LMFDB - Embedded newform 304.2.k.b.77.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (of order $4$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.13
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.472113 - 1.33308i) q^{2} +(-0.194303 - 0.194303i) q^{3} +(-1.55422 + 1.25873i) q^{4} +(-1.01947 + 1.01947i) q^{5} +(-0.167289 + 0.350755i) q^{6} +2.78994i q^{7} +(2.41176 + 1.47764i) q^{8} -2.92449i q^{9} +O(q^{10})$	\(q+(-0.472113 - 1.33308i) q^{2} +(-0.194303 - 0.194303i) q^{3} +(-1.55422 + 1.25873i) q^{4} +(-1.01947 + 1.01947i) q^{5} +(-0.167289 + 0.350755i) q^{6} +2.78994i q^{7} +(2.41176 + 1.47764i) q^{8} -2.92449i q^{9} +(1.84035 + 0.877735i) q^{10} +(4.15707 - 4.15707i) q^{11} +(0.546564 + 0.0574138i) q^{12} +(3.85908 + 3.85908i) q^{13} +(3.71923 - 1.31717i) q^{14} +0.396173 q^{15} +(0.831187 - 3.91269i) q^{16} +4.48546 q^{17} +(-3.89859 + 1.38069i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(0.301240 - 2.86773i) q^{20} +(0.542094 - 0.542094i) q^{21} +(-7.50433 - 3.57911i) q^{22} +3.66625i q^{23} +(-0.181503 - 0.755721i) q^{24} +2.92135i q^{25} +(3.32255 - 6.96639i) q^{26} +(-1.15115 + 1.15115i) q^{27} +(-3.51179 - 4.33618i) q^{28} +(2.04427 + 2.04427i) q^{29} +(-0.187039 - 0.528131i) q^{30} -2.97474 q^{31} +(-5.60835 + 0.739191i) q^{32} -1.61546 q^{33} +(-2.11764 - 5.97948i) q^{34} +(-2.84427 - 2.84427i) q^{35} +(3.68115 + 4.54530i) q^{36} +(8.39019 - 8.39019i) q^{37} +(-0.608797 + 1.27647i) q^{38} -1.49966i q^{39} +(-3.96514 + 0.952314i) q^{40} +5.02958i q^{41} +(-0.978586 - 0.466726i) q^{42} +(-5.43835 + 5.43835i) q^{43} +(-1.22836 + 11.6936i) q^{44} +(2.98144 + 2.98144i) q^{45} +(4.88741 - 1.73088i) q^{46} -6.73925 q^{47} +(-0.921748 + 0.598744i) q^{48} -0.783793 q^{49} +(3.89440 - 1.37921i) q^{50} +(-0.871537 - 0.871537i) q^{51} +(-10.8554 - 1.14030i) q^{52} +(6.12560 - 6.12560i) q^{53} +(2.07804 + 0.991101i) q^{54} +8.47605i q^{55} +(-4.12253 + 6.72868i) q^{56} +0.274786i q^{57} +(1.76005 - 3.69030i) q^{58} +(6.65292 - 6.65292i) q^{59} +(-0.615739 + 0.498676i) q^{60} +(-2.39148 - 2.39148i) q^{61} +(1.40441 + 3.96558i) q^{62} +8.15917 q^{63} +(3.63318 + 7.12741i) q^{64} -7.86845 q^{65} +(0.762681 + 2.15354i) q^{66} +(-8.65383 - 8.65383i) q^{67} +(-6.97138 + 5.64599i) q^{68} +(0.712362 - 0.712362i) q^{69} +(-2.44883 + 5.13447i) q^{70} -3.99706i q^{71} +(4.32134 - 7.05318i) q^{72} +10.2021i q^{73} +(-15.1459 - 7.22369i) q^{74} +(0.567626 - 0.567626i) q^{75} +(1.98906 + 0.208940i) q^{76} +(11.5980 + 11.5980i) q^{77} +(-1.99917 + 0.708009i) q^{78} -8.69044 q^{79} +(3.14151 + 4.83625i) q^{80} -8.32614 q^{81} +(6.70484 - 2.37453i) q^{82} +(8.43335 + 8.43335i) q^{83} +(-0.160181 + 1.52488i) q^{84} +(-4.57280 + 4.57280i) q^{85} +(9.81729 + 4.68225i) q^{86} -0.794414i q^{87} +(16.1685 - 3.88322i) q^{88} +4.30916i q^{89} +(2.56693 - 5.38209i) q^{90} +(-10.7666 + 10.7666i) q^{91} +(-4.61482 - 5.69815i) q^{92} +(0.578001 + 0.578001i) q^{93} +(3.18169 + 8.98398i) q^{94} +1.44175 q^{95} +(1.23335 + 0.946091i) q^{96} -4.86879 q^{97} +(0.370039 + 1.04486i) q^{98} +(-12.1573 - 12.1573i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.472113	−	1.33308i	−0.333835	−	0.942632i
$2$	−0.472113	−	1.33308i	−0.333835	−	0.942632i
$3$	−0.194303	−	0.194303i	−0.112181	−	0.112181i	0.648788	−	0.760969i	$-0.275276\pi$
$3$	−0.194303	−	0.194303i	−0.112181	−	0.112181i	−0.760969	+	0.648788i	$0.775276\pi$
$4$	−1.55422	+	1.25873i	−0.777109	+	0.629366i
$5$	−1.01947	+	1.01947i	−0.455922	+	0.455922i	−0.897314	−	0.441392i	$-0.854485\pi$
$5$	−1.01947	+	1.01947i	−0.455922	+	0.455922i	0.441392	+	0.897314i	$0.354485\pi$
$6$	−0.167289	+	0.350755i	−0.0682953	+	0.143195i
$7$			2.78994i			1.05450i	0.849710	+	0.527250i	$0.176777\pi$
$7$			2.78994i			1.05450i	−0.849710	+	0.527250i	$0.823223\pi$
$8$	2.41176	+	1.47764i	0.852686	+	0.522423i
$9$		−	2.92449i		−	0.974831i
$10$	1.84035	+	0.877735i	0.581969	+	0.277564i
$11$	4.15707	−	4.15707i	1.25341	−	1.25341i	0.299221	−	0.954184i	$-0.403273\pi$
$11$	4.15707	−	4.15707i	1.25341	−	1.25341i	0.954184	−	0.299221i	$-0.0967269\pi$
$12$	0.546564	+	0.0574138i	0.157779	+	0.0165739i
$13$	3.85908	+	3.85908i	1.07032	+	1.07032i	0.997333	+	0.0729826i	$0.0232518\pi$
$13$	3.85908	+	3.85908i	1.07032	+	1.07032i	0.0729826	+	0.997333i	$0.476748\pi$
$14$	3.71923	−	1.31717i	0.994005	−	0.352029i
$15$	0.396173			0.102291
$16$	0.831187	−	3.91269i	0.207797	−	0.978172i
$17$	4.48546			1.08788			0.543941	−	0.839123i	$-0.316931\pi$
$17$	4.48546			1.08788			0.543941	+	0.839123i	$0.316931\pi$
$18$	−3.89859	+	1.38069i	−0.918907	+	0.325432i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$20$	0.301240	−	2.86773i	0.0673593	−	0.641243i
$21$	0.542094	−	0.542094i	0.118295	−	0.118295i
$22$	−7.50433	−	3.57911i	−1.59993	−	0.763069i
$23$			3.66625i			0.764466i	0.924066	+	0.382233i	$0.124845\pi$
$23$			3.66625i			0.764466i	−0.924066	+	0.382233i	$0.875155\pi$
$24$	−0.181503	−	0.755721i	−0.0370491	−	0.154261i
$25$			2.92135i			0.584270i
$26$	3.32255	−	6.96639i	0.651605	−	1.36622i
$27$	−1.15115	+	1.15115i	−0.221538	+	0.221538i
$28$	−3.51179	−	4.33618i	−0.663667	−	0.819462i
$29$	2.04427	+	2.04427i	0.379611	+	0.379611i	0.870962	−	0.491351i	$-0.163497\pi$
$29$	2.04427	+	2.04427i	0.379611	+	0.379611i	−0.491351	+	0.870962i	$0.663497\pi$
$30$	−0.187039	−	0.528131i	−0.0341484	−	0.0964231i
$31$	−2.97474			−0.534279			−0.267140	−	0.963658i	$-0.586078\pi$
$31$	−2.97474			−0.534279			−0.267140	+	0.963658i	$0.586078\pi$
$32$	−5.60835	+	0.739191i	−0.991426	+	0.130672i
$33$	−1.61546			−0.281216
$34$	−2.11764	−	5.97948i	−0.363173	−	1.02547i
$35$	−2.84427	−	2.84427i	−0.480770	−	0.480770i
$36$	3.68115	+	4.54530i	0.613525	+	0.757550i
$37$	8.39019	−	8.39019i	1.37934	−	1.37934i	0.533603	−	0.845735i	$-0.320838\pi$
$37$	8.39019	−	8.39019i	1.37934	−	1.37934i	0.845735	−	0.533603i	$-0.179162\pi$
$38$	−0.608797	+	1.27647i	−0.0987599	+	0.207070i
$39$		−	1.49966i		−	0.240138i
$40$	−3.96514	+	0.952314i	−0.626943	+	0.150574i
$41$			5.02958i			0.785488i	0.919648	+	0.392744i	$0.128474\pi$
$41$			5.02958i			0.785488i	−0.919648	+	0.392744i	$0.871526\pi$
$42$	−0.978586	−	0.466726i	−0.150999	−	0.0720174i
$43$	−5.43835	+	5.43835i	−0.829341	+	0.829341i	−0.987426	−	0.158085i	$-0.949468\pi$
$43$	−5.43835	+	5.43835i	−0.829341	+	0.829341i	0.158085	+	0.987426i	$0.449468\pi$
$44$	−1.22836	+	11.6936i	−0.185182	+	1.76288i
$45$	2.98144	+	2.98144i	0.444447	+	0.444447i
$46$	4.88741	−	1.73088i	0.720610	−	0.255205i
$47$	−6.73925			−0.983021			−0.491510	−	0.870872i	$-0.663555\pi$
$47$	−6.73925			−0.983021			−0.491510	+	0.870872i	$0.663555\pi$
$48$	−0.921748	+	0.598744i	−0.133043	+	0.0864213i
$49$	−0.783793			−0.111970
$50$	3.89440	−	1.37921i	0.550751	−	0.195049i
$51$	−0.871537	−	0.871537i	−0.122040	−	0.122040i
$52$	−10.8554	−	1.14030i	−1.50537	−	0.158132i
$53$	6.12560	−	6.12560i	0.841416	−	0.841416i	−0.147627	−	0.989043i	$-0.547164\pi$
$53$	6.12560	−	6.12560i	0.841416	−	0.841416i	0.989043	+	0.147627i	$0.0471636\pi$
$54$	2.07804	+	0.991101i	0.282786	+	0.134872i
$55$			8.47605i			1.14291i
$56$	−4.12253	+	6.72868i	−0.550896	+	0.899158i
$57$			0.274786i			0.0363963i
$58$	1.76005	−	3.69030i	0.231106	−	0.484561i
$59$	6.65292	−	6.65292i	0.866137	−	0.866137i	−0.125906	−	0.992042i	$-0.540184\pi$
$59$	6.65292	−	6.65292i	0.866137	−	0.866137i	0.992042	+	0.125906i	$0.0401836\pi$
$60$	−0.615739	+	0.498676i	−0.0794916	+	0.0643787i
$61$	−2.39148	−	2.39148i	−0.306198	−	0.306198i	0.537235	−	0.843433i	$-0.319469\pi$
$61$	−2.39148	−	2.39148i	−0.306198	−	0.306198i	−0.843433	+	0.537235i	$0.819469\pi$
$62$	1.40441	+	3.96558i	0.178361	+	0.503629i
$63$	8.15917			1.02796
$64$	3.63318	+	7.12741i	0.454147	+	0.890927i
$65$	−7.86845			−0.975962
$66$	0.762681	+	2.15354i	0.0938796	+	0.265083i
$67$	−8.65383	−	8.65383i	−1.05723	−	1.05723i	−0.998259	−	0.0589745i	$-0.981217\pi$
$67$	−8.65383	−	8.65383i	−1.05723	−	1.05723i	−0.0589745	−	0.998259i	$-0.518783\pi$
$68$	−6.97138	+	5.64599i	−0.845404	+	0.684677i
$69$	0.712362	−	0.712362i	0.0857584	−	0.0857584i
$70$	−2.44883	+	5.13447i	−0.292691	+	0.613687i
$71$		−	3.99706i		−	0.474364i	−0.971465	−	0.237182i	$-0.923776\pi$
$71$		−	3.99706i		−	0.474364i	0.971465	−	0.237182i	$-0.0762238\pi$
$72$	4.32134	−	7.05318i	0.509275	−	0.831225i
$73$			10.2021i			1.19407i	0.802216	+	0.597034i	$0.203654\pi$
$73$			10.2021i			1.19407i	−0.802216	+	0.597034i	$0.796346\pi$
$74$	−15.1459	−	7.22369i	−1.76068	−	0.839737i
$75$	0.567626	−	0.567626i	0.0655438	−	0.0655438i
$76$	1.98906	+	0.208940i	0.228160	+	0.0239671i
$77$	11.5980	+	11.5980i	1.32172	+	1.32172i
