LMFDB - Embedded newform 429.2.m.b.109.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(109,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("429.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.m (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.11
Character	$\chi$	$=$	429.109
Dual form			429.2.m.b.307.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20600 + 1.20600i) q^{2} +1.00000 q^{3} +0.908895i q^{4} +(-0.200991 + 0.200991i) q^{5} +(1.20600 + 1.20600i) q^{6} +(3.33407 - 3.33407i) q^{7} +(1.31588 - 1.31588i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.20600 + 1.20600i) q^{2} +1.00000 q^{3} +0.908895i q^{4} +(-0.200991 + 0.200991i) q^{5} +(1.20600 + 1.20600i) q^{6} +(3.33407 - 3.33407i) q^{7} +(1.31588 - 1.31588i) q^{8} +1.00000 q^{9} -0.484791 q^{10} +(-1.51398 + 2.95091i) q^{11} +0.908895i q^{12} +(-2.46083 - 2.63521i) q^{13} +8.04182 q^{14} +(-0.200991 + 0.200991i) q^{15} +4.99170 q^{16} -7.25513 q^{17} +(1.20600 + 1.20600i) q^{18} +(1.18165 + 1.18165i) q^{19} +(-0.182679 - 0.182679i) q^{20} +(3.33407 - 3.33407i) q^{21} +(-5.38468 + 1.73295i) q^{22} +3.26417i q^{23} +(1.31588 - 1.31588i) q^{24} +4.91921i q^{25} +(0.210296 - 6.14585i) q^{26} +1.00000 q^{27} +(3.03032 + 3.03032i) q^{28} +5.67492i q^{29} -0.484791 q^{30} +(-3.86547 + 3.86547i) q^{31} +(3.38826 + 3.38826i) q^{32} +(-1.51398 + 2.95091i) q^{33} +(-8.74972 - 8.74972i) q^{34} +1.34024i q^{35} +0.908895i q^{36} +(2.95704 + 2.95704i) q^{37} +2.85014i q^{38} +(-2.46083 - 2.63521i) q^{39} +0.528958i q^{40} +(-4.75377 - 4.75377i) q^{41} +8.04182 q^{42} +2.81887 q^{43} +(-2.68207 - 1.37605i) q^{44} +(-0.200991 + 0.200991i) q^{45} +(-3.93660 + 3.93660i) q^{46} +(3.39398 + 3.39398i) q^{47} +4.99170 q^{48} -15.2321i q^{49} +(-5.93259 + 5.93259i) q^{50} -7.25513 q^{51} +(2.39513 - 2.23664i) q^{52} -5.44413 q^{53} +(1.20600 + 1.20600i) q^{54} +(-0.288811 - 0.897400i) q^{55} -8.77447i q^{56} +(1.18165 + 1.18165i) q^{57} +(-6.84397 + 6.84397i) q^{58} +(-5.68655 - 5.68655i) q^{59} +(-0.182679 - 0.182679i) q^{60} -14.3278i q^{61} -9.32355 q^{62} +(3.33407 - 3.33407i) q^{63} -1.81089i q^{64} +(1.02426 + 0.0350475i) q^{65} +(-5.38468 + 1.73295i) q^{66} +(-0.748559 + 0.748559i) q^{67} -6.59415i q^{68} +3.26417i q^{69} +(-1.61633 + 1.61633i) q^{70} +(6.94874 - 6.94874i) q^{71} +(1.31588 - 1.31588i) q^{72} +(-2.84928 + 2.84928i) q^{73} +7.13242i q^{74} +4.91921i q^{75} +(-1.07399 + 1.07399i) q^{76} +(4.79085 + 14.8863i) q^{77} +(0.210296 - 6.14585i) q^{78} +3.04264i q^{79} +(-1.00328 + 1.00328i) q^{80} +1.00000 q^{81} -11.4661i q^{82} +(4.10311 + 4.10311i) q^{83} +(3.03032 + 3.03032i) q^{84} +(1.45821 - 1.45821i) q^{85} +(3.39957 + 3.39957i) q^{86} +5.67492i q^{87} +(1.89083 + 5.87525i) q^{88} +(6.08327 + 6.08327i) q^{89} -0.484791 q^{90} +(-16.9906 - 0.581376i) q^{91} -2.96679 q^{92} +(-3.86547 + 3.86547i) q^{93} +8.18631i q^{94} -0.475000 q^{95} +(3.38826 + 3.38826i) q^{96} +(-1.76445 + 1.76445i) q^{97} +(18.3700 - 18.3700i) q^{98} +(-1.51398 + 2.95091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9}+O(q^{10}) $ 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9	$ 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9} - 4 q^{15} - 20 q^{16} - 16 q^{20} - 8 q^{22} + 12 q^{26} + 28 q^{27} + 8 q^{31} - 32 q^{34} - 12 q^{37} + 36 q^{44} - 4 q^{45} - 40 q^{47} - 20 q^{48} + 8 q^{53} - 16 q^{55} + 16 q^{58} - 44 q^{59} - 16 q^{60} - 8 q^{66} - 20 q^{67} - 36 q^{70} - 60 q^{71} + 12 q^{78} - 8 q^{80} + 28 q^{81} + 48 q^{86} + 32 q^{89} + 4 q^{91} + 64 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) $ 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9 - 4 * q^15 - 20 * q^16 - 16 * q^20 - 8 * q^22 + 12 * q^26 + 28 * q^27 + 8 * q^31 - 32 * q^34 - 12 * q^37 + 36 * q^44 - 4 * q^45 - 40 * q^47 - 20 * q^48 + 8 * q^53 - 16 * q^55 + 16 * q^58 - 44 * q^59 - 16 * q^60 - 8 * q^66 - 20 * q^67 - 36 * q^70 - 60 * q^71 + 12 * q^78 - 8 * q^80 + 28 * q^81 + 48 * q^86 + 32 * q^89 + 4 * q^91 + 64 * q^92 + 8 * q^93 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	1.20600	+	1.20600i	0.852774	+	0.852774i	0.990474	−	0.137700i	$-0.0439709\pi$
$2$	1.20600	+	1.20600i	0.852774	+	0.852774i	−0.137700	+	0.990474i	$0.543971\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$			0.908895i			0.454448i
$5$	−0.200991	+	0.200991i	−0.0898857	+	0.0898857i	−0.750620	−	0.660734i	$-0.770245\pi$
$5$	−0.200991	+	0.200991i	−0.0898857	+	0.0898857i	0.660734	+	0.750620i	$0.270245\pi$
$6$	1.20600	+	1.20600i	0.492349	+	0.492349i
$7$	3.33407	−	3.33407i	1.26016	−	1.26016i	0.309147	−	0.951014i	$-0.399956\pi$
$7$	3.33407	−	3.33407i	1.26016	−	1.26016i	0.951014	−	0.309147i	$-0.100044\pi$
$8$	1.31588	−	1.31588i	0.465233	−	0.465233i
$9$	1.00000			0.333333
$10$	−0.484791			−0.153304
$11$	−1.51398	+	2.95091i	−0.456481	+	0.889733i
$11$	−1.51398	+	2.95091i	−0.456481	+	0.889733i
$12$			0.908895i			0.262375i
$13$	−2.46083	−	2.63521i	−0.682512	−	0.730875i
$13$	−2.46083	−	2.63521i	−0.682512	−	0.730875i
$14$	8.04182			2.14927
$15$	−0.200991	+	0.200991i	−0.0518956	+	0.0518956i
$16$	4.99170			1.24792
$17$	−7.25513			−1.75963			−0.879814	−	0.475319i	$-0.842333\pi$
$17$	−7.25513			−1.75963			−0.879814	+	0.475319i	$0.842333\pi$
$18$	1.20600	+	1.20600i	0.284258	+	0.284258i
$19$	1.18165	+	1.18165i	0.271089	+	0.271089i	0.829538	−	0.558450i	$-0.188604\pi$
$19$	1.18165	+	1.18165i	0.271089	+	0.271089i	−0.558450	+	0.829538i	$0.688604\pi$
$20$	−0.182679	−	0.182679i	−0.0408484	−	0.0408484i
$21$	3.33407	−	3.33407i	0.727554	−	0.727554i
$22$	−5.38468	+	1.73295i	−1.14802	+	0.369466i
$23$			3.26417i			0.680626i	0.940312	+	0.340313i	$0.110533\pi$
$23$			3.26417i			0.680626i	−0.940312	+	0.340313i	$0.889467\pi$
$24$	1.31588	−	1.31588i	0.268602	−	0.268602i
$25$			4.91921i			0.983841i
$26$	0.210296	−	6.14585i	0.0412424	−	1.20530i
$27$	1.00000			0.192450
$28$	3.03032	+	3.03032i	0.572677	+	0.572677i
$29$			5.67492i			1.05381i	0.849926	+	0.526903i	$0.176647\pi$
$29$			5.67492i			1.05381i	−0.849926	+	0.526903i	$0.823353\pi$
$30$	−0.484791			−0.0885104
$31$	−3.86547	+	3.86547i	−0.694259	+	0.694259i	−0.963166	−	0.268907i	$-0.913338\pi$
$31$	−3.86547	+	3.86547i	−0.694259	+	0.694259i	0.268907	+	0.963166i	$0.413338\pi$
$32$	3.38826	+	3.38826i	0.598965	+	0.598965i
$33$	−1.51398	+	2.95091i	−0.263549	+	0.513688i
$34$	−8.74972	−	8.74972i	−1.50056	−	1.50056i
$35$			1.34024i			0.226541i
$36$			0.908895i			0.151483i
$37$	2.95704	+	2.95704i	0.486135	+	0.486135i	0.907084	−	0.420949i	$-0.138303\pi$
$37$	2.95704	+	2.95704i	0.486135	+	0.486135i	−0.420949	+	0.907084i	$0.638303\pi$
$38$			2.85014i			0.462355i
$39$	−2.46083	−	2.63521i	−0.394048	−	0.421971i
$40$			0.528958i			0.0836356i
$41$	−4.75377	−	4.75377i	−0.742413	−	0.742413i	0.230628	−	0.973042i	$-0.425922\pi$
$41$	−4.75377	−	4.75377i	−0.742413	−	0.742413i	−0.973042	+	0.230628i	$0.925922\pi$
$42$	8.04182			1.24088
$43$	2.81887			0.429873			0.214937	−	0.976628i	$-0.431046\pi$
$43$	2.81887			0.429873			0.214937	+	0.976628i	$0.431046\pi$
$44$	−2.68207	−	1.37605i	−0.404337	−	0.207447i
$45$	−0.200991	+	0.200991i	−0.0299619	+	0.0299619i
$46$	−3.93660	+	3.93660i	−0.580420	+	0.580420i
$47$	3.39398	+	3.39398i	0.495063	+	0.495063i	0.909897	−	0.414834i	$-0.136160\pi$
$47$	3.39398	+	3.39398i	0.495063	+	0.495063i	−0.414834	+	0.909897i	$0.636160\pi$
$48$	4.99170			0.720490
$49$		−	15.2321i		−	2.17601i
$50$	−5.93259	+	5.93259i	−0.838994	+	0.838994i
$51$	−7.25513			−1.01592
$52$	2.39513	−	2.23664i	0.332144	−	0.310166i
$53$	−5.44413			−0.747809			−0.373904	−	0.927467i	$-0.621981\pi$
$53$	−5.44413			−0.747809			−0.373904	+	0.927467i	$0.621981\pi$
$54$	1.20600	+	1.20600i	0.164116	+	0.164116i
$55$	−0.288811	−	0.897400i	−0.0389432	−	0.121005i
$56$		−	8.77447i		−	1.17254i
$57$	1.18165	+	1.18165i	0.156513	+	0.156513i
$58$	−6.84397	+	6.84397i	−0.898658	+	0.898658i
$59$	−5.68655	−	5.68655i	−0.740325	−	0.740325i	0.232315	−	0.972641i	$-0.425370\pi$
$59$	−5.68655	−	5.68655i	−0.740325	−	0.740325i	−0.972641	+	0.232315i	$0.925370\pi$
$60$	−0.182679	−	0.182679i	−0.0235838	−	0.0235838i
$61$		−	14.3278i		−	1.83448i	−0.398330	−	0.917242i	$-0.630410\pi$
$61$		−	14.3278i		−	1.83448i	0.398330	−	0.917242i	$-0.369590\pi$
$62$	−9.32355			−1.18409
$63$	3.33407	−	3.33407i	0.420054	−	0.420054i
$64$		−	1.81089i		−	0.226361i
$65$	1.02426	+	0.0350475i	0.127043	+	0.00434711i
