LMFDB - Embedded newform 930.2.bn.b.19.10

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			19.10
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.b.49.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.23144 + 0.143766i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.807100 - 0.726716i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.23144 + 0.143766i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.807100 - 0.726716i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(-1.19530 + 1.88978i) q^{10} +(-4.94583 - 1.05127i) q^{11} +(-0.994522 - 0.104528i) q^{12} +(0.895778 - 0.0941500i) q^{13} +(-1.06233 + 0.225805i) q^{14} +(-0.776272 + 2.09700i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.764742 + 3.59783i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(-0.638594 + 6.07582i) q^{19} +(0.826283 + 2.07780i) q^{20} +(-0.992165 + 0.441740i) q^{21} +(-3.75758 + 3.38334i) q^{22} +(2.75261 + 0.894378i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(4.95866 - 0.641611i) q^{25} +(0.450356 - 0.780039i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-0.441740 + 0.992165i) q^{28} +(-6.50920 - 4.72921i) q^{29} +(1.24023 + 1.86060i) q^{30} +(-0.321878 + 5.55845i) q^{31} +1.00000i q^{32} +(-2.97203 + 4.09065i) q^{33} +(3.36021 + 1.49606i) q^{34} +(1.90547 + 1.50559i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.47884 - 1.43116i) q^{37} +(4.54008 + 4.08791i) q^{38} +(0.278335 - 0.856628i) q^{39} +(2.16665 + 0.552824i) q^{40} +(-2.95110 + 1.31392i) q^{41} +(-0.225805 + 1.06233i) q^{42} +(-10.8246 - 1.13771i) q^{43} +(0.528529 + 5.02862i) q^{44} +(1.59996 + 1.56209i) q^{45} +(2.34151 - 1.70121i) q^{46} +(-5.43877 - 7.48582i) q^{47} +(0.207912 + 0.978148i) q^{48} +(-0.608405 - 5.78859i) q^{49} +(2.39555 - 4.38877i) q^{50} +(3.59783 + 0.764742i) q^{51} +(-0.366352 - 0.822841i) q^{52} +(-2.70026 + 2.43133i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(11.1875 + 1.63480i) q^{55} +(0.543030 + 0.940556i) q^{56} +(5.29080 + 3.05464i) q^{57} +(-7.65202 + 2.48629i) q^{58} +(-12.3992 - 5.52048i) q^{59} +(2.23425 + 0.0902706i) q^{60} -15.1454 q^{61} +(4.30769 + 3.52758i) q^{62} +1.08606i q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.98534 + 0.338873i) q^{65} +(1.56249 + 4.80885i) q^{66} +(9.19572 + 5.30915i) q^{67} +(3.18542 - 1.83910i) q^{68} +(1.93664 - 2.15086i) q^{69} +(2.33806 - 0.656596i) q^{70} +(7.40784 + 8.22724i) q^{71} +(0.406737 + 0.913545i) q^{72} +(2.00223 - 9.41973i) q^{73} +(0.299194 - 2.84664i) q^{74} +(1.43073 - 4.79093i) q^{75} +(5.97578 - 1.27019i) q^{76} +(3.22780 + 4.44269i) q^{77} +(-0.529425 - 0.728691i) q^{78} +(8.62895 - 1.83414i) q^{79} +(1.72077 - 1.42792i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-0.671634 + 3.15979i) q^{82} +(5.88824 + 13.2252i) q^{83} +(0.726716 + 0.807100i) q^{84} +(-2.22372 - 7.91840i) q^{85} +(-7.28299 + 8.08857i) q^{86} +(-6.96788 + 4.02291i) q^{87} +(4.37890 + 2.52816i) q^{88} +(-3.90805 - 12.0278i) q^{89} +(2.20419 - 0.376228i) q^{90} +(-0.791402 - 0.574987i) q^{91} -2.89427i q^{92} +(4.94698 + 2.55488i) q^{93} -9.25299 q^{94} +(0.551489 - 13.6496i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-9.42485 + 3.06232i) q^{97} +(-5.04068 - 2.91024i) q^{98} +(2.52816 + 4.37890i) 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
$5$	−2.23144	+	0.143766i	−0.997931	+	0.0642941i
$5$	−2.23144	+	0.143766i	−0.997931	+	0.0642941i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.807100	−	0.726716i	−0.305055	−	0.274673i	0.502358	−	0.864660i	$-0.332466\pi$
$7$	−0.807100	−	0.726716i	−0.305055	−	0.274673i	−0.807413	+	0.589987i	$0.799133\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	−1.19530	+	1.88978i	−0.377987	+	0.597600i
$11$	−4.94583	−	1.05127i	−1.49122	−	0.316969i	−0.611038	−	0.791601i	$-0.709248\pi$
$11$	−4.94583	−	1.05127i	−1.49122	−	0.316969i	−0.880184	+	0.474632i	$0.842581\pi$
$12$	−0.994522	−	0.104528i	−0.287094	−	0.0301748i
$13$	0.895778	−	0.0941500i	0.248444	−	0.0261125i	0.0205121	−	0.999790i	$-0.493470\pi$
$13$	0.895778	−	0.0941500i	0.248444	−	0.0261125i	0.227932	+	0.973677i	$0.426804\pi$
$14$	−1.06233	+	0.225805i	−0.283919	+	0.0603488i
$15$	−0.776272	+	2.09700i	−0.200433	+	0.541443i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.764742	+	3.59783i	0.185477	+	0.872602i	0.968190	+	0.250218i	$0.0805023\pi$
$17$	0.764742	+	3.59783i	0.185477	+	0.872602i	−0.782712	+	0.622384i	$0.786164\pi$
$18$	−0.994522	+	0.104528i	−0.234411	+	0.0246376i
$19$	−0.638594	+	6.07582i	−0.146504	+	1.39389i	0.636215	+	0.771512i	$0.280499\pi$
$19$	−0.638594	+	6.07582i	−0.146504	+	1.39389i	−0.782718	+	0.622376i	$0.786167\pi$
$20$	0.826283	+	2.07780i	0.184763	+	0.464610i
$21$	−0.992165	+	0.441740i	−0.216508	+	0.0963957i
$22$	−3.75758	+	3.38334i	−0.801118	+	0.721330i
$23$	2.75261	+	0.894378i	0.573959	+	0.186491i	0.581593	−	0.813480i	$-0.302430\pi$
$23$	2.75261	+	0.894378i	0.573959	+	0.186491i	−0.00763334	+	0.999971i	$0.502430\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	4.95866	−	0.641611i	0.991733	−	0.128322i
$26$	0.450356	−	0.780039i	0.0883221	−	0.152978i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	−0.441740	+	0.992165i	−0.0834811	+	0.187502i
$29$	−6.50920	−	4.72921i	−1.20873	−	0.878192i	−0.213613	−	0.976918i	$-0.568523\pi$
$29$	−6.50920	−	4.72921i	−1.20873	−	0.878192i	−0.995115	+	0.0987259i	$0.968523\pi$
$30$	1.24023	+	1.86060i	0.226433	+	0.339698i
$31$	−0.321878	+	5.55845i	−0.0578110	+	0.998328i
$31$	−0.321878	+	5.55845i	−0.0578110	+	0.998328i
$32$			1.00000i			0.176777i
$33$	−2.97203	+	4.09065i	−0.517364	+	0.712090i
$34$	3.36021	+	1.49606i	0.576271	+	0.256572i
$35$	1.90547	+	1.50559i	0.322084	+	0.254491i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	2.47884	−	1.43116i	0.407519	−	0.235281i	−0.282204	−	0.959354i	$-0.591066\pi$
$37$	2.47884	−	1.43116i	0.407519	−	0.235281i	0.689723	+	0.724073i	$0.257732\pi$
$38$	4.54008	+	4.08791i	0.736499	+	0.663146i
$39$	0.278335	−	0.856628i	0.0445693	−	0.137170i
$40$	2.16665	+	0.552824i	0.342578	+	0.0874091i
$41$	−2.95110	+	1.31392i	−0.460885	+	0.205199i	−0.624026	−	0.781404i	$-0.714504\pi$
$41$	−2.95110	+	1.31392i	−0.460885	+	0.205199i	0.163141	+	0.986603i	$0.447837\pi$
$42$	−0.225805	+	1.06233i	−0.0348424	+	0.163921i
$43$	−10.8246	−	1.13771i	−1.65074	−	0.173500i	−0.767055	−	0.641582i	$-0.778279\pi$
$43$	−10.8246	−	1.13771i	−1.65074	−	0.173500i	−0.883685	+	0.468082i	$0.844945\pi$
$44$	0.528529	+	5.02862i	0.0796788	+	0.758093i
$45$	1.59996	+	1.56209i	0.238509	+	0.232862i
$46$	2.34151	−	1.70121i	0.345237	−	0.250829i
$47$	−5.43877	−	7.48582i	−0.793326	−	1.09192i	−0.993686	−	0.112197i	$-0.964211\pi$
$47$	−5.43877	−	7.48582i	−0.793326	−	1.09192i	0.200360	−	0.979722i	$-0.435789\pi$
$48$	0.207912	+	0.978148i	0.0300095	+	0.141183i
$49$	−0.608405	−	5.78859i	−0.0869150	−	0.826941i
$50$	2.39555	−	4.38877i	0.338783	−	0.620666i
$51$	3.59783	+	0.764742i	0.503797	+	0.107085i
$52$	−0.366352	−	0.822841i	−0.0508039	−	0.114108i
$53$	−2.70026	+	2.43133i	−0.370910	+	0.333969i	−0.833415	−	0.552648i	$-0.813617\pi$
$53$	−2.70026	+	2.43133i	−0.370910	+	0.333969i	0.462505	+	0.886617i	$0.346951\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	11.1875	+	1.63480i	1.50852	+	0.220436i
$56$	0.543030	+	0.940556i	0.0725654	+	0.125687i
$57$	5.29080	+	3.05464i	0.700783	+	0.404597i
$58$	−7.65202	+	2.48629i	−1.00476	+	0.326466i
$59$	−12.3992	−	5.52048i	−1.61424	−	0.718705i	−0.616592	−	0.787283i	$-0.711487\pi$
$59$	−12.3992	−	5.52048i	−1.61424	−	0.718705i	−0.997646	+	0.0685783i	$0.978154\pi$
$60$	2.23425	+	0.0902706i	0.288440	+	0.0116539i
$61$	−15.1454			−1.93917			−0.969583	−	0.244764i	$-0.921290\pi$
$61$	−15.1454			−1.93917			−0.969583	+	0.244764i	$0.921290\pi$
$62$	4.30769	+	3.52758i	0.547077	+	0.448003i
$63$			1.08606i			0.136831i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−1.98534	+	0.338873i	−0.246251	+	0.0420320i
$66$	1.56249	+	4.80885i	0.192329	+	0.591928i
$67$	9.19572	+	5.30915i	1.12344	+	0.648616i	0.942276	−	0.334838i	$-0.108682\pi$
$67$	9.19572	+	5.30915i	1.12344	+	0.648616i	0.181160	+	0.983454i	$0.442015\pi$
$68$	3.18542	−	1.83910i	0.386289	−	0.223024i
$69$	1.93664	−	2.15086i	0.233144	−	0.258933i
$70$	2.33806	−	0.656596i	0.279451	−	0.0784783i
$71$	7.40784	+	8.22724i	0.879149	+	0.976394i	0.999867	−	0.0162932i	$-0.00518651\pi$
$71$	7.40784	+	8.22724i	0.879149	+	0.976394i	−0.120719	+	0.992687i	$0.538520\pi$
$72$	0.406737	+	0.913545i	0.0479344	+	0.107662i
$73$	2.00223	−	9.41973i	0.234343	−	1.10250i	−0.690850	−	0.722998i	$-0.742763\pi$
$73$	2.00223	−	9.41973i	0.234343	−	1.10250i	0.925193	−	0.379498i	$-0.123903\pi$
$74$	0.299194	−	2.84664i	0.0347806	−	0.330915i
$75$	1.43073	−	4.79093i	0.165206	−	0.553209i
$76$	5.97578	−	1.27019i	0.685469	−	0.145701i
$77$	3.22780	+	4.44269i	0.367842	+	0.506291i
$78$	−0.529425	−	0.728691i	−0.0599456	−	0.0825080i
$79$	8.62895	−	1.83414i	0.970832	−	0.206357i	0.304913	−	0.952380i	$-0.401373\pi$
$79$	8.62895	−	1.83414i	0.970832	−	0.206357i	0.665920	+	0.746024i	$0.268039\pi$
$80$	1.72077	−	1.42792i	0.192388	−	0.159646i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−0.671634	+	3.15979i	−0.0741696	+	0.348941i
$83$	5.88824	+	13.2252i	0.646318	+	1.45165i	0.877903	+	0.478839i	$0.158942\pi$
