LMFDB - Embedded newform 728.2.c.b.365.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(365,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.365"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			365.1
Character	$\chi$	$=$	728.365
Dual form			728.2.c.b.365.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40887 - 0.122797i) q^{2} +0.192506i q^{3} +(1.96984 + 0.346010i) q^{4} +2.98429i q^{5} +(0.0236391 - 0.271216i) q^{6} +1.00000 q^{7} +(-2.73277 - 0.729373i) q^{8} +2.96294 q^{9} +(0.366461 - 4.20449i) q^{10} +1.00336i q^{11} +(-0.0666089 + 0.379206i) q^{12} +1.00000i q^{13} +(-1.40887 - 0.122797i) q^{14} -0.574494 q^{15} +(3.76055 + 1.36317i) q^{16} +5.01819 q^{17} +(-4.17441 - 0.363839i) q^{18} -3.05501i q^{19} +(-1.03259 + 5.87859i) q^{20} +0.192506i q^{21} +(0.123209 - 1.41360i) q^{22} +1.46785 q^{23} +(0.140409 - 0.526074i) q^{24} -3.90601 q^{25} +(0.122797 - 1.40887i) q^{26} +1.14790i q^{27} +(1.96984 + 0.346010i) q^{28} +7.00104i q^{29} +(0.809389 + 0.0705460i) q^{30} -5.32922 q^{31} +(-5.13075 - 2.38231i) q^{32} -0.193152 q^{33} +(-7.06998 - 0.616216i) q^{34} +2.98429i q^{35} +(5.83653 + 1.02521i) q^{36} -5.29400i q^{37} +(-0.375145 + 4.30412i) q^{38} -0.192506 q^{39} +(2.17666 - 8.15538i) q^{40} -2.79082 q^{41} +(0.0236391 - 0.271216i) q^{42} +1.27667i q^{43} +(-0.347171 + 1.97645i) q^{44} +8.84229i q^{45} +(-2.06801 - 0.180247i) q^{46} -3.77337 q^{47} +(-0.262418 + 0.723929i) q^{48} +1.00000 q^{49} +(5.50307 + 0.479645i) q^{50} +0.966031i q^{51} +(-0.346010 + 1.96984i) q^{52} +3.46579i q^{53} +(0.140958 - 1.61725i) q^{54} -2.99431 q^{55} +(-2.73277 - 0.729373i) q^{56} +0.588108 q^{57} +(0.859704 - 9.86357i) q^{58} +14.0940i q^{59} +(-1.13166 - 0.198781i) q^{60} +6.82042i q^{61} +(7.50819 + 0.654410i) q^{62} +2.96294 q^{63} +(6.93603 + 3.98641i) q^{64} -2.98429 q^{65} +(0.272127 + 0.0237184i) q^{66} -11.1751i q^{67} +(9.88503 + 1.73634i) q^{68} +0.282569i q^{69} +(0.366461 - 4.20449i) q^{70} +7.60183 q^{71} +(-8.09703 - 2.16109i) q^{72} +9.74653 q^{73} +(-0.650085 + 7.45857i) q^{74} -0.751930i q^{75} +(1.05706 - 6.01789i) q^{76} +1.00336i q^{77} +(0.271216 + 0.0236391i) q^{78} +1.42324 q^{79} +(-4.06809 + 11.2226i) q^{80} +8.66785 q^{81} +(3.93191 + 0.342704i) q^{82} +4.59820i q^{83} +(-0.0666089 + 0.379206i) q^{84} +14.9757i q^{85} +(0.156770 - 1.79866i) q^{86} -1.34774 q^{87} +(0.731821 - 2.74194i) q^{88} +1.30979 q^{89} +(1.08580 - 12.4577i) q^{90} +1.00000i q^{91} +(2.89142 + 0.507889i) q^{92} -1.02591i q^{93} +(5.31620 + 0.463357i) q^{94} +9.11705 q^{95} +(0.458610 - 0.987700i) q^{96} -16.6675 q^{97} +(-1.40887 - 0.122797i) q^{98} +2.97289i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{4} + 14 q^{6} + 38 q^{7} - 6 q^{8} - 46 q^{9} - 4 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 4 q^{18} - 24 q^{20} + 10 q^{22} + 12 q^{23} + 10 q^{24} - 50 q^{25} + 8 q^{28} + 4 q^{30} + 16 q^{31}+ \cdots + 82 q^{96}+O(q^{100}) $ 38 * q + 8 * q^4 + 14 * q^6 + 38 * q^7 - 6 * q^8 - 46 * q^9 - 4 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 4 * q^18 - 24 * q^20 + 10 * q^22 + 12 * q^23 + 10 * q^24 - 50 * q^25 + 8 * q^28 + 4 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 - 4 * q^34 - 38 * q^36 - 28 * q^38 + 8 * q^39 + 4 * q^40 + 8 * q^41 + 14 * q^42 - 40 * q^44 - 16 * q^46 + 4 * q^48 + 38 * q^49 + 24 * q^50 - 4 * q^52 - 14 * q^54 - 6 * q^56 + 8 * q^57 - 24 * q^58 + 44 * q^60 - 12 * q^62 - 46 * q^63 + 32 * q^64 + 20 * q^65 - 76 * q^66 - 52 * q^68 + 42 * q^72 + 50 * q^74 - 28 * q^76 - 12 * q^79 - 16 * q^80 + 62 * q^81 - 4 * q^84 + 44 * q^86 - 56 * q^87 - 6 * q^88 + 48 * q^90 + 2 * q^92 - 48 * q^94 + 82 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	−1.40887	−	0.122797i	−0.996223	−	0.0868304i
$2$	−1.40887	−	0.122797i	−0.996223	−	0.0868304i
$3$			0.192506i			0.111143i	0.998455	+	0.0555717i	$0.0176981\pi$
$3$			0.192506i			0.111143i	−0.998455	+	0.0555717i	$0.982302\pi$
$4$	1.96984	+	0.346010i	0.984921	+	0.173005i
$5$			2.98429i			1.33462i	0.744782	+	0.667308i	$0.232554\pi$
$5$			2.98429i			1.33462i	−0.744782	+	0.667308i	$0.767446\pi$
$6$	0.0236391	−	0.271216i	0.00965062	−	0.110724i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.73277	−	0.729373i	−0.966179	−	0.257872i
$9$	2.96294			0.987647
$10$	0.366461	−	4.20449i	0.115885	−	1.32958i
$11$			1.00336i			0.302523i	0.988494	+	0.151262i	$0.0483336\pi$
$11$			1.00336i			0.302523i	−0.988494	+	0.151262i	$0.951666\pi$
$12$	−0.0666089	+	0.379206i	−0.0192283	+	0.109467i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−1.40887	−	0.122797i	−0.376537	−	0.0328188i
$15$	−0.574494			−0.148334
$16$	3.76055	+	1.36317i	0.940139	+	0.340792i
$17$	5.01819			1.21709			0.608544	−	0.793520i	$-0.291754\pi$
$17$	5.01819			1.21709			0.608544	+	0.793520i	$0.291754\pi$
$18$	−4.17441	−	0.363839i	−0.983917	−	0.0857577i
$19$		−	3.05501i		−	0.700868i	−0.936588	−	0.350434i	$-0.886034\pi$
$19$		−	3.05501i		−	0.700868i	0.936588	−	0.350434i	$-0.113966\pi$
$20$	−1.03259	+	5.87859i	−0.230895	+	1.31449i
$21$			0.192506i			0.0420082i
$22$	0.123209	−	1.41360i	0.0262682	−	0.301381i
$23$	1.46785			0.306067			0.153033	−	0.988221i	$-0.451096\pi$
$23$	1.46785			0.306067			0.153033	+	0.988221i	$0.451096\pi$
$24$	0.140409	−	0.526074i	0.0286608	−	0.107384i
$25$	−3.90601			−0.781202
$26$	0.122797	−	1.40887i	0.0240824	−	0.276303i
$27$			1.14790i			0.220914i
$28$	1.96984	+	0.346010i	0.372265	+	0.0653897i
$29$			7.00104i			1.30006i	0.759908	+	0.650030i	$0.225244\pi$
$29$			7.00104i			1.30006i	−0.759908	+	0.650030i	$0.774756\pi$
$30$	0.809389	+	0.0705460i	0.147774	+	0.0128799i
$31$	−5.32922			−0.957156			−0.478578	−	0.878045i	$-0.658848\pi$
$31$	−5.32922			−0.957156			−0.478578	+	0.878045i	$0.658848\pi$
$32$	−5.13075	−	2.38231i	−0.906997	−	0.421138i
$33$	−0.193152			−0.0336235
$34$	−7.06998	−	0.616216i	−1.21249	−	0.105680i
$35$			2.98429i			0.504438i
$36$	5.83653	+	1.02521i	0.972754	+	0.170868i
$37$		−	5.29400i		−	0.870328i	−0.900351	−	0.435164i	$-0.856690\pi$
$37$		−	5.29400i		−	0.870328i	0.900351	−	0.435164i	$-0.143310\pi$
$38$	−0.375145	+	4.30412i	−0.0608566	+	0.698220i
$39$	−0.192506			−0.0308256
$40$	2.17666	−	8.15538i	0.344161	−	1.28948i
$41$	−2.79082			−0.435853			−0.217927	−	0.975965i	$-0.569929\pi$
$41$	−2.79082			−0.435853			−0.217927	+	0.975965i	$0.569929\pi$
$42$	0.0236391	−	0.271216i	0.00364759	−	0.0418496i
$43$			1.27667i			0.194690i	0.995251	+	0.0973448i	$0.0310350\pi$
$43$			1.27667i			0.194690i	−0.995251	+	0.0973448i	$0.968965\pi$
$44$	−0.347171	+	1.97645i	−0.0523380	+	0.297962i
$45$			8.84229i			1.31813i
$46$	−2.06801	−	0.180247i	−0.304911	−	0.0265759i
$47$	−3.77337			−0.550403			−0.275201	−	0.961387i	$-0.588745\pi$
$47$	−3.77337			−0.550403			−0.275201	+	0.961387i	$0.588745\pi$
$48$	−0.262418	+	0.723929i	−0.0378768	+	0.104490i
$49$	1.00000			0.142857
$50$	5.50307	+	0.479645i	0.778251	+	0.0678320i
$51$			0.966031i			0.135271i
$52$	−0.346010	+	1.96984i	−0.0479829	+	0.273168i
$53$			3.46579i			0.476062i	0.971258	+	0.238031i	$0.0765020\pi$
$53$			3.46579i			0.476062i	−0.971258	+	0.238031i	$0.923498\pi$
$54$	0.140958	−	1.61725i	0.0191820	−	0.220079i
$55$	−2.99431			−0.403753
$56$	−2.73277	−	0.729373i	−0.365181	−	0.0974666i
$57$	0.588108			0.0778968
$58$	0.859704	−	9.86357i	0.112885	−	1.29515i
$59$			14.0940i			1.83488i	0.397878	+	0.917438i	$0.369747\pi$
$59$			14.0940i			1.83488i	−0.397878	+	0.917438i	$0.630253\pi$
$60$	−1.13166	−	0.198781i	−0.146097	−	0.0256625i
$61$			6.82042i			0.873265i	0.899640	+	0.436632i	$0.143829\pi$
$61$			6.82042i			0.873265i	−0.899640	+	0.436632i	$0.856171\pi$
$62$	7.50819	+	0.654410i	0.953541	+	0.0831102i
$63$	2.96294			0.373296
$64$	6.93603	+	3.98641i	0.867004	+	0.498302i
$65$	−2.98429			−0.370156
$66$	0.272127	+	0.0237184i	0.0334965	+	0.00291954i
$67$		−	11.1751i		−	1.36525i	−0.730767	−	0.682627i	$-0.760837\pi$
$67$		−	11.1751i		−	1.36525i	0.730767	−	0.682627i	$-0.239163\pi$
