LMFDB - Embedded newform 403.2.r.a.218.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(218,403)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("403.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			218.19
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.228638 - 0.132004i) q^{2} +(-0.254003 - 0.439946i) q^{3} +(-0.965150 + 1.67169i) q^{4} +2.92638i q^{5} +(-0.116149 - 0.0670588i) q^{6} +(-4.12569 - 2.38197i) q^{7} +1.03763i q^{8} +(1.37097 - 2.37458i) q^{9} +O(q^{10})$	\(q+(0.228638 - 0.132004i) q^{2} +(-0.254003 - 0.439946i) q^{3} +(-0.965150 + 1.67169i) q^{4} +2.92638i q^{5} +(-0.116149 - 0.0670588i) q^{6} +(-4.12569 - 2.38197i) q^{7} +1.03763i q^{8} +(1.37097 - 2.37458i) q^{9} +(0.386294 + 0.669081i) q^{10} +(-2.57882 + 1.48888i) q^{11} +0.980603 q^{12} +(-2.23785 - 2.82701i) q^{13} -1.25772 q^{14} +(1.28745 - 0.743309i) q^{15} +(-1.79333 - 3.10614i) q^{16} +(0.577155 - 0.999662i) q^{17} -0.723892i q^{18} +(-4.39810 - 2.53924i) q^{19} +(-4.89200 - 2.82440i) q^{20} +2.42010i q^{21} +(-0.393077 + 0.680830i) q^{22} +(1.48522 + 2.57248i) q^{23} +(0.456501 - 0.263561i) q^{24} -3.56371 q^{25} +(-0.884835 - 0.350956i) q^{26} -2.91693 q^{27} +(7.96381 - 4.59791i) q^{28} +(3.93096 + 6.80862i) q^{29} +(0.196240 - 0.339897i) q^{30} +1.00000i q^{31} +(-2.61727 - 1.51108i) q^{32} +(1.31006 + 0.756362i) q^{33} -0.304747i q^{34} +(6.97054 - 12.0733i) q^{35} +(2.64637 + 4.58365i) q^{36} +(-4.20241 + 2.42626i) q^{37} -1.34076 q^{38} +(-0.675312 + 1.70260i) q^{39} -3.03650 q^{40} +(-9.21786 + 5.32194i) q^{41} +(0.319464 + 0.553327i) q^{42} +(-1.91930 + 3.32433i) q^{43} -5.74799i q^{44} +(6.94893 + 4.01197i) q^{45} +(0.679156 + 0.392111i) q^{46} +6.99193i q^{47} +(-0.911021 + 1.57793i) q^{48} +(7.84753 + 13.5923i) q^{49} +(-0.814799 + 0.470424i) q^{50} -0.586396 q^{51} +(6.88575 - 1.01250i) q^{52} +1.93549 q^{53} +(-0.666921 + 0.385047i) q^{54} +(-4.35705 - 7.54662i) q^{55} +(2.47160 - 4.28094i) q^{56} +2.57990i q^{57} +(1.79753 + 1.03780i) q^{58} +(-6.49462 - 3.74967i) q^{59} +2.86962i q^{60} +(-2.89343 + 5.01157i) q^{61} +(0.132004 + 0.228638i) q^{62} +(-11.3123 + 6.53118i) q^{63} +6.37544 q^{64} +(8.27293 - 6.54881i) q^{65} +0.399371 q^{66} +(7.65399 - 4.41904i) q^{67} +(1.11408 + 1.92965i) q^{68} +(0.754501 - 1.30683i) q^{69} -3.68056i q^{70} +(-3.58302 - 2.06866i) q^{71} +(2.46394 + 1.42256i) q^{72} -14.6633i q^{73} +(-0.640552 + 1.10947i) q^{74} +(0.905193 + 1.56784i) q^{75} +(8.48964 - 4.90150i) q^{76} +14.1859 q^{77} +(0.0703488 + 0.478423i) q^{78} -12.2095 q^{79} +(9.08974 - 5.24796i) q^{80} +(-3.37199 - 5.84045i) q^{81} +(-1.40503 + 2.43359i) q^{82} -2.51973i q^{83} +(-4.04566 - 2.33576i) q^{84} +(2.92539 + 1.68898i) q^{85} +1.01342i q^{86} +(1.99695 - 3.45882i) q^{87} +(-1.54491 - 2.67587i) q^{88} +(8.72750 - 5.03883i) q^{89} +2.11838 q^{90} +(2.49883 + 16.9939i) q^{91} -5.73385 q^{92} +(0.439946 - 0.254003i) q^{93} +(0.922963 + 1.59862i) q^{94} +(7.43079 - 12.8705i) q^{95} +1.53528i q^{96} +(11.7859 + 6.80461i) q^{97} +(3.58848 + 2.07181i) q^{98} +8.16484i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) $ 68 * q + 32 * q^4 - 34 * q^9	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.228638	−	0.132004i	0.161671	−	0.0933409i	−0.416981	−	0.908915i	$-0.636912\pi$
$2$	0.228638	−	0.132004i	0.161671	−	0.0933409i	0.578653	+	0.815574i	$0.303579\pi$
$3$	−0.254003	−	0.439946i	−0.146649	−	0.254003i	0.783338	−	0.621596i	$-0.213515\pi$
$3$	−0.254003	−	0.439946i	−0.146649	−	0.254003i	−0.929987	+	0.367593i	$0.880182\pi$
$4$	−0.965150	+	1.67169i	−0.482575	+	0.835844i
$5$			2.92638i			1.30872i	0.756184	+	0.654359i	$0.227061\pi$
$5$			2.92638i			1.30872i	−0.756184	+	0.654359i	$0.772939\pi$
$6$	−0.116149	−	0.0670588i	−0.0474177	−	0.0273766i
$7$	−4.12569	−	2.38197i	−1.55936	−	0.900299i	−0.997318	−	0.0731919i	$-0.976681\pi$
$7$	−4.12569	−	2.38197i	−1.55936	−	0.900299i	−0.562045	−	0.827107i	$-0.689985\pi$
$8$			1.03763i			0.366858i
$9$	1.37097	−	2.37458i	0.456988	−	0.791527i
$10$	0.386294	+	0.669081i	0.122157	+	0.211582i
$11$	−2.57882	+	1.48888i	−0.777545	+	0.448916i	−0.835559	−	0.549400i	$-0.814856\pi$
$11$	−2.57882	+	1.48888i	−0.777545	+	0.448916i	0.0580148	+	0.998316i	$0.481523\pi$
$12$	0.980603			0.283076
$13$	−2.23785	−	2.82701i	−0.620669	−	0.784073i
$13$	−2.23785	−	2.82701i	−0.620669	−	0.784073i
$14$	−1.25772			−0.336139
$15$	1.28745	−	0.743309i	0.332418	−	0.191922i
$16$	−1.79333	−	3.10614i	−0.448332	−	0.776534i
$17$	0.577155	−	0.999662i	0.139981	−	0.242454i	−0.787508	−	0.616304i	$-0.788629\pi$
$17$	0.577155	−	0.999662i	0.139981	−	0.242454i	0.927489	+	0.373850i	$0.121963\pi$
$18$		−	0.723892i		−	0.170623i
$19$	−4.39810	−	2.53924i	−1.00899	−	0.582542i	−0.0980959	−	0.995177i	$-0.531275\pi$
$19$	−4.39810	−	2.53924i	−1.00899	−	0.582542i	−0.910896	+	0.412635i	$0.864609\pi$
$20$	−4.89200	−	2.82440i	−1.09388	−	0.631554i
$21$			2.42010i			0.528110i
$22$	−0.393077	+	0.680830i	−0.0838044	+	0.145153i
$23$	1.48522	+	2.57248i	0.309690	+	0.536399i	0.978295	−	0.207219i	$-0.0664413\pi$
$23$	1.48522	+	2.57248i	0.309690	+	0.536399i	−0.668604	+	0.743618i	$0.733108\pi$
$24$	0.456501	−	0.263561i	0.0931829	−	0.0537992i
$25$	−3.56371			−0.712742
$26$	−0.884835	−	0.350956i	−0.173530	−	0.0688282i
$27$	−2.91693			−0.561364
$28$	7.96381	−	4.59791i	1.50502	−	0.868923i
$29$	3.93096	+	6.80862i	0.729960	+	1.26433i	0.956899	+	0.290420i	$0.0937949\pi$
$29$	3.93096	+	6.80862i	0.729960	+	1.26433i	−0.226939	+	0.973909i	$0.572872\pi$
$30$	0.196240	−	0.339897i	0.0358283	−	0.0620564i
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$	−2.61727	−	1.51108i	−0.462673	−	0.267124i
$33$	1.31006	+	0.756362i	0.228052	+	0.131666i
$34$		−	0.304747i		−	0.0522637i
$35$	6.97054	−	12.0733i	1.17824	−	2.04077i
$36$	2.64637	+	4.58365i	0.441062	+	0.763942i
$37$	−4.20241	+	2.42626i	−0.690871	+	0.398875i	−0.803938	−	0.594713i	$-0.797266\pi$
$37$	−4.20241	+	2.42626i	−0.690871	+	0.398875i	0.113067	+	0.993587i	$0.463933\pi$
$38$	−1.34076			−0.217500
$39$	−0.675312	+	1.70260i	−0.108137	+	0.272635i
$40$	−3.03650			−0.480113
$41$	−9.21786	+	5.32194i	−1.43959	+	0.831147i	−0.997821	−	0.0659828i	$-0.978982\pi$
$41$	−9.21786	+	5.32194i	−1.43959	+	0.831147i	−0.441768	+	0.897130i	$0.645648\pi$
$42$	0.319464	+	0.553327i	0.0492943	+	0.0853802i
$43$	−1.91930	+	3.32433i	−0.292691	+	0.506956i	−0.974445	−	0.224626i	$-0.927884\pi$
$43$	−1.91930	+	3.32433i	−0.292691	+	0.506956i	0.681754	+	0.731581i	$0.261217\pi$
$44$		−	5.74799i		−	0.866542i
$45$	6.94893	+	4.01197i	1.03589	+	0.598069i
$46$	0.679156	+	0.392111i	0.100136	+	0.0578136i
$47$			6.99193i			1.01988i	0.860210	+	0.509939i	$0.170332\pi$
$47$			6.99193i			1.01988i	−0.860210	+	0.509939i	$0.829668\pi$
$48$	−0.911021	+	1.57793i	−0.131495	+	0.227755i
$49$	7.84753	+	13.5923i	1.12108	+	1.94176i
$50$	−0.814799	+	0.470424i	−0.115230	+	0.0665280i
$51$	−0.586396			−0.0821119
$52$	6.88575	−	1.01250i	0.954882	−	0.140409i
$53$	1.93549			0.265859			0.132930	−	0.991125i	$-0.457562\pi$
$53$	1.93549			0.265859			0.132930	+	0.991125i	$0.457562\pi$
$54$	−0.666921	+	0.385047i	−0.0907564	+	0.0523982i
$55$	−4.35705	−	7.54662i	−0.587504	−	1.01759i
$56$	2.47160	−	4.28094i	0.330282	−	0.572065i
$57$			2.57990i			0.341716i
$58$	1.79753	+	1.03780i	0.236027	+	0.136270i
$59$	−6.49462	−	3.74967i	−0.845527	−	0.488165i	0.0136121	−	0.999907i	$-0.495667\pi$
$59$	−6.49462	−	3.74967i	−0.845527	−	0.488165i	−0.859139	+	0.511742i	$0.829000\pi$
$60$			2.86962i			0.370466i
$61$	−2.89343	+	5.01157i	−0.370466	+	0.641666i	−0.989637	−	0.143590i	$-0.954135\pi$
$61$	−2.89343	+	5.01157i	−0.370466	+	0.641666i	0.619171	+	0.785256i	$0.287469\pi$
$62$	0.132004	+	0.228638i	0.0167645	+	0.0290370i
$63$	−11.3123	+	6.53118i	−1.42522	+	0.822852i
$64$	6.37544			0.796930
$65$	8.27293	−	6.54881i	1.02613	−	0.812280i
$66$	0.399371			0.0491592
$67$	7.65399	−	4.41904i	0.935084	−	0.539871i	0.0466682	−	0.998910i	$-0.485140\pi$
$67$	7.65399	−	4.41904i	0.935084	−	0.539871i	0.888416	+	0.459039i	$0.151806\pi$
$68$	1.11408	+	1.92965i	0.135102	+	0.234004i
$69$	0.754501	−	1.30683i	0.0908313	−	0.157324i
$70$		−	3.68056i		−	0.439911i
$71$	−3.58302	−	2.06866i	−0.425226	−	0.245505i	0.272085	−	0.962273i	$-0.412287\pi$
$71$	−3.58302	−	2.06866i	−0.425226	−	0.245505i	−0.697311	+	0.716769i	$0.745620\pi$
$72$	2.46394	+	1.42256i	0.290378	+	0.167650i
$73$		−	14.6633i		−	1.71621i	−0.513471	−	0.858107i	$-0.671641\pi$
$73$		−	14.6633i		−	1.71621i	0.513471	−	0.858107i	$-0.328359\pi$
$74$	−0.640552	+	1.10947i	−0.0744627	+	0.128973i