$66$	−5.38468	+	1.73295i	−0.662808	+	0.213312i
$67$	−0.748559	+	0.748559i	−0.0914511	+	0.0914511i	−0.751352	−	0.659901i	$-0.770598\pi$
$67$	−0.748559	+	0.748559i	−0.0914511	+	0.0914511i	0.659901	+	0.751352i	$0.270598\pi$
$68$		−	6.59415i		−	0.799658i
$69$			3.26417i			0.392960i
$70$	−1.61633	+	1.61633i	−0.193188	+	0.193188i
$71$	6.94874	−	6.94874i	0.824664	−	0.824664i	−0.162109	−	0.986773i	$-0.551829\pi$
$71$	6.94874	−	6.94874i	0.824664	−	0.824664i	0.986773	+	0.162109i	$0.0518295\pi$
$72$	1.31588	−	1.31588i	0.155078	−	0.155078i
$73$	−2.84928	+	2.84928i	−0.333483	+	0.333483i	−0.853908	−	0.520424i	$-0.825774\pi$
$73$	−2.84928	+	2.84928i	−0.333483	+	0.333483i	0.520424	+	0.853908i	$0.325774\pi$
$74$			7.13242i			0.829127i
$75$			4.91921i			0.568021i
$76$	−1.07399	+	1.07399i	−0.123196	+	0.123196i
$77$	4.79085	+	14.8863i	0.545968	+	1.69645i
$78$	0.210296	−	6.14585i	0.0238113	−	0.695880i
$79$			3.04264i			0.342323i	0.985243	+	0.171162i	$0.0547520\pi$
$79$			3.04264i			0.342323i	−0.985243	+	0.171162i	$0.945248\pi$
$80$	−1.00328	+	1.00328i	−0.112171	+	0.112171i
$81$	1.00000			0.111111
$82$		−	11.4661i		−	1.26622i
$83$	4.10311	+	4.10311i	0.450375	+	0.450375i	0.895479	−	0.445104i	$-0.146833\pi$
$83$	4.10311	+	4.10311i	0.450375	+	0.450375i	−0.445104	+	0.895479i	$0.646833\pi$
$84$	3.03032	+	3.03032i	0.330635	+	0.330635i
$85$	1.45821	−	1.45821i	0.158165	−	0.158165i
$86$	3.39957	+	3.39957i	0.366585	+	0.366585i
$87$			5.67492i			0.608415i
$88$	1.89083	+	5.87525i	0.201563	+	0.626303i
$89$	6.08327	+	6.08327i	0.644826	+	0.644826i	0.951738	−	0.306912i	$-0.0992958\pi$
$89$	6.08327	+	6.08327i	0.644826	+	0.644826i	−0.306912	+	0.951738i	$0.599296\pi$
$90$	−0.484791			−0.0511015
$91$	−16.9906	−	0.581376i	−1.78109	−	0.0609447i
$92$	−2.96679			−0.309309
$93$	−3.86547	+	3.86547i	−0.400831	+	0.400831i
$94$			8.18631i			0.844354i
$95$	−0.475000			−0.0487340
$96$	3.38826	+	3.38826i	0.345813	+	0.345813i
$97$	−1.76445	+	1.76445i	−0.179153	+	0.179153i	−0.790987	−	0.611833i	$-0.790432\pi$
$97$	−1.76445	+	1.76445i	−0.179153	+	0.179153i	0.611833	+	0.790987i	$0.290432\pi$
$98$	18.3700	−	18.3700i	1.85565	−	1.85565i
$99$	−1.51398	+	2.95091i	−0.152160	+	0.296578i
$100$	−4.47104			−0.447104
$101$	17.5489			1.74618			0.873089	−	0.487561i	$-0.162113\pi$
$101$	17.5489			1.74618			0.873089	+	0.487561i	$0.162113\pi$
$102$	−8.74972	−	8.74972i	−0.866352	−	0.866352i
$103$		−	3.92179i		−	0.386426i	−0.981157	−	0.193213i	$-0.938109\pi$
$103$		−	3.92179i		−	0.386426i	0.981157	−	0.193213i	$-0.0618908\pi$
$104$	−6.70576	−	0.229455i	−0.657554	−	0.0224999i
$105$			1.34024i			0.130794i
$106$	−6.56565	−	6.56565i	−0.637712	−	0.637712i
$107$		−	0.546231i		−	0.0528062i	−0.999651	−	0.0264031i	$-0.991595\pi$
$107$		−	0.546231i		−	0.0528062i	0.999651	−	0.0264031i	$-0.00840534\pi$
$108$			0.908895i			0.0874585i
$109$	−4.52795	−	4.52795i	−0.433699	−	0.433699i	0.456186	−	0.889885i	$-0.349215\pi$
$109$	−4.52795	−	4.52795i	−0.433699	−	0.433699i	−0.889885	+	0.456186i	$0.849215\pi$
$110$	0.733962	−	1.43058i	0.0699806	−	0.136400i
$111$	2.95704	+	2.95704i	0.280670	+	0.280670i
$112$	16.6427	−	16.6427i	1.57259	−	1.57259i
$113$	5.58972			0.525836			0.262918	−	0.964818i	$-0.415315\pi$
$113$	5.58972			0.525836			0.262918	+	0.964818i	$0.415315\pi$
$114$			2.85014i			0.266941i
$115$	−0.656067	−	0.656067i	−0.0611786	−	0.0611786i
$116$	−5.15790			−0.478899
$117$	−2.46083	−	2.63521i	−0.227504	−	0.243625i
$118$		−	13.7160i		−	1.26266i
$119$	−24.1891	+	24.1891i	−2.21741	+	2.21741i
$120$			0.528958i			0.0482871i
$121$	−6.41575	−	8.93522i	−0.583250	−	0.812292i
$122$	17.2794	−	17.2794i	1.56440	−	1.56440i
$123$	−4.75377	−	4.75377i	−0.428633	−	0.428633i
$124$	−3.51331	−	3.51331i	−0.315504	−	0.315504i
$125$	−1.99367	−	1.99367i	−0.178319	−	0.178319i
$126$	8.04182			0.716422
$127$	−10.9493			−0.971598			−0.485799	−	0.874071i	$-0.661471\pi$
$127$	−10.9493			−0.971598			−0.485799	+	0.874071i	$0.661471\pi$
$128$	8.96046	−	8.96046i	0.792000	−	0.792000i
$129$	2.81887			0.248187
$130$	1.19299	+	1.27752i	0.104632	+	0.112046i
$131$		−	13.8031i		−	1.20598i	−0.797747	−	0.602992i	$-0.793975\pi$
$131$		−	13.8031i		−	1.20598i	0.797747	−	0.602992i	$-0.206025\pi$
$132$	−2.68207	−	1.37605i	−0.233444	−	0.119769i
$133$	7.87940			0.683231
$134$	−1.80553			−0.155974
$135$	−0.200991	+	0.200991i	−0.0172985	+	0.0172985i
$136$	−9.54686	+	9.54686i	−0.818637	+	0.818637i
$137$	−12.6531	−	12.6531i	−1.08103	−	1.08103i	−0.996414	−	0.0846164i	$-0.973034\pi$
$137$	−12.6531	−	12.6531i	−1.08103	−	1.08103i	−0.0846164	−	0.996414i	$-0.526966\pi$
$138$	−3.93660	+	3.93660i	−0.335106	+	0.335106i
$139$			16.0680i			1.36287i	0.731880	+	0.681433i	$0.238643\pi$
$139$			16.0680i			1.36287i	−0.731880	+	0.681433i	$0.761357\pi$
$140$	−1.21813			−0.102951
$141$	3.39398	+	3.39398i	0.285825	+	0.285825i
$142$	16.7604			1.40650
$143$	11.5019	−	3.27206i	0.961837	−	0.273623i
$144$	4.99170			0.415975
$145$	−1.14060	−	1.14060i	−0.0947221	−	0.0947221i
$146$	−6.87250			−0.568772
$147$		−	15.2321i		−	1.25632i
$148$	−2.68764	+	2.68764i	−0.220923	+	0.220923i
$149$	10.6538	+	10.6538i	0.872794	+	0.872794i	0.992776	−	0.119982i	$-0.0382838\pi$
$149$	10.6538	+	10.6538i	0.872794	+	0.872794i	−0.119982	+	0.992776i	$0.538284\pi$
$150$	−5.93259	+	5.93259i	−0.484394	+	0.484394i
$151$	2.70436	−	2.70436i	0.220078	−	0.220078i	−0.588453	−	0.808531i	$-0.700263\pi$
$151$	2.70436	−	2.70436i	0.220078	−	0.220078i	0.808531	+	0.588453i	$0.200263\pi$
$152$	3.10981			0.252239
$153$	−7.25513			−0.586543
$154$	−12.1751	+	23.7307i	−0.981099	+	1.91227i
$155$		−	1.55385i		−	0.124808i
$156$	2.39513	−	2.23664i	0.191764	−	0.179074i
$157$	13.0749			1.04349			0.521746	−	0.853101i	$-0.325281\pi$
$157$	13.0749			1.04349			0.521746	+	0.853101i	$0.325281\pi$
$158$	−3.66943	+	3.66943i	−0.291924	+	0.291924i
$159$	−5.44413			−0.431748
$160$	−1.36202			−0.107677
$161$	10.8830	+	10.8830i	0.857698	+	0.857698i
$162$	1.20600	+	1.20600i	0.0947527	+	0.0947527i
$163$	−3.24947	−	3.24947i	−0.254518	−	0.254518i	0.568302	−	0.822820i	$-0.307601\pi$
$163$	−3.24947	−	3.24947i	−0.254518	−	0.254518i	−0.822820	+	0.568302i	$0.807601\pi$
$164$	4.32067	−	4.32067i	0.337388	−	0.337388i
$165$	−0.288811	−	0.897400i	−0.0224839	−	0.0698625i
$166$			9.89674i			0.768136i
$167$	−3.87790	+	3.87790i	−0.300081	+	0.300081i	−0.841046	−	0.540964i	$-0.818059\pi$
$167$	−3.87790	+	3.87790i	−0.300081	+	0.300081i	0.540964	+	0.841046i	$0.318059\pi$
$168$		−	8.77447i		−	0.676965i
$169$	−0.888616	+	12.9696i	−0.0683551	+	0.997661i
$170$	3.51722			0.269759
$171$	1.18165	+	1.18165i	0.0903628	+	0.0903628i
$172$			2.56205i			0.195355i
$173$	−8.75558			−0.665675			−0.332837	−	0.942984i	$-0.608006\pi$
$173$	−8.75558			−0.665675			−0.332837	+	0.942984i	$0.608006\pi$
$174$	−6.84397	+	6.84397i	−0.518840	+	0.518840i
$175$	16.4010	+	16.4010i	1.23980	+	1.23980i
$176$	−7.55731	+	14.7301i	−0.569654	+	1.11032i
$177$	−5.68655	−	5.68655i	−0.427427	−	0.427427i
$178$			14.6729i			1.09978i
$179$		−	8.37650i		−	0.626089i	−0.949738	−	0.313044i	$-0.898651\pi$
$179$		−	8.37650i		−	0.626089i	0.949738	−	0.313044i	$-0.101349\pi$
$180$	−0.182679	−	0.182679i	−0.0136161	−	0.0136161i
$181$		−	8.13564i		−	0.604717i	−0.953194	−	0.302359i	$-0.902226\pi$
$181$		−	8.13564i		−	0.604717i	0.953194	−	0.302359i	$-0.0977740\pi$
$182$	−19.7896	−	21.1918i	−1.46690	−	1.57084i
$183$		−	14.3278i		−	1.05914i
$184$	4.29524	+	4.29524i	0.316650	+	0.316650i
$185$	−1.18868			−0.0873932
$186$	−9.32355			−0.683636
$187$	10.9841	−	21.4092i	0.803236	−	1.56560i
$188$	−3.08477	+	3.08477i	−0.224980	+	0.224980i
$189$	3.33407	−	3.33407i	0.242518	−	0.242518i
$190$	−0.572852	−	0.572852i	−0.0415591	−	0.0415591i
$191$	−1.28415			−0.0929180			−0.0464590	−	0.998920i	$-0.514794\pi$
$191$	−1.28415			−0.0929180			−0.0464590	+	0.998920i	$0.514794\pi$
$192$		−	1.81089i		−	0.130690i
$193$	−18.7908	+	18.7908i	−1.35259	+	1.35259i	−0.469838	+	0.882753i	$0.655688\pi$
$193$	−18.7908	+	18.7908i	−1.35259	+	1.35259i	−0.882753	+	0.469838i	$0.844312\pi$
$194$	−4.25588			−0.305555
$195$	1.02426	+	0.0350475i	0.0733485	+	0.00250981i
$196$	13.8444			0.988884
$197$	12.3045	+	12.3045i	0.876663	+	0.876663i	0.993188	−	0.116525i	$-0.0371755\pi$
$197$	12.3045	+	12.3045i	0.876663	+	0.876663i	−0.116525	+	0.993188i	$0.537176\pi$
$198$	−5.38468	+	1.73295i	−0.382672	+	0.123155i
