LMFDB - Embedded newform 234.2.z.a.227.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.13
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(1.41563 + 0.997997i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.175000 - 0.653109i) q^{5} +(1.33038 - 1.10909i) q^{6} +(2.85512 + 2.85512i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00801 + 2.82558i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(1.41563 + 0.997997i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.175000 - 0.653109i) q^{5} +(1.33038 - 1.10909i) q^{6} +(2.85512 + 2.85512i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00801 + 2.82558i) q^{9} +(-0.585562 - 0.338074i) q^{10} +(-0.686168 - 0.183858i) q^{11} +(-0.726972 - 1.57210i) q^{12} +(-1.25625 - 3.37962i) q^{13} +(3.49679 - 2.01888i) q^{14} +(0.899536 - 0.749910i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.24443 - 5.61952i) q^{17} +(2.99020 - 0.242344i) q^{18} +(-0.253608 - 0.0679541i) q^{19} +(-0.478109 + 0.478109i) q^{20} +(1.19239 + 6.89119i) q^{21} +(-0.355187 + 0.615201i) q^{22} +1.72101 q^{23} +(-1.70669 + 0.295310i) q^{24} +(3.93420 + 2.27141i) q^{25} +(-3.58960 + 0.338733i) q^{26} +(-1.39296 + 5.00596i) q^{27} +(-1.04505 - 3.90017i) q^{28} +(-1.11417 + 0.643269i) q^{29} +(-0.491541 - 1.06298i) q^{30} +(-3.89881 - 1.04468i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.787869 - 0.945068i) q^{33} +(-6.26776 + 1.67944i) q^{34} +(2.36435 - 1.36506i) q^{35} +(0.539833 - 2.95103i) q^{36} +(-7.96159 + 2.13330i) q^{37} +(-0.131277 + 0.227379i) q^{38} +(1.59447 - 6.03802i) q^{39} +(0.338074 + 0.585562i) q^{40} +(-6.55152 - 6.55152i) q^{41} +(6.96499 + 0.631813i) q^{42} +6.55772i q^{43} +(0.502310 + 0.502310i) q^{44} +(2.02182 - 0.163860i) q^{45} +(0.445430 - 1.66237i) q^{46} +(-2.43087 - 9.07214i) q^{47} +(-0.156476 + 1.72497i) q^{48} +9.30343i q^{49} +(3.21226 - 3.21226i) q^{50} +(1.01535 - 11.1931i) q^{51} +(-0.601867 + 3.55496i) q^{52} +6.34328i q^{53} +(4.47486 + 2.64114i) q^{54} +(-0.240159 + 0.415967i) q^{55} -4.03775 q^{56} +(-0.291197 - 0.349298i) q^{57} +(0.332981 + 1.24270i) q^{58} +(1.28969 + 4.81321i) q^{59} +(-1.15398 + 0.199673i) q^{60} +3.29863 q^{61} +(-2.01817 + 3.49557i) q^{62} +(-5.18941 + 10.9454i) q^{63} -1.00000i q^{64} +(-2.42711 + 0.229034i) q^{65} +(-1.11678 + 0.516421i) q^{66} +(-7.38704 + 7.38704i) q^{67} +6.48886i q^{68} +(2.43631 + 1.71756i) q^{69} +(-0.706607 - 2.63709i) q^{70} +(2.09577 - 7.82153i) q^{71} +(-2.71076 - 1.28522i) q^{72} +(-1.40415 - 1.40415i) q^{73} +8.24244i q^{74} +(3.30250 + 7.14179i) q^{75} +(0.185654 + 0.185654i) q^{76} +(-1.43416 - 2.48403i) q^{77} +(-5.41960 - 3.10289i) q^{78} +(7.29283 - 12.6316i) q^{79} +(0.653109 - 0.175000i) q^{80} +(-6.96785 + 5.69641i) q^{81} +(-8.02394 + 4.63262i) q^{82} +(3.90968 - 1.04760i) q^{83} +(2.41296 - 6.56414i) q^{84} +(-4.23794 + 1.13555i) q^{85} +(6.33427 + 1.69726i) q^{86} +(-2.21924 - 0.201313i) q^{87} +(0.615201 - 0.355187i) q^{88} +(2.64065 + 9.85503i) q^{89} +(0.365007 - 1.99533i) q^{90} +(6.06248 - 13.2360i) q^{91} +(-1.49044 - 0.860504i) q^{92} +(-4.47667 - 5.36988i) q^{93} -9.39217 q^{94} +(-0.0887629 + 0.153742i) q^{95} +(1.62569 + 0.597599i) q^{96} +(1.42324 - 1.42324i) q^{97} +(8.98642 + 2.40791i) q^{98} +(-0.172155 - 2.12416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	1.41563	+	0.997997i	0.817313	+	0.576194i
$3$	1.41563	+	0.997997i	0.817313	+	0.576194i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.175000	−	0.653109i	0.0782624	−	0.292079i	−0.915691	−	0.401883i	$-0.868356\pi$
$5$	0.175000	−	0.653109i	0.0782624	−	0.292079i	0.993953	+	0.109804i	$0.0350224\pi$
$6$	1.33038	−	1.10909i	0.543126	−	0.452785i
$7$	2.85512	+	2.85512i	1.07913	+	1.07913i	0.996587	+	0.0825471i	$0.0263055\pi$
$7$	2.85512	+	2.85512i	1.07913	+	1.07913i	0.0825471	+	0.996587i	$0.473694\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.00801	+	2.82558i	0.336002	+	0.941861i
$10$	−0.585562	−	0.338074i	−0.185171	−	0.106908i
$11$	−0.686168	−	0.183858i	−0.206887	−	0.0554353i	0.153887	−	0.988088i	$-0.450821\pi$
$11$	−0.686168	−	0.183858i	−0.206887	−	0.0554353i	−0.360774	+	0.932653i	$0.617488\pi$
$12$	−0.726972	−	1.57210i	−0.209859	−	0.453827i
$13$	−1.25625	−	3.37962i	−0.348421	−	0.937338i
$13$	−1.25625	−	3.37962i	−0.348421	−	0.937338i
$14$	3.49679	−	2.01888i	0.934558	−	0.539567i
$15$	0.899536	−	0.749910i	0.232259	−	0.193626i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−3.24443	−	5.61952i	−0.786890	−	1.36293i	−0.927863	−	0.372920i	$-0.878356\pi$
$17$	−3.24443	−	5.61952i	−0.786890	−	1.36293i	0.140973	−	0.990013i	$-0.454977\pi$
$18$	2.99020	−	0.242344i	0.704796	−	0.0571210i
$19$	−0.253608	−	0.0679541i	−0.0581817	−	0.0155897i	0.229611	−	0.973283i	$-0.426255\pi$
$19$	−0.253608	−	0.0679541i	−0.0581817	−	0.0155897i	−0.287792	+	0.957693i	$0.592921\pi$
$20$	−0.478109	+	0.478109i	−0.106908	+	0.106908i
$21$	1.19239	+	6.89119i	0.260200	+	1.50378i
$22$	−0.355187	+	0.615201i	−0.0757261	+	0.131161i
$23$	1.72101			0.358855			0.179427	−	0.983771i	$-0.442575\pi$
$23$	1.72101			0.358855			0.179427	+	0.983771i	$0.442575\pi$
$24$	−1.70669	+	0.295310i	−0.348377	+	0.0602799i
$25$	3.93420	+	2.27141i	0.786840	+	0.454282i
$26$	−3.58960	+	0.338733i	−0.703979	+	0.0664310i
$27$	−1.39296	+	5.00596i	−0.268076	+	0.963398i
$28$	−1.04505	−	3.90017i	−0.197495	−	0.737062i
$29$	−1.11417	+	0.643269i	−0.206897	+	0.119452i	−0.599869	−	0.800099i	$-0.704780\pi$
$29$	−1.11417	+	0.643269i	−0.206897	+	0.119452i	0.392971	+	0.919551i	$0.371447\pi$
$30$	−0.491541	−	1.06298i	−0.0897426	−	0.194072i
$31$	−3.89881	−	1.04468i	−0.700246	−	0.187630i	−0.108905	−	0.994052i	$-0.534735\pi$
$31$	−3.89881	−	1.04468i	−0.700246	−	0.187630i	−0.591341	+	0.806422i	$0.701401\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−0.787869	−	0.945068i	−0.137150	−	0.164515i
$34$	−6.26776	+	1.67944i	−1.07491	+	0.288022i
$35$	2.36435	−	1.36506i	0.399648	−	0.230737i
$36$	0.539833	−	2.95103i	0.0899722	−	0.491838i
$37$	−7.96159	+	2.13330i	−1.30888	+	0.350713i	−0.844800	−	0.535082i	$-0.820281\pi$
$37$	−7.96159	+	2.13330i	−1.30888	+	0.350713i	−0.464077	+	0.885795i	$0.653614\pi$
$38$	−0.131277	+	0.227379i	−0.0212960	+	0.0368857i
$39$	1.59447	−	6.03802i	0.255319	−	0.966857i
$40$	0.338074	+	0.585562i	0.0534542	+	0.0925854i
$41$	−6.55152	−	6.55152i	−1.02318	−	1.02318i	−0.999725	−	0.0234500i	$-0.992535\pi$
$41$	−6.55152	−	6.55152i	−1.02318	−	1.02318i	−0.0234500	−	0.999725i	$-0.507465\pi$
$42$	6.96499	+	0.631813i	1.07472	+	0.0974908i
$43$			6.55772i			1.00004i	0.866013	+	0.500021i	$0.166674\pi$
$43$			6.55772i			1.00004i	−0.866013	+	0.500021i	$0.833326\pi$
$44$	0.502310	+	0.502310i	0.0757261	+	0.0757261i
$45$	2.02182	−	0.163860i	0.301394	−	0.0244269i
$46$	0.445430	−	1.66237i	0.0656750	−	0.245102i
$47$	−2.43087	−	9.07214i	−0.354579	−	1.32331i	−0.881013	−	0.473092i	$-0.843138\pi$
$47$	−2.43087	−	9.07214i	−0.354579	−	1.32331i	0.526434	−	0.850216i	$-0.323529\pi$
$48$	−0.156476	+	1.72497i	−0.0225854	+	0.248978i
$49$			9.30343i			1.32906i
$50$	3.21226	−	3.21226i	0.454282	−	0.454282i
$51$	1.01535	−	11.1931i	0.142178	−	1.56735i
$52$	−0.601867	+	3.55496i	−0.0834640	+	0.492985i
$53$			6.34328i			0.871317i	0.900112	+	0.435658i	$0.143484\pi$