$75$	0.905193	+	1.56784i	0.104523	+	0.181039i
$76$	8.48964	−	4.90150i	0.973829	−	0.562240i
$77$	14.1859			1.61663
$78$	0.0703488	+	0.478423i	0.00796543	+	0.0541708i
$79$	−12.2095			−1.37368			−0.686838	−	0.726810i	$-0.741002\pi$
$79$	−12.2095			−1.37368			−0.686838	+	0.726810i	$0.741002\pi$
$80$	9.08974	−	5.24796i	1.01626	−	0.586740i
$81$	−3.37199	−	5.84045i	−0.374665	−	0.648939i
$82$	−1.40503	+	2.43359i	−0.155160	+	0.268745i
$83$		−	2.51973i		−	0.276576i	−0.990392	−	0.138288i	$-0.955840\pi$
$83$		−	2.51973i		−	0.276576i	0.990392	−	0.138288i	$-0.0441600\pi$
$84$	−4.04566	−	2.33576i	−0.441418	−	0.254853i
$85$	2.92539	+	1.68898i	0.317303	+	0.183195i
$86$			1.01342i			0.109280i
$87$	1.99695	−	3.45882i	0.214095	−	0.370824i
$88$	−1.54491	−	2.67587i	−0.164688	−	0.285248i
$89$	8.72750	−	5.03883i	0.925113	−	0.534115i	0.0398507	−	0.999206i	$-0.487312\pi$
$89$	8.72750	−	5.03883i	0.925113	−	0.534115i	0.885263	+	0.465091i	$0.153978\pi$
$90$	2.11838			0.223297
$91$	2.49883	+	16.9939i	0.261948	+	1.78144i
$92$	−5.73385			−0.597795
$93$	0.439946	−	0.254003i	0.0456203	−	0.0263389i
$94$	0.922963	+	1.59862i	0.0951964	+	0.164885i
$95$	7.43079	−	12.8705i	0.762383	−	1.32049i
$96$			1.53528i			0.156694i
$97$	11.7859	+	6.80461i	1.19668	+	0.690903i	0.959813	−	0.280639i	$-0.0905464\pi$
$97$	11.7859	+	6.80461i	1.19668	+	0.690903i	0.236866	+	0.971542i	$0.423880\pi$
$98$	3.58848	+	2.07181i	0.362491	+	0.209284i
$99$			8.16484i			0.820597i
$100$	3.43952	−	5.95742i	0.343952	−	0.595742i
$101$	−4.70395	−	8.14748i	−0.468060	−	0.810704i	0.531273	−	0.847200i	$-0.321714\pi$
$101$	−4.70395	−	8.14748i	−0.468060	−	0.810704i	−0.999334	+	0.0364961i	$0.988380\pi$
$102$	−0.134072	+	0.0774067i	−0.0132751	+	0.00766440i
$103$	0.837079			0.0824798			0.0412399	−	0.999149i	$-0.486869\pi$
$103$	0.837079			0.0824798			0.0412399	+	0.999149i	$0.486869\pi$
$104$	2.93340	−	2.32207i	0.287643	−	0.227697i
$105$	−7.08215			−0.691147
$106$	0.442525	−	0.255492i	0.0429818	−	0.0248156i
$107$	3.67058	+	6.35763i	0.354848	+	0.614615i	0.987092	−	0.160154i	$-0.0511992\pi$
$107$	3.67058	+	6.35763i	0.354848	+	0.614615i	−0.632244	+	0.774770i	$0.717866\pi$
$108$	2.81528	−	4.87620i	0.270900	−	0.469213i
$109$			8.51607i			0.815692i	0.913051	+	0.407846i	$0.133720\pi$
$109$			8.51607i			0.815692i	−0.913051	+	0.407846i	$0.866280\pi$
$110$	−1.99237	−	1.15029i	−0.189965	−	0.109676i
$111$	2.13485	+	1.23255i	0.202631	+	0.116989i
$112$			17.0866i			1.61453i
$113$	4.74897	−	8.22546i	0.446745	−	0.773786i	−0.551427	−	0.834223i	$-0.685916\pi$
$113$	4.74897	−	8.22546i	0.446745	−	0.773786i	0.998172	+	0.0604377i	$0.0192496\pi$
$114$	0.340557	+	0.589862i	0.0318961	+	0.0552456i
$115$	−7.52806	+	4.34633i	−0.701995	+	0.405297i
$116$	−15.1759			−1.40904
$117$	−9.78099	+	1.43823i	−0.904253	+	0.132964i
$118$	−1.97989			−0.182263
$119$	−4.76232	+	2.74953i	−0.436561	+	0.252049i
$120$	0.771281	+	1.33590i	0.0704080	+	0.121950i
$121$	−1.06645	+	1.84714i	−0.0969496	+	0.167922i
$122$			1.52778i			0.138319i
$123$	4.68273	+	2.70357i	0.422227	+	0.243773i
$124$	−1.67169	−	0.965150i	−0.150122	−	0.0866730i
$125$			4.20313i			0.375939i
$126$	−1.72429	+	2.98655i	−0.153612	+	0.266063i
$127$	−8.30444	−	14.3837i	−0.736900	−	1.27635i	−0.953885	−	0.300173i	$-0.902956\pi$
$127$	−8.30444	−	14.3837i	−0.736900	−	1.27635i	0.216985	−	0.976175i	$-0.430378\pi$
$128$	6.69221	−	3.86375i	0.591514	−	0.341511i
$129$	1.95003			0.171691
$130$	1.02703	−	2.58936i	0.0900767	−	0.227102i
$131$	−14.5209			−1.26870			−0.634350	−	0.773046i	$-0.718732\pi$
$131$	−14.5209			−1.26870			−0.634350	+	0.773046i	$0.718732\pi$
$132$	−2.52880	+	1.46001i	−0.220104	+	0.127077i
$133$	12.0968	+	20.9522i	1.04892	+	1.81679i
$134$	1.16666	−	2.02072i	0.100784	−	0.174563i
$135$		−	8.53606i		−	0.734667i
$136$	1.03728	+	0.598874i	0.0889460	+	0.0513530i
$137$	−18.4568	−	10.6560i	−1.57687	−	0.910407i	−0.995292	−	0.0969171i	$-0.969102\pi$
$137$	−18.4568	−	10.6560i	−1.57687	−	0.910407i	−0.581579	−	0.813490i	$-0.697565\pi$
$138$		−	0.398389i		−	0.0339131i
$139$	−7.18968	+	12.4529i	−0.609821	+	1.05624i	0.381449	+	0.924390i	$0.375425\pi$
$139$	−7.18968	+	12.4529i	−0.609821	+	1.05624i	−0.991270	+	0.131851i	$0.957908\pi$
$140$	13.4552	+	23.3052i	1.13718	+	1.96965i
$141$	3.07607	−	1.77597i	0.259052	−	0.149564i
$142$	−1.09228			−0.0916625
$143$	9.98013	+	3.95847i	0.834580	+	0.331024i
$144$	−9.83436			−0.819530
$145$	−19.9246	+	11.5035i	−1.65465	+	0.955312i
$146$	−1.93562	−	3.35259i	−0.160193	−	0.277462i
$147$	3.98659	−	6.90497i	0.328808	−	0.569513i
$148$		−	9.36682i		−	0.769948i
$149$	18.1919	+	10.5031i	1.49033	+	0.860445i	0.999939	−	0.0110550i	$-0.00351899\pi$
$149$	18.1919	+	10.5031i	1.49033	+	0.860445i	0.490396	+	0.871500i	$0.336852\pi$
$150$	0.413922	+	0.238978i	0.0337966	+	0.0195125i
$151$		−	0.926361i		−	0.0753862i	−0.999289	−	0.0376931i	$-0.987999\pi$
$151$		−	0.926361i		−	0.0753862i	0.999289	−	0.0376931i	$-0.0120009\pi$
$152$	2.63480	−	4.56360i	0.213710	−	0.370157i
$153$	−1.58252	−	2.74100i	−0.127939	−	0.221597i
$154$	3.24343	−	1.87259i	0.261363	−	0.150898i
$155$	−2.92638			−0.235053
$156$	−2.19445	−	2.77218i	−0.175696	−	0.221952i
$157$	21.9913			1.75509			0.877547	−	0.479491i	$-0.159179\pi$
$157$	21.9913			1.75509			0.877547	+	0.479491i	$0.159179\pi$
$158$	−2.79155	+	1.61170i	−0.222084	+	0.128220i
$159$	−0.491619	−	0.851509i	−0.0389879	−	0.0675290i
$160$	4.42201	−	7.65914i	0.349590	−	0.605508i
$161$		−	14.1510i		−	1.11525i
$162$	−1.54193	−	0.890231i	−0.121145	−	0.0699432i
$163$	−6.93747	−	4.00535i	−0.543384	−	0.313723i	0.203065	−	0.979165i	$-0.434910\pi$
$163$	−6.93747	−	4.00535i	−0.543384	−	0.313723i	−0.746449	+	0.665442i	$0.768243\pi$
$164$		−	20.5459i		−	1.60436i
$165$	−2.21340	+	3.83373i	−0.172313	+	0.298455i
$166$	−0.332614	−	0.576105i	−0.0258159	−	0.0447144i
$167$	20.3430	−	11.7450i	1.57419	−	0.908856i	0.578538	−	0.815655i	$-0.303623\pi$
$167$	20.3430	−	11.7450i	1.57419	−	0.908856i	0.995647	−	0.0932010i	$-0.0297099\pi$
$168$	−2.51118			−0.193741
$169$	−2.98402	+	12.6529i	−0.229540	+	0.973299i
$170$	0.891807			0.0683985
$171$	−12.0593	+	6.96242i	−0.922196	+	0.532430i
$172$	−3.70483	−	6.41696i	−0.282491	−	0.489288i
$173$	3.36158	−	5.82243i	0.255576	−	0.442671i	−0.709476	−	0.704730i	$-0.751068\pi$
$173$	3.36158	−	5.82243i	0.255576	−	0.442671i	0.965052	+	0.262059i	$0.0844015\pi$
$174$		−	1.05442i		−	0.0799354i
$175$	14.7028	+	8.48864i	1.11142	+	0.641681i
$176$	9.24936	+	5.34012i	0.697196	+	0.402527i
$177$			3.80971i			0.286355i
$178$	1.33029	−	2.30413i	0.0997095	−	0.172702i
$179$	6.85610	+	11.8751i	0.512449	+	0.887588i	0.999896	+	0.0144354i	$0.00459510\pi$
$179$	6.85610	+	11.8751i	0.512449	+	0.887588i	−0.487446	+	0.873153i	$0.662072\pi$
$180$	−13.4135	+	7.74430i	−0.999785	+	0.577226i
$181$	−2.24442			−0.166826			−0.0834131	−	0.996515i	$-0.526582\pi$
$181$	−2.24442			−0.166826			−0.0834131	+	0.996515i	$0.526582\pi$
$182$	2.81458	+	3.55558i	0.208631	+	0.263557i
$183$	2.93976			0.217313
$184$	−2.66928	+	1.54111i	−0.196782	+	0.113612i
$185$	−7.10017	−	12.2978i	−0.522015	−	0.904156i
$186$	0.0670588	−	0.116149i	0.00491699	−	0.00851648i
$187$			3.43727i			0.251358i
$188$	−11.6883	−	6.74827i	−0.852460	−	0.492168i
$189$	12.0344	+	6.94804i	0.875370	+	0.505395i
$190$		−	3.92358i		−	0.284646i
$191$	−0.868763	+	1.50474i	−0.0628615	+	0.108879i	−0.895743	−	0.444571i	$-0.853356\pi$
$191$	−0.868763	+	1.50474i	−0.0628615	+	0.108879i	0.832882	+	0.553451i	$0.186689\pi$
$192$	−1.61938	−	2.80485i	−0.116869	−	0.202422i
$193$	−10.8510	+	6.26483i	−0.781072	+	0.450952i	−0.836810	−	0.547493i	$-0.815582\pi$
$193$	−10.8510	+	6.26483i	−0.781072	+	0.450952i	0.0557379	+	0.998445i	$0.482249\pi$
$194$	3.59294			0.257958
$195$	−4.98247	−	1.97622i	−0.356802	−	0.141520i
$196$	−30.2962			−2.16401
$197$	−18.9104	+	10.9179i	−1.34731	+	0.777868i	−0.987867	−	0.155300i	$-0.950366\pi$
$197$	−18.9104	+	10.9179i	−1.34731	+	0.777868i	−0.359440	+	0.933168i	$0.617032\pi$
$198$	1.07779	+	1.86679i	0.0765953	+	0.132667i
$199$	3.71517	−	6.43486i	0.263361	−	0.456155i	−0.703772	−	0.710426i	$-0.748502\pi$
$199$	3.71517	−	6.43486i	0.263361	−	0.456155i	0.967133	+	0.254271i	$0.0818355\pi$
$200$		−	3.69782i		−	0.261475i
$201$	−3.88827	−	2.24490i	−0.274258	−	0.158343i
$202$	−2.15100	−	1.24188i	−0.151344	−	0.0873784i
$203$		−	37.4536i		−	2.62873i
$204$	0.565960	−	0.980272i	0.0396251	−	0.0686328i
$205$	−15.5740	−	26.9750i	−1.08774	−	1.88401i
$206$	0.191388	−	0.110498i	0.0133346	−	0.00769874i
$207$	8.14475			0.566099