$68$	9.88503	+	1.73634i	1.19874	+	0.210562i
$69$			0.282569i			0.0340173i
$70$	0.366461	−	4.20449i	0.0438005	−	0.502532i
$71$	7.60183			0.902171			0.451086	−	0.892481i	$-0.351037\pi$
$71$	7.60183			0.902171			0.451086	+	0.892481i	$0.351037\pi$
$72$	−8.09703	−	2.16109i	−0.954244	−	0.254687i
$73$	9.74653			1.14075			0.570373	−	0.821386i	$-0.306799\pi$
$73$	9.74653			1.14075			0.570373	+	0.821386i	$0.306799\pi$
$74$	−0.650085	+	7.45857i	−0.0755709	+	0.867041i
$75$		−	0.751930i		−	0.0868254i
$76$	1.05706	−	6.01789i	0.121253	−	0.690299i
$77$			1.00336i			0.114343i
$78$	0.271216	+	0.0236391i	0.0307092	+	0.00267660i
$79$	1.42324			0.160127			0.0800635	−	0.996790i	$-0.474488\pi$
$79$	1.42324			0.160127			0.0800635	+	0.996790i	$0.474488\pi$
$80$	−4.06809	+	11.2226i	−0.454827	+	1.25472i
$81$	8.66785			0.963094
$82$	3.93191	+	0.342704i	0.434207	+	0.0378453i
$83$			4.59820i			0.504718i	0.967634	+	0.252359i	$0.0812063\pi$
$83$			4.59820i			0.504718i	−0.967634	+	0.252359i	$0.918794\pi$
$84$	−0.0666089	+	0.379206i	−0.00726763	+	0.0413748i
$85$			14.9757i			1.62435i
$86$	0.156770	−	1.79866i	0.0169050	−	0.193954i
$87$	−1.34774			−0.144493
$88$	0.731821	−	2.74194i	0.0780124	−	0.292292i
$89$	1.30979			0.138838			0.0694188	−	0.997588i	$-0.477886\pi$
$89$	1.30979			0.138838			0.0694188	+	0.997588i	$0.477886\pi$
$90$	1.08580	−	12.4577i	0.114454	−	1.31315i
$91$			1.00000i			0.104828i
$92$	2.89142	+	0.507889i	0.301452	+	0.0529510i
$93$		−	1.02591i		−	0.106382i
$94$	5.31620	+	0.463357i	0.548324	+	0.0477917i
$95$	9.11705			0.935389
$96$	0.458610	−	0.987700i	0.0468066	−	0.100807i
$97$	−16.6675			−1.69233			−0.846165	−	0.532921i	$-0.821094\pi$
$97$	−16.6675			−1.69233			−0.846165	+	0.532921i	$0.821094\pi$
$98$	−1.40887	−	0.122797i	−0.142318	−	0.0124043i
$99$			2.97289i			0.298786i
$100$	−7.69422	−	1.35152i	−0.769422	−	0.135152i
$101$			15.5451i			1.54680i	0.633920	+	0.773398i	$0.281445\pi$
$101$			15.5451i			1.54680i	−0.633920	+	0.773398i	$0.718555\pi$
$102$	0.118625	−	1.36101i	0.0117457	−	0.134760i
$103$	−9.35343			−0.921620			−0.460810	−	0.887499i	$-0.652441\pi$
$103$	−9.35343			−0.921620			−0.460810	+	0.887499i	$0.652441\pi$
$104$	0.729373	−	2.73277i	0.0715209	−	0.267970i
$105$	−0.574494			−0.0560649
$106$	0.425587	−	4.88285i	0.0413367	−	0.474264i
$107$		−	20.1201i		−	1.94509i	−0.232719	−	0.972544i	$-0.574762\pi$
$107$		−	20.1201i		−	1.94509i	0.232719	−	0.972544i	$-0.425238\pi$
$108$	−0.397185	+	2.26118i	−0.0382191	+	0.217583i
$109$			9.27587i			0.888467i	0.895911	+	0.444234i	$0.146524\pi$
$109$			9.27587i			0.888467i	−0.895911	+	0.444234i	$0.853476\pi$
$110$	4.21860	+	0.367691i	0.402228	+	0.0350580i
$111$	1.01913			0.0967312
$112$	3.76055	+	1.36317i	0.355339	+	0.128807i
$113$	−15.7978			−1.48613			−0.743066	−	0.669219i	$-0.766629\pi$
$113$	−15.7978			−1.48613			−0.743066	+	0.669219i	$0.766629\pi$
$114$	−0.828569	−	0.0722177i	−0.0776026	−	0.00676380i
$115$			4.38048i			0.408482i
$116$	−2.42243	+	13.7909i	−0.224917	+	1.28046i
$117$			2.96294i			0.273924i
$118$	1.73069	−	19.8566i	0.159323	−	1.82795i
$119$	5.01819			0.460016
$120$	1.56996	+	0.419021i	0.143317	+	0.0382512i
$121$	9.99328			0.908480
$122$	0.837524	−	9.60909i	0.0758259	−	0.869967i
$123$		−	0.537250i		−	0.0484422i
$124$	−10.4977	−	1.84396i	−0.942723	−	0.165593i
$125$			3.26479i			0.292012i
$126$	−4.17441	−	0.363839i	−0.371886	−	0.0324134i
$127$	8.10472			0.719178			0.359589	−	0.933111i	$-0.382917\pi$
$127$	8.10472			0.719178			0.359589	+	0.933111i	$0.382917\pi$
$128$	−9.28246	−	6.46807i	−0.820461	−	0.571702i
$129$	−0.245766			−0.0216385
$130$	4.20449	+	0.366461i	0.368758	+	0.0321408i
$131$		−	6.30484i		−	0.550857i	−0.961322	−	0.275428i	$-0.911180\pi$
$131$		−	6.30484i		−	0.550857i	0.961322	−	0.275428i	$-0.0888197\pi$
$132$	−0.380479	−	0.0668325i	−0.0331165	−	0.00581702i
$133$		−	3.05501i		−	0.264903i
$134$	−1.37226	+	15.7443i	−0.118545	+	1.36010i
$135$	−3.42568			−0.294835
$136$	−13.7135	−	3.66013i	−1.17593	−	0.313854i
$137$	−1.54638			−0.132117			−0.0660583	−	0.997816i	$-0.521042\pi$
$137$	−1.54638			−0.132117			−0.0660583	+	0.997816i	$0.521042\pi$
$138$	0.0346985	−	0.398104i	0.00295373	−	0.0338888i
$139$		−	6.77925i		−	0.575008i	−0.957779	−	0.287504i	$-0.907175\pi$
$139$		−	6.77925i		−	0.575008i	0.957779	−	0.287504i	$-0.0928255\pi$
$140$	−1.03259	+	5.87859i	−0.0872701	+	0.496831i
$141$		−	0.726396i		−	0.0611736i
$142$	−10.7100	−	0.933479i	−0.898764	−	0.0783359i
$143$	−1.00336			−0.0839049
$144$	11.1423	+	4.03899i	0.928525	+	0.336582i
$145$	−20.8932			−1.73508
$146$	−13.7316	−	1.19684i	−1.13644	−	0.0990513i
$147$			0.192506i			0.0158776i
$148$	1.83177	−	10.4283i	0.150571	−	0.857204i
$149$		−	13.3703i		−	1.09534i	−0.836695	−	0.547669i	$-0.815515\pi$
$149$		−	13.3703i		−	1.09534i	0.836695	−	0.547669i	$-0.184485\pi$
$150$	−0.0923345	+	1.05937i	−0.00753908	+	0.0864974i
$151$	3.67367			0.298959			0.149479	−	0.988765i	$-0.452240\pi$
$151$	3.67367			0.298959			0.149479	+	0.988765i	$0.452240\pi$
$152$	−2.22824	+	8.34863i	−0.180734	+	0.677163i
$153$	14.8686			1.20205
$154$	0.123209	−	1.41360i	0.00992845	−	0.113911i
$155$		−	15.9040i		−	1.27744i
$156$	−0.379206	−	0.0666089i	−0.0303608	−	0.00533298i
$157$		−	2.33182i		−	0.186099i	−0.995661	−	0.0930496i	$-0.970338\pi$
$157$		−	2.33182i		−	0.186099i	0.995661	−	0.0930496i	$-0.0296615\pi$
$158$	−2.00516	−	0.174769i	−0.159522	−	0.0139039i
$159$	−0.667184			−0.0529112
$160$	7.10952	−	15.3117i	0.562057	−	1.21049i
$161$	1.46785			0.115682
$162$	−12.2119	−	1.06438i	−0.959457	−	0.0836258i
$163$		−	20.5746i		−	1.61152i	−0.592239	−	0.805762i	$-0.701756\pi$
$163$		−	20.5746i		−	1.61152i	0.592239	−	0.805762i	$-0.298244\pi$
$164$	−5.49748	−	0.965651i	−0.429281	−	0.0754047i
$165$		−	0.576422i		−	0.0448744i
$166$	0.564643	−	6.47827i	0.0438248	−	0.502811i
$167$	17.9718			1.39070			0.695350	−	0.718671i	$-0.255249\pi$
$167$	17.9718			1.39070			0.695350	+	0.718671i	$0.255249\pi$
$168$	0.140409	−	0.526074i	0.0108328	−	0.0405875i
$169$	−1.00000			−0.0769231
$170$	1.83897	−	21.0989i	0.141043	−	1.61821i
$171$		−	9.05182i		−	0.692210i
$172$	−0.441738	+	2.51483i	−0.0336822	+	0.191754i
$173$		−	22.1185i		−	1.68164i	−0.541314	−	0.840821i	$-0.682073\pi$
$173$		−	22.1185i		−	1.68164i	0.541314	−	0.840821i	$-0.317927\pi$
$174$	1.89880	+	0.165498i	0.143947	+	0.0125464i
$175$	−3.90601			−0.295266
$176$	−1.36774	+	3.77318i	−0.103098	+	0.284414i
$177$	−2.71317			−0.203934
$178$	−1.84533	−	0.160838i	−0.138313	−	0.0120553i
$179$		−	22.1673i		−	1.65686i	−0.560093	−	0.828429i	$-0.689235\pi$
$179$		−	22.1673i		−	1.65686i	0.560093	−	0.828429i	$-0.310765\pi$
$180$	−3.05952	+	17.4179i	−0.228043	+	1.29825i
$181$		−	10.9406i		−	0.813210i	−0.913604	−	0.406605i	$-0.866713\pi$
$181$		−	10.9406i		−	0.813210i	0.913604	−	0.406605i	$-0.133287\pi$
$182$	0.122797	−	1.40887i	0.00910229	−	0.104433i
$183$	−1.31297			−0.0970576
$184$	−4.01128	−	1.07061i	−0.295715	−	0.0789262i
$185$	15.7988			1.16155
$186$	−0.125978	+	1.44537i	−0.00923715	+	0.105980i
$187$			5.03503i			0.368198i
$188$	−7.43294	−	1.30562i	−0.542103	−	0.0952223i
$189$			1.14790i			0.0834976i
$190$	−12.8448	−	1.11954i	−0.931857	−	0.0812202i
$191$	−23.1767			−1.67701			−0.838503	−	0.544897i	$-0.816569\pi$
$191$	−23.1767			−1.67701			−0.838503	+	0.544897i	$0.816569\pi$
$192$	−0.767408	+	1.33523i	−0.0553829	+	0.0963617i
$193$	−4.80618			−0.345956			−0.172978	−	0.984926i	$-0.555339\pi$
$193$	−4.80618			−0.345956			−0.172978	+	0.984926i	$0.555339\pi$
$194$	23.4824	+	2.04671i	1.68594	+	0.146946i
$195$		−	0.574494i		−	0.0411404i
$196$	1.96984	+	0.346010i	0.140703	+	0.0247150i
$197$			10.2280i			0.728716i	0.931259	+	0.364358i	$0.118712\pi$
$197$			10.2280i			0.728716i	−0.931259	+	0.364358i	$0.881288\pi$
$198$	0.365061	−	4.18842i	0.0259437	−	0.297658i
$199$	1.69234			0.119967			0.0599833	−	0.998199i	$-0.480895\pi$
$199$	1.69234			0.119967			0.0599833	+	0.998199i	$0.480895\pi$
