LMFDB - Embedded newform 735.2.v.a.472.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(178,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("735.178");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.v (of order $12$, degree $4$, not 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			472.3
Character	$\chi$	$=$	735.472
Dual form			735.2.v.a.313.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0611467 + 0.228203i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.68371 + 0.972092i) q^{4} +(-1.04485 - 1.97694i) q^{5} -0.236253i q^{6} +(-0.658899 + 0.658899i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.0611467 + 0.228203i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.68371 + 0.972092i) q^{4} +(-1.04485 - 1.97694i) q^{5} -0.236253i q^{6} +(-0.658899 + 0.658899i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.515032 - 0.117555i) q^{10} +(-1.99301 + 3.45200i) q^{11} +(-1.87794 - 0.503192i) q^{12} +(0.500437 + 0.500437i) q^{13} +(1.52092 + 1.63915i) q^{15} +(1.83411 + 3.17677i) q^{16} +(-0.614336 - 2.29273i) q^{17} +(0.0611467 + 0.228203i) q^{18} +(3.60925 + 6.25141i) q^{19} +(0.162536 - 4.34429i) q^{20} +(-0.665888 - 0.665888i) q^{22} +(7.04878 + 1.88872i) q^{23} +(0.465912 - 0.806983i) q^{24} +(-2.81657 + 4.13121i) q^{25} +(-0.144801 + 0.0836010i) q^{26} +(-0.707107 + 0.707107i) q^{27} -3.65191i q^{29} +(-0.467057 + 0.246849i) q^{30} +(4.27662 + 2.46911i) q^{31} +(-2.63724 + 0.706647i) q^{32} +(1.03166 - 3.85020i) q^{33} +0.560773 q^{34} +1.94418 q^{36} +(0.106980 - 0.399255i) q^{37} +(-1.64728 + 0.441387i) q^{38} +(-0.612908 - 0.353863i) q^{39} +(1.99105 + 0.614151i) q^{40} +7.63184i q^{41} +(3.65191 - 3.65191i) q^{43} +(-6.71132 + 3.87478i) q^{44} +(-1.89334 - 1.18965i) q^{45} +(-0.862019 + 1.49306i) q^{46} +(0.417052 + 0.111749i) q^{47} +(-2.59383 - 2.59383i) q^{48} +(-0.770530 - 0.895358i) q^{50} +(1.18681 + 2.05561i) q^{51} +(0.356122 + 1.32906i) q^{52} +(1.97527 + 7.37179i) q^{53} +(-0.118126 - 0.204601i) q^{54} +(8.90678 + 0.333235i) q^{55} +(-5.10425 - 5.10425i) q^{57} +(0.833375 + 0.223302i) q^{58} +(-3.05480 + 5.29106i) q^{59} +(0.967387 + 4.23833i) q^{60} +(-6.15784 + 3.55523i) q^{61} +(-0.824957 + 0.824957i) q^{62} +6.69141i q^{64} +(0.466451 - 1.51222i) q^{65} +(0.815543 + 0.470854i) q^{66} +(-1.28978 + 0.345596i) q^{67} +(1.19438 - 4.45750i) q^{68} -7.29744 q^{69} +1.19297 q^{71} +(-0.241174 + 0.900073i) q^{72} +(-1.88918 + 0.506205i) q^{73} +(0.0845694 + 0.0488262i) q^{74} +(1.65136 - 4.71943i) q^{75} +14.0341i q^{76} +(0.118230 - 0.118230i) q^{78} +(7.48269 - 4.32013i) q^{79} +(4.36391 - 6.94518i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.74161 - 0.466662i) q^{82} +(-11.9895 - 11.9895i) q^{83} +(-3.89070 + 3.61007i) q^{85} +(0.610073 + 1.05668i) q^{86} +(0.945184 + 3.52747i) q^{87} +(-0.961324 - 3.58771i) q^{88} +(-3.91290 - 6.77735i) q^{89} +(0.387253 - 0.359321i) q^{90} +(10.0321 + 10.0321i) q^{92} +(-4.76995 - 1.27810i) q^{93} +(-0.0510027 + 0.0883393i) q^{94} +(8.58751 - 13.6671i) q^{95} +(2.36449 - 1.36514i) q^{96} +(7.43671 - 7.43671i) q^{97} +3.98602i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 48 q^{8}+O(q^{10}) $ 32 * q + 48 * q^8	$ 32 q + 48 q^{8} + 16 q^{11} + 16 q^{15} + 48 q^{16} - 32 q^{22} + 40 q^{23} + 8 q^{30} - 48 q^{32} - 32 q^{36} - 32 q^{37} - 32 q^{43} - 64 q^{46} - 144 q^{50} + 16 q^{51} - 24 q^{53} + 16 q^{57} - 32 q^{58} - 40 q^{60} - 40 q^{65} + 32 q^{67} + 128 q^{71} - 24 q^{72} - 16 q^{78} + 16 q^{81} + 96 q^{85} - 64 q^{86} + 64 q^{88} - 80 q^{92} - 24 q^{93} + 72 q^{95}+O(q^{100}) $ 32 * q + 48 * q^8 + 16 * q^11 + 16 * q^15 + 48 * q^16 - 32 * q^22 + 40 * q^23 + 8 * q^30 - 48 * q^32 - 32 * q^36 - 32 * q^37 - 32 * q^43 - 64 * q^46 - 144 * q^50 + 16 * q^51 - 24 * q^53 + 16 * q^57 - 32 * q^58 - 40 * q^60 - 40 * q^65 + 32 * q^67 + 128 * q^71 - 24 * q^72 - 16 * q^78 + 16 * q^81 + 96 * q^85 - 64 * q^86 + 64 * q^88 - 80 * q^92 - 24 * q^93 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.0611467	+	0.228203i	−0.0432372	+	0.161364i	−0.984169	−	0.177233i	$-0.943285\pi$
$2$	−0.0611467	+	0.228203i	−0.0432372	+	0.161364i	0.940932	+	0.338596i	$0.109952\pi$
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	1.68371	+	0.972092i	0.841857	+	0.486046i
$5$	−1.04485	−	1.97694i	−0.467272	−	0.884114i
$5$	−1.04485	−	1.97694i	−0.467272	−	0.884114i
$6$		−	0.236253i		−	0.0964497i
$7$		0			0
$7$		0			0
$8$	−0.658899	+	0.658899i	−0.232956	+	0.232956i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	0.515032	−	0.117555i	0.162867	−	0.0371740i
$11$	−1.99301	+	3.45200i	−0.600915	+	1.04082i	0.391767	+	0.920064i	$0.371864\pi$
$11$	−1.99301	+	3.45200i	−0.600915	+	1.04082i	−0.992683	+	0.120752i	$0.961470\pi$
$12$	−1.87794	−	0.503192i	−0.542114	−	0.145259i
$13$	0.500437	+	0.500437i	0.138796	+	0.138796i	0.773091	−	0.634295i	$-0.218709\pi$
$13$	0.500437	+	0.500437i	0.138796	+	0.138796i	−0.634295	+	0.773091i	$0.718709\pi$
$14$		0			0
$15$	1.52092	+	1.63915i	0.392699	+	0.423226i
$16$	1.83411	+	3.17677i	0.458528	+	0.794194i
$17$	−0.614336	−	2.29273i	−0.148998	−	0.556070i	−0.999545	−	0.0301697i	$-0.990395\pi$
$17$	−0.614336	−	2.29273i	−0.148998	−	0.556070i	0.850546	−	0.525900i	$-0.176271\pi$
$18$	0.0611467	+	0.228203i	0.0144124	+	0.0537879i
$19$	3.60925	+	6.25141i	0.828019	+	1.43417i	0.899590	+	0.436735i	$0.143865\pi$
$19$	3.60925	+	6.25141i	0.828019	+	1.43417i	−0.0715711	+	0.997435i	$0.522801\pi$
$20$	0.162536	−	4.34429i	0.0363441	−	0.971413i
$21$		0			0
$22$	−0.665888	−	0.665888i	−0.141968	−	0.141968i
$23$	7.04878	+	1.88872i	1.46977	+	0.393824i	0.902853	−	0.429949i	$-0.141468\pi$
$23$	7.04878	+	1.88872i	1.46977	+	0.393824i	0.566919	+	0.823773i	$0.308135\pi$
$24$	0.465912	−	0.806983i	0.0951039	−	0.164725i
$25$	−2.81657	+	4.13121i	−0.563314	+	0.826243i
$26$	−0.144801	+	0.0836010i	−0.0283978	+	0.0163955i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	3.65191i		−	0.678143i	−0.940761	−	0.339071i	$-0.889887\pi$
$29$		−	3.65191i		−	0.678143i	0.940761	−	0.339071i	$-0.110113\pi$
$30$	−0.467057	+	0.246849i	−0.0852725	+	0.0450683i
$31$	4.27662	+	2.46911i	0.768103	+	0.443465i	0.832198	−	0.554479i	$-0.187083\pi$
$31$	4.27662	+	2.46911i	0.768103	+	0.443465i	−0.0640944	+	0.997944i	$0.520416\pi$
$32$	−2.63724	+	0.706647i	−0.466203	+	0.124919i
$33$	1.03166	−	3.85020i	0.179589	−	0.670234i
$34$	0.560773			0.0961717
$35$		0			0
$36$	1.94418			0.324031
$37$	0.106980	−	0.399255i	0.0175874	−	0.0656371i	−0.956574	−	0.291488i	$-0.905850\pi$
$37$	0.106980	−	0.399255i	0.0175874	−	0.0656371i	0.974162	+	0.225851i	$0.0725163\pi$
$38$	−1.64728	+	0.441387i	−0.267224	+	0.0716025i
$39$	−0.612908	−	0.353863i	−0.0981438	−	0.0566634i
$40$	1.99105	+	0.614151i	0.314813	+	0.0971058i
$41$			7.63184i			1.19189i	0.803024	+	0.595947i	$0.203223\pi$
$41$			7.63184i			1.19189i	−0.803024	+	0.595947i	$0.796777\pi$
$42$		0			0
$43$	3.65191	−	3.65191i	0.556911	−	0.556911i	−0.371516	−	0.928427i	$-0.621162\pi$
$43$	3.65191	−	3.65191i	0.556911	−	0.556911i	0.928427	+	0.371516i	$0.121162\pi$
$44$	−6.71132	+	3.87478i	−1.01177	+	0.584145i
$45$	−1.89334	−	1.18965i	−0.282242	−	0.177343i
$46$	−0.862019	+	1.49306i	−0.127098	+	0.220140i
$47$	0.417052	+	0.111749i	0.0608333	+	0.0163002i	0.289107	−	0.957297i	$-0.406642\pi$
$47$	0.417052	+	0.111749i	0.0608333	+	0.0163002i	−0.228274	+	0.973597i	$0.573308\pi$
$48$	−2.59383	−	2.59383i	−0.374386	−	0.374386i
$49$		0			0
$50$	−0.770530	−	0.895358i	−0.108969	−	0.126623i
$51$	1.18681	+	2.05561i	0.166186	+	0.287843i
$52$	0.356122	+	1.32906i	0.0493852	+	0.184308i
$53$	1.97527	+	7.37179i	0.271324	+	1.01259i	0.958265	+	0.285881i	$0.0922861\pi$
$53$	1.97527	+	7.37179i	0.271324	+	1.01259i	−0.686942	+	0.726713i	$0.741047\pi$
$54$	−0.118126	−	0.204601i	−0.0160750	−	0.0278426i
$55$	8.90678	+	0.333235i	1.20099	+	0.0449335i
$56$		0			0
$57$	−5.10425	−	5.10425i	−0.676075	−	0.676075i
$58$	0.833375	+	0.223302i	0.109428	+	0.0293210i
$59$	−3.05480	+	5.29106i	−0.397701	+	0.688838i	−0.993442	−	0.114339i	$-0.963525\pi$
$59$	−3.05480	+	5.29106i	−0.397701	+	0.688838i	0.595741	+	0.803176i	$0.296858\pi$
$60$	0.967387	+	4.23833i	0.124889	+	0.547166i
$61$	−6.15784	+	3.55523i	−0.788431	+	0.455201i	−0.839410	−	0.543499i	$-0.817099\pi$
$61$	−6.15784	+	3.55523i	−0.788431	+	0.455201i	0.0509788	+	0.998700i	$0.483766\pi$
$62$	−0.824957	+	0.824957i	−0.104770	+	0.104770i
$63$		0			0
$64$			6.69141i			0.836426i
$65$	0.466451	−	1.51222i	0.0578561	−	0.187567i
$66$	0.815543	+	0.470854i	0.100386	+	0.0579581i
$67$	−1.28978	+	0.345596i	−0.157572	+	0.0422212i	−0.336743	−	0.941597i	$-0.609325\pi$
$67$	−1.28978	+	0.345596i	−0.157572	+	0.0422212i	0.179171	+	0.983818i	$0.442659\pi$
$68$	1.19438	−	4.45750i	0.144840	−	0.540551i
$69$	−7.29744			−0.878508
$70$		0			0
$71$	1.19297			0.141579			0.0707897	−	0.997491i	$-0.477448\pi$
