238584	−	0.734285i
$334$	−4.56592	−	3.31734i	−0.249836	−	0.181517i
$335$	11.4739	+	27.6437i	0.626887	+	1.51034i
$336$	−2.76266	+	2.00719i	−0.150716	+	0.109501i
$337$	−18.6711	−	13.5654i	−1.01708	−	0.738953i	−0.0513986	−	0.998678i	$-0.516368\pi$
$337$	−18.6711	−	13.5654i	−1.01708	−	0.738953i	−0.965682	+	0.259726i	$0.916368\pi$
$338$	−6.20908	−	4.51116i	−0.337730	−	0.245375i
$339$	4.84412	−	3.51946i	0.263096	−	0.191151i
$340$	3.27413	−	0.260071i	0.177565	−	0.0141043i
$341$	34.4774	+	25.0493i	1.86706	+	1.35650i
$342$	1.31079	+	4.03421i	0.0708796	+	0.218145i
$343$	−19.4352			−1.04940
$344$	−3.41583	−	10.5128i	−0.184169	−	0.566815i
$345$	3.97239	+	9.57055i	0.213866	+	0.515261i
$346$	2.82628	−	8.69839i	0.151942	−	0.467628i
$347$	−2.90862	+	8.95182i	−0.156143	+	0.480559i	−0.998275	−	0.0587129i	$-0.981300\pi$
$347$	−2.90862	+	8.95182i	−0.156143	+	0.480559i	0.842132	+	0.539272i	$0.181300\pi$
$348$	0.402729	−	0.292600i	0.0215885	−	0.0156850i
$349$	−14.5274			−0.777632			−0.388816	−	0.921316i	$-0.627116\pi$
$349$	−14.5274			−0.777632			−0.388816	+	0.921316i	$0.627116\pi$
$350$	6.39912	−	6.41773i	0.342048	−	0.343042i
$351$	−8.72371			−0.465637
$352$	−30.2651	+	21.9889i	−1.61313	+	1.17201i
$353$	−4.87045	+	14.9897i	−0.259228	+	0.797822i	0.733739	+	0.679431i	$0.237773\pi$
$353$	−4.87045	+	14.9897i	−0.259228	+	0.797822i	−0.992967	+	0.118390i	$0.962227\pi$
$354$	1.89057	−	5.81859i	0.100483	−	0.309255i
$355$	−7.06604	+	29.5266i	−0.375026	+	1.56711i
$356$	−2.42857	−	7.47436i	−0.128714	−	0.396140i
$357$	3.11797			0.165020
$358$	−2.39316	−	7.36537i	−0.126482	−	0.389272i
$359$	−3.53423	−	2.56777i	−0.186529	−	0.135521i	0.490602	−	0.871384i	$-0.336777\pi$
$359$	−3.53423	−	2.56777i	−0.186529	−	0.135521i	−0.677131	+	0.735862i	$0.736777\pi$
$360$	1.87919	−	7.85248i	0.0990419	−	0.413862i
$361$	1.93742	−	1.40762i	0.101969	−	0.0740850i
$362$	5.97363	+	4.34010i	0.313967	+	0.228111i
$363$	−30.2572	−	21.9831i	−1.58809	−	1.15382i
$364$	4.64410	−	3.37414i	0.243417	−	0.176853i
$365$	−1.95737	+	1.67421i	−0.102453	+	0.0876322i
$366$	8.36510	+	6.07760i	0.437251	+	0.317681i
$367$	3.26979	+	10.0634i	0.170682	+	0.525304i	0.999410	−	0.0343469i	$-0.0109351\pi$
$367$	3.26979	+	10.0634i	0.170682	+	0.525304i	−0.828728	+	0.559651i	$0.810935\pi$
$368$	−4.04838			−0.211036
$369$	−1.02694	−	3.16061i	−0.0534606	−	0.164535i
$370$	16.0246	−	1.27287i	0.833082	−	0.0661734i
$371$	1.02689	−	3.16044i	0.0533134	−	0.164082i
$372$	−3.79507	+	11.6800i	−0.196765	+	0.605580i
$373$	7.99266	−	5.80701i	0.413844	−	0.300676i	−0.361312	−	0.932445i	$-0.617671\pi$
$373$	7.99266	−	5.80701i	0.413844	−	0.300676i	0.775156	+	0.631769i	$0.217671\pi$
$374$	4.65705			0.240810
$375$	−1.06929	+	13.9756i	−0.0552180	+	0.721699i
$376$	−16.3841			−0.844946
$377$	−0.343662	+	0.249685i	−0.0176995	+	0.0128594i
$378$	3.10957	−	9.57028i	0.159939	−	0.492242i
$379$	0.217902	−	0.670633i	0.0111929	−	0.0344481i	−0.945304	−	0.326190i	$-0.894235\pi$
$379$	0.217902	−	0.670633i	0.0111929	−	0.0344481i	0.956497	+	0.291742i	$0.0942350\pi$
$380$	13.3419	−	1.05978i	0.684426	−	0.0543654i
$381$	5.23445	+	16.1100i	0.268169	+	0.825340i
$382$	6.71016			0.343322
$383$	−0.319558	−	0.983499i	−0.0163287	−	0.0502545i	0.942560	−	0.334036i	$-0.108411\pi$
$383$	−0.319558	−	0.983499i	−0.0163287	−	0.0502545i	−0.958889	+	0.283782i	$0.908411\pi$
$384$	−10.3408	−	7.51305i	−0.527703	−	0.383399i
$385$	−27.0054	+	23.0987i	−1.37632	+	1.17722i
$386$	6.50074	−	4.72306i	0.330879	−	0.240397i
$387$	−5.05240	−	3.67078i	−0.256828	−	0.186596i
$388$	−8.52088	−	6.19078i	−0.432582	−	0.314289i
$389$	18.3745	−	13.3498i	0.931622	−	0.676863i	−0.0147672	−	0.999891i	$-0.504701\pi$
$389$	18.3745	−	13.3498i	0.931622	−	0.676863i	0.946390	+	0.323028i	$0.104701\pi$
$390$	0.747185	−	3.12223i	0.0378352	−	0.158100i
$391$	2.99048	+	2.17271i	0.151235	+	0.109879i
$392$	−0.636305	−	1.95835i	−0.0321383	−	0.0989115i
$393$	−25.0117			−1.26168
$394$	−1.52272	−	4.68644i	−0.0767133	−	0.236099i
$395$	6.96816	−	29.1176i	0.350606	−	1.46506i
$396$	−4.14268	+	12.7499i	−0.208178	+	0.640705i
$397$	−7.58206	+	23.3352i	−0.380533	+	1.17116i	0.559137	+	0.829075i	$0.311133\pi$
$397$	−7.58206	+	23.3352i	−0.380533	+	1.17116i	−0.939669	+	0.342084i	$0.888867\pi$
$398$	−2.85235	+	2.07235i	−0.142975	+	0.103878i
$399$	12.7056			0.636074
$400$	−4.88281	−	2.47899i	−0.244141	−	0.123950i
$401$	26.2001			1.30837			0.654186	−	0.756333i	$-0.273011\pi$
$401$	26.2001			1.30837			0.654186	+	0.756333i	$0.273011\pi$
$402$	−9.89415	+	7.18852i	−0.493475	+	0.358531i
$403$	3.23845	−	9.96693i	0.161319	−	0.496488i
$404$	5.34626	−	16.4541i	0.265986	−	0.818622i
$405$	2.29306	+	5.52459i	0.113943	+	0.274519i
$406$	−0.151416	−	0.466012i	−0.00751467	−	0.0231278i
$407$	−63.0321			−3.12439
$408$	0.979403	+	3.01429i	0.0484877	+	0.149230i
$409$	−8.35647	−	6.07133i	−0.413201	−	0.300208i	0.361695	−	0.932296i	$-0.382198\pi$
$409$	−8.35647	−	6.07133i	−0.413201	−	0.300208i	−0.774896	+	0.632088i	$0.782198\pi$
$410$	3.77983	−	0.300240i	0.186673	−	0.0148278i
$411$	0.400317	−	0.290847i	0.0197462	−	0.0143464i
$412$	20.4392	+	14.8500i	1.00697	+	0.731605i
$413$	13.4730	+	9.78868i	0.662961	+	0.481669i
$414$	3.11294	−	2.26168i	0.152992	−	0.111156i
$415$	−4.54694	−	10.9548i	−0.223201	−	0.537750i
$416$	7.44251	+	5.40730i	0.364899	+	0.265115i
$417$	5.00518	+	15.4044i	0.245105	+	0.754354i
$418$	18.9773			0.928208
$419$	0.932757	+	2.87073i	0.0455682	+	0.140244i	0.971252	−	0.238054i	$-0.0765094\pi$
$419$	0.932757	+	2.87073i	0.0455682	+	0.140244i	−0.925684	+	0.378298i	$0.876509\pi$
$420$	−8.73560	−	5.34447i	−0.426254	−	0.260783i
