LMFDB - Embedded newform 930.2.bn.b.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (of order $30$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.b.49.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.02048 - 0.957953i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.95080 + 1.75650i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.02048 - 0.957953i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.95080 + 1.75650i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(-0.412606 + 2.19767i) q^{10} +(-0.831899 - 0.176825i) q^{11} +(0.994522 + 0.104528i) q^{12} +(-3.90436 + 0.410364i) q^{13} +(-2.56769 + 0.545780i) q^{14} +(0.0533318 + 2.23543i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.467968 + 2.20162i) q^{17} +(0.994522 - 0.104528i) q^{18} +(-0.440154 + 4.18778i) q^{19} +(-1.53543 - 1.62556i) q^{20} +(-2.39811 + 1.06771i) q^{21} +(0.632033 - 0.569085i) q^{22} +(4.82156 + 1.56662i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(3.16465 - 3.87104i) q^{25} +(1.96293 - 3.39990i) q^{26} +(0.951057 - 0.309017i) q^{27} +(1.06771 - 2.39811i) q^{28} +(7.54172 + 5.47938i) q^{29} +(-1.83985 - 1.27081i) q^{30} +(3.20557 - 4.55240i) q^{31} -1.00000i q^{32} +(0.499902 - 0.688056i) q^{33} +(-2.05621 - 0.915483i) q^{34} +(5.62419 + 1.68021i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.363402 + 0.209811i) q^{37} +(-3.12927 - 2.81761i) q^{38} +(1.21316 - 3.73372i) q^{39} +(2.21761 - 0.286706i) q^{40} +(-11.0497 + 4.91966i) q^{41} +(0.545780 - 2.56769i) q^{42} +(4.44487 + 0.467175i) q^{43} +(0.0888997 + 0.845825i) q^{44} +(-2.06386 - 0.860511i) q^{45} +(-4.10146 + 2.97989i) q^{46} +(5.67524 + 7.81130i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(-0.0114024 - 0.108486i) q^{49} +(1.27160 + 4.83560i) q^{50} +(-2.20162 - 0.467968i) q^{51} +(1.59679 + 3.58645i) q^{52} +(-6.59729 + 5.94022i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.85022 + 0.439648i) q^{55} +(1.31253 + 2.27336i) q^{56} +(-3.64670 - 2.10542i) q^{57} +(-8.86583 + 2.88068i) q^{58} +(8.02930 + 3.57487i) q^{59} +(2.10954 - 0.741508i) q^{60} +10.8920 q^{61} +(1.79878 + 5.26919i) q^{62} -2.62506i q^{63} +(0.809017 + 0.587785i) q^{64} +(-7.49555 + 4.56932i) q^{65} +(0.262814 + 0.808858i) q^{66} +(-8.75212 - 5.05304i) q^{67} +(1.94925 - 1.12540i) q^{68} +(-3.39228 + 3.76751i) q^{69} +(-4.66513 + 3.56246i) q^{70} +(-6.07223 - 6.74390i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(-0.702164 + 3.30342i) q^{73} +(0.0438623 - 0.417322i) q^{74} +(2.24919 + 4.46555i) q^{75} +(4.11883 - 0.875485i) q^{76} +(-1.31227 - 1.80618i) q^{77} +(2.30756 + 3.17609i) q^{78} +(-3.45357 + 0.734080i) q^{79} +(-1.07153 + 1.96261i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(2.51478 - 11.8311i) q^{82} +(6.79440 + 15.2605i) q^{83} +(1.75650 + 1.95080i) q^{84} +(3.05456 + 4.00002i) q^{85} +(-2.99058 + 3.32138i) q^{86} +(-8.07316 + 4.66104i) q^{87} +(-0.736540 - 0.425242i) q^{88} +(-1.10589 - 3.40357i) q^{89} +(1.90927 - 1.16390i) q^{90} +(-8.33741 - 6.05748i) q^{91} -5.06969i q^{92} +(2.85500 + 4.78006i) q^{93} -9.65529 q^{94} +(3.12238 + 8.88296i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-7.95184 + 2.58371i) q^{97} +(0.0944694 + 0.0545419i) q^{98} +(0.425242 + 0.736540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	2.02048	−	0.957953i	0.903585	−	0.428410i
$5$	2.02048	−	0.957953i	0.903585	−	0.428410i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.95080	+	1.75650i	0.737332	+	0.663896i	0.949653	−	0.313303i	$-0.101436\pi$
$7$	1.95080	+	1.75650i	0.737332	+	0.663896i	−0.212321	+	0.977200i	$0.568102\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	−0.412606	+	2.19767i	−0.130477	+	0.694964i
$11$	−0.831899	−	0.176825i	−0.250827	−	0.0533149i	0.0807822	−	0.996732i	$-0.474258\pi$
$11$	−0.831899	−	0.176825i	−0.250827	−	0.0533149i	−0.331609	+	0.943417i	$0.607591\pi$
$12$	0.994522	+	0.104528i	0.287094	+	0.0301748i
$13$	−3.90436	+	0.410364i	−1.08287	+	0.113815i	−0.629117	−	0.777311i	$-0.716583\pi$
$13$	−3.90436	+	0.410364i	−1.08287	+	0.113815i	−0.453757	+	0.891126i	$0.649917\pi$
$14$	−2.56769	+	0.545780i	−0.686244	+	0.145866i
$15$	0.0533318	+	2.23543i	0.0137702	+	0.577186i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.467968	+	2.20162i	0.113499	+	0.533970i	0.997755	+	0.0669682i	$0.0213326\pi$
$17$	0.467968	+	2.20162i	0.113499	+	0.533970i	−0.884256	+	0.467002i	$0.845334\pi$
$18$	0.994522	−	0.104528i	0.234411	−	0.0246376i
$19$	−0.440154	+	4.18778i	−0.100978	+	0.960743i	0.820325	+	0.571898i	$0.193793\pi$
$19$	−0.440154	+	4.18778i	−0.100978	+	0.960743i	−0.921303	+	0.388845i	$0.872874\pi$
$20$	−1.53543	−	1.62556i	−0.343332	−	0.363487i
$21$	−2.39811	+	1.06771i	−0.523310	+	0.232993i
$22$	0.632033	−	0.569085i	0.134750	−	0.121329i
$23$	4.82156	+	1.56662i	1.00536	+	0.326663i	0.765007	−	0.644022i	$-0.222735\pi$
$23$	4.82156	+	1.56662i	1.00536	+	0.326663i	0.240358	+	0.970684i	$0.422735\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	3.16465	−	3.87104i	0.632930	−	0.774209i
$26$	1.96293	−	3.39990i	0.384962	−	0.666774i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	1.06771	−	2.39811i	0.201778	−	0.453200i
$29$	7.54172	+	5.47938i	1.40046	+	1.01750i	0.994624	+	0.103551i	$0.0330205\pi$
$29$	7.54172	+	5.47938i	1.40046	+	1.01750i	0.405839	+	0.913945i	$0.366979\pi$
$30$	−1.83985	−	1.27081i	−0.335909	−	0.232017i
$31$	3.20557	−	4.55240i	0.575738	−	0.817634i
$31$	3.20557	−	4.55240i	0.575738	−	0.817634i
$32$		−	1.00000i		−	0.176777i
$33$	0.499902	−	0.688056i	0.0870217	−	0.119775i
$34$	−2.05621	−	0.915483i	−0.352637	−	0.157004i
$35$	5.62419	+	1.68021i	0.950661	+	0.284007i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.363402	+	0.209811i	−0.0597430	+	0.0344926i	−0.529574	−	0.848264i	$-0.677648\pi$
$37$	−0.363402	+	0.209811i	−0.0597430	+	0.0344926i	0.469831	+	0.882756i	$0.344315\pi$
$38$	−3.12927	−	2.81761i	−0.507635	−	0.457076i
$39$	1.21316	−	3.73372i	0.194261	−	0.597873i
$40$	2.21761	−	0.286706i	0.350635	−	0.0453322i
$41$	−11.0497	+	4.91966i	−1.72568	+	0.768321i	−0.729215	+	0.684285i	$0.760115\pi$
$41$	−11.0497	+	4.91966i	−1.72568	+	0.768321i	−0.996463	+	0.0840366i	$0.973219\pi$
$42$	0.545780	−	2.56769i	0.0842156	−	0.396203i
$43$	4.44487	+	0.467175i	0.677837	+	0.0712435i	0.437190	−	0.899369i	$-0.355974\pi$
$43$	4.44487	+	0.467175i	0.677837	+	0.0712435i	0.240647	+	0.970613i	$0.422640\pi$
$44$	0.0888997	+	0.845825i	0.0134021	+	0.127513i
$45$	−2.06386	−	0.860511i	−0.307662	−	0.128277i
$46$	−4.10146	+	2.97989i	−0.604728	+	0.439361i
$47$	5.67524	+	7.81130i	0.827819	+	1.13939i	0.988325	+	0.152360i	$0.0486873\pi$
$47$	5.67524	+	7.81130i	0.827819	+	1.13939i	−0.160506	+	0.987035i	$0.551313\pi$
$48$	−0.207912	−	0.978148i	−0.0300095	−	0.141183i
$49$	−0.0114024	−	0.108486i	−0.00162891	−	0.0154980i
$50$	1.27160	+	4.83560i	0.179832	+	0.683857i
$51$	−2.20162	−	0.467968i	−0.308288	−	0.0655286i
$52$	1.59679	+	3.58645i	0.221435	+	0.497352i
$53$	−6.59729	+	5.94022i	−0.906207	+	0.815952i	−0.983472	−	0.181058i	$-0.942048\pi$
$53$	−6.59729	+	5.94022i	−0.906207	+	0.815952i	0.0772654	+	0.997011i	$0.475381\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−1.85022	+	0.439648i	−0.249484	+	0.0592821i
$56$	1.31253	+	2.27336i	0.175394	+	0.303791i
$57$	−3.64670	−	2.10542i	−0.483017	−	0.278870i
$58$	−8.86583	+	2.88068i	−1.16414	+	0.378252i
$59$	8.02930	+	3.57487i	1.04533	+	0.465409i	0.856254	−	0.516554i	$-0.172786\pi$
$59$	8.02930	+	3.57487i	1.04533	+	0.465409i	0.189071	+	0.981963i	$0.439452\pi$
$60$	2.10954	−	0.741508i	0.272341	−	0.0957283i
$61$	10.8920			1.39458			0.697288	−	0.716791i	$-0.254390\pi$
$61$	10.8920			1.39458			0.697288	+	0.716791i	$0.254390\pi$
$62$	1.79878	+	5.26919i	0.228445	+	0.669188i
$63$		−	2.62506i		−	0.330726i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−7.49555	+	4.56932i	−0.929708	+	0.566755i
$66$	0.262814	+	0.808858i	0.0323502	+	0.0995635i
$67$	−8.75212	−	5.05304i	−1.06924	−	0.617327i	−0.141267	−	0.989971i	$-0.545118\pi$
$67$	−8.75212	−	5.05304i	−1.06924	−	0.617327i	−0.927974	+	0.372645i	$0.878451\pi$
$68$	1.94925	−	1.12540i	0.236381	−	0.136475i
$69$	−3.39228	+	3.76751i	−0.408383	+	0.453555i
$70$	−4.66513	+	3.56246i	−0.557590	+	0.425796i
$71$	−6.07223	−	6.74390i	−0.720641	−	0.800353i	0.265876	−	0.964007i	$-0.414339\pi$
$71$	−6.07223	−	6.74390i	−0.720641	−	0.800353i	−0.986518	+	0.163654i	$0.947672\pi$
$72$	−0.406737	−	0.913545i	−0.0479344	−	0.107662i
$73$	−0.702164	+	3.30342i	−0.0821821	+	0.386636i	−0.999945	−	0.0104926i	$-0.996660\pi$
$73$	−0.702164	+	3.30342i	−0.0821821	+	0.386636i	0.917763	+	0.397129i	$0.129993\pi$
$74$	0.0438623	−	0.417322i	0.00509889	−	0.0485127i
$75$	2.24919	+	4.46555i	0.259715	+	0.515637i
$76$	4.11883	−	0.875485i	0.472462	−	0.100425i
$77$	−1.31227	−	1.80618i	−0.149547	−	0.205834i
$78$	2.30756	+	3.17609i	0.261280	+	0.359621i
$79$	−3.45357	+	0.734080i	−0.388557	+	0.0825904i	−0.398048	−	0.917365i	$-0.630312\pi$
$79$	−3.45357	+	0.734080i	−0.388557	+	0.0825904i	0.00949073	+	0.999955i	$0.496979\pi$
$80$	−1.07153	+	1.96261i	−0.119801	+	0.219426i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	2.51478	−	11.8311i	0.277711	−	1.30653i
$83$	6.79440	+	15.2605i	0.745782	+	1.67505i	0.737739	+	0.675086i	$0.235893\pi$