$83$	5.88824	+	13.2252i	0.646318	+	1.45165i	−0.231584	+	0.972815i	$0.574391\pi$
$84$	0.726716	+	0.807100i	0.0792912	+	0.0880618i
$85$	−2.22372	−	7.91840i	−0.241197	−	0.858871i
$86$	−7.28299	+	8.08857i	−0.785345	+	0.872213i
$87$	−6.96788	+	4.02291i	−0.747035	+	0.431301i
$88$	4.37890	+	2.52816i	0.466792	+	0.269503i
$89$	−3.90805	−	12.0278i	−0.414253	−	1.27494i	−0.912917	−	0.408144i	$-0.866176\pi$
$89$	−3.90805	−	12.0278i	−0.414253	−	1.27494i	0.498665	−	0.866795i	$-0.333824\pi$
$90$	2.20419	−	0.376228i	0.232342	−	0.0396579i
$91$	−0.791402	−	0.574987i	−0.0829615	−	0.0602751i
$92$		−	2.89427i		−	0.301748i
$93$	4.94698	+	2.55488i	0.512978	+	0.264928i
$94$	−9.25299			−0.954373
$95$	0.551489	−	13.6496i	0.0565816	−	1.40042i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	−9.42485	+	3.06232i	−0.956949	+	0.310931i	−0.745536	−	0.666465i	$-0.767806\pi$
$97$	−9.42485	+	3.06232i	−0.956949	+	0.310931i	−0.211413	+	0.977397i	$0.567806\pi$
$98$	−5.04068	−	2.91024i	−0.509185	−	0.293978i
$99$	2.52816	+	4.37890i	0.254090	+	0.440096i
$100$	−2.14252	−	4.51770i	−0.214252	−	0.451770i
$101$	−0.0562367	+	0.173079i	−0.00559576	+	0.0172220i	−0.953815	−	0.300393i	$-0.902882\pi$
$101$	−0.0562367	+	0.173079i	−0.00559576	+	0.0172220i	0.948220	+	0.317615i	$0.102882\pi$
$102$	2.73344	−	2.46120i	0.270651	−	0.243695i
$103$	1.49914	+	3.36712i	0.147715	+	0.331772i	0.972215	−	0.234089i	$-0.0752106\pi$
$103$	1.49914	+	3.36712i	0.147715	+	0.331772i	−0.824501	+	0.565861i	$0.808544\pi$
$104$	−0.881029	−	0.187268i	−0.0863920	−	0.0183632i
$105$	2.15045	−	1.12836i	0.209863	−	0.110116i
$106$	0.379811	+	3.61366i	0.0368905	+	0.350990i
$107$	−3.44854	−	16.2241i	−0.333383	−	1.56844i	−0.751302	−	0.659958i	$-0.770574\pi$
$107$	−3.44854	−	16.2241i	−0.333383	−	1.56844i	0.417920	−	0.908484i	$-0.362759\pi$
$108$	0.587785	+	0.809017i	0.0565597	+	0.0778477i
$109$	9.35950	−	6.80007i	0.896477	−	0.651329i	−0.0410815	−	0.999156i	$-0.513080\pi$
$109$	9.35950	−	6.80007i	0.896477	−	0.651329i	0.937559	+	0.347827i	$0.113080\pi$
$110$	7.89841	−	8.08993i	0.753083	−	0.771345i
$111$	−0.299194	−	2.84664i	−0.0283982	−	0.270191i
$112$	1.08011	+	0.113524i	0.102061	+	0.0107270i
$113$	2.36727	−	11.1371i	0.222694	−	1.04769i	−0.714702	−	0.699429i	$-0.753438\pi$
$113$	2.36727	−	11.1371i	0.222694	−	1.04769i	0.937396	−	0.348265i	$-0.113229\pi$
$114$	5.58111	−	2.48487i	0.522719	−	0.232729i
$115$	−6.27087	−	1.60002i	−0.584762	−	0.149203i
$116$	−2.48629	+	7.65202i	−0.230847	+	0.710473i
$117$	−0.669359	−	0.602694i	−0.0618823	−	0.0557191i
$118$	−11.7542	+	6.78630i	−1.08206	+	0.624730i
$119$	1.99738	−	3.45956i	0.183099	−	0.317137i
$120$	1.38629	−	1.75448i	0.126550	−	0.160162i
$121$	13.3070	+	5.92468i	1.20973	+	0.538607i
$122$	−8.90222	+	12.2529i	−0.805969	+	1.10932i
$123$			3.23038i			0.291274i
$124$	5.38587	−	1.41153i	0.483665	−	0.126759i
$125$	−10.9727	+	2.14461i	−0.981430	+	0.191819i
$126$	0.878641	+	0.638370i	0.0782756	+	0.0568705i
$127$	6.81850	−	15.3146i	0.605044	−	1.35895i	−0.308116	−	0.951349i	$-0.599698\pi$
$127$	6.81850	−	15.3146i	0.605044	−	1.35895i	0.913160	−	0.407602i	$-0.133635\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	−5.44213	+	9.42604i	−0.479152	+	0.829916i
$130$	−0.892800	+	1.80536i	−0.0783037	+	0.158340i
$131$	−8.64173	+	9.59761i	−0.755031	+	0.838547i	−0.991090	−	0.133191i	$-0.957478\pi$
$131$	−8.64173	+	9.59761i	−0.755031	+	0.838547i	0.236059	+	0.971739i	$0.424144\pi$
$132$	4.80885	+	1.56249i	0.418556	+	0.135997i
$133$	4.93080	−	4.43971i	0.427555	−	0.384972i
$134$	9.70030	−	4.31885i	0.837978	−	0.373092i
$135$	2.07780	−	0.826283i	0.178829	−	0.0711151i
$136$	0.384477	−	3.65806i	0.0329687	−	0.313676i
$137$	−10.1397	+	1.06572i	−0.866289	+	0.0910507i	−0.527238	−	0.849717i	$-0.676773\pi$
$137$	−10.1397	+	1.06572i	−0.866289	+	0.0910507i	−0.339051	+	0.940768i	$0.610106\pi$
$138$	−0.601752	−	2.83102i	−0.0512245	−	0.240992i
$139$	12.3423	−	8.96724i	1.04686	−	0.760591i	0.0752505	−	0.997165i	$-0.476024\pi$
$139$	12.3423	−	8.96724i	1.04686	−	0.760591i	0.971614	+	0.236573i	$0.0760244\pi$
$140$	0.843078	−	2.27747i	0.0712531	−	0.192481i
$141$	−9.05079	+	1.92380i	−0.762214	+	0.162014i
$142$	11.0102	−	1.15722i	0.923955	−	0.0971116i
$143$	−4.52934	−	0.476053i	−0.378762	−	0.0398095i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	15.2048	+	9.61715i	1.26269	+	0.798661i
$146$	−6.44384	−	7.15661i	−0.533296	−	0.592285i
$147$	−5.53560	−	1.79863i	−0.456569	−	0.148348i
$148$	−2.12712	−	1.91527i	−0.174848	−	0.157434i
$149$	3.18677	+	5.51965i	0.261071	+	0.452188i	0.966527	−	0.256566i	$-0.0825911\pi$
$149$	3.18677	+	5.51965i	0.261071	+	0.452188i	−0.705456	+	0.708754i	$0.749258\pi$
$150$	−3.03498	−	3.97352i	−0.247805	−	0.324437i
$151$	1.22188	+	3.76057i	0.0994356	+	0.306031i	0.988384	−	0.151976i	$-0.0485635\pi$
$151$	1.22188	+	3.76057i	0.0994356	+	0.306031i	−0.888949	+	0.458007i	$0.848564\pi$
$152$	2.48487	−	5.58111i	0.201550	−	0.452688i
$153$	2.16200	−	2.97573i	0.174787	−	0.240574i
$154$	5.49147			0.442515
$155$	−0.0808645	−	12.4496i	−0.00649519	−	0.999979i
$156$	−0.900712			−0.0721147
$157$	1.13963	−	1.56857i	0.0909527	−	0.125186i	−0.761116	−	0.648616i	$-0.775348\pi$
$157$	1.13963	−	1.56857i	0.0909527	−	0.125186i	0.852068	+	0.523431i	$0.175348\pi$
$158$	3.58812	−	8.05904i	0.285455	−	0.641143i
$159$	1.12283	+	3.45573i	0.0890465	+	0.274057i
$160$	−0.143766	−	2.23144i	−0.0113657	−	0.176411i
$161$	−1.57167	−	2.72222i	−0.123865	−	0.214541i
$162$	0.743145	+	0.669131i	0.0583870	+	0.0525719i
$163$	−9.30078	−	3.02201i	−0.728493	−	0.236702i	−0.0787915	−	0.996891i	$-0.525106\pi$
$163$	−9.30078	−	3.02201i	−0.728493	−	0.236702i	−0.649702	+	0.760189i	$0.725106\pi$
$164$	2.16155	+	2.40064i	0.168789	+	0.187459i
$165$	6.04381	−	9.55532i	0.470510	−	0.743881i
$166$	14.1604	+	3.00989i	1.09906	+	0.233613i
$167$	−3.89118	−	0.408979i	−0.301108	−	0.0316478i	−0.0472303	−	0.998884i	$-0.515039\pi$
$167$	−3.89118	−	0.408979i	−0.301108	−	0.0316478i	−0.253878	+	0.967236i	$0.581706\pi$
$168$	1.08011	−	0.113524i	0.0833323	−	0.00875858i
$169$	−11.9224	+	2.53418i	−0.917105	+	0.194937i
$170$	−7.71319	−	2.85529i	−0.591575	−	0.218991i
$171$	4.94251	−	3.59095i	0.377964	−	0.274607i
$172$	2.26296	+	10.6464i	0.172549	+	0.811781i
$173$	1.50541	−	0.158225i	0.114454	−	0.0120296i	−0.0471281	−	0.998889i	$-0.515007\pi$
$173$	1.50541	−	0.158225i	0.114454	−	0.0120296i	0.161582	+	0.986859i	$0.448340\pi$
$174$	−0.841017	+	8.00174i	−0.0637573	+	0.606610i
$175$	−4.46840	−	3.08569i	−0.337780	−	0.233257i
$176$	4.61918	−	2.05659i	0.348184	−	0.155021i
$177$	−10.0864	+	9.08185i	−0.758141	+	0.682633i
$178$	−12.0278	−	3.90805i	−0.901518	−	0.292921i
$179$	−4.00607	+	4.44919i	−0.299428	+	0.332548i	−0.874018	−	0.485893i	$-0.838495\pi$
$179$	−4.00607	+	4.44919i	−0.299428	+	0.332548i	0.574591	+	0.818441i	$0.305161\pi$
$180$	0.991216	−	2.00437i	0.0738809	−	0.149397i
$181$	−12.1835	+	21.1024i	−0.905592	+	1.56853i	−0.0854711	+	0.996341i	$0.527240\pi$
$181$	−12.1835	+	21.1024i	−0.905592	+	1.56853i	−0.820121	+	0.572190i	$0.806094\pi$
$182$	−0.930349	+	0.302289i	−0.0689621	+	0.0224071i
$183$	−6.16018	+	13.8360i	−0.455373	+	1.02279i
$184$	−2.34151	−	1.70121i	−0.172619	−	0.125415i
$185$	−5.32564	+	3.54992i	−0.391549	+	0.260995i
$186$	4.97470	−	2.50047i	0.364763	−	0.183343i
$187$		−	18.5982i		−	1.36003i
$188$	−5.43877	+	7.48582i	−0.396663	+	0.545960i
$189$	0.992165	+	0.441740i	0.0721694	+	0.0321319i
$190$	−10.7186	−	8.46922i	−0.777611	−	0.614422i
$191$	−9.13386	+	15.8203i	−0.660903	+	1.14472i	0.319476	+	0.947594i	$0.396493\pi$
$191$	−9.13386	+	15.8203i	−0.660903	+	1.14472i	−0.980379	+	0.197123i	$0.936840\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−2.24884	−	2.02486i	−0.161875	−	0.145753i	0.584213	−	0.811600i	$-0.301403\pi$
$193$	−2.24884	−	2.02486i	−0.161875	−	0.145753i	−0.746088	+	0.665848i	$0.768070\pi$
$194$	−3.06232	+	9.42485i	−0.219862	+	0.676665i
$195$	−0.497935	+	1.95153i	−0.0356578	+	0.139752i
$196$	−5.31727	+	2.36740i	−0.379805	+	0.169100i
$197$	2.62410	−	12.3454i	0.186959	−	0.879573i	−0.780225	−	0.625498i	$-0.784896\pi$
$197$	2.62410	−	12.3454i	0.186959	−	0.879573i	0.967185	−	0.254075i	$-0.0817710\pi$
$198$	5.02862	+	0.528529i	0.357368	+	0.0375609i
$199$	2.13779	+	20.3397i	0.151544	+	1.44184i	0.760861	+	0.648915i	$0.224777\pi$
$199$	2.13779	+	20.3397i	0.151544	+	1.44184i	−0.609317	+	0.792927i	$0.708556\pi$
$200$	−4.91424	−	0.922102i	−0.347489	−	0.0652025i
$201$	8.59038	−	6.24128i	0.605919	−	0.440226i
$202$	0.106969	+	0.147230i	0.00752628	+	0.0103590i
$203$	1.81678	+	8.54728i	0.127513	+	0.599902i
$204$	−0.384477	−	3.65806i	−0.0269188	−	0.256115i
$205$	6.39632	−	3.35619i	0.446738	−	0.234407i
$206$	3.60523	+	0.766315i	0.251188	+	0.0533917i
$207$	−1.17720	−	2.64404i	−0.0818214	−	0.183774i
$208$	−0.669359	+	0.602694i	−0.0464117	+	0.0417893i
$209$	9.54569	−	29.3786i	0.660289	−	2.03216i
$210$	0.351143	−	2.40298i	0.0242312	−	0.165822i
$211$	−0.638824	−	1.10648i	−0.0439785	−	0.0761730i	0.843198	−	0.537603i	$-0.180670\pi$
$211$	−0.638824	−	1.10648i	−0.0439785	−	0.0761730i	−0.887177	+	0.461430i	$0.847337\pi$
$212$	3.14676	+	1.81678i	0.216120	+	0.124777i
$213$	10.5290	−	3.42108i	0.721435	−	0.234408i
$214$	−15.1526	−	6.74636i	−1.03581	−	0.461171i