$421$	0.284323	−	0.875055i	0.0138570	−	0.0426476i	−0.943889	−	0.330263i	$-0.892863\pi$
$421$	0.284323	−	0.875055i	0.0138570	−	0.0426476i	0.957746	+	0.287616i	$0.0928625\pi$
$422$	−5.50984	+	16.9575i	−0.268215	+	0.825480i
$423$	−7.48870	+	5.44086i	−0.364113	+	0.264544i
$424$	3.37791			0.164046
$425$	2.27642	+	4.45173i	0.110422	+	0.215941i
$426$	−12.4055			−0.601049
$427$	−22.7701	+	16.5434i	−1.10192	+	0.800593i
$428$	−2.84430	+	8.75385i	−0.137484	+	0.423133i
$429$	−3.88999	+	11.9721i	−0.187810	+	0.578021i
$430$	5.41489	−	4.63155i	0.261129	−	0.223353i
$431$	9.38715	+	28.8907i	0.452163	+	1.39161i	0.874434	+	0.485145i	$0.161233\pi$
$431$	9.38715	+	28.8907i	0.452163	+	1.39161i	−0.422271	+	0.906470i	$0.638767\pi$
$432$	−6.08023			−0.292535
$433$	3.95311	+	12.1664i	0.189974	+	0.584680i	0.999999	−	0.00171585i	$-0.000546174\pi$
$433$	3.95311	+	12.1664i	0.189974	+	0.584680i	−0.810024	+	0.586396i	$0.800546\pi$
$434$	9.77980	+	7.10544i	0.469446	+	0.341072i
$435$	0.646431	+	0.395488i	0.0309940	+	0.0189622i
$436$	−3.55642	+	2.58389i	−0.170321	+	0.123746i
$437$	12.1860	+	8.85368i	0.582938	+	0.423529i
$438$	−0.851458	−	0.618620i	−0.0406842	−	0.0295588i
$439$	23.4010	−	17.0018i	1.11687	−	0.811454i	0.133138	−	0.991097i	$-0.457495\pi$
$439$	23.4010	−	17.0018i	1.11687	−	0.811454i	0.983732	+	0.179644i	$0.0574946\pi$
$440$	−30.8134	−	18.8518i	−1.46897	−	0.898722i
$441$	−0.941167	−	0.683798i	−0.0448175	−	0.0325618i
$442$	−0.353892	−	1.08917i	−0.0168329	−	0.0518065i
$443$	−13.5802			−0.645214			−0.322607	−	0.946533i	$-0.604559\pi$
$443$	−13.5802			−0.645214			−0.322607	+	0.946533i	$0.604559\pi$
$444$	−5.61311	−	17.2754i	−0.266386	−	0.819853i
$445$	9.09184	−	7.77659i	0.430995	−	0.368645i
$446$	−4.90803	+	15.1054i	−0.232402	+	0.715259i
$447$	−3.01180	+	9.26937i	−0.142453	+	0.438426i
$448$	−4.17762	+	3.03522i	−0.197374	+	0.143400i
$449$	−30.6775			−1.44776			−0.723880	−	0.689926i	$-0.757643\pi$
$449$	−30.6775			−1.44776			−0.723880	+	0.689926i	$0.757643\pi$
$450$	5.13948	−	0.821663i	0.242277	−	0.0387336i
$451$	−14.8678			−0.700096
$452$	−5.67554	+	4.12352i	−0.266955	+	0.193954i
$453$	3.34897	−	10.3071i	0.157348	−	0.484268i
$454$	3.64560	−	11.2200i	0.171096	−	0.526580i
$455$	7.45437	+	4.56060i	0.349466	+	0.213804i
$456$	3.99102	+	12.2831i	0.186897	+	0.575208i
$457$	12.8720			0.602127			0.301064	−	0.953604i	$-0.402658\pi$
$457$	12.8720			0.602127			0.301064	+	0.953604i	$0.402658\pi$
$458$	−0.554850	−	1.70765i	−0.0259265	−	0.0797934i
$459$	4.49138	+	3.26318i	0.209639	+	0.152312i
$460$	−4.65420	−	11.2132i	−0.217003	−	0.522818i
$461$	2.71288	−	1.97102i	0.126351	−	0.0917996i	−0.522815	−	0.852446i	$-0.675118\pi$
$461$	2.71288	−	1.97102i	0.126351	−	0.0917996i	0.649166	+	0.760647i	$0.275118\pi$
$462$	−11.7474	−	8.53496i	−0.546537	−	0.397082i
$463$	−29.5397	−	21.4618i	−1.37283	−	0.997416i	−0.997510	−	0.0705187i	$-0.977535\pi$
$463$	−29.5397	−	21.4618i	−1.37283	−	0.997416i	−0.375315	−	0.926897i	$-0.622465\pi$
$464$	−0.239524	+	0.174025i	−0.0111196	+	0.00807889i
$465$	−18.6371	+	1.48039i	−0.864277	+	0.0686513i
$466$	6.50564	+	4.72663i	0.301368	+	0.218957i
$467$	−0.0865019	−	0.266226i	−0.00400283	−	0.0123194i	0.949035	−	0.315170i	$-0.102062\pi$
$467$	−0.0865019	−	0.266226i	−0.00400283	−	0.0123194i	−0.953038	+	0.302851i	$0.902062\pi$
$468$	3.29668			0.152389
$469$	−10.2872	−	31.6607i	−0.475019	−	1.46196i
$470$	−4.04877	−	9.75455i	−0.186756	−	0.449944i
$471$	−1.45524	+	4.47876i	−0.0670538	+	0.206370i
$472$	−5.23112	+	16.0997i	−0.240782	+	0.741050i
$473$	−22.6037	+	16.4225i	−1.03932	+	0.755108i
$474$	12.2337			0.561911
$475$	9.27629	+	18.1406i	0.425625	+	0.832347i
$476$	−3.65313			−0.167441
$477$	1.54394	−	1.12174i	0.0706923	−	0.0513610i
$478$	−3.62874	+	11.1681i	−0.165975	+	0.510818i
$479$	−3.48963	+	10.7400i	−0.159445	+	0.490723i	−0.998584	−	0.0531949i	$-0.983060\pi$
$479$	−3.48963	+	10.7400i	−0.159445	+	0.490723i	0.839139	+	0.543917i	$0.183060\pi$
$480$	3.81963	−	15.9609i	0.174342	−	0.728514i
$481$	4.78985	+	14.7416i	0.218398	+	0.672161i
$482$	1.47410			0.0671432
$483$	−3.56154	−	10.9613i	−0.162055	−	0.498755i
$484$	35.4504	+	25.7562i	1.61138	+	1.17074i
$485$	3.73169	−	15.5934i	0.169447	−	0.708062i
$486$	7.84262	−	5.69800i	0.355749	−	0.258466i
$487$	24.6329	+	17.8969i	1.11622	+	0.810984i	0.983633	−	0.180186i	$-0.0576701\pi$
$487$	24.6329	+	17.8969i	1.11622	+	0.810984i	0.132592	+	0.991171i	$0.457670\pi$
$488$	−23.1458	−	16.8164i	−1.04776	−	0.761242i
$489$	−19.6531	+	14.2788i	−0.888745	+	0.645711i
$490$	1.00869	−	0.862772i	0.0455681	−	0.0389761i
$491$	−5.48926	−	3.98818i	−0.247727	−	0.179984i	0.456992	−	0.889471i	$-0.348927\pi$
$491$	−5.48926	−	3.98818i	−0.247727	−	0.179984i	−0.704719	+	0.709487i	$0.748927\pi$
$492$	−1.32400	−	4.07485i	−0.0596905	−	0.183708i
$493$	0.270330			0.0121750
$494$	−1.44209	−	4.43831i	−0.0648829	−	0.199689i
$495$	−20.3442	+	1.61598i	−0.914405	+	0.0726331i
$496$	2.25713	−	6.94673i	0.101348	−	0.311917i
$497$	10.4350	−	32.1155i	0.468072	−	1.44058i
$498$	3.92090	−	2.84870i	0.175700	−	0.127653i
$499$	34.6960			1.55320			0.776602	−	0.629991i	$-0.216942\pi$
$499$	34.6960			1.55320			0.776602	+	0.629991i	$0.216942\pi$
$500$	1.25282	−	16.3744i	0.0560279	−	0.732284i
$501$	−9.70837			−0.433738
$502$	12.3861	−	8.99902i	0.552818	−	0.401646i
$503$	12.0178	−	36.9870i	0.535847	−	1.64917i	−0.205964	−	0.978559i	$-0.566033\pi$
$503$	12.0178	−	36.9870i	0.535847	−	1.64917i	0.741811	−	0.670608i	$-0.233967\pi$
$504$	−2.77514	+	8.54100i	−0.123615	+	0.380446i
$505$	26.2549	−	2.08548i	1.16833	−	0.0928026i
$506$	−5.31957	−	16.3719i	−0.236484	−	0.727822i
$507$	−13.2022			−0.586329