$83$	6.79440	+	15.2605i	0.745782	+	1.67505i	0.00804236	+	0.999968i	$0.497440\pi$
$84$	1.75650	+	1.95080i	0.191650	+	0.212849i
$85$	3.05456	+	4.00002i	0.331314	+	0.433863i
$86$	−2.99058	+	3.32138i	−0.322483	+	0.358154i
$87$	−8.07316	+	4.66104i	−0.865534	+	0.499716i
$88$	−0.736540	−	0.425242i	−0.0785155	−	0.0453309i
$89$	−1.10589	−	3.40357i	−0.117224	−	0.360777i	0.875181	−	0.483796i	$-0.160742\pi$
$89$	−1.10589	−	3.40357i	−0.117224	−	0.360777i	−0.992404	+	0.123019i	$0.960742\pi$
$90$	1.90927	−	1.16390i	0.201255	−	0.122686i
$91$	−8.33741	−	6.05748i	−0.873998	−	0.634997i
$92$		−	5.06969i		−	0.528552i
$93$	2.85500	+	4.78006i	0.296049	+	0.495669i
$94$	−9.65529			−0.995867
$95$	3.12238	+	8.88296i	0.320349	+	0.911372i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	−7.95184	+	2.58371i	−0.807387	+	0.262336i	−0.683491	−	0.729959i	$-0.739539\pi$
$97$	−7.95184	+	2.58371i	−0.807387	+	0.262336i	−0.123897	+	0.992295i	$0.539539\pi$
$98$	0.0944694	+	0.0545419i	0.00954285	+	0.00550957i
$99$	0.425242	+	0.736540i	0.0427384	+	0.0740251i
$100$	−4.65951	−	1.81354i	−0.465951	−	0.181354i
$101$	3.78818	−	11.6588i	0.376938	−	1.16009i	−0.565224	−	0.824937i	$-0.691210\pi$
$101$	3.78818	−	11.6588i	0.376938	−	1.16009i	0.942162	−	0.335158i	$-0.108790\pi$
$102$	1.67267	−	1.50608i	0.165619	−	0.149124i
$103$	−4.70434	−	10.5661i	−0.463532	−	1.04111i	−0.982491	−	0.186311i	$-0.940347\pi$
$103$	−4.70434	−	10.5661i	−0.463532	−	1.04111i	0.518958	−	0.854799i	$-0.326320\pi$
$104$	−3.84007	−	0.816233i	−0.376550	−	0.0800382i
$105$	−3.82251	+	4.45455i	−0.373039	+	0.434720i
$106$	−0.927954	−	8.82889i	−0.0901309	−	0.857538i
$107$	0.397192	+	1.86864i	0.0383980	+	0.180648i	0.993167	−	0.116699i	$-0.0372313\pi$
$107$	0.397192	+	1.86864i	0.0383980	+	0.180648i	−0.954769	+	0.297348i	$0.903898\pi$
$108$	−0.587785	−	0.809017i	−0.0565597	−	0.0778477i
$109$	−7.07515	+	5.14039i	−0.677676	+	0.492360i	−0.872586	−	0.488461i	$-0.837559\pi$
$109$	−7.07515	+	5.14039i	−0.677676	+	0.492360i	0.194910	+	0.980821i	$0.437559\pi$
$110$	0.731851	−	1.75528i	0.0697792	−	0.167359i
$111$	−0.0438623	−	0.417322i	−0.00416323	−	0.0396105i
$112$	−2.61068	−	0.274393i	−0.246686	−	0.0259277i
$113$	−2.25264	+	10.5978i	−0.211910	+	0.996959i	0.735645	+	0.677367i	$0.236879\pi$
$113$	−2.25264	+	10.5978i	−0.211910	+	0.996959i	−0.947555	+	0.319592i	$0.896454\pi$
$114$	3.84680	−	1.71271i	0.360286	−	0.160410i
$115$	11.2426	−	1.45351i	1.04838	−	0.135541i
$116$	2.88068	−	8.86583i	0.267465	−	0.823171i
$117$	2.91748	+	2.62691i	0.269721	+	0.242858i
$118$	−7.61164	+	4.39458i	−0.700708	+	0.404554i
$119$	−2.95424	+	5.11689i	−0.270815	+	0.469065i
$120$	−0.640065	+	2.14250i	−0.0584297	+	0.195583i
$121$	−9.38821	−	4.17990i	−0.853474	−	0.379991i
$122$	−6.40215	+	8.81181i	−0.579624	+	0.797784i
$123$		−	12.0954i		−	1.09061i
$124$	−5.32016	−	1.64191i	−0.477765	−	0.147448i
$125$	2.68583	−	10.8529i	0.240228	−	0.970717i
$126$	2.12371	+	1.54297i	0.189196	+	0.137459i
$127$	6.09966	−	13.7001i	0.541257	−	1.21568i	−0.411349	−	0.911478i	$-0.634942\pi$
$127$	6.09966	−	13.7001i	0.541257	−	1.21568i	0.952606	−	0.304206i	$-0.0983911\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−2.23468	+	3.87058i	−0.196752	+	0.340785i
$130$	0.709115	−	8.74981i	0.0621935	−	0.767409i
$131$	8.44514	−	9.37928i	0.737856	−	0.819472i	−0.251057	−	0.967972i	$-0.580778\pi$
$131$	8.44514	−	9.37928i	0.737856	−	0.819472i	0.988912	+	0.148501i	$0.0474447\pi$
$132$	−0.808858	−	0.262814i	−0.0704021	−	0.0228750i
$133$	−8.21451	+	7.39638i	−0.712288	+	0.641347i
$134$	9.23236	−	4.11051i	0.797554	−	0.355094i
$135$	1.62556	−	1.53543i	0.139906	−	0.132149i
$136$	−0.235273	+	2.23847i	−0.0201745	+	0.191947i
$137$	−4.78113	+	0.502517i	−0.408479	+	0.0429329i	−0.306540	−	0.951858i	$-0.599171\pi$
$137$	−4.78113	+	0.502517i	−0.408479	+	0.0429329i	−0.101939	+	0.994791i	$0.532505\pi$
$138$	−1.05405	−	4.95890i	−0.0897265	−	0.422130i
$139$	10.0265	−	7.28465i	0.850433	−	0.617876i	−0.0748325	−	0.997196i	$-0.523842\pi$
$139$	10.0265	−	7.28465i	0.850433	−	0.617876i	0.925265	+	0.379320i	$0.123842\pi$
$140$	−0.139999	−	5.86813i	−0.0118321	−	0.495948i
$141$	−9.44430	+	2.00745i	−0.795354	+	0.169058i
$142$	9.02510	−	0.948576i	0.757369	−	0.0796027i
$143$	3.32059	+	0.349008i	0.277682	+	0.0291855i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	20.4869	+	3.84635i	1.70134	+	0.319422i
$146$	−2.25980	−	2.50976i	−0.187023	−	0.207710i
$147$	0.103745	+	0.0337088i	0.00855674	+	0.00278025i
$148$	0.311839	+	0.280781i	0.0256330	+	0.0230801i
$149$	8.48769	+	14.7011i	0.695339	+	1.20436i	0.970066	+	0.242840i	$0.0780791\pi$
$149$	8.48769	+	14.7011i	0.695339	+	1.20436i	−0.274727	+	0.961522i	$0.588588\pi$
$150$	−4.93475	−	0.805147i	−0.402920	−	0.0657400i
$151$	2.18831	+	6.73494i	0.178082	+	0.548081i	0.999761	−	0.0218701i	$-0.00696201\pi$
$151$	2.18831	+	6.73494i	0.178082	+	0.548081i	−0.821678	+	0.569951i	$0.806962\pi$
$152$	−1.71271	+	3.84680i	−0.138919	+	0.312017i
$153$	1.32299	−	1.82094i	0.106957	−	0.147214i
$154$	2.23257			0.179905
$155$	2.11580	−	12.2688i	0.169945	−	0.985453i
$156$	−3.92586			−0.314321
$157$	−0.854998	+	1.17680i	−0.0682363	+	0.0939192i	−0.841771	−	0.539835i	$-0.818487\pi$
$157$	−0.854998	+	1.17680i	−0.0682363	+	0.0939192i	0.773535	+	0.633754i	$0.218487\pi$
$158$	1.43608	−	3.22548i	0.114248	−	0.256605i
$159$	−2.74331	−	8.44303i	−0.217558	−	0.669576i
$160$	−0.957953	−	2.02048i	−0.0757328	−	0.159733i
$161$	6.65411	+	11.5253i	0.524417	+	0.908317i
$162$	−0.743145	−	0.669131i	−0.0583870	−	0.0525719i
$163$	−0.230639	−	0.0749391i	−0.0180650	−	0.00586968i	0.299971	−	0.953948i	$-0.403023\pi$
$163$	−0.230639	−	0.0749391i	−0.0180650	−	0.00586968i	−0.318036	+	0.948079i	$0.603023\pi$
$164$	8.09343	+	8.98866i	0.631990	+	0.701896i
$165$	0.350915	−	1.86908i	0.0273187	−	0.145508i
$166$	−16.3396	−	3.47309i	−1.26820	−	0.269564i
$167$	0.544400	+	0.0572187i	0.0421269	+	0.00442772i	0.125568	−	0.992085i	$-0.459925\pi$
$167$	0.544400	+	0.0572187i	0.0421269	+	0.00442772i	−0.0834416	+	0.996513i	$0.526591\pi$
$168$	−2.61068	+	0.274393i	−0.201418	+	0.0211699i
$169$	2.35967	−	0.501564i	0.181513	−	0.0385819i
$170$	−5.03151	+	0.120039i	−0.385899	+	0.00920660i
$171$	3.40665	−	2.47507i	0.260513	−	0.189274i
$172$	−0.929232	−	4.37169i	−0.0708532	−	0.333338i
$173$	14.8524	−	1.56105i	1.12921	−	0.118684i	0.478553	−	0.878059i	$-0.341162\pi$
$173$	14.8524	−	1.56105i	1.12921	−	0.118684i	0.650654	+	0.759374i	$0.274495\pi$
$174$	0.974423	−	9.27102i	0.0738708	−	0.702834i
$175$	12.9731	−	1.99289i	0.980674	−	0.150648i
$176$	0.776955	−	0.345923i	0.0585652	−	0.0260749i
$177$	−6.53162	+	5.88110i	−0.490947	+	0.442050i
$178$	3.40357	+	1.10589i	0.255108	+	0.0828897i
$179$	6.11119	−	6.78716i	0.456772	−	0.507296i	−0.470132	−	0.882596i	$-0.655794\pi$
$179$	6.11119	−	6.78716i	0.456772	−	0.507296i	0.926903	+	0.375300i	$0.122460\pi$
$180$	−0.180627	+	2.22876i	−0.0134631	+	0.166122i
$181$	7.77994	−	13.4752i	0.578278	−	1.00161i	−0.417399	−	0.908723i	$-0.637058\pi$
$181$	7.77994	−	13.4752i	0.578278	−	1.00161i	0.995677	−	0.0928838i	$-0.0296085\pi$
$182$	9.80121	−	3.18461i	0.726514	−	0.236059i
$183$	−4.43017	+	9.95033i	−0.327488	+	0.735550i
$184$	4.10146	+	2.97989i	0.302364	+	0.219680i
$185$	−0.533258	+	0.772040i	−0.0392059	+	0.0567615i
$186$	−5.54528	−	0.499909i	−0.406599	−	0.0366551i
$187$		−	1.91427i		−	0.139985i
$188$	5.67524	−	7.81130i	0.413909	−	0.569697i
$189$	2.39811	+	1.06771i	0.174437	+	0.0776642i
$190$	−9.02175	−	2.69522i	−0.654507	−	0.195532i
$191$	13.2738	−	22.9908i	0.960455	−	1.66356i	0.239097	−	0.970996i	$-0.423149\pi$
$191$	13.2738	−	22.9908i	0.960455	−	1.66356i	0.721359	−	0.692562i	$-0.243518\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−16.4030	−	14.7693i	−1.18071	−	1.06312i	−0.996780	−	0.0801803i	$-0.974450\pi$
$193$	−16.4030	−	14.7693i	−1.18071	−	1.06312i	−0.183933	−	0.982939i	$-0.558883\pi$
$194$	2.58371	−	7.95184i	0.185500	−	0.570909i
$195$	−1.12557	−	8.70604i	−0.0806036	−	0.623452i
$196$	−0.0996531	+	0.0443684i	−0.00711808	+	0.00316917i
$197$	−0.169941	+	0.799510i	−0.0121078	+	0.0569627i	−0.983787	−	0.179342i	$-0.942603\pi$
$197$	−0.169941	+	0.799510i	−0.0121078	+	0.0569627i	0.971679	+	0.236305i	$0.0759364\pi$
$198$	−0.845825	−	0.0888997i	−0.0601101	−	0.00631783i
$199$	1.85816	+	17.6792i	0.131721	+	1.25324i	0.838142	+	0.545451i	$0.183642\pi$
$199$	1.85816	+	17.6792i	0.131721	+	1.25324i	−0.706421	+	0.707792i	$0.749692\pi$
$200$	4.20598	−	2.70365i	0.297408	−	0.191177i
$201$	8.17599	−	5.94020i	0.576690	−	0.418990i
$202$	7.20554	+	9.91758i	0.506980	+	0.697798i
$203$	5.08780	+	23.9362i	0.357094	+	1.67999i
$204$	0.235273	+	2.23847i	0.0164724	+	0.156724i
$205$	−17.6129	+	20.5252i	−1.23014	+	1.43354i
$206$	11.3133	+	2.40472i	0.788236	+	0.167545i
$207$	−2.06203	−	4.63139i	−0.143321	−	0.321904i
$208$	2.91748	−	2.62691i	0.202291	−	0.182144i
$209$	1.10667	−	3.40598i	0.0765499	−	0.235596i
$210$	−1.35699	−	5.71079i	−0.0936414	−	0.394082i
$211$	−8.63300	−	14.9528i	−0.594320	−	1.02939i	−0.993642	−	0.112582i	$-0.964088\pi$
$211$	−8.63300	−	14.9528i	−0.594320	−	1.02939i	0.399322	−	0.916811i	$-0.369246\pi$
$212$	7.68816	+	4.43876i	0.528025	+	0.304855i
$213$	8.63066	−	2.80427i	0.591363	−	0.192145i
$214$	−1.74523	−	0.777025i	−0.119301	−	0.0531163i