$215$	24.3181	+	0.982528i	1.65848	+	0.0670079i
$216$	1.00000			0.0680414
$217$	4.29920	−	4.25231i	0.291849	−	0.288666i
$218$		−	11.5690i		−	0.783550i
$219$	−7.79097	−	5.66047i	−0.526465	−	0.382499i
$220$	−1.90233	−	11.1451i	−0.128255	−	0.751402i
$221$	1.02377	+	3.15085i	0.0688665	+	0.211949i
$222$	−2.47884	−	1.43116i	−0.166369	−	0.0960531i
$223$	−10.1632	+	5.86774i	−0.680580	+	0.392933i	−0.800074	−	0.599902i	$-0.795206\pi$
$223$	−10.1632	+	5.86774i	−0.680580	+	0.392933i	0.119493	+	0.992835i	$0.461873\pi$
$224$	0.726716	−	0.807100i	0.0485558	−	0.0539266i
$225$	−3.79480	−	3.25568i	−0.252987	−	0.217046i
$226$	−7.61869	−	8.46141i	−0.506788	−	0.562845i
$227$	−2.32072	−	5.21243i	−0.154032	−	0.345961i	0.820003	−	0.572359i	$-0.193972\pi$
$227$	−2.32072	−	5.21243i	−0.154032	−	0.345961i	−0.974035	+	0.226398i	$0.927305\pi$
$228$	1.27019	−	5.97578i	0.0841205	−	0.395756i
$229$	0.814447	−	7.74895i	0.0538202	−	0.512065i	−0.934090	−	0.357038i	$-0.883787\pi$
$229$	0.814447	−	7.74895i	0.0538202	−	0.512065i	0.987910	−	0.155027i	$-0.0495465\pi$
$230$	−4.98037	+	4.13278i	−0.328396	+	0.272507i
$231$	5.37146	−	1.14174i	0.353416	−	0.0751210i
$232$	4.72921	+	6.50920i	0.310488	+	0.427350i
$233$	−6.60127	−	9.08587i	−0.432463	−	0.595235i	0.536053	−	0.844184i	$-0.319915\pi$
$233$	−6.60127	−	9.08587i	−0.432463	−	0.595235i	−0.968516	+	0.248949i	$0.919915\pi$
$234$	−0.881029	+	0.187268i	−0.0575947	+	0.0122421i
$235$	13.2125	+	15.9223i	0.861889	+	1.03865i
$236$	−1.41872	+	13.4983i	−0.0923510	+	0.878662i
$237$	1.83414	−	8.62895i	0.119140	−	0.560510i
$238$	−1.62481	−	3.64939i	−0.105321	−	0.236555i
$239$	−1.36695	−	1.51815i	−0.0884204	−	0.0982008i	0.697311	−	0.716769i	$-0.254380\pi$
$239$	−1.36695	−	1.51815i	−0.0884204	−	0.0982008i	−0.785731	+	0.618568i	$0.787713\pi$
$240$	−0.604567	−	2.15279i	−0.0390246	−	0.138962i
$241$	14.8946	−	16.5421i	0.959444	−	1.06557i	−0.0383555	−	0.999264i	$-0.512212\pi$
$241$	14.8946	−	16.5421i	0.959444	−	1.06557i	0.997799	−	0.0663061i	$-0.0211214\pi$
$242$	12.6148	−	7.28318i	0.810913	−	0.468181i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	4.68018	+	14.4041i	0.299618	+	0.922128i
$245$	2.18982	+	12.8294i	0.139903	+	0.819642i
$246$	2.61344	+	1.89877i	0.166627	+	0.121061i
$247$			5.50270i			0.350129i
$248$	2.02378	−	5.18694i	0.128510	−	0.329371i
$249$	14.4768			0.917429
$250$	−4.71458	+	10.1377i	−0.298176	+	0.641164i
$251$	−1.29356	−	0.575928i	−0.0816485	−	0.0363522i	0.365506	−	0.930809i	$-0.380896\pi$
$251$	−1.29356	−	0.575928i	−0.0816485	−	0.0363522i	−0.447155	+	0.894457i	$0.647563\pi$
$252$	1.03290	−	0.335611i	0.0650669	−	0.0211415i
$253$	−12.6737	−	7.31717i	−0.796789	−	0.460027i
$254$	−8.38196	−	14.5180i	−0.525931	−	0.910939i
$255$	−8.13829	−	1.18923i	−0.509640	−	0.0744726i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	7.39677	−	6.66008i	0.461398	−	0.415445i	−0.405373	−	0.914151i	$-0.632858\pi$
$257$	7.39677	−	6.66008i	0.461398	−	0.415445i	0.866771	+	0.498707i	$0.166192\pi$
$258$	4.42702	+	9.94326i	0.275614	+	0.619040i
$259$	−3.04072	−	0.646325i	−0.188941	−	0.0401607i
$260$	0.935791	+	1.78345i	0.0580353	+	0.110605i
$261$	0.841017	+	8.00174i	0.0520576	+	0.495295i
$262$	2.68515	+	12.6326i	0.165889	+	0.780447i
$263$	−14.4569	−	19.8982i	−0.891449	−	1.22697i	−0.973116	−	0.230315i	$-0.926024\pi$
$263$	−14.4569	−	19.8982i	−0.891449	−	1.22697i	0.0816667	−	0.996660i	$-0.473976\pi$
$264$	4.09065	−	2.97203i	0.251762	−	0.182916i
$265$	5.67594	−	5.81358i	0.348670	−	0.357125i
$266$	−0.693551	−	6.59870i	−0.0425244	−	0.404592i
$267$	−12.5774	−	1.32194i	−0.769727	−	0.0809016i
$268$	2.20767	−	10.3863i	0.134855	−	0.634442i
$269$	6.69247	−	2.97968i	0.408047	−	0.181674i	−0.192440	−	0.981309i	$-0.561640\pi$
$269$	6.69247	−	2.97968i	0.408047	−	0.181674i	0.600487	+	0.799634i	$0.294973\pi$
$270$	0.552824	−	2.16665i	0.0336438	−	0.131858i
$271$	−9.91674	+	30.5206i	−0.602399	+	1.85399i	−0.0886309	+	0.996065i	$0.528249\pi$
$271$	−9.91674	+	30.5206i	−0.602399	+	1.85399i	−0.513768	+	0.857929i	$0.671751\pi$
$272$	−2.73344	−	2.46120i	−0.165739	−	0.149232i
$273$	−0.847169	+	0.489113i	−0.0512730	+	0.0296025i
$274$	−5.09775	+	8.82957i	−0.307967	+	0.533414i
$275$	−25.1992	−	2.03958i	−1.51957	−	0.122992i
$276$	−2.64404	−	1.17720i	−0.159153	−	0.0708594i
$277$	13.9227	−	19.1629i	0.836531	−	1.15139i	−0.150141	−	0.988665i	$-0.547973\pi$
$277$	13.9227	−	19.1629i	0.836531	−	1.15139i	0.986672	−	0.162722i	$-0.0520272\pi$
$278$		−	15.2560i		−	0.914993i
$279$	4.34611	−	3.48013i	0.260195	−	0.208350i
$280$	−1.34696	−	2.02073i	−0.0804962	−	0.120761i
$281$	−0.229193	−	0.166518i	−0.0136725	−	0.00993364i	0.580928	−	0.813955i	$-0.302690\pi$
$281$	−0.229193	−	0.166518i	−0.0136725	−	0.00993364i	−0.594601	+	0.804021i	$0.702690\pi$
$282$	−3.76353	+	8.45303i	−0.224115	+	0.503370i
$283$	22.2756	−	7.23779i	1.32415	−	0.430242i	0.440231	−	0.897884i	$-0.354896\pi$
$283$	22.2756	−	7.23779i	1.32415	−	0.430242i	0.883918	+	0.467642i	$0.154896\pi$
$284$	5.53542	−	9.58763i	0.328467	−	0.568921i
$285$	−12.2453	−	6.05562i	−0.725346	−	0.358704i
$286$	−3.04741	+	3.38449i	−0.180197	+	0.200129i
$287$	3.33668	+	1.08415i	0.196958	+	0.0639955i
$288$	0.743145	−	0.669131i	0.0437902	−	0.0394289i
$289$	3.17073	−	1.41170i	0.186513	−	0.0830411i
$290$	16.7176	−	6.64812i	0.981691	−	0.390391i
$291$	−1.03586	+	9.85559i	−0.0607234	+	0.577745i
$292$	−9.57742	+	1.00663i	−0.560476	+	0.0589084i
$293$	4.01013	+	18.8662i	0.234274	+	1.10217i	0.925268	+	0.379313i	$0.123840\pi$
$293$	4.01013	+	18.8662i	0.234274	+	1.10217i	−0.690994	+	0.722860i	$0.742827\pi$
$294$	−4.70886	+	3.42119i	−0.274626	+	0.199528i
$295$	28.4617	+	10.5360i	1.65711	+	0.613432i
$296$	−2.79977	+	0.595110i	−0.162733	+	0.0345900i
$297$	5.02862	−	0.528529i	0.291790	−	0.0306684i
$298$	6.33863	+	0.666217i	0.367187	+	0.0385929i
$299$	2.54993	+	0.542005i	0.147466	+	0.0313450i
$300$	−4.99857	+	0.119775i	−0.288592	+	0.00691522i
$301$	7.90976	+	8.78468i	0.455911	+	0.506340i
$302$	3.76057	+	1.22188i	0.216397	+	0.0703116i
$303$	0.135242	+	0.121772i	0.00776943	+	0.00699563i
$304$	−3.05464	−	5.29080i	−0.175196	−	0.303448i
$305$	33.7960	−	2.17739i	1.93515	−	0.124677i
$306$	−1.13663	−	3.49818i	−0.0649767	−	0.199978i
$307$	−7.53792	+	16.9304i	−0.430212	+	0.966272i	0.560230	+	0.828337i	$0.310713\pi$
$307$	−7.53792	+	16.9304i	−0.430212	+	0.966272i	−0.990441	+	0.137934i	$0.955954\pi$
$308$	3.22780	−	4.44269i	0.183921	−	0.253146i
$309$	3.68577			0.209676
$310$	−10.1195	−	7.25229i	−0.574749	−	0.411903i
$311$	2.20222			0.124876			0.0624382	−	0.998049i	$-0.480112\pi$
$311$	2.20222			0.124876			0.0624382	+	0.998049i	$0.480112\pi$
$312$	−0.529425	+	0.728691i	−0.0299728	+	0.0412540i
$313$	3.20258	−	7.19311i	0.181021	−	0.406579i	−0.800129	−	0.599828i	$-0.795236\pi$
$313$	3.20258	−	7.19311i	0.181021	−	0.406579i	0.981150	+	0.193249i	$0.0619025\pi$
$314$	−0.599141	−	1.84397i	−0.0338115	−	0.104061i
$315$	−0.156139	−	2.42348i	−0.00879741	−	0.136548i
$316$	−4.41086	−	7.63984i	−0.248130	−	0.429774i
$317$	4.38569	+	3.94889i	0.246325	+	0.221792i	0.783040	−	0.621972i	$-0.213668\pi$
$317$	4.38569	+	3.94889i	0.246325	+	0.221792i	−0.536715	+	0.843764i	$0.680335\pi$
$318$	3.45573	+	1.12283i	0.193787	+	0.0629654i
$319$	27.2217	+	30.2328i	1.52412	+	1.69271i
$320$	−1.88978	−	1.19530i	−0.105642	−	0.0668193i
$321$	−16.2241	−	3.44854i	−0.905541	−	0.192479i
$322$	−3.12613	−	0.328569i	−0.174212	−	0.0183105i
$323$	−22.3481	+	2.34888i	−1.24348	+	0.130695i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	4.38145	−	1.04160i	0.243039	−	0.0577775i
$326$	−7.91171	+	5.74820i	−0.438189	+	0.318363i
$327$	−2.40533	−	11.3162i	−0.133015	−	0.625785i
$328$	3.21269	−	0.337667i	0.177391	−	0.0186445i
$329$	−1.05044	+	9.99425i	−0.0579125	+	0.551001i
$330$	−4.17795	−	10.5060i	−0.229989	−	0.578338i
$331$	−8.25729	+	3.67638i	−0.453862	+	0.202072i	−0.620919	−	0.783875i	$-0.713240\pi$
$331$	−8.25729	+	3.67638i	−0.453862	+	0.202072i	0.167057	+	0.985947i	$0.446574\pi$
$332$	10.7583	−	9.68686i	0.590441	−	0.531635i
$333$	−2.72223	−	0.884505i	−0.149177	−	0.0484706i
$334$	−2.61805	+	2.90764i	−0.143253	+	0.159099i
$335$	−21.2830	−	10.5250i	−1.16281	−	0.575044i
$336$	0.543030	−	0.940556i	0.0296247	−	0.0513115i
$337$	−19.4822	+	6.33014i	−1.06126	+	0.344825i	−0.787079	−	0.616853i	$-0.788407\pi$
$337$	−19.4822	+	6.33014i	−1.06126	+	0.344825i	−0.274183	+	0.961677i	$0.588407\pi$
$338$	−4.95760	+	11.1349i	−0.269658	+	0.605661i
$339$	−9.21143	−	6.69249i	−0.500296	−	0.363486i
$340$	−6.84368	+	4.56181i	−0.371151	+	0.247399i
$341$	7.43538	−	27.1528i	0.402648	−	1.47040i
$342$		−	6.10928i		−	0.330352i
$343$	−8.18421	+	11.2646i	−0.441906	+	0.608231i
$344$	9.94326	+	4.42702i	0.536105	+	0.238689i
$345$	−4.01228	+	5.07794i	−0.216014	+	0.273387i
$346$	0.756852	−	1.31091i	0.0406886	−	0.0704748i
$347$	−2.67153	+	1.54241i	−0.143415	+	0.0828008i	−0.569991	−	0.821651i	$-0.693053\pi$
$347$	−2.67153	+	1.54241i	−0.143415	+	0.0828008i	0.426575	+	0.904452i	$0.359720\pi$
$348$	5.97920	+	5.38370i	0.320519	+	0.288597i
$349$	6.23967	−	19.2037i	0.334002	−	1.02795i	−0.633210	−	0.773980i	$-0.718263\pi$
$349$	6.23967	−	19.2037i	0.334002	−	1.02795i	0.967212	−	0.253972i	$-0.0817371\pi$
$350$	−5.12284	+	1.80129i	−0.273827	+	0.0962830i