$199$		−	20.0985i		−	1.42475i	−0.701801	−	0.712373i	$-0.747621\pi$
$199$		−	20.0985i		−	1.42475i	0.701801	−	0.712373i	$-0.252379\pi$
$200$	6.47307	+	6.47307i	0.457715	+	0.457715i
$201$	−0.748559	+	0.748559i	−0.0527993	+	0.0527993i
$202$	21.1640	+	21.1640i	1.48910	+	1.48910i
$203$	18.9206	+	18.9206i	1.32796	+	1.32796i
$204$		−	6.59415i		−	0.461683i
$205$	1.91092			0.133465
$206$	4.72970	−	4.72970i	0.329534	−	0.329534i
$207$			3.26417i			0.226875i
$208$	−12.2837	−	13.1542i	−0.851724	−	0.912077i
$209$	−5.27592	+	1.69795i	−0.364943	+	0.117450i
$210$	−1.61633	+	1.61633i	−0.111537	+	0.111537i
$211$		−	21.6318i		−	1.48919i	−0.667515	−	0.744597i	$-0.732642\pi$
$211$		−	21.6318i		−	1.48919i	0.667515	−	0.744597i	$-0.267358\pi$
$212$		−	4.94814i		−	0.339840i
$213$	6.94874	−	6.94874i	0.476120	−	0.476120i
$214$	0.658758	−	0.658758i	0.0450317	−	0.0450317i
$215$	−0.566566	+	0.566566i	−0.0386395	+	0.0386395i
$216$	1.31588	−	1.31588i	0.0895341	−	0.0895341i
$217$			25.7755i			1.74976i
$218$		−	10.9215i		−	0.739695i
$219$	−2.84928	+	2.84928i	−0.192537	+	0.192537i
$220$	0.815643	−	0.262499i	0.0549906	−	0.0176976i
$221$	17.8537	+	19.1188i	1.20097	+	1.28607i
$222$			7.13242i			0.478697i
$223$	−18.0992	+	18.0992i	−1.21201	+	1.21201i	−0.241651	+	0.970363i	$0.577689\pi$
$223$	−18.0992	+	18.0992i	−1.21201	+	1.21201i	−0.970363	+	0.241651i	$0.922311\pi$
$224$	22.5934			1.50959
$225$			4.91921i			0.327947i
$226$	6.74123	+	6.74123i	0.448420	+	0.448420i
$227$	0.513536	+	0.513536i	0.0340846	+	0.0340846i	0.723944	−	0.689859i	$-0.242328\pi$
$227$	0.513536	+	0.513536i	0.0340846	+	0.0340846i	−0.689859	+	0.723944i	$0.742328\pi$
$228$	−1.07399	+	1.07399i	−0.0711270	+	0.0711270i
$229$	12.6249	+	12.6249i	0.834274	+	0.834274i	0.988098	−	0.153824i	$-0.0491589\pi$
$229$	12.6249	+	12.6249i	0.834274	+	0.834274i	−0.153824	+	0.988098i	$0.549159\pi$
$230$		−	1.58244i		−	0.104343i
$231$	4.79085	+	14.8863i	0.315215	+	0.979444i
$232$	7.46749	+	7.46749i	0.490265	+	0.490265i
$233$	−22.5952			−1.48026			−0.740130	−	0.672464i	$-0.765236\pi$
$233$	−22.5952			−1.48026			−0.740130	+	0.672464i	$0.765236\pi$
$234$	0.210296	−	6.14585i	0.0137475	−	0.401766i
$235$	−1.36432			−0.0889982
$236$	5.16847	−	5.16847i	0.336439	−	0.336439i
$237$			3.04264i			0.197640i
$238$	−58.3444			−3.78191
$239$	3.72061	+	3.72061i	0.240666	+	0.240666i	0.817126	−	0.576459i	$-0.195566\pi$
$239$	3.72061	+	3.72061i	0.240666	+	0.240666i	−0.576459	+	0.817126i	$0.695566\pi$
$240$	−1.00328	+	1.00328i	−0.0647618	+	0.0647618i
$241$	7.81915	−	7.81915i	0.503676	−	0.503676i	−0.408902	−	0.912578i	$-0.634088\pi$
$241$	7.81915	−	7.81915i	0.503676	−	0.503676i	0.912578	+	0.408902i	$0.134088\pi$
$242$	3.03848	−	18.5133i	0.195321	−	1.19008i
$243$	1.00000			0.0641500
$244$	13.0225			0.833677
$245$	3.06151	+	3.06151i	0.195593	+	0.195593i
$246$		−	11.4661i		−	0.731054i
$247$	0.206049	−	6.02172i	0.0131106	−	0.383153i
$248$			10.1730i			0.645984i
$249$	4.10311	+	4.10311i	0.260024	+	0.260024i
$250$		−	4.80874i		−	0.304132i
$251$		−	14.5266i		−	0.916911i	−0.888717	−	0.458456i	$-0.848403\pi$
$251$		−	14.5266i		−	0.916911i	0.888717	−	0.458456i	$-0.151597\pi$
$252$	3.03032	+	3.03032i	0.190892	+	0.190892i
$253$	−9.63227	−	4.94187i	−0.605575	−	0.310693i
$254$	−13.2050	−	13.2050i	−0.828553	−	0.828553i
$255$	1.45821	−	1.45821i	0.0913169	−	0.0913169i
$256$	17.9909			1.12443
$257$		−	2.83504i		−	0.176845i	−0.996083	−	0.0884226i	$-0.971817\pi$
$257$		−	2.83504i		−	0.176845i	0.996083	−	0.0884226i	$-0.0281826\pi$
$258$	3.39957	+	3.39957i	0.211648	+	0.211648i
$259$	19.7180			1.22522
$260$	−0.0318545	+	0.930941i	−0.00197553	+	0.0577345i
$261$			5.67492i			0.351268i
$262$	16.6466	−	16.6466i	1.02843	−	1.02843i
$263$		−	14.5178i		−	0.895209i	−0.894232	−	0.447604i	$-0.852277\pi$
$263$		−	14.5178i		−	0.895209i	0.894232	−	0.447604i	$-0.147723\pi$
$264$	1.89083	+	5.87525i	0.116373	+	0.361596i
$265$	1.09422	−	1.09422i	0.0672174	−	0.0672174i
$266$	9.50259	+	9.50259i	0.582641	+	0.582641i
$267$	6.08327	+	6.08327i	0.372290	+	0.372290i
$268$	−0.680362	−	0.680362i	−0.0415597	−	0.0415597i
$269$	−23.0188			−1.40348			−0.701740	−	0.712433i	$-0.747593\pi$
$269$	−23.0188			−1.40348			−0.701740	+	0.712433i	$0.747593\pi$
$270$	−0.484791			−0.0295035
$271$	−17.0008	+	17.0008i	−1.03272	+	1.03272i	−0.0332760	+	0.999446i	$0.510594\pi$
$271$	−17.0008	+	17.0008i	−1.03272	+	1.03272i	−0.999446	+	0.0332760i	$0.989406\pi$
$272$	−36.2154			−2.19588
$273$	−16.9906	−	0.581376i	−1.02832	−	0.0351865i
$274$		−	30.5195i		−	1.84375i
$275$	−14.5161	−	7.44756i	−0.875356	−	0.449105i
$276$	−2.96679			−0.178579
$277$	27.4149			1.64720			0.823601	−	0.567169i	$-0.191962\pi$
$277$	27.4149			1.64720			0.823601	+	0.567169i	$0.191962\pi$
$278$	−19.3780	+	19.3780i	−1.16222	+	1.16222i
$279$	−3.86547	+	3.86547i	−0.231420	+	0.231420i
$280$	1.76359	+	1.76359i	0.105394	+	0.105394i
$281$	−3.55759	+	3.55759i	−0.212228	+	0.212228i	−0.805213	−	0.592985i	$-0.797949\pi$
$281$	−3.55759	+	3.55759i	−0.212228	+	0.212228i	0.592985	+	0.805213i	$0.297949\pi$
$282$			8.18631i			0.487488i
$283$	25.2088			1.49851			0.749253	−	0.662284i	$-0.230413\pi$
$283$	25.2088			1.49851			0.749253	+	0.662284i	$0.230413\pi$
$284$	6.31568	+	6.31568i	0.374767	+	0.374767i
$285$	−0.475000			−0.0281366
$286$	17.8175	+	9.92523i	1.05357	+	0.586891i
$287$	−31.6988			−1.87112
$288$	3.38826	+	3.38826i	0.199655	+	0.199655i
$289$	35.6369			2.09629
$290$		−	2.75115i		−	0.161553i
$291$	−1.76445	+	1.76445i	−0.103434	+	0.103434i
$292$	−2.58970	−	2.58970i	−0.151551	−	0.151551i
$293$	−14.1743	+	14.1743i	−0.828069	+	0.828069i	−0.987250	−	0.159180i	$-0.949115\pi$
$293$	−14.1743	+	14.1743i	−0.828069	+	0.828069i	0.159180	+	0.987250i	$0.449115\pi$
$294$	18.3700	−	18.3700i	1.07136	−	1.07136i
$295$	2.28588			0.133089
$296$	7.78222			0.452332
$297$	−1.51398	+	2.95091i	−0.0878498	+	0.171229i
$298$			25.6971i			1.48859i
$299$	8.60175	−	8.03256i	0.497452	−	0.464535i
$300$	−4.47104			−0.258136
$301$	9.39831	−	9.39831i	0.541709	−	0.541709i
$302$	6.52295			0.375353
$303$	17.5489			1.00816
$304$	5.89843	+	5.89843i	0.338298	+	0.338298i
$305$	2.87975	+	2.87975i	0.164894	+	0.164894i
$306$	−8.74972	−	8.74972i	−0.500188	−	0.500188i
$307$	8.82445	−	8.82445i	0.503638	−	0.503638i	−0.408929	−	0.912566i	$-0.634097\pi$
$307$	8.82445	−	8.82445i	0.503638	−	0.503638i	0.912566	+	0.408929i	$0.134097\pi$
$308$	−13.5301	+	4.35438i	−0.770946	+	0.248114i
$309$		−	3.92179i		−	0.223103i
$310$	1.87395	−	1.87395i	0.106433	−	0.106433i
$311$		−	15.5102i		−	0.879502i	−0.898120	−	0.439751i	$-0.855067\pi$
$311$		−	15.5102i		−	0.879502i	0.898120	−	0.439751i	$-0.144933\pi$
$312$	−6.70576	−	0.229455i	−0.379639	−	0.0129903i
$313$	28.7631			1.62579			0.812895	−	0.582411i	$-0.197891\pi$
$313$	28.7631			1.62579			0.812895	+	0.582411i	$0.197891\pi$
$314$	15.7684	+	15.7684i	0.889863	+	0.889863i
$315$			1.34024i			0.0755137i
$316$	−2.76544			−0.155568
$317$	11.7770	−	11.7770i	0.661463	−	0.661463i	−0.294262	−	0.955725i	$-0.595074\pi$
$317$	11.7770	−	11.7770i	0.661463	−	0.661463i	0.955725	+	0.294262i	$0.0950737\pi$
$318$	−6.56565	−	6.56565i	−0.368183	−	0.368183i
$319$	−16.7462	−	8.59168i	−0.937606	−	0.481042i
$320$	0.363971	+	0.363971i	0.0203466	+	0.0203466i
$321$		−	0.546231i		−	0.0304877i
$322$			26.2498i			1.46285i
$323$	−8.57301	−	8.57301i	−0.477015	−	0.477015i
$324$			0.908895i			0.0504942i
$325$	12.9631	−	12.1053i	0.719064	−	0.671483i
$326$		−	7.83776i		−	0.434093i
$327$	−4.52795	−	4.52795i	−0.250396	−	0.250396i
$328$	−12.5107			−0.690790
$329$	22.6316			1.24772
$330$	0.733962	−	1.43058i	0.0404033	−	0.0787506i
$331$	0.0573492	−	0.0573492i	0.00315220	−	0.00315220i	−0.705529	−	0.708681i	$-0.749291\pi$
$331$	0.0573492	−	0.0573492i	0.00315220	−	0.00315220i	0.708681	+	0.705529i	$0.249291\pi$
$332$	−3.72930	+	3.72930i	−0.204672	+	0.204672i
$333$	2.95704	+	2.95704i	0.162045	+	0.162045i
$334$	−9.35354			−0.511803
$335$		−	0.300907i		−	0.0164403i
$336$	16.6427	−	16.6427i	0.907933	−	0.907933i
$337$	3.94748			0.215033			0.107516	−	0.994203i	$-0.465710\pi$
$337$	3.94748			0.215033			0.107516	+	0.994203i	$0.465710\pi$
$338$	−16.7131	+	14.5697i	−0.909071	+	0.792488i
$339$	5.58972			0.303592
$340$	1.32536	+	1.32536i	0.0718779	+	0.0718779i
$341$	−5.55443	−	17.2589i	−0.300789	−	0.934621i
$342$			2.85014i			0.154118i