$508$	−6.13287	−	18.8750i	−0.272102	−	0.837445i
$509$	−23.9525	−	17.4025i	−1.06168	−	0.771353i	−0.0872784	−	0.996184i	$-0.527817\pi$
$509$	−23.9525	−	17.4025i	−1.06168	−	0.771353i	−0.974398	+	0.224831i	$0.927817\pi$
$510$	−1.55258	+	1.32798i	−0.0687495	+	0.0588040i
$511$	2.31770	−	1.68391i	0.102529	−	0.0744917i
$512$	9.66729	+	7.02370i	0.427238	+	0.310406i
$513$	18.3021	+	13.2973i	0.808059	+	0.587089i
$514$	0.139730	−	0.101520i	0.00616325	−	0.00447786i
$515$	−8.95128	+	37.4043i	−0.394440	+	1.64823i
$516$	−6.51386	−	4.73260i	−0.286757	−	0.208341i
$517$	12.7971	+	39.3855i	0.562817	+	1.73217i
$518$	−17.8796			−0.785583
$519$	−4.86172	−	14.9628i	−0.213406	−	0.656796i
$520$	−2.06742	+	8.63905i	−0.0906625	+	0.378848i
$521$	12.0270	−	37.0153i	0.526912	−	1.62167i	−0.233591	−	0.972335i	$-0.575048\pi$
$521$	12.0270	−	37.0153i	0.526912	−	1.62167i	0.760503	−	0.649334i	$-0.224952\pi$
$522$	0.0869572	−	0.267627i	0.00380602	−	0.0117137i
$523$	9.87493	−	7.17456i	0.431801	−	0.313722i	−0.350568	−	0.936537i	$-0.614011\pi$
$523$	9.87493	−	7.17456i	0.431801	−	0.313722i	0.782369	+	0.622816i	$0.214011\pi$
$524$	29.3046			1.28018
$525$	2.41644	−	15.4014i	0.105462	−	0.672174i
$526$	−16.4794			−0.718537
$527$	−5.39552	+	3.92007i	−0.235033	+	0.170761i
$528$	−2.71123	+	8.34432i	−0.117991	+	0.363140i
$529$	−2.88510	+	8.87942i	−0.125439	+	0.386062i
$530$	0.834733	+	2.01109i	0.0362585	+	0.0873563i
$531$	2.95543	+	9.09588i	0.128255	+	0.394727i
$532$	−14.8863			−0.645403
$533$	1.12981	+	3.47720i	0.0489376	+	0.150614i
$534$	3.95496	+	2.87345i	0.171148	+	0.124346i
$535$	−13.9680	+	1.10951i	−0.603890	+	0.0479683i
$536$	27.3766	−	19.8903i	1.18249	−	0.859128i
$537$	−10.7776	−	7.83037i	−0.465087	−	0.337905i
$538$	13.8057	+	10.0304i	0.595207	+	0.432443i
$539$	−4.21064	+	3.05921i	−0.181365	+	0.131769i
$540$	−6.99010	−	16.8410i	−0.300806	−	0.724722i
$541$	15.2260	+	11.0623i	0.654616	+	0.475606i	0.864840	−	0.502047i	$-0.167420\pi$
$541$	15.2260	+	11.0623i	0.654616	+	0.475606i	−0.210225	+	0.977653i	$0.567420\pi$
$542$	1.43557	+	4.41823i	0.0616630	+	0.189779i
$543$	12.7015			0.545075
$544$	−1.80911	−	5.56786i	−0.0775649	−	0.238720i
$545$	−5.70850	−	3.49248i	−0.244525	−	0.149601i
$546$	−1.10343	+	3.39600i	−0.0472223	+	0.145335i
$547$	−5.57415	+	17.1555i	−0.238334	+	0.733515i	0.758328	+	0.651873i	$0.226017\pi$
$547$	−5.57415	+	17.1555i	−0.238334	+	0.733515i	−0.996662	+	0.0816423i	$0.973983\pi$
$548$	−0.469026	+	0.340767i	−0.0200358	+	0.0145568i
$549$	−16.1637			−0.689849
$550$	3.60923	−	23.0038i	0.153898	−	0.980887i
$551$	1.10158			0.0469289
$552$	9.47806	−	6.88622i	0.403413	−	0.293097i
$553$	−10.2904	+	31.6706i	−0.437593	+	1.34677i
$554$	1.74267	−	5.36338i	0.0740389	−	0.227868i
$555$	21.0138	−	17.9739i	0.891988	−	0.762950i
$556$	−5.86425	−	18.0483i	−0.248699	−	0.765418i
$557$	18.6234			0.789100			0.394550	−	0.918874i	$-0.370900\pi$
$557$	18.6234			0.789100			0.394550	+	0.918874i	$0.370900\pi$
$558$	2.14530	+	6.60255i	0.0908177	+	0.279508i
$559$	5.55849	+	4.03848i	0.235099	+	0.170809i
$560$	5.19553	+	3.17864i	0.219551	+	0.134322i
$561$	6.48103	−	4.70874i	0.273629	−	0.198803i
$562$	17.4453	+	12.6747i	0.735885	+	0.534651i
$563$	−1.87499	−	1.36226i	−0.0790215	−	0.0574125i	0.547573	−	0.836758i	$-0.315552\pi$
$563$	−1.87499	−	1.36226i	−0.0790215	−	0.0574125i	−0.626595	+	0.779345i	$0.715552\pi$
$564$	−9.65490	+	7.01469i	−0.406544	+	0.295372i
$565$	−9.10996	−	5.57350i	−0.383259	−	0.234479i
$566$	−1.71693	−	1.24742i	−0.0721680	−	0.0524331i
$567$	−2.05589	−	6.32739i	−0.0863394	−	0.265725i
$568$	34.3254			1.44026
$569$	9.01729	+	27.7524i	0.378024	+	1.16344i	0.941416	+	0.337249i	$0.109496\pi$
$569$	9.01729	+	27.7524i	0.378024	+	1.16344i	−0.563391	+	0.826190i	$0.690504\pi$
$570$	−6.32670	+	5.41146i	−0.264996	+	0.226661i
$571$	6.72180	−	20.6876i	0.281299	−	0.865749i	−0.706185	−	0.708027i	$-0.749585\pi$
$571$	6.72180	−	20.6876i	0.281299	−	0.865749i	0.987484	−	0.157721i	$-0.0504147\pi$
$572$	4.55765	−	14.0270i	0.190565	−	0.586498i
$573$	9.33826	−	6.78464i	0.390111	−	0.283432i
$574$	−4.21736			−0.176029
$575$	13.0499	−	13.0878i	0.544218	−	0.545800i
$576$	−2.96554			−0.123564
$577$	−23.6846	+	17.2079i	−0.986002	+	0.716372i	−0.959042	−	0.283264i	$-0.908583\pi$
$577$	−23.6846	+	17.2079i	−0.986002	+	0.716372i	−0.0269599	+	0.999637i	$0.508583\pi$
$578$	−0.225212	+	0.693131i	−0.00936759	+	0.0288305i
$579$	4.27132	−	13.1458i	0.177510	−	0.546320i
$580$	−0.757381	−	0.463368i	−0.0314485	−	0.0192403i
$581$	4.07666	+	12.5467i	0.169128	+	0.520524i
$582$	6.55154			0.271570
$583$	−2.63838	−	8.12010i	−0.109271	−	0.336300i
$584$	2.35594	+	1.71169i	0.0974895	+	0.0708302i
$585$	1.92391	+	4.63521i	0.0795439	+	0.191642i
$586$	−1.82105	+	1.32307i	−0.0752270	+	0.0546556i
$587$	−28.2489	−	20.5241i	−1.16596	−	0.847118i	−0.175439	−	0.984490i	$-0.556134\pi$
$587$	−28.2489	−	20.5241i	−1.16596	−	0.847118i	−0.990520	+	0.137372i	$0.956134\pi$
$588$	−1.21341	−	0.881594i	−0.0500402	−	0.0363563i
$589$	−21.9865	+	15.9741i	−0.905937	+	0.658202i
$590$	−10.8779	+	0.864057i	−0.447837	+	0.0355726i
$591$	−6.85756	−	4.98231i	−0.282082	−	0.204945i
$592$	3.33842	+	10.2746i	0.137208	+	0.422283i
$593$	−17.4668			−0.717274			−0.358637	−	0.933477i	$-0.616758\pi$
$593$	−17.4668			−0.717274			−0.358637	+	0.933477i	$0.616758\pi$
$594$	−7.98942	−	24.5889i	−0.327810	−	1.00889i
$595$	−2.13193	−	5.13638i	−0.0874005	−	0.210571i
$596$	3.52873	−	10.8603i	0.144543	−	0.444856i
$597$	−1.87414	+	5.76801i	−0.0767034	+	0.236069i
$598$	−3.42475	+	2.48823i	−0.140049	+	0.101751i
$599$	−15.8563			−0.647870			−0.323935	−	0.946079i	$-0.605006\pi$
