LMFDB - Embedded newform 783.2.v.b.26.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(26,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 19])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.26"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.v (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$20$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			26.9
Character	$\chi$	$=$	783.26
Dual form			783.2.v.b.512.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.561561 - 0.352852i) q^{2} +(-0.676921 - 1.40564i) q^{4} +(0.901677 + 3.95051i) q^{5} +(3.71421 + 1.78867i) q^{7} +(-0.264364 + 2.34630i) q^{8} +(0.887598 - 2.53661i) q^{10} +(-0.0605415 - 0.537321i) q^{11} +(1.03994 + 0.829323i) q^{13} +(-1.45462 - 2.31501i) q^{14} +(-0.969115 + 1.21523i) q^{16} +(-3.42739 + 3.42739i) q^{17} +(-6.17677 - 2.16134i) q^{19} +(4.94263 - 3.94162i) q^{20} +(-0.155597 + 0.323101i) q^{22} +(1.09932 + 0.250912i) q^{23} +(-10.2886 + 4.95474i) q^{25} +(-0.291360 - 0.832660i) q^{26} -6.43163i q^{28} +(-3.20978 + 4.32404i) q^{29} +(2.17681 - 3.46437i) q^{31} +(5.43031 - 1.90015i) q^{32} +(3.13405 - 0.715326i) q^{34} +(-3.71713 + 16.2858i) q^{35} +(-0.116634 - 0.0131415i) q^{37} +(2.70600 + 3.39321i) q^{38} +(-9.50744 + 1.07123i) q^{40} +(1.85162 + 1.85162i) q^{41} +(-2.37879 + 1.49469i) q^{43} +(-0.714298 + 0.448823i) q^{44} +(-0.528799 - 0.528799i) q^{46} +(-4.54606 + 0.512218i) q^{47} +(6.23158 + 7.81416i) q^{49} +(7.52598 + 0.847975i) q^{50} +(0.461775 - 2.02317i) q^{52} +(13.8470 - 3.16050i) q^{53} +(2.06810 - 0.723659i) q^{55} +(-5.17866 + 8.24178i) q^{56} +(3.32823 - 1.29563i) q^{58} -5.24021i q^{59} +(2.86526 + 8.18845i) q^{61} +(-2.44482 + 1.17736i) q^{62} +(-0.689180 - 0.157301i) q^{64} +(-2.33856 + 4.85606i) q^{65} +(11.0783 - 8.83463i) q^{67} +(7.13775 + 2.49761i) q^{68} +(7.83388 - 7.83388i) q^{70} +(-1.86371 + 2.33702i) q^{71} +(7.33708 + 11.6769i) q^{73} +(0.0608602 + 0.0485344i) q^{74} +(1.14311 + 10.1454i) q^{76} +(0.736225 - 2.10401i) q^{77} +(0.573293 - 5.08811i) q^{79} +(-5.67461 - 2.73275i) q^{80} +(-0.386450 - 1.69315i) q^{82} +(5.49290 + 11.4061i) q^{83} +(-16.6303 - 10.4495i) q^{85} +1.86324 q^{86} +1.27672 q^{88} +(-12.0422 - 7.56663i) q^{89} +(2.37916 + 4.94039i) q^{91} +(-0.391459 - 1.71509i) q^{92} +(2.73363 + 1.31645i) q^{94} +(2.96895 - 26.3502i) q^{95} +(-0.400010 + 1.14316i) q^{97} +(-0.742172 - 6.58696i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 72 q^{16} + 8 q^{19} - 40 q^{25} + 8 q^{31} - 32 q^{37} - 16 q^{40} - 16 q^{43} - 104 q^{46} - 8 q^{49} + 8 q^{52} - 128 q^{55} + 272 q^{58} - 24 q^{61} + 112 q^{67} - 56 q^{70} - 64 q^{73} - 160 q^{76}+ \cdots + 40 q^{97}+O(q^{100}) $ 240 * q + 72 * q^16 + 8 * q^19 - 40 * q^25 + 8 * q^31 - 32 * q^37 - 16 * q^40 - 16 * q^43 - 104 * q^46 - 8 * q^49 + 8 * q^52 - 128 * q^55 + 272 * q^58 - 24 * q^61 + 112 * q^67 - 56 * q^70 - 64 * q^73 - 160 * q^76 - 96 * q^79 - 80 * q^82 - 104 * q^85 - 464 * q^88 - 168 * q^91 - 88 * q^94 + 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{19}{28}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.561561	−	0.352852i	−0.397084	−	0.249504i	0.318657	−	0.947870i	$-0.396768\pi$
$2$	−0.561561	−	0.352852i	−0.397084	−	0.249504i	−0.715741	+	0.698366i	$0.753911\pi$
$3$		0			0
$3$		0			0
$4$	−0.676921	−	1.40564i	−0.338461	−	0.702821i
$5$	0.901677	+	3.95051i	0.403242	+	1.76672i	0.614125	+	0.789209i	$0.289509\pi$
$5$	0.901677	+	3.95051i	0.403242	+	1.76672i	−0.210883	+	0.977511i	$0.567634\pi$
$6$		0			0
$7$	3.71421	+	1.78867i	1.40384	+	0.676053i	0.973936	−	0.226822i	$-0.0728335\pi$
$7$	3.71421	+	1.78867i	1.40384	+	0.676053i	0.429903	+	0.902875i	$0.358548\pi$
$8$	−0.264364	+	2.34630i	−0.0934669	+	0.829542i
$9$		0			0
$10$	0.887598	−	2.53661i	0.280683	−	0.802146i
$11$	−0.0605415	−	0.537321i	−0.0182539	−	0.162008i	0.981278	−	0.192596i	$-0.0616907\pi$
$11$	−0.0605415	−	0.537321i	−0.0182539	−	0.162008i	−0.999532	+	0.0305877i	$0.990262\pi$
$12$		0			0
$13$	1.03994	+	0.829323i	0.288427	+	0.230013i	0.757005	−	0.653409i	$-0.226662\pi$
$13$	1.03994	+	0.829323i	0.288427	+	0.230013i	−0.468578	+	0.883422i	$0.655233\pi$
$14$	−1.45462	−	2.31501i	−0.388763	−	0.618713i
$15$		0			0
$16$	−0.969115	+	1.21523i	−0.242279	+	0.303808i
$17$	−3.42739	+	3.42739i	−0.831263	+	0.831263i	−0.987690	−	0.156426i	$-0.950003\pi$
$17$	−3.42739	+	3.42739i	−0.831263	+	0.831263i	0.156426	+	0.987690i	$0.450003\pi$
$18$		0			0
$19$	−6.17677	−	2.16134i	−1.41705	−	0.495846i	−0.490307	−	0.871550i	$-0.663116\pi$
$19$	−6.17677	−	2.16134i	−1.41705	−	0.495846i	−0.926740	+	0.375703i	$0.877401\pi$
$20$	4.94263	−	3.94162i	1.10521	−	0.881372i
$21$		0			0
$22$	−0.155597	+	0.323101i	−0.0331734	+	0.0688853i
$23$	1.09932	+	0.250912i	0.229224	+	0.0523188i	0.335590	−	0.942008i	$-0.391064\pi$
$23$	1.09932	+	0.250912i	0.229224	+	0.0523188i	−0.106366	+	0.994327i	$0.533922\pi$
$24$		0			0
$25$	−10.2886	+	4.95474i	−2.05773	+	0.990948i
$26$	−0.291360	−	0.832660i	−0.0571405	−	0.163298i
$27$		0			0
$28$		−	6.43163i		−	1.21546i
$29$	−3.20978	+	4.32404i	−0.596041	+	0.802954i
$29$	−3.20978	+	4.32404i	−0.596041	+	0.802954i
$30$		0			0
$31$	2.17681	−	3.46437i	0.390966	−	0.622219i	−0.592015	−	0.805927i	$-0.701667\pi$
$31$	2.17681	−	3.46437i	0.390966	−	0.622219i	0.982981	+	0.183708i	$0.0588101\pi$
$32$	5.43031	−	1.90015i	0.959951	−	0.335902i
$33$		0			0
$34$	3.13405	−	0.715326i	0.537485	−	0.122677i
$35$	−3.71713	+	16.2858i	−0.628309	+	2.75280i
$36$		0			0
$37$	−0.116634	−	0.0131415i	−0.0191745	−	0.00216045i	0.102372	−	0.994746i	$-0.467357\pi$
$37$	−0.116634	−	0.0131415i	−0.0191745	−	0.00216045i	−0.121547	+	0.992586i	$0.538785\pi$
$38$	2.70600	+	3.39321i	0.438971	+	0.550452i
$39$		0			0
$40$	−9.50744	+	1.07123i	−1.50326	+	0.169376i
$41$	1.85162	+	1.85162i	0.289175	+	0.289175i	0.836754	−	0.547579i	$-0.184450\pi$
$41$	1.85162	+	1.85162i	0.289175	+	0.289175i	−0.547579	+	0.836754i	$0.684450\pi$
$42$		0			0
$43$	−2.37879	+	1.49469i	−0.362762	+	0.227938i	−0.701063	−	0.713100i	$-0.747291\pi$
$43$	−2.37879	+	1.49469i	−0.362762	+	0.227938i	0.338301	+	0.941038i	$0.390148\pi$
$44$	−0.714298	+	0.448823i	−0.107685	+	0.0676627i
$45$		0			0
$46$	−0.528799	−	0.528799i	−0.0779672	−	0.0779672i
$47$	−4.54606	+	0.512218i	−0.663111	+	0.0747147i	−0.437104	−	0.899411i	$-0.643996\pi$
$47$	−4.54606	+	0.512218i	−0.663111	+	0.0747147i	−0.226007	+	0.974126i	$0.572567\pi$
$48$		0			0
$49$	6.23158	+	7.81416i	0.890226	+	1.11631i
$50$	7.52598	+	0.847975i	1.06433	+	0.119922i
$51$		0			0
$52$	0.461775	−	2.02317i	0.0640366	−	0.280563i
$53$	13.8470	−	3.16050i	1.90204	−	0.434128i	0.902041	−	0.431650i	$-0.142068\pi$
$53$	13.8470	−	3.16050i	1.90204	−	0.434128i	0.999997	−	0.00247771i	$-0.000788680\pi$
$54$		0			0
$55$	2.06810	−	0.723659i	0.278862	−	0.0975782i
$56$	−5.17866	+	8.24178i	−0.692027	+	1.10135i
$57$		0			0
$58$	3.32823	−	1.29563i	0.437019	−	0.170125i
$59$		−	5.24021i		−	0.682218i	−0.940024	−	0.341109i	$-0.889198\pi$
$59$		−	5.24021i		−	0.682218i	0.940024	−	0.341109i	$-0.110802\pi$
$60$		0			0
$61$	2.86526	+	8.18845i	0.366859	+	1.04842i	0.968361	+	0.249552i	$0.0802834\pi$
$61$	2.86526	+	8.18845i	0.366859	+	1.04842i	−0.601502	+	0.798871i	$0.705431\pi$
$62$	−2.44482	+	1.17736i	−0.310493	+	0.149525i
$63$		0			0
$64$	−0.689180	−	0.157301i	−0.0861475	−	0.0196626i
$65$	−2.33856	+	4.85606i	−0.290062	+	0.602321i
$66$		0			0
$67$	11.0783	−	8.83463i	1.35343	−	1.07932i	0.364454	−	0.931222i	$-0.381256\pi$
$67$	11.0783	−	8.83463i	1.35343	−	1.07932i	0.988972	−	0.148100i	$-0.0473156\pi$
$68$	7.13775	+	2.49761i	0.865579	+	0.302879i
$69$		0			0
$70$	7.83388	−	7.83388i	0.936327	−	0.936327i
$71$	−1.86371	+	2.33702i	−0.221182	+	0.277353i	−0.880025	−	0.474927i	$-0.842475\pi$