$343$	−27.4464	−	27.4464i	−1.48197	−	1.48197i
$344$	3.70928	−	3.70928i	0.199991	−	0.199991i
$345$	−0.656067	−	0.656067i	−0.0353215	−	0.0353215i
$346$	−10.5593	−	10.5593i	−0.567670	−	0.567670i
$347$		−	3.45221i		−	0.185324i	−0.995698	−	0.0926622i	$-0.970462\pi$
$347$		−	3.45221i		−	0.185324i	0.995698	−	0.0926622i	$-0.0295377\pi$
$348$	−5.15790			−0.276493
$349$	5.50942	−	5.50942i	0.294912	−	0.294912i	−0.544105	−	0.839017i	$-0.683131\pi$
$349$	5.50942	−	5.50942i	0.294912	−	0.294912i	0.839017	+	0.544105i	$0.183131\pi$
$350$			39.5594i			2.11454i
$351$	−2.46083	−	2.63521i	−0.131349	−	0.140657i
$352$	−15.1282	+	4.86871i	−0.806335	+	0.259503i
$353$	7.13058	−	7.13058i	0.379522	−	0.379522i	−0.491407	−	0.870930i	$-0.663517\pi$
$353$	7.13058	−	7.13058i	0.379522	−	0.379522i	0.870930	+	0.491407i	$0.163517\pi$
$354$		−	13.7160i		−	0.728997i
$355$			2.79327i			0.148251i
$356$	−5.52906	+	5.52906i	−0.293040	+	0.293040i
$357$	−24.1891	+	24.1891i	−1.28022	+	1.28022i
$358$	10.1021	−	10.1021i	0.533912	−	0.533912i
$359$	−16.0603	+	16.0603i	−0.847632	+	0.847632i	−0.989837	−	0.142205i	$-0.954581\pi$
$359$	−16.0603	+	16.0603i	−0.847632	+	0.847632i	0.142205	+	0.989837i	$0.454581\pi$
$360$			0.528958i			0.0278785i
$361$		−	16.2074i		−	0.853022i
$362$	9.81162	−	9.81162i	0.515687	−	0.515687i
$363$	−6.41575	−	8.93522i	−0.336740	−	0.468977i
$364$	0.528410	−	15.4426i	0.0276962	−	0.809414i
$365$		−	1.14536i		−	0.0599508i
$366$	17.2794	−	17.2794i	0.903207	−	0.903207i
$367$	−35.5649			−1.85647			−0.928236	−	0.371993i	$-0.878675\pi$
$367$	−35.5649			−1.85647			−0.928236	+	0.371993i	$0.878675\pi$
$368$			16.2937i			0.849370i
$369$	−4.75377	−	4.75377i	−0.247471	−	0.247471i
$370$	−1.43355	−	1.43355i	−0.0745267	−	0.0745267i
$371$	−18.1511	+	18.1511i	−0.942360	+	0.942360i
$372$	−3.51331	−	3.51331i	−0.182156	−	0.182156i
$373$			21.1566i			1.09545i	0.836659	+	0.547724i	$0.184506\pi$
$373$			21.1566i			1.09545i	−0.836659	+	0.547724i	$0.815494\pi$
$374$	39.0665	−	12.5728i	2.02008	−	0.650123i
$375$	−1.99367	−	1.99367i	−0.102953	−	0.102953i
$376$	8.93213			0.460639
$377$	14.9546	−	13.9650i	0.770199	−	0.719235i
$378$	8.04182			0.413626
$379$	12.9964	−	12.9964i	0.667579	−	0.667579i	−0.289576	−	0.957155i	$-0.593514\pi$
$379$	12.9964	−	12.9964i	0.667579	−	0.667579i	0.957155	+	0.289576i	$0.0935143\pi$
$380$		−	0.431725i		−	0.0221470i
$381$	−10.9493			−0.560952
$382$	−1.54869	−	1.54869i	−0.0792381	−	0.0792381i
$383$	15.7374	−	15.7374i	0.804144	−	0.804144i	−0.179596	−	0.983740i	$-0.557479\pi$
$383$	15.7374	−	15.7374i	0.804144	−	0.804144i	0.983740	+	0.179596i	$0.0574792\pi$
$384$	8.96046	−	8.96046i	0.457261	−	0.457261i
$385$	−3.95491	−	2.02908i	−0.201561	−	0.103412i
$386$	−45.3236			−2.30691
$387$	2.81887			0.143291
$388$	−1.60370	−	1.60370i	−0.0814158	−	0.0814158i
$389$			6.41847i			0.325429i	0.986673	+	0.162715i	$0.0520250\pi$
$389$			6.41847i			0.325429i	−0.986673	+	0.162715i	$0.947975\pi$
$390$	1.19299	+	1.27752i	0.0604094	+	0.0646900i
$391$		−	23.6820i		−	1.19765i
$392$	−20.0436	−	20.0436i	−1.01235	−	1.01235i
$393$		−	13.8031i		−	0.696275i
$394$			29.6787i			1.49519i
$395$	−0.611541	−	0.611541i	−0.0307700	−	0.0307700i
$396$	−2.68207	−	1.37605i	−0.134779	−	0.0691489i
$397$	13.2341	+	13.2341i	0.664198	+	0.664198i	0.956367	−	0.292168i	$-0.0943768\pi$
$397$	13.2341	+	13.2341i	0.664198	+	0.664198i	−0.292168	+	0.956367i	$0.594377\pi$
$398$	24.2389	−	24.2389i	1.21499	−	1.21499i
$399$	7.87940			0.394463
$400$			24.5552i			1.22776i
$401$	2.12792	+	2.12792i	0.106263	+	0.106263i	0.758239	−	0.651976i	$-0.226060\pi$
$401$	2.12792	+	2.12792i	0.106263	+	0.106263i	−0.651976	+	0.758239i	$0.726060\pi$
$402$	−1.80553			−0.0900517
$403$	19.6986	+	0.674038i	0.981256	+	0.0335762i
$404$			15.9501i			0.793546i
$405$	−0.200991	+	0.200991i	−0.00998730	+	0.00998730i
$406$			45.6366i			2.26491i
$407$	−13.2029	+	4.24908i	−0.654442	+	0.210619i
$408$	−9.54686	+	9.54686i	−0.472640	+	0.472640i
$409$	5.55755	+	5.55755i	0.274803	+	0.274803i	0.831030	−	0.556227i	$-0.187752\pi$
$409$	5.55755	+	5.55755i	0.274803	+	0.274803i	−0.556227	+	0.831030i	$0.687752\pi$
$410$	2.30458	+	2.30458i	0.113815	+	0.113815i
$411$	−12.6531	−	12.6531i	−0.624133	−	0.624133i
$412$	3.56450			0.175610
$413$	−37.9187			−1.86586
$414$	−3.93660	+	3.93660i	−0.193473	+	0.193473i
$415$	−1.64937			−0.0809646
$416$	0.590824	−	17.2667i	0.0289675	−	0.846569i
$417$			16.0680i			0.786852i
$418$	−8.41052	−	4.31505i	−0.411372	−	0.211056i
$419$	−11.0697			−0.540791			−0.270396	−	0.962749i	$-0.587155\pi$
$419$	−11.0697			−0.540791			−0.270396	+	0.962749i	$0.587155\pi$
$420$	−1.21813			−0.0594388
$421$	3.62745	−	3.62745i	0.176791	−	0.176791i	−0.613164	−	0.789955i	$-0.710104\pi$
$421$	3.62745	−	3.62745i	0.176791	−	0.176791i	0.789955	+	0.613164i	$0.210104\pi$
$422$	26.0880	−	26.0880i	1.26995	−	1.26995i
$423$	3.39398	+	3.39398i	0.165021	+	0.165021i
$424$	−7.16381	+	7.16381i	−0.347905	+	0.347905i
$425$		−	35.6895i		−	1.73119i
$426$	16.7604			0.812046
$427$	−47.7699	−	47.7699i	−2.31175	−	2.31175i
$428$	0.496467			0.0239976
$429$	11.5019	−	3.27206i	0.555317	−	0.157976i
$430$	−1.36656			−0.0659015
$431$	5.17800	+	5.17800i	0.249415	+	0.249415i	0.820731	−	0.571315i	$-0.193567\pi$
$431$	5.17800	+	5.17800i	0.249415	+	0.249415i	−0.571315	+	0.820731i	$0.693567\pi$
$432$	4.99170			0.240163
$433$			29.3459i			1.41027i	0.709072	+	0.705137i	$0.249114\pi$
$433$			29.3459i			1.41027i	−0.709072	+	0.705137i	$0.750886\pi$
$434$	−31.0854	+	31.0854i	−1.49215	+	1.49215i
$435$	−1.14060	−	1.14060i	−0.0546878	−	0.0546878i
$436$	4.11543	−	4.11543i	0.197093	−	0.197093i
$437$	−3.85709	+	3.85709i	−0.184510	+	0.184510i
$438$	−6.87250			−0.328381
$439$	−28.6462			−1.36721			−0.683604	−	0.729854i	$-0.739588\pi$
$439$	−28.6462			−1.36721			−0.683604	+	0.729854i	$0.739588\pi$
$440$	−1.56091	−	0.800830i	−0.0744134	−	0.0381781i
$441$		−	15.2321i		−	0.725338i
$442$	−1.52572	+	44.5889i	−0.0725713	+	2.12088i
$443$	−16.3682			−0.777679			−0.388839	−	0.921306i	$-0.627124\pi$
$443$	−16.3682			−0.777679			−0.388839	+	0.921306i	$0.627124\pi$
$444$	−2.68764	+	2.68764i	−0.127550	+	0.127550i
$445$	−2.44536			−0.115921
$446$	−43.6555			−2.06715
$447$	10.6538	+	10.6538i	0.503908	+	0.503908i
$448$	−6.03763	−	6.03763i	−0.285251	−	0.285251i
$449$	−5.62755	−	5.62755i	−0.265580	−	0.265580i	0.561736	−	0.827316i	$-0.310134\pi$
$449$	−5.62755	−	5.62755i	−0.265580	−	0.265580i	−0.827316	+	0.561736i	$0.810134\pi$
$450$	−5.93259	+	5.93259i	−0.279665	+	0.279665i
$451$	21.2250	−	6.83085i	0.999447	−	0.321652i
$452$			5.08047i			0.238965i
$453$	2.70436	−	2.70436i	0.127062	−	0.127062i
$454$			1.23865i			0.0581329i
$455$	3.53179	−	3.29809i	0.165573	−	0.154617i
$456$	3.10981			0.145630
$457$	17.4431	+	17.4431i	0.815955	+	0.815955i	0.985519	−	0.169564i	$-0.0542360\pi$
$457$	17.4431	+	17.4431i	0.815955	+	0.815955i	−0.169564	+	0.985519i	$0.554236\pi$
$458$			30.4513i			1.42290i
$459$	−7.25513			−0.338640
$460$	0.596296	−	0.596296i	0.0278024	−	0.0278024i
$461$	−12.6607	−	12.6607i	−0.589669	−	0.589669i	0.347873	−	0.937542i	$-0.386904\pi$
$461$	−12.6607	−	12.6607i	−0.589669	−	0.589669i	−0.937542	+	0.347873i	$0.886904\pi$
$462$	−12.1751	+	23.7307i	−0.566438	+	1.10405i
$463$	14.2561	+	14.2561i	0.662535	+	0.662535i	0.955977	−	0.293442i	$-0.0948007\pi$
$463$	14.2561	+	14.2561i	0.662535	+	0.662535i	−0.293442	+	0.955977i	$0.594801\pi$
$464$			28.3275i			1.31507i
$465$		−	1.55385i		−	0.0720579i
$466$	−27.2499	−	27.2499i	−1.26233	−	1.26233i
$467$			3.80081i			0.175880i	0.996126	+	0.0879402i	$0.0280285\pi$
$467$			3.80081i			0.175880i	−0.996126	+	0.0879402i	$0.971972\pi$
$468$	2.39513	−	2.23664i	0.110715	−	0.103389i
$469$			4.99150i			0.230486i
$470$	−1.64537	−	1.64537i	−0.0758954	−	0.0758954i
$471$	13.0749			0.602461
$472$	−14.9656			−0.688847
$473$	−4.26769	+	8.31822i	−0.196229	+	0.382472i
$474$	−3.66943	+	3.66943i	−0.168543	+	0.168543i
$475$	−5.81277	+	5.81277i	−0.266708	+	0.266708i
$476$	−21.9854	−	21.9854i	−1.00770	−	1.00770i
$477$	−5.44413			−0.249270
$478$			8.97415i			0.410468i
$479$	−15.4257	+	15.4257i	−0.704818	+	0.704818i	−0.965441	−	0.260623i	$-0.916072\pi$
$479$	−15.4257	+	15.4257i	−0.704818	+	0.704818i	0.260623	+	0.965441i	$0.416072\pi$
$480$	−1.36202			−0.0621673
$481$	0.515632	−	15.0692i	0.0235108	−	0.687097i
$482$	18.8599			0.859044
$483$	10.8830	+	10.8830i	0.495192	+	0.495192i