$351$	−0.822841	+	0.366352i	−0.0439200	+	0.0195544i
$352$	1.05127	−	4.94583i	0.0560328	−	0.263613i
$353$	25.9011	+	2.72232i	1.37858	+	0.144894i	0.764638	−	0.644460i	$-0.222918\pi$
$353$	25.9011	+	2.72232i	1.37858	+	0.144894i	0.613938	+	0.789354i	$0.289584\pi$
$354$	1.41872	+	13.4983i	0.0754043	+	0.717424i
$355$	−17.7130	−	17.2936i	−0.940106	−	0.917849i
$356$	−10.2314	+	7.43356i	−0.542264	+	0.393978i
$357$	−2.34806	−	3.23182i	−0.124272	−	0.171046i
$358$	1.24476	+	5.85615i	0.0657877	+	0.309507i
$359$	−1.10617	−	10.5245i	−0.0583816	−	0.555464i	−0.984146	−	0.177362i	$-0.943244\pi$
$359$	−1.10617	−	10.5245i	−0.0583816	−	0.555464i	0.925764	−	0.378102i	$-0.123423\pi$
$360$	−1.03895	−	1.98005i	−0.0547573	−	0.104358i
$361$	−17.9229	−	3.80964i	−0.943313	−	0.200507i
$362$	9.91095	+	22.2603i	0.520908	+	1.16998i
$363$	10.8249	−	9.74680i	0.568161	−	0.511574i
$364$	−0.302289	+	0.930349i	−0.0158442	+	0.0487635i
$365$	−3.11361	+	21.3074i	−0.162974	+	1.11528i
$366$	7.57268	+	13.1163i	0.395831	+	0.685599i
$367$	19.5066	+	11.2621i	1.01824	+	0.587879i	0.913593	−	0.406631i	$-0.133296\pi$
$367$	19.5066	+	11.2621i	1.01824	+	0.587879i	0.104644	+	0.994510i	$0.466630\pi$
$368$	−2.75261	+	0.894378i	−0.143490	+	0.0466227i
$369$	2.95110	+	1.31392i	0.153628	+	0.0683997i
$370$	−0.258383	+	6.39512i	−0.0134327	+	0.332467i
$371$	3.94627			0.204880
$372$	0.901131	−	5.49436i	0.0467215	−	0.284869i
$373$			16.4070i			0.849520i	0.905306	+	0.424760i	$0.139642\pi$
$373$			16.4070i			0.849520i	−0.905306	+	0.424760i	$0.860358\pi$
$374$	−15.0463	−	10.9317i	−0.778023	−	0.565267i
$375$	−2.50381	+	10.8964i	−0.129296	+	0.562686i
$376$	2.85933	+	8.80012i	0.147459	+	0.453831i
$377$	−6.27605	−	3.62348i	−0.323233	−	0.186619i
$378$	0.940556	−	0.543030i	0.0483770	−	0.0279304i
$379$	−13.5684	+	15.0692i	−0.696962	+	0.774055i	−0.982889	−	0.184197i	$-0.941032\pi$
$379$	−13.5684	+	15.0692i	−0.696962	+	0.774055i	0.285927	+	0.958251i	$0.407698\pi$
$380$	−13.1520	+	3.69347i	−0.674683	+	0.189471i
$381$	−11.2173	−	12.4580i	−0.574677	−	0.638244i
$382$	7.43015	+	16.6884i	0.380160	+	0.853852i
$383$	−0.317050	+	1.49160i	−0.0162005	+	0.0762174i	−0.985505	−	0.169645i	$-0.945738\pi$
$383$	−0.317050	+	1.49160i	−0.0162005	+	0.0762174i	0.969305	+	0.245863i	$0.0790712\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	−7.84136	−	9.44955i	−0.399633	−	0.481594i
$386$	−2.95998	+	0.629163i	−0.150659	+	0.0320235i
$387$	6.39760	+	8.80554i	0.325208	+	0.447611i
$388$	5.82488	+	8.01726i	0.295713	+	0.407015i
$389$	21.9058	−	4.65622i	1.11067	−	0.236080i	0.384179	−	0.923259i	$-0.374485\pi$
$389$	21.9058	−	4.65622i	1.11067	−	0.236080i	0.726488	+	0.687179i	$0.241151\pi$
$390$	1.28614	+	1.54992i	0.0651263	+	0.0784832i
$391$	−1.11278	+	10.5874i	−0.0562757	+	0.535428i
$392$	−1.21014	+	5.69328i	−0.0611215	+	0.287554i
$393$	5.25295	+	11.7983i	0.264976	+	0.595146i
$394$	−8.44523	−	9.37938i	−0.425465	−	0.472527i
$395$	−18.9913	+	5.33332i	−0.955556	+	0.268349i
$396$	3.38334	−	3.75758i	0.170019	−	0.188825i
$397$	9.01617	−	5.20549i	0.452509	−	0.261256i	−0.256380	−	0.966576i	$-0.582530\pi$
$397$	9.01617	−	5.20549i	0.452509	−	0.261256i	0.708889	+	0.705320i	$0.249197\pi$
$398$	17.7117	+	10.2259i	0.887808	+	0.512576i
$399$	−2.05034	−	6.31031i	−0.102646	−	0.315910i
$400$	−3.63451	+	3.43370i	−0.181726	+	0.171685i
$401$	2.92667	+	2.12635i	0.146151	+	0.106185i	0.658458	−	0.752617i	$-0.271209\pi$
$401$	2.92667	+	2.12635i	0.146151	+	0.106185i	−0.512307	+	0.858802i	$0.671209\pi$
$402$		−	10.6183i		−	0.529593i
$403$	0.234997	+	5.00944i	0.0117060	+	0.249538i
$404$	0.181986			0.00905413
$405$	0.0902706	−	2.23425i	0.00448558	−	0.111021i
$406$	7.98278	+	3.55416i	0.396179	+	0.176390i
$407$	−13.7644	+	4.47234i	−0.682278	+	0.221686i
$408$	−3.18542	−	1.83910i	−0.157702	−	0.0910492i
$409$	2.70111	+	4.67846i	0.133561	+	0.231335i	0.925047	−	0.379853i	$-0.124025\pi$
$409$	2.70111	+	4.67846i	0.133561	+	0.231335i	−0.791486	+	0.611188i	$0.790692\pi$
$410$	1.04444	−	7.14745i	0.0515813	−	0.352987i
$411$	−3.15059	+	9.69651i	−0.155407	+	0.478293i
$412$	2.73906	−	2.46626i	0.134944	−	0.121504i
$413$	5.99557	+	13.4663i	0.295023	+	0.662632i
$414$	−2.83102	−	0.601752i	−0.139137	−	0.0295745i
$415$	−15.0406	−	28.6647i	−0.738314	−	1.40710i
$416$	0.0941500	+	0.895778i	0.00461608	+	0.0439191i
$417$	−3.17190	−	14.9226i	−0.155328	−	0.730763i
$418$	−18.1570	−	24.9909i	−0.888087	−	1.22235i
$419$	12.7267	−	9.24649i	0.621740	−	0.451720i	−0.231789	−	0.972766i	$-0.574458\pi$
$419$	12.7267	−	9.24649i	0.621740	−	0.451720i	0.853529	+	0.521046i	$0.174458\pi$
$420$	−1.73766	−	1.69652i	−0.0847890	−	0.0827817i
$421$	−0.585892	−	5.57439i	−0.0285546	−	0.271679i	−0.999479	−	0.0322907i	$-0.989720\pi$
$421$	−0.585892	−	5.57439i	−0.0285546	−	0.271679i	0.970924	−	0.239388i	$-0.0769469\pi$
$422$	−1.27065	−	0.133551i	−0.0618543	−	0.00650114i
$423$	−1.92380	+	9.05079i	−0.0935386	+	0.440064i
$424$	3.31943	−	1.47790i	0.161206	−	0.0717734i
$425$	6.10051	+	17.3498i	0.295918	+	0.841587i
$426$	3.42108	−	10.5290i	0.165752	−	0.510132i
$427$	12.2238	+	11.0064i	0.591552	+	0.532636i
$428$	−14.3644	+	8.29327i	−0.694328	+	0.400871i
$429$	−2.27714	+	3.94413i	−0.109942	+	0.190424i
$430$	15.0887	−	19.0962i	0.727641	−	0.920902i
$431$	21.0418	+	9.36841i	1.01355	+	0.451261i	0.845190	−	0.534465i	$-0.179487\pi$
$431$	21.0418	+	9.36841i	1.01355	+	0.451261i	0.168358	+	0.985726i	$0.446154\pi$
$432$	0.587785	−	0.809017i	0.0282798	−	0.0389238i
$433$		−	30.4634i		−	1.46398i	−0.681316	−	0.731989i	$-0.738592\pi$
$433$		−	30.4634i		−	1.46398i	0.681316	−	0.731989i	$-0.261408\pi$
$434$	−0.913184	−	5.97758i	−0.0438342	−	0.286933i
$435$	14.9701	−	9.97863i	0.717759	−	0.478438i
$436$	−9.35950	−	6.80007i	−0.448239	−	0.325664i
$437$	−7.19188	+	16.1532i	−0.344034	+	0.772713i
$438$	−9.15884	+	2.97589i	−0.437626	+	0.142193i
$439$	−9.34524	+	16.1864i	−0.446024	+	0.772536i	−0.998123	−	0.0612425i	$-0.980494\pi$
$439$	−9.34524	+	16.1864i	−0.446024	+	0.772536i	0.552099	+	0.833779i	$0.313827\pi$
$440$	−10.1347	−	5.01190i	−0.483154	−	0.238933i
$441$	−3.89466	+	4.32545i	−0.185460	+	0.205974i
$442$	3.15085	+	1.02377i	0.149871	+	0.0486960i
$443$	−14.8469	+	13.3682i	−0.705396	+	0.635141i	−0.941667	−	0.336546i	$-0.890741\pi$
$443$	−14.8469	+	13.3682i	−0.705396	+	0.635141i	0.236271	+	0.971687i	$0.424075\pi$
$444$	−2.61486	+	1.16421i	−0.124096	+	0.0552510i
$445$	10.4498	+	26.2774i	0.495367	+	1.24567i
$446$	−1.22669	+	11.6712i	−0.0580856	+	0.552647i
$447$	6.33863	−	0.666217i	0.299807	−	0.0315110i
$448$	−0.225805	−	1.06233i	−0.0106683	−	0.0501902i
$449$	−5.38259	+	3.91068i	−0.254020	+	0.184556i	−0.707507	−	0.706707i	$-0.750180\pi$
$449$	−5.38259	+	3.91068i	−0.254020	+	0.184556i	0.453487	+	0.891263i	$0.350180\pi$
$450$	−4.86443	+	1.15642i	−0.229312	+	0.0545141i
$451$	15.9769	−	3.39600i	0.752324	−	0.159911i
$452$	−11.3236	+	1.19016i	−0.532616	+	0.0559802i
$453$	3.93244	+	0.413316i	0.184762	+	0.0194193i
$454$	−5.58103	−	1.18629i	−0.261931	−	0.0556751i
$455$	1.84863	+	1.16927i	0.0866652	+	0.0548164i
$456$	−4.08791	−	4.54008i	−0.191434	−	0.212609i
$457$	−7.05019	−	2.29074i	−0.329794	−	0.107157i	0.139440	−	0.990231i	$-0.455470\pi$
$457$	−7.05019	−	2.29074i	−0.329794	−	0.107157i	−0.469234	+	0.883074i	$0.655470\pi$
$458$	−5.79031	−	5.21362i	−0.270563	−	0.243616i
$459$	−1.83910	−	3.18542i	−0.0858420	−	0.148683i
$460$	0.416098	+	6.45839i	0.0194006	+	0.301124i
$461$	8.28140	+	25.4875i	0.385703	+	1.18707i	0.935969	+	0.352083i	$0.114527\pi$
$461$	8.28140	+	25.4875i	0.385703	+	1.18707i	−0.550265	+	0.834990i	$0.685473\pi$
$462$	2.23358	−	5.01670i	0.103916	−	0.233398i
$463$	−5.34109	+	7.35138i	−0.248222	+	0.341648i	−0.914887	−	0.403709i	$-0.867721\pi$
$463$	−5.34109	+	7.35138i	−0.248222	+	0.341648i	0.666666	+	0.745357i	$0.267721\pi$
$464$	8.04581			0.373518
$465$	−11.4062	−	4.98985i	−0.528950	−	0.231399i
$466$	−11.2307			−0.520254
$467$	−7.37316	+	10.1483i	−0.341189	+	0.469607i	−0.944788	−	0.327681i	$-0.893733\pi$
$467$	−7.37316	+	10.1483i	−0.341189	+	0.469607i	0.603599	+	0.797288i	$0.293733\pi$
$468$	−0.366352	+	0.822841i	−0.0169346	+	0.0380358i
$469$	−3.56362	−	10.9677i	−0.164553	−	0.506441i
$470$	20.6475	−	1.33027i	0.952398	−	0.0613606i
$471$	−0.969431	−	1.67910i	−0.0446690	−	0.0773690i
$472$	10.0864	+	9.08185i	0.464265	+	0.418026i
$473$	52.3407	+	17.0065i	2.40663	+	0.781961i
$474$	−5.90288	−	6.55582i	−0.271128	−	0.301119i
$475$	0.731740	+	30.5377i	0.0335745	+	1.40116i
$476$	−3.90746	−	0.830556i	−0.179098	−	0.0380685i
$477$	3.61366	+	0.379811i	0.165458	+	0.0173903i
$478$	−2.03168	+	0.213538i	−0.0929268	+	0.00976700i
$479$	−2.65906	+	0.565200i	−0.121496	+	0.0258247i	−0.268258	−	0.963347i	$-0.586448\pi$
$479$	−2.65906	+	0.565200i	−0.121496	+	0.0258247i	0.146763	+	0.989172i	$0.453115\pi$
$480$	−2.09700	−	0.776272i	−0.0957144	−	0.0354318i
$481$	2.08575	−	1.51538i	0.0951018	−	0.0690955i
$482$	−4.62803	−	21.7732i	−0.210801	−	0.991740i
$483$	−3.12613	+	0.328569i	−0.142244	+	0.0149504i
$484$	1.52260	−	14.4866i	0.0692091	−	0.658481i
$485$	20.5907	−	8.18836i	0.934978	−	0.371814i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	−12.7697	+	11.4979i	−0.578650	+	0.521019i	−0.905662	−	0.424001i	$-0.860625\pi$
$487$	−12.7697	+	11.4979i	−0.578650	+	0.521019i	0.327011	+	0.945020i	$0.393958\pi$