$215$	9.42830	−	3.31406i	0.643004	−	0.226017i
$216$	1.00000			0.0680414
$217$	14.2497	−	3.25019i	0.967334	−	0.220638i
$218$		−	8.74536i		−	0.592311i
$219$	−2.73223	−	1.98508i	−0.184627	−	0.134139i
$220$	0.989880	+	1.62381i	0.0667377	+	0.109477i
$221$	−2.73058	−	8.40385i	−0.183678	−	0.565304i
$222$	0.363402	+	0.209811i	0.0243900	+	0.0140816i
$223$	−2.51488	+	1.45197i	−0.168409	+	0.0972310i	−0.581835	−	0.813307i	$-0.697665\pi$
$223$	−2.51488	+	1.45197i	−0.168409	+	0.0972310i	0.413426	+	0.910538i	$0.364332\pi$
$224$	1.75650	−	1.95080i	0.117361	−	0.130343i
$225$	−4.99431	+	0.238439i	−0.332954	+	0.0158960i
$226$	−7.24975	−	8.05166i	−0.482246	−	0.535589i
$227$	−4.99254	−	11.2134i	−0.331367	−	0.744262i	−1.00000		0.000669382i	$-0.999787\pi$
$227$	−4.99254	−	11.2134i	−0.331367	−	0.744262i	0.668633	−	0.743593i	$-0.266880\pi$
$228$	−0.875485	+	4.11883i	−0.0579804	+	0.272776i
$229$	−0.308662	+	2.93672i	−0.0203970	+	0.194064i	−0.999976	−	0.00699773i	$-0.997773\pi$
$229$	−0.308662	+	2.93672i	−0.0203970	+	0.194064i	0.979579	+	0.201062i	$0.0644392\pi$
$230$	−5.43232	+	9.94981i	−0.358197	+	0.656071i
$231$	2.18378	−	0.464177i	0.143682	−	0.0305406i
$232$	5.47938	+	7.54172i	0.359739	+	0.495138i
$233$	−7.82498	−	10.7702i	−0.512632	−	0.705577i	0.471729	−	0.881744i	$-0.343630\pi$
$233$	−7.82498	−	10.7702i	−0.512632	−	0.705577i	−0.984360	+	0.176167i	$0.943630\pi$
$234$	−3.84007	+	0.816233i	−0.251033	+	0.0533588i
$235$	18.9495	+	10.3459i	1.23613	+	0.674894i
$236$	0.918718	−	8.74102i	0.0598034	−	0.568992i
$237$	0.734080	−	3.45357i	0.0476836	−	0.224334i
$238$	−2.40319	−	5.39766i	−0.155776	−	0.349878i
$239$	−6.29432	−	6.99055i	−0.407146	−	0.452181i	0.504345	−	0.863502i	$-0.331734\pi$
$239$	−6.29432	−	6.99055i	−0.407146	−	0.452181i	−0.911490	+	0.411321i	$0.865067\pi$
$240$	−1.35710	−	1.77715i	−0.0876004	−	0.114715i
$241$	13.7192	−	15.2367i	0.883732	−	0.981484i	−0.116199	−	0.993226i	$-0.537071\pi$
$241$	13.7192	−	15.2367i	0.883732	−	0.981484i	0.999931	+	0.0117419i	$0.00373766\pi$
$242$	8.89986	−	5.13834i	0.572105	−	0.330305i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.36581	−	10.3589i	−0.215474	−	0.663161i
$245$	−0.126963	−	0.208271i	−0.00811137	−	0.0133060i
$246$	9.78541	+	7.10952i	0.623895	+	0.453286i
$247$		−	16.5312i		−	1.05186i
$248$	4.45545	−	3.33901i	0.282921	−	0.212027i
$249$	−16.7047			−1.05861
$250$	7.20153	+	8.55208i	0.455464	+	0.540881i
$251$	−13.8783	−	6.17903i	−0.875992	−	0.390017i	−0.0810556	−	0.996710i	$-0.525829\pi$
$251$	−13.8783	−	6.17903i	−0.875992	−	0.390017i	−0.794936	+	0.606693i	$0.792496\pi$
$252$	−2.49658	+	0.811187i	−0.157270	+	0.0511000i
$253$	−3.73403	−	2.15584i	−0.234757	−	0.135537i
$254$	7.49829	+	12.9874i	0.470485	+	0.814903i
$255$	−4.89660	+	1.16353i	−0.306637	+	0.0728628i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−23.3679	+	21.0405i	−1.45765	+	1.31247i	−0.598093	+	0.801426i	$0.704075\pi$
$257$	−23.3679	+	21.0405i	−1.45765	+	1.31247i	−0.859554	+	0.511045i	$0.829258\pi$
$258$	−1.81785	−	4.08296i	−0.113174	−	0.254194i
$259$	−1.07746	−	0.229021i	−0.0669500	−	0.0142307i
$260$	6.66193	+	5.71669i	0.413156	+	0.354534i
$261$	−0.974423	−	9.27102i	−0.0603153	−	0.573861i
$262$	2.62407	+	12.3453i	0.162115	+	0.762693i
$263$	7.64534	+	10.5229i	0.471432	+	0.648870i	0.976830	−	0.214016i	$-0.0686544\pi$
$263$	7.64534	+	10.5229i	0.471432	+	0.648870i	−0.505398	+	0.862886i	$0.668654\pi$
$264$	0.688056	−	0.499902i	0.0423469	−	0.0307668i
$265$	−7.63921	+	18.3220i	−0.469273	+	1.12551i
$266$	−1.15543	−	10.9932i	−0.0708438	−	0.674034i
$267$	3.55912	+	0.374078i	0.217815	+	0.0228932i
$268$	−2.10117	+	9.88523i	−0.128349	+	0.603837i
$269$	13.8382	−	6.16116i	0.843729	−	0.375652i	0.0610931	−	0.998132i	$-0.480541\pi$
$269$	13.8382	−	6.16116i	0.843729	−	0.375652i	0.782636	+	0.622480i	$0.213875\pi$
$270$	0.286706	+	2.21761i	0.0174484	+	0.134960i
$271$	−5.20589	+	16.0221i	−0.316235	+	0.973273i	0.659007	+	0.752136i	$0.270977\pi$
$271$	−5.20589	+	16.0221i	−0.316235	+	0.973273i	−0.975243	+	0.221136i	$0.929023\pi$
$272$	−1.67267	−	1.50608i	−0.101421	−	0.0913195i
$273$	8.92492	−	5.15280i	0.540160	−	0.311862i
$274$	2.40373	−	4.16339i	0.145215	−	0.251519i
$275$	−3.31717	+	2.66072i	−0.200033	+	0.160448i
$276$	4.63139	+	2.06203i	0.278777	+	0.124120i
$277$	0.439357	−	0.604723i	0.0263984	−	0.0363343i	−0.795614	−	0.605804i	$-0.792851\pi$
$277$	0.439357	−	0.604723i	0.0263984	−	0.0363343i	0.822012	+	0.569470i	$0.192851\pi$
$278$			12.3934i			0.743306i
$279$	−5.52804	+	0.663943i	−0.330955	+	0.0397492i
$280$	4.82971	+	3.33594i	0.288630	+	0.199361i
$281$	0.280386	+	0.203712i	0.0167264	+	0.0121525i	0.596117	−	0.802898i	$-0.296709\pi$
$281$	0.280386	+	0.203712i	0.0167264	+	0.0121525i	−0.579391	+	0.815050i	$0.696709\pi$
$282$	3.92716	−	8.82055i	0.233859	−	0.525256i
$283$	−10.9365	+	3.55349i	−0.650108	+	0.211233i	−0.615462	−	0.788167i	$-0.711031\pi$
$283$	−10.9365	+	3.55349i	−0.650108	+	0.211233i	−0.0346464	+	0.999400i	$0.511031\pi$
$284$	−4.53740	+	7.85901i	−0.269245	+	0.466347i
$285$	−9.38497	−	0.760591i	−0.555918	−	0.0450535i
$286$	−2.23415	+	2.48127i	−0.132108	+	0.146721i
$287$	−30.1972	−	9.81166i	−1.78248	−	0.579164i
$288$	−0.743145	+	0.669131i	−0.0437902	+	0.0394289i
$289$	10.9022	−	4.85395i	0.641303	−	0.285527i
$290$	−15.1536	+	14.3134i	−0.889852	+	0.840512i
$291$	0.873969	−	8.31526i	0.0512330	−	0.487449i
$292$	3.35872	−	0.353016i	0.196554	−	0.0206587i
$293$	−6.54768	−	30.8044i	−0.382520	−	1.79961i	−0.574823	−	0.818278i	$-0.694929\pi$
$293$	−6.54768	−	30.8044i	−0.382520	−	1.79961i	0.192303	−	0.981336i	$-0.438404\pi$
$294$	−0.0882507	+	0.0641179i	−0.00514689	+	0.00373943i
$295$	19.6476	−	0.468742i	1.14393	−	0.0272912i
$296$	−0.410451	+	0.0872441i	−0.0238570	+	0.00507096i
$297$	−0.845825	+	0.0888997i	−0.0490797	+	0.00515849i
$298$	−16.8824	−	1.77441i	−0.977971	−	0.102789i
$299$	−19.4680	−	4.13805i	−1.12586	−	0.239309i
$300$	3.55195	−	3.51904i	0.205072	−	0.203172i
$301$	7.85045	+	8.71881i	0.452492	+	0.502544i
$302$	−6.73494	−	2.18831i	−0.387552	−	0.125923i
$303$	9.11006	+	8.20274i	0.523359	+	0.471235i
$304$	−2.10542	−	3.64670i	−0.120754	−	0.209153i
$305$	22.0070	−	10.4340i	1.26012	−	0.597450i
$306$	0.695536	+	2.14064i	0.0397611	+	0.122372i
$307$	8.42417	−	18.9210i	0.480793	−	1.07988i	−0.496510	−	0.868031i	$-0.665385\pi$
$307$	8.42417	−	18.9210i	0.480793	−	1.07988i	0.977303	−	0.211847i	$-0.0679480\pi$
$308$	−1.31227	+	1.80618i	−0.0747735	+	0.102917i
$309$	11.5661			0.657970
$310$	8.68203	+	8.92314i	0.493106	+	0.506800i
$311$	−12.3264			−0.698967			−0.349484	−	0.936943i	$-0.613643\pi$
$311$	−12.3264			−0.698967			−0.349484	+	0.936943i	$0.613643\pi$
$312$	2.30756	−	3.17609i	0.130640	−	0.179811i
$313$	0.498318	−	1.11924i	0.0281666	−	0.0632632i	−0.898914	−	0.438124i	$-0.855643\pi$
$313$	0.498318	−	1.11924i	0.0281666	−	0.0632632i	0.927081	+	0.374861i	$0.122310\pi$
$314$	−0.449499	−	1.38342i	−0.0253667	−	0.0780707i
$315$	−2.51468	−	5.30386i	−0.141686	−	0.298839i
$316$	1.76536	+	3.05770i	0.0993095	+	0.172009i
$317$	2.45657	+	2.21191i	0.137975	+	0.124233i	0.735229	−	0.677819i	$-0.237075\pi$
$317$	2.45657	+	2.21191i	0.137975	+	0.124233i	−0.597254	+	0.802052i	$0.703742\pi$
$318$	8.44303	+	2.74331i	0.473462	+	0.153837i
$319$	−5.30505	−	5.89186i	−0.297026	−	0.329881i
$320$	2.19767	+	0.412606i	0.122854	+	0.0230654i
$321$	−1.86864	−	0.397192i	−0.104297	−	0.0221691i
$322$	−13.2353	−	1.39109i	−0.737575	−	0.0775223i
$323$	−9.42586	+	0.990698i	−0.524469	+	0.0551239i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	−10.7674	+	16.4126i	−0.597267	+	0.910407i
$326$	0.196193	−	0.142543i	0.0108661	−	0.00789471i
$327$	−1.81826	−	8.55425i	−0.100550	−	0.473051i
$328$	−12.0292	+	1.26432i	−0.664200	+	0.0698102i
$329$	−2.64934	+	25.2068i	−0.146063	+	1.38970i
$330$	1.30586	+	1.38252i	0.0718851	+	0.0761050i
$331$	3.65829	−	1.62878i	0.201078	−	0.0895257i	−0.303727	−	0.952759i	$-0.598231\pi$
$331$	3.65829	−	1.62878i	0.201078	−	0.0895257i	0.504805	+	0.863233i	$0.331564\pi$
$332$	12.4140	−	11.1776i	0.681306	−	0.613450i
$333$	0.399083	+	0.129670i	0.0218696	+	0.00710587i
$334$	−0.366281	+	0.406796i	−0.0200420	+	0.0222589i
$335$	−22.5240	−	1.82543i	−1.23062	−	0.0997337i
$336$	1.31253	−	2.27336i	0.0716043	−	0.124022i
$337$	12.9790	−	4.21713i	0.707011	−	0.229722i	0.0666286	−	0.997778i	$-0.478776\pi$
$337$	12.9790	−	4.21713i	0.707011	−	0.229722i	0.640383	+	0.768056i	$0.278776\pi$
$338$	−0.981208	+	2.20383i	−0.0533707	+	0.119873i
$339$	−8.76536	−	6.36841i	−0.476069	−	0.345884i
$340$	2.86033	−	4.14114i	0.155123	−	0.224585i
$341$	−3.47169	+	3.22030i	−0.188003	+	0.174389i
$342$			4.21085i			0.227697i
$343$	10.9691	−	15.0977i	0.592275	−	0.815197i
$344$	4.08296	+	1.81785i	0.220139	+	0.0980120i
$345$	−3.24493	+	10.8618i	−0.174701	+	0.584781i
$346$	−7.46710	+	12.9334i	−0.401434	+	0.695304i
$347$	26.7700	−	15.4557i	1.43709	−	0.829704i	0.439442	−	0.898271i	$-0.355176\pi$
$347$	26.7700	−	15.4557i	1.43709	−	0.829704i	0.997647	+	0.0685671i	$0.0218427\pi$
$348$	6.92766	+	6.23769i	0.371361	+	0.334375i
$349$	−2.43761	+	7.50219i	−0.130482	+	0.401583i	−0.994860	−	0.101260i	$-0.967713\pi$
$349$	−2.43761	+	7.50219i	−0.130482	+	0.401583i	0.864378	+	0.502843i	$0.167713\pi$
$350$	−6.01311	+	11.6668i	−0.321414	+	0.623619i