$71$	1.19297			0.141579			0.0707897	+	0.997491i	$0.477448\pi$
$72$	−0.241174	+	0.900073i	−0.0284226	+	0.106075i
$73$	−1.88918	+	0.506205i	−0.221112	+	0.0592469i	−0.367674	−	0.929955i	$-0.619846\pi$
$73$	−1.88918	+	0.506205i	−0.221112	+	0.0592469i	0.146562	+	0.989201i	$0.453179\pi$
$74$	0.0845694	+	0.0488262i	0.00983100	+	0.00567593i
$75$	1.65136	−	4.71943i	0.190683	−	0.544953i
$76$			14.0341i			1.60982i
$77$		0			0
$78$	0.118230	−	0.118230i	0.0133869	−	0.0133869i
$79$	7.48269	−	4.32013i	0.841868	−	0.486053i	−0.0160304	−	0.999872i	$-0.505103\pi$
$79$	7.48269	−	4.32013i	0.841868	−	0.486053i	0.857899	+	0.513819i	$0.171770\pi$
$80$	4.36391	−	6.94518i	0.487900	−	0.776495i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−1.74161	−	0.466662i	−0.192328	−	0.0515342i
$83$	−11.9895	−	11.9895i	−1.31602	−	1.31602i	−0.916898	−	0.399122i	$-0.869315\pi$
$83$	−11.9895	−	11.9895i	−1.31602	−	1.31602i	−0.399122	−	0.916898i	$-0.630685\pi$
$84$		0			0
$85$	−3.89070	+	3.61007i	−0.422006	+	0.391567i
$86$	0.610073	+	1.05668i	0.0657859	+	0.113944i
$87$	0.945184	+	3.52747i	0.101334	+	0.378185i
$88$	−0.961324	−	3.58771i	−0.102477	−	0.382451i
$89$	−3.91290	−	6.77735i	−0.414767	−	0.718397i	0.580637	−	0.814163i	$-0.302804\pi$
$89$	−3.91290	−	6.77735i	−0.414767	−	0.718397i	−0.995404	+	0.0957652i	$0.969470\pi$
$90$	0.387253	−	0.359321i	0.0408201	−	0.0378758i
$91$		0			0
$92$	10.0321	+	10.0321i	1.04592	+	1.04592i
$93$	−4.76995	−	1.27810i	−0.494620	−	0.132533i
$94$	−0.0510027	+	0.0883393i	−0.00526053	+	0.00911150i
$95$	8.58751	−	13.6671i	0.881060	−	1.40221i
$96$	2.36449	−	1.36514i	0.241325	−	0.139329i
$97$	7.43671	−	7.43671i	0.755083	−	0.755083i	−0.220340	−	0.975423i	$-0.570717\pi$
$97$	7.43671	−	7.43671i	0.755083	−	0.755083i	0.975423	+	0.220340i	$0.0707167\pi$
$98$		0			0
$99$			3.98602i			0.400610i
$100$	−8.75822	+	4.21782i	−0.875822	+	0.421782i
$101$	5.47010	+	3.15816i	0.544295	+	0.314249i	0.746818	−	0.665028i	$-0.231581\pi$
$101$	5.47010	+	3.15816i	0.544295	+	0.314249i	−0.202523	+	0.979278i	$0.564914\pi$
$102$	−0.541665	+	0.145139i	−0.0536328	+	0.0143709i
$103$	−4.59031	+	17.1313i	−0.452296	+	1.68799i	0.243620	+	0.969871i	$0.421665\pi$
$103$	−4.59031	+	17.1313i	−0.452296	+	1.68799i	−0.695917	+	0.718122i	$0.745002\pi$
$104$	−0.659476			−0.0646669
$105$		0			0
$106$	−1.80304			−0.175127
$107$	2.73794	−	10.2181i	0.264687	−	0.987825i	−0.697755	−	0.716337i	$-0.745817\pi$
$107$	2.73794	−	10.2181i	0.264687	−	0.987825i	0.962442	−	0.271488i	$-0.0875159\pi$
$108$	−1.87794	+	0.503192i	−0.180705	+	0.0484197i
$109$	−0.578698	−	0.334112i	−0.0554293	−	0.0320021i	0.472029	−	0.881583i	$-0.343522\pi$
$109$	−0.578698	−	0.334112i	−0.0554293	−	0.0320021i	−0.527459	+	0.849581i	$0.676855\pi$
$110$	−0.620666	+	2.01217i	−0.0591781	+	0.191853i
$111$			0.413339i			0.0392324i
$112$		0			0
$113$	−3.39653	+	3.39653i	−0.319518	+	0.319518i	−0.848582	−	0.529064i	$-0.822543\pi$
$113$	−3.39653	+	3.39653i	−0.319518	+	0.319518i	0.529064	+	0.848582i	$0.322543\pi$
$114$	1.47691	−	0.852695i	0.138325	−	0.0798622i
$115$	−3.63106	−	15.9084i	−0.338598	−	1.48347i
$116$	3.54999	−	6.14877i	0.329609	−	0.570899i
$117$	0.683610	+	0.183173i	0.0631998	+	0.0169343i
$118$	−1.02064	−	1.02064i	−0.0939578	−	0.0939578i
$119$		0			0
$120$	−2.08217	−	0.0779014i	−0.190075	−	0.00711139i
$121$	−2.44418	−	4.23345i	−0.222199	−	0.384859i
$122$	−0.434781	−	1.62263i	−0.0393633	−	0.146906i
$123$	−1.97527	−	7.37179i	−0.178104	−	0.664692i
$124$	4.80040	+	8.31453i	0.431088	+	0.746667i
$125$	11.1101	+	1.25168i	0.993713	+	0.111953i
$126$		0			0
$127$	−5.88837	−	5.88837i	−0.522508	−	0.522508i	0.395820	−	0.918328i	$-0.370460\pi$
$127$	−5.88837	−	5.88837i	−0.522508	−	0.522508i	−0.918328	+	0.395820i	$0.870460\pi$
$128$	−6.80149	−	1.82245i	−0.601172	−	0.161084i
$129$	−2.58229	+	4.47266i	−0.227358	+	0.393796i
$130$	0.316570	+	0.198912i	0.0277650	+	0.0174458i
$131$	16.2938	−	9.40722i	1.42359	−	0.821913i	0.426991	−	0.904256i	$-0.359574\pi$
$131$	16.2938	−	9.40722i	1.42359	−	0.821913i	0.996604	+	0.0823433i	$0.0262404\pi$
$132$	5.47977	−	5.47977i	0.476953	−	0.476953i
$133$		0			0
$134$		−	0.315463i		−	0.0272519i
$135$	2.13673	+	0.659085i	0.183900	+	0.0567250i
$136$	1.91547	+	1.10590i	0.164250	+	0.0948297i
$137$	1.10918	−	0.297204i	0.0947637	−	0.0253919i	−0.211126	−	0.977459i	$-0.567713\pi$
$137$	1.10918	−	0.297204i	0.0947637	−	0.0253919i	0.305889	+	0.952067i	$0.401046\pi$
$138$	0.446214	−	1.66529i	0.0379843	−	0.141759i
$139$	−0.442439			−0.0375272			−0.0187636	−	0.999824i	$-0.505973\pi$
$139$	−0.442439			−0.0375272			−0.0187636	+	0.999824i	$0.505973\pi$
$140$		0			0
$141$	−0.431764			−0.0363611
$142$	−0.0729461	+	0.272239i	−0.00612150	+	0.0228458i
$143$	−2.72489	+	0.730131i	−0.227866	+	0.0610566i
$144$	3.17677	+	1.83411i	0.264731	+	0.152843i
$145$	−7.21960	+	3.81570i	−0.599555	+	0.316877i
$146$		−	0.462070i		−	0.0382411i
$147$		0			0
$148$	0.568236	−	0.568236i	0.0467087	−	0.0467087i
$149$	−2.72031	+	1.57057i	−0.222856	+	0.128666i	−0.607272	−	0.794494i	$-0.707736\pi$
$149$	−2.72031	+	1.57057i	−0.222856	+	0.128666i	0.384416	+	0.923160i	$0.374403\pi$
$150$	0.976010	+	0.665422i	0.0796909	+	0.0543315i
$151$	7.36197	−	12.7513i	0.599109	−	1.03769i	−0.393844	−	0.919177i	$-0.628855\pi$
$151$	7.36197	−	12.7513i	0.599109	−	1.03769i	0.992953	−	0.118509i	$-0.0378116\pi$
$152$	−6.49718	−	1.74091i	−0.526991	−	0.141207i
$153$	−1.67840	−	1.67840i	−0.135690	−	0.135690i
$154$		0			0
$155$	0.412839	−	11.0345i	0.0331601	−	0.886309i
$156$	−0.687974	−	1.19161i	−0.0550820	−	0.0954049i
$157$	−2.91542	−	10.8805i	−0.232676	−	0.868358i	−0.979183	−	0.202980i	$-0.934937\pi$
$157$	−2.91542	−	10.8805i	−0.232676	−	0.868358i	0.746507	−	0.665378i	$-0.231729\pi$
$158$	0.528324	+	1.97173i	0.0420312	+	0.156862i
$159$	−3.81592	−	6.60937i	−0.302622	−	0.524157i
$160$	4.15253	+	4.47533i	0.328286	+	0.353806i
$161$		0			0
$162$	0.167056	+	0.167056i	0.0131251	+	0.0131251i
$163$	−14.2681	−	3.82312i	−1.11756	−	0.299450i	−0.347666	−	0.937619i	$-0.613026\pi$
$163$	−14.2681	−	3.82312i	−1.11756	−	0.299450i	−0.769897	+	0.638169i	$0.779692\pi$
$164$	−7.41885	+	12.8498i	−0.579315	+	1.00340i
$165$	−8.68954	+	1.98336i	−0.676480	+	0.154405i
$166$	3.46916	−	2.00292i	0.269259	−	0.155457i
$167$	4.63621	−	4.63621i	0.358761	−	0.358761i	−0.504595	−	0.863356i	$-0.668358\pi$
$167$	4.63621	−	4.63621i	0.358761	−	0.358761i	0.863356	+	0.504595i	$0.168358\pi$
$168$		0			0
$169$		−	12.4991i		−	0.961471i
$170$	−0.585924	−	1.10861i	−0.0449383	−	0.0850267i
$171$	6.25141	+	3.60925i	0.478057	+	0.276006i
$172$	9.69876	−	2.59878i	0.739524	−	0.198155i
$173$	−0.909686	+	3.39499i	−0.0691621	+	0.258117i	−0.991846	−	0.127440i	$-0.959324\pi$
$173$	−0.909686	+	3.39499i	−0.0691621	+	0.258117i	0.922684	+	0.385557i	$0.125991\pi$
$174$	−0.862773			−0.0654067
$175$		0			0
$176$	−14.6216			−1.10215
$177$	1.58128	−	5.90141i	0.118856	−	0.443577i
$178$	1.78587	−	0.478522i	0.133857	−	0.0358667i
$179$	−19.1486	−	11.0554i	−1.43123	−	0.826321i	−0.434016	−	0.900905i	$-0.642904\pi$
$179$	−19.1486	−	11.0554i	−1.43123	−	0.826321i	−0.997215	+	0.0745840i	$0.976237\pi$
$180$	−2.03138	−	3.84353i	−0.151410	−	0.286480i
$181$			8.48528i			0.630706i	0.948974	+	0.315353i	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$		0			0
$183$	5.02786	−	5.02786i	0.371670	−	0.371670i
$184$	−5.88891	+	3.39996i	−0.434136	+	0.250649i
$185$	−0.901080	+	0.205669i	−0.0662487	+	0.0151211i
$186$	0.583333	−	1.01036i	0.0427720	−	0.0740833i
$187$	9.13889	+	2.44876i	0.668302	+	0.179071i
$188$	0.593566	+	0.593566i	0.0432903	+	0.0432903i
$189$		0			0
$190$	2.59376	+	2.79539i	0.188171	+	0.202799i
$191$	−7.64492	−	13.2414i	−0.553167	−	0.958113i	−0.998044	−	0.0625216i	$-0.980086\pi$
$191$	−7.64492	−	13.2414i	−0.553167	−	0.958113i	0.444877	−	0.895592i	$-0.353248\pi$
$192$	−1.73186	−	6.46341i	−0.124987	−	0.466456i
$193$	−3.26783	−	12.1957i	−0.235223	−	0.877866i	−0.978048	−	0.208380i	$-0.933181\pi$
$193$	−3.26783	−	12.1957i	−0.235223	−	0.877866i	0.742825	−	0.669486i	$-0.233486\pi$
$194$	1.24235	+	2.15181i	0.0891952	+	0.154491i
$195$	−0.0591665	+	1.58142i	−0.00423700	+	0.113248i
$196$		0			0
$197$	−2.68715	−	2.68715i	−0.191451	−	0.191451i	0.604872	−	0.796323i	$-0.293224\pi$
$197$	−2.68715	−	2.68715i	−0.191451	−	0.191451i	−0.796323	+	0.604872i	$0.793224\pi$
$198$	−0.909620	−	0.243732i	−0.0646439	−	0.0173213i
$199$	−0.308318	+	0.534023i	−0.0218561	+	0.0378559i	−0.876747	−	0.480953i	$-0.840291\pi$
$199$	−0.308318	+	0.534023i	−0.0218561	+	0.0378559i	0.854890	+	0.518809i	$0.173624\pi$
$200$	−0.866218	−	4.57789i	−0.0612509	−	0.323706i
$201$	1.15639	−	0.667639i	0.0815651	−	0.0470917i
$202$	−1.05518	+	1.05518i	−0.0742422	+	0.0742422i
$203$		0			0
$204$			4.61474i			0.323097i
$205$	15.0877	−	7.97414i	1.05377	−	0.556938i