$208$	−4.76789	+	12.0208i	−0.330593	+	0.833495i
$209$	15.1226			1.04605
$210$	−1.61925	+	0.934872i	−0.111739	+	0.0645123i
$211$	−0.332875	−	0.576556i	−0.0229160	−	0.0396918i	0.854340	−	0.519715i	$-0.173962\pi$
$211$	−0.332875	−	0.576556i	−0.0229160	−	0.0396918i	−0.877256	+	0.480023i	$0.840628\pi$
$212$	−1.86803	+	3.23553i	−0.128297	+	0.222217i
$213$			2.10178i			0.144012i
$214$	1.67847	+	0.969063i	0.114738	+	0.0662438i
$215$	−9.72826	−	5.61662i	−0.663462	−	0.383050i
$216$		−	3.02670i		−	0.205941i
$217$	2.38197	−	4.12569i	0.161698	−	0.280070i
$218$	1.12416	+	1.94709i	0.0761374	+	0.131874i
$219$	−6.45108	+	3.72453i	−0.435923	+	0.251680i
$220$	16.8208			1.13406
$221$	−4.11765	+	0.605471i	−0.276983	+	0.0407284i
$222$	0.650808			0.0436794
$223$	−4.90993	+	2.83475i	−0.328793	+	0.189829i	−0.655305	−	0.755364i	$-0.727460\pi$
$223$	−4.90993	+	2.83475i	−0.328793	+	0.189829i	0.326512	+	0.945193i	$0.394127\pi$
$224$	7.19870	+	12.4685i	0.480983	+	0.833088i
$225$	−4.88573	+	8.46232i	−0.325715	+	0.564155i
$226$		−	2.50753i		−	0.166799i
$227$	9.82144	+	5.67041i	0.651872	+	0.376358i	0.789173	−	0.614171i	$-0.210509\pi$
$227$	9.82144	+	5.67041i	0.651872	+	0.376358i	−0.137301	+	0.990529i	$0.543843\pi$
$228$	−4.31279	−	2.48999i	−0.285621	−	0.164904i
$229$			0.237767i			0.0157121i	0.999969	+	0.00785604i	$0.00250068\pi$
$229$			0.237767i			0.0157121i	−0.999969	+	0.00785604i	$0.997499\pi$
$230$	−1.14747	+	1.98747i	−0.0756616	+	0.131050i
$231$	−3.60326	−	6.24102i	−0.237077	−	0.410629i
$232$	−7.06483	+	4.07888i	−0.463829	+	0.267792i
$233$	−2.15412			−0.141121			−0.0705604	−	0.997508i	$-0.522479\pi$
$233$	−2.15412			−0.141121			−0.0705604	+	0.997508i	$0.522479\pi$
$234$	−2.04645	+	1.61996i	−0.133781	+	0.105900i
$235$	−20.4611			−1.33473
$236$	12.5366	−	7.23798i	0.816060	−	0.471153i
$237$	3.10125	+	5.37152i	0.201448	+	0.348918i
$238$	−0.725898	+	1.25729i	−0.0470529	+	0.0814981i
$239$			2.86126i			0.185080i	0.995709	+	0.0925398i	$0.0294985\pi$
$239$			2.86126i			0.185080i	−0.995709	+	0.0925398i	$0.970501\pi$
$240$	−4.61764	−	2.66600i	−0.298067	−	0.172089i
$241$	−25.2739	−	14.5919i	−1.62803	−	0.939946i	−0.984679	−	0.174378i	$-0.944208\pi$
$241$	−25.2739	−	14.5919i	−1.62803	−	0.939946i	−0.643356	−	0.765568i	$-0.722458\pi$
$242$			0.563100i			0.0361975i
$243$	−6.08839	+	10.5454i	−0.390570	+	0.676488i
$244$	−5.58519	−	9.67383i	−0.357555	−	0.619304i
$245$	−39.7763	+	22.9649i	−2.54121	+	1.46717i
$246$	1.42753			0.0910160
$247$	2.66382	+	18.1159i	0.169495	+	1.15269i
$248$	−1.03763			−0.0658896
$249$	−1.10854	+	0.640018i	−0.0702511	+	0.0405595i
$250$	0.554830	+	0.960993i	0.0350905	+	0.0607785i
$251$	4.51004	−	7.81163i	0.284671	−	0.493065i	−0.687858	−	0.725845i	$-0.741449\pi$
$251$	4.51004	−	7.81163i	0.284671	−	0.493065i	0.972529	+	0.232780i	$0.0747822\pi$
$252$		−	25.2143i		−	1.58835i
$253$	−7.66025	−	4.42265i	−0.481596	−	0.278050i
$254$	−3.79742	−	2.19244i	−0.238271	−	0.137566i
$255$		−	1.71602i		−	0.107461i
$256$	−5.35538	+	9.27578i	−0.334711	+	0.579736i
$257$	1.48317	+	2.56893i	0.0925178	+	0.160245i	0.908570	−	0.417733i	$-0.137175\pi$
$257$	1.48317	+	2.56893i	0.0925178	+	0.160245i	−0.816052	+	0.577978i	$0.803842\pi$
$258$	0.445851	−	0.257412i	0.0277575	−	0.0160258i
$259$	23.1171			1.43643
$260$	2.96297	+	20.1503i	0.183755	+	1.24967i
$261$	21.5568			1.33433
$262$	−3.32003	+	1.91682i	−0.205112	+	0.118422i
$263$	0.120104	+	0.208026i	0.00740593	+	0.0128275i	0.869705	−	0.493573i	$-0.164309\pi$
$263$	0.120104	+	0.208026i	0.00740593	+	0.0128275i	−0.862299	+	0.506400i	$0.830976\pi$
$264$	−0.784824	+	1.35936i	−0.0483026	+	0.0836626i
$265$			5.66397i			0.347935i
$266$	5.53156	+	3.19365i	0.339162	+	0.195815i
$267$	−4.43362	−	2.55975i	−0.271333	−	0.156654i
$268$			17.0601i			1.04211i
$269$	−2.36716	+	4.10004i	−0.144328	+	0.249984i	−0.929122	−	0.369773i	$-0.879435\pi$
$269$	−2.36716	+	4.10004i	−0.144328	+	0.249984i	0.784794	+	0.619757i	$0.212769\pi$
$270$	−1.12679	−	1.95167i	−0.0685745	−	0.118775i
$271$	11.2631	−	6.50273i	0.684182	−	0.395013i	−0.117247	−	0.993103i	$-0.537407\pi$
$271$	11.2631	−	6.50273i	0.684182	−	0.395013i	0.801429	+	0.598090i	$0.204073\pi$
$272$	−4.14012			−0.251031
$273$	6.84167	−	5.41584i	0.414077	−	0.327782i
$274$	−5.62656			−0.339913
$275$	9.19019	−	5.30596i	0.554189	−	0.319961i
$276$	1.45641	+	2.52258i	0.0876658	+	0.151842i
$277$	7.77243	−	13.4622i	0.467000	−	0.808868i	−0.532289	−	0.846563i	$-0.678668\pi$
$277$	7.77243	−	13.4622i	0.467000	−	0.808868i	0.999289	+	0.0376945i	$0.0120014\pi$
$278$			3.79627i			0.227685i
$279$	2.37458	+	1.37097i	0.142162	+	0.0820775i
$280$	12.5277	+	7.23285i	0.748671	+	0.432245i
$281$			13.5044i			0.805605i	0.915287	+	0.402803i	$0.131964\pi$
$281$			13.5044i			0.805605i	−0.915287	+	0.402803i	$0.868036\pi$
$282$	0.468871	−	0.812108i	0.0279208	−	0.0483603i
$283$	−2.16571	−	3.75111i	−0.128738	−	0.222980i	0.794450	−	0.607330i	$-0.207759\pi$
$283$	−2.16571	−	3.75111i	−0.128738	−	0.222980i	−0.923188	+	0.384349i	$0.874426\pi$
$284$	6.91631	−	3.99313i	0.410407	−	0.236949i
$285$	−7.54977			−0.447210
$286$	2.80437	−	0.412362i	0.165826	−	0.0243835i
$287$	50.7067			2.99312
$288$	−7.17638	+	4.14329i	−0.422872	+	0.244145i
$289$	7.83378	+	13.5685i	0.460811	+	0.798148i
$290$	−3.03701	+	5.26026i	−0.178339	+	0.308893i
$291$		−	6.91356i		−	0.405280i
$292$	24.5125	+	14.1523i	1.43449	+	0.828202i
$293$	−15.2922	−	8.82893i	−0.893378	−	0.515792i	−0.0183318	−	0.999832i	$-0.505836\pi$
$293$	−15.2922	−	8.82893i	−0.893378	−	0.515792i	−0.875046	+	0.484040i	$0.839169\pi$
$294$		−	2.10498i		−	0.122765i
$295$	10.9730	−	19.0057i	0.638871	−	1.10656i
$296$	−2.51756	−	4.36055i	−0.146330	−	0.253452i
$297$	7.52226	−	4.34298i	0.436486	−	0.252005i
$298$	5.54579			0.321259
$299$	3.94873	−	9.95558i	0.228361	−	0.575746i
$300$	−3.49459			−0.201760
$301$	15.8369	−	9.14343i	0.912823	−	0.527019i
$302$	−0.122283	−	0.211801i	−0.00703662	−	0.0121878i
$303$	−2.38963	+	4.13897i	−0.137281	+	0.237777i
$304$			18.2148i			1.04469i
$305$	−14.6658	−	8.46729i	−0.839760	−	0.484835i
$306$	−0.723647	−	0.417798i	−0.0413681	−	0.0238839i
$307$			3.68921i			0.210555i	0.994443	+	0.105277i	$0.0335730\pi$
$307$			3.68921i			0.210555i	−0.994443	+	0.105277i	$0.966427\pi$
$308$	−13.6915	+	23.7144i	−0.780146	+	1.35125i
$309$	−0.212620	−	0.368269i	−0.0120956	−	0.0209501i
$310$	−0.669081	+	0.386294i	−0.0380013	+	0.0219400i
$311$	−25.5595			−1.44935			−0.724674	−	0.689092i	$-0.758010\pi$
$311$	−25.5595			−1.44935			−0.724674	+	0.689092i	$0.758010\pi$
$312$	−1.76667	−	0.700725i	−0.100018	−	0.0396707i
$313$	−21.2515			−1.20120			−0.600602	−	0.799548i	$-0.705072\pi$
$313$	−21.2515			−1.20120			−0.600602	+	0.799548i	$0.705072\pi$
$314$	5.02803	−	2.90294i	0.283748	−	0.163822i
$315$	−19.1127	−	33.1042i	−1.07688	−	1.86521i
$316$	11.7840	−	20.4105i	0.662902	−	1.14818i
$317$			2.78104i			0.156199i	0.996946	+	0.0780993i	$0.0248851\pi$
$317$			2.78104i			0.156199i	−0.996946	+	0.0780993i	$0.975115\pi$
$318$	−0.224805	−	0.129791i	−0.0126064	−	0.00727834i
$319$	−20.2745	−	11.7055i	−1.13515	−	0.655381i
$320$			18.6570i			1.04296i
$321$	1.86468	−	3.22971i	0.104076	−	0.180265i
$322$	−1.86799	−	3.23545i	−0.104099	−	0.180305i
$323$	−5.07677	+	2.93107i	−0.282479	+	0.163089i
$324$	13.0179			0.723216
$325$	7.97507	+	10.0747i	0.442377	+	0.558842i
$326$	−2.11489			−0.117133
$327$	3.74661	−	2.16311i	0.207188	−	0.119620i
$328$	−5.52220	−	9.56474i	−0.304913	−	0.528124i
$329$	16.6546	−	28.8465i	0.918195	−	1.59036i
$330$			1.16871i			0.0643355i
$331$	4.37819	+	2.52775i	0.240647	+	0.138938i	0.615474	−	0.788157i	$-0.288965\pi$
$331$	4.37819	+	2.52775i	0.240647	+	0.138938i	−0.374827	+	0.927095i	$0.622298\pi$
$332$	4.21220	+	2.43192i	0.231175	+	0.133469i
$333$			13.3053i			0.729125i
$334$	3.10078	−	5.37070i	0.169667	−	0.293872i
$335$	12.9318	+	22.3985i	0.706539	+	1.22376i
$336$	7.51717	−	4.34004i	0.410095	−	0.236769i
$337$	4.77143			0.259917			0.129958	−	0.991519i	$-0.458516\pi$
$337$	4.77143			0.259917			0.129958	+	0.991519i	$0.458516\pi$
$338$	0.987972	+	3.28683i	0.0537386	+	0.178780i
$339$	−4.82501			−0.262058
$340$	−5.64689	+	3.26023i	−0.306245	+	0.176811i
$341$	−1.48888	−	2.57882i	−0.0806276	−	0.139651i
$342$	−1.83814	+	3.18374i	−0.0993950	+	0.172157i
$343$		−	41.4226i		−	2.23661i
$344$	−3.44943	−	1.99153i	−0.185981	−	0.107376i
$345$	3.82430	+	2.20796i	0.205893	+	0.118873i
$346$		−	1.77497i		−	0.0954229i
$347$	2.44468	−	4.23431i	0.131237	−	0.227310i	−0.792916	−	0.609330i	$-0.791438\pi$