$71$	−1.86371	+	2.33702i	−0.221182	+	0.277353i	0.658843	+	0.752280i	$0.271046\pi$
$72$		0			0
$73$	7.33708	+	11.6769i	0.858741	+	1.36668i	0.929360	+	0.369175i	$0.120360\pi$
$73$	7.33708	+	11.6769i	0.858741	+	1.36668i	−0.0706193	+	0.997503i	$0.522498\pi$
$74$	0.0608602	+	0.0485344i	0.00707485	+	0.00564200i
$75$		0			0
$76$	1.14311	+	10.1454i	0.131124	+	1.16375i
$77$	0.736225	−	2.10401i	0.0839006	−	0.239774i
$78$		0			0
$79$	0.573293	−	5.08811i	0.0645005	−	0.572457i	−0.919347	−	0.393448i	$-0.871282\pi$
$79$	0.573293	−	5.08811i	0.0645005	−	0.572457i	0.983847	−	0.179009i	$-0.0572893\pi$
$80$	−5.67461	−	2.73275i	−0.634441	−	0.305530i
$81$		0			0
$82$	−0.386450	−	1.69315i	−0.0426763	−	0.186977i
$83$	5.49290	+	11.4061i	0.602924	+	1.25198i	0.949442	+	0.313941i	$0.101649\pi$
$83$	5.49290	+	11.4061i	0.602924	+	1.25198i	−0.346519	+	0.938043i	$0.612636\pi$
$84$		0			0
$85$	−16.6303	−	10.4495i	−1.80381	−	1.13341i
$86$	1.86324			0.200918
$87$		0			0
$88$	1.27672			0.136099
$89$	−12.0422	−	7.56663i	−1.27647	−	0.802061i	−0.288618	−	0.957444i	$-0.593196\pi$
$89$	−12.0422	−	7.56663i	−1.27647	−	0.802061i	−0.987854	+	0.155383i	$0.950339\pi$
$90$		0			0
$91$	2.37916	+	4.94039i	0.249404	+	0.517893i
$92$	−0.391459	−	1.71509i	−0.0408124	−	0.178811i
$93$		0			0
$94$	2.73363	+	1.31645i	0.281952	+	0.135781i
$95$	2.96895	−	26.3502i	0.304608	−	2.70347i
$96$		0			0
$97$	−0.400010	+	1.14316i	−0.0406148	+	0.116071i	−0.962405	−	0.271619i	$-0.912441\pi$
$97$	−0.400010	+	1.14316i	−0.0406148	+	0.116071i	0.921790	+	0.387689i	$0.126727\pi$
$98$	−0.742172	−	6.58696i	−0.0749707	−	0.665383i
$99$		0			0
$100$	13.9292	+	11.1082i	1.39292	+	1.11082i
$101$	−7.94123	−	12.6384i	−0.790182	−	1.25757i	−0.962165	−	0.272467i	$-0.912160\pi$
$101$	−7.94123	−	12.6384i	−0.790182	−	1.25757i	0.171984	−	0.985100i	$-0.444982\pi$
$102$		0			0
$103$	5.03284	−	6.31098i	0.495900	−	0.621839i	−0.469399	−	0.882986i	$-0.655529\pi$
$103$	5.03284	−	6.31098i	0.495900	−	0.621839i	0.965299	+	0.261147i	$0.0841008\pi$
$104$	−2.22076	+	2.22076i	−0.217764	+	0.217764i
$105$		0			0
$106$	−8.89115	−	3.11115i	−0.863585	−	0.302181i
$107$	−8.75922	+	6.98525i	−0.846786	+	0.675289i	−0.947545	−	0.319621i	$-0.896444\pi$
$107$	−8.75922	+	6.98525i	−0.846786	+	0.675289i	0.100759	+	0.994911i	$0.467873\pi$
$108$		0			0
$109$	−7.45388	+	15.4781i	−0.713952	+	1.48254i	0.155143	+	0.987892i	$0.450416\pi$
$109$	−7.45388	+	15.4781i	−0.713952	+	1.48254i	−0.869095	+	0.494645i	$0.835298\pi$
$110$	−1.41671	−	0.323355i	−0.135078	−	0.0308306i
$111$		0			0
$112$	−5.77314	+	2.78020i	−0.545511	+	0.262704i
$113$	3.83624	+	10.9633i	0.360883	+	1.03134i	0.971010	+	0.239040i	$0.0768327\pi$
$113$	3.83624	+	10.9633i	0.360883	+	1.03134i	−0.610127	+	0.792304i	$0.708882\pi$
$114$		0			0
$115$			4.56910i			0.426071i
$116$	8.25082	+	1.58477i	0.766069	+	0.147142i
$117$		0			0
$118$	−1.84902	+	2.94270i	−0.170216	+	0.270898i
$119$	−18.8605	+	6.59957i	−1.72894	+	0.604982i
$120$		0			0
$121$	10.4392	−	2.38267i	0.949014	−	0.216606i
$122$	1.28029	−	5.60933i	0.115912	−	0.507845i
$123$		0			0
$124$	−6.34319	−	0.714706i	−0.569635	−	0.0641825i
$125$	−16.2185	−	20.3374i	−1.45063	−	1.81903i
$126$		0			0
$127$	12.7918	−	1.44129i	1.13509	−	0.127894i	0.475636	−	0.879642i	$-0.342218\pi$
$127$	12.7918	−	1.44129i	1.13509	−	0.127894i	0.659450	+	0.751748i	$0.270789\pi$
$128$	−7.80467	−	7.80467i	−0.689842	−	0.689842i
$129$		0			0
$130$	3.02672	−	1.90181i	0.265461	−	0.166800i
$131$	0.416771	−	0.261874i	0.0364134	−	0.0228801i	−0.513702	−	0.857968i	$-0.671726\pi$
$131$	0.416771	−	0.261874i	0.0364134	−	0.0228801i	0.550116	+	0.835088i	$0.314584\pi$
$132$		0			0
$133$	−19.0759	−	19.0759i	−1.65409	−	1.65409i
$134$	−9.33844	+	1.05219i	−0.806718	+	0.0908953i
$135$		0			0
$136$	−7.13559	−	8.94775i	−0.611872	−	0.767263i
$137$	3.47111	+	0.391100i	0.296557	+	0.0334139i	0.258989	−	0.965880i	$-0.416611\pi$
$137$	3.47111	+	0.391100i	0.296557	+	0.0334139i	0.0375674	+	0.999294i	$0.488039\pi$
$138$		0			0
$139$	−1.20207	+	5.26660i	−0.101958	+	0.446707i	0.898019	+	0.439956i	$0.145006\pi$
$139$	−1.20207	+	5.26660i	−0.101958	+	0.446707i	−0.999977	+	0.00675108i	$0.997851\pi$
$140$	25.4082	−	5.79926i	2.14739	−	0.490127i
$141$		0			0
$142$	1.87121	−	0.654765i	0.157029	−	0.0549467i
$143$	0.382653	−	0.608989i	0.0319991	−	0.0509262i
$144$		0			0
$145$	−19.9763	−	8.78137i	−1.65894	−	0.729253i
$146$		−	9.14620i		−	0.756945i
$147$		0			0
$148$	0.0604799	+	0.172842i	0.00497141	+	0.0142075i
$149$	−1.04175	+	0.501679i	−0.0853433	+	0.0410992i	−0.476068	−	0.879408i	$-0.657939\pi$
$149$	−1.04175	+	0.501679i	−0.0853433	+	0.0410992i	0.390725	+	0.920507i	$0.372224\pi$
$150$		0			0
$151$	11.4192	+	2.60636i	0.929283	+	0.212103i	0.660265	−	0.751032i	$-0.270444\pi$
$151$	11.4192	+	2.60636i	0.929283	+	0.212103i	0.269018	+	0.963135i	$0.413301\pi$
$152$	6.70408	−	13.9212i	0.543772	−	1.12915i
$153$		0			0
$154$	−1.15584	+	0.921751i	−0.0931402	+	0.0742768i
$155$	15.6488	+	5.47575i	1.25694	+	0.439823i
$156$		0			0
$157$	0.882364	−	0.882364i	0.0704203	−	0.0704203i	−0.671019	−	0.741440i	$-0.734143\pi$
$157$	0.882364	−	0.882364i	0.0704203	−	0.0704203i	0.741440	+	0.671019i	$0.234143\pi$
$158$	−2.11729	+	2.65500i	−0.168443	+	0.211220i
$159$		0			0
$160$	12.4029	+	19.7391i	0.980537	+	1.56052i
$161$	3.63430	+	2.89825i	0.286423	+	0.228414i
$162$		0			0
$163$	−1.48504	−	13.1801i	−0.116317	−	1.03235i	−0.907293	−	0.420498i	$-0.861855\pi$
$163$	−1.48504	−	13.1801i	−0.116317	−	1.03235i	0.790976	−	0.611847i	$-0.209573\pi$
$164$	1.34932	−	3.85613i	0.105364	−	0.301113i
$165$		0			0
$166$	0.940077	−	8.34341i	0.0729641	−	0.647574i
$167$	−0.446853	−	0.215193i	−0.0345785	−	0.0166521i	0.416515	−	0.909129i	$-0.363251\pi$
$167$	−0.446853	−	0.215193i	−0.0345785	−	0.0166521i	−0.451093	+	0.892477i	$0.648966\pi$
$168$		0			0
$169$	−2.49908	−	10.9492i	−0.192237	−	0.842244i
$170$	5.65180	+	11.7361i	0.433473	+	0.900116i
$171$		0			0
$172$	3.71125	+	2.33193i	0.282980	+	0.177808i
$173$	22.7723			1.73135			0.865674	−	0.500608i	$-0.166890\pi$
$173$	22.7723			1.73135			0.865674	+	0.500608i	$0.166890\pi$
$174$		0			0
$175$	−47.0765			−3.55865
$176$	0.711641	+	0.447154i	0.0536419	+	0.0337055i
$177$		0			0
$178$	4.09254	+	8.49825i	0.306749	+	0.636971i
$179$	1.94996	+	8.54333i	0.145747	+	0.638558i	0.994039	+	0.109029i	$0.0347742\pi$
$179$	1.94996	+	8.54333i	0.145747	+	0.638558i	−0.848292	+	0.529529i	$0.822369\pi$
$180$		0			0
$181$	1.73920	+	0.837555i	0.129274	+	0.0622550i	0.497403	−	0.867520i	$-0.334287\pi$
$181$	1.73920	+	0.837555i	0.129274	+	0.0622550i	−0.368129	+	0.929775i	$0.620001\pi$
$182$	0.407180	−	3.61382i	0.0301822	−	0.267874i
$183$		0			0
$184$	−0.879335	+	2.51300i	−0.0648254	+	0.185260i
$185$	−0.0532507	−	0.472613i	−0.00391507	−	0.0347472i
$186$		0			0
$187$	2.04910	+	1.63411i	0.149845	+	0.119498i
$188$	3.79732	+	6.04340i	0.276948	+	0.440761i
$189$		0			0
$190$	−10.9650	+	13.7496i	−0.795483	+	0.997504i
$191$	7.21934	−	7.21934i	0.522373	−	0.522373i	−0.395914	−	0.918288i	$-0.629572\pi$
$191$	7.21934	−	7.21934i	0.522373	−	0.522373i	0.918288	+	0.395914i	$0.129572\pi$
$192$		0			0
$193$	−3.49934	−	1.22447i	−0.251888	−	0.0881394i	0.201382	−	0.979513i	$-0.435457\pi$
$193$	−3.49934	−	1.22447i	−0.251888	−	0.0881394i	−0.453270	+	0.891373i	$0.649743\pi$
$194$	0.627997	−	0.500811i	0.0450876	−	0.0359561i
$195$		0			0
$196$	6.76561	−	14.0489i	0.483258	−	1.00350i
$197$	−14.9878	−	3.42087i	−1.06784	−	0.243727i	−0.347733	−	0.937594i	$-0.613048\pi$
$197$	−14.9878	−	3.42087i	−1.06784	−	0.243727i	−0.720103	+	0.693867i	$0.755905\pi$
$198$		0			0
$199$	5.80624	−	2.79614i	0.411593	−	0.198213i	−0.216617	−	0.976257i	$-0.569502\pi$