$484$	8.12117	−	5.83125i	0.369144	−	0.265057i
$485$		−	0.709278i		−	0.0322066i
$486$	1.20600	+	1.20600i	0.0547055	+	0.0547055i
$487$	−7.87086	+	7.87086i	−0.356663	+	0.356663i	−0.862581	−	0.505918i	$-0.831154\pi$
$487$	−7.87086	+	7.87086i	−0.356663	+	0.356663i	0.505918	+	0.862581i	$0.331154\pi$
$488$	−18.8536	−	18.8536i	−0.853463	−	0.853463i
$489$	−3.24947	−	3.24947i	−0.146946	−	0.146946i
$490$			7.38439i			0.333593i
$491$	33.4183			1.50815			0.754074	−	0.656789i	$-0.228086\pi$
$491$	33.4183			1.50815			0.754074	+	0.656789i	$0.228086\pi$
$492$	4.32067	−	4.32067i	0.194791	−	0.194791i
$493$		−	41.1722i		−	1.85430i
$494$	7.51072	−	7.01373i	0.337923	−	0.315562i
$495$	−0.288811	−	0.897400i	−0.0129811	−	0.0403352i
$496$	−19.2953	+	19.2953i	−0.866383	+	0.866383i
$497$		−	46.3353i		−	2.07842i
$498$			9.89674i			0.443484i
$499$	−13.6017	+	13.6017i	−0.608896	+	0.608896i	−0.942658	−	0.333761i	$-0.891682\pi$
$499$	−13.6017	+	13.6017i	−0.608896	+	0.608896i	0.333761	+	0.942658i	$0.391682\pi$
$500$	1.81203	−	1.81203i	0.0810367	−	0.0810367i
$501$	−3.87790	+	3.87790i	−0.173252	+	0.173252i
$502$	17.5192	−	17.5192i	0.781918	−	0.781918i
$503$		−	12.4724i		−	0.556117i	−0.960564	−	0.278058i	$-0.910309\pi$
$503$		−	12.4724i		−	0.556117i	0.960564	−	0.278058i	$-0.0896909\pi$
$504$		−	8.77447i		−	0.390846i
$505$	−3.52716	+	3.52716i	−0.156957	+	0.156957i
$506$	−5.65664	−	17.5765i	−0.251468	−	0.781370i
$507$	−0.888616	+	12.9696i	−0.0394648	+	0.576000i
$508$		−	9.95181i		−	0.441540i
$509$	22.4584	−	22.4584i	0.995450	−	0.995450i	−0.00454003	−	0.999990i	$-0.501445\pi$
$509$	22.4584	−	22.4584i	0.995450	−	0.995450i	0.999990	+	0.00454003i	$0.00144514\pi$
$510$	3.51722			0.155745
$511$			18.9994i			0.840485i
$512$	3.77624	+	3.77624i	0.166888	+	0.166888i
$513$	1.18165	+	1.18165i	0.0521710	+	0.0521710i
$514$	3.41908	−	3.41908i	0.150809	−	0.150809i
$515$	0.788243	+	0.788243i	0.0347342	+	0.0347342i
$516$			2.56205i			0.112788i
$517$	−15.1537	+	4.87693i	−0.666461	+	0.214487i
$518$	23.7800	+	23.7800i	1.04483	+	1.04483i
$519$	−8.75558			−0.384327
$520$	1.39391	−	1.30168i	0.0611272	−	0.0570823i
$521$	40.1278			1.75803			0.879014	−	0.476795i	$-0.158202\pi$
$521$	40.1278			1.75803			0.879014	+	0.476795i	$0.158202\pi$
$522$	−6.84397	+	6.84397i	−0.299553	+	0.299553i
$523$		−	22.0859i		−	0.965747i	−0.875690	−	0.482874i	$-0.839593\pi$
$523$		−	22.0859i		−	0.965747i	0.875690	−	0.482874i	$-0.160407\pi$
$524$	12.5456			0.548057
$525$	16.4010	+	16.4010i	0.715798	+	0.715798i
$526$	17.5086	−	17.5086i	0.763411	−	0.763411i
$527$	28.0445	−	28.0445i	1.22164	−	1.22164i
$528$	−7.55731	+	14.7301i	−0.328890	+	0.641044i
$529$	12.3452			0.536748
$530$	2.63927			0.114642
$531$	−5.68655	−	5.68655i	−0.246775	−	0.246775i
$532$			7.16155i			0.310492i
$533$	−0.828933	+	24.2254i	−0.0359051	+	1.04932i
$534$			14.6729i			0.634959i
$535$	0.109787	+	0.109787i	0.00474652	+	0.00474652i
$536$			1.97002i			0.0850921i
$537$		−	8.37650i		−	0.361473i
$538$	−27.7608	−	27.7608i	−1.19685	−	1.19685i
$539$	44.9486	+	23.0610i	1.93607	+	0.993308i
$540$	−0.182679	−	0.182679i	−0.00786127	−	0.00786127i
$541$	−8.27698	+	8.27698i	−0.355855	+	0.355855i	−0.862283	−	0.506427i	$-0.830966\pi$
$541$	−8.27698	+	8.27698i	−0.355855	+	0.355855i	0.506427	+	0.862283i	$0.330966\pi$
$542$	−41.0060			−1.76136
$543$		−	8.13564i		−	0.349134i
$544$	−24.5823	−	24.5823i	−1.05396	−	1.05396i
$545$	1.82015			0.0779667
$546$	−19.7896	−	21.1918i	−0.846915	−	0.906927i
$547$		−	13.3885i		−	0.572451i	−0.958162	−	0.286225i	$-0.907599\pi$
$547$		−	13.3885i		−	0.572451i	0.958162	−	0.286225i	$-0.0924006\pi$
$548$	11.5004	−	11.5004i	0.491271	−	0.491271i
$549$		−	14.3278i		−	0.611495i
$550$	−8.52474	−	26.4883i	−0.363496	−	1.12947i
$551$	−6.70575	+	6.70575i	−0.285674	+	0.285674i
$552$	4.29524	+	4.29524i	0.182818	+	0.182818i
$553$	10.1444	+	10.1444i	0.431383	+	0.431383i
$554$	33.0625	+	33.0625i	1.40469	+	1.40469i
$555$	−1.18868			−0.0504565
$556$	−14.6041			−0.619351
$557$	−1.84660	+	1.84660i	−0.0782429	+	0.0782429i	−0.745145	−	0.666902i	$-0.767620\pi$
$557$	−1.84660	+	1.84660i	−0.0782429	+	0.0782429i	0.666902	+	0.745145i	$0.267620\pi$
$558$	−9.32355			−0.394697
$559$	−6.93675	−	7.42829i	−0.293393	−	0.314183i
$560$			6.69005i			0.282706i
$561$	10.9841	−	21.4092i	0.463749	−	0.903899i
$562$	−8.58094			−0.361965
$563$	−13.1782			−0.555396			−0.277698	−	0.960668i	$-0.589571\pi$
$563$	−13.1782			−0.555396			−0.277698	+	0.960668i	$0.589571\pi$
$564$	−3.08477	+	3.08477i	−0.129892	+	0.129892i
$565$	−1.12348	+	1.12348i	−0.0472652	+	0.0472652i
$566$	30.4019	+	30.4019i	1.27789	+	1.27789i
$567$	3.33407	−	3.33407i	0.140018	−	0.140018i
$568$		−	18.2874i		−	0.767322i
$569$	−4.97172			−0.208426			−0.104213	−	0.994555i	$-0.533232\pi$
$569$	−4.97172			−0.208426			−0.104213	+	0.994555i	$0.533232\pi$
$570$	−0.572852	−	0.572852i	−0.0239941	−	0.0239941i
$571$	17.0888			0.715145			0.357572	−	0.933885i	$-0.383605\pi$
$571$	17.0888			0.715145			0.357572	+	0.933885i	$0.383605\pi$
$572$	2.97396	+	10.4540i	0.124347	+	0.437104i
$573$	−1.28415			−0.0536462
$574$	−38.2289	−	38.2289i	−1.59564	−	1.59564i
$575$	−16.0571			−0.669628
$576$		−	1.81089i		−	0.0754536i
$577$	4.06432	−	4.06432i	0.169200	−	0.169200i	−0.617428	−	0.786628i	$-0.711825\pi$
$577$	4.06432	−	4.06432i	0.169200	−	0.169200i	0.786628	+	0.617428i	$0.211825\pi$
$578$	42.9783	+	42.9783i	1.78766	+	1.78766i
$579$	−18.7908	+	18.7908i	−0.780919	+	0.780919i
$580$	1.03669	−	1.03669i	0.0430462	−	0.0430462i
$581$	27.3602			1.13509
$582$	−4.25588			−0.176412
$583$	8.24228	−	16.0651i	0.341360	−	0.665350i
$584$			7.49861i			0.310295i
$585$	1.02426	+	0.0350475i	0.0423478	+	0.00144904i
$586$	−34.1885			−1.41231
$587$	−4.92139	+	4.92139i	−0.203127	+	0.203127i	−0.801339	−	0.598211i	$-0.795878\pi$
$587$	−4.92139	+	4.92139i	−0.203127	+	0.203127i	0.598211	+	0.801339i	$0.295878\pi$
$588$	13.8444			0.570932
$589$	−9.13525			−0.376411
$590$	2.75679	+	2.75679i	0.113495	+	0.113495i
$591$	12.3045	+	12.3045i	0.506141	+	0.506141i
$592$	14.7607	+	14.7607i	0.606660	+	0.606660i
$593$	8.10376	−	8.10376i	0.332781	−	0.332781i	−0.520860	−	0.853642i	$-0.674389\pi$
$593$	8.10376	−	8.10376i	0.332781	−	0.332781i	0.853642	+	0.520860i	$0.174389\pi$
$594$	−5.38468	+	1.73295i	−0.220936	+	0.0711038i
$595$		−	9.72358i		−	0.398628i
$596$	−9.68319	+	9.68319i	−0.396639	+	0.396639i
$597$		−	20.0985i		−	0.822577i
$598$	20.0611	+	0.686441i	0.820358	+	0.0280707i
$599$	−8.72506			−0.356496			−0.178248	−	0.983986i	$-0.557043\pi$
$599$	−8.72506			−0.356496			−0.178248	+	0.983986i	$0.557043\pi$
$600$	6.47307	+	6.47307i	0.264262	+	0.264262i
$601$			13.9440i			0.568786i	0.958708	+	0.284393i	$0.0917921\pi$
$601$			13.9440i			0.568786i	−0.958708	+	0.284393i	$0.908208\pi$
$602$	22.6688			0.923911
$603$	−0.748559	+	0.748559i	−0.0304837	+	0.0304837i
$604$	2.45798	+	2.45798i	0.100014	+	0.100014i
$605$	3.08540	+	0.506388i	0.125439	+	0.0205876i
$606$	21.1640	+	21.1640i	0.859730	+	0.859730i
$607$			45.9267i			1.86411i	0.362323	+	0.932053i	$0.381984\pi$
$607$			45.9267i			1.86411i	−0.362323	+	0.932053i	$0.618016\pi$
$608$			8.00745i			0.324745i
$609$	18.9206	+	18.9206i	0.766701	+	0.766701i
$610$			6.94598i			0.281235i
$611$	0.591822	−	17.2959i	0.0239426	−	0.699715i
$612$		−	6.59415i		−	0.266553i
$613$	3.85718	+	3.85718i	0.155790	+	0.155790i	0.780698	−	0.624908i	$-0.214864\pi$
$613$	3.85718	+	3.85718i	0.155790	+	0.155790i	−0.624908	+	0.780698i	$0.714864\pi$
$614$	21.2847			0.858979
$615$	1.91092			0.0770559
$616$	25.8927	+	13.2843i	1.04325	+	0.535241i
$617$	3.08121	−	3.08121i	0.124045	−	0.124045i	−0.642359	−	0.766404i	$-0.722044\pi$
$617$	3.08121	−	3.08121i	0.124045	−	0.124045i	0.766404	+	0.642359i	$0.222044\pi$
$618$	4.72970	−	4.72970i	0.190256	−	0.190256i
$619$	−18.4046	−	18.4046i	−0.739743	−	0.739743i	0.232785	−	0.972528i	$-0.425216\pi$
$619$	−18.4046	−	18.4046i	−0.739743	−	0.739743i	−0.972528	+	0.232785i	$0.925216\pi$
$620$	1.41228			0.0567187
$621$			3.26417i			0.130987i
$622$	18.7054	−	18.7054i	0.750017	−	0.750017i
$623$	40.5642			1.62517
$624$	−12.2837	−	13.1542i	−0.491743	−	0.526588i
$625$	−23.7946			−0.951784
$626$	34.6885	+	34.6885i	1.38643	+	1.38643i
$627$	−5.27592	+	1.69795i	−0.210700	+	0.0678096i
$628$			11.8837i			0.474213i
$629$	−21.4537	−	21.4537i	−0.855417	−	0.855417i