$599$	−15.8563			−0.647870			−0.323935	+	0.946079i	$0.605006\pi$
$600$	15.6484	−	2.50175i	0.638841	−	0.102133i
$601$	−14.4325			−0.588715			−0.294358	−	0.955695i	$-0.595106\pi$
$601$	−14.4325			−0.588715			−0.294358	+	0.955695i	$0.595106\pi$
$602$	−6.41171	+	4.65838i	−0.261322	+	0.189861i
$603$	5.90786	−	18.1825i	0.240586	−	0.740449i
$604$	−3.92377	+	12.0761i	−0.159656	+	0.491371i
$605$	−15.5254	+	64.8752i	−0.631196	+	2.63755i
$606$	3.32558	+	10.2351i	0.135092	+	0.415771i
$607$	9.86763			0.400515			0.200257	−	0.979743i	$-0.435822\pi$
$607$	9.86763			0.400515			0.200257	+	0.979743i	$0.435822\pi$
$608$	−7.37202	−	22.6888i	−0.298975	−	0.920151i
$609$	−0.681904	−	0.495432i	−0.0276322	−	0.0200759i
$610$	4.29224	−	17.9358i	0.173788	−	0.726200i
$611$	8.23883	−	5.98586i	0.333308	−	0.242162i
$612$	−1.69729	−	1.23315i	−0.0686087	−	0.0498471i
$613$	8.74092	+	6.35065i	0.353042	+	0.256500i	0.750144	−	0.661274i	$-0.229984\pi$
$613$	8.74092	+	6.35065i	0.353042	+	0.256500i	−0.397102	+	0.917775i	$0.629984\pi$
$614$	14.0818	−	10.2311i	0.568297	−	0.412892i
$615$	4.95666	−	4.23962i	0.199872	−	0.170958i
$616$	32.5044	+	23.6158i	1.30964	+	0.951508i
$617$	9.29399	+	28.6040i	0.374162	+	1.15155i	0.944042	+	0.329825i	$0.106990\pi$
$617$	9.29399	+	28.6040i	0.374162	+	1.15155i	−0.569880	+	0.821728i	$0.693010\pi$
$618$	−15.7153			−0.632163
$619$	−11.2756	−	34.7028i	−0.453205	−	1.39482i	−0.873229	−	0.487309i	$-0.837978\pi$
$619$	−11.2756	−	34.7028i	−0.453205	−	1.39482i	0.420024	−	0.907513i	$-0.362022\pi$
$620$	21.8359	−	1.73447i	0.876952	−	0.0696581i
$621$	6.34143	−	19.5169i	0.254473	−	0.783187i
$622$	−1.47494	+	4.53939i	−0.0591396	+	0.182013i
$623$	−10.7655	+	7.82162i	−0.431312	+	0.313367i
$624$	2.15756			0.0863714
$625$	23.7539	−	7.79442i	0.950155	−	0.311777i
$626$	10.9775			0.438751
$627$	26.4099	−	19.1879i	1.05471	−	0.766291i
$628$	1.70501	−	5.24748i	0.0680373	−	0.209397i
$629$	3.04819	−	9.38137i	0.121539	−	0.374060i
$630$	−5.77080	+	0.458387i	−0.229914	+	0.0182626i
$631$	−0.0335021	−	0.103109i	−0.00133370	−	0.00410470i	0.950387	−	0.311069i	$-0.100687\pi$
$631$	−0.0335021	−	0.103109i	−0.00133370	−	0.00410470i	−0.951721	+	0.306964i	$0.900687\pi$
$632$	−33.8499			−1.34648
$633$	9.47794	+	29.1701i	0.376714	+	1.15941i
$634$	−9.95394	−	7.23196i	−0.395321	−	0.287218i
$635$	22.9597	−	19.6383i	0.911127	−	0.779320i
$636$	1.99055	−	1.44622i	0.0789303	−	0.0573462i
$637$	1.03544	+	0.752293i	0.0410257	+	0.0298069i
$638$	−1.01850	−	0.739986i	−0.0403229	−	0.0292963i
$639$	15.6891	−	11.3988i	0.620652	−	0.450930i
$640$	−5.30601	+	22.1720i	−0.209739	+	0.876426i
$641$	−6.13477	−	4.45717i	−0.242309	−	0.176048i	0.460002	−	0.887918i	$-0.347849\pi$
$641$	−6.13477	−	4.45717i	−0.242309	−	0.176048i	−0.702311	+	0.711870i	$0.747849\pi$
$642$	−1.76926	−	5.44522i	−0.0698271	−	0.214906i
$643$	10.7933			0.425645			0.212822	−	0.977091i	$-0.431734\pi$
$643$	10.7933			0.425645			0.212822	+	0.977091i	$0.431734\pi$
$644$	4.17282	+	12.8426i	0.164432	+	0.506070i
$645$	2.85272	−	11.9205i	0.112326	−	0.469371i
$646$	−0.917728	+	2.82448i	−0.0361075	+	0.111128i
$647$	10.9360	−	33.6576i	0.429939	−	1.32322i	−0.468245	−	0.883599i	$-0.655114\pi$
$647$	10.9360	−	33.6576i	0.429939	−	1.32322i	0.898185	−	0.439619i	$-0.144886\pi$
$648$	5.47120	−	3.97506i	0.214929	−	0.156155i
$649$	42.7878			1.67957
$650$	−5.65429	+	0.903968i	−0.221780	+	0.0354565i
$651$	20.7945			0.814999
$652$	23.0263	−	16.7296i	0.901780	−	0.655181i
$653$	−2.72411	+	8.38396i	−0.106603	+	0.328090i	−0.990103	−	0.140341i	$-0.955180\pi$
$653$	−2.72411	+	8.38396i	−0.106603	+	0.328090i	0.883501	+	0.468430i	$0.155180\pi$
$654$	0.844995	−	2.60063i	0.0330419	−	0.101693i
$655$	17.1019	+	41.2030i	0.668226	+	1.60994i
$656$	0.787453	+	2.42353i	0.0307449	+	0.0946230i
$657$	1.64525			0.0641874
$658$	3.63001	+	11.1720i	0.141512	+	0.435531i
$659$	0.512840	+	0.372600i	0.0199774	+	0.0145144i	0.597729	−	0.801698i	$-0.296070\pi$
$659$	0.512840	+	0.372600i	0.0199774	+	0.0145144i	−0.577752	+	0.816213i	$0.696070\pi$
$660$	−26.2290	+	2.08343i	−1.02096	+	0.0810973i
$661$	−14.8822	+	10.8125i	−0.578850	+	0.420559i	−0.838309	−	0.545195i	$-0.816456\pi$
$661$	−14.8822	+	10.8125i	−0.578850	+	0.420559i	0.259459	+	0.965754i	$0.416456\pi$
$662$	16.6484	+	12.0958i	0.647058	+	0.470115i
$663$	−1.59376	−	1.15793i	−0.0618963	−	0.0449703i
$664$	−10.8489	+	7.88221i	−0.421020	+	0.305889i
$665$	−8.68750	−	20.9305i	−0.336887	−	0.811650i
$666$	−8.30706	−	6.03543i	−0.321892	−	0.233868i
$667$	−0.308787	−	0.950349i	−0.0119563	−	0.0367977i
$668$	11.3747			0.440099
$669$	8.44272	+	25.9840i	0.326414	+	1.00460i
$670$	18.6072	+	11.3839i	0.718857	+	0.439799i
$671$	−22.3462	+	68.7746i	−0.862666	+	2.65501i
$672$	−5.64074	+	17.3604i	−0.217596	+	0.669693i
$673$	25.4820	−	18.5138i	0.982259	−	0.713653i	0.0240466	−	0.999711i	$-0.492345\pi$
$673$	25.4820	−	18.5138i	0.982259	−	0.713653i	0.958212	+	0.286058i	$0.0923450\pi$
$674$	−16.8199			−0.647876
$675$	19.5995	−	19.6565i	0.754386	−	0.756579i
$676$	15.4681			0.594928
$677$	27.4018	−	19.9086i	1.05314	−	0.765150i	0.0803316	−	0.996768i	$-0.474402\pi$
$677$	27.4018	−	19.9086i	1.05314	−	0.765150i	0.972807	+	0.231618i	$0.0744021\pi$
$678$	1.34849	−	4.15024i	0.0517886	−	0.159389i
$679$	−5.51087	+	16.9607i	−0.211488	+	0.650892i
$680$	4.29591	−	3.67445i	0.164741	−	0.140909i
$681$	−6.27110	−	19.3005i	−0.240309	−	0.739595i
$682$	31.0589			1.18931
$683$	3.76855	+	11.5984i	0.144200	+	0.443801i	0.996907	−	0.0785876i	$-0.0250410\pi$
$683$	3.76855	+	11.5984i	0.144200	+	0.443801i	−0.852707	+	0.522389i	$0.825041\pi$
$684$	−6.91636	−	5.02503i	−0.264453	−	0.192137i
$685$	−0.752845	−	0.460593i	−0.0287647	−	0.0175983i