$199$	5.80624	−	2.79614i	0.411593	−	0.198213i	0.628210	+	0.778044i	$0.283788\pi$
$200$	−8.90536	−	25.4501i	−0.629704	−	1.79959i
$201$		0			0
$202$			9.89931i			0.696513i
$203$	−19.6561	+	10.3192i	−1.37959	+	0.724262i
$204$		0			0
$205$	−5.64529	+	8.98442i	−0.394284	+	0.627499i
$206$	−5.05309	+	1.76815i	−0.352065	+	0.123193i
$207$		0			0
$208$	−2.01564	+	0.460057i	−0.139759	+	0.0318992i
$209$	−0.787384	+	3.44976i	−0.0544645	+	0.238625i
$210$		0			0
$211$	15.2933	+	1.72314i	1.05283	+	0.118626i	0.621380	−	0.783510i	$-0.286572\pi$
$211$	15.2933	+	1.72314i	1.05283	+	0.118626i	0.431453	+	0.902135i	$0.358001\pi$
$212$	−13.8159	−	17.3246i	−0.948879	−	1.18986i
$213$		0			0
$214$	7.38360	−	0.831932i	0.504733	−	0.0568697i
$215$	−8.04969	−	8.04969i	−0.548984	−	0.548984i
$216$		0			0
$217$	14.2817	−	8.97381i	0.969507	−	0.609182i
$218$	9.64730	−	6.06180i	0.653398	−	0.410557i
$219$		0			0
$220$	−2.41715	−	2.41715i	−0.162964	−	0.162964i
$221$	−6.40668	+	0.721860i	−0.430960	+	0.0485575i
$222$		0			0
$223$	3.76337	+	4.71912i	0.252014	+	0.316016i	0.891705	−	0.452616i	$-0.149509\pi$
$223$	3.76337	+	4.71912i	0.252014	+	0.316016i	−0.639691	+	0.768632i	$0.720938\pi$
$224$	23.5680	+	2.65548i	1.57470	+	0.177427i
$225$		0			0
$226$	1.71416	−	7.51020i	0.114024	−	0.499571i
$227$	10.3888	−	2.37116i	0.689526	−	0.157380i	0.136620	−	0.990624i	$-0.456376\pi$
$227$	10.3888	−	2.37116i	0.689526	−	0.157380i	0.552906	+	0.833244i	$0.313519\pi$
$228$		0			0
$229$	17.6455	−	6.17441i	1.16604	−	0.408017i	0.323282	−	0.946303i	$-0.395214\pi$
$229$	17.6455	−	6.17441i	1.16604	−	0.408017i	0.842762	+	0.538286i	$0.180928\pi$
$230$	1.61222	−	2.56583i	0.106306	−	0.169186i
$231$		0			0
$232$	−9.29694	−	8.67422i	−0.610374	−	0.569491i
$233$		−	25.2819i		−	1.65627i	−0.560526	−	0.828137i	$-0.689401\pi$
$233$		−	25.2819i		−	1.65627i	0.560526	−	0.828137i	$-0.310599\pi$
$234$		0			0
$235$	−6.12260	−	17.4974i	−0.399395	−	1.14140i
$236$	−7.36586	+	3.54721i	−0.479477	+	0.230904i
$237$		0			0
$238$	12.9200	+	2.94890i	0.837479	+	0.191149i
$239$	11.9320	−	24.7771i	0.771819	−	1.60270i	−0.0258962	−	0.999665i	$-0.508244\pi$
$239$	11.9320	−	24.7771i	0.771819	−	1.60270i	0.797715	−	0.603034i	$-0.206042\pi$
$240$		0			0
$241$	8.87070	−	7.07415i	0.571412	−	0.455686i	−0.294662	−	0.955602i	$-0.595207\pi$
$241$	8.87070	−	7.07415i	0.571412	−	0.455686i	0.866074	+	0.499916i	$0.166636\pi$
$242$	−6.70296	−	2.34547i	−0.430882	−	0.150772i
$243$		0			0
$244$	9.57047	−	9.57047i	0.612686	−	0.612686i
$245$	−25.2510	+	31.6638i	−1.61323	+	2.02292i
$246$		0			0
$247$	−4.63100	−	7.37020i	−0.294664	−	0.468955i
$248$	7.55298	+	6.02330i	0.479615	+	0.382480i
$249$		0			0
$250$	1.93160	+	17.1434i	0.122165	+	1.08425i
$251$	−5.48814	+	15.6842i	−0.346408	+	0.989978i	0.630476	+	0.776209i	$0.282860\pi$
$251$	−5.48814	+	15.6842i	−0.346408	+	0.989978i	−0.976884	+	0.213769i	$0.931426\pi$
$252$		0			0
$253$	0.0682659	−	0.605877i	0.00429184	−	0.0380911i
$254$	−7.69192	−	3.70423i	−0.482634	−	0.232424i
$255$		0			0
$256$	1.94351	+	8.51506i	0.121469	+	0.532191i
$257$	−8.20818	−	17.0445i	−0.512012	−	1.06320i	−0.983429	−	0.181293i	$-0.941972\pi$
$257$	−8.20818	−	17.0445i	−0.512012	−	1.06320i	0.471417	−	0.881910i	$-0.343743\pi$
$258$		0			0
$259$	−0.409698	−	0.257430i	−0.0254574	−	0.0159959i
$260$	8.40891			0.521498
$261$		0			0
$262$	−0.326445			−0.0201679
$263$	−26.7374	−	16.8002i	−1.64870	−	1.03595i	−0.945848	−	0.324609i	$-0.894767\pi$
$263$	−26.7374	−	16.8002i	−1.64870	−	1.03595i	−0.702851	−	0.711337i	$-0.748090\pi$
$264$		0			0
$265$	24.9711	+	51.8531i	1.53396	+	3.18531i
$266$	3.98130	+	17.4432i	0.244109	+	1.06951i
$267$		0			0
$268$	−19.9174	−	9.59173i	−1.21665	−	0.585908i
$269$	−1.21694	+	10.8007i	−0.0741983	+	0.658528i	0.900477	+	0.434903i	$0.143218\pi$
$269$	−1.21694	+	10.8007i	−0.0741983	+	0.658528i	−0.974675	+	0.223625i	$0.928211\pi$
$270$		0			0
$271$	−1.10464	+	3.15688i	−0.0671022	+	0.191767i	−0.972552	−	0.232687i	$-0.925248\pi$
$271$	−1.10464	+	3.15688i	−0.0671022	+	0.191767i	0.905450	+	0.424454i	$0.139534\pi$
$272$	−0.843537	−	7.48660i	−0.0511470	−	0.453942i
$273$		0			0
$274$	−1.81124	−	1.44441i	−0.109421	−	0.0872603i
$275$	3.28517	+	5.22832i	0.198103	+	0.315280i
$276$		0			0
$277$	1.73796	−	2.17934i	0.104424	−	0.130944i	−0.726873	−	0.686772i	$-0.759027\pi$
$277$	1.73796	−	2.17934i	0.104424	−	0.130944i	0.831297	+	0.555828i	$0.187599\pi$
$278$	2.53337	−	2.53337i	0.151941	−	0.151941i
$279$		0			0
$280$	−37.2287	−	13.0269i	−2.22484	−	0.778505i
$281$	1.35528	−	1.08080i	0.0808490	−	0.0644749i	−0.582231	−	0.813023i	$-0.697820\pi$
$281$	1.35528	−	1.08080i	0.0808490	−	0.0644749i	0.663080	+	0.748548i	$0.269249\pi$
$282$		0			0
$283$	−6.88206	+	14.2908i	−0.409096	+	0.849497i	0.590017	+	0.807391i	$0.299121\pi$
$283$	−6.88206	+	14.2908i	−0.409096	+	0.849497i	−0.999113	+	0.0421063i	$0.986593\pi$
$284$	4.54660	+	1.03773i	0.269791	+	0.0615781i
$285$		0			0
$286$	−0.429766	+	0.206964i	−0.0254126	+	0.0122381i
$287$	3.56538	+	10.1893i	0.210458	+	0.601453i
$288$		0			0
$289$		−	6.49396i		−	0.381998i
$290$	8.11940	+	11.9800i	0.476788	+	0.703488i
$291$		0			0
$292$	11.4469	−	18.2177i	0.669880	−	1.06611i
$293$	10.2053	−	3.57099i	0.596199	−	0.208619i	−0.0152751	−	0.999883i	$-0.504862\pi$
$293$	10.2053	−	3.57099i	0.596199	−	0.208619i	0.611475	+	0.791264i	$0.290577\pi$
$294$		0			0
$295$	20.7015	−	4.72498i	1.20529	−	0.275099i
$296$	0.0616678	−	0.270184i	0.00358437	−	0.0157041i
$297$		0			0
$298$	0.762024	+	0.0858595i	0.0441429	+	0.00497371i
$299$	0.935135	+	1.17262i	0.0540803	+	0.0678145i
$300$		0			0
$301$	−11.5088	+	1.29673i	−0.663358	+	0.0747424i
$302$	−5.49293	−	5.49293i	−0.316083	−	0.316083i
$303$		0			0
$304$	8.61253	−	5.41161i	0.493963	−	0.310377i
$305$	−29.7650	+	18.7026i	−1.70434	+	1.07091i
$306$		0			0
$307$	10.8666	+	10.8666i	0.620191	+	0.620191i	0.945580	−	0.325389i	$-0.105495\pi$
$307$	10.8666	+	10.8666i	0.620191	+	0.620191i	−0.325389	+	0.945580i	$0.605495\pi$
$308$	−3.45585	+	0.389381i	−0.196915	+	0.0221870i
$309$		0			0
$310$	−6.85562	−	8.59668i	−0.389373	−	0.488259i
$311$	11.2187	+	1.26404i	0.636152	+	0.0716771i	0.424150	−	0.905592i	$-0.360573\pi$
$311$	11.2187	+	1.26404i	0.636152	+	0.0716771i	0.212002	+	0.977269i	$0.432002\pi$
$312$		0			0
$313$	−1.78340	+	7.81360i	−0.100804	+	0.441651i	0.899188	+	0.437563i	$0.144158\pi$
$313$	−1.78340	+	7.81360i	−0.100804	+	0.441651i	−0.999992	+	0.00408780i	$0.998699\pi$
$314$	−0.806845	+	0.184157i	−0.0455329	+	0.0103926i
$315$		0			0
$316$	−7.54014	+	2.63841i	−0.424166	+	0.148422i
$317$	−8.75043	+	13.9262i	−0.491473	+	0.782175i	−0.996731	−	0.0807937i	$-0.974255\pi$
$317$	−8.75043	+	13.9262i	−0.491473	+	0.782175i	0.505258	+	0.862968i	$0.331397\pi$
$318$		0			0
$319$	2.51772	+	1.46290i	0.140965	+	0.0819065i
$320$		−	2.86444i		−	0.160127i
$321$		0			0
$322$	−1.01822	−	2.90992i	−0.0567434	−	0.162163i
$323$	28.5779	−	13.7624i	1.59012	−	0.765761i
$324$		0			0
$325$	−14.8086	−	3.37997i	−0.821435	−	0.187487i
$326$	−3.81669	+	7.92543i	−0.211387	+	0.438949i
$327$		0			0
$328$	−4.83397	+	3.85496i	−0.266911	+	0.212855i
$329$	−17.8012	−	6.22892i	−0.981413	−	0.343411i
$330$		0			0
$331$	3.35519	−	3.35519i	0.184418	−	0.184418i	−0.608860	−	0.793278i	$-0.708373\pi$
$331$	3.35519	−	3.35519i	0.184418	−	0.184418i	0.793278	+	0.608860i	$0.208373\pi$
$332$	12.3147	−	15.4421i	0.675855	−	0.847495i
$333$		0			0
$334$	0.175004	+	0.278517i	0.00957579	+	0.0152398i
$335$	44.8903	+	35.7988i	2.45262	+	1.95590i
$336$		0			0
$337$	−1.07577	−	9.54770i	−0.0586008	−	0.520096i	−0.988383	−	0.151986i	$-0.951433\pi$
$337$	−1.07577	−	9.54770i	−0.0586008	−	0.520096i	0.929782	−	0.368111i	$-0.119995\pi$
$338$	−2.46006	+	7.03043i	−0.133809	+	0.382405i
$339$		0			0