$200$	10.6742	+	2.84894i	0.754781	+	0.201450i
$201$	2.15127			0.151739
$202$	1.90889	−	21.9011i	0.134309	−	1.54095i
$203$			7.00104i			0.491377i
$204$	−0.334256	+	1.90293i	−0.0234026	+	0.133232i
$205$		−	8.32863i		−	0.581697i
$206$	13.1778	+	1.14857i	0.918140	+	0.0800246i
$207$	4.34914			0.302286
$208$	−1.36317	+	3.76055i	−0.0945187	+	0.260748i
$209$	3.06526			0.212029
$210$	0.809389	+	0.0705460i	0.0558531	+	0.00486813i
$211$			3.70828i			0.255288i	0.991820	+	0.127644i	$0.0407415\pi$
$211$			3.70828i			0.255288i	−0.991820	+	0.127644i	$0.959258\pi$
$212$	−1.19920	+	6.82705i	−0.0823611	+	0.468884i
$213$			1.46340i			0.100270i
$214$	−2.47069	+	28.3467i	−0.168893	+	1.93774i
$215$	−3.80994			−0.259836
$216$	0.837249	−	3.13695i	0.0569676	−	0.213442i
$217$	−5.32922			−0.361771
$218$	1.13905	−	13.0685i	0.0771459	−	0.885112i
$219$			1.87626i			0.126786i
$220$	−5.89832	−	1.03606i	−0.397665	−	0.0698512i
$221$			5.01819i			0.337560i
$222$	−1.43582	−	0.125145i	−0.0963658	−	0.00839920i
$223$	−15.9566			−1.06853			−0.534266	−	0.845316i	$-0.679412\pi$
$223$	−15.9566			−1.06853			−0.534266	+	0.845316i	$0.679412\pi$
$224$	−5.13075	−	2.38231i	−0.342813	−	0.159175i
$225$	−11.5733			−0.771551
$226$	22.2571	+	1.93992i	1.48052	+	0.129041i
$227$			1.84030i			0.122145i	0.998133	+	0.0610724i	$0.0194521\pi$
$227$			1.84030i			0.122145i	−0.998133	+	0.0610724i	$0.980548\pi$
$228$	1.15848	+	0.203491i	0.0767222	+	0.0134765i
$229$		−	9.57637i		−	0.632825i	−0.948622	−	0.316412i	$-0.897522\pi$
$229$		−	9.57637i		−	0.632825i	0.948622	−	0.316412i	$-0.102478\pi$
$230$	0.537909	−	6.17154i	0.0354686	−	0.406939i
$231$	−0.193152			−0.0127085
$232$	5.10637	−	19.1322i	0.335250	−	1.25609i
$233$	−8.11239			−0.531460			−0.265730	−	0.964047i	$-0.585613\pi$
$233$	−8.11239			−0.531460			−0.265730	+	0.964047i	$0.585613\pi$
$234$	0.363839	−	4.17441i	0.0237849	−	0.272889i
$235$		−	11.2608i		−	0.734577i
$236$	−4.87664	+	27.7629i	−0.317442	+	1.80721i
$237$			0.273982i			0.0177971i
$238$	−7.06998	−	0.616216i	−0.458279	−	0.0399434i
$239$	16.8998			1.09316			0.546578	−	0.837408i	$-0.315930\pi$
$239$	16.8998			1.09316			0.546578	+	0.837408i	$0.315930\pi$
$240$	−2.16042	−	0.783132i	−0.139454	−	0.0505510i
$241$	11.4349			0.736584			0.368292	−	0.929710i	$-0.379943\pi$
$241$	11.4349			0.736584			0.368292	+	0.929710i	$0.379943\pi$
$242$	−14.0792	−	1.22714i	−0.905048	−	0.0788836i
$243$			5.11232i			0.327955i
$244$	−2.35993	+	13.4351i	−0.151079	+	0.860097i
$245$			2.98429i			0.190660i
$246$	−0.0659725	+	0.756916i	−0.00420625	+	0.0482592i
$247$	3.05501			0.194386
$248$	14.5635	+	3.88699i	0.924784	+	0.246824i
$249$	−0.885180			−0.0560960
$250$	0.400906	−	4.59968i	0.0253555	−	0.290909i
$251$		−	5.94790i		−	0.375428i	−0.982224	−	0.187714i	$-0.939892\pi$
$251$		−	5.94790i		−	0.375428i	0.982224	−	0.187714i	$-0.0601078\pi$
$252$	5.83653	+	1.02521i	0.367667	+	0.0645819i
$253$			1.47277i			0.0925924i
$254$	−11.4185	−	0.995233i	−0.716462	−	0.0624465i
$255$	−2.88292			−0.180535
$256$	12.2835	+	10.2525i	0.767721	+	0.640784i
$257$	21.2037			1.32265			0.661325	−	0.750100i	$-0.269995\pi$
$257$	21.2037			1.32265			0.661325	+	0.750100i	$0.269995\pi$
$258$	0.346252	+	0.0301792i	0.0215567	+	0.00187887i
$259$		−	5.29400i		−	0.328953i
$260$	−5.87859	−	1.03259i	−0.364574	−	0.0640388i
$261$			20.7437i			1.28400i
$262$	−0.774214	+	8.88272i	−0.0478311	+	0.548776i
$263$	−8.45169			−0.521154			−0.260577	−	0.965453i	$-0.583913\pi$
$263$	−8.45169			−0.521154			−0.260577	+	0.965453i	$0.583913\pi$
$264$	0.527840	+	0.140880i	0.0324863	+	0.00867056i
$265$	−10.3429			−0.635361
$266$	−0.375145	+	4.30412i	−0.0230016	+	0.263903i
$267$			0.252142i			0.0154309i
$268$	3.86669	−	22.0132i	0.236195	−	1.34467i
$269$			19.7776i			1.20586i	0.797794	+	0.602930i	$0.206000\pi$
$269$			19.7776i			1.20586i	−0.797794	+	0.602930i	$0.794000\pi$
$270$	4.82634	+	0.420661i	0.293722	+	0.0256006i
$271$	4.60443			0.279699			0.139850	−	0.990173i	$-0.455338\pi$
$271$	4.60443			0.279699			0.139850	+	0.990173i	$0.455338\pi$
$272$	18.8712	+	6.84063i	1.14423	+	0.414774i
$273$	−0.192506			−0.0116510
$274$	2.17866	+	0.189891i	0.131618	+	0.0114717i
$275$		−	3.91912i		−	0.236332i
$276$	−0.0977716	+	0.556616i	−0.00588516	+	0.0335044i
$277$		−	7.51131i		−	0.451311i	−0.974207	−	0.225656i	$-0.927548\pi$
$277$		−	7.51131i		−	0.451311i	0.974207	−	0.225656i	$-0.0724524\pi$
$278$	−0.832469	+	9.55109i	−0.0499282	+	0.572836i
$279$	−15.7902			−0.945333
$280$	2.17666	−	8.15538i	0.130081	−	0.487377i
$281$	11.6161			0.692959			0.346480	−	0.938057i	$-0.387377\pi$
$281$	11.6161			0.692959			0.346480	+	0.938057i	$0.387377\pi$
$282$	−0.0891990	+	1.02340i	−0.00531172	+	0.0609425i
$283$		−	9.43050i		−	0.560585i	−0.959915	−	0.280292i	$-0.909569\pi$
$283$		−	9.43050i		−	0.560585i	0.959915	−	0.280292i	$-0.0904315\pi$
$284$	14.9744	+	2.63031i	0.888567	+	0.156080i
$285$			1.75509i			0.103962i
$286$	1.41360	+	0.123209i	0.0835880	+	0.00728549i
$287$	−2.79082			−0.164737
$288$	−15.2021	−	7.05866i	−0.895793	−	0.415935i
$289$	8.18219			0.481305
$290$	29.4358	+	2.56561i	1.72853	+	0.150658i
$291$		−	3.20860i		−	0.188091i
$292$	19.1991	+	3.37239i	1.12354	+	0.197354i
$293$		−	17.4997i		−	1.02234i	−0.859479	−	0.511171i	$-0.829212\pi$
$293$		−	17.4997i		−	1.02234i	0.859479	−	0.511171i	$-0.170788\pi$
$294$	0.0236391	−	0.271216i	0.00137866	−	0.0158177i
$295$	−42.0605			−2.44886
$296$	−3.86130	+	14.4673i	−0.224434	+	0.840893i
$297$	−1.15175			−0.0668316
$298$	−1.64183	+	18.8370i	−0.0951086	+	1.09120i
$299$			1.46785i			0.0848877i
$300$	0.260175	−	1.48118i	0.0150212	−	0.0855161i
$301$			1.27667i			0.0735858i
$302$	−5.17573	−	0.451114i	−0.297830	−	0.0259587i
$303$	−2.99253			−0.171916
$304$	4.16449	−	11.4885i	0.238850	−	0.658913i
$305$	−20.3541			−1.16547
$306$	−20.9479	−	1.82581i	−1.19751	−	0.104375i
$307$			30.6469i			1.74911i	0.484925	+	0.874556i	$0.338847\pi$
$307$			30.6469i			1.74911i	−0.484925	+	0.874556i	$0.661153\pi$
$308$	−0.347171	+	1.97645i	−0.0197819	+	0.112619i
$309$		−	1.80059i		−	0.102432i
$310$	−1.95295	+	22.4066i	−0.110920	+	1.27261i
$311$	−12.5674			−0.712634			−0.356317	−	0.934365i	$-0.615968\pi$
$311$	−12.5674			−0.712634			−0.356317	+	0.934365i	$0.615968\pi$
$312$	0.526074	+	0.140409i	0.0297831	+	0.00794908i
$313$	20.1689			1.14002			0.570008	−	0.821639i	$-0.306940\pi$
$313$	20.1689			1.14002			0.570008	+	0.821639i	$0.306940\pi$
$314$	−0.286339	+	3.28523i	−0.0161591	+	0.185396i
$315$			8.84229i			0.498206i
$316$	2.80356	+	0.492455i	0.157712	+	0.0277027i
$317$		−	3.46083i		−	0.194380i	−0.995266	−	0.0971898i	$-0.969015\pi$
$317$		−	3.46083i		−	0.194380i	0.995266	−	0.0971898i	$-0.0309854\pi$
$318$	0.939977	+	0.0819280i	0.0527113	+	0.00459429i
$319$	−7.02454			−0.393299
$320$	−11.8966	+	20.6991i	−0.665042	+	1.15712i
$321$	3.87325			0.216184
$322$	−2.06801	−	0.180247i	−0.115246	−	0.0100447i
$323$		−	15.3306i		−	0.853018i
$324$	17.0743	+	2.99916i	0.948572	+	0.166620i
$325$		−	3.90601i		−	0.216666i
$326$	−2.52649	+	28.9869i	−0.139929	+	1.60544i
$327$	−1.78566			−0.0987472
$328$	7.62667	+	2.03555i	0.421112	+	0.112395i
$329$	−3.77337			−0.208033
$330$	−0.0707828	+	0.812106i	−0.00389646	+	0.0447049i
$331$			27.9694i			1.53734i	0.639648	+	0.768668i	$0.279080\pi$
$331$			27.9694i			1.53734i	−0.639648	+	0.768668i	$0.720920\pi$
$332$	−1.59102	+	9.05772i	−0.0873186	+	0.497107i
$333$		−	15.6858i		−	0.859577i
$334$	−25.3200	−	2.20688i	−1.38545	−	0.120755i
$335$	33.3497			1.82209
$336$	−0.262418	+	0.723929i	−0.0143161	+	0.0394936i
$337$	20.7057			1.12791			0.563957	−	0.825804i	$-0.309278\pi$
$337$	20.7057			1.12791			0.563957	+	0.825804i	$0.309278\pi$
$338$	1.40887	+	0.122797i	0.0766325	+	0.00667926i
$339$		−	3.04117i		−	0.165174i
$340$	−5.18175	+	29.4998i	−0.281020	+	1.59985i
$341$		−	5.34711i		−	0.289562i
$342$	−1.11153	+	12.7529i	−0.0601048	+	0.689595i
$343$	1.00000			0.0539949
$344$	0.931166	−	3.48883i	0.0502051	−	0.188105i