$351$	−3.58645	+	1.59679i	−0.191431	+	0.0852304i
$352$	−0.176825	+	0.831899i	−0.00942483	+	0.0443403i
$353$	−7.21467	−	0.758292i	−0.383998	−	0.0403598i	−0.0894369	−	0.995992i	$-0.528507\pi$
$353$	−7.21467	−	0.758292i	−0.383998	−	0.0403598i	−0.294561	+	0.955633i	$0.595173\pi$
$354$	−0.918718	−	8.74102i	−0.0488293	−	0.464580i
$355$	−18.7291	−	7.80897i	−0.994040	−	0.414457i
$356$	−2.89525	+	2.10352i	−0.153448	+	0.111486i
$357$	−3.47292	−	4.78006i	−0.183806	−	0.252988i
$358$	1.89886	+	8.93345i	0.100358	+	0.472147i
$359$	0.756503	+	7.19765i	0.0399267	+	0.379877i	0.996179	+	0.0873342i	$0.0278348\pi$
$359$	0.756503	+	7.19765i	0.0399267	+	0.379877i	−0.956252	+	0.292543i	$0.905499\pi$
$360$	−1.69694	−	1.45616i	−0.0894364	−	0.0767465i
$361$	1.24103	+	0.263789i	0.0653173	+	0.0138836i
$362$	6.32877	+	14.2147i	0.332633	+	0.747106i
$363$	7.63706	−	6.87644i	0.400842	−	0.360919i
$364$	−3.18461	+	9.80121i	−0.166919	+	0.513723i
$365$	1.74582	+	7.34713i	0.0913802	+	0.384566i
$366$	−5.44600	−	9.43274i	−0.284667	−	0.493057i
$367$	1.38524	+	0.799768i	0.0723089	+	0.0417476i	0.535719	−	0.844397i	$-0.320041\pi$
$367$	1.38524	+	0.799768i	0.0723089	+	0.0417476i	−0.463410	+	0.886144i	$0.653374\pi$
$368$	−4.82156	+	1.56662i	−0.251341	+	0.0816657i
$369$	11.0497	+	4.91966i	0.575226	+	0.256107i
$370$	−0.311152	−	0.885208i	−0.0161760	−	0.0460198i
$371$	−23.3040			−1.20988
$372$	3.66387	−	4.19238i	0.189963	−	0.217365i
$373$			0.276806i			0.0143325i	0.999974	+	0.00716624i	$0.00228111\pi$
$373$			0.276806i			0.0143325i	−0.999974	+	0.00716624i	$0.997719\pi$
$374$	1.54868	+	1.12518i	0.0800802	+	0.0581816i
$375$	8.82223	+	6.86791i	0.455578	+	0.354658i
$376$	2.98365	+	9.18273i	0.153870	+	0.473563i
$377$	−31.6941	−	18.2986i	−1.63233	−	0.942426i
$378$	−2.27336	+	1.31253i	−0.116929	+	0.0675091i
$379$	5.63867	−	6.26238i	0.289639	−	0.321677i	−0.580711	−	0.814109i	$-0.697226\pi$
$379$	5.63867	−	6.26238i	0.289639	−	0.321677i	0.870351	+	0.492433i	$0.163892\pi$
$380$	7.48333	−	5.71454i	0.383887	−	0.293150i
$381$	10.0347	+	11.1446i	0.514092	+	0.570957i
$382$	10.7978	+	24.2524i	0.552466	+	1.24086i
$383$	4.13905	−	19.4727i	0.211496	−	0.995009i	−0.736429	−	0.676515i	$-0.763490\pi$
$383$	4.13905	−	19.4727i	0.211496	−	0.995009i	0.947925	−	0.318494i	$-0.103177\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	−4.38165	−	2.39226i	−0.223310	−	0.121921i
$386$	21.5901	−	4.58911i	1.09891	−	0.233580i
$387$	−2.62702	−	3.61579i	−0.133539	−	0.183801i
$388$	4.91451	+	6.76424i	0.249496	+	0.343402i
$389$	−2.31081	+	0.491179i	−0.117163	+	0.0249037i	−0.266120	−	0.963940i	$-0.585742\pi$
$389$	−2.31081	+	0.491179i	−0.117163	+	0.0249037i	0.148957	+	0.988844i	$0.452408\pi$
$390$	7.70492	+	4.20668i	0.390154	+	0.213013i
$391$	−1.19276	+	11.3484i	−0.0603204	+	0.573911i
$392$	0.0226798	−	0.106700i	0.00114550	−	0.00538917i
$393$	5.13345	+	11.5299i	0.258948	+	0.581608i
$394$	−0.546928	−	0.607426i	−0.0275539	−	0.0306017i
$395$	−6.27465	+	4.79155i	−0.315712	+	0.241089i
$396$	0.569085	−	0.632033i	0.0285976	−	0.0317608i
$397$	−9.61850	+	5.55325i	−0.482739	+	0.278709i	−0.721557	−	0.692355i	$-0.756573\pi$
$397$	−9.61850	+	5.55325i	−0.482739	+	0.278709i	0.238818	+	0.971064i	$0.423240\pi$
$398$	−15.3949	−	8.88827i	−0.771679	−	0.445529i
$399$	−3.41578	−	10.5127i	−0.171003	−	0.526293i
$400$	−0.284914	+	4.99188i	−0.0142457	+	0.249594i
$401$	−15.5023	−	11.2631i	−0.774147	−	0.562451i	0.129069	−	0.991636i	$-0.458801\pi$
$401$	−15.5023	−	11.2631i	−0.774147	−	0.562451i	−0.903217	+	0.429184i	$0.858801\pi$
$402$			10.1061i			0.504045i
$403$	−10.6476	+	19.0896i	−0.530392	+	0.950922i
$404$	−12.2588			−0.609898
$405$	0.741508	+	2.10954i	0.0368458	+	0.104824i
$406$	−22.3554	−	9.95325i	−1.10948	−	0.493971i
$407$	0.339414	−	0.110282i	0.0168241	−	0.00546649i
$408$	−1.94925	−	1.12540i	−0.0965023	−	0.0557156i
$409$	11.8472	+	20.5200i	0.585807	+	1.01465i	0.994774	+	0.102098i	$0.0325555\pi$
$409$	11.8472	+	20.5200i	0.585807	+	1.01465i	−0.408968	+	0.912549i	$0.634111\pi$
$410$	−6.25260	−	26.3135i	−0.308794	−	1.29953i
$411$	1.48559	−	4.57217i	0.0732786	−	0.225528i
$412$	−8.59526	+	7.73920i	−0.423458	+	0.381283i
$413$	9.38424	+	21.0774i	0.461768	+	1.03715i
$414$	4.95890	+	1.05405i	0.243717	+	0.0518036i
$415$	28.3467	+	24.3247i	1.39149	+	1.19405i
$416$	0.410364	+	3.90436i	0.0201198	+	0.191427i
$417$	2.57673	+	12.1226i	0.126183	+	0.593644i
$418$	2.10501	+	2.89730i	0.102959	+	0.141712i
$419$	−20.4757	+	14.8765i	−1.00030	+	0.726762i	−0.962153	−	0.272510i	$-0.912146\pi$
$419$	−20.4757	+	14.8765i	−1.00030	+	0.726762i	−0.0381493	+	0.999272i	$0.512146\pi$
$420$	5.41775	+	2.25889i	0.264359	+	0.110223i
$421$	−2.13845	−	20.3460i	−0.104222	−	0.991603i	−0.914233	−	0.405189i	$-0.867206\pi$
$421$	−2.13845	−	20.3460i	−0.104222	−	0.991603i	0.810011	−	0.586414i	$-0.199461\pi$
$422$	17.1714	+	1.80479i	0.835892	+	0.0878558i
$423$	2.00745	−	9.44430i	0.0976055	−	0.459198i
$424$	−8.11002	+	3.61081i	−0.393858	+	0.175357i
$425$	10.0035	+	5.15582i	0.485241	+	0.250094i
$426$	−2.80427	+	8.63066i	−0.135867	+	0.418157i
$427$	21.2481	+	19.1318i	1.02827	+	0.925855i
$428$	1.65444	−	0.955194i	0.0799706	−	0.0461710i
$429$	−1.66944	+	2.89156i	−0.0806014	+	0.139606i
$430$	−2.86068	+	9.57561i	−0.137954	+	0.461777i
$431$	27.0755	+	12.0548i	1.30418	+	0.580658i	0.936947	−	0.349472i	$-0.113639\pi$
$431$	27.0755	+	12.0548i	1.30418	+	0.580658i	0.367232	+	0.930129i	$0.380306\pi$
$432$	−0.587785	+	0.809017i	−0.0282798	+	0.0389238i
$433$		−	37.5809i		−	1.80602i	−0.429615	−	0.903012i	$-0.641351\pi$
$433$		−	37.5809i		−	1.80602i	0.429615	−	0.903012i	$-0.358649\pi$
$434$	−5.74632	+	13.4387i	−0.275832	+	0.645078i
$435$	−11.8466	+	17.1512i	−0.568000	+	0.822339i
$436$	7.07515	+	5.14039i	0.338838	+	0.246180i
$437$	−8.68289	+	19.5021i	−0.415359	+	0.932911i
$438$	3.21193	−	1.04362i	0.153472	−	0.0498660i
$439$	4.84351	−	8.38921i	0.231168	−	0.400395i	−0.726984	−	0.686654i	$-0.759079\pi$
$439$	4.84351	−	8.38921i	0.231168	−	0.400395i	0.958152	+	0.286259i	$0.0924119\pi$
$440$	−1.89552	−	0.153620i	−0.0903656	−	0.00732354i
$441$	−0.0729914	+	0.0810651i	−0.00347578	+	0.00386024i
$442$	8.40385	+	2.73058i	0.399730	+	0.129880i
$443$	10.1822	−	9.16811i	0.483772	−	0.435590i	−0.390808	−	0.920472i	$-0.627804\pi$
$443$	10.1822	−	9.16811i	0.483772	−	0.435590i	0.874579	+	0.484882i	$0.161138\pi$
$444$	−0.383343	+	0.170675i	−0.0181926	+	0.00809989i
$445$	−5.49488	−	5.81744i	−0.260482	−	0.275773i
$446$	0.303544	−	2.88803i	0.0143732	−	0.136752i
$447$	−16.8824	+	1.77441i	−0.798510	+	0.0839268i
$448$	0.545780	+	2.56769i	0.0257857	+	0.121312i
$449$	−5.31402	+	3.86086i	−0.250784	+	0.182205i	−0.706074	−	0.708138i	$-0.749536\pi$
$449$	−5.31402	+	3.86086i	−0.250784	+	0.182205i	0.455290	+	0.890343i	$0.349536\pi$
$450$	2.74268	−	4.18063i	0.129291	−	0.197077i
$451$	10.0622	−	2.13878i	0.473809	−	0.100711i
$452$	10.7752	−	1.13252i	0.506824	−	0.0532694i
$453$	−7.04274	−	0.740222i	−0.330897	−	0.0347786i
$454$	12.0064	+	2.55204i	0.563488	+	0.119773i
$455$	−22.6483	−	4.25215i	−1.06177	−	0.199344i
$456$	−2.81761	−	3.12927i	−0.131947	−	0.146542i
$457$	−16.5892	−	5.39015i	−0.776009	−	0.252140i	−0.105873	−	0.994380i	$-0.533764\pi$
$457$	−16.5892	−	5.39015i	−0.776009	−	0.252140i	−0.670135	+	0.742239i	$0.733764\pi$
$458$	−2.19443	−	1.97587i	−0.102539	−	0.0923266i
$459$	1.12540	+	1.94925i	0.0525292	+	0.0909832i
$460$	−4.85652	−	10.2432i	−0.226437	−	0.477591i
$461$	−2.50706	−	7.71595i	−0.116766	−	0.359367i	0.875546	−	0.483135i	$-0.160502\pi$
$461$	−2.50706	−	7.71595i	−0.116766	−	0.359367i	−0.992311	+	0.123768i	$0.960502\pi$
$462$	−0.908067	+	2.03955i	−0.0422471	+	0.0948885i
$463$	7.55748	−	10.4020i	0.351226	−	0.483421i	−0.596452	−	0.802649i	$-0.703423\pi$
$463$	7.55748	−	10.4020i	0.351226	−	0.483421i	0.947678	+	0.319228i	$0.103423\pi$
$464$	−9.32208			−0.432767
$465$	10.3475	+	6.92305i	0.479855	+	0.321049i
$466$	13.3127			0.616697
$467$	24.4874	−	33.7040i	1.13314	−	1.55964i	0.351182	−	0.936307i	$-0.385780\pi$
$467$	24.4874	−	33.7040i	1.13314	−	1.55964i	0.781960	−	0.623329i	$-0.214220\pi$
$468$	1.59679	−	3.58645i	0.0738117	−	0.165784i
$469$	−8.19791	−	25.2306i	−0.378544	−	1.16504i
$470$	−19.5083	+	9.24932i	−0.899850	+	0.426639i
$471$	−0.727305	−	1.25973i	−0.0335124	−	0.0580453i
$472$	6.53162	+	5.88110i	0.300642	+	0.270699i
$473$	−3.61508	−	1.17461i	−0.166221	−	0.0540086i
$474$	2.36252	+	2.62384i	0.108514	+	0.120517i
$475$	14.8182	+	14.9567i	0.679903	+	0.686261i
$476$	5.77936	+	1.22844i	0.264897	+	0.0563055i
$477$	8.82889	+	0.927954i	0.404247	+	0.0424881i
$478$	9.35518	−	0.983269i	0.427896	−	0.0449737i
$479$	2.26134	−	0.480663i	0.103323	−	0.0219620i	−0.155960	−	0.987763i	$-0.549847\pi$
$479$	2.26134	−	0.480663i	0.103323	−	0.0219620i	0.259283	+	0.965801i	$0.416514\pi$
$480$	2.23543	−	0.0533318i	0.102033	−	0.00243425i
$481$	1.33275	−	0.968302i	0.0607683	−	0.0441508i
$482$	4.26282	+	20.0550i	0.194166	+	0.913480i
$483$	−13.2353	+	1.39109i	−0.602228	+	0.0632967i
$484$	−1.07421	+	10.2204i	−0.0488275	+	0.464563i
$485$	−13.5914	+	12.8378i	−0.617156	+	0.582935i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	−11.7816	+	10.6082i	−0.533877	+	0.480705i	−0.891411	−	0.453195i	$-0.850284\pi$
$487$	−11.7816	+	10.6082i	−0.533877	+	0.480705i	0.357534	+	0.933900i	$0.383617\pi$