$630$	−1.61633	+	1.61633i	−0.0643961	+	0.0643961i
$631$	−17.6559	−	17.6559i	−0.702872	−	0.702872i	0.262154	−	0.965026i	$-0.415567\pi$
$631$	−17.6559	−	17.6559i	−0.702872	−	0.702872i	−0.965026	+	0.262154i	$0.915567\pi$
$632$	4.00374	+	4.00374i	0.159260	+	0.159260i
$633$		−	21.6318i		−	0.859786i
$634$	28.4063			1.12816
$635$	2.20072	−	2.20072i	0.0873328	−	0.0873328i
$636$		−	4.94814i		−	0.196207i
$637$	−40.1397	+	37.4836i	−1.59039	+	1.48515i
$638$	−9.83435	−	30.5576i	−0.389346	−	1.20979i
$639$	6.94874	−	6.94874i	0.274888	−	0.274888i
$640$			3.60194i			0.142379i
$641$			7.41695i			0.292952i	0.989214	+	0.146476i	$0.0467931\pi$
$641$			7.41695i			0.292952i	−0.989214	+	0.146476i	$0.953207\pi$
$642$	0.658758	−	0.658758i	0.0259991	−	0.0259991i
$643$	−23.3090	+	23.3090i	−0.919217	+	0.919217i	−0.996972	−	0.0777551i	$-0.975225\pi$
$643$	−23.3090	+	23.3090i	−0.919217	+	0.919217i	0.0777551	+	0.996972i	$0.475225\pi$
$644$	−9.89148	+	9.89148i	−0.389779	+	0.389779i
$645$	−0.566566	+	0.566566i	−0.0223085	+	0.0223085i
$646$		−	20.6782i		−	0.813572i
$647$			23.8718i			0.938499i	0.883066	+	0.469249i	$0.155475\pi$
$647$			23.8718i			0.938499i	−0.883066	+	0.469249i	$0.844525\pi$
$648$	1.31588	−	1.31588i	0.0516926	−	0.0516926i
$649$	25.3898	−	8.17120i	0.996636	−	0.320748i
$650$	30.2327	+	1.03449i	1.18582	+	0.0405760i
$651$			25.7755i			1.01022i
$652$	2.95343	−	2.95343i	0.115665	−	0.115665i
$653$	−31.2998			−1.22486			−0.612429	−	0.790526i	$-0.709807\pi$
$653$	−31.2998			−1.22486			−0.612429	+	0.790526i	$0.709807\pi$
$654$		−	10.9215i		−	0.427063i
$655$	2.77430	+	2.77430i	0.108401	+	0.108401i
$656$	−23.7294	−	23.7294i	−0.926476	−	0.926476i
$657$	−2.84928	+	2.84928i	−0.111161	+	0.111161i
$658$	27.2938	+	27.2938i	1.06402	+	1.06402i
$659$			33.7688i			1.31544i	0.753261	+	0.657722i	$0.228480\pi$
$659$			33.7688i			1.31544i	−0.753261	+	0.657722i	$0.771520\pi$
$660$	0.815643	−	0.262499i	0.0317489	−	0.0102177i
$661$	4.49941	+	4.49941i	0.175007	+	0.175007i	0.789175	−	0.614168i	$-0.210508\pi$
$661$	4.49941	+	4.49941i	0.175007	+	0.175007i	−0.614168	+	0.789175i	$0.710508\pi$
$662$	0.138327			0.00537623
$663$	17.8537	+	19.1188i	0.693378	+	0.742511i
$664$	10.7984			0.419059
$665$	−1.58369	+	1.58369i	−0.0614127	+	0.0614127i
$666$			7.13242i			0.276376i
$667$	−18.5239			−0.717247
$668$	−3.52461	−	3.52461i	−0.136371	−	0.136371i
$669$	−18.0992	+	18.0992i	−0.699757	+	0.699757i
$670$	0.362895	−	0.362895i	0.0140199	−	0.0140199i
$671$	42.2800	+	21.6919i	1.63220	+	0.837407i
$672$	22.5934			0.871560
$673$	26.4783			1.02066			0.510332	−	0.859977i	$-0.329522\pi$
$673$	26.4783			1.02066			0.510332	+	0.859977i	$0.329522\pi$
$674$	4.76068	+	4.76068i	0.183374	+	0.183374i
$675$			4.91921i			0.189340i
$676$	−11.7880	−	0.807659i	−0.453385	−	0.0310638i
$677$		−	45.1205i		−	1.73412i	−0.498201	−	0.867062i	$-0.666006\pi$
$677$		−	45.1205i		−	1.73412i	0.498201	−	0.867062i	$-0.333994\pi$
$678$	6.74123	+	6.74123i	0.258895	+	0.258895i
$679$			11.7656i			0.451524i
$680$		−	3.83766i		−	0.147168i
$681$	0.513536	+	0.513536i	0.0196787	+	0.0196787i
$682$	14.1156	−	27.5130i	0.540515	−	1.05353i
$683$	18.7464	+	18.7464i	0.717310	+	0.717310i	0.968053	−	0.250744i	$-0.0806752\pi$
$683$	18.7464	+	18.7464i	0.717310	+	0.717310i	−0.250744	+	0.968053i	$0.580675\pi$
$684$	−1.07399	+	1.07399i	−0.0410652	+	0.0410652i
$685$	5.08632			0.194338
$686$		−	66.2010i		−	2.52757i
$687$	12.6249	+	12.6249i	0.481668	+	0.481668i
$688$	14.0709			0.536449
$689$	13.3971	+	14.3464i	0.510388	+	0.546555i
$690$		−	1.58244i		−	0.0602425i
$691$	24.0218	−	24.0218i	0.913834	−	0.913834i	−0.0827376	−	0.996571i	$-0.526366\pi$
$691$	24.0218	−	24.0218i	0.913834	−	0.913834i	0.996571	+	0.0827376i	$0.0263663\pi$
$692$		−	7.95791i		−	0.302514i
$693$	4.79085	+	14.8863i	0.181989	+	0.565482i
$694$	4.16338	−	4.16338i	0.158040	−	0.158040i
$695$	−3.22951	−	3.22951i	−0.122502	−	0.122502i
$696$	7.46749	+	7.46749i	0.283055	+	0.283055i
$697$	34.4892	+	34.4892i	1.30637	+	1.30637i
$698$	13.2888			0.502987
$699$	−22.5952			−0.854629
$700$	−14.9068	+	14.9068i	−0.563423	+	0.563423i
$701$	−3.82750			−0.144563			−0.0722814	−	0.997384i	$-0.523028\pi$
$701$	−3.82750			−0.144563			−0.0722814	+	0.997384i	$0.523028\pi$
$702$	0.210296	−	6.14585i	0.00793711	−	0.231960i
$703$			6.98837i			0.263571i
$704$	5.34377	+	2.74164i	0.201401	+	0.103329i
$705$	−1.36432			−0.0513831
$706$	17.1990			0.647294
$707$	58.5092	−	58.5092i	2.20047	−	2.20047i
$708$	5.16847	−	5.16847i	0.194243	−	0.194243i
$709$	17.0851	+	17.0851i	0.641643	+	0.641643i	0.950959	−	0.309317i	$-0.100100\pi$
$709$	17.0851	+	17.0851i	0.641643	+	0.641643i	−0.309317	+	0.950959i	$0.600100\pi$
$710$	−3.36869	+	3.36869i	−0.126425	+	0.126425i
$711$			3.04264i			0.114108i
$712$	16.0097			0.599989
$713$	−12.6175	−	12.6175i	−0.472531	−	0.472531i
$714$	−58.3444			−2.18349
$715$	−1.65412	+	2.96943i	−0.0618606	+	0.111050i
$716$	7.61336			0.284525
$717$	3.72061	+	3.72061i	0.138949	+	0.138949i
$718$	−38.7377			−1.44568
$719$			50.3816i			1.87892i	0.342663	+	0.939459i	$0.388671\pi$
$719$			50.3816i			1.87892i	−0.342663	+	0.939459i	$0.611329\pi$
$720$	−1.00328	+	1.00328i	−0.0373902	+	0.0373902i
$721$	−13.0755	−	13.0755i	−0.486959	−	0.486959i
$722$	19.5462	−	19.5462i	0.727435	−	0.727435i
$723$	7.81915	−	7.81915i	0.290797	−	0.290797i
$724$	7.39444			0.274812
$725$	−27.9161			−1.03678
$726$	3.03848	−	18.5133i	0.112769	−	0.687095i
$727$		−	14.1485i		−	0.524740i	−0.964967	−	0.262370i	$-0.915496\pi$
$727$		−	14.1485i		−	0.524740i	0.964967	−	0.262370i	$-0.0845041\pi$
$728$	−23.1225	+	21.5925i	−0.856978	+	0.800271i
$729$	1.00000			0.0370370
$730$	1.38131	−	1.38131i	0.0511245	−	0.0511245i
$731$	−20.4512			−0.756416
$732$	13.0225			0.481324
$733$	7.13792	+	7.13792i	0.263645	+	0.263645i	0.826533	−	0.562888i	$-0.190310\pi$
$733$	7.13792	+	7.13792i	0.263645	+	0.263645i	−0.562888	+	0.826533i	$0.690310\pi$
$734$	−42.8914	−	42.8914i	−1.58315	−	1.58315i
$735$	3.06151	+	3.06151i	0.112925	+	0.112925i
$736$	−11.0598	+	11.0598i	−0.407671	+	0.407671i
$737$	−1.07563	−	3.34223i	−0.0396214	−	0.123113i
$738$		−	11.4661i		−	0.422074i
$739$	−6.21124	+	6.21124i	−0.228484	+	0.228484i	−0.812059	−	0.583575i	$-0.801653\pi$
$739$	−6.21124	+	6.21124i	−0.228484	+	0.228484i	0.583575	+	0.812059i	$0.301653\pi$
$740$		−	1.08038i		−	0.0397156i
$741$	0.206049	−	6.02172i	0.00756938	−	0.221213i
$742$	−43.7807			−1.60724
$743$	−22.0058	−	22.0058i	−0.807314	−	0.807314i	0.176913	−	0.984227i	$-0.443389\pi$
$743$	−22.0058	−	22.0058i	−0.807314	−	0.807314i	−0.984227	+	0.176913i	$0.943389\pi$
$744$			10.1730i			0.372959i
$745$	−4.28263			−0.156903
$746$	−25.5150	+	25.5150i	−0.934170	+	0.934170i
$747$	4.10311	+	4.10311i	0.150125	+	0.150125i
$748$	19.4588	+	9.98339i	0.711483	+	0.365029i
$749$	−1.82118	−	1.82118i	−0.0665443	−	0.0665443i
$750$		−	4.80874i		−	0.175591i
$751$			30.0145i			1.09525i	0.836725	+	0.547623i	$0.184467\pi$
$751$			30.0145i			1.09525i	−0.836725	+	0.547623i	$0.815533\pi$
$752$	16.9417	+	16.9417i	0.617801	+	0.617801i
$753$		−	14.5266i		−	0.529379i
$754$	34.8771	+	1.19341i	1.27015	+	0.0434615i
$755$			1.08710i			0.0395637i
$756$	3.03032	+	3.03032i	0.110212	+	0.110212i
$757$	−42.5187			−1.54537			−0.772684	−	0.634790i	$-0.781086\pi$
$757$	−42.5187			−1.54537			−0.772684	+	0.634790i	$0.781086\pi$
$758$	31.3474			1.13859
$759$	−9.63227	−	4.94187i	−0.349629	−	0.179378i
$760$	−0.625042	+	0.625042i	−0.0226727	+	0.0226727i
$761$	5.20061	−	5.20061i	0.188522	−	0.188522i	−0.606535	−	0.795057i	$-0.707441\pi$
$761$	5.20061	−	5.20061i	0.188522	−	0.188522i	0.795057	+	0.606535i	$0.207441\pi$
$762$	−13.2050	−	13.2050i	−0.478366	−	0.478366i
$763$	−30.1930			−1.09306
$764$		−	1.16716i		−	0.0422264i
$765$	1.45821	−	1.45821i	0.0527218	−	0.0527218i
$766$	37.9588			1.37151
$767$	−0.991586	+	28.9788i	−0.0358041	+	1.04637i
$768$	17.9909			0.649192
$769$	−4.65425	−	4.65425i	−0.167836	−	0.167836i	0.618191	−	0.786028i	$-0.287866\pi$
$769$	−4.65425	−	4.65425i	−0.167836	−	0.167836i	−0.786028	+	0.618191i	$0.787866\pi$
$770$	−2.32256	−	7.21673i	−0.0836993	−	0.260073i
$771$		−	2.83504i		−	0.102102i
$772$	−17.0789	−	17.0789i	−0.614682	−	0.614682i
$773$	−13.3308	+	13.3308i	−0.479476	+	0.479476i	−0.904964	−	0.425488i	$-0.860102\pi$
$773$	−13.3308	+	13.3308i	−0.479476	+	0.479476i	0.425488	+	0.904964i	$0.360102\pi$
$774$	3.39957	+	3.39957i	0.122195	+	0.122195i