$78$	−1.99917	+	0.708009i	−0.226361	+	0.0801663i
$79$	−8.69044			−0.977751			−0.488876	−	0.872354i	$-0.662593\pi$
$79$	−8.69044			−0.977751			−0.488876	+	0.872354i	$0.662593\pi$
$80$	3.14151	+	4.83625i	0.351231	+	0.540710i
$81$	−8.32614			−0.925126
$82$	6.70484	−	2.37453i	0.740426	−	0.262223i
$83$	8.43335	+	8.43335i	0.925680	+	0.925680i	0.997423	−	0.0717428i	$-0.0228561\pi$
$83$	8.43335	+	8.43335i	0.925680	+	0.925680i	−0.0717428	+	0.997423i	$0.522856\pi$
$84$	−0.160181	+	1.52488i	−0.0174772	+	0.166378i
$85$	−4.57280	+	4.57280i	−0.495990	+	0.495990i
$86$	9.81729	+	4.68225i	1.05863	+	0.504900i
$87$		−	0.794414i		−	0.0851701i
$88$	16.1685	−	3.88322i	1.72357	−	0.413953i
$89$			4.30916i			0.456770i	0.973571	+	0.228385i	$0.0733445\pi$
$89$			4.30916i			0.456770i	−0.973571	+	0.228385i	$0.926656\pi$
$90$	2.56693	−	5.38209i	0.270578	−	0.567322i
$91$	−10.7666	+	10.7666i	−1.12865	+	1.12865i
$92$	−4.61482	−	5.69815i	−0.481129	−	0.594073i
$93$	0.578001	+	0.578001i	0.0599359	+	0.0599359i
$94$	3.18169	+	8.98398i	0.328166	+	0.926626i
$95$	1.44175			0.147921
$96$	1.23335	+	0.946091i	0.125878	+	0.0965601i
$97$	−4.86879			−0.494350			−0.247175	−	0.968971i	$-0.579502\pi$
$97$	−4.86879			−0.494350			−0.247175	+	0.968971i	$0.579502\pi$
$98$	0.370039	+	1.04486i	0.0373796	+	0.105547i
$99$	−12.1573	−	12.1573i	−1.22186	−	1.22186i
$100$	−3.67720	−	4.54041i	−0.367720	−	0.454041i
$101$	−12.2592	+	12.2592i	−1.21984	+	1.21984i	−0.252152	+	0.967688i	$0.581138\pi$
$101$	−12.2592	+	12.2592i	−1.21984	+	1.21984i	−0.967688	+	0.252152i	$0.918862\pi$
$102$	−0.750366	+	1.57329i	−0.0742973	+	0.155779i
$103$		−	8.95867i		−	0.882724i	−0.897329	−	0.441362i	$-0.854496\pi$
$103$		−	8.95867i		−	0.882724i	0.897329	−	0.441362i	$-0.145504\pi$
$104$	3.60486	+	15.0095i	0.353485	+	1.47180i
$105$			1.10530i			0.107866i
$106$	−11.0579	−	5.27395i	−1.07404	−	0.512252i
$107$	7.88215	−	7.88215i	0.761996	−	0.761996i	−0.214687	−	0.976683i	$-0.568873\pi$
$107$	7.88215	−	7.88215i	0.761996	−	0.761996i	0.976683	+	0.214687i	$0.0688731\pi$
$108$	0.340147	−	3.23812i	0.0327307	−	0.311588i
$109$	−1.56866	−	1.56866i	−0.150251	−	0.150251i	0.627979	−	0.778230i	$-0.283882\pi$
$109$	−1.56866	−	1.56866i	−0.150251	−	0.150251i	−0.778230	+	0.627979i	$0.783882\pi$
$110$	11.2993	−	4.00166i	1.07734	−	0.381543i
$111$	−3.26047			−0.309470
$112$	10.9162	+	2.31897i	1.03148	+	0.219122i
$113$	9.86218			0.927756			0.463878	−	0.885899i	$-0.346458\pi$
$113$	9.86218			0.927756			0.463878	+	0.885899i	$0.346458\pi$
$114$	0.366312	−	0.129730i	0.0343083	−	0.0121503i
$115$	−3.73764	−	3.73764i	−0.348537	−	0.348537i
$116$	−5.75042	−	0.604053i	−0.533913	−	0.0560849i
$117$	11.2858	−	11.2858i	1.04338	−	1.04338i
$118$	−12.0098	−	5.72796i	−1.10559	−	0.527302i
$119$			12.5142i			1.14717i
$120$	0.955474	+	0.585400i	0.0872225	+	0.0534394i
$121$		−	23.5625i		−	2.14205i
$122$	−2.05899	+	4.31709i	−0.186412	+	0.390851i
$123$	0.977262	−	0.977262i	0.0881167	−	0.0881167i
$124$	4.62340	−	3.74440i	0.415193	−	0.336257i
$125$	−8.07560	−	8.07560i	−0.722304	−	0.722304i
$126$	−3.85205	−	10.8769i	−0.343168	−	0.968987i
$127$	−15.8360			−1.40522			−0.702608	−	0.711577i	$-0.747981\pi$
$127$	−15.8360			−1.40522			−0.702608	+	0.711577i	$0.747981\pi$
$128$	7.78616	−	8.20827i	0.688206	−	0.725516i
$129$	2.11337			0.186072
$130$	3.71480	+	10.4893i	0.325810	+	0.919972i
$131$	−4.25193	−	4.25193i	−0.371493	−	0.371493i	0.496528	−	0.868021i	$-0.334608\pi$
$131$	−4.25193	−	4.25193i	−0.371493	−	0.371493i	−0.868021	+	0.496528i	$0.834608\pi$
$132$	2.51078	−	2.03343i	0.218535	−	0.176988i
$133$	1.97279	−	1.97279i	0.171063	−	0.171063i
$134$	−7.45068	+	15.6219i	−0.643641	+	1.34952i
$135$		−	2.34712i		−	0.202008i
$136$	10.8178	+	6.62788i	0.927623	+	0.568336i
$137$		−	18.6776i		−	1.59573i	−0.602835	−	0.797866i	$-0.705962\pi$
$137$		−	18.6776i		−	1.59573i	0.602835	−	0.797866i	$-0.294038\pi$
$138$	−1.28595	−	0.613322i	−0.109468	−	0.0522094i
$139$	2.09390	−	2.09390i	0.177603	−	0.177603i	−0.612707	−	0.790310i	$-0.709920\pi$
$139$	2.09390	−	2.09390i	0.177603	−	0.177603i	0.790310	+	0.612707i	$0.209920\pi$
$140$	8.00080	+	0.840443i	0.676191	+	0.0710304i
$141$	1.30946	+	1.30946i	0.110276	+	0.110276i
$142$	−5.32842	+	1.88707i	−0.447151	+	0.158359i
$143$	32.0850			2.68308
$144$	−11.4426	−	2.43080i	−0.953552	−	0.202567i
$145$	−4.16815			−0.346146
$146$	13.6003	−	4.81656i	1.12557	−	0.398621i
$147$	0.152293	+	0.152293i	0.0125609	+	0.0125609i
$148$	−2.47918	+	23.6012i	−0.203788	+	1.94000i
$149$	2.79759	−	2.79759i	0.229187	−	0.229187i	−0.583166	−	0.812353i	$-0.698186\pi$
$149$	2.79759	−	2.79759i	0.229187	−	0.229187i	0.812353	+	0.583166i	$0.198186\pi$
$150$	−1.02468	−	0.488709i	−0.0836645	−	0.0399029i
$151$			10.3747i			0.844280i	0.906531	+	0.422140i	$0.138721\pi$
$151$			10.3747i			0.844280i	−0.906531	+	0.422140i	$0.861279\pi$
$152$	−0.660525	−	2.75022i	−0.0535757	−	0.223072i
$153$		−	13.1177i		−	1.06050i
$154$	9.98553	−	20.9367i	0.804657	−	1.68713i
$155$	3.03267	−	3.03267i	0.243590	−	0.243590i
$156$	1.88767	+	2.33080i	0.151135	+	0.186613i
$157$	0.188683	+	0.188683i	0.0150585	+	0.0150585i	0.714596	−	0.699537i	$-0.246611\pi$
$157$	0.188683	+	0.188683i	0.0150585	+	0.0150585i	−0.699537	+	0.714596i	$0.746611\pi$
$158$	4.10287	+	11.5851i	0.326407	+	0.921659i
$159$	−2.38044			−0.188781
$160$	4.96398	−	6.47115i	0.392437	−	0.511589i
$161$	−10.2286			−0.806129
$162$	3.93088	+	11.0994i	0.308839	+	0.872053i
$163$	9.34084	+	9.34084i	0.731631	+	0.731631i	0.970943	−	0.239312i	$-0.0769218\pi$
$163$	9.34084	+	9.34084i	0.731631	+	0.731631i	−0.239312	+	0.970943i	$0.576922\pi$
$164$	−6.33089	−	7.81706i	−0.494360	−	0.610410i
$165$	1.64692	−	1.64692i	0.128213	−	0.128213i
$166$	7.26085	−	15.2238i	0.563552	−	1.18160i
$167$			10.3312i			0.799453i	0.916634	+	0.399727i	$0.130895\pi$
$167$			10.3312i			0.799453i	−0.916634	+	0.399727i	$0.869105\pi$
$168$	2.10842	−	0.506383i	0.162668	−	0.0390683i
$169$			16.7850i			1.29115i
$170$	8.25480	+	3.93704i	0.633114	+	0.301957i
$171$	−2.06793	+	2.06793i	−0.158138	+	0.158138i
$172$	1.60696	−	15.2978i	0.122529	−	1.16645i
$173$	−8.72113	−	8.72113i	−0.663055	−	0.663055i	0.293044	−	0.956099i	$-0.405332\pi$
$173$	−8.72113	−	8.72113i	−0.663055	−	0.663055i	−0.956099	+	0.293044i	$0.905332\pi$
$174$	−1.05902	+	0.375053i	−0.0802840	+	0.0284327i
$175$	−8.15040			−0.616113
$176$	−12.8100	−	19.7206i	−0.965592	−	1.48650i
$177$	−2.58536			−0.194328
$178$	5.74446	−	2.03441i	0.430566	−	0.152486i
$179$	−9.88623	−	9.88623i	−0.738931	−	0.738931i	0.233440	−	0.972371i	$-0.425002\pi$
$179$	−9.88623	−	9.88623i	−0.738931	−	0.738931i	−0.972371	+	0.233440i	$0.925002\pi$
$180$	−8.38665	−	0.880974i	−0.625104	−	0.0656639i
$181$	11.2826	−	11.2826i	0.838631	−	0.838631i	−0.150048	−	0.988679i	$-0.547943\pi$
$181$	11.2826	−	11.2826i	0.838631	−	0.838631i	0.988679	+	0.150048i	$0.0479428\pi$
$182$	19.4359	+	9.26973i	1.44068	+	0.687118i
$183$			0.929343i			0.0686990i
$184$	−5.41738	+	8.84211i	−0.399375	+	0.651849i
$185$			17.1071i			1.25774i
$186$	0.497641	−	1.04340i	0.0364888	−	0.0765061i
$187$	18.6464	−	18.6464i	1.36356	−	1.36356i
$188$	10.4743	−	8.48291i	0.763914	−	0.618680i
$189$	−3.21163	−	3.21163i	−0.233612	−	0.233612i
$190$	−0.680671	−	1.92198i	−0.0493810	−	0.139435i
$191$	0.743260			0.0537804			0.0268902	−	0.999638i	$-0.491440\pi$
$191$	0.743260			0.0537804			0.0268902	+	0.999638i	$0.491440\pi$
$192$	0.678939	−	2.09081i	0.0489982	−	0.150891i
$193$	−17.9171			−1.28970			−0.644852	−	0.764308i	$-0.723081\pi$
$193$	−17.9171			−1.28970			−0.644852	+	0.764308i	$0.723081\pi$
$194$	2.29862	+	6.49050i	0.165031	+	0.465990i
$195$	1.52886	+	1.52886i	0.109484	+	0.109484i
$196$	1.21819	−	0.986585i	0.0870132	−	0.0704704i
$197$	−0.0237789	+	0.0237789i	−0.00169418	+	0.00169418i	−0.707953	−	0.706259i	$-0.750381\pi$
$197$	−0.0237789	+	0.0237789i	−0.00169418	+	0.00169418i	0.706259	+	0.707953i	$0.250381\pi$
$198$	−10.4671	+	21.9464i	−0.743864	+	1.55966i
$199$			11.3012i			0.801119i	0.916271	+	0.400559i	$0.131184\pi$
$199$			11.3012i			0.801119i	−0.916271	+	0.400559i	$0.868816\pi$
$200$	−4.31669	+	7.04560i	−0.305236	+	0.498199i
$201$			3.36293i			0.237203i
$202$	22.1303	+	10.5548i	1.55708	+	0.742635i
$203$	−5.70339	+	5.70339i	−0.400300	+	0.400300i
$204$	2.45159	+	0.257527i	0.171646	+	0.0180305i
$205$	−5.12752	−	5.12752i	−0.358122	−	0.358122i
$206$	−11.9426	+	4.22951i	−0.832083	+	0.294684i
$207$	10.7219			0.745225
$208$	18.3070	−	11.8918i	1.26936	−	0.824545i
$209$	−5.87899			−0.406658
$210$	1.47346	−	0.521827i	0.101678	−	0.0360095i