$53$			6.34328i			0.871317i	−0.900112	+	0.435658i	$0.856516\pi$
$54$	4.47486	+	2.64114i	0.608952	+	0.359413i
$55$	−0.240159	+	0.415967i	−0.0323830	+	0.0560890i
$56$	−4.03775			−0.539567
$57$	−0.291197	−	0.349298i	−0.0385700	−	0.0462656i
$58$	0.332981	+	1.24270i	0.0437225	+	0.163175i
$59$	1.28969	+	4.81321i	0.167904	+	0.626626i	0.997652	+	0.0684878i	$0.0218174\pi$
$59$	1.28969	+	4.81321i	0.167904	+	0.626626i	−0.829748	+	0.558138i	$0.811516\pi$
$60$	−1.15398	+	0.199673i	−0.148978	+	0.0257777i
$61$	3.29863			0.422346			0.211173	−	0.977449i	$-0.432272\pi$
$61$	3.29863			0.422346			0.211173	+	0.977449i	$0.432272\pi$
$62$	−2.01817	+	3.49557i	−0.256308	+	0.443938i
$63$	−5.18941	+	10.9454i	−0.653804	+	1.37899i
$64$		−	1.00000i		−	0.125000i
$65$	−2.42711	+	0.229034i	−0.301045	+	0.0284081i
$66$	−1.11678	+	0.516421i	−0.137466	+	0.0635671i
$67$	−7.38704	+	7.38704i	−0.902471	+	0.902471i	−0.995649	−	0.0931784i	$-0.970297\pi$
$67$	−7.38704	+	7.38704i	−0.902471	+	0.902471i	0.0931784	+	0.995649i	$0.470297\pi$
$68$			6.48886i			0.786890i
$69$	2.43631	+	1.71756i	0.293297	+	0.206770i
$70$	−0.706607	−	2.63709i	−0.0844556	−	0.315193i
$71$	2.09577	−	7.82153i	0.248722	−	0.928245i	−0.722753	−	0.691106i	$-0.757124\pi$
$71$	2.09577	−	7.82153i	0.248722	−	0.928245i	0.971476	−	0.237139i	$-0.0762096\pi$
$72$	−2.71076	−	1.28522i	−0.319466	−	0.151465i
$73$	−1.40415	−	1.40415i	−0.164343	−	0.164343i	0.620145	−	0.784488i	$-0.287074\pi$
$73$	−1.40415	−	1.40415i	−0.164343	−	0.164343i	−0.784488	+	0.620145i	$0.787074\pi$
$74$			8.24244i			0.958165i
$75$	3.30250	+	7.14179i	0.381340	+	0.824663i
$76$	0.185654	+	0.185654i	0.0212960	+	0.0212960i
$77$	−1.43416	−	2.48403i	−0.163437	−	0.283081i
$78$	−5.41960	−	3.10289i	−0.613649	−	0.351333i
$79$	7.29283	−	12.6316i	0.820507	−	1.42116i	−0.0847976	−	0.996398i	$-0.527024\pi$
$79$	7.29283	−	12.6316i	0.820507	−	1.42116i	0.905305	−	0.424762i	$-0.139642\pi$
$80$	0.653109	−	0.175000i	0.0730198	−	0.0195656i
$81$	−6.96785	+	5.69641i	−0.774205	+	0.632934i
$82$	−8.02394	+	4.63262i	−0.886096	+	0.511588i
$83$	3.90968	−	1.04760i	0.429144	−	0.114989i	−0.0377806	−	0.999286i	$-0.512029\pi$
$83$	3.90968	−	1.04760i	0.429144	−	0.114989i	0.466924	+	0.884297i	$0.345362\pi$
$84$	2.41296	−	6.56414i	0.263275	−	0.716206i
$85$	−4.23794	+	1.13555i	−0.459669	+	0.123168i
$86$	6.33427	+	1.69726i	0.683042	+	0.183020i
$87$	−2.21924	−	0.201313i	−0.237927	−	0.0215830i
$88$	0.615201	−	0.355187i	0.0655807	−	0.0378630i
$89$	2.64065	+	9.85503i	0.279908	+	1.04463i	0.952481	+	0.304600i	$0.0985226\pi$
$89$	2.64065	+	9.85503i	0.279908	+	1.04463i	−0.672573	+	0.740031i	$0.734811\pi$
$90$	0.365007	−	1.99533i	0.0384752	−	0.210327i
$91$	6.06248	−	13.2360i	0.635521	−	1.38751i
$92$	−1.49044	−	0.860504i	−0.155389	−	0.0897137i
$93$	−4.47667	−	5.36988i	−0.464209	−	0.556830i
$94$	−9.39217			−0.968729
$95$	−0.0887629	+	0.153742i	−0.00910688	+	0.0157736i
$96$	1.62569	+	0.597599i	0.165922	+	0.0609922i
$97$	1.42324	−	1.42324i	0.144508	−	0.144508i	−0.631151	−	0.775660i	$-0.717417\pi$
$97$	1.42324	−	1.42324i	0.144508	−	0.144508i	0.775660	+	0.631151i	$0.217417\pi$
$98$	8.98642	+	2.40791i	0.907766	+	0.243235i
$99$	−0.172155	−	2.12416i	−0.0173022	−	0.213486i
$100$	−2.27141	−	3.93420i	−0.227141	−	0.393420i
$101$	7.26007	+	12.5748i	0.722404	+	1.25124i	0.960034	+	0.279884i	$0.0902961\pi$
$101$	7.26007	+	12.5748i	0.722404	+	1.25124i	−0.237630	+	0.971356i	$0.576371\pi$
$102$	−10.5489	−	3.87774i	−1.04450	−	0.383953i
$103$	16.7121	−	9.64874i	1.64669	−	0.950719i	0.668319	−	0.743874i	$-0.267014\pi$
$103$	16.7121	−	9.64874i	1.64669	−	0.950719i	0.978374	−	0.206844i	$-0.0663194\pi$
$104$	3.27806	+	1.50145i	0.321440	+	0.147229i
$105$	4.70937	+	0.427199i	0.459587	+	0.0416904i
$106$	6.12714	+	1.64176i	0.595121	+	0.159462i
$107$	−11.5211	−	6.65169i	−1.11378	−	0.643043i	−0.173977	−	0.984750i	$-0.555662\pi$
$107$	−11.5211	−	6.65169i	−1.11378	−	0.643043i	−0.939807	+	0.341706i	$0.888995\pi$
$108$	3.70932	−	3.63881i	0.356930	−	0.350145i
$109$	7.63616	−	7.63616i	0.731412	−	0.731412i	−0.239488	−	0.970899i	$-0.576979\pi$
$109$	7.63616	−	7.63616i	0.731412	−	0.731412i	0.970899	+	0.239488i	$0.0769794\pi$
$110$	0.339636	+	0.339636i	0.0323830	+	0.0323830i
$111$	−13.3997	−	4.92568i	−1.27184	−	0.467525i
$112$	−1.04505	+	3.90017i	−0.0987476	+	0.368531i
$113$	13.1742	+	7.60612i	1.23932	+	0.715524i	0.968956	−	0.247233i	$-0.0795214\pi$
$113$	13.1742	+	7.60612i	1.23932	+	0.715524i	0.270368	+	0.962757i	$0.412855\pi$
$114$	−0.412763	+	0.190870i	−0.0386588	+	0.0178766i
$115$	0.301176	−	1.12401i	0.0280849	−	0.104814i
$116$	1.28654			0.119452
$117$	8.28310	−	6.95631i	0.765773	−	0.643111i
$118$	4.98300			0.458722
$119$	6.78117	−	25.3077i	0.621628	−	2.31995i
$120$	−0.105801	+	1.16633i	−0.00965829	+	0.106471i
$121$	−9.08926	−	5.24768i	−0.826296	−	0.477062i
$122$	0.853749	−	3.18623i	0.0772948	−	0.288468i
$123$	−2.73612	−	15.8129i	−0.246708	−	1.42580i
$124$	2.85412	+	2.85412i	0.256308	+	0.256308i
$125$	4.56251	−	4.56251i	0.408083	−	0.408083i
$126$	9.22929	+	7.84545i	0.822211	+	0.698928i
$127$	16.8933	+	9.75334i	1.49904	+	0.865469i	0.999999	−	0.00111133i	$-0.000353747\pi$
$127$	16.8933	+	9.75334i	1.49904	+	0.865469i	0.499037	+	0.866581i	$0.333687\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−6.54458	+	9.28329i	−0.576218	+	0.817348i
$130$	−0.406951	+	2.40368i	−0.0356920	+	0.210817i
$131$	−4.87564	+	2.81495i	−0.425986	+	0.245943i	−0.697635	−	0.716453i	$-0.745764\pi$
$131$	−4.87564	+	2.81495i	−0.425986	+	0.245943i	0.271649	+	0.962396i	$0.412431\pi$
$132$	0.209780	+	1.21239i	0.0182590	+	0.105525i
$133$	−0.530065	−	0.918099i	−0.0459625	−	0.0796093i
$134$	5.22343	+	9.04724i	0.451236	+	0.781563i
$135$	3.02567	+	1.78580i	0.260408	+	0.153697i
$136$	6.26776	+	1.67944i	0.537456	+	0.144011i
$137$	−8.31760	+	8.31760i	−0.710621	+	0.710621i	−0.966665	−	0.256044i	$-0.917581\pi$
$137$	−8.31760	+	8.31760i	−0.710621	+	0.710621i	0.256044	+	0.966665i	$0.417581\pi$
$138$	2.28960	−	1.90875i	0.194904	−	0.162484i
$139$	−1.48106	+	2.56527i	−0.125622	+	0.217584i	−0.921976	−	0.387247i	$-0.873426\pi$
$139$	−1.48106	+	2.56527i	−0.125622	+	0.217584i	0.796354	+	0.604831i	$0.206759\pi$
$140$	−2.73012			−0.230737
$141$	5.61276	−	15.2688i	0.472679	−	1.28586i
$142$	−7.01259	−	4.04872i	−0.588484	−	0.339761i
$143$	0.240627	+	2.54996i	0.0201222	+	0.213238i
$144$	−1.94302	+	2.28575i	−0.161919	+	0.190479i
$145$	0.225144	+	0.840250i	0.0186972	+	0.0697790i
$146$	−1.71972	+	0.992882i	−0.142325	+	0.0821715i
$147$	−9.28479	+	13.1702i	−0.765797	+	1.08626i
$148$	7.96159	+	2.13330i	0.654439	+	0.175356i
$149$	−22.4219	+	6.00794i	−1.83688	+	0.492189i	−0.998592	−	0.0530449i	$-0.983107\pi$
$149$	−22.4219	+	6.00794i	−1.83688	+	0.492189i	−0.838284	+	0.545234i	$0.816441\pi$
$150$	7.75319	−	1.34154i	0.633046	−	0.109536i
$151$	6.65733	−	1.78383i	0.541766	−	0.145166i	0.0224496	−	0.999748i	$-0.492853\pi$
$151$	6.65733	−	1.78383i	0.541766	−	0.145166i	0.519316	+	0.854582i	$0.326187\pi$
$152$	0.227379	−	0.131277i	0.0184429	−	0.0106480i
$153$	12.6080	−	14.8319i	1.01930	−	1.19909i
$154$	−2.77058	+	0.742373i	−0.223259	+	0.0598222i
$155$	−1.36458	+	2.36353i	−0.109606	+	0.189843i
$156$	−4.39986	+	4.43184i	−0.352271	+	0.354831i
