LMFDB - Embedded newform 1380.2.p.b.91.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(91,1380)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1380.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.p (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.14
Character	$\chi$	$=$	1380.91
Dual form			1380.2.p.b.91.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01915 + 0.980473i) q^{2} -1.00000i q^{3} +(0.0773439 - 1.99850i) q^{4} +1.00000i q^{5} +(0.980473 + 1.01915i) q^{6} -2.01213 q^{7} +(1.88065 + 2.11261i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.01915 + 0.980473i) q^{2} -1.00000i q^{3} +(0.0773439 - 1.99850i) q^{4} +1.00000i q^{5} +(0.980473 + 1.01915i) q^{6} -2.01213 q^{7} +(1.88065 + 2.11261i) q^{8} -1.00000 q^{9} +(-0.980473 - 1.01915i) q^{10} +0.838109 q^{11} +(-1.99850 - 0.0773439i) q^{12} +3.05381 q^{13} +(2.05067 - 1.97284i) q^{14} +1.00000 q^{15} +(-3.98804 - 0.309144i) q^{16} -3.47052i q^{17} +(1.01915 - 0.980473i) q^{18} -7.38055 q^{19} +(1.99850 + 0.0773439i) q^{20} +2.01213i q^{21} +(-0.854161 + 0.821743i) q^{22} +(-0.669578 + 4.74886i) q^{23} +(2.11261 - 1.88065i) q^{24} -1.00000 q^{25} +(-3.11230 + 2.99418i) q^{26} +1.00000i q^{27} +(-0.155626 + 4.02125i) q^{28} +2.05264 q^{29} +(-1.01915 + 0.980473i) q^{30} +6.36885i q^{31} +(4.36752 - 3.59510i) q^{32} -0.838109i q^{33} +(3.40276 + 3.53699i) q^{34} -2.01213i q^{35} +(-0.0773439 + 1.99850i) q^{36} -3.67292i q^{37} +(7.52191 - 7.23643i) q^{38} -3.05381i q^{39} +(-2.11261 + 1.88065i) q^{40} -2.79566 q^{41} +(-1.97284 - 2.05067i) q^{42} -3.75094 q^{43} +(0.0648226 - 1.67496i) q^{44} -1.00000i q^{45} +(-3.97373 - 5.49632i) q^{46} -10.8748i q^{47} +(-0.309144 + 3.98804i) q^{48} -2.95133 q^{49} +(1.01915 - 0.980473i) q^{50} -3.47052 q^{51} +(0.236194 - 6.10305i) q^{52} +3.38684i q^{53} +(-0.980473 - 1.01915i) q^{54} +0.838109i q^{55} +(-3.78412 - 4.25086i) q^{56} +7.38055i q^{57} +(-2.09196 + 2.01256i) q^{58} +2.21667i q^{59} +(0.0773439 - 1.99850i) q^{60} +14.3017i q^{61} +(-6.24449 - 6.49083i) q^{62} +2.01213 q^{63} +(-0.926277 + 7.94619i) q^{64} +3.05381i q^{65} +(0.821743 + 0.854161i) q^{66} -5.95010 q^{67} +(-6.93585 - 0.268424i) q^{68} +(4.74886 + 0.669578i) q^{69} +(1.97284 + 2.05067i) q^{70} +9.84155i q^{71} +(-1.88065 - 2.11261i) q^{72} +2.33425 q^{73} +(3.60120 + 3.74327i) q^{74} +1.00000i q^{75} +(-0.570841 + 14.7501i) q^{76} -1.68638 q^{77} +(2.99418 + 3.11230i) q^{78} -12.4986 q^{79} +(0.309144 - 3.98804i) q^{80} +1.00000 q^{81} +(2.84921 - 2.74107i) q^{82} -8.62575 q^{83} +(4.02125 + 0.155626i) q^{84} +3.47052 q^{85} +(3.82278 - 3.67770i) q^{86} -2.05264i q^{87} +(1.57619 + 1.77060i) q^{88} -3.93051i q^{89} +(0.980473 + 1.01915i) q^{90} -6.14467 q^{91} +(9.43883 + 1.70545i) q^{92} +6.36885 q^{93} +(10.6624 + 11.0831i) q^{94} -7.38055i q^{95} +(-3.59510 - 4.36752i) q^{96} +17.4142i q^{97} +(3.00786 - 2.89370i) q^{98} -0.838109 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	−1.01915	+	0.980473i	−0.720650	+	0.693299i
$2$	−1.01915	+	0.980473i	−0.720650	+	0.693299i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.0773439	−	1.99850i	0.0386720	−	0.999252i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.980473	+	1.01915i	0.400277	+	0.416067i
$7$	−2.01213			−0.760514			−0.380257	−	0.924881i	$-0.624164\pi$
$7$	−2.01213			−0.760514			−0.380257	+	0.924881i	$0.624164\pi$
$8$	1.88065	+	2.11261i	0.664912	+	0.746922i
$9$	−1.00000			−0.333333
$10$	−0.980473	−	1.01915i	−0.310053	−	0.322284i
$11$	0.838109			0.252699			0.126350	−	0.991986i	$-0.459674\pi$
$11$	0.838109			0.252699			0.126350	+	0.991986i	$0.459674\pi$
$12$	−1.99850	−	0.0773439i	−0.576918	−	0.0223273i
$13$	3.05381			0.846975			0.423487	−	0.905902i	$-0.360806\pi$
$13$	3.05381			0.846975			0.423487	+	0.905902i	$0.360806\pi$
$14$	2.05067	−	1.97284i	0.548064	−	0.527264i
$15$	1.00000			0.258199
$16$	−3.98804	−	0.309144i	−0.997009	−	0.0772861i
$17$		−	3.47052i		−	0.841725i	−0.907124	−	0.420863i	$-0.861727\pi$
$17$		−	3.47052i		−	0.841725i	0.907124	−	0.420863i	$-0.138273\pi$
$18$	1.01915	−	0.980473i	0.240217	−	0.231100i
$19$	−7.38055			−1.69321			−0.846607	−	0.532218i	$-0.821359\pi$
$19$	−7.38055			−1.69321			−0.846607	+	0.532218i	$0.821359\pi$
$20$	1.99850	+	0.0773439i	0.446879	+	0.0172946i
$21$			2.01213i			0.439083i
$22$	−0.854161	+	0.821743i	−0.182108	+	0.175196i
$23$	−0.669578	+	4.74886i	−0.139617	+	0.990206i
$23$	−0.669578	+	4.74886i	−0.139617	+	0.990206i
$24$	2.11261	−	1.88065i	0.431236	−	0.383887i
$25$	−1.00000			−0.200000
$26$	−3.11230	+	2.99418i	−0.610372	+	0.587207i
$27$			1.00000i			0.192450i
$28$	−0.155626	+	4.02125i	−0.0294106	+	0.759945i
$29$	2.05264			0.381166			0.190583	−	0.981671i	$-0.438962\pi$
$29$	2.05264			0.381166			0.190583	+	0.981671i	$0.438962\pi$
$30$	−1.01915	+	0.980473i	−0.186071	+	0.179009i
$31$			6.36885i			1.14388i	0.820296	+	0.571939i	$0.193809\pi$
$31$			6.36885i			1.14388i	−0.820296	+	0.571939i	$0.806191\pi$
$32$	4.36752	−	3.59510i	0.772077	−	0.635529i
$33$		−	0.838109i		−	0.145896i
$34$	3.40276	+	3.53699i	0.583568	+	0.606589i
$35$		−	2.01213i		−	0.340112i
$36$	−0.0773439	+	1.99850i	−0.0128907	+	0.333084i
$37$		−	3.67292i		−	0.603825i	−0.953336	−	0.301912i	$-0.902375\pi$
$37$		−	3.67292i		−	0.603825i	0.953336	−	0.301912i	$-0.0976250\pi$
$38$	7.52191	−	7.23643i	1.22021	−	1.17390i
$39$		−	3.05381i		−	0.489001i
$40$	−2.11261	+	1.88065i	−0.334034	+	0.297358i
$41$	−2.79566			−0.436609			−0.218305	−	0.975881i	$-0.570053\pi$
$41$	−2.79566			−0.436609			−0.218305	+	0.975881i	$0.570053\pi$
$42$	−1.97284	−	2.05067i	−0.304416	−	0.316425i
$43$	−3.75094			−0.572013			−0.286007	−	0.958228i	$-0.592328\pi$
$43$	−3.75094			−0.572013			−0.286007	+	0.958228i	$0.592328\pi$
$44$	0.0648226	−	1.67496i	0.00977238	−	0.252510i
$45$		−	1.00000i		−	0.149071i
$46$	−3.97373	−	5.49632i	−0.585894	−	0.810388i
$47$		−	10.8748i		−	1.58625i	−0.609060	−	0.793124i	$-0.708453\pi$
$47$		−	10.8748i		−	1.58625i	0.609060	−	0.793124i	$-0.291547\pi$
$48$	−0.309144	+	3.98804i	−0.0446211	+	0.575623i