$211$	1.59189	+	1.59189i	0.109590	+	0.109590i	0.759775	−	0.650186i	$-0.225309\pi$
$211$	1.59189	+	1.59189i	0.109590	+	0.109590i	−0.650186	+	0.759775i	$0.725309\pi$
$212$	−1.81003	+	17.2310i	−0.124313	+	1.18343i
$213$	−0.776641	+	0.776641i	−0.0532145	+	0.0532145i
$214$	−14.2288	−	6.78629i	−0.972662	−	0.463901i
$215$		−	11.0885i		−	0.756230i
$216$	−4.47726	+	1.07531i	−0.304639	+	0.0731658i
$217$		−	8.29936i		−	0.563398i
$218$	−1.35057	+	2.83175i	−0.0914722	+	0.191790i
$219$	1.98230	−	1.98230i	0.133951	−	0.133951i
$220$	−10.6691	−	13.1736i	−0.719309	−	0.888166i
$221$	17.3097	+	17.3097i	1.16438	+	1.16438i
$222$	1.53931	+	4.34648i	0.103312	+	0.291717i
$223$	3.16215			0.211754			0.105877	−	0.994379i	$-0.466235\pi$
$223$	3.16215			0.211754			0.105877	+	0.994379i	$0.466235\pi$
$224$	−2.06230	−	15.6470i	−0.137793	−	1.04546i
$225$	8.54347			0.569564
$226$	−4.65607	−	13.1471i	−0.309717	−	0.874532i
$227$	−10.2342	−	10.2342i	−0.679270	−	0.679270i	0.280565	−	0.959835i	$-0.409478\pi$
$227$	−10.2342	−	10.2342i	−0.679270	−	0.679270i	−0.959835	+	0.280565i	$0.909478\pi$
$228$	−0.345882	−	0.427077i	−0.0229066	−	0.0282839i
$229$	−16.1996	+	16.1996i	−1.07050	+	1.07050i	−0.0731796	+	0.997319i	$0.523315\pi$
$229$	−16.1996	+	16.1996i	−1.07050	+	1.07050i	−0.997319	+	0.0731796i	$0.976685\pi$
$230$	−3.21799	+	6.74717i	−0.212188	+	0.444896i
$231$		−	4.50705i		−	0.296542i
$232$	1.90960	+	7.95097i	0.125371	+	0.522007i
$233$			15.6544i			1.02555i	0.858523	+	0.512775i	$0.171383\pi$
$233$			15.6544i			1.02555i	−0.858523	+	0.512775i	$0.828617\pi$
$234$	−20.3732	−	9.71677i	−1.33184	−	0.635205i
$235$	6.87048	−	6.87048i	0.448181	−	0.448181i
$236$	−1.96585	+	18.7143i	−0.127966	+	1.21820i
$237$	1.68858	+	1.68858i	0.109685	+	0.109685i
$238$	16.6824	−	5.90811i	1.08136	−	0.382966i
$239$	−11.0219			−0.712948			−0.356474	−	0.934305i	$-0.616021\pi$
$239$	−11.0219			−0.712948			−0.356474	+	0.934305i	$0.616021\pi$
$240$	0.329294	−	1.55010i	0.0212558	−	0.100059i
$241$	−10.6351			−0.685069			−0.342535	−	0.939505i	$-0.611285\pi$
$241$	−10.6351			−0.685069			−0.342535	+	0.939505i	$0.611285\pi$
$242$	−31.4108	+	11.1242i	−2.01916	+	0.715090i
$243$	5.07123	+	5.07123i	0.325319	+	0.325319i
$244$	6.72712	+	0.706649i	0.430660	+	0.0452386i
$245$	0.799056	−	0.799056i	0.0510498	−	0.0510498i
$246$	−1.76415	−	0.841392i	−0.112478	−	0.0536452i
$247$		−	5.45756i		−	0.347256i
$248$	−7.17436	−	4.39559i	−0.455573	−	0.279120i
$249$		−	3.27725i		−	0.207687i
$250$	−6.95284	+	14.5780i	−0.439737	+	0.921996i
$251$	1.14182	−	1.14182i	0.0720710	−	0.0720710i	−0.670152	−	0.742223i	$-0.733771\pi$
$251$	1.14182	−	1.14182i	0.0720710	−	0.0720710i	0.742223	+	0.670152i	$0.233771\pi$
$252$	−12.6811	+	10.2702i	−0.798836	+	0.646963i
$253$	15.2409	+	15.2409i	0.958185	+	0.958185i
$254$	7.47638	+	21.1107i	0.469110	+	1.32460i
$255$	1.77702			0.111281
$256$	−14.6183	−	6.50435i	−0.913641	−	0.406522i
$257$	−5.47516			−0.341531			−0.170766	−	0.985312i	$-0.554624\pi$
$257$	−5.47516			−0.341531			−0.170766	+	0.985312i	$0.554624\pi$
$258$	−0.997752	−	2.81730i	−0.0621173	−	0.175398i
$259$	23.4082	+	23.4082i	1.45451	+	1.45451i
$260$	12.2293	−	9.90427i	0.758429	−	0.614237i
$261$	5.97845	−	5.97845i	0.370057	−	0.370057i
$262$	−3.66078	+	7.67557i	−0.226164	+	0.474198i
$263$			1.29508i			0.0798581i	0.999203	+	0.0399291i	$0.0127132\pi$
$263$			1.29508i			0.0798581i	−0.999203	+	0.0399291i	$0.987287\pi$
$264$	−3.89611	−	2.38707i	−0.239789	−	0.146914i
$265$			12.4898i			0.767240i
$266$	−3.56127	−	1.69851i	−0.218356	−	0.104142i
$267$	0.837281	−	0.837281i	0.0512408	−	0.0512408i
$268$	24.3428	+	2.55709i	1.48697	+	0.156199i
$269$	−3.75872	−	3.75872i	−0.229173	−	0.229173i	0.583174	−	0.812347i	$-0.301811\pi$
$269$	−3.75872	−	3.75872i	−0.229173	−	0.229173i	−0.812347	+	0.583174i	$0.801811\pi$
$270$	−3.12891	+	1.10811i	−0.190419	+	0.0674373i
$271$	20.4586			1.24277			0.621387	−	0.783504i	$-0.286569\pi$
$271$	20.4586			1.24277			0.621387	+	0.783504i	$0.286569\pi$
$272$	3.72825	−	17.5502i	0.226059	−	1.06414i
$273$	4.18397			0.253225
$274$	−24.8987	+	8.81793i	−1.50419	+	0.532711i
$275$	12.1443	+	12.1443i	0.732327	+	0.732327i
$276$	−0.210493	+	2.00384i	−0.0126702	+	0.120617i
$277$	−8.82768	+	8.82768i	−0.530404	+	0.530404i	−0.920693	−	0.390289i	$-0.872375\pi$
$277$	−8.82768	+	8.82768i	−0.530404	+	0.530404i	0.390289	+	0.920693i	$0.372375\pi$
$278$	−3.77991	−	1.80279i	−0.226704	−	0.108124i
$279$			8.69961i			0.520832i
$280$	−2.65690	−	11.0625i	−0.158780	−	0.661111i
$281$		−	7.98183i		−	0.476156i	−0.971246	−	0.238078i	$-0.923483\pi$
$281$		−	7.98183i		−	0.476156i	0.971246	−	0.238078i	$-0.0765174\pi$
$282$	1.12740	−	2.36382i	0.0671357	−	0.140764i
$283$	−6.00158	+	6.00158i	−0.356757	+	0.356757i	−0.862616	−	0.505859i	$-0.831175\pi$
$283$	−6.00158	+	6.00158i	−0.356757	+	0.356757i	0.505859	+	0.862616i	$0.331175\pi$
$284$	5.03123	+	6.21231i	0.298549	+	0.368633i
$285$	−0.280137	−	0.280137i	−0.0165939	−	0.0165939i
$286$	−15.1477	−	42.7719i	−0.895704	−	2.52915i
$287$	−14.0323			−0.828298
$288$	2.16176	+	16.4016i	0.127383	+	0.966472i
$289$	3.11932			0.183489
$290$	1.96784	+	5.55649i	0.115556	+	0.326288i
$291$	0.946019	+	0.946019i	0.0554566	+	0.0554566i
$292$	−12.8417	−	15.8563i	−0.751506	−	0.927921i
$293$	−1.34587	+	1.34587i	−0.0786266	+	0.0786266i	−0.745326	−	0.666700i	$-0.767706\pi$
$293$	−1.34587	+	1.34587i	−0.0786266	+	0.0786266i	0.666700	+	0.745326i	$0.267706\pi$
$294$	0.131120	−	0.274919i	0.00764706	−	0.0160336i
$295$			13.5649i			0.789782i
$296$	32.6328	−	7.83747i	1.89674	−	0.455544i
$297$			9.57080i			0.555354i
$298$	−5.05019	−	2.40863i	−0.292550	−	0.139528i
$299$	−14.1483	+	14.1483i	−0.818220	+	0.818220i
$300$	−0.167726	+	1.59670i	−0.00968365	+	0.0921858i
$301$	−15.1727	−	15.1727i	−0.874540	−	0.874540i
$302$	13.8303	−	4.89803i	0.795845	−	0.281850i
$303$	4.76401			0.273685
$304$	−3.35443	+	2.17895i	−0.192390	+	0.124971i
$305$	4.87610			0.279205
$306$	−17.4870	+	6.19303i	−0.999663	+	0.354032i
$307$	4.02175	+	4.02175i	0.229533	+	0.229533i	0.812498	−	0.582964i	$-0.198107\pi$
$307$	4.02175	+	4.02175i	0.229533	+	0.229533i	−0.582964	+	0.812498i	$0.698107\pi$
$308$	−32.6246	−	3.42705i	−1.85896	−	0.195274i
$309$	−1.74069	+	1.74069i	−0.0990246	+	0.0990246i
$310$	−5.47456	−	2.61103i	−0.310934	−	0.148297i
$311$		−	17.2825i		−	0.980002i	−0.871722	−	0.490001i	$-0.836996\pi$
$311$		−	17.2825i		−	0.980002i	0.871722	−	0.490001i	$-0.163004\pi$
$312$	2.21595	−	3.61682i	0.125454	−	0.204762i
$313$		−	26.3237i		−	1.48790i	−0.668234	−	0.743951i	$-0.732950\pi$
$313$		−	26.3237i		−	1.48790i	0.668234	−	0.743951i	$-0.267050\pi$
$314$	0.162450	−	0.340609i	0.00916758	−	0.0192217i
$315$	−8.31806	+	8.31806i	−0.468669	+	0.468669i
$316$	13.5068	−	10.9389i	0.759819	−	0.615363i
$317$	−4.32214	−	4.32214i	−0.242756	−	0.242756i	0.575234	−	0.817989i	$-0.304911\pi$
$317$	−4.32214	−	4.32214i	−0.242756	−	0.242756i	−0.817989	+	0.575234i	$0.804911\pi$
$318$	1.12384	+	3.17333i	0.0630217	+	0.177951i
$319$	16.9963			0.951613
$320$	−10.9701	−	3.56228i	−0.613249	−	0.199137i
$321$	−3.06305			−0.170963
$322$	4.82907	+	13.6356i	0.269114	+	0.759883i
$323$	−3.17170	−	3.17170i	−0.176478	−	0.176478i
$324$	12.9406	−	10.4804i	0.718924	−	0.582243i
$325$	−11.2737	+	11.2737i	−0.625353	+	0.625353i
$326$	8.04217	−	16.8620i	0.445415	−	0.933902i
$327$			0.609592i			0.0337105i
$328$	−7.43189	+	12.1301i	−0.410358	+	0.669775i
$329$		−	18.8021i		−	1.03660i
$330$	−2.97301	−	1.41795i	−0.163659	−	0.0780555i
$331$	1.87060	−	1.87060i	0.102818	−	0.102818i	−0.653827	−	0.756644i	$-0.726837\pi$
$331$	1.87060	−	1.87060i	0.102818	−	0.102818i	0.756644	+	0.653827i	$0.226837\pi$
$332$	−23.7226	−	2.49194i	−1.30195	−	0.136763i
$333$	−24.5370	−	24.5370i	−1.34462	−	1.34462i
$334$	13.7724	−	4.87750i	0.753590	−	0.266885i
$335$	17.6447			0.964033
$336$	−1.67046	−	2.57163i	−0.0911313	−	0.140294i
$337$	5.47332			0.298151			0.149076	−	0.988826i	$-0.452370\pi$
$337$	5.47332			0.298151			0.149076	+	0.988826i	$0.452370\pi$
$338$	22.3758	−	7.92441i	1.21708	−	0.431031i
$339$	−1.91625	−	1.91625i	−0.104076	−	0.104076i
$340$	1.35120	−	12.8631i	0.0732791	−	0.697598i
$341$	−12.3662	+	12.3662i	−0.669668	+	0.669668i
$342$	3.73302	+	1.78042i	0.201858	+	0.0962742i
$343$			17.3429i			0.936427i
$344$	−21.1519	+	5.08009i	−1.14043	+	0.273900i
$345$			1.45247i			0.0781983i
$346$	−7.50863	+	15.7433i	−0.403666	+	0.846368i
$347$	−4.05692	+	4.05692i	−0.217787	+	0.217787i	−0.807565	−	0.589778i	$-0.799215\pi$
$347$	−4.05692	+	4.05692i	−0.217787	+	0.217787i	0.589778	+	0.807565i	$0.299215\pi$
