LMFDB - Embedded newform 153.2.f.b.55.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,2,Mod(55,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.55"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.836829184.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 $ x^8 + 14x^6 + 61x^4 + 84*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			55.3
Root			$1.65222i$ of defining polynomial
Character	$\chi$	$=$	153.55
Dual form			153.2.f.b.64.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.65222i q^{2} -0.729840 q^{4} +(2.87540 - 2.87540i) q^{5} +(0.652223 + 0.652223i) q^{7} +2.09859i q^{8} +(4.75081 + 4.75081i) q^{10} +(-1.60525 - 1.60525i) q^{11} -3.57461 q^{13} +(-1.07762 + 1.07762i) q^{14} -4.92701 q^{16} +(-3.79779 + 1.60525i) q^{17} +1.72984i q^{19} +(-2.09859 + 2.09859i) q^{20} +(2.65222 - 2.65222i) q^{22} +(3.60525 + 3.60525i) q^{23} -11.5359i q^{25} -5.90604i q^{26} +(-0.476019 - 0.476019i) q^{28} +(1.55827 - 1.55827i) q^{29} +(-2.92238 + 2.92238i) q^{31} -3.94335i q^{32} +(-2.65222 - 6.27479i) q^{34} +3.75081 q^{35} +(4.21049 - 4.21049i) q^{37} -2.85808 q^{38} +(6.03429 + 6.03429i) q^{40} +(-3.57096 - 3.57096i) q^{41} +5.23146i q^{43} +(1.17157 + 1.17157i) q^{44} +(-5.95667 + 5.95667i) q^{46} -6.96130 q^{47} -6.14921i q^{49} +19.0599 q^{50} +2.60889 q^{52} +2.69555i q^{53} -9.23146 q^{55} +(-1.36875 + 1.36875i) q^{56} +(2.57461 + 2.57461i) q^{58} -7.39840i q^{59} +(-2.75081 - 2.75081i) q^{61} +(-4.82843 - 4.82843i) q^{62} -3.33873 q^{64} +(-10.2784 + 10.2784i) q^{65} +12.0419 q^{67} +(2.77178 - 1.17157i) q^{68} +6.19717i q^{70} +(-1.07762 + 1.07762i) q^{71} +(0.823796 - 0.823796i) q^{73} +(6.95667 + 6.95667i) q^{74} -1.26251i q^{76} -2.09396i q^{77} +(8.40303 + 8.40303i) q^{79} +(-14.1672 + 14.1672i) q^{80} +(5.90002 - 5.90002i) q^{82} +6.38508i q^{83} +(-6.30445 + 15.5359i) q^{85} -8.64354 q^{86} +(3.36875 - 3.36875i) q^{88} +10.3597 q^{89} +(-2.33144 - 2.33144i) q^{91} +(-2.63125 - 2.63125i) q^{92} -11.5016i q^{94} +(4.97399 + 4.97399i) q^{95} +(-10.2315 + 10.2315i) q^{97} +10.1599 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{13} - 24 q^{14} + 12 q^{16} + 4 q^{17} + 12 q^{20} + 12 q^{22} + 16 q^{23} - 8 q^{28} - 4 q^{29} - 8 q^{31} - 12 q^{34} - 8 q^{35} + 8 q^{37} - 24 q^{38} + 36 q^{40}+ \cdots + 76 q^{98}+O(q^{100}) $ 8 * q - 12 * q^4 + 4 * q^5 - 4 * q^7 - 4 * q^13 - 24 * q^14 + 12 * q^16 + 4 * q^17 + 12 * q^20 + 12 * q^22 + 16 * q^23 - 8 * q^28 - 4 * q^29 - 8 * q^31 - 12 * q^34 - 8 * q^35 + 8 * q^37 - 24 * q^38 + 36 * q^40 - 28 * q^41 + 32 * q^44 - 20 * q^46 + 8 * q^47 + 60 * q^50 - 16 * q^52 - 4 * q^55 + 24 * q^56 - 4 * q^58 + 16 * q^61 - 16 * q^62 + 4 * q^64 - 16 * q^65 + 8 * q^67 - 60 * q^68 - 24 * q^71 + 20 * q^73 + 28 * q^74 + 20 * q^79 - 60 * q^80 - 40 * q^82 - 32 * q^85 + 8 * q^86 - 8 * q^88 + 8 * q^89 - 36 * q^91 - 56 * q^92 - 8 * q^95 - 12 * q^97 + 76 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$			1.65222i			1.16830i	0.811646	+	0.584149i	$0.198572\pi$
$2$			1.65222i			1.16830i	−0.811646	+	0.584149i	$0.801428\pi$
$3$		0			0
$3$		0			0
$4$	−0.729840			−0.364920
$5$	2.87540	−	2.87540i	1.28592	−	1.28592i	0.348677	−	0.937243i	$-0.386631\pi$
$5$	2.87540	−	2.87540i	1.28592	−	1.28592i	0.937243	−	0.348677i	$-0.113369\pi$
$6$		0			0
$7$	0.652223	+	0.652223i	0.246517	+	0.246517i	0.819540	−	0.573023i	$-0.194229\pi$
$7$	0.652223	+	0.652223i	0.246517	+	0.246517i	−0.573023	+	0.819540i	$0.694229\pi$
$8$			2.09859i			0.741962i
$9$		0			0
$10$	4.75081	+	4.75081i	1.50234	+	1.50234i
$11$	−1.60525	−	1.60525i	−0.484000	−	0.484000i	0.422407	−	0.906406i	$-0.361185\pi$
$11$	−1.60525	−	1.60525i	−0.484000	−	0.484000i	−0.906406	+	0.422407i	$0.861185\pi$
$12$		0			0
$13$	−3.57461			−0.991417			−0.495709	−	0.868489i	$-0.665092\pi$
$13$	−3.57461			−0.991417			−0.495709	+	0.868489i	$0.665092\pi$
$14$	−1.07762	+	1.07762i	−0.288005	+	0.288005i
$15$		0			0
$16$	−4.92701			−1.23175
$17$	−3.79779	+	1.60525i	−0.921099	+	0.389329i
$17$	−3.79779	+	1.60525i	−0.921099	+	0.389329i
$18$		0			0
$19$			1.72984i			0.396853i	0.980116	+	0.198426i	$0.0635830\pi$
$19$			1.72984i			0.396853i	−0.980116	+	0.198426i	$0.936417\pi$
$20$	−2.09859	+	2.09859i	−0.469258	+	0.469258i
$21$		0			0
$22$	2.65222	−	2.65222i	0.565456	−	0.565456i
$23$	3.60525	+	3.60525i	0.751746	+	0.751746i	0.974805	−	0.223059i	$-0.0716044\pi$
$23$	3.60525	+	3.60525i	0.751746	+	0.751746i	−0.223059	+	0.974805i	$0.571604\pi$
$24$		0			0
$25$		−	11.5359i		−	2.30718i
$26$		−	5.90604i		−	1.15827i
$27$		0			0
$28$	−0.476019	−	0.476019i	−0.0899591	−	0.0899591i
$29$	1.55827	−	1.55827i	0.289363	−	0.289363i	−0.547465	−	0.836828i	$-0.684407\pi$
$29$	1.55827	−	1.55827i	0.289363	−	0.289363i	0.836828	+	0.547465i	$0.184407\pi$
$30$		0			0
$31$	−2.92238	+	2.92238i	−0.524875	+	0.524875i	−0.919040	−	0.394165i	$-0.871034\pi$
$31$	−2.92238	+	2.92238i	−0.524875	+	0.524875i	0.394165	+	0.919040i	$0.371034\pi$
$32$		−	3.94335i		−	0.697093i
$33$		0			0
$34$	−2.65222	−	6.27479i	−0.454852	−	1.07612i
$35$	3.75081			0.634003
$36$		0			0
$37$	4.21049	−	4.21049i	0.692200	−	0.692200i	−0.270515	−	0.962716i	$-0.587194\pi$
$37$	4.21049	−	4.21049i	0.692200	−	0.692200i	0.962716	+	0.270515i	$0.0871941\pi$
$38$	−2.85808			−0.463642
$39$		0			0
$40$	6.03429	+	6.03429i	0.954104	+	0.954104i
$41$	−3.57096	−	3.57096i	−0.557690	−	0.557690i	0.370959	−	0.928649i	$-0.379029\pi$
$41$	−3.57096	−	3.57096i	−0.557690	−	0.557690i	−0.928649	+	0.370959i	$0.879029\pi$
$42$		0			0
$43$			5.23146i			0.797790i	0.916997	+	0.398895i	$0.130606\pi$
$43$			5.23146i			0.797790i	−0.916997	+	0.398895i	$0.869394\pi$
$44$	1.17157	+	1.17157i	0.176621	+	0.176621i
$45$		0			0
$46$	−5.95667	+	5.95667i	−0.878263	+	0.878263i
$47$	−6.96130			−1.01541			−0.507705	−	0.861531i	$-0.669506\pi$
$47$	−6.96130			−1.01541			−0.507705	+	0.861531i	$0.669506\pi$
$48$		0			0
$49$		−	6.14921i		−	0.878459i
$50$	19.0599			2.69548
$51$		0			0
$52$	2.60889			0.361788
$53$			2.69555i			0.370263i	0.982714	+	0.185131i	$0.0592711\pi$
$53$			2.69555i			0.370263i	−0.982714	+	0.185131i	$0.940729\pi$
$54$		0			0
$55$	−9.23146			−1.24477
$56$	−1.36875	+	1.36875i	−0.182906	+	0.182906i
$57$		0			0
$58$	2.57461	+	2.57461i	0.338062	+	0.338062i
$59$		−	7.39840i		−	0.963190i	−0.876394	−	0.481595i	$-0.840058\pi$
$59$		−	7.39840i		−	0.963190i	0.876394	−	0.481595i	$-0.159942\pi$
$60$		0			0
$61$	−2.75081	−	2.75081i	−0.352205	−	0.352205i	0.508724	−	0.860929i	$-0.330117\pi$
$61$	−2.75081	−	2.75081i	−0.352205	−	0.352205i	−0.860929	+	0.508724i	$0.830117\pi$
$62$	−4.82843	−	4.82843i	−0.613211	−	0.613211i
$63$		0			0
$64$	−3.33873			−0.417341
$65$	−10.2784	+	10.2784i	−1.27488	+	1.27488i
$66$		0			0
$67$	12.0419			1.47116			0.735578	−	0.677440i	$-0.236910\pi$
$67$	12.0419			1.47116			0.735578	+	0.677440i	$0.236910\pi$
$68$	2.77178	−	1.17157i	0.336128	−	0.142074i
$69$		0			0
$70$			6.19717i			0.740704i
$71$	−1.07762	+	1.07762i	−0.127890	+	0.127890i	−0.768154	−	0.640265i	$-0.778825\pi$