$49$	−2.95133			−0.421619
$50$	1.01915	−	0.980473i	0.144130	−	0.138660i
$51$	−3.47052			−0.485970
$52$	0.236194	−	6.10305i	0.0327542	−	0.846341i
$53$			3.38684i			0.465218i	0.972570	+	0.232609i	$0.0747262\pi$
$53$			3.38684i			0.465218i	−0.972570	+	0.232609i	$0.925274\pi$
$54$	−0.980473	−	1.01915i	−0.133426	−	0.138689i
$55$			0.838109i			0.113011i
$56$	−3.78412	−	4.25086i	−0.505675	−	0.568044i
$57$			7.38055i			0.977578i
$58$	−2.09196	+	2.01256i	−0.274687	+	0.264262i
$59$			2.21667i			0.288586i	0.989535	+	0.144293i	$0.0460908\pi$
$59$			2.21667i			0.288586i	−0.989535	+	0.144293i	$0.953909\pi$
$60$	0.0773439	−	1.99850i	0.00998506	−	0.258006i
$61$			14.3017i			1.83114i	0.402153	+	0.915572i	$0.368262\pi$
$61$			14.3017i			1.83114i	−0.402153	+	0.915572i	$0.631738\pi$
$62$	−6.24449	−	6.49083i	−0.793051	−	0.824336i
$63$	2.01213			0.253505
$64$	−0.926277	+	7.94619i	−0.115785	+	0.993274i
$65$			3.05381i			0.378779i
$66$	0.821743	+	0.854161i	0.101150	+	0.105140i
$67$	−5.95010			−0.726920			−0.363460	−	0.931610i	$-0.618405\pi$
$67$	−5.95010			−0.726920			−0.363460	+	0.931610i	$0.618405\pi$
$68$	−6.93585	−	0.268424i	−0.841096	−	0.0325512i
$69$	4.74886	+	0.669578i	0.571695	+	0.0806077i
$70$	1.97284	+	2.05067i	0.235800	+	0.245102i
$71$			9.84155i			1.16798i	0.811762	+	0.583988i	$0.198509\pi$
$71$			9.84155i			1.16798i	−0.811762	+	0.583988i	$0.801491\pi$
$72$	−1.88065	−	2.11261i	−0.221637	−	0.248974i
$73$	2.33425			0.273203			0.136601	−	0.990626i	$-0.456382\pi$
$73$	2.33425			0.273203			0.136601	+	0.990626i	$0.456382\pi$
$74$	3.60120	+	3.74327i	0.418631	+	0.435146i
$75$			1.00000i			0.115470i
$76$	−0.570841	+	14.7501i	−0.0654799	+	1.69195i
$77$	−1.68638			−0.192181
$78$	2.99418	+	3.11230i	0.339024	+	0.352398i
$79$	−12.4986			−1.40621			−0.703104	−	0.711087i	$-0.748203\pi$
$79$	−12.4986			−1.40621			−0.703104	+	0.711087i	$0.748203\pi$
$80$	0.309144	−	3.98804i	0.0345634	−	0.445876i
$81$	1.00000			0.111111
$82$	2.84921	−	2.74107i	0.314642	−	0.302701i
$83$	−8.62575			−0.946799			−0.473400	−	0.880848i	$-0.656973\pi$
$83$	−8.62575			−0.946799			−0.473400	+	0.880848i	$0.656973\pi$
$84$	4.02125	+	0.155626i	0.438754	+	0.0169802i
$85$	3.47052			0.376431
$86$	3.82278	−	3.67770i	0.412221	−	0.396576i
$87$		−	2.05264i		−	0.220066i
$88$	1.57619	+	1.77060i	0.168023	+	0.188747i
$89$		−	3.93051i		−	0.416633i	−0.978061	−	0.208317i	$-0.933202\pi$
$89$		−	3.93051i		−	0.416633i	0.978061	−	0.208317i	$-0.0667984\pi$
$90$	0.980473	+	1.01915i	0.103351	+	0.107428i
$91$	−6.14467			−0.644136
$92$	9.43883	+	1.70545i	0.984066	+	0.177805i
$93$	6.36885			0.660419
$94$	10.6624	+	11.0831i	1.09974	+	1.14313i
$95$		−	7.38055i		−	0.757228i
$96$	−3.59510	−	4.36752i	−0.366923	−	0.445759i
$97$			17.4142i			1.76814i	0.467354	+	0.884070i	$0.345207\pi$
$97$			17.4142i			1.76814i	−0.467354	+	0.884070i	$0.654793\pi$
$98$	3.00786	−	2.89370i	0.303839	−	0.292308i
$99$	−0.838109			−0.0842331
$100$	−0.0773439	+	1.99850i	−0.00773439	+	0.199850i
$101$	−9.27908			−0.923303			−0.461652	−	0.887061i	$-0.652743\pi$
$101$	−9.27908			−0.923303			−0.461652	+	0.887061i	$0.652743\pi$
$102$	3.53699	−	3.40276i	0.350214	−	0.336923i
$103$	−12.5904			−1.24057			−0.620284	−	0.784378i	$-0.712983\pi$
$103$	−12.5904			−1.24057			−0.620284	+	0.784378i	$0.712983\pi$
$104$	5.74316	+	6.45152i	0.563163	+	0.632624i
$105$	−2.01213			−0.196364
$106$	−3.32070	−	3.45170i	−0.322535	−	0.335259i
$107$	−1.91110			−0.184753			−0.0923763	−	0.995724i	$-0.529446\pi$
$107$	−1.91110			−0.184753			−0.0923763	+	0.995724i	$0.529446\pi$
$108$	1.99850	+	0.0773439i	0.192306	+	0.00744242i
$109$			6.97931i			0.668496i	0.942485	+	0.334248i	$0.108482\pi$
$109$			6.97931i			0.668496i	−0.942485	+	0.334248i	$0.891518\pi$
$110$	−0.821743	−	0.854161i	−0.0783502	−	0.0814410i
$111$	−3.67292			−0.348618
$112$	8.02445	+	0.622039i	0.758239	+	0.0587772i
$113$			0.0437717i			0.00411769i	0.999998	+	0.00205885i	$0.000655351\pi$
$113$			0.0437717i			0.00411769i	−0.999998	+	0.00205885i	$0.999345\pi$
$114$	−7.23643	−	7.52191i	−0.677754	−	0.704491i
$115$	−4.74886	−	0.669578i	−0.442833	−	0.0624385i
$116$	0.158759	−	4.10221i	0.0147404	−	0.380881i
$117$	−3.05381			−0.282325
$118$	−2.17339	−	2.25913i	−0.200077	−	0.207969i
$119$			6.98315i			0.640144i
$120$	1.88065	+	2.11261i	0.171679	+	0.192854i
$121$	−10.2976			−0.936143
$122$	−14.0224	−	14.5756i	−1.26953	−	1.31961i
$123$			2.79566i			0.252076i
$124$	12.7282	+	0.492592i	1.14302	+	0.0442361i
$125$		−	1.00000i		−	0.0894427i
$126$	−2.05067	+	1.97284i	−0.182688	+	0.175755i
$127$		−	10.1347i		−	0.899308i	−0.893203	−	0.449654i	$-0.851547\pi$
$127$		−	10.1347i		−	0.899308i	0.893203	−	0.449654i	$-0.148453\pi$
$128$	−6.84702	−	9.00657i	−0.605196	−	0.796076i
$129$			3.75094i			0.330252i
$130$	−2.99418	−	3.11230i	−0.262607	−	0.272967i
$131$			17.9661i			1.56970i	0.619683	+	0.784852i	$0.287261\pi$
$131$			17.9661i			1.56970i	−0.619683	+	0.784852i	$0.712739\pi$
$132$	−1.67496	−	0.0648226i	−0.145787	−	0.00564209i
$133$	14.8506			1.28771
$134$	6.06406	−	5.83391i	0.523855	−	0.503973i
$135$	−1.00000			−0.0860663
$136$	7.33188	−	6.52685i	0.628703	−	0.559673i
$137$			2.44756i			0.209109i	0.994519	+	0.104555i	$0.0333417\pi$
$137$			2.44756i			0.209109i	−0.994519	+	0.104555i	$0.966658\pi$
$138$	−5.49632	+	3.97373i	−0.467877	+	0.338266i
$139$			9.31856i			0.790390i	0.918597	+	0.395195i	$0.129323\pi$
$139$			9.31856i			0.790390i	−0.918597	+	0.395195i	$0.870677\pi$
$140$	−4.02125	−	0.155626i	−0.339858	−	0.0131528i
$141$	−10.8748			−0.915821
$142$	−9.64938	−	10.0300i	−0.809758	−	0.841702i
$143$	2.55943			0.214030
$144$	3.98804	+	0.309144i	0.332336	+	0.0257620i
$145$			2.05264i			0.170463i
$146$	−2.37895	+	2.28867i	−0.196884	+	0.189411i
$147$			2.95133i			0.243422i
$148$	−7.34035	−	0.284078i	−0.603373	−	0.0233511i
$149$		−	5.60863i		−	0.459477i	−0.973252	−	0.229738i	$-0.926213\pi$
$149$		−	5.60863i		−	0.459477i	0.973252	−	0.229738i	$-0.0737871\pi$
$150$	−0.980473	−	1.01915i	−0.0800553	−	0.0832135i
$151$			5.87537i			0.478131i	0.971003	+	0.239065i	$0.0768411\pi$