$488$	10.3589	+	3.36581i	0.468925	+	0.152363i
$489$	0.162270	−	0.180219i	0.00733808	−	0.00814977i
$490$	0.243122	+	0.0197034i	0.0109831	+	0.000890111i
$491$	−11.1928	+	19.3864i	−0.505122	+	0.874897i	0.494861	+	0.868972i	$0.335219\pi$
$491$	−11.1928	+	19.3864i	−0.505122	+	0.874897i	−0.999982	+	0.00592423i	$0.998114\pi$
$492$	−11.5034	+	3.73769i	−0.518615	+	0.168508i
$493$	−8.53421	+	19.1681i	−0.384361	+	0.863290i
$494$	13.3740	+	9.71680i	0.601726	+	0.437180i
$495$	1.56476	+	1.08080i	0.0703308	+	0.0485784i
$496$	0.0824687	+	5.56715i	0.00370295	+	0.249973i
$497$		−	23.8219i		−	1.06856i
$498$	9.81875	−	13.5143i	0.439989	−	0.605592i
$499$	−22.3947	−	9.97075i	−1.00252	−	0.446352i	−0.161222	−	0.986918i	$-0.551543\pi$
$499$	−22.3947	−	9.97075i	−1.00252	−	0.446352i	−0.841302	+	0.540566i	$0.818210\pi$
$500$	−11.1517	+	0.799371i	−0.498720	+	0.0357490i
$501$	−0.273699	+	0.474061i	−0.0122280	+	0.0211795i
$502$	13.1564	−	7.59586i	0.587199	−	0.339020i
$503$	−3.33825	−	3.00578i	−0.148845	−	0.134021i	0.591344	−	0.806419i	$-0.298598\pi$
$503$	−3.33825	−	3.00578i	−0.148845	−	0.134021i	−0.740189	+	0.672398i	$0.765264\pi$
$504$	0.811187	−	2.49658i	0.0361331	−	0.111206i
$505$	−3.51467	−	27.1852i	−0.156401	−	1.20973i
$506$	3.93892	−	1.75372i	0.175106	−	0.0779624i
$507$	−0.501564	+	2.35967i	−0.0222753	+	0.104797i
$508$	−14.9144	−	1.56757i	−0.661721	−	0.0695497i
$509$	4.12672	+	39.2631i	0.182913	+	1.74031i	0.573025	+	0.819538i	$0.305770\pi$
$509$	4.12672	+	39.2631i	0.182913	+	1.74031i	−0.390112	+	0.920767i	$0.627564\pi$
$510$	1.93684	−	4.64534i	0.0857647	−	0.205699i
$511$	−7.17225	+	5.21095i	−0.317282	+	0.230519i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	0.875485	+	4.11883i	0.0386536	+	0.181851i
$514$	−3.28685	−	31.2723i	−0.144977	−	1.37936i
$515$	−19.6269	−	16.8421i	−0.864863	−	0.742150i
$516$	4.37169	+	0.929232i	0.192453	+	0.0409071i
$517$	−3.33999	−	7.50173i	−0.146892	−	0.329926i
$518$	0.818595	−	0.737066i	0.0359670	−	0.0323848i
$519$	−4.61492	+	14.2033i	−0.202573	+	0.623455i
$520$	−8.54069	+	2.02943i	−0.374534	+	0.0889964i
$521$	0.863173	+	1.49506i	0.0378163	+	0.0654997i	0.884314	−	0.466892i	$-0.154626\pi$
$521$	0.863173	+	1.49506i	0.0378163	+	0.0654997i	−0.846498	+	0.532392i	$0.821293\pi$
$522$	8.07316	+	4.66104i	0.353353	+	0.204008i
$523$	6.68781	−	2.17300i	0.292438	−	0.0950187i	−0.159124	−	0.987259i	$-0.550867\pi$
$523$	6.68781	−	2.17300i	0.292438	−	0.0950187i	0.451562	+	0.892240i	$0.350867\pi$
$524$	−11.5299	−	5.13345i	−0.503687	−	0.224256i
$525$	−3.45604	+	12.6621i	−0.150834	+	0.552619i
$526$	−13.0070			−0.567134
$527$	11.5227	+	4.92706i	0.501938	+	0.214626i
$528$			0.850484i			0.0370126i
$529$	2.18576	+	1.58805i	0.0950330	+	0.0690455i
$530$	−10.3326	−	16.9496i	−0.448818	−	0.736245i
$531$	−2.71600	−	8.35899i	−0.117864	−	0.362749i
$532$	9.57279	+	5.52686i	0.415033	+	0.239620i
$533$	41.1232	−	23.7425i	1.78124	−	1.02840i
$534$	−2.39463	+	2.65951i	−0.103626	+	0.115088i
$535$	2.59259	+	3.39505i	0.112087	+	0.146781i
$536$	−6.76228	−	7.51028i	−0.292086	−	0.324395i
$537$	3.71474	+	8.34344i	0.160303	+	0.360046i
$538$	−3.14940	+	14.8168i	−0.135780	+	0.638796i
$539$	−0.00969753	+	0.0922658i	−0.000417702	+	0.00397417i
$540$	−1.96261	−	1.07153i	−0.0844571	−	0.0461113i
$541$	−20.7081	+	4.40164i	−0.890310	+	0.189241i	−0.630288	−	0.776361i	$-0.717063\pi$
$541$	−20.7081	+	4.40164i	−0.890310	+	0.189241i	−0.260022	+	0.965603i	$0.583730\pi$
$542$	−9.90220	−	13.6292i	−0.425336	−	0.585424i
$543$	9.14587	+	12.5882i	0.392487	+	0.540212i
$544$	2.20162	−	0.467968i	0.0943935	−	0.0200640i
$545$	−9.37091	+	17.1637i	−0.401406	+	0.735212i
$546$	−1.07723	+	10.2491i	−0.0461011	+	0.438623i
$547$	−7.67350	+	36.1010i	−0.328095	+	1.54357i	0.436887	+	0.899516i	$0.356081\pi$
$547$	−7.67350	+	36.1010i	−0.328095	+	1.54357i	−0.764983	+	0.644051i	$0.777252\pi$
$548$	1.95537	+	4.39184i	0.0835293	+	0.187610i
$549$	−7.28817	−	8.09433i	−0.311051	−	0.345457i
$550$	−0.202789	−	4.24758i	−0.00864694	−	0.181117i
$551$	−26.2660	+	29.1713i	−1.11897	+	1.24274i
$552$	−4.39048	+	2.53484i	−0.186871	+	0.107890i
$553$	−8.02663	−	4.63418i	−0.341327	−	0.197065i
$554$	0.230984	+	0.710894i	0.00981355	+	0.0302030i
$555$	−0.488398	−	0.801172i	−0.0207313	−	0.0340079i
$556$	−10.0265	−	7.28465i	−0.425216	−	0.308938i
$557$			0.603986i			0.0255917i	0.999918	+	0.0127959i	$0.00407316\pi$
$557$			0.603986i			0.0255917i	−0.999918	+	0.0127959i	$0.995927\pi$
$558$	2.71216	−	4.86253i	0.114815	−	0.205847i
$559$	−17.5461			−0.742120
$560$	−5.53766	+	1.94650i	−0.234009	+	0.0822546i
$561$	1.74877	+	0.778603i	0.0738332	+	0.0328727i
$562$	−0.329613	+	0.107098i	−0.0139039	+	0.00451765i
$563$	20.2240	+	11.6764i	0.852342	+	0.492100i	0.861440	−	0.507859i	$-0.169563\pi$
$563$	20.2240	+	11.6764i	0.852342	+	0.492100i	−0.00909846	+	0.999959i	$0.502896\pi$
$564$	4.82765	+	8.36173i	0.203281	+	0.352092i
$565$	5.60082	+	23.5706i	0.235628	+	0.991621i
$566$	3.55349	−	10.9365i	0.149364	−	0.459696i
$567$	−1.95080	+	1.75650i	−0.0819257	+	0.0737663i
$568$	−3.69106	−	8.29025i	−0.154873	−	0.347851i
$569$	−13.6749	−	2.90668i	−0.573280	−	0.121855i	−0.0878561	−	0.996133i	$-0.528002\pi$
$569$	−13.6749	−	2.90668i	−0.573280	−	0.121855i	−0.485424	+	0.874279i	$0.661335\pi$
$570$	6.13168	−	7.14554i	0.256828	−	0.299294i
$571$	3.75794	+	35.7544i	0.157265	+	1.49628i	0.733890	+	0.679268i	$0.237703\pi$
$571$	3.75794	+	35.7544i	0.157265	+	1.49628i	−0.576625	+	0.817009i	$0.695631\pi$
$572$	−0.694192	−	3.26592i	−0.0290256	−	0.136555i
$573$	15.6042	+	21.4774i	0.651876	+	0.897231i
$574$	25.6872	−	18.6629i	1.07217	−	0.778973i
$575$	21.3230	−	13.7067i	0.889231	−	0.571607i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	6.90141	+	0.725367i	0.287309	+	0.0301974i	0.247087	−	0.968993i	$-0.420527\pi$
$577$	6.90141	+	0.725367i	0.287309	+	0.0301974i	0.0402225	+	0.999191i	$0.487193\pi$
$578$	−2.48120	+	11.6731i	−0.103204	+	0.485537i
$579$	20.1641	−	8.97766i	0.837993	−	0.373099i
$580$	−2.67270	−	20.6728i	−0.110978	−	0.858389i
$581$	−13.5506	+	41.7044i	−0.562173	+	1.73019i
$582$	6.21348	+	5.59464i	0.257557	+	0.231905i
$583$	6.53866	−	3.77510i	0.270803	−	0.156348i
$584$	−1.68861	+	2.92476i	−0.0698752	+	0.121027i
$585$	8.41117	+	2.51281i	0.347759	+	0.103892i
$586$	28.7699	+	12.8092i	1.18847	+	0.529143i
$587$	−25.4027	+	34.9638i	−1.04848	+	1.44311i	−0.158364	+	0.987381i	$0.550622\pi$
$587$	−25.4027	+	34.9638i	−1.04848	+	1.44311i	−0.890118	+	0.455730i	$0.849378\pi$
$588$		−	0.109084i		−	0.00449854i
$589$	17.6535	+	15.4280i	0.727400	+	0.635699i
$590$	−11.1693	+	16.1707i	−0.459834	+	0.665739i
$591$	−0.661268	−	0.480439i	−0.0272009	−	0.0197626i
$592$	0.170675	−	0.383343i	0.00701471	−	0.0157553i
$593$	24.4087	−	7.93085i	1.00234	−	0.325681i	0.238542	−	0.971132i	$-0.423331\pi$
$593$	24.4087	−	7.93085i	1.00234	−	0.325681i	0.763802	+	0.645451i	$0.223331\pi$
$594$	0.425242	−	0.736540i	0.0174479	−	0.0302206i
$595$	−1.06723	+	13.1686i	−0.0437521	+	0.539859i
$596$	11.3588	−	12.6152i	0.465273	−	0.516738i
$597$	−16.9065	−	5.49326i	−0.691937	−	0.224824i
$598$	14.7907	−	13.3176i	0.604838	−	0.544599i
$599$	3.81298	−	1.69765i	0.155794	−	0.0693639i	−0.327358	−	0.944900i	$-0.606158\pi$
$599$	3.81298	−	1.69765i	0.155794	−	0.0693639i	0.483152	+	0.875536i	$0.339492\pi$
$600$	0.759181	+	4.94203i	0.0309934	+	0.201757i
$601$	−1.22943	+	11.6972i	−0.0501493	+	0.477139i	0.940409	+	0.340046i	$0.110443\pi$
$601$	−1.22943	+	11.6972i	−0.0501493	+	0.477139i	−0.990558	+	0.137093i	$0.956224\pi$
$602$	−11.6680	+	1.22636i	−0.475554	+	0.0499827i
$603$	2.10117	+	9.88523i	0.0855663	+	0.402558i
$604$	5.72908	−	4.16242i	0.233113	−	0.169366i
$605$	−22.9728	+	0.548074i	−0.933978	+	0.0222824i
$606$	−11.9909	+	2.54875i	−0.487098	+	0.103536i
$607$	−17.7563	+	1.86626i	−0.720706	+	0.0757493i	−0.457779	−	0.889066i	$-0.651355\pi$
$607$	−17.7563	+	1.86626i	−0.720706	+	0.0757493i	−0.262928	+	0.964816i	$0.584688\pi$
$608$	4.18778	+	0.440154i	0.169837	+	0.0178506i
$609$	−23.9362	−	5.08780i	−0.969945	−	0.206168i
$610$	−4.49410	+	23.9370i	−0.181961	+	0.969181i
$611$	−25.3636	−	28.1692i	−1.02610	−	1.13960i
$612$	−2.14064	−	0.695536i	−0.0865302	−	0.0281154i
$613$	−25.6121	−	23.0612i	−1.03446	−	0.931434i	−0.0367691	−	0.999324i	$-0.511707\pi$
$613$	−25.6121	−	23.0612i	−1.03446	−	0.931434i	−0.997693	+	0.0678901i	$0.978373\pi$
$614$	10.3558	+	17.9368i	0.417926	+	0.723870i
$615$	−11.5869	−	24.4385i	−0.467227	−	0.985457i
$616$	−0.689901	−	2.12330i	−0.0277969	−	0.0855501i
$617$	−10.5195	+	23.6272i	−0.423500	+	0.951196i	0.568232	+	0.822868i	$0.307628\pi$
$617$	−10.5195	+	23.6272i	−0.423500	+	0.951196i	−0.991732	+	0.128327i	$0.959039\pi$
$618$	−6.79836	+	9.35714i	−0.273470	+	0.376399i
$619$	40.2236			1.61672			0.808362	−	0.588685i	$-0.200354\pi$
$619$	40.2236			1.61672			0.808362	+	0.588685i	$0.200354\pi$
$620$	−12.3221	+	1.77902i	−0.494869	+	0.0714471i
$621$	5.06969			0.203440
$622$	7.24529	−	9.97228i	0.290510	−	0.399852i
$623$	3.82103	−	8.58216i	0.153086	−	0.343837i
$624$	1.21316	+	3.73372i	0.0485652	+	0.149468i
$625$	−4.96996	−	24.5010i	−0.198798	−	0.980040i
$626$	0.612580	+	1.06102i	0.0244836	+	0.0424069i
$627$	2.66139	+	2.39633i	0.106286	+	0.0957002i
$628$	1.38342	+	0.449499i	0.0552043	+	0.0179370i
$629$	−0.631983	−	0.701888i	−0.0251988	−	0.0279861i
