LMFDB - Embedded newform 392.2.m.c.19.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(19,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Root			$1.60021 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	392.19
Dual form			392.2.m.c.227.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(2.26303 - 1.30656i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.60021 - 2.77164i) q^{5} +(3.20041 + 1.84776i) q^{6} -2.82843 q^{8} +(1.91421 - 3.31552i) q^{9} +4.52607 q^{10} +(1.00000 + 1.73205i) q^{11} +5.22625i q^{12} -5.07517 q^{13} -8.36308i q^{15} +(-2.00000 - 3.46410i) q^{16} +(-0.274552 + 0.158513i) q^{17} +5.41421 q^{18} +(4.13779 + 2.38896i) q^{19} +(3.20041 + 5.54328i) q^{20} +(-1.41421 + 2.44949i) q^{22} +(-1.24264 - 0.717439i) q^{23} +(-6.40083 + 3.69552i) q^{24} +(-2.62132 - 4.54026i) q^{25} +(-3.58869 - 6.21579i) q^{26} -2.16478i q^{27} +9.37769i q^{29} +(10.2426 - 5.91359i) q^{30} +(-1.32565 - 2.29610i) q^{31} +(2.82843 - 4.89898i) q^{32} +(4.52607 + 2.61313i) q^{33} +(-0.388275 - 0.224171i) q^{34} +(3.82843 + 6.63103i) q^{36} +(2.12132 + 1.22474i) q^{37} +6.75699i q^{38} +(-11.4853 + 6.63103i) q^{39} +(-4.52607 + 7.83938i) q^{40} +4.46088i q^{41} -8.82843 q^{43} -4.00000 q^{44} +(-6.12627 - 10.6110i) q^{45} -2.02922i q^{46} +(2.65131 - 4.59220i) q^{47} +(-9.05213 - 5.22625i) q^{48} +(3.70711 - 6.42090i) q^{50} +(-0.414214 + 0.717439i) q^{51} +(5.07517 - 8.79045i) q^{52} +(-3.00000 + 1.73205i) q^{53} +(2.65131 - 1.53073i) q^{54} +6.40083 q^{55} +12.4853 q^{57} +(-11.4853 + 6.63103i) q^{58} +(2.26303 - 1.30656i) q^{59} +(14.4853 + 8.36308i) q^{60} +(-1.98848 + 3.44415i) q^{61} +(1.87476 - 3.24718i) q^{62} +8.00000 q^{64} +(-8.12132 + 14.0665i) q^{65} +7.39104i q^{66} +(-6.00000 - 10.3923i) q^{67} -0.634051i q^{68} -3.74952 q^{69} +(-5.41421 + 9.37769i) q^{72} +(1.21193 - 0.699709i) q^{73} +3.46410i q^{74} +(-11.8643 - 6.84984i) q^{75} +(-8.27558 + 4.77791i) q^{76} +(-16.2426 - 9.37769i) q^{78} +(10.2426 + 5.91359i) q^{79} -12.8017 q^{80} +(2.91421 + 5.04757i) q^{81} +(-5.46345 + 3.15432i) q^{82} -8.47343i q^{83} +1.01461i q^{85} +(-6.24264 - 10.8126i) q^{86} +(12.2525 + 21.2220i) q^{87} +(-2.82843 - 4.89898i) q^{88} +(-8.55014 - 4.93642i) q^{89} +(8.66386 - 15.0062i) q^{90} +(2.48528 - 1.43488i) q^{92} +(-6.00000 - 3.46410i) q^{93} +7.49903 q^{94} +(13.2426 - 7.64564i) q^{95} -14.7821i q^{96} -3.82683i q^{97} +7.65685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 4 q^{9} + 8 q^{11} - 16 q^{16} + 32 q^{18} + 24 q^{23} - 4 q^{25} + 48 q^{30} + 8 q^{36} - 24 q^{39} - 48 q^{43} - 32 q^{44} + 24 q^{50} + 8 q^{51} - 24 q^{53} + 32 q^{57} - 24 q^{58} + 48 q^{60}+ \cdots + 16 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^9 + 8 * q^11 - 16 * q^16 + 32 * q^18 + 24 * q^23 - 4 * q^25 + 48 * q^30 + 8 * q^36 - 24 * q^39 - 48 * q^43 - 32 * q^44 + 24 * q^50 + 8 * q^51 - 24 * q^53 + 32 * q^57 - 24 * q^58 + 48 * q^60 + 64 * q^64 - 48 * q^65 - 48 * q^67 - 32 * q^72 - 96 * q^78 + 48 * q^79 + 12 * q^81 - 16 * q^86 - 48 * q^92 - 48 * q^93 + 72 * q^95 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.500000	+	0.866025i
$2$	0.707107	+	1.22474i	0.500000	+	0.866025i
$3$	2.26303	−	1.30656i	1.30656	−	0.754344i	0.325042	−	0.945700i	$-0.394622\pi$
$3$	2.26303	−	1.30656i	1.30656	−	0.754344i	0.981521	+	0.191355i	$0.0612882\pi$
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	1.60021	−	2.77164i	0.715634	−	1.23951i	−0.247080	−	0.968995i	$-0.579471\pi$
$5$	1.60021	−	2.77164i	0.715634	−	1.23951i	0.962714	−	0.270520i	$-0.0871955\pi$
$6$	3.20041	+	1.84776i	1.30656	+	0.754344i
$7$		0			0
$7$		0			0
$8$	−2.82843			−1.00000
$9$	1.91421	−	3.31552i	0.638071	−	1.10517i
$10$	4.52607			1.43127
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$			5.22625i			1.50869i
$13$	−5.07517			−1.40760			−0.703800	−	0.710399i	$-0.748515\pi$
$13$	−5.07517			−1.40760			−0.703800	+	0.710399i	$0.748515\pi$
$14$		0			0
$15$		−	8.36308i		−	2.15934i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−0.274552	+	0.158513i	−0.0665886	+	0.0384450i	−0.532925	−	0.846163i	$-0.678907\pi$
$17$	−0.274552	+	0.158513i	−0.0665886	+	0.0384450i	0.466336	+	0.884608i	$0.345574\pi$
$18$	5.41421			1.27614
$19$	4.13779	+	2.38896i	0.949275	+	0.548064i	0.892855	−	0.450343i	$-0.148698\pi$
$19$	4.13779	+	2.38896i	0.949275	+	0.548064i	0.0564190	+	0.998407i	$0.482032\pi$
$20$	3.20041	+	5.54328i	0.715634	+	1.23951i
$21$		0			0
$22$	−1.41421	+	2.44949i	−0.301511	+	0.522233i
$23$	−1.24264	−	0.717439i	−0.259108	−	0.149596i	0.364819	−	0.931078i	$-0.381131\pi$
$23$	−1.24264	−	0.717439i	−0.259108	−	0.149596i	−0.623928	+	0.781482i	$0.714464\pi$
$24$	−6.40083	+	3.69552i	−1.30656	+	0.754344i
$25$	−2.62132	−	4.54026i	−0.524264	−	0.908052i
$26$	−3.58869	−	6.21579i	−0.703800	−	1.21902i
$27$		−	2.16478i		−	0.416613i
$28$		0			0
$29$			9.37769i			1.74139i	0.491820	+	0.870697i	$0.336332\pi$
$29$			9.37769i			1.74139i	−0.491820	+	0.870697i	$0.663668\pi$
$30$	10.2426	−	5.91359i	1.87004	−	1.07967i
$31$	−1.32565	−	2.29610i	−0.238095	−	0.412392i	0.722073	−	0.691817i	$-0.243189\pi$
$31$	−1.32565	−	2.29610i	−0.238095	−	0.412392i	−0.960168	+	0.279425i	$0.909856\pi$
$32$	2.82843	−	4.89898i	0.500000	−	0.866025i
$33$	4.52607	+	2.61313i	0.787887	+	0.454887i
$34$	−0.388275	−	0.224171i	−0.0665886	−	0.0384450i
$35$		0			0
$36$	3.82843	+	6.63103i	0.638071	+	1.10517i
$37$	2.12132	+	1.22474i	0.348743	+	0.201347i	0.664131	−	0.747616i	$-0.268802\pi$
$37$	2.12132	+	1.22474i	0.348743	+	0.201347i	−0.315389	+	0.948963i	$0.602135\pi$
$38$			6.75699i			1.09613i
$39$	−11.4853	+	6.63103i	−1.83912	+	1.06181i
$40$	−4.52607	+	7.83938i	−0.715634	+	1.23951i
$41$			4.46088i			0.696673i	0.937370	+	0.348337i	$0.113253\pi$
$41$			4.46088i			0.696673i	−0.937370	+	0.348337i	$0.886747\pi$
$42$		0			0
$43$	−8.82843			−1.34632			−0.673161	−	0.739496i	$-0.735064\pi$
$43$	−8.82843			−1.34632			−0.673161	+	0.739496i	$0.735064\pi$
$44$	−4.00000			−0.603023
$45$	−6.12627	−	10.6110i	−0.913251	−	1.58180i
$46$		−	2.02922i		−	0.299193i
$47$	2.65131	−	4.59220i	0.386733	−	0.669841i	−0.605275	−	0.796017i	$-0.706937\pi$
$47$	2.65131	−	4.59220i	0.386733	−	0.669841i	0.992008	+	0.126175i	$0.0402701\pi$
$48$	−9.05213	−	5.22625i	−1.30656	−	0.754344i
$49$		0			0
$50$	3.70711	−	6.42090i	0.524264	−	0.908052i
$51$	−0.414214	+	0.717439i	−0.0580015	+	0.100462i
$52$	5.07517	−	8.79045i	0.703800	−	1.21902i
$53$	−3.00000	+	1.73205i	−0.412082	+	0.237915i	−0.691684	−	0.722200i	$-0.743131\pi$
$53$	−3.00000	+	1.73205i	−0.412082	+	0.237915i	0.279602	+	0.960116i	$0.409797\pi$
$54$	2.65131	−	1.53073i	0.360797	−	0.208306i
$55$	6.40083			0.863087
$56$		0			0
$57$	12.4853			1.65372
$58$	−11.4853	+	6.63103i	−1.50809	+	0.870697i
$59$	2.26303	−	1.30656i	0.294622	−	0.170100i	−0.345402	−	0.938455i	$-0.612258\pi$
$59$	2.26303	−	1.30656i	0.294622	−	0.170100i	0.640024	+	0.768355i	$0.278924\pi$
$60$	14.4853	+	8.36308i	1.87004	+	1.07967i
$61$	−1.98848	+	3.44415i	−0.254599	+	0.440978i	−0.964787	−	0.263034i	$-0.915277\pi$
$61$	−1.98848	+	3.44415i	−0.254599	+	0.440978i	0.710188	+	0.704013i	$0.248610\pi$
$62$	1.87476	−	3.24718i	0.238095	−	0.412392i
$63$		0			0
$64$	8.00000			1.00000
$65$	−8.12132	+	14.0665i	−1.00733	+	1.74474i
$66$			7.39104i			0.909774i
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$		−	0.634051i		−	0.0768899i
$69$	−3.74952			−0.451389
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−5.41421	+	9.37769i	−0.638071	+	1.10517i
$73$	1.21193	−	0.699709i	0.141846	−	0.0818947i	−0.427398	−	0.904064i	$-0.640570\pi$
$73$	1.21193	−	0.699709i	0.141846	−	0.0818947i	0.569243	+	0.822169i	$0.307236\pi$
$74$			3.46410i			0.402694i
$75$	−11.8643	−	6.84984i	−1.36997	−	0.790951i
$76$	−8.27558	+	4.77791i	−0.949275	+	0.548064i
$77$		0			0
$78$	−16.2426	−	9.37769i	−1.83912	−	1.06181i
$79$	10.2426	+	5.91359i	1.15239	+	0.665331i	0.949468	−	0.313864i	$-0.101624\pi$