$71$	−1.07762	+	1.07762i	−0.127890	+	0.127890i	0.640265	+	0.768154i	$0.278825\pi$
$72$		0			0
$73$	0.823796	−	0.823796i	0.0964180	−	0.0964180i	−0.657252	−	0.753670i	$-0.728281\pi$
$73$	0.823796	−	0.823796i	0.0964180	−	0.0964180i	0.753670	+	0.657252i	$0.228281\pi$
$74$	6.95667	+	6.95667i	0.808696	+	0.808696i
$75$		0			0
$76$		−	1.26251i		−	0.144820i
$77$		−	2.09396i		−	0.238628i
$78$		0			0
$79$	8.40303	+	8.40303i	0.945415	+	0.945415i	0.998585	−	0.0531704i	$-0.0169327\pi$
$79$	8.40303	+	8.40303i	0.945415	+	0.945415i	−0.0531704	+	0.998585i	$0.516933\pi$
$80$	−14.1672	+	14.1672i	−1.58394	+	1.58394i
$81$		0			0
$82$	5.90002	−	5.90002i	0.651548	−	0.651548i
$83$			6.38508i			0.700854i	0.936590	+	0.350427i	$0.113964\pi$
$83$			6.38508i			0.700854i	−0.936590	+	0.350427i	$0.886036\pi$
$84$		0			0
$85$	−6.30445	+	15.5359i	−0.683813	+	1.68511i
$86$	−8.64354			−0.932057
$87$		0			0
$88$	3.36875	−	3.36875i	0.359110	−	0.359110i
$89$	10.3597			1.09813			0.549063	−	0.835781i	$-0.314985\pi$
$89$	10.3597			1.09813			0.549063	+	0.835781i	$0.314985\pi$
$90$		0			0
$91$	−2.33144	−	2.33144i	−0.244401	−	0.244401i
$92$	−2.63125	−	2.63125i	−0.274327	−	0.274327i
$93$		0			0
$94$		−	11.5016i		−	1.18630i
$95$	4.97399	+	4.97399i	0.510321	+	0.510321i
$96$		0			0
$97$	−10.2315	+	10.2315i	−1.03885	+	1.03885i	−0.0396330	+	0.999214i	$0.512619\pi$
$97$	−10.2315	+	10.2315i	−1.03885	+	1.03885i	−0.999214	+	0.0396330i	$0.987381\pi$
$98$	10.1599			1.02630
$99$		0			0
$100$			8.41937i			0.841937i
$101$	−0.265746			−0.0264427			−0.0132213	−	0.999913i	$-0.504209\pi$
$101$	−0.265746			−0.0264427			−0.0132213	+	0.999913i	$0.504209\pi$
$102$		0			0
$103$	−3.03429			−0.298977			−0.149489	−	0.988763i	$-0.547763\pi$
$103$	−3.03429			−0.298977			−0.149489	+	0.988763i	$0.547763\pi$
$104$		−	7.50162i		−	0.735594i
$105$		0			0
$106$	−4.45366			−0.432577
$107$	13.8964	−	13.8964i	1.34341	−	1.34341i	0.450776	−	0.892637i	$-0.351147\pi$
$107$	13.8964	−	13.8964i	1.34341	−	1.34341i	0.892637	−	0.450776i	$-0.148853\pi$
$108$		0			0
$109$	−0.506033	−	0.506033i	−0.0484692	−	0.0484692i	0.682457	−	0.730926i	$-0.260912\pi$
$109$	−0.506033	−	0.506033i	−0.0484692	−	0.0484692i	−0.730926	+	0.682457i	$0.760912\pi$
$110$		−	15.2524i		−	1.45426i
$111$		0			0
$112$	−3.21351	−	3.21351i	−0.303648	−	0.303648i
$113$	8.33509	+	8.33509i	0.784099	+	0.784099i	0.980520	−	0.196421i	$-0.0629319\pi$
$113$	8.33509	+	8.33509i	0.784099	+	0.784099i	−0.196421	+	0.980520i	$0.562932\pi$
$114$		0			0
$115$	20.7331			1.93337
$116$	−1.13729	+	1.13729i	−0.105594	+	0.105594i
$117$		0			0
$118$	12.2238			1.12529
$119$	−3.52398	−	1.43003i	−0.323043	−	0.131090i
$120$		0			0
$121$		−	5.84638i		−	0.531489i
$122$	4.54495	−	4.54495i	0.411480	−	0.411480i
$123$		0			0
$124$	2.13287	−	2.13287i	0.191538	−	0.191538i
$125$	−18.7934	−	18.7934i	−1.68093	−	1.68093i
$126$		0			0
$127$		−	2.81048i		−	0.249390i	−0.992195	−	0.124695i	$-0.960205\pi$
$127$		−	2.81048i		−	0.249390i	0.992195	−	0.124695i	$-0.0397952\pi$
$128$		−	13.4030i		−	1.18467i
$129$		0			0
$130$	−16.9823	−	16.9823i	−1.48944	−	1.48944i
$131$	−5.60525	+	5.60525i	−0.489733	+	0.489733i	−0.908222	−	0.418489i	$-0.862560\pi$
$131$	−5.60525	+	5.60525i	−0.489733	+	0.489733i	0.418489	+	0.908222i	$0.362560\pi$
$132$		0			0
$133$	−1.12824	+	1.12824i	−0.0978309	+	0.0978309i
$134$			19.8960i			1.71875i
$135$		0			0
$136$	−3.36875	−	7.96999i	−0.288868	−	0.683421i
$137$	0.103218			0.00881851			0.00440926	−	0.999990i	$-0.498596\pi$
$137$	0.103218			0.00881851			0.00440926	+	0.999990i	$0.498596\pi$
$138$		0			0
$139$	−10.2151	+	10.2151i	−0.866435	+	0.866435i	−0.992076	−	0.125641i	$-0.959901\pi$
$139$	−10.2151	+	10.2151i	−0.866435	+	0.866435i	0.125641	+	0.992076i	$0.459901\pi$
$140$	−2.73749			−0.231360
$141$		0			0
$142$	−1.78046	−	1.78046i	−0.149413	−	0.149413i
$143$	5.73812	+	5.73812i	0.479846	+	0.479846i
$144$		0			0
$145$		−	8.96130i		−	0.744195i
$146$	1.36109	+	1.36109i	0.112645	+	0.112645i
$147$		0			0
$148$	−3.07299	+	3.07299i	−0.252598	+	0.252598i
$149$	3.59557			0.294561			0.147280	−	0.989095i	$-0.452948\pi$
$149$	3.59557			0.294561			0.147280	+	0.989095i	$0.452948\pi$
$150$		0			0
$151$			7.58828i			0.617526i	0.951139	+	0.308763i	$0.0999149\pi$
$151$			7.58828i			0.617526i	−0.951139	+	0.308763i	$0.900085\pi$
$152$	−3.63022			−0.294450
$153$		0			0
$154$	3.45968			0.278789
$155$			16.8061i			1.34990i
$156$		0			0
$157$	18.9569			1.51292			0.756462	−	0.654038i	$-0.226926\pi$
$157$	18.9569			1.51292			0.756462	+	0.654038i	$0.226926\pi$
$158$	−13.8837	+	13.8837i	−1.10453	+	1.10453i
$159$		0			0
$160$	−11.3387	−	11.3387i	−0.896405	−	0.896405i
$161$			4.70285i			0.370636i
$162$		0			0
$163$	−9.49860	−	9.49860i	−0.743988	−	0.743988i	0.229355	−	0.973343i	$-0.426338\pi$
$163$	−9.49860	−	9.49860i	−0.743988	−	0.743988i	−0.973343	+	0.229355i	$0.926338\pi$
$164$	2.60623	+	2.60623i	0.203512	+	0.203512i
$165$		0			0
$166$	−10.5496			−0.818806
$167$	1.51129	−	1.51129i	0.116947	−	0.116947i	−0.646211	−	0.763158i	$-0.723648\pi$
$167$	1.51129	−	1.51129i	0.116947	−	0.116947i	0.763158	+	0.646211i	$0.223648\pi$
$168$		0			0
$169$	−0.222197			−0.0170921
$170$	−25.6688	−	10.4163i	−1.96871	−	0.798898i
$171$		0			0
$172$		−	3.81813i		−	0.291130i
$173$	3.73349	−	3.73349i	0.283852	−	0.283852i	−0.550791	−	0.834643i	$-0.685674\pi$
$173$	3.73349	−	3.73349i	0.283852	−	0.283852i	0.834643	+	0.550791i	$0.185674\pi$
$174$		0			0
$175$	7.52398	−	7.52398i	0.568760	−	0.568760i
$176$	7.90907	+	7.90907i	0.596168	+	0.596168i
$177$		0			0
$178$			17.1165i			1.28294i
$179$		−	7.77619i		−	0.581220i	−0.956842	−	0.290610i	$-0.906142\pi$
$179$		−	7.77619i		−	0.581220i	0.956842	−	0.290610i	$-0.0938582\pi$
$180$		0			0
$181$	0.647592	+	0.647592i	0.0481351	+	0.0481351i	0.730765	−	0.682630i	$-0.239164\pi$
$181$	0.647592	+	0.647592i	0.0481351	+	0.0481351i	−0.682630	+	0.730765i	$0.739164\pi$
$182$	3.85206	−	3.85206i	0.285533	−	0.285533i
$183$		0			0
$184$	−7.56592	+	7.56592i	−0.557767	+	0.557767i
$185$		−	24.2137i		−	1.78023i
$186$		0			0
$187$	8.67319	+	3.51957i	0.634247	+	0.257376i
$188$	5.08064			0.370544
$189$		0			0
$190$	−8.21814	+	8.21814i	−0.596207	+	0.596207i
$191$	−19.1658			−1.38679			−0.693393	−	0.720560i	$-0.743885\pi$
$191$	−19.1658			−1.38679			−0.693393	+	0.720560i	$0.743885\pi$
$192$		0			0
$193$	3.33144	+	3.33144i	0.239802	+	0.239802i	0.816768	−	0.576966i	$-0.195763\pi$
$193$	3.33144	+	3.33144i	0.239802	+	0.239802i	−0.576966	+	0.816768i	$0.695763\pi$
$194$	−16.9047	−	16.9047i	−1.21368	−	1.21368i
$195$		0			0
$196$			4.48794i			0.320567i
$197$	10.5323	+	10.5323i	0.750392	+	0.750392i	0.974552	−	0.224160i	$-0.0719638\pi$
$197$	10.5323	+	10.5323i	0.750392	+	0.750392i	−0.224160	+	0.974552i	$0.571964\pi$
$198$		0			0
$199$	13.2821	−	13.2821i	0.941542	−	0.941542i	−0.0568413	−	0.998383i	$-0.518103\pi$
$199$	13.2821	−	13.2821i	0.941542	−	0.941542i	0.998383	+	0.0568413i	$0.0181029\pi$
$200$	24.2091			1.71184
$201$		0			0
$202$		−	0.439071i		−	0.0308929i
$203$	2.03268			0.142666
$204$		0			0