$151$			5.87537i			0.478131i	−0.971003	+	0.239065i	$0.923159\pi$
$152$	−13.8803	−	15.5923i	−1.12584	−	1.26470i
$153$			3.47052i			0.280575i
$154$	1.71868	−	1.65346i	0.138495	−	0.133239i
$155$	−6.36885			−0.511558
$156$	−6.10305	−	0.236194i	−0.488635	−	0.0189106i
$157$			3.93437i			0.313997i	0.987599	+	0.156999i	$0.0501818\pi$
$157$			3.93437i			0.313997i	−0.987599	+	0.156999i	$0.949818\pi$
$158$	12.7380	−	12.2546i	1.01338	−	0.974923i
$159$	3.38684			0.268594
$160$	3.59510	+	4.36752i	0.284217	+	0.345283i
$161$	1.34728	−	9.55533i	0.106180	−	0.753065i
$162$	−1.01915	+	0.980473i	−0.0800722	+	0.0770333i
$163$		−	9.32869i		−	0.730680i	−0.930874	−	0.365340i	$-0.880953\pi$
$163$		−	9.32869i		−	0.730680i	0.930874	−	0.365340i	$-0.119047\pi$
$164$	−0.216228	+	5.58714i	−0.0168845	+	0.436283i
$165$	0.838109			0.0652467
$166$	8.79096	−	8.45732i	0.682311	−	0.656415i
$167$		−	12.3005i		−	0.951837i	−0.879489	−	0.475919i	$-0.842116\pi$
$167$		−	12.3005i		−	0.951837i	0.879489	−	0.475919i	$-0.157884\pi$
$168$	−4.25086	+	3.78412i	−0.327961	+	0.291951i
$169$	−3.67424			−0.282634
$170$	−3.53699	+	3.40276i	−0.271275	+	0.260979i
$171$	7.38055			0.564405
$172$	−0.290113	+	7.49627i	−0.0221209	+	0.571585i
$173$	−11.5739			−0.879949			−0.439975	−	0.898010i	$-0.645013\pi$
$173$	−11.5739			−0.879949			−0.439975	+	0.898010i	$0.645013\pi$
$174$	2.01256	+	2.09196i	0.152572	+	0.158591i
$175$	2.01213			0.152103
$176$	−3.34241	−	0.259097i	−0.251943	−	0.0195301i
$177$	2.21667			0.166615
$178$	3.85376	+	4.00579i	0.288851	+	0.300246i
$179$		−	4.53328i		−	0.338833i	−0.985545	−	0.169417i	$-0.945812\pi$
$179$		−	4.53328i		−	0.338833i	0.985545	−	0.169417i	$-0.0541883\pi$
$180$	−1.99850	−	0.0773439i	−0.148960	−	0.00576488i
$181$		−	21.5833i		−	1.60428i	−0.597138	−	0.802139i	$-0.703695\pi$
$181$		−	21.5833i		−	1.60428i	0.597138	−	0.802139i	$-0.296305\pi$
$182$	6.26235	−	6.02468i	0.464196	−	0.446579i
$183$	14.3017			1.05721
$184$	−11.2918	+	7.51640i	−0.832439	+	0.554117i
$185$	3.67292			0.270039
$186$	−6.49083	+	6.24449i	−0.475931	+	0.457868i
$187$		−	2.90868i		−	0.212703i
$188$	−21.7333	−	0.841098i	−1.58506	−	0.0613434i
$189$		−	2.01213i		−	0.146361i
$190$	7.23643	+	7.52191i	0.524986	+	0.545696i
$191$	−24.4980			−1.77261			−0.886306	−	0.463099i	$-0.846737\pi$
$191$	−24.4980			−1.77261			−0.886306	+	0.463099i	$0.846737\pi$
$192$	7.94619	+	0.926277i	0.573467	+	0.0668483i
$193$	3.78506			0.272455			0.136227	−	0.990678i	$-0.456502\pi$
$193$	3.78506			0.272455			0.136227	+	0.990678i	$0.456502\pi$
$194$	−17.0741	−	17.7477i	−1.22585	−	1.27421i
$195$	3.05381			0.218688
$196$	−0.228268	+	5.89824i	−0.0163048	+	0.421303i
$197$	18.0777			1.28798			0.643992	−	0.765033i	$-0.277277\pi$
$197$	18.0777			1.28798			0.643992	+	0.765033i	$0.277277\pi$
$198$	0.854161	−	0.821743i	0.0607026	−	0.0583988i
$199$	15.0594			1.06754			0.533768	−	0.845631i	$-0.320776\pi$
$199$	15.0594			1.06754			0.533768	+	0.845631i	$0.320776\pi$
$200$	−1.88065	−	2.11261i	−0.132982	−	0.149384i
$201$			5.95010i			0.419688i
$202$	9.45680	−	9.09790i	0.665378	−	0.640126i
$203$	−4.13019			−0.289882
$204$	−0.268424	+	6.93585i	−0.0187934	+	0.485607i
$205$		−	2.79566i		−	0.195258i
$206$	12.8315	−	12.3445i	0.894014	−	0.860085i
$207$	0.669578	−	4.74886i	0.0465389	−	0.330069i
$208$	−12.1787	−	0.944068i	−0.844441	−	0.0654594i
$209$	−6.18570			−0.427874
$210$	2.05067	−	1.97284i	0.141510	−	0.136139i
$211$		−	4.56590i		−	0.314330i	−0.987572	−	0.157165i	$-0.949765\pi$
$211$		−	4.56590i		−	0.314330i	0.987572	−	0.157165i	$-0.0502354\pi$
$212$	6.76861	+	0.261951i	0.464870	+	0.0179909i
$213$	9.84155			0.674332
$214$	1.94770	−	1.87378i	0.133142	−	0.128089i
$215$		−	3.75094i		−	0.255812i
$216$	−2.11261	+	1.88065i	−0.143745	+	0.127962i
$217$		−	12.8150i		−	0.869936i
$218$	−6.84302	−	7.11298i	−0.463468	−	0.481752i
$219$		−	2.33425i		−	0.157734i
$220$	1.67496	+	0.0648226i	0.112926	+	0.00437034i
$221$		−	10.5983i		−	0.712920i
$222$	3.74327	−	3.60120i	0.251232	−	0.241697i
$223$			14.9169i			0.998908i	0.866341	+	0.499454i	$0.166466\pi$
$223$			14.9169i			0.998908i	−0.866341	+	0.499454i	$0.833534\pi$
$224$	−8.78803	+	7.23381i	−0.587175	+	0.483329i
$225$	1.00000			0.0666667
$226$	−0.0429169	−	0.0446100i	−0.00285479	−	0.00296741i
$227$	13.3851			0.888399			0.444199	−	0.895928i	$-0.353488\pi$
$227$	13.3851			0.888399			0.444199	+	0.895928i	$0.353488\pi$
$228$	14.7501	+	0.570841i	0.976846	+	0.0378049i
$229$		−	2.36318i		−	0.156163i	−0.996947	−	0.0780817i	$-0.975120\pi$
$229$		−	2.36318i		−	0.156163i	0.996947	−	0.0780817i	$-0.0248795\pi$
$230$	5.49632	−	3.97373i	0.362416	−	0.262020i
$231$			1.68638i			0.110956i
$232$	3.86031	+	4.33644i	0.253442	+	0.284701i
$233$	13.7390			0.900073			0.450037	−	0.893010i	$-0.351411\pi$
$233$	13.7390			0.900073			0.450037	+	0.893010i	$0.351411\pi$
$234$	3.11230	−	2.99418i	0.203457	−	0.195736i
$235$	10.8748			0.709392
$236$	4.43003	+	0.171446i	0.288370	+	0.0111602i
$237$			12.4986i			0.811875i
$238$	−6.84679	−	7.11689i	−0.443811	−	0.461320i
$239$		−	26.8900i		−	1.73937i	−0.493610	−	0.869684i	$-0.664323\pi$
$239$		−	26.8900i		−	1.73937i	0.493610	−	0.869684i	$-0.335677\pi$
$240$	−3.98804	−	0.309144i	−0.257427	−	0.0199552i
$241$			7.43614i			0.479004i	0.970896	+	0.239502i	$0.0769841\pi$
$241$			7.43614i			0.479004i	−0.970896	+	0.239502i	$0.923016\pi$
$242$	10.4948	−	10.0965i	0.674631	−	0.649027i
$243$		−	1.00000i		−	0.0641500i
$244$	28.5820	+	1.10615i	1.82978	+	0.0708140i
$245$		−	2.95133i		−	0.188554i
$246$	−2.74107	−	2.84921i	−0.174764	−	0.181659i
$247$	−22.5388			−1.43411
$248$	−13.4549	+	11.9776i	−0.854388	+	0.760579i
$249$			8.62575i			0.546635i
$250$	0.980473	+	1.01915i	0.0620106	+	0.0644569i
$251$	26.1926			1.65326			0.826632	−	0.562743i	$-0.190254\pi$
$251$	26.1926			1.65326			0.826632	+	0.562743i	$0.190254\pi$
$252$	0.155626	−	4.02125i	0.00980353	−	0.253315i
$253$	−0.561179	+	3.98006i	−0.0352810	+	0.250224i
$254$	9.93679	+	10.3288i	0.623490	+	0.648086i
$255$		−	3.47052i		−	0.217333i
$256$	15.8089	+	2.46576i	0.988054	+	0.154110i