$157$	−5.48299	−	9.49681i	−0.437590	−	0.757928i	0.559913	−	0.828551i	$-0.310835\pi$
$157$	−5.48299	−	9.49681i	−0.437590	−	0.757928i	−0.997503	+	0.0706232i	$0.977501\pi$
$158$	−10.3136	−	10.3136i	−0.820507	−	0.820507i
$159$	−6.33057	+	8.97973i	−0.502047	+	0.712139i
$160$		−	0.676148i		−	0.0534542i
$161$	4.91369	+	4.91369i	0.387253	+	0.387253i
$162$	3.69890	+	8.20476i	0.290613	+	0.644627i
$163$	3.31255	−	12.3626i	0.259459	−	0.968315i	−0.706096	−	0.708116i	$-0.749545\pi$
$163$	3.31255	−	12.3626i	0.259459	−	0.968315i	0.965555	−	0.260198i	$-0.0837880\pi$
$164$	2.39802	+	8.94954i	0.187254	+	0.698842i
$165$	−0.755110	+	0.349177i	−0.0587852	+	0.0271834i
$166$		−	4.04760i		−	0.314155i
$167$	−0.593992	+	0.593992i	−0.0459645	+	0.0459645i	−0.729715	−	0.683751i	$-0.760347\pi$
$167$	−0.593992	+	0.593992i	−0.0459645	+	0.0459645i	0.683751	+	0.729715i	$0.260347\pi$
$168$	−5.71595	−	4.02966i	−0.440995	−	0.310895i
$169$	−9.84368	+	8.49129i	−0.757206	+	0.653176i
$170$			4.38743i			0.336501i
$171$	−0.0636284	−	0.785089i	−0.00486579	−	0.0600373i
$172$	3.27886	−	5.67915i	0.250011	−	0.433031i
$173$	21.3169			1.62070			0.810349	−	0.585948i	$-0.199278\pi$
$173$	21.3169			1.62070			0.810349	+	0.585948i	$0.199278\pi$
$174$	−0.768834	+	2.09152i	−0.0582852	+	0.158557i
$175$	4.74746	+	17.7178i	0.358874	+	1.33934i
$176$	−0.183858	−	0.686168i	−0.0138588	−	0.0517219i
$177$	−2.97783	+	8.10082i	−0.223828	+	0.608895i
$178$	10.2027			0.764723
$179$	−0.120767	+	0.209175i	−0.00902656	+	0.0156345i	−0.870503	−	0.492162i	$-0.836207\pi$
$179$	−0.120767	+	0.209175i	−0.00902656	+	0.0156345i	0.861477	+	0.507797i	$0.169540\pi$
$180$	−1.83287	−	0.869001i	−0.136614	−	0.0647715i
$181$			1.73952i			0.129298i	0.997908	+	0.0646488i	$0.0205927\pi$
$181$			1.73952i			0.129298i	−0.997908	+	0.0646488i	$0.979407\pi$
$182$	−11.2159	−	9.28163i	−0.831376	−	0.688000i
$183$	4.66964	+	3.29202i	0.345189	+	0.243353i
$184$	−1.21694	+	1.21694i	−0.0897137	+	0.0897137i
$185$			5.57311i			0.409744i
$186$	−6.34555	+	2.93431i	−0.465278	+	0.215154i
$187$	1.19303	+	4.45245i	0.0872430	+	0.325595i
$188$	−2.43087	+	9.07214i	−0.177290	+	0.661654i
$189$	−18.2697	+	10.3156i	−1.32893	+	0.750346i
$190$	0.125530	+	0.125530i	0.00910688	+	0.00910688i
$191$			8.44838i			0.611304i	0.952143	+	0.305652i	$0.0988744\pi$
$191$			8.44838i			0.611304i	−0.952143	+	0.305652i	$0.901126\pi$
$192$	0.997997	−	1.41563i	0.0720242	−	0.102164i
$193$	0.0379467	+	0.0379467i	0.00273147	+	0.00273147i	0.708471	−	0.705740i	$-0.249385\pi$
$193$	0.0379467	+	0.0379467i	0.00273147	+	0.00273147i	−0.705740	+	0.708471i	$0.749385\pi$
$194$	−1.00638	−	1.74311i	−0.0722541	−	0.125148i
$195$	−3.66445	−	2.09802i	−0.262417	−	0.150242i
$196$	4.65172	−	8.05701i	0.332265	−	0.575501i
$197$	−2.56942	+	0.688475i	−0.183064	+	0.0490518i	−0.349186	−	0.937053i	$-0.613542\pi$
$197$	−2.56942	+	0.688475i	−0.183064	+	0.0490518i	0.166122	+	0.986105i	$0.446875\pi$
$198$	−2.09633	−	0.383483i	−0.148980	−	0.0272530i
$199$	−1.51087	+	0.872302i	−0.107103	+	0.0618359i	−0.552595	−	0.833450i	$-0.686362\pi$
$199$	−1.51087	+	0.872302i	−0.107103	+	0.0618359i	0.445492	+	0.895286i	$0.353029\pi$
$200$	−4.38803	+	1.17577i	−0.310281	+	0.0831394i
$201$	−17.8296	+	3.08506i	−1.25760	+	0.217604i
$202$	14.0254	−	3.75809i	0.986822	−	0.264418i
$203$	−5.01771	−	1.34449i	−0.352175	−	0.0943649i
$204$	−6.47586	+	9.18582i	−0.453401	+	0.643136i
$205$	−5.42537	+	3.13234i	−0.378924	+	0.218772i
$206$	−4.99456	−	18.6399i	−0.347987	−	1.29871i
$207$	1.73479	+	4.86285i	0.120576	+	0.337992i
$208$	2.29871	−	2.77775i	0.159387	−	0.192603i
$209$	0.161524	+	0.0932559i	0.0111728	+	0.00645064i
$210$	1.63152	−	4.43833i	0.112585	−	0.306274i
$211$	−1.30223			−0.0896495			−0.0448248	−	0.998995i	$-0.514273\pi$
$211$	−1.30223			−0.0896495			−0.0448248	+	0.998995i	$0.514273\pi$
$212$	3.17164	−	5.49344i	0.217829	−	0.377291i
$213$	10.7727	−	8.98080i	0.738133	−	0.615354i
$214$	−9.40691	+	9.40691i	−0.643043	+	0.643043i
$215$	4.28290	+	1.14760i	0.292092	+	0.0782657i
$216$	−2.55478	−	4.52472i	−0.173831	−	0.307868i
$217$	−8.14887	−	14.1143i	−0.553181	−	0.958138i
$218$	−5.39958	−	9.35235i	−0.365706	−	0.633421i
$219$	−0.586416	−	3.38908i	−0.0396263	−	0.229013i
$220$	0.415967	−	0.240159i	0.0280445	−	0.0161915i
$221$	−14.9160	+	18.0245i	−1.00336	+	1.21246i
$222$	−8.22593	+	11.6682i	−0.552088	+	0.783121i
$223$	18.4364	+	4.94002i	1.23459	+	0.330808i	0.816366	−	0.577535i	$-0.195985\pi$
$223$	18.4364	+	4.94002i	1.23459	+	0.330808i	0.418227	+	0.908343i	$0.362652\pi$
$224$	3.49679	+	2.01888i	0.233639	+	0.134892i
$225$	−2.45237	+	13.4060i	−0.163491	+	0.893734i
$226$	10.7567	−	10.7567i	0.715524	−	0.715524i
$227$	11.6214	+	11.6214i	0.771338	+	0.771338i	0.978340	−	0.207002i	$-0.0663708\pi$
$227$	11.6214	+	11.6214i	0.771338	+	0.771338i	−0.207002	+	0.978340i	$0.566371\pi$
$228$	0.0775350	+	0.448099i	0.00513488	+	0.0296761i
$229$	3.52092	−	13.1402i	0.232669	−	0.868332i	−0.746517	−	0.665366i	$-0.768275\pi$
$229$	3.52092	−	13.1402i	0.232669	−	0.868332i	0.979186	−	0.202965i	$-0.0650579\pi$
$230$	−1.00776	−	0.581828i	−0.0664495	−	0.0383646i
$231$	0.448823	−	4.94774i	0.0295304	−	0.325538i
$232$	0.332981	−	1.24270i	0.0218612	−	0.0815873i
$233$	−3.89618			−0.255247			−0.127623	−	0.991823i	$-0.540735\pi$
$233$	−3.89618			−0.255247			−0.127623	+	0.991823i	$0.540735\pi$
$234$	−4.57546	−	9.80128i	−0.299107	−	0.640730i
$235$	−6.35050			−0.414261
$236$	1.28969	−	4.81321i	0.0839520	−	0.313313i
$237$	22.9302	−	10.6034i	1.48948	−	0.688762i
$238$	−22.6902	−	13.1002i	−1.47079	−	0.849160i
$239$	0.407977	−	1.52259i	0.0263898	−	0.0984882i	−0.951475	−	0.307727i	$-0.900432\pi$
$239$	0.407977	−	1.52259i	0.0263898	−	0.0984882i	0.977865	+	0.209238i	$0.0670985\pi$
$240$	1.09921	+	0.404066i	0.0709536	+	0.0260823i
$241$	3.65205	+	3.65205i	0.235249	+	0.235249i	0.814879	−	0.579630i	$-0.196803\pi$
$241$	3.65205	+	3.65205i	0.235249	+	0.235249i	−0.579630	+	0.814879i	$0.696803\pi$
$242$	−7.42135	+	7.42135i	−0.477062	+	0.477062i
$243$	−15.5489	+	1.11011i	−0.997461	+	0.0712134i
$244$	−2.85670	−	1.64932i	−0.182881	−	0.105587i
$245$	6.07616	+	1.62810i	0.388191	+	0.104016i
$246$	−15.9823	−	1.44979i	−1.01899	−	0.0924353i
$247$	0.0889359	+	0.942467i	0.00565885	+	0.0599677i
$248$	3.49557	−	2.01817i	0.221969	−	0.128154i
$249$	6.58016	+	2.41884i	0.417000	+	0.153288i
$250$	−3.22618	−	5.58791i	−0.204042	−	0.353411i
$251$	−3.50515	−	6.07109i	−0.221243	−	0.383204i	0.733943	−	0.679211i	$-0.237678\pi$
$251$	−3.50515	−	6.07109i	−0.221243	−	0.383204i	−0.955186	+	0.296007i	$0.904345\pi$
$252$	9.96684	−	6.88426i	0.627852	−	0.433668i
$253$	−1.18090	−	0.316421i	−0.0742426	−	0.0198932i
$254$	13.7933	−	13.7933i	0.865469	−	0.865469i
$255$	−7.13262	−	2.62193i	−0.446662	−	0.164191i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.79217			0.236549			0.118275	−	0.992981i	$-0.462264\pi$
$257$	3.79217			0.236549			0.118275	+	0.992981i	$0.462264\pi$
$258$	7.27311	+	8.72427i	0.452804	+	0.543149i
$259$	−28.8221	−	16.6405i	−1.79092	−	1.03399i
$260$	2.21645	+	1.01520i	0.137458	+	0.0629603i
$261$	−2.94071	−	2.49978i	−0.182025	−	0.154732i
$262$	1.45713	+	5.43807i	0.0900215	+	0.335965i
$263$	−7.23499	+	4.17712i	−0.446129	+	0.257573i	−0.706194	−	0.708019i	$-0.749589\pi$