$686$	−11.4592	+	8.32562i	−0.437515	+	0.317874i
$687$	−2.49877	−	1.81546i	−0.0953340	−	0.0692642i
$688$	3.87414	+	2.81473i	0.147700	+	0.107310i
$689$	−1.69860	+	1.23410i	−0.0647114	+	0.0470156i
$690$	6.44200	+	3.94123i	0.245243	+	0.150040i
$691$	36.6749	+	26.6459i	1.39518	+	1.01366i	0.995275	+	0.0971011i	$0.0309570\pi$
$691$	36.6749	+	26.6459i	1.39518	+	1.01366i	0.399905	+	0.916556i	$0.369043\pi$
$692$	5.69617	+	17.5310i	0.216536	+	0.666428i
$693$	22.6992			0.862270
$694$	2.11981	+	6.52410i	0.0804668	+	0.247651i
$695$	21.9540	−	18.7781i	0.832763	−	0.712293i
$696$	0.264762	−	0.814853i	0.0100358	−	0.0308869i
$697$	0.718996	−	2.21284i	0.0272339	−	0.0838174i
$698$	−8.56551	+	6.22321i	−0.324210	+	0.235552i
$699$	13.8327			0.523202
$700$	−2.83118	+	18.0449i	−0.107009	+	0.682032i
$701$	12.0942			0.456792			0.228396	−	0.973568i	$-0.426652\pi$
$701$	12.0942			0.456792			0.228396	+	0.973568i	$0.426652\pi$
$702$	−5.14361	+	3.73705i	−0.194133	+	0.141046i
$703$	12.4212	−	38.2286i	0.468476	−	1.44182i
$704$	−4.09985	+	12.6180i	−0.154519	+	0.475560i
$705$	−15.4973	−	9.48131i	−0.583663	−	0.357087i
$706$	3.54959	+	10.9245i	0.133591	+	0.411150i
$707$	−29.2940			−1.10171
$708$	3.81032	+	11.7270i	0.143201	+	0.440726i
$709$	−19.8336	−	14.4100i	−0.744868	−	0.541178i	0.149364	−	0.988782i	$-0.452277\pi$
$709$	−19.8336	−	14.4100i	−0.744868	−	0.541178i	−0.894232	+	0.447604i	$0.852277\pi$
$710$	8.48233	+	20.4362i	0.318336	+	0.766956i
$711$	−15.4718	+	11.2409i	−0.580238	+	0.421568i
$712$	−10.9432	−	7.95067i	−0.410112	−	0.297964i
$713$	19.9442	+	14.4903i	0.746915	+	0.542666i
$714$	1.83840	−	1.33567i	0.0688002	−	0.0499863i
$715$	22.3821	−	1.77786i	0.837043	−	0.0664880i
$716$	12.6274	+	9.17434i	0.471908	+	0.342861i
$717$	6.24211	+	19.2112i	0.233116	+	0.717456i
$718$	−3.18380			−0.118818
$719$	−1.60187	−	4.93004i	−0.0597396	−	0.183859i	0.916733	−	0.399500i	$-0.130816\pi$
$719$	−1.60187	−	4.93004i	−0.0597396	−	0.183859i	−0.976473	+	0.215640i	$0.930816\pi$
$720$	1.34092	+	3.23064i	0.0499732	+	0.120399i
$721$	13.2190	−	40.6840i	0.492303	−	1.51515i
$722$	0.539333	−	1.65990i	0.0200719	−	0.0617750i
$723$	2.05144	−	1.49046i	0.0762938	−	0.0554307i
$724$	−14.8816			−0.553069
$725$	0.209506	−	1.33531i	0.00778087	−	0.0495923i
$726$	−27.2571			−1.01161
$727$	−25.0627	+	18.2091i	−0.929523	+	0.675338i	−0.945876	−	0.324528i	$-0.894794\pi$
$727$	−25.0627	+	18.2091i	−0.929523	+	0.675338i	0.0163529	+	0.999866i	$0.494794\pi$
$728$	3.05312	−	9.39654i	0.113156	−	0.348259i
$729$	7.63291	−	23.4917i	0.282700	−	0.870062i
$730$	−0.436894	+	1.82563i	−0.0161702	+	0.0675697i
$731$	−1.35114	−	4.15839i	−0.0499739	−	0.153804i
$732$	−20.8392			−0.770239
$733$	−11.4544	−	35.2531i	−0.423079	−	1.30210i	−0.904822	−	0.425791i	$-0.859996\pi$
$733$	−11.4544	−	35.2531i	−0.423079	−	1.30210i	0.481743	−	0.876313i	$-0.340004\pi$
$734$	6.23885	+	4.53279i	0.230280	+	0.167308i
$735$	0.531408	−	2.22057i	0.0196013	−	0.0819071i
$736$	−17.5074	+	12.7199i	−0.645333	+	0.468862i
$737$	−69.1969	−	50.2745i	−2.54890	−	1.85188i
$738$	−1.95944	−	1.42361i	−0.0721279	−	0.0524040i
$739$	8.28665	−	6.02060i	0.304829	−	0.221471i	−0.424845	−	0.905266i	$-0.639672\pi$
$739$	8.28665	−	6.02060i	0.304829	−	0.221471i	0.729675	+	0.683794i	$0.239672\pi$
$740$	−24.6206	+	21.0589i	−0.905070	+	0.774140i
$741$	−6.49447	−	4.71851i	−0.238580	−	0.173339i
$742$	−0.748398	−	2.30333i	−0.0274745	−	0.0845580i
$743$	−5.74985			−0.210941			−0.105471	−	0.994422i	$-0.533635\pi$
$743$	−5.74985			−0.210941			−0.105471	+	0.994422i	$0.533635\pi$
$744$	6.53186	+	20.1030i	0.239470	+	0.737012i
$745$	17.3292	−	1.37650i	0.634893	−	0.0504309i
$746$	2.22498	−	6.84777i	0.0814622	−	0.250715i
$747$	−2.34119	+	7.20545i	−0.0856598	+	0.263634i
$748$	−7.59340	+	5.51693i	−0.277642	+	0.201719i
$749$	15.5849			0.569459
$750$	5.35640	+	8.69828i	0.195588	+	0.317616i
$751$	25.4330			0.928063			0.464032	−	0.885819i	$-0.346402\pi$
$751$	25.4330			0.928063			0.464032	+	0.885819i	$0.346402\pi$
$752$	5.74228	−	4.17201i	0.209400	−	0.152138i
$753$	8.13831	−	25.0471i	0.296576	−	0.912768i
$754$	−0.0956676	+	0.294435i	−0.00348401	+	0.0107227i
$755$	−19.2692	+	1.53059i	−0.701278	+	0.0557040i
$756$	6.26713	+	19.2882i	0.227933	+	0.701507i
$757$	6.87254			0.249787			0.124893	−	0.992170i	$-0.460141\pi$
$757$	6.87254			0.249787			0.124893	+	0.992170i	$0.460141\pi$
$758$	−0.158807	−	0.488759i	−0.00576814	−	0.0177525i
$759$	−23.9567	−	17.4056i	−0.869573	−	0.631782i
$760$	17.5056	−	14.9732i	0.634996	−	0.543136i
$761$	25.3041	−	18.3845i	0.917273	−	0.666438i	−0.0255706	−	0.999673i	$-0.508140\pi$
$761$	25.3041	−	18.3845i	0.917273	−	0.666438i	0.942844	+	0.333235i	$0.108140\pi$
$762$	9.98748	+	7.25633i	0.361808	+	0.262869i
$763$	6.02176	+	4.37506i	0.218002	+	0.158388i
$764$	−10.9410	+	7.94913i	−0.395833	+	0.287589i
$765$	0.743320	−	3.10608i	0.0268748	−	0.112301i
$766$	−0.609726	−	0.442992i	−0.0220303	−	0.0160059i
$767$	−3.25147	−	10.0070i	−0.117404	−	0.361332i
$768$	−14.5214			−0.523997
$769$	−5.47477	−	16.8496i	−0.197425	−	0.607613i	−0.999940	−	0.0109799i	$-0.996505\pi$
$769$	−5.47477	−	16.8496i	−0.197425	−	0.607613i	0.802514	−	0.596633i	$-0.203495\pi$
$770$	−6.02773	+	25.1878i	−0.217224	+	0.907706i
$771$	0.0918102	−	0.282563i	0.00330646	−	0.0101762i
$772$	−5.00443	+	15.4021i	−0.180114	+	0.554332i
$773$	−42.1402	+	30.6166i	−1.51568	+	1.10120i	−0.552099	+	0.833779i	$0.686173\pi$
$773$	−42.1402	+	30.6166i	−1.51568	+	1.10120i	−0.963579	+	0.267425i	$0.913827\pi$
$774$	−4.55144			−0.163598
$775$	15.1819	+	29.6896i	0.545352	+	1.06648i
$776$	−18.1278			−0.650749