$347$	2.44468	−	4.23431i	0.131237	−	0.227310i	0.924154	+	0.382021i	$0.124772\pi$
$348$	3.85471	+	6.67655i	0.206634	+	0.357901i
$349$	−8.83227	+	5.09931i	−0.472781	+	0.272960i	−0.717403	−	0.696658i	$-0.754669\pi$
$349$	−8.83227	+	5.09931i	−0.472781	+	0.272960i	0.244622	+	0.969618i	$0.421336\pi$
$350$	4.48214			0.239580
$351$	6.52767	+	8.24621i	0.348421	+	0.440150i
$352$	8.99932			0.479665
$353$	−18.6591	+	10.7728i	−0.993121	+	0.573379i	−0.906206	−	0.422837i	$-0.861034\pi$
$353$	−18.6591	+	10.7728i	−0.993121	+	0.573379i	−0.0869155	+	0.996216i	$0.527701\pi$
$354$	0.502897	+	0.871042i	0.0267286	+	0.0462954i
$355$	6.05368	−	10.4853i	0.321296	−	0.556501i
$356$			19.4529i			1.03100i
$357$	2.41929	+	1.39678i	0.128042	+	0.0739252i
$358$	3.13513	+	1.81007i	0.165697	+	0.0956650i
$359$		−	3.78918i		−	0.199985i	−0.994988	−	0.0999927i	$-0.968118\pi$
$359$		−	3.78918i		−	0.199985i	0.994988	−	0.0999927i	$-0.0318819\pi$
$360$	−4.16294	+	7.21043i	−0.219406	+	0.380023i
$361$	3.39550	+	5.88117i	0.178710	+	0.309536i
$362$	−0.513158	+	0.296272i	−0.0269710	+	0.0155717i
$363$	1.08352			0.0568701
$364$	−30.8202	−	12.2244i	−1.61542	−	0.640731i
$365$	42.9105			2.24604
$366$	0.672140	−	0.388060i	0.0351333	−	0.0202842i
$367$	−5.43893	−	9.42050i	−0.283910	−	0.491746i	0.688435	−	0.725298i	$-0.258298\pi$
$367$	−5.43893	−	9.42050i	−0.283910	−	0.491746i	−0.972344	+	0.233553i	$0.924965\pi$
$368$	5.32698	−	9.22660i	0.277688	−	0.480970i
$369$			29.1848i			1.51930i
$370$	−3.24673	−	1.87450i	−0.168789	−	0.0974507i
$371$	−7.98521	−	4.61026i	−0.414571	−	0.239353i
$372$			0.980603i			0.0508419i
$373$	−1.43491	+	2.48534i	−0.0742968	+	0.128686i	−0.900780	−	0.434275i	$-0.857005\pi$
$373$	−1.43491	+	2.48534i	−0.0742968	+	0.128686i	0.826483	+	0.562961i	$0.190338\pi$
$374$	0.453733	+	0.785889i	0.0234620	+	0.0406374i
$375$	1.84915	−	1.06761i	0.0954896	−	0.0551309i
$376$	−7.25505			−0.374150
$377$	10.4512	−	26.3496i	0.538262	−	1.35707i
$378$	3.66867			0.188696
$379$	8.68672	−	5.01528i	0.446207	−	0.257618i	−0.260020	−	0.965603i	$-0.583729\pi$
$379$	8.68672	−	5.01528i	0.446207	−	0.257618i	0.706227	+	0.707986i	$0.250396\pi$
$380$	14.3437	+	24.8439i	0.735814	+	1.27447i
$381$	−4.21870	+	7.30701i	−0.216131	+	0.374349i
$382$			0.458721i			0.0234702i
$383$	5.79028	+	3.34302i	0.295869	+	0.170820i	0.640586	−	0.767887i	$-0.278692\pi$
$383$	5.79028	+	3.34302i	0.295869	+	0.170820i	−0.344716	+	0.938707i	$0.612025\pi$
$384$	−3.39968	−	1.96281i	−0.173489	−	0.100164i
$385$			41.5133i			2.11572i
$386$	−1.65397	+	2.86475i	−0.0841846	+	0.145812i
$387$	5.26260	+	9.11509i	0.267513	+	0.463346i
$388$	−22.7504	+	13.1349i	−1.15498	+	0.666825i
$389$	28.4088			1.44038			0.720192	−	0.693775i	$-0.244054\pi$
$389$	28.4088			1.44038			0.720192	+	0.693775i	$0.244054\pi$
$390$	−1.40005	+	0.205867i	−0.0708943	+	0.0104245i
$391$	3.42882			0.173403
$392$	−14.1038	+	8.14283i	−0.712350	+	0.411275i
$393$	3.68836	+	6.38843i	0.186053	+	0.322254i
$394$	−2.88241	+	4.99249i	−0.145214	+	0.251518i
$395$		−	35.7297i		−	1.79776i
$396$	−13.6491	−	7.88029i	−0.685891	−	0.395999i
$397$	1.24775	+	0.720392i	0.0626230	+	0.0361554i	0.530985	−	0.847381i	$-0.321822\pi$
$397$	1.24775	+	0.720392i	0.0626230	+	0.0361554i	−0.468362	+	0.883537i	$0.655156\pi$
$398$		−	1.96167i		−	0.0983295i
$399$	6.14523	−	10.6439i	0.307646	−	0.532859i
$400$	6.39091	+	11.0694i	0.319545	+	0.553469i
$401$	−10.0731	+	5.81571i	−0.503027	+	0.290423i	−0.729963	−	0.683487i	$-0.760463\pi$
$401$	−10.0731	+	5.81571i	−0.503027	+	0.290423i	0.226936	+	0.973910i	$0.427129\pi$
$402$	−1.18534			−0.0591194
$403$	2.82701	−	2.23785i	0.140824	−	0.111475i
$404$	18.1601			0.903497
$405$	17.0914	−	9.86772i	0.849278	−	0.490331i
$406$	−4.94403	−	8.56331i	−0.245368	−	0.424990i
$407$	7.22484	−	12.5138i	0.358122	−	0.620286i
$408$		−	0.608463i		−	0.0301234i
$409$	−9.49659	−	5.48286i	−0.469576	−	0.271110i	0.246486	−	0.969146i	$-0.420724\pi$
$409$	−9.49659	−	5.48286i	−0.469576	−	0.271110i	−0.716062	+	0.698036i	$0.754057\pi$
$410$	−7.12161	−	4.11167i	−0.351711	−	0.203061i
$411$			10.8267i			0.534040i
$412$	−0.807906	+	1.39934i	−0.0398027	+	0.0689403i
$413$	17.8632	+	30.9399i	0.878989	+	1.52245i
$414$	1.86220	−	1.07514i	0.0915220	−	0.0528402i
$415$	7.37369			0.361960
$416$	1.58522	+	10.7807i	0.0777218	+	0.528565i
$417$	7.30480			0.357718
$418$	3.45758	−	1.99624i	0.169116	−	0.0976392i
$419$	−6.39930	−	11.0839i	−0.312626	−	0.541485i	0.666304	−	0.745681i	$-0.267875\pi$
$419$	−6.39930	−	11.0839i	−0.312626	−	0.541485i	−0.978930	+	0.204196i	$0.934542\pi$
$420$	6.83534	−	11.8392i	0.333530	−	0.577691i
$421$			17.1106i			0.833922i	0.908924	+	0.416961i	$0.136905\pi$
$421$			17.1106i			0.833922i	−0.908924	+	0.416961i	$0.863095\pi$
$422$	−0.152215	−	0.0878816i	−0.00740973	−	0.00427801i
$423$	16.6029	+	9.58570i	0.807261	+	0.466073i
$424$			2.00832i			0.0975326i
$425$	−2.05682	+	3.56251i	−0.0997702	+	0.172807i
$426$	0.277443	+	0.480546i	0.0134422	+	0.0232825i
$427$	23.8748	−	13.7841i	1.15538	−	0.667060i
$428$	−14.1706			−0.684964
$429$	−0.793470	−	5.39618i	−0.0383091	−	0.260530i
$430$	−2.96566			−0.143017
$431$	15.4024	−	8.89260i	0.741909	−	0.428341i	−0.0808541	−	0.996726i	$-0.525765\pi$
$431$	15.4024	−	8.89260i	0.741909	−	0.428341i	0.822763	+	0.568385i	$0.192431\pi$
$432$	5.23102	+	9.06039i	0.251678	+	0.435918i
$433$	11.8749	−	20.5680i	0.570674	−	0.988436i	−0.425823	−	0.904806i	$-0.640015\pi$
$433$	11.8749	−	20.5680i	0.570674	−	0.988436i	0.996497	−	0.0836293i	$-0.0266512\pi$
$434$		−	1.25772i		−	0.0603723i
$435$	10.1218	+	5.84383i	0.485304	+	0.280190i
$436$	−14.2362	−	8.21928i	−0.681791	−	0.393632i
$437$		−	15.0854i		−	0.721630i
$438$	−0.983306	+	1.70314i	−0.0469842	+	0.0813790i
$439$	3.02383	+	5.23743i	0.144320	+	0.249969i	0.929119	−	0.369781i	$-0.120567\pi$
$439$	3.02383	+	5.23743i	0.144320	+	0.249969i	−0.784799	+	0.619750i	$0.787234\pi$
$440$	7.83061	−	4.52100i	0.373310	−	0.215530i
$441$	43.0347			2.04927
$442$	−0.861525	+	0.681980i	−0.0409786	+	0.0324385i
$443$	2.00826			0.0954153			0.0477076	−	0.998861i	$-0.484808\pi$
$443$	2.00826			0.0954153			0.0477076	+	0.998861i	$0.484808\pi$
$444$	−4.12089	+	2.37920i	−0.195569	+	0.112912i
$445$	14.7455	+	25.5400i	0.699005	+	1.21071i
$446$	−0.748396	+	1.29626i	−0.0354376	+	0.0613797i
$447$		−	10.6712i		−	0.504732i
$448$	−26.3031	−	15.1861i	−1.24270	−	0.717475i
$449$	−20.6141	−	11.9016i	−0.972841	−	0.561670i	−0.0727401	−	0.997351i	$-0.523174\pi$
$449$	−20.6141	−	11.9016i	−0.972841	−	0.561670i	−0.900101	+	0.435681i	$0.856508\pi$
$450$			2.57974i			0.121610i
$451$	15.8475	−	27.4487i	0.746229	−	1.29251i
$452$	9.16693	+	15.8776i	0.431176	+	0.746819i
$453$	−0.407549	+	0.235298i	−0.0191483	+	0.0110553i
$454$	2.99407			0.140519
$455$	−49.7305	+	7.31253i	−2.33140	+	0.342817i
$456$	−2.67698			−0.125361
$457$	19.7513	−	11.4034i	0.923926	−	0.533429i	0.0390404	−	0.999238i	$-0.487570\pi$
$457$	19.7513	−	11.4034i	0.923926	−	0.533429i	0.884885	+	0.465809i	$0.154237\pi$
$458$	0.0313862	+	0.0543625i	0.00146658	+	0.00254019i
$459$	−1.68352	+	2.91595i	−0.0785801	+	0.136105i
$460$		−	16.7794i		−	0.782345i
$461$	−21.2932	−	12.2937i	−0.991725	−	0.572573i	−0.0859357	−	0.996301i	$-0.527388\pi$
$461$	−21.2932	−	12.2937i	−0.991725	−	0.572573i	−0.905790	+	0.423728i	$0.860721\pi$
$462$	−1.64768	−	0.951289i	−0.0766570	−	0.0442580i
$463$			31.7357i			1.47488i	0.675411	+	0.737441i	$0.263966\pi$
$463$			31.7357i			1.47488i	−0.675411	+	0.737441i	$0.736034\pi$
$464$	14.0990	−	24.4202i	0.654529	−	1.13368i
$465$	0.743309	+	1.28745i	0.0344701	+	0.0597040i
$466$	−0.492512	+	0.284352i	−0.0228152	+	0.0131724i
$467$	−10.9225			−0.505434			−0.252717	−	0.967540i	$-0.581324\pi$
$467$	−10.9225			−0.505434			−0.252717	+	0.967540i	$0.581324\pi$
$468$	7.03586	−	17.7389i	0.325233	−	0.819980i
$469$	−42.1040			−1.94418
$470$	−4.67817	+	2.70094i	−0.215788	+	0.124585i
$471$	−5.58584	−	9.67497i	−0.257382	−	0.445799i
$472$	3.89077	−	6.73901i	0.179087	−	0.310188i
$473$		−	11.4305i		−	0.525574i
$474$	1.41812	+	0.818755i	0.0651366	+	0.0376067i
$475$	15.6735	+	9.04913i	0.719152	+	0.415202i
$476$		−	10.6148i		−	0.486530i
$477$	2.65348	−	4.59597i	0.121495	−	0.210435i
$478$	0.377698	+	0.654192i	0.0172755	+	0.0299221i
$479$	12.4563	−	7.19166i	0.569144	−	0.328595i	−0.187663	−	0.982233i	$-0.560091\pi$
$479$	12.4563	−	7.19166i	0.569144	−	0.328595i	0.756807	+	0.653638i	$0.226758\pi$
$480$	−4.49281			−0.205068
$481$	16.2634	+	6.45065i	0.741549	+	0.294124i
$482$	−7.70475			−0.350942
$483$	−6.22567	+	3.59439i	−0.283278	+	0.163551i