$206$	−3.62871	−	2.09504i	−0.252825	−	0.145968i
$207$	7.04878	−	1.88872i	0.489924	−	0.131275i
$208$	−0.671919	+	2.50763i	−0.0465892	+	0.173873i
$209$	−28.7731			−1.99028
$210$		0			0
$211$	9.30849			0.640823			0.320411	−	0.947278i	$-0.396179\pi$
$211$	9.30849			0.640823			0.320411	+	0.947278i	$0.396179\pi$
$212$	−3.84028	+	14.3321i	−0.263752	+	0.984334i
$213$	−1.15232	+	0.308763i	−0.0789557	+	0.0211561i
$214$	2.16439	+	1.24961i	0.147955	+	0.0854217i
$215$	−11.0353	−	3.40390i	−0.752602	−	0.232144i
$216$		−	0.931824i		−	0.0634026i
$217$		0			0
$218$	0.111631	−	0.111631i	0.00756058	−	0.00756058i
$219$	1.69380	−	0.977914i	0.114456	−	0.0660813i
$220$	14.6725	+	9.21929i	0.989222	+	0.621564i
$221$	0.839933	−	1.45481i	0.0565000	−	0.0978609i
$222$	−0.0943250	−	0.0252743i	−0.00633068	−	0.00169630i
$223$	−1.35505	−	1.35505i	−0.0907407	−	0.0907407i	0.660279	−	0.751020i	$-0.270438\pi$
$223$	−1.35505	−	1.35505i	−0.0907407	−	0.0907407i	−0.751020	+	0.660279i	$0.770438\pi$
$224$		0			0
$225$	−0.373614	+	4.98602i	−0.0249076	+	0.332401i
$226$	−0.567410	−	0.982782i	−0.0377435	−	0.0653737i
$227$	1.52061	+	5.67498i	0.100926	+	0.376662i	0.997851	−	0.0655211i	$-0.0208710\pi$
$227$	1.52061	+	5.67498i	0.100926	+	0.376662i	−0.896925	+	0.442183i	$0.854204\pi$
$228$	−3.63229	−	13.5559i	−0.240554	−	0.897761i
$229$	−6.49500	−	11.2497i	−0.429202	−	0.743399i	0.567601	−	0.823304i	$-0.307872\pi$
$229$	−6.49500	−	11.2497i	−0.429202	−	0.743399i	−0.996802	+	0.0799049i	$0.974538\pi$
$230$	3.85237	+	0.144131i	0.254018	+	0.00950374i
$231$		0			0
$232$	2.40624	+	2.40624i	0.157977	+	0.157977i
$233$	22.4901	+	6.02620i	1.47337	+	0.394790i	0.904087	−	0.427349i	$-0.140552\pi$
$233$	22.4901	+	6.02620i	1.47337	+	0.394790i	0.569288	+	0.822138i	$0.307219\pi$
$234$	−0.0836010	+	0.144801i	−0.00546517	+	0.00946595i
$235$	−0.214837	−	0.941247i	−0.0140144	−	0.0614002i
$236$	−10.2868	+	5.93909i	−0.669614	+	0.386602i
$237$	−6.10959	+	6.10959i	−0.396861	+	0.396861i
$238$		0			0
$239$			5.48048i			0.354503i	0.984166	+	0.177251i	$0.0567205\pi$
$239$			5.48048i			0.354503i	−0.984166	+	0.177251i	$0.943279\pi$
$240$	−2.41767	+	7.83800i	−0.156060	+	0.505940i
$241$	12.6879	+	7.32537i	0.817300	+	0.471868i	0.849485	−	0.527613i	$-0.176913\pi$
$241$	12.6879	+	7.32537i	0.817300	+	0.471868i	−0.0321844	+	0.999482i	$0.510246\pi$
$242$	1.11554	−	0.298908i	0.0717095	−	0.0192145i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−13.8241			−0.884995
$245$		0			0
$246$	1.80304			0.114958
$247$	−1.32223	+	4.93464i	−0.0841317	+	0.313984i
$248$	−4.44475	+	1.19097i	−0.282242	+	0.0756265i
$249$	14.6841	+	8.47787i	0.930567	+	0.537263i
$250$	−0.964979	+	2.45881i	−0.0610306	+	0.155509i
$251$			21.1506i			1.33501i	0.744604	+	0.667507i	$0.232639\pi$
$251$			21.1506i			1.33501i	−0.744604	+	0.667507i	$0.767361\pi$
$252$		0			0
$253$	−20.5681	+	20.5681i	−1.29311	+	1.29311i
$254$	1.70380	−	0.983687i	0.106906	−	0.0617220i
$255$	2.82378	−	4.49405i	0.176832	−	0.281428i
$256$	−5.85964	+	10.1492i	−0.366227	+	0.634324i
$257$	12.8304	+	3.43788i	0.800336	+	0.214449i	0.635731	−	0.771910i	$-0.280699\pi$
$257$	12.8304	+	3.43788i	0.800336	+	0.214449i	0.164604	+	0.986360i	$0.447365\pi$
$258$	−0.862773	−	0.862773i	−0.0537139	−	0.0537139i
$259$		0			0
$260$	2.25538	−	2.09271i	0.139873	−	0.129784i
$261$	−1.82596	−	3.16265i	−0.113024	−	0.195763i
$262$	1.15044	+	4.29350i	0.0710745	+	0.265254i
$263$	5.62869	+	21.0066i	0.347080	+	1.29532i	0.890163	+	0.455642i	$0.150590\pi$
$263$	5.62869	+	21.0066i	0.347080	+	1.29532i	−0.543083	+	0.839679i	$0.682743\pi$
$264$	1.85714	+	3.21665i	0.114299	+	0.197971i
$265$	12.5097	−	11.6074i	0.768466	−	0.713037i
$266$		0			0
$267$	5.53368	+	5.53368i	0.338656	+	0.338656i
$268$	−2.50757	−	0.671902i	−0.153174	−	0.0410429i
$269$	11.4926	−	19.9057i	0.700714	−	1.21367i	−0.267501	−	0.963557i	$-0.586198\pi$
$269$	11.4926	−	19.9057i	0.700714	−	1.21367i	0.968216	−	0.250116i	$-0.0804686\pi$
$270$	−0.281059	+	0.447306i	−0.0171047	+	0.0272222i
$271$	13.6483	−	7.87982i	0.829072	−	0.478665i	−0.0244625	−	0.999701i	$-0.507787\pi$
$271$	13.6483	−	7.87982i	0.829072	−	0.478665i	0.853535	+	0.521036i	$0.174454\pi$
$272$	6.15674	−	6.15674i	0.373307	−	0.373307i
$273$		0			0
$274$			0.271291i			0.0163893i
$275$	−8.64748	−	17.9563i	−0.521463	−	1.08281i
$276$	−12.2868	−	7.09378i	−0.739578	−	0.426995i
$277$	−6.56746	+	1.75975i	−0.394600	+	0.105733i	−0.450662	−	0.892694i	$-0.648812\pi$
$277$	−6.56746	+	1.75975i	−0.394600	+	0.105733i	0.0560621	+	0.998427i	$0.482146\pi$
$278$	0.0270537	−	0.100966i	0.00162257	−	0.00605553i
$279$	4.93821			0.295643
$280$		0			0
$281$	−9.65658			−0.576063			−0.288032	−	0.957621i	$-0.593001\pi$
$281$	−9.65658			−0.576063			−0.288032	+	0.957621i	$0.593001\pi$
$282$	0.0264009	−	0.0985297i	0.00157215	−	0.00586736i
$283$	−20.3668	+	5.45726i	−1.21068	+	0.324400i	−0.807028	−	0.590513i	$-0.798925\pi$
$283$	−20.3668	+	5.45726i	−1.21068	+	0.324400i	−0.403650	+	0.914913i	$0.632259\pi$
$284$	2.00862	+	1.15968i	0.119190	+	0.0688141i
$285$	−4.75760	+	15.4240i	−0.281816	+	0.913637i
$286$		−	0.666471i		−	0.0394092i
$287$		0			0
$288$	−1.93060	+	1.93060i	−0.113761	+	0.113761i
$289$	9.84321	−	5.68298i	0.579012	−	0.334293i
$290$	−0.429299	−	1.88085i	−0.0252093	−	0.110447i
$291$	−5.25855	+	9.10807i	−0.308261	+	0.533924i
$292$	−3.67292	−	0.984157i	−0.214942	−	0.0575934i
$293$	4.79236	+	4.79236i	0.279973	+	0.279973i	0.833098	−	0.553125i	$-0.186565\pi$
$293$	4.79236	+	4.79236i	0.279973	+	0.279973i	−0.553125	+	0.833098i	$0.686565\pi$
$294$		0			0
$295$	13.6519	+	0.510768i	0.794845	+	0.0297381i
$296$	0.192580	+	0.333558i	0.0111935	+	0.0193876i
$297$	−1.03166	−	3.85020i	−0.0598629	−	0.223411i
$298$	−0.192070	−	0.716817i	−0.0111263	−	0.0415241i
$299$	2.58229	+	4.47266i	0.149338	+	0.258660i
$300$	7.36814	−	6.34089i	0.425400	−	0.366091i
$301$		0			0
$302$	2.45972	+	2.45972i	0.141541	+	0.141541i
$303$	−6.10111	−	1.63479i	−0.350499	−	0.0939160i
$304$	−13.2395	+	22.9316i	−0.759340	+	1.31521i
$305$	13.4625	+	8.45899i	0.770861	+	0.484360i
$306$	0.485643	−	0.280386i	0.0277624	−	0.0160286i
$307$	9.85063	−	9.85063i	0.562205	−	0.562205i	−0.367728	−	0.929933i	$-0.619864\pi$
$307$	9.85063	−	9.85063i	0.562205	−	0.562205i	0.929933	+	0.367728i	$0.119864\pi$
$308$		0			0
$309$		−	17.7356i		−	1.00894i
$310$	2.49285	+	0.768932i	0.141584	+	0.0436724i
$311$	23.6480	+	13.6532i	1.34095	+	0.774200i	0.986947	−	0.161043i	$-0.0514858\pi$
$311$	23.6480	+	13.6532i	1.34095	+	0.774200i	0.354006	+	0.935243i	$0.384819\pi$
$312$	0.637004	−	0.170685i	0.0360633	−	0.00966313i
$313$	6.77439	−	25.2824i	0.382911	−	1.42904i	−0.458523	−	0.888683i	$-0.651621\pi$
$313$	6.77439	−	25.2824i	0.382911	−	1.42904i	0.841434	−	0.540361i	$-0.181712\pi$
$314$	2.66123			0.150182
$315$		0			0
$316$	16.7983			0.944977
$317$	−8.00839	+	29.8877i	−0.449796	+	1.67866i	0.253156	+	0.967425i	$0.418531\pi$
$317$	−8.00839	+	29.8877i	−0.449796	+	1.67866i	−0.702952	+	0.711237i	$0.748135\pi$
$318$	1.74161	−	0.466662i	0.0976644	−	0.0261691i
$319$	12.6064	+	7.27830i	0.705822	+	0.407506i
$320$	13.2285	−	6.99153i	0.739496	−	0.390839i
$321$			10.5786i			0.590440i
$322$		0			0
$323$	12.1155	−	12.1155i	0.674126	−	0.674126i
$324$	1.68371	−	0.972092i	0.0935396	−	0.0540051i
$325$	−3.47693	+	0.657897i	−0.192865	+	0.0364936i
$326$	1.74489	−	3.02224i	0.0966406	−	0.167386i
$327$	0.645454	+	0.172949i	0.0356937	+	0.00956410i
$328$	−5.02861	−	5.02861i	−0.277659	−	0.277659i
$329$		0			0
$330$	0.0787277	−	2.10425i	0.00433382	−	0.115835i
$331$	8.34566	+	14.4551i	0.458719	+	0.794524i	0.998894	−	0.0470286i	$-0.0149752\pi$
$331$	8.34566	+	14.4551i	0.458719	+	0.794524i	−0.540175	+	0.841553i	$0.681642\pi$
$332$	−8.53199	−	31.8418i	−0.468254	−	1.74755i
$333$	−0.106980	−	0.399255i	−0.00586246	−	0.0218790i
$334$	0.774506	+	1.34148i	0.0423791	+	0.0734027i
$335$	2.03085	+	2.18872i	0.110957	+	0.119583i
$336$		0			0
$337$	2.54028	+	2.54028i	0.138378	+	0.138378i	0.772903	−	0.634525i	$-0.218804\pi$
$337$	2.54028	+	2.54028i	0.138378	+	0.138378i	−0.634525	+	0.772903i	$0.718804\pi$
$338$	2.85233	+	0.764280i	0.155146	+	0.0415714i
$339$	2.40171	−	4.15988i	0.130443	−	0.225934i
$340$	−10.0602	+	2.29620i	−0.545589	+	0.124529i
$341$	−17.0467	+	9.84191i	−0.923130	+	0.532969i
$342$	−1.20589	+	1.20589i	−0.0652072	+	0.0652072i
$343$		0			0
$344$			4.81248i			0.259472i
$345$	7.62474	+	14.4266i	0.410502	+	0.776701i
$346$	−0.719122	−	0.415185i	−0.0386602	−	0.0223205i
$347$	−18.7118	+	5.01382i	−1.00450	+	0.269156i	−0.723331	−	0.690501i	$-0.757390\pi$
$347$	−18.7118	+	5.01382i	−1.00450	+	0.269156i	−0.281173	+	0.959657i	$0.590723\pi$
$348$	−1.83761	+	6.85806i	−0.0985063	+	0.367631i
$349$	0.508601			0.0272248			0.0136124	−	0.999907i	$-0.495667\pi$
$349$	0.508601			0.0272248			0.0136124	+	0.999907i	$0.495667\pi$
$350$		0			0
$351$	−0.707725			−0.0377756