$79$	10.2426	+	5.91359i	1.15239	+	0.665331i	0.202919	+	0.979195i	$0.434957\pi$
$80$	−12.8017			−1.43127
$81$	2.91421	+	5.04757i	0.323802	+	0.560841i
$82$	−5.46345	+	3.15432i	−0.603337	+	0.348337i
$83$		−	8.47343i		−	0.930080i	−0.885290	−	0.465040i	$-0.846040\pi$
$83$		−	8.47343i		−	0.930080i	0.885290	−	0.465040i	$-0.153960\pi$
$84$		0			0
$85$			1.01461i			0.110050i
$86$	−6.24264	−	10.8126i	−0.673161	−	1.16595i
$87$	12.2525	+	21.2220i	1.31361	+	2.27524i
$88$	−2.82843	−	4.89898i	−0.301511	−	0.522233i
$89$	−8.55014	−	4.93642i	−0.906313	−	0.523260i	−0.0270697	−	0.999634i	$-0.508618\pi$
$89$	−8.55014	−	4.93642i	−0.906313	−	0.523260i	−0.879243	+	0.476374i	$0.841951\pi$
$90$	8.66386	−	15.0062i	0.913251	−	1.58180i
$91$		0			0
$92$	2.48528	−	1.43488i	0.259108	−	0.149596i
$93$	−6.00000	−	3.46410i	−0.622171	−	0.359211i
$94$	7.49903			0.773466
$95$	13.2426	−	7.64564i	1.35867	−	0.784426i
$96$		−	14.7821i		−	1.50869i
$97$		−	3.82683i		−	0.388556i	−0.980946	−	0.194278i	$-0.937764\pi$
$97$		−	3.82683i		−	0.388556i	0.980946	−	0.194278i	$-0.0622364\pi$
$98$		0			0
$99$	7.65685			0.769543
$100$	10.4853			1.04853
$101$	−3.86324	−	6.69133i	−0.384407	−	0.665812i	0.607280	−	0.794488i	$-0.292261\pi$
$101$	−3.86324	−	6.69133i	−0.384407	−	0.665812i	−0.991687	+	0.128676i	$0.958927\pi$
$102$	−1.17157			−0.116003
$103$	7.72648	−	13.3827i	0.761313	−	1.31863i	−0.180862	−	0.983509i	$-0.557889\pi$
$103$	7.72648	−	13.3827i	0.761313	−	1.31863i	0.942174	−	0.335124i	$-0.108778\pi$
$104$	14.3548			1.40760
$105$		0			0
$106$	−4.24264	−	2.44949i	−0.412082	−	0.237915i
$107$	4.24264	−	7.34847i	0.410152	−	0.710403i	−0.584754	−	0.811210i	$-0.698809\pi$
$107$	4.24264	−	7.34847i	0.410152	−	0.710403i	0.994906	+	0.100807i	$0.0321425\pi$
$108$	3.74952	+	2.16478i	0.360797	+	0.208306i
$109$	0.363961	−	0.210133i	0.0348611	−	0.0201271i	−0.482468	−	0.875914i	$-0.660260\pi$
$109$	0.363961	−	0.210133i	0.0348611	−	0.0201271i	0.517329	+	0.855786i	$0.326926\pi$
$110$	4.52607	+	7.83938i	0.431544	+	0.747455i
$111$	6.40083			0.607539
$112$		0			0
$113$	−16.4853			−1.55080			−0.775402	−	0.631467i	$-0.782453\pi$
$113$	−16.4853			−1.55080			−0.775402	+	0.631467i	$0.782453\pi$
$114$	8.82843	+	15.2913i	0.826858	+	1.43216i
$115$	−3.97696	+	2.29610i	−0.370854	+	0.214112i
$116$	−16.2426	−	9.37769i	−1.50809	−	0.870697i
$117$	−9.71496	+	16.8268i	−0.898148	+	1.55564i
$118$	3.20041	+	1.84776i	0.294622	+	0.170100i
$119$		0			0
$120$			23.6544i			2.15934i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−5.62427			−0.509198
$123$	5.82843	+	10.0951i	0.525532	+	0.910247i
$124$	5.30262			0.476189
$125$	−0.776550			−0.0694568
$126$		0			0
$127$		−	5.49333i		−	0.487454i	−0.969844	−	0.243727i	$-0.921630\pi$
$127$		−	5.49333i		−	0.487454i	0.969844	−	0.243727i	$-0.0783701\pi$
$128$	5.65685	+	9.79796i	0.500000	+	0.866025i
$129$	−19.9790	+	11.5349i	−1.75906	+	1.01559i
$130$	−22.9706			−2.01465
$131$	−3.03958	−	1.75490i	−0.265570	−	0.153327i	0.361303	−	0.932448i	$-0.382332\pi$
$131$	−3.03958	−	1.75490i	−0.265570	−	0.153327i	−0.626873	+	0.779122i	$0.715665\pi$
$132$	−9.05213	+	5.22625i	−0.787887	+	0.454887i
$133$		0			0
$134$	8.48528	−	14.6969i	0.733017	−	1.26962i
$135$	−6.00000	−	3.46410i	−0.516398	−	0.298142i
$136$	0.776550	−	0.448342i	0.0665886	−	0.0384450i
$137$	−0.121320	−	0.210133i	−0.0103651	−	0.0179529i	0.860796	−	0.508950i	$-0.169966\pi$
$137$	−0.121320	−	0.210133i	−0.0103651	−	0.0179529i	−0.871161	+	0.490997i	$0.836633\pi$
$138$	−2.65131	−	4.59220i	−0.225694	−	0.390914i
$139$		−	5.04054i		−	0.427533i	−0.976885	−	0.213767i	$-0.931427\pi$
$139$		−	5.04054i		−	0.427533i	0.976885	−	0.213767i	$-0.0685732\pi$
$140$		0			0
$141$		−	13.8564i		−	1.16692i
$142$		0			0
$143$	−5.07517	−	8.79045i	−0.424407	−	0.735095i
$144$	−15.3137			−1.27614
$145$	25.9916	+	15.0062i	2.15848	+	1.24620i
$146$	1.71393	+	0.989538i	0.141846	+	0.0818947i
$147$		0			0
$148$	−4.24264	+	2.44949i	−0.348743	+	0.201347i
$149$	−17.4853	−	10.0951i	−1.43245	−	0.827025i	−0.435143	−	0.900361i	$-0.643302\pi$
$149$	−17.4853	−	10.0951i	−1.43245	−	0.827025i	−0.997307	+	0.0733360i	$0.976635\pi$
$150$		−	19.3743i		−	1.58190i
$151$	13.2426	−	7.64564i	1.07767	−	0.622194i	0.147404	−	0.989076i	$-0.452908\pi$
$151$	13.2426	−	7.64564i	1.07767	−	0.622194i	0.930267	+	0.366883i	$0.119575\pi$
$152$	−11.7034	−	6.75699i	−0.949275	−	0.548064i
$153$			1.21371i			0.0981225i
$154$		0			0
$155$	−8.48528			−0.681554
$156$		−	26.5241i		−	2.12363i
$157$	11.9780	+	20.7465i	0.955948	+	1.65575i	0.732184	+	0.681107i	$0.238501\pi$
$157$	11.9780	+	20.7465i	0.955948	+	1.65575i	0.223764	+	0.974643i	$0.428165\pi$
$158$			16.7262i			1.33066i
$159$	−4.52607	+	7.83938i	−0.358940	+	0.621703i
$160$	−9.05213	−	15.6788i	−0.715634	−	1.23951i
$161$		0			0
$162$	−4.12132	+	7.13834i	−0.323802	+	0.560841i
$163$	−4.07107	+	7.05130i	−0.318871	+	0.552300i	−0.980253	−	0.197749i	$-0.936637\pi$
$163$	−4.07107	+	7.05130i	−0.318871	+	0.552300i	0.661382	+	0.750049i	$0.269970\pi$
$164$	−7.72648	−	4.46088i	−0.603337	−	0.348337i
$165$	14.4853	−	8.36308i	1.12768	−	0.651065i
$166$	10.3778	−	5.99162i	0.805473	−	0.465040i
$167$	−14.3548			−1.11080			−0.555402	−	0.831582i	$-0.687436\pi$
$167$	−14.3548			−1.11080			−0.555402	+	0.831582i	$0.687436\pi$
$168$		0			0
$169$	12.7574			0.981335
$170$	−1.24264	+	0.717439i	−0.0953062	+	0.0550251i
$171$	15.8412	−	9.14594i	1.21141	−	0.699408i
$172$	8.82843	−	15.2913i	0.673161	−	1.16595i
$173$	−3.47496	+	6.01882i	−0.264197	+	0.457602i	−0.967353	−	0.253433i	$-0.918440\pi$
$173$	−3.47496	+	6.01882i	−0.264197	+	0.457602i	0.703156	+	0.711035i	$0.251773\pi$
$174$	−17.3277	+	30.0125i	−1.31361	+	2.27524i
$175$		0			0
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$	3.41421	−	5.91359i	0.256628	−	0.444493i
$178$		−	13.9623i		−	1.04652i
$179$	10.2426	+	17.7408i	0.765571	+	1.32601i	0.939944	+	0.341328i	$0.110877\pi$
$179$	10.2426	+	17.7408i	0.765571	+	1.32601i	−0.174373	+	0.984680i	$0.555790\pi$
$180$	24.5051			1.82650
$181$	−2.10220			−0.156256			−0.0781278	−	0.996943i	$-0.524894\pi$
$181$	−2.10220			−0.156256			−0.0781278	+	0.996943i	$0.524894\pi$
$182$		0			0
$183$			10.3923i			0.768221i
$184$	3.51472	+	2.02922i	0.259108	+	0.149596i
$185$	6.78910	−	3.91969i	0.499145	−	0.288181i
$186$		−	9.79796i		−	0.718421i
$187$	−0.549104	−	0.317025i	−0.0401545	−	0.0231832i
$188$	5.30262	+	9.18440i	0.386733	+	0.669841i
$189$		0			0
$190$	18.7279	+	10.8126i	1.35867	+	0.784426i
$191$	10.2426	+	5.91359i	0.741131	+	0.427892i	0.822481	−	0.568793i	$-0.192590\pi$
$191$	10.2426	+	5.91359i	0.741131	+	0.427892i	−0.0813491	+	0.996686i	$0.525923\pi$
$192$	18.1043	−	10.4525i	1.30656	−	0.754344i
$193$	7.07107	+	12.2474i	0.508987	+	0.881591i	0.999946	+	0.0104081i	$0.00331306\pi$
$193$	7.07107	+	12.2474i	0.508987	+	0.881591i	−0.490959	+	0.871183i	$0.663354\pi$
$194$	4.68690	−	2.70598i	0.336500	−	0.194278i
$195$			42.4441i			3.03948i
$196$		0			0
$197$			26.5241i			1.88977i	0.327409	+	0.944883i	$0.393824\pi$
$197$			26.5241i			1.88977i	−0.327409	+	0.944883i	$0.606176\pi$
$198$	5.41421	+	9.37769i	0.384771	+	0.666444i
$199$	−1.32565	−	2.29610i	−0.0939731	−	0.162766i	0.815206	−	0.579170i	$-0.196623\pi$
$199$	−1.32565	−	2.29610i	−0.0939731	−	0.162766i	−0.909180	+	0.416404i	$0.863290\pi$
$200$	7.41421	+	12.8418i	0.524264	+	0.908052i
$201$	−27.1564	−	15.6788i	−1.91546	−	1.10589i
$202$	5.46345	−	9.46297i	0.384407	−	0.665812i
$203$		0			0
$204$	−0.828427	−	1.43488i	−0.0580015	−	0.100462i
$205$	12.3640	+	7.13834i	0.863536	+	0.498563i
$206$	21.8538			1.52263
$207$	−4.75736	+	2.74666i	−0.330659	+	0.190906i
$208$	10.1503	+	17.5809i	0.703800	+	1.21902i
$209$			9.55582i			0.660990i
$210$		0			0
$211$	20.4853			1.41026			0.705132	−	0.709076i	$-0.250888\pi$
$211$	20.4853			1.41026			0.705132	+	0.709076i	$0.250888\pi$
$212$		−	6.92820i		−	0.475831i
$213$		0			0
$214$	12.0000			0.820303