$484$	−2.05856	−	3.56553i	−0.0935709	−	0.162070i
$485$	−19.9129	+	34.4901i	−0.904197	+	1.56612i
$486$			3.21477i			0.145825i
$487$	8.17135	+	4.71773i	0.370279	+	0.213781i	0.673580	−	0.739114i	$-0.264756\pi$
$487$	8.17135	+	4.71773i	0.370279	+	0.213781i	−0.303301	+	0.952895i	$0.598089\pi$
$488$	−5.20016	−	3.00231i	−0.235400	−	0.135908i
$489$			4.06948i			0.184028i
$490$	−6.06291	+	10.5013i	−0.273894	+	0.474399i
$491$	−0.559011	−	0.968235i	−0.0252278	−	0.0436958i	0.853136	−	0.521689i	$-0.174698\pi$
$491$	−0.559011	−	0.968235i	−0.0252278	−	0.0436958i	−0.878364	+	0.477993i	$0.841364\pi$
$492$	−9.03907	+	5.21871i	−0.407513	+	0.235278i
$493$	9.07509			0.408721
$494$	3.00043	+	3.79035i	0.134996	+	0.170536i
$495$	−23.8934			−1.07393
$496$	3.10614	−	1.79333i	0.139470	−	0.0805228i
$497$	9.85495	+	17.0693i	0.442055	+	0.765661i
$498$	−0.168970	+	0.292665i	−0.00757173	+	0.0131146i
$499$			43.3626i			1.94118i	0.240747	+	0.970588i	$0.422608\pi$
$499$			43.3626i			1.94118i	−0.240747	+	0.970588i	$0.577392\pi$
$500$	−7.02632	−	4.05665i	−0.314227	−	0.181419i
$501$	−10.3343	−	5.96653i	−0.461704	−	0.266565i
$502$		−	2.38138i		−	0.106286i
$503$	−5.44007	+	9.42248i	−0.242561	+	0.420127i	−0.961443	−	0.275004i	$-0.911321\pi$
$503$	−5.44007	+	9.42248i	−0.242561	+	0.420127i	0.718882	+	0.695132i	$0.244654\pi$
$504$	−6.77696	−	11.7380i	−0.301870	−	0.522854i
$505$	23.8426	−	13.7656i	1.06098	−	0.612559i
$506$	−2.33523			−0.103814
$507$	6.32454	−	1.90106i	0.280883	−	0.0844291i
$508$	32.0601			1.42244
$509$	−14.5599	+	8.40618i	−0.645358	+	0.372598i	−0.786675	−	0.617367i	$-0.788199\pi$
$509$	−14.5599	+	8.40618i	−0.645358	+	0.372598i	0.141318	+	0.989964i	$0.454866\pi$
$510$	−0.226521	−	0.392347i	−0.0100305	−	0.0173734i
$511$	−34.9276	+	60.4963i	−1.54510	+	2.67620i
$512$			18.2827i			0.807990i
$513$	12.8290	+	7.40680i	0.566412	+	0.327018i
$514$	0.678218	+	0.391569i	0.0299149	+	0.0172714i
$515$			2.44961i			0.107943i
$516$	−1.88208	+	3.25985i	−0.0828538	+	0.143507i
$517$	−10.4102	−	18.0310i	−0.457839	−	0.793001i
$518$	5.28544	−	3.05155i	0.232229	−	0.134077i
$519$	−3.41540			−0.149920
$520$	6.79525	+	8.58424i	0.297991	+	0.376444i
$521$	−28.2673			−1.23841			−0.619207	−	0.785228i	$-0.712546\pi$
$521$	−28.2673			−1.23841			−0.619207	+	0.785228i	$0.712546\pi$
$522$	4.92870	−	2.84559i	0.215723	−	0.124548i
$523$	−18.2168	−	31.5524i	−0.796565	−	1.37969i	−0.921841	−	0.387568i	$-0.873315\pi$
$523$	−18.2168	−	31.5524i	−0.796565	−	1.37969i	0.125276	−	0.992122i	$-0.460018\pi$
$524$	14.0149	−	24.2745i	0.612243	−	1.06044i
$525$		−	8.62456i		−	0.376407i
$526$	0.0549206	+	0.0317084i	0.00239465	+	0.00138255i
$527$	0.999662	+	0.577155i	0.0435460	+	0.0251413i
$528$		−	5.42562i		−	0.236120i
$529$	7.08823	−	12.2772i	0.308184	−	0.533790i
$530$	0.747667	+	1.29500i	0.0324766	+	0.0562511i
$531$	−17.8078	+	10.2813i	−0.772792	+	0.446172i
$532$	−46.7008			−2.02474
$533$	35.6734	+	14.1493i	1.54519	+	0.612875i
$534$	−1.35159			−0.0584890
$535$	−18.6049	+	10.7415i	−0.804358	+	0.464396i
$536$	4.58533	+	7.94202i	0.198056	+	0.343043i
$537$	3.48294	−	6.03263i	0.150300	−	0.260327i
$538$			1.24990i			0.0538869i
$539$	−40.4748	−	23.3681i	−1.74337	−	1.00654i
$540$	14.2696	+	8.23858i	0.614067	+	0.354532i
$541$			42.1010i			1.81006i	0.425345	+	0.905031i	$0.360153\pi$
$541$			42.1010i			1.81006i	−0.425345	+	0.905031i	$0.639847\pi$
$542$	1.71677	−	2.97354i	0.0737417	−	0.127724i
$543$	0.570088	+	0.987422i	0.0244648	+	0.0423743i
$544$	−3.02115	+	1.74426i	−0.129531	+	0.0747845i
$545$	−24.9213			−1.06751
$546$	0.849351	−	2.14139i	0.0363489	−	0.0916432i
$547$	−16.3782			−0.700283			−0.350142	−	0.936697i	$-0.613867\pi$
$547$	−16.3782			−0.700283			−0.350142	+	0.936697i	$0.613867\pi$
$548$	35.6272	−	20.5694i	1.52192	−	0.878679i
$549$	7.93359	+	13.7414i	0.338597	+	0.586468i
$550$	1.40082	−	2.42628i	0.0597310	−	0.103457i
$551$		−	39.9266i		−	1.70093i
$552$	1.35601	+	0.782894i	0.0577157	+	0.0333222i
$553$	50.3726	+	29.0826i	2.14206	+	1.23672i
$554$		−	4.10397i		−	0.174361i
$555$	−3.60692	+	6.24738i	−0.153105	+	0.265186i
$556$	−13.8782	−	24.0378i	−0.588569	−	1.01943i
$557$	5.52144	−	3.18780i	0.233951	−	0.135072i	−0.378442	−	0.925625i	$-0.623540\pi$
$557$	5.52144	−	3.18780i	0.233951	−	0.135072i	0.612393	+	0.790553i	$0.290207\pi$
$558$	0.723892			0.0306448
$559$	13.6931	−	2.01347i	0.579155	−	0.0851606i
$560$	−50.0019			−2.11297
$561$	1.51221	−	0.873076i	0.0638457	−	0.0368613i
$562$	1.78264	+	3.08762i	0.0751959	+	0.130243i
$563$	−9.30625	+	16.1189i	−0.392212	+	0.679331i	−0.992741	−	0.120272i	$-0.961623\pi$
$563$	−9.30625	+	16.1189i	−0.392212	+	0.679331i	0.600529	+	0.799603i	$0.294957\pi$
$564$			6.85631i			0.288703i
$565$	24.0708	+	13.8973i	1.01267	+	0.584664i
$566$	−0.990324	−	0.571764i	−0.0416264	−	0.0240330i
$567$			32.1278i			1.34924i
$568$	2.14650	−	3.71785i	0.0900653	−	0.155998i
$569$	−15.9196	−	27.5736i	−0.667386	−	1.15595i	−0.978632	−	0.205618i	$-0.934080\pi$
$569$	−15.9196	−	27.5736i	−0.667386	−	1.15595i	0.311246	−	0.950329i	$-0.399254\pi$
$570$	−1.72616	+	0.996600i	−0.0723010	+	0.0417430i
$571$	−9.07200			−0.379652			−0.189826	−	0.981818i	$-0.560792\pi$
$571$	−9.07200			−0.379652			−0.189826	+	0.981818i	$0.560792\pi$
$572$	−16.2496	+	12.8632i	−0.679432	+	0.537835i
$573$	0.882673			0.0368742
$574$	11.5935	−	6.69349i	0.483902	−	0.279381i
$575$	−5.29291	−	9.16758i	−0.220729	−	0.382315i
$576$	8.74050	−	15.1390i	0.364188	−	0.630791i
$577$		−	15.5034i		−	0.645417i	−0.946498	−	0.322708i	$-0.895407\pi$
$577$		−	15.5034i		−	0.645417i	0.946498	−	0.322708i	$-0.104593\pi$
$578$	3.58220	+	2.06818i	0.149000	+	0.0860250i
$579$	5.51237	+	3.18257i	0.229086	+	0.132263i
$580$		−	44.4103i		−	1.84404i
$581$	−6.00191	+	10.3956i	−0.249001	+	0.431283i
$582$	−0.912618	−	1.58070i	−0.0378292	−	0.0655221i
$583$	−4.99128	+	2.88171i	−0.206718	+	0.119348i
$584$	15.2151			0.629607
$585$	−4.20880	−	28.6229i	−0.174012	−	1.18341i
$586$	−4.66182			−0.192578
$587$	−21.6731	+	12.5130i	−0.894544	+	0.516465i	−0.875426	−	0.483352i	$-0.839419\pi$
$587$	−21.6731	+	12.5130i	−0.894544	+	0.516465i	−0.0191177	+	0.999817i	$0.506086\pi$
$588$	7.69531	+	13.3287i	0.317349	+	0.549665i
$589$	2.53924	−	4.39810i	0.104628	−	0.181220i
$590$		−	5.79390i		−	0.238531i
$591$	9.60657	+	5.54636i	0.395162	+	0.228147i
$592$	15.0726	+	8.70216i	0.619480	+	0.357657i
$593$		−	36.1835i		−	1.48588i	−0.669360	−	0.742938i	$-0.733432\pi$
$593$		−	36.1835i		−	1.48588i	0.669360	−	0.742938i	$-0.266568\pi$
$594$	1.14658	−	1.98594i	0.0470448	−	0.0814840i
$595$	−8.04617	−	13.9364i	−0.329861	−	0.571336i
$596$	−35.1157	+	20.2741i	−1.43840	+	0.830458i
$597$	−3.77465			−0.154486
$598$	−0.411348	−	2.79747i	−0.0168213	−	0.114397i
$599$	−13.4927			−0.551295			−0.275647	−	0.961259i	$-0.588892\pi$
$599$	−13.4927			−0.551295			−0.275647	+	0.961259i	$0.588892\pi$
$600$	−1.62684	+	0.939256i	−0.0664154	+	0.0383450i
$601$	−4.06257	−	7.03658i	−0.165716	−	0.287028i	0.771194	−	0.636601i	$-0.219660\pi$
$601$	−4.06257	−	7.03658i	−0.165716	−	0.287028i	−0.936909	+	0.349573i	$0.886327\pi$
$602$	2.41394	−	4.18107i	0.0983848	−	0.170408i
$603$		−	24.2334i		−	0.986859i
$604$	1.54859	+	0.894078i	0.0630111	+	0.0363795i
$605$	−5.40543	−	3.12083i	−0.219762	−	0.126880i
$606$			1.26176i			0.0512557i
$607$	−20.0565	+	34.7389i	−0.814068	+	1.41001i	0.0959270	+	0.995388i	$0.469418\pi$
$607$	−20.0565	+	34.7389i	−0.814068	+	1.41001i	−0.909995	+	0.414619i	$0.863915\pi$
$608$	7.67401	+	13.2918i	0.311222	+	0.539053i
$609$	−16.4776	+	9.51333i	−0.667705	+	0.385500i
$610$	−4.47086			−0.181020
$611$	19.7663	−	15.6469i	0.799659	−	0.633007i
$612$	6.10947			0.246961
$613$	11.2432	−	6.49127i	0.454109	−	0.262180i	−0.255455	−	0.966821i	$-0.582225\pi$
$613$	11.2432	−	6.49127i	0.454109	−	0.262180i	0.709564	+	0.704641i	$0.248892\pi$
$614$	0.486991	+	0.843493i	0.0196534	+	0.0340406i
$615$	−7.91169	+	13.7034i	−0.319030	+	0.552576i
$616$			14.7197i			0.593074i
$617$	−0.827121	−	0.477539i	−0.0332987	−	0.0192250i	0.483258	−	0.875478i	$-0.339453\pi$
$617$	−0.827121	−	0.477539i	−0.0332987	−	0.0192250i	−0.516557	+	0.856253i	$0.672787\pi$
$618$	−0.0972261	−	0.0561335i	−0.00391101	−	0.00225802i
$619$		−	19.9823i		−	0.803155i	−0.915825	−	0.401578i	$-0.868462\pi$
$619$		−	19.9823i		−	0.803155i	0.915825	−	0.401578i	$-0.131538\pi$
$620$	2.82440	−	4.89200i	0.113431	−	0.196467i
$621$	−4.33229	−	7.50375i	−0.173849	−	0.301115i
$622$	−5.84387	+	3.37396i	−0.234318	+	0.135283i
$623$	−48.0093			−1.92345
$624$	6.49958	−	0.955717i	0.260191	−	0.0382593i