$348$	0.999954	+	1.23469i	0.0536032	+	0.0661865i
$349$	11.5352	+	11.5352i	0.617468	+	0.617468i	0.944881	−	0.327413i	$-0.106177\pi$
$349$	11.5352	+	11.5352i	0.617468	+	0.617468i	−0.327413	+	0.944881i	$0.606177\pi$
$350$	3.84791	+	10.8652i	0.205680	+	0.580767i
$351$	−8.88472			−0.474231
$352$	−20.2415	+	26.3872i	−1.07887	+	1.40644i
$353$	12.7164			0.676827			0.338414	−	0.940997i	$-0.390110\pi$
$353$	12.7164			0.676827			0.338414	+	0.940997i	$0.390110\pi$
$354$	1.22058	+	3.44650i	0.0648733	+	0.183180i
$355$	4.07490	+	4.07490i	0.216273	+	0.216273i
$356$	−5.42407	−	6.69737i	−0.287475	−	0.354960i
$357$	2.43154	−	2.43154i	0.128691	−	0.128691i
$358$	−8.51174	+	17.8466i	−0.449859	+	0.943221i
$359$		−	10.6459i		−	0.561870i	−0.959727	−	0.280935i	$-0.909355\pi$
$359$		−	10.6459i		−	0.561870i	0.959727	−	0.280935i	$-0.0906445\pi$
$360$	2.78504	+	11.5960i	0.146784	+	0.611163i
$361$			1.00000i			0.0526316i
$362$	−20.3673	−	9.71399i	−1.07048	−	0.510556i
$363$	−4.57827	+	4.57827i	−0.240297	+	0.240297i
$364$	3.18138	−	30.2860i	0.166750	−	1.58742i
$365$	−10.4008	−	10.4008i	−0.544402	−	0.544402i
$366$	1.23889	−	0.438755i	0.0647579	−	0.0229341i
$367$	−7.98708			−0.416922			−0.208461	−	0.978031i	$-0.566845\pi$
$367$	−7.98708			−0.416922			−0.208461	+	0.978031i	$0.566845\pi$
$368$	14.3449	+	3.04734i	0.747779	+	0.158854i
$369$	14.7090			0.765718
$370$	22.8052	−	8.07651i	1.18559	−	0.419878i
$371$	17.0901	+	17.0901i	0.887273	+	0.887273i
$372$	−1.62589	−	0.170791i	−0.0842983	−	0.00885510i
$373$	2.96433	−	2.96433i	0.153487	−	0.153487i	−0.626186	−	0.779673i	$-0.715385\pi$
$373$	2.96433	−	2.96433i	0.153487	−	0.153487i	0.779673	+	0.626186i	$0.215385\pi$
$374$	−33.6604	−	16.0540i	−1.74054	−	0.830130i
$375$			3.13822i			0.162057i
$376$	−16.2535	−	9.95816i	−0.838208	−	0.513553i
$377$			15.7780i			0.812607i
$378$	−2.76512	+	5.79763i	−0.142222	+	0.298198i
$379$	16.4915	−	16.4915i	0.847111	−	0.847111i	−0.142661	−	0.989772i	$-0.545566\pi$
$379$	16.4915	−	16.4915i	0.847111	−	0.847111i	0.989772	+	0.142661i	$0.0455659\pi$
$380$	−2.24080	+	1.81478i	−0.114951	+	0.0930963i
$381$	3.07698	+	3.07698i	0.157638	+	0.157638i
$382$	−0.350903	−	0.990828i	−0.0179538	−	0.0506951i
$383$	26.4007			1.34901			0.674507	−	0.738269i	$-0.264356\pi$
$383$	26.4007			1.34901			0.674507	+	0.738269i	$0.264356\pi$
$384$	−3.10776	+	0.0820186i	−0.158592	+	0.00418550i
$385$	−23.6477			−1.20520
$386$	8.45891	+	23.8850i	0.430547	+	1.21572i
$387$	15.9044	+	15.9044i	0.808467	+	0.808467i
$388$	7.56716	−	6.12850i	0.384164	−	0.311127i
$389$	2.23164	−	2.23164i	0.113149	−	0.113149i	−0.648266	−	0.761414i	$-0.724505\pi$
$389$	2.23164	−	2.23164i	0.113149	−	0.113149i	0.761414	+	0.648266i	$0.224505\pi$
$390$	1.31630	−	2.75990i	0.0666536	−	0.139753i
$391$			16.4448i			0.831649i
$392$	−1.89032	−	1.15816i	−0.0954756	−	0.0584960i
$393$			1.65233i			0.0833488i
$394$	0.0429256	+	0.0204729i	0.00216256	+	0.00103141i
$395$	8.85967	−	8.85967i	0.445778	−	0.445778i
$396$	34.1980	+	3.59232i	1.71851	+	0.180521i
$397$	13.4381	+	13.4381i	0.674438	+	0.674438i	0.958736	−	0.284298i	$-0.0917604\pi$
$397$	13.4381	+	13.4381i	0.674438	+	0.674438i	−0.284298	+	0.958736i	$0.591760\pi$
$398$	15.0654	−	5.33543i	0.755160	−	0.267441i
$399$	−0.766637			−0.0383798
$400$	11.4303	+	2.42819i	0.571516	+	0.121409i
$401$	−4.56977			−0.228203			−0.114102	−	0.993469i	$-0.536399\pi$
$401$	−4.56977			−0.228203			−0.114102	+	0.993469i	$0.536399\pi$
$402$	4.48306	−	1.58768i	0.223595	−	0.0791864i
$403$	−11.4798	−	11.4798i	−0.571848	−	0.571848i
$404$	3.62243	−	34.4846i	0.180223	−	1.71567i
$405$	8.48827	−	8.48827i	0.421786	−	0.421786i
$406$	10.2957	+	4.91045i	0.510969	+	0.243701i
$407$		−	69.7572i		−	3.45774i
$408$	−0.814123	−	3.38975i	−0.0403051	−	0.167818i
$409$		−	35.1068i		−	1.73592i	−0.496633	−	0.867961i	$-0.665431\pi$
$409$		−	35.1068i		−	1.73592i	0.496633	−	0.867961i	$-0.334569\pi$
$410$	−4.41464	+	9.25618i	−0.218023	+	0.457130i
$411$	−3.62910	+	3.62910i	−0.179011	+	0.179011i
$412$	11.2766	+	13.9237i	0.555556	+	0.685973i
$413$	18.5613	+	18.5613i	0.913341	+	0.913341i
$414$	−5.06196	−	14.2932i	−0.248782	−	0.702472i
$415$	−17.1951			−0.844077
$416$	−24.4957	−	18.7905i	−1.20100	−	0.921279i
$417$	−0.813703			−0.0398472
$418$	2.77555	+	7.83718i	0.135757	+	0.383329i
$419$	−11.7778	−	11.7778i	−0.575385	−	0.575385i	0.358243	−	0.933628i	$-0.383376\pi$
$419$	−11.7778	−	11.7778i	−0.575385	−	0.575385i	−0.933628	+	0.358243i	$0.883376\pi$
$420$	−1.39128	−	1.71788i	−0.0678874	−	0.0838239i
$421$	−11.2656	+	11.2656i	−0.549050	+	0.549050i	−0.926166	−	0.377116i	$-0.876916\pi$
$421$	−11.2656	+	11.2656i	−0.549050	+	0.549050i	0.377116	+	0.926166i	$0.376916\pi$
$422$	1.37056	−	2.87367i	0.0667180	−	0.139888i
$423$			19.7089i			0.958279i
$424$	23.8249	−	5.72207i	1.15704	−	0.277888i
$425$			13.1036i			0.635617i
$426$	1.40199	+	0.668664i	0.0679266	+	0.0323969i
$427$	6.67210	−	6.67210i	0.322886	−	0.322886i
$428$	−2.32907	+	22.1721i	−0.112580	+	1.07173i
$429$	−6.23420	−	6.23420i	−0.300990	−	0.300990i
$430$	−14.7819	+	5.23503i	−0.712846	+	0.252456i
$431$	4.85909			0.234054			0.117027	−	0.993129i	$-0.462664\pi$
$431$	4.85909			0.234054			0.117027	+	0.993129i	$0.462664\pi$
$432$	3.54726	+	5.46089i	0.170667	+	0.262737i
$433$	16.0771			0.772618			0.386309	−	0.922370i	$-0.373750\pi$
$433$	16.0771			0.772618			0.386309	+	0.922370i	$0.373750\pi$
$434$	−11.0637	+	3.91824i	−0.531076	+	0.188082i
$435$	0.809884	+	0.809884i	0.0388309	+	0.0388309i
$436$	4.41257	+	0.463518i	0.211324	+	0.0221985i
$437$	2.59243	−	2.59243i	0.124013	−	0.124013i
$438$	−3.57844	−	1.70670i	−0.170984	−	0.0815493i
$439$			4.37413i			0.208766i	0.994537	+	0.104383i	$0.0332868\pi$
$439$			4.37413i			0.208766i	−0.994537	+	0.104383i	$0.966713\pi$
$440$	−12.5245	+	20.4422i	−0.597083	+	0.974544i
$441$			2.29220i			0.109152i
$442$	14.9031	−	31.2474i	0.708870	−	1.48629i
$443$	−11.6989	+	11.6989i	−0.555833	+	0.555833i	−0.928118	−	0.372285i	$-0.878574\pi$
$443$	−11.6989	+	11.6989i	−0.555833	+	0.555833i	0.372285	+	0.928118i	$0.378574\pi$
$444$	5.06749	−	4.10406i	0.240492	−	0.194770i
$445$	−4.39307	−	4.39307i	−0.208251	−	0.208251i
$446$	−1.49290	−	4.21541i	−0.0706906	−	0.199606i
$447$	−1.08716			−0.0514208
$448$	−19.8851	+	10.1364i	−0.939482	+	0.478898i
$449$	15.0954			0.712398			0.356199	−	0.934410i	$-0.384073\pi$
$449$	15.0954			0.712398			0.356199	+	0.934410i	$0.384073\pi$
$450$	−4.03348	−	11.3891i	−0.190140	−	0.536889i
$451$	20.9083	+	20.9083i	0.984535	+	0.984535i
$452$	−15.3280	+	12.4138i	−0.720967	+	0.583898i
$453$	2.01583	−	2.01583i	0.0947120	−	0.0947120i
$454$	−8.81136	+	18.4748i	−0.413538	+	0.867065i
$455$		−	21.9526i		−	1.02915i
$456$	−0.406033	+	0.662717i	−0.0190143	+	0.0310346i
$457$			31.9424i			1.49420i	0.664711	+	0.747101i	$0.268555\pi$
$457$			31.9424i			1.49420i	−0.664711	+	0.747101i	$0.731445\pi$
$458$	29.2434	+	13.9473i	1.36645	+	0.651716i
$459$	−5.16341	+	5.16341i	−0.241007	+	0.241007i
$460$	10.5138	+	1.10442i	0.490208	+	0.0514939i
$461$	−10.8170	−	10.8170i	−0.503800	−	0.503800i	0.408817	−	0.912617i	$-0.365942\pi$
$461$	−10.8170	−	10.8170i	−0.503800	−	0.503800i	−0.912617	+	0.408817i	$0.865942\pi$
$462$	−6.00827	+	2.12784i	−0.279530	+	0.0989960i
$463$	−34.7007			−1.61268			−0.806339	−	0.591454i	$-0.798554\pi$
$463$	−34.7007			−1.61268			−0.806339	+	0.591454i	$0.798554\pi$
$464$	9.69775	−	6.29941i	0.450207	−	0.292443i
$465$	−1.17851			−0.0546522
$466$	20.8685	−	7.39063i	0.966717	−	0.342364i
$467$	−13.6677	−	13.6677i	−0.632466	−	0.632466i	0.316220	−	0.948686i	$-0.397586\pi$
$467$	−13.6677	−	13.6677i	−0.632466	−	0.632466i	−0.948686	+	0.316220i	$0.897586\pi$
$468$	−3.33481	+	31.7465i	−0.154152	+	1.46748i
$469$	24.1437	−	24.1437i	1.11485	−	1.11485i
$470$	−12.4026	−	5.91528i	−0.572088	−	0.272851i
$471$		−	0.0733231i		−	0.00337855i
$472$	25.8759	−	6.21465i	1.19103	−	0.286053i
$473$			45.2153i			2.07900i
$474$	1.45381	−	3.04821i	0.0667758	−	0.140009i
$475$	2.06571	−	2.06571i	0.0947811	−	0.0947811i
$476$	−15.7520	−	19.4498i	−0.721991	−	0.891478i
$477$	−17.9143	−	17.9143i	−0.820238	−	0.820238i
$478$	5.20359	+	14.6931i	0.238007	+	0.672048i
$479$	14.3826			0.657159			0.328580	−	0.944476i	$-0.393430\pi$
$479$	14.3826			0.657159			0.328580	+	0.944476i	$0.393430\pi$
$480$	−2.22188	+	0.292847i	−0.101414	+	0.0133666i
$481$	64.7568			2.95265
$482$	5.02099	+	14.1775i	0.228700	+	0.645768i
$483$	1.98745	+	1.98745i	0.0904322	+	0.0904322i
$484$	29.6589	+	36.6213i	1.34813	+	1.66461i
$485$	4.96360	−	4.96360i	0.225385	−	0.225385i
$486$	4.36617	−	9.15456i	0.198054	−	0.415259i