$215$	−14.1273	+	24.4692i	−0.963474	+	1.66879i
$216$			6.12293i			0.416613i
$217$		0			0
$218$	0.514719	+	0.297173i	0.0348611	+	0.0201271i
$219$	1.82843	−	3.16693i	0.123554	−	0.214001i
$220$	−6.40083	+	11.0866i	−0.431544	+	0.747455i
$221$	1.39340	−	0.804479i	0.0937301	−	0.0541151i
$222$	4.52607	+	7.83938i	0.303770	+	0.526145i
$223$	24.5051			1.64098			0.820491	−	0.571659i	$-0.193700\pi$
$223$	24.5051			1.64098			0.820491	+	0.571659i	$0.193700\pi$
$224$		0			0
$225$	−20.0711			−1.33807
$226$	−11.6569	−	20.1903i	−0.775402	−	1.34304i
$227$	−20.1399	+	11.6278i	−1.33673	+	0.771761i	−0.986321	−	0.164836i	$-0.947290\pi$
$227$	−20.1399	+	11.6278i	−1.33673	+	0.771761i	−0.350408	+	0.936597i	$0.613957\pi$
$228$	−12.4853	+	21.6251i	−0.826858	+	1.43216i
$229$	8.77758	−	15.2032i	0.580039	−	1.00466i	−0.415435	−	0.909623i	$-0.636371\pi$
$229$	8.77758	−	15.2032i	0.580039	−	1.00466i	0.995474	−	0.0950341i	$-0.0302960\pi$
$230$	−5.62427	−	3.24718i	−0.370854	−	0.214112i
$231$		0			0
$232$		−	26.5241i		−	1.74139i
$233$	10.1213	−	17.5306i	0.663070	−	1.14847i	−0.316735	−	0.948514i	$-0.602587\pi$
$233$	10.1213	−	17.5306i	0.663070	−	1.14847i	0.979805	−	0.199956i	$-0.0640801\pi$
$234$	−27.4781			−1.79630
$235$	−8.48528	−	14.6969i	−0.553519	−	0.958723i
$236$			5.22625i			0.340200i
$237$	30.9059			2.00756
$238$		0			0
$239$			13.2621i			0.857851i	0.903340	+	0.428926i	$0.141108\pi$
$239$			13.2621i			0.857851i	−0.903340	+	0.428926i	$0.858892\pi$
$240$	−28.9706	+	16.7262i	−1.87004	+	1.07967i
$241$	19.1554	−	11.0594i	1.23391	−	0.712396i	0.266064	−	0.963955i	$-0.414277\pi$
$241$	19.1554	−	11.0594i	1.23391	−	0.712396i	0.967842	+	0.251559i	$0.0809434\pi$
$242$	9.89949			0.636364
$243$	18.8142	+	10.8624i	1.20693	+	0.696822i
$244$	−3.97696	−	6.88830i	−0.254599	−	0.440978i
$245$		0			0
$246$	−8.24264	+	14.2767i	−0.525532	+	0.910247i
$247$	−21.0000	−	12.1244i	−1.33620	−	0.771454i
$248$	3.74952	+	6.49435i	0.238095	+	0.412392i
$249$	−11.0711	−	19.1757i	−0.701600	−	1.21521i
$250$	−0.549104	−	0.951076i	−0.0347284	−	0.0601513i
$251$		−	19.1886i		−	1.21117i	−0.795780	−	0.605586i	$-0.792939\pi$
$251$		−	19.1886i		−	1.21117i	0.795780	−	0.605586i	$-0.207061\pi$
$252$		0			0
$253$		−	2.86976i		−	0.180420i
$254$	6.72792	−	3.88437i	0.422147	−	0.243727i
$255$	1.32565	+	2.29610i	0.0830157	+	0.143787i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−7.06365	−	4.07820i	−0.440619	−	0.254391i	0.263241	−	0.964730i	$-0.415208\pi$
$257$	−7.06365	−	4.07820i	−0.440619	−	0.254391i	−0.703860	+	0.710339i	$0.748542\pi$
$258$	−28.2546	−	16.3128i	−1.75906	−	1.01559i
$259$		0			0
$260$	−16.2426	−	28.1331i	−1.00733	−	1.74474i
$261$	31.0919	+	17.9509i	1.92454	+	1.11113i
$262$		−	4.96362i		−	0.306653i
$263$	−7.75736	+	4.47871i	−0.478339	+	0.276169i	−0.719724	−	0.694260i	$-0.755732\pi$
$263$	−7.75736	+	4.47871i	−0.478339	+	0.276169i	0.241385	+	0.970429i	$0.422398\pi$
$264$	−12.8017	−	7.39104i	−0.787887	−	0.454887i
$265$			11.0866i			0.681042i
$266$		0			0
$267$	−25.7990			−1.57887
$268$	24.0000			1.46603
$269$	1.21193	+	2.09913i	0.0738927	+	0.127986i	0.900604	−	0.434640i	$-0.143124\pi$
$269$	1.21193	+	2.09913i	0.0738927	+	0.127986i	−0.826711	+	0.562626i	$0.809791\pi$
$270$		−	9.79796i		−	0.596285i
$271$	−6.62827	+	11.4805i	−0.402639	+	0.697391i	−0.994044	−	0.108984i	$-0.965240\pi$
$271$	−6.62827	+	11.4805i	−0.402639	+	0.697391i	0.591405	+	0.806375i	$0.298574\pi$
$272$	1.09821	+	0.634051i	0.0665886	+	0.0384450i
$273$		0			0
$274$	0.171573	−	0.297173i	0.0103651	−	0.0179529i
$275$	5.24264	−	9.08052i	0.316143	−	0.547576i
$276$	3.74952	−	6.49435i	0.225694	−	0.390914i
$277$	−14.4853	+	8.36308i	−0.870336	+	0.502489i	−0.867460	−	0.497507i	$-0.834249\pi$
$277$	−14.4853	+	8.36308i	−0.870336	+	0.502489i	−0.00287626	+	0.999996i	$0.500916\pi$
$278$	6.17338	−	3.56420i	0.370255	−	0.213767i
$279$	−10.1503			−0.607685
$280$		0			0
$281$	8.72792			0.520664			0.260332	−	0.965519i	$-0.416168\pi$
$281$	8.72792			0.520664			0.260332	+	0.965519i	$0.416168\pi$
$282$	16.9706	−	9.79796i	1.01058	−	0.583460i
$283$	0.160829	−	0.0928546i	0.00956028	−	0.00551963i	−0.495212	−	0.868772i	$-0.664910\pi$
$283$	0.160829	−	0.0928546i	0.00956028	−	0.00551963i	0.504773	+	0.863252i	$0.331576\pi$
$284$		0			0
$285$	19.9790	−	34.6047i	1.18346	−	2.04980i
$286$	7.17738	−	12.4316i	0.424407	−	0.735095i
$287$		0			0
$288$	−10.8284	−	18.7554i	−0.638071	−	1.10517i
$289$	−8.44975	+	14.6354i	−0.497044	+	0.860905i
$290$			42.4441i			2.49240i
$291$	−5.00000	−	8.66025i	−0.293105	−	0.507673i
$292$			2.79884i			0.163789i
$293$	5.07517			0.296495			0.148247	−	0.988950i	$-0.452637\pi$
$293$	5.07517			0.296495			0.148247	+	0.988950i	$0.452637\pi$
$294$		0			0
$295$		−	8.36308i		−	0.486917i
$296$	−6.00000	−	3.46410i	−0.348743	−	0.201347i
$297$	3.74952	−	2.16478i	0.217569	−	0.125614i
$298$		−	28.5533i		−	1.65405i
$299$	6.30661	+	3.64113i	0.364721	+	0.210572i
$300$	23.7285	−	13.6997i	1.36997	−	0.790951i
$301$		0			0
$302$	18.7279	+	10.8126i	1.07767	+	0.622194i
$303$	−17.4853	−	10.0951i	−1.00450	−	0.579950i
$304$		−	19.1116i		−	1.09613i
$305$	6.36396	+	11.0227i	0.364399	+	0.631158i
$306$	−1.48648	+	0.858221i	−0.0849766	+	0.0490613i
$307$		−	6.04601i		−	0.345064i	−0.985004	−	0.172532i	$-0.944805\pi$
$307$		−	6.04601i		−	0.345064i	0.985004	−	0.172532i	$-0.0551948\pi$
$308$		0			0
$309$		−	40.3805i		−	2.29717i
$310$	−6.00000	−	10.3923i	−0.340777	−	0.590243i
$311$	−13.5782	−	23.5181i	−0.769949	−	1.33359i	−0.937590	−	0.347743i	$-0.886948\pi$
$311$	−13.5782	−	23.5181i	−0.769949	−	1.33359i	0.167641	−	0.985848i	$-0.446385\pi$
$312$	32.4853	−	18.7554i	1.83912	−	1.06181i
$313$	−9.16586	−	5.29191i	−0.518085	−	0.299116i	0.218066	−	0.975934i	$-0.430025\pi$
$313$	−9.16586	−	5.29191i	−0.518085	−	0.299116i	−0.736151	+	0.676818i	$0.763359\pi$
$314$	−16.9394	+	29.3400i	−0.955948	+	1.65575i
$315$		0			0
$316$	−20.4853	+	11.8272i	−1.15239	+	0.665331i
$317$	3.51472	+	2.02922i	0.197406	+	0.113973i	0.595445	−	0.803396i	$-0.296976\pi$
$317$	3.51472	+	2.02922i	0.197406	+	0.113973i	−0.398039	+	0.917369i	$0.630309\pi$
$318$	−12.8017			−0.717881
$319$	−16.2426	+	9.37769i	−0.909413	+	0.525050i
$320$	12.8017	−	22.1731i	0.715634	−	1.23951i
$321$		−	22.1731i		−	1.23758i
$322$		0			0
$323$	−1.51472			−0.0842812
$324$	−11.6569			−0.647603
$325$	13.3036	+	23.0426i	0.737954	+	1.27817i
$326$	−11.5147			−0.637741
$327$	0.549104	−	0.951076i	0.0303655	−	0.0525946i
$328$		−	12.6173i		−	0.696673i
$329$		0			0
$330$	20.4853	+	11.8272i	1.12768	+	0.651065i
$331$	−10.4142	+	18.0379i	−0.572417	+	0.991455i	0.423900	+	0.905709i	$0.360661\pi$
$331$	−10.4142	+	18.0379i	−0.572417	+	0.991455i	−0.996317	+	0.0857463i	$0.972673\pi$
$332$	14.6764	+	8.47343i	0.805473	+	0.465040i
$333$	8.12132	−	4.68885i	0.445046	−	0.256947i
$334$	−10.1503	−	17.5809i	−0.555402	−	0.961984i
$335$	−38.4050			−2.09829
$336$		0			0
$337$	4.24264			0.231111			0.115556	−	0.993301i	$-0.463135\pi$
$337$	4.24264			0.231111			0.115556	+	0.993301i	$0.463135\pi$
$338$	9.02082	+	15.6245i	0.490668	+	0.849861i
$339$	−37.3067	+	21.5391i	−2.02622	+	1.16984i
$340$	−1.75736	−	1.01461i	−0.0953062	−	0.0550251i
$341$	2.65131	−	4.59220i	0.143576	−	0.248682i
$342$	22.4029	+	12.9343i	1.21141	+	0.699408i
$343$		0			0
$344$	24.9706			1.34632
$345$	−6.00000	+	10.3923i	−0.323029	+	0.559503i
$346$	−9.82868			−0.528393
$347$	−3.48528	−	6.03668i	−0.187100	−	0.324066i	0.757182	−	0.653204i	$-0.226575\pi$
$347$	−3.48528	−	6.03668i	−0.187100	−	0.324066i	−0.944282	+	0.329137i	$0.893242\pi$
$348$	−49.0102			−2.62722
$349$	−22.4029			−1.19920			−0.599600	−	0.800300i	$-0.704673\pi$
$349$	−22.4029			−1.19920			−0.599600	+	0.800300i	$0.704673\pi$
$350$		0			0
$351$			10.9867i			0.586424i
$352$	11.3137			0.603023
$353$	11.3623	−	6.56001i	0.604753	−	0.349154i	−0.166156	−	0.986099i	$-0.553136\pi$
$353$	11.3623	−	6.56001i	0.604753	−	0.349154i	0.770909	+	0.636945i	$0.219802\pi$