$205$	−20.5359			−1.43429
$206$		−	5.01332i		−	0.349294i
$207$		0			0
$208$	17.6121			1.22118
$209$	2.77682	−	2.77682i	0.192077	−	0.192077i
$210$		0			0
$211$	4.15826	+	4.15826i	0.286266	+	0.286266i	0.835602	−	0.549336i	$-0.185119\pi$
$211$	4.15826	+	4.15826i	0.286266	+	0.286266i	−0.549336	+	0.835602i	$0.685119\pi$
$212$		−	1.96732i		−	0.135116i
$213$		0			0
$214$	22.9599	+	22.9599i	1.56951	+	1.56951i
$215$	15.0426	+	15.0426i	1.02589	+	1.02589i
$216$		0			0
$217$	−3.81209			−0.258781
$218$	0.836079	−	0.836079i	0.0566264	−	0.0566264i
$219$		0			0
$220$	6.73749			0.454242
$221$	13.5756	−	5.73812i	0.913193	−	0.385988i
$222$		0			0
$223$		−	5.58387i		−	0.373923i	−0.982367	−	0.186962i	$-0.940136\pi$
$223$		−	5.58387i		−	0.373923i	0.982367	−	0.186962i	$-0.0598640\pi$
$224$	2.57194	−	2.57194i	0.171845	−	0.171845i
$225$		0			0
$226$	−13.7714	+	13.7714i	−0.916061	+	0.916061i
$227$	19.4666	+	19.4666i	1.29204	+	1.29204i	0.933522	+	0.358519i	$0.116718\pi$
$227$	19.4666	+	19.4666i	1.29204	+	1.29204i	0.358519	+	0.933522i	$0.383282\pi$
$228$		0			0
$229$			3.57019i			0.235925i	0.993018	+	0.117962i	$0.0376362\pi$
$229$			3.57019i			0.235925i	−0.993018	+	0.117962i	$0.962364\pi$
$230$			34.2557i			2.25875i
$231$		0			0
$232$	3.27016	+	3.27016i	0.214696	+	0.214696i
$233$	−0.969360	+	0.969360i	−0.0635049	+	0.0635049i	−0.738146	−	0.674641i	$-0.764298\pi$
$233$	−0.969360	+	0.969360i	−0.0635049	+	0.0635049i	0.674641	+	0.738146i	$0.264298\pi$
$234$		0			0
$235$	−20.0166	+	20.0166i	−1.30574	+	1.30574i
$236$			5.39965i			0.351487i
$237$		0			0
$238$	2.36272	−	5.82240i	0.153153	−	0.377410i
$239$	−21.6121			−1.39797			−0.698986	−	0.715135i	$-0.746365\pi$
$239$	−21.6121			−1.39797			−0.698986	+	0.715135i	$0.746365\pi$
$240$		0			0
$241$	0.750810	−	0.750810i	0.0483639	−	0.0483639i	−0.682511	−	0.730875i	$-0.739112\pi$
$241$	0.750810	−	0.750810i	0.0483639	−	0.0483639i	0.730875	+	0.682511i	$0.239112\pi$
$242$	9.65952			0.620937
$243$		0			0
$244$	2.00765	+	2.00765i	0.128527	+	0.128527i
$245$	−17.6815	−	17.6815i	−1.12963	−	1.12963i
$246$		0			0
$247$		−	6.18350i		−	0.393446i
$248$	−6.13287	−	6.13287i	−0.389438	−	0.389438i
$249$		0			0
$250$	31.0508	−	31.0508i	1.96383	−	1.96383i
$251$	−7.29715			−0.460592			−0.230296	−	0.973121i	$-0.573969\pi$
$251$	−7.29715			−0.460592			−0.230296	+	0.973121i	$0.573969\pi$
$252$		0			0
$253$		−	11.5746i		−	0.727689i
$254$	4.64354			0.291361
$255$		0			0
$256$	15.4673			0.966708
$257$			22.5569i			1.40706i	0.710666	+	0.703530i	$0.248394\pi$
$257$			22.5569i			1.40706i	−0.710666	+	0.703530i	$0.751606\pi$
$258$		0			0
$259$	5.49236			0.341278
$260$	7.50162	−	7.50162i	0.465231	−	0.465231i
$261$		0			0
$262$	−9.26111	−	9.26111i	−0.572154	−	0.572154i
$263$		−	4.24919i		−	0.262016i	−0.991381	−	0.131008i	$-0.958179\pi$
$263$		−	4.24919i		−	0.262016i	0.991381	−	0.131008i	$-0.0418214\pi$
$264$		0			0
$265$	7.75081	+	7.75081i	0.476128	+	0.476128i
$266$	−1.86411	−	1.86411i	−0.114296	−	0.114296i
$267$		0			0
$268$	−8.78869			−0.536855
$269$	8.36776	−	8.36776i	0.510191	−	0.510191i	−0.404394	−	0.914585i	$-0.632517\pi$
$269$	8.36776	−	8.36776i	0.510191	−	0.510191i	0.914585	+	0.404394i	$0.132517\pi$
$270$		0			0
$271$	−11.8045			−0.717070			−0.358535	−	0.933516i	$-0.616724\pi$
$271$	−11.8045			−0.717070			−0.358535	+	0.933516i	$0.616724\pi$
$272$	18.7118	−	7.90907i	1.13457	−	0.479558i
$273$		0			0
$274$			0.170539i			0.0103027i
$275$	−18.5180	+	18.5180i	−1.11667	+	1.11667i
$276$		0			0
$277$	−7.37338	+	7.37338i	−0.443023	+	0.443023i	−0.893027	−	0.450003i	$-0.851423\pi$
$277$	−7.37338	+	7.37338i	−0.443023	+	0.443023i	0.450003	+	0.893027i	$0.351423\pi$
$278$	−16.8777	−	16.8777i	−1.01225	−	1.01225i
$279$		0			0
$280$			7.87140i			0.470406i
$281$		−	5.46697i		−	0.326132i	−0.986615	−	0.163066i	$-0.947862\pi$
$281$		−	5.46697i		−	0.326132i	0.986615	−	0.163066i	$-0.0521384\pi$
$282$		0			0
$283$	12.4716	+	12.4716i	0.741360	+	0.741360i	0.972840	−	0.231480i	$-0.0743567\pi$
$283$	12.4716	+	12.4716i	0.741360	+	0.741360i	−0.231480	+	0.972840i	$0.574357\pi$
$284$	0.786489	−	0.786489i	0.0466695	−	0.0466695i
$285$		0			0
$286$	−9.48065	+	9.48065i	−0.560603	+	0.560603i
$287$		−	4.65812i		−	0.274960i
$288$		0			0
$289$	11.8464	−	12.1928i	0.696846	−	0.717221i
$290$	14.8061			0.869442
$291$		0			0
$292$	−0.601239	+	0.601239i	−0.0351849	+	0.0351849i
$293$	−8.25845			−0.482464			−0.241232	−	0.970467i	$-0.577551\pi$
$293$	−8.25845			−0.482464			−0.241232	+	0.970467i	$0.577551\pi$
$294$		0			0
$295$	−21.2734	−	21.2734i	−1.23859	−	1.23859i
$296$	8.83608	+	8.83608i	0.513587	+	0.513587i
$297$		0			0
$298$			5.94069i			0.344135i
$299$	−12.8873	−	12.8873i	−0.745293	−	0.745293i
$300$		0			0
$301$	−3.41208	+	3.41208i	−0.196669	+	0.196669i
$302$	−12.5375			−0.721454
$303$		0			0
$304$		−	8.52295i		−	0.488825i
$305$	−15.8194			−0.905815
$306$		0			0
$307$	−9.94601			−0.567649			−0.283824	−	0.958876i	$-0.591603\pi$
$307$	−9.94601			−0.567649			−0.283824	+	0.958876i	$0.591603\pi$
$308$			1.52825i			0.0870803i
$309$		0			0
$310$	−27.7674			−1.57708
$311$	−11.7284	+	11.7284i	−0.665059	+	0.665059i	−0.956568	−	0.291509i	$-0.905843\pi$
$311$	−11.7284	+	11.7284i	−0.665059	+	0.665059i	0.291509	+	0.956568i	$0.405843\pi$
$312$		0			0
$313$	−14.5746	−	14.5746i	−0.823805	−	0.823805i	0.162846	−	0.986651i	$-0.447933\pi$
$313$	−14.5746	−	14.5746i	−0.823805	−	0.823805i	−0.986651	+	0.162846i	$0.947933\pi$
$314$			31.3210i			1.76755i
$315$		0			0
$316$	−6.13287	−	6.13287i	−0.345001	−	0.345001i
$317$	−3.01795	−	3.01795i	−0.169505	−	0.169505i	0.617257	−	0.786762i	$-0.288244\pi$
$317$	−3.01795	−	3.01795i	−0.169505	−	0.169505i	−0.786762	+	0.617257i	$0.788244\pi$
$318$		0			0
$319$	−5.00280			−0.280103
$320$	−9.60021	+	9.60021i	−0.536668	+	0.536668i
$321$		0			0
$322$	−7.77015			−0.433014
$323$	−2.77682	−	6.56957i	−0.154506	−	0.365540i
$324$		0			0
$325$			41.2363i			2.28738i
$326$	15.6938	−	15.6938i	0.869199	−	0.869199i
$327$		0			0
$328$	7.49397	−	7.49397i	0.413785	−	0.413785i
$329$	−4.54032	−	4.54032i	−0.250316	−	0.250316i
$330$		0			0
$331$			28.6105i			1.57258i	0.617860	+	0.786288i	$0.288000\pi$
$331$			28.6105i			1.57258i	−0.617860	+	0.786288i	$0.712000\pi$
$332$		−	4.66009i		−	0.255756i
$333$		0			0
$334$	2.49699	+	2.49699i	0.136629	+	0.136629i
$335$	34.6254	−	34.6254i	1.89179	−	1.89179i
$336$		0			0
$337$	22.1585	−	22.1585i	1.20705	−	1.20705i	0.235071	−	0.971978i	$-0.424468\pi$
$337$	22.1585	−	22.1585i	1.20705	−	1.20705i	0.971978	−	0.235071i	$-0.0755322\pi$
$338$		−	0.367119i		−	0.0199686i
$339$		0			0
$340$	4.60124	−	11.3387i	0.249537	−	0.614929i
$341$	9.38228			0.508079
$342$		0			0
$343$	8.57622	−	8.57622i	0.463072	−	0.463072i
$344$	−10.9787			−0.591930
$345$		0			0
$346$	6.16855	+	6.16855i	0.331623	+	0.331623i
$347$	8.51066	+	8.51066i	0.456876	+	0.456876i	0.897629	−	0.440752i	$-0.145288\pi$
$347$	8.51066	+	8.51066i	0.456876	+	0.456876i	−0.440752	+	0.897629i	$0.645288\pi$
$348$		0			0
$349$		−	33.3512i		−	1.78525i	−0.450799	−	0.892625i	$-0.648861\pi$
