LMFDB - Embedded newform 783.2.v.b.26.12

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			26.12
Character	$\chi$	$=$	783.26
Dual form			783.2.v.b.512.12

$q$-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	0.715741	−	0.698366i	$-0.246089\pi$
$2$	0.561561	+	0.352852i	0.397084	+	0.249504i	−0.318657	+	0.947870i	$0.603232\pi$
$3$		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	$-0.710491\pi$
$5$	−0.901677	−	3.95051i	−0.403242	−	1.76672i	0.210883	−	0.977511i	$-0.432366\pi$
$6$		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	0.999532	−	0.0305877i	$-0.00973789\pi$
$11$	0.0605415	+	0.537321i	0.0182539	+	0.162008i	−0.981278	+	0.192596i	$0.938309\pi$
$12$		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	−0.156426	−	0.987690i	$-0.549997\pi$
$17$	3.42739	−	3.42739i	0.831263	−	0.831263i	0.987690	+	0.156426i	$0.0499974\pi$
$18$		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	0.106366	−	0.994327i	$-0.466078\pi$
$23$	−1.09932	−	0.250912i	−0.229224	−	0.0523188i	−0.335590	+	0.942008i	$0.608936\pi$
$24$		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	0.547579	−	0.836754i	$-0.315550\pi$
$41$	−1.85162	−	1.85162i	−0.289175	−	0.289175i	−0.836754	+	0.547579i	$0.815550\pi$
$42$		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	0.226007	−	0.974126i	$-0.427433\pi$
$47$	4.54606	−	0.512218i	0.663111	−	0.0747147i	0.437104	+	0.899411i	$0.356004\pi$
$48$		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	$0.857932\pi$
$53$	−13.8470	+	3.16050i	−1.90204	+	0.434128i	−0.999997	+	0.00247771i	$0.999211\pi$
$54$		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	$0.110802\pi$
$59$			5.24021i			0.682218i	−0.940024	+	0.341109i	$0.889198\pi$
$60$		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	−0.658843	−	0.752280i	$-0.728954\pi$
$71$	1.86371	−	2.33702i	0.221182	−	0.277353i	0.880025	+	0.474927i	$0.157525\pi$
$72$		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	$-0.898351\pi$
$83$	−5.49290	−	11.4061i	−0.602924	−	1.25198i	0.346519	−	0.938043i	$-0.387364\pi$
$84$		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	0.987854	−	0.155383i	$-0.0496613\pi$
$89$	12.0422	+	7.56663i	1.27647	+	0.802061i	0.288618	+	0.957444i	$0.406804\pi$
$90$		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	$0.0878395\pi$
$101$	7.94123	+	12.6384i	0.790182	+	1.25757i	−0.171984	+	0.985100i	$0.555018\pi$
$102$		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	−0.100759	−	0.994911i	$-0.532127\pi$
$107$	8.75922	−	6.98525i	0.846786	−	0.675289i	0.947545	+	0.319621i	$0.103556\pi$
$108$		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	$-0.923167\pi$
$113$	−3.83624	−	10.9633i	−0.360883	−	1.03134i	0.610127	−	0.792304i	$-0.291118\pi$
$114$		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	−0.550116	−	0.835088i	$-0.685416\pi$
$131$	−0.416771	+	0.261874i	−0.0364134	+	0.0228801i	0.513702	+	0.857968i	$0.328274\pi$
$132$		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	−0.0375674	−	0.999294i	$-0.511961\pi$
$137$	−3.47111	−	0.391100i	−0.296557	−	0.0334139i	−0.258989	+	0.965880i	$0.583389\pi$
$138$		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	−0.390725	−	0.920507i	$-0.627776\pi$
$149$	1.04175	−	0.501679i	0.0853433	−	0.0410992i	0.476068	+	0.879408i	$0.342061\pi$
$150$		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	0.451093	−	0.892477i	$-0.351034\pi$
$167$	0.446853	+	0.215193i	0.0345785	+	0.0166521i	−0.416515	+	0.909129i	$0.636749\pi$
$168$		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	$-0.833110\pi$
$173$	−22.7723			−1.73135			−0.865674	+	0.500608i	$0.833110\pi$
$174$		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	$-0.965226\pi$
$179$	−1.94996	−	8.54333i	−0.145747	−	0.638558i	0.848292	−	0.529529i	$-0.177631\pi$
$180$		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	−0.918288	−	0.395914i	$-0.870428\pi$