$487$		−	4.55985i		−	0.206627i	−0.994649	−	0.103313i	$-0.967056\pi$
$487$		−	4.55985i		−	0.206627i	0.994649	−	0.103313i	$-0.0329444\pi$
$488$	−2.23394	−	9.30142i	−0.101126	−	0.421056i
$489$		−	3.62990i		−	0.164150i
$490$	−1.44245	−	0.687962i	−0.0651633	−	0.0310790i
$491$	−13.1235	+	13.1235i	−0.592254	+	0.592254i	−0.938240	−	0.345986i	$-0.887544\pi$
$491$	−13.1235	+	13.1235i	−0.592254	+	0.592254i	0.345986	+	0.938240i	$0.387544\pi$
$492$	−0.288767	+	2.74899i	−0.0130186	+	0.123934i
$493$	9.16947	+	9.16947i	0.412972	+	0.412972i
$494$	−7.27538	+	2.57659i	−0.327335	+	0.115926i
$495$	24.7881			1.11414
$496$	−2.47257	+	11.6392i	−0.111022	+	0.522617i
$497$	11.1516			0.500217
$498$	−4.36884	+	1.54723i	−0.195772	+	0.0693331i
$499$	−0.0196504	−	0.0196504i	−0.000879674	−	0.000879674i	0.706667	−	0.707546i	$-0.250198\pi$
$499$	−0.0196504	−	0.0196504i	−0.000879674	−	0.000879674i	−0.707546	+	0.706667i	$0.750198\pi$
$500$	22.7163	+	2.38623i	1.01590	+	0.106715i
$501$	2.00738	−	2.00738i	0.0896833	−	0.0896833i
$502$	−2.06121	−	0.983072i	−0.0919962	−	0.0438766i
$503$		−	40.1576i		−	1.79054i	−0.445524	−	0.895270i	$-0.646983\pi$
$503$		−	40.1576i		−	1.79054i	0.445524	−	0.895270i	$-0.353017\pi$
$504$	19.6780	+	12.0563i	0.876527	+	0.537030i
$505$		−	24.9959i		−	1.11230i
$506$	13.1219	−	27.5127i	0.583340	−	1.22309i
$507$	3.26137	−	3.26137i	0.144842	−	0.144842i
$508$	24.6126	−	19.9333i	1.09201	−	0.884395i
$509$	−7.72987	−	7.72987i	−0.342620	−	0.342620i	0.514731	−	0.857352i	$-0.327892\pi$
$509$	−7.72987	−	7.72987i	−0.342620	−	0.342620i	−0.857352	+	0.514731i	$0.827892\pi$
$510$	−0.838953	−	2.36891i	−0.0371495	−	0.104897i
$511$	−28.4633			−1.25914
$512$	−1.76937	+	22.5581i	−0.0781957	+	0.996938i
$513$	1.62797			0.0718764
$514$	2.58490	+	7.29884i	0.114015	+	0.321938i
$515$	9.13312	+	9.13312i	0.402453	+	0.402453i
$516$	−3.28464	+	2.66017i	−0.144598	+	0.117108i
$517$	−28.0156	+	28.0156i	−1.23212	+	1.23212i
$518$	20.1537	−	42.2563i	0.885503	−	1.85664i
$519$			3.38908i			0.148764i
$520$	−18.9768	−	11.6267i	−0.832189	−	0.509865i
$521$			4.07442i			0.178504i	0.996009	+	0.0892518i	$0.0284476\pi$
$521$			4.07442i			0.178504i	−0.996009	+	0.0892518i	$0.971552\pi$
$522$	−10.7923	−	5.14726i	−0.472365	−	0.225289i
$523$	−15.4424	+	15.4424i	−0.675251	+	0.675251i	−0.958922	−	0.283671i	$-0.908448\pi$
$523$	−15.4424	+	15.4424i	−0.675251	+	0.675251i	0.283671	+	0.958922i	$0.408448\pi$
$524$	11.9605	+	1.25639i	0.522496	+	0.0548855i
$525$	1.58365	+	1.58365i	0.0691160	+	0.0691160i
$526$	1.72645	−	0.611425i	0.0752768	−	0.0266594i
$527$	−13.3431			−0.581233
$528$	−1.34275	+	6.32080i	−0.0584358	+	0.275078i
$529$	9.55862			0.415592
$530$	16.6499	−	5.89659i	0.723225	−	0.256131i
$531$	−19.4564	−	19.4564i	−0.844337	−	0.844337i
$532$	−0.582932	+	5.54936i	−0.0252733	+	0.240595i
$533$	−19.4095	+	19.4095i	−0.840721	+	0.840721i
$534$	−1.51146	−	0.720873i	−0.0654071	−	0.0311952i
$535$			16.0713i			0.694822i
$536$	−8.08375	−	33.6582i	−0.349165	−	1.45381i
$537$			3.84184i			0.165788i
$538$	−3.23614	+	6.78523i	−0.139520	+	0.292532i
$539$	−3.25829	+	3.25829i	−0.140344	+	0.140344i
$540$	2.95440	+	3.64794i	0.127137	+	0.156982i
$541$	−22.3906	−	22.3906i	−0.962648	−	0.962648i	0.0366792	−	0.999327i	$-0.488322\pi$
$541$	−22.3906	−	22.3906i	−0.962648	−	0.962648i	−0.999327	+	0.0366792i	$0.988322\pi$
$542$	−9.65880	−	27.2731i	−0.414881	−	1.17148i
$543$	−4.38449			−0.188157
$544$	−25.1560	+	3.31561i	−1.07856	+	0.142156i
$545$	3.19842			0.137005
$546$	−1.97531	−	5.57757i	−0.0845353	−	0.238698i
$547$	23.9736	+	23.9736i	1.02504	+	1.02504i	0.999678	+	0.0253598i	$0.00807313\pi$
$547$	23.9736	+	23.9736i	1.02504	+	1.02504i	0.0253598	+	0.999678i	$0.491927\pi$
$548$	23.5101	+	29.0290i	1.00430	+	1.24006i
$549$	−6.99387	+	6.99387i	−0.298491	+	0.298491i
$550$	10.4558	−	21.9228i	0.445838	−	0.934790i
$551$		−	2.89103i		−	0.123162i
$552$	2.77066	−	0.665435i	0.117927	−	0.0283228i
$553$		−	24.2459i		−	1.03104i
$554$	15.9357	+	7.60036i	0.677043	+	0.322908i
$555$	3.32396	−	3.32396i	0.141094	−	0.141094i
$556$	−0.618719	+	5.89005i	−0.0262395	+	0.249794i
$557$	−20.0817	−	20.0817i	−0.850890	−	0.850890i	0.139353	−	0.990243i	$-0.455498\pi$
$557$	−20.0817	−	20.0817i	−0.850890	−	0.850890i	−0.990243	+	0.139353i	$0.955498\pi$
$558$	11.5973	−	4.10720i	0.490953	−	0.173872i
$559$	−41.9740			−1.77531
$560$	−13.4929	+	8.76463i	−0.570178	+	0.370373i
$561$	−7.24609			−0.305930
$562$	−10.6404	+	3.76833i	−0.448840	+	0.158957i
$563$	−24.7774	−	24.7774i	−1.04424	−	1.04424i	−0.998975	−	0.0452696i	$-0.985585\pi$
$563$	−24.7774	−	24.7774i	−1.04424	−	1.04424i	−0.0452696	−	0.998975i	$-0.514415\pi$
$564$	−3.68343	−	0.386926i	−0.155100	−	0.0162925i
$565$	−10.0542	+	10.0542i	−0.422984	+	0.422984i
$566$	10.8340	+	5.16717i	0.455388	+	0.217192i
$567$		−	23.2295i		−	0.975546i
$568$	5.90621	−	9.63996i	0.247819	−	0.404484i
$569$		−	42.4666i		−	1.78029i	−0.455674	−	0.890147i	$-0.650602\pi$
$569$		−	42.4666i		−	1.78029i	0.455674	−	0.890147i	$-0.349398\pi$
$570$	−0.241189	+	0.505701i	−0.0101023	+	0.0211815i
$571$	−22.4682	+	22.4682i	−0.940266	+	0.940266i	−0.998314	−	0.0580482i	$-0.981512\pi$
$571$	−22.4682	+	22.4682i	−0.940266	+	0.940266i	0.0580482	+	0.998314i	$0.481512\pi$
$572$	−49.8670	+	40.3864i	−2.08504	+	1.68864i
$573$	−0.144418	−	0.144418i	−0.00603313	−	0.00603313i
$574$	6.62481	+	18.7061i	0.276514	+	0.780780i
$575$	−10.7104			−0.446654
$576$	20.8441	−	10.6252i	0.868503	−	0.442717i
$577$	6.29771			0.262177			0.131088	−	0.991371i	$-0.458153\pi$
$577$	6.29771			0.262177			0.131088	+	0.991371i	$0.458153\pi$
$578$	−1.47267	−	4.15831i	−0.0612551	−	0.172963i
$579$	3.48135	+	3.48135i	0.144680	+	0.144680i
$580$	6.47822	−	5.24659i	0.268993	−	0.217853i
$581$	−23.5286	+	23.5286i	−0.976130	+	0.976130i
$582$	0.814493	−	1.70775i	0.0337618	−	0.0707885i
$583$		−	50.9291i		−	2.10927i
$584$	−15.0750	+	24.6051i	−0.623809	+	1.01816i
$585$			23.0112i			0.951398i
$586$	2.42956	+	1.15875i	0.100364	+	0.0478677i
$587$	27.7401	−	27.7401i	1.14496	−	1.14496i	0.157428	−	0.987531i	$-0.449680\pi$
$587$	27.7401	−	27.7401i	1.14496	−	1.14496i	0.987531	−	0.157428i	$-0.0503201\pi$
$588$	−0.428393	−	0.0450005i	−0.0176666	−	0.00185579i
$589$	2.10346	+	2.10346i	0.0866715	+	0.0866715i
$590$	18.0832	−	6.40419i	0.744473	−	0.263656i
$591$	0.00924063			0.000380109
$592$	−25.8544	−	39.8020i	−1.06261	−	1.63585i
$593$	16.2722			0.668221			0.334111	−	0.942534i	$-0.391564\pi$
$593$	16.2722			0.668221			0.334111	+	0.942534i	$0.391564\pi$
$594$	12.7587	−	4.51850i	0.523494	−	0.185396i
$595$	−12.7579	−	12.7579i	−0.523022	−	0.523022i
$596$	−0.826647	+	7.86947i	−0.0338608	+	0.322346i
$597$	2.19585	−	2.19585i	0.0898702	−	0.0898702i
$598$	25.5405	+	12.1813i	1.04443	+	0.498130i
$599$			13.9442i			0.569745i	0.958565	+	0.284872i	$0.0919513\pi$
$599$			13.9442i			0.569745i	−0.958565	+	0.284872i	$0.908049\pi$
$600$	2.20772	−	0.530233i	0.0901300	−	0.0216467i
$601$			10.0406i			0.409565i	0.978807	+	0.204783i	$0.0656488\pi$
$601$			10.0406i			0.409565i	−0.978807	+	0.204783i	$0.934351\pi$
$602$	−13.0632	+	27.3897i	−0.532417	+	1.11632i
$603$	−25.3081	+	25.3081i	−1.03062	+	1.03062i
$604$	−13.0590	−	16.1245i	−0.531361	−	0.656098i
$605$	24.0214	+	24.0214i	0.976607	+	0.976607i
$606$	−2.24915	−	6.35082i	−0.0913656	−	0.257984i
$607$	33.1122			1.34398			0.671991	−	0.740559i	$-0.265439\pi$
$607$	33.1122			1.34398			0.671991	+	0.740559i	$0.265439\pi$
$608$	4.48839	+	3.44302i	0.182028	+	0.139633i
$609$	2.21637			0.0898119
$610$	−2.30207	−	6.50025i	−0.0932082	−	0.263187i
$611$	−26.0073	−	26.0073i	−1.05214	−	1.05214i
$612$	16.5117	+	20.3877i	0.667444	+	0.824126i
$613$	1.97069	−	1.97069i	0.0795954	−	0.0795954i	−0.666188	−	0.745784i	$-0.732075\pi$
$613$	1.97069	−	1.97069i	0.0795954	−	0.0795954i	0.745784	+	0.666188i	$0.232075\pi$
$614$	3.46260	−	7.26004i	0.139739	−	0.292991i
$615$			1.99258i			0.0803487i
$616$	10.8340	+	45.1093i	0.436513	+	1.81750i
$617$			13.2574i			0.533723i	0.963735	+	0.266862i	$0.0859867\pi$
$617$			13.2574i			0.533723i	−0.963735	+	0.266862i	$0.914013\pi$
$618$	3.14229	+	1.49868i	0.126402	+	0.0602859i
$619$	−17.3336	+	17.3336i	−0.696698	+	0.696698i	−0.963697	−	0.266999i	$-0.913968\pi$
$619$	−17.3336	+	17.3336i	−0.696698	+	0.696698i	0.266999	+	0.963697i	$0.413968\pi$
$620$	−0.896111	+	8.53074i	−0.0359887	+	0.342603i
$621$	−4.22039	−	4.22039i	−0.169358	−	0.169358i
$622$	−23.0390	+	8.15931i	−0.923781	+	0.327158i
$623$	−12.0223			−0.481664
$624$	−5.86770	−	1.24650i	−0.234896	−	0.0498999i
$625$	1.85897			0.0743589
$626$	−35.0916	+	12.4278i	−1.40254	+	0.496713i