$340$	−3.43086	+	30.4498i	−0.186065	+	1.65137i
$341$	−1.99326	−	0.959906i	−0.107941	−	0.0519818i
$342$		0			0
$343$	2.74713	+	12.0359i	0.148331	+	0.649880i
$344$	−2.87813	−	5.97649i	−0.155178	−	0.322231i
$345$		0			0
$346$	−12.7881	−	8.03527i	−0.687490	−	0.431979i
$347$	3.15691			0.169472			0.0847360	−	0.996403i	$-0.472995\pi$
$347$	3.15691			0.169472			0.0847360	+	0.996403i	$0.472995\pi$
$348$		0			0
$349$	−13.5471			−0.725158			−0.362579	−	0.931953i	$-0.618104\pi$
$349$	−13.5471			−0.725158			−0.362579	+	0.931953i	$0.618104\pi$
$350$	26.4363	+	16.6110i	1.41308	+	0.887898i
$351$		0			0
$352$	−1.34975	−	2.80278i	−0.0719417	−	0.149389i
$353$	−4.10593	−	17.9893i	−0.218537	−	0.957471i	−0.958560	−	0.284890i	$-0.908043\pi$
$353$	−4.10593	−	17.9893i	−0.218537	−	0.957471i	0.740024	−	0.672581i	$-0.234814\pi$
$354$		0			0
$355$	−10.9129	−	5.25537i	−0.579196	−	0.278926i
$356$	−2.48433	+	22.0491i	−0.131669	+	1.16860i
$357$		0			0
$358$	1.91951	−	5.48565i	0.101449	−	0.289926i
$359$	1.71399	+	15.2121i	0.0904608	+	0.802862i	0.954250	+	0.299009i	$0.0966560\pi$
$359$	1.71399	+	15.2121i	0.0904608	+	0.802862i	−0.863790	+	0.503853i	$0.831915\pi$
$360$		0			0
$361$	18.6262	+	14.8539i	0.980329	+	0.781786i
$362$	−0.681134	−	1.08402i	−0.0357996	−	0.0569748i
$363$		0			0
$364$	5.33390	−	6.68850i	0.279573	−	0.350573i
$365$	−39.5140	+	39.5140i	−2.06826	+	2.06826i
$366$		0			0
$367$	−10.6427	−	3.72403i	−0.555543	−	0.194393i	0.0378820	−	0.999282i	$-0.487939\pi$
$367$	−10.6427	−	3.72403i	−0.555543	−	0.194393i	−0.593425	+	0.804889i	$0.702225\pi$
$368$	−1.37028	+	1.09276i	−0.0714309	+	0.0569642i
$369$		0			0
$370$	−0.136859	+	0.284191i	−0.00711496	+	0.0147744i
$371$	57.0839	+	13.0290i	2.96365	+	0.676433i
$372$		0			0
$373$	−23.3176	+	11.2292i	−1.20734	+	0.581425i	−0.925760	−	0.378112i	$-0.876573\pi$
$373$	−23.3176	+	11.2292i	−1.20734	+	0.581425i	−0.281582	+	0.959537i	$0.590859\pi$
$374$	−0.574099	−	1.64068i	−0.0296860	−	0.0848376i
$375$		0			0
$376$		−	10.8018i		−	0.557062i
$377$	−6.92400	+	1.83479i	−0.356604	+	0.0944965i
$378$		0			0
$379$	8.05998	−	12.8274i	0.414013	−	0.658898i	−0.572997	−	0.819558i	$-0.694219\pi$
$379$	8.05998	−	12.8274i	0.414013	−	0.658898i	0.987010	+	0.160659i	$0.0513621\pi$
$380$	−39.0487	+	13.6637i	−2.00315	+	0.700934i
$381$		0			0
$382$	−6.60146	+	1.50674i	−0.337760	+	0.0770916i
$383$	−6.31524	+	27.6689i	−0.322693	+	1.41381i	0.510046	+	0.860147i	$0.329628\pi$
$383$	−6.31524	+	27.6689i	−0.322693	+	1.41381i	−0.832739	+	0.553665i	$0.813229\pi$
$384$		0			0
$385$	8.97574	+	1.01132i	0.457446	+	0.0515418i
$386$	1.53304	+	1.92237i	0.0780295	+	0.0978458i
$387$		0			0
$388$	1.87765	−	0.211561i	0.0953233	−	0.0107404i
$389$	−15.2482	−	15.2482i	−0.773116	−	0.773116i	0.205534	−	0.978650i	$-0.434107\pi$
$389$	−15.2482	−	15.2482i	−0.773116	−	0.773116i	−0.978650	+	0.205534i	$0.934107\pi$
$390$		0			0
$391$	−4.62776	+	2.90781i	−0.234036	+	0.147054i
$392$	−19.9818	+	12.5554i	−1.00923	+	0.634142i
$393$		0			0
$394$	7.20950	+	7.20950i	0.363209	+	0.363209i
$395$	20.6175	−	2.32304i	1.03738	−	0.116885i
$396$		0			0
$397$	5.67395	+	7.11491i	0.284767	+	0.357087i	0.903556	−	0.428471i	$-0.140948\pi$
$397$	5.67395	+	7.11491i	0.284767	+	0.357087i	−0.618788	+	0.785558i	$0.712376\pi$
$398$	−4.24718	−	0.478542i	−0.212892	−	0.0239872i
$399$		0			0
$400$	3.94970	−	17.3048i	0.197485	−	0.865239i
$401$	21.6183	−	4.93424i	1.07957	−	0.246404i	0.354482	−	0.935063i	$-0.384657\pi$
$401$	21.6183	−	4.93424i	1.07957	−	0.246404i	0.725086	+	0.688659i	$0.241800\pi$
$402$		0			0
$403$	5.13683	−	1.79745i	0.255884	−	0.0895376i
$404$	−12.3895	+	19.7177i	−0.616399	+	0.980993i
$405$		0			0
$406$	14.6792	+	1.14085i	0.728517	+	0.0566196i
$407$			0.0634655i			0.00314587i
$408$		0			0
$409$	5.55810	+	15.8841i	0.274830	+	0.785420i	0.995724	+	0.0923748i	$0.0294458\pi$
$409$	5.55810	+	15.8841i	0.274830	+	0.785420i	−0.720894	+	0.693045i	$0.756268\pi$
$410$	6.34035	−	3.05335i	0.313127	−	0.150794i
$411$		0			0
$412$	−12.2778	−	2.80233i	−0.604884	−	0.138061i
$413$	9.37301	−	19.4633i	0.461216	−	0.957724i
$414$		0			0
$415$	−40.1071	+	31.9844i	−1.96878	+	1.57005i
$416$	7.22302	+	2.52744i	0.354138	+	0.123918i
$417$		0			0
$418$	1.65942	−	1.65942i	0.0811648	−	0.0811648i
$419$	0.592078	−	0.742442i	0.0289249	−	0.0362707i	−0.767159	−	0.641457i	$-0.778330\pi$
$419$	0.592078	−	0.742442i	0.0289249	−	0.0362707i	0.796084	+	0.605187i	$0.206902\pi$
$420$		0			0
$421$	−13.0848	−	20.8243i	−0.637714	−	1.01492i	−0.996668	−	0.0815612i	$-0.974009\pi$
$421$	−13.0848	−	20.8243i	−0.637714	−	1.01492i	0.358954	−	0.933355i	$-0.383133\pi$
$422$	−7.98010	−	6.36391i	−0.388465	−	0.309790i
$423$		0			0
$424$	3.75481	+	33.3248i	0.182350	+	1.61840i
$425$	18.2813	−	52.2449i	0.886773	−	2.53425i
$426$		0			0
$427$	−4.00424	+	35.5386i	−0.193779	+	1.71983i
$428$	15.7481	+	7.58387i	0.761211	+	0.366580i
$429$		0			0
$430$	1.68004	+	7.36074i	0.0810188	+	0.354966i
$431$	0.210702	+	0.437527i	0.0101491	+	0.0210749i	0.905982	−	0.423317i	$-0.139134\pi$
$431$	0.210702	+	0.437527i	0.0101491	+	0.0210749i	−0.895833	+	0.444392i	$0.853420\pi$
$432$		0			0
$433$	25.3408	+	15.9227i	1.21780	+	0.765195i	0.978599	−	0.205775i	$-0.0659714\pi$
$433$	25.3408	+	15.9227i	1.21780	+	0.765195i	0.239202	+	0.970970i	$0.423114\pi$
$434$	−11.1865			−0.536969
$435$		0			0
$436$	26.8024			1.28360
$437$	−6.24792	−	3.92583i	−0.298879	−	0.187798i
$438$		0			0
$439$	−9.93931	−	20.6392i	−0.474377	−	0.985055i	−0.991617	−	0.129214i	$-0.958755\pi$
$439$	−9.93931	−	20.6392i	−0.474377	−	0.985055i	0.517239	−	0.855841i	$-0.326960\pi$
$440$	1.15119	+	5.04369i	0.0548808	+	0.240448i
$441$		0			0
$442$	3.85245	+	1.85524i	0.183243	+	0.0882449i
$443$	−3.22774	+	28.6470i	−0.153354	+	1.36106i	0.647439	+	0.762117i	$0.275840\pi$
$443$	−3.22774	+	28.6470i	−0.153354	+	1.36106i	−0.800794	+	0.598941i	$0.795589\pi$
$444$		0			0
$445$	19.0338	−	54.3955i	0.902289	−	2.57859i
$446$	−0.448212	−	3.97799i	−0.0212234	−	0.188363i
$447$		0			0
$448$	−2.27840	−	1.81696i	−0.107644	−	0.0858434i
$449$	−6.74252	−	10.7307i	−0.318199	−	0.506411i	0.648879	−	0.760892i	$-0.275238\pi$
$449$	−6.74252	−	10.7307i	−0.318199	−	0.506411i	−0.967078	+	0.254481i	$0.918095\pi$
$450$		0			0
$451$	0.882816	−	1.10702i	0.0415702	−	0.0521274i
$452$	12.8137	−	12.8137i	0.602705	−	0.602705i
$453$		0			0
$454$	−6.67059	−	2.33414i	−0.313066	−	0.109547i
$455$	−17.3718	+	13.8535i	−0.814402	+	0.649464i
$456$		0			0
$457$	−0.653651	+	1.35732i	−0.0305765	+	0.0634928i	−0.915698	−	0.401868i	$-0.868361\pi$
$457$	−0.653651	+	1.35732i	−0.0305765	+	0.0634928i	0.885121	+	0.465361i	$0.154075\pi$
$458$	−12.0877	−	2.75893i	−0.564819	−	0.128916i
$459$		0			0
$460$	6.42252	−	3.09292i	0.299452	−	0.144208i
$461$	8.19989	+	23.4339i	0.381907	+	1.09143i	0.961091	+	0.276230i	$0.0890853\pi$
$461$	8.19989	+	23.4339i	0.381907	+	1.09143i	−0.579185	+	0.815196i	$0.696629\pi$
$462$		0			0
$463$		−	24.5107i		−	1.13911i	−0.821953	−	0.569555i	$-0.807116\pi$
$463$		−	24.5107i		−	1.13911i	0.821953	−	0.569555i	$-0.192884\pi$
$464$	−2.14406	−	8.09112i	−0.0995357	−	0.375621i
$465$		0			0
$466$	−8.92078	+	14.1973i	−0.413247	+	0.657679i
$467$	27.2756	−	9.54416i	1.26217	−	0.441651i	0.385481	−	0.922716i	$-0.374036\pi$
$467$	27.2756	−	9.54416i	1.26217	−	0.441651i	0.876685	+	0.481065i	$0.159750\pi$
$468$		0			0
$469$	56.9492	−	12.9983i	2.62967	−	0.600205i
$470$	−2.73578	+	11.9862i	−0.126192	+	0.552883i
$471$		0			0
$472$	12.2951	+	1.38533i	0.565928	+	0.0637648i
$473$	0.947144	+	1.18768i	0.0435497	+	0.0546096i
$474$		0			0
$475$	74.2594	−	8.36702i	3.40725	−	0.383905i
$476$	22.0437	+	22.0437i	1.01037	+	1.01037i
$477$		0			0
$478$	−15.4432	+	9.70362i	−0.706357	+	0.443833i