$345$	−0.843269			−0.0454001
$346$	−2.71608	+	31.1622i	−0.146018	+	1.67529i
$347$			7.14734i			0.383689i	0.981425	+	0.191845i	$0.0614470\pi$
$347$			7.14734i			0.383689i	−0.981425	+	0.191845i	$0.938553\pi$
$348$	−2.65484	−	0.466332i	−0.142314	−	0.0249980i
$349$		−	10.9558i		−	0.586451i	−0.956043	−	0.293225i	$-0.905271\pi$
$349$		−	10.9558i		−	0.586451i	0.956043	−	0.293225i	$-0.0947286\pi$
$350$	5.50307	+	0.479645i	0.294151	+	0.0256381i
$351$	−1.14790			−0.0612705
$352$	2.39031	−	5.14797i	0.127404	−	0.274388i
$353$	−18.4422			−0.981577			−0.490788	−	0.871279i	$-0.663291\pi$
$353$	−18.4422			−0.981577			−0.490788	+	0.871279i	$0.663291\pi$
$354$	3.82251	+	0.333168i	0.203164	+	0.0177077i
$355$			22.6861i			1.20405i
$356$	2.58008	+	0.453200i	0.136744	+	0.0240196i
$357$			0.966031i			0.0511278i
$358$	−2.72207	+	31.2308i	−0.143866	+	1.65060i
$359$	11.8687			0.626405			0.313202	−	0.949686i	$-0.398598\pi$
$359$	11.8687			0.626405			0.313202	+	0.949686i	$0.398598\pi$
$360$	6.44933	−	24.1639i	0.339909	−	1.27355i
$361$	9.66691			0.508785
$362$	−1.34347	+	15.4139i	−0.0706113	+	0.810138i
$363$			1.92376i			0.100971i
$364$	−0.346010	+	1.96984i	−0.0181358	+	0.103248i
$365$			29.0865i			1.52246i
$366$	1.84981	+	0.161228i	0.0966910	+	0.00842754i
$367$	−2.19123			−0.114381			−0.0571905	−	0.998363i	$-0.518214\pi$
$367$	−2.19123			−0.114381			−0.0571905	+	0.998363i	$0.518214\pi$
$368$	5.51991	+	2.00092i	0.287745	+	0.104305i
$369$	−8.26904			−0.430469
$370$	−22.2586	−	1.94005i	−1.15717	−	0.100858i
$371$			3.46579i			0.179935i
$372$	0.354974	−	2.02087i	0.0184045	−	0.104777i
$373$		−	28.2440i		−	1.46242i	−0.682152	−	0.731211i	$-0.738956\pi$
$373$		−	28.2440i		−	1.46242i	0.682152	−	0.731211i	$-0.261044\pi$
$374$	0.618285	−	7.09371i	0.0319707	−	0.366807i
$375$	−0.628492			−0.0324552
$376$	10.3117	+	2.75220i	0.531787	+	0.141934i
$377$	−7.00104			−0.360572
$378$	0.140958	−	1.61725i	0.00725012	−	0.0831822i
$379$		−	18.7465i		−	0.962942i	−0.876462	−	0.481471i	$-0.840103\pi$
$379$		−	18.7465i		−	0.962942i	0.876462	−	0.481471i	$-0.159897\pi$
$380$	17.9591	+	3.15459i	0.921285	+	0.161827i
$381$			1.56021i			0.0799319i
$382$	32.6530	+	2.84602i	1.67067	+	0.145615i
$383$	20.5013			1.04757			0.523785	−	0.851851i	$-0.324520\pi$
$383$	20.5013			1.04757			0.523785	+	0.851851i	$0.324520\pi$
$384$	1.24514	−	1.78693i	0.0635409	−	0.0911888i
$385$	−2.99431			−0.152604
$386$	6.77129	+	0.590183i	0.344650	+	0.0300395i
$387$			3.78268i			0.192285i
$388$	−32.8324	−	5.76712i	−1.66681	−	0.292781i
$389$		−	28.1868i		−	1.42913i	−0.699572	−	0.714563i	$-0.746626\pi$
$389$		−	28.1868i		−	1.42913i	0.699572	−	0.714563i	$-0.253374\pi$
$390$	−0.0705460	+	0.809389i	−0.00357223	+	0.0409850i
$391$	7.36592			0.372511
$392$	−2.73277	−	0.729373i	−0.138026	−	0.0368389i
$393$	1.21372			0.0612241
$394$	1.25597	−	14.4100i	0.0632747	−	0.725964i
$395$			4.24737i			0.213708i
$396$	−1.02865	+	5.85612i	−0.0516915	+	0.294281i
$397$		−	13.0095i		−	0.652927i	−0.945210	−	0.326464i	$-0.894143\pi$
$397$		−	13.0095i		−	0.652927i	0.945210	−	0.326464i	$-0.105857\pi$
$398$	−2.38428	−	0.207813i	−0.119513	−	0.0104167i
$399$	0.588108			0.0294422
$400$	−14.6888	−	5.32455i	−0.734438	−	0.266227i
$401$	−21.1050			−1.05393			−0.526967	−	0.849885i	$-0.676671\pi$
$401$	−21.1050			−1.05393			−0.526967	+	0.849885i	$0.676671\pi$
$402$	−3.03086	−	0.264169i	−0.151166	−	0.0131755i
$403$		−	5.32922i		−	0.265467i
$404$	−5.37876	+	30.6214i	−0.267603	+	1.52347i
$405$			25.8674i			1.28536i
$406$	0.859704	−	9.86357i	0.0426664	−	0.489521i
$407$	5.31177			0.263295
$408$	0.704597	−	2.63994i	0.0348827	−	0.130696i
$409$	15.8968			0.786047			0.393024	−	0.919528i	$-0.371429\pi$
$409$	15.8968			0.786047			0.393024	+	0.919528i	$0.371429\pi$
$410$	−1.02273	+	11.7340i	−0.0505089	+	0.579500i
$411$		−	0.297688i		−	0.0146839i
$412$	−18.4248	−	3.23638i	−0.907723	−	0.159445i
$413$			14.0940i			0.693518i
$414$	−6.12738	−	0.534060i	−0.301144	−	0.0262476i
$415$	−13.7224			−0.673605
$416$	2.38231	−	5.13075i	0.116803	−	0.251556i
$417$	1.30504			0.0639083
$418$	−4.31857	−	0.376404i	−0.211228	−	0.0184105i
$419$		−	17.9388i		−	0.876367i	−0.898886	−	0.438183i	$-0.855622\pi$
$419$		−	17.9388i		−	0.876367i	0.898886	−	0.438183i	$-0.144378\pi$
$420$	−1.13166	−	0.198781i	−0.0552195	−	0.00969950i
$421$		−	13.0158i		−	0.634349i	−0.948367	−	0.317174i	$-0.897266\pi$
$421$		−	13.0158i		−	0.634349i	0.948367	−	0.317174i	$-0.102734\pi$
$422$	0.455364	−	5.22449i	0.0221668	−	0.254324i
$423$	−11.1803			−0.543604
$424$	2.52785	−	9.47118i	0.122763	−	0.459961i
$425$	−19.6011			−0.950792
$426$	0.179700	−	2.06174i	0.00870651	−	0.0998916i
$427$			6.82042i			0.330063i
$428$	6.96176	−	39.6335i	0.336510	−	1.91576i
$429$		−	0.193152i		−	0.00932547i
$430$	5.36772	+	0.467848i	0.258855	+	0.0225616i
$431$	17.8703			0.860781			0.430390	−	0.902643i	$-0.358376\pi$
$431$	17.8703			0.860781			0.430390	+	0.902643i	$0.358376\pi$
$432$	−1.56478	+	4.31675i	−0.0752857	+	0.207690i
$433$	8.67996			0.417132			0.208566	−	0.978008i	$-0.433120\pi$
$433$	8.67996			0.417132			0.208566	+	0.978008i	$0.433120\pi$
$434$	7.50819	+	0.654410i	0.360405	+	0.0314127i
$435$		−	4.02206i		−	0.192843i
$436$	−3.20954	+	18.2720i	−0.153709	+	0.875070i
$437$		−	4.48428i		−	0.214512i
$438$	0.230399	−	2.64342i	0.0110089	−	0.126307i
$439$	40.1155			1.91461			0.957305	−	0.289079i	$-0.0933491\pi$
$439$	40.1155			1.91461			0.957305	+	0.289079i	$0.0933491\pi$
$440$	8.18275	+	2.18397i	0.390097	+	0.104117i
$441$	2.96294			0.141092
$442$	0.616216	−	7.06998i	0.0293104	−	0.336285i
$443$			10.0772i			0.478784i	0.970923	+	0.239392i	$0.0769481\pi$
$443$			10.0772i			0.478784i	−0.970923	+	0.239392i	$0.923052\pi$
$444$	2.00752	+	0.352628i	0.0952726	+	0.0167350i
$445$			3.90880i			0.185295i
$446$	22.4808	+	1.95942i	1.06450	+	0.0927810i
$447$	2.57386			0.121740
$448$	6.93603	+	3.98641i	0.327697	+	0.188340i
$449$	22.9511			1.08313			0.541565	−	0.840659i	$-0.317832\pi$
$449$	22.9511			1.08313			0.541565	+	0.840659i	$0.317832\pi$
$450$	16.3053	+	1.42116i	0.768637	+	0.0669941i
$451$		−	2.80019i		−	0.131856i
$452$	−31.1192	−	5.46619i	−1.46372	−	0.257108i
$453$			0.707202i			0.0332273i
$454$	0.225982	−	2.59274i	0.0106059	−	0.121684i
$455$	−2.98429			−0.139906
$456$	−1.60716	−	0.428950i	−0.0752622	−	0.0200874i
$457$	39.5146			1.84842			0.924208	−	0.381890i	$-0.124727\pi$
$457$	39.5146			1.84842			0.924208	+	0.381890i	$0.124727\pi$
$458$	−1.17595	+	13.4919i	−0.0549484	+	0.630434i
$459$			5.76038i			0.268872i
$460$	−1.51569	+	8.62886i	−0.0706694	+	0.402323i
$461$			28.6519i			1.33445i	0.744856	+	0.667225i	$0.232518\pi$
$461$			28.6519i			1.33445i	−0.744856	+	0.667225i	$0.767482\pi$
$462$	0.272127	+	0.0237184i	0.0126605	+	0.00110348i
$463$	35.3773			1.64412			0.822062	−	0.569398i	$-0.192824\pi$
$463$	35.3773			1.64412			0.822062	+	0.569398i	$0.192824\pi$
$464$	−9.54360	+	26.3278i	−0.443050	+	1.22224i
$465$	3.06161			0.141979
$466$	11.4293	+	0.996174i	0.529453	+	0.0461469i
$467$		−	1.25168i		−	0.0579208i	−0.999581	−	0.0289604i	$-0.990780\pi$
$467$		−	1.25168i		−	0.0579208i	0.999581	−	0.0289604i	$-0.00921967\pi$
$468$	−1.02521	+	5.83653i	−0.0473902	+	0.269794i
$469$		−	11.1751i		−	0.516017i
$470$	−1.38279	+	15.8651i	−0.0637835	+	0.731802i
$471$	0.448889			0.0206837
$472$	10.2798	−	38.5155i	0.473164	−	1.77282i
$473$	−1.28095			−0.0588982
$474$	0.0336441	−	0.386006i	0.00154532	−	0.0177298i
$475$			11.9329i			0.547519i
$476$	9.88503	+	1.73634i	0.453080	+	0.0795850i
$477$			10.2689i			0.470182i
$478$	−23.8096	−	2.07524i	−1.08903	−	0.0949190i
$479$	−36.3649			−1.66155			−0.830777	−	0.556605i	$-0.812104\pi$
$479$	−36.3649			−1.66155			−0.830777	+	0.556605i	$0.812104\pi$
$480$	2.94759	+	1.36863i	0.134538	+	0.0624689i
$481$	5.29400			0.241386
$482$	−16.1103	−	1.40416i	−0.733802	−	0.0639578i
$483$			0.282569i			0.0128573i
$484$	19.6852	+	3.45777i	0.894781	+	0.157171i