$627$	1.14230	+	1.14230i	0.0456192	+	0.0456192i
$628$	−0.530755	−	0.0557531i	−0.0211794	−	0.00222479i
$629$	37.6338	−	37.6338i	1.50056	−	1.50056i
$630$	15.0157	+	7.16159i	0.598241	+	0.285325i
$631$		−	10.5465i		−	0.419848i	−0.977718	−	0.209924i	$-0.932678\pi$
$631$		−	10.5465i		−	0.419848i	0.977718	−	0.209924i	$-0.0673217\pi$
$632$	−20.9593	−	12.8413i	−0.833715	−	0.510800i
$633$		−	0.618616i		−	0.0245878i
$634$	−3.72123	+	7.80231i	−0.147789	+	0.309869i
$635$	16.1444	−	16.1444i	0.640669	−	0.640669i
$636$	3.69973	−	2.99634i	0.146704	−	0.118813i
$637$	−3.02472	−	3.02472i	−0.119844	−	0.119844i
$638$	−8.02420	−	22.6575i	−0.317681	−	0.897020i
$639$	−11.6894			−0.462425
$640$	0.430338	+	16.3059i	0.0170106	+	0.644547i
$641$	−16.5992			−0.655630			−0.327815	−	0.944742i	$-0.606312\pi$
$641$	−16.5992			−0.655630			−0.327815	+	0.944742i	$0.606312\pi$
$642$	1.44611	+	4.08330i	0.0570732	+	0.161155i
$643$	−18.0603	−	18.0603i	−0.712229	−	0.712229i	0.254772	−	0.967001i	$-0.418000\pi$
$643$	−18.0603	−	18.0603i	−0.712229	−	0.712229i	−0.967001	+	0.254772i	$0.918000\pi$
$644$	15.8975	−	12.8751i	0.626450	−	0.507350i
$645$	−2.15453	+	2.15453i	−0.0848344	+	0.0848344i
$646$	−2.73073	+	5.72553i	−0.107439	+	0.225268i
$647$			12.8473i			0.505080i	0.967586	+	0.252540i	$0.0812659\pi$
$647$			12.8473i			0.505080i	−0.967586	+	0.252540i	$0.918734\pi$
$648$	−20.0806	−	12.3030i	−0.788842	−	0.483308i
$649$		−	55.3134i		−	2.17124i
$650$	20.3513	+	9.70632i	0.798242	+	0.380713i
$651$	−1.61259	+	1.61259i	−0.0632024	+	0.0632024i
$652$	−26.2753	−	2.76009i	−1.02902	−	0.108093i
$653$	−27.8294	−	27.8294i	−1.08905	−	1.08905i	−0.995627	−	0.0934201i	$-0.970220\pi$
$653$	−27.8294	−	27.8294i	−1.08905	−	1.08905i	−0.0934201	−	0.995627i	$-0.529780\pi$
$654$	0.812636	−	0.287796i	0.0317766	−	0.0112537i
$655$	8.66946			0.338744
$656$	19.6792	+	4.18052i	0.768343	+	0.163222i
$657$	29.8360			1.16401
$658$	−25.0648	+	8.87674i	−0.977128	+	0.346051i
$659$	28.2472	+	28.2472i	1.10036	+	1.10036i	0.994367	+	0.105988i	$0.0338007\pi$
$659$	28.2472	+	28.2472i	1.10036	+	1.10036i	0.105988	+	0.994367i	$0.466199\pi$
$660$	−0.486642	+	4.63270i	−0.0189425	+	0.180328i
$661$	−24.6588	+	24.6588i	−0.959117	+	0.959117i	−0.999197	−	0.0400792i	$-0.987239\pi$
$661$	−24.6588	+	24.6588i	−0.959117	+	0.959117i	0.0400792	+	0.999197i	$0.487239\pi$
$662$	−3.37680	−	1.61053i	−0.131243	−	0.0625951i
$663$		−	6.72666i		−	0.261242i
$664$	7.87779	+	32.8006i	0.305718	+	1.27291i
$665$			4.02241i			0.155982i
$666$	−21.1256	+	44.2942i	−0.818602	+	1.71636i
$667$	−7.49479	+	7.49479i	−0.290200	+	0.290200i
$668$	−13.0042	−	16.0570i	−0.503149	−	0.621262i
$669$	−0.614415	−	0.614415i	−0.0237547	−	0.0237547i
$670$	−8.33030	−	23.5218i	−0.321827	−	0.908728i
$671$	−19.8831			−0.767580
$672$	−2.63954	+	3.44097i	−0.101823	+	0.132738i
$673$	−34.4233			−1.32692			−0.663459	−	0.748212i	$-0.730912\pi$
$673$	−34.4233			−1.32692			−0.663459	+	0.748212i	$0.730912\pi$
$674$	−2.58403	−	7.29639i	−0.0995331	−	0.281047i
$675$	−3.36290	−	3.36290i	−0.129438	−	0.129438i
$676$	−21.1278	−	26.0875i	−0.812607	−	1.00337i
$677$	3.37597	−	3.37597i	0.129749	−	0.129749i	−0.639250	−	0.768999i	$-0.720755\pi$
$677$	3.37597	−	3.37597i	0.129749	−	0.129749i	0.768999	+	0.639250i	$0.220755\pi$
$678$	−1.64983	+	3.45920i	−0.0633614	+	0.132850i
$679$		−	13.5836i		−	0.521293i
$680$	−17.7854	+	4.27156i	−0.682041	+	0.163807i
$681$			3.97708i			0.152402i
$682$	22.3234	+	10.6469i	0.854809	+	0.407692i
$683$	−6.78881	+	6.78881i	−0.259767	+	0.259767i	−0.824959	−	0.565193i	$-0.808802\pi$
$683$	−6.78881	+	6.78881i	−0.259767	+	0.259767i	0.565193	+	0.824959i	$0.308802\pi$
$684$	0.611044	−	5.81698i	0.0233639	−	0.222418i
$685$	19.0413	+	19.0413i	0.727530	+	0.727530i
$686$	23.1195	−	8.18780i	0.882706	−	0.312612i
$687$	6.29525			0.240179
$688$	16.7583	+	25.7989i	0.638904	+	0.983572i
$689$	47.2783			1.80116
$690$	1.93626	−	0.685730i	0.0737122	−	0.0261053i
$691$	−8.77925	−	8.77925i	−0.333978	−	0.333978i	0.520117	−	0.854095i	$-0.325888\pi$
$691$	−8.77925	−	8.77925i	−0.333978	−	0.333978i	−0.854095	+	0.520117i	$0.825888\pi$
$692$	24.5321	+	2.57697i	0.932571	+	0.0979618i
$693$	33.9183	−	33.9183i	1.28845	−	1.28845i
$694$	7.32354	+	3.49289i	0.277998	+	0.132588i
$695$			4.26936i			0.161946i
$696$	1.17386	−	1.91594i	0.0444949	−	0.0726234i
$697$			22.5600i			0.854519i
$698$	9.93149	−	20.8234i	0.375913	−	0.788177i
$699$	3.04168	−	3.04168i	0.115047	−	0.115047i
$700$	12.6675	−	10.2592i	0.478787	−	0.387760i
$701$	19.6265	+	19.6265i	0.741284	+	0.741284i	0.972825	−	0.231541i	$-0.0743768\pi$
$701$	19.6265	+	19.6265i	0.741284	+	0.741284i	−0.231541	+	0.972825i	$0.574377\pi$
$702$	4.19460	+	11.8441i	0.158315	+	0.447026i
$703$	−11.8655			−0.447516
$704$	44.7326	+	14.5258i	1.68592	+	0.547461i
$705$	−2.66991			−0.100555
$706$	−6.00360	−	16.9521i	−0.225948	−	0.637999i
$707$	−34.2026	−	34.2026i	−1.28632	−	1.28632i
$708$	4.01822	−	3.25428i	0.151014	−	0.122303i
$709$	−7.75356	+	7.75356i	−0.291191	+	0.291191i	−0.837551	−	0.546360i	$-0.816013\pi$
$709$	−7.75356	+	7.75356i	−0.291191	+	0.291191i	0.546360	+	0.837551i	$0.316013\pi$
$710$	3.50836	−	7.35599i	0.131666	−	0.276065i
$711$			25.4151i			0.953142i
$712$	−6.36737	+	10.3927i	−0.238627	+	0.389481i
$713$		−	10.9061i		−	0.408438i
$714$	−4.38941	−	2.09348i	−0.164269	−	0.0783465i
$715$	−32.7097	+	32.7097i	−1.22328	+	1.22328i
$716$	27.8095	+	2.92124i	1.03929	+	0.109172i
$717$	2.14159	+	2.14159i	0.0799791	+	0.0799791i
$718$	−14.1919	+	5.02608i	−0.529636	+	0.187572i
$719$	−10.1767			−0.379528			−0.189764	−	0.981830i	$-0.560772\pi$
$719$	−10.1767			−0.379528			−0.189764	+	0.981830i	$0.560772\pi$
$720$	14.1436	−	9.18731i	0.527100	−	0.342391i
$721$	24.9942			0.930832
$722$	1.33308	−	0.472113i	0.0496122	−	0.0175702i
$723$	2.06644	+	2.06644i	0.0768516	+	0.0768516i
$724$	−3.33386	+	31.7375i	−0.123902	+	1.17951i
$725$	−5.97202	+	5.97202i	−0.221795	+	0.221795i
$726$	8.26467	+	3.94175i	0.306731	+	0.146292i
$727$			19.0184i			0.705354i	0.935745	+	0.352677i	$0.114728\pi$
$727$			19.0184i			0.705354i	−0.935745	+	0.352677i	$0.885272\pi$
$728$	−41.8757	+	10.0574i	−1.55201	+	0.372750i
$729$			23.0077i			0.852137i
$730$	−8.95476	+	18.7755i	−0.331430	+	0.694911i
$731$	−24.3935	+	24.3935i	−0.902226	+	0.902226i
$732$	−1.16979	−	1.44440i	−0.0432368	−	0.0533866i
$733$	37.1906	+	37.1906i	1.37366	+	1.37366i	0.854943	+	0.518722i	$0.173592\pi$
$733$	37.1906	+	37.1906i	1.37366	+	1.37366i	0.518722	+	0.854943i	$0.326408\pi$
$734$	3.77081	+	10.6474i	0.139183	+	0.393004i
$735$	−0.310518			−0.0114536
$736$	−2.71006	−	20.5616i	−0.0998940	−	0.757911i
$737$	−71.9493			−2.65028
$738$	−6.94430	−	19.6083i	−0.255623	−	0.721790i
$739$	22.8071	+	22.8071i	0.838974	+	0.838974i	0.988724	−	0.149750i	$-0.0478469\pi$
$739$	22.8071	+	22.8071i	0.838974	+	0.838974i	−0.149750	+	0.988724i	$0.547847\pi$
$740$	−21.5333	−	26.5882i	−0.791580	−	0.977402i
$741$	−1.06042	+	1.06042i	−0.0389555	+	0.0389555i
$742$	14.7140	−	30.8510i	0.540169	−	1.13257i
$743$			36.8449i			1.35171i	0.737035	+	0.675854i	$0.236225\pi$
$743$			36.8449i			1.35171i	−0.737035	+	0.675854i	$0.763775\pi$
$744$	0.539924	+	2.24807i	0.0197946	+	0.0824184i
$745$			5.70413i			0.208983i
$746$	−5.35119	−	2.55220i	−0.195921	−	0.0934425i
$747$	24.6633	−	24.6633i	0.902382	−	0.902382i
$748$	−5.50974	+	52.4513i	−0.201456	+	1.91781i
$749$	21.9908	+	21.9908i	0.803525	+	0.803525i
$750$	4.18351	−	1.48160i	0.152760	−	0.0541003i
$751$	−22.7422			−0.829874			−0.414937	−	0.909850i	$-0.636196\pi$
$751$	−22.7422			−0.829874			−0.414937	+	0.909850i	$0.636196\pi$
$752$	−5.60158	+	26.3686i	−0.204269	+	0.961563i
$753$	−0.443718			−0.0161700
$754$	21.0333	−	7.44899i	0.765989	−	0.271276i
$755$	−10.5767	−	10.5767i	−0.384926	−	0.384926i
$756$	9.03416	+	0.948993i	0.328569	+	0.0345145i
$757$	−3.61197	+	3.61197i	−0.131279	+	0.131279i	−0.769693	−	0.638414i	$-0.779591\pi$
$757$	−3.61197	+	3.61197i	−0.131279	+	0.131279i	0.638414	+	0.769693i	$0.279591\pi$
$758$	−29.7704	−	14.1987i	−1.08131	−	0.515719i
$759$		−	5.92269i		−	0.214980i
$760$	3.47716	+	2.13039i	0.126130	+	0.0772772i
$761$			46.2680i			1.67721i	0.544737	+	0.838607i	$0.316629\pi$
$761$			46.2680i			1.67721i	−0.544737	+	0.838607i	$0.683371\pi$
$762$	2.64918	−	5.55454i	0.0959697	−	0.201220i
$763$	4.37649	−	4.37649i	0.158439	−	0.158439i
$764$	−1.15519	+	0.935566i	−0.0417933	+	0.0338476i
$765$	13.3731	+	13.3731i	0.483506	+	0.483506i
$766$	−12.4641	−	35.1943i	−0.450347	−	1.27162i
$767$	51.3483			1.85408
$768$	1.57655	+	4.10418i	0.0568890	+	0.148097i