$775$	−19.0150	−	19.0150i	−0.683041	−	0.683041i
$776$			4.64361i			0.166696i
$777$	19.7180			0.707380
$778$	−7.74070	+	7.74070i	−0.277518	+	0.277518i
$779$		−	11.2345i		−	0.402519i
$780$	−0.0318545	+	0.930941i	−0.00114058	+	0.0333330i
$781$	9.98490	+	31.0254i	0.357288	+	1.11017i
$782$	28.5606	−	28.5606i	1.02132	−	1.02132i
$783$			5.67492i			0.202805i
$784$		−	76.0340i		−	2.71550i
$785$	−2.62794	+	2.62794i	−0.0937951	+	0.0937951i
$786$	16.6466	−	16.6466i	0.593766	−	0.593766i
$787$	11.1342	−	11.1342i	0.396890	−	0.396890i	−0.480244	−	0.877135i	$-0.659452\pi$
$787$	11.1342	−	11.1342i	0.396890	−	0.396890i	0.877135	+	0.480244i	$0.159452\pi$
$788$	−11.1835	+	11.1835i	−0.398397	+	0.398397i
$789$		−	14.5178i		−	0.516849i
$790$		−	1.47504i		−	0.0524797i
$791$	18.6365	−	18.6365i	0.662639	−	0.662639i
$792$	1.89083	+	5.87525i	0.0671878	+	0.208768i
$793$	−37.7566	+	35.2583i	−1.34078	+	1.25206i
$794$			31.9207i			1.13282i
$795$	1.09422	−	1.09422i	0.0388080	−	0.0388080i
$796$	18.2674			0.647472
$797$		−	19.7275i		−	0.698784i	−0.936977	−	0.349392i	$-0.886388\pi$
$797$		−	19.7275i		−	0.698784i	0.936977	−	0.349392i	$-0.113612\pi$
$798$	9.50259	+	9.50259i	0.336388	+	0.336388i
$799$	−24.6238	−	24.6238i	−0.871126	−	0.871126i
$800$	−16.6675	+	16.6675i	−0.589287	+	0.589287i
$801$	6.08327	+	6.08327i	0.214942	+	0.214942i
$802$			5.13256i			0.181237i
$803$	−4.09423	−	12.7217i	−0.144482	−	0.448940i
$804$	−0.680362	−	0.680362i	−0.0239945	−	0.0239945i
$805$	−4.37475			−0.154190
$806$	22.9437	+	24.5695i	0.808157	+	0.865423i
$807$	−23.0188			−0.810300
$808$	23.0922	−	23.0922i	0.812380	−	0.812380i
$809$			3.53428i			0.124259i	0.998068	+	0.0621294i	$0.0197891\pi$
$809$			3.53428i			0.124259i	−0.998068	+	0.0621294i	$0.980211\pi$
$810$	−0.484791			−0.0170338
$811$	−11.8959	−	11.8959i	−0.417723	−	0.417723i	0.466695	−	0.884418i	$-0.345444\pi$
$811$	−11.8959	−	11.8959i	−0.417723	−	0.417723i	−0.884418	+	0.466695i	$0.845444\pi$
$812$	−17.1968	+	17.1968i	−0.603490	+	0.603490i
$813$	−17.0008	+	17.0008i	−0.596242	+	0.596242i
$814$	−21.0471	−	10.7983i	−0.737702	−	0.378481i
$815$	1.30623			0.0457552
$816$	−36.2154			−1.26779
$817$	3.33091	+	3.33091i	0.116534	+	0.116534i
$818$			13.4049i			0.468690i
$819$	−16.9906	−	0.581376i	−0.593698	−	0.0203149i
$820$			1.73683i			0.0606527i
$821$	21.4198	+	21.4198i	0.747556	+	0.747556i	0.974020	−	0.226464i	$-0.0727164\pi$
$821$	21.4198	+	21.4198i	0.747556	+	0.747556i	−0.226464	+	0.974020i	$0.572716\pi$
$822$		−	30.5195i		−	1.06449i
$823$			43.7848i			1.52624i	0.646255	+	0.763122i	$0.276334\pi$
$823$			43.7848i			1.52624i	−0.646255	+	0.763122i	$0.723666\pi$
$824$	−5.16060	−	5.16060i	−0.179778	−	0.179778i
$825$	−14.5161	−	7.44756i	−0.505387	−	0.259291i
$826$	−45.7302	−	45.7302i	−1.59116	−	1.59116i
$827$	−16.0478	+	16.0478i	−0.558036	+	0.558036i	−0.928748	−	0.370712i	$-0.879114\pi$
$827$	−16.0478	+	16.0478i	−0.558036	+	0.558036i	0.370712	+	0.928748i	$0.379114\pi$
$828$	−2.96679			−0.103103
$829$		−	42.1586i		−	1.46423i	−0.681182	−	0.732114i	$-0.738534\pi$
$829$		−	42.1586i		−	1.46423i	0.681182	−	0.732114i	$-0.261466\pi$
$830$	−1.98915	−	1.98915i	−0.0690445	−	0.0690445i
$831$	27.4149			0.951013
$832$	−4.77206	+	4.45629i	−0.165441	+	0.154494i
$833$			110.511i			3.82897i
$834$	−19.3780	+	19.3780i	−0.671007	+	0.671007i
$835$		−	1.55884i		−	0.0539460i
$836$	−1.54326	−	4.79526i	−0.0533747	−	0.165848i
$837$	−3.86547	+	3.86547i	−0.133610	+	0.133610i
$838$	−13.3501	−	13.3501i	−0.461173	−	0.461173i
$839$	13.9581	+	13.9581i	0.481887	+	0.481887i	0.905734	−	0.423847i	$-0.139321\pi$
$839$	13.9581	+	13.9581i	0.481887	+	0.481887i	−0.423847	+	0.905734i	$0.639321\pi$
$840$	1.76359	+	1.76359i	0.0608495	+	0.0608495i
$841$	−3.20466			−0.110506
$842$	8.74943			0.301525
$843$	−3.55759	+	3.55759i	−0.122530	+	0.122530i
$844$	19.6610			0.676760
$845$	−2.42816	−	2.78537i	−0.0835314	−	0.0958197i
$846$			8.18631i			0.281451i
$847$	−51.1813	−	8.40007i	−1.75861	−	0.288630i
$848$	−27.1755			−0.933209
$849$	25.2088			0.865163
$850$	43.0417	−	43.0417i	1.47632	−	1.47632i
$851$	−9.65229	+	9.65229i	−0.330876	+	0.330876i
$852$	6.31568	+	6.31568i	0.216372	+	0.216372i
$853$	−40.7704	+	40.7704i	−1.39595	+	1.39595i	−0.584702	+	0.811248i	$0.698789\pi$
$853$	−40.7704	+	40.7704i	−1.39595	+	1.39595i	−0.811248	+	0.584702i	$0.801211\pi$
$854$		−	115.221i		−	3.94280i
$855$	−0.475000			−0.0162447
$856$	−0.718774	−	0.718774i	−0.0245672	−	0.0245672i
$857$	−31.5605			−1.07809			−0.539043	−	0.842278i	$-0.681214\pi$
$857$	−31.5605			−1.07809			−0.539043	+	0.842278i	$0.681214\pi$
$858$	17.8175	+	9.92523i	0.608278	+	0.338842i
$859$	31.4713			1.07379			0.536894	−	0.843650i	$-0.319598\pi$
$859$	31.4713			1.07379			0.536894	+	0.843650i	$0.319598\pi$
$860$	−0.514949	−	0.514949i	−0.0175596	−	0.0175596i
$861$	−31.6988			−1.08029
$862$			12.4894i			0.425390i
$863$	16.5706	−	16.5706i	0.564070	−	0.564070i	−0.366391	−	0.930461i	$-0.619407\pi$
$863$	16.5706	−	16.5706i	0.564070	−	0.564070i	0.930461	+	0.366391i	$0.119407\pi$
$864$	3.38826	+	3.38826i	0.115271	+	0.115271i
$865$	1.75979	−	1.75979i	0.0598347	−	0.0598347i
$866$	−35.3913	+	35.3913i	−1.20264	+	1.20264i
$867$	35.6369			1.21029
$868$	−23.4272			−0.795173
$869$	−8.97855	−	4.60648i	−0.304576	−	0.156264i
$870$		−	2.75115i		−	0.0932727i
$871$	3.81469	+	0.130529i	0.129256	+	0.00442282i
$872$	−11.9165			−0.403542
$873$	−1.76445	+	1.76445i	−0.0597177	+	0.0597177i
$874$	−9.30335			−0.314690
$875$	−13.2941			−0.449422
$876$	−2.58970	−	2.58970i	−0.0874978	−	0.0874978i
$877$	14.7471	+	14.7471i	0.497973	+	0.497973i	0.910807	−	0.412833i	$-0.135461\pi$
$877$	14.7471	+	14.7471i	0.497973	+	0.497973i	−0.412833	+	0.910807i	$0.635461\pi$
$878$	−34.5474	−	34.5474i	−1.16592	−	1.16592i
$879$	−14.1743	+	14.1743i	−0.478086	+	0.478086i
$880$	−1.44166	−	4.47955i	−0.0485982	−	0.151006i
$881$		−	25.4247i		−	0.856579i	−0.903642	−	0.428289i	$-0.859116\pi$
$881$		−	25.4247i		−	0.856579i	0.903642	−	0.428289i	$-0.140884\pi$
$882$	18.3700	−	18.3700i	0.618549	−	0.618549i
$883$			16.4770i			0.554494i	0.960799	+	0.277247i	$0.0894221\pi$
$883$			16.4770i			0.554494i	−0.960799	+	0.277247i	$0.910578\pi$
$884$	−17.3769	+	16.2271i	−0.584450	+	0.545776i
$885$	2.28588			0.0768392
$886$	−19.7402	−	19.7402i	−0.663184	−	0.663184i
$887$			4.46850i			0.150037i	0.997182	+	0.0750187i	$0.0239017\pi$
$887$			4.46850i			0.150037i	−0.997182	+	0.0750187i	$0.976098\pi$
$888$	7.78222			0.261154
$889$	−36.5059	+	36.5059i	−1.22437	+	1.22437i
$890$	−2.94912	−	2.94912i	−0.0988547	−	0.0988547i
$891$	−1.51398	+	2.95091i	−0.0507201	+	0.0988592i
$892$	−16.4503	−	16.4503i	−0.550797	−	0.550797i
$893$			8.02098i			0.268412i
$894$			25.6971i			0.859439i
$895$	1.68360	+	1.68360i	0.0562765	+	0.0562765i
$896$		−	59.7496i		−	1.99610i
$897$	8.60175	−	8.03256i	0.287204	−	0.268200i
$898$		−	13.5737i		−	0.452960i
$899$	−21.9362	−	21.9362i	−0.731614	−	0.731614i
$900$	−4.47104			−0.149035
$901$	39.4979			1.31587
$902$	33.8355	+	17.3594i	1.12660	+	0.578006i
$903$	9.39831	−	9.39831i	0.312756	−	0.312756i
$904$	7.35539	−	7.35539i	0.244637	−	0.244637i
$905$	1.63519	+	1.63519i	0.0543555	+	0.0543555i
$906$	6.52295			0.216710
$907$			26.6927i			0.886316i	0.896443	+	0.443158i	$0.146142\pi$
$907$			26.6927i			0.886316i	−0.896443	+	0.443158i	$0.853858\pi$
$908$	−0.466751	+	0.466751i	−0.0154897	+	0.0154897i
$909$	17.5489			0.582059
$910$	8.23688	+	0.281846i	0.273050	+	0.00934310i
$911$	−24.1348			−0.799622			−0.399811	−	0.916598i	$-0.630924\pi$
$911$	−24.1348			−0.799622			−0.399811	+	0.916598i	$0.630924\pi$
$912$	5.89843	+	5.89843i	0.195317	+	0.195317i
$913$	−18.3199	+	5.89591i	−0.606301	+	0.195126i
$914$			42.0730i			1.39165i
$915$	2.87975	+	2.87975i	0.0952016	+	0.0952016i
$916$	−11.4747	+	11.4747i	−0.379134	+	0.379134i
$917$	−46.0206	−	46.0206i	−1.51973	−	1.51973i
$918$	−8.74972	−	8.74972i	−0.288784	−	0.288784i
$919$		−	41.7170i		−	1.37612i	−0.725655	−	0.688059i	$-0.758463\pi$
$919$		−	41.7170i		−	1.37612i	0.725655	−	0.688059i	$-0.241537\pi$
$920$	−1.72661			−0.0569246
$921$	8.82445	−	8.82445i	0.290775	−	0.290775i
$922$		−	30.5378i		−	1.00571i
$923$	−35.4111	−	1.21168i	−1.16557	−	0.0398829i
$924$	−13.5301	+	4.35438i	−0.445106	+	0.143249i
$925$	−14.5463	+	14.5463i	−0.478280	+	0.478280i
$926$			34.3857i			1.12999i
$927$		−	3.92179i		−	0.128809i