$257$	15.8897			0.991174			0.495587	−	0.868558i	$-0.334953\pi$
$257$	15.8897			0.991174			0.495587	+	0.868558i	$0.334953\pi$
$258$	−3.67770	−	3.82278i	−0.228963	−	0.237996i
$259$			7.39040i			0.459217i
$260$	6.10305	+	0.236194i	0.378495	+	0.0146481i
$261$	−2.05264			−0.127055
$262$	−17.6153	−	18.3102i	−1.08828	−	1.13121i
$263$	20.2265			1.24722			0.623609	−	0.781736i	$-0.285666\pi$
$263$	20.2265			1.24722			0.623609	+	0.781736i	$0.285666\pi$
$264$	1.77060	−	1.57619i	0.108973	−	0.0970080i
$265$	−3.38684			−0.208052
$266$	−15.1351	+	14.5606i	−0.927990	+	0.892771i
$267$	−3.93051			−0.240543
$268$	−0.460204	+	11.8913i	−0.0281114	+	0.726377i
$269$	−10.9893			−0.670032			−0.335016	−	0.942212i	$-0.608742\pi$
$269$	−10.9893			−0.670032			−0.335016	+	0.942212i	$0.608742\pi$
$270$	1.01915	−	0.980473i	0.0620237	−	0.0596697i
$271$		−	14.7411i		−	0.895456i	−0.894170	−	0.447728i	$-0.852233\pi$
$271$		−	14.7411i		−	0.895456i	0.894170	−	0.447728i	$-0.147767\pi$
$272$	−1.07289	+	13.8406i	−0.0650537	+	0.839208i
$273$			6.14467i			0.371892i
$274$	−2.39977	−	2.49444i	−0.144975	−	0.150695i
$275$	−0.838109			−0.0505399
$276$	1.70545	−	9.43883i	0.102656	−	0.568151i
$277$	−22.5583			−1.35539			−0.677697	−	0.735341i	$-0.737022\pi$
$277$	−22.5583			−1.35539			−0.677697	+	0.735341i	$0.737022\pi$
$278$	−9.13660	−	9.49703i	−0.547977	−	0.569594i
$279$		−	6.36885i		−	0.381293i
$280$	4.25086	−	3.78412i	0.254037	−	0.226145i
$281$			33.3197i			1.98769i	0.110783	+	0.993845i	$0.464664\pi$
$281$			33.3197i			1.98769i	−0.110783	+	0.993845i	$0.535336\pi$
$282$	11.0831	−	10.6624i	0.659986	−	0.634938i
$283$	−16.5981			−0.986658			−0.493329	−	0.869843i	$-0.664220\pi$
$283$	−16.5981			−0.986658			−0.493329	+	0.869843i	$0.664220\pi$
$284$	19.6684	+	0.761184i	1.16710	+	0.0451680i
$285$	−7.38055			−0.437186
$286$	−2.60844	+	2.50945i	−0.154241	+	0.148387i
$287$	5.62524			0.332047
$288$	−4.36752	+	3.59510i	−0.257359	+	0.211843i
$289$	4.95547			0.291498
$290$	−2.01256	−	2.09196i	−0.118182	−	0.122844i
$291$	17.4142			1.02084
$292$	0.180540	−	4.66500i	0.0105653	−	0.272999i
$293$		−	7.44141i		−	0.434732i	−0.976090	−	0.217366i	$-0.930253\pi$
$293$		−	7.44141i		−	0.434732i	0.976090	−	0.217366i	$-0.0697465\pi$
$294$	−2.89370	−	3.00786i	−0.168764	−	0.175422i
$295$	−2.21667			−0.129060
$296$	7.75947	−	6.90750i	0.451010	−	0.401490i
$297$			0.838109i			0.0486320i
$298$	5.49911	+	5.71605i	0.318555	+	0.331122i
$299$	−2.04476	+	14.5021i	−0.118252	+	0.838679i
$300$	1.99850	+	0.0773439i	0.115384	+	0.00446545i
$301$	7.54738			0.435024
$302$	−5.76065	−	5.98790i	−0.331488	−	0.344565i
$303$			9.27908i			0.533069i
$304$	29.4339	+	2.28166i	1.68815	+	0.130862i
$305$	−14.3017			−0.818913
$306$	−3.40276	−	3.53699i	−0.194523	−	0.202196i
$307$		−	5.60524i		−	0.319908i	−0.987124	−	0.159954i	$-0.948865\pi$
$307$		−	5.60524i		−	0.319908i	0.987124	−	0.159954i	$-0.0511346\pi$
$308$	−0.130432	+	3.37025i	−0.00743203	+	0.192038i
$309$			12.5904i			0.716242i
$310$	6.49083	−	6.24449i	0.368654	−	0.354663i
$311$			24.6632i			1.39852i	0.714867	+	0.699261i	$0.246487\pi$
$311$			24.6632i			1.39852i	−0.714867	+	0.699261i	$0.753513\pi$
$312$	6.45152	−	5.74316i	0.365246	−	0.325143i
$313$		−	10.8619i		−	0.613953i	−0.951717	−	0.306976i	$-0.900683\pi$
$313$		−	10.8619i		−	0.613953i	0.951717	−	0.306976i	$-0.0993172\pi$
$314$	−3.85755	−	4.00973i	−0.217694	−	0.226282i
$315$			2.01213i			0.113371i
$316$	−0.966695	+	24.9786i	−0.0543808	+	1.40516i
$317$	19.0344			1.06908			0.534540	−	0.845143i	$-0.320485\pi$
$317$	19.0344			1.06908			0.534540	+	0.845143i	$0.320485\pi$
$318$	−3.45170	+	3.32070i	−0.193562	+	0.186216i
$319$	1.72034			0.0963204
$320$	−7.94619	−	0.926277i	−0.444206	−	0.0517804i
$321$			1.91110i			0.106667i
$322$	7.99566	+	11.0593i	0.445581	+	0.616311i
$323$			25.6144i			1.42522i
$324$	0.0773439	−	1.99850i	0.00429689	−	0.111028i
$325$	−3.05381			−0.169395
$326$	9.14654	+	9.50736i	0.506580	+	0.526564i
$327$	6.97931			0.385957
$328$	−5.25768	−	5.90616i	−0.290307	−	0.326113i
$329$			21.8815i			1.20636i
$330$	−0.854161	+	0.821743i	−0.0470200	+	0.0452355i
$331$			7.97792i			0.438506i	0.975668	+	0.219253i	$0.0703621\pi$
$331$			7.97792i			0.438506i	−0.975668	+	0.219253i	$0.929638\pi$
$332$	−0.667150	+	17.2386i	−0.0366146	+	0.946091i
$333$			3.67292i			0.201275i
$334$	12.0603	+	12.5360i	0.659908	+	0.685941i
$335$		−	5.95010i		−	0.325089i
$336$	0.622039	−	8.02445i	0.0339350	−	0.437770i
$337$		−	7.52091i		−	0.409690i	−0.978794	−	0.204845i	$-0.934331\pi$
$337$		−	7.52091i		−	0.409690i	0.978794	−	0.204845i	$-0.0656690\pi$
$338$	3.74461	−	3.60250i	0.203680	−	0.195950i
$339$	0.0437717			0.00237735
$340$	0.268424	−	6.93585i	0.0145573	−	0.376149i
$341$			5.33779i			0.289057i
$342$	−7.52191	+	7.23643i	−0.406738	+	0.391301i
$343$	20.0234			1.08116
$344$	−7.05422	−	7.92429i	−0.380338	−	0.427249i
$345$	−0.669578	+	4.74886i	−0.0360489	+	0.255670i
$346$	11.7956	−	11.3479i	0.634135	−	0.610068i
$347$		−	10.5698i		−	0.567415i	−0.958911	−	0.283708i	$-0.908435\pi$
$347$		−	10.5698i		−	0.567415i	0.958911	−	0.283708i	$-0.0915645\pi$
$348$	−4.10221	−	0.158759i	−0.219902	−	0.00851040i
$349$	−6.27423			−0.335852			−0.167926	−	0.985800i	$-0.553707\pi$
$349$	−6.27423			−0.335852			−0.167926	+	0.985800i	$0.553707\pi$
$350$	−2.05067	+	1.97284i	−0.109613	+	0.105453i
$351$			3.05381i			0.163000i
$352$	3.66046	−	3.01308i	0.195103	−	0.160598i
$353$	−5.22486			−0.278091			−0.139046	−	0.990286i	$-0.544403\pi$
$353$	−5.22486			−0.278091			−0.139046	+	0.990286i	$0.544403\pi$
$354$	−2.25913	+	2.17339i	−0.120071	+	0.115514i
$355$	−9.84155			−0.522335
$356$	−7.85514	−	0.304001i	−0.416321	−	0.0161120i
$357$	6.98315			0.369587
$358$	4.44476	+	4.62010i	0.234913	+	0.244180i
$359$	11.2250			0.592432			0.296216	−	0.955121i	$-0.404275\pi$
$359$	11.2250			0.592432			0.296216	+	0.955121i	$0.404275\pi$
$360$	2.11261	−	1.88065i	0.111345	−	0.0991192i
$361$	35.4725			1.86697
$362$	21.1619	+	21.9967i	1.11224	+	1.15612i
$363$			10.2976i			0.540482i