$488$	14.4041	+	4.68018i	0.652043	+	0.211862i
$489$	−6.54371	+	7.26752i	−0.295917	+	0.328649i
$490$	11.6664	+	5.76934i	0.527033	+	0.260632i
$491$	−16.5405	+	28.6489i	−0.746461	+	1.29291i	0.203048	+	0.979169i	$0.434915\pi$
$491$	−16.5405	+	28.6489i	−0.746461	+	1.29291i	−0.949509	+	0.313739i	$0.898418\pi$
$492$	3.07228	−	0.998243i	0.138509	−	0.0450043i
$493$	12.0370	−	27.0356i	0.542121	−	1.21762i
$494$	4.45178	+	3.23441i	0.200295	+	0.145523i
$495$	−6.27098	−	9.40780i	−0.281860	−	0.422849i
$496$	−3.00677	−	4.68608i	−0.135008	−	0.210411i
$497$		−	12.0236i		−	0.539332i
$498$	8.50924	−	11.7120i	0.381308	−	0.524826i
$499$	−33.3271	−	14.8382i	−1.49193	−	0.664249i	−0.511170	−	0.859479i	$-0.670788\pi$
$499$	−33.3271	−	14.8382i	−1.49193	−	0.664249i	−0.980757	+	0.195230i	$0.937455\pi$
$500$	5.43040	+	9.77296i	0.242855	+	0.437060i
$501$	−1.95630	+	3.38842i	−0.0874013	+	0.151383i
$502$	−1.22627	+	0.707986i	−0.0547310	+	0.0315990i
$503$	24.7304	+	22.2674i	1.10268	+	0.992853i	0.999998	−	0.00186133i	$-0.000592482\pi$
$503$	24.7304	+	22.2674i	1.10268	+	0.992853i	0.102677	+	0.994715i	$0.467259\pi$
$504$	0.335611	−	1.03290i	0.0149493	−	0.0460092i
$505$	0.100606	−	0.394300i	0.00447691	−	0.0175461i
$506$	−13.3691	+	5.95232i	−0.594331	+	0.264613i
$507$	−2.53418	+	11.9224i	−0.112547	+	0.529491i
$508$	−16.6721	−	1.75231i	−0.739704	−	0.0777460i
$509$	0.814292	+	7.74747i	0.0360929	+	0.343401i	0.997635	+	0.0687415i	$0.0218984\pi$
$509$	0.814292	+	7.74747i	0.0360929	+	0.343401i	−0.961542	+	0.274659i	$0.911435\pi$
$510$	−5.74568	+	5.88500i	−0.254423	+	0.260592i
$511$	−8.46146	+	6.14761i	−0.374313	+	0.271954i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−1.27019	−	5.97578i	−0.0560803	−	0.263837i
$514$	−1.04041	−	9.89881i	−0.0458904	−	0.436618i
$515$	−3.82932	−	7.29801i	−0.168740	−	0.321589i
$516$	10.6464	+	2.26296i	0.468682	+	0.0996214i
$517$	19.0296	+	42.7412i	0.836921	+	1.87976i
$518$	−2.31018	+	2.08009i	−0.101503	+	0.0913940i
$519$	0.467760	−	1.43962i	0.0205324	−	0.0631922i
$520$	1.99289	+	0.291217i	0.0873939	+	0.0127707i
$521$	0.170333	+	0.295026i	0.00746243	+	0.0129253i	0.869733	−	0.493523i	$-0.164291\pi$
$521$	0.170333	+	0.295026i	0.00746243	+	0.0129253i	−0.862270	+	0.506449i	$0.830958\pi$
$522$	6.96788	+	4.02291i	0.304976	+	0.176078i
$523$	−2.24535	+	0.729558i	−0.0981822	+	0.0319013i	−0.357696	−	0.933838i	$-0.616438\pi$
$523$	−2.24535	+	0.729558i	−0.0981822	+	0.0319013i	0.259514	+	0.965739i	$0.416438\pi$
$524$	11.7983	+	5.25295i	0.515412	+	0.229476i
$525$	−4.63639	+	2.82703i	−0.202349	+	0.123382i
$526$	−24.5955			−1.07242
$527$	−20.2445	+	3.09272i	−0.881865	+	0.134721i
$528$		−	5.05632i		−	0.220048i
$529$	−11.8304	−	8.59531i	−0.514367	−	0.373709i
$530$	−1.36705	−	8.00907i	−0.0593808	−	0.347892i
$531$	4.19417	+	12.9083i	0.182011	+	0.560173i
$532$	−5.74612	−	3.31752i	−0.249126	−	0.143833i
$533$	−2.51983	+	1.45482i	−0.109146	+	0.0630153i
$534$	−8.46231	+	9.39835i	−0.366200	+	0.406706i
$535$	10.0277	+	35.7073i	0.433535	+	1.54376i
$536$	−7.10503	−	7.89093i	−0.306890	−	0.340836i
$537$	2.43512	+	5.46937i	0.105083	+	0.236021i
$538$	1.52312	−	7.16574i	0.0656666	−	0.308937i
$539$	−3.07629	+	29.2690i	−0.132505	+	1.26070i
$540$	−1.42792	−	1.72077i	−0.0614478	−	0.0740502i
$541$	19.4446	−	4.13307i	0.835988	−	0.177695i	0.230022	−	0.973185i	$-0.426120\pi$
$541$	19.4446	−	4.13307i	0.835988	−	0.177695i	0.605966	+	0.795491i	$0.292787\pi$
$542$	18.8628	+	25.9624i	0.810225	+	1.11518i
$543$	14.3226	+	19.7133i	0.614640	+	0.845979i
$544$	−3.59783	+	0.764742i	−0.154256	+	0.0327881i
$545$	−19.9076	+	16.5195i	−0.852746	+	0.707619i
$546$	−0.102253	+	0.972868i	−0.00437601	+	0.0416349i
$547$	7.80182	−	36.7047i	0.333582	−	1.56938i	−0.417192	−	0.908819i	$-0.636986\pi$
$547$	7.80182	−	36.7047i	0.333582	−	1.56938i	0.750773	−	0.660560i	$-0.229681\pi$
$548$	4.14689	+	9.31406i	0.177146	+	0.397877i
$549$	10.1342	+	11.2552i	0.432518	+	0.480360i
$550$	−16.4618	+	19.1877i	−0.701932	+	0.818168i
$551$	32.8906	−	36.5287i	1.40118	−	1.55617i
$552$	−2.50651	+	1.44713i	−0.106684	+	0.0615941i
$553$	−8.29732	−	4.79046i	−0.352838	−	0.203711i
$554$	−7.31957	−	22.5273i	−0.310979	−	0.957094i
$555$	1.07688	+	6.30909i	0.0457112	+	0.267806i
$556$	−12.3423	−	8.96724i	−0.523432	−	0.380296i
$557$			9.29921i			0.394020i	0.980401	+	0.197010i	$0.0631232\pi$
$557$			9.29921i			0.394020i	−0.980401	+	0.197010i	$0.936877\pi$
$558$	−0.260902	−	5.56165i	−0.0110448	−	0.235443i
$559$	−9.80357			−0.414647
$560$	−2.42652	−	0.0980393i	−0.102539	−	0.00414292i
$561$	−16.9903	−	7.56457i	−0.717331	−	0.319376i
$562$	−0.269432	+	0.0875438i	−0.0113653	+	0.00369281i
$563$	8.70777	+	5.02743i	0.366989	+	0.211881i	0.672142	−	0.740422i	$-0.265374\pi$
$563$	8.70777	+	5.02743i	0.366989	+	0.211881i	−0.305153	+	0.952303i	$0.598708\pi$
$564$	4.62649	+	8.01332i	0.194811	+	0.337422i
$565$	−3.68129	+	25.1922i	−0.154873	+	1.05984i
$566$	7.23779	−	22.2756i	0.304227	−	0.936315i
$567$	0.807100	−	0.726716i	0.0338950	−	0.0305192i
$568$	−4.50292	−	10.1137i	−0.188938	−	0.424362i
$569$	−23.3218	−	4.95721i	−0.977702	−	0.207817i	−0.308767	−	0.951138i	$-0.599916\pi$
$569$	−23.3218	−	4.95721i	−0.977702	−	0.207817i	−0.668935	+	0.743321i	$0.733250\pi$
$570$	−12.0967	+	6.34722i	−0.506674	+	0.265856i
$571$	−3.48211	−	33.1301i	−0.145722	−	1.38645i	−0.785961	−	0.618276i	$-0.787832\pi$
$571$	−3.48211	−	33.1301i	−0.145722	−	1.38645i	0.640240	−	0.768175i	$-0.278835\pi$
$572$	0.946889	+	4.45476i	0.0395914	+	0.186263i
$573$	10.7375	+	14.7789i	0.448565	+	0.617397i
$574$	2.83835	−	2.06218i	0.118470	−	0.0860737i
$575$	14.2231	+	2.66881i	0.593145	+	0.111297i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−35.0583	−	3.68478i	−1.45950	−	0.153399i	−0.658732	−	0.752378i	$-0.728907\pi$
$577$	−35.0583	−	3.68478i	−1.45950	−	0.153399i	−0.800765	+	0.598979i	$0.795573\pi$
$578$	0.721618	−	3.39495i	0.0300154	−	0.141211i
$579$	−2.76449	+	1.23083i	−0.114888	+	0.0511515i
$580$	4.44792	−	17.4325i	0.184690	−	0.723845i
$581$	4.85857	−	14.9531i	0.201567	−	0.620360i
$582$	7.36447	+	6.63100i	0.305267	+	0.274864i
$583$	15.9110	−	9.18623i	0.658967	−	0.380455i
$584$	−4.81509	+	8.33997i	−0.199250	+	0.345111i
$585$	1.58028	+	1.24864i	0.0653367	+	0.0516251i
$586$	17.6201	+	7.84499i	0.727881	+	0.324074i
$587$	5.17771	−	7.12651i	0.213707	−	0.294143i	−0.688683	−	0.725062i	$-0.741811\pi$
$587$	5.17771	−	7.12651i	0.213707	−	0.294143i	0.902390	+	0.430920i	$0.141811\pi$
$588$			5.82047i			0.240032i
$589$	−33.5666	−	5.50527i	−1.38309	−	0.226841i
$590$	25.2532	−	16.8331i	1.03966	−	0.693008i
$591$	−10.2108	−	7.41856i	−0.420015	−	0.305159i
$592$	−1.16421	+	2.61486i	−0.0478487	+	0.107470i
$593$	26.3505	−	8.56179i	1.08208	−	0.351591i	0.286902	−	0.957960i	$-0.407375\pi$
$593$	26.3505	−	8.56179i	1.08208	−	0.351591i	0.795183	+	0.606369i	$0.207375\pi$
$594$	2.52816	−	4.37890i	0.103732	−	0.179668i
$595$	−3.95966	+	8.00696i	−0.162330	+	0.328253i
$596$	4.26474	−	4.73647i	0.174690	−	0.194013i
$597$	19.4507	+	6.31993i	0.796066	+	0.258657i
$598$	1.93730	−	1.74436i	0.0792223	−	0.0713321i
$599$	17.9140	−	7.97583i	0.731946	−	0.325883i	−0.00669927	−	0.999978i	$-0.502132\pi$
$599$	17.9140	−	7.97583i	0.731946	−	0.325883i	0.738645	+	0.674094i	$0.235466\pi$
$600$	−2.84118	+	4.11433i	−0.115991	+	0.167967i
$601$	3.03753	−	28.9001i	0.123903	−	1.17886i	−0.739076	−	0.673622i	$-0.764738\pi$
$601$	3.03753	−	28.9001i	0.123903	−	1.17886i	0.862980	−	0.505239i	$-0.168596\pi$
$602$	11.7562	−	1.23563i	0.479147	−	0.0503603i
$603$	−2.20767	−	10.3863i	−0.0899032	−	0.422961i
$604$	3.19894	−	2.32416i	0.130163	−	0.0945688i
$605$	−30.5456	−	11.3075i	−1.24186	−	0.459714i
$606$	0.178009	−	0.0378370i	0.00723112	−	0.00153702i
$607$	4.36497	−	0.458777i	0.177169	−	0.0186212i	−0.0155286	−	0.999879i	$-0.504943\pi$
$607$	4.36497	−	0.458777i	0.177169	−	0.0186212i	0.192697	+	0.981258i	$0.438276\pi$
$608$	−6.07582	−	0.638594i	−0.246407	−	0.0258984i
$609$	8.54728	+	1.81678i	0.346353	+	0.0736197i
$610$	18.1032	−	28.6214i	0.732979	−	1.15885i
$611$	−5.57672	−	6.19357i	−0.225610	−	0.250565i
$612$	−3.49818	−	1.13663i	−0.141406	−	0.0459455i
$613$	−14.1357	−	12.7278i	−0.570934	−	0.514071i	0.332326	−	0.943164i	$-0.392166\pi$
$613$	−14.1357	−	12.7278i	−0.570934	−	0.514071i	−0.903260	+	0.429093i	$0.858833\pi$
$614$	9.26634	+	16.0498i	0.373959	+	0.647716i
$615$	−0.464420	−	7.20841i	−0.0187272	−	0.290671i
$616$	−1.69696	−	5.22269i	−0.0683723	−	0.210428i
$617$	−16.8344	+	37.8108i	−0.677729	+	1.52221i	0.166396	+	0.986059i	$0.446787\pi$
$617$	−16.8344	+	37.8108i	−0.677729	+	1.52221i	−0.844125	+	0.536146i	$0.819880\pi$
$618$	2.16644	−	2.98185i	0.0871471	−	0.119948i
$619$	−22.9239			−0.921391			−0.460695	−	0.887558i	$-0.652400\pi$
$619$	−22.9239			−0.921391			−0.460695	+	0.887558i	$0.652400\pi$
$620$	−11.8153	+	3.92406i	−0.474515	+	0.157594i
$621$	−2.89427			−0.116143
$622$	1.29443	−	1.78163i	0.0519020	−	0.0714370i
$623$	−5.58657	+	12.5476i	−0.223821	+	0.502711i
$624$	0.278335	+	0.856628i	0.0111423	+	0.0342926i
$625$	24.1767	−	6.36307i	0.967067	−	0.254523i
$626$	−3.93692	−	6.81895i	−0.157351	−	0.272540i
$627$	−22.9561	−	20.6698i	−0.916779	−	0.825471i
$628$	−1.84397	−	0.599141i	−0.0735823	−	0.0239083i
$629$	7.04474	+	7.82398i	0.280892	+	0.311962i