$769$	−29.3923			−1.05991			−0.529957	−	0.848024i	$-0.677792\pi$
$769$	−29.3923			−1.05991			−0.529957	+	0.848024i	$0.677792\pi$
$770$	11.1644	+	31.5244i	0.402337	+	1.13606i
$771$	1.06384	+	1.06384i	0.0383132	+	0.0383132i
$772$	27.8471	−	22.5529i	1.00224	−	0.811695i
$773$	−0.588045	+	0.588045i	−0.0211505	+	0.0211505i	−0.717603	−	0.696452i	$-0.754761\pi$
$773$	−0.588045	+	0.588045i	−0.0211505	+	0.0211505i	0.696452	+	0.717603i	$0.254761\pi$
$774$	13.6932	−	28.7106i	0.492192	−	1.03198i
$775$		−	8.69026i		−	0.312163i
$776$	−11.7424	−	7.19430i	−0.421526	−	0.258260i
$777$		−	9.09654i		−	0.326337i
$778$	−4.02855	−	1.92138i	−0.144431	−	0.0688847i
$779$	3.55645	−	3.55645i	0.127423	−	0.127423i
$780$	−4.30061	−	0.451758i	−0.153987	−	0.0161755i
$781$	−16.6161	−	16.6161i	−0.594570	−	0.594570i
$782$	21.9223	−	7.76381i	0.783939	−	0.277633i
$783$	−4.70650			−0.168197
$784$	−0.651479	+	3.06674i	−0.0232671	+	0.109526i
$785$	−0.384714			−0.0137310
$786$	2.20269	−	0.780085i	0.0785672	−	0.0278247i
$787$	13.3041	+	13.3041i	0.474240	+	0.474240i	0.903284	−	0.429044i	$-0.141149\pi$
$787$	13.3041	+	13.3041i	0.474240	+	0.474240i	−0.429044	+	0.903284i	$0.641149\pi$
$788$	0.00702634	−	0.0668890i	0.000250303	−	0.00238282i
$789$	0.251638	−	0.251638i	0.00895855	−	0.00895855i
$790$	−15.9934	−	7.62790i	−0.569021	−	0.271389i
$791$			27.5149i			0.978318i
$792$	−11.3565	−	47.2847i	−0.403534	−	1.68019i
$793$		−	18.4578i		−	0.655457i
$794$	11.5698	−	24.2584i	0.410596	−	0.860898i
$795$	2.42680	−	2.42680i	0.0860696	−	0.0860696i
$796$	−14.2251	−	17.5645i	−0.504197	−	0.622557i
$797$	0.475928	+	0.475928i	0.0168582	+	0.0168582i	0.715486	−	0.698627i	$-0.246205\pi$
$797$	0.475928	+	0.475928i	0.0168582	+	0.0168582i	−0.698627	+	0.715486i	$0.746205\pi$
$798$	0.361939	+	1.02199i	0.0128125	+	0.0361781i
$799$	−30.2286			−1.06941
$800$	−2.15943	−	16.3840i	−0.0763475	−	0.579260i
$801$	12.6021			0.445273
$802$	2.15745	+	6.09188i	0.0761822	+	0.215112i
$803$	42.4110	+	42.4110i	1.49665	+	1.49665i
$804$	−4.23303	−	5.22672i	−0.149287	−	0.184332i
$805$	10.4278	−	10.4278i	0.367532	−	0.367532i
$806$	−9.88372	+	20.7232i	−0.348139	+	0.729944i
$807$			1.46066i			0.0514177i
$808$	−47.6810	+	11.4516i	−1.67741	+	0.402868i
$809$		−	35.3512i		−	1.24288i	−0.783461	−	0.621441i	$-0.786547\pi$
$809$		−	35.3512i		−	1.24288i	0.783461	−	0.621441i	$-0.213453\pi$
$810$	−15.3230	−	7.30814i	−0.538395	−	0.256782i
$811$	12.3618	−	12.3618i	0.434081	−	0.434081i	−0.455933	−	0.890014i	$-0.650694\pi$
$811$	12.3618	−	12.3618i	0.434081	−	0.434081i	0.890014	+	0.455933i	$0.150694\pi$
$812$	1.68527	−	16.0434i	0.0591415	−	0.563012i
$813$	−3.97517	−	3.97517i	−0.139415	−	0.139415i
$814$	−92.9922	+	32.9333i	−3.25937	+	1.15431i
$815$	−19.0455			−0.667134
$816$	−4.13446	+	2.68564i	−0.144735	+	0.0940162i
$817$	7.69099			0.269074
$818$	−46.8003	+	16.5744i	−1.63633	+	0.579510i
$819$	31.4869	+	31.4869i	1.10024	+	1.10024i
$820$	14.4235	+	1.51511i	0.503689	+	0.0529100i
$821$	8.72352	−	8.72352i	0.304453	−	0.304453i	−0.538300	−	0.842753i	$-0.680933\pi$
$821$	8.72352	−	8.72352i	0.304453	−	0.304453i	0.842753	+	0.538300i	$0.180933\pi$
$822$	6.55124	+	3.12455i	0.228501	+	0.108981i
$823$			3.77440i			0.131567i	0.997834	+	0.0657836i	$0.0209547\pi$
$823$			3.77440i			0.131567i	−0.997834	+	0.0657836i	$0.979045\pi$
$824$	13.2377	−	21.6062i	0.461156	−	0.752686i
$825$		−	4.71933i		−	0.164306i
$826$	15.9807	−	33.5068i	0.556039	−	1.16585i
$827$	12.8479	−	12.8479i	0.446767	−	0.446767i	−0.447511	−	0.894278i	$-0.647690\pi$
$827$	12.8479	−	12.8479i	0.446767	−	0.446767i	0.894278	+	0.447511i	$0.147690\pi$
$828$	−16.6642	+	13.4960i	−0.579121	+	0.469019i
$829$	−2.76471	−	2.76471i	−0.0960224	−	0.0960224i	0.657464	−	0.753486i	$-0.271629\pi$
$829$	−2.76471	−	2.76471i	−0.0960224	−	0.0960224i	−0.753486	+	0.657464i	$0.771629\pi$
$830$	8.11806	+	22.9225i	0.281782	+	0.795653i
$831$	3.43049			0.119002
$832$	−13.4845	+	41.5260i	−0.467492	+	1.43965i
$833$	−3.51567			−0.121811
$834$	0.384160	+	1.08473i	0.0133024	+	0.0375612i
$835$	−10.5324	−	10.5324i	−0.364489	−	0.364489i
$836$	9.13723	−	7.40007i	0.316018	−	0.255937i
$837$	3.42436	−	3.42436i	0.118363	−	0.118363i
$838$	−10.1404	+	21.2613i	−0.350293	+	0.734460i
$839$		−	41.6266i		−	1.43711i	−0.695471	−	0.718554i	$-0.744804\pi$
$839$		−	41.6266i		−	1.43711i	0.695471	−	0.718554i	$-0.255196\pi$
$840$	−1.63323	+	2.66572i	−0.0563519	+	0.0919761i
$841$		−	20.6419i		−	0.711791i
$842$	20.3366	+	9.69931i	0.700844	+	0.334260i
$843$	−1.55089	+	1.55089i	−0.0534155	+	0.0534155i
$844$	−4.47790	−	0.470380i	−0.154136	−	0.0161911i
$845$	−17.1118	−	17.1118i	−0.588665	−	0.588665i
$846$	26.2736	−	9.30483i	0.903304	−	0.319907i
$847$	65.7382			2.25879
$848$	−18.8760	−	29.0591i	−0.648206	−	0.997893i
$849$	2.33225			0.0800425
$850$	17.4682	−	6.18638i	0.599153	−	0.212191i
$851$	30.7605	+	30.7605i	1.05446	+	1.05446i
$852$	0.229486	−	2.18465i	0.00786208	−	0.0748449i
$853$	23.9935	−	23.9935i	0.821521	−	0.821521i	−0.164805	−	0.986326i	$-0.552700\pi$
$853$	23.9935	−	23.9935i	0.821521	−	0.821521i	0.986326	+	0.164805i	$0.0526996\pi$
$854$	−12.0444	−	5.74447i	−0.412153	−	0.196572i
$855$		−	4.21640i		−	0.144198i
$856$	30.6568	−	7.36291i	1.04783	−	0.251659i
$857$			20.7533i			0.708919i	0.935071	+	0.354460i	$0.115335\pi$
$857$			20.7533i			0.708919i	−0.935071	+	0.354460i	$0.884665\pi$
$858$	−5.36745	+	11.2539i	−0.183242	+	0.384203i
$859$	14.4211	−	14.4211i	0.492040	−	0.492040i	−0.416908	−	0.908949i	$-0.636886\pi$
$859$	14.4211	−	14.4211i	0.492040	−	0.492040i	0.908949	+	0.416908i	$0.136886\pi$
$860$	13.9575	+	17.2340i	0.475945	+	0.587673i
$861$	2.72651	+	2.72651i	0.0929191	+	0.0929191i
$862$	−2.29404	−	6.47757i	−0.0781354	−	0.220627i
$863$	4.10084			0.139594			0.0697971	−	0.997561i	$-0.477765\pi$
$863$	4.10084			0.139594			0.0697971	+	0.997561i	$0.477765\pi$
$864$	5.60511	−	7.30694i	0.190690	−	0.248587i
$865$	17.7819			0.604603
$866$	−7.59023	−	21.4321i	−0.257926	−	0.728294i
$867$	−0.606092	−	0.606092i	−0.0205840	−	0.0205840i
$868$	10.4467	+	12.8990i	0.354583	+	0.437821i
$869$	−36.1268	+	36.1268i	−1.22552	+	1.22552i
$870$	0.697285	−	1.46200i	0.0236402	−	0.0495664i
$871$		−	66.7916i		−	2.26315i
$872$	−1.46533	−	6.10116i	−0.0496222	−	0.206611i
$873$			14.2387i			0.481908i
$874$	−4.67984	−	2.23200i	−0.158298	−	0.0754986i
$875$	22.5305	−	22.5305i	0.761669	−	0.761669i
$876$	−0.585742	+	5.57611i	−0.0197904	+	0.188399i
$877$	−13.0371	−	13.0371i	−0.440233	−	0.440233i	0.451857	−	0.892090i	$-0.350762\pi$
$877$	−13.0371	−	13.0371i	−0.440233	−	0.440233i	−0.892090	+	0.451857i	$0.850762\pi$
$878$	5.83108	−	2.06509i	0.196789	−	0.0696933i
$879$	0.523013			0.0176408
$880$	33.1641	+	7.04519i	1.11796	+	0.237493i
$881$	−58.7727			−1.98010			−0.990051	−	0.140710i	$-0.955062\pi$
$881$	−58.7727			−1.98010			−0.990051	+	0.140710i	$0.955062\pi$
$882$	3.05569	−	1.08218i	0.102890	−	0.0364388i
$883$	−0.781334	−	0.781334i	−0.0262940	−	0.0262940i	0.693838	−	0.720132i	$-0.255919\pi$
$883$	−0.781334	−	0.781334i	−0.0262940	−	0.0262940i	−0.720132	+	0.693838i	$0.755919\pi$
$884$	−48.6914	−	5.11478i	−1.63767	−	0.172029i
$885$	2.63571	−	2.63571i	0.0885983	−	0.0885983i
$886$	21.1189	+	10.0724i	0.709502	+	0.338390i
$887$		−	26.9751i		−	0.905735i	−0.891578	−	0.452868i	$-0.850401\pi$
$887$		−	26.9751i		−	0.905735i	0.891578	−	0.452868i	$-0.149599\pi$
$888$	−7.86348	−	4.81780i	−0.263881	−	0.161675i
$889$		−	44.1815i		−	1.48180i
$890$	−3.78230	+	7.93035i	−0.126783	+	0.265826i
$891$	−34.6124	+	34.6124i	−1.15956	+	1.15956i
$892$	−4.91468	+	3.98030i	−0.164556	+	0.133270i
$893$	4.76537	+	4.76537i	0.159467	+	0.159467i
$894$	0.513261	+	1.44927i	0.0171660	+	0.0484709i
$895$	20.1575			0.673790
$896$	22.9006	+	21.7229i	0.765056	+	0.725713i
$897$	5.49812			0.183577
$898$	−7.12676	−	20.1235i	−0.237823	−	0.671529i
$899$	−6.08117	−	6.08117i	−0.202818	−	0.202818i
$900$	−13.2784	+	10.7539i	−0.442614	+	0.358464i
$901$	27.4761	−	27.4761i	0.915362	−	0.915362i
$902$	18.0014	−	37.7436i	0.599382	−	1.25673i
$903$			5.89620i			0.196213i
$904$	23.7852	+	14.5727i	0.791084	+	0.484681i
$905$			23.0047i			0.764701i
$906$	−3.63897	−	1.73557i	−0.120897	−	0.0576604i
$907$	37.6300	−	37.6300i	1.24948	−	1.24948i	0.293533	−	0.955949i	$-0.405169\pi$
$907$	37.6300	−	37.6300i	1.24948	−	1.24948i	0.955949	−	0.293533i	$-0.0948312\pi$
$908$	28.7884	+	3.02407i	0.955376	+	0.100357i
$909$	35.8521	+	35.8521i	1.18914	+	1.18914i
$910$	−29.2646	+	10.3641i	−0.970111	+	0.343566i
$911$	−26.9253			−0.892076			−0.446038	−	0.895014i	$-0.647165\pi$
$911$	−26.9253			−0.892076			−0.446038	+	0.895014i	$0.647165\pi$