$928$	−19.2281	+	19.2281i	−0.631193	+	0.631193i
$929$	−26.8941	+	26.8941i	−0.882367	+	0.882367i	−0.993775	−	0.111408i	$-0.964464\pi$
$929$	−26.8941	+	26.8941i	−0.882367	+	0.882367i	0.111408	+	0.993775i	$0.464464\pi$
$930$	1.87395	−	1.87395i	0.0614491	−	0.0614491i
$931$	17.9990	−	17.9990i	0.589892	−	0.589892i
$932$		−	20.5367i		−	0.672701i
$933$		−	15.5102i		−	0.507781i
$934$	−4.58379	+	4.58379i	−0.149986	+	0.149986i
$935$	2.09536	+	6.51076i	0.0685255	+	0.212925i
$936$	−6.70576	−	0.229455i	−0.219185	−	0.00749997i
$937$		−	36.3852i		−	1.18865i	−0.804224	−	0.594326i	$-0.797419\pi$
$937$		−	36.3852i		−	1.18865i	0.804224	−	0.594326i	$-0.202581\pi$
$938$	−6.01978	+	6.01978i	−0.196553	+	0.196553i
$939$	28.7631			0.938650
$940$		−	1.24002i		−	0.0404450i
$941$	35.8119	+	35.8119i	1.16743	+	1.16743i	0.982809	+	0.184626i	$0.0591073\pi$
$941$	35.8119	+	35.8119i	1.16743	+	1.16743i	0.184626	+	0.982809i	$0.440893\pi$
$942$	15.7684	+	15.7684i	0.513763	+	0.513763i
$943$	15.5171	−	15.5171i	0.505306	−	0.505306i
$944$	−28.3855	−	28.3855i	−0.923870	−	0.923870i
$945$			1.34024i			0.0435979i
$946$	−15.1787	+	4.88496i	−0.493501	+	0.158824i
$947$	−35.8340	−	35.8340i	−1.16445	−	1.16445i	−0.983491	−	0.180956i	$-0.942081\pi$
$947$	−35.8340	−	35.8340i	−1.16445	−	1.16445i	−0.180956	−	0.983491i	$-0.557919\pi$
$948$	−2.76544			−0.0898172
$949$	14.5200	+	0.496841i	0.471341	+	0.0161281i
$950$	−14.0204			−0.454883
$951$	11.7770	−	11.7770i	0.381896	−	0.381896i
$952$			63.6599i			2.06323i
$953$	56.4922			1.82996			0.914981	−	0.403497i	$-0.132206\pi$
$953$	56.4922			1.82996			0.914981	+	0.403497i	$0.132206\pi$
$954$	−6.56565	−	6.56565i	−0.212571	−	0.212571i
$955$	0.258103	−	0.258103i	0.00835200	−	0.00835200i
$956$	−3.38165	+	3.38165i	−0.109370	+	0.109370i
$957$	−16.7462	−	8.59168i	−0.541327	−	0.277730i
$958$	−37.2069			−1.20210
$959$	−84.3729			−2.72454
$960$	0.363971	+	0.363971i	0.0117471	+	0.0117471i
$961$			1.11628i			0.0360089i
$962$	18.7954	−	17.5517i	0.605988	−	0.565889i
$963$		−	0.546231i		−	0.0176021i
$964$	7.10679	+	7.10679i	0.228894	+	0.228894i
$965$		−	7.55355i		−	0.243157i
$966$			26.2498i			0.844575i
$967$	−41.1339	−	41.1339i	−1.32278	−	1.32278i	−0.911520	−	0.411257i	$-0.865090\pi$
$967$	−41.1339	−	41.1339i	−1.32278	−	1.32278i	−0.411257	−	0.911520i	$-0.634910\pi$
$968$	−20.2000	−	3.31530i	−0.649253	−	0.106558i
$969$	−8.57301	−	8.57301i	−0.275405	−	0.275405i
$970$	0.855392	−	0.855392i	0.0274650	−	0.0274650i
$971$	28.2094			0.905281			0.452641	−	0.891693i	$-0.350482\pi$
$971$	28.2094			0.905281			0.452641	+	0.891693i	$0.350482\pi$
$972$			0.908895i			0.0291528i
$973$	53.5718	+	53.5718i	1.71743	+	1.71743i
$974$	−18.9846			−0.608306
$975$	12.9631	−	12.1053i	0.415152	−	0.387681i
$976$		−	71.5200i		−	2.28930i
$977$	−35.5051	+	35.5051i	−1.13591	+	1.13591i	−0.146732	+	0.989176i	$0.546876\pi$
$977$	−35.5051	+	35.5051i	−1.13591	+	1.13591i	−0.989176	+	0.146732i	$0.953124\pi$
$978$		−	7.83776i		−	0.250624i
$979$	−27.1611	+	8.74127i	−0.868074	+	0.279372i
$980$	−2.78259	+	2.78259i	−0.0888866	+	0.0888866i
$981$	−4.52795	−	4.52795i	−0.144566	−	0.144566i
$982$	40.3027	+	40.3027i	1.28611	+	1.28611i
$983$	0.418033	+	0.418033i	0.0133332	+	0.0133332i	0.713742	−	0.700409i	$-0.246999\pi$
$983$	0.418033	+	0.418033i	0.0133332	+	0.0133332i	−0.700409	+	0.713742i	$0.746999\pi$
$984$	−12.5107			−0.398828
$985$	−4.94620			−0.157599
$986$	49.6539	−	49.6539i	1.58130	−	1.58130i
$987$	22.6316			0.720371
$988$	5.47311	+	0.187277i	0.174123	+	0.00595806i
$989$			9.20125i			0.292583i
$990$	0.733962	−	1.43058i	0.0233269	−	0.0454667i
$991$	18.9713			0.602644			0.301322	−	0.953522i	$-0.402572\pi$
$991$	18.9713			0.602644			0.301322	+	0.953522i	$0.402572\pi$
$992$	−26.1944			−0.831674
$993$	0.0573492	−	0.0573492i	0.00181992	−	0.00181992i
$994$	55.8805	−	55.8805i	1.77242	−	1.77242i
$995$	4.03961	+	4.03961i	0.128064	+	0.128064i
$996$	−3.72930	+	3.72930i	−0.118167	+	0.118167i
$997$		−	14.2729i		−	0.452029i	−0.974124	−	0.226014i	$-0.927430\pi$
$997$		−	14.2729i		−	0.452029i	0.974124	−	0.226014i	$-0.0725696\pi$
$998$	−32.8075			−1.03850
$999$	2.95704	+	2.95704i	0.0935568	+	0.0935568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.b.109.11	yes	28
11.10	odd	2	inner	429.2.m.b.109.4	✓	28
13.8	odd	4	inner	429.2.m.b.307.4	yes	28
143.21	even	4	inner	429.2.m.b.307.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.b.109.4	✓	28	11.10	odd	2	inner
429.2.m.b.109.11	yes	28	1.1	even	1	trivial
429.2.m.b.307.4	yes	28	13.8	odd	4	inner
429.2.m.b.307.11	yes	28	143.21	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20600 + 1.20600i) q^{2} +1.00000 q^{3} +0.908895i q^{4} +(-0.200991 + 0.200991i) q^{5} +(1.20600 + 1.20600i) q^{6} +(3.33407 - 3.33407i) q^{7} +(1.31588 - 1.31588i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.20600 + 1.20600i) q^{2} +1.00000 q^{3} +0.908895i q^{4} +(-0.200991 + 0.200991i) q^{5} +(1.20600 + 1.20600i) q^{6} +(3.33407 - 3.33407i) q^{7} +(1.31588 - 1.31588i) q^{8} +1.00000 q^{9} -0.484791 q^{10} +(-1.51398 + 2.95091i) q^{11} +0.908895i q^{12} +(-2.46083 - 2.63521i) q^{13} +8.04182 q^{14} +(-0.200991 + 0.200991i) q^{15} +4.99170 q^{16} -7.25513 q^{17} +(1.20600 + 1.20600i) q^{18} +(1.18165 + 1.18165i) q^{19} +(-0.182679 - 0.182679i) q^{20} +(3.33407 - 3.33407i) q^{21} +(-5.38468 + 1.73295i) q^{22} +3.26417i q^{23} +(1.31588 - 1.31588i) q^{24} +4.91921i q^{25} +(0.210296 - 6.14585i) q^{26} +1.00000 q^{27} +(3.03032 + 3.03032i) q^{28} +5.67492i q^{29} -0.484791 q^{30} +(-3.86547 + 3.86547i) q^{31} +(3.38826 + 3.38826i) q^{32} +(-1.51398 + 2.95091i) q^{33} +(-8.74972 - 8.74972i) q^{34} +1.34024i q^{35} +0.908895i q^{36} +(2.95704 + 2.95704i) q^{37} +2.85014i q^{38} +(-2.46083 - 2.63521i) q^{39} +0.528958i q^{40} +(-4.75377 - 4.75377i) q^{41} +8.04182 q^{42} +2.81887 q^{43} +(-2.68207 - 1.37605i) q^{44} +(-0.200991 + 0.200991i) q^{45} +(-3.93660 + 3.93660i) q^{46} +(3.39398 + 3.39398i) q^{47} +4.99170 q^{48} -15.2321i q^{49} +(-5.93259 + 5.93259i) q^{50} -7.25513 q^{51} +(2.39513 - 2.23664i) q^{52} -5.44413 q^{53} +(1.20600 + 1.20600i) q^{54} +(-0.288811 - 0.897400i) q^{55} -8.77447i q^{56} +(1.18165 + 1.18165i) q^{57} +(-6.84397 + 6.84397i) q^{58} +(-5.68655 - 5.68655i) q^{59} +(-0.182679 - 0.182679i) q^{60} -14.3278i q^{61} -9.32355 q^{62} +(3.33407 - 3.33407i) q^{63} -1.81089i q^{64} +(1.02426 + 0.0350475i) q^{65} +(-5.38468 + 1.73295i) q^{66} +(-0.748559 + 0.748559i) q^{67} -6.59415i q^{68} +3.26417i q^{69} +(-1.61633 + 1.61633i) q^{70} +(6.94874 - 6.94874i) q^{71} +(1.31588 - 1.31588i) q^{72} +(-2.84928 + 2.84928i) q^{73} +7.13242i q^{74} +4.91921i q^{75} +(-1.07399 + 1.07399i) q^{76} +(4.79085 + 14.8863i) q^{77} +(0.210296 - 6.14585i) q^{78} +3.04264i q^{79} +(-1.00328 + 1.00328i) q^{80} +1.00000 q^{81} -11.4661i q^{82} +(4.10311 + 4.10311i) q^{83} +(3.03032 + 3.03032i) q^{84} +(1.45821 - 1.45821i) q^{85} +(3.39957 + 3.39957i) q^{86} +5.67492i q^{87} +(1.89083 + 5.87525i) q^{88} +(6.08327 + 6.08327i) q^{89} -0.484791 q^{90} +(-16.9906 - 0.581376i) q^{91} -2.96679 q^{92} +(-3.86547 + 3.86547i) q^{93} +8.18631i q^{94} -0.475000 q^{95} +(3.38826 + 3.38826i) q^{96} +(-1.76445 + 1.76445i) q^{97} +(18.3700 - 18.3700i) q^{98} +(-1.51398 + 2.95091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9}+O(q^{10}) \) 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9	\( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9} - 4 q^{15} - 20 q^{16} - 16 q^{20} - 8 q^{22} + 12 q^{26} + 28 q^{27} + 8 q^{31} - 32 q^{34} - 12 q^{37} + 36 q^{44} - 4 q^{45} - 40 q^{47} - 20 q^{48} + 8 q^{53} - 16 q^{55} + 16 q^{58} - 44 q^{59} - 16 q^{60} - 8 q^{66} - 20 q^{67} - 36 q^{70} - 60 q^{71} + 12 q^{78} - 8 q^{80} + 28 q^{81} + 48 q^{86} + 32 q^{89} + 4 q^{91} + 64 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) \) 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9 - 4 * q^15 - 20 * q^16 - 16 * q^20 - 8 * q^22 + 12 * q^26 + 28 * q^27 + 8 * q^31 - 32 * q^34 - 12 * q^37 + 36 * q^44 - 4 * q^45 - 40 * q^47 - 20 * q^48 + 8 * q^53 - 16 * q^55 + 16 * q^58 - 44 * q^59 - 16 * q^60 - 8 * q^66 - 20 * q^67 - 36 * q^70 - 60 * q^71 + 12 * q^78 - 8 * q^80 + 28 * q^81 + 48 * q^86 + 32 * q^89 + 4 * q^91 + 64 * q^92 + 8 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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