$263$	−7.23499	+	4.17712i	−0.446129	+	0.257573i	0.260065	+	0.965591i	$0.416256\pi$
$264$	1.22537	+	0.111157i	0.0754164	+	0.00684122i
$265$	4.14286	+	1.11007i	0.254494	+	0.0681914i
$266$	−1.02401	+	0.274382i	−0.0627859	+	0.0168234i
$267$	−6.09711	+	16.5864i	−0.373137	+	1.01507i
$268$	10.0909	−	2.70385i	0.616399	−	0.165164i
$269$	−3.60032	+	2.07864i	−0.219515	+	0.126737i	−0.605726	−	0.795674i	$-0.707117\pi$
$269$	−3.60032	+	2.07864i	−0.219515	+	0.126737i	0.386211	+	0.922411i	$0.373784\pi$
$270$	2.50805	−	2.46037i	0.152635	−	0.149734i
$271$	−20.1972	+	5.41182i	−1.22689	+	0.328745i	−0.813368	−	0.581749i	$-0.802369\pi$
$271$	−20.1972	+	5.41182i	−1.22689	+	0.328745i	−0.413523	+	0.910494i	$0.635702\pi$
$272$	3.24443	−	5.61952i	0.196723	−	0.340733i
$273$	21.7917	−	12.6869i	1.31889	−	0.767844i
$274$	5.88143	+	10.1869i	0.355310	+	0.615416i
$275$	−2.28190	−	2.28190i	−0.137604	−	0.137604i
$276$	−1.25112	−	2.70560i	−0.0753088	−	0.162858i
$277$		−	15.1838i		−	0.912308i	−0.889901	−	0.456154i	$-0.849227\pi$
$277$		−	15.1838i		−	0.912308i	0.889901	−	0.456154i	$-0.150773\pi$
$278$	2.09454	+	2.09454i	0.125622	+	0.125622i
$279$	−0.978182	−	12.0694i	−0.0585622	−	0.722579i
$280$	−0.706607	+	2.63709i	−0.0422278	+	0.157596i
$281$	7.82648	+	29.2088i	0.466889	+	1.74245i	0.650550	+	0.759463i	$0.274538\pi$
$281$	7.82648	+	29.2088i	0.466889	+	1.74245i	−0.183662	+	0.982990i	$0.558795\pi$
$282$	−13.2958	−	9.37336i	−0.791755	−	0.558175i
$283$			19.6844i			1.17012i	0.810991	+	0.585059i	$0.198928\pi$
$283$			19.6844i			1.17012i	−0.810991	+	0.585059i	$0.801072\pi$
$284$	−5.72576	+	5.72576i	−0.339761	+	0.339761i
$285$	−0.279089	+	0.129056i	−0.0165318	+	0.00764463i
$286$	2.52535	+	0.427550i	0.149327	+	0.0252816i
$287$		−	37.4107i		−	2.20829i
$288$	1.70497	+	2.46841i	0.100467	+	0.145453i
$289$	−12.5527	+	21.7419i	−0.738393	+	1.27893i
$290$	0.869891			0.0510817
$291$	3.43517	−	0.594390i	0.201373	−	0.0348438i
$292$	0.513954	+	1.91810i	0.0300769	+	0.112248i
$293$	−2.57173	−	9.59784i	−0.150242	−	0.560712i	−0.999466	−	0.0326785i	$-0.989596\pi$
$293$	−2.57173	−	9.59784i	−0.150242	−	0.560712i	0.849224	−	0.528033i	$-0.177070\pi$
$294$	10.3184	+	12.3771i	0.601779	+	0.721848i
$295$	3.36924			0.196165
$296$	4.12122	−	7.13817i	0.239541	−	0.414897i
$297$	1.87619	−	3.17882i	0.108868	−	0.184454i
$298$			23.2129i			1.34469i
$299$	−2.16201	−	5.81635i	−0.125033	−	0.336368i
$300$	0.710844	−	7.83623i	0.0410406	−	0.452425i
$301$	−18.7231	+	18.7231i	−1.07918	+	1.07918i
$302$		−	6.89217i		−	0.396600i
$303$	−2.27206	+	25.0468i	−0.130526	+	1.43890i
$304$	−0.0679541	−	0.253608i	−0.00389744	−	0.0145454i
$305$	0.577261	−	2.15437i	0.0330539	−	0.123359i
$306$	−11.0633	−	16.0172i	−0.632449	−	0.915642i
$307$	14.4825	+	14.4825i	0.826560	+	0.826560i	0.987039	−	0.160479i	$-0.0513040\pi$
$307$	14.4825	+	14.4825i	0.826560	+	0.826560i	−0.160479	+	0.987039i	$0.551304\pi$
$308$			2.86831i			0.163437i
$309$	33.2875	+	3.01960i	1.89366	+	0.171779i
$310$	1.92981	+	1.92981i	0.109606	+	0.109606i
$311$	11.3091	+	19.5879i	0.641281	+	1.11073i	0.985147	+	0.171712i	$0.0549299\pi$
$311$	11.3091	+	19.5879i	0.641281	+	1.11073i	−0.343866	+	0.939019i	$0.611737\pi$
$312$	3.14206	+	5.39698i	0.177884	+	0.305544i
$313$	−9.43419	+	16.3405i	−0.533252	+	0.923619i	0.465994	+	0.884788i	$0.345697\pi$
$313$	−9.43419	+	16.3405i	−0.533252	+	0.923619i	−0.999246	+	0.0388313i	$0.987636\pi$
$314$	−10.5923	+	2.83820i	−0.597759	+	0.160169i
$315$	6.24037	+	5.30469i	0.351605	+	0.298885i
$316$	−12.6316	+	7.29283i	−0.710580	+	0.410254i
$317$	−18.3643	+	4.92071i	−1.03144	+	0.276375i	−0.734563	−	0.678540i	$-0.762613\pi$
$317$	−18.3643	+	4.92071i	−1.03144	+	0.276375i	−0.296881	+	0.954915i	$0.595946\pi$
$318$	7.03528	+	8.43899i	0.394519	+	0.473235i
$319$	0.882781	−	0.236541i	0.0494263	−	0.0132437i
$320$	−0.653109	−	0.175000i	−0.0365099	−	0.00978280i
$321$	−9.67118	−	20.9143i	−0.539793	−	1.16732i
$322$	6.01801	−	3.47450i	0.335371	−	0.193626i
$323$	0.440945	+	1.64563i	0.0245348	+	0.0915652i
$324$	8.88254	−	1.44931i	0.493474	−	0.0805172i
$325$	2.73418	−	16.1496i	0.151665	−	0.895817i
$326$	−11.0840	−	6.39936i	−0.613887	−	0.354428i
$327$	18.4308	−	3.18910i	1.01923	−	0.176358i
$328$	9.26524			0.511588
$329$	18.9616	−	32.8425i	1.04539	−	1.81067i
$330$	0.141843	+	0.819754i	0.00780818	+	0.0451260i
$331$	−18.7189	+	18.7189i	−1.02889	+	1.02889i	−0.0293155	+	0.999570i	$0.509333\pi$
$331$	−18.7189	+	18.7189i	−1.02889	+	1.02889i	−0.999570	+	0.0293155i	$0.990667\pi$
$332$	−3.90968	−	1.04760i	−0.214572	−	0.0574943i
$333$	−14.0531	−	20.3458i	−0.770108	−	1.11494i
$334$	0.420016	+	0.727488i	0.0229822	+	0.0398064i
$335$	3.53181	+	6.11728i	0.192964	+	0.334223i
$336$	−5.37175	+	4.47823i	−0.293053	+	0.244308i
$337$	19.6500	−	11.3449i	1.07040	−	0.617996i	0.142110	−	0.989851i	$-0.454611\pi$
$337$	19.6500	−	11.3449i	1.07040	−	0.617996i	0.928291	+	0.371854i	$0.121278\pi$
$338$	5.65423	+	11.7060i	0.307549	+	0.636721i
$339$	11.0589	+	23.9152i	0.600635	+	1.29890i
$340$	4.23794	+	1.13555i	0.229834	+	0.0615839i
$341$	2.48316	+	1.43365i	0.134471	+	0.0776368i
$342$	−0.774806	−	0.141736i	−0.0418967	−	0.00766419i
$343$	−6.57658	+	6.57658i	−0.355102	+	0.355102i
$344$	−4.63701	−	4.63701i	−0.250011	−	0.250011i
$345$	1.54811	−	1.29060i	0.0833473	−	0.0694836i
$346$	5.51723	−	20.5906i	0.296608	−	1.10696i
$347$	14.3861	+	8.30581i	0.772286	+	0.445879i	0.833689	−	0.552234i	$-0.186224\pi$
$347$	14.3861	+	8.30581i	0.772286	+	0.445879i	−0.0614037	+	0.998113i	$0.519558\pi$
$348$	1.82126	+	1.28396i	0.0976298	+	0.0688275i
$349$	−0.581079	+	2.16862i	−0.0311044	+	0.116083i	−0.979733	−	0.200310i	$-0.935805\pi$
$349$	−0.581079	+	2.16862i	−0.0311044	+	0.116083i	0.948628	+	0.316393i	$0.102472\pi$
$350$	18.3428			0.980463
$351$	18.6682	−	1.58105i	0.996433	−	0.0843902i
$352$	−0.710373			−0.0378630
$353$	2.32242	−	8.66739i	0.123610	−	0.461319i	−0.876176	−	0.481991i	$-0.839914\pi$
$353$	2.32242	−	8.66739i	0.123610	−	0.461319i	0.999786	+	0.0206720i	$0.00658057\pi$
$354$	7.05407	+	4.97301i	0.374920	+	0.264313i
$355$	−4.74155	−	2.73754i	−0.251655	−	0.145293i
$356$	2.64065	−	9.85503i	0.139954	−	0.522315i
$357$	34.8566	−	29.0586i	1.84480	−	1.53795i
$358$	0.170790	+	0.170790i	0.00902656	+	0.00902656i
$359$	25.1620	−	25.1620i	1.32800	−	1.32800i	0.420885	−	0.907114i	$-0.361720\pi$
$359$	25.1620	−	25.1620i	1.32800	−	1.32800i	0.907114	−	0.420885i	$-0.138280\pi$
$360$	−1.31377	+	1.54551i	−0.0692419	+	0.0814553i
$361$	−16.3948	−	9.46553i	−0.862883	−	0.498186i
$362$	1.68025	+	0.450221i	0.0883119	+	0.0236631i
$363$	−7.62984	−	16.4998i	−0.400463	−	0.866016i
$364$	−11.8683	+	8.43144i	−0.622065	+	0.441928i
$365$	−1.16279	+	0.671335i	−0.0608631	+	0.0351393i
$366$	4.38844	−	3.65848i	0.229387	−	0.191232i
$367$	−11.5999	−	20.0916i	−0.605509	−	1.04877i	−0.991971	−	0.126467i	$-0.959636\pi$
$367$	−11.5999	−	20.0916i	−0.605509	−	1.04877i	0.386462	−	0.922305i	$-0.373697\pi$
$368$	0.860504	+	1.49044i	0.0448569	+	0.0776944i
$369$	11.9079	−	25.1158i	0.619900	−	1.30748i
$370$	5.38322	+	1.44243i	0.279860	+	0.0749883i
$371$	−18.1108	+	18.1108i	−0.940268	+	0.940268i
$372$	1.19197	+	6.88878i	0.0618009	+	0.357167i
$373$	15.0231	−	26.0208i	0.777866	−	1.34730i	−0.155303	−	0.987867i	$-0.549635\pi$