$349$		−	33.3512i		−	1.78525i	0.450799	−	0.892625i	$-0.351139\pi$
$350$	12.4313	+	12.4313i	0.664481	+	0.664481i
$351$		0			0
$352$	−6.33005	+	6.33005i	−0.337393	+	0.337393i
$353$	−6.56570			−0.349457			−0.174729	−	0.984617i	$-0.555905\pi$
$353$	−6.56570			−0.349457			−0.174729	+	0.984617i	$0.555905\pi$
$354$		0			0
$355$			6.19717i			0.328912i
$356$	−7.56093			−0.400728
$357$		0			0
$358$	12.8480			0.679038
$359$		−	21.5508i		−	1.13741i	−0.822541	−	0.568705i	$-0.807445\pi$
$359$		−	21.5508i		−	1.13741i	0.822541	−	0.568705i	$-0.192555\pi$
$360$		0			0
$361$	16.0077			0.842508
$362$	−1.06997	+	1.06997i	−0.0562361	+	0.0562361i
$363$		0			0
$364$	1.70158	+	1.70158i	0.0891870	+	0.0891870i
$365$		−	4.73749i		−	0.247972i
$366$		0			0
$367$	−25.1478	−	25.1478i	−1.31271	−	1.31271i	−0.919414	−	0.393292i	$-0.871336\pi$
$367$	−25.1478	−	25.1478i	−1.31271	−	1.31271i	−0.393292	−	0.919414i	$-0.628664\pi$
$368$	−17.7631	−	17.7631i	−0.925965	−	0.925965i
$369$		0			0
$370$	40.0065			2.07984
$371$	−1.75810	+	1.75810i	−0.0912761	+	0.0912761i
$372$		0			0
$373$	−35.8452			−1.85599			−0.927997	−	0.372588i	$-0.878471\pi$
$373$	−35.8452			−1.85599			−0.927997	+	0.372588i	$0.878471\pi$
$374$	−5.81511	+	14.3300i	−0.300692	+	0.740989i
$375$		0			0
$376$		−	14.6089i		−	0.753396i
$377$	−5.57019	+	5.57019i	−0.286879	+	0.286879i
$378$		0			0
$379$	15.5002	−	15.5002i	0.796193	−	0.796193i	−0.186300	−	0.982493i	$-0.559650\pi$
$379$	15.5002	−	15.5002i	0.796193	−	0.796193i	0.982493	+	0.186300i	$0.0596496\pi$
$380$	−3.63022	−	3.63022i	−0.186226	−	0.186226i
$381$		0			0
$382$		−	31.6661i		−	1.62018i
$383$		−	34.3109i		−	1.75321i	−0.481215	−	0.876603i	$-0.659804\pi$
$383$		−	34.3109i		−	1.75321i	0.481215	−	0.876603i	$-0.340196\pi$
$384$		0			0
$385$	−6.02097	−	6.02097i	−0.306857	−	0.306857i
$386$	−5.50428	+	5.50428i	−0.280160	+	0.280160i
$387$		0			0
$388$	7.46733	−	7.46733i	0.379096	−	0.379096i
$389$			34.1956i			1.73379i	0.498493	+	0.866894i	$0.333887\pi$
$389$			34.1956i			1.73379i	−0.498493	+	0.866894i	$0.666113\pi$
$390$		0			0
$391$	−19.4793	−	7.90465i	−0.985108	−	0.399755i
$392$	12.9047			0.651783
$393$		0			0
$394$	−17.4016	+	17.4016i	−0.876682	+	0.876682i
$395$	48.3242			2.43146
$396$		0			0
$397$	0.162887	+	0.162887i	0.00817507	+	0.00817507i	0.711183	−	0.703007i	$-0.248160\pi$
$397$	0.162887	+	0.162887i	0.00817507	+	0.00817507i	−0.703007	+	0.711183i	$0.748160\pi$
$398$	21.9450	+	21.9450i	1.10000	+	1.10000i
$399$		0			0
$400$			56.8376i			2.84188i
$401$	0.429041	+	0.429041i	0.0214253	+	0.0214253i	0.717738	−	0.696313i	$-0.245177\pi$
$401$	0.429041	+	0.429041i	0.0214253	+	0.0214253i	−0.696313	+	0.717738i	$0.745177\pi$
$402$		0			0
$403$	10.4464	−	10.4464i	0.520370	−	0.520370i
$404$	0.193952			0.00964947
$405$		0			0
$406$			3.35843i			0.166676i
$407$	−13.5177			−0.670049
$408$		0			0
$409$	−1.50925			−0.0746278			−0.0373139	−	0.999304i	$-0.511880\pi$
$409$	−1.50925			−0.0746278			−0.0373139	+	0.999304i	$0.511880\pi$
$410$		−	33.9299i		−	1.67568i
$411$		0			0
$412$	2.21454			0.109103
$413$	4.82541	−	4.82541i	0.237443	−	0.237443i
$414$		0			0
$415$	18.3597	+	18.3597i	0.901242	+	0.901242i
$416$			14.0959i			0.691110i
$417$		0			0
$418$	4.58792	+	4.58792i	0.224403	+	0.224403i
$419$	8.56997	+	8.56997i	0.418671	+	0.418671i	0.884745	−	0.466075i	$-0.154332\pi$
$419$	8.56997	+	8.56997i	0.418671	+	0.418671i	−0.466075	+	0.884745i	$0.654332\pi$
$420$		0			0
$421$	17.8730			0.871078			0.435539	−	0.900170i	$-0.356558\pi$
$421$	17.8730			0.871078			0.435539	+	0.900170i	$0.356558\pi$
$422$	−6.87037	+	6.87037i	−0.334444	+	0.334444i
$423$		0			0
$424$	−5.65685			−0.274721
$425$	18.5180	+	43.8109i	0.898253	+	2.12514i
$426$		0			0
$427$		−	3.58828i		−	0.173649i
$428$	−10.1421	+	10.1421i	−0.490239	+	0.490239i
$429$		0			0
$430$	−24.8537	+	24.8537i	−1.19855	+	1.19855i
$431$	−7.87442	−	7.87442i	−0.379297	−	0.379297i	0.491551	−	0.870849i	$-0.336430\pi$
$431$	−7.87442	−	7.87442i	−0.379297	−	0.379297i	−0.870849	+	0.491551i	$0.836430\pi$
$432$		0			0
$433$			29.1182i			1.39933i	0.714471	+	0.699665i	$0.246667\pi$
$433$			29.1182i			1.39933i	−0.714471	+	0.699665i	$0.753333\pi$
$434$		−	6.29842i		−	0.302334i
$435$		0			0
$436$	0.369323	+	0.369323i	0.0176874	+	0.0176874i
$437$	−6.23650	+	6.23650i	−0.298332	+	0.298332i
$438$		0			0
$439$	15.9776	−	15.9776i	0.762571	−	0.762571i	−0.214215	−	0.976786i	$-0.568719\pi$
$439$	15.9776	−	15.9776i	0.762571	−	0.762571i	0.976786	+	0.214215i	$0.0687194\pi$
$440$		−	19.3730i		−	0.923572i
$441$		0			0
$442$	9.48065	+	22.4299i	0.450949	+	1.06688i
$443$	−32.1976			−1.52975			−0.764877	−	0.644176i	$-0.777200\pi$
$443$	−32.1976			−1.52975			−0.764877	+	0.644176i	$0.777200\pi$
$444$		0			0
$445$	29.7883	−	29.7883i	1.41210	−	1.41210i
$446$	9.22579			0.436854
$447$		0			0
$448$	−2.17760	−	2.17760i	−0.102882	−	0.102882i
$449$	0.792171	+	0.792171i	0.0373849	+	0.0373849i	0.725552	−	0.688167i	$-0.241584\pi$
$449$	0.792171	+	0.792171i	0.0373849	+	0.0373849i	−0.688167	+	0.725552i	$0.741584\pi$
$450$		0			0
$451$			11.4645i			0.539844i
$452$	−6.08328	−	6.08328i	−0.286134	−	0.286134i
$453$		0			0
$454$	−32.1631	+	32.1631i	−1.50949	+	1.50949i
$455$	−13.4077			−0.628561
$456$		0			0
$457$			40.0795i			1.87484i	0.348203	+	0.937419i	$0.386792\pi$
$457$			40.0795i			1.87484i	−0.348203	+	0.937419i	$0.613208\pi$
$458$	−5.89875			−0.275631
$459$		0			0
$460$	−15.1318			−0.705526
$461$		−	4.99595i		−	0.232684i	−0.993209	−	0.116342i	$-0.962883\pi$
$461$		−	4.99595i		−	0.232684i	0.993209	−	0.116342i	$-0.0371169\pi$
$462$		0			0
$463$	−39.0452			−1.81458			−0.907292	−	0.420502i	$-0.861854\pi$
$463$	−39.0452			−1.81458			−0.907292	+	0.420502i	$0.861854\pi$
$464$	−7.67761	+	7.67761i	−0.356424	+	0.356424i
$465$		0			0
$466$	−1.60160	−	1.60160i	−0.0741926	−	0.0741926i
$467$			10.5242i			0.487002i	0.969901	+	0.243501i	$0.0782959\pi$
$467$			10.5242i			0.487002i	−0.969901	+	0.243501i	$0.921704\pi$
$468$		0			0
$469$	7.85403	+	7.85403i	0.362665	+	0.362665i
$470$	−33.0718	−	33.0718i	−1.52549	−	1.52549i
$471$		0			0
$472$	15.5262			0.714651
$473$	8.39778	−	8.39778i	0.386130	−	0.386130i
$474$		0			0
$475$	19.9553			0.915611
$476$	2.57194	+	1.04369i	0.117885	+	0.0478375i
$477$		0			0
$478$		−	35.7081i		−	1.63325i
$479$	18.3593	−	18.3593i	0.838858	−	0.838858i	−0.149851	−	0.988709i	$-0.547879\pi$
$479$	18.3593	−	18.3593i	0.838858	−	0.838858i	0.988709	+	0.149851i	$0.0478794\pi$
$480$		0			0
$481$	−15.0508	+	15.0508i	−0.686259	+	0.686259i
$482$	1.24050	+	1.24050i	0.0565034	+	0.0565034i
$483$		0			0
$484$			4.26692i			0.193951i
$485$			58.8392i			2.67175i
$486$		0			0
$487$	18.0599	+	18.0599i	0.818372	+	0.818372i	0.985872	−	0.167500i	$-0.0535696\pi$
$487$	18.0599	+	18.0599i	0.818372	+	0.818372i	−0.167500	+	0.985872i	$0.553570\pi$
$488$	5.77281	−	5.77281i	0.261323	−	0.261323i
$489$		0			0
$490$	29.2137	−	29.2137i	1.31974	−	1.31974i
$491$			2.50764i			0.113168i	0.998398	+	0.0565842i	$0.0180209\pi$