$479$	34.1452	−	21.4548i	1.56013	−	0.980296i	0.573153	−	0.819449i	$-0.305720\pi$
$479$	34.1452	−	21.4548i	1.56013	−	0.980296i	0.986979	−	0.160847i	$-0.0514227\pi$
$480$		0			0
$481$	−0.110394	−	0.110394i	−0.00503352	−	0.00503352i
$482$	−7.47757	+	0.842520i	−0.340594	+	0.0383757i
$483$		0			0
$484$	−10.4157	−	13.0608i	−0.473440	−	0.593674i
$485$	−4.87675	−	0.549478i	−0.221442	−	0.0249505i
$486$		0			0
$487$	−5.15038	+	22.5653i	−0.233386	+	1.02253i	0.713423	+	0.700734i	$0.247144\pi$
$487$	−5.15038	+	22.5653i	−0.233386	+	1.02253i	−0.946809	+	0.321797i	$0.895713\pi$
$488$	−19.9700	+	4.55803i	−0.904000	+	0.206332i
$489$		0			0
$490$	25.3526	−	8.87126i	1.14531	−	0.400763i
$491$	−3.36323	+	5.35254i	−0.151780	+	0.241557i	−0.913956	−	0.405813i	$-0.866988\pi$
$491$	−3.36323	+	5.35254i	−0.151780	+	0.241557i	0.762176	+	0.647370i	$0.224131\pi$
$492$		0			0
$493$	−3.81900	−	25.8213i	−0.171999	−	1.16293i
$494$			5.77288i			0.259734i
$495$		0			0
$496$	2.10044	+	6.00270i	0.0943124	+	0.269529i
$497$	−11.1024	+	5.34662i	−0.498010	+	0.239829i
$498$		0			0
$499$	−10.9765	−	2.50531i	−0.491374	−	0.112153i	−0.0303478	−	0.999539i	$-0.509661\pi$
$499$	−10.9765	−	2.50531i	−0.491374	−	0.112153i	−0.461026	+	0.887386i	$0.652519\pi$
$500$	−17.6084	+	36.5643i	−0.787473	+	1.63520i
$501$		0			0
$502$	8.61613	−	6.87114i	0.384557	−	0.306674i
$503$	24.2139	+	8.47280i	1.07964	+	0.377784i	0.810754	−	0.585387i	$-0.199058\pi$
$503$	24.2139	+	8.47280i	1.07964	+	0.377784i	0.268890	+	0.963171i	$0.413343\pi$
$504$		0			0
$505$	42.7676	−	42.7676i	1.90313	−	1.90313i
$506$	−0.252120	+	0.316149i	−0.0112081	+	0.0140545i
$507$		0			0
$508$	−10.6850	−	17.0050i	−0.474068	−	0.754475i
$509$	−19.8602	−	15.8380i	−0.880288	−	0.702006i	0.0751585	−	0.997172i	$-0.476054\pi$
$509$	−19.8602	−	15.8380i	−0.880288	−	0.702006i	−0.955446	+	0.295166i	$0.904625\pi$
$510$		0			0
$511$	6.36535	+	56.4941i	0.281587	+	2.49915i
$512$	−5.37774	+	15.3687i	−0.237665	+	0.679206i
$513$		0			0
$514$	−1.40478	+	12.4678i	−0.0619622	+	0.549930i
$515$	29.4695	+	14.1918i	1.29858	+	0.625365i
$516$		0			0
$517$	0.550451	+	2.41168i	0.0242088	+	0.106066i
$518$	0.139235	+	0.289125i	0.00611765	+	0.0127034i
$519$		0			0
$520$	−10.7755	−	6.77072i	−0.472539	−	0.296916i
$521$	6.74973			0.295711			0.147855	−	0.989009i	$-0.452763\pi$
$521$	6.74973			0.295711			0.147855	+	0.989009i	$0.452763\pi$
$522$		0			0
$523$	−13.9628			−0.610553			−0.305276	−	0.952264i	$-0.598749\pi$
$523$	−13.9628			−0.610553			−0.305276	+	0.952264i	$0.598749\pi$
$524$	−0.650223	−	0.408562i	−0.0284051	−	0.0178481i
$525$		0			0
$526$	9.08669	+	18.8687i	0.396198	+	0.822715i
$527$	4.41297	+	19.3345i	0.192232	+	0.842224i
$528$		0			0
$529$	−19.5767	−	9.42766i	−0.851163	−	0.409898i
$530$	4.27366	−	37.9298i	0.185636	−	1.64756i
$531$		0			0
$532$	−13.9010	+	39.7267i	−0.602684	+	1.72237i
$533$	0.389980	+	3.46117i	0.0168919	+	0.149920i
$534$		0			0
$535$	−35.4933	−	28.3049i	−1.53451	−	1.22373i
$536$	17.8000	+	28.3285i	0.768842	+	1.22360i
$537$		0			0
$538$	4.49442	−	5.63583i	0.193768	−	0.242978i
$539$	3.82144	−	3.82144i	0.164601	−	0.164601i
$540$		0			0
$541$	−26.5010	−	9.27311i	−1.13937	−	0.398682i	−0.306345	−	0.951921i	$-0.599106\pi$
$541$	−26.5010	−	9.27311i	−1.13937	−	0.398682i	−0.833023	+	0.553238i	$0.813392\pi$
$542$	1.73424	−	1.38301i	0.0744918	−	0.0594053i
$543$		0			0
$544$	−12.0992	+	25.1243i	−0.518750	+	1.07720i
$545$	−67.8675	−	15.4903i	−2.90712	−	0.663532i
$546$		0			0
$547$	−38.6354	+	18.6058i	−1.65193	+	0.795528i	−0.652649	+	0.757661i	$0.726342\pi$
$547$	−38.6354	+	18.6058i	−1.65193	+	0.795528i	−0.999283	+	0.0378678i	$0.987943\pi$
$548$	−1.79992	−	5.14388i	−0.0768888	−	0.219736i
$549$		0			0
$550$		−	4.09520i		−	0.174620i
$551$	29.1718	−	19.7711i	1.24276	−	0.842279i
$552$		0			0
$553$	11.2303	−	17.8729i	0.477560	−	0.760032i
$554$	−1.74496	+	0.610587i	−0.0741361	+	0.0259414i
$555$		0			0
$556$	8.21666	−	1.87540i	0.348464	−	0.0795347i
$557$	6.81818	−	29.8724i	0.288896	−	1.26573i	−0.597148	−	0.802131i	$-0.703699\pi$
$557$	6.81818	−	29.8724i	0.288896	−	1.26573i	0.886043	−	0.463603i	$-0.153444\pi$
$558$		0			0
$559$	−3.71338	−	0.418397i	−0.157059	−	0.0176963i
$560$	−16.1887	−	20.3000i	−0.684098	−	0.857831i
$561$		0			0
$562$	−1.14243	+	0.128721i	−0.0481906	+	0.00542977i
$563$	−25.1567	−	25.1567i	−1.06023	−	1.06023i	−0.998066	−	0.0621640i	$-0.980200\pi$
$563$	−25.1567	−	25.1567i	−1.06023	−	1.06023i	−0.0621640	−	0.998066i	$-0.519800\pi$
$564$		0			0
$565$	−39.8517	+	25.0405i	−1.67657	+	1.05346i
$566$	8.90722	−	5.59678i	0.374399	−	0.235250i
$567$		0			0
$568$	−4.99065	−	4.99065i	−0.209403	−	0.209403i
$569$	25.2658	−	2.84677i	1.05920	−	0.119343i	0.434860	−	0.900498i	$-0.356798\pi$
$569$	25.2658	−	2.84677i	1.05920	−	0.119343i	0.624336	+	0.781156i	$0.285369\pi$
$570$		0			0
$571$	−2.88233	−	3.61433i	−0.120622	−	0.151255i	0.717854	−	0.696193i	$-0.245124\pi$
$571$	−2.88233	−	3.61433i	−0.120622	−	0.151255i	−0.838476	+	0.544938i	$0.816553\pi$
$572$	−1.11505	−	0.125636i	−0.0466224	−	0.00525308i
$573$		0			0
$574$	1.59313	−	6.97995i	0.0664958	−	0.291337i
$575$	−12.5537	+	2.86529i	−0.523524	+	0.119491i
$576$		0			0
$577$	−21.5333	+	7.53483i	−0.896443	+	0.313679i	−0.738886	−	0.673831i	$-0.764648\pi$
$577$	−21.5333	+	7.53483i	−0.896443	+	0.313679i	−0.157557	+	0.987510i	$0.550362\pi$
$578$	−2.29141	+	3.64675i	−0.0953100	+	0.151685i
$579$		0			0
$580$	1.17895	+	34.0238i	0.0489531	+	1.41276i
$581$			52.1897i			2.16519i
$582$		0			0
$583$	−2.53652	−	7.24896i	−0.105052	−	0.300221i
$584$	−29.3372	+	14.1280i	−1.21398	+	0.584622i
$585$		0			0
$586$	−6.99092	−	1.59563i	−0.288792	−	0.0659150i
$587$	−4.13272	+	8.58169i	−0.170576	+	0.354204i	−0.968679	−	0.248317i	$-0.920123\pi$
$587$	−4.13272	+	8.58169i	−0.170576	+	0.354204i	0.798103	+	0.602521i	$0.205837\pi$
$588$		0			0
$589$	−20.9333	+	16.6938i	−0.862543	+	0.687855i
$590$	−13.2924	−	4.65120i	−0.547238	−	0.191487i
$591$		0			0
$592$	0.129002	−	0.129002i	0.00530194	−	0.00530194i
$593$	0.358513	−	0.449561i	0.0147223	−	0.0184612i	−0.774416	−	0.632677i	$-0.781956\pi$
$593$	0.358513	−	0.449561i	0.0147223	−	0.0184612i	0.789138	+	0.614216i	$0.210528\pi$
$594$		0			0
$595$	−43.0777	−	68.5578i	−1.76601	−	2.81060i
$596$	1.41036	+	1.12473i	0.0577707	+	0.0460706i
$597$		0			0
$598$	−0.111373	−	0.988464i	−0.00455439	−	0.0404213i
$599$	8.41878	−	24.0595i	0.343982	−	0.983044i	−0.633814	−	0.773486i	$-0.718512\pi$
$599$	8.41878	−	24.0595i	0.343982	−	0.983044i	0.977796	−	0.209559i	$-0.0672028\pi$
$600$		0			0
$601$	2.55298	−	22.6583i	0.104138	−	0.924253i	−0.827648	−	0.561247i	$-0.810322\pi$
$601$	2.55298	−	22.6583i	0.104138	−	0.924253i	0.931787	−	0.363006i	$-0.118250\pi$
$602$	6.92046	+	3.33272i	0.282057	+	0.135831i
$603$		0			0
$604$	−4.06630	−	17.8156i	−0.165456	−	0.724908i
$605$	18.8255	+	39.0916i	0.765365	+	1.58930i
$606$		0			0
$607$	26.6597	+	16.7514i	1.08208	+	0.679919i	0.950293	−	0.311358i	$-0.100784\pi$
$607$	26.6597	+	16.7514i	1.08208	+	0.679919i	0.131792	+	0.991277i	$0.457927\pi$
$608$	−37.6486			−1.52685
$609$		0			0
$610$	23.3141			0.943960
$611$	−5.15242	−	3.23748i	−0.208445	−	0.130974i
$612$		0			0
$613$	−16.3387	−	33.9277i	−0.659914	−	1.37033i	−0.915019	−	0.403412i	$-0.867824\pi$
$613$	−16.3387	−	33.9277i	−0.659914	−	1.37033i	0.255105	−	0.966913i	$-0.417890\pi$
$614$	−2.26796	−	9.93658i	−0.0915274	−	0.401008i
$615$		0			0
$616$	4.74200	+	2.28363i	0.191061	+	0.0920100i
$617$	0.532966	−	4.73020i	0.0214564	−	0.190431i	−0.978412	−	0.206665i	$-0.933739\pi$
$617$	0.532966	−	4.73020i	0.0214564	−	0.190431i	0.999868	+	0.0162339i	$0.00516764\pi$
$618$		0			0
$619$	−8.97421	+	25.6468i	−0.360704	+	1.03083i	0.610383	+	0.792106i	$0.291016\pi$
$619$	−8.97421	+	25.6468i	−0.360704	+	1.03083i	−0.971087	+	0.238726i	$0.923270\pi$