$373$	15.0231	−	26.0208i	0.777866	−	1.34730i	0.933169	−	0.359437i	$-0.117031\pi$
$374$	4.60952			0.238352
$375$	11.0122	−	1.90545i	0.568667	−	0.0983969i
$376$	8.13386	+	4.69609i	0.419472	+	0.242182i
$377$	3.57369	+	2.95738i	0.184054	+	0.152313i
$378$	5.23551	+	20.3170i	0.269286	+	1.04500i
$379$	7.34807	+	27.4234i	0.377445	+	1.40864i	0.849739	+	0.527203i	$0.176759\pi$
$379$	7.34807	+	27.4234i	0.377445	+	1.40864i	−0.472294	+	0.881441i	$0.656574\pi$
$380$	0.153742	−	0.0887629i	0.00788679	−	0.00455344i
$381$	14.1808	+	30.6665i	0.726505	+	1.57109i
$382$	8.16051	+	2.18660i	0.417528	+	0.111876i
$383$	−3.58594	+	0.960849i	−0.183233	+	0.0490971i	−0.349269	−	0.937023i	$-0.613570\pi$
$383$	−3.58594	+	0.960849i	−0.183233	+	0.0490971i	0.166036	+	0.986120i	$0.446903\pi$
$384$	−1.10909	−	1.33038i	−0.0565981	−	0.0678908i
$385$	−1.87332	+	0.501955i	−0.0954732	+	0.0255820i
$386$	0.0464751	−	0.0268324i	0.00236552	−	0.00136573i
$387$	−18.5294	+	6.61022i	−0.941901	+	0.336016i
$388$	−1.94418	+	0.520942i	−0.0987009	+	0.0264468i
$389$	−1.01593	+	1.75965i	−0.0515099	+	0.0892178i	−0.890631	−	0.454727i	$-0.849737\pi$
$389$	−1.01593	+	1.75965i	−0.0515099	+	0.0892178i	0.839121	+	0.543945i	$0.183070\pi$
$390$	−2.97496	+	2.99658i	−0.150643	+	0.151738i
$391$	−5.58369	−	9.67124i	−0.282379	−	0.489096i
$392$	−6.57852	−	6.57852i	−0.332265	−	0.332265i
$393$	−9.71140	−	0.880946i	−0.489875	−	0.0444379i
$394$			2.66006i			0.134012i
$395$	−6.97354	−	6.97354i	−0.350877	−	0.350877i
$396$	−0.912987	+	1.92565i	−0.0458793	+	0.0967675i
$397$	−2.23806	+	8.35257i	−0.112325	+	0.419203i	−0.999073	−	0.0430503i	$-0.986292\pi$
$397$	−2.23806	+	8.35257i	−0.112325	+	0.419203i	0.886748	+	0.462254i	$0.152959\pi$
$398$	0.451537	+	1.68516i	0.0226335	+	0.0844694i
$399$	0.165885	−	1.82869i	0.00830465	−	0.0915490i
$400$			4.54282i			0.227141i
$401$	27.8080	−	27.8080i	1.38866	−	1.38866i	0.560528	−	0.828136i	$-0.310598\pi$
$401$	27.8080	−	27.8080i	1.38866	−	1.38866i	0.828136	−	0.560528i	$-0.189402\pi$
$402$	−1.63469	+	18.0205i	−0.0815307	+	0.898781i
$403$	1.36724	+	14.4889i	0.0681072	+	0.721742i
$404$		−	14.5201i		−	0.722404i
$405$	2.50100	+	5.54764i	0.124276	+	0.275664i
$406$	−2.59736	+	4.49876i	−0.128905	+	0.223270i
$407$	5.85521			0.290232
$408$	7.19674	+	8.63267i	0.356292	+	0.427381i
$409$	−7.69913	−	28.7335i	−0.380697	−	1.42078i	−0.844839	−	0.535021i	$-0.820304\pi$
$409$	−7.69913	−	28.7335i	−0.380697	−	1.42078i	0.464141	−	0.885761i	$-0.346363\pi$
$410$	1.62142	+	6.05122i	0.0800761	+	0.298848i
$411$	−20.0756	+	3.47369i	−0.990255	+	0.171345i
$412$	−19.2975			−0.950719
$413$	−10.0600	+	17.4245i	−0.495023	+	0.857404i
$414$	5.14615	−	0.417076i	0.252919	−	0.0204981i
$415$		−	2.73678i		−	0.134343i
$416$	−2.08815	−	2.93932i	−0.102380	−	0.144112i
$417$	−4.65677	+	2.15338i	−0.228043	+	0.105451i
$418$	0.131884	−	0.131884i	0.00645064	−	0.00645064i
$419$			14.0759i			0.687655i	0.939033	+	0.343827i	$0.111724\pi$
$419$			14.0759i			0.687655i	−0.939033	+	0.343827i	$0.888276\pi$
$420$	−3.86483	−	2.72465i	−0.188585	−	0.132949i
$421$	−1.25055	−	4.66713i	−0.0609482	−	0.227462i	0.928733	−	0.370750i	$-0.120899\pi$
$421$	−1.25055	−	4.66713i	−0.0609482	−	0.227462i	−0.989681	+	0.143288i	$0.954233\pi$
$422$	−0.337043	+	1.25786i	−0.0164070	+	0.0612318i
$423$	23.1838	−	16.0134i	1.12723	−	0.778599i
$424$	−4.48538	−	4.48538i	−0.217829	−	0.217829i
$425$		−	29.4778i		−	1.42988i
$426$	−5.88661	−	12.7300i	−0.285207	−	0.616772i
$427$	9.41799	+	9.41799i	0.455769	+	0.455769i
$428$	6.65169	+	11.5211i	0.321522	+	0.556892i
$429$	−2.20421	+	3.84994i	−0.106420	+	0.185877i
$430$	2.21699	−	3.83995i	0.106913	−	0.185179i
$431$	−16.0936	+	4.31228i	−0.775203	+	0.207715i	−0.624669	−	0.780890i	$-0.714766\pi$
$431$	−16.0936	+	4.31228i	−0.775203	+	0.207715i	−0.150534	+	0.988605i	$0.548099\pi$
$432$	−5.03177	+	1.29664i	−0.242091	+	0.0623846i
$433$	5.53229	−	3.19407i	0.265865	−	0.153497i	−0.361142	−	0.932511i	$-0.617613\pi$
$433$	5.53229	−	3.19407i	0.265865	−	0.153497i	0.627007	+	0.779014i	$0.284280\pi$
$434$	−15.7424	+	4.21817i	−0.755660	+	0.202478i
$435$	−0.519846	+	1.41417i	−0.0249247	+	0.0678045i
$436$	−10.4312	+	2.79503i	−0.499564	+	0.133858i
$437$	−0.436462	−	0.116950i	−0.0208788	−	0.00559446i
$438$	−3.42538	−	0.310725i	−0.163671	−	0.0148470i
$439$	−11.5041	+	6.64188i	−0.549060	+	0.317000i	−0.748743	−	0.662861i	$-0.769342\pi$
$439$	−11.5041	+	6.64188i	−0.549060	+	0.317000i	0.199683	+	0.979861i	$0.436009\pi$
$440$	−0.124315	−	0.463951i	−0.00592650	−	0.0221180i
$441$	−26.2876	+	9.37791i	−1.25179	+	0.446567i
$442$	13.5497	+	19.0729i	0.644496	+	0.907203i
$443$	19.0340	+	10.9893i	0.904332	+	0.522117i	0.878603	−	0.477552i	$-0.158476\pi$
$443$	19.0340	+	10.9893i	0.904332	+	0.522117i	0.0257292	+	0.999669i	$0.491809\pi$
$444$	9.14162	+	10.9656i	0.433842	+	0.520404i
$445$	6.89852			0.327021
$446$	9.54338	−	16.5296i	0.451892	−	0.782700i
$447$	−37.7370	−	13.8720i	−1.78490	−	0.656123i
$448$	2.85512	−	2.85512i	0.134892	−	0.134892i
$449$	−8.04520	−	2.15570i	−0.379676	−	0.101734i	0.0639330	−	0.997954i	$-0.479636\pi$
$449$	−8.04520	−	2.15570i	−0.379676	−	0.101734i	−0.443609	+	0.896220i	$0.646302\pi$
$450$	12.3145	+	5.83854i	0.580511	+	0.275231i
$451$	3.29089	+	5.69999i	0.154962	+	0.268402i
$452$	−7.60612	−	13.1742i	−0.357762	−	0.619662i
$453$	11.2045	+	4.11876i	0.526436	+	0.193516i
$454$	14.2332	−	8.21756i	0.667998	−	0.385669i
$455$	−7.58360	−	6.27576i	−0.355525	−	0.294212i
$456$	0.452898	+	0.0410836i	0.0212089	+	0.00192391i
$457$	−13.1545	−	3.52474i	−0.615343	−	0.164881i	−0.0623330	−	0.998055i	$-0.519854\pi$
$457$	−13.1545	−	3.52474i	−0.615343	−	0.164881i	−0.553010	+	0.833175i	$0.686521\pi$
$458$	−11.7812	−	6.80189i	−0.550500	−	0.317831i
$459$	32.6505	−	8.41372i	1.52399	−	0.392719i
$460$	−0.822829	+	0.822829i	−0.0383646	+	0.0383646i
$461$	−25.2856	−	25.2856i	−1.17767	−	1.17767i	−0.980337	−	0.197331i	$-0.936773\pi$
$461$	−25.2856	−	25.2856i	−1.17767	−	1.17767i	−0.197331	−	0.980337i	$-0.563227\pi$
$462$	−4.66299	−	1.71410i	−0.216942	−	0.0797472i
$463$	−3.23386	+	12.0689i	−0.150290	+	0.560891i	0.849172	+	0.528116i	$0.177101\pi$
$463$	−3.23386	+	12.0689i	−0.150290	+	0.560891i	−0.999463	+	0.0327754i	$0.989565\pi$
$464$	−1.11417	−	0.643269i	−0.0517243	−	0.0298630i
$465$	−4.29053	+	1.98403i	−0.198969	+	0.0920070i
$466$	−1.00840	+	3.76342i	−0.0467134	+	0.174337i
$467$	−11.9847			−0.554587			−0.277293	−	0.960785i	$-0.589437\pi$
$467$	−11.9847			−0.554587			−0.277293	+	0.960785i	$0.589437\pi$
$468$	−10.6515	+	1.88280i	−0.492367	+	0.0870323i
$469$	−42.1818			−1.94777
$470$	−1.64363	+	6.13412i	−0.0758151	+	0.282946i
$471$	1.71592	−	18.9160i	0.0790652	−	0.871601i
$472$	−4.31540	−	2.49150i	−0.198632	−	0.114681i
$473$	1.20569	−	4.49970i	0.0554377	−	0.206896i
$474$	−4.30729	−	24.8932i	−0.197840	−	1.14338i
$475$	−0.843394	−	0.843394i	−0.0386976	−	0.0386976i
$476$	−18.5265	+	18.5265i	−0.849160	+	0.849160i
$477$	−17.9235	+	6.39406i	−0.820660	+	0.292764i
$478$	−1.36512	−	0.788151i	−0.0624390	−	0.0360492i
$479$	13.8839	+	3.72019i	0.634373	+	0.169980i	0.561653	−	0.827373i	$-0.310165\pi$
$479$	13.8839	+	3.72019i	0.634373	+	0.169980i	0.0727198	+	0.997352i	$0.476832\pi$
$480$	0.674794	−	0.957175i	0.0308000	−	0.0436888i
$481$	17.2115	+	24.2272i	0.784776	+	1.10467i