$625$	−30.1185			−1.20474
$626$	−4.85888	+	2.80528i	−0.194200	+	0.112121i
$627$	−3.84117	−	6.65310i	−0.153402	−	0.265699i
$628$	−21.2249	+	36.7625i	−0.846964	+	1.46699i
$629$			5.60132i			0.223339i
$630$	−8.73979	−	5.04592i	−0.348201	−	0.201034i
$631$	−21.3121	−	12.3046i	−0.848422	−	0.489837i	0.0116960	−	0.999932i	$-0.496277\pi$
$631$	−21.3121	−	12.3046i	−0.848422	−	0.489837i	−0.860118	+	0.510095i	$0.829610\pi$
$632$		−	12.6690i		−	0.503944i
$633$	−0.169102	+	0.292894i	−0.00672121	+	0.0116415i
$634$	0.367108	+	0.635850i	0.0145797	+	0.0252528i
$635$	42.0922	−	24.3020i	1.67038	−	0.964394i
$636$	1.89794			0.0752584
$637$	20.8641	−	52.6027i	0.826664	−	2.08419i
$638$	−6.18068			−0.244696
$639$	−9.82439	+	5.67212i	−0.388647	+	0.224385i
$640$	11.3068	+	19.5840i	0.446941	+	0.774124i
$641$	−10.4836	+	18.1581i	−0.414077	+	0.717203i	−0.995331	−	0.0965193i	$-0.969229\pi$
$641$	−10.4836	+	18.1581i	−0.414077	+	0.717203i	0.581254	+	0.813722i	$0.302562\pi$
$642$		−	0.984579i		−	0.0388582i
$643$	−18.7575	−	10.8296i	−0.739723	−	0.427079i	0.0822457	−	0.996612i	$-0.473791\pi$
$643$	−18.7575	−	10.8296i	−0.739723	−	0.427079i	−0.821969	+	0.569533i	$0.807124\pi$
$644$	23.6561	+	13.6578i	0.932179	+	0.538194i
$645$			5.70655i			0.224695i
$646$	−0.773827	+	1.34031i	−0.0304458	+	0.0527337i
$647$	20.0267	+	34.6873i	0.787331	+	1.36370i	0.927597	+	0.373583i	$0.121871\pi$
$647$	20.0267	+	34.6873i	0.787331	+	1.36370i	−0.140266	+	0.990114i	$0.544796\pi$
$648$	6.06023	−	3.49888i	0.238068	−	0.137449i
$649$	22.3313			0.876580
$650$	3.15330	+	1.25071i	0.123682	+	0.0490568i
$651$	−2.42010			−0.0948514
$652$	13.3914	−	7.73152i	0.524447	−	0.302790i
$653$	−0.754361	−	1.30659i	−0.0295204	−	0.0511309i	0.850888	−	0.525348i	$-0.176065\pi$
$653$	−0.754361	−	1.30659i	−0.0295204	−	0.0511309i	−0.880408	+	0.474217i	$0.842731\pi$
$654$	0.571077	−	0.989135i	0.0223309	−	0.0386782i
$655$		−	42.4938i		−	1.66037i
$656$	33.0613	+	19.0880i	1.29083	+	0.745259i
$657$	−34.8193	−	20.1029i	−1.35843	−	0.784290i
$658$		−	8.79387i		−	0.342821i
$659$	0.210825	−	0.365159i	0.00821257	−	0.0142246i	−0.861890	−	0.507095i	$-0.830719\pi$
$659$	0.210825	−	0.365159i	0.00821257	−	0.0142246i	0.870102	+	0.492871i	$0.164052\pi$
$660$	−4.27253	−	7.40024i	−0.166308	−	0.288054i
$661$	−10.7038	+	6.17985i	−0.416330	+	0.240368i	−0.693506	−	0.720451i	$-0.743935\pi$
$661$	−10.7038	+	6.17985i	−0.416330	+	0.240368i	0.277176	+	0.960819i	$0.410601\pi$
$662$	1.33469			0.0518743
$663$	1.31227	+	1.65775i	0.0509643	+	0.0643817i
$664$	2.61455			0.101464
$665$	−61.3142	+	35.3998i	−2.37766	+	1.37274i
$666$	1.75635	+	3.04209i	0.0680572	+	0.117878i
$667$	−11.6767	+	20.2246i	−0.452123	+	0.783100i
$668$			45.3428i			1.75437i
$669$	2.49427	+	1.44007i	0.0964341	+	0.0556763i
$670$	5.91339	+	3.41410i	0.228454	+	0.131898i
$671$		−	17.2319i		−	0.665232i
$672$	3.65698	−	6.33408i	0.141071	−	0.244342i
$673$	12.2216	+	21.1683i	0.471106	+	0.815980i	0.999454	−	0.0330484i	$-0.0105215\pi$
$673$	12.2216	+	21.1683i	0.471106	+	0.815980i	−0.528348	+	0.849028i	$0.677188\pi$
$674$	1.09093	−	0.629848i	0.0420210	−	0.0242609i
$675$	10.3951			0.400108
$676$	−18.2717	−	17.2003i	−0.702756	−	0.661550i
$677$	12.8321			0.493177			0.246588	−	0.969120i	$-0.420690\pi$
$677$	12.8321			0.493177			0.246588	+	0.969120i	$0.420690\pi$
$678$	−1.10318	+	0.636920i	−0.0423673	+	0.0244608i
$679$	−32.4167	−	56.1474i	−1.24404	−	2.15474i
$680$	−1.75253	+	3.03548i	−0.0672066	+	0.116405i
$681$		−	5.76120i		−	0.220770i
$682$	−0.680830	−	0.393077i	−0.0260703	−	0.0150517i
$683$	41.1019	+	23.7302i	1.57272	+	0.908010i	0.995834	+	0.0911855i	$0.0290656\pi$
$683$	41.1019	+	23.7302i	1.57272	+	0.908010i	0.576886	+	0.816825i	$0.304268\pi$
$684$		−	26.8791i		−	1.02775i
$685$	31.1837	−	54.0117i	1.19147	−	2.06368i
$686$	−5.46795	−	9.47077i	−0.208767	−	0.361596i
$687$	0.104605	−	0.0603935i	0.00399091	−	0.00230416i
$688$	13.7678			0.524891
$689$	−4.33133	−	5.47165i	−0.165011	−	0.208453i
$690$	1.16584			0.0443827
$691$	31.3916	−	18.1240i	1.19419	−	0.689468i	0.234939	−	0.972010i	$-0.424511\pi$
$691$	31.3916	−	18.1240i	1.19419	−	0.689468i	0.959255	+	0.282542i	$0.0911777\pi$
$692$	6.48886	+	11.2390i	0.246669	+	0.427244i
$693$	19.4484	−	33.6855i	0.738782	−	1.27961i
$694$		−	1.29083i		−	0.0489992i
$695$	−36.4419	−	21.0398i	−1.38232	−	0.798084i
$696$	3.58897	+	2.07210i	0.136040	+	0.0785426i
$697$			12.2863i			0.465378i
$698$	−1.34626	+	2.33179i	−0.0509567	+	0.0882596i
$699$	0.547152	+	0.947695i	0.0206952	+	0.0358451i
$700$	−28.3807	+	16.3856i	−1.07269	+	0.619318i
$701$	−3.43354			−0.129683			−0.0648414	−	0.997896i	$-0.520654\pi$
$701$	−3.43354			−0.129683			−0.0648414	+	0.997896i	$0.520654\pi$
$702$	2.58100	+	1.02372i	0.0974137	+	0.0386377i
$703$	24.6434			0.929445
$704$	−16.4411	+	9.49229i	−0.619648	+	0.357754i
$705$	5.19717	+	9.00176i	0.195737	+	0.339026i
$706$	−2.84411	+	4.92614i	−0.107039	+	0.185398i
$707$			44.8186i			1.68558i
$708$	−6.36864	−	3.67694i	−0.239348	−	0.138188i
$709$	13.4430	+	7.76129i	0.504861	+	0.291481i	0.730719	−	0.682679i	$-0.239185\pi$
$709$	13.4430	+	7.76129i	0.504861	+	0.291481i	−0.225858	+	0.974160i	$0.572519\pi$
$710$		−	3.19644i		−	0.119960i
$711$	−16.7388	+	28.9925i	−0.627754	+	1.08730i
$712$	5.22844	+	9.05592i	0.195944	+	0.339385i
$713$	−2.57248	+	1.48522i	−0.0963402	+	0.0556220i
$714$	0.737520			0.0276010
$715$	−11.5840	+	29.2057i	−0.433217	+	1.09223i
$716$	−26.4687			−0.989181
$717$	1.25880	−	0.726769i	0.0470108	−	0.0271417i
$718$	−0.500187	−	0.866350i	−0.0186668	−	0.0323319i
$719$	−9.57781	+	16.5893i	−0.357192	+	0.618675i	−0.987491	−	0.157678i	$-0.949599\pi$
$719$	−9.57781	+	16.5893i	−0.357192	+	0.618675i	0.630299	+	0.776353i	$0.282932\pi$
$720$		−	28.7791i		−	1.07253i
$721$	−3.45352	−	1.99389i	−0.128616	−	0.0742565i
$722$	1.55268	+	0.896439i	0.0577847	+	0.0333620i
$723$			14.8255i			0.551367i
$724$	2.16620	−	3.75197i	0.0805062	−	0.139441i
$725$	−14.0088	−	24.2640i	−0.520274	−	0.901141i
$726$	0.247734	−	0.143029i	0.00919426	−	0.00530831i
$727$	12.3181			0.456855			0.228427	−	0.973561i	$-0.426642\pi$
$727$	12.3181			0.456855			0.228427	+	0.973561i	$0.426642\pi$
$728$	−17.6334	+	2.59286i	−0.653536	+	0.0960978i
$729$	−14.0460			−0.520224
$730$	9.81096	−	5.66436i	0.363120	−	0.209647i
$731$	2.21547	+	3.83731i	0.0819422	+	0.141928i
$732$	−2.83731	+	4.91436i	−0.104870	+	0.181640i
$733$			8.67737i			0.320506i	0.987076	+	0.160253i	$0.0512310\pi$
$733$			8.67737i			0.320506i	−0.987076	+	0.160253i	$0.948769\pi$
$734$	−2.48709	−	1.43592i	−0.0918000	−	0.0530008i
$735$	20.2066	+	11.6663i	0.745331	+	0.430317i
$736$		−	8.97718i		−	0.330903i
$737$	−13.1589	+	22.7918i	−0.484713	+	0.839548i
$738$	3.85250	+	6.67273i	0.141813	+	0.245627i
$739$	24.7954	−	14.3156i	0.912114	−	0.526609i	0.0310031	−	0.999519i	$-0.490130\pi$
$739$	24.7954	−	14.3156i	0.912114	−	0.526609i	0.881111	+	0.472910i	$0.156796\pi$
$740$	27.4109			1.00764
$741$	7.29341	−	5.77344i	0.267930	−	0.212092i
$742$	−2.43429			−0.0893657
$743$	−6.15757	+	3.55507i	−0.225899	+	0.130423i	−0.608679	−	0.793417i	$-0.708300\pi$
$743$	−6.15757	+	3.55507i	−0.225899	+	0.130423i	0.382780	+	0.923840i	$0.374967\pi$
$744$	0.263561	+	0.456501i	0.00966262	+	0.0167362i
$745$	−30.7360	+	53.2363i	−1.12608	+	1.95043i
$746$			0.757656i			0.0277397i
$747$	−5.98330	−	3.45446i	−0.218918	−	0.126392i
$748$	−5.74604	−	3.31748i	−0.210096	−	0.121299i
$749$		−	34.9728i		−	1.27788i
$750$	0.281857	−	0.488190i	0.0102919	−	0.0178262i
$751$	19.0438	+	32.9849i	0.694919	+	1.20364i	0.970208	+	0.242274i	$0.0778933\pi$
$751$	19.0438	+	32.9849i	0.694919	+	1.20364i	−0.275288	+	0.961362i	$0.588773\pi$
$752$	21.7179	−	12.5388i	0.791970	−	0.457244i
$753$	−4.58226			−0.166987
$754$	−1.08872	−	7.40410i	−0.0396488	−	0.269641i
$755$	2.71089			0.0986593
$756$	−23.2299	+	13.4118i	−0.844864	+	0.487782i
$757$	−4.82590	−	8.35871i	−0.175400	−	0.303802i	0.764899	−	0.644150i	$-0.222789\pi$
$757$	−4.82590	−	8.35871i	−0.175400	−	0.303802i	−0.940300	+	0.340347i	$0.889455\pi$
$758$	1.32407	−	2.29336i	0.0480925	−	0.0832987i
$759$			4.49346i			0.163102i
$760$	13.3548	+	7.71042i	0.484431	+	0.279686i
$761$	−33.4646	−	19.3208i	−1.21309	−	0.700379i	−0.249661	−	0.968333i	$-0.580319\pi$
$761$	−33.4646	−	19.3208i	−1.21309	−	0.700379i	−0.963432	+	0.267954i	$0.913652\pi$
$762$			2.22754i			0.0806954i
$763$	20.2850	−	35.1346i	0.734366	−	1.27196i
$764$	−1.67697	−	2.90460i	−0.0606708	−	0.105085i
$765$	8.02122	−	4.63106i	0.290008	−	0.167436i
$766$	1.76517			0.0637781