$630$	5.76901	+	1.08311i	0.229843	+	0.0431523i
$631$	−30.9144	−	6.57106i	−1.23068	−	0.261590i	−0.453724	−	0.891142i	$-0.649905\pi$
$631$	−30.9144	−	6.57106i	−1.23068	−	0.261590i	−0.776958	+	0.629552i	$0.783238\pi$
$632$	−3.51139	−	0.369062i	−0.139675	−	0.0146805i
$633$	17.1714	−	1.80479i	0.682503	−	0.0717339i
$634$	−3.23340	+	0.687281i	−0.128415	+	0.0272954i
$635$	−0.799796	−	33.5238i	−0.0317389	−	1.33035i
$636$	−7.18207	+	5.21808i	−0.284788	+	0.206910i
$637$	0.0890378	+	0.418890i	0.00352781	+	0.0165970i
$638$	7.88485	−	0.828731i	0.312164	−	0.0328098i
$639$	−0.948576	+	9.02510i	−0.0375251	+	0.357027i
$640$	−1.62556	+	1.53543i	−0.0642560	+	0.0606932i
$641$	33.9669	−	15.1230i	1.34161	−	0.597324i	0.394697	−	0.918811i	$-0.370850\pi$
$641$	33.9669	−	15.1230i	1.34161	−	0.597324i	0.946914	+	0.321488i	$0.104183\pi$
$642$	1.41969	−	1.27830i	0.0560309	−	0.0504504i
$643$	23.6343	+	7.67926i	0.932047	+	0.302840i	0.735399	−	0.677634i	$-0.236995\pi$
$643$	23.6343	+	7.67926i	0.932047	+	0.302840i	0.196647	+	0.980474i	$0.436995\pi$
$644$	8.90493	−	9.88993i	0.350904	−	0.389718i
$645$	−0.807285	+	9.96113i	−0.0317868	+	0.392219i
$646$	4.73889	−	8.20800i	0.186449	−	0.322939i
$647$	−0.285148	+	0.0926502i	−0.0112103	+	0.00364246i	−0.314617	−	0.949219i	$-0.601876\pi$
$647$	−0.285148	+	0.0926502i	−0.0112103	+	0.00364246i	0.303406	+	0.952861i	$0.401876\pi$
$648$	−0.406737	+	0.913545i	−0.0159781	+	0.0358875i
$649$	−6.04743	−	4.39372i	−0.237383	−	0.172469i
$650$	−6.94915	−	18.3581i	−0.272568	−	0.720063i
$651$	−2.82669	+	14.3397i	−0.110787	+	0.562019i
$652$			0.242508i			0.00949735i
$653$	0.555573	−	0.764680i	0.0217412	−	0.0299243i	−0.798008	−	0.602647i	$-0.794113\pi$
$653$	0.555573	−	0.764680i	0.0217412	−	0.0299243i	0.819749	+	0.572723i	$0.194113\pi$
$654$	7.98928	+	3.55706i	0.312406	+	0.139092i
$655$	8.07830	−	27.0407i	0.315645	−	1.05657i
$656$	6.04772	−	10.4750i	0.236124	−	0.408978i
$657$	2.92476	−	1.68861i	0.114106	−	0.0658790i
$658$	−18.8355	−	16.9596i	−0.734285	−	0.661153i
$659$	10.8902	−	33.5166i	0.424222	−	1.30562i	−0.479515	−	0.877534i	$-0.659187\pi$
$659$	10.8902	−	33.5166i	0.424222	−	1.30562i	0.903737	−	0.428088i	$-0.140813\pi$
$660$	−1.88604	+	0.243839i	−0.0734141	+	0.00949141i
$661$	30.8099	−	13.7175i	1.19837	−	0.533548i	0.292155	−	0.956371i	$-0.405628\pi$
$661$	30.8099	−	13.7175i	1.19837	−	0.533548i	0.906212	+	0.422823i	$0.138961\pi$
$662$	−0.832582	+	3.91699i	−0.0323592	+	0.152238i
$663$	8.78793	+	0.923648i	0.341295	+	0.0358715i
$664$	1.74611	+	16.6131i	0.0677623	+	0.644715i
$665$	−9.51184	+	22.8133i	−0.368853	+	0.884663i
$666$	−0.339481	+	0.246647i	−0.0131546	+	0.00955738i
$667$	27.7788	+	38.2342i	1.07560	+	1.48043i
$668$	−0.113811	−	0.535436i	−0.00440346	−	0.0207167i
$669$	−0.303544	−	2.88803i	−0.0117357	−	0.111658i
$670$	14.7161	−	17.1494i	0.568532	−	0.662538i
$671$	−9.06103	−	1.92598i	−0.349797	−	0.0743517i
$672$	1.06771	+	2.39811i	0.0411877	+	0.0925090i
$673$	−31.0136	+	27.9248i	−1.19549	+	1.07642i	−0.200168	+	0.979762i	$0.564149\pi$
$673$	−31.0136	+	27.9248i	−1.19549	+	1.07642i	−0.995318	+	0.0966585i	$0.969185\pi$
$674$	−4.21713	+	12.9790i	−0.162438	+	0.499933i
$675$	1.81354	−	4.65951i	0.0698034	−	0.179345i
$676$	−1.20620	−	2.08919i	−0.0463921	−	0.0803535i
$677$	−33.0029	−	19.0542i	−1.26840	−	0.732313i	−0.293717	−	0.955892i	$-0.594892\pi$
$677$	−33.0029	−	19.0542i	−1.26840	−	0.732313i	−0.974686	+	0.223580i	$0.928226\pi$
$678$	10.3043	−	3.34807i	0.395734	−	0.128582i
$679$	−20.0507	−	8.92716i	−0.769476	−	0.342593i
$680$	1.66899	+	4.74816i	0.0640027	+	0.182084i
$681$	12.2746			0.470365
$682$	−0.564673	−	4.70150i	−0.0216224	−	0.180030i
$683$		−	0.381710i		−	0.0146057i	−0.999973	−	0.00730286i	$-0.997675\pi$
$683$		−	0.381710i		−	0.0146057i	0.999973	−	0.00730286i	$-0.00232459\pi$
$684$	−3.40665	−	2.47507i	−0.130256	−	0.0946368i
$685$	−9.17877	+	5.59542i	−0.350703	+	0.213790i
$686$	5.76679	+	17.7484i	0.220177	+	0.677636i
$687$	−2.55728	−	1.47645i	−0.0975665	−	0.0563300i
$688$	−3.87058	+	2.23468i	−0.147564	+	0.0851963i
$689$	23.3205	−	25.9000i	0.888440	−	0.986713i
$690$	−6.88008	−	9.00962i	−0.261920	−	0.342990i
$691$	15.2975	+	16.9896i	0.581946	+	0.646317i	0.960176	−	0.279395i	$-0.0901339\pi$
$691$	15.2975	+	16.9896i	0.581946	+	0.646317i	−0.378230	+	0.925712i	$0.623467\pi$
$692$	−6.07429	−	13.6431i	−0.230910	−	0.518632i
$693$	−0.464177	+	2.18378i	−0.0176326	+	0.0829549i
$694$	−3.23111	+	30.7420i	−0.122651	+	1.16695i
$695$	13.2799	−	24.3233i	0.503734	−	0.922637i
$696$	−9.11837	+	1.93817i	−0.345631	+	0.0734661i
$697$	−16.0021	−	22.0250i	−0.606123	−	0.834257i
$698$	−4.63661	−	6.38174i	−0.175498	−	0.241552i
$699$	13.0217	−	2.76786i	0.492528	−	0.104690i
$700$	−5.90426	−	11.7223i	−0.223160	−	0.443062i
$701$	−4.76515	+	45.3373i	−0.179977	+	1.71237i	0.415999	+	0.909365i	$0.363432\pi$
$701$	−4.76515	+	45.3373i	−0.179977	+	1.71237i	−0.595976	+	0.803002i	$0.703235\pi$
$702$	0.816233	−	3.84007i	0.0308067	−	0.144934i
$703$	−0.718688	−	1.61420i	−0.0271058	−	0.0608807i
$704$	−0.569085	−	0.632033i	−0.0214482	−	0.0238206i
$705$	−17.1589	+	13.1032i	−0.646243	+	0.493495i
$706$	4.85415	−	5.39107i	0.182688	−	0.202896i
$707$	27.8687	−	16.0900i	1.04811	−	0.605127i
$708$	7.61164	+	4.39458i	0.286063	+	0.165158i
$709$	−0.0612120	−	0.188391i	−0.00229887	−	0.00707518i	0.949901	−	0.312552i	$-0.101184\pi$
$709$	−0.0612120	−	0.188391i	−0.00229887	−	0.00707518i	−0.952199	+	0.305477i	$0.901184\pi$
$710$	17.3263	−	10.5622i	0.650245	−	0.396392i
$711$	2.85642	+	2.07531i	0.107124	+	0.0778302i
$712$		−	3.57872i		−	0.134118i
$713$	22.5877	−	16.9277i	0.845917	−	0.633949i
$714$	5.90848			0.221119
$715$	7.04351	−	2.47581i	0.263412	−	0.0925899i
$716$	−8.34344	−	3.71474i	−0.311809	−	0.138826i
$717$	8.94632	−	2.90683i	0.334106	−	0.108558i
$718$	−6.26768	−	3.61865i	−0.233908	−	0.135047i
$719$	−8.30522	−	14.3851i	−0.309732	−	0.536472i	0.668571	−	0.743648i	$-0.266906\pi$
$719$	−8.30522	−	14.3851i	−0.309732	−	0.536472i	−0.978304	+	0.207176i	$0.933573\pi$
$720$	2.17549	−	0.516939i	0.0810759	−	0.0192652i
$721$	9.38223	−	28.8755i	0.349413	−	1.07538i
$722$	−0.942868	+	0.848962i	−0.0350899	+	0.0315951i
$723$	8.33934	+	18.7305i	0.310143	+	0.696593i
$724$	−15.2199	−	3.23508i	−0.565641	−	0.120231i
$725$	45.0779	−	11.8540i	1.67415	−	0.440247i
$726$	1.07421	+	10.2204i	0.0398675	+	0.379314i
$727$	−6.17499	−	29.0510i	−0.229018	−	1.07744i	−0.930935	−	0.365185i	$-0.881006\pi$
$727$	−6.17499	−	29.0510i	−0.229018	−	1.07744i	0.701917	−	0.712258i	$-0.252328\pi$
$728$	−6.05748	−	8.33741i	−0.224505	−	0.309005i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−6.97012	−	2.90614i	−0.257976	−	0.107561i
$731$	1.05152	+	10.0045i	0.0388918	+	0.370031i
$732$	10.8323	+	1.13852i	0.400374	+	0.0420810i
$733$	0.556907	−	2.62004i	0.0205698	−	0.0967735i	−0.966665	−	0.256044i	$-0.917581\pi$
$733$	0.556907	−	2.62004i	0.0205698	−	0.0967735i	0.987235	+	0.159270i	$0.0509142\pi$
$734$	−1.46125	+	0.650590i	−0.0539357	+	0.0240137i
$735$	0.241906	−	0.0312750i	0.00892282	−	0.00115360i
$736$	1.56662	−	4.82156i	0.0577464	−	0.177725i
$737$	6.38737	+	5.75121i	0.235282	+	0.211849i
$738$	−10.4750	+	6.04772i	−0.385588	+	0.222620i
$739$	10.1549	−	17.5889i	0.373555	−	0.647016i	−0.616555	−	0.787312i	$-0.711472\pi$
$739$	10.1549	−	17.5889i	0.373555	−	0.647016i	0.990110	+	0.140296i	$0.0448053\pi$
$740$	0.899039	+	0.268585i	0.0330493	+	0.00987337i
$741$	15.1020	+	6.72385i	0.554786	+	0.247007i
$742$	13.6977	−	18.8533i	0.502860	−	0.692127i
$743$		−	4.37599i		−	0.160539i	−0.996773	−	0.0802697i	$-0.974422\pi$
$743$		−	4.37599i		−	0.160539i	0.996773	−	0.0802697i	$-0.0255782\pi$
$744$	1.23814	+	5.42835i	0.0453925	+	0.199013i
$745$	31.2322	+	21.5724i	1.14426	+	0.790353i
$746$	−0.223941	−	0.162703i	−0.00819906	−	0.00595697i
$747$	6.79440	−	15.2605i	0.248594	−	0.558351i
$748$	−1.82058	+	0.591542i	−0.0665669	+	0.0216289i
$749$	−2.50744	+	4.34301i	−0.0916197	+	0.158690i
$750$	−10.7418	+	3.10048i	−0.392236	+	0.113213i
$751$	16.9700	−	18.8471i	0.619246	−	0.687742i	−0.349177	−	0.937057i	$-0.613539\pi$
$751$	16.9700	−	18.8471i	0.619246	−	0.687742i	0.968422	+	0.249315i	$0.0802054\pi$
$752$	−9.18273	−	2.98365i	−0.334860	−	0.108803i
$753$	11.2896	−	10.1652i	0.411418	−	0.370442i
$754$	33.4332	−	14.8854i	1.21757	−	0.542095i
$755$	10.8732	+	11.5115i	0.395716	+	0.418946i
$756$	0.274393	−	2.61068i	0.00997958	−	0.0949493i
$757$	−38.8937	+	4.08790i	−1.41362	+	0.148577i	−0.780344	−	0.625351i	$-0.784956\pi$
$757$	−38.8937	+	4.08790i	−1.41362	+	0.148577i	−0.633273	+	0.773928i	$0.718289\pi$
$758$	1.75204	+	8.24272i	0.0636371	+	0.299389i
$759$	3.48823	−	2.53435i	0.126615	−	0.0919909i
$760$	0.224572	+	9.41307i	0.00814609	+	0.341448i
$761$	−24.3205	+	5.16948i	−0.881617	+	0.187393i	−0.626411	−	0.779493i	$-0.715477\pi$
$761$	−24.3205	+	5.16948i	−0.881617	+	0.187393i	−0.255206	+	0.966887i	$0.582143\pi$
$762$	−14.9144	+	1.56757i	−0.540293	+	0.0567871i
$763$	−22.8313	−	2.39967i	−0.826548	−	0.0868737i
$764$	−25.9674	−	5.51954i	−0.939467	−	0.199690i
$765$	0.928694	−	4.94652i	0.0335770	−	0.178842i
$766$	13.3209	+	14.7943i	0.481303	+	0.534541i
$767$	−32.8162	−	10.6626i	−1.18493	−	0.385006i
$768$	0.743145	+	0.669131i	0.0268159	+	0.0241452i