$630$	−2.05241	−	1.29817i	−0.0817700	−	0.0517202i
$631$	1.19292	+	0.253564i	0.0474896	+	0.0100942i	0.231595	−	0.972812i	$-0.425606\pi$
$631$	1.19292	+	0.253564i	0.0474896	+	0.0100942i	−0.184106	+	0.982906i	$0.558939\pi$
$632$	−8.77340	−	0.922121i	−0.348987	−	0.0366800i
$633$	−1.27065	+	0.133551i	−0.0505038	+	0.00530816i
$634$	5.77257	−	1.22700i	0.229258	−	0.0487303i
$635$	−13.0134	+	35.1539i	−0.516420	+	1.39504i
$636$	2.93962	−	2.13576i	0.116563	−	0.0846882i
$637$	−1.08999	−	5.12801i	−0.0431870	−	0.203179i
$638$	40.4593	−	4.25245i	1.60180	−	0.168356i
$639$	1.15722	−	11.0102i	0.0457788	−	0.435557i
$640$	−2.07780	+	0.826283i	−0.0821323	+	0.0326617i
$641$	−23.9374	+	10.6576i	−0.945471	+	0.420951i	−0.820780	−	0.571245i	$-0.806461\pi$
$641$	−23.9374	+	10.6576i	−0.945471	+	0.420951i	−0.124691	+	0.992196i	$0.539794\pi$
$642$	−12.3262	+	11.0986i	−0.486477	+	0.438026i
$643$	−39.4456	−	12.8167i	−1.55558	−	0.505440i	−0.599960	−	0.800030i	$-0.704817\pi$
$643$	−39.4456	−	12.8167i	−1.55558	−	0.505440i	−0.955624	+	0.294590i	$0.904817\pi$
$644$	−2.10331	+	2.33596i	−0.0828820	+	0.0920498i
$645$	10.7886	−	21.8160i	0.424802	−	0.859006i
$646$	−11.2356	+	19.4606i	−0.442059	+	0.765669i
$647$	29.7265	−	9.65874i	1.16867	−	0.379724i	0.340524	−	0.940236i	$-0.389395\pi$
$647$	29.7265	−	9.65874i	1.16867	−	0.379724i	0.828147	+	0.560512i	$0.189395\pi$
$648$	0.406737	−	0.913545i	0.0159781	−	0.0358875i
$649$	55.5208	+	40.3382i	2.17938	+	1.58341i
$650$	1.73268	−	4.15690i	0.0679613	−	0.163047i
$651$	−2.13604	−	5.65709i	−0.0837179	−	0.221719i
$652$			9.77942i			0.382991i
$653$	−10.9028	+	15.0064i	−0.426660	+	0.587247i	−0.967183	−	0.254083i	$-0.918226\pi$
$653$	−10.9028	+	15.0064i	−0.426660	+	0.587247i	0.540523	+	0.841329i	$0.318226\pi$
$654$	−10.5688	−	4.70553i	−0.413272	−	0.184001i
$655$	17.9037	−	22.6589i	0.699556	−	0.885357i
$656$	1.61519	−	2.79759i	0.0630626	−	0.109228i
$657$	−8.33997	+	4.81509i	−0.325373	+	0.187854i
$658$	7.46809	+	6.72429i	0.291136	+	0.262140i
$659$	−7.26616	+	22.3629i	−0.283049	+	0.871136i	0.703927	+	0.710272i	$0.251428\pi$
$659$	−7.26616	+	22.3629i	−0.283049	+	0.871136i	−0.986977	+	0.160864i	$0.948572\pi$
$660$	−10.9553	−	2.79525i	−0.426434	−	0.108805i
$661$	−2.55452	+	1.13735i	−0.0993595	+	0.0442377i	−0.455815	−	0.890075i	$-0.650652\pi$
$661$	−2.55452	+	1.13735i	−0.0993595	+	0.0442377i	0.356455	+	0.934312i	$0.383985\pi$
$662$	−1.87926	+	8.84121i	−0.0730394	+	0.343623i
$663$	3.29486	+	0.346303i	0.127962	+	0.0134493i
$664$	−1.51324	−	14.3975i	−0.0587249	−	0.558730i
$665$	−10.3645	+	10.6158i	−0.401919	+	0.411665i
$666$	−2.31566	+	1.68243i	−0.0897302	+	0.0651928i
$667$	−13.6876	−	18.8394i	−0.529986	−	0.729463i
$668$	0.813477	+	3.82711i	0.0314744	+	0.148075i
$669$	1.22669	+	11.6712i	0.0474267	+	0.451235i
$670$	−21.0247	+	11.0318i	−0.812257	+	0.426197i
$671$	74.9064	+	15.9218i	2.89173	+	0.614656i
$672$	−0.441740	−	0.992165i	−0.0170405	−	0.0382736i
$673$	12.7432	−	11.4740i	0.491214	−	0.442291i	−0.385923	−	0.922531i	$-0.626117\pi$
$673$	12.7432	−	11.4740i	0.491214	−	0.442291i	0.877137	+	0.480240i	$0.159450\pi$
$674$	−6.33014	+	19.4822i	−0.243828	+	0.750425i
$675$	−4.51770	+	2.14252i	−0.173886	+	0.0824656i
$676$	6.09436	+	10.5557i	0.234398	+	0.405990i
$677$	−1.93376	−	1.11645i	−0.0743203	−	0.0429088i	0.462379	−	0.886682i	$-0.346996\pi$
$677$	−1.93376	−	1.11645i	−0.0743203	−	0.0429088i	−0.536700	+	0.843773i	$0.680329\pi$
$678$	−10.8287	+	3.51845i	−0.415873	+	0.135125i
$679$	9.83223	+	4.37759i	0.377326	+	0.167997i
$680$	−0.332034	+	8.21802i	−0.0127329	+	0.315147i
$681$	−5.70572			−0.218644
$682$	−17.5966	−	21.9753i	−0.673810	−	0.841479i
$683$		−	38.7965i		−	1.48451i	−0.670120	−	0.742253i	$-0.733757\pi$
$683$		−	38.7965i		−	1.48451i	0.670120	−	0.742253i	$-0.266243\pi$
$684$	−4.94251	−	3.59095i	−0.188982	−	0.137303i
$685$	22.4728	−	3.83583i	0.858643	−	0.146560i
$686$	4.30269	+	13.2423i	0.164278	+	0.505594i
$687$	−6.74775	−	3.89582i	−0.257443	−	0.148635i
$688$	9.42604	−	5.44213i	0.359364	−	0.207479i
$689$	−2.18993	+	2.43216i	−0.0834296	+	0.0926579i
$690$	1.74978	+	6.23075i	0.0666130	+	0.237200i
$691$	−1.41766	−	1.57447i	−0.0539304	−	0.0598958i	0.715576	−	0.698535i	$-0.246164\pi$
$691$	−1.41766	−	1.57447i	−0.0539304	−	0.0598958i	−0.769506	+	0.638639i	$0.779498\pi$
$692$	−0.615679	−	1.38284i	−0.0234046	−	0.0525676i
$693$	1.14174	−	5.37146i	0.0433711	−	0.204045i
$694$	−0.322451	+	3.06792i	−0.0122401	+	0.116457i
$695$	−26.2520	+	21.7843i	−0.995797	+	0.826325i
$696$	7.86999	−	1.67282i	0.298311	−	0.0634080i
$697$	−6.98408	−	9.61276i	−0.264541	−	0.364109i
$698$	−11.8686	−	16.3357i	−0.449232	−	0.618314i
$699$	−10.9853	+	2.33500i	−0.415503	+	0.0883180i
$700$	−1.55386	+	5.20324i	−0.0587303	+	0.196664i
$701$	−2.76124	+	26.2715i	−0.104291	+	0.992260i	0.809788	+	0.586723i	$0.199582\pi$
$701$	−2.76124	+	26.2715i	−0.104291	+	0.992260i	−0.914079	+	0.405537i	$0.867085\pi$
$702$	−0.187268	+	0.881029i	−0.00706799	+	0.0332523i
$703$	7.11249	+	15.9749i	0.268253	+	0.602505i
$704$	−3.38334	−	3.75758i	−0.127514	−	0.141619i
$705$	19.9197	−	5.59405i	0.750220	−	0.210684i
$706$	17.4267	−	19.3543i	0.655862	−	0.728409i
$707$	0.171168	−	0.0988237i	0.00643742	−	0.00371665i
$708$	11.7542	+	6.78630i	0.441751	+	0.255045i
$709$	−8.15140	−	25.0874i	−0.306132	−	0.942179i	−0.979252	−	0.202645i	$-0.935046\pi$
$709$	−8.15140	−	25.0874i	−0.306132	−	0.942179i	0.673120	−	0.739533i	$-0.264954\pi$
$710$	−24.4022	+	4.16516i	−0.915800	+	0.156316i
$711$	−7.13692	−	5.18528i	−0.267656	−	0.194463i
$712$			12.6467i			0.473956i
$713$	−5.85736	+	15.0124i	−0.219360	+	0.562218i
$714$	−3.99475			−0.149500
$715$	10.1754	+	0.411118i	0.380538	+	0.0153750i
$716$	5.46937	+	2.43512i	0.204400	+	0.0910048i
$717$	−1.94288	+	0.631281i	−0.0725583	+	0.0235756i
$718$	−9.16472	−	5.29125i	−0.342024	−	0.197468i
$719$	−19.1486	−	33.1664i	−0.714124	−	1.23690i	−0.963296	−	0.268440i	$-0.913492\pi$
$719$	−19.1486	−	33.1664i	−0.714124	−	1.23690i	0.249172	−	0.968459i	$-0.419841\pi$
$720$	−2.21257	−	0.323318i	−0.0824576	−	0.0120494i
$721$	1.23699	−	3.80705i	0.0460678	−	0.141782i
$722$	−13.6169	+	12.2607i	−0.506769	+	0.456297i
$723$	−9.05379	−	20.3351i	−0.336714	−	0.756272i
$724$	23.8345	+	5.06618i	0.885802	+	0.188283i
$725$	−35.3112	−	19.2742i	−1.31143	−	0.715825i
$726$	−1.52260	−	14.4866i	−0.0565090	−	0.537647i
$727$	3.48613	+	16.4009i	0.129293	+	0.608277i	0.994309	+	0.106533i	$0.0339749\pi$
$727$	3.48613	+	16.4009i	0.129293	+	0.608277i	−0.865016	+	0.501744i	$0.832692\pi$
$728$	0.574987	+	0.791402i	0.0213104	+	0.0293313i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	15.4079	+	15.0432i	0.570273	+	0.556772i
$731$	−4.18475	−	39.8152i	−0.154778	−	1.47262i
$732$	15.0624	+	1.58312i	0.556722	+	0.0585139i
$733$	−5.72453	+	26.9318i	−0.211440	+	0.994749i	0.736533	+	0.676401i	$0.236461\pi$
$733$	−5.72453	+	26.9318i	−0.211440	+	0.994749i	−0.947974	+	0.318348i	$0.896872\pi$
$734$	20.5770	−	9.16145i	0.759509	−	0.338155i
$735$	12.6109	+	3.21770i	0.465162	+	0.118686i
$736$	−0.894378	+	2.75261i	−0.0329672	+	0.101463i
$737$	−39.8991	−	35.9253i	−1.46970	−	1.32333i
$738$	2.79759	−	1.61519i	0.102981	−	0.0594560i
$739$	−8.07877	+	13.9928i	−0.297183	+	0.514735i	−0.975490	−	0.220043i	$-0.929380\pi$
$739$	−8.07877	+	13.9928i	−0.297183	+	0.514735i	0.678308	+	0.734778i	$0.262714\pi$
$740$	5.02189	+	3.96799i	0.184608	+	0.145866i
$741$	5.02697	+	2.23815i	0.184670	+	0.0822205i
$742$	2.31956	−	3.19260i	0.0851537	−	0.117204i
$743$			10.8306i			0.397337i	0.980067	+	0.198669i	$0.0636618\pi$
$743$			10.8306i			0.397337i	−0.980067	+	0.198669i	$0.936338\pi$
$744$	−3.91536	−	3.95853i	−0.143544	−	0.145127i
$745$	−7.90464	−	11.8586i	−0.289604	−	0.434467i
$746$	13.2735	+	9.64377i	0.485978	+	0.353083i
$747$	5.88824	−	13.2252i	0.215439	−	0.483885i
$748$	−17.6879	+	5.74716i	−0.646735	+	0.210137i
$749$	−9.00699	+	15.6006i	−0.329108	+	0.570032i
$750$	7.34364	+	8.43035i	0.268152	+	0.307833i
$751$	22.4413	−	24.9236i	0.818896	−	0.909476i	−0.178325	−	0.983972i	$-0.557068\pi$
$751$	22.4413	−	24.9236i	0.818896	−	0.909476i	0.997221	+	0.0744954i	$0.0237346\pi$
$752$	8.80012	+	2.85933i	0.320907	+	0.104269i
$753$	−1.05227	+	0.947471i	−0.0383469	+	0.0345277i
$754$	−6.62043	+	2.94760i	−0.241102	+	0.107345i
$755$	−3.26721	−	8.21584i	−0.118906	−	0.299005i
$756$	0.113524	−	1.08011i	0.00412883	−	0.0392832i
$757$	−25.8377	+	2.71566i	−0.939088	+	0.0987022i	−0.561689	−	0.827348i	$-0.689848\pi$
$757$	−25.8377	+	2.71566i	−0.939088	+	0.0987022i	−0.377399	+	0.926051i	$0.623182\pi$
$758$	4.21596	+	19.8345i	0.153131	+	0.720423i
$759$	−11.8394	+	8.60185i	−0.429744	+	0.312227i
$760$	−4.74247	+	12.8112i	−0.172027	+	0.464710i
$761$	10.7591	−	2.28691i	0.390015	−	0.0829003i	−0.00873022	−	0.999962i	$-0.502779\pi$
$761$	10.7591	−	2.28691i	0.390015	−	0.0829003i	0.398746	+	0.917062i	$0.369446\pi$
$762$	−16.6721	+	1.75231i	−0.603966	+	0.0634794i
$763$	−12.4958	−	1.31336i	−0.452377	−	0.0475468i
$764$	17.8685	+	3.79807i	0.646460	+	0.137409i
$765$	−4.39656	+	6.95099i	−0.158958	+	0.251314i
$766$	1.02038	+	1.13324i	0.0368677	+	0.0409457i
$767$	−11.6267	−	3.77773i	−0.419815	−	0.136406i
$768$	−0.743145	−	0.669131i	−0.0268159	−	0.0241452i
$769$	12.3715	+	21.4281i	0.446128	+	0.772716i	0.998130	−	0.0611265i	$-0.0194693\pi$