$352$	2.81671	−	10.5121i	0.150131	−	0.560297i
$353$	−14.9193	+	3.99763i	−0.794077	+	0.212772i	−0.632982	−	0.774167i	$-0.718169\pi$
$353$	−14.9193	+	3.99763i	−0.794077	+	0.212772i	−0.161095	+	0.986939i	$0.551503\pi$
$354$	1.25003	+	0.721704i	0.0664382	+	0.0383581i
$355$	−1.24648	−	2.35843i	−0.0661561	−	0.125172i
$356$		−	15.2148i		−	0.806383i
$357$		0			0
$358$	3.69375	−	3.69375i	0.195221	−	0.195221i
$359$	−13.8443	+	7.99301i	−0.730674	+	0.421855i	−0.818669	−	0.574266i	$-0.805288\pi$
$359$	−13.8443	+	7.99301i	−0.730674	+	0.421855i	0.0879945	+	0.996121i	$0.471954\pi$
$360$	2.03138	−	0.463657i	0.107063	−	0.0244369i
$361$	−16.5534	+	28.6713i	−0.871231	+	1.50902i
$362$	−1.93636	−	0.518847i	−0.101773	−	0.0272700i
$363$	3.45660	+	3.45660i	0.181424	+	0.181424i
$364$		0			0
$365$	2.97465	+	3.20589i	0.155701	+	0.167804i
$366$	0.839933	+	1.45481i	0.0439040	+	0.0760440i
$367$	0.150084	+	0.560120i	0.00783431	+	0.0292380i	0.969732	−	0.244170i	$-0.0785156\pi$
$367$	0.150084	+	0.560120i	0.00783431	+	0.0292380i	−0.961898	+	0.273408i	$0.911849\pi$
$368$	6.92823	+	25.8565i	0.361159	+	1.34786i
$369$	3.81592	+	6.60937i	0.198649	+	0.344070i
$370$	0.00816384	−	0.218205i	0.000424418	−	0.0113439i
$371$		0			0
$372$	−6.78879	−	6.78879i	−0.351982	−	0.351982i
$373$	4.70591	+	1.26094i	0.243663	+	0.0652892i	0.378583	−	0.925567i	$-0.376411\pi$
$373$	4.70591	+	1.26094i	0.243663	+	0.0652892i	−0.134921	+	0.990856i	$0.543078\pi$
$374$	−1.11763	+	1.93578i	−0.0577911	+	0.100097i
$375$	−11.0554	+	1.66647i	−0.570901	+	0.0860559i
$376$	−0.348426	+	0.201164i	−0.0179687	+	0.0103742i
$377$	1.82755	−	1.82755i	0.0941237	−	0.0941237i
$378$		0			0
$379$		−	12.9179i		−	0.663547i	−0.943359	−	0.331773i	$-0.892353\pi$
$379$		−	12.9179i		−	0.663547i	0.943359	−	0.331773i	$-0.107647\pi$
$380$	27.7445	−	14.6636i	1.42327	−	0.752224i
$381$	7.21175	+	4.16371i	0.369469	+	0.213313i
$382$	3.48918	−	0.934923i	0.178522	−	0.0478348i
$383$	−3.68844	+	13.7654i	−0.188470	+	0.703381i	0.805391	+	0.592744i	$0.201956\pi$
$383$	−3.68844	+	13.7654i	−0.188470	+	0.703381i	−0.993861	+	0.110636i	$0.964711\pi$
$384$	7.04142			0.359331
$385$		0			0
$386$	2.98291			0.151826
$387$	1.33669	−	4.98860i	0.0679479	−	0.253585i
$388$	19.7504	−	5.29212i	1.00268	−	0.268666i
$389$	−21.0704	−	12.1650i	−1.06831	−	0.616791i	−0.140593	−	0.990068i	$-0.544901\pi$
$389$	−21.0704	−	12.1650i	−1.06831	−	0.616791i	−0.927720	+	0.373277i	$0.878234\pi$
$390$	−0.357265	−	0.110200i	−0.0180908	−	0.00558021i
$391$		−	17.3213i		−	0.875976i
$392$		0			0
$393$	−13.3038	+	13.3038i	−0.671089	+	0.671089i
$394$	0.777524	−	0.448904i	0.0391711	−	0.0226154i
$395$	−16.3589	−	10.2789i	−0.823108	−	0.517189i
$396$	−3.87478	+	6.71132i	−0.194715	+	0.337256i
$397$	−9.29762	−	2.49129i	−0.466634	−	0.125034i	0.0178380	−	0.999841i	$-0.494322\pi$
$397$	−9.29762	−	2.49129i	−0.466634	−	0.125034i	−0.484472	+	0.874807i	$0.660988\pi$
$398$	−0.103013	−	0.103013i	−0.00516356	−	0.00516356i
$399$		0			0
$400$	−18.2898	−	1.37050i	−0.914492	−	0.0685249i
$401$	4.41545	+	7.64778i	0.220497	+	0.381912i	0.954959	−	0.296738i	$-0.0958987\pi$
$401$	4.41545	+	7.64778i	0.220497	+	0.381912i	−0.734462	+	0.678650i	$0.762565\pi$
$402$	0.0816479	+	0.304714i	0.00407223	+	0.0151978i
$403$	0.904546	+	3.37581i	0.0450587	+	0.168161i
$404$	6.14006	+	10.6349i	0.305479	+	0.529105i
$405$	−2.23450	−	0.0836010i	−0.111033	−	0.00415417i
$406$		0			0
$407$	1.16501	+	1.16501i	0.0577476	+	0.0577476i
$408$	−2.13643	−	0.572453i	−0.105769	−	0.0283407i
$409$	11.5992	−	20.0905i	0.573546	−	0.993410i	−0.422652	−	0.906292i	$-0.638901\pi$
$409$	11.5992	−	20.0905i	0.573546	−	0.993410i	0.996198	−	0.0871183i	$-0.0277658\pi$
$410$	0.897158	+	3.93064i	0.0443075	+	0.194120i
$411$	−0.994464	+	0.574154i	−0.0490533	+	0.0283209i
$412$	−24.3819	+	24.3819i	−1.20121	+	1.20121i
$413$		0			0
$414$			1.72404i			0.0847319i
$415$	−11.1753	+	36.2298i	−0.548572	+	1.77845i
$416$	−1.67341	−	0.966143i	−0.0820456	−	0.0473690i
$417$	0.427364	−	0.114512i	0.0209281	−	0.00560766i
$418$	1.75938	−	6.56610i	0.0860541	−	0.321158i
$419$	13.0393			0.637009			0.318505	−	0.947921i	$-0.396819\pi$
$419$	13.0393			0.637009			0.318505	+	0.947921i	$0.396819\pi$
$420$		0			0
$421$	−31.3549			−1.52814			−0.764071	−	0.645132i	$-0.776802\pi$
$421$	−31.3549			−1.52814			−0.764071	+	0.645132i	$0.776802\pi$
$422$	−0.569183	+	2.12422i	−0.0277074	+	0.103405i
$423$	0.417052	−	0.111749i	0.0202778	−	0.00543341i
$424$	−6.15877	−	3.55577i	−0.299096	−	0.172683i
$425$	11.2021	+	3.91969i	0.543382	+	0.190133i
$426$		−	0.281842i		−	0.0136553i
$427$		0			0
$428$	14.5429	−	14.5429i	0.702957	−	0.702957i
$429$	2.44307	−	1.41050i	0.117952	−	0.0680998i
$430$	1.45155	−	2.31015i	0.0700000	−	0.111405i
$431$	11.2779	−	19.5339i	0.543238	−	0.940915i	−0.455478	−	0.890247i	$-0.650532\pi$
$431$	11.2779	−	19.5339i	0.543238	−	0.940915i	0.998716	−	0.0506681i	$-0.0161351\pi$
$432$	−3.54323	−	0.949406i	−0.170474	−	0.0456783i
$433$	−19.9639	−	19.9639i	−0.959405	−	0.959405i	0.0398028	−	0.999208i	$-0.487327\pi$
$433$	−19.9639	−	19.9639i	−0.959405	−	0.959405i	−0.999208	+	0.0398028i	$0.987327\pi$
$434$		0			0
$435$	5.98602	−	5.55426i	0.287008	−	0.266306i
$436$	−0.649575	−	1.12510i	−0.0311090	−	0.0538824i
$437$	13.6337	+	50.8816i	0.652188	+	2.43400i
$438$	0.119592	+	0.446325i	0.00571435	+	0.0213262i
$439$	−15.0972	−	26.1490i	−0.720548	−	1.24803i	−0.960780	−	0.277310i	$-0.910557\pi$
$439$	−15.0972	−	26.1490i	−0.720548	−	1.24803i	0.240232	−	0.970715i	$-0.422776\pi$
$440$	−6.08824	+	5.64910i	−0.290246	+	0.269310i
$441$		0			0
$442$	0.280632	+	0.280632i	0.0133483	+	0.0133483i
$443$	17.4063	+	4.66400i	0.826997	+	0.221593i	0.647403	−	0.762148i	$-0.275855\pi$
$443$	17.4063	+	4.66400i	0.826997	+	0.221593i	0.179594	+	0.983741i	$0.442522\pi$
$444$	−0.401803	+	0.695944i	−0.0190687	+	0.0330280i
$445$	−9.30999	+	14.8169i	−0.441336	+	0.702388i
$446$	0.392082	−	0.226369i	0.0185656	−	0.0107189i
$447$	2.22112	−	2.22112i	0.105056	−	0.105056i
$448$		0			0
$449$			30.4170i			1.43547i	0.696318	+	0.717734i	$0.254820\pi$
$449$			30.4170i			1.43547i	−0.696318	+	0.717734i	$0.745180\pi$
$450$	−1.11498	−	0.390138i	−0.0525605	−	0.0183913i
$451$	−26.3451	−	15.2103i	−1.24054	−	0.716227i
$452$	−9.02051	+	2.41704i	−0.424289	+	0.113688i
$453$	−3.81084	+	14.2222i	−0.179049	+	0.668219i
$454$	−1.38802			−0.0651432
$455$		0			0
$456$	6.72637			0.314991
$457$	0.481493	−	1.79696i	0.0225233	−	0.0840581i	−0.953749	−	0.300603i	$-0.902812\pi$
$457$	0.481493	−	1.79696i	0.0225233	−	0.0840581i	0.976273	+	0.216545i	$0.0694788\pi$
$458$	2.96435	−	0.794295i	0.138515	−	0.0371150i
$459$	2.05561	+	1.18681i	0.0959476	+	0.0553954i
$460$	9.35081	−	30.3150i	0.435984	−	1.41344i
$461$		−	1.29957i		−	0.0605272i	−0.999542	−	0.0302636i	$-0.990365\pi$
$461$		−	1.29957i		−	0.0605272i	0.999542	−	0.0302636i	$-0.00963467\pi$
$462$		0			0
$463$	16.5240	−	16.5240i	0.767934	−	0.767934i	−0.209809	−	0.977742i	$-0.567284\pi$
$463$	16.5240	−	16.5240i	0.767934	−	0.767934i	0.977742	+	0.209809i	$0.0672841\pi$
$464$	11.6013	−	6.69801i	0.538577	−	0.310947i
$465$	2.45716	+	10.7653i	0.113948	+	0.499230i
$466$	−2.75039	+	4.76381i	−0.127409	+	0.220679i
$467$	−27.4583	−	7.35742i	−1.27062	−	0.340461i	−0.440350	−	0.897826i	$-0.645146\pi$
$467$	−27.4583	−	7.35742i	−1.27062	−	0.340461i	−0.830267	+	0.557365i	$0.811812\pi$
$468$	0.972943	+	0.972943i	0.0449743	+	0.0449743i
$469$		0			0
$470$	0.227932	+	0.00852775i	0.0105137	+	0.000393356i
$471$	5.63216	+	9.75519i	0.259516	+	0.449495i
$472$	−1.47347	−	5.49908i	−0.0678221	−	0.253116i
$473$	5.32808	+	19.8847i	0.244986	+	0.914298i
$474$	−1.02064	−	1.76781i	−0.0468797	−	0.0811980i
$475$	−35.9916	−	2.69693i	−1.65141	−	0.123744i
$476$		0			0
$477$	5.39653	+	5.39653i	0.247090	+	0.247090i
$478$	−1.25066	−	0.335113i	−0.0572038	−	0.0153277i
$479$	5.54182	−	9.59872i	0.253212	−	0.438577i	−0.711196	−	0.702994i	$-0.751846\pi$
$479$	5.54182	−	9.59872i	0.253212	−	0.438577i	0.964408	+	0.264417i	$0.0851795\pi$
$480$	−5.16933	−	3.24808i	−0.235947	−	0.148254i
$481$	0.253339	−	0.146265i	0.0115513	−	0.00666912i
$482$	−2.44749	+	2.44749i	−0.111480	+	0.111480i
$483$		0			0
$484$		−	9.50389i		−	0.431995i
$485$	−22.4722	−	6.93165i	−1.02041	−	0.314750i
$486$	−0.204601	−	0.118126i	−0.00928088	−	0.00535832i
$487$	18.6489	−	4.99695i	0.845060	−	0.226433i	0.189787	−	0.981825i	$-0.439220\pi$
$487$	18.6489	−	4.99695i	0.845060	−	0.226433i	0.655273	+	0.755392i	$0.272554\pi$
$488$	1.71486	−	6.39994i	0.0776280	−	0.289712i
$489$	14.7714			0.667986
$490$		0			0
$491$	32.1155			1.44935			0.724677	−	0.689089i	$-0.241989\pi$
$491$	32.1155			1.44935			0.724677	+	0.689089i	$0.241989\pi$
$492$	3.84028	−	14.3321i	0.173133	−	0.646142i
$493$	−8.37286	+	2.24350i	−0.377095	+	0.101042i
$494$	−1.04525	−	0.603474i	−0.0470279	−	0.0271516i
$495$	7.88012	−	4.16480i	0.354185	−	0.187194i