$485$		−	49.7408i		−	2.25861i
$486$	0.627775	−	7.20260i	0.0284765	−	0.326717i
$487$	−31.8906			−1.44510			−0.722551	−	0.691317i	$-0.757031\pi$
$487$	−31.8906			−1.44510			−0.722551	+	0.691317i	$0.757031\pi$
$488$	4.97463	−	18.6386i	0.225191	−	0.843730i
$489$	3.96073			0.179110
$490$	0.366461	−	4.20449i	0.0165550	−	0.189939i
$491$		−	39.2263i		−	1.77026i	−0.465346	−	0.885129i	$-0.654070\pi$
$491$		−	39.2263i		−	1.77026i	0.465346	−	0.885129i	$-0.345930\pi$
$492$	0.185894	−	1.05830i	0.00838073	−	0.0477117i
$493$			35.1325i			1.58229i
$494$	−4.30412	−	0.375145i	−0.193652	−	0.0168786i
$495$	−8.87197			−0.398765
$496$	−20.0408	−	7.26463i	−0.899860	−	0.326191i
$497$	7.60183			0.340989
$498$	1.24711	+	0.108697i	0.0558841	+	0.00487084i
$499$		−	7.62400i		−	0.341297i	−0.985332	−	0.170649i	$-0.945414\pi$
$499$		−	7.62400i		−	0.341297i	0.985332	−	0.170649i	$-0.0545863\pi$
$500$	−1.12965	+	6.43113i	−0.0505195	+	0.287609i
$501$			3.45968i			0.154567i
$502$	−0.730382	+	8.37983i	−0.0325986	+	0.374010i
$503$	−1.85374			−0.0826540			−0.0413270	−	0.999146i	$-0.513159\pi$
$503$	−1.85374			−0.0826540			−0.0413270	+	0.999146i	$0.513159\pi$
$504$	−8.09703	−	2.16109i	−0.360670	−	0.0962626i
$505$	−46.3912			−2.06438
$506$	0.180852	−	2.07495i	0.00803983	−	0.0922427i
$507$		−	0.192506i		−	0.00854949i
$508$	15.9650	+	2.80431i	0.708334	+	0.124421i
$509$		−	1.69436i		−	0.0751011i	−0.999295	−	0.0375505i	$-0.988044\pi$
$509$		−	1.69436i		−	0.0751011i	0.999295	−	0.0375505i	$-0.0119555\pi$
$510$	4.06166	+	0.354013i	0.179854	+	0.0156760i
$511$	9.74653			0.431161
$512$	−16.0470	−	15.9529i	−0.709182	−	0.705025i
$513$	3.50685			0.154831
$514$	−29.8733	−	2.60374i	−1.31765	−	0.114846i
$515$		−	27.9134i		−	1.23001i
$516$	−0.484119	−	0.0850373i	−0.0213122	−	0.00374356i
$517$		−	3.78604i		−	0.166510i
$518$	−0.650085	+	7.45857i	−0.0285631	+	0.327711i
$519$	4.25795			0.186903
$520$	8.15538	+	2.17666i	0.357637	+	0.0954530i
$521$	−23.6564			−1.03641			−0.518203	−	0.855258i	$-0.673399\pi$
$521$	−23.6564			−1.03641			−0.518203	+	0.855258i	$0.673399\pi$
$522$	2.54725	−	29.2252i	0.111490	−	1.27915i
$523$			1.75108i			0.0765693i	0.999267	+	0.0382847i	$0.0121894\pi$
$523$			1.75108i			0.0765693i	−0.999267	+	0.0382847i	$0.987811\pi$
$524$	2.18154	−	12.4195i	0.0953009	−	0.542550i
$525$		−	0.751930i		−	0.0328169i
$526$	11.9074	+	1.03784i	0.519185	+	0.0452519i
$527$	−26.7430			−1.16494
$528$	−0.726359	−	0.263299i	−0.0316107	−	0.0114586i
$529$	−20.8454			−0.906323
$530$	14.5719	+	1.27008i	0.632961	+	0.0551686i
$531$			41.7596i			1.81221i
$532$	1.05706	−	6.01789i	0.0458295	−	0.260909i
$533$		−	2.79082i		−	0.120884i
$534$	0.0309623	−	0.355237i	0.00133987	−	0.0153726i
$535$	60.0444			2.59595
$536$	−8.15081	+	30.5389i	−0.352061	+	1.31908i
$537$	4.26733			0.184149
$538$	2.42862	−	27.8641i	0.104705	−	1.20131i
$539$			1.00336i			0.0432176i
$540$	−6.74804	−	1.18532i	−0.290389	−	0.0510079i
$541$		−	4.77614i		−	0.205342i	−0.994715	−	0.102671i	$-0.967261\pi$
$541$		−	4.77614i		−	0.205342i	0.994715	−	0.102671i	$-0.0327389\pi$
$542$	−6.48705	−	0.565409i	−0.278643	−	0.0242864i
$543$	2.10613			0.0903829
$544$	−25.7471	−	11.9549i	−1.10390	−	0.512562i
$545$	−27.6819			−1.18576
$546$	0.271216	+	0.0236391i	0.0116070	+	0.00101166i
$547$			22.4810i			0.961216i	0.876936	+	0.480608i	$0.159584\pi$
$547$			22.4810i			0.961216i	−0.876936	+	0.480608i	$0.840416\pi$
$548$	−3.04613	−	0.535064i	−0.130124	−	0.0228568i
$549$			20.2085i			0.862477i
$550$	−0.481255	+	5.52154i	−0.0205208	+	0.235439i
$551$	21.3883			0.911170
$552$	0.206098	−	0.772195i	0.00877212	−	0.0328668i
$553$	1.42324			0.0605223
$554$	−0.922364	+	10.5825i	−0.0391875	+	0.449607i
$555$			3.04137i			0.129099i
$556$	2.34568	−	13.3540i	0.0994792	−	0.566338i
$557$		−	23.4582i		−	0.993956i	−0.867763	−	0.496978i	$-0.834443\pi$
$557$		−	23.4582i		−	0.993956i	0.867763	−	0.496978i	$-0.165557\pi$
$558$	22.2463	+	1.93898i	0.941762	+	0.0820836i
$559$	−1.27667			−0.0539972
$560$	−4.06809	+	11.2226i	−0.171908	+	0.474241i
$561$	−0.969273			−0.0409227
$562$	−16.3656	−	1.42642i	−0.690342	−	0.0601699i
$563$			15.3821i			0.648278i	0.946009	+	0.324139i	$0.105075\pi$
$563$			15.3821i			0.648278i	−0.946009	+	0.324139i	$0.894925\pi$
$564$	0.251340	−	1.43089i	0.0105833	−	0.0602512i
$565$		−	47.1452i		−	1.98342i
$566$	−1.15803	+	13.2864i	−0.0486758	+	0.558468i
$567$	8.66785			0.364015
$568$	−20.7740	−	5.54457i	−0.871659	−	0.232645i
$569$	−34.5507			−1.44844			−0.724221	−	0.689568i	$-0.757800\pi$
$569$	−34.5507			−1.44844			−0.724221	+	0.689568i	$0.757800\pi$
$570$	0.215519	−	2.47269i	0.00902708	−	0.103570i
$571$			39.3464i			1.64660i	0.567608	+	0.823299i	$0.307869\pi$
$571$			39.3464i			1.64660i	−0.567608	+	0.823299i	$0.692131\pi$
$572$	−1.97645	−	0.347171i	−0.0826397	−	0.0145159i
$573$		−	4.46165i		−	0.186388i
$574$	3.93191	+	0.342704i	0.164115	+	0.0143042i
$575$	−5.73342			−0.239100
$576$	20.5510	+	11.8115i	0.856294	+	0.492146i
$577$	−29.2664			−1.21838			−0.609189	−	0.793025i	$-0.708505\pi$
$577$	−29.2664			−1.21838			−0.609189	+	0.793025i	$0.708505\pi$
$578$	−11.5277	−	1.00475i	−0.479487	−	0.0417919i
$579$		−	0.925218i		−	0.0384508i
$580$	−41.1562	−	7.22923i	−1.70892	−	0.300178i
$581$			4.59820i			0.190765i
$582$	−0.394005	+	4.52050i	−0.0163320	+	0.187381i
$583$	−3.47742			−0.144020
$584$	−26.6350	−	7.10886i	−1.10216	−	0.294167i
$585$	−8.84229			−0.365584
$586$	−2.14890	+	24.6548i	−0.0887703	+	1.01848i
$587$			20.2321i			0.835067i	0.908662	+	0.417533i	$0.137105\pi$
$587$			20.2321i			0.835067i	−0.908662	+	0.417533i	$0.862895\pi$
$588$	−0.0666089	+	0.379206i	−0.00274690	+	0.0156382i
$589$			16.2808i			0.670840i
$590$	59.2579	+	5.16489i	2.43961	+	0.212635i
$591$	−1.96895			−0.0809919
$592$	7.21661	−	19.9084i	0.296601	−	0.818229i
$593$	20.3894			0.837291			0.418646	−	0.908150i	$-0.362505\pi$
$593$	20.3894			0.837291			0.418646	+	0.908150i	$0.362505\pi$
$594$	1.62267	+	0.141432i	0.0665792	+	0.00580301i
$595$			14.9757i			0.613945i
$596$	4.62625	−	26.3374i	0.189499	−	1.07882i
$597$			0.325785i			0.0133335i
$598$	0.180247	−	2.06801i	0.00737083	−	0.0845671i
$599$	−36.8376			−1.50514			−0.752571	−	0.658511i	$-0.771186\pi$
$599$	−36.8376			−1.50514			−0.752571	+	0.658511i	$0.771186\pi$
$600$	−0.548437	+	2.05485i	−0.0223899	+	0.0838888i
$601$	4.24761			0.173264			0.0866318	−	0.996240i	$-0.472390\pi$
$601$	4.24761			0.173264			0.0866318	+	0.996240i	$0.472390\pi$
$602$	0.156770	−	1.79866i	0.00638948	−	0.0733078i
$603$		−	33.1111i		−	1.34839i
$604$	7.23654	+	1.27112i	0.294451	+	0.0517213i
$605$			29.8229i			1.21247i
$606$	4.21609	+	0.367472i	0.171267	+	0.0149275i
$607$	−22.9363			−0.930955			−0.465477	−	0.885060i	$-0.654117\pi$
$607$	−22.9363			−0.930955			−0.465477	+	0.885060i	$0.654117\pi$
$608$	−7.27799	+	15.6745i	−0.295162	+	0.635685i
$609$	−1.34774			−0.0546133
$610$	28.6764	+	2.49942i	1.16107	+	0.101198i
$611$		−	3.77337i		−	0.152654i
$612$	29.2888	+	5.14468i	1.18393	+	0.207961i
$613$		−	37.1446i		−	1.50026i	−0.661292	−	0.750129i	$-0.729992\pi$
$613$		−	37.1446i		−	1.50026i	0.661292	−	0.750129i	$-0.270008\pi$
$614$	3.76334	−	43.1776i	0.151876	−	1.74251i
$615$	1.60331			0.0646517
$616$	0.731821	−	2.74194i	0.0294859	−	0.110476i
$617$	7.62484			0.306965			0.153482	−	0.988151i	$-0.450951\pi$
$617$	7.62484			0.306965			0.153482	+	0.988151i	$0.450951\pi$
$618$	−0.221106	+	2.53680i	−0.00889421	+	0.102045i
$619$			5.36732i			0.215731i	0.994166	+	0.107865i	$0.0344015\pi$
$619$			5.36732i			0.215731i	−0.994166	+	0.107865i	$0.965598\pi$
$620$	5.50292	−	31.3283i	0.221003	−	1.25817i
$621$			1.68494i			0.0676144i
$622$	17.7059	+	1.54324i	0.709943	+	0.0618783i
$623$	1.30979			0.0524757
$624$	−0.723929	−	0.262418i	−0.0289804	−	0.0105051i
$625$	−29.2731			−1.17093
$626$	−28.4154	−	2.47668i	−1.13571	−	0.0989879i
$627$			0.590082i			0.0235656i
$628$	0.806831	−	4.59331i	0.0321961	−	0.183293i
$629$		−	26.5663i		−	1.05927i