$364$	−0.475253	+	12.2801i	−0.0249100	+	0.643654i
$365$			2.33425i			0.122180i
$366$	−14.5756	+	14.0224i	−0.761880	+	0.732964i
$367$	18.6461			0.973317			0.486658	−	0.873592i	$-0.338216\pi$
$367$	18.6461			0.973317			0.486658	+	0.873592i	$0.338216\pi$
$368$	4.13838	−	18.7316i	0.215728	−	0.976453i
$369$	2.79566			0.145536
$370$	−3.74327	+	3.60120i	−0.194603	+	0.187218i
$371$		−	6.81476i		−	0.353805i
$372$	0.492592	−	12.7282i	0.0255397	−	0.659925i
$373$		−	23.9409i		−	1.23961i	−0.784755	−	0.619807i	$-0.787211\pi$
$373$		−	23.9409i		−	1.23961i	0.784755	−	0.619807i	$-0.212789\pi$
$374$	2.85188	+	2.96438i	0.147467	+	0.153285i
$375$	−1.00000			−0.0516398
$376$	22.9742	−	20.4517i	1.18480	−	1.05472i
$377$	6.26838			0.322838
$378$	1.97284	+	2.05067i	0.101472	+	0.105475i
$379$	−1.42762			−0.0733318			−0.0366659	−	0.999328i	$-0.511674\pi$
$379$	−1.42762			−0.0733318			−0.0366659	+	0.999328i	$0.511674\pi$
$380$	−14.7501	−	0.570841i	−0.756662	−	0.0292835i
$381$	−10.1347			−0.519216
$382$	24.9672	−	24.0196i	1.27743	−	1.22895i
$383$	28.6784			1.46540			0.732699	−	0.680553i	$-0.238260\pi$
$383$	28.6784			1.46540			0.732699	+	0.680553i	$0.238260\pi$
$384$	−9.00657	+	6.84702i	−0.459615	+	0.349410i
$385$		−	1.68638i		−	0.0859461i
$386$	−3.85755	+	3.71115i	−0.196344	+	0.188893i
$387$	3.75094			0.190671
$388$	34.8023	+	1.34688i	1.76682	+	0.0683775i
$389$		−	8.42510i		−	0.427169i	−0.976925	−	0.213585i	$-0.931486\pi$
$389$		−	8.42510i		−	0.427169i	0.976925	−	0.213585i	$-0.0685139\pi$
$390$	−3.11230	+	2.99418i	−0.157597	+	0.151616i
$391$	16.4810	+	2.32379i	0.833481	+	0.117519i
$392$	−5.55043	−	6.23502i	−0.280339	−	0.314916i
$393$	17.9661			0.906269
$394$	−18.4239	+	17.7247i	−0.928185	+	0.892958i
$395$		−	12.4986i		−	0.628875i
$396$	−0.0648226	+	1.67496i	−0.00325746	+	0.0841701i
$397$	−36.8283			−1.84836			−0.924180	−	0.381958i	$-0.875250\pi$
$397$	−36.8283			−1.84836			−0.924180	+	0.381958i	$0.875250\pi$
$398$	−15.3479	+	14.7654i	−0.769319	+	0.740121i
$399$		−	14.8506i		−	0.743461i
$400$	3.98804	+	0.309144i	0.199402	+	0.0154572i
$401$			18.4159i			0.919645i	0.888011	+	0.459823i	$0.152087\pi$
$401$			18.4159i			0.919645i	−0.888011	+	0.459823i	$0.847913\pi$
$402$	−5.83391	−	6.06406i	−0.290969	−	0.302448i
$403$			19.4493i			0.968836i
$404$	−0.717681	+	18.5443i	−0.0357060	+	0.922613i
$405$			1.00000i			0.0496904i
$406$	4.20929	−	4.04954i	0.208904	−	0.200975i
$407$		−	3.07831i		−	0.152586i
$408$	−6.52685	−	7.33188i	−0.323127	−	0.362982i
$409$	−38.5213			−1.90476			−0.952378	−	0.304919i	$-0.901371\pi$
$409$	−38.5213			−1.90476			−0.952378	+	0.304919i	$0.901371\pi$
$410$	2.74107	+	2.84921i	0.135372	+	0.140712i
$411$	2.44756			0.120729
$412$	−0.973790	+	25.1619i	−0.0479752	+	1.23964i
$413$		−	4.46023i		−	0.219474i
$414$	3.97373	+	5.49632i	0.195298	+	0.270129i
$415$		−	8.62575i		−	0.423422i
$416$	13.3376	−	10.9787i	0.653929	−	0.538277i
$417$	9.31856			0.456332
$418$	6.30418	−	6.06492i	0.308347	−	0.296645i
$419$	10.8734			0.531200			0.265600	−	0.964083i	$-0.414430\pi$
$419$	10.8734			0.531200			0.265600	+	0.964083i	$0.414430\pi$
$420$	−0.155626	+	4.02125i	−0.00759378	+	0.196217i
$421$		−	37.6787i		−	1.83635i	−0.396177	−	0.918174i	$-0.629663\pi$
$421$		−	37.6787i		−	1.83635i	0.396177	−	0.918174i	$-0.370337\pi$
$422$	4.47674	+	4.65335i	0.217924	+	0.226522i
$423$			10.8748i			0.528749i
$424$	−7.15508	+	6.36947i	−0.347481	+	0.309329i
$425$			3.47052i			0.168345i
$426$	−10.0300	+	9.64938i	−0.485957	+	0.467514i
$427$		−	28.7769i		−	1.39261i
$428$	−0.147812	+	3.81933i	−0.00714475	+	0.184614i
$429$		−	2.55943i		−	0.123570i
$430$	3.67770	+	3.82278i	0.177354	+	0.184351i
$431$	11.9852			0.577306			0.288653	−	0.957434i	$-0.406793\pi$
$431$	11.9852			0.577306			0.288653	+	0.957434i	$0.406793\pi$
$432$	0.309144	−	3.98804i	0.0148737	−	0.191874i
$433$			35.1094i			1.68725i	0.536934	+	0.843624i	$0.319583\pi$
$433$			35.1094i			1.68725i	−0.536934	+	0.843624i	$0.680417\pi$
$434$	12.5647	+	13.0604i	0.603126	+	0.626919i
$435$	2.05264			0.0984167
$436$	13.9482	+	0.539807i	0.667996	+	0.0258521i
$437$	4.94185	−	35.0492i	0.236401	−	1.67663i
$438$	2.28867	+	2.37895i	0.109357	+	0.113671i
$439$			3.53171i			0.168559i	0.996442	+	0.0842796i	$0.0268589\pi$
$439$			3.53171i			0.168559i	−0.996442	+	0.0842796i	$0.973141\pi$
$440$	−1.77060	+	1.57619i	−0.0844101	+	0.0751421i
$441$	2.95133			0.140540
$442$	10.3914	+	10.8013i	0.494267	+	0.513766i
$443$		−	12.5136i		−	0.594540i	−0.954793	−	0.297270i	$-0.903924\pi$
$443$		−	12.5136i		−	0.594540i	0.954793	−	0.297270i	$-0.0960762\pi$
$444$	−0.284078	+	7.34035i	−0.0134818	+	0.348358i
$445$	3.93051			0.186324
$446$	−14.6256	−	15.2026i	−0.692542	−	0.719862i
$447$	−5.60863			−0.265279
$448$	1.86379	−	15.9888i	0.0880558	−	0.755399i
$449$	−36.5846			−1.72653			−0.863267	−	0.504748i	$-0.831585\pi$
$449$	−36.5846			−1.72653			−0.863267	+	0.504748i	$0.831585\pi$
$450$	−1.01915	+	0.980473i	−0.0480433	+	0.0462200i
$451$	−2.34307			−0.110331
$452$	0.0874778	+	0.00338547i	0.00411461	+	0.000159239i
$453$	5.87537			0.276049
$454$	−13.6414	+	13.1237i	−0.640224	+	0.615926i
$455$		−	6.14467i		−	0.288066i
$456$	−15.5923	+	13.8803i	−0.730174	+	0.650003i
$457$		−	20.8600i		−	0.975788i	−0.872903	−	0.487894i	$-0.837765\pi$
$457$		−	20.8600i		−	0.975788i	0.872903	−	0.487894i	$-0.162235\pi$
$458$	2.31704	+	2.40844i	0.108268	+	0.112539i
$459$	3.47052			0.161990
$460$	−1.70545	+	9.43883i	−0.0795170	+	0.440088i
$461$	34.0378			1.58530			0.792650	−	0.609677i	$-0.208701\pi$
$461$	34.0378			1.58530			0.792650	+	0.609677i	$0.208701\pi$
$462$	−1.65346	−	1.71868i	−0.0769257	−	0.0799604i
$463$			0.309688i			0.0143924i	0.999974	+	0.00719622i	$0.00229065\pi$
$463$			0.309688i			0.0143924i	−0.999974	+	0.00719622i	$0.997709\pi$
$464$	−8.18601	−	0.634563i	−0.380026	−	0.0294588i
$465$			6.36885i			0.295348i
$466$	−14.0022	+	13.4707i	−0.648637	+	0.624020i
$467$	−36.4222			−1.68542			−0.842708	−	0.538370i	$-0.819040\pi$
$467$	−36.4222			−1.68542			−0.842708	+	0.538370i	$0.819040\pi$
$468$	−0.236194	+	6.10305i	−0.0109181	+	0.282114i