$354$	9.65685			0.513256
$355$		0			0
$356$	17.1003	−	9.87285i	0.906313	−	0.523260i
$357$		0			0
$358$	−14.4853	+	25.0892i	−0.765571	+	1.32601i
$359$	15.0000	+	8.66025i	0.791670	+	0.457071i	0.840550	−	0.541734i	$-0.182232\pi$
$359$	15.0000	+	8.66025i	0.791670	+	0.457071i	−0.0488803	+	0.998805i	$0.515565\pi$
$360$	17.3277	+	30.0125i	0.913251	+	1.58180i
$361$	1.91421	+	3.31552i	0.100748	+	0.174501i
$362$	−1.48648	−	2.57466i	−0.0781278	−	0.135321i
$363$		−	18.2919i		−	0.960075i
$364$		0			0
$365$		−	4.47871i		−	0.234427i
$366$	−12.7279	+	7.34847i	−0.665299	+	0.384111i
$367$	−8.50303	−	14.7277i	−0.443855	−	0.768779i	0.554117	−	0.832439i	$-0.313056\pi$
$367$	−8.50303	−	14.7277i	−0.443855	−	0.768779i	−0.997972	+	0.0636601i	$0.979723\pi$
$368$			5.73951i			0.299193i
$369$	14.7901	+	8.53909i	0.769944	+	0.444527i
$370$	9.60124	+	5.54328i	0.499145	+	0.288181i
$371$		0			0
$372$	12.0000	−	6.92820i	0.622171	−	0.359211i
$373$	−7.97056	−	4.60181i	−0.412700	−	0.238273i	0.279249	−	0.960219i	$-0.409914\pi$
$373$	−7.97056	−	4.60181i	−0.412700	−	0.238273i	−0.691949	+	0.721946i	$0.743248\pi$
$374$		−	0.896683i		−	0.0463664i
$375$	−1.75736	+	1.01461i	−0.0907496	+	0.0523943i
$376$	−7.49903	+	12.9887i	−0.386733	+	0.669841i
$377$		−	47.5934i		−	2.45118i
$378$		0			0
$379$	17.3137			0.889345			0.444673	−	0.895693i	$-0.353320\pi$
$379$	17.3137			0.889345			0.444673	+	0.895693i	$0.353320\pi$
$380$			30.5826i			1.56885i
$381$	−7.17738	−	12.4316i	−0.367708	−	0.636889i
$382$			16.7262i			0.855785i
$383$	2.65131	−	4.59220i	0.135476	−	0.234651i	−0.790303	−	0.612716i	$-0.790077\pi$
$383$	2.65131	−	4.59220i	0.135476	−	0.234651i	0.925779	+	0.378065i	$0.123410\pi$
$384$	25.6033	+	14.7821i	1.30656	+	0.754344i
$385$		0			0
$386$	−10.0000	+	17.3205i	−0.508987	+	0.881591i
$387$	−16.8995	+	29.2708i	−0.859050	+	1.48792i
$388$	6.62827	+	3.82683i	0.336500	+	0.194278i
$389$	3.15076	−	1.81909i	0.159750	−	0.0922316i	−0.417994	−	0.908450i	$-0.637267\pi$
$389$	3.15076	−	1.81909i	0.159750	−	0.0922316i	0.577744	+	0.816218i	$0.303933\pi$
$390$	−51.9832	+	30.0125i	−2.63227	+	1.51974i
$391$	0.454893			0.0230049
$392$		0			0
$393$	−9.17157			−0.462645
$394$	−32.4853	+	18.7554i	−1.63658	+	0.944883i
$395$	32.7807	−	18.9259i	1.64937	−	0.952267i
$396$	−7.65685	+	13.2621i	−0.384771	+	0.666444i
$397$	−12.1388	+	21.0251i	−0.609230	+	1.05522i	0.382137	+	0.924105i	$0.375188\pi$
$397$	−12.1388	+	21.0251i	−0.609230	+	1.05522i	−0.991368	+	0.131112i	$0.958145\pi$
$398$	1.87476	−	3.24718i	0.0939731	−	0.162766i
$399$		0			0
$400$	−10.4853	+	18.1610i	−0.524264	+	0.908052i
$401$	−3.87868	+	6.71807i	−0.193692	+	0.335484i	−0.946471	−	0.322789i	$-0.895380\pi$
$401$	−3.87868	+	6.71807i	−0.193692	+	0.335484i	0.752779	+	0.658273i	$0.228713\pi$
$402$		−	44.3462i		−	2.21179i
$403$	6.72792	+	11.6531i	0.335142	+	0.580482i
$404$	15.4530			0.768813
$405$	18.6534			0.926893
$406$		0			0
$407$			4.89898i			0.242833i
$408$	1.17157	−	2.02922i	0.0580015	−	0.100462i
$409$	3.31414	−	1.91342i	0.163873	−	0.0946124i	−0.415820	−	0.909447i	$-0.636505\pi$
$409$	3.31414	−	1.91342i	0.163873	−	0.0946124i	0.579694	+	0.814834i	$0.303172\pi$
$410$			20.1903i			0.997126i
$411$	−0.549104	−	0.317025i	−0.0270853	−	0.0156377i
$412$	15.4530	+	26.7653i	0.761313	+	1.31863i
$413$		0			0
$414$	−6.72792	−	3.88437i	−0.330659	−	0.190906i
$415$	−23.4853	−	13.5592i	−1.15285	−	0.665597i
$416$	−14.3548	+	24.8632i	−0.703800	+	1.21902i
$417$	−6.58579	−	11.4069i	−0.322507	−	0.558599i
$418$	−11.7034	+	6.75699i	−0.572434	+	0.330495i
$419$			39.8309i			1.94587i	0.231082	+	0.972934i	$0.425774\pi$
$419$			39.8309i			1.94587i	−0.231082	+	0.972934i	$0.574226\pi$
$420$		0			0
$421$		−	26.5241i		−	1.29271i	−0.763038	−	0.646353i	$-0.776293\pi$
$421$		−	26.5241i		−	1.29271i	0.763038	−	0.646353i	$-0.223707\pi$
$422$	14.4853	+	25.0892i	0.705132	+	1.22133i
$423$	−10.1503	−	17.5809i	−0.493527	−	0.854813i
$424$	8.48528	−	4.89898i	0.412082	−	0.237915i
$425$	1.43938	+	0.831025i	0.0698201	+	0.0403106i
$426$		0			0
$427$		0			0
$428$	8.48528	+	14.6969i	0.410152	+	0.710403i
$429$	−22.9706	−	13.2621i	−1.10903	−	0.640298i
$430$	−39.9581			−1.92695
$431$	6.51472	−	3.76127i	0.313803	−	0.181174i	−0.334824	−	0.942281i	$-0.608677\pi$
$431$	6.51472	−	3.76127i	0.313803	−	0.181174i	0.648627	+	0.761106i	$0.275344\pi$
$432$	−7.49903	+	4.32957i	−0.360797	+	0.208306i
$433$			5.17186i			0.248544i	0.992248	+	0.124272i	$0.0396595\pi$
$433$			5.17186i			0.248544i	−0.992248	+	0.124272i	$0.960341\pi$
$434$		0			0
$435$	78.4264			3.76026
$436$			0.840532i			0.0402542i
$437$	−3.42786	−	5.93723i	−0.163977	−	0.284016i
$438$	5.17157			0.247107
$439$	17.8768	−	30.9636i	0.853214	−	1.47781i	−0.0250778	−	0.999686i	$-0.507983\pi$
$439$	17.8768	−	30.9636i	0.853214	−	1.47781i	0.878292	−	0.478125i	$-0.158683\pi$
$440$	−18.1043			−0.863087
$441$		0			0
$442$	1.97056	+	1.13770i	0.0937301	+	0.0541151i
$443$	14.1421	−	24.4949i	0.671913	−	1.16379i	−0.305448	−	0.952209i	$-0.598806\pi$
$443$	14.1421	−	24.4949i	0.671913	−	1.16379i	0.977361	−	0.211579i	$-0.0678605\pi$
$444$	−6.40083	+	11.0866i	−0.303770	+	0.526145i
$445$	−27.3640	+	15.7986i	−1.29718	+	0.748925i
$446$	17.3277	+	30.0125i	0.820491	+	1.42113i
$447$	−52.7597			−2.49545
$448$		0			0
$449$	−5.65685			−0.266963			−0.133482	−	0.991051i	$-0.542616\pi$
$449$	−5.65685			−0.266963			−0.133482	+	0.991051i	$0.542616\pi$
$450$	−14.1924	−	24.5819i	−0.669036	−	1.15880i
$451$	−7.72648	+	4.46088i	−0.363826	+	0.210055i
$452$	16.4853	−	28.5533i	0.775402	−	1.34304i
$453$	19.9790	−	34.6047i	0.938697	−	1.62587i
$454$	−28.4821	−	16.4441i	−1.33673	−	0.771761i
$455$		0			0
$456$	−35.3137			−1.65372
$457$	10.5858	−	18.3351i	0.495182	−	0.857681i	−0.504802	−	0.863235i	$-0.668435\pi$
$457$	10.5858	−	18.3351i	0.495182	−	0.857681i	0.999985	+	0.00555421i	$0.00176797\pi$
$458$	24.8268			1.16008
$459$	0.343146	+	0.594346i	0.0160167	+	0.0277417i
$460$		−	9.18440i		−	0.428225i
$461$	−26.6073			−1.23923			−0.619613	−	0.784908i	$-0.712710\pi$
$461$	−26.6073			−1.23923			−0.619613	+	0.784908i	$0.712710\pi$
$462$		0			0
$463$			18.7554i			0.871637i	0.900035	+	0.435818i	$0.143541\pi$
$463$			18.7554i			0.871637i	−0.900035	+	0.435818i	$0.856459\pi$
$464$	32.4853	−	18.7554i	1.50809	−	0.870697i
$465$	−19.2025	+	11.0866i	−0.890493	+	0.514127i
$466$	28.6274			1.32614
$467$	−0.0666175	−	0.0384616i	−0.00308269	−	0.00177979i	0.498458	−	0.866914i	$-0.333900\pi$
$467$	−0.0666175	−	0.0384616i	−0.00308269	−	0.00177979i	−0.501541	+	0.865134i	$0.667233\pi$
$468$	−19.4299	−	33.6536i	−0.898148	−	1.55564i
$469$		0			0
$470$	12.0000	−	20.7846i	0.553519	−	0.958723i
$471$	54.2132	+	31.3000i	2.49801	+	1.44223i
$472$	−6.40083	+	3.69552i	−0.294622	+	0.170100i
$473$	−8.82843	−	15.2913i	−0.405932	−	0.703094i
$474$	21.8538	+	37.8519i	1.00378	+	1.73859i
$475$		−	25.0489i		−	1.14932i
$476$		0			0
$477$			13.2621i			0.607228i
$478$	−16.2426	+	9.37769i	−0.742921	+	0.428926i
$479$	5.85172	+	10.1355i	0.267372	+	0.463102i	0.968182	−	0.250246i	$-0.0805114\pi$
$479$	5.85172	+	10.1355i	0.267372	+	0.463102i	−0.700810	+	0.713348i	$0.747178\pi$
$480$	−40.9706	−	23.6544i	−1.87004	−	1.07967i
$481$	−10.7661	−	6.21579i	−0.490890	−	0.283416i
$482$	27.0898	+	15.6403i	1.23391	+	0.712396i
$483$		0			0
$484$	7.00000	+	12.1244i	0.318182	+	0.551107i
$485$	−10.6066	−	6.12372i	−0.481621	−	0.278064i
$486$			30.7235i			1.39364i
$487$	29.4853	−	17.0233i	1.33611	−	0.771401i	0.349878	−	0.936795i	$-0.386223\pi$
$487$	29.4853	−	17.0233i	1.33611	−	0.771401i	0.986228	+	0.165394i	$0.0528897\pi$
$488$	5.62427	−	9.74153i	0.254599	−	0.440978i
$489$			21.2764i			0.962153i
$490$		0			0
$491$	−31.7990			−1.43507			−0.717534	−	0.696523i	$-0.754729\pi$
$491$	−31.7990			−1.43507			−0.717534	+	0.696523i	$0.754729\pi$
$492$	−23.3137			−1.05106
$493$	−1.48648	−	2.57466i	−0.0669478	−	0.115957i
$494$		−	34.2929i		−	1.54291i