$496$			18.1145i			0.813364i
$497$		0			0
$498$	−2.83255	+	2.83255i	−0.126930	+	0.126930i
$499$	3.70166	−	2.13715i	0.165709	−	0.0956722i	−0.414852	−	0.909889i	$-0.636167\pi$
$499$	3.70166	−	2.13715i	0.165709	−	0.0956722i	0.580561	+	0.814217i	$0.302833\pi$
$500$	17.4894	+	12.9075i	0.782150	+	0.577239i
$501$	−3.27830	+	5.67818i	−0.146463	+	0.253682i
$502$	−4.82662	−	1.29329i	−0.215423	−	0.0577223i
$503$	17.5637	+	17.5637i	0.783128	+	0.783128i	0.980357	−	0.197229i	$-0.0631943\pi$
$503$	17.5637	+	17.5637i	0.783128	+	0.783128i	−0.197229	+	0.980357i	$0.563194\pi$
$504$		0			0
$505$	0.528051	−	14.1139i	0.0234980	−	0.628059i
$506$	−3.43603	−	5.95138i	−0.152750	−	0.264571i
$507$	3.23501	+	12.0732i	0.143672	+	0.536191i
$508$	−4.19029	−	15.6384i	−0.185914	−	0.693840i
$509$	13.9581	+	24.1762i	0.618682	+	1.07159i	0.989726	+	0.142974i	$0.0456666\pi$
$509$	13.9581	+	24.1762i	0.618682	+	1.07159i	−0.371044	+	0.928615i	$0.621000\pi$
$510$	0.852889	+	0.919189i	0.0377666	+	0.0407024i
$511$		0			0
$512$	−11.9158	−	11.9158i	−0.526611	−	0.526611i
$513$	−6.97254	−	1.86829i	−0.307845	−	0.0824868i
$514$	−1.56907	+	2.71771i	−0.0692086	+	0.119873i
$515$	38.6636	−	8.82487i	1.70372	−	0.388870i
$516$	−8.69567	+	5.02045i	−0.382806	+	0.221013i
$517$	−1.21695	+	1.21695i	−0.0535212	+	0.0535212i
$518$		0			0
$519$		−	3.51476i		−	0.154281i
$520$	0.689054	+	1.30374i	0.0302170	+	0.0571729i
$521$	−24.9975	−	14.4323i	−1.09516	−	0.632292i	−0.160216	−	0.987082i	$-0.551219\pi$
$521$	−24.9975	−	14.4323i	−1.09516	−	0.632292i	−0.934946	+	0.354790i	$0.884552\pi$
$522$	0.833375	−	0.223302i	0.0364758	−	0.00977367i
$523$	−1.29832	+	4.84539i	−0.0567715	+	0.211874i	−0.988485	−	0.151321i	$-0.951647\pi$
$523$	−1.29832	+	4.84539i	−0.0567715	+	0.211874i	0.931713	+	0.363195i	$0.118314\pi$
$524$	36.5788			1.59795
$525$		0			0
$526$	−5.13793			−0.224024
$527$	3.03372	−	11.3220i	0.132151	−	0.493195i
$528$	14.1234	−	3.78435i	0.614642	−	0.164693i
$529$	26.1995	+	15.1263i	1.13911	+	0.657665i
$530$	1.88391	+	3.56450i	0.0818319	+	0.154832i
$531$			6.10959i			0.265134i
$532$		0			0
$533$	−3.81926	+	3.81926i	−0.165430	+	0.165430i
$534$	−1.60117	+	0.924434i	−0.0692892	+	0.0400042i
$535$	−23.0614	+	5.26370i	−0.997031	+	0.227570i
$536$	0.622122	−	1.07755i	0.0268716	−	0.0465430i
$537$	21.3574	+	5.72271i	0.921642	+	0.246953i
$538$	3.83980	+	3.83980i	0.165546	+	0.165546i
$539$		0			0
$540$	2.95695	+	3.18681i	0.127247	+	0.137138i
$541$	2.04349	+	3.53943i	0.0878565	+	0.152172i	0.906605	−	0.421981i	$-0.138665\pi$
$541$	2.04349	+	3.53943i	0.0878565	+	0.152172i	−0.818748	+	0.574153i	$0.805332\pi$
$542$	0.963650	+	3.59639i	0.0413923	+	0.154478i
$543$	−2.19615	−	8.19615i	−0.0942459	−	0.351731i
$544$	3.24031	+	5.61238i	0.138927	+	0.240629i
$545$	−0.0558641	+	1.49315i	−0.00239296	+	0.0639594i
$546$		0			0
$547$	28.2200	+	28.2200i	1.20660	+	1.20660i	0.972121	+	0.234482i	$0.0753392\pi$
$547$	28.2200	+	28.2200i	1.20660	+	1.20660i	0.234482	+	0.972121i	$0.424661\pi$
$548$	2.15645	+	0.577820i	0.0921191	+	0.0246832i
$549$	−3.55523	+	6.15784i	−0.151734	+	0.262810i
$550$	4.62645	−	0.875407i	0.197272	−	0.0373275i
$551$	22.8296	−	13.1807i	0.972572	−	0.561515i
$552$	4.80827	−	4.80827i	0.204654	−	0.204654i
$553$		0			0
$554$		−	1.60631i		−	0.0682457i
$555$	0.817145	−	0.431878i	0.0346859	−	0.0183322i
$556$	−0.744941	−	0.430092i	−0.0315925	−	0.0182400i
$557$	−38.4695	+	10.3079i	−1.63000	+	0.436758i	−0.953919	−	0.300065i	$-0.902992\pi$
$557$	−38.4695	+	10.3079i	−1.63000	+	0.436758i	−0.676086	+	0.736823i	$0.736325\pi$
$558$	−0.301955	+	1.12691i	−0.0127828	+	0.0477060i
$559$	3.65510			0.154594
$560$		0			0
$561$	−9.46128			−0.399455
$562$	0.590468	−	2.20366i	0.0249074	−	0.0929556i
$563$	37.3806	−	10.0161i	1.57541	−	0.422129i	0.637906	−	0.770114i	$-0.279801\pi$
$563$	37.3806	−	10.0161i	1.57541	−	0.422129i	0.937500	+	0.347985i	$0.113134\pi$
$564$	−0.726967	−	0.419715i	−0.0306108	−	0.0176732i
$565$	10.2636	+	3.16586i	0.431792	+	0.133189i
$566$		−	4.98144i		−	0.209386i
$567$		0			0
$568$	−0.786047	+	0.786047i	−0.0329818	+	0.0329818i
$569$	−15.3951	+	8.88837i	−0.645396	+	0.372620i	−0.786690	−	0.617348i	$-0.788207\pi$
$569$	−15.3951	+	8.88837i	−0.645396	+	0.372620i	0.141294	+	0.989968i	$0.454874\pi$
$570$	−3.22888	−	2.02882i	−0.135243	−	0.0849780i
$571$	8.44331	−	14.6242i	0.353342	−	0.612005i	−0.633491	−	0.773750i	$-0.718379\pi$
$571$	8.44331	−	14.6242i	0.353342	−	0.612005i	0.986833	+	0.161744i	$0.0517120\pi$
$572$	−5.29768	−	1.41951i	−0.221507	−	0.0593527i
$573$	10.8116	+	10.8116i	0.451659	+	0.451659i
$574$		0			0
$575$	−27.6561	+	23.8003i	−1.15334	+	0.992543i
$576$	3.34571	+	5.79493i	0.139404	+	0.241456i
$577$	1.42632	+	5.32309i	0.0593784	+	0.221603i	0.989239	−	0.146309i	$-0.0467394\pi$
$577$	1.42632	+	5.32309i	0.0593784	+	0.221603i	−0.929861	+	0.367912i	$0.880073\pi$
$578$	0.694991	+	2.59374i	0.0289078	+	0.107885i
$579$	6.31296	+	10.9344i	0.262358	+	0.454417i
$580$	−15.8650	−	0.593566i	−0.658756	−	0.0246465i
$581$		0			0
$582$	−1.75694	−	1.75694i	−0.0728276	−	0.0728276i
$583$	−29.3841	−	7.87345i	−1.21697	−	0.326085i
$584$	0.911244	−	1.57832i	0.0377075	−	0.0653114i
$585$	−0.352150	−	1.54284i	−0.0145596	−	0.0637887i
$586$	−1.38667	+	0.800592i	−0.0572826	+	0.0330721i
$587$	−15.1058	+	15.1058i	−0.623484	+	0.623484i	−0.946420	−	0.322937i	$-0.895330\pi$
$587$	−15.1058	+	15.1058i	−0.623484	+	0.623484i	0.322937	+	0.946420i	$0.395330\pi$
$588$		0			0
$589$			35.6465i			1.46879i
$590$	−0.951328	+	3.08417i	−0.0391655	+	0.126973i
$591$	3.29107	+	1.90010i	0.135377	+	0.0781597i
$592$	1.46456	−	0.392426i	0.0601928	−	0.0161286i
$593$	−1.25558	+	4.68590i	−0.0515606	+	0.192427i	−0.986902	−	0.161318i	$-0.948425\pi$
$593$	−1.25558	+	4.68590i	−0.0515606	+	0.192427i	0.935342	+	0.353745i	$0.115092\pi$
$594$	0.941708			0.0386388
$595$		0			0
$596$	−6.10696			−0.250151
$597$	0.159597	−	0.595625i	0.00653188	−	0.0243773i
$598$	−1.17857	+	0.315797i	−0.0481953	+	0.0129139i
$599$	−8.74769	−	5.05048i	−0.357421	−	0.206357i	0.310528	−	0.950564i	$-0.399494\pi$
$599$	−8.74769	−	5.05048i	−0.357421	−	0.206357i	−0.667949	+	0.744207i	$0.732827\pi$
$600$	2.02155	+	4.19771i	0.0825293	+	0.171371i
$601$		−	38.4063i		−	1.56663i	−0.621628	−	0.783313i	$-0.713528\pi$
$601$		−	38.4063i		−	1.56663i	0.621628	−	0.783313i	$-0.286472\pi$
$602$		0			0
$603$	−0.944185	+	0.944185i	−0.0384502	+	0.0384502i
$604$	24.7909	−	14.3130i	1.00873	−	0.582389i
$605$	−5.81546	+	9.25533i	−0.236432	+	0.376283i
$606$	0.746125	−	1.29233i	0.0303093	−	0.0524972i
$607$	−14.0606	−	3.76752i	−0.570702	−	0.152919i	−0.0380833	−	0.999275i	$-0.512125\pi$
$607$	−14.0606	−	3.76752i	−0.570702	−	0.152919i	−0.532618	+	0.846356i	$0.678792\pi$
$608$	−13.9360	−	13.9360i	−0.565180	−	0.565180i
$609$		0			0
$610$	−2.75355	+	2.55494i	−0.111488	+	0.103447i
$611$	0.152785	+	0.264632i	0.00618103	+	0.0107059i
$612$	−1.19438	−	4.45750i	−0.0482801	−	0.180184i
$613$	−5.27642	−	19.6919i	−0.213113	−	0.795347i	−0.986822	−	0.161807i	$-0.948268\pi$
$613$	−5.27642	−	19.6919i	−0.213113	−	0.795347i	0.773710	−	0.633540i	$-0.218399\pi$
$614$	1.64560	+	2.85027i	0.0664112	+	0.115028i
$615$	−12.5097	+	11.6074i	−0.504440	+	0.468056i
$616$		0			0
$617$	−25.4196	−	25.4196i	−1.02336	−	1.02336i	−0.999721	−	0.0236346i	$-0.992476\pi$
$617$	−25.4196	−	25.4196i	−1.02336	−	1.02336i	−0.0236346	−	0.999721i	$-0.507524\pi$
$618$	4.04731	+	1.08447i	0.162807	+	0.0436239i
$619$	5.59953	−	9.69868i	0.225064	−	0.389823i	−0.731274	−	0.682083i	$-0.761074\pi$
$619$	5.59953	−	9.69868i	0.225064	−	0.389823i	0.956339	+	0.292261i	$0.0944075\pi$
$620$	11.4216	−	18.1775i	0.458703	−	0.730028i
$621$	−6.31977	+	3.64872i	−0.253603	+	0.146418i
$622$	−4.56168	+	4.56168i	−0.182907	+	0.182907i
$623$		0			0
$624$		−	2.59609i		−	0.103927i
$625$	−9.13387	−	23.2717i	−0.365355	−	0.930868i
$626$	5.35527	+	3.09186i	0.214040	+	0.123576i
$627$	27.7927	−	7.44703i	1.10993	−	0.297406i
$628$	5.66812	−	21.1537i	0.226182	−	0.844124i
$629$	−0.981107			−0.0391193
$630$		0			0
$631$	21.2015			0.844020			0.422010	−	0.906591i	$-0.361325\pi$
$631$	21.2015			0.844020			0.422010	+	0.906591i	$0.361325\pi$
$632$	−2.08381	+	7.77687i	−0.0828894	+	0.309347i
$633$	−8.99131	+	2.40921i	−0.357373	+	0.0957577i
$634$	−6.33077	−	3.65507i	−0.251427	−	0.145161i
$635$	−5.48847	+	17.7934i	−0.217803	+	0.706110i
$636$		−	14.8377i		−	0.588353i
$637$		0			0
$638$	−2.43176	+	2.43176i	−0.0962745	+	0.0962745i
$639$	1.03314	−	0.596485i	0.0408705	−	0.0235966i
$640$	3.50367	+	15.3503i	0.138495	+	0.606774i
$641$	14.9484	−	25.8915i	0.590428	−	1.02265i	−0.403746	−	0.914871i	$-0.632292\pi$
$641$	14.9484	−	25.8915i	0.590428	−	1.02265i	0.994175	−	0.107781i	$-0.0343745\pi$
$642$	−2.41406	−	0.646846i	−0.0952755	−	0.0255290i
$643$	11.2813	+	11.2813i	0.444891	+	0.444891i	0.893652	−	0.448761i	$-0.148134\pi$