$777$	−24.8822	+	18.0780i	−0.892645	+	0.648545i
$778$	5.11504	−	15.7425i	0.183383	−	0.564395i
$779$	2.92987	−	9.01722i	0.104974	−	0.323075i
$780$	2.48042	+	5.97600i	0.0888134	+	0.213975i
$781$	−26.8105	−	82.5143i	−0.959355	−	2.95259i
$782$	2.69397			0.0963360
$783$	−0.463765	−	1.42732i	−0.0165736	−	0.0510083i
$784$	0.721680	+	0.524331i	0.0257743	+	0.0187261i
$785$	8.37311	−	0.665093i	0.298849	−	0.0237382i
$786$	−14.7472	+	10.7145i	−0.526017	+	0.382173i
$787$	−40.2696	−	29.2576i	−1.43546	−	1.04292i	−0.988968	−	0.148132i	$-0.952674\pi$
$787$	−40.2696	−	29.2576i	−1.43546	−	1.04292i	−0.446490	−	0.894789i	$-0.647326\pi$
$788$	8.03456	+	5.83745i	0.286219	+	0.207950i
$789$	−22.9337	+	16.6623i	−0.816462	+	0.593195i
$790$	−8.36483	−	20.1531i	−0.297607	−	0.717015i
$791$	9.60988	+	6.98199i	0.341688	+	0.248251i
$792$	7.13016	+	21.9444i	0.253359	+	0.779759i
$793$	17.7828			0.631484
$794$	5.52582	+	17.0067i	0.196104	+	0.603546i
$795$	3.19508	+	1.95476i	0.113318	+	0.0693281i
$796$	2.19581	−	6.75801i	0.0778284	−	0.239531i
$797$	1.32002	−	4.06262i	0.0467577	−	0.143905i	−0.924952	−	0.380084i	$-0.875895\pi$
$797$	1.32002	−	4.06262i	0.0467577	−	0.143905i	0.971710	+	0.236179i	$0.0758951\pi$
$798$	7.49137	−	5.44280i	0.265192	−	0.192673i
$799$	−6.48080			−0.229274
$800$	−28.9049	+	4.62111i	−1.02194	+	0.163381i
$801$	−7.64207			−0.270019
$802$	15.4479	−	11.2236i	0.545486	−	0.396319i
$803$	2.27455	−	7.00035i	0.0802672	−	0.247037i
$804$	7.61677	−	23.4420i	0.268623	−	0.826736i
$805$	−15.6218	+	13.3619i	−0.550597	+	0.470946i
$806$	−2.36019	−	7.26391i	−0.0831341	−	0.255860i
$807$	29.3546			1.03333
$808$	−9.20169	−	28.3199i	−0.323714	−	0.996291i
$809$	−31.2347	−	22.6933i	−1.09815	−	0.797855i	−0.117396	−	0.993085i	$-0.537455\pi$
$809$	−31.2347	−	22.6933i	−1.09815	−	0.797855i	−0.980757	+	0.195230i	$0.937455\pi$
$810$	3.71863	+	2.27507i	0.130660	+	0.0799379i
$811$	6.97957	−	5.07095i	0.245086	−	0.178065i	−0.458460	−	0.888715i	$-0.651599\pi$
$811$	6.97957	−	5.07095i	0.245086	−	0.178065i	0.703546	+	0.710650i	$0.251599\pi$
$812$	0.798943	+	0.580466i	0.0280374	+	0.0203704i
$813$	6.46509	+	4.69717i	0.226741	+	0.164737i
$814$	−37.1645	+	27.0016i	−1.30262	+	0.946406i
$815$	36.9601	+	22.6123i	1.29466	+	0.792074i
$816$	−1.11081	−	0.807052i	−0.0388862	−	0.0282525i
$817$	−5.50585	−	16.9452i	−0.192625	−	0.592839i
$818$	−7.52791			−0.263207
$819$	−1.72492	−	5.30877i	−0.0602737	−	0.185503i
$820$	−5.80741	+	4.96729i	−0.202803	+	0.173465i
$821$	15.3833	−	47.3451i	0.536883	−	1.65235i	−0.202664	−	0.979248i	$-0.564960\pi$
$821$	15.3833	−	47.3451i	0.536883	−	1.65235i	0.739546	−	0.673106i	$-0.235040\pi$
$822$	0.111439	−	0.342975i	0.00388689	−	0.0119626i
$823$	−22.9165	+	16.6498i	−0.798820	+	0.580377i	−0.910568	−	0.413360i	$-0.864355\pi$
$823$	−22.9165	+	16.6498i	−0.798820	+	0.580377i	0.111748	+	0.993737i	$0.464355\pi$
$824$	43.4835			1.51482
$825$	−18.2364	−	35.6628i	−0.634908	−	1.24162i
$826$	12.1371			0.422303
$827$	−31.2453	+	22.7010i	−1.08651	+	0.789393i	−0.978806	−	0.204791i	$-0.934349\pi$
$827$	−31.2453	+	22.7010i	−1.08651	+	0.789393i	−0.107700	+	0.994183i	$0.534349\pi$
$828$	−2.39642	+	7.37542i	−0.0832813	+	0.256313i
$829$	−1.76423	+	5.42974i	−0.0612742	+	0.188583i	−0.977008	−	0.213203i	$-0.931610\pi$
$829$	−1.76423	+	5.42974i	−0.0612742	+	0.188583i	0.915734	+	0.401786i	$0.131610\pi$
$830$	−7.37374	−	4.51127i	−0.255946	−	0.156589i
$831$	−2.99771	−	9.22601i	−0.103989	−	0.320047i
$832$	3.26259			0.113110
$833$	−0.251693	−	0.774631i	−0.00872064	−	0.0268394i
$834$	9.55001	+	6.93849i	0.330690	+	0.240260i
$835$	6.63815	+	15.9931i	0.229723	+	0.553463i
$836$	−30.9427	+	22.4812i	−1.07018	+	0.777529i
$837$	29.9540	+	21.7629i	1.03536	+	0.752235i
$838$	1.77973	+	1.29305i	0.0614796	+	0.0446675i
$839$	19.9336	−	14.4826i	0.688185	−	0.499996i	−0.187878	−	0.982192i	$-0.560161\pi$
$839$	19.9336	−	14.4826i	0.688185	−	0.499996i	0.876063	+	0.482197i	$0.160161\pi$
$840$	−17.5706	+	1.39567i	−0.606242	+	0.0481551i
$841$	23.4024	+	17.0028i	0.806978	+	0.586304i
$842$	−0.207215	−	0.637742i	−0.00714109	−	0.0219780i
$843$	37.0933			1.27756
$844$	−11.1047	−	34.1767i	−0.382239	−	1.17641i
$845$	9.02704	+	21.7486i	0.310540	+	0.748173i
$846$	−2.08469	+	6.41600i	−0.0716730	+	0.220587i
$847$	22.9275	−	70.5635i	0.787798	−	2.42459i
$848$	−1.18388	+	0.860142i	−0.0406548	+	0.0295374i
$849$	−3.65065			−0.125290
$850$	3.24923	+	1.64963i	0.111448	+	0.0565818i
$851$	−36.4622			−1.24991
$852$	20.2274	−	14.6961i	0.692979	−	0.503479i
$853$	6.07450	−	18.6954i	0.207987	−	0.640118i	−0.791591	−	0.611052i	$-0.790747\pi$
$853$	6.07450	−	18.6954i	0.207987	−	0.640118i	0.999577	−	0.0290662i	$-0.00925335\pi$
$854$	−6.33868	+	19.5084i	−0.216905	+	0.667565i
$855$	3.02899	−	12.6571i	0.103589	−	0.432864i
$856$	4.89545	+	15.0666i	0.167323	+	0.514967i
$857$	−3.33902			−0.114059			−0.0570294	−	0.998372i	$-0.518163\pi$
$857$	−3.33902			−0.114059			−0.0570294	+	0.998372i	$0.518163\pi$
$858$	2.83503	+	8.72532i	0.0967863	+	0.297877i
$859$	−5.85780	−	4.25594i	−0.199866	−	0.145211i	0.483351	−	0.875427i	$-0.339419\pi$
$859$	−5.85780	−	4.25594i	−0.199866	−	0.145211i	−0.683217	+	0.730216i	$0.739419\pi$
$860$	−3.34235	+	13.9665i	−0.113973	+	0.476255i
$861$	−5.86913	+	4.26417i	−0.200019	+	0.145323i
$862$	17.9109	+	13.0130i	0.610049	+	0.443226i
$863$	−33.3481	−	24.2288i	−1.13518	−	0.824759i	−0.148742	−	0.988876i	$-0.547522\pi$
$863$	−33.3481	−	24.2288i	−1.13518	−	0.824759i	−0.986441	+	0.164117i	$0.947522\pi$
$864$	−26.2943	+	19.1039i	−0.894550	+	0.649929i
$865$	−21.3248	+	18.2399i	−0.725064	+	0.620174i
$866$	7.54263	+	5.48004i	0.256309	+	0.186219i
$867$	0.387406	+	1.19231i	0.0131570	+	0.0404931i