$495$	12.2525	−	21.2220i	0.550711	−	0.953859i
$496$	−5.30262	+	9.18440i	−0.238095	+	0.412392i
$497$		0			0
$498$	15.6569	−	27.1185i	0.701600	−	1.21521i
$499$	4.24264	−	7.34847i	0.189927	−	0.328963i	−0.755299	−	0.655380i	$-0.772508\pi$
$499$	4.24264	−	7.34847i	0.189927	−	0.328963i	0.945226	+	0.326418i	$0.105842\pi$
$500$	0.776550	−	1.34502i	0.0347284	−	0.0601513i
$501$	−32.4853	+	18.7554i	−1.45134	+	0.837929i
$502$	23.5011	−	13.5684i	1.04891	−	0.605586i
$503$	24.5051			1.09263			0.546314	−	0.837580i	$-0.316031\pi$
$503$	24.5051			1.09263			0.546314	+	0.837580i	$0.316031\pi$
$504$		0			0
$505$	−24.7279			−1.10038
$506$	3.51472	−	2.02922i	0.156248	−	0.0902100i
$507$	28.8703	−	16.6683i	1.28218	−	0.740265i
$508$	9.51472	+	5.49333i	0.422147	+	0.243727i
$509$	−7.06365	+	12.2346i	−0.313091	+	0.542289i	−0.979030	−	0.203717i	$-0.934698\pi$
$509$	−7.06365	+	12.2346i	−0.313091	+	0.542289i	0.665939	+	0.746006i	$0.268031\pi$
$510$	−1.87476	+	3.24718i	−0.0830157	+	0.143787i
$511$		0			0
$512$	−22.6274			−1.00000
$513$	5.17157	−	8.95743i	0.228331	−	0.395480i
$514$		−	11.5349i		−	0.508782i
$515$	−24.7279	−	42.8300i	−1.08964	−	1.88732i
$516$		−	46.1396i		−	2.03118i
$517$	10.6052			0.466418
$518$		0			0
$519$			18.1610i			0.797181i
$520$	22.9706	−	39.7862i	1.00733	−	1.74474i
$521$	−16.1158	+	9.30445i	−0.706045	+	0.407636i	−0.809595	−	0.586989i	$-0.800313\pi$
$521$	−16.1158	+	9.30445i	−0.706045	+	0.407636i	0.103550	+	0.994624i	$0.466980\pi$
$522$			50.7728i			2.22227i
$523$	−28.4154	−	16.4057i	−1.24252	−	0.717369i	−0.272914	−	0.962039i	$-0.587987\pi$
$523$	−28.4154	−	16.4057i	−1.24252	−	0.717369i	−0.969607	+	0.244669i	$0.921321\pi$
$524$	6.07917	−	3.50981i	0.265570	−	0.153327i
$525$		0			0
$526$	−10.9706	−	6.33386i	−0.478339	−	0.276169i
$527$	0.727922	+	0.420266i	0.0317088	+	0.0183071i
$528$		−	20.9050i		−	0.909774i
$529$	−10.4706	−	18.1355i	−0.455242	−	0.788502i
$530$	−13.5782	+	7.83938i	−0.589799	+	0.340521i
$531$		−	10.0042i		−	0.434144i
$532$		0			0
$533$		−	22.6398i		−	0.980637i
$534$	−18.2426	−	31.5972i	−0.789436	−	1.36734i
$535$	−13.5782	−	23.5181i	−0.587037	−	1.01678i
$536$	16.9706	+	29.3939i	0.733017	+	1.26962i
$537$	46.3589	+	26.7653i	2.00053	+	1.15501i
$538$	−1.71393	+	2.96861i	−0.0738927	+	0.127986i
$539$		0			0
$540$	12.0000	−	6.92820i	0.516398	−	0.298142i
$541$	28.4558	+	16.4290i	1.22341	+	0.706337i	0.965644	−	0.259869i	$-0.0836795\pi$
$541$	28.4558	+	16.4290i	1.22341	+	0.706337i	0.257768	+	0.966207i	$0.417013\pi$
$542$	−18.7476			−0.805278
$543$	−4.75736	+	2.74666i	−0.204158	+	0.117871i
$544$			1.79337i			0.0768899i
$545$		−	1.34502i		−	0.0576145i
$546$		0			0
$547$	−15.1716			−0.648690			−0.324345	−	0.945939i	$-0.605144\pi$
$547$	−15.1716			−0.648690			−0.324345	+	0.945939i	$0.605144\pi$
$548$	0.485281			0.0207302
$549$	7.61276	+	13.1857i	0.324905	+	0.562751i
$550$	14.8284			0.632286
$551$	−22.4029	+	38.8029i	−0.954395	+	1.65306i
$552$	10.6052			0.451389
$553$		0			0
$554$	−20.4853	−	11.8272i	−0.870336	−	0.502489i
$555$	10.2426	−	17.7408i	0.434776	−	0.753054i
$556$	8.73048	+	5.04054i	0.370255	+	0.213767i
$557$	−14.4853	+	8.36308i	−0.613761	+	0.354355i	−0.774436	−	0.632652i	$-0.781966\pi$
$557$	−14.4853	+	8.36308i	−0.613761	+	0.354355i	0.160675	+	0.987007i	$0.448633\pi$
$558$	−7.17738	−	12.4316i	−0.303843	−	0.526271i
$559$	44.8058			1.89508
$560$		0			0
$561$	−1.65685			−0.0699524
$562$	6.17157	+	10.6895i	0.260332	+	0.450908i
$563$	14.5156	−	8.38057i	0.611759	−	0.353199i	−0.161895	−	0.986808i	$-0.551760\pi$
$563$	14.5156	−	8.38057i	0.611759	−	0.353199i	0.773653	+	0.633609i	$0.218427\pi$
$564$	24.0000	+	13.8564i	1.01058	+	0.583460i
$565$	−26.3799	+	45.6912i	−1.10981	+	1.92225i
$566$	0.227446	+	0.131316i	0.00956028	+	0.00551963i
$567$		0			0
$568$		0			0
$569$	−7.05025	+	12.2114i	−0.295562	+	0.511928i	−0.975115	−	0.221698i	$-0.928840\pi$
$569$	−7.05025	+	12.2114i	−0.295562	+	0.511928i	0.679554	+	0.733626i	$0.262174\pi$
$570$	56.5092			2.36691
$571$	11.8284	+	20.4874i	0.495004	+	0.857373i	0.999983	−	0.00575900i	$-0.00183316\pi$
$571$	11.8284	+	20.4874i	0.495004	+	0.857373i	−0.504979	+	0.863132i	$0.668500\pi$
$572$	20.3007			0.848814
$573$	30.9059			1.29111
$574$		0			0
$575$			7.52255i			0.313712i
$576$	15.3137	−	26.5241i	0.638071	−	1.10517i
$577$	1.82765	−	1.05520i	0.0760862	−	0.0439284i	−0.461474	−	0.887154i	$-0.652679\pi$
$577$	1.82765	−	1.05520i	0.0760862	−	0.0439284i	0.537560	+	0.843225i	$0.319346\pi$
$578$	−23.8995			−0.994088
$579$	32.0041	+	18.4776i	1.33005	+	0.767902i
$580$	−51.9832	+	30.0125i	−2.15848	+	1.24620i
$581$		0			0
$582$	7.07107	−	12.2474i	0.293105	−	0.507673i
$583$	−6.00000	−	3.46410i	−0.248495	−	0.143468i
$584$	−3.42786	+	1.97908i	−0.141846	+	0.0818947i
$585$	31.0919	+	53.8527i	1.28549	+	2.22654i
$586$	3.58869	+	6.21579i	0.148247	+	0.256772i
$587$			43.2638i			1.78569i	0.450365	+	0.892845i	$0.351294\pi$
$587$			43.2638i			1.78569i	−0.450365	+	0.892845i	$0.648706\pi$
$588$		0			0
$589$		−	12.6677i		−	0.521964i
$590$	10.2426	−	5.91359i	0.421683	−	0.243459i
$591$	34.6554	+	60.0250i	1.42553	+	2.46910i
$592$		−	9.79796i		−	0.402694i
$593$	−10.6523	−	6.15013i	−0.437439	−	0.252556i	0.265072	−	0.964229i	$-0.414604\pi$
$593$	−10.6523	−	6.15013i	−0.437439	−	0.252556i	−0.702511	+	0.711673i	$0.747938\pi$
$594$	5.30262	+	3.06147i	0.217569	+	0.125614i
$595$		0			0
$596$	34.9706	−	20.1903i	1.43245	−	0.827025i
$597$	−6.00000	−	3.46410i	−0.245564	−	0.141776i
$598$			10.2987i			0.421143i
$599$	−30.7279	+	17.7408i	−1.25551	+	0.724868i	−0.972198	−	0.234160i	$-0.924766\pi$
$599$	−30.7279	+	17.7408i	−1.25551	+	0.724868i	−0.283311	+	0.959028i	$0.591433\pi$
$600$	33.5572	+	19.3743i	1.36997	+	0.790951i
$601$			35.1843i			1.43520i	0.696456	+	0.717600i	$0.254759\pi$
$601$			35.1843i			1.43520i	−0.696456	+	0.717600i	$0.745241\pi$
$602$		0			0
$603$	−45.9411			−1.87087
$604$			30.5826i			1.24439i
$605$	−11.2014	−	19.4015i	−0.455403	−	0.788782i
$606$		−	28.5533i		−	1.15990i
$607$	12.8017	−	22.1731i	0.519603	−	0.899979i	−0.480137	−	0.877193i	$-0.659413\pi$
$607$	12.8017	−	22.1731i	0.519603	−	0.899979i	0.999740	−	0.0227854i	$-0.00725346\pi$
$608$	23.4069	−	13.5140i	0.949275	−	0.548064i
$609$		0			0
$610$	−9.00000	+	15.5885i	−0.364399	+	0.631158i
$611$	−13.4558	+	23.3062i	−0.544365	+	0.942868i
$612$	−2.10220	−	1.21371i	−0.0849766	−	0.0490613i
$613$	23.3345	−	13.4722i	0.942473	−	0.544137i	0.0517380	−	0.998661i	$-0.483524\pi$
$613$	23.3345	−	13.4722i	0.942473	−	0.544137i	0.890735	+	0.454524i	$0.150191\pi$
$614$	7.40482	−	4.27518i	0.298834	−	0.172532i
$615$	37.3067			1.50435
$616$		0			0
$617$	−9.21320			−0.370910			−0.185455	−	0.982653i	$-0.559376\pi$
$617$	−9.21320			−0.370910			−0.185455	+	0.982653i	$0.559376\pi$
$618$	49.4558	−	28.5533i	1.98941	−	1.14858i
$619$	−25.2150	+	14.5579i	−1.01348	+	0.585131i	−0.912208	−	0.409728i	$-0.865624\pi$
$619$	−25.2150	+	14.5579i	−1.01348	+	0.585131i	−0.101270	+	0.994859i	$0.532290\pi$
$620$	8.48528	−	14.6969i	0.340777	−	0.590243i
$621$	−1.55310	+	2.69005i	−0.0623238	+	0.107948i
$622$	19.2025	−	33.2597i	0.769949	−	1.33359i
$623$		0			0
$624$	45.9411	+	26.5241i	1.83912	+	1.06181i
$625$	11.8640	−	20.5490i	0.474558	−	0.821959i
$626$		−	14.9678i		−	0.598233i
$627$	12.4853	+	21.6251i	0.498614	+	0.863625i
$628$	−47.9120			−1.91190
$629$	−0.776550			−0.0309631
$630$		0			0
$631$		−	29.7420i		−	1.18401i	−0.805934	−	0.592006i	$-0.798336\pi$
$631$		−	29.7420i		−	1.18401i	0.805934	−	0.592006i	$-0.201664\pi$
$632$	−28.9706	−	16.7262i	−1.15239	−	0.665331i
$633$	46.3589	−	26.7653i	1.84260	−	1.06383i
$634$			5.73951i			0.227945i
$635$	−15.2255	−	8.79045i	−0.604206	−	0.348839i
$636$	−9.05213	−	15.6788i	−0.358940	−	0.621703i
$637$		0			0
$638$	−22.9706	−	13.2621i	−0.909413	−	0.525050i
$639$		0			0
$640$	36.2085			1.43127
$641$	8.46447	+	14.6609i	0.334326	+	0.579070i	0.983355	−	0.181694i	$-0.0581579\pi$