$620$	−2.89606	−	25.7032i	−0.116309	−	1.03227i
$621$		0			0
$622$	−5.85394	−	4.66836i	−0.234722	−	0.187184i
$623$	−31.1931	−	49.6436i	−1.24973	−	1.98893i
$624$		0			0
$625$	30.1194	−	37.7685i	1.20478	−	1.51074i
$626$	3.75854	−	3.75854i	0.150221	−	0.150221i
$627$		0			0
$628$	−1.83758	−	0.642996i	−0.0733273	−	0.0256583i
$629$	0.444791	−	0.354709i	0.0177350	−	0.0141432i
$630$		0			0
$631$	0.961079	−	1.99570i	0.0382600	−	0.0794476i	−0.880963	−	0.473186i	$-0.843104\pi$
$631$	0.961079	−	1.99570i	0.0382600	−	0.0794476i	0.919223	+	0.393738i	$0.128818\pi$
$632$	11.7867	+	2.69023i	0.468849	+	0.107012i
$633$		0			0
$634$	9.82780	−	4.73282i	0.390312	−	0.187964i
$635$	17.2279	+	49.2344i	0.683667	+	1.95381i
$636$		0			0
$637$			13.2942i			0.526737i
$638$	−0.897667	−	1.70989i	−0.0355390	−	0.0676952i
$639$		0			0
$640$	23.7951	−	37.8697i	0.940584	−	1.49693i
$641$	−4.96248	+	1.73645i	−0.196006	+	0.0685855i	−0.426497	−	0.904489i	$-0.640253\pi$
$641$	−4.96248	+	1.73645i	−0.196006	+	0.0685855i	0.230491	+	0.973074i	$0.425967\pi$
$642$		0			0
$643$	−19.5291	+	4.45740i	−0.770154	+	0.175783i	−0.589505	−	0.807765i	$-0.700677\pi$
$643$	−19.5291	+	4.45740i	−0.770154	+	0.175783i	−0.180649	+	0.983548i	$0.557820\pi$
$644$	1.61377	−	7.07041i	0.0635916	−	0.278613i
$645$		0			0
$646$	−20.9043	−	2.35535i	−0.822471	−	0.0926702i
$647$	−2.13062	−	2.67172i	−0.0837634	−	0.105036i	0.738184	−	0.674600i	$-0.235684\pi$
$647$	−2.13062	−	2.67172i	−0.0837634	−	0.105036i	−0.821947	+	0.569564i	$0.807112\pi$
$648$		0			0
$649$	−2.81568	+	0.317250i	−0.110525	+	0.0124532i
$650$	7.12332	+	7.12332i	0.279399	+	0.279399i
$651$		0			0
$652$	−17.5212	+	11.0093i	−0.686185	+	0.431159i
$653$	−2.06425	+	1.29705i	−0.0807802	+	0.0507575i	−0.571817	−	0.820382i	$-0.693761\pi$
$653$	−2.06425	+	1.29705i	−0.0807802	+	0.0507575i	0.491036	+	0.871139i	$0.336618\pi$
$654$		0			0
$655$	1.41033	+	1.41033i	0.0551061	+	0.0551061i
$656$	−4.04459	+	0.455716i	−0.157915	+	0.0177927i
$657$		0			0
$658$	7.79858	+	9.77911i	0.304020	+	0.381230i
$659$	−38.6654	−	4.35655i	−1.50619	−	0.169707i	−0.680048	−	0.733168i	$-0.738041\pi$
$659$	−38.6654	−	4.35655i	−1.50619	−	0.169707i	−0.826143	+	0.563461i	$0.809470\pi$
$660$		0			0
$661$	−9.84055	+	43.1143i	−0.382753	+	1.67695i	0.306060	+	0.952012i	$0.400989\pi$
$661$	−9.84055	+	43.1143i	−0.382753	+	1.67695i	−0.688813	+	0.724939i	$0.741868\pi$
$662$	−3.06803	+	0.700258i	−0.119242	+	0.0272163i
$663$		0			0
$664$	−28.2143	+	9.87261i	−1.09493	+	0.383131i
$665$	58.1591	−	92.5596i	2.25531	−	3.58931i
$666$		0			0
$667$	−4.61352	+	3.94812i	−0.178636	+	0.152872i
$668$			0.773784i			0.0299386i
$669$		0			0
$670$	−12.5769	−	35.9428i	−0.485890	−	1.38859i
$671$	4.22636	−	2.03531i	0.163157	−	0.0785721i
$672$		0			0
$673$	15.6749	+	3.57770i	0.604224	+	0.137910i	0.513679	−	0.857982i	$-0.328282\pi$
$673$	15.6749	+	3.57770i	0.604224	+	0.137910i	0.0905444	+	0.995892i	$0.471139\pi$
$674$	−2.76482	+	5.74120i	−0.106497	+	0.221143i
$675$		0			0
$676$	−13.6989	+	10.9245i	−0.526882	+	0.420174i
$677$	−14.2726	−	4.99419i	−0.548539	−	0.191942i	0.0417586	−	0.999128i	$-0.486704\pi$
$677$	−14.2726	−	4.99419i	−0.548539	−	0.191942i	−0.590298	+	0.807186i	$0.700990\pi$
$678$		0			0
$679$	−3.53046	+	3.53046i	−0.135487	+	0.135487i
$680$	28.9141	−	36.2572i	1.10881	−	1.39040i
$681$		0			0
$682$	0.780635	+	1.24237i	0.0298921	+	0.0475729i
$683$	−29.4103	−	23.4539i	−1.12535	−	0.897439i	−0.129790	−	0.991541i	$-0.541430\pi$
$683$	−29.4103	−	23.4539i	−1.12535	−	0.897439i	−0.995563	+	0.0941026i	$0.970002\pi$
$684$		0			0
$685$	1.58478	+	14.0653i	0.0605512	+	0.537407i
$686$	2.70423	−	7.72824i	0.103248	−	0.295066i
$687$		0			0
$688$	0.488922	−	4.33931i	0.0186400	−	0.165435i
$689$	17.0211	+	8.19695i	0.648454	+	0.312279i
$690$		0			0
$691$	4.75600	+	20.8374i	0.180927	+	0.792693i	0.981190	+	0.193044i	$0.0618359\pi$
$691$	4.75600	+	20.8374i	0.180927	+	0.792693i	−0.800263	+	0.599649i	$0.795307\pi$
$692$	−15.4151	−	32.0097i	−0.585993	−	1.21683i
$693$		0			0
$694$	−1.77280	−	1.11392i	−0.0672945	−	0.0422839i
$695$	−21.8896			−0.830321
$696$		0			0
$697$	−12.6925			−0.480761
$698$	7.60751	+	4.78011i	0.287948	+	0.180930i
$699$		0			0
$700$	31.8671	+	66.1727i	1.20446	+	2.50109i
$701$	4.53501	+	19.8692i	0.171285	+	0.750449i	0.985471	+	0.169845i	$0.0543266\pi$
$701$	4.53501	+	19.8692i	0.171285	+	0.750449i	−0.814186	+	0.580605i	$0.802816\pi$
$702$		0			0
$703$	0.692018	+	0.333258i	0.0261000	+	0.0125691i
$704$	−0.0427970	+	0.379834i	−0.00161297	+	0.0143155i
$705$		0			0
$706$	−4.04182	+	11.5508i	−0.152116	+	0.434722i
$707$	−6.88948	−	61.1458i	−0.259106	−	2.29963i
$708$		0			0
$709$	14.5947	+	11.6389i	0.548116	+	0.437108i	0.857988	−	0.513670i	$-0.171715\pi$
$709$	14.5947	+	11.6389i	0.548116	+	0.437108i	−0.309871	+	0.950779i	$0.600286\pi$
$710$	4.27388	+	6.80185i	0.160396	+	0.255269i
$711$		0			0
$712$	20.9371	−	26.2543i	0.784651	−	0.983921i
$713$	3.26226	−	3.26226i	0.122172	−	0.122172i
$714$		0			0
$715$	2.75084	+	0.962562i	0.102876	+	0.0359978i
$716$	10.6889	−	8.52411i	0.399463	−	0.318561i
$717$		0			0
$718$	4.40510	−	9.14728i	0.164397	−	0.341374i
$719$	36.8464	+	8.40995i	1.37414	+	0.313638i	0.844940	−	0.534860i	$-0.179636\pi$
$719$	36.8464	+	8.40995i	1.37414	+	0.313638i	0.529198	+	0.848499i	$0.322493\pi$
$720$		0			0
$721$	29.9813	−	14.4382i	1.11656	−	0.537707i
$722$	−5.21853	−	14.9137i	−0.194214	−	0.555030i
$723$		0			0
$724$		−	3.01165i		−	0.111927i
$725$	11.5997	−	60.3921i	0.430803	−	2.24290i
$726$		0			0
$727$	26.5998	−	42.3334i	0.986534	−	1.57006i	0.175981	−	0.984394i	$-0.443690\pi$
$727$	26.5998	−	42.3334i	0.986534	−	1.57006i	0.810553	−	0.585666i	$-0.199167\pi$
$728$	−12.2206	+	4.27617i	−0.452925	+	0.158485i
$729$		0			0
$730$	36.1321	−	8.24692i	1.33731	−	0.305232i
$731$	3.03014	−	13.2759i	0.112074	−	0.491027i
$732$		0			0
$733$	18.5172	+	2.08639i	0.683948	+	0.0770625i	0.447100	−	0.894484i	$-0.352457\pi$
$733$	18.5172	+	2.08639i	0.683948	+	0.0770625i	0.236849	+	0.971547i	$0.423885\pi$
$734$	4.66248	+	5.84656i	0.172095	+	0.215801i
$735$		0			0
$736$	6.44640	−	0.726335i	0.237617	−	0.0267731i
$737$	−5.41772	−	5.41772i	−0.199564	−	0.199564i
$738$		0			0
$739$	5.79153	−	3.63906i	0.213045	−	0.133865i	−0.421283	−	0.906929i	$-0.638420\pi$
$739$	5.79153	−	3.63906i	0.213045	−	0.133865i	0.634328	+	0.773064i	$0.281277\pi$
$740$	−0.628278	+	0.394773i	−0.0230960	+	0.0145122i
$741$		0			0
$742$	−27.4588	−	27.4588i	−1.00804	−	1.00804i
$743$	−4.77591	+	0.538116i	−0.175211	+	0.0197415i	−0.199134	−	0.979972i	$-0.563813\pi$
$743$	−4.77591	+	0.538116i	−0.175211	+	0.0197415i	0.0239230	+	0.999714i	$0.492384\pi$
$744$		0			0
$745$	−2.92121	−	3.66308i	−0.107025	−	0.134205i
$746$	17.0565	+	1.92181i	0.624484	+	0.0703624i
$747$		0			0
$748$	0.909885	−	3.98647i	0.0332687	−	0.145760i
$749$	−45.0279	+	10.2773i	−1.64528	+	0.375525i
$750$		0			0
$751$	41.9736	−	14.6872i	1.53164	−	0.535944i	0.572752	−	0.819729i	$-0.305876\pi$
$751$	41.9736	−	14.6872i	1.53164	−	0.535944i	0.958888	+	0.283785i	$0.0915900\pi$
$752$	3.78319	−	6.02092i	0.137959	−	0.219560i
$753$		0			0
$754$	4.53566	+	1.41280i	0.165179	+	0.0514512i
$755$			47.4618i			1.72731i
$756$		0			0
$757$	−12.0529	−	34.4452i	−0.438070	−	1.25193i	−0.925493	−	0.378765i	$-0.876349\pi$
$757$	−12.0529	−	34.4452i	−0.438070	−	1.25193i	0.487423	−	0.873166i	$-0.337937\pi$
$758$	−9.05234	+	4.35938i	−0.328796	+	0.158340i
$759$		0			0
$760$	61.0405	+	13.9321i	2.21417	+	0.505370i
$761$	2.75922	−	5.72957i	0.100022	−	0.207697i	−0.844953	−	0.534840i	$-0.820372\pi$
$761$	2.75922	−	5.72957i	0.100022	−	0.207697i	0.944975	+	0.327143i	$0.106086\pi$
$762$		0			0
$763$	−55.3705	+	44.1565i	−2.00455	+	1.59857i