$643$	11.2813	+	11.2813i	0.444891	+	0.444891i	−0.448761	+	0.893652i	$0.648134\pi$
$644$		0			0
$645$	11.5403	+	0.431764i	0.454398	+	0.0170007i
$646$	2.02397	+	3.50562i	0.0796320	+	0.137927i
$647$	−9.60434	−	35.8439i	−0.377586	−	1.40917i	−0.849530	−	0.527540i	$-0.823114\pi$
$647$	−9.60434	−	35.8439i	−0.377586	−	1.40917i	0.471944	−	0.881628i	$-0.343552\pi$
$648$	0.241174	+	0.900073i	0.00947420	+	0.0353582i
$649$	−12.1765	−	21.0903i	−0.477969	−	0.827866i
$650$	0.0624689	−	0.833673i	0.00245023	−	0.0326993i
$651$		0			0
$652$	−20.3069	−	20.3069i	−0.795281	−	0.795281i
$653$	2.69982	+	0.723414i	0.105652	+	0.0283094i	0.311258	−	0.950326i	$-0.399250\pi$
$653$	2.69982	+	0.723414i	0.105652	+	0.0283094i	−0.205606	+	0.978635i	$0.565916\pi$
$654$	−0.0789348	+	0.136719i	−0.00308659	+	0.00534614i
$655$	−35.6221	−	22.3827i	−1.39187	−	0.874563i
$656$	−24.2446	+	13.9976i	−0.946594	+	0.546516i
$657$	−1.38298	+	1.38298i	−0.0539552	+	0.0539552i
$658$		0			0
$659$		−	15.1044i		−	0.588385i	−0.955746	−	0.294193i	$-0.904949\pi$
$659$		−	15.1044i		−	0.588385i	0.955746	−	0.294193i	$-0.0950507\pi$
$660$	−16.5587	−	5.10762i	−0.644547	−	0.198814i
$661$	0.953098	+	0.550272i	0.0370712	+	0.0214031i	0.518421	−	0.855125i	$-0.326520\pi$
$661$	0.953098	+	0.550272i	0.0370712	+	0.0214031i	−0.481350	+	0.876529i	$0.659853\pi$
$662$	−3.80900	+	1.02062i	−0.148041	+	0.0396675i
$663$	−0.434781	+	1.62263i	−0.0168855	+	0.0630176i
$664$	15.7998			0.613150
$665$		0			0
$666$	0.0976524			0.00378395
$667$	6.89742	−	25.7415i	0.267069	−	0.996716i
$668$	12.3129	−	3.29923i	0.476399	−	0.127651i
$669$	1.65959	+	0.958163i	0.0641633	+	0.0370447i
$670$	−0.623651	+	0.329612i	−0.0240937	+	0.0127340i
$671$		−	28.3425i		−	1.09415i
$672$		0			0
$673$	−11.4381	+	11.4381i	−0.440906	+	0.440906i	−0.892316	−	0.451411i	$-0.850921\pi$
$673$	−11.4381	+	11.4381i	−0.440906	+	0.440906i	0.451411	+	0.892316i	$0.350921\pi$
$674$	−0.735028	+	0.424369i	−0.0283122	+	0.0163461i
$675$	−0.929594	−	4.91283i	−0.0357801	−	0.189095i
$676$	12.1503	−	21.0449i	0.467319	−	0.809421i
$677$	33.6052	+	9.00447i	1.29155	+	0.346070i	0.838249	−	0.545287i	$-0.183579\pi$
$677$	33.6052	+	9.00447i	1.29155	+	0.346070i	0.453302	+	0.891357i	$0.350246\pi$
$678$	0.802438	+	0.802438i	0.0308175	+	0.0308175i
$679$		0			0
$680$	0.184908	−	4.94226i	0.00709089	−	0.189527i
$681$	−2.93759	−	5.08805i	−0.112569	−	0.194974i
$682$	−1.20360	−	4.49190i	−0.0460882	−	0.172004i
$683$	−5.07507	−	18.9404i	−0.194192	−	0.724736i	−0.992474	−	0.122452i	$-0.960924\pi$
$683$	−5.07507	−	18.9404i	−0.194192	−	0.724736i	0.798282	−	0.602284i	$-0.205742\pi$
$684$	7.01705	+	12.1539i	0.268304	+	0.464715i
$685$	−1.74648	−	1.88225i	−0.0667297	−	0.0719170i
$686$		0			0
$687$	9.18531	+	9.18531i	0.350442	+	0.350442i
$688$	18.2993	+	4.90328i	0.697655	+	0.186936i
$689$	−2.70062	+	4.67762i	−0.102886	+	0.178203i
$690$	−3.75841	+	0.857847i	−0.143080	+	0.0326577i
$691$	−10.7439	+	6.20301i	−0.408718	+	0.235974i	−0.690239	−	0.723582i	$-0.742495\pi$
$691$	−10.7439	+	6.20301i	−0.408718	+	0.235974i	0.281521	+	0.959555i	$0.409161\pi$
$692$	−4.83190	+	4.83190i	−0.183681	+	0.183681i
$693$		0			0
$694$		−	4.57667i		−	0.173728i
$695$	0.462284	+	0.874675i	0.0175354	+	0.0331783i
$696$	−2.94703	−	1.70147i	−0.111707	−	0.0644940i
$697$	17.4978	−	4.68852i	0.662776	−	0.177590i
$698$	−0.0310993	+	0.116064i	−0.00117713	+	0.00439309i
$699$	−23.2835			−0.880661
$700$		0			0
$701$	1.45193			0.0548388			0.0274194	−	0.999624i	$-0.491271\pi$
$701$	1.45193			0.0548388			0.0274194	+	0.999624i	$0.491271\pi$
$702$	0.0432751	−	0.161505i	0.00163331	−	0.00609560i
$703$	2.88202	−	0.772235i	0.108697	−	0.0291254i
$704$	−23.0987	−	13.3361i	−0.870566	−	0.502622i
$705$	0.451129	+	0.853571i	0.0169905	+	0.0321473i
$706$		−	3.64907i		−	0.137335i
$707$		0			0
$708$	8.39914	−	8.39914i	0.315659	−	0.315659i
$709$	−42.0269	+	24.2642i	−1.57835	+	0.911262i	−0.583262	+	0.812284i	$0.698224\pi$
$709$	−42.0269	+	24.2642i	−1.57835	+	0.911262i	−0.995090	+	0.0989781i	$0.968443\pi$
$710$	0.614417	−	0.140239i	0.0230587	−	0.00526308i
$711$	4.32013	−	7.48269i	0.162018	−	0.280623i
$712$	7.04380	+	1.88738i	0.263977	+	0.0707325i
$713$	25.4815	+	25.4815i	0.954290	+	0.954290i
$714$		0			0
$715$	4.29052	+	4.62405i	0.160457	+	0.172930i
$716$	−21.4938	−	37.2283i	−0.803261	−	1.39129i
$717$	−1.41845	−	5.29373i	−0.0529730	−	0.197698i
$718$	−0.977492	−	3.64805i	−0.0364797	−	0.136144i
$719$	−21.7936	−	37.7476i	−0.812764	−	1.40775i	−0.910922	−	0.412578i	$-0.864628\pi$
$719$	−21.7936	−	37.7476i	−0.812764	−	1.40775i	0.0981578	−	0.995171i	$-0.468705\pi$
$720$	0.306667	−	8.19666i	0.0114288	−	0.305472i
$721$		0			0
$722$	−5.53068	−	5.53068i	−0.205831	−	0.205831i
$723$	−14.1515	−	3.79189i	−0.526301	−	0.141022i
$724$	−8.24848	+	14.2868i	−0.306552	+	0.530964i
$725$	15.0868	+	10.2859i	0.560311	+	0.382007i
$726$	−1.00016	+	0.577445i	−0.0371196	+	0.0214310i
$727$	10.4498	−	10.4498i	0.387563	−	0.387563i	−0.486254	−	0.873817i	$-0.661637\pi$
$727$	10.4498	−	10.4498i	0.387563	−	0.387563i	0.873817	+	0.486254i	$0.161637\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−0.913483	+	0.482794i	−0.0338095	+	0.0178690i
$731$	−10.6164	−	6.12936i	−0.392660	−	0.226703i
$732$	13.3530	−	3.57793i	0.493542	−	0.132244i
$733$	6.90644	−	25.7752i	0.255095	−	0.952028i	−0.712942	−	0.701223i	$-0.752638\pi$
$733$	6.90644	−	25.7752i	0.255095	−	0.952028i	0.968037	−	0.250806i	$-0.0806955\pi$
$734$	−0.136998			−0.00505669
$735$		0			0
$736$	−19.9240			−0.734409
$737$	1.37755	−	5.14109i	0.0507428	−	0.189375i
$738$	−1.74161	+	0.466662i	−0.0641094	+	0.0171781i
$739$	−18.1596	−	10.4845i	−0.668013	−	0.385677i	0.127311	−	0.991863i	$-0.459366\pi$
$739$	−18.1596	−	10.4845i	−0.668013	−	0.385677i	−0.795323	+	0.606186i	$0.792699\pi$
$740$	−1.71709	−	0.529645i	−0.0631215	−	0.0194701i
$741$		−	5.10872i		−	0.187673i
$742$		0			0
$743$	9.18724	−	9.18724i	0.337047	−	0.337047i	−0.518208	−	0.855255i	$-0.673401\pi$
$743$	9.18724	−	9.18724i	0.337047	−	0.337047i	0.855255	+	0.518208i	$0.173401\pi$
$744$	3.98506	−	2.30077i	0.146099	−	0.0843504i
$745$	5.94724	+	3.73687i	0.217890	+	0.136908i
$746$	−0.575501	+	0.996797i	−0.0210706	+	0.0364953i
$747$	−16.3780	−	4.38847i	−0.599239	−	0.160566i
$748$	13.0069	+	13.0069i	0.475578	+	0.475578i
$749$		0			0
$750$	0.295712	−	2.62478i	0.0107979	−	0.0958434i
$751$	−5.59843	−	9.69676i	−0.204290	−	0.353840i	0.745617	−	0.666375i	$-0.232155\pi$
$751$	−5.59843	−	9.69676i	−0.204290	−	0.353840i	−0.949906	+	0.312535i	$0.898822\pi$
$752$	0.409919	+	1.52984i	0.0149482	+	0.0557875i
$753$	−5.47418	−	20.4299i	−0.199490	−	0.744507i
$754$	0.305303	+	0.528801i	0.0111185	+	0.0192578i
$755$	−32.9007	−	1.23094i	−1.19738	−	0.0447984i
$756$		0			0
$757$	−13.9324	−	13.9324i	−0.506383	−	0.506383i	0.407031	−	0.913414i	$-0.366564\pi$
$757$	−13.9324	−	13.9324i	−0.506383	−	0.506383i	−0.913414	+	0.407031i	$0.866564\pi$
$758$	2.94789	+	0.789886i	0.107072	+	0.0286899i
$759$	14.5439	−	25.1907i	0.527909	−	0.914365i
$760$	3.34691	+	14.6635i	0.121405	+	0.531902i
$761$	−7.61085	+	4.39412i	−0.275893	+	0.159287i	−0.631563	−	0.775325i	$-0.717586\pi$
$761$	−7.61085	+	4.39412i	−0.275893	+	0.159287i	0.355670	+	0.934612i	$0.384253\pi$
$762$	−1.39114	+	1.39114i	−0.0503958	+	0.0503958i
$763$		0			0
$764$		−	29.7263i		−	1.07546i
$765$	−1.56441	+	5.07177i	−0.0565615	+	0.183370i
$766$	−2.91577	−	1.68342i	−0.105351	−	0.0608245i
$767$	−4.17658	+	1.11911i	−0.150808	+	0.0404088i
$768$	3.03317	−	11.3199i	0.109450	−	0.408473i
$769$	−11.2183			−0.404543			−0.202271	−	0.979330i	$-0.564832\pi$
$769$	−11.2183			−0.404543			−0.202271	+	0.979330i	$0.564832\pi$
$770$		0			0
$771$	−13.2830			−0.478374
$772$	6.35326	−	23.7107i	0.228659	−	0.853366i
$773$	−29.3784	+	7.87192i	−1.05667	+	0.283133i	−0.745005	−	0.667059i	$-0.767553\pi$
$773$	−29.3784	+	7.87192i	−1.05667	+	0.283133i	−0.311663	+	0.950193i	$0.600886\pi$
$774$	1.05668	+	0.610073i	0.0379815	+	0.0219286i
$775$	−22.2458	+	10.7132i	−0.799093	+	0.384830i
$776$			9.80008i			0.351802i
$777$		0			0
$778$	4.06447	−	4.06447i	0.145718	−	0.145718i
$779$	−47.7097	+	27.5452i	−1.70938	+	0.986910i
$780$	−1.63690	+	2.60514i	−0.0586105	+	0.0932788i
$781$	−2.37760	+	4.11813i	−0.0850773	+	0.147358i
$782$	3.95276	+	1.05914i	0.141351	+	0.0378748i
$783$	2.58229	+	2.58229i	0.0922835	+	0.0922835i
$784$		0			0
$785$	−18.4639	+	17.1321i	−0.659004	+	0.611471i
$786$	−2.22248	−	3.84945i	−0.0792733	−	0.137305i
$787$	13.7140	+	51.1813i	0.488851	+	1.82442i	0.562055	+	0.827100i	$0.310011\pi$
$787$	13.7140	+	51.1813i	0.488851	+	1.82442i	−0.0732040	+	0.997317i	$0.523322\pi$
$788$	−1.91223	−	7.13654i	−0.0681204	−	0.254229i
$789$	−10.8738	−	18.8340i	−0.387118	−	0.670507i
$790$	3.34597	−	3.10463i	0.119044	−	0.110458i
$791$		0			0
$792$	−2.62639	−	2.62639i	−0.0933246	−	0.0933246i