$641$	8.46447	+	14.6609i	0.334326	+	0.579070i	−0.649029	+	0.760764i	$0.724825\pi$
$642$	27.1564	−	15.6788i	1.07178	−	0.618791i
$643$			36.3981i			1.43540i	0.696353	+	0.717700i	$0.254805\pi$
$643$			36.3981i			1.43540i	−0.696353	+	0.717700i	$0.745195\pi$
$644$		0			0
$645$			73.8329i			2.90717i
$646$	−1.07107	−	1.85514i	−0.0421406	−	0.0729897i
$647$	5.85172	+	10.1355i	0.230055	+	0.398467i	0.957824	−	0.287355i	$-0.0927761\pi$
$647$	5.85172	+	10.1355i	0.230055	+	0.398467i	−0.727769	+	0.685822i	$0.759443\pi$
$648$	−8.24264	−	14.2767i	−0.323802	−	0.560841i
$649$	4.52607	+	2.61313i	0.177664	+	0.102574i
$650$	−18.8142	+	32.5872i	−0.737954	+	1.27817i
$651$		0			0
$652$	−8.14214	−	14.1026i	−0.318871	−	0.552300i
$653$	−30.3640	−	17.5306i	−1.18823	−	0.686027i	−0.230329	−	0.973113i	$-0.573980\pi$
$653$	−30.3640	−	17.5306i	−1.18823	−	0.686027i	−0.957905	+	0.287086i	$0.907313\pi$
$654$	1.55310			0.0607310
$655$	−9.72792	+	5.61642i	−0.380101	+	0.219452i
$656$	15.4530	−	8.92177i	0.603337	−	0.348337i
$657$		−	5.35757i		−	0.209019i
$658$		0			0
$659$	25.5147			0.993912			0.496956	−	0.867776i	$-0.334451\pi$
$659$	25.5147			0.993912			0.496956	+	0.867776i	$0.334451\pi$
$660$			33.4523i			1.30213i
$661$	−10.4249	−	18.0564i	−0.405481	−	0.702314i	0.588896	−	0.808209i	$-0.299563\pi$
$661$	−10.4249	−	18.0564i	−0.405481	−	0.702314i	−0.994377	+	0.105894i	$0.966229\pi$
$662$	−29.4558			−1.14483
$663$	2.10220	−	3.64113i	0.0816429	−	0.141410i
$664$			23.9665i			0.930080i
$665$		0			0
$666$	11.4853	+	6.63103i	0.445046	+	0.256947i
$667$	6.72792	−	11.6531i	0.260506	−	0.451210i
$668$	14.3548	−	24.8632i	0.555402	−	0.961984i
$669$	55.4558	−	32.0174i	2.14405	−	1.23787i
$670$	−27.1564	−	47.0363i	−1.04914	−	1.81717i
$671$	−7.95393			−0.307058
$672$		0			0
$673$	30.3848			1.17125			0.585624	−	0.810583i	$-0.300850\pi$
$673$	30.3848			1.17125			0.585624	+	0.810583i	$0.300850\pi$
$674$	3.00000	+	5.19615i	0.115556	+	0.200148i
$675$	−9.82868	+	5.67459i	−0.378306	+	0.218415i
$676$	−12.7574	+	22.0964i	−0.490668	+	0.849861i
$677$	−0.501998	+	0.869487i	−0.0192934	+	0.0334171i	−0.875511	−	0.483198i	$-0.839475\pi$
$677$	−0.501998	+	0.869487i	−0.0192934	+	0.0334171i	0.856218	+	0.516615i	$0.172808\pi$
$678$	−52.7597	−	30.4608i	−2.02622	−	1.16984i
$679$		0			0
$680$		−	2.86976i		−	0.110050i
$681$	−30.3848	+	52.6280i	−1.16435	+	2.01671i
$682$	7.49903			0.287153
$683$	7.07107	+	12.2474i	0.270567	+	0.468636i	0.969007	−	0.247033i	$-0.0794555\pi$
$683$	7.07107	+	12.2474i	0.270567	+	0.468636i	−0.698440	+	0.715668i	$0.746122\pi$
$684$			36.5838i			1.39882i
$685$	−0.776550			−0.0296705
$686$		0			0
$687$		−	45.8739i		−	1.75020i
$688$	17.6569	+	30.5826i	0.673161	+	1.16595i
$689$	15.2255	−	8.79045i	0.580046	−	0.334890i
$690$	−16.9706			−0.646058
$691$	17.2611	+	9.96570i	0.656643	+	0.379113i	0.790997	−	0.611820i	$-0.209562\pi$
$691$	17.2611	+	9.96570i	0.656643	+	0.379113i	−0.134354	+	0.990933i	$0.542896\pi$
$692$	−6.94993	−	12.0376i	−0.264197	−	0.457602i
$693$		0			0
$694$	4.92893	−	8.53716i	0.187100	−	0.324066i
$695$	−13.9706	−	8.06591i	−0.529934	−	0.305957i
$696$	−34.6554	−	60.0250i	−1.31361	−	2.27524i
$697$	−0.707107	−	1.22474i	−0.0267836	−	0.0463905i
$698$	−15.8412	−	27.4378i	−0.599600	−	1.03854i
$699$		−	52.8966i		−	2.00073i
$700$		0			0
$701$			6.15978i			0.232652i	0.993211	+	0.116326i	$0.0371117\pi$
$701$			6.15978i			0.232652i	−0.993211	+	0.116326i	$0.962888\pi$
$702$	−13.4558	+	7.76874i	−0.507858	+	0.293212i
$703$	5.85172	+	10.1355i	0.220702	+	0.382267i
$704$	8.00000	+	13.8564i	0.301511	+	0.522233i
$705$	−38.4050	−	22.1731i	−1.44641	−	0.835088i
$706$	16.0687	+	9.27726i	0.604753	+	0.349154i
$707$		0			0
$708$	6.82843	+	11.8272i	0.256628	+	0.444493i
$709$	31.8198	+	18.3712i	1.19502	+	0.689944i	0.959440	−	0.281912i	$-0.0909685\pi$
$709$	31.8198	+	18.3712i	1.19502	+	0.689944i	0.235578	+	0.971856i	$0.424302\pi$
$710$		0			0
$711$	39.2132	−	22.6398i	1.47061	−	0.849057i
$712$	24.1834	+	13.9623i	0.906313	+	0.523260i
$713$			3.80430i			0.142472i
$714$		0			0
$715$	−32.4853			−1.21488
$716$	−40.9706			−1.53114
$717$	17.3277	+	30.0125i	0.647115	+	1.12084i
$718$			24.4949i			0.914141i
$719$	−14.6764	+	25.4203i	−0.547338	+	0.948017i	0.451118	+	0.892464i	$0.351025\pi$
$719$	−14.6764	+	25.4203i	−0.547338	+	0.948017i	−0.998456	+	0.0555524i	$0.982308\pi$
$720$	−24.5051	+	42.4441i	−0.913251	+	1.58180i
$721$		0			0
$722$	−2.70711	+	4.68885i	−0.100748	+	0.174501i
$723$	28.8995	−	50.0554i	1.07478	−	1.86158i
$724$	2.10220	−	3.64113i	0.0781278	−	0.135321i
$725$	42.5772	−	24.5819i	1.58128	−	0.912950i
$726$	22.4029	−	12.9343i	0.831449	−	0.480037i
$727$	−43.0643			−1.59716			−0.798582	−	0.601886i	$-0.794416\pi$
$727$	−43.0643			−1.59716			−0.798582	+	0.601886i	$0.794416\pi$
$728$		0			0
$729$	39.2843			1.45497
$730$	5.48528	−	3.16693i	0.203019	−	0.117213i
$731$	2.42386	−	1.39942i	0.0896498	−	0.0517593i
$732$	−18.0000	−	10.3923i	−0.665299	−	0.384111i
$733$	3.70241	−	6.41276i	0.136752	−	0.236861i	−0.789514	−	0.613733i	$-0.789667\pi$
$733$	3.70241	−	6.41276i	0.136752	−	0.236861i	0.926265	+	0.376872i	$0.123000\pi$
$734$	12.0251	−	20.8281i	0.443855	−	0.768779i
$735$		0			0
$736$	−7.02944	+	4.05845i	−0.259108	+	0.149596i
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$			24.1522i			0.889054i
$739$	−7.58579	−	13.1390i	−0.279048	−	0.483325i	0.692101	−	0.721801i	$-0.256685\pi$
$739$	−7.58579	−	13.1390i	−0.279048	−	0.483325i	−0.971148	+	0.238476i	$0.923352\pi$
$740$			15.6788i			0.576363i
$741$	−63.3649			−2.32777
$742$		0			0
$743$		−	13.2621i		−	0.486538i	−0.969959	−	0.243269i	$-0.921780\pi$
$743$		−	13.2621i		−	0.486538i	0.969959	−	0.243269i	$-0.0782197\pi$
$744$	16.9706	+	9.79796i	0.622171	+	0.359211i
$745$	−55.9601	+	32.3086i	−2.05022	+	1.18370i
$746$		−	13.0159i		−	0.476545i
$747$	−28.0938	−	16.2200i	−1.02790	−	0.593457i
$748$	1.09821	−	0.634051i	0.0401545	−	0.0231832i
$749$		0			0
$750$	−2.48528	−	1.43488i	−0.0907496	−	0.0523943i
$751$	−30.9411	−	17.8639i	−1.12906	−	0.651862i	−0.185360	−	0.982671i	$-0.559345\pi$
$751$	−30.9411	−	17.8639i	−1.12906	−	0.651862i	−0.943698	+	0.330809i	$0.892678\pi$
$752$	−21.2105			−0.773466
$753$	−25.0711	−	43.4244i	−0.913641	−	1.58247i
$754$	58.2898	−	33.6536i	2.12279	−	1.22559i
$755$		−	48.9384i		−	1.78105i
$756$		0			0
$757$			35.9018i			1.30487i	0.757843	+	0.652437i	$0.226253\pi$
$757$			35.9018i			1.30487i	−0.757843	+	0.652437i	$0.773747\pi$
$758$	12.2426	+	21.2049i	0.444673	+	0.770196i
$759$	−3.74952	−	6.49435i	−0.136099	−	0.235730i
$760$	−37.4558	+	21.6251i	−1.35867	+	0.784426i
$761$	18.9279	+	10.9280i	0.686137	+	0.396141i	0.802163	−	0.597105i	$-0.203682\pi$
$761$	18.9279	+	10.9280i	0.686137	+	0.396141i	−0.116026	+	0.993246i	$0.537016\pi$
$762$	10.1503	−	17.5809i	0.367708	−	0.636889i
$763$		0			0
$764$	−20.4853	+	11.8272i	−0.741131	+	0.427892i
$765$	3.36396	+	1.94218i	0.121624	+	0.0702198i
$766$	7.49903			0.270951
$767$	−11.4853	+	6.63103i	−0.414709	+	0.239433i
$768$			41.8100i			1.50869i
$769$			46.1940i			1.66580i	0.553425	+	0.832899i	$0.313320\pi$
$769$			46.1940i			1.66580i	−0.553425	+	0.832899i	$0.686680\pi$
$770$		0			0
$771$	−21.3137			−0.767594
$772$	−28.2843			−1.01797
$773$	−15.5001	−	26.8469i	−0.557499	−	0.965616i	−0.997704	−	0.0677190i	$-0.978428\pi$
$773$	−15.5001	−	26.8469i	−0.557499	−	0.965616i	0.440206	−	0.897897i	$-0.354905\pi$
$774$	−47.7990			−1.71810
$775$	−6.94993	+	12.0376i	−0.249649	+	0.432404i
$776$			10.8239i			0.388556i
$777$		0			0
$778$	4.45584	+	2.57258i	0.159750	+	0.0922316i
$779$	−10.6569	+	18.4582i	−0.381821	+	0.661334i
$780$	−73.5153	−	42.4441i	−2.63227	−	1.51974i
$781$		0			0
$782$	0.321658	+	0.557127i	0.0115025	+	0.0199228i
$783$	20.3007			0.725487
$784$		0			0
$785$	76.6690			2.73644
$786$	−6.48528	−	11.2328i	−0.231322	−	0.400662i
$787$	−33.6238	+	19.4127i	−1.19856	+	0.691989i	−0.960234	−	0.279196i	$-0.909932\pi$