$482$	4.47282	−	2.58239i	0.203732	−	0.117624i
$483$	2.05211	+	11.8598i	0.0933742	+	0.539639i
$484$	5.24768	+	9.08926i	0.238531	+	0.413148i
$485$	−0.680464	−	1.17860i	−0.0308983	−	0.0535174i
$486$	−2.95207	+	15.3064i	−0.133908	+	0.694312i
$487$	21.7160	+	5.81879i	0.984047	+	0.263675i	0.714748	−	0.699382i	$-0.246541\pi$
$487$	21.7160	+	5.81879i	0.984047	+	0.263675i	0.269299	+	0.963057i	$0.413208\pi$
$488$	−2.33248	+	2.33248i	−0.105587	+	0.105587i
$489$	17.0272	−	14.1949i	0.769996	−	0.641918i
$490$	3.14525	−	5.44773i	0.142088	−	0.246103i
$491$	−43.3748			−1.95748			−0.978738	−	0.205114i	$-0.934243\pi$
$491$	−43.3748			−1.95748			−0.978738	+	0.205114i	$0.934243\pi$
$492$	−5.53690	+	15.0624i	−0.249623	+	0.679067i
$493$	7.22973	+	4.17409i	0.325611	+	0.187991i
$494$	0.933371	+	0.158023i	0.0419944	+	0.00710979i
$495$	−1.41743	−	0.259292i	−0.0637088	−	0.0116543i
$496$	−1.04468	−	3.89881i	−0.0469076	−	0.175062i
$497$	28.3151	−	16.3477i	1.27011	−	0.733296i
$498$	4.03949	−	5.72990i	0.181014	−	0.256763i
$499$	−27.8176	−	7.45370i	−1.24529	−	0.333673i	−0.424772	−	0.905300i	$-0.639646\pi$
$499$	−27.8176	−	7.45370i	−1.24529	−	0.333673i	−0.820514	+	0.571627i	$0.806313\pi$
$500$	−6.23251	+	1.66999i	−0.278726	+	0.0746844i
$501$	−1.43367	+	0.248070i	−0.0640518	+	0.0110829i
$502$	−6.77143	+	1.81440i	−0.302224	+	0.0809805i
$503$	−13.3453	+	7.70492i	−0.595038	+	0.343545i	−0.767087	−	0.641543i	$-0.778295\pi$
$503$	−13.3453	+	7.70492i	−0.595038	+	0.343545i	0.172049	+	0.985088i	$0.444961\pi$
$504$	−4.07008	−	11.4090i	−0.181296	−	0.508197i
$505$	9.48323	−	2.54102i	0.421998	−	0.113074i
$506$	−0.611279	+	1.05877i	−0.0271747	+	0.0470679i
$507$	−22.4093	+	2.19655i	−0.995230	+	0.0975523i
$508$	−9.75334	−	16.8933i	−0.432735	−	0.749518i
$509$	−4.97121	−	4.97121i	−0.220345	−	0.220345i	0.588299	−	0.808644i	$-0.299798\pi$
$509$	−4.97121	−	4.97121i	−0.220345	−	0.220345i	−0.808644	+	0.588299i	$0.799798\pi$
$510$	−4.37864	+	6.21097i	−0.193890	+	0.275027i
$511$		−	8.01802i		−	0.354696i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.693442	−	1.17490i	0.0306162	−	0.0518729i
$514$	0.981486	−	3.66296i	0.0432915	−	0.161566i
$515$	−3.37706	−	12.6034i	−0.148811	−	0.555371i
$516$	10.3094	−	4.76727i	0.453847	−	0.209868i
$517$			6.67195i			0.293432i
$518$	−23.5332	+	23.5332i	−1.03399	+	1.03399i
$519$	30.1769	+	21.2742i	1.32462	+	0.933835i
$520$	1.55427	−	1.87817i	0.0681593	−	0.0823634i
$521$			42.4222i			1.85855i	0.369391	+	0.929274i	$0.379566\pi$
$521$			42.4222i			1.85855i	−0.369391	+	0.929274i	$0.620434\pi$
$522$	−3.17571	+	2.19351i	−0.138997	+	0.0960075i
$523$	1.58272	−	2.74135i	0.0692074	−	0.119871i	−0.829345	−	0.558737i	$-0.811286\pi$
$523$	1.58272	−	2.74135i	0.0692074	−	0.119871i	0.898553	+	0.438866i	$0.144620\pi$
$524$	5.62990			0.245943
$525$	−10.9616	+	29.8197i	−0.478405	+	1.30144i
$526$	2.16224	+	8.06959i	0.0942781	+	0.351851i
$527$	6.77880	+	25.2988i	0.295289	+	1.10203i
$528$	0.424519	−	1.15485i	0.0184748	−	0.0502583i
$529$	−20.0381			−0.871223
$530$	2.14450	−	3.71438i	0.0931511	−	0.161342i
$531$	−12.3001	+	8.49588i	−0.533779	+	0.368690i
$532$			1.06013i			0.0459625i
$533$	−13.9113	+	30.3720i	−0.602566	+	1.31556i
$534$	14.4432	+	10.1822i	0.625018	+	0.440628i
$535$	−6.36047	+	6.36047i	−0.274987	+	0.274987i
$536$		−	10.4469i		−	0.451236i
$537$	−0.379717	+	0.175588i	−0.0163860	+	0.00757720i
$538$	1.07599	+	4.01563i	0.0463890	+	0.173126i
$539$	1.71051	−	6.38372i	0.0736770	−	0.274966i
$540$	−1.72741	−	3.05938i	−0.0743358	−	0.131655i
$541$	−5.91918	−	5.91918i	−0.254486	−	0.254486i	0.568321	−	0.822807i	$-0.307593\pi$
$541$	−5.91918	−	5.91918i	−0.254486	−	0.254486i	−0.822807	+	0.568321i	$0.807593\pi$
$542$			20.9097i			0.898147i
$543$	−1.73604	+	2.46252i	−0.0745004	+	0.105677i
$544$	−4.58832	−	4.58832i	−0.196723	−	0.196723i
$545$	−3.65092	−	6.32358i	−0.156388	−	0.270872i
$546$	−6.61448	−	24.3327i	−0.283073	−	1.04135i
$547$	16.9449	−	29.3493i	0.724510	−	1.25489i	−0.234666	−	0.972076i	$-0.575400\pi$
$547$	16.9449	−	29.3493i	0.724510	−	1.25489i	0.959176	−	0.282811i	$-0.0912670\pi$
$548$	11.3621	−	3.04445i	0.485363	−	0.130053i
$549$	3.32504	+	9.32056i	0.141909	+	0.397792i
$550$	−2.79475	+	1.61355i	−0.119169	+	0.0688020i
$551$	0.326277	−	0.0874256i	0.0138999	−	0.00372445i
$552$	−2.93723	+	0.508231i	−0.125017	+	0.0216317i
$553$	56.8865	−	15.2427i	2.41906	−	0.648185i
$554$	−14.6665	−	3.92987i	−0.623118	−	0.166964i
$555$	−5.56195	+	7.88946i	−0.236092	+	0.334889i
$556$	2.56527	−	1.48106i	0.108792	−	0.0628110i
$557$	2.17805	+	8.12858i	0.0922868	+	0.344419i	0.996594	−	0.0824630i	$-0.0262786\pi$
$557$	2.17805	+	8.12858i	0.0922868	+	0.344419i	−0.904307	+	0.426882i	$0.859612\pi$
$558$	−11.9114	−	2.17895i	−0.504248	−	0.0922424i
$559$	22.1626	−	8.23812i	0.937378	−	0.348436i
$560$	2.36435	+	1.36506i	0.0999121	+	0.0576843i
$561$	−2.75464	+	7.49365i	−0.116301	+	0.316382i
$562$	30.2392			1.27556
$563$	15.9438	−	27.6155i	0.671951	−	1.16385i	−0.305400	−	0.952224i	$-0.598790\pi$
$563$	15.9438	−	27.6155i	0.671951	−	1.16385i	0.977350	−	0.211628i	$-0.0678766\pi$
$564$	−12.4952	+	10.4168i	−0.526142	+	0.438625i
$565$	7.27311	−	7.27311i	0.305982	−	0.305982i
$566$	19.0137	+	5.09470i	0.799205	+	0.214146i
$567$	−36.1580	−	3.63011i	−1.51849	−	0.152450i
$568$	4.04872	+	7.01259i	0.169881	+	0.294242i
$569$	−16.2401	−	28.1287i	−0.680821	−	1.17922i	−0.974731	−	0.223383i	$-0.928290\pi$
$569$	−16.2401	−	28.1287i	−0.680821	−	1.17922i	0.293910	−	0.955833i	$-0.405043\pi$
$570$	0.0524252	+	0.302982i	0.00219585	+	0.0126905i
$571$	27.2576	−	15.7372i	1.14070	−	0.658582i	0.194094	−	0.980983i	$-0.437823\pi$
$571$	27.2576	−	15.7372i	1.14070	−	0.658582i	0.946603	+	0.322401i	$0.104490\pi$
$572$	1.06659	−	2.32864i	0.0445964	−	0.0973655i
$573$	−8.43146	+	11.9598i	−0.352229	+	0.499627i
$574$	−36.1360	−	9.68261i	−1.50829	−	0.404144i
$575$	6.77079	+	3.90912i	0.282361	+	0.163021i
$576$	2.82558	−	1.00801i	0.117733	−	0.0420002i
$577$	3.78292	−	3.78292i	0.157485	−	0.157485i	−0.623966	−	0.781451i	$-0.714480\pi$
$577$	3.78292	−	3.78292i	0.157485	−	0.157485i	0.781451	+	0.623966i	$0.214480\pi$
$578$	17.7522	+	17.7522i	0.738393	+	0.738393i
$579$	0.0158478	+	0.0915892i	0.000658610	+	0.00380632i
$580$	0.225144	−	0.840250i	0.00934861	−	0.0348895i
$581$	14.1536	+	8.17160i	0.587192	+	0.339015i
$582$	0.314950	−	3.47196i	0.0130551	−	0.143917i
$583$	1.16626	−	4.35256i	0.0483017	−	0.180265i
$584$	1.98576			0.0821715
$585$	−3.09369	−	6.62712i	−0.127908	−	0.273998i
$586$	−9.93642			−0.410470
$587$	11.2947	−	42.1526i	0.466184	−	1.73982i	−0.186750	−	0.982408i	$-0.559795\pi$
$587$	11.2947	−	42.1526i	0.466184	−	1.73982i	0.652934	−	0.757415i	$-0.273538\pi$
$588$	14.6260	−	6.76333i	0.603165	−	0.278915i
$589$	0.917779	+	0.529880i	0.0378164	+	0.0218333i
$590$	0.872025	−	3.25444i	0.0359007	−	0.133983i
$591$	−4.32444	−	1.58965i	−0.177884	−	0.0653895i
$592$	−5.82829	−	5.82829i	−0.239541	−	0.239541i
$593$	3.43157	−	3.43157i	0.140918	−	0.140918i	−0.633129	−	0.774047i	$-0.718230\pi$
$593$	3.43157	−	3.43157i	0.140918	−	0.140918i	0.774047	+	0.633129i	$0.218230\pi$
$594$	−2.58491	−	2.63500i	−0.106060	−	0.108115i
$595$	−15.3420	−	8.85768i	−0.628959	−	0.363130i
$596$	22.4219	+	6.00794i	0.918438	+	0.246095i