$769$	12.3715	+	21.4281i	0.446128	+	0.772716i	−0.552002	+	0.833843i	$0.686136\pi$
$770$	−12.2539	+	0.789487i	−0.441599	+	0.0284511i
$771$	−3.07575	−	9.46619i	−0.110770	−	0.340916i
$772$	−1.23083	+	2.76449i	−0.0442985	+	0.0994960i
$773$	−4.70062	+	6.46985i	−0.169070	+	0.232704i	−0.885141	−	0.465322i	$-0.845938\pi$
$773$	−4.70062	+	6.46985i	−0.169070	+	0.232704i	0.716072	+	0.698027i	$0.245938\pi$
$774$	10.8843			0.391226
$775$	1.97028	+	27.7690i	0.0707745	+	0.997492i
$776$	9.90987			0.355744
$777$	−1.82722	+	2.51495i	−0.0655511	+	0.0902234i
$778$	9.10893	−	20.4590i	0.326571	−	0.733491i
$779$	−6.09855	−	18.7694i	−0.218503	−	0.672484i
$780$	2.00989	−	0.129492i	0.0719654	−	0.00463655i
$781$	−27.9889	−	48.4781i	−1.00152	−	1.73468i
$782$	7.91131	+	7.12337i	0.282908	+	0.254731i
$783$	7.65202	+	2.48629i	0.273461	+	0.0888529i
$784$	3.89466	+	4.32545i	0.139095	+	0.154481i
$785$	−2.31752	+	3.66402i	−0.0827158	+	0.130774i
$786$	12.6326	+	2.68515i	0.450591	+	0.0957762i
$787$	13.6844	+	1.43829i	0.487796	+	0.0512694i	0.345234	−	0.938517i	$-0.387799\pi$
$787$	13.6844	+	1.43829i	0.487796	+	0.0512694i	0.142562	+	0.989786i	$0.454466\pi$
$788$	−12.5521	+	1.31928i	−0.447149	+	0.0469972i
$789$	−24.0580	+	5.11369i	−0.856489	+	0.182052i
$790$	−6.84806	+	18.4991i	−0.243643	+	0.658170i
$791$	−10.0042	+	7.26845i	−0.355707	+	0.258436i
$792$	−1.05127	−	4.94583i	−0.0373552	−	0.175742i
$793$	−13.5669	+	1.42594i	−0.481774	+	0.0506365i
$794$	1.08824	−	10.3539i	0.0386203	−	0.367448i
$795$	−3.00235	−	7.54982i	−0.106482	−	0.267765i
$796$	18.6836	−	8.31846i	0.662222	−	0.294840i
$797$	9.98741	−	8.99270i	0.353772	−	0.318538i	−0.473013	−	0.881055i	$-0.656834\pi$
$797$	9.98741	−	8.99270i	0.353772	−	0.318538i	0.826785	+	0.562517i	$0.190167\pi$
$798$	−6.31031	−	2.05034i	−0.223382	−	0.0725814i
$799$	22.7735	−	25.2925i	0.805667	−	0.894784i
$800$	0.641611	+	4.95866i	0.0226844	+	0.175315i
$801$	−6.32336	+	10.9524i	−0.223425	+	0.386984i
$802$	3.44051	−	1.11789i	0.121489	−	0.0394740i
$803$	−19.8053	+	44.4835i	−0.698914	+	1.56979i
$804$	−8.59038	−	6.24128i	−0.302959	−	0.220113i
$805$	3.89846	+	5.84852i	0.137403	+	0.206133i
$806$	4.19085	+	2.75436i	0.147616	+	0.0970182i
$807$		−	7.32582i		−	0.257881i
$808$	0.106969	−	0.147230i	0.00376314	−	0.00517952i
$809$	15.8517	+	7.05764i	0.557317	+	0.248133i	0.666011	−	0.745942i	$-0.268000\pi$
$809$	15.8517	+	7.05764i	0.557317	+	0.248133i	−0.108694	+	0.994075i	$0.534667\pi$
$810$	−1.75448	−	1.38629i	−0.0616462	−	0.0487092i
$811$	−13.6460	+	23.6355i	−0.479175	+	0.829956i	−0.999715	−	0.0238818i	$-0.992397\pi$
$811$	−13.6460	+	23.6355i	−0.479175	+	0.829956i	0.520540	+	0.853838i	$0.325731\pi$
$812$	7.56753	−	4.36912i	0.265568	−	0.153326i
$813$	23.8484	+	21.4732i	0.836401	+	0.753099i
$814$	−4.47234	+	13.7644i	−0.156755	+	0.482444i
$815$	21.1886	+	5.40629i	0.742204	+	0.189374i
$816$	−3.36021	+	1.49606i	−0.117631	+	0.0523726i
$817$	13.8251	−	65.0419i	0.483678	−	2.27553i
$818$	5.37263	+	0.564686i	0.187850	+	0.0197438i
$819$	0.102253	+	0.972868i	0.00357299	+	0.0339948i
$820$	−5.16850	−	5.04614i	−0.180492	−	0.176219i
$821$	31.1624	−	22.6408i	1.08757	−	0.790169i	0.108586	−	0.994087i	$-0.465368\pi$
$821$	31.1624	−	22.6408i	1.08757	−	0.790169i	0.978988	+	0.203919i	$0.0653678\pi$
$822$	5.99277	+	8.24834i	0.209022	+	0.287694i
$823$	−10.2126	−	48.0465i	−0.355989	−	1.67480i	−0.683501	−	0.729949i	$-0.739544\pi$
$823$	−10.2126	−	48.0465i	−0.355989	−	1.67480i	0.327512	−	0.944847i	$-0.393790\pi$
$824$	−0.385268	−	3.66558i	−0.0134215	−	0.127697i
$825$	−12.1127	+	22.1910i	−0.421710	+	0.772593i
$826$	14.4185	+	3.06476i	0.501685	+	0.106637i
$827$	−14.4833	−	32.5301i	−0.503635	−	1.13118i	−0.969224	−	0.246181i	$-0.920824\pi$
$827$	−14.4833	−	32.5301i	−0.503635	−	1.13118i	0.465589	−	0.885001i	$-0.345842\pi$
$828$	−2.15086	+	1.93664i	−0.0747476	+	0.0673030i
$829$	4.54197	−	13.9787i	0.157749	−	0.485502i	−0.840680	−	0.541532i	$-0.817844\pi$
$829$	4.54197	−	13.9787i	0.157749	−	0.485502i	0.998429	+	0.0560304i	$0.0178444\pi$
$830$	−32.0309	−	4.68061i	−1.11181	−	0.162466i
$831$	−11.8433	−	20.5132i	−0.410840	−	0.711596i
$832$	0.780039	+	0.450356i	0.0270430	+	0.0156133i
$833$	20.3611	−	6.61572i	0.705470	−	0.229221i
$834$	−13.9370	−	6.20517i	−0.482600	−	0.214867i
$835$	8.74173	+	0.353194i	0.302520	+	0.0122228i
$836$	−30.8905			−1.06837
$837$	−1.41153	−	5.38587i	−0.0487897	−	0.186163i
$838$		−	15.7311i		−	0.543421i
$839$	24.8753	+	18.0730i	0.858790	+	0.623948i	0.927556	−	0.373685i	$-0.121906\pi$
$839$	24.8753	+	18.0730i	0.858790	+	0.623948i	−0.0687654	+	0.997633i	$0.521906\pi$
$840$	−2.39388	+	0.408606i	−0.0825968	+	0.0140982i
$841$	11.0428	+	33.9861i	0.380785	+	1.17193i
$842$	−4.85415	−	2.80255i	−0.167285	−	0.0965821i
$843$	−0.245343	+	0.141649i	−0.00845006	+	0.00487864i
$844$	−0.854914	+	0.949478i	−0.0294273	+	0.0326824i
$845$	26.2397	−	7.36890i	0.902674	−	0.253498i
$846$	6.19146	+	6.87631i	0.212867	+	0.236412i
$847$	−6.43455	−	14.4522i	−0.221094	−	0.496585i
$848$	0.755461	−	3.55416i	0.0259426	−	0.122050i
$849$	2.44826	−	23.2937i	0.0840242	−	0.799437i
$850$	17.6220	+	5.26252i	0.604431	+	0.180503i
$851$	8.10328	−	1.72241i	0.277777	−	0.0590433i
$852$	−6.50728	−	8.95650i	−0.222936	−	0.306845i
$853$	−11.4154	−	15.7120i	−0.390856	−	0.537967i	0.567564	−	0.823330i	$-0.307886\pi$
$853$	−11.4154	−	15.7120i	−0.390856	−	0.537967i	−0.958420	+	0.285362i	$0.907886\pi$
$854$	16.0893	−	3.41989i	0.550566	−	0.117026i
$855$	−10.5127	+	8.72355i	−0.359526	+	0.298339i
$856$	−1.73377	+	16.4957i	−0.0592589	+	0.563811i
$857$	6.18601	−	29.1029i	0.211310	−	0.994135i	−0.736780	−	0.676133i	$-0.763655\pi$
$857$	6.18601	−	29.1029i	0.211310	−	0.994135i	0.948090	−	0.318002i	$-0.103012\pi$
$858$	1.85240	+	4.16055i	0.0632397	+	0.142039i
$859$	−5.52531	−	6.13648i	−0.188521	−	0.209374i	0.641474	−	0.767145i	$-0.278323\pi$
$859$	−5.52531	−	6.13648i	−0.188521	−	0.209374i	−0.829995	+	0.557771i	$0.811657\pi$
$860$	−6.58026	−	23.4315i	−0.224385	−	0.799007i
$861$	2.34757	−	2.60724i	0.0800050	−	0.0888546i
$862$	19.9473	−	11.5166i	0.679407	−	0.392256i
$863$	9.40124	+	5.42781i	0.320022	+	0.184765i	0.651402	−	0.758733i	$-0.274181\pi$
$863$	9.40124	+	5.42781i	0.320022	+	0.184765i	−0.331380	+	0.943497i	$0.607514\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−3.33649	+	0.569498i	−0.113444	+	0.0193635i
$866$	−24.6454	−	17.9059i	−0.837485	−	0.608469i
$867$		−	3.47079i		−	0.117874i
$868$	−5.37272	−	2.77475i	−0.182362	−	0.0941811i
$869$	−44.6054			−1.51314
$870$	0.726301	−	17.9763i	0.0246239	−	0.609454i
$871$	8.73717	+	3.89004i	0.296048	+	0.131809i
$872$	−11.0027	+	3.57501i	−0.372600	+	0.121065i
$873$	8.58220	+	4.95494i	0.290464	+	0.167699i
$874$	8.84095	+	15.3130i	0.299050	+	0.517969i
$875$	10.4146	+	6.24314i	0.352078	+	0.211057i
$876$	−2.97589	+	9.15884i	−0.100546	+	0.309448i
$877$	−3.10267	+	2.79366i	−0.104770	+	0.0943351i	−0.719851	−	0.694129i	$-0.755790\pi$
$877$	−3.10267	+	2.79366i	−0.104770	+	0.0943351i	0.615081	+	0.788464i	$0.289123\pi$
$878$	7.60210	+	17.0746i	0.256559	+	0.576240i
$879$	18.8662	+	4.01013i	0.636340	+	0.135258i
$880$	−10.0118	+	5.25324i	−0.337496	+	0.177087i
$881$	1.55294	+	14.7753i	0.0523200	+	0.497792i	0.989033	+	0.147694i	$0.0471850\pi$
$881$	1.55294	+	14.7753i	0.0523200	+	0.497792i	−0.936713	+	0.350098i	$0.886148\pi$
$882$	1.21014	+	5.69328i	0.0407477	+	0.191703i
$883$	−0.270320	−	0.372063i	−0.00909698	−	0.0125209i	0.804444	−	0.594028i	$-0.202463\pi$
$883$	−0.270320	−	0.372063i	−0.00909698	−	0.0125209i	−0.813541	+	0.581507i	$0.802463\pi$
$884$	2.68028	−	1.94734i	0.0901475	−	0.0654960i
$885$	21.2016	−	21.7157i	0.712683	−	0.729965i
$886$	2.08831	+	19.8690i	0.0701583	+	0.667512i
$887$	−51.1051	−	5.37137i	−1.71594	−	0.180353i	−0.805109	−	0.593127i	$-0.797893\pi$
$887$	−51.1051	−	5.37137i	−1.71594	−	0.180353i	−0.910833	+	0.412774i	$0.864560\pi$
$888$	−0.595110	+	2.79977i	−0.0199706	+	0.0939541i
$889$	−16.6326	+	7.40530i	−0.557839	+	0.248366i
$890$	27.4011	+	6.99141i	0.918486	+	0.234353i
$891$	1.56249	−	4.80885i	0.0523453	−	0.161102i
$892$	8.72117	+	7.85257i	0.292006	+	0.262924i
$893$	48.9557	−	28.2646i	1.63824	−	0.945838i
$894$	3.18677	−	5.51965i	0.106582	−	0.184605i
$895$	8.29967	−	10.5040i	0.277427	−	0.351111i
$896$	−0.992165	−	0.441740i	−0.0331459	−	0.0147575i
$897$	1.53230	−	2.10903i	0.0511619	−	0.0704184i
$898$			6.65324i			0.222022i
$899$	28.3823	−	34.6588i	0.946601	−	1.15594i
$900$	−1.92368	+	4.61513i	−0.0641227	+	0.153838i
$901$	−10.8125	−	7.85575i	−0.360217	−	0.261713i
$902$	6.64358	−	14.9217i	0.221207	−	0.496839i
$903$	11.2424	−	3.65287i	0.374123	−	0.121560i
$904$	−5.69298	+	9.86052i	−0.189346	+	0.327956i
$905$	24.1529	−	48.8404i	0.802871	−	1.62351i
$906$	2.64581	−	2.93847i	0.0879012	−	0.0976241i
$907$	−3.57884	−	1.16284i	−0.118833	−	0.0386113i	0.248997	−	0.968504i	$-0.419899\pi$
$907$	−3.57884	−	1.16284i	−0.118833	−	0.0386113i	−0.367830	+	0.929893i	$0.619899\pi$
$908$	−4.24017	+	3.81787i	−0.140715	+	0.126700i
$909$	0.166252	−	0.0740202i	0.00551424	−	0.00245510i
$910$	2.03256	−	0.808292i	0.0673787	−	0.0267946i
$911$	3.43517	−	32.6834i	0.113812	−	1.08285i	−0.777320	−	0.629106i	$-0.783421\pi$
$911$	3.43517	−	32.6834i	0.113812	−	1.08285i	0.891132	−	0.453744i	$-0.149912\pi$
$912$	−6.07582	+	0.638594i	−0.201190	+	0.0211460i