$787$	−33.6238	+	19.4127i	−1.19856	+	0.691989i	−0.238326	+	0.971185i	$0.576599\pi$
$788$	−45.9411	−	26.5241i	−1.63658	−	0.944883i
$789$	−11.7034	+	20.2710i	−0.416654	+	0.721665i
$790$	46.3589	+	26.7653i	1.64937	+	0.952267i
$791$		0			0
$792$	−21.6569			−0.769543
$793$	10.0919	−	17.4797i	0.358373	−	0.620721i
$794$	−34.3338			−1.21846
$795$	14.4853	+	25.0892i	0.513740	+	0.889824i
$796$	5.30262			0.187946
$797$	13.4840			0.477627			0.238814	−	0.971065i	$-0.423241\pi$
$797$	13.4840			0.477627			0.238814	+	0.971065i	$0.423241\pi$
$798$		0			0
$799$			1.68106i			0.0594718i
$800$	−29.6569			−1.04853
$801$	−32.7336	+	18.8987i	−1.15658	+	0.667754i
$802$	−10.9706			−0.387384
$803$	2.42386	+	1.39942i	0.0855362	+	0.0493844i
$804$	54.3128	−	31.3575i	1.91546	−	1.10589i
$805$		0			0
$806$	−9.51472	+	16.4800i	−0.335142	+	0.580482i
$807$	5.48528	+	3.16693i	0.193091	+	0.111481i
$808$	10.9269	+	18.9259i	0.384407	+	0.665812i
$809$	7.72792	+	13.3852i	0.271699	+	0.470597i	0.969297	−	0.245893i	$-0.0790811\pi$
$809$	7.72792	+	13.3852i	0.271699	+	0.470597i	−0.697598	+	0.716490i	$0.745748\pi$
$810$	13.1899	+	22.8456i	0.463447	+	0.802713i
$811$		−	28.4818i		−	1.00013i	−0.865988	−	0.500065i	$-0.833310\pi$
$811$		−	28.4818i		−	1.00013i	0.865988	−	0.500065i	$-0.166690\pi$
$812$		0			0
$813$			34.6410i			1.21491i
$814$	−6.00000	+	3.46410i	−0.210300	+	0.121417i
$815$	13.0291	+	22.5671i	0.456389	+	0.790490i
$816$	3.31371			0.116003
$817$	−36.5302	−	21.0907i	−1.27803	−	0.737871i
$818$	4.68690	+	2.70598i	0.163873	+	0.0946124i
$819$		0			0
$820$	−24.7279	+	14.2767i	−0.863536	+	0.498563i
$821$	−15.5147	−	8.95743i	−0.541467	−	0.312616i	0.204206	−	0.978928i	$-0.434539\pi$
$821$	−15.5147	−	8.95743i	−0.541467	−	0.312616i	−0.745673	+	0.666312i	$0.767872\pi$
$822$		−	0.896683i		−	0.0312754i
$823$	18.0000	−	10.3923i	0.627441	−	0.362253i	−0.152320	−	0.988331i	$-0.548674\pi$
$823$	18.0000	−	10.3923i	0.627441	−	0.362253i	0.779760	+	0.626078i	$0.215341\pi$
$824$	−21.8538	+	37.8519i	−0.761313	+	1.31863i
$825$		−	27.3994i		−	0.953923i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		−	10.9867i		−	0.381813i
$829$	8.38931	+	14.5307i	0.291373	+	0.504672i	0.974135	−	0.225969i	$-0.0725547\pi$
$829$	8.38931	+	14.5307i	0.291373	+	0.504672i	−0.682762	+	0.730641i	$0.739221\pi$
$830$		−	38.3513i		−	1.33119i
$831$	−21.8538	+	37.8519i	−0.758099	+	1.31307i
$832$	−40.6014			−1.40760
$833$		0			0
$834$	9.31371	−	16.1318i	0.322507	−	0.558599i
$835$	−22.9706	+	39.7862i	−0.794929	+	1.37686i
$836$	−16.5512	−	9.55582i	−0.572434	−	0.330495i
$837$	−4.97056	+	2.86976i	−0.171808	+	0.0991933i
$838$	−48.7827	+	28.1647i	−1.68517	+	0.972934i
$839$	30.4510			1.05129			0.525643	−	0.850705i	$-0.323825\pi$
$839$	30.4510			1.05129			0.525643	+	0.850705i	$0.323825\pi$
$840$		0			0
$841$	−58.9411			−2.03245
$842$	32.4853	−	18.7554i	1.11952	−	0.646353i
$843$	19.7516	−	11.4036i	0.680281	−	0.392760i
$844$	−20.4853	+	35.4815i	−0.705132	+	1.22133i
$845$	20.4144	−	35.3588i	0.702277	−	1.21638i
$846$	14.3548	−	24.8632i	0.493527	−	0.854813i
$847$		0			0
$848$	12.0000	+	6.92820i	0.412082	+	0.237915i
$849$	0.242641	−	0.420266i	0.00832741	−	0.0144235i
$850$			2.35049i			0.0806213i
$851$	−1.75736	−	3.04384i	−0.0602415	−	0.104341i
$852$		0			0
$853$	−32.5532			−1.11460			−0.557301	−	0.830311i	$-0.688163\pi$
$853$	−32.5532			−1.11460			−0.557301	+	0.830311i	$0.688163\pi$
$854$		0			0
$855$		−	58.5416i		−	2.00208i
$856$	−12.0000	+	20.7846i	−0.410152	+	0.710403i
$857$	−29.8548	+	17.2367i	−1.01982	+	0.588794i	−0.914052	−	0.405597i	$-0.867064\pi$
$857$	−29.8548	+	17.2367i	−1.01982	+	0.588794i	−0.105769	+	0.994391i	$0.533730\pi$
$858$		−	37.5108i		−	1.28060i
$859$	−38.5658	−	22.2660i	−1.31585	−	0.759705i	−0.332790	−	0.943001i	$-0.607990\pi$
$859$	−38.5658	−	22.2660i	−1.31585	−	0.759705i	−0.983058	+	0.183296i	$0.941323\pi$
$860$	−28.2546	−	48.9384i	−0.963474	−	1.66879i
$861$		0			0
$862$	9.21320	+	5.31925i	0.313803	+	0.181174i
$863$	3.51472	+	2.02922i	0.119642	+	0.0690756i	0.558627	−	0.829419i	$-0.311328\pi$
$863$	3.51472	+	2.02922i	0.119642	+	0.0690756i	−0.438985	+	0.898495i	$0.644662\pi$
$864$	−10.6052	−	6.12293i	−0.360797	−	0.208306i
$865$	11.1213	+	19.2627i	0.378136	+	0.654951i
$866$	−6.33421	+	3.65706i	−0.215245	+	0.124272i
$867$			44.1605i			1.49977i
$868$		0			0
$869$			23.6544i			0.802419i
$870$	55.4558	+	96.0523i	1.88013	+	3.25648i
$871$	30.4510	+	52.7427i	1.03179	+	1.78712i
$872$	−1.02944	+	0.594346i	−0.0348611	+	0.0201271i
$873$	−12.6879	−	7.32538i	−0.429421	−	0.247926i
$874$	4.84772	−	8.39651i	0.163977	−	0.284016i
$875$		0			0
$876$	3.65685	+	6.33386i	0.123554	+	0.214001i
$877$	27.8787	+	16.0958i	0.941396	+	0.543515i	0.890398	−	0.455183i	$-0.150426\pi$
$877$	27.8787	+	16.0958i	0.941396	+	0.543515i	0.0509984	+	0.998699i	$0.483760\pi$
$878$	50.5633			1.70643
$879$	11.4853	−	6.63103i	0.387389	−	0.223659i
$880$	−12.8017	−	22.1731i	−0.431544	−	0.747455i
$881$		−	34.8448i		−	1.17395i	−0.809605	−	0.586975i	$-0.800319\pi$
$881$		−	34.8448i		−	1.17395i	0.809605	−	0.586975i	$-0.199681\pi$
$882$		0			0
$883$	38.4264			1.29315			0.646576	−	0.762850i	$-0.276200\pi$
$883$	38.4264			1.29315			0.646576	+	0.762850i	$0.276200\pi$
$884$			3.21792i			0.108230i
$885$	−10.9269	−	18.9259i	−0.367303	−	0.636188i
$886$	40.0000			1.34383
$887$	19.9790	−	34.6047i	0.670830	−	1.16191i	−0.306839	−	0.951761i	$-0.599271\pi$
$887$	19.9790	−	34.6047i	0.670830	−	1.16191i	0.977669	−	0.210150i	$-0.0673953\pi$
$888$	−18.1043			−0.607539
$889$		0			0
$890$	−38.6985	−	22.3426i	−1.29718	−	0.748925i
$891$	−5.82843	+	10.0951i	−0.195260	+	0.338200i
$892$	−24.5051	+	42.4441i	−0.820491	+	1.42113i
$893$	21.9411	−	12.6677i	0.734232	−	0.423909i
$894$	−37.3067	−	64.6172i	−1.24772	−	2.16112i
$895$	65.5614			2.19147
$896$		0			0
$897$	19.0294			0.635374
$898$	−4.00000	−	6.92820i	−0.133482	−	0.231197i
$899$	21.5321	−	12.4316i	0.718137	−	0.414616i
$900$	20.0711	−	34.7641i	0.669036	−	1.15880i
$901$	0.549104	−	0.951076i	0.0182933	−	0.0316849i
$902$	−10.9269	−	6.30864i	−0.363826	−	0.210055i
$903$		0			0
$904$	46.6274			1.55080
$905$	−3.36396	+	5.82655i	−0.111822	+	0.193681i
$906$	56.5092			1.87739
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	0.967730	−	0.251990i	$-0.0810849\pi$
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	−0.702094	+	0.712084i	$0.747752\pi$
$908$		−	46.5110i		−	1.54352i
$909$	−29.5803			−0.981115
$910$		0			0
$911$			5.49333i			0.182002i	0.995851	+	0.0910010i	$0.0290066\pi$
$911$			5.49333i			0.182002i	−0.995851	+	0.0910010i	$0.970993\pi$
$912$	−24.9706	−	43.2503i	−0.826858	−	1.43216i
$913$	14.6764	−	8.47343i	0.485718	−	0.280430i
$914$	29.9411			0.990364
$915$	28.8037	+	16.6298i	0.952221	+	0.549765i
$916$	17.5552	+	30.4064i	0.580039	+	1.00466i
$917$		0			0
$918$	−0.485281	+	0.840532i	−0.0160167	+	0.0277417i
$919$	−15.5147	−	8.95743i	−0.511783	−	0.295478i	0.221783	−	0.975096i	$-0.428812\pi$
$919$	−15.5147	−	8.95743i	−0.511783	−	0.295478i	−0.733566	+	0.679618i	$0.762146\pi$
$920$	11.2485	−	6.49435i	0.370854	−	0.214112i
$921$	−7.89949	−	13.6823i	−0.260297	−	0.450848i
$922$	−18.8142	−	32.5872i	−0.619613	−	1.07320i
$923$		0			0
$924$		0			0
$925$		−	12.8418i		−	0.422236i
$926$	−22.9706	+	13.2621i	−0.754860	+	0.435818i
$927$	−29.5803	−	51.2345i	−0.971543	−	1.68276i
$928$	45.9411	+	26.5241i	1.50809	+	0.870697i
$929$	−1.37276	−	0.792563i	−0.0450388	−	0.0260032i	0.477312	−	0.878734i	$-0.341611\pi$
$929$	−1.37276	−	0.792563i	−0.0450388	−	0.0260032i	−0.522350	+	0.852731i	$0.674945\pi$
$930$	−27.1564	−	15.6788i	−0.890493	−	0.514127i
$931$		0			0
$932$	20.2426	+	35.0613i	0.663070	+	1.14847i
$933$	−61.4558	−	35.4815i	−2.01197	−	1.16161i
$934$		−	0.108786i		−	0.00355958i
$935$	−1.75736	+	1.01461i	−0.0574718	+	0.0331814i
$936$	27.4781	−	47.5934i	0.898148	−	1.55564i
$937$		−	16.9694i		−	0.554366i	−0.960817	−	0.277183i	$-0.910599\pi$