$491$			2.50764i			0.113168i	−0.998398	+	0.0565842i	$0.981979\pi$
$492$		0			0
$493$	−3.41657	+	8.41937i	−0.153874	+	0.379189i
$494$	10.2165			0.459663
$495$		0			0
$496$	14.3986	−	14.3986i	0.646517	−	0.646517i
$497$	−1.40569			−0.0630540
$498$		0			0
$499$	10.7671	+	10.7671i	0.482004	+	0.482004i	0.905771	−	0.423767i	$-0.139293\pi$
$499$	10.7671	+	10.7671i	0.482004	+	0.482004i	−0.423767	+	0.905771i	$0.639293\pi$
$500$	13.7162	+	13.7162i	0.613405	+	0.613405i
$501$		0			0
$502$		−	12.0565i		−	0.538109i
$503$	−27.6472	−	27.6472i	−1.23273	−	1.23273i	−0.962912	−	0.269815i	$-0.913038\pi$
$503$	−27.6472	−	27.6472i	−1.23273	−	1.23273i	−0.269815	−	0.962912i	$-0.586962\pi$
$504$		0			0
$505$	−0.764127	+	0.764127i	−0.0340032	+	0.0340032i
$506$	19.1238			0.850158
$507$		0			0
$508$			2.05120i			0.0910073i
$509$	31.9138			1.41455			0.707277	−	0.706937i	$-0.249924\pi$
$509$	31.9138			1.41455			0.707277	+	0.706937i	$0.249924\pi$
$510$		0			0
$511$	1.07460			0.0475374
$512$		−	1.25058i		−	0.0552685i
$513$		0			0
$514$	−37.2690			−1.64386
$515$	−8.72480	+	8.72480i	−0.384461	+	0.384461i
$516$		0			0
$517$	11.1746	+	11.1746i	0.491458	+	0.491458i
$518$			9.07460i			0.398715i
$519$		0			0
$520$	−21.5702	−	21.5702i	−0.945915	−	0.945915i
$521$	3.41572	+	3.41572i	0.149646	+	0.149646i	0.777960	−	0.628314i	$-0.216255\pi$
$521$	3.41572	+	3.41572i	0.149646	+	0.149646i	−0.628314	+	0.777960i	$0.716255\pi$
$522$		0			0
$523$	−36.5734			−1.59924			−0.799622	−	0.600503i	$-0.794967\pi$
$523$	−36.5734			−1.59924			−0.799622	+	0.600503i	$0.794967\pi$
$524$	4.09093	−	4.09093i	0.178713	−	0.178713i
$525$		0			0
$526$	7.02061			0.306113
$527$	6.40745	−	15.7897i	0.279113	−	0.687811i
$528$		0			0
$529$			2.99559i			0.130243i
$530$	−12.8061	+	12.8061i	−0.556260	+	0.556260i
$531$		0			0
$532$	0.823436	−	0.823436i	0.0357005	−	0.0357005i
$533$	12.7648	+	12.7648i	0.552904	+	0.552904i
$534$		0			0
$535$		−	79.9154i		−	3.45504i
$536$			25.2711i			1.09154i
$537$		0			0
$538$	13.8254	+	13.8254i	0.596056	+	0.596056i
$539$	−9.87099	+	9.87099i	−0.425174	+	0.425174i
$540$		0			0
$541$	7.79877	−	7.79877i	0.335295	−	0.335295i	−0.519298	−	0.854593i	$-0.673806\pi$
$541$	7.79877	−	7.79877i	0.335295	−	0.335295i	0.854593	+	0.519298i	$0.173806\pi$
$542$		−	19.5036i		−	0.837751i
$543$		0			0
$544$	6.33005	+	14.9760i	0.271398	+	0.642091i
$545$	−2.91010			−0.124655
$546$		0			0
$547$	−19.0046	+	19.0046i	−0.812579	+	0.812579i	−0.985020	−	0.172441i	$-0.944835\pi$
$547$	−19.0046	+	19.0046i	−0.812579	+	0.812579i	0.172441	+	0.985020i	$0.444835\pi$
$548$	−0.0753327			−0.00321805
$549$		0			0
$550$	−30.5958	−	30.5958i	−1.30461	−	1.30461i
$551$	2.69555	+	2.69555i	0.114834	+	0.114834i
$552$		0			0
$553$			10.9613i			0.466122i
$554$	−12.1825	−	12.1825i	−0.517583	−	0.517583i
$555$		0			0
$556$	7.45541	−	7.45541i	0.316180	−	0.316180i
$557$	−34.9146			−1.47938			−0.739690	−	0.672948i	$-0.765028\pi$
$557$	−34.9146			−1.47938			−0.739690	+	0.672948i	$0.765028\pi$
$558$		0			0
$559$		−	18.7004i		−	0.790943i
$560$	−18.4803			−0.780935
$561$		0			0
$562$	9.03266			0.381020
$563$			7.91334i			0.333507i	0.985999	+	0.166754i	$0.0533285\pi$
$563$			7.91334i			0.333507i	−0.985999	+	0.166754i	$0.946672\pi$
$564$		0			0
$565$	47.9335			2.01658
$566$	−20.6059	+	20.6059i	−0.866129	+	0.866129i
$567$		0			0
$568$	−2.26147	−	2.26147i	−0.0948893	−	0.0948893i
$569$		−	17.2956i		−	0.725070i	−0.931970	−	0.362535i	$-0.881911\pi$
$569$		−	17.2956i		−	0.725070i	0.931970	−	0.362535i	$-0.118089\pi$
$570$		0			0
$571$	13.7031	+	13.7031i	0.573455	+	0.573455i	0.933092	−	0.359637i	$-0.117099\pi$
$571$	13.7031	+	13.7031i	0.573455	+	0.573455i	−0.359637	+	0.933092i	$0.617099\pi$
$572$	−4.18791	−	4.18791i	−0.175105	−	0.175105i
$573$		0			0
$574$	7.69626			0.321236
$575$	41.5898	−	41.5898i	1.73441	−	1.73441i
$576$		0			0
$577$	−2.89714			−0.120610			−0.0603048	−	0.998180i	$-0.519207\pi$
$577$	−2.89714			−0.120610			−0.0603048	+	0.998180i	$0.519207\pi$
$578$	20.1452	+	19.5729i	0.837928	+	0.814123i
$579$		0			0
$580$			6.54032i			0.271572i
$581$	−4.16450	+	4.16450i	−0.172772	+	0.172772i
$582$		0			0
$583$	4.32703	−	4.32703i	0.179207	−	0.179207i
$584$	1.72881	+	1.72881i	0.0715385	+	0.0715385i
$585$		0			0
$586$		−	13.6448i		−	0.563662i
$587$			12.3165i			0.508357i	0.967157	+	0.254178i	$0.0818050\pi$
$587$			12.3165i			0.508357i	−0.967157	+	0.254178i	$0.918195\pi$
$588$		0			0
$589$	−5.05526	−	5.05526i	−0.208298	−	0.208298i
$590$	35.1484	−	35.1484i	1.44704	−	1.44704i
$591$		0			0
$592$	−20.7451	+	20.7451i	−0.852620	+	0.852620i
$593$		−	43.1763i		−	1.77304i	−0.462693	−	0.886519i	$-0.653117\pi$
$593$		−	43.1763i		−	1.77304i	0.462693	−	0.886519i	$-0.346883\pi$
$594$		0			0
$595$	−14.2448	+	6.02097i	−0.583979	+	0.246836i
$596$	−2.62420			−0.107491
$597$		0			0
$598$	21.2927	−	21.2927i	0.870725	−	0.870725i
$599$	6.70607			0.274003			0.137001	−	0.990571i	$-0.456254\pi$
$599$	6.70607			0.274003			0.137001	+	0.990571i	$0.456254\pi$
$600$		0			0
$601$	22.5138	+	22.5138i	0.918355	+	0.918355i	0.996910	−	0.0785544i	$-0.0250304\pi$
$601$	22.5138	+	22.5138i	0.918355	+	0.918355i	−0.0785544	+	0.996910i	$0.525030\pi$
$602$	−5.63751	−	5.63751i	−0.229768	−	0.229768i
$603$		0			0
$604$		−	5.53823i		−	0.225348i
$605$	−16.8107	−	16.8107i	−0.683452	−	0.683452i
$606$		0			0
$607$	−19.7402	+	19.7402i	−0.801228	+	0.801228i	−0.983288	−	0.182059i	$-0.941724\pi$
$607$	−19.7402	+	19.7402i	−0.801228	+	0.801228i	0.182059	+	0.983288i	$0.441724\pi$
$608$	6.82137			0.276643
$609$		0			0
$610$		−	26.1371i		−	1.05826i
$611$	24.8839			1.00669
$612$		0			0
$613$	−5.84314			−0.236002			−0.118001	−	0.993013i	$-0.537649\pi$
$613$	−5.84314			−0.236002			−0.118001	+	0.993013i	$0.537649\pi$
$614$		−	16.4330i		−	0.663183i
$615$		0			0
$616$	4.39435			0.177053
$617$	26.1998	−	26.1998i	1.05477	−	1.05477i	0.0563548	−	0.998411i	$-0.482052\pi$
$617$	26.1998	−	26.1998i	1.05477	−	1.05477i	0.998411	−	0.0563548i	$-0.0179478\pi$
$618$		0			0
$619$	11.4329	+	11.4329i	0.459527	+	0.459527i	0.898500	−	0.438973i	$-0.144658\pi$
$619$	11.4329	+	11.4329i	0.459527	+	0.459527i	−0.438973	+	0.898500i	$0.644658\pi$
$620$		−	12.2657i		−	0.492604i
$621$		0			0
$622$	−19.3780	−	19.3780i	−0.776987	−	0.776987i
$623$	6.75683	+	6.75683i	0.270707	+	0.270707i
$624$		0			0
$625$	−50.3976			−2.01590
$626$	24.0805	−	24.0805i	0.962450	−	0.962450i
$627$		0			0
$628$	−13.8355			−0.552097
$629$	−9.23168	+	22.7494i	−0.368091	+	0.907079i
$630$		0			0
$631$		−	31.6670i		−	1.26064i	−0.776334	−	0.630322i	$-0.782923\pi$
$631$		−	31.6670i		−	1.26064i	0.776334	−	0.630322i	$-0.217077\pi$
$632$	−17.6345	+	17.6345i	−0.701462	+	0.701462i
$633$		0			0
$634$	4.98632	−	4.98632i	0.198032	−	0.198032i
$635$	−8.08126	−	8.08126i	−0.320695	−	0.320695i
$636$		0			0
$637$			21.9810i			0.870919i
$638$		−	8.26575i		−	0.327244i
$639$		0			0
$640$	−38.5391	−	38.5391i	−1.52339	−	1.52339i
$641$	−11.2637	+	11.2637i	−0.444890	+	0.444890i	−0.893651	−	0.448762i	$-0.851865\pi$
$641$	−11.2637	+	11.2637i	−0.444890	+	0.444890i	0.448762	+	0.893651i	$0.351865\pi$