$868$	−24.3635			−0.826952
$869$	26.4391	+	81.3713i	0.896886	+	2.76033i
$870$	0.550563	−	0.0437323i	0.0186658	−	0.00148266i
$871$	−6.49964	+	20.0038i	−0.220232	+	0.677804i
$872$	−2.33806	+	7.19580i	−0.0791766	+	0.243680i
$873$	−8.28568	+	6.01990i	−0.280428	+	0.203743i
$874$	10.9778			0.371329
$875$	−27.0238	+	6.55010i	−0.913570	+	0.221434i
$876$	2.12116			0.0716673
$877$	−8.12733	+	5.90485i	−0.274440	+	0.199393i	−0.716489	−	0.697599i	$-0.754252\pi$
$877$	−8.12733	+	5.90485i	−0.274440	+	0.199393i	0.442049	+	0.896991i	$0.354252\pi$
$878$	6.51432	−	20.0490i	0.219848	−	0.676621i
$879$	−1.19653	+	3.68253i	−0.0403579	+	0.124209i
$880$	15.5998	−	1.23913i	0.525870	−	0.0417709i
$881$	−15.7695	−	48.5335i	−0.531288	−	1.63514i	−0.751535	−	0.659693i	$-0.770686\pi$
$881$	−15.7695	−	48.5335i	−0.531288	−	1.63514i	0.220247	−	0.975444i	$-0.429314\pi$
$882$	−0.847849			−0.0285485
$883$	9.03943	+	27.8205i	0.304201	+	0.936235i	0.979974	+	0.199125i	$0.0638099\pi$
$883$	9.03943	+	27.8205i	0.304201	+	0.936235i	−0.675773	+	0.737110i	$0.736190\pi$
$884$	1.86730	+	1.35667i	0.0628041	+	0.0456299i
$885$	−14.2647	+	12.2011i	−0.479503	+	0.410137i
$886$	−8.00705	+	5.81746i	−0.269002	+	0.195441i
$887$	15.9993	+	11.6242i	0.537205	+	0.390303i	0.823046	−	0.567975i	$-0.192273\pi$
$887$	15.9993	+	11.6242i	0.537205	+	0.390303i	−0.285841	+	0.958277i	$0.592273\pi$
$888$	−25.2928	−	18.3763i	−0.848770	−	0.616668i
$889$	−27.1863	+	19.7520i	−0.911799	+	0.662461i
$890$	2.02934	−	8.47993i	0.0680237	−	0.284248i
$891$	−13.8290	−	10.0473i	−0.463288	−	0.336598i
$892$	−9.89179	−	30.4438i	−0.331202	−	1.01933i
$893$	−26.4089			−0.883741
$894$	2.19501	+	6.75553i	0.0734120	+	0.225939i
$895$	−5.53012	+	23.1085i	−0.184851	+	0.772431i
$896$	7.83579	−	24.1161i	0.261775	−	0.805662i
$897$	−2.25024	+	6.92553i	−0.0751334	+	0.231237i
$898$	−18.0878	+	13.1416i	−0.603599	+	0.438540i
$899$	1.80289			0.0601298
$900$	−7.40664	+	7.42817i	−0.246888	+	0.247606i
$901$	1.33614			0.0445134
$902$	−8.76623	+	6.36904i	−0.291883	+	0.212066i
$903$	−4.21283	+	12.9657i	−0.140194	+	0.431473i
$904$	−3.73121	+	11.4835i	−0.124098	+	0.381935i
$905$	−8.68474	−	20.9238i	−0.288690	−	0.695532i
$906$	−2.44073	−	7.51181i	−0.0810880	−	0.249563i
$907$	−0.0795572			−0.00264165			−0.00132083	−	0.999999i	$-0.500420\pi$
$907$	−0.0795572			−0.00264165			−0.00132083	+	0.999999i	$0.500420\pi$
$908$	7.34745	+	22.6131i	0.243834	+	0.750443i
$909$	−13.6103	−	9.88849i	−0.451426	−	0.327980i
$910$	6.34886	−	0.504303i	0.210463	−	0.0167175i
$911$	−28.4972	+	20.7044i	−0.944155	+	0.685969i	−0.949417	−	0.314017i	$-0.898325\pi$
$911$	−28.4972	+	20.7044i	−0.944155	+	0.685969i	0.00526217	+	0.999986i	$0.498325\pi$
$912$	−4.52650	−	3.28870i	−0.149887	−	0.108900i
$913$	27.4217	+	19.9230i	0.907525	+	0.659356i
$914$	7.58950	−	5.51409i	0.251038	−	0.182390i
$915$	−12.1616	−	29.3004i	−0.402048	−	0.968642i
$916$	2.92765	+	2.12706i	0.0967322	+	0.0702801i
$917$	−15.3331	−	47.1904i	−0.506343	−	1.55836i
$918$	4.04605			0.133539
$919$	15.7231	+	48.3907i	0.518657	+	1.59626i	0.776527	+	0.630084i	$0.216979\pi$
$919$	15.7231	+	48.3907i	0.518657	+	1.59626i	−0.257870	+	0.966180i	$0.583021\pi$
$920$	−17.8247	−	10.9052i	−0.587662	−	0.359533i
$921$	9.25251	−	28.4763i	0.304881	−	0.938326i
$922$	0.755203	−	2.32428i	0.0248713	−	0.0765460i
$923$	−17.2607	+	12.5406i	−0.568142	+	0.412780i
$924$	29.2652			0.962753
$925$	−43.9776	−	22.3273i	−1.44597	−	0.734119i
$926$	−26.6108			−0.874484
$927$	19.8750	−	14.4401i	0.652782	−	0.474274i
$928$	−0.489056	+	1.50516i	−0.0160540	+	0.0494092i
$929$	16.4039	−	50.4860i	0.538194	−	1.65639i	−0.198451	−	0.980111i	$-0.563591\pi$
$929$	16.4039	−	50.4860i	0.538194	−	1.65639i	0.736645	−	0.676280i	$-0.236409\pi$
$930$	−10.3545	+	8.85661i	−0.339538	+	0.290420i
$931$	−1.02564	−	3.15658i	−0.0336139	−	0.103453i
$932$	−16.2069			−0.530875
$933$	2.53717	+	7.80860i	0.0830631	+	0.255642i
$934$	−0.165048	−	0.119914i	−0.00540054	−	0.00392372i
$935$	−12.1884	−	7.45688i	−0.398602	−	0.243866i
$936$	4.59042	−	3.33513i	0.150042	−	0.109012i
$937$	12.0123	+	8.72743i	0.392424	+	0.285113i	0.766448	−	0.642306i	$-0.222022\pi$
$937$	12.0123	+	8.72743i	0.392424	+	0.285113i	−0.374024	+	0.927419i	$0.622022\pi$
$938$	−19.6282	−	14.2608i	−0.640885	−	0.465630i
$939$	15.2770	−	11.0994i	0.498546	−	0.362215i
$940$	18.1572	+	11.1086i	0.592223	+	0.362324i
$941$	−11.9004	−	8.64614i	−0.387942	−	0.281856i	0.376670	−	0.926348i	$-0.377069\pi$
$941$	−11.9004	−	8.64614i	−0.387942	−	0.281856i	−0.764611	+	0.644491i	$0.777069\pi$
$942$	1.06058	+	3.26413i	0.0345556	+	0.106351i
$943$	−8.60057			−0.280073
$944$	−2.26620	−	6.97465i	−0.0737586	−	0.227006i
$945$	−23.4623	+	20.0682i	−0.763228	+	0.652817i
$946$	−6.29235	+	19.3659i	−0.204582	+	0.629638i
$947$	14.3547	−	44.1792i	0.466465	−	1.43563i	−0.390665	−	0.920533i	$-0.627755\pi$
$947$	14.3547	−	44.1792i	0.466465	−	1.43563i	0.857130	−	0.515099i	$-0.172245\pi$
$948$	−19.9472	+	14.4925i	−0.647855	+	0.470694i
$949$	−1.81005			−0.0587568
$950$	13.2405	+	6.72216i	0.429577	+	0.218096i
$951$	−21.1647			−0.686313
$952$	−5.08674	+	3.69573i	−0.164862	+	0.119779i
$953$	−9.93850	+	30.5876i	−0.321940	+	0.990829i	0.650863	+	0.759195i	$0.274407\pi$
$953$	−9.93850	+	30.5876i	−0.321940	+	0.990829i	−0.972803	+	0.231634i	$0.925593\pi$
$954$	0.429799	−	1.32278i	0.0139153	−	0.0428267i
$955$	−17.5617	−	10.7443i	−0.568285	−	0.347678i
$956$	−7.31347	−	22.5086i	−0.236535	−	0.727979i
$957$	−2.16561			−0.0700042
$958$	2.54325	+	7.82732i	0.0821687	+	0.252889i
$959$	0.794158	+	0.576990i	0.0256447	+	0.0186320i
$960$	−2.23127	−	5.37573i	−0.0720140	−	0.173501i