$764$	−15.0347	−	5.26088i	−0.543938	−	0.190332i
$765$		0			0
$766$	13.3094	−	13.3094i	0.480888	−	0.480888i
$767$	4.34583	−	5.44950i	0.156919	−	0.196770i
$768$		0			0
$769$	3.51156	+	5.58861i	0.126630	+	0.201531i	0.904022	−	0.427486i	$-0.140601\pi$
$769$	3.51156	+	5.58861i	0.126630	+	0.201531i	−0.777392	+	0.629016i	$0.783458\pi$
$770$	−4.68358	−	3.73503i	−0.168784	−	0.134601i
$771$		0			0
$772$	0.647609	+	5.74769i	0.0233080	+	0.206864i
$773$	7.68076	−	21.9504i	0.276258	−	0.789500i	−0.719244	−	0.694758i	$-0.755512\pi$
$773$	7.68076	−	21.9504i	0.276258	−	0.789500i	0.995502	−	0.0947420i	$-0.0302026\pi$
$774$		0			0
$775$	−5.23131	+	46.4291i	−0.187914	+	1.66778i
$776$	−2.57645	−	1.24075i	−0.0924892	−	0.0445405i
$777$		0			0
$778$	3.18244	+	13.9432i	0.114096	+	0.499887i
$779$	−7.43506	−	15.4391i	−0.266389	−	0.553161i
$780$		0			0
$781$	1.36856	+	0.859925i	0.0489710	+	0.0307705i
$782$	3.62480			0.129623
$783$		0			0
$784$	−15.5351			−0.554826
$785$	4.28139	+	2.69018i	0.152809	+	0.0960165i
$786$		0			0
$787$	13.9613	+	28.9909i	0.497666	+	1.03341i	0.986911	+	0.161268i	$0.0515583\pi$
$787$	13.9613	+	28.9909i	0.497666	+	1.03341i	−0.489244	+	0.872147i	$0.662727\pi$
$788$	5.33704	+	23.3831i	0.190124	+	0.832989i
$789$		0			0
$790$	−12.3977	−	5.97042i	−0.441090	−	0.212418i
$791$	−5.36119	+	47.5819i	−0.190622	+	1.69182i
$792$		0			0
$793$	−3.81117	+	10.8917i	−0.135339	+	0.386776i
$794$	−0.675758	−	5.99752i	−0.0239818	−	0.212844i
$795$		0			0
$796$	−7.86073	−	6.26873i	−0.278616	−	0.222189i
$797$	2.71716	+	4.32434i	0.0962468	+	0.153176i	0.891377	−	0.453263i	$-0.149740\pi$
$797$	2.71716	+	4.32434i	0.0962468	+	0.153176i	−0.795130	+	0.606439i	$0.792597\pi$
$798$		0			0
$799$	13.8255	−	17.3367i	0.489113	−	0.613328i
$800$	−46.4557	+	46.4557i	−1.64246	+	1.64246i
$801$		0			0
$802$	−13.8811	−	4.85720i	−0.490158	−	0.171514i
$803$	5.83004	−	4.64930i	0.205738	−	0.164070i
$804$		0			0
$805$	−8.17261	+	16.9706i	−0.288047	+	0.598135i
$806$	−3.51888	−	0.803161i	−0.123947	−	0.0282901i
$807$		0			0
$808$	31.7528	−	15.2913i	1.11706	−	0.537948i
$809$	−2.02647	−	5.79133i	−0.0712470	−	0.203612i	0.902753	−	0.430158i	$-0.141542\pi$
$809$	−2.02647	−	5.79133i	−0.0712470	−	0.203612i	−0.974000	+	0.226546i	$0.927257\pi$
$810$		0			0
$811$			15.2737i			0.536332i	0.963373	+	0.268166i	$0.0864176\pi$
$811$			15.2737i			0.536332i	−0.963373	+	0.268166i	$0.913582\pi$
$812$	27.8106	+	20.6441i	0.975962	+	0.724467i
$813$		0			0
$814$	0.0223939	−	0.0356398i	0.000784907	−	0.00124917i
$815$	50.7291	−	17.7509i	1.77696	−	0.621786i
$816$		0			0
$817$	17.9238	−	4.09098i	0.627073	−	0.143125i
$818$	2.48354	−	10.8811i	0.0868350	−	0.380449i
$819$		0			0
$820$	16.4503	+	1.85350i	0.574469	+	0.0647271i
$821$	32.3595	+	40.5775i	1.12935	+	1.41616i	0.896158	+	0.443735i	$0.146347\pi$
$821$	32.3595	+	40.5775i	1.12935	+	1.41616i	0.233196	+	0.972430i	$0.425082\pi$
$822$		0			0
$823$	47.3526	−	5.33535i	1.65061	−	0.185979i	0.762942	−	0.646468i	$-0.223754\pi$
$823$	47.3526	−	5.33535i	1.65061	−	0.185979i	0.887666	+	0.460489i	$0.152326\pi$
$824$	13.4769	+	13.4769i	0.469491	+	0.469491i
$825$		0			0
$826$	−12.1312	+	7.62252i	−0.422097	+	0.265221i
$827$	15.3143	−	9.62258i	0.532529	−	0.334610i	−0.238777	−	0.971074i	$-0.576747\pi$
$827$	15.3143	−	9.62258i	0.532529	−	0.334610i	0.771306	+	0.636464i	$0.219604\pi$
$828$		0			0
$829$	−32.0906	−	32.0906i	−1.11455	−	1.11455i	−0.992527	−	0.122025i	$-0.961061\pi$
$829$	−32.0906	−	32.0906i	−1.11455	−	1.11455i	−0.122025	−	0.992527i	$-0.538939\pi$
$830$	33.8083	−	3.80929i	1.17350	−	0.132222i
$831$		0			0
$832$	−0.586251	−	0.735136i	−0.0203246	−	0.0254863i
$833$	−48.1402	−	5.42410i	−1.66796	−	0.187934i
$834$		0			0
$835$	0.447204	−	1.95933i	0.0154761	−	0.0678054i
$836$	5.38212	−	1.22843i	0.186144	−	0.0424862i
$837$		0			0
$838$	−0.594460	+	0.208011i	−0.0205353	+	0.00718561i
$839$	1.76116	−	2.80288i	0.0608021	−	0.0967661i	−0.814940	−	0.579546i	$-0.803230\pi$
$839$	1.76116	−	2.80288i	0.0608021	−	0.0967661i	0.875742	+	0.482780i	$0.160373\pi$
$840$		0			0
$841$	−8.39463	−	27.7584i	−0.289470	−	0.957187i
$842$			16.3111i			0.562119i
$843$		0			0
$844$	−7.93023	−	22.6633i	−0.272970	−	0.780103i
$845$	41.0014	−	19.7452i	1.41049	−	0.679257i
$846$		0			0
$847$	43.0350	+	9.82246i	1.47870	+	0.337504i
$848$	−9.57864	+	19.8903i	−0.328932	+	0.683034i
$849$		0			0
$850$	−28.7008	+	22.8881i	−0.984429	+	0.785056i
$851$	−0.124921	−	0.0437116i	−0.00428222	−	0.00149841i
$852$		0			0
$853$	3.88408	−	3.88408i	0.132988	−	0.132988i	−0.637479	−	0.770468i	$-0.720023\pi$
$853$	3.88408	−	3.88408i	0.132988	−	0.132988i	0.770468	+	0.637479i	$0.220023\pi$
$854$	14.7885	−	18.5442i	0.506052	−	0.634569i
$855$		0			0
$856$	−14.0739	−	22.3984i	−0.481034	−	0.765562i
$857$	3.88843	+	3.10092i	0.132826	+	0.105925i	0.687649	−	0.726043i	$-0.258643\pi$
$857$	3.88843	+	3.10092i	0.132826	+	0.105925i	−0.554823	+	0.831968i	$0.687214\pi$
$858$		0			0
$859$	0.628263	+	5.57599i	0.0214361	+	0.190250i	0.999867	−	0.0163252i	$-0.00519669\pi$
$859$	0.628263	+	5.57599i	0.0214361	+	0.190250i	−0.978431	+	0.206575i	$0.933768\pi$
$860$	−5.86597	+	16.7640i	−0.200028	+	0.571647i
$861$		0			0
$862$	0.0360604	−	0.320045i	0.00122822	−	0.0109008i
$863$	−9.32653	−	4.49142i	−0.317479	−	0.152890i	0.268357	−	0.963320i	$-0.413519\pi$
$863$	−9.32653	−	4.49142i	−0.317479	−	0.152890i	−0.585836	+	0.810430i	$0.699234\pi$
$864$		0			0
$865$	20.5333	+	89.9622i	0.698153	+	3.05881i
$866$	−8.61205	−	17.8831i	−0.292650	−	0.607693i
$867$		0			0
$868$	−22.2816	−	14.0004i	−0.756286	−	0.475206i
$869$	−2.76866			−0.0939202
$870$		0			0
$871$	18.8475			0.638622
$872$	−34.3458	−	21.5809i	−1.16310	−	0.730821i
$873$		0			0
$874$	2.12335	+	4.40919i	0.0718234	+	0.149143i
$875$	−23.8622	−	104.547i	−0.806689	−	3.53433i
$876$		0			0
$877$	4.27851	+	2.06042i	0.144475	+	0.0695755i	0.504724	−	0.863281i	$-0.331594\pi$
$877$	4.27851	+	2.06042i	0.144475	+	0.0695755i	−0.360249	+	0.932856i	$0.617308\pi$
$878$	−1.70105	+	15.0973i	−0.0574078	+	0.509508i
$879$		0			0
$880$	−1.12481	+	3.21453i	−0.0379174	+	0.108362i
$881$	3.38332	+	30.0278i	0.113987	+	1.01166i	0.912329	+	0.409458i	$0.134282\pi$
$881$	3.38332	+	30.0278i	0.113987	+	1.01166i	−0.798342	+	0.602204i	$0.794289\pi$
$882$		0			0
$883$	−26.5058	−	21.1376i	−0.891990	−	0.711338i	0.0660976	−	0.997813i	$-0.478945\pi$
$883$	−26.5058	−	21.1376i	−0.891990	−	0.711338i	−0.958088	+	0.286475i	$0.907517\pi$
$884$	5.35150	+	8.51686i	0.179990	+	0.286453i
$885$		0			0
$886$	11.9207	−	14.9481i	0.400484	−	0.502191i
$887$	14.0492	−	14.0492i	0.471726	−	0.471726i	−0.430747	−	0.902473i	$-0.641750\pi$
$887$	14.0492	−	14.0492i	0.471726	−	0.471726i	0.902473	+	0.430747i	$0.141750\pi$
$888$		0			0
$889$	50.0893	+	17.5270i	1.67994	+	0.587837i
$890$	−29.8822	+	23.8303i	−1.00165	+	0.798793i
$891$		0			0
$892$	4.08588	−	8.48442i	0.136805	−	0.284080i
$893$	29.1871	+	6.66175i	0.976707	+	0.222927i
$894$		0			0
$895$	−31.9922	+	15.4067i	−1.06938	+	0.514988i
$896$	−15.0282	−	42.9482i	−0.502057	−	1.43480i
$897$		0			0
$898$			8.40503i			0.280479i
$899$	7.99300	+	20.5325i	0.266581	+	0.684796i
$900$		0			0
$901$	−36.6269	+	58.2914i	−1.22022	+	1.94197i
$902$	−0.886368	+	0.310154i	−0.0295128	+	0.0103270i
$903$		0			0
$904$	−26.7374	+	6.10264i	−0.889273	+	0.202971i
$905$	−1.74057	+	7.62593i	−0.0578584	+	0.253494i
$906$		0			0
$907$	−35.8138	−	4.03525i	−1.18918	−	0.133988i	−0.504879	−	0.863190i	$-0.668463\pi$
$907$	−35.8138	−	4.03525i	−1.18918	−	0.133988i	−0.684299	+	0.729202i	$0.739892\pi$
$908$	−10.3654	−	12.9978i	−0.343987	−	0.431346i
$909$		0			0
$910$	14.6436	−	1.64993i	0.485429	−	0.0546948i
$911$	24.0144	+	24.0144i	0.795632	+	0.795632i	0.982403	−	0.186772i	$-0.0598025\pi$