$469$	11.9724			0.552833
$470$	−11.0831	+	10.6624i	−0.511223	+	0.491821i
$471$	3.93437			0.181286
$472$	−4.68297	+	4.16879i	−0.215551	+	0.191884i
$473$	−3.14370			−0.144547
$474$	−12.2546	−	12.7380i	−0.562872	−	0.585077i
$475$	7.38055			0.338643
$476$	13.9558	+	0.540104i	0.639665	+	0.0247556i
$477$		−	3.38684i		−	0.155073i
$478$	26.3649	+	27.4050i	1.20590	+	1.25347i
$479$	12.0846			0.552158			0.276079	−	0.961135i	$-0.410965\pi$
$479$	12.0846			0.552158			0.276079	+	0.961135i	$0.410965\pi$
$480$	4.36752	−	3.59510i	0.199349	−	0.164093i
$481$		−	11.2164i		−	0.511424i
$482$	−7.29093	−	7.57856i	−0.332093	−	0.345194i
$483$	−9.55533	−	1.34728i	−0.434782	−	0.0613033i
$484$	−0.796455	+	20.5797i	−0.0362025	+	0.935443i
$485$	−17.4142			−0.790736
$486$	0.980473	+	1.01915i	0.0444752	+	0.0462297i
$487$			14.8852i			0.674513i	0.941413	+	0.337256i	$0.109499\pi$
$487$			14.8852i			0.674513i	−0.941413	+	0.337256i	$0.890501\pi$
$488$	−30.2140	+	26.8966i	−1.36772	+	1.21755i
$489$	−9.32869			−0.421858
$490$	2.89370	+	3.00786i	0.130724	+	0.135881i
$491$			10.5855i			0.477719i	0.971054	+	0.238859i	$0.0767735\pi$
$491$			10.5855i			0.477719i	−0.971054	+	0.238859i	$0.923227\pi$
$492$	5.58714	+	0.216228i	0.251888	+	0.00974829i
$493$		−	7.12374i		−	0.320837i
$494$	22.9705	−	22.0987i	1.03349	−	0.994267i
$495$		−	0.838109i		−	0.0376702i
$496$	1.96889	−	25.3992i	0.0884059	−	1.14046i
$497$		−	19.8025i		−	0.888263i
$498$	−8.45732	−	8.79096i	−0.378982	−	0.393932i
$499$		−	12.3123i		−	0.551175i	−0.961276	−	0.275588i	$-0.911128\pi$
$499$		−	12.3123i		−	0.551175i	0.961276	−	0.275588i	$-0.0888724\pi$
$500$	−1.99850	−	0.0773439i	−0.0893758	−	0.00345893i
$501$	−12.3005			−0.549544
$502$	−26.6943	+	25.6812i	−1.19142	+	1.14621i
$503$	13.4558			0.599966			0.299983	−	0.953945i	$-0.403019\pi$
$503$	13.4558			0.599966			0.299983	+	0.953945i	$0.403019\pi$
$504$	3.78412	+	4.25086i	0.168558	+	0.189348i
$505$		−	9.27908i		−	0.412914i
$506$	−3.33042	−	4.60651i	−0.148055	−	0.204784i
$507$			3.67424i			0.163179i
$508$	−20.2542	−	0.783857i	−0.898635	−	0.0347780i
$509$	−7.06555			−0.313175			−0.156588	−	0.987664i	$-0.550049\pi$
$509$	−7.06555			−0.313175			−0.156588	+	0.987664i	$0.550049\pi$
$510$	3.40276	+	3.53699i	0.150677	+	0.156621i
$511$	−4.69681			−0.207775
$512$	−18.5292	+	12.9872i	−0.818885	+	0.573958i
$513$		−	7.38055i		−	0.325859i
$514$	−16.1940	+	15.5794i	−0.714289	+	0.687180i
$515$		−	12.5904i		−	0.554799i
$516$	7.49627	+	0.290113i	0.330005	+	0.0127715i
$517$		−	9.11424i		−	0.400844i
$518$	−7.24609	−	7.53195i	−0.318375	−	0.330935i
$519$			11.5739i			0.508039i
$520$	−6.45152	+	5.74316i	−0.282918	+	0.251854i
$521$		−	6.25136i		−	0.273877i	−0.990580	−	0.136939i	$-0.956274\pi$
$521$		−	6.25136i		−	0.273877i	0.990580	−	0.136939i	$-0.0437263\pi$
$522$	2.09196	−	2.01256i	0.0915624	−	0.0880874i
$523$	−9.50085			−0.415443			−0.207722	−	0.978188i	$-0.566605\pi$
$523$	−9.50085			−0.415443			−0.207722	+	0.978188i	$0.566605\pi$
$524$	35.9053	+	1.38957i	1.56853	+	0.0607036i
$525$		−	2.01213i		−	0.0878166i
$526$	−20.6139	+	19.8315i	−0.898807	+	0.864695i
$527$	22.1032			0.962832
$528$	−0.259097	+	3.34241i	−0.0112757	+	0.145460i
$529$	−22.1033	−	6.35946i	−0.961014	−	0.276498i
$530$	3.45170	−	3.32070i	0.149932	−	0.144242i
$531$		−	2.21667i		−	0.0961953i
$532$	1.14861	−	29.6790i	0.0497984	−	1.28675i
$533$	−8.53742			−0.369797
$534$	4.00579	−	3.85376i	0.173347	−	0.166768i
$535$		−	1.91110i		−	0.0826239i
$536$	−11.1901	−	12.5703i	−0.483338	−	0.542953i
$537$	−4.53328			−0.195625
$538$	11.1998	−	10.7748i	0.482858	−	0.464533i
$539$	−2.47354			−0.106543
$540$	−0.0773439	+	1.99850i	−0.00332835	+	0.0860019i
$541$	14.7050			0.632215			0.316108	−	0.948723i	$-0.397624\pi$
$541$	14.7050			0.632215			0.316108	+	0.948723i	$0.397624\pi$
$542$	14.4532	+	15.0234i	0.620819	+	0.645310i
$543$	−21.5833			−0.926230
$544$	−12.4769	−	15.1576i	−0.534941	−	0.649877i
$545$	−6.97931			−0.298961
$546$	−6.02468	−	6.26235i	−0.257833	−	0.268004i
$547$		−	8.03207i		−	0.343427i	−0.985147	−	0.171713i	$-0.945070\pi$
$547$		−	8.03207i		−	0.343427i	0.985147	−	0.171713i	$-0.0549303\pi$
$548$	4.89146	+	0.189304i	0.208953	+	0.00808667i
$549$		−	14.3017i		−	0.610382i
$550$	0.854161	−	0.821743i	0.0364215	−	0.0350393i
$551$	−15.1496			−0.645396
$552$	7.51640	+	11.2918i	0.319919	+	0.480609i
$553$	25.1489			1.06944
$554$	22.9903	−	22.1178i	0.976765	−	0.939694i
$555$		−	3.67292i		−	0.155907i
$556$	18.6232	+	0.720734i	0.789799	+	0.0305659i
$557$		−	19.1240i		−	0.810310i	−0.914248	−	0.405155i	$-0.867218\pi$
$557$		−	19.1240i		−	0.810310i	0.914248	−	0.405155i	$-0.132782\pi$
$558$	6.24449	+	6.49083i	0.264350	+	0.274779i
$559$	−11.4547			−0.484480
$560$	−0.622039	+	8.02445i	−0.0262859	+	0.339095i
$561$	−2.90868			−0.122804
$562$	−32.6691	−	33.9579i	−1.37806	−	1.43243i
$563$	−23.0912			−0.973177			−0.486588	−	0.873631i	$-0.661759\pi$
$563$	−23.0912			−0.973177			−0.486588	+	0.873631i	$0.661759\pi$
$564$	−0.841098	+	21.7333i	−0.0354166	+	0.915136i
$565$	−0.0437717			−0.00184149
$566$	16.9160	−	16.2740i	0.711034	−	0.684049i
$567$	−2.01213			−0.0845015
$568$	−20.7914	+	18.5086i	−0.872388	+	0.776602i
$569$			3.18426i			0.133491i	0.997770	+	0.0667456i	$0.0212616\pi$
$569$			3.18426i			0.133491i	−0.997770	+	0.0667456i	$0.978738\pi$
$570$	7.52191	−	7.23643i	0.315058	−	0.303101i
$571$	−4.77519			−0.199836			−0.0999178	−	0.994996i	$-0.531858\pi$
$571$	−4.77519			−0.199836			−0.0999178	+	0.994996i	$0.531858\pi$
$572$	0.197956	−	5.11502i	0.00827696	−	0.213870i
$573$			24.4980i			1.02342i
$574$	−5.73298	+	5.51540i	−0.239290	+	0.230208i
$575$	0.669578	−	4.74886i	0.0279233	−	0.198041i
$576$	0.926277	−	7.94619i	0.0385949	−	0.331091i
$577$	−11.4670			−0.477377			−0.238688	−	0.971096i	$-0.576717\pi$
$577$	−11.4670			−0.477377			−0.238688	+	0.971096i	$0.576717\pi$
$578$	−5.05038	+	4.85871i	−0.210068	+	0.202096i
$579$		−	3.78506i		−	0.157302i
$580$	4.10221	+	0.158759i	0.170335	+	0.00659213i
$581$	17.3561			0.720054
$582$	−17.7477	+	17.0741i	−0.735665	+	0.707745i