$912$	1.07515	+	0.228398i	0.0356018	+	0.00756303i
$913$	70.1161			2.32050
$914$	42.5818	−	15.0804i	1.40848	−	0.498816i
$915$	−0.947440	−	0.947440i	−0.0313214	−	0.0313214i
$916$	4.78675	−	45.5686i	0.158159	−	1.50563i
$917$	11.8627	−	11.8627i	0.391740	−	0.391740i
$918$	9.32097	+	4.44554i	0.307638	+	0.146725i
$919$		−	16.7032i		−	0.550986i	−0.961303	−	0.275493i	$-0.911159\pi$
$919$		−	16.7032i		−	0.550986i	0.961303	−	0.275493i	$-0.0888411\pi$
$920$	−3.49142	−	14.5372i	−0.115109	−	0.479276i
$921$		−	1.56287i		−	0.0514984i
$922$	−9.31314	+	19.5269i	−0.306712	+	0.643084i
$923$	15.4250	−	15.4250i	0.507719	−	0.507719i
$924$	5.67317	+	7.00494i	0.186634	+	0.230446i
$925$	24.5107	+	24.5107i	0.805906	+	0.805906i
$926$	16.3827	+	46.2589i	0.538368	+	1.52016i
$927$	−26.1996			−0.860506
$928$	−12.9761	−	9.95387i	−0.425961	−	0.326752i
$929$	3.92025			0.128619			0.0643097	−	0.997930i	$-0.479515\pi$
$929$	3.92025			0.128619			0.0643097	+	0.997930i	$0.479515\pi$
$930$	0.556391	+	1.57105i	0.0182448	+	0.0515169i
$931$	0.554225	+	0.554225i	0.0181640	+	0.0181640i
$932$	−19.7046	−	24.3303i	−0.645447	−	0.796965i
$933$	−3.35804	+	3.35804i	−0.109937	+	0.109937i
$934$	−11.7675	+	24.6729i	−0.385044	+	0.807322i
$935$			38.0190i			1.24335i
$936$	43.8951	−	10.5424i	1.43476	−	0.344588i
$937$			18.9021i			0.617505i	0.951142	+	0.308752i	$0.0999115\pi$
$937$			18.9021i			0.617505i	−0.951142	+	0.308752i	$0.900089\pi$
$938$	−43.5841	−	20.7870i	−1.42307	−	0.678720i
$939$	−5.11476	+	5.11476i	−0.166914	+	0.166914i
$940$	−2.03013	+	19.3263i	−0.0662156	+	0.630355i
$941$	−19.1160	−	19.1160i	−0.623164	−	0.623164i	0.323175	−	0.946339i	$-0.395250\pi$
$941$	−19.1160	−	19.1160i	−0.623164	−	0.623164i	−0.946339	+	0.323175i	$0.895250\pi$
$942$	−0.0977458	+	0.0346168i	−0.00318473	+	0.00112788i
$943$	−18.4397			−0.600479
$944$	−20.5010	−	31.5606i	−0.667250	−	1.02721i
$945$	6.54835			0.213018
$946$	60.2757	−	21.3467i	1.95973	−	0.694042i
$947$	−3.15712	−	3.15712i	−0.102592	−	0.102592i	0.653947	−	0.756540i	$-0.273112\pi$
$947$	−3.15712	−	3.15712i	−0.102592	−	0.102592i	−0.756540	+	0.653947i	$0.773112\pi$
$948$	−4.74988	−	0.498951i	−0.154269	−	0.0162052i
$949$	−39.3708	+	39.3708i	−1.27803	+	1.27803i
$950$	−3.72900	−	1.77851i	−0.120985	−	0.0577025i
$951$			1.67961i			0.0544650i
$952$	−18.4914	+	30.1812i	−0.599310	+	0.978178i
$953$		−	3.25616i		−	0.105478i	−0.998608	−	0.0527388i	$-0.983205\pi$
$953$		−	3.25616i		−	0.105478i	0.998608	−	0.0527388i	$-0.0167951\pi$
$954$	−15.4236	+	32.3388i	−0.499359	+	1.04701i
$955$	−0.757734	+	0.757734i	−0.0245197	+	0.0245197i
$956$	17.1305	−	13.8736i	0.554039	−	0.448705i
$957$	−3.30244	−	3.30244i	−0.106753	−	0.106753i
$958$	−6.79023	−	19.1732i	−0.219382	−	0.619459i
$959$	52.1094			1.68270
$960$	1.43937	+	2.82369i	0.0464554	+	0.0911341i
$961$	−22.1509			−0.714546
$962$	−30.5725	−	86.3261i	−0.985698	−	2.78327i
$963$	−23.0513	−	23.0513i	−0.742818	−	0.742818i
$964$	16.5293	−	13.3868i	0.532374	−	0.431159i
$965$	18.2660	−	18.2660i	0.588004	−	0.588004i
$966$	1.71113	−	3.58774i	0.0550549	−	0.115434i
$967$		−	5.24108i		−	0.168542i	−0.996443	−	0.0842709i	$-0.973144\pi$
$967$		−	5.24108i		−	0.168542i	0.996443	−	0.0842709i	$-0.0268561\pi$
$968$	34.8169	−	56.8272i	1.11906	−	1.82649i
$969$			1.23254i			0.0395949i
$970$	−8.96027	−	4.27350i	−0.287697	−	0.137214i
$971$	−11.6711	+	11.6711i	−0.374543	+	0.374543i	−0.869129	−	0.494586i	$-0.835320\pi$
$971$	−11.6711	+	11.6711i	−0.374543	+	0.374543i	0.494586	+	0.869129i	$0.335320\pi$
$972$	−14.2651	−	1.49848i	−0.457554	−	0.0480637i
$973$	5.84188	+	5.84188i	0.187282	+	0.187282i
$974$	−6.07866	+	2.15277i	−0.194773	+	0.0689791i
$975$	4.38103			0.140305
$976$	−11.3449	+	7.36935i	−0.363141	+	0.235887i
$977$	38.6122			1.23531			0.617657	−	0.786448i	$-0.288082\pi$
$977$	38.6122			1.23531			0.617657	+	0.786448i	$0.288082\pi$
$978$	−4.83896	+	1.71373i	−0.154733	+	0.0547989i
$979$	17.9135	+	17.9135i	0.572517	+	0.572517i
$980$	−0.236110	+	2.24770i	−0.00754225	+	0.0718003i
$981$	−4.58755	+	4.58755i	−0.146469	+	0.146469i
$982$	23.6904	+	11.2989i	0.755992	+	0.360562i
$983$			44.1515i			1.40821i	0.710094	+	0.704107i	$0.248652\pi$
$983$			44.1515i			1.40821i	−0.710094	+	0.704107i	$0.751348\pi$
$984$	3.80096	−	0.912883i	0.121170	−	0.0291017i
$985$		−	0.0484840i		−	0.00154483i
$986$	7.89463	−	16.5527i	0.251416	−	0.527145i
$987$	−3.65331	+	3.65331i	−0.116286	+	0.116286i
$988$	6.86961	+	8.48224i	0.218551	+	0.269856i
$989$	−19.9383	−	19.9383i	−0.634003	−	0.634003i
$990$	−11.7028	−	33.0446i	−0.371940	−	1.05023i
$991$	33.3274			1.05868			0.529339	−	0.848410i	$-0.322440\pi$
$991$	33.3274			1.05868			0.529339	+	0.848410i	$0.322440\pi$
$992$	16.6834	−	2.19890i	0.529698	−	0.0698152i
$993$	−0.726927			−0.0230683
$994$	−5.26481	−	14.8660i	−0.166990	−	0.471520i
$995$	−11.5212	−	11.5212i	−0.365248	−	0.365248i
$996$	4.12518	+	5.09356i	0.130711	+	0.161396i
$997$	6.30027	−	6.30027i	0.199532	−	0.199532i	−0.600268	−	0.799799i	$-0.704939\pi$
$997$	6.30027	−	6.30027i	0.199532	−	0.199532i	0.799799	+	0.600268i	$0.204939\pi$
$998$	−0.0169184	+	0.0354729i	−0.000535543	+	0.00112287i
$999$			19.3167i			0.611152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.13	✓	68
4.3	odd	2		1216.2.k.b.913.21		68
16.5	even	4	inner	304.2.k.b.229.13	yes	68
16.11	odd	4		1216.2.k.b.305.21		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.13	✓	68	1.1	even	1	trivial
304.2.k.b.229.13	yes	68	16.5	even	4	inner
1216.2.k.b.305.21		68	16.11	odd	4
1216.2.k.b.913.21		68	4.3	odd	2

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.472113 - 1.33308i) q^{2} +(-0.194303 - 0.194303i) q^{3} +(-1.55422 + 1.25873i) q^{4} +(-1.01947 + 1.01947i) q^{5} +(-0.167289 + 0.350755i) q^{6} +2.78994i q^{7} +(2.41176 + 1.47764i) q^{8} -2.92449i q^{9} +O(q^{10})\)	\(q+(-0.472113 - 1.33308i) q^{2} +(-0.194303 - 0.194303i) q^{3} +(-1.55422 + 1.25873i) q^{4} +(-1.01947 + 1.01947i) q^{5} +(-0.167289 + 0.350755i) q^{6} +2.78994i q^{7} +(2.41176 + 1.47764i) q^{8} -2.92449i q^{9} +(1.84035 + 0.877735i) q^{10} +(4.15707 - 4.15707i) q^{11} +(0.546564 + 0.0574138i) q^{12} +(3.85908 + 3.85908i) q^{13} +(3.71923 - 1.31717i) q^{14} +0.396173 q^{15} +(0.831187 - 3.91269i) q^{16} +4.48546 q^{17} +(-3.89859 + 1.38069i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(0.301240 - 2.86773i) q^{20} +(0.542094 - 0.542094i) q^{21} +(-7.50433 - 3.57911i) q^{22} +3.66625i q^{23} +(-0.181503 - 0.755721i) q^{24} +2.92135i q^{25} +(3.32255 - 6.96639i) q^{26} +(-1.15115 + 1.15115i) q^{27} +(-3.51179 - 4.33618i) q^{28} +(2.04427 + 2.04427i) q^{29} +(-0.187039 - 0.528131i) q^{30} -2.97474 q^{31} +(-5.60835 + 0.739191i) q^{32} -1.61546 q^{33} +(-2.11764 - 5.97948i) q^{34} +(-2.84427 - 2.84427i) q^{35} +(3.68115 + 4.54530i) q^{36} +(8.39019 - 8.39019i) q^{37} +(-0.608797 + 1.27647i) q^{38} -1.49966i q^{39} +(-3.96514 + 0.952314i) q^{40} +5.02958i q^{41} +(-0.978586 - 0.466726i) q^{42} +(-5.43835 + 5.43835i) q^{43} +(-1.22836 + 11.6936i) q^{44} +(2.98144 + 2.98144i) q^{45} +(4.88741 - 1.73088i) q^{46} -6.73925 q^{47} +(-0.921748 + 0.598744i) q^{48} -0.783793 q^{49} +(3.89440 - 1.37921i) q^{50} +(-0.871537 - 0.871537i) q^{51} +(-10.8554 - 1.14030i) q^{52} +(6.12560 - 6.12560i) q^{53} +(2.07804 + 0.991101i) q^{54} +8.47605i q^{55} +(-4.12253 + 6.72868i) q^{56} +0.274786i q^{57} +(1.76005 - 3.69030i) q^{58} +(6.65292 - 6.65292i) q^{59} +(-0.615739 + 0.498676i) q^{60} +(-2.39148 - 2.39148i) q^{61} +(1.40441 + 3.96558i) q^{62} +8.15917 q^{63} +(3.63318 + 7.12741i) q^{64} -7.86845 q^{65} +(0.762681 + 2.15354i) q^{66} +(-8.65383 - 8.65383i) q^{67} +(-6.97138 + 5.64599i) q^{68} +(0.712362 - 0.712362i) q^{69} +(-2.44883 + 5.13447i) q^{70} -3.99706i q^{71} +(4.32134 - 7.05318i) q^{72} +10.2021i q^{73} +(-15.1459 - 7.22369i) q^{74} +(0.567626 - 0.567626i) q^{75} +(1.98906 + 0.208940i) q^{76} +(11.5980 + 11.5980i) q^{77} +(-1.99917 + 0.708009i) q^{78} -8.69044 q^{79} +(3.14151 + 4.83625i) q^{80} -8.32614 q^{81} +(6.70484 - 2.37453i) q^{82} +(8.43335 + 8.43335i) q^{83} +(-0.160181 + 1.52488i) q^{84} +(-4.57280 + 4.57280i) q^{85} +(9.81729 + 4.68225i) q^{86} -0.794414i q^{87} +(16.1685 - 3.88322i) q^{88} +4.30916i q^{89} +(2.56693 - 5.38209i) q^{90} +(-10.7666 + 10.7666i) q^{91} +(-4.61482 - 5.69815i) q^{92} +(0.578001 + 0.578001i) q^{93} +(3.18169 + 8.98398i) q^{94} +1.44175 q^{95} +(1.23335 + 0.946091i) q^{96} -4.86879 q^{97} +(0.370039 + 1.04486i) q^{98} +(-12.1573 - 12.1573i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

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