$767$	3.93363	+	26.7516i	0.142035	+	0.965944i
$768$	5.44112			0.196340
$769$	−9.55464	+	5.51637i	−0.344549	+	0.198925i	−0.662282	−	0.749255i	$-0.730412\pi$
$769$	−9.55464	+	5.51637i	−0.344549	+	0.198925i	0.317733	+	0.948180i	$0.397078\pi$
$770$	5.47993	+	9.49151i	0.197483	+	0.342050i
$771$	0.753460	−	1.30503i	0.0271352	−	0.0469996i
$772$		−	24.1860i		−	0.870473i
$773$	13.4300	+	7.75383i	0.483045	+	0.278886i	0.721684	−	0.692222i	$-0.243368\pi$
$773$	13.4300	+	7.75383i	0.483045	+	0.278886i	−0.238640	+	0.971108i	$0.576702\pi$
$774$	2.40646	+	1.38937i	0.0864983	+	0.0499398i
$775$		−	3.56371i		−	0.128012i
$776$	−7.06067	+	12.2294i	−0.253463	+	0.439011i
$777$	−5.87181	−	10.1703i	−0.210650	−	0.364856i
$778$	6.49532	−	3.75008i	0.232869	−	0.134447i
$779$	54.0547			1.93671
$780$	8.11246	−	6.42179i	0.290473	−	0.229937i
$781$	12.3200			0.440843
$782$	0.783956	−	0.452617i	0.0280342	−	0.0161856i
$783$	−11.4663	−	19.8603i	−0.409774	−	0.709749i
$784$	28.1464	−	48.7510i	1.00523	−	1.74111i
$785$			64.3548i			2.29692i
$786$	1.68660	+	0.973757i	0.0601589	+	0.0347328i
$787$	−7.06527	−	4.07914i	−0.251850	−	0.145406i	0.368761	−	0.929524i	$-0.379782\pi$
$787$	−7.06527	−	4.07914i	−0.251850	−	0.145406i	−0.620611	+	0.784119i	$0.713115\pi$
$788$		−	42.1497i		−	1.50152i
$789$	0.0610135	−	0.105679i	0.00217214	−	0.00376226i
$790$	−4.71646	−	8.16915i	−0.167804	−	0.290645i
$791$	−39.1855	+	22.6238i	−1.39328	+	0.804409i
$792$	−8.47208			−0.301042
$793$	20.6429	−	3.03539i	0.733049	−	0.107790i
$794$	0.380378			0.0134991
$795$	2.49184	−	1.43866i	0.0883765	−	0.0510242i
$796$	7.17139	+	12.4212i	0.254183	+	0.440258i
$797$	−13.5010	+	23.3844i	−0.478229	+	0.828317i	−0.999688	−	0.0249588i	$-0.992055\pi$
$797$	−13.5010	+	23.3844i	−0.478229	+	0.828317i	0.521459	+	0.853276i	$0.325388\pi$
$798$		−	3.24478i		−	0.114864i
$799$	6.98957	+	4.03543i	0.247273	+	0.142763i
$800$	9.32721	+	5.38507i	0.329767	+	0.190391i
$801$		−	27.6322i		−	0.976336i
$802$	−1.53539	+	2.65938i	−0.0542166	+	0.0939060i
$803$	21.8320	+	37.8142i	0.770435	+	1.33443i
$804$	7.50553	−	4.33332i	0.264700	−	0.152824i
$805$	41.4112			1.45955
$806$	0.350956	−	0.884835i	0.0123619	−	0.0311670i
$807$	2.40506			0.0846621
$808$	8.45407	−	4.88096i	0.297413	−	0.171712i
$809$	−21.4704	−	37.1877i	−0.754857	−	1.30745i	−0.945445	−	0.325781i	$-0.894373\pi$
$809$	−21.4704	−	37.1877i	−0.754857	−	1.30745i	0.190588	−	0.981670i	$-0.438961\pi$
$810$	2.60516	−	4.51226i	0.0915359	−	0.158545i
$811$			43.5429i			1.52900i	0.644625	+	0.764499i	$0.277013\pi$
$811$			43.5429i			1.52900i	−0.644625	+	0.764499i	$0.722987\pi$
$812$	62.6108	+	36.1484i	2.19721	+	1.26856i
$813$	−5.72170	−	3.30343i	−0.200669	−	0.115856i
$814$		−	3.81483i		−	0.133710i
$815$	11.7212	−	20.3017i	0.410575	−	0.711137i
$816$	1.05160	+	1.82143i	0.0368134	+	0.0637627i
$817$	16.8826	−	9.74715i	0.590646	−	0.341010i
$818$	−2.89504			−0.101223
$819$	43.7791	+	17.3643i	1.52977	+	0.606759i
$820$	60.1250			2.09966
$821$	−6.55566	+	3.78491i	−0.228794	+	0.132094i	−0.610016	−	0.792389i	$-0.708837\pi$
$821$	−6.55566	+	3.78491i	−0.228794	+	0.132094i	0.381221	+	0.924484i	$0.375504\pi$
$822$	1.42916	+	2.47538i	0.0498478	+	0.0863389i
$823$	15.9735	−	27.6668i	0.556799	−	0.964405i	−0.440962	−	0.897526i	$-0.645363\pi$
$823$	15.9735	−	27.6668i	0.556799	−	0.964405i	0.997761	−	0.0668790i	$-0.0213042\pi$
$824$			0.868579i			0.0302584i
$825$	−4.66867	−	2.69546i	−0.162542	−	0.0938437i
$826$	8.16839	+	4.71602i	0.284214	+	0.164091i
$827$			54.9232i			1.90987i	0.296819	+	0.954934i	$0.404074\pi$
$827$			54.9232i			1.90987i	−0.296819	+	0.954934i	$0.595926\pi$
$828$	−7.86091	+	13.6155i	−0.273185	+	0.473171i
$829$	−20.3518	−	35.2504i	−0.706849	−	1.22430i	−0.966020	−	0.258467i	$-0.916783\pi$
$829$	−20.3518	−	35.2504i	−0.706849	−	1.22430i	0.259171	−	0.965831i	$-0.416551\pi$
$830$	1.68590	−	0.973357i	0.0585186	−	0.0337857i
$831$	−7.89688			−0.273940
$832$	−14.2673	−	18.0235i	−0.494629	−	0.624851i
$833$	18.1170			0.627715
$834$	1.67015	−	0.964263i	0.0578326	−	0.0333897i
$835$	34.3704	+	59.5313i	1.18944	+	2.06016i
$836$	−14.5955	+	25.2802i	−0.504797	+	0.874334i
$837$		−	2.91693i		−	0.100824i
$838$	−2.92624	−	1.68947i	−0.101085	−	0.0583617i
$839$	0.951251	+	0.549205i	0.0328408	+	0.0189607i	0.516331	−	0.856389i	$-0.327298\pi$
$839$	0.951251	+	0.549205i	0.0328408	+	0.0189607i	−0.483490	+	0.875350i	$0.660631\pi$
$840$		−	7.34866i		−	0.253553i
$841$	−16.4048	+	28.4140i	−0.565684	+	0.979794i
$842$	2.25867	+	3.91214i	0.0778390	+	0.134821i
$843$	5.94121	−	3.43016i	0.204626	−	0.118141i
$844$	1.28510			0.0442348
$845$	−37.0272	−	8.73239i	−1.27377	−	0.300404i
$846$	5.06140			0.174015
$847$	8.79964	−	5.08047i	0.302359	−	0.174567i
$848$	−3.47096	−	6.01188i	−0.119193	−	0.206449i
$849$	−1.10019	+	1.90559i	−0.0377584	+	0.0653996i
$850$			1.08603i			0.0372506i
$851$	−12.4830	−	7.20707i	−0.427912	−	0.247055i
$852$	−3.51352	−	2.02853i	−0.120371	−	0.0694964i
$853$			1.88630i			0.0645855i	0.999478	+	0.0322928i	$0.0102809\pi$
$853$			1.88630i			0.0645855i	−0.999478	+	0.0322928i	$0.989719\pi$
$854$	3.63912	−	6.30313i	0.124528	−	0.215689i
$855$	−20.3747	−	35.2900i	−0.696800	−	1.20689i
$856$	−6.59687	+	3.80871i	−0.225476	+	0.130179i
$857$	−28.3622			−0.968836			−0.484418	−	0.874837i	$-0.660969\pi$
$857$	−28.3622			−0.968836			−0.484418	+	0.874837i	$0.660969\pi$
$858$	−0.893734	−	1.12903i	−0.0305116	−	0.0385444i
$859$	−17.5578			−0.599066			−0.299533	−	0.954086i	$-0.596831\pi$
$859$	−17.5578			−0.599066			−0.299533	+	0.954086i	$0.596831\pi$
$860$	18.7785	−	10.8418i	0.640340	−	0.369701i
$861$	−12.8796	−	22.3082i	−0.438937	−	0.760261i
$862$	2.34772	−	4.06636i	0.0799635	−	0.138501i
$863$			50.6609i			1.72452i	0.506467	+	0.862259i	$0.330951\pi$
$863$			50.6609i			1.72452i	−0.506467	+	0.862259i	$0.669049\pi$
$864$	7.63441	+	4.40773i	0.259728	+	0.149954i
$865$	17.0386	+	9.83727i	0.579331	+	0.334477i
$866$		−	6.27016i		−	0.213069i
$867$	3.97961	−	6.89288i	0.135155	−	0.234095i
$868$	4.59791	+	7.96381i	0.156063	+	0.270309i
$869$	31.4862	−	18.1785i	1.06810	−	0.616665i
$870$	3.08564			0.104613
$871$	−29.6212	−	11.7488i	−1.00368	−	0.398093i
$872$	−8.83654			−0.299243
$873$	32.3162	−	18.6578i	1.09374	−	0.631470i
$874$	−1.99133	−	3.44908i	−0.0673577	−	0.116667i
$875$	10.0117	−	17.3408i	0.338457	−	0.586225i
$876$		−	14.3789i		−	0.485819i
$877$	−36.1342	−	20.8621i	−1.22016	−	0.704462i	−0.255211	−	0.966885i	$-0.582145\pi$
$877$	−36.1342	−	20.8621i	−1.22016	−	0.704462i	−0.964953	+	0.262423i	$0.915478\pi$
$878$	1.38272	+	0.798316i	0.0466647	+	0.0269419i
$879$			8.97030i			0.302561i
$880$	−15.6272	+	27.0671i	−0.526794	+	0.912433i
$881$	−3.78411	−	6.55428i	−0.127490	−	0.220819i	0.795213	−	0.606330i	$-0.207359\pi$
$881$	−3.78411	−	6.55428i	−0.127490	−	0.220819i	−0.922704	+	0.385510i	$0.874025\pi$
$882$	9.83936	−	5.68076i	0.331309	−	0.191281i
$883$	−46.0225			−1.54878			−0.774390	−	0.632708i	$-0.781943\pi$
$883$	−46.0225			−1.54878			−0.774390	+	0.632708i	$0.781943\pi$
$884$	2.96199	−	7.46780i	0.0996225	−	0.251169i
$885$	−11.1487			−0.374758
$886$	0.459164	−	0.265098i	0.0154259	−	0.00890615i
$887$	24.0392	+	41.6372i	0.807158	+	1.39804i	0.914824	+	0.403852i	$0.132329\pi$
$887$	24.0392	+	41.6372i	0.807158	+	1.39804i	−0.107666	+	0.994187i	$0.534338\pi$
$888$	−1.27894	+	2.21518i	−0.0429183	+	0.0743367i
$889$			79.1236i			2.65372i
$890$	6.74277	+	3.89294i	0.226018	+	0.130492i
$891$	17.3915	+	10.0410i	0.582638	+	0.336386i
$892$		−	10.9438i		−	0.366426i
$893$	17.7542	−	30.7512i	0.594122	−	1.02905i
$894$	−1.40865	−	2.43985i	−0.0471122	−	0.0816007i
$895$	−34.7511	+	20.0636i	−1.16160	+	0.670652i
$896$	−36.8133			−1.22985
$897$	−5.38291	+	0.791518i	−0.179730	+	0.0264280i
$898$	−6.28422			−0.209707
$899$	−6.80862	+	3.93096i	−0.227080	+	0.131105i
$900$	−9.43091	−	16.3348i	−0.314364	−	0.544494i
$901$	1.11708	−	1.93483i	0.0372152	−	0.0644586i
$902$		−	8.36773i		−	0.278615i
$903$	−8.04523	−	4.64492i	−0.267729	−	0.154573i
$904$	8.53498	+	4.92768i	0.283869	+	0.163892i
$905$		−	6.56802i		−	0.218328i
$906$	−0.0621207	+	0.107596i	−0.00206382	+	0.00357464i
$907$	−14.4095	−	24.9581i	−0.478461	−	0.828719i	0.521234	−	0.853414i	$-0.325472\pi$
$907$	−14.4095	−	24.9581i	−0.478461	−	0.828719i	−0.999695	+	0.0246950i	$0.992139\pi$
$908$	−18.9583	+	10.9456i	−0.629154	+	0.363242i
$909$	−25.7958			−0.855593
$910$	−10.4050	+	8.23655i	−0.344922	+	0.273039i
$911$	37.2528			1.23424			0.617121	−	0.786869i	$-0.288299\pi$
$911$	37.2528			1.23424			0.617121	+	0.786869i	$0.288299\pi$