$937$		−	16.9694i		−	0.554366i	0.960817	−	0.277183i	$-0.0894008\pi$
$938$		0			0
$939$	−27.6569			−0.902547
$940$	33.9411			1.10704
$941$	1.21193	+	2.09913i	0.0395078	+	0.0684296i	0.885103	−	0.465395i	$-0.154088\pi$
$941$	1.21193	+	2.09913i	0.0395078	+	0.0684296i	−0.845595	+	0.533824i	$0.820754\pi$
$942$			88.5298i			2.88446i
$943$	3.20041	−	5.54328i	0.104220	−	0.180514i
$944$	−9.05213	−	5.22625i	−0.294622	−	0.170100i
$945$		0			0
$946$	12.4853	−	21.6251i	0.405932	−	0.703094i
$947$	−25.7279	+	44.5621i	−0.836045	+	1.44807i	0.0571315	+	0.998367i	$0.481805\pi$
$947$	−25.7279	+	44.5621i	−0.836045	+	1.44807i	−0.893177	+	0.449706i	$0.851529\pi$
$948$	−30.9059	+	53.5306i	−1.00378	+	1.73859i
$949$	−6.15076	+	3.55114i	−0.199662	+	0.115275i
$950$	30.6785	−	17.7122i	0.995341	−	0.574660i
$951$	10.6052			0.343898
$952$		0			0
$953$	−41.3137			−1.33828			−0.669141	−	0.743135i	$-0.733338\pi$
$953$	−41.3137			−1.33828			−0.669141	+	0.743135i	$0.733338\pi$
$954$	−16.2426	+	9.37769i	−0.525875	+	0.303614i
$955$	32.7807	−	18.9259i	1.06076	−	0.612429i
$956$	−22.9706	−	13.2621i	−0.742921	−	0.428926i
$957$	−24.5051	+	42.4441i	−0.792137	+	1.37202i
$958$	−8.27558	+	14.3337i	−0.267372	+	0.463102i
$959$		0			0
$960$		−	66.9046i		−	2.15934i
$961$	11.9853	−	20.7591i	0.386622	−	0.669649i
$962$		−	17.5809i		−	0.566831i
$963$	−16.2426	−	28.1331i	−0.523412	−	0.906576i
$964$			44.2374i			1.42479i
$965$	45.2607			1.45699
$966$		0			0
$967$		−	21.0308i		−	0.676305i	−0.941091	−	0.338152i	$-0.890198\pi$
$967$		−	21.0308i		−	0.676305i	0.941091	−	0.338152i	$-0.109802\pi$
$968$	−9.89949	+	17.1464i	−0.318182	+	0.551107i
$969$	−3.42786	+	1.97908i	−0.110119	+	0.0635771i
$970$		−	17.3205i		−	0.556128i
$971$	21.4655	+	12.3931i	0.688861	+	0.397714i	0.803185	−	0.595729i	$-0.203137\pi$
$971$	21.4655	+	12.3931i	0.688861	+	0.397714i	−0.114324	+	0.993443i	$0.536470\pi$
$972$	−37.6284	+	21.7248i	−1.20693	+	0.696822i
$973$		0			0
$974$	41.6985	+	24.0746i	1.33611	+	0.771401i
$975$	60.2132	+	34.7641i	1.92837	+	1.11334i
$976$	15.9079			0.509198
$977$	−18.6066	−	32.2276i	−0.595278	−	1.03105i	−0.993508	−	0.113766i	$-0.963709\pi$
$977$	−18.6066	−	32.2276i	−0.595278	−	1.03105i	0.398230	−	0.917286i	$-0.369625\pi$
$978$	−26.0582	+	15.0447i	−0.833249	+	0.481077i
$979$		−	19.7457i		−	0.631075i
$980$		0			0
$981$		−	1.60896i		−	0.0513701i
$982$	−22.4853	−	38.9456i	−0.717534	−	1.24281i
$983$	13.0291	+	22.5671i	0.415564	+	0.719777i	0.995487	−	0.0948934i	$-0.0302510\pi$
$983$	13.0291	+	22.5671i	0.415564	+	0.719777i	−0.579924	+	0.814671i	$0.696918\pi$
$984$	−16.4853	−	28.5533i	−0.525532	−	0.910247i
$985$	73.5153	+	42.4441i	2.34239	+	1.35238i
$986$	2.10220	−	3.64113i	0.0669478	−	0.115957i
$987$		0			0
$988$	42.0000	−	24.2487i	1.33620	−	0.771454i
$989$	10.9706	+	6.33386i	0.348844	+	0.201405i
$990$	34.6554			1.10142
$991$	−27.9411	+	16.1318i	−0.887579	+	0.512444i	−0.873150	−	0.487452i	$-0.837926\pi$
$991$	−27.9411	+	16.1318i	−0.887579	+	0.512444i	−0.0144292	+	0.999896i	$0.504593\pi$
$992$	−14.9981			−0.476189
$993$			54.4273i			1.72720i
$994$		0			0
$995$	−8.48528			−0.269002
$996$	44.2843			1.40320
$997$	2.69841	+	4.67379i	0.0854596	+	0.148020i	0.905587	−	0.424161i	$-0.139431\pi$
$997$	2.69841	+	4.67379i	0.0854596	+	0.148020i	−0.820127	+	0.572181i	$0.806097\pi$
$998$	12.0000			0.379853
$999$	2.65131	−	4.59220i	0.0838837	−	0.145291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.m.c.19.4		8
4.3	odd	2		1568.2.q.c.1391.1		8
7.2	even	3		392.2.e.c.195.6	yes	8
7.3	odd	6		392.2.m.e.227.2		8
7.4	even	3		392.2.m.e.227.1		8
7.5	odd	6		392.2.e.c.195.5	✓	8
7.6	odd	2	inner	392.2.m.c.19.3		8
8.3	odd	2		392.2.m.e.19.2		8
8.5	even	2		1568.2.q.d.1391.1		8
28.3	even	6		1568.2.q.d.815.1		8
28.11	odd	6		1568.2.q.d.815.4		8
28.19	even	6		1568.2.e.c.783.8		8
28.23	odd	6		1568.2.e.c.783.1		8
28.27	even	2		1568.2.q.c.1391.4		8
56.3	even	6	inner	392.2.m.c.227.4		8
56.5	odd	6		1568.2.e.c.783.7		8
56.11	odd	6	inner	392.2.m.c.227.3		8
56.13	odd	2		1568.2.q.d.1391.4		8
56.19	even	6		392.2.e.c.195.7	yes	8
56.27	even	2		392.2.m.e.19.1		8
56.37	even	6		1568.2.e.c.783.2		8
56.45	odd	6		1568.2.q.c.815.1		8
56.51	odd	6		392.2.e.c.195.8	yes	8
56.53	even	6		1568.2.q.c.815.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.e.c.195.5	✓	8	7.5	odd	6
392.2.e.c.195.6	yes	8	7.2	even	3
392.2.e.c.195.7	yes	8	56.19	even	6
392.2.e.c.195.8	yes	8	56.51	odd	6
392.2.m.c.19.3		8	7.6	odd	2	inner
392.2.m.c.19.4		8	1.1	even	1	trivial
392.2.m.c.227.3		8	56.11	odd	6	inner
392.2.m.c.227.4		8	56.3	even	6	inner
392.2.m.e.19.1		8	56.27	even	2
392.2.m.e.19.2		8	8.3	odd	2
392.2.m.e.227.1		8	7.4	even	3
392.2.m.e.227.2		8	7.3	odd	6
1568.2.e.c.783.1		8	28.23	odd	6
1568.2.e.c.783.2		8	56.37	even	6
1568.2.e.c.783.7		8	56.5	odd	6
1568.2.e.c.783.8		8	28.19	even	6
1568.2.q.c.815.1		8	56.45	odd	6
1568.2.q.c.815.4		8	56.53	even	6
1568.2.q.c.1391.1		8	4.3	odd	2
1568.2.q.c.1391.4		8	28.27	even	2
1568.2.q.d.815.1		8	28.3	even	6
1568.2.q.d.815.4		8	28.11	odd	6
1568.2.q.d.1391.1		8	8.5	even	2
1568.2.q.d.1391.4		8	56.13	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(2.26303 - 1.30656i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.60021 - 2.77164i) q^{5} +(3.20041 + 1.84776i) q^{6} -2.82843 q^{8} +(1.91421 - 3.31552i) q^{9} +4.52607 q^{10} +(1.00000 + 1.73205i) q^{11} +5.22625i q^{12} -5.07517 q^{13} -8.36308i q^{15} +(-2.00000 - 3.46410i) q^{16} +(-0.274552 + 0.158513i) q^{17} +5.41421 q^{18} +(4.13779 + 2.38896i) q^{19} +(3.20041 + 5.54328i) q^{20} +(-1.41421 + 2.44949i) q^{22} +(-1.24264 - 0.717439i) q^{23} +(-6.40083 + 3.69552i) q^{24} +(-2.62132 - 4.54026i) q^{25} +(-3.58869 - 6.21579i) q^{26} -2.16478i q^{27} +9.37769i q^{29} +(10.2426 - 5.91359i) q^{30} +(-1.32565 - 2.29610i) q^{31} +(2.82843 - 4.89898i) q^{32} +(4.52607 + 2.61313i) q^{33} +(-0.388275 - 0.224171i) q^{34} +(3.82843 + 6.63103i) q^{36} +(2.12132 + 1.22474i) q^{37} +6.75699i q^{38} +(-11.4853 + 6.63103i) q^{39} +(-4.52607 + 7.83938i) q^{40} +4.46088i q^{41} -8.82843 q^{43} -4.00000 q^{44} +(-6.12627 - 10.6110i) q^{45} -2.02922i q^{46} +(2.65131 - 4.59220i) q^{47} +(-9.05213 - 5.22625i) q^{48} +(3.70711 - 6.42090i) q^{50} +(-0.414214 + 0.717439i) q^{51} +(5.07517 - 8.79045i) q^{52} +(-3.00000 + 1.73205i) q^{53} +(2.65131 - 1.53073i) q^{54} +6.40083 q^{55} +12.4853 q^{57} +(-11.4853 + 6.63103i) q^{58} +(2.26303 - 1.30656i) q^{59} +(14.4853 + 8.36308i) q^{60} +(-1.98848 + 3.44415i) q^{61} +(1.87476 - 3.24718i) q^{62} +8.00000 q^{64} +(-8.12132 + 14.0665i) q^{65} +7.39104i q^{66} +(-6.00000 - 10.3923i) q^{67} -0.634051i q^{68} -3.74952 q^{69} +(-5.41421 + 9.37769i) q^{72} +(1.21193 - 0.699709i) q^{73} +3.46410i q^{74} +(-11.8643 - 6.84984i) q^{75} +(-8.27558 + 4.77791i) q^{76} +(-16.2426 - 9.37769i) q^{78} +(10.2426 + 5.91359i) q^{79} -12.8017 q^{80} +(2.91421 + 5.04757i) q^{81} +(-5.46345 + 3.15432i) q^{82} -8.47343i q^{83} +1.01461i q^{85} +(-6.24264 - 10.8126i) q^{86} +(12.2525 + 21.2220i) q^{87} +(-2.82843 - 4.89898i) q^{88} +(-8.55014 - 4.93642i) q^{89} +(8.66386 - 15.0062i) q^{90} +(2.48528 - 1.43488i) q^{92} +(-6.00000 - 3.46410i) q^{93} +7.49903 q^{94} +(13.2426 - 7.64564i) q^{95} -14.7821i q^{96} -3.82683i q^{97} +7.65685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{9} + 8 q^{11} - 16 q^{16} + 32 q^{18} + 24 q^{23} - 4 q^{25} + 48 q^{30} + 8 q^{36} - 24 q^{39} - 48 q^{43} - 32 q^{44} + 24 q^{50} + 8 q^{51} - 24 q^{53} + 32 q^{57} - 24 q^{58} + 48 q^{60}+ \cdots + 16 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^9 + 8 * q^11 - 16 * q^16 + 32 * q^18 + 24 * q^23 - 4 * q^25 + 48 * q^30 + 8 * q^36 - 24 * q^39 - 48 * q^43 - 32 * q^44 + 24 * q^50 + 8 * q^51 - 24 * q^53 + 32 * q^57 - 24 * q^58 + 48 * q^60 + 64 * q^64 - 48 * q^65 - 48 * q^67 - 32 * q^72 - 96 * q^78 + 48 * q^79 + 12 * q^81 - 16 * q^86 - 48 * q^92 - 48 * q^93 + 72 * q^95 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more