$769$	−26.2490	−	45.4646i	−0.946564	−	1.63950i	−0.752590	−	0.658490i	$-0.771196\pi$
$769$	−26.2490	−	45.4646i	−0.946564	−	1.63950i	−0.193974	−	0.981007i	$-0.562138\pi$
$770$	4.51085	−	2.13869i	0.162560	−	0.0770732i
$771$	−9.71690	−	29.9056i	−0.349946	−	1.07702i
$772$	−8.97766	+	20.1641i	−0.323113	+	0.725723i
$773$	18.1889	−	25.0349i	0.654211	−	0.900444i	−0.345062	−	0.938580i	$-0.612142\pi$
$773$	18.1889	−	25.0349i	0.654211	−	0.900444i	0.999273	+	0.0381362i	$0.0121421\pi$
$774$	4.46936			0.160648
$775$	−7.47800	−	26.8157i	−0.268618	−	0.963247i
$776$	−8.36106			−0.300145
$777$	0.647462	−	0.891155i	0.0232276	−	0.0319700i
$778$	0.960890	−	2.15820i	0.0344496	−	0.0773751i
$779$	−15.7389	−	48.4392i	−0.563903	−	1.73552i
$780$	−7.93211	+	3.76079i	−0.284015	+	0.134658i
$781$	3.85899	+	6.68396i	0.138085	+	0.239171i
$782$	−8.47992	−	7.63536i	−0.303241	−	0.273040i
$783$	8.86583	+	2.88068i	0.316839	+	0.102947i
$784$	0.0729914	+	0.0810651i	0.00260683	+	0.00289518i
$785$	−0.600181	+	3.19675i	−0.0214214	+	0.114097i
$786$	−12.3453	−	2.62407i	−0.440341	−	0.0935974i
$787$	22.4824	+	2.36299i	0.801410	+	0.0842315i	0.496373	−	0.868109i	$-0.334665\pi$
$787$	22.4824	+	2.36299i	0.801410	+	0.0842315i	0.305036	+	0.952341i	$0.401331\pi$
$788$	0.812894	−	0.0854386i	0.0289581	−	0.00304362i
$789$	−12.7228	+	2.70431i	−0.452944	+	0.0962761i
$790$	−0.188300	−	7.89270i	−0.00669942	−	0.280810i
$791$	−23.0096	+	16.7174i	−0.818126	+	0.594403i
$792$	0.176825	+	0.831899i	0.00628322	+	0.0295602i
$793$	−42.5262	+	4.46968i	−1.51015	+	0.158723i
$794$	1.16094	−	11.0456i	0.0412004	−	0.391995i
$795$	−13.6308	−	14.4310i	−0.483435	−	0.511814i
$796$	16.2397	−	7.23037i	0.575600	−	0.256274i
$797$	19.4814	−	17.5411i	0.690065	−	0.621338i	−0.247606	−	0.968861i	$-0.579644\pi$
$797$	19.4814	−	17.5411i	0.690065	−	0.621338i	0.937671	+	0.347523i	$0.112977\pi$
$798$	10.5127	+	3.41578i	0.372146	+	0.120917i
$799$	−14.5416	+	16.1501i	−0.514446	+	0.571350i
$800$	−3.87104	−	3.16465i	−0.136862	−	0.111887i
$801$	−1.78936	+	3.09927i	−0.0632240	+	0.109507i
$802$	18.2240	−	5.92135i	0.643513	−	0.209090i
$803$	1.16826	−	2.62395i	0.0412269	−	0.0925972i
$804$	−8.17599	−	5.94020i	−0.288345	−	0.209495i
$805$	24.4851	+	16.9122i	0.862987	+	0.596076i
$806$	−9.18536	−	19.8347i	−0.323540	−	0.698646i
$807$			15.1478i			0.533227i
$808$	7.20554	−	9.91758i	0.253490	−	0.348899i
$809$	2.70581	+	1.20471i	0.0951313	+	0.0423552i	0.453751	−	0.891129i	$-0.350086\pi$
$809$	2.70581	+	1.20471i	0.0951313	+	0.0423552i	−0.358619	+	0.933484i	$0.616752\pi$
$810$	−2.14250	−	0.640065i	−0.0752799	−	0.0224896i
$811$	13.3628	−	23.1450i	0.469230	−	0.812730i	−0.530151	−	0.847903i	$-0.677865\pi$
$811$	13.3628	−	23.1450i	0.469230	−	0.812730i	0.999381	+	0.0351729i	$0.0111982\pi$
$812$	21.1925	−	12.2355i	0.743711	−	0.429382i
$813$	−12.5195	−	11.2726i	−0.439077	−	0.395347i
$814$	−0.110282	+	0.339414i	−0.00386539	+	0.0118964i
$815$	−0.537789	+	0.0695285i	−0.0188379	+	0.00243548i
$816$	2.05621	−	0.915483i	0.0719817	−	0.0320483i
$817$	−3.91285	+	18.4085i	−0.136893	+	0.644033i
$818$	−23.5646	−	2.47674i	−0.823917	−	0.0865972i
$819$	1.07723	+	10.2491i	0.0376414	+	0.358134i
$820$	24.9633	+	10.4083i	0.871756	+	0.363472i
$821$	1.76630	−	1.28329i	0.0616444	−	0.0447873i	−0.556536	−	0.830823i	$-0.687870\pi$
$821$	1.76630	−	1.28329i	0.0616444	−	0.0447873i	0.618181	+	0.786036i	$0.287870\pi$
$822$	2.82576	+	3.88932i	0.0985596	+	0.135656i
$823$	6.08982	+	28.6504i	0.212278	+	0.998689i	0.947226	+	0.320566i	$0.103873\pi$
$823$	6.08982	+	28.6504i	0.212278	+	0.998689i	−0.734948	+	0.678123i	$0.762794\pi$
$824$	−1.20898	−	11.5027i	−0.0421169	−	0.400715i
$825$	−1.08148	−	4.11260i	−0.0376523	−	0.143182i
$826$	−22.5679	−	4.79695i	−0.785236	−	0.166907i
$827$	−18.2824	−	41.0631i	−0.635743	−	1.42790i	−0.887818	−	0.460195i	$-0.847780\pi$
$827$	−18.2824	−	41.0631i	−0.635743	−	1.42790i	0.252075	−	0.967708i	$-0.418887\pi$
$828$	−3.76751	+	3.39228i	−0.130930	+	0.117890i
$829$	8.24425	−	25.3732i	0.286335	−	0.881247i	−0.699661	−	0.714475i	$-0.746666\pi$
$829$	8.24425	−	25.3732i	0.286335	−	0.881247i	0.985995	−	0.166772i	$-0.0533344\pi$
$830$	−36.3409	+	8.63528i	−1.26141	+	0.299735i
$831$	0.373739	+	0.647335i	0.0129649	+	0.0224558i
$832$	−3.39990	−	1.96293i	−0.117870	−	0.0680524i
$833$	0.233509	−	0.0758717i	0.00809061	−	0.00262880i
$834$	−11.3219	−	5.04084i	−0.392046	−	0.174550i
$835$	1.15476	−	0.405900i	0.0399621	−	0.0140468i
$836$	−3.58126			−0.123860
$837$	1.64191	−	5.32016i	0.0567528	−	0.183892i
$838$		−	25.3093i		−	0.874296i
$839$	30.9887	+	22.5146i	1.06985	+	0.777290i	0.975885	−	0.218286i	$-0.0700465\pi$
$839$	30.9887	+	22.5146i	1.06985	+	0.777290i	0.0939628	+	0.995576i	$0.470047\pi$
$840$	−5.01195	+	3.05531i	−0.172929	+	0.105418i
$841$	17.8925	+	55.0673i	0.616981	+	1.89887i
$842$	17.7172	+	10.2290i	0.610575	+	0.352516i
$843$	−0.300144	+	0.173288i	−0.0103375	+	0.00596836i
$844$	−11.5532	+	12.8311i	−0.397678	+	0.441666i
$845$	4.28719	−	3.27386i	0.147484	−	0.112624i
$846$	6.46065	+	7.17528i	0.222122	+	0.246691i
$847$	−10.9725	−	24.6446i	−0.377019	−	0.846798i
$848$	1.84574	−	8.68353i	0.0633830	−	0.298194i
$849$	1.20201	−	11.4363i	0.0412528	−	0.392494i
$850$	−10.0511	+	5.06249i	−0.344749	+	0.173642i
$851$	−2.08086	+	0.442301i	−0.0713310	+	0.0151619i
$852$	−5.33404	−	7.34167i	−0.182741	−	0.251522i
$853$	12.3123	+	16.9464i	0.421564	+	0.580233i	0.965991	−	0.258575i	$-0.0832530\pi$
$853$	12.3123	+	16.9464i	0.421564	+	0.580233i	−0.544427	+	0.838808i	$0.683253\pi$
$854$	−27.9673	+	5.94463i	−0.957021	+	0.203421i
$855$	4.51205	−	8.26424i	0.154309	−	0.282631i
$856$	−0.199690	+	1.89992i	−0.00682526	+	0.0649380i
$857$	−5.50710	+	25.9089i	−0.188119	+	0.885029i	0.778267	+	0.627933i	$0.216099\pi$
$857$	−5.50710	+	25.9089i	−0.188119	+	0.885029i	−0.966386	+	0.257096i	$0.917234\pi$
$858$	−1.35805	−	3.05022i	−0.0463629	−	0.104133i
$859$	31.3418	+	34.8086i	1.06937	+	1.18765i	0.981488	+	0.191523i	$0.0613426\pi$
$859$	31.3418	+	34.8086i	1.06937	+	1.18765i	0.0878802	+	0.996131i	$0.471991\pi$
$860$	−6.06537	−	7.94274i	−0.206827	−	0.270845i
$861$	21.2457	−	23.5957i	0.724051	−	0.804140i
$862$	−25.6671	+	14.8189i	−0.874224	+	0.504733i
$863$	−23.0184	−	13.2897i	−0.783557	−	0.452387i	0.0541326	−	0.998534i	$-0.482761\pi$
$863$	−23.0184	−	13.2897i	−0.783557	−	0.452387i	−0.837689	+	0.546147i	$0.816094\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	28.5135	−	17.3820i	0.969488	−	0.591005i
$866$	30.4036	+	22.0895i	1.03316	+	0.750632i
$867$			11.9339i			0.405296i
$868$	−7.49452	−	12.5479i	−0.254381	−	0.425904i
$869$	3.00283			0.101864
$870$	−6.91240	−	19.6653i	−0.234352	−	0.666717i
$871$	36.2450	+	16.1373i	1.22811	+	0.546791i
$872$	−8.31733	+	2.70247i	−0.281660	+	0.0915170i
$873$	7.24089	+	4.18053i	0.245067	+	0.141490i
$874$	−10.6738	−	18.4876i	−0.361048	−	0.625354i
$875$	24.3027	−	16.4542i	0.821583	−	0.556254i
$876$	−1.04362	+	3.21193i	−0.0352606	+	0.108521i
$877$	−13.9323	+	12.5447i	−0.470459	+	0.423603i	−0.869955	−	0.493132i	$-0.835852\pi$
$877$	−13.9323	+	12.5447i	−0.470459	+	0.423603i	0.399495	+	0.916735i	$0.369185\pi$
$878$	3.94007	+	8.84954i	0.132971	+	0.298657i
$879$	30.8044	+	6.54768i	1.03901	+	0.220848i
$880$	1.23844	−	1.44322i	0.0417479	−	0.0486508i
$881$	3.15372	+	30.0057i	0.106252	+	1.01092i	0.909622	+	0.415437i	$0.136371\pi$
$881$	3.15372	+	30.0057i	0.106252	+	1.01092i	−0.803370	+	0.595480i	$0.796962\pi$
$882$	−0.0226798	−	0.106700i	−0.000763669	−	0.00359278i
$883$	14.3256	+	19.7174i	0.482093	+	0.663544i	0.978905	−	0.204314i	$-0.0654963\pi$
$883$	14.3256	+	19.7174i	0.482093	+	0.663544i	−0.496812	+	0.867858i	$0.665496\pi$
$884$	−7.14874	+	5.19387i	−0.240438	+	0.174689i
$885$	−7.56317	+	18.1396i	−0.254233	+	0.609756i
$886$	1.43220	+	13.6265i	0.0481157	+	0.457790i
$887$	−41.0057	−	4.30987i	−1.37684	−	0.144711i	−0.612980	−	0.790099i	$-0.710029\pi$
$887$	−41.0057	−	4.30987i	−1.37684	−	0.144711i	−0.763855	+	0.645387i	$0.776696\pi$
$888$	0.0872441	−	0.410451i	0.00292772	−	0.0137738i
$889$	35.9634	−	16.0119i	1.20617	−	0.537023i
$890$	7.93622	−	1.02604i	0.266023	−	0.0343930i
$891$	0.262814	−	0.808858i	0.00880460	−	0.0270978i
$892$	2.15805	+	1.94311i	0.0722567	+	0.0650602i
$893$	−35.2100	+	20.3285i	−1.17826	+	0.680267i
$894$	8.48769	−	14.7011i	0.283871	−	0.491679i
$895$	5.84573	−	19.5675i	0.195401	−	0.654071i
$896$	−2.39811	−	1.06771i	−0.0801151	−	0.0356696i
$897$	11.6986	−	16.1018i	0.390606	−	0.537623i
$898$		−	6.56849i		−	0.219193i
$899$	49.1199	−	16.7684i	1.63824	−	0.559256i
$900$	1.77010	+	4.67619i	0.0590032	+	0.155873i
$901$	−16.1654	−	11.7449i	−0.538548	−	0.391278i
$902$	−4.18409	+	9.39761i	−0.139315	+	0.312906i
$903$	−11.1581	+	3.62548i	−0.371318	+	0.120649i
$904$	−5.41729	+	9.38302i	−0.180176	+	0.312075i
$905$	2.81053	−	34.6792i	0.0934251	−	1.15278i
$906$	4.73847	−	5.26260i	0.157425	−	0.174838i
$907$	9.46014	+	3.07379i	0.314119	+	0.102063i	0.461834	−	0.886967i	$-0.347192\pi$
$907$	9.46014	+	3.07379i	0.314119	+	0.102063i	−0.147715	+	0.989030i	$0.547192\pi$
$908$	−9.12183	+	8.21333i	−0.302719	+	0.272569i
$909$	−11.1990	+	4.98610i	−0.371446	+	0.165379i
$910$	16.7524	−	15.8235i	0.555337	−	0.524545i
$911$	−3.25598	+	30.9786i	−0.107876	+	1.02637i	0.797952	+	0.602721i	$0.205917\pi$
$911$	−3.25598	+	30.9786i	−0.107876	+	1.02637i	−0.905828	+	0.423646i	$0.860750\pi$