$597$	−3.00939	−	0.272989i	−0.123166	−	0.0111727i
$598$	−6.17774	+	0.582962i	−0.252626	+	0.0238391i
$599$	6.49912	−	3.75227i	0.265547	−	0.153313i	−0.361315	−	0.932444i	$-0.617672\pi$
$599$	6.49912	−	3.75227i	0.265547	−	0.153313i	0.626862	+	0.779130i	$0.284339\pi$
$600$	−7.38523	−	2.71479i	−0.301501	−	0.110831i
$601$	−8.71312	−	15.0916i	−0.355416	−	0.615598i	0.631773	−	0.775153i	$-0.282327\pi$
$601$	−8.71312	−	15.0916i	−0.355416	−	0.615598i	−0.987189	+	0.159555i	$0.948994\pi$
$602$	13.2392	+	22.9310i	0.539590	+	0.934597i
$603$	−28.3189	−	13.4265i	−1.15323	−	0.546771i
$604$	−6.65733	−	1.78383i	−0.270883	−	0.0725828i
$605$	−5.01793	+	5.01793i	−0.204008	+	0.204008i
$606$	23.6053	+	8.67722i	0.958899	+	0.352488i
$607$	15.4563	−	26.7710i	0.627350	−	1.08660i	−0.360731	−	0.932670i	$-0.617473\pi$
$607$	15.4563	−	26.7710i	0.627350	−	1.08660i	0.988081	−	0.153933i	$-0.0491939\pi$
$608$	−0.262555			−0.0106480
$609$	−5.76142	−	6.91096i	−0.233464	−	0.280046i
$610$	−1.93155	−	1.11518i	−0.0782063	−	0.0451524i
$611$	−27.6066	+	19.6123i	−1.11684	+	0.793429i
$612$	−18.3348	+	6.54081i	−0.741141	+	0.264397i
$613$	11.1528	+	41.6227i	0.450456	+	1.68113i	0.701113	+	0.713050i	$0.252687\pi$
$613$	11.1528	+	41.6227i	0.450456	+	1.68113i	−0.250657	+	0.968076i	$0.580646\pi$
$614$	17.7374	−	10.2407i	0.715822	−	0.413280i
$615$	−10.8064	−	0.980274i	−0.435755	−	0.0395285i
$616$	2.77058	+	0.742373i	0.111630	+	0.0299111i
$617$	−12.2280	+	3.27648i	−0.492280	+	0.131906i	−0.496415	−	0.868086i	$-0.665350\pi$
$617$	−12.2280	+	3.27648i	−0.492280	+	0.131906i	0.00413506	+	0.999991i	$0.498684\pi$
$618$	11.5322	−	31.3718i	0.463892	−	1.26196i
$619$	−1.08632	+	0.291078i	−0.0436628	+	0.0116994i	−0.280584	−	0.959829i	$-0.590528\pi$
$619$	−1.08632	+	0.291078i	−0.0436628	+	0.0116994i	0.236922	+	0.971529i	$0.423862\pi$
$620$	2.36353	−	1.36458i	0.0949215	−	0.0548030i
$621$	−2.39730	+	8.61530i	−0.0962003	+	0.345720i
$622$	21.8475	−	5.85403i	0.876006	−	0.234725i
$623$	−20.5979	+	35.6767i	−0.825239	+	1.42936i
$624$	6.02631	−	1.63816i	0.241246	−	0.0655788i
$625$	9.17568	+	15.8927i	0.367027	+	0.635710i
$626$	13.3420	+	13.3420i	0.533252	+	0.533252i
$627$	0.135589	+	0.293216i	0.00541489	+	0.0117099i
$628$			10.9660i			0.437590i
$629$	37.8190	+	37.8190i	1.50794	+	1.50794i
$630$	6.73906	−	4.65478i	0.268491	−	0.185451i
$631$	−3.51015	+	13.1000i	−0.139737	+	0.521505i	0.860197	+	0.509962i	$0.170341\pi$
$631$	−3.51015	+	13.1000i	−0.139737	+	0.521505i	−0.999933	+	0.0115421i	$0.996326\pi$
$632$	3.77505	+	14.0887i	0.150163	+	0.560417i
$633$	−1.84348	−	1.29963i	−0.0732717	−	0.0516555i
$634$			19.0122i			0.755069i
$635$	9.32632	−	9.32632i	0.370104	−	0.370104i
$636$	9.97230	−	4.61139i	0.395428	−	0.182853i
$637$	31.4421	−	11.6874i	1.24578	−	0.463073i
$638$		−	0.913923i		−	0.0361825i
$639$	24.2129	−	1.96236i	0.957849	−	0.0776299i
$640$	−0.338074	+	0.585562i	−0.0133636	+	0.0231464i
$641$	−47.3161			−1.86887			−0.934436	−	0.356130i	$-0.884096\pi$
$641$	−47.3161			−1.86887			−0.934436	+	0.356130i	$0.884096\pi$
$642$	−22.7048	+	3.92862i	−0.896085	+	0.155050i
$643$	2.46650	+	9.20510i	0.0972692	+	0.363014i	0.997354	−	0.0727016i	$-0.0231621\pi$
$643$	2.46650	+	9.20510i	0.0972692	+	0.363014i	−0.900084	+	0.435715i	$0.856495\pi$
$644$	−1.79853	−	6.71222i	−0.0708722	−	0.264498i
$645$	4.91770	+	5.89890i	0.193634	+	0.232269i
$646$	1.70368			0.0670304
$647$	8.42061	−	14.5849i	0.331048	−	0.573392i	−0.651669	−	0.758503i	$-0.725931\pi$
$647$	8.42061	−	14.5849i	0.331048	−	0.573392i	0.982718	+	0.185111i	$0.0592644\pi$
$648$	0.899044	−	8.95498i	0.0353178	−	0.351785i
$649$		−	3.53979i		−	0.138949i
$650$	−14.8916	−	6.82083i	−0.584098	−	0.267535i
$651$	2.55021	−	28.1131i	0.0999506	−	1.10184i
$652$	−9.05006	+	9.05006i	−0.354428	+	0.354428i
$653$			29.2126i			1.14318i	0.820540	+	0.571589i	$0.193673\pi$
$653$			29.2126i			1.14318i	−0.820540	+	0.571589i	$0.806327\pi$
$654$	1.68981	−	18.6282i	0.0660770	−	0.728421i
$655$	0.985233	+	3.67694i	0.0384962	+	0.143670i
$656$	2.39802	−	8.94954i	0.0936270	−	0.349421i
$657$	2.55215	−	5.38292i	0.0995687	−	0.210008i
$658$	−26.8158	−	26.8158i	−1.04539	−	1.04539i
$659$		−	14.3659i		−	0.559615i	−0.960056	−	0.279807i	$-0.909729\pi$
$659$		−	14.3659i		−	0.559615i	0.960056	−	0.279807i	$-0.0902706\pi$
$660$	0.828533	+	0.0751584i	0.0322506	+	0.00292554i
$661$	−29.3026	−	29.3026i	−1.13974	−	1.13974i	−0.988496	−	0.151245i	$-0.951672\pi$
$661$	−29.3026	−	29.3026i	−1.13974	−	1.13974i	−0.151245	−	0.988496i	$-0.548328\pi$
$662$	13.2363	+	22.9259i	0.514443	+	0.891041i
$663$	−39.1039	+	10.6298i	−1.51867	+	0.412827i
$664$	−2.02380	+	3.50533i	−0.0785387	+	0.136033i
$665$	−0.692380	+	0.185523i	−0.0268494	+	0.00719426i
$666$	−23.2897	+	8.30843i	−0.902458	+	0.321945i
$667$	−1.91750	+	1.10707i	−0.0742460	+	0.0428660i
$668$	0.811408	−	0.217416i	0.0313943	−	0.00841208i
$669$	21.1690	+	25.3927i	0.818439	+	0.981738i
$670$	6.82294	−	1.82820i	0.263593	−	0.0706296i
$671$	−2.26342	−	0.606480i	−0.0873782	−	0.0234129i
$672$	2.93533	+	6.34777i	0.113233	+	0.244870i
$673$	34.2005	−	19.7457i	1.31833	−	0.761140i	0.334873	−	0.942263i	$-0.391307\pi$
$673$	34.2005	−	19.7457i	1.31833	−	0.761140i	0.983460	+	0.181124i	$0.0579734\pi$
$674$	−5.87256	−	21.9167i	−0.226202	−	0.844199i
$675$	−16.8508	+	16.5305i	−0.648587	+	0.636258i
$676$	12.7705	−	2.43183i	0.491174	−	0.0935321i
$677$	14.7062	+	8.49064i	0.565206	+	0.326322i	0.755232	−	0.655457i	$-0.227524\pi$
$677$	14.7062	+	8.49064i	0.565206	+	0.326322i	−0.190026	+	0.981779i	$0.560857\pi$
$678$	25.9626	−	4.49233i	0.997087	−	0.172527i
$679$	8.12705			0.311888
$680$	2.19372	−	3.79963i	0.0841252	−	0.145709i
$681$	4.85345	+	28.0496i	0.185985	+	1.07486i
$682$	2.02749	−	2.02749i	0.0776368	−	0.0776368i
$683$	1.34228	+	0.359662i	0.0513607	+	0.0137621i	0.284408	−	0.958703i	$-0.408203\pi$
$683$	1.34228	+	0.359662i	0.0513607	+	0.0137621i	−0.233047	+	0.972465i	$0.574870\pi$
$684$	−0.337441	+	0.711722i	−0.0129024	+	0.0272134i
$685$	3.97672	+	6.88788i	0.151943	+	0.263173i
$686$	4.65034	+	8.05463i	0.177551	+	0.307527i
$687$	18.0982	−	15.0878i	0.690490	−	0.575637i
$688$	−5.67915	+	3.27886i	−0.216516	+	0.125005i
$689$	21.4379	−	7.96874i	0.816719	−	0.303585i
$690$	−0.845945	−	1.82939i	−0.0322046	−	0.0696437i
$691$	9.95590	+	2.66767i	0.378740	+	0.101483i	0.443166	−	0.896439i	$-0.353855\pi$
$691$	9.95590	+	2.66767i	0.378740	+	0.101483i	−0.0644263	+	0.997922i	$0.520522\pi$
$692$	−18.4610	−	10.6585i	−0.701782	−	0.405174i
$693$	5.57320	−	6.55624i	0.211708	−	0.249051i
$694$	11.7462	−	11.7462i	0.445879	−	0.445879i
$695$	1.41622	+	1.41622i	0.0537202	+	0.0537202i
$696$	1.71159	−	1.42689i	0.0648776	−	0.0540861i
$697$	−15.5604	+	58.0723i	−0.589393	+	2.19965i
$698$	1.94433	+	1.12256i	0.0735939	+	0.0424895i
$699$	−5.51553	−	3.88837i	−0.208617	−	0.147072i
$700$	4.74746	−	17.7178i	0.179437	−	0.669669i
$701$	26.3023			0.993423			0.496712	−	0.867916i	$-0.334541\pi$
$701$	26.3023			0.993423			0.496712	+	0.867916i	$0.334541\pi$
$702$	3.30450	−	18.4413i	0.124720	−	0.696021i
$703$	2.16409			0.0816202
$704$	−0.183858	+	0.686168i	−0.00692942	+	0.0258609i
$705$	−8.98995	−	6.33778i	−0.338581	−	0.238695i
$706$	−7.77097	−	4.48657i	−0.292464	−	0.168854i
$707$	−15.1742	+	56.6310i	−0.570685	+	2.12983i