$642$		0			0
$643$	−11.7990	+	11.7990i	−0.465307	+	0.465307i	−0.900390	−	0.435083i	$-0.856719\pi$
$643$	−11.7990	+	11.7990i	−0.465307	+	0.465307i	0.435083	+	0.900390i	$0.356719\pi$
$644$		−	3.43233i		−	0.135253i
$645$		0			0
$646$	10.8544	−	4.58792i	0.427060	−	0.180509i
$647$	8.35044			0.328290			0.164145	−	0.986436i	$-0.447514\pi$
$647$	8.35044			0.328290			0.164145	+	0.986436i	$0.447514\pi$
$648$		0			0
$649$	−11.8762	+	11.8762i	−0.466184	+	0.466184i
$650$	−68.1316			−2.67234
$651$		0			0
$652$	6.93246	+	6.93246i	0.271496	+	0.271496i
$653$	20.2923	+	20.2923i	0.794100	+	0.794100i	0.982158	−	0.188058i	$-0.0602192\pi$
$653$	20.2923	+	20.2923i	0.794100	+	0.794100i	−0.188058	+	0.982158i	$0.560219\pi$
$654$		0			0
$655$			32.2347i			1.25951i
$656$	17.5942	+	17.5942i	0.686937	+	0.686937i
$657$		0			0
$658$	7.50162	−	7.50162i	0.292444	−	0.292444i
$659$	−40.3690			−1.57255			−0.786276	−	0.617876i	$-0.787993\pi$
$659$	−40.3690			−1.57255			−0.786276	+	0.617876i	$0.787993\pi$
$660$		0			0
$661$		−	39.4706i		−	1.53523i	−0.640913	−	0.767614i	$-0.721444\pi$
$661$		−	39.4706i		−	1.53523i	0.640913	−	0.767614i	$-0.278556\pi$
$662$	−47.2710			−1.83724
$663$		0			0
$664$	−13.3997			−0.520007
$665$			6.48830i			0.251606i
$666$		0			0
$667$	11.2359			0.435055
$668$	−1.10300	+	1.10300i	−0.0426764	+	0.0426764i
$669$		0			0
$670$	57.2090	+	57.2090i	2.21017	+	2.21017i
$671$			8.83145i			0.340934i
$672$		0			0
$673$	15.2775	+	15.2775i	0.588903	+	0.588903i	0.937334	−	0.348432i	$-0.113286\pi$
$673$	15.2775	+	15.2775i	0.588903	+	0.588903i	−0.348432	+	0.937334i	$0.613286\pi$
$674$	36.6107	+	36.6107i	1.41019	+	1.41019i
$675$		0			0
$676$	0.162168			0.00623724
$677$	−1.77542	+	1.77542i	−0.0682351	+	0.0682351i	−0.740401	−	0.672166i	$-0.765364\pi$
$677$	−1.77542	+	1.77542i	−0.0682351	+	0.0682351i	0.672166	+	0.740401i	$0.265364\pi$
$678$		0			0
$679$	−13.3464			−0.512187
$680$	−32.6034	−	13.2304i	−1.25029	−	0.507364i
$681$		0			0
$682$			15.5016i			0.593588i
$683$	−13.2528	+	13.2528i	−0.507106	+	0.507106i	−0.913637	−	0.406531i	$-0.866738\pi$
$683$	−13.2528	+	13.2528i	−0.507106	+	0.507106i	0.406531	+	0.913637i	$0.366738\pi$
$684$		0			0
$685$	0.296794	−	0.296794i	0.0113399	−	0.0113399i
$686$	14.1698	+	14.1698i	0.541006	+	0.541006i
$687$		0			0
$688$		−	25.7755i		−	0.982681i
$689$		−	9.63554i		−	0.367085i
$690$		0			0
$691$	−27.2733	−	27.2733i	−1.03752	−	1.03752i	−0.999268	−	0.0382556i	$-0.987820\pi$
$691$	−27.2733	−	27.2733i	−1.03752	−	1.03752i	−0.0382556	−	0.999268i	$-0.512180\pi$
$692$	−2.72485	+	2.72485i	−0.103583	+	0.103583i
$693$		0			0
$694$	−14.0615	+	14.0615i	−0.533768	+	0.533768i
$695$			58.7452i			2.22833i
$696$		0			0
$697$	19.2940	+	7.82948i	0.730813	+	0.296563i
$698$	55.1037			2.08570
$699$		0			0
$700$	−5.49131	+	5.49131i	−0.207552	+	0.207552i
$701$	−28.7827			−1.08711			−0.543553	−	0.839375i	$-0.682921\pi$
$701$	−28.7827			−1.08711			−0.543553	+	0.839375i	$0.682921\pi$
$702$		0			0
$703$	7.28348	+	7.28348i	0.274702	+	0.274702i
$704$	5.35948	+	5.35948i	0.201993	+	0.201993i
$705$		0			0
$706$		−	10.8480i		−	0.408270i
$707$	−0.173325	−	0.173325i	−0.00651858	−	0.00651858i
$708$		0			0
$709$	3.63869	−	3.63869i	0.136654	−	0.136654i	−0.635471	−	0.772125i	$-0.719194\pi$
$709$	3.63869	−	3.63869i	0.136654	−	0.136654i	0.772125	+	0.635471i	$0.219194\pi$
$710$	−10.2391			−0.384267
$711$		0			0
$712$			21.7407i			0.814768i
$713$	−21.0718			−0.789146
$714$		0			0
$715$	32.9988			1.23409
$716$			5.67538i			0.212099i
$717$		0			0
$718$	35.6068			1.32883
$719$	−22.2754	+	22.2754i	−0.830733	+	0.830733i	−0.987617	−	0.156884i	$-0.949855\pi$
$719$	−22.2754	+	22.2754i	−0.830733	+	0.830733i	0.156884	+	0.987617i	$0.449855\pi$
$720$		0			0
$721$	−1.97903	−	1.97903i	−0.0737030	−	0.0737030i
$722$			26.4482i			0.984300i
$723$		0			0
$724$	−0.472638	−	0.472638i	−0.0175655	−	0.0175655i
$725$	−17.9760	−	17.9760i	−0.667613	−	0.667613i
$726$		0			0
$727$	−31.2775			−1.16002			−0.580010	−	0.814610i	$-0.696951\pi$
$727$	−31.2775			−1.16002			−0.580010	+	0.814610i	$0.696951\pi$
$728$	4.89273	−	4.89273i	0.181337	−	0.181337i
$729$		0			0
$730$	7.82739			0.289705
$731$	−8.39778	−	19.8680i	−0.310603	−	0.734843i
$732$		0			0
$733$			18.8153i			0.694960i	0.937687	+	0.347480i	$0.112963\pi$
$733$			18.8153i			0.694960i	−0.937687	+	0.347480i	$0.887037\pi$
$734$	41.5498	−	41.5498i	1.53363	−	1.53363i
$735$		0			0
$736$	14.2167	−	14.2167i	0.524036	−	0.524036i
$737$	−19.3303	−	19.3303i	−0.712039	−	0.712039i
$738$		0			0
$739$		−	6.94762i		−	0.255572i	−0.991802	−	0.127786i	$-0.959213\pi$
$739$		−	6.94762i		−	0.255572i	0.991802	−	0.127786i	$-0.0407871\pi$
$740$			17.6722i			0.649641i
$741$		0			0
$742$	−2.90478	−	2.90478i	−0.106638	−	0.106638i
$743$	−24.0107	+	24.0107i	−0.880869	+	0.880869i	−0.993623	−	0.112754i	$-0.964033\pi$
$743$	−24.0107	+	24.0107i	−0.880869	+	0.880869i	0.112754	+	0.993623i	$0.464033\pi$
$744$		0			0
$745$	10.3387	−	10.3387i	0.378782	−	0.378782i
$746$		−	59.2243i		−	2.16835i
$747$		0			0
$748$	−6.33005	−	2.56872i	−0.231449	−	0.0939218i
$749$	18.1271			0.662349
$750$		0			0
$751$	−4.88971	+	4.88971i	−0.178428	+	0.178428i	−0.790670	−	0.612242i	$-0.790268\pi$
$751$	−4.88971	+	4.88971i	−0.178428	+	0.178428i	0.612242	+	0.790670i	$0.290268\pi$
$752$	34.2984			1.25073
$753$		0			0
$754$	−9.20320	−	9.20320i	−0.335161	−	0.335161i
$755$	21.8194	+	21.8194i	0.794089	+	0.794089i
$756$		0			0
$757$		−	1.86166i		−	0.0676633i	−0.999428	−	0.0338316i	$-0.989229\pi$
$757$		−	1.86166i		−	0.0676633i	0.999428	−	0.0338316i	$-0.0107710\pi$
$758$	25.6098	+	25.6098i	0.930191	+	0.930191i
$759$		0			0
$760$	−10.4384	+	10.4384i	−0.378639	+	0.378639i
$761$	49.2335			1.78471			0.892357	−	0.451330i	$-0.149050\pi$
$761$	49.2335			1.78471			0.892357	+	0.451330i	$0.149050\pi$
$762$		0			0
$763$		−	0.660093i		−	0.0238970i
$764$	13.9880			0.506066
$765$		0			0
$766$	56.6893			2.04827
$767$			26.4464i			0.954923i
$768$		0			0
$769$	−50.9303			−1.83659			−0.918296	−	0.395895i	$-0.870435\pi$
$769$	−50.9303			−1.83659			−0.918296	+	0.395895i	$0.870435\pi$
$770$	9.94798	−	9.94798i	0.358500	−	0.358500i
$771$		0			0
$772$	−2.43142	−	2.43142i	−0.0875087	−	0.0875087i
$773$			2.91614i			0.104886i	0.998624	+	0.0524431i	$0.0167008\pi$
$773$			2.91614i			0.104886i	−0.998624	+	0.0524431i	$0.983299\pi$
$774$		0			0
$775$	33.7123	+	33.7123i	1.21098	+	1.21098i
$776$	−21.4716	−	21.4716i	−0.770786	−	0.770786i
$777$		0			0
$778$	−56.4988			−2.02558
$779$	6.17719	−	6.17719i	0.221321	−	0.221321i
$780$		0			0
$781$	3.45968			0.123797
$782$	13.0602	−	32.1841i	0.467033	−	1.15090i
$783$		0			0
$784$			30.2972i			1.08204i
$785$	54.5087	−	54.5087i	1.94550	−	1.94550i
$786$		0			0
$787$	35.9869	−	35.9869i	1.28279	−	1.28279i	0.343724	−	0.939071i	$-0.388312\pi$
$787$	35.9869	−	35.9869i	1.28279	−	1.28279i	0.939071	−	0.343724i	$-0.111688\pi$
$788$	−7.68687	−	7.68687i	−0.273833	−	0.273833i
$789$		0			0
$790$			79.8424i			2.84067i
$791$			10.8727i			0.386588i