$191$	−7.21934	+	7.21934i	−0.522373	+	0.522373i	0.395914	+	0.918288i	$0.370428\pi$
$192$		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	0.720103	−	0.693867i	$-0.244095\pi$
$197$	14.9878	+	3.42087i	1.06784	+	0.243727i	0.347733	+	0.937594i	$0.386952\pi$
$198$		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	−0.552906	−	0.833244i	$-0.686481\pi$
$227$	−10.3888	+	2.37116i	−0.689526	+	0.157380i	−0.136620	+	0.990624i	$0.543624\pi$
$228$		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	$0.310599\pi$
$233$			25.2819i			1.65627i	−0.560526	+	0.828137i	$0.689401\pi$
$234$		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	$0.491756\pi$
$239$	−11.9320	+	24.7771i	−0.771819	+	1.60270i	−0.797715	+	0.603034i	$0.793958\pi$
$240$		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	$-0.717140\pi$
$251$	5.48814	−	15.6842i	0.346408	−	0.989978i	0.976884	−	0.213769i	$-0.0685741\pi$
$252$		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	$0.0580284\pi$
$257$	8.20818	+	17.0445i	0.512012	+	1.06320i	−0.471417	+	0.881910i	$0.656257\pi$
$258$		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	$0.105233\pi$
$263$	26.7374	+	16.8002i	1.64870	+	1.03595i	0.702851	+	0.711337i	$0.251910\pi$
$264$		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	$-0.856782\pi$
$269$	1.21694	−	10.8007i	0.0741983	−	0.658528i	0.974675	−	0.223625i	$-0.0717889\pi$
$270$		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	−0.663080	−	0.748548i	$-0.730751\pi$
$281$	−1.35528	+	1.08080i	−0.0808490	+	0.0644749i	0.582231	+	0.813023i	$0.302180\pi$
$282$		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	−0.611475	−	0.791264i	$-0.709423\pi$
$293$	−10.2053	+	3.57099i	−0.596199	+	0.208619i	0.0152751	+	0.999883i	$0.495138\pi$
$294$		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	−0.212002	−	0.977269i	$-0.567998\pi$
$311$	−11.2187	−	1.26404i	−0.636152	−	0.0716771i	−0.424150	+	0.905592i	$0.639427\pi$
$312$		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	−0.505258	−	0.862968i	$-0.668603\pi$
$317$	8.75043	−	13.9262i	0.491473	−	0.782175i	0.996731	+	0.0807937i	$0.0257455\pi$
$318$		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	$-0.527005\pi$
$347$	−3.15691			−0.169472			−0.0847360	+	0.996403i	$0.527005\pi$
$348$		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	$0.0919572\pi$
$353$	4.10593	+	17.9893i	0.218537	+	0.957471i	−0.740024	+	0.672581i	$0.765186\pi$
$354$		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	$-0.903344\pi$
$359$	−1.71399	−	15.2121i	−0.0904608	−	0.802862i	0.863790	−	0.503853i	$-0.168085\pi$
$360$		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	$-0.670372\pi$
$383$	6.31524	−	27.6689i	0.322693	−	1.41381i	0.832739	−	0.553665i	$-0.186771\pi$
$384$		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	0.978650	−	0.205534i	$-0.0658932\pi$
$389$	15.2482	+	15.2482i	0.773116	+	0.773116i	−0.205534	+	0.978650i	$0.565893\pi$
$390$		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	−0.725086	−	0.688659i	$-0.758200\pi$
$401$	−21.6183	+	4.93424i	−1.07957	+	0.246404i	−0.354482	+	0.935063i	$0.615343\pi$
$402$		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	−0.796084	−	0.605187i	$-0.793098\pi$
$419$	−0.592078	+	0.742442i	−0.0289249	+	0.0362707i	0.767159	+	0.641457i	$0.221670\pi$
$420$		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	0.895833	−	0.444392i	$-0.146580\pi$
$431$	−0.210702	−	0.437527i	−0.0101491	−	0.0210749i	−0.905982	+	0.423317i	$0.860866\pi$
$432$		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	$-0.724160\pi$
$443$	3.22774	−	28.6470i	0.153354	−	1.36106i	0.800794	−	0.598941i	$-0.204411\pi$
$444$		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	0.967078	−	0.254481i	$-0.0819046\pi$
$449$	6.74252	+	10.7307i	0.318199	+	0.506411i	−0.648879	+	0.760892i	$0.724762\pi$