$793$	−4.86079	−	1.30244i	−0.172612	−	0.0462511i
$794$	1.13704	−	1.96941i	0.0403520	−	0.0698916i
$795$	−9.07924	+	14.4496i	−0.322007	+	0.512476i
$796$	−1.03824	+	0.599428i	−0.0367994	+	0.0212462i
$797$	6.96365	−	6.96365i	0.246665	−	0.246665i	−0.572935	−	0.819601i	$-0.694195\pi$
$797$	6.96365	−	6.96365i	0.246665	−	0.246665i	0.819601	+	0.572935i	$0.194195\pi$
$798$		0			0
$799$		−	1.02484i		−	0.0362563i
$800$	4.50867	−	12.8853i	0.159406	−	0.455566i
$801$	−6.77735	−	3.91290i	−0.239466	−	0.138256i
$802$	−2.01523	+	0.539980i	−0.0711604	+	0.0190674i
$803$	2.01775	−	7.53033i	0.0712047	−	0.265740i
$804$	2.59603			0.0915549
$805$		0			0
$806$	−0.825679			−0.0290833
$807$	−5.94899	+	22.2019i	−0.209414	+	0.781545i
$808$	−5.68516	+	1.52333i	−0.200003	+	0.0535907i
$809$	36.5817	+	21.1205i	1.28614	+	0.742556i	0.977964	−	0.208772i	$-0.0669466\pi$
$809$	36.5817	+	21.1205i	1.28614	+	0.742556i	0.308180	+	0.951328i	$0.400280\pi$
$810$	0.155711	−	0.504808i	0.00547111	−	0.0177371i
$811$		−	34.9480i		−	1.22719i	−0.789620	−	0.613596i	$-0.789723\pi$
$811$		−	34.9480i		−	1.22719i	0.789620	−	0.613596i	$-0.210277\pi$
$812$		0			0
$813$	−11.1438	+	11.1438i	−0.390828	+	0.390828i
$814$	−0.337096	+	0.194622i	−0.0118152	+	0.00682151i
$815$	7.34996	+	32.2017i	0.257458	+	1.12798i
$816$	−4.35347	+	7.54044i	−0.152402	+	0.263968i
$817$	36.0102	+	9.64891i	1.25984	+	0.337573i
$818$	3.87544	+	3.87544i	0.135502	+	0.135502i
$819$		0			0
$820$	33.1549	+	1.24045i	1.15782	+	0.0433183i
$821$	2.06708	+	3.58030i	0.0721418	+	0.124953i	0.899840	−	0.436221i	$-0.143683\pi$
$821$	2.06708	+	3.58030i	0.0721418	+	0.124953i	−0.827698	+	0.561174i	$0.810350\pi$
$822$	−0.0702153	−	0.262047i	−0.00244904	−	0.00913994i
$823$	−2.09404	−	7.81506i	−0.0729936	−	0.272416i	0.919777	−	0.392441i	$-0.128369\pi$
$823$	−2.09404	−	7.81506i	−0.0729936	−	0.272416i	−0.992771	+	0.120025i	$0.961703\pi$
$824$	−8.26322	−	14.3123i	−0.287863	−	0.498593i
$825$	13.0003	+	15.1064i	0.452611	+	0.525936i
$826$		0			0
$827$	17.0630	+	17.0630i	0.593339	+	0.593339i	0.938532	−	0.345193i	$-0.112187\pi$
$827$	17.0630	+	17.0630i	0.593339	+	0.593339i	−0.345193	+	0.938532i	$0.612187\pi$
$828$	13.7041	+	3.67201i	0.476252	+	0.127611i
$829$	18.8573	−	32.6618i	0.654940	−	1.13439i	−0.326968	−	0.945035i	$-0.606027\pi$
$829$	18.8573	−	32.6618i	0.654940	−	1.13439i	0.981909	−	0.189355i	$-0.0606396\pi$
$830$	−7.58440	−	4.76555i	−0.263258	−	0.165415i
$831$	5.88822	−	3.39957i	0.204260	−	0.117930i
$832$	−3.34863	+	3.34863i	−0.116093	+	0.116093i
$833$		0			0
$834$			0.104527i			0.00361949i
$835$	−14.0097	−	4.32135i	−0.484824	−	0.149546i
$836$	−48.4457	−	27.9701i	−1.67553	−	0.967367i
$837$	−4.76995	+	1.27810i	−0.164873	+	0.0441777i
$838$	−0.797307	+	2.97559i	−0.0275425	+	0.102790i
$839$	22.3652			0.772133			0.386066	−	0.922471i	$-0.373834\pi$
$839$	22.3652			0.772133			0.386066	+	0.922471i	$0.373834\pi$
$840$		0			0
$841$	15.6636			0.540123
$842$	1.91725	−	7.15526i	0.0660727	−	0.246587i
$843$	9.32754	−	2.49931i	0.321258	−	0.0860807i
$844$	15.6728	+	9.04871i	0.539481	+	0.311470i
$845$	−24.7100	+	13.0597i	−0.850050	+	0.449268i
$846$			0.102005i			0.00350702i
$847$		0			0
$848$	−19.7957	+	19.7957i	−0.679786	+	0.679786i
$849$	18.2603	−	10.5426i	0.626693	−	0.361822i
$850$	−1.57945	+	2.31667i	−0.0541749	+	0.0794612i
$851$	1.50816	−	2.61220i	0.0516989	−	0.0895452i
$852$	−2.24032	−	0.600293i	−0.0767522	−	0.0205657i
$853$	24.1276	+	24.1276i	0.826114	+	0.826114i	0.986977	−	0.160863i	$-0.0514276\pi$
$853$	24.1276	+	24.1276i	0.826114	+	0.826114i	−0.160863	+	0.986977i	$0.551428\pi$
$854$		0			0
$855$	0.603474	−	16.1298i	0.0206384	−	0.551627i
$856$	4.92870	+	8.53675i	0.168459	+	0.291780i
$857$	−0.560372	−	2.09134i	−0.0191419	−	0.0714387i	0.955694	−	0.294361i	$-0.0951069\pi$
$857$	−0.560372	−	2.09134i	−0.0191419	−	0.0714387i	−0.974836	+	0.222923i	$0.928440\pi$
$858$	0.172495	+	0.643761i	0.00588889	+	0.0219777i
$859$	20.9047	+	36.2081i	0.713261	+	1.23540i	0.963627	+	0.267253i	$0.0861158\pi$
$859$	20.9047	+	36.2081i	0.713261	+	1.23540i	−0.250366	+	0.968151i	$0.580551\pi$
$860$	−15.2714	−	16.4585i	−0.520750	−	0.561231i
$861$		0			0
$862$	3.76808	+	3.76808i	0.128341	+	0.128341i
$863$	19.2128	+	5.14806i	0.654011	+	0.175242i	0.570542	−	0.821268i	$-0.306733\pi$
$863$	19.2128	+	5.14806i	0.654011	+	0.175242i	0.0834696	+	0.996510i	$0.473400\pi$
$864$	1.36514	−	2.36449i	0.0464429	−	0.0804415i
$865$	7.66218	−	1.74887i	0.260522	−	0.0594634i
$866$	5.77654	−	3.33509i	0.196295	−	0.113331i
$867$	−8.03695	+	8.03695i	−0.272949	+	0.272949i
$868$		0			0
$869$			34.4403i			1.16831i
$870$	0.901470	+	1.70565i	0.0305627	+	0.0578269i
$871$	−0.818403	−	0.472505i	−0.0277305	−	0.0160102i
$872$	0.601450	−	0.161158i	0.0203677	−	0.00545750i
$873$	2.72202	−	10.1587i	0.0921265	−	0.343821i
$874$	−12.4450			−0.420958
$875$		0			0
$876$	3.80249			0.128474
$877$	−14.4157	+	53.8001i	−0.486783	+	1.81670i	0.0851110	+	0.996371i	$0.472876\pi$
$877$	−14.4157	+	53.8001i	−0.486783	+	1.81670i	−0.571894	+	0.820328i	$0.693791\pi$
$878$	6.89042	−	1.84628i	0.232540	−	0.0623090i
$879$	−5.86942	−	3.38871i	−0.197971	−	0.114298i
$880$	15.2774	+	28.9060i	0.515002	+	0.974422i
$881$		−	25.7205i		−	0.866546i	−0.901263	−	0.433273i	$-0.857359\pi$
$881$		−	25.7205i		−	0.866546i	0.901263	−	0.433273i	$-0.142641\pi$
$882$		0			0
$883$	−25.0968	+	25.0968i	−0.844574	+	0.844574i	−0.989450	−	0.144876i	$-0.953722\pi$
$883$	−25.0968	+	25.0968i	−0.844574	+	0.844574i	0.144876	+	0.989450i	$0.453722\pi$
$884$	2.82841	−	1.63299i	0.0951298	−	0.0549232i
$885$	−13.3189	+	3.04001i	−0.447711	+	0.102189i
$886$	−2.12867	+	3.68697i	−0.0715142	+	0.123866i
$887$	51.7651	+	13.8704i	1.73810	+	0.465723i	0.982023	−	0.188760i	$-0.0604467\pi$
$887$	51.7651	+	13.8704i	1.73810	+	0.465723i	0.756077	+	0.654482i	$0.227113\pi$
$888$	−0.272349	−	0.272349i	−0.00913942	−	0.00913942i
$889$		0			0
$890$	−2.81198	−	3.03057i	−0.0942577	−	0.101585i
$891$	1.99301	+	3.45200i	0.0667684	+	0.115646i
$892$	−0.964280	−	3.59874i	−0.0322865	−	0.120495i
$893$	0.806659	+	3.01049i	0.0269938	+	0.100742i
$894$	0.371052	+	0.642680i	0.0124098	+	0.0214944i
$895$	−1.84849	+	49.4068i	−0.0617882	+	1.65149i
$896$		0			0
$897$	−3.65191	−	3.65191i	−0.121934	−	0.121934i
$898$	−6.94124	−	1.85990i	−0.231632	−	0.0620656i
$899$	9.01695	−	15.6178i	0.300732	−	0.520883i
$900$	−5.47593	+	8.03184i	−0.182531	+	0.267728i
$901$	15.6881	−	9.05752i	0.522646	−	0.301750i
$902$	5.08195	−	5.08195i	0.169211	−	0.169211i
$903$		0			0
$904$		−	4.47594i		−	0.148867i
$905$	16.7749	−	8.86586i	0.557616	−	0.294711i
$906$	−3.01253	−	1.73929i	−0.100085	−	0.0577839i
$907$	41.7950	−	11.1989i	1.38778	−	0.371855i	0.513840	−	0.857886i	$-0.328222\pi$
$907$	41.7950	−	11.1989i	1.38778	−	0.371855i	0.873942	+	0.486031i	$0.161556\pi$
$908$	−2.95634	+	11.0332i	−0.0981096	+	0.366150i
$909$	6.31633			0.209499
$910$		0			0
$911$	20.7843			0.688614			0.344307	−	0.938857i	$-0.388114\pi$
$911$	20.7843			0.688614			0.344307	+	0.938857i	$0.388114\pi$
$912$	6.85329	−	25.5768i	0.226935	−	0.846933i
$913$	65.2830	−	17.4925i	2.16055	−	0.578918i
$914$	0.380628	+	0.219756i	0.0125901	+	0.00726888i
$915$	−15.1931	−	4.68640i	−0.502269	−	0.154928i
$916$		−	25.2550i		−	0.834447i
$917$		0			0
$918$	−0.396526	+	0.396526i	−0.0130873	+	0.0130873i
$919$	41.2267	−	23.8023i	1.35994	−	0.785164i	0.370328	−	0.928901i	$-0.379245\pi$
$919$	41.2267	−	23.8023i	1.35994	−	0.785164i	0.989616	+	0.143737i	$0.0459119\pi$
$920$	12.8746	+	8.08955i	0.424462	+	0.266705i
$921$	−6.96544	+	12.0645i	−0.229519	+	0.397539i
$922$	0.296566	+	0.0794646i	0.00976688	+	0.00261703i
$923$	0.597007	+	0.597007i	0.0196507	+	0.0196507i
$924$		0			0
$925$	1.34809	+	1.56649i	0.0443249	+	0.0515057i
$926$	2.76043	+	4.78120i	0.0907132	+	0.157120i
$927$	4.59031	+	17.1313i	0.150765	+	0.562664i
$928$	2.58061	+	9.63098i	0.0847128	+	0.316152i
$929$	−20.3266	−	35.2067i	−0.666895	−	1.15510i	−0.978768	−	0.204972i	$-0.934290\pi$
$929$	−20.3266	−	35.2067i	−0.666895	−	1.15510i	0.311873	−	0.950124i	$-0.399044\pi$
$930$	−2.60692	−	0.0975344i	−0.0854843	−	0.00319828i
$931$		0			0
$932$	32.0088	+	32.0088i	1.04848	+	1.04848i
$933$	−26.3759	−	7.06740i	−0.863508	−	0.231376i
$934$	3.35797	−	5.81617i	0.109876	−	0.190311i
$935$	−4.70774	−	20.6256i	−0.153960	−	0.674530i
$936$	−0.571123	+	0.329738i	−0.0186677	+	0.0107778i
$937$	−8.25994	+	8.25994i	−0.269841	+	0.269841i	−0.829036	−	0.559195i	$-0.811110\pi$
$937$	−8.25994	+	8.25994i	−0.269841	+	0.269841i	0.559195	+	0.829036i	$0.311110\pi$
$938$		0			0
$939$			26.1742i			0.854163i
$940$	0.553255	−	1.79363i	0.0180452	−	0.0585018i
$941$	24.9263	+	14.3912i	0.812575	+	0.469140i	0.847849	−	0.530237i	$-0.177897\pi$
$941$	24.9263	+	14.3912i	0.812575	+	0.469140i	−0.0352744	+	0.999378i	$0.511231\pi$
$942$	−2.57055	+	0.688776i	−0.0837529	+	0.0224415i