$792$		0			0
$793$	9.83306	+	9.83306i	0.349182	+	0.349182i
$794$	−0.269126	+	0.269126i	−0.00955092	+	0.00955092i
$795$		0			0
$796$	−9.69380	+	9.69380i	−0.343588	+	0.343588i
$797$			13.6061i			0.481952i	0.970531	+	0.240976i	$0.0774676\pi$
$797$			13.6061i			0.481952i	−0.970531	+	0.240976i	$0.922532\pi$
$798$		0			0
$799$	26.4375	−	11.1746i	0.935293	−	0.395329i
$800$	−45.4901			−1.60832
$801$		0			0
$802$	−0.708871	+	0.708871i	−0.0250311	+	0.0250311i
$803$	−2.64479			−0.0933326
$804$		0			0
$805$	13.5226	+	13.5226i	0.476609	+	0.476609i
$806$	17.2597	+	17.2597i	0.607948	+	0.607948i
$807$		0			0
$808$		−	0.557691i		−	0.0196195i
$809$	12.2992	+	12.2992i	0.432416	+	0.432416i	0.889450	−	0.457033i	$-0.151088\pi$
$809$	12.2992	+	12.2992i	0.432416	+	0.432416i	−0.457033	+	0.889450i	$0.651088\pi$
$810$		0			0
$811$	23.2841	−	23.2841i	0.817614	−	0.817614i	−0.168148	−	0.985762i	$-0.553779\pi$
$811$	23.2841	−	23.2841i	0.817614	−	0.817614i	0.985762	+	0.168148i	$0.0537787\pi$
$812$	−1.48353			−0.0520617
$813$		0			0
$814$		−	22.3343i		−	0.782817i
$815$	−54.6246			−1.91342
$816$		0			0
$817$	−9.04959			−0.316605
$818$		−	2.49362i		−	0.0871875i
$819$		0			0
$820$	14.9879			0.523401
$821$	30.9266	−	30.9266i	1.07935	−	1.07935i	0.0827780	−	0.996568i	$-0.473621\pi$
$821$	30.9266	−	30.9266i	1.07935	−	1.07935i	0.996568	−	0.0827780i	$-0.0263792\pi$
$822$		0			0
$823$	−1.18371	−	1.18371i	−0.0412617	−	0.0412617i	0.686175	−	0.727437i	$-0.259288\pi$
$823$	−1.18371	−	1.18371i	−0.0412617	−	0.0412617i	−0.727437	+	0.686175i	$0.759288\pi$
$824$		−	6.36771i		−	0.221830i
$825$		0			0
$826$	7.97265	+	7.97265i	0.277404	+	0.277404i
$827$	1.60525	+	1.60525i	0.0558198	+	0.0558198i	0.734466	−	0.678646i	$-0.237433\pi$
$827$	1.60525	+	1.60525i	0.0558198	+	0.0558198i	−0.678646	+	0.734466i	$0.737433\pi$
$828$		0			0
$829$	−19.2597			−0.668918			−0.334459	−	0.942410i	$-0.608554\pi$
$829$	−19.2597			−0.668918			−0.334459	+	0.942410i	$0.608554\pi$
$830$	−30.3343	+	30.3343i	−1.05292	+	1.05292i
$831$		0			0
$832$	11.9346			0.413760
$833$	9.87099	+	23.3534i	0.342010	+	0.809147i
$834$		0			0
$835$		−	8.69114i		−	0.300769i
$836$	−2.02663	+	2.02663i	−0.0700926	+	0.0700926i
$837$		0			0
$838$	−14.1595	+	14.1595i	−0.489132	+	0.489132i
$839$	−10.4694	−	10.4694i	−0.361443	−	0.361443i	0.502901	−	0.864344i	$-0.332266\pi$
$839$	−10.4694	−	10.4694i	−0.361443	−	0.361443i	−0.864344	+	0.502901i	$0.832266\pi$
$840$		0			0
$841$			24.1436i			0.832538i
$842$			29.5302i			1.01768i
$843$		0			0
$844$	−3.03486	−	3.03486i	−0.104464	−	0.104464i
$845$	−0.638906	+	0.638906i	−0.0219790	+	0.0219790i
$846$		0			0
$847$	3.81314	−	3.81314i	0.131021	−	0.131021i
$848$		−	13.2810i		−	0.456073i
$849$		0			0
$850$	−72.3854	+	30.5958i	−2.48280	+	1.04943i
$851$	30.3597			1.04072
$852$		0			0
$853$	4.49558	−	4.49558i	0.153926	−	0.153926i	−0.625943	−	0.779869i	$-0.715286\pi$
$853$	4.49558	−	4.49558i	0.153926	−	0.153926i	0.779869	+	0.625943i	$0.215286\pi$
$854$	5.92864			0.202874
$855$		0			0
$856$	29.1627	+	29.1627i	0.996762	+	0.996762i
$857$	−28.8720	−	28.8720i	−0.986248	−	0.986248i	0.0136588	−	0.999907i	$-0.495652\pi$
$857$	−28.8720	−	28.8720i	−0.986248	−	0.986248i	−0.999907	+	0.0136588i	$0.995652\pi$
$858$		0			0
$859$		−	22.1464i		−	0.755626i	−0.925882	−	0.377813i	$-0.876676\pi$
$859$		−	22.1464i		−	0.755626i	0.925882	−	0.377813i	$-0.123324\pi$
$860$	−10.9787	−	10.9787i	−0.374370	−	0.374370i
$861$		0			0
$862$	13.0103	−	13.0103i	0.443132	−	0.443132i
$863$	17.3423			0.590339			0.295170	−	0.955445i	$-0.404624\pi$
$863$	17.3423			0.590339			0.295170	+	0.955445i	$0.404624\pi$
$864$		0			0
$865$		−	21.4706i		−	0.730021i
$866$	−48.1097			−1.63483
$867$		0			0
$868$	2.78222			0.0944346
$869$		−	26.9779i		−	0.915161i
$870$		0			0
$871$	−43.0452			−1.45853
$872$	1.06195	−	1.06195i	0.0359623	−	0.0359623i
$873$		0			0
$874$	−10.3041	−	10.3041i	−0.348541	−	0.348541i
$875$		−	24.5149i		−	0.828756i
$876$		0			0
$877$	−21.3763	−	21.3763i	−0.721825	−	0.721825i	0.247152	−	0.968977i	$-0.420505\pi$
$877$	−21.3763	−	21.3763i	−0.721825	−	0.721825i	−0.968977	+	0.247152i	$0.920505\pi$
$878$	26.3986	+	26.3986i	0.890910	+	0.890910i
$879$		0			0
$880$	45.4835			1.53325
$881$	−7.47035	+	7.47035i	−0.251683	+	0.251683i	−0.821660	−	0.569978i	$-0.806952\pi$
$881$	−7.47035	+	7.47035i	−0.251683	+	0.251683i	0.569978	+	0.821660i	$0.306952\pi$
$882$		0			0
$883$	13.9150			0.468276			0.234138	−	0.972203i	$-0.424773\pi$
$883$	13.9150			0.468276			0.234138	+	0.972203i	$0.424773\pi$
$884$	−9.90801	+	4.18791i	−0.333243	+	0.140855i
$885$		0			0
$886$		−	53.1976i		−	1.78721i
$887$	−25.4307	+	25.4307i	−0.853878	+	0.853878i	−0.990608	−	0.136730i	$-0.956341\pi$
$887$	−25.4307	+	25.4307i	−0.853878	+	0.853878i	0.136730	+	0.990608i	$0.456341\pi$
$888$		0			0
$889$	1.83306	−	1.83306i	0.0614788	−	0.0614788i
$890$	49.2170	+	49.2170i	1.64976	+	1.64976i
$891$		0			0
$892$			4.07533i			0.136452i
$893$		−	12.0419i		−	0.402968i
$894$		0			0
$895$	−22.3597	−	22.3597i	−0.747402	−	0.747402i
$896$	8.74176	−	8.74176i	0.292042	−	0.292042i
$897$		0			0
$898$	−1.30884	+	1.30884i	−0.0436766	+	0.0436766i
$899$			9.10771i			0.303759i
$900$		0			0
$901$	−4.32703	−	10.2371i	−0.144154	−	0.341049i
$902$	−18.9420			−0.630698
$903$		0			0
$904$	−17.4919	+	17.4919i	−0.581772	+	0.581772i
$905$	3.72418			0.123796
$906$		0			0
$907$	−27.7075	−	27.7075i	−0.920012	−	0.920012i	0.0770180	−	0.997030i	$-0.475460\pi$
$907$	−27.7075	−	27.7075i	−0.920012	−	0.920012i	−0.997030	+	0.0770180i	$0.975460\pi$
$908$	−14.2075	−	14.2075i	−0.471492	−	0.471492i
$909$		0			0
$910$		−	22.1524i		−	0.734347i
$911$	7.02020	+	7.02020i	0.232590	+	0.232590i	0.813773	−	0.581183i	$-0.197410\pi$
$911$	7.02020	+	7.02020i	0.232590	+	0.232590i	−0.581183	+	0.813773i	$0.697410\pi$
$912$		0			0
$913$	10.2496	−	10.2496i	0.339213	−	0.339213i
$914$	−66.2202			−2.19037
$915$		0			0
$916$		−	2.60567i		−	0.0860938i
$917$	−7.31174			−0.241455
$918$		0			0
$919$	42.8795			1.41446			0.707232	−	0.706982i	$-0.249944\pi$
$919$	42.8795			1.41446			0.707232	+	0.706982i	$0.249944\pi$
$920$			43.5102i			1.43449i
$921$		0			0
$922$	8.25442			0.271845
$923$	3.85206	−	3.85206i	0.126792	−	0.126792i
$924$		0			0
$925$	−48.5718	−	48.5718i	−1.59703	−	1.59703i
$926$		−	64.5113i		−	2.11997i
$927$		0			0
$928$	−6.14480	−	6.14480i	−0.201713	−	0.201713i
$929$	12.8427	+	12.8427i	0.421356	+	0.421356i	0.885671	−	0.464314i	$-0.153699\pi$
$929$	12.8427	+	12.8427i	0.421356	+	0.421356i	−0.464314	+	0.885671i	$0.653699\pi$
$930$		0			0
$931$	10.6372			0.348619
$932$	0.707478	−	0.707478i	0.0231742	−	0.0231742i
$933$		0			0
$934$	−17.3883			−0.568963
$935$	35.0591	−	14.8188i	1.14656	−	0.484625i
$936$		0			0
$937$			1.60243i			0.0523492i	0.999657	+	0.0261746i	$0.00833258\pi$
$937$			1.60243i			0.0523492i	−0.999657	+	0.0261746i	$0.991667\pi$
$938$	−12.9766	+	12.9766i	−0.423701	+	0.423701i
$939$		0			0
$940$	14.6089	−	14.6089i	0.476490	−	0.476490i
$941$	−22.8780	−	22.8780i	−0.745802	−	0.745802i	0.227886	−	0.973688i	$-0.426819\pi$