$961$	−10.9044	+	7.92253i	−0.351756	+	0.255566i
$962$	9.13916	+	6.63999i	0.294658	+	0.214082i
$963$	7.24092	+	5.26084i	0.233335	+	0.169528i
$964$	−2.40354	+	1.74627i	−0.0774128	+	0.0562437i
$965$	−24.5762	+	1.95214i	−0.791136	+	0.0628416i
$966$	−6.79551	−	4.93722i	−0.218642	−	0.158853i
$967$	8.11936	+	24.9888i	0.261101	+	0.803586i	0.992566	+	0.121707i	$0.0388369\pi$
$967$	8.11936	+	24.9888i	0.261101	+	0.803586i	−0.731465	+	0.681879i	$0.761163\pi$
$968$	75.4191			2.42406
$969$	1.57866	+	4.85862i	0.0507139	+	0.156081i
$970$	−4.47965	−	10.7927i	−0.143833	−	0.346532i
$971$	−8.48795	+	26.1232i	−0.272391	+	0.838334i	0.717507	+	0.696552i	$0.245283\pi$
$971$	−8.48795	+	26.1232i	−0.272391	+	0.838334i	−0.989898	+	0.141782i	$0.954717\pi$
$972$	−6.03745	+	18.5814i	−0.193651	+	0.595998i
$973$	−25.9955	+	18.8868i	−0.833377	+	0.605484i
$974$	22.1905			0.711030
$975$	−6.95485	+	6.97507i	−0.222733	+	0.223381i
$976$	12.3942			0.396728
$977$	25.0469	−	18.1976i	0.801321	−	0.582194i	−0.109980	−	0.993934i	$-0.535079\pi$
$977$	25.0469	−	18.1976i	0.801321	−	0.582194i	0.911301	+	0.411740i	$0.135079\pi$
$978$	−5.47099	+	16.8380i	−0.174943	+	0.538419i
$979$	−10.5651	+	32.5161i	−0.337663	+	1.03922i
$980$	−0.622617	+	2.60170i	−0.0198888	+	0.0831084i
$981$	1.32093	+	4.06541i	0.0421741	+	0.129799i
$982$	−4.94499			−0.157801
$983$	12.1874	+	37.5090i	0.388718	+	1.19635i	0.933747	+	0.357933i	$0.116519\pi$
$983$	12.1874	+	37.5090i	0.388718	+	1.19635i	−0.545029	+	0.838417i	$0.683481\pi$
$984$	−5.96596	−	4.33453i	−0.190188	−	0.138180i
$985$	−3.51870	+	14.7035i	−0.112115	+	0.468491i
$986$	0.159390	−	0.115804i	0.00507601	−	0.00368794i
$987$	16.3478	+	11.8773i	0.520355	+	0.378060i
$988$	7.60916	+	5.52838i	0.242079	+	0.175881i
$989$	−13.0755	+	9.49994i	−0.415778	+	0.302081i
$990$	−11.3030	+	9.66784i	−0.359232	+	0.307264i
$991$	19.7330	+	14.3368i	0.626838	+	0.455424i	0.855303	−	0.518128i	$-0.173371\pi$
$991$	19.7330	+	14.3368i	0.626838	+	0.455424i	−0.228465	+	0.973552i	$0.573371\pi$
$992$	−12.0654	−	37.1333i	−0.383075	−	1.17898i
$993$	35.3989			1.12335
$994$	−7.60501	−	23.4058i	−0.241216	−	0.742388i
$995$	10.7834	−	0.856545i	0.341856	−	0.0271543i
$996$	−3.01841	+	9.28971i	−0.0956420	+	0.294356i
$997$	13.5558	−	41.7206i	0.429318	−	1.32130i	−0.469481	−	0.882942i	$-0.655559\pi$
$997$	13.5558	−	41.7206i	0.429318	−	1.32130i	0.898799	−	0.438361i	$-0.144441\pi$
$998$	20.4572	−	14.8630i	0.647561	−	0.470480i
$999$	−54.7623			−1.73260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.13	✓	76
25.16	even	5	inner	425.2.k.b.341.13	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.13	✓	76	1.1	even	1	trivial
425.2.k.b.341.13	yes	76	25.16	even	5	inner

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.589613 - 0.428379i) q^{2} +(0.387406 - 1.19231i) q^{3} +(-0.453899 + 1.39696i) q^{4} +(-2.22905 + 0.177058i) q^{5} +(-0.282342 - 0.868960i) q^{6} +2.48707 q^{7} +(0.781226 + 2.40437i) q^{8} +(1.15552 + 0.839535i) q^{9} +(-1.23843 + 1.05927i) q^{10} +(5.16963 - 3.75596i) q^{11} +(1.48977 + 1.08238i) q^{12} +(-1.27127 - 0.923630i) q^{13} +(1.46641 - 1.06541i) q^{14} +(-0.652438 + 2.72632i) q^{15} +(-0.886046 - 0.643750i) q^{16} +(0.309017 + 0.951057i) q^{17} +1.04095 q^{18} +(1.25923 + 3.87551i) q^{19} +(0.764420 - 3.19425i) q^{20} +(0.963506 - 2.96537i) q^{21} +(1.43911 - 4.42912i) q^{22} +(2.99048 - 2.17271i) q^{23} +3.16941 q^{24} +(4.93730 - 0.789340i) q^{25} -1.14522 q^{26} +(4.49138 - 3.26318i) q^{27} +(-1.12888 + 3.47433i) q^{28} +(0.0835365 - 0.257099i) q^{29} +(0.783211 + 1.88696i) q^{30} +(2.06091 + 6.34281i) q^{31} -5.85440 q^{32} +(-2.47553 - 7.61891i) q^{33} +(0.589613 + 0.428379i) q^{34} +(-5.54379 + 0.440355i) q^{35} +(-1.69729 + 1.23315i) q^{36} +(-7.98027 - 5.79801i) q^{37} +(2.40264 + 1.74562i) q^{38} +(-1.59376 + 1.15793i) q^{39} +(-2.16710 - 5.22113i) q^{40} +(-1.88236 - 1.36761i) q^{41} +(-0.702204 - 2.16116i) q^{42} -4.37239 q^{43} +(2.90042 + 8.92658i) q^{44} +(-2.72436 - 1.66677i) q^{45} +(0.832481 - 2.56211i) q^{46} +(-2.00268 + 6.16361i) q^{47} +(-1.11081 + 0.807052i) q^{48} -0.814496 q^{49} +(2.57296 - 2.58044i) q^{50} +1.25367 q^{51} +(1.86730 - 1.35667i) q^{52} +(0.412891 - 1.27075i) q^{53} +(1.25030 - 3.84802i) q^{54} +(-10.8583 + 9.28753i) q^{55} +(1.94296 + 5.97982i) q^{56} +5.10866 q^{57} +(-0.0608815 - 0.187374i) q^{58} +(5.41721 + 3.93583i) q^{59} +(-3.51241 - 2.14890i) q^{60} +(-9.15540 + 6.65179i) q^{61} +(3.93226 + 2.85696i) q^{62} +(2.87386 + 2.08798i) q^{63} +(-1.67974 + 1.22040i) q^{64} +(2.99725 + 1.83373i) q^{65} +(-4.72338 - 3.43174i) q^{66} +(-4.13628 - 12.7301i) q^{67} -1.46885 q^{68} +(-1.43202 - 4.40731i) q^{69} +(-3.08005 + 2.63448i) q^{70} +(4.19569 - 12.9130i) q^{71} +(-1.11583 + 3.43417i) q^{72} +(0.931900 - 0.677065i) q^{73} -7.18901 q^{74} +(0.971600 - 6.19261i) q^{75} -5.98548 q^{76} +(12.8572 - 9.34132i) q^{77} +(-0.443665 + 1.36546i) q^{78} +(-4.13757 + 12.7341i) q^{79} +(2.08902 + 1.27807i) q^{80} +(-0.826633 - 2.54412i) q^{81} -1.69572 q^{82} +(1.63914 + 5.04476i) q^{83} +(3.70516 + 2.69195i) q^{84} +(-0.857205 - 2.06524i) q^{85} +(-2.57802 + 1.87304i) q^{86} +(-0.274180 - 0.199203i) q^{87} +(13.0694 + 9.49544i) q^{88} +(-4.32861 + 3.14492i) q^{89} +(-2.32033 + 0.184308i) q^{90} +(-3.16173 - 2.29713i) q^{91} +(1.67781 + 5.16376i) q^{92} +8.36103 q^{93} +(1.45955 + 4.49205i) q^{94} +(-3.49307 - 8.41573i) q^{95} +(-2.26803 + 6.98028i) q^{96} +(-2.21581 + 6.81956i) q^{97} +(-0.480237 + 0.348913i) q^{98} +9.12688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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