$943$	−14.4144	+	53.7952i	−0.469397	+	1.75181i
$944$	−22.4113			−0.729427
$945$		0			0
$946$	−4.86353			−0.158127
$947$	1.56270	−	5.83206i	0.0507808	−	0.189516i	−0.935876	−	0.352329i	$-0.885390\pi$
$947$	1.56270	−	5.83206i	0.0507808	−	0.189516i	0.986657	+	0.162812i	$0.0520565\pi$
$948$	−16.2259	+	4.34771i	−0.526992	+	0.141207i
$949$	−1.19874	−	0.692094i	−0.0389128	−	0.0224663i
$950$	2.81621	−	8.04847i	0.0913700	−	0.261127i
$951$		−	30.9421i		−	1.00336i
$952$		0			0
$953$	31.8382	−	31.8382i	1.03134	−	1.03134i	0.0318472	−	0.999493i	$-0.489861\pi$
$953$	31.8382	−	31.8382i	1.03134	−	1.03134i	0.999493	−	0.0318472i	$-0.0101390\pi$
$954$	−1.56148	+	0.901521i	−0.0505548	+	0.0291878i
$955$	−18.1896	+	28.9488i	−0.588602	+	0.936762i
$956$	−5.32753	+	9.22755i	−0.172305	+	0.298440i
$957$	−14.0606	−	3.76752i	−0.454514	−	0.121787i
$958$	1.85159	+	1.85159i	0.0598221	+	0.0598221i
$959$		0			0
$960$	−10.9682	+	10.1771i	−0.353998	+	0.328464i
$961$	−3.30703	−	5.72794i	−0.106678	−	0.184772i
$962$	0.0178873	+	0.0667562i	0.000576708	+	0.00215231i
$963$	−2.73794	−	10.2181i	−0.0882290	−	0.329275i
$964$	14.2419	+	24.6676i	0.458700	+	0.794491i
$965$	−20.6957	+	19.2030i	−0.666220	+	0.618166i
$966$		0			0
$967$	−17.5518	−	17.5518i	−0.564429	−	0.564429i	0.366134	−	0.930562i	$-0.380681\pi$
$967$	−17.5518	−	17.5518i	−0.564429	−	0.564429i	−0.930562	+	0.366134i	$0.880681\pi$
$968$	4.39989	+	1.17895i	0.141418	+	0.0378928i
$969$	−8.56697	+	14.8384i	−0.275211	+	0.476679i
$970$	2.95592	−	4.70436i	0.0949089	−	0.151048i
$971$	0.0805953	−	0.0465317i	0.00258643	−	0.00149327i	−0.498706	−	0.866771i	$-0.666191\pi$
$971$	0.0805953	−	0.0465317i	0.00258643	−	0.00149327i	0.501293	+	0.865278i	$0.332858\pi$
$972$	−1.37475	+	1.37475i	−0.0440950	+	0.0440950i
$973$		0			0
$974$			4.56126i			0.146152i
$975$	3.18818	−	1.53538i	0.102104	−	0.0491714i
$976$	−22.5883	−	13.0414i	−0.723035	−	0.417445i
$977$	−7.10049	+	1.90257i	−0.227165	+	0.0608686i	−0.370606	−	0.928790i	$-0.620850\pi$
$977$	−7.10049	+	1.90257i	−0.227165	+	0.0608686i	0.143441	+	0.989659i	$0.454183\pi$
$978$	−0.903223	+	3.37087i	−0.0288819	+	0.107789i
$979$	31.1938			0.996959
$980$		0			0
$981$	−0.668223			−0.0213347
$982$	−1.96376	+	7.32884i	−0.0626660	+	0.233873i
$983$	41.5189	−	11.1249i	1.32425	−	0.354831i	0.473679	−	0.880697i	$-0.342926\pi$
$983$	41.5189	−	11.1249i	1.32425	−	0.354831i	0.850567	+	0.525867i	$0.176259\pi$
$984$	6.15877	+	3.55577i	0.196334	+	0.113354i
$985$	−2.50465	+	8.12000i	−0.0798049	+	0.258725i
$986$		−	2.04789i		−	0.0652181i
$987$		0			0
$988$	−7.02319	+	7.02319i	−0.223437	+	0.223437i
$989$	32.6389	−	18.8441i	1.03786	−	0.599208i
$990$	0.468575	+	2.05293i	0.0148923	+	0.0652463i
$991$	−17.1324	+	29.6742i	−0.544228	+	0.942631i	0.454427	+	0.890784i	$0.349844\pi$
$991$	−17.1324	+	29.6742i	−0.544228	+	0.942631i	−0.998655	+	0.0518468i	$0.983489\pi$
$992$	−13.0233	−	3.48957i	−0.413489	−	0.110794i
$993$	−11.8025	−	11.8025i	−0.374542	−	0.374542i
$994$		0			0
$995$	1.37788	+	0.0515514i	0.0436817	+	0.00163429i
$996$	16.4825	+	28.5486i	0.522269	+	0.904597i
$997$	−7.75273	−	28.9336i	−0.245532	−	0.916336i	−0.973116	−	0.230318i	$-0.926023\pi$
$997$	−7.75273	−	28.9336i	−0.245532	−	0.916336i	0.727584	−	0.686019i	$-0.240643\pi$
$998$	0.261360	+	0.975408i	0.00827320	+	0.0308760i
$999$	0.206669	+	0.357962i	0.00653873	+	0.0113254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.v.a.472.3		32
5.3	odd	4	inner	735.2.v.a.178.5		32
7.2	even	3	inner	735.2.v.a.607.6		32
7.3	odd	6		105.2.m.a.97.3	yes	16
7.4	even	3		105.2.m.a.97.4	yes	16
7.5	odd	6	inner	735.2.v.a.607.5		32
7.6	odd	2	inner	735.2.v.a.472.4		32
21.11	odd	6		315.2.p.e.307.5		16
21.17	even	6		315.2.p.e.307.6		16
28.3	even	6		1680.2.cz.d.97.5		16
28.11	odd	6		1680.2.cz.d.97.4		16
35.3	even	12		105.2.m.a.13.4	yes	16
35.4	even	6		525.2.m.b.307.5		16
35.13	even	4	inner	735.2.v.a.178.6		32
35.17	even	12		525.2.m.b.118.5		16
35.18	odd	12		105.2.m.a.13.3	✓	16
35.23	odd	12	inner	735.2.v.a.313.4		32
35.24	odd	6		525.2.m.b.307.6		16
35.32	odd	12		525.2.m.b.118.6		16
35.33	even	12	inner	735.2.v.a.313.3		32
105.38	odd	12		315.2.p.e.118.5		16
105.53	even	12		315.2.p.e.118.6		16
140.3	odd	12		1680.2.cz.d.433.4		16
140.123	even	12		1680.2.cz.d.433.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.3	✓	16	35.18	odd	12
105.2.m.a.13.4	yes	16	35.3	even	12
105.2.m.a.97.3	yes	16	7.3	odd	6
105.2.m.a.97.4	yes	16	7.4	even	3
315.2.p.e.118.5		16	105.38	odd	12
315.2.p.e.118.6		16	105.53	even	12
315.2.p.e.307.5		16	21.11	odd	6
315.2.p.e.307.6		16	21.17	even	6
525.2.m.b.118.5		16	35.17	even	12
525.2.m.b.118.6		16	35.32	odd	12
525.2.m.b.307.5		16	35.4	even	6
525.2.m.b.307.6		16	35.24	odd	6
735.2.v.a.178.5		32	5.3	odd	4	inner
735.2.v.a.178.6		32	35.13	even	4	inner
735.2.v.a.313.3		32	35.33	even	12	inner
735.2.v.a.313.4		32	35.23	odd	12	inner
735.2.v.a.472.3		32	1.1	even	1	trivial
735.2.v.a.472.4		32	7.6	odd	2	inner
735.2.v.a.607.5		32	7.5	odd	6	inner
735.2.v.a.607.6		32	7.2	even	3	inner
1680.2.cz.d.97.4		16	28.11	odd	6
1680.2.cz.d.97.5		16	28.3	even	6
1680.2.cz.d.433.4		16	140.3	odd	12
1680.2.cz.d.433.5		16	140.123	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0611467 + 0.228203i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.68371 + 0.972092i) q^{4} +(-1.04485 - 1.97694i) q^{5} -0.236253i q^{6} +(-0.658899 + 0.658899i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.0611467 + 0.228203i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.68371 + 0.972092i) q^{4} +(-1.04485 - 1.97694i) q^{5} -0.236253i q^{6} +(-0.658899 + 0.658899i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.515032 - 0.117555i) q^{10} +(-1.99301 + 3.45200i) q^{11} +(-1.87794 - 0.503192i) q^{12} +(0.500437 + 0.500437i) q^{13} +(1.52092 + 1.63915i) q^{15} +(1.83411 + 3.17677i) q^{16} +(-0.614336 - 2.29273i) q^{17} +(0.0611467 + 0.228203i) q^{18} +(3.60925 + 6.25141i) q^{19} +(0.162536 - 4.34429i) q^{20} +(-0.665888 - 0.665888i) q^{22} +(7.04878 + 1.88872i) q^{23} +(0.465912 - 0.806983i) q^{24} +(-2.81657 + 4.13121i) q^{25} +(-0.144801 + 0.0836010i) q^{26} +(-0.707107 + 0.707107i) q^{27} -3.65191i q^{29} +(-0.467057 + 0.246849i) q^{30} +(4.27662 + 2.46911i) q^{31} +(-2.63724 + 0.706647i) q^{32} +(1.03166 - 3.85020i) q^{33} +0.560773 q^{34} +1.94418 q^{36} +(0.106980 - 0.399255i) q^{37} +(-1.64728 + 0.441387i) q^{38} +(-0.612908 - 0.353863i) q^{39} +(1.99105 + 0.614151i) q^{40} +7.63184i q^{41} +(3.65191 - 3.65191i) q^{43} +(-6.71132 + 3.87478i) q^{44} +(-1.89334 - 1.18965i) q^{45} +(-0.862019 + 1.49306i) q^{46} +(0.417052 + 0.111749i) q^{47} +(-2.59383 - 2.59383i) q^{48} +(-0.770530 - 0.895358i) q^{50} +(1.18681 + 2.05561i) q^{51} +(0.356122 + 1.32906i) q^{52} +(1.97527 + 7.37179i) q^{53} +(-0.118126 - 0.204601i) q^{54} +(8.90678 + 0.333235i) q^{55} +(-5.10425 - 5.10425i) q^{57} +(0.833375 + 0.223302i) q^{58} +(-3.05480 + 5.29106i) q^{59} +(0.967387 + 4.23833i) q^{60} +(-6.15784 + 3.55523i) q^{61} +(-0.824957 + 0.824957i) q^{62} +6.69141i q^{64} +(0.466451 - 1.51222i) q^{65} +(0.815543 + 0.470854i) q^{66} +(-1.28978 + 0.345596i) q^{67} +(1.19438 - 4.45750i) q^{68} -7.29744 q^{69} +1.19297 q^{71} +(-0.241174 + 0.900073i) q^{72} +(-1.88918 + 0.506205i) q^{73} +(0.0845694 + 0.0488262i) q^{74} +(1.65136 - 4.71943i) q^{75} +14.0341i q^{76} +(0.118230 - 0.118230i) q^{78} +(7.48269 - 4.32013i) q^{79} +(4.36391 - 6.94518i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.74161 - 0.466662i) q^{82} +(-11.9895 - 11.9895i) q^{83} +(-3.89070 + 3.61007i) q^{85} +(0.610073 + 1.05668i) q^{86} +(0.945184 + 3.52747i) q^{87} +(-0.961324 - 3.58771i) q^{88} +(-3.91290 - 6.77735i) q^{89} +(0.387253 - 0.359321i) q^{90} +(10.0321 + 10.0321i) q^{92} +(-4.76995 - 1.27810i) q^{93} +(-0.0510027 + 0.0883393i) q^{94} +(8.58751 - 13.6671i) q^{95} +(2.36449 - 1.36514i) q^{96} +(7.43671 - 7.43671i) q^{97} +3.98602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 48 q^{8}+O(q^{10}) \) 32 * q + 48 * q^8	\( 32 q + 48 q^{8} + 16 q^{11} + 16 q^{15} + 48 q^{16} - 32 q^{22} + 40 q^{23} + 8 q^{30} - 48 q^{32} - 32 q^{36} - 32 q^{37} - 32 q^{43} - 64 q^{46} - 144 q^{50} + 16 q^{51} - 24 q^{53} + 16 q^{57} - 32 q^{58} - 40 q^{60} - 40 q^{65} + 32 q^{67} + 128 q^{71} - 24 q^{72} - 16 q^{78} + 16 q^{81} + 96 q^{85} - 64 q^{86} + 64 q^{88} - 80 q^{92} - 24 q^{93} + 72 q^{95}+O(q^{100}) \) 32 * q + 48 * q^8 + 16 * q^11 + 16 * q^15 + 48 * q^16 - 32 * q^22 + 40 * q^23 + 8 * q^30 - 48 * q^32 - 32 * q^36 - 32 * q^37 - 32 * q^43 - 64 * q^46 - 144 * q^50 + 16 * q^51 - 24 * q^53 + 16 * q^57 - 32 * q^58 - 40 * q^60 - 40 * q^65 + 32 * q^67 + 128 * q^71 - 24 * q^72 - 16 * q^78 + 16 * q^81 + 96 * q^85 - 64 * q^86 + 64 * q^88 - 80 * q^92 - 24 * q^93 + 72 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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