$583$			2.83854i			0.117560i
$584$	4.38991	+	4.93136i	0.181656	+	0.204061i
$585$		−	3.05381i		−	0.126260i
$586$	7.29611	+	7.58393i	0.301399	+	0.313289i
$587$		−	22.2604i		−	0.918785i	−0.888233	−	0.459392i	$-0.848067\pi$
$587$		−	22.2604i		−	0.918785i	0.888233	−	0.459392i	$-0.151933\pi$
$588$	5.89824	+	0.228268i	0.243239	+	0.00941359i
$589$		−	47.0056i		−	1.93683i
$590$	2.25913	−	2.17339i	0.0930068	−	0.0894769i
$591$		−	18.0777i		−	0.743617i
$592$	−1.13546	+	14.6477i	−0.0466673	+	0.602019i
$593$	13.4007			0.550299			0.275149	−	0.961401i	$-0.411273\pi$
$593$	13.4007			0.550299			0.275149	+	0.961401i	$0.411273\pi$
$594$	−0.821743	−	0.854161i	−0.0337165	−	0.0350466i
$595$	−6.98315			−0.286281
$596$	−11.2089	−	0.433794i	−0.459133	−	0.0177689i
$597$		−	15.0594i		−	0.616342i
$598$	−12.1350	−	16.7847i	−0.496238	−	0.686378i
$599$			25.5681i			1.04469i	0.852736	+	0.522343i	$0.174942\pi$
$599$			25.5681i			1.04469i	−0.852736	+	0.522343i	$0.825058\pi$
$600$	−2.11261	+	1.88065i	−0.0862471	+	0.0767774i
$601$	18.3245			0.747472			0.373736	−	0.927535i	$-0.378077\pi$
$601$	18.3245			0.747472			0.373736	+	0.927535i	$0.378077\pi$
$602$	−7.69193	+	7.40001i	−0.313500	+	0.301602i
$603$	5.95010			0.242307
$604$	11.7420	+	0.454424i	0.477773	+	0.0184903i
$605$		−	10.2976i		−	0.418656i
$606$	−9.09790	−	9.45680i	−0.369577	−	0.384156i
$607$			46.1975i			1.87510i	0.347853	+	0.937549i	$0.386911\pi$
$607$			46.1975i			1.87510i	−0.347853	+	0.937549i	$0.613089\pi$
$608$	−32.2347	+	26.5338i	−1.30729	+	1.07609i
$609$			4.13019i			0.167364i
$610$	14.5756	−	14.0224i	0.590149	−	0.567752i
$611$		−	33.2095i		−	1.34351i
$612$	6.93585	+	0.268424i	0.280365	+	0.0108504i
$613$		−	43.2388i		−	1.74640i	−0.487364	−	0.873199i	$-0.662041\pi$
$613$		−	43.2388i		−	1.74640i	0.487364	−	0.873199i	$-0.337959\pi$
$614$	5.49579	+	5.71260i	0.221792	+	0.230542i
$615$	−2.79566			−0.112732
$616$	−3.17151	−	3.56268i	−0.127784	−	0.143544i
$617$			36.3664i			1.46406i	0.681274	+	0.732029i	$0.261426\pi$
$617$			36.3664i			1.46406i	−0.681274	+	0.732029i	$0.738574\pi$
$618$	−12.3445	−	12.8315i	−0.496570	−	0.516160i
$619$	−1.14354			−0.0459627			−0.0229814	−	0.999736i	$-0.507316\pi$
$619$	−1.14354			−0.0459627			−0.0229814	+	0.999736i	$0.507316\pi$
$620$	−0.492592	+	12.7282i	−0.0197830	+	0.511176i
$621$	−4.74886	−	0.669578i	−0.190565	−	0.0268692i
$622$	−24.1816	−	25.1356i	−0.969594	−	1.00784i
$623$			7.90870i			0.316855i
$624$	−0.944068	+	12.1787i	−0.0377930	+	0.487538i
$625$	1.00000			0.0400000
$626$	10.6498	+	11.0700i	0.425653	+	0.442445i
$627$			6.18570i			0.247033i
$628$	7.86286	+	0.304300i	0.313762	+	0.0121429i
$629$	−12.7470			−0.508255
$630$	−1.97284	−	2.05067i	−0.0785999	−	0.0817006i
$631$	−6.37336			−0.253719			−0.126860	−	0.991921i	$-0.540490\pi$
$631$	−6.37336			−0.253719			−0.126860	+	0.991921i	$0.540490\pi$
$632$	−23.5056	−	26.4048i	−0.935004	−	1.05033i
$633$	−4.56590			−0.181478
$634$	−19.3990	+	18.6627i	−0.770432	+	0.741192i
$635$	10.1347			0.402183
$636$	0.261951	−	6.76861i	0.0103870	−	0.268393i
$637$	−9.01280			−0.357100
$638$	−1.75329	+	1.68675i	−0.0694133	+	0.0667789i
$639$		−	9.84155i		−	0.389326i
$640$	9.00657	−	6.84702i	0.356016	−	0.270652i
$641$		−	2.63541i		−	0.104092i	−0.998645	−	0.0520462i	$-0.983426\pi$
$641$		−	2.63541i		−	0.104092i	0.998645	−	0.0520462i	$-0.0165743\pi$
$642$	−1.87378	−	1.94770i	−0.0739522	−	0.0768695i
$643$	41.5256			1.63761			0.818806	−	0.574071i	$-0.194637\pi$
$643$	41.5256			1.63761			0.818806	+	0.574071i	$0.194637\pi$
$644$	−18.9922	−	3.43159i	−0.748396	−	0.135223i
$645$	−3.75094			−0.147693
$646$	−25.1142	−	26.1049i	−0.988105	−	1.02709i
$647$			7.39042i			0.290547i	0.989392	+	0.145274i	$0.0464063\pi$
$647$			7.39042i			0.290547i	−0.989392	+	0.145274i	$0.953594\pi$
$648$	1.88065	+	2.11261i	0.0738791	+	0.0829913i
$649$			1.85781i			0.0729255i
$650$	3.11230	−	2.99418i	0.122074	−	0.117441i
$651$	−12.8150			−0.502258
$652$	−18.6434	−	0.721518i	−0.730133	−	0.0282568i
$653$	34.8573			1.36407			0.682035	−	0.731319i	$-0.261095\pi$
$653$	34.8573			1.36407			0.682035	+	0.731319i	$0.261095\pi$
$654$	−7.11298	+	6.84302i	−0.278139	+	0.267583i
$655$	−17.9661			−0.701993
$656$	11.1492	+	0.864263i	0.435303	+	0.0337438i
$657$	−2.33425			−0.0910676
$658$	−21.4542	−	22.3005i	−0.836371	−	0.869366i
$659$	−27.2076			−1.05986			−0.529929	−	0.848042i	$-0.677782\pi$
$659$	−27.2076			−1.05986			−0.529929	+	0.848042i	$0.677782\pi$
$660$	0.0648226	−	1.67496i	0.00252322	−	0.0651979i
$661$		−	30.8126i		−	1.19847i	−0.800572	−	0.599236i	$-0.795471\pi$
$661$		−	30.8126i		−	1.19847i	0.800572	−	0.599236i	$-0.204529\pi$
$662$	−7.82214	−	8.13072i	−0.304016	−	0.316009i
$663$	−10.5983			−0.411605
$664$	−16.2221	−	18.2229i	−0.629538	−	0.707185i
$665$			14.8506i			0.575883i
$666$	−3.60120	−	3.74327i	−0.139544	−	0.145049i
$667$	−1.37440	+	9.74771i	−0.0532171	+	0.377433i
$668$	−24.5825	−	0.951365i	−0.951125	−	0.0368094i
$669$	14.9169			0.576720
$670$	5.83391	+	6.06406i	0.225384	+	0.234275i
$671$			11.9864i			0.462729i
$672$	7.23381	+	8.78803i	0.279050	+	0.339006i
$673$	12.5520			0.483843			0.241922	−	0.970296i	$-0.422222\pi$
$673$	12.5520			0.483843			0.241922	+	0.970296i	$0.422222\pi$
$674$	7.37405	+	7.66495i	0.284038	+	0.295243i
$675$		−	1.00000i		−	0.0384900i
$676$	−0.284181	+	7.34299i	−0.0109300	+	0.282423i
$677$			49.0419i			1.88483i	0.334443	+	0.942416i	$0.391452\pi$
$677$			49.0419i			1.88483i	−0.334443	+	0.942416i	$0.608548\pi$
$678$	−0.0446100	+	0.0429169i	−0.00171324	+	0.00164822i
$679$		−	35.0396i		−	1.34470i
$680$	6.52685	+	7.33188i	0.250293	+	0.281165i
$681$		−	13.3851i		−	0.512917i
$682$	−5.23356	−	5.44002i	−0.200403	−	0.208309i
$683$		−	18.5848i		−	0.711126i	−0.934652	−	0.355563i	$-0.884289\pi$
$683$		−	18.5848i		−	0.711126i	0.934652	−	0.355563i	$-0.115711\pi$
$684$	0.570841	−	14.7501i	0.0218266	−	0.563983i
$685$	−2.44756			−0.0935166
$686$	−20.4069	+	19.6324i	−0.779138	+	0.749568i
$687$	−2.36318			−0.0901610
$688$	14.9589	+	1.15958i	0.570302	+	0.0442087i
$689$			10.3428i			0.394028i