$941$	−22.8780	−	22.8780i	−0.745802	−	0.745802i	−0.973688	+	0.227886i	$0.926819\pi$
$942$		0			0
$943$		−	25.7484i		−	0.838482i
$944$			36.4520i			1.18641i
$945$		0			0
$946$	13.8750	+	13.8750i	0.451115	+	0.451115i
$947$	17.8063	−	17.8063i	0.578626	−	0.578626i	−0.355898	−	0.934525i	$-0.615825\pi$
$947$	17.8063	−	17.8063i	0.578626	−	0.578626i	0.934525	+	0.355898i	$0.115825\pi$
$948$		0			0
$949$	−2.94474	+	2.94474i	−0.0955905	+	0.0955905i
$950$			32.9706i			1.06971i
$951$		0			0
$952$	3.00103	−	7.39538i	0.0972641	−	0.239686i
$953$	−54.0658			−1.75136			−0.875681	−	0.482889i	$-0.839587\pi$
$953$	−54.0658			−1.75136			−0.875681	+	0.482889i	$0.839587\pi$
$954$		0			0
$955$	−55.1093	+	55.1093i	−1.78330	+	1.78330i
$956$	15.7734			0.510148
$957$		0			0
$958$	30.3336	+	30.3336i	0.980036	+	0.980036i
$959$	0.0673212	+	0.0673212i	0.00217391	+	0.00217391i
$960$		0			0
$961$			13.9194i			0.449012i
$962$	−24.8673	−	24.8673i	−0.801755	−	0.801755i
$963$		0			0
$964$	−0.547971	+	0.547971i	−0.0176490	+	0.0176490i
$965$	19.1585			0.616733
$966$		0			0
$967$		−	2.17495i		−	0.0699418i	−0.999388	−	0.0349709i	$-0.988866\pi$
$967$		−	2.17495i		−	0.0699418i	0.999388	−	0.0349709i	$-0.0111338\pi$
$968$	12.2691			0.394345
$969$		0			0
$970$	−97.2154			−3.12140
$971$		−	47.4481i		−	1.52268i	−0.648352	−	0.761340i	$-0.724542\pi$
$971$		−	47.4481i		−	1.52268i	0.648352	−	0.761340i	$-0.275458\pi$
$972$		0			0
$973$	−13.3251			−0.427182
$974$	−29.8390	+	29.8390i	−0.956102	+	0.956102i
$975$		0			0
$976$	13.5533	+	13.5533i	0.433830	+	0.433830i
$977$		−	20.8226i		−	0.666175i	−0.942896	−	0.333087i	$-0.891910\pi$
$977$		−	20.8226i		−	0.666175i	0.942896	−	0.333087i	$-0.108090\pi$
$978$		0			0
$979$	−16.6299	−	16.6299i	−0.531493	−	0.531493i
$980$	12.9047	+	12.9047i	0.412224	+	0.412224i
$981$		0			0
$982$	−4.14319			−0.132214
$983$	−1.71854	+	1.71854i	−0.0548130	+	0.0548130i	−0.733982	−	0.679169i	$-0.762340\pi$
$983$	−1.71854	+	1.71854i	−0.0548130	+	0.0548130i	0.679169	+	0.733982i	$0.262340\pi$
$984$		0			0
$985$	60.5690			1.92989
$986$	−13.9107	−	5.64493i	−0.443006	−	0.179771i
$987$		0			0
$988$			4.51297i			0.143577i
$989$	−18.8607	+	18.8607i	−0.599735	+	0.599735i
$990$		0			0
$991$	−25.8643	+	25.8643i	−0.821608	+	0.821608i	−0.986339	−	0.164731i	$-0.947324\pi$
$991$	−25.8643	+	25.8643i	−0.821608	+	0.821608i	0.164731	+	0.986339i	$0.447324\pi$
$992$	11.5240	+	11.5240i	0.365887	+	0.365887i
$993$		0			0
$994$		−	2.32252i		−	0.0736658i
$995$		−	76.3827i		−	2.42150i
$996$		0			0
$997$	14.6448	+	14.6448i	0.463806	+	0.463806i	0.899901	−	0.436095i	$-0.143639\pi$
$997$	14.6448	+	14.6448i	0.463806	+	0.463806i	−0.436095	+	0.899901i	$0.643639\pi$
$998$	−17.7897	+	17.7897i	−0.563124	+	0.563124i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.f.b.55.3		8
3.2	odd	2		51.2.e.a.4.2	✓	8
4.3	odd	2		2448.2.be.x.1585.4		8
12.11	even	2		816.2.bd.e.769.1		8
17.8	even	8		2601.2.a.bf.1.3		4
17.9	even	8		2601.2.a.be.1.3		4
17.13	even	4	inner	153.2.f.b.64.2		8
51.2	odd	8		867.2.d.f.577.5		8
51.5	even	16		867.2.h.i.712.4		16
51.8	odd	8		867.2.a.k.1.2		4
51.11	even	16		867.2.h.i.688.3		16
51.14	even	16		867.2.h.k.733.1		16
51.20	even	16		867.2.h.k.733.2		16
51.23	even	16		867.2.h.i.688.4		16
51.26	odd	8		867.2.a.l.1.2		4
51.29	even	16		867.2.h.i.712.3		16
51.32	odd	8		867.2.d.f.577.6		8
51.38	odd	4		867.2.e.g.829.3		8
51.41	even	16		867.2.h.k.757.1		16
51.44	even	16		867.2.h.k.757.2		16
51.47	odd	4		51.2.e.a.13.3	yes	8
51.50	odd	2		867.2.e.g.616.2		8
68.47	odd	4		2448.2.be.x.1441.4		8
204.47	even	4		816.2.bd.e.625.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.2	✓	8	3.2	odd	2
51.2.e.a.13.3	yes	8	51.47	odd	4
153.2.f.b.55.3		8	1.1	even	1	trivial
153.2.f.b.64.2		8	17.13	even	4	inner
816.2.bd.e.625.1		8	204.47	even	4
816.2.bd.e.769.1		8	12.11	even	2
867.2.a.k.1.2		4	51.8	odd	8
867.2.a.l.1.2		4	51.26	odd	8
867.2.d.f.577.5		8	51.2	odd	8
867.2.d.f.577.6		8	51.32	odd	8
867.2.e.g.616.2		8	51.50	odd	2
867.2.e.g.829.3		8	51.38	odd	4
867.2.h.i.688.3		16	51.11	even	16
867.2.h.i.688.4		16	51.23	even	16
867.2.h.i.712.3		16	51.29	even	16
867.2.h.i.712.4		16	51.5	even	16
867.2.h.k.733.1		16	51.14	even	16
867.2.h.k.733.2		16	51.20	even	16
867.2.h.k.757.1		16	51.41	even	16
867.2.h.k.757.2		16	51.44	even	16
2448.2.be.x.1441.4		8	68.47	odd	4
2448.2.be.x.1585.4		8	4.3	odd	2
2601.2.a.be.1.3		4	17.9	even	8
2601.2.a.bf.1.3		4	17.8	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.65222i q^{2} -0.729840 q^{4} +(2.87540 - 2.87540i) q^{5} +(0.652223 + 0.652223i) q^{7} +2.09859i q^{8} +(4.75081 + 4.75081i) q^{10} +(-1.60525 - 1.60525i) q^{11} -3.57461 q^{13} +(-1.07762 + 1.07762i) q^{14} -4.92701 q^{16} +(-3.79779 + 1.60525i) q^{17} +1.72984i q^{19} +(-2.09859 + 2.09859i) q^{20} +(2.65222 - 2.65222i) q^{22} +(3.60525 + 3.60525i) q^{23} -11.5359i q^{25} -5.90604i q^{26} +(-0.476019 - 0.476019i) q^{28} +(1.55827 - 1.55827i) q^{29} +(-2.92238 + 2.92238i) q^{31} -3.94335i q^{32} +(-2.65222 - 6.27479i) q^{34} +3.75081 q^{35} +(4.21049 - 4.21049i) q^{37} -2.85808 q^{38} +(6.03429 + 6.03429i) q^{40} +(-3.57096 - 3.57096i) q^{41} +5.23146i q^{43} +(1.17157 + 1.17157i) q^{44} +(-5.95667 + 5.95667i) q^{46} -6.96130 q^{47} -6.14921i q^{49} +19.0599 q^{50} +2.60889 q^{52} +2.69555i q^{53} -9.23146 q^{55} +(-1.36875 + 1.36875i) q^{56} +(2.57461 + 2.57461i) q^{58} -7.39840i q^{59} +(-2.75081 - 2.75081i) q^{61} +(-4.82843 - 4.82843i) q^{62} -3.33873 q^{64} +(-10.2784 + 10.2784i) q^{65} +12.0419 q^{67} +(2.77178 - 1.17157i) q^{68} +6.19717i q^{70} +(-1.07762 + 1.07762i) q^{71} +(0.823796 - 0.823796i) q^{73} +(6.95667 + 6.95667i) q^{74} -1.26251i q^{76} -2.09396i q^{77} +(8.40303 + 8.40303i) q^{79} +(-14.1672 + 14.1672i) q^{80} +(5.90002 - 5.90002i) q^{82} +6.38508i q^{83} +(-6.30445 + 15.5359i) q^{85} -8.64354 q^{86} +(3.36875 - 3.36875i) q^{88} +10.3597 q^{89} +(-2.33144 - 2.33144i) q^{91} +(-2.63125 - 2.63125i) q^{92} -11.5016i q^{94} +(4.97399 + 4.97399i) q^{95} +(-10.2315 + 10.2315i) q^{97} +10.1599 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4} + 4 q^{5} - 4 q^{7} - 4 q^{13} - 24 q^{14} + 12 q^{16} + 4 q^{17} + 12 q^{20} + 12 q^{22} + 16 q^{23} - 8 q^{28} - 4 q^{29} - 8 q^{31} - 12 q^{34} - 8 q^{35} + 8 q^{37} - 24 q^{38} + 36 q^{40}+ \cdots + 76 q^{98}+O(q^{100}) \) 8 * q - 12 * q^4 + 4 * q^5 - 4 * q^7 - 4 * q^13 - 24 * q^14 + 12 * q^16 + 4 * q^17 + 12 * q^20 + 12 * q^22 + 16 * q^23 - 8 * q^28 - 4 * q^29 - 8 * q^31 - 12 * q^34 - 8 * q^35 + 8 * q^37 - 24 * q^38 + 36 * q^40 - 28 * q^41 + 32 * q^44 - 20 * q^46 + 8 * q^47 + 60 * q^50 - 16 * q^52 - 4 * q^55 + 24 * q^56 - 4 * q^58 + 16 * q^61 - 16 * q^62 + 4 * q^64 - 16 * q^65 + 8 * q^67 - 60 * q^68 - 24 * q^71 + 20 * q^73 + 28 * q^74 + 20 * q^79 - 60 * q^80 - 40 * q^82 - 32 * q^85 + 8 * q^86 - 8 * q^88 + 8 * q^89 - 36 * q^91 - 56 * q^92 - 8 * q^95 - 12 * q^97 + 76 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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