$630$	1.08580	−	12.4577i	0.0432594	−	0.496325i
$631$	1.69179			0.0673491			0.0336745	−	0.999433i	$-0.489279\pi$
$631$	1.69179			0.0673491			0.0336745	+	0.999433i	$0.489279\pi$
$632$	−3.88938	−	1.03807i	−0.154711	−	0.0412923i
$633$	−0.713865			−0.0283736
$634$	−0.424978	+	4.87587i	−0.0168780	+	0.193645i
$635$			24.1869i			0.959827i
$636$	−1.31425	−	0.230852i	−0.0521133	−	0.00915388i
$637$			1.00000i			0.0396214i
$638$	9.89668	+	0.862590i	0.391813	+	0.0341503i
$639$	22.5238			0.891027
$640$	19.3026	−	27.7016i	0.763003	−	1.09500i
$641$	−1.81368			−0.0716359			−0.0358180	−	0.999358i	$-0.511404\pi$
$641$	−1.81368			−0.0716359			−0.0358180	+	0.999358i	$0.511404\pi$
$642$	−5.45691	−	0.475622i	−0.215367	−	0.0187713i
$643$			26.1858i			1.03267i	0.856387	+	0.516334i	$0.172704\pi$
$643$			26.1858i			1.03267i	−0.856387	+	0.516334i	$0.827296\pi$
$644$	2.89142	+	0.507889i	0.113938	+	0.0200136i
$645$		−	0.733437i		−	0.0288790i
$646$	−1.88255	+	21.5989i	−0.0740679	+	0.849796i
$647$	28.6859			1.12776			0.563879	−	0.825857i	$-0.309308\pi$
$647$	28.6859			1.12776			0.563879	+	0.825857i	$0.309308\pi$
$648$	−23.6872	−	6.32210i	−0.930521	−	0.248355i
$649$	−14.1413			−0.555093
$650$	−0.479645	+	5.50307i	−0.0188132	+	0.215848i
$651$		−	1.02591i		−	0.0402084i
$652$	7.11900	−	40.5286i	0.278801	−	1.58722i
$653$		−	30.4022i		−	1.18973i	−0.803825	−	0.594866i	$-0.797205\pi$
$653$		−	30.4022i		−	1.18973i	0.803825	−	0.594866i	$-0.202795\pi$
$654$	2.51577	+	0.219273i	0.0983743	+	0.00857426i
$655$	18.8155			0.735183
$656$	−10.4950	−	3.80436i	−0.409762	−	0.148535i
$657$	28.8784			1.12665
$658$	5.31620	+	0.463357i	0.207247	+	0.0180635i
$659$			3.86352i			0.150501i	0.997165	+	0.0752507i	$0.0239757\pi$
$659$			3.86352i			0.150501i	−0.997165	+	0.0752507i	$0.976024\pi$
$660$	0.199448	−	1.13546i	0.00776349	−	0.0441978i
$661$		−	13.0419i		−	0.507270i	−0.967300	−	0.253635i	$-0.918374\pi$
$661$		−	13.0419i		−	0.507270i	0.967300	−	0.253635i	$-0.0816262\pi$
$662$	3.43455	−	39.4053i	0.133487	−	1.53153i
$663$	−0.966031			−0.0375175
$664$	3.35380	−	12.5658i	0.130153	−	0.487648i
$665$	9.11705			0.353544
$666$	−1.92617	+	22.0993i	−0.0746374	+	0.856331i
$667$			10.2764i			0.397906i
$668$	35.4016	+	6.21842i	1.36973	+	0.240598i
$669$		−	3.07174i		−	0.118760i
$670$	−46.9855	−	4.09524i	−1.81521	−	0.158213i
$671$	−6.84331			−0.264183
$672$	0.458610	−	0.987700i	0.0176912	−	0.0381013i
$673$	10.5564			0.406918			0.203459	−	0.979083i	$-0.434782\pi$
$673$	10.5564			0.406918			0.203459	+	0.979083i	$0.434782\pi$
$674$	−29.1717	−	2.54260i	−1.12365	−	0.0979371i
$675$		−	4.48371i		−	0.172578i
$676$	−1.96984	−	0.346010i	−0.0757632	−	0.0133081i
$677$		−	41.5579i		−	1.59720i	−0.601863	−	0.798599i	$-0.705575\pi$
$677$		−	41.5579i		−	1.59720i	0.601863	−	0.798599i	$-0.294425\pi$
$678$	−0.373445	+	4.28462i	−0.0143421	+	0.164550i
$679$	−16.6675			−0.639640
$680$	10.9229	−	40.9252i	0.418874	−	1.56941i
$681$	−0.354268			−0.0135756
$682$	−0.656607	+	7.53339i	−0.0251428	+	0.288468i
$683$		−	32.5216i		−	1.24440i	−0.782857	−	0.622202i	$-0.786238\pi$
$683$		−	32.5216i		−	1.24440i	0.782857	−	0.622202i	$-0.213762\pi$
$684$	3.13202	−	17.8307i	0.119756	−	0.681772i
$685$		−	4.61487i		−	0.176325i
$686$	−1.40887	−	0.122797i	−0.0537910	−	0.00468840i
$687$	1.84351			0.0703342
$688$	−1.74031	+	4.80097i	−0.0663487	+	0.183035i
$689$	−3.46579			−0.132036
$690$	1.18806	+	0.103551i	0.0452286	+	0.00394210i
$691$			28.3095i			1.07694i	0.842643	+	0.538472i	$0.180998\pi$
$691$			28.3095i			1.07694i	−0.842643	+	0.538472i	$0.819002\pi$
$692$	7.65323	−	43.5700i	0.290932	−	1.65628i
$693$			2.97289i			0.112931i
$694$	0.877670	−	10.0697i	0.0333159	−	0.382240i
$695$	20.2313			0.767415
$696$	3.68306	+	0.983007i	0.139606	+	0.0372608i
$697$	−14.0049			−0.530472
$698$	−1.34534	+	15.4353i	−0.0509217	+	0.584236i
$699$		−	1.56168i		−	0.0590683i
$700$	−7.69422	−	1.35152i	−0.290814	−	0.0510825i
$701$			32.9514i			1.24456i	0.782796	+	0.622278i	$0.213793\pi$
$701$			32.9514i			1.24456i	−0.782796	+	0.622278i	$0.786207\pi$
$702$	1.61725	+	0.140958i	0.0610390	+	0.00532014i
$703$	−16.1732			−0.609985
$704$	−3.99979	+	6.95931i	−0.150748	+	0.262289i
$705$	2.16778			0.0816433
$706$	25.9826	+	2.26464i	0.977870	+	0.0852307i
$707$			15.5451i			0.584634i
$708$	−5.34452	−	0.938783i	−0.200859	−	0.0352816i
$709$		−	33.9034i		−	1.27327i	−0.771166	−	0.636634i	$-0.780326\pi$
$709$		−	33.9034i		−	1.27327i	0.771166	−	0.636634i	$-0.219674\pi$
$710$	2.78578	−	31.9618i	0.104548	−	1.19951i
$711$	4.21698			0.158149
$712$	−3.57935	−	0.955326i	−0.134142	−	0.0358024i
$713$	−7.82247			−0.292954
$714$	0.118625	−	1.36101i	0.00443944	−	0.0509347i
$715$		−	2.99431i		−	0.111981i
$716$	7.67009	−	43.6660i	0.286645	−	1.63188i
$717$			3.25331i			0.121497i
$718$	−16.7214	−	1.45743i	−0.624039	−	0.0543909i
$719$	−32.4362			−1.20967			−0.604833	−	0.796352i	$-0.706760\pi$
$719$	−32.4362			−1.20967			−0.604833	+	0.796352i	$0.706760\pi$
$720$	−12.0535	+	33.2519i	−0.449208	+	1.23923i
$721$	−9.35343			−0.348340
$722$	−13.6194	−	1.18706i	−0.506863	−	0.0441780i
$723$			2.20128i			0.0818664i
$724$	3.78556	−	21.5513i	0.140689	−	0.800947i
$725$		−	27.3461i		−	1.01561i
$726$	0.236232	−	2.71034i	0.00876739	−	0.100590i
$727$	−27.4351			−1.01751			−0.508756	−	0.860911i	$-0.669894\pi$
$727$	−27.4351			−1.01751			−0.508756	+	0.860911i	$0.669894\pi$
$728$	0.729373	−	2.73277i	0.0270324	−	0.101283i
$729$	25.0194			0.926644
$730$	3.57173	−	40.9792i	0.132196	−	1.51671i
$731$			6.40654i			0.236955i
$732$	−2.58634	−	0.454300i	−0.0955940	−	0.0167914i
$733$			17.5680i			0.648888i	0.945905	+	0.324444i	$0.105177\pi$
$733$			17.5680i			0.648888i	−0.945905	+	0.324444i	$0.894823\pi$
$734$	3.08716	+	0.269075i	0.113949	+	0.00993175i
$735$	−0.574494			−0.0211905
$736$	−7.53115	−	3.49687i	−0.277602	−	0.128896i
$737$	11.2126			0.413021
$738$	11.6500	+	1.01541i	0.428843	+	0.0373778i
$739$		−	17.4117i		−	0.640500i	−0.947333	−	0.320250i	$-0.896233\pi$
$739$		−	17.4117i		−	0.640500i	0.947333	−	0.320250i	$-0.103767\pi$
$740$	31.1212	+	5.46655i	1.14404	+	0.200954i
$741$			0.588108i			0.0216047i
$742$	0.425587	−	4.88285i	0.0156238	−	0.179255i
$743$	−43.3041			−1.58867			−0.794336	−	0.607478i	$-0.792181\pi$
$743$	−43.3041			−1.58867			−0.794336	+	0.607478i	$0.792181\pi$
$744$	−0.748269	+	2.80356i	−0.0274329	+	0.102784i
$745$	39.9009			1.46186
$746$	−3.46827	+	39.7923i	−0.126983	+	1.45690i
$747$			13.6242i			0.498483i
$748$	−1.74217	+	9.91821i	−0.0637000	+	0.362646i
$749$		−	20.1201i		−	0.735174i
$750$	0.885465	+	0.0771767i	0.0323326	+	0.00281810i
$751$	54.1254			1.97506			0.987531	−	0.157422i	$-0.0503184\pi$
$751$	54.1254			1.97506			0.987531	+	0.157422i	$0.0503184\pi$
$752$	−14.1900	−	5.14374i	−0.517455	−	0.187573i
$753$	1.14501			0.0417263
$754$	9.86357	+	0.859704i	0.359210	+	0.0313086i
$755$			10.9633i			0.398995i
$756$	−0.397185	+	2.26118i	−0.0144455	+	0.0822385i
$757$			24.1649i			0.878287i	0.898417	+	0.439143i	$0.144718\pi$
$757$			24.1649i			0.878287i	−0.898417	+	0.439143i	$0.855282\pi$
$758$	−2.30201	+	26.4114i	−0.0836126	+	0.959305i
$759$	−0.283517			−0.0102910
$760$	−24.9148	−	6.64973i	−0.903754	−	0.241211i
$761$	11.9453			0.433016			0.216508	−	0.976281i	$-0.430533\pi$
$761$	11.9453			0.433016			0.216508	+	0.976281i	$0.430533\pi$
$762$	0.191588	−	2.19813i	0.00694051	−	0.0796300i
$763$			9.27587i			0.335809i
$764$	−45.6544	−	8.01936i	−1.65172	−	0.290130i
$765$			44.3722i			1.60428i
$766$	−28.8838	−	2.51750i	−1.04361	−	0.0909608i
$767$	−14.0940			−0.508903
$768$	−1.97367	+	2.36465i	−0.0712189	+	0.0853271i
$769$	22.2885			0.803745			0.401872	−	0.915696i	$-0.368360\pi$
$769$	22.2885			0.803745			0.401872	+	0.915696i	$0.368360\pi$
$770$	4.21860	+	0.367691i	0.152028	+	0.0132507i
$771$			4.08183i			0.147004i
$772$	−9.46742	−	1.66298i	−0.340740	−	0.0598521i
$773$		−	34.3914i		−	1.23697i	−0.785796	−	0.618486i	$-0.787746\pi$