$450$		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	$-0.910915\pi$
$461$	−8.19989	−	23.4339i	−0.381907	−	1.09143i	0.579185	−	0.815196i	$-0.303371\pi$
$462$		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	−0.876685	−	0.481065i	$-0.840250\pi$
$467$	−27.2756	+	9.54416i	−1.26217	+	0.441651i	−0.385481	+	0.922716i	$0.625964\pi$
$468$		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	$0.694280\pi$
$479$	−34.1452	+	21.4548i	−1.56013	+	0.980296i	−0.986979	+	0.160847i	$0.948577\pi$
$480$		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	−0.762176	−	0.647370i	$-0.775869\pi$
$491$	3.36323	−	5.35254i	0.151780	−	0.241557i	0.913956	+	0.405813i	$0.133012\pi$
$492$		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	−0.268890	−	0.963171i	$-0.586657\pi$
$503$	−24.2139	−	8.47280i	−1.07964	−	0.377784i	−0.810754	+	0.585387i	$0.800942\pi$
$504$		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	0.955446	−	0.295166i	$-0.0953748\pi$
$509$	19.8602	+	15.8380i	0.880288	+	0.702006i	−0.0751585	+	0.997172i	$0.523946\pi$
$510$		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	$-0.547237\pi$
$521$	−6.74973			−0.295711			−0.147855	+	0.989009i	$0.547237\pi$
$522$		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	$0.296301\pi$
$557$	−6.81818	+	29.8724i	−0.288896	+	1.26573i	−0.886043	+	0.463603i	$0.846556\pi$
$558$		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	$0.0198002\pi$
$563$	25.1567	+	25.1567i	1.06023	+	1.06023i	0.0621640	+	0.998066i	$0.480200\pi$
$564$		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	−0.624336	−	0.781156i	$-0.714631\pi$
$569$	−25.2658	+	2.84677i	−1.05920	+	0.119343i	−0.434860	+	0.900498i	$0.643202\pi$
$570$		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	−0.798103	−	0.602521i	$-0.794163\pi$
$587$	4.13272	−	8.58169i	0.170576	−	0.354204i	0.968679	+	0.248317i	$0.0798773\pi$
$588$		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	−0.789138	−	0.614216i	$-0.789472\pi$
$593$	−0.358513	+	0.449561i	−0.0147223	+	0.0184612i	0.774416	+	0.632677i	$0.218044\pi$
$594$		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	$0.281488\pi$
$599$	−8.41878	+	24.0595i	−0.343982	+	0.983044i	−0.977796	+	0.209559i	$0.932797\pi$
$600$		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	−0.999868	−	0.0162339i	$-0.994832\pi$
$617$	−0.532966	+	4.73020i	−0.0214564	+	0.190431i	0.978412	+	0.206665i	$0.0662609\pi$
$618$		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	−0.230491	−	0.973074i	$-0.574033\pi$
$641$	4.96248	−	1.73645i	0.196006	−	0.0685855i	0.426497	+	0.904489i	$0.359747\pi$
$642$		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	0.821947	−	0.569564i	$-0.192888\pi$
$647$	2.13062	+	2.67172i	0.0837634	+	0.105036i	−0.738184	+	0.674600i	$0.764316\pi$
$648$		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	−0.491036	−	0.871139i	$-0.663382\pi$
$653$	2.06425	−	1.29705i	0.0807802	−	0.0507575i	0.571817	+	0.820382i	$0.306239\pi$
$654$		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	0.826143	−	0.563461i	$-0.190530\pi$
$659$	38.6654	+	4.35655i	1.50619	+	0.169707i	0.680048	+	0.733168i	$0.261959\pi$
$660$		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	0.590298	−	0.807186i	$-0.299010\pi$
$677$	14.2726	+	4.99419i	0.548539	+	0.191942i	−0.0417586	+	0.999128i	$0.513296\pi$
$678$		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	0.995563	−	0.0941026i	$-0.0299982\pi$
$683$	29.4103	+	23.4539i	1.12535	+	0.897439i	0.129790	+	0.991541i	$0.458570\pi$
$684$		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	$-0.945673\pi$
$701$	−4.53501	−	19.8692i	−0.171285	−	0.750449i	0.814186	−	0.580605i	$-0.197184\pi$
$702$		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	−0.529198	−	0.848499i	$-0.677507\pi$
$719$	−36.8464	−	8.40995i	−1.37414	−	0.313638i	−0.844940	+	0.534860i	$0.820364\pi$