$913$	−15.2190	−	71.5997i	−0.503675	−	2.36960i
$914$	−5.99725	+	4.35725i	−0.198371	+	0.144125i
$915$	11.7569	−	31.7598i	0.388672	−	1.04995i
$916$	−7.62136	+	1.61997i	−0.251817	+	0.0535253i
$917$	13.9495	−	1.46615i	0.460652	−	0.0484165i
$918$	−3.65806	−	0.384477i	−0.120734	−	0.0126896i
$919$	−6.83768	−	1.45339i	−0.225554	−	0.0479430i	0.0937480	−	0.995596i	$-0.470115\pi$
$919$	−6.83768	−	1.45339i	−0.225554	−	0.0479430i	−0.319302	+	0.947653i	$0.603449\pi$
$920$	5.46952	+	3.45952i	0.180325	+	0.114057i
$921$	12.4008	+	13.7725i	0.408620	+	0.453818i
$922$	25.4875	+	8.28140i	0.839387	+	0.272733i
$923$	7.41037	+	6.67233i	0.243915	+	0.219622i
$924$	−2.74573	−	4.75575i	−0.0903280	−	0.156453i
$925$	11.3735	−	8.68709i	0.373958	−	0.285630i
$926$	2.80798	+	8.64207i	0.0922759	+	0.283996i
$927$	1.49914	−	3.36712i	0.0492382	−	0.110591i
$928$	4.72921	−	6.50920i	0.155244	−	0.213675i
$929$	−11.1404			−0.365505			−0.182752	−	0.983159i	$-0.558501\pi$
$929$	−11.1404			−0.365505			−0.182752	+	0.983159i	$0.558501\pi$
$930$	−10.7413	+	6.29485i	−0.352220	+	0.206416i
$931$	35.5589			1.16540
$932$	−6.60127	+	9.08587i	−0.216232	+	0.297617i
$933$	0.895724	−	2.01183i	0.0293247	−	0.0658643i
$934$	3.87630	+	11.9300i	0.126836	+	0.390362i
$935$	2.67379	+	41.5008i	0.0874423	+	1.35722i
$936$	0.450356	+	0.780039i	0.0147203	+	0.0254964i
$937$	−10.2512	−	9.23025i	−0.334893	−	0.301539i	0.484477	−	0.874804i	$-0.339010\pi$
$937$	−10.2512	−	9.23025i	−0.334893	−	0.301539i	−0.819370	+	0.573265i	$0.805677\pi$
$938$	−10.9677	−	3.56362i	−0.358108	−	0.116356i
$939$	−5.26863	−	5.85141i	−0.171935	−	0.190953i
$940$	11.0601	−	17.4861i	0.360740	−	0.570333i
$941$	−10.2518	−	2.17909i	−0.334200	−	0.0710364i	0.0377553	−	0.999287i	$-0.487979\pi$
$941$	−10.2518	−	2.17909i	−0.334200	−	0.0710364i	−0.371955	+	0.928251i	$0.621313\pi$
$942$	−1.92824	−	0.202666i	−0.0628255	−	0.00660322i
$943$	−9.29838	+	0.977299i	−0.302797	+	0.0318252i
$944$	13.2760	−	2.82190i	0.432097	−	0.0918451i
$945$	−2.27747	−	0.843078i	−0.0740860	−	0.0274253i
$946$	44.5236	−	32.3483i	1.44759	−	1.05173i
$947$	10.7075	+	50.3749i	0.347947	+	1.63696i	0.709567	+	0.704638i	$0.248891\pi$
$947$	10.7075	+	50.3749i	0.347947	+	1.63696i	−0.361620	+	0.932326i	$0.617776\pi$
$948$	−8.77340	+	0.922121i	−0.284947	+	0.0299491i
$949$	0.906681	−	8.62649i	0.0294321	−	0.280028i
$950$	25.1356	+	17.3576i	0.815506	+	0.563155i
$951$	5.39132	−	2.40037i	0.174825	−	0.0778373i
$952$	−2.96868	+	2.67301i	−0.0962155	+	0.0866328i
$953$	−14.0470	−	4.56416i	−0.455028	−	0.147848i	0.0725306	−	0.997366i	$-0.476893\pi$
$953$	−14.0470	−	4.56416i	−0.455028	−	0.147848i	−0.527559	+	0.849519i	$0.676893\pi$
$954$	2.43133	−	2.70026i	0.0787172	−	0.0874243i
$955$	18.1072	−	36.6152i	0.585937	−	1.18484i
$956$	−1.02143	+	1.76918i	−0.0330355	+	0.0572192i
$957$	38.6911	−	12.5715i	1.25070	−	0.406379i
$958$	−1.10570	+	2.48344i	−0.0357235	+	0.0802363i
$959$	8.95819	+	6.50851i	0.289275	+	0.210171i
$960$	−1.86060	+	1.24023i	−0.0600507	+	0.0400281i
$961$	−30.7928	−	3.57829i	−0.993316	−	0.115429i
$962$		−	2.57812i		−	0.0831221i
$963$	−9.74933	+	13.4188i	−0.314168	+	0.432415i
$964$	−20.3351	−	9.05379i	−0.654951	−	0.291603i
$965$	5.30925	+	4.19505i	0.170911	+	0.135043i
$966$	−1.57167	+	2.72222i	−0.0505678	+	0.0875860i
$967$	−35.6017	+	20.5546i	−1.14487	+	0.660993i	−0.947633	−	0.319363i	$-0.896531\pi$
$967$	−35.6017	+	20.5546i	−1.14487	+	0.660993i	−0.197240	+	0.980355i	$0.563198\pi$
$968$	−10.8249	−	9.74680i	−0.347926	−	0.313274i
$969$	−6.94399	+	21.3714i	−0.223073	+	0.686548i
$970$	5.47841	−	21.4713i	0.175901	−	0.689401i
$971$	37.0038	−	16.4751i	1.18751	−	0.528713i	0.284642	−	0.958634i	$-0.408125\pi$
$971$	37.0038	−	16.4751i	1.18751	−	0.528713i	0.902866	+	0.429921i	$0.141459\pi$
$972$	0.207912	−	0.978148i	0.00666877	−	0.0313741i
$973$	−16.4781	−	1.73192i	−0.528265	−	0.0555229i
$974$	1.79615	+	17.0892i	0.0575522	+	0.547573i
$975$	0.830549	−	4.42631i	0.0265988	−	0.141755i
$976$	12.2529	−	8.90222i	0.392204	−	0.284953i
$977$	28.3170	+	38.9750i	0.905941	+	1.24692i	0.968534	+	0.248881i	$0.0800629\pi$
$977$	28.3170	+	38.9750i	0.905941	+	1.24692i	−0.0625933	+	0.998039i	$0.519937\pi$
$978$	2.03325	+	9.56571i	0.0650163	+	0.305878i
$979$	6.68417	+	63.5956i	0.213627	+	2.03252i
$980$	11.5248	−	6.04716i	0.368147	−	0.193169i
$981$	−11.3162	−	2.40533i	−0.361297	−	0.0767961i
$982$	13.4552	+	30.2209i	0.429374	+	0.964389i
$983$	16.2460	−	14.6280i	0.518168	−	0.466561i	−0.368065	−	0.929800i	$-0.619980\pi$
$983$	16.2460	−	14.6280i	0.518168	−	0.466561i	0.886233	+	0.463239i	$0.153313\pi$
$984$	0.998243	−	3.07228i	0.0318228	−	0.0979406i
$985$	−4.08067	+	27.9253i	−0.130021	+	0.889774i
$986$	−14.7971	−	25.6293i	−0.471235	−	0.816203i
$987$	8.70295	+	5.02465i	0.277018	+	0.159936i
$988$	5.23338	−	1.70043i	0.166496	−	0.0540979i
$989$	−28.7784	−	12.8130i	−0.915101	−	0.407429i
$990$	−11.2971	−	0.456437i	−0.359044	−	0.0145065i
$991$	−9.58489			−0.304474			−0.152237	−	0.988344i	$-0.548648\pi$
$991$	−9.58489			−0.304474			−0.152237	+	0.988344i	$0.548648\pi$
$992$	−5.55845	−	0.321878i	−0.176481	−	0.0102196i
$993$			9.03873i			0.286835i
$994$	−9.72730	−	7.06729i	−0.308531	−	0.224161i
$995$	−7.69450	−	45.0795i	−0.243932	−	1.42912i
$996$	−4.47357	−	13.7682i	−0.141751	−	0.436263i
$997$	32.7906	+	18.9317i	1.03849	+	0.599572i	0.919405	−	0.393312i	$-0.128671\pi$
$997$	32.7906	+	18.9317i	1.03849	+	0.599572i	0.119084	+	0.992884i	$0.462004\pi$
$998$	−31.5936	+	18.2406i	−1.00008	+	0.577395i
$999$	−1.91527	+	2.12712i	−0.0605963	+	0.0672990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.b.19.10	yes	144
5.4	even	2	inner	930.2.bn.b.19.6	✓	144
31.18	even	15	inner	930.2.bn.b.49.6	yes	144
155.49	even	30	inner	930.2.bn.b.49.10	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.b.19.6	✓	144	5.4	even	2	inner
930.2.bn.b.19.10	yes	144	1.1	even	1	trivial
930.2.bn.b.49.6	yes	144	31.18	even	15	inner
930.2.bn.b.49.10	yes	144	155.49	even	30	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)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.23144 + 0.143766i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.807100 - 0.726716i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.23144 + 0.143766i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.807100 - 0.726716i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(-1.19530 + 1.88978i) q^{10} +(-4.94583 - 1.05127i) q^{11} +(-0.994522 - 0.104528i) q^{12} +(0.895778 - 0.0941500i) q^{13} +(-1.06233 + 0.225805i) q^{14} +(-0.776272 + 2.09700i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.764742 + 3.59783i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(-0.638594 + 6.07582i) q^{19} +(0.826283 + 2.07780i) q^{20} +(-0.992165 + 0.441740i) q^{21} +(-3.75758 + 3.38334i) q^{22} +(2.75261 + 0.894378i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(4.95866 - 0.641611i) q^{25} +(0.450356 - 0.780039i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(-0.441740 + 0.992165i) q^{28} +(-6.50920 - 4.72921i) q^{29} +(1.24023 + 1.86060i) q^{30} +(-0.321878 + 5.55845i) q^{31} +1.00000i q^{32} +(-2.97203 + 4.09065i) q^{33} +(3.36021 + 1.49606i) q^{34} +(1.90547 + 1.50559i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.47884 - 1.43116i) q^{37} +(4.54008 + 4.08791i) q^{38} +(0.278335 - 0.856628i) q^{39} +(2.16665 + 0.552824i) q^{40} +(-2.95110 + 1.31392i) q^{41} +(-0.225805 + 1.06233i) q^{42} +(-10.8246 - 1.13771i) q^{43} +(0.528529 + 5.02862i) q^{44} +(1.59996 + 1.56209i) q^{45} +(2.34151 - 1.70121i) q^{46} +(-5.43877 - 7.48582i) q^{47} +(0.207912 + 0.978148i) q^{48} +(-0.608405 - 5.78859i) q^{49} +(2.39555 - 4.38877i) q^{50} +(3.59783 + 0.764742i) q^{51} +(-0.366352 - 0.822841i) q^{52} +(-2.70026 + 2.43133i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(11.1875 + 1.63480i) q^{55} +(0.543030 + 0.940556i) q^{56} +(5.29080 + 3.05464i) q^{57} +(-7.65202 + 2.48629i) q^{58} +(-12.3992 - 5.52048i) q^{59} +(2.23425 + 0.0902706i) q^{60} -15.1454 q^{61} +(4.30769 + 3.52758i) q^{62} +1.08606i q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.98534 + 0.338873i) q^{65} +(1.56249 + 4.80885i) q^{66} +(9.19572 + 5.30915i) q^{67} +(3.18542 - 1.83910i) q^{68} +(1.93664 - 2.15086i) q^{69} +(2.33806 - 0.656596i) q^{70} +(7.40784 + 8.22724i) q^{71} +(0.406737 + 0.913545i) q^{72} +(2.00223 - 9.41973i) q^{73} +(0.299194 - 2.84664i) q^{74} +(1.43073 - 4.79093i) q^{75} +(5.97578 - 1.27019i) q^{76} +(3.22780 + 4.44269i) q^{77} +(-0.529425 - 0.728691i) q^{78} +(8.62895 - 1.83414i) q^{79} +(1.72077 - 1.42792i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-0.671634 + 3.15979i) q^{82} +(5.88824 + 13.2252i) q^{83} +(0.726716 + 0.807100i) q^{84} +(-2.22372 - 7.91840i) q^{85} +(-7.28299 + 8.08857i) q^{86} +(-6.96788 + 4.02291i) q^{87} +(4.37890 + 2.52816i) q^{88} +(-3.90805 - 12.0278i) q^{89} +(2.20419 - 0.376228i) q^{90} +(-0.791402 - 0.574987i) q^{91} -2.89427i q^{92} +(4.94698 + 2.55488i) q^{93} -9.25299 q^{94} +(0.551489 - 13.6496i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-9.42485 + 3.06232i) q^{97} +(-5.04068 - 2.91024i) q^{98} +(2.52816 + 4.37890i) 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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