$773$		−	34.3914i		−	1.23697i	0.785796	−	0.618486i	$-0.212254\pi$
$774$	0.464501	−	5.32932i	0.0166961	−	0.191558i
$775$	20.8160			0.747732
$776$	45.5484	+	12.1568i	1.63509	+	0.436405i
$777$	1.01913			0.0365610
$778$	−3.46124	+	39.7115i	−0.124091	+	1.42373i
$779$			8.52599i			0.305475i
$780$	0.198781	−	1.13166i	0.00711748	−	0.0405200i
$781$			7.62735i			0.272928i
$782$	−10.3776	−	0.904511i	−0.371104	−	0.0323452i
$783$	−8.03651			−0.287201
$784$	3.76055	+	1.36317i	0.134306	+	0.0486846i
$785$	6.95883			0.248371
$786$	−1.70998	−	0.149041i	−0.0609928	−	0.00531611i
$787$			20.2618i			0.722253i	0.932517	+	0.361127i	$0.117608\pi$
$787$			20.2618i			0.722253i	−0.932517	+	0.361127i	$0.882392\pi$
$788$	−3.53899	+	20.1476i	−0.126071	+	0.717728i
$789$		−	1.62700i		−	0.0579228i
$790$	0.521562	−	5.98400i	0.0185564	−	0.212901i
$791$	−15.7978			−0.561705
$792$	2.16834	−	8.12421i	0.0770488	−	0.288681i
$793$	−6.82042			−0.242200
$794$	−1.59752	+	18.3287i	−0.0566939	+	0.650461i
$795$		−	1.99107i		−	0.0706161i
$796$	3.33363	+	0.585564i	0.118158	+	0.0207548i
$797$			15.6850i			0.555593i	0.960640	+	0.277796i	$0.0896040\pi$
$797$			15.6850i			0.555593i	−0.960640	+	0.277796i	$0.910396\pi$
$798$	−0.828569	−	0.0722177i	−0.0293310	−	0.00255648i
$799$	−18.9355			−0.669889
$800$	20.0407	+	9.30534i	0.708547	+	0.328993i
$801$	3.88083			0.137122
$802$	29.7343	+	2.59163i	1.04995	+	0.0915135i
$803$			9.77924i			0.345102i
$804$	4.23766	+	0.744360i	0.149451	+	0.0262516i
$805$			4.38048i			0.154392i
$806$	−0.654410	+	7.50819i	−0.0230506	+	0.264465i
$807$	−3.80730			−0.134023
$808$	11.3382	−	42.4812i	0.398876	−	1.49448i
$809$	17.6658			0.621096			0.310548	−	0.950558i	$-0.399488\pi$
$809$	17.6658			0.621096			0.310548	+	0.950558i	$0.399488\pi$
$810$	3.17643	−	36.4439i	0.111608	−	1.28051i
$811$			43.2600i			1.51906i	0.650471	+	0.759531i	$0.274572\pi$
$811$			43.2600i			1.51906i	−0.650471	+	0.759531i	$0.725428\pi$
$812$	−2.42243	+	13.7909i	−0.0850105	+	0.483967i
$813$			0.886380i			0.0310867i
$814$	−7.48360	−	0.652267i	−0.262300	−	0.0228620i
$815$	61.4005			2.15077
$816$	−1.31686	+	3.63281i	−0.0460994	+	0.127174i
$817$	3.90023			0.136452
$818$	−22.3966	−	1.95208i	−0.783078	−	0.0682527i
$819$			2.96294i			0.103534i
$820$	2.88179	−	16.4061i	0.100636	−	0.572925i
$821$			42.8024i			1.49381i	0.664928	+	0.746907i	$0.268462\pi$
$821$			42.8024i			1.49381i	−0.664928	+	0.746907i	$0.731538\pi$
$822$	−0.0365551	+	0.419405i	−0.00127501	+	0.0146284i
$823$	14.1848			0.494452			0.247226	−	0.968958i	$-0.420481\pi$
$823$	14.1848			0.494452			0.247226	+	0.968958i	$0.420481\pi$
$824$	25.5607	+	6.82214i	0.890450	+	0.237661i
$825$	0.754454			0.0262667
$826$	1.73069	−	19.8566i	0.0602184	−	0.690899i
$827$		−	17.5635i		−	0.610741i	−0.952234	−	0.305371i	$-0.901220\pi$
$827$		−	17.5635i		−	0.610741i	0.952234	−	0.305371i	$-0.0987804\pi$
$828$	8.56712	+	1.50484i	0.297728	+	0.0522970i
$829$			7.94783i			0.276040i	0.990429	+	0.138020i	$0.0440738\pi$
$829$			7.94783i			0.276040i	−0.990429	+	0.138020i	$0.955926\pi$
$830$	19.3331	+	1.68506i	0.671060	+	0.0584893i
$831$	1.44597			0.0501602
$832$	−3.98641	+	6.93603i	−0.138204	+	0.240464i
$833$	5.01819			0.173870
$834$	−1.83864	−	0.160255i	−0.0636669	−	0.00554918i
$835$			53.6331i			1.85605i
$836$	6.03809	+	1.06061i	0.208832	+	0.0366820i
$837$		−	6.11742i		−	0.211449i
$838$	−2.20282	+	25.2734i	−0.0760952	+	0.873057i
$839$	−24.3769			−0.841584			−0.420792	−	0.907157i	$-0.638248\pi$
$839$	−24.3769			−0.841584			−0.420792	+	0.907157i	$0.638248\pi$
$840$	1.56996	+	0.419021i	0.0541687	+	0.0144576i
$841$	−20.0146			−0.690158
$842$	−1.59829	+	18.3375i	−0.0550807	+	0.631953i
$843$			2.23617i			0.0770178i
$844$	−1.28310	+	7.30472i	−0.0441661	+	0.251439i
$845$		−	2.98429i		−	0.102663i
$846$	15.7516	+	1.37290i	0.541550	+	0.0472013i
$847$	9.99328			0.343373
$848$	−4.72445	+	13.0333i	−0.162238	+	0.447565i
$849$	1.81543			0.0623053
$850$	27.6154	+	2.40695i	0.947201	+	0.0825576i
$851$		−	7.77077i		−	0.266379i
$852$	−0.506350	+	2.88266i	−0.0173473	+	0.0987584i
$853$		−	11.9274i		−	0.408385i	−0.978931	−	0.204193i	$-0.934543\pi$
$853$		−	11.9274i		−	0.408385i	0.978931	−	0.204193i	$-0.0654569\pi$
$854$	0.837524	−	9.60909i	0.0286595	−	0.328816i
$855$	27.0133			0.923835
$856$	−14.6751	+	54.9837i	−0.501585	+	1.87930i
$857$	−58.4117			−1.99531			−0.997654	−	0.0684640i	$-0.978190\pi$
$857$	−58.4117			−1.99531			−0.997654	+	0.0684640i	$0.978190\pi$
$858$	−0.0237184	+	0.272127i	−0.000809734	+	0.00929025i
$859$		−	42.6940i		−	1.45670i	−0.685206	−	0.728350i	$-0.740288\pi$
$859$		−	42.6940i		−	1.45670i	0.685206	−	0.728350i	$-0.259712\pi$
$860$	−7.50499	−	1.31828i	−0.255918	−	0.0449529i
$861$		−	0.537250i		−	0.0183094i
$862$	−25.1769	−	2.19441i	−0.857530	−	0.0747419i
$863$	−26.5317			−0.903149			−0.451574	−	0.892233i	$-0.649137\pi$
$863$	−26.5317			−0.903149			−0.451574	+	0.892233i	$0.649137\pi$
$864$	2.73466	−	5.88959i	0.0930351	−	0.200368i
$865$	66.0082			2.24435
$866$	−12.2290	−	1.06587i	−0.415557	−	0.0362197i
$867$			1.57512i			0.0534939i
$868$	−10.4977	−	1.84396i	−0.356316	−	0.0625881i
$869$			1.42802i			0.0484422i
$870$	−0.493895	+	5.66657i	−0.0167446	+	0.192115i
$871$	11.1751			0.378653
$872$	6.76557	−	25.3488i	0.229111	−	0.858418i
$873$	−49.3849			−1.67142
$874$	−0.550655	+	6.31778i	−0.0186262	+	0.213702i
$875$			3.26479i			0.110370i
$876$	−0.649206	+	3.69595i	−0.0219346	+	0.124874i
$877$			43.2917i			1.46186i	0.682454	+	0.730929i	$0.260913\pi$
$877$			43.2917i			1.46186i	−0.682454	+	0.730929i	$0.739087\pi$
$878$	−56.5177	−	4.92605i	−1.90738	−	0.166246i
$879$	3.36879			0.113626
$880$	−11.2603	−	4.08175i	−0.379584	−	0.137596i
$881$	35.7110			1.20313			0.601567	−	0.798822i	$-0.294543\pi$
$881$	35.7110			1.20313			0.601567	+	0.798822i	$0.294543\pi$
$882$	−4.17441	−	0.363839i	−0.140560	−	0.0122511i
$883$			2.31339i			0.0778519i	0.999242	+	0.0389259i	$0.0123936\pi$
$883$			2.31339i			0.0778519i	−0.999242	+	0.0389259i	$0.987606\pi$
$884$	−1.73634	+	9.88503i	−0.0583995	+	0.332470i
$885$		−	8.09689i		−	0.272174i
$886$	1.23745	−	14.1975i	0.0415730	−	0.476976i
$887$	−13.5959			−0.456507			−0.228253	−	0.973602i	$-0.573301\pi$
$887$	−13.5959			−0.456507			−0.228253	+	0.973602i	$0.573301\pi$
$888$	−2.78503	−	0.743324i	−0.0934596	−	0.0249443i
$889$	8.10472			0.271824
$890$	0.479988	−	5.50700i	0.0160892	−	0.184595i
$891$			8.69694i			0.291358i
$892$	−31.4320	−	5.52113i	−1.05242	−	0.184861i
$893$			11.5277i			0.385759i
$894$	−3.62624	−	0.316062i	−0.121280	−	0.0105707i
$895$	66.1536			2.21127
$896$	−9.28246	−	6.46807i	−0.310105	−	0.216083i
$897$	−0.282569			−0.00943470
$898$	−32.3352	−	2.81832i	−1.07904	−	0.0940485i
$899$		−	37.3101i		−	1.24436i
$900$	−22.7975	−	4.00446i	−0.759917	−	0.133482i
$901$			17.3920i			0.579410i
$902$	−0.343854	+	3.94511i	−0.0114491	+	0.131358i
$903$	−0.245766			−0.00817857
$904$	43.1717	+	11.5225i	1.43587	+	0.383232i
$905$	32.6500			1.08532
$906$	0.0868421	−	0.996358i	0.00288514	−	0.0331018i
$907$			53.1606i			1.76517i	0.470153	+	0.882585i	$0.344199\pi$
$907$			53.1606i			1.76517i	−0.470153	+	0.882585i	$0.655801\pi$
$908$	−0.636761	+	3.62510i	−0.0211317	+	0.120303i
$909$			46.0593i			1.52769i
$910$	4.20449	+	0.366461i	0.139377	+	0.0121481i
$911$	−51.9490			−1.72115			−0.860573	−	0.509326i	$-0.829895\pi$
$911$	−51.9490			−1.72115			−0.860573	+	0.509326i	$0.829895\pi$
$912$	2.21161	+	0.801690i	0.0732338	+	0.0265466i
$913$	−4.61363			−0.152689
$914$	−55.6710	−	4.85226i	−1.84143	−	0.160499i
$915$		−	3.91829i		−	0.129535i
$916$	3.31352	−	18.8639i	0.109482	−	0.623282i
$917$		−	6.30484i		−	0.208204i
$918$	0.707356	−	8.11564i	0.0233462	−	0.267856i
$919$	15.9201			0.525156			0.262578	−	0.964911i	$-0.415427\pi$
$919$	15.9201			0.525156			0.262578	+	0.964911i	$0.415427\pi$
$920$	3.19501	−	11.9708i	0.105336	−	0.394667i
$921$	−5.89971			−0.194402
$922$	3.51835	−	40.3668i	0.115871	−	1.32941i
$923$			7.60183i			0.250217i