$720$		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	−0.0239230	−	0.999714i	$-0.507616\pi$
$743$	4.77591	−	0.538116i	0.175211	−	0.0197415i	0.199134	+	0.979972i	$0.436187\pi$
$744$		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	−0.944975	−	0.327143i	$-0.893914\pi$
$761$	−2.75922	+	5.72957i	−0.100022	+	0.207697i	0.844953	+	0.534840i	$0.179628\pi$
$762$		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	$0.244488\pi$
$773$	−7.68076	+	21.9504i	−0.276258	+	0.789500i	−0.995502	+	0.0947420i	$0.969797\pi$
$774$		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	0.795130	−	0.606439i	$-0.207403\pi$
$797$	−2.71716	−	4.32434i	−0.0962468	−	0.153176i	−0.891377	+	0.453263i	$0.850260\pi$
$798$		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	0.974000	−	0.226546i	$-0.0727434\pi$
$809$	2.02647	+	5.79133i	0.0712470	+	0.203612i	−0.902753	+	0.430158i	$0.858458\pi$
$810$		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	$-0.853653\pi$
$821$	−32.3595	−	40.5775i	−1.12935	−	1.41616i	−0.233196	−	0.972430i	$-0.574918\pi$
$822$		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	−0.771306	−	0.636464i	$-0.780396\pi$
$827$	−15.3143	+	9.62258i	−0.532529	+	0.334610i	0.238777	+	0.971074i	$0.423253\pi$
$828$		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	−0.875742	−	0.482780i	$-0.839627\pi$
$839$	−1.76116	+	2.80288i	−0.0608021	+	0.0967661i	0.814940	+	0.579546i	$0.196770\pi$
$840$		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	0.554823	−	0.831968i	$-0.312786\pi$
$857$	−3.88843	−	3.10092i	−0.132826	−	0.105925i	−0.687649	+	0.726043i	$0.741357\pi$
$858$		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	0.585836	−	0.810430i	$-0.300766\pi$
$863$	9.32653	+	4.49142i	0.317479	+	0.152890i	−0.268357	+	0.963320i	$0.586481\pi$
$864$		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	$-0.865718\pi$
$881$	−3.38332	−	30.0278i	−0.113987	−	1.01166i	0.798342	−	0.602204i	$-0.205711\pi$
$882$		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	−0.902473	−	0.430747i	$-0.858250\pi$
$887$	−14.0492	+	14.0492i	−0.471726	+	0.471726i	0.430747	+	0.902473i	$0.358250\pi$
$888$		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	0.186772	−	0.982403i	$-0.440198\pi$
$911$	−24.0144	−	24.0144i	−0.795632	−	0.795632i	−0.982403	+	0.186772i	$0.940198\pi$
$912$		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	$0.208816\pi$
$929$			37.1827i			1.21993i	−0.792430	+	0.609963i	$0.791184\pi$
$930$		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	−0.966381	−	0.257116i	$-0.917228\pi$
$941$	−15.3585	+	19.2589i	−0.500672	+	0.627822i	0.465709	+	0.884938i	$0.345799\pi$
$942$		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	$-0.725325\pi$
$947$	10.2116	−	29.1832i	0.331834	−	0.948327i	0.982057	−	0.188584i	$-0.0603897\pi$
$948$		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	$0.0974820\pi$
$953$	18.3588	+	38.1225i	0.594701	+	1.23491i	−0.358770	+	0.933426i	$0.616804\pi$
$954$		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	$-0.967158\pi$
$971$	−20.4384	−	32.5275i	−0.655899	−	1.04386i	0.338783	−	0.940865i	$-0.389985\pi$
$972$		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	−0.774454	−	0.632630i	$-0.781975\pi$
$977$	−10.3154	+	8.22623i	−0.330018	+	0.263181i	0.444436	+	0.895810i	$0.353404\pi$
$978$		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	0.922974	−	0.384862i	$-0.125751\pi$
$983$	−1.21002	−	3.45804i	−0.0385937	−	0.110294i	−0.961568	+	0.274568i	$0.911465\pi$
$984$		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.26.12	yes	240
3.2	odd	2	inner	783.2.v.b.26.9	✓	240
29.19	odd	28	inner	783.2.v.b.512.9	yes	240
87.77	even	28	inner	783.2.v.b.512.12	yes	240

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

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