$912$	8.01352	−	4.62661i	0.265354	−	0.153202i
$913$	3.75159	+	6.49794i	0.124159	+	0.215050i
$914$	3.01059	−	5.21450i	0.0995815	−	0.172480i
$915$			8.60286i			0.284402i
$916$	−0.397472	−	0.229481i	−0.0131329	−	0.00758226i
$917$	59.9088	+	34.5884i	1.97836	+	1.14221i
$918$			0.888927i			0.0293390i
$919$	−18.3084	+	31.7111i	−0.603938	+	1.04605i	0.388280	+	0.921541i	$0.373069\pi$
$919$	−18.3084	+	31.7111i	−0.603938	+	1.04605i	−0.992218	+	0.124510i	$0.960264\pi$
$920$	−4.50988	−	7.81135i	−0.148686	−	0.257533i
$921$	1.62305	−	0.937071i	0.0534815	−	0.0308775i
$922$	−6.49125			−0.213778
$923$	2.17015	+	14.7586i	0.0714313	+	0.485785i
$924$	13.9107			0.457629
$925$	14.9762	−	8.64649i	0.492413	−	0.284295i
$926$	4.18924	+	7.25597i	0.137667	+	0.238446i
$927$	1.14761	−	1.98771i	0.0376923	−	0.0652850i
$928$		−	23.7600i		−	0.779961i
$929$	33.9661	+	19.6103i	1.11439	+	0.643394i	0.939963	−	0.341276i	$-0.110859\pi$
$929$	33.9661	+	19.6103i	1.11439	+	0.643394i	0.174428	+	0.984670i	$0.444192\pi$
$930$	0.339897	+	0.196240i	0.0111457	+	0.00643495i
$931$		−	79.7071i		−	2.61229i
$932$	2.07905	−	3.60101i	0.0681014	−	0.117955i
$933$	6.49219	+	11.2448i	0.212545	+	0.368139i
$934$	−2.49730	+	1.44182i	−0.0817141	+	0.0471777i
$935$	−10.0588			−0.328957
$936$	−1.49235	−	10.1491i	−0.0487789	−	0.331732i
$937$	−12.0107			−0.392371			−0.196186	−	0.980567i	$-0.562856\pi$
$937$	−12.0107			−0.392371			−0.196186	+	0.980567i	$0.562856\pi$
$938$	−9.62655	+	5.55789i	−0.314318	+	0.181472i
$939$	5.39793	+	9.34949i	0.176155	+	0.305109i
$940$	19.7480	−	34.2045i	0.644109	−	1.11563i
$941$		−	39.8591i		−	1.29937i	−0.760203	−	0.649685i	$-0.774901\pi$
$941$		−	39.8591i		−	1.29937i	0.760203	−	0.649685i	$-0.225099\pi$
$942$	−2.55427	−	1.47471i	−0.0832226	−	0.0480486i
$943$	−27.3812	−	15.8085i	−0.891653	−	0.514796i
$944$			26.8975i			0.875441i
$945$	−20.3326	+	35.2171i	−0.661420	+	1.14561i
$946$	−1.50887	−	2.61344i	−0.0490576	−	0.0849703i
$947$	13.9573	−	8.05824i	0.453550	−	0.261857i	−0.255778	−	0.966736i	$-0.582332\pi$
$947$	13.9573	−	8.05824i	0.453550	−	0.261857i	0.709328	+	0.704878i	$0.248998\pi$
$948$	−11.9727			−0.388855
$949$	−41.4535	+	32.8144i	−1.34564	+	1.06520i
$950$	4.77808			0.155022
$951$	1.22351	−	0.706391i	0.0396749	−	0.0229063i
$952$	−2.85299	−	4.94153i	−0.0924661	−	0.160156i
$953$	−23.5475	+	40.7855i	−0.762779	+	1.32117i	0.178633	+	0.983916i	$0.442832\pi$
$953$	−23.5475	+	40.7855i	−0.762779	+	1.32117i	−0.941413	+	0.337257i	$0.890501\pi$
$954$		−	1.40108i		−	0.0453617i
$955$	−4.40345	−	2.54233i	−0.142492	−	0.0822680i
$956$	−4.78314	−	2.76155i	−0.154698	−	0.0893148i
$957$			11.8929i			0.384443i
$958$	1.89866	−	3.28857i	0.0613428	−	0.106249i
$959$	50.7647	+	87.9270i	1.63928	+	2.83931i
$960$	8.20805	−	4.73892i	0.264914	−	0.152948i
$961$	−1.00000			−0.0322581
$962$	4.56995	−	0.671979i	0.147341	−	0.0216655i
$963$	20.1289			0.648646
$964$	48.7862	−	28.1667i	1.57130	−	0.907189i
$965$	−18.3333	−	31.7542i	−0.590169	−	1.02220i
$966$	−0.948949	+	1.64363i	−0.0305319	+	0.0528829i
$967$		−	24.7836i		−	0.796986i	−0.917171	−	0.398493i	$-0.869533\pi$
$967$		−	24.7836i		−	0.796986i	0.917171	−	0.398493i	$-0.130467\pi$
$968$	−1.91665	−	1.10658i	−0.0616034	−	0.0355667i
$969$	2.57903	+	1.48900i	0.0828503	+	0.0478336i
$970$			10.5143i			0.337595i
$971$	25.6718	−	44.4648i	0.823847	−	1.42694i	−0.0789511	−	0.996878i	$-0.525157\pi$
$971$	25.6718	−	44.4648i	0.823847	−	1.42694i	0.902798	−	0.430066i	$-0.141510\pi$
$972$	−11.7524	−	20.3558i	−0.376959	−	0.652912i
$973$	59.3248	−	34.2512i	1.90186	−	1.09804i
$974$	2.49104			0.0798180
$975$	2.40662	−	6.06759i	0.0770735	−	0.194318i
$976$	20.7555			0.664367
$977$	5.11844	−	2.95513i	0.163753	−	0.0945431i	−0.415884	−	0.909418i	$-0.636528\pi$
$977$	5.11844	−	2.95513i	0.163753	−	0.0945431i	0.579637	+	0.814875i	$0.303194\pi$
$978$	0.537188	+	0.930437i	0.0171774	+	0.0297521i
$979$	−15.0045	+	25.9885i	−0.479545	+	0.830596i
$980$		−	88.6581i		−	2.83208i
$981$	20.2221	+	11.6752i	0.645642	+	0.372762i
$982$	−0.255622	−	0.147583i	−0.00815722	−	0.00470957i
$983$		−	54.1966i		−	1.72860i	−0.502975	−	0.864301i	$-0.667761\pi$
$983$		−	54.1966i		−	1.72860i	0.502975	−	0.864301i	$-0.332239\pi$
$984$	−2.80531	+	4.85894i	−0.0894301	+	0.154897i
$985$	−31.9500	−	55.3390i	−1.01801	−	1.76325i
$986$	2.07491	−	1.19795i	0.0660785	−	0.0381504i
$987$	−16.9212			−0.538608
$988$	−32.8552	−	13.0315i	−1.04526	−	0.414588i
$989$	−11.4024			−0.362574
$990$	−5.46294	+	3.15403i	−0.173624	+	0.100242i
$991$	−19.8054	−	34.3039i	−0.629139	−	1.08970i	−0.987725	−	0.156204i	$-0.950074\pi$
$991$	−19.8054	−	34.3039i	−0.629139	−	1.08970i	0.358586	−	0.933497i	$-0.383259\pi$
$992$	1.51108	−	2.61727i	0.0479770	−	0.0830985i
$993$		−	2.56822i		−	0.0815001i
$994$	4.50642	+	2.60179i	0.142935	+	0.0825236i
$995$	18.8309	+	10.8720i	0.596978	+	0.344666i
$996$		−	2.47085i		−	0.0782920i
$997$	−6.73038	+	11.6574i	−0.213153	+	0.369192i	−0.952700	−	0.303913i	$-0.901707\pi$
$997$	−6.73038	+	11.6574i	−0.213153	+	0.369192i	0.739547	+	0.673105i	$0.235040\pi$
$998$	5.72404	+	9.91432i	0.181191	+	0.313832i
$999$	12.2581	−	7.07724i	0.387830	−	0.223914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.19	✓	68
13.2	odd	12		5239.2.a.q.1.20		34
13.4	even	6	inner	403.2.r.a.342.19	yes	68
13.11	odd	12		5239.2.a.r.1.15		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.19	✓	68	1.1	even	1	trivial
403.2.r.a.342.19	yes	68	13.4	even	6	inner
5239.2.a.q.1.20		34	13.2	odd	12
5239.2.a.r.1.15		34	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.228638 - 0.132004i) q^{2} +(-0.254003 - 0.439946i) q^{3} +(-0.965150 + 1.67169i) q^{4} +2.92638i q^{5} +(-0.116149 - 0.0670588i) q^{6} +(-4.12569 - 2.38197i) q^{7} +1.03763i q^{8} +(1.37097 - 2.37458i) q^{9} +O(q^{10})\)	\(q+(0.228638 - 0.132004i) q^{2} +(-0.254003 - 0.439946i) q^{3} +(-0.965150 + 1.67169i) q^{4} +2.92638i q^{5} +(-0.116149 - 0.0670588i) q^{6} +(-4.12569 - 2.38197i) q^{7} +1.03763i q^{8} +(1.37097 - 2.37458i) q^{9} +(0.386294 + 0.669081i) q^{10} +(-2.57882 + 1.48888i) q^{11} +0.980603 q^{12} +(-2.23785 - 2.82701i) q^{13} -1.25772 q^{14} +(1.28745 - 0.743309i) q^{15} +(-1.79333 - 3.10614i) q^{16} +(0.577155 - 0.999662i) q^{17} -0.723892i q^{18} +(-4.39810 - 2.53924i) q^{19} +(-4.89200 - 2.82440i) q^{20} +2.42010i q^{21} +(-0.393077 + 0.680830i) q^{22} +(1.48522 + 2.57248i) q^{23} +(0.456501 - 0.263561i) q^{24} -3.56371 q^{25} +(-0.884835 - 0.350956i) q^{26} -2.91693 q^{27} +(7.96381 - 4.59791i) q^{28} +(3.93096 + 6.80862i) q^{29} +(0.196240 - 0.339897i) q^{30} +1.00000i q^{31} +(-2.61727 - 1.51108i) q^{32} +(1.31006 + 0.756362i) q^{33} -0.304747i q^{34} +(6.97054 - 12.0733i) q^{35} +(2.64637 + 4.58365i) q^{36} +(-4.20241 + 2.42626i) q^{37} -1.34076 q^{38} +(-0.675312 + 1.70260i) q^{39} -3.03650 q^{40} +(-9.21786 + 5.32194i) q^{41} +(0.319464 + 0.553327i) q^{42} +(-1.91930 + 3.32433i) q^{43} -5.74799i q^{44} +(6.94893 + 4.01197i) q^{45} +(0.679156 + 0.392111i) q^{46} +6.99193i q^{47} +(-0.911021 + 1.57793i) q^{48} +(7.84753 + 13.5923i) q^{49} +(-0.814799 + 0.470424i) q^{50} -0.586396 q^{51} +(6.88575 - 1.01250i) q^{52} +1.93549 q^{53} +(-0.666921 + 0.385047i) q^{54} +(-4.35705 - 7.54662i) q^{55} +(2.47160 - 4.28094i) q^{56} +2.57990i q^{57} +(1.79753 + 1.03780i) q^{58} +(-6.49462 - 3.74967i) q^{59} +2.86962i q^{60} +(-2.89343 + 5.01157i) q^{61} +(0.132004 + 0.228638i) q^{62} +(-11.3123 + 6.53118i) q^{63} +6.37544 q^{64} +(8.27293 - 6.54881i) q^{65} +0.399371 q^{66} +(7.65399 - 4.41904i) q^{67} +(1.11408 + 1.92965i) q^{68} +(0.754501 - 1.30683i) q^{69} -3.68056i q^{70} +(-3.58302 - 2.06866i) q^{71} +(2.46394 + 1.42256i) q^{72} -14.6633i q^{73} +(-0.640552 + 1.10947i) q^{74} +(0.905193 + 1.56784i) q^{75} +(8.48964 - 4.90150i) q^{76} +14.1859 q^{77} +(0.0703488 + 0.478423i) q^{78} -12.2095 q^{79} +(9.08974 - 5.24796i) q^{80} +(-3.37199 - 5.84045i) q^{81} +(-1.40503 + 2.43359i) q^{82} -2.51973i q^{83} +(-4.04566 - 2.33576i) q^{84} +(2.92539 + 1.68898i) q^{85} +1.01342i q^{86} +(1.99695 - 3.45882i) q^{87} +(-1.54491 - 2.67587i) q^{88} +(8.72750 - 5.03883i) q^{89} +2.11838 q^{90} +(2.49883 + 16.9939i) q^{91} -5.73385 q^{92} +(0.439946 - 0.254003i) q^{93} +(0.922963 + 1.59862i) q^{94} +(7.43079 - 12.8705i) q^{95} +1.53528i q^{96} +(11.7859 + 6.80461i) q^{97} +(3.58848 + 2.07181i) q^{98} +8.16484i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) \) 68 * q + 32 * q^4 - 34 * q^9	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

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