$708$	6.62929	−	5.52660i	0.249144	−	0.207702i
$709$	−22.9263	−	22.9263i	−0.861016	−	0.861016i	0.130440	−	0.991456i	$-0.458361\pi$
$709$	−22.9263	−	22.9263i	−0.861016	−	0.861016i	−0.991456	+	0.130440i	$0.958361\pi$
$710$	−3.87146	+	3.87146i	−0.145293	+	0.145293i
$711$	43.0427	+	7.87383i	1.61423	+	0.295292i
$712$	−8.83578	−	5.10134i	−0.331135	−	0.191181i
$713$	−6.70988	−	1.79791i	−0.251287	−	0.0673321i
$714$	−19.0470	−	41.1898i	−0.712814	−	1.54149i
$715$	1.70751	+	0.289087i	0.0638573	+	0.0108113i
$716$	0.209175	−	0.120767i	0.00781723	−	0.00451328i
$717$	2.09708	−	1.74826i	0.0783171	−	0.0652901i
$718$	−17.7922	−	30.8170i	−0.663999	−	1.15008i
$719$	−8.65353	−	14.9884i	−0.322722	−	0.558971i	0.658326	−	0.752733i	$-0.271265\pi$
$719$	−8.65353	−	14.9884i	−0.322722	−	0.558971i	−0.981049	+	0.193761i	$0.937931\pi$
$720$	1.15282	+	1.66901i	0.0429629	+	0.0622005i
$721$	75.2634	+	20.1668i	2.80296	+	0.751050i
$722$	−13.3863	+	13.3863i	−0.498186	+	0.498186i
$723$	1.52521	+	8.81467i	0.0567232	+	0.327821i
$724$	0.869761	−	1.50647i	0.0323244	−	0.0559875i
$725$	−5.84452			−0.217060
$726$	−17.9123	+	3.09939i	−0.664790	+	0.115029i
$727$	−8.04825	−	4.64666i	−0.298493	−	0.172335i	0.343273	−	0.939236i	$-0.388464\pi$
$727$	−8.04825	−	4.64666i	−0.298493	−	0.172335i	−0.641766	+	0.766901i	$0.721798\pi$
$728$	5.07242	+	13.6461i	0.187996	+	0.505757i
$729$	−23.1193	−	13.9462i	−0.856271	−	0.516527i
$730$	0.347509	+	1.29692i	0.0128619	+	0.0480012i
$731$	36.8512	−	21.2761i	1.36299	−	0.786924i
$732$	−2.39801	−	5.18579i	−0.0886330	−	0.191672i
$733$	−34.0522	−	9.12426i	−1.25775	−	0.337012i	−0.432422	−	0.901671i	$-0.642341\pi$
$733$	−34.0522	−	9.12426i	−1.25775	−	0.337012i	−0.825324	+	0.564659i	$0.809008\pi$
$734$	−22.4093	+	6.00454i	−0.827141	+	0.221632i
$735$	6.97674	+	8.36877i	0.257341	+	0.308687i
$736$	1.66237	−	0.445430i	0.0612756	−	0.0164188i
$737$	6.42692	−	3.71058i	0.236739	−	0.136681i
$738$	−21.1780	−	18.0026i	−0.779574	−	0.662685i
$739$	32.7392	−	8.77244i	1.20433	−	0.322699i	0.399795	−	0.916604i	$-0.369081\pi$
$739$	32.7392	−	8.77244i	1.20433	−	0.322699i	0.804535	+	0.593905i	$0.202415\pi$
$740$	2.78656	−	4.82646i	0.102436	−	0.177424i
$741$	−0.814679	+	1.42294i	−0.0299280	+	0.0522730i
$742$	12.8063	+	22.1812i	0.470134	+	0.814296i
$743$	7.56862	+	7.56862i	0.277666	+	0.277666i	0.832177	−	0.554511i	$-0.187095\pi$
$743$	7.56862	+	7.56862i	0.277666	+	0.277666i	−0.554511	+	0.832177i	$0.687095\pi$
$744$	6.96256	+	0.631592i	0.255260	+	0.0231553i
$745$			15.6954i			0.575033i
$746$	−21.2459	−	21.2459i	−0.777866	−	0.777866i
$747$	6.90106	+	9.99116i	0.252496	+	0.365557i
$748$	1.19303	−	4.45245i	0.0436215	−	0.162798i
$749$	−13.9027	−	51.8854i	−0.507992	−	1.89585i
$750$	1.00964	−	11.1301i	0.0368669	−	0.406415i
$751$		−	14.0001i		−	0.510871i	−0.966826	−	0.255436i	$-0.917781\pi$
$751$		−	14.0001i		−	0.510871i	0.966826	−	0.255436i	$-0.0822189\pi$
$752$	6.64127	−	6.64127i	0.242182	−	0.242182i
$753$	1.09695	−	12.0925i	0.0399749	−	0.440677i
$754$	3.78155	−	2.68649i	0.137716	−	0.0978362i
$755$		−	4.66013i		−	0.169600i
$756$	20.9798	+	0.201321i	0.763028	+	0.00732197i
$757$	−4.20269	+	7.27928i	−0.152749	+	0.264570i	−0.932237	−	0.361848i	$-0.882146\pi$
$757$	−4.20269	+	7.27928i	−0.152749	+	0.264570i	0.779488	+	0.626417i	$0.215479\pi$
$758$	28.3908			1.03120
$759$	−1.35593	−	1.62647i	−0.0492171	−	0.0590371i
$760$	−0.0459471	−	0.171477i	−0.00166667	−	0.00622012i
$761$	−7.60908	−	28.3975i	−0.275829	−	1.02941i	−0.955284	−	0.295690i	$-0.904450\pi$
$761$	−7.60908	−	28.3975i	−0.275829	−	1.02941i	0.679455	−	0.733717i	$-0.262216\pi$
$762$	33.2919	−	5.76052i	1.20604	−	0.208682i
$763$	43.6043			1.57858
$764$	4.22419	−	7.31652i	0.152826	−	0.264702i
$765$	−7.48046	−	10.8300i	−0.270457	−	0.391560i
$766$			3.71244i			0.134136i
$767$	14.6466	−	10.4053i	0.528859	−	0.375712i
$768$	−1.57210	+	0.726972i	−0.0567284	+	0.0262323i
$769$	−25.7163	+	25.7163i	−0.927354

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.41563 + 0.997997i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.175000 - 0.653109i) q^{5} +(1.33038 - 1.10909i) q^{6} +(2.85512 + 2.85512i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00801 + 2.82558i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.41563 + 0.997997i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.175000 - 0.653109i) q^{5} +(1.33038 - 1.10909i) q^{6} +(2.85512 + 2.85512i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00801 + 2.82558i) q^{9} +(-0.585562 - 0.338074i) q^{10} +(-0.686168 - 0.183858i) q^{11} +(-0.726972 - 1.57210i) q^{12} +(-1.25625 - 3.37962i) q^{13} +(3.49679 - 2.01888i) q^{14} +(0.899536 - 0.749910i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.24443 - 5.61952i) q^{17} +(2.99020 - 0.242344i) q^{18} +(-0.253608 - 0.0679541i) q^{19} +(-0.478109 + 0.478109i) q^{20} +(1.19239 + 6.89119i) q^{21} +(-0.355187 + 0.615201i) q^{22} +1.72101 q^{23} +(-1.70669 + 0.295310i) q^{24} +(3.93420 + 2.27141i) q^{25} +(-3.58960 + 0.338733i) q^{26} +(-1.39296 + 5.00596i) q^{27} +(-1.04505 - 3.90017i) q^{28} +(-1.11417 + 0.643269i) q^{29} +(-0.491541 - 1.06298i) q^{30} +(-3.89881 - 1.04468i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.787869 - 0.945068i) q^{33} +(-6.26776 + 1.67944i) q^{34} +(2.36435 - 1.36506i) q^{35} +(0.539833 - 2.95103i) q^{36} +(-7.96159 + 2.13330i) q^{37} +(-0.131277 + 0.227379i) q^{38} +(1.59447 - 6.03802i) q^{39} +(0.338074 + 0.585562i) q^{40} +(-6.55152 - 6.55152i) q^{41} +(6.96499 + 0.631813i) q^{42} +6.55772i q^{43} +(0.502310 + 0.502310i) q^{44} +(2.02182 - 0.163860i) q^{45} +(0.445430 - 1.66237i) q^{46} +(-2.43087 - 9.07214i) q^{47} +(-0.156476 + 1.72497i) q^{48} +9.30343i q^{49} +(3.21226 - 3.21226i) q^{50} +(1.01535 - 11.1931i) q^{51} +(-0.601867 + 3.55496i) q^{52} +6.34328i q^{53} +(4.47486 + 2.64114i) q^{54} +(-0.240159 + 0.415967i) q^{55} -4.03775 q^{56} +(-0.291197 - 0.349298i) q^{57} +(0.332981 + 1.24270i) q^{58} +(1.28969 + 4.81321i) q^{59} +(-1.15398 + 0.199673i) q^{60} +3.29863 q^{61} +(-2.01817 + 3.49557i) q^{62} +(-5.18941 + 10.9454i) q^{63} -1.00000i q^{64} +(-2.42711 + 0.229034i) q^{65} +(-1.11678 + 0.516421i) q^{66} +(-7.38704 + 7.38704i) q^{67} +6.48886i q^{68} +(2.43631 + 1.71756i) q^{69} +(-0.706607 - 2.63709i) q^{70} +(2.09577 - 7.82153i) q^{71} +(-2.71076 - 1.28522i) q^{72} +(-1.40415 - 1.40415i) q^{73} +8.24244i q^{74} +(3.30250 + 7.14179i) q^{75} +(0.185654 + 0.185654i) q^{76} +(-1.43416 - 2.48403i) q^{77} +(-5.41960 - 3.10289i) q^{78} +(7.29283 - 12.6316i) q^{79} +(0.653109 - 0.175000i) q^{80} +(-6.96785 + 5.69641i) q^{81} +(-8.02394 + 4.63262i) q^{82} +(3.90968 - 1.04760i) q^{83} +(2.41296 - 6.56414i) q^{84} +(-4.23794 + 1.13555i) q^{85} +(6.33427 + 1.69726i) q^{86} +(-2.21924 - 0.201313i) q^{87} +(0.615201 - 0.355187i) q^{88} +(2.64065 + 9.85503i) q^{89} +(0.365007 - 1.99533i) q^{90} +(6.06248 - 13.2360i) q^{91} +(-1.49044 - 0.860504i) q^{92} +(-4.47667 - 5.36988i) q^{93} -9.39217 q^{94} +(-0.0887629 + 0.153742i) q^{95} +(1.62569 + 0.597599i) q^{96} +(1.42324 - 1.42324i) q^{97} +(8.98642 + 2.40791i) q^{98} +(-0.172155 - 2.12416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

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