$911$	24.0144	+	24.0144i	0.795632	+	0.795632i	−0.186772	+	0.982403i	$0.559802\pi$
$912$		0			0
$913$	5.79619	−	3.64199i	0.191826	−	0.120532i
$914$	0.845998	−	0.531576i	0.0279831	−	0.0175830i
$915$		0			0
$916$	−20.6236	−	20.6236i	−0.681423	−	0.681423i
$917$	2.01638	−	0.227191i	0.0665867	−	0.00750252i
$918$		0			0
$919$	10.9781	+	13.7661i	0.362135	+	0.454103i	0.929204	−	0.369567i	$-0.120494\pi$
$919$	10.9781	+	13.7661i	0.362135	+	0.454103i	−0.567069	+	0.823670i	$0.691923\pi$
$920$	−10.7205	−	1.20791i	−0.353444	−	0.0398235i
$921$		0			0
$922$	3.66398	−	16.0529i	0.120667	−	0.528675i
$923$	−3.87629	+	0.884739i	−0.127590	+	0.0291215i
$924$		0			0
$925$	1.26512	−	0.442684i	0.0415968	−	0.0145554i
$926$	−8.64866	+	13.7643i	−0.284213	+	0.452322i
$927$		0			0
$928$	−9.21378	+	29.5799i	−0.302457	+	0.971008i
$929$		−	37.1827i		−	1.21993i	−0.792430	−	0.609963i	$-0.791184\pi$
$929$		−	37.1827i		−	1.21993i	0.792430	−	0.609963i	$-0.208816\pi$
$930$		0			0
$931$	−21.6020	−	61.7348i	−0.707975	−	2.02328i
$932$	−35.5373	+	17.1139i	−1.16406	+	0.560584i
$933$		0			0
$934$	−18.6846	−	4.26464i	−0.611379	−	0.139543i
$935$	−4.60792	+	9.56844i	−0.150695	+	0.312921i
$936$		0			0
$937$	−30.9134	+	24.6526i	−1.00990	+	0.805366i	−0.980959	−	0.194215i	$-0.937784\pi$
$937$	−30.9134	+	24.6526i	−1.00990	+	0.805366i	−0.0289385	+	0.999581i	$0.509213\pi$
$938$	−36.5669	−	12.7953i	−1.19395	−	0.417782i
$939$		0			0
$940$	−20.4505	+	20.4505i	−0.667023	+	0.667023i
$941$	15.3585	−	19.2589i	0.500672	−	0.627822i	−0.465709	−	0.884938i	$-0.654201\pi$
$941$	15.3585	−	19.2589i	0.500672	−	0.627822i	0.966381	+	0.257116i	$0.0827721\pi$
$942$		0			0
$943$	1.57093	+	2.50012i	0.0511565	+	0.0814151i
$944$	6.36808	+	5.07837i	0.207263	+	0.165287i
$945$		0			0
$946$	−0.112803	−	1.00116i	−0.00366755	−	0.0325504i
$947$	−10.2116	+	29.1832i	−0.331834	+	0.948327i	0.650223	+	0.759743i	$0.274675\pi$
$947$	−10.2116	+	29.1832i	−0.331834	+	0.948327i	−0.982057	+	0.188584i	$0.939610\pi$
$948$		0			0
$949$	−2.05381	+	18.2281i	−0.0666695	+	0.591708i
$950$	−44.6535	−	21.5040i	−1.44875	−	0.697681i
$951$		0			0
$952$	−10.4985	−	45.9970i	−0.340259	−	1.49077i
$953$	−18.3588	−	38.1225i	−0.594701	−	1.23491i	−0.953471	−	0.301484i	$-0.902518\pi$
$953$	−18.3588	−	38.1225i	−0.594701	−	1.23491i	0.358770	−	0.933426i	$-0.383196\pi$
$954$		0			0
$955$	35.0296	+	22.0105i	1.13353	+	0.712244i
$956$	−42.9048			−1.38764
$957$		0			0
$958$	−26.7450			−0.864091
$959$	12.1929	+	7.66129i	0.393728	+	0.247396i
$960$		0			0
$961$	6.18703	+	12.8475i	0.199581	+	0.414435i
$962$	0.0230401	+	0.100945i	0.000742844	+	0.00325461i
$963$		0			0
$964$	−15.9485	−	7.68038i	−0.513666	−	0.247369i
$965$	1.68201	−	14.9282i	0.0541458	−	0.480557i
$966$		0			0
$967$	−4.59839	+	13.1414i	−0.147874	+	0.422600i	−0.993865	−	0.110597i	$-0.964724\pi$
$967$	−4.59839	+	13.1414i	−0.147874	+	0.422600i	0.845991	+	0.533197i	$0.179010\pi$
$968$	2.83071	+	25.1233i	0.0909826	+	0.807493i
$969$		0			0
$970$	2.54471	+	2.02934i	0.0817056	+	0.0651581i
$971$	20.4384	+	32.5275i	0.655899	+	1.04386i	0.994682	+	0.102993i	$0.0328419\pi$
$971$	20.4384	+	32.5275i	0.655899	+	1.04386i	−0.338783	+	0.940865i	$0.610015\pi$
$972$		0			0
$973$	−13.8849	+	17.4112i	−0.445131	+	0.558176i
$974$	10.8545	−	10.8545i	0.347799	−	0.347799i
$975$		0			0
$976$	−12.7276	−	4.45359i	−0.407402	−	0.142556i
$977$	10.3154	−	8.22623i	0.330018	−	0.263181i	−0.444436	−	0.895810i	$-0.646596\pi$
$977$	10.3154	−	8.22623i	0.330018	−	0.263181i	0.774454	+	0.632630i	$0.218025\pi$
$978$		0			0
$979$	−3.33665	+	6.92863i	−0.106640	+	0.221440i
$980$	61.6008	+	14.0600i	1.96777	+	0.449130i
$981$		0			0
$982$	3.77731	−	1.81906i	0.120539	−	0.0580485i
$983$	1.21002	+	3.45804i	0.0385937	+	0.110294i	0.961568	−	0.274568i	$-0.0885347\pi$
$983$	1.21002	+	3.45804i	0.0385937	+	0.110294i	−0.922974	+	0.384862i	$0.874249\pi$
$984$		0			0
$985$		−	62.2939i		−	1.98485i
$986$	−6.96651	+	15.8478i	−0.221859	+	0.504696i
$987$		0			0
$988$	−7.22504	+	11.4986i	−0.229859	+	0.365819i
$989$	−2.99008	+	1.04627i	−0.0950790	+	0.0332696i
$990$		0			0
$991$	−5.42316	+	1.23780i	−0.172272	+	0.0393201i	−0.307787	−	0.951455i	$-0.599588\pi$
$991$	−5.42316	+	1.23780i	−0.172272	+	0.0393201i	0.135515	+	0.990775i	$0.456731\pi$
$992$	5.23792	−	22.9488i	0.166304	−	0.728627i
$993$		0			0
$994$	8.12123	+	0.915043i	0.257590	+	0.0290234i
$995$	16.2815	+	20.4164i	0.516158	+	0.647242i
$996$		0			0
$997$	14.8919	−	1.67792i	0.471633	−	0.0531402i	0.127050	−	0.991896i	$-0.459449\pi$
$997$	14.8919	−	1.67792i	0.471633	−	0.0531402i	0.344582	+	0.938756i	$0.388021\pi$
$998$	5.27995	+	5.27995i	0.167134	+	0.167134i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.v.b.26.9	✓	240
3.2	odd	2	inner	783.2.v.b.26.12	yes	240
29.19	odd	28	inner	783.2.v.b.512.12	yes	240
87.77	even	28	inner	783.2.v.b.512.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.v.b.26.9	✓	240	1.1	even	1	trivial
783.2.v.b.26.12	yes	240	3.2	odd	2	inner
783.2.v.b.512.9	yes	240	87.77	even	28	inner
783.2.v.b.512.12	yes	240	29.19	odd	28	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.v (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.561561 - 0.352852i) q^{2} +(-0.676921 - 1.40564i) q^{4} +(0.901677 + 3.95051i) q^{5} +(3.71421 + 1.78867i) q^{7} +(-0.264364 + 2.34630i) q^{8} +(0.887598 - 2.53661i) q^{10} +(-0.0605415 - 0.537321i) q^{11} +(1.03994 + 0.829323i) q^{13} +(-1.45462 - 2.31501i) q^{14} +(-0.969115 + 1.21523i) q^{16} +(-3.42739 + 3.42739i) q^{17} +(-6.17677 - 2.16134i) q^{19} +(4.94263 - 3.94162i) q^{20} +(-0.155597 + 0.323101i) q^{22} +(1.09932 + 0.250912i) q^{23} +(-10.2886 + 4.95474i) q^{25} +(-0.291360 - 0.832660i) q^{26} -6.43163i q^{28} +(-3.20978 + 4.32404i) q^{29} +(2.17681 - 3.46437i) q^{31} +(5.43031 - 1.90015i) q^{32} +(3.13405 - 0.715326i) q^{34} +(-3.71713 + 16.2858i) q^{35} +(-0.116634 - 0.0131415i) q^{37} +(2.70600 + 3.39321i) q^{38} +(-9.50744 + 1.07123i) q^{40} +(1.85162 + 1.85162i) q^{41} +(-2.37879 + 1.49469i) q^{43} +(-0.714298 + 0.448823i) q^{44} +(-0.528799 - 0.528799i) q^{46} +(-4.54606 + 0.512218i) q^{47} +(6.23158 + 7.81416i) q^{49} +(7.52598 + 0.847975i) q^{50} +(0.461775 - 2.02317i) q^{52} +(13.8470 - 3.16050i) q^{53} +(2.06810 - 0.723659i) q^{55} +(-5.17866 + 8.24178i) q^{56} +(3.32823 - 1.29563i) q^{58} -5.24021i q^{59} +(2.86526 + 8.18845i) q^{61} +(-2.44482 + 1.17736i) q^{62} +(-0.689180 - 0.157301i) q^{64} +(-2.33856 + 4.85606i) q^{65} +(11.0783 - 8.83463i) q^{67} +(7.13775 + 2.49761i) q^{68} +(7.83388 - 7.83388i) q^{70} +(-1.86371 + 2.33702i) q^{71} +(7.33708 + 11.6769i) q^{73} +(0.0608602 + 0.0485344i) q^{74} +(1.14311 + 10.1454i) q^{76} +(0.736225 - 2.10401i) q^{77} +(0.573293 - 5.08811i) q^{79} +(-5.67461 - 2.73275i) q^{80} +(-0.386450 - 1.69315i) q^{82} +(5.49290 + 11.4061i) q^{83} +(-16.6303 - 10.4495i) q^{85} +1.86324 q^{86} +1.27672 q^{88} +(-12.0422 - 7.56663i) q^{89} +(2.37916 + 4.94039i) q^{91} +(-0.391459 - 1.71509i) q^{92} +(2.73363 + 1.31645i) q^{94} +(2.96895 - 26.3502i) q^{95} +(-0.400010 + 1.14316i) q^{97} +(-0.742172 - 6.58696i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 72 q^{16} + 8 q^{19} - 40 q^{25} + 8 q^{31} - 32 q^{37} - 16 q^{40} - 16 q^{43} - 104 q^{46} - 8 q^{49} + 8 q^{52} - 128 q^{55} + 272 q^{58} - 24 q^{61} + 112 q^{67} - 56 q^{70} - 64 q^{73} - 160 q^{76}+ \cdots + 40 q^{97}+O(q^{100}) \) 240 * q + 72 * q^16 + 8 * q^19 - 40 * q^25 + 8 * q^31 - 32 * q^37 - 16 * q^40 - 16 * q^43 - 104 * q^46 - 8 * q^49 + 8 * q^52 - 128 * q^55 + 272 * q^58 - 24 * q^61 + 112 * q^67 - 56 * q^70 - 64 * q^73 - 160 * q^76 - 96 * q^79 - 80 * q^82 - 104 * q^85 - 464 * q^88 - 168 * q^91 - 88 * q^94 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more