$912$	4.18778	−	0.440154i	0.138671	−	0.0145749i
$913$	−2.95381	−	13.8966i	−0.0977568	−	0.459910i
$914$	14.1116	−	10.2527i	0.466770	−	0.339128i
$915$	0.580890	+	24.3483i	0.0192036	+	0.804930i
$916$	2.88837	−	0.613942i	0.0954344	−	0.0202852i
$917$	32.9495	−	3.46313i	1.08809	−	0.114363i
$918$	−2.23847	−	0.235273i	−0.0738805	−	0.00776516i
$919$	−0.794932	−	0.168968i	−0.0262224	−	0.00557374i	0.194782	−	0.980847i	$-0.437600\pi$
$919$	−0.794932	−	0.168968i	−0.0262224	−	0.00557374i	−0.221004	+	0.975273i	$0.570933\pi$
$920$	11.1415	+	2.09178i	0.367325	+	0.0689641i
$921$	13.8588	+	15.3917i	0.456662	+	0.507175i
$922$	7.71595	+	2.50706i	0.254111	+	0.0825657i
$923$	26.4756	+	23.8387i	0.871455	+	0.784662i
$924$	−1.11628	−	1.93346i	−0.0367230	−	0.0636061i
$925$	−0.337857	+	2.07072i	−0.0111087	+	0.0680850i
$926$	3.97320	+	12.2283i	0.130568	+	0.401846i
$927$	−4.70434	+	10.5661i	−0.154511	+	0.347037i
$928$	5.47938	−	7.54172i	0.179870	−	0.247569i
$929$	−15.9058			−0.521854			−0.260927	−	0.965359i	$-0.584028\pi$
$929$	−15.9058			−0.521854			−0.260927	+	0.965359i	$0.584028\pi$
$930$	−11.6830	+	4.30206i	−0.383100	+	0.141070i
$931$	0.459336			0.0150541
$932$	−7.82498	+	10.7702i	−0.256316	+	0.352789i
$933$	5.01361	−	11.2607i	0.164138	−	0.368660i
$934$	12.8738	+	39.6215i	0.421243	+	1.29645i
$935$	−1.83378	−	3.86774i	−0.0599710	−	0.126489i
$936$	1.96293	+	3.39990i	0.0641604	+	0.111129i
$937$	5.18967	+	4.67280i	0.169539	+	0.152654i	0.749533	−	0.661967i	$-0.230278\pi$
$937$	5.18967	+	4.67280i	0.169539	+	0.152654i	−0.579993	+	0.814621i	$0.696945\pi$
$938$	25.2306	+	8.19791i	0.823808	+	0.267671i
$939$	0.819793	+	0.910472i	0.0267529	+	0.0297121i
$940$	3.98383	−	21.2192i	0.129938	−	0.692092i
$941$	−6.36043	−	1.35195i	−0.207344	−	0.0440724i	0.103069	−	0.994674i	$-0.467134\pi$
$941$	−6.36043	−	1.35195i	−0.207344	−	0.0440724i	−0.310413	+	0.950602i	$0.600467\pi$
$942$	1.44664	+	0.152048i	0.0471341	+	0.00495400i
$943$	−60.9842	+	6.40969i	−1.98592	+	0.208728i
$944$	−8.59710	+	1.82737i	−0.279812	+	0.0594758i
$945$	5.86813	−	0.139999i	0.190890	−	0.00455417i
$946$	3.07517	−	2.23424i	0.0999823	−	0.0726414i
$947$	9.04441	+	42.5506i	0.293904	+	1.38271i	0.838907	+	0.544275i	$0.183195\pi$
$947$	9.04441	+	42.5506i	0.293904	+	1.38271i	−0.545003	+	0.838434i	$0.683472\pi$
$948$	−3.51139	+	0.369062i	−0.114045	+	0.0119866i
$949$	1.38589	−	13.1859i	0.0449879	−	0.428032i
$950$	−20.8101	+	3.19680i	−0.675170	+	0.103718i
$951$	−3.01985	+	1.34453i	−0.0979254	+	0.0435992i
$952$	−4.39085	+	3.95354i	−0.142308	+	0.128135i
$953$	−7.00295	−	2.27540i	−0.226848	−	0.0737073i	0.193388	−	0.981122i	$-0.438052\pi$
$953$	−7.00295	−	2.27540i	−0.226848	−	0.0737073i	−0.420235	+	0.907415i	$0.638052\pi$
$954$	−5.94022	+	6.59729i	−0.192322	+	0.213595i
$955$	4.79519	−	59.1681i	0.155169	−	1.91463i
$956$	−4.70336	+	8.14645i	−0.152117	+	0.263475i
$957$	7.54024	−	2.44997i	0.243741	−	0.0791964i
$958$	−0.940318	+	2.11199i	−0.0303803	+	0.0682353i
$959$	−10.2097	−	7.41777i	−0.329688	−	0.239532i
$960$	−1.27081	+	1.83985i	−0.0410151	+	0.0593809i
$961$	−10.4486	−	29.1861i	−0.337052	−	0.941486i
$962$			1.64737i			0.0531135i
$963$	1.12290	−	1.54554i	0.0361849	−	0.0498042i
$964$	−18.7305	−	8.33934i	−0.603268	−	0.268592i
$965$	−47.2902	−	14.1278i	−1.52232	−	0.454789i
$966$	6.65411	−	11.5253i	0.214092	−	0.370819i
$967$	−6.88930	+	3.97754i	−0.221545	+	0.127909i	−0.606665	−	0.794957i	$-0.707493\pi$
$967$	−6.88930	+	3.97754i	−0.221545	+	0.127909i	0.385121	+	0.922866i	$0.374160\pi$
$968$	−7.63706	−	6.87644i	−0.245464	−	0.221017i
$969$	2.92880	−	9.01391i	0.0940865	−	0.289568i
$970$	−2.39717	−	18.5416i	−0.0769684	−	0.595335i
$971$	37.0256	−	16.4848i	1.18821	−	0.529024i	0.285124	−	0.958491i	$-0.407965\pi$
$971$	37.0256	−	16.4848i	1.18821	−	0.529024i	0.903083	+	0.429467i	$0.141299\pi$
$972$	−0.207912	+	0.978148i	−0.00666877	+	0.0313741i
$973$	32.3551	+	3.40066i	1.03726	+	0.109020i
$974$	−1.65717	−	15.7669i	−0.0530991	−	0.505204i
$975$	−10.6142	−	16.5121i	−0.339925	−	0.528810i
$976$	−8.81181	+	6.40215i	−0.282059	+	0.204928i
$977$	−7.65528	−	10.5366i	−0.244914	−	0.337095i	0.668808	−	0.743435i	$-0.266805\pi$
$977$	−7.65528	−	10.5366i	−0.244914	−	0.337095i	−0.913722	+	0.406340i	$0.866805\pi$
$978$	0.0504203	+	0.237209i	0.00161226	+	0.00758510i
$979$	0.318148	+	3.02697i	0.0101680	+	0.0967424i
$980$	−0.158844	+	0.185108i	−0.00507408	+	0.00591307i
$981$	8.55425	+	1.81826i	0.273116	+	0.0580527i
$982$	−9.10500	−	20.4502i	−0.290552	−	0.652591i
$983$	−28.1847	+	25.3776i	−0.898952	+	0.809420i	−0.982341	−	0.187097i	$-0.940092\pi$
$983$	−28.1847	+	25.3776i	−0.898952	+	0.809420i	0.0833898	+	0.996517i	$0.473425\pi$
$984$	3.73769	−	11.5034i	0.119153	−	0.366716i
$985$	0.422531	+	1.77819i	0.0134630	+	0.0566578i
$986$	−10.4911	−	18.1711i	−0.334104	−	0.578685i
$987$	−21.9500	−	12.6728i	−0.698676	−	0.403381i
$988$	−15.7221	+	5.10842i	−0.500187	+	0.162521i
$989$	20.6993	+	9.21594i	0.658201	+	0.293050i
$990$	−1.79413	+	0.630640i	−0.0570212	+	0.0200431i
$991$	−26.5290			−0.842721			−0.421361	−	0.906893i	$-0.638447\pi$
$991$	−26.5290			−0.842721			−0.421361	+	0.906893i	$0.638447\pi$
$992$	−4.55240	−	3.20557i	−0.144539	−	0.101777i
$993$			4.00450i			0.127079i
$994$	19.2723	+	14.0021i	0.611280	+	0.444121i
$995$	20.6902	+	33.9403i	0.655923	+	1.07598i
$996$	5.16202	+	15.8871i	0.163565	+	0.503401i
$997$	29.7726	+	17.1892i	0.942909	+	0.544388i	0.890871	−	0.454257i	$-0.150095\pi$
$997$	29.7726	+	17.1892i	0.942909	+	0.544388i	0.0520377	+	0.998645i	$0.483428\pi$
$998$	21.2298	−	12.2570i	0.672016	−	0.387989i
$999$	−0.280781	+	0.311839i	−0.00888353	+	0.00986616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.b.19.8	✓	144
5.4	even	2	inner	930.2.bn.b.19.14	yes	144
31.18	even	15	inner	930.2.bn.b.49.14	yes	144
155.49	even	30	inner	930.2.bn.b.49.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.b.19.8	✓	144	1.1	even	1	trivial
930.2.bn.b.19.14	yes	144	5.4	even	2	inner
930.2.bn.b.49.8	yes	144	155.49	even	30	inner
930.2.bn.b.49.14	yes	144	31.18	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.02048 - 0.957953i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.95080 + 1.75650i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.02048 - 0.957953i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.95080 + 1.75650i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(-0.412606 + 2.19767i) q^{10} +(-0.831899 - 0.176825i) q^{11} +(0.994522 + 0.104528i) q^{12} +(-3.90436 + 0.410364i) q^{13} +(-2.56769 + 0.545780i) q^{14} +(0.0533318 + 2.23543i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.467968 + 2.20162i) q^{17} +(0.994522 - 0.104528i) q^{18} +(-0.440154 + 4.18778i) q^{19} +(-1.53543 - 1.62556i) q^{20} +(-2.39811 + 1.06771i) q^{21} +(0.632033 - 0.569085i) q^{22} +(4.82156 + 1.56662i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(3.16465 - 3.87104i) q^{25} +(1.96293 - 3.39990i) q^{26} +(0.951057 - 0.309017i) q^{27} +(1.06771 - 2.39811i) q^{28} +(7.54172 + 5.47938i) q^{29} +(-1.83985 - 1.27081i) q^{30} +(3.20557 - 4.55240i) q^{31} -1.00000i q^{32} +(0.499902 - 0.688056i) q^{33} +(-2.05621 - 0.915483i) q^{34} +(5.62419 + 1.68021i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.363402 + 0.209811i) q^{37} +(-3.12927 - 2.81761i) q^{38} +(1.21316 - 3.73372i) q^{39} +(2.21761 - 0.286706i) q^{40} +(-11.0497 + 4.91966i) q^{41} +(0.545780 - 2.56769i) q^{42} +(4.44487 + 0.467175i) q^{43} +(0.0888997 + 0.845825i) q^{44} +(-2.06386 - 0.860511i) q^{45} +(-4.10146 + 2.97989i) q^{46} +(5.67524 + 7.81130i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(-0.0114024 - 0.108486i) q^{49} +(1.27160 + 4.83560i) q^{50} +(-2.20162 - 0.467968i) q^{51} +(1.59679 + 3.58645i) q^{52} +(-6.59729 + 5.94022i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.85022 + 0.439648i) q^{55} +(1.31253 + 2.27336i) q^{56} +(-3.64670 - 2.10542i) q^{57} +(-8.86583 + 2.88068i) q^{58} +(8.02930 + 3.57487i) q^{59} +(2.10954 - 0.741508i) q^{60} +10.8920 q^{61} +(1.79878 + 5.26919i) q^{62} -2.62506i q^{63} +(0.809017 + 0.587785i) q^{64} +(-7.49555 + 4.56932i) q^{65} +(0.262814 + 0.808858i) q^{66} +(-8.75212 - 5.05304i) q^{67} +(1.94925 - 1.12540i) q^{68} +(-3.39228 + 3.76751i) q^{69} +(-4.66513 + 3.56246i) q^{70} +(-6.07223 - 6.74390i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(-0.702164 + 3.30342i) q^{73} +(0.0438623 - 0.417322i) q^{74} +(2.24919 + 4.46555i) q^{75} +(4.11883 - 0.875485i) q^{76} +(-1.31227 - 1.80618i) q^{77} +(2.30756 + 3.17609i) q^{78} +(-3.45357 + 0.734080i) q^{79} +(-1.07153 + 1.96261i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(2.51478 - 11.8311i) q^{82} +(6.79440 + 15.2605i) q^{83} +(1.75650 + 1.95080i) q^{84} +(3.05456 + 4.00002i) q^{85} +(-2.99058 + 3.32138i) q^{86} +(-8.07316 + 4.66104i) q^{87} +(-0.736540 - 0.425242i) q^{88} +(-1.10589 - 3.40357i) q^{89} +(1.90927 - 1.16390i) q^{90} +(-8.33741 - 6.05748i) q^{91} -5.06969i q^{92} +(2.85500 + 4.78006i) q^{93} -9.65529 q^{94} +(3.12238 + 8.88296i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-7.95184 + 2.58371i) q^{97} +(0.0944694 + 0.0545419i) q^{98} +(0.425242 + 0.736540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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