$924$	−0.380479	−	0.0668325i	−0.0125168	−	0.00219863i
$925$			20.6784i			0.679902i
$926$	−49.8421	−	4.34422i	−1.63791	−	0.142760i
$927$	−27.7137			−0.910236
$928$	16.6787	−	35.9206i	0.547504	−	1.17915i
$929$	−3.61460			−0.118591			−0.0592956	−	0.998240i	$-0.518885\pi$
$929$	−3.61460			−0.118591			−0.0592956	+	0.998240i	$0.518885\pi$
$930$	−4.31341	−	0.375955i	−0.141442	−	0.0123281i
$931$		−	3.05501i		−	0.100124i
$932$	−15.9801	−	2.80696i	−0.523446	−	0.0919451i
$933$		−	2.41931i		−	0.0792046i
$934$	−0.153702	+	1.76345i	−0.00502928	+	0.0577020i
$935$	−15.0260			−0.491403
$936$	2.16109	−	8.09703i	0.0706375	−	0.264660i
$937$	38.7807			1.26691			0.633456	−	0.773779i	$-0.281636\pi$
$937$	38.7807			1.26691			0.633456	+	0.773779i	$0.281636\pi$
$938$	−1.37226	+	15.7443i	−0.0448060	+	0.514069i
$939$			3.88264i			0.126705i
$940$	3.89636	−	22.1821i	0.127085	−	0.723500i
$941$		−	27.0826i		−	0.882869i	−0.897294	−	0.441434i	$-0.854470\pi$
$941$		−	27.0826i		−	0.882869i	0.897294	−	0.441434i	$-0.145530\pi$
$942$	−0.632427	−	0.0551220i	−0.0206056	−	0.00179597i
$943$	−4.09650			−0.133400
$944$	−19.2124	+	53.0011i	−0.625311	+	1.72504i
$945$	−3.42568			−0.111437
$946$	1.80470	+	0.157296i	0.0586757	+	0.00511415i
$947$			4.94904i			0.160822i	0.996762	+	0.0804110i	$0.0256233\pi$
$947$			4.94904i			0.160822i	−0.996762	+	0.0804110i	$0.974377\pi$
$948$	−0.0948005	+	0.539702i	−0.00307898	+	0.0175287i
$949$			9.74653i			0.316386i
$950$	1.46532	−	16.8119i	0.0475412	−	0.545451i
$951$	0.666230			0.0216040
$952$	−13.7135	−	3.66013i	−0.444458	−	0.118626i
$953$	27.9839			0.906487			0.453244	−	0.891387i	$-0.350267\pi$
$953$	27.9839			0.906487			0.453244	+	0.891387i	$0.350267\pi$
$954$	1.26099	−	14.4676i	0.0408260	−	0.468406i
$955$		−	69.1660i		−	2.23816i
$956$	33.2899	+	5.84748i	1.07667	+	0.189121i
$957$		−	1.35227i		−	0.0437125i
$958$	51.2335	+	4.46549i	1.65528	+	0.144273i
$959$	−1.54638			−0.0499354
$960$	−3.98471	−	2.29017i	−0.128606	−	0.0739150i
$961$	−2.59941			−0.0838520
$962$	−7.45857	−	0.650085i	−0.240474	−	0.0209596i
$963$		−	59.6148i		−	1.92106i
$964$	22.5249	+	3.95657i	0.725477	+	0.127433i
$965$		−	14.3431i		−	0.461719i
$966$	0.0346985	−	0.398104i	0.00111641	−	0.0128088i
$967$	−7.90194			−0.254109			−0.127055	−	0.991896i	$-0.540552\pi$
$967$	−7.90194			−0.254109			−0.127055	+	0.991896i	$0.540552\pi$
$968$	−27.3093	−	7.28883i	−0.877754	−	0.234272i
$969$	2.95123			0.0948073
$970$	−6.10800	+	70.0784i	−0.196116	+	2.25008i
$971$			32.3464i			1.03805i	0.854760	+	0.519023i	$0.173704\pi$
$971$			32.3464i			1.03805i	−0.854760	+	0.519023i	$0.826296\pi$
$972$	−1.76891	+	10.0705i	−0.0567378	+	0.323010i
$973$		−	6.77925i		−	0.217333i
$974$	44.9298	+	3.91606i	1.43964	+	0.125479i
$975$	0.751930			0.0240810
$976$	−9.29738	+	25.6485i	−0.297602	+	0.820990i
$977$	33.6243			1.07574			0.537868	−	0.843029i	$-0.319230\pi$
$977$	33.6243			1.07574			0.537868	+	0.843029i	$0.319230\pi$
$978$	−5.58016	−	0.486364i	−0.178434	−	0.0155522i
$979$			1.31419i			0.0420016i
$980$	−1.03259	+	5.87859i	−0.0329850	+	0.187785i
$981$			27.4839i			0.877492i
$982$	−4.81686	+	55.2648i	−0.153712	+	1.76357i
$983$	24.6726			0.786934			0.393467	−	0.919339i	$-0.371276\pi$
$983$	24.6726			0.786934			0.393467	+	0.919339i	$0.371276\pi$
$984$	−0.391856	+	1.46818i	−0.0124919	+	0.0468038i
$985$	−30.5234			−0.972556
$986$	4.31416	−	49.4972i	0.137391	−	1.57631i
$987$		−	0.726396i		−	0.0231214i
$988$	6.01789	+	1.05706i	0.191455	+	0.0336297i
$989$			1.87395i			0.0595880i
$990$	12.4995	+	1.08945i	0.397259	+	0.0346249i
$991$	−44.3738			−1.40958			−0.704791	−	0.709415i	$-0.748959\pi$
$991$	−44.3738			−1.40958			−0.704791	+	0.709415i	$0.748959\pi$
$992$	27.3429	+	12.6959i	0.868138	+	0.403094i
$993$	−5.38427			−0.170865
$994$	−10.7100	−	0.933479i	−0.339701	−	0.0296082i
$995$			5.05043i			0.160109i
$996$	−1.74366	−	0.306281i	−0.0552501	−	0.00970488i
$997$		−	6.74589i		−	0.213644i	−0.994278	−	0.106822i	$-0.965932\pi$
$997$		−	6.74589i		−	0.213644i	0.994278	−	0.106822i	$-0.0340676\pi$
$998$	−0.936202	+	10.7412i	−0.0296349	+	0.340008i
$999$	6.07699			0.192267

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.c.b.365.1	✓	38
4.3	odd	2		2912.2.c.b.1457.19		38
8.3	odd	2		2912.2.c.b.1457.20		38
8.5	even	2	inner	728.2.c.b.365.2	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.c.b.365.1	✓	38	1.1	even	1	trivial
728.2.c.b.365.2	yes	38	8.5	even	2	inner
2912.2.c.b.1457.19		38	4.3	odd	2
2912.2.c.b.1457.20		38	8.3	odd	2

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40887 - 0.122797i) q^{2} +0.192506i q^{3} +(1.96984 + 0.346010i) q^{4} +2.98429i q^{5} +(0.0236391 - 0.271216i) q^{6} +1.00000 q^{7} +(-2.73277 - 0.729373i) q^{8} +2.96294 q^{9} +(0.366461 - 4.20449i) q^{10} +1.00336i q^{11} +(-0.0666089 + 0.379206i) q^{12} +1.00000i q^{13} +(-1.40887 - 0.122797i) q^{14} -0.574494 q^{15} +(3.76055 + 1.36317i) q^{16} +5.01819 q^{17} +(-4.17441 - 0.363839i) q^{18} -3.05501i q^{19} +(-1.03259 + 5.87859i) q^{20} +0.192506i q^{21} +(0.123209 - 1.41360i) q^{22} +1.46785 q^{23} +(0.140409 - 0.526074i) q^{24} -3.90601 q^{25} +(0.122797 - 1.40887i) q^{26} +1.14790i q^{27} +(1.96984 + 0.346010i) q^{28} +7.00104i q^{29} +(0.809389 + 0.0705460i) q^{30} -5.32922 q^{31} +(-5.13075 - 2.38231i) q^{32} -0.193152 q^{33} +(-7.06998 - 0.616216i) q^{34} +2.98429i q^{35} +(5.83653 + 1.02521i) q^{36} -5.29400i q^{37} +(-0.375145 + 4.30412i) q^{38} -0.192506 q^{39} +(2.17666 - 8.15538i) q^{40} -2.79082 q^{41} +(0.0236391 - 0.271216i) q^{42} +1.27667i q^{43} +(-0.347171 + 1.97645i) q^{44} +8.84229i q^{45} +(-2.06801 - 0.180247i) q^{46} -3.77337 q^{47} +(-0.262418 + 0.723929i) q^{48} +1.00000 q^{49} +(5.50307 + 0.479645i) q^{50} +0.966031i q^{51} +(-0.346010 + 1.96984i) q^{52} +3.46579i q^{53} +(0.140958 - 1.61725i) q^{54} -2.99431 q^{55} +(-2.73277 - 0.729373i) q^{56} +0.588108 q^{57} +(0.859704 - 9.86357i) q^{58} +14.0940i q^{59} +(-1.13166 - 0.198781i) q^{60} +6.82042i q^{61} +(7.50819 + 0.654410i) q^{62} +2.96294 q^{63} +(6.93603 + 3.98641i) q^{64} -2.98429 q^{65} +(0.272127 + 0.0237184i) q^{66} -11.1751i q^{67} +(9.88503 + 1.73634i) q^{68} +0.282569i q^{69} +(0.366461 - 4.20449i) q^{70} +7.60183 q^{71} +(-8.09703 - 2.16109i) q^{72} +9.74653 q^{73} +(-0.650085 + 7.45857i) q^{74} -0.751930i q^{75} +(1.05706 - 6.01789i) q^{76} +1.00336i q^{77} +(0.271216 + 0.0236391i) q^{78} +1.42324 q^{79} +(-4.06809 + 11.2226i) q^{80} +8.66785 q^{81} +(3.93191 + 0.342704i) q^{82} +4.59820i q^{83} +(-0.0666089 + 0.379206i) q^{84} +14.9757i q^{85} +(0.156770 - 1.79866i) q^{86} -1.34774 q^{87} +(0.731821 - 2.74194i) q^{88} +1.30979 q^{89} +(1.08580 - 12.4577i) q^{90} +1.00000i q^{91} +(2.89142 + 0.507889i) q^{92} -1.02591i q^{93} +(5.31620 + 0.463357i) q^{94} +9.11705 q^{95} +(0.458610 - 0.987700i) q^{96} -16.6675 q^{97} +(-1.40887 - 0.122797i) q^{98} +2.97289i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{4} + 14 q^{6} + 38 q^{7} - 6 q^{8} - 46 q^{9} - 4 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{17} + 4 q^{18} - 24 q^{20} + 10 q^{22} + 12 q^{23} + 10 q^{24} - 50 q^{25} + 8 q^{28} + 4 q^{30} + 16 q^{31}+ \cdots + 82 q^{96}+O(q^{100}) \) 38 * q + 8 * q^4 + 14 * q^6 + 38 * q^7 - 6 * q^8 - 46 * q^9 - 4 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^17 + 4 * q^18 - 24 * q^20 + 10 * q^22 + 12 * q^23 + 10 * q^24 - 50 * q^25 + 8 * q^28 + 4 * q^30 + 16 * q^31 + 10 * q^32 - 8 * q^33 - 4 * q^34 - 38 * q^36 - 28 * q^38 + 8 * q^39 + 4 * q^40 + 8 * q^41 + 14 * q^42 - 40 * q^44 - 16 * q^46 + 4 * q^48 + 38 * q^49 + 24 * q^50 - 4 * q^52 - 14 * q^54 - 6 * q^56 + 8 * q^57 - 24 * q^58 + 44 * q^60 - 12 * q^62 - 46 * q^63 + 32 * q^64 + 20 * q^65 - 76 * q^66 - 52 * q^68 + 42 * q^72 + 50 * q^74 - 28 * q^76 - 12 * q^79 - 16 * q^80 + 62 * q^81 - 4 * q^84 + 44 * q^86 - 56 * q^87 - 6 * q^88 + 48 * q^90 + 2 * q^92 - 48 * q^94 + 82 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more