$690$	−3.97373	−	5.49632i	−0.151277	−	0.209241i
$691$			9.03153i			0.343576i	0.985134	+	0.171788i	$0.0549544\pi$
$691$			9.03153i			0.343576i	−0.985134	+	0.171788i	$0.945046\pi$
$692$	−0.895173	+	23.1305i	−0.0340294	+	0.879291i
$693$	1.68638			0.0640604
$694$	10.3634	+	10.7722i	0.393389	+	0.408908i
$695$	−9.31856			−0.353473
$696$	4.33644	−	3.86031i	0.164372	−	0.146325i
$697$			9.70241i			0.367505i
$698$	6.39440	−	6.15171i	0.242031	−	0.232846i
$699$		−	13.7390i		−	0.519657i
$700$	0.155626	−	4.02125i	0.00588212	−	0.151989i
$701$		−	24.7906i		−	0.936328i	−0.883642	−	0.468164i	$-0.844916\pi$
$701$		−	24.7906i		−	0.936328i	0.883642	−	0.468164i	$-0.155084\pi$
$702$	−2.99418	−	3.11230i	−0.113008	−	0.117466i
$703$			27.1082i			1.02240i
$704$	−0.776321	+	6.65978i	−0.0292587	+	0.251000i
$705$		−	10.8748i		−	0.409568i
$706$	5.32493	−	5.12284i	0.200407	−	0.192801i
$707$	18.6707			0.702185
$708$	0.171446	−	4.43003i	0.00644334	−	0.166491i
$709$			33.2164i			1.24747i	0.781637	+	0.623733i	$0.214385\pi$
$709$			33.2164i			1.24747i	−0.781637	+	0.623733i	$0.785615\pi$
$710$	10.0300	−	9.64938i	0.376421	−	0.362135i
$711$	12.4986			0.468736
$712$	8.30365	−	7.39193i	0.311192	−	0.277024i
$713$	−30.2448	−	4.26444i	−1.13268	−	0.159705i
$714$	−7.11689	+	6.84679i	−0.266343	+	0.256235i
$715$			2.55943i			0.0957171i
$716$	−9.05977	−	0.350622i	−0.338580	−	0.0131033i
$717$	−26.8900			−1.00422
$718$	−11.4400	+	11.0058i	−0.426936	+	0.410732i
$719$			7.12071i			0.265558i	0.991146	+	0.132779i	$0.0423900\pi$
$719$			7.12071i			0.265558i	−0.991146	+	0.132779i	$0.957610\pi$
$720$	−0.309144	+	3.98804i	−0.0115211	+	0.148625i
$721$	25.3335			0.943469
$722$	−36.1519	+	34.7799i	−1.34543	+	1.29437i
$723$	7.43614			0.276553
$724$	−43.1344	−	1.66934i	−1.60308	−	0.0620406i
$725$	−2.05264			−0.0762332
$726$	−10.0965	−	10.4948i	−0.374716	−	0.389499i
$727$	−3.84921			−0.142759			−0.0713797	−	0.997449i	$-0.522740\pi$
$727$	−3.84921			−0.142759			−0.0713797	+	0.997449i	$0.522740\pi$
$728$	−11.5560	−	12.9813i	−0.428294	−	0.481119i
$729$	−1.00000			−0.0370370
$730$	−2.28867	−	2.37895i	−0.0847074	−	0.0880490i
$731$			13.0177i			0.481478i
$732$	1.10615	−	28.5820i	0.0408845	−	1.05642i
$733$		−	48.1251i		−	1.77754i	−0.458351	−	0.888771i	$-0.651560\pi$
$733$		−	48.1251i		−	1.77754i	0.458351	−	0.888771i	$-0.348440\pi$
$734$	−19.0032	+	18.2820i	−0.701421	+	0.674800i
$735$	−2.95133			−0.108861
$736$	14.1482	+	23.1480i	0.521510	+	0.853245i
$737$	−4.98683			−0.183692
$738$	−2.84921	+	2.74107i	−0.104881	+	0.100900i
$739$		−	8.37169i		−	0.307957i	−0.988074	−	0.153979i	$-0.950791\pi$
$739$		−	8.37169i		−	0.307957i	0.988074	−	0.153979i	$-0.0492087\pi$
$740$	0.284078	−	7.34035i	0.0104429	−	0.269837i
$741$			22.5388i			0.827983i
$742$	6.68169	+	6.94528i	0.245292	+	0.254969i
$743$	−18.3004			−0.671375			−0.335687	−	0.941973i	$-0.608969\pi$
$743$	−18.3004			−0.671375			−0.335687	+	0.941973i	$0.608969\pi$
$744$	11.9776	+	13.4549i	0.439120	+	0.493281i
$745$	5.60863			0.205484
$746$	23.4734	+	24.3994i	0.859423	+	0.893327i
$747$	8.62575			0.315600
$748$	−5.81300	−	0.224968i	−0.212544	−	0.00822566i
$749$	3.84538			0.140507
$750$	1.01915	−	0.980473i	0.0372142	−	0.0358018i
$751$	−39.4451			−1.43937			−0.719686	−	0.694300i	$-0.755714\pi$
$751$	−39.4451			−1.43937			−0.719686	+	0.694300i	$0.755714\pi$
$752$	−3.36187	+	43.3690i	−0.122595	+	1.58150i
$753$		−	26.1926i		−	0.954512i
$754$	−6.38844	+	6.14598i	−0.232653	+	0.223823i
$755$	−5.87537			−0.213827
$756$	−4.02125	−	0.155626i	−0.146251	−	0.00566007i
$757$			2.49205i			0.0905749i	0.998974	+	0.0452875i	$0.0144204\pi$
$757$			2.49205i			0.0905749i	−0.998974	+	0.0452875i	$0.985580\pi$
$758$	1.45496	−	1.39974i	0.0528466	−	0.0508409i
$759$	3.98006	+	0.561179i	0.144467	+	0.0203695i
$760$	15.5923	−	13.8803i	0.565590	−	0.503490i
$761$	19.1210			0.693136			0.346568	−	0.938025i	$-0.387347\pi$
$761$	19.1210			0.693136			0.346568	+	0.938025i	$0.387347\pi$
$762$	10.3288	−	9.93679i	0.374173	−	0.359972i
$763$		−	14.0433i		−	0.508401i
$764$	−1.89477	+	48.9593i	−0.0685504	+	1.77129i
$765$	−3.47052			−0.125477
$766$	−29.2277	+	28.1184i	−1.05604	+	1.01596i
$767$			6.76929i			0.244425i
$768$	2.46576	−	15.8089i	0.0889754	−	0.570453i
$769$		−	25.4632i		−	0.918225i	−0.888378	−	0.459113i	$-0.848167\pi$
$769$		−	25.4632i		−	0.918225i	0.888378	−	0.459113i	$-0.151833\pi$
$770$	1.65346	+	1.71868i	0.0595864	+	0.0619370i
$771$		−	15.8897i		−	0.572254i
$772$	0.292751	−	7.56446i	0.0105364	−	0.272251i
$773$		−	20.2943i		−	0.729936i	−0.931020	−	0.364968i	$-0.881080\pi$
$773$		−	20.2943i		−	0.729936i	0.931020	−	0.364968i	$-0.118920\pi$
$774$	−3.82278	+	3.67770i	−0.137407	+	0.132192i
$775$		−	6.36885i		−	0.228776i
$776$	−36.7894	+	32.7500i	−1.32066	+	1.17566i
$777$	7.39040			0.265129
$778$	8.26058	+	8.58646i	0.296156	+	0.307840i
$779$	20.6335			0.739273
$780$	0.236194	−	6.10305i	0.00845709	−	0.218524i
$781$			8.24829i			0.295147i
$782$	−19.0751	+	13.7909i	−0.682124	+	0.493162i
$783$			2.05264i			0.0733555i
$784$	11.7700	+	0.912387i	0.420357	+	0.0325853i
$785$	−3.93437			−0.140424
$786$	−18.3102	+	17.6153i	−0.653103	+	0.628316i
$787$	−50.2889			−1.79261			−0.896303	−	0.443443i	$-0.853757\pi$
$787$	−50.2889			−1.79261			−0.896303	+	0.443443i	$0.853757\pi$
$788$	1.39820	−	36.1284i	0.0498089	−	1.28702i
$789$		−	20.2265i		−	0.720082i
$790$	12.2546	+	12.7380i	0.435999	+	0.453199i
$791$		−	0.0880743i		−	0.00313156i
$792$	−1.57619	−	1.77060i	−0.0560076	−	0.0629155i
$793$			43.6747i			1.55093i
$794$	37.5337	−	36.1092i	1.33202	−	1.28147i
$795$			3.38684i			0.120119i
$796$	1.16476	−	30.0963i	0.0412837	−	1.06674i
$797$			13.0786i			0.463266i	0.972803	+	0.231633i	$0.0744069\pi$
$797$			13.0786i			0.463266i	−0.972803	+	0.231633i	$0.925593\pi$
$798$	14.5606	+	15.1351i	0.515441	+	0.535775i
$799$	−37.7411			−1.33519
$800$	−4.36752	+	3.59510i	−0.154415	+	0.127106i
$801$			3.93051i			0.138878i
$802$	−18.0563	−	18.7686i	−0.637589	−	0.662742i
$803$	1.95635			0.0690382
$804$	11.8913	+	0.460204i	0.419374	+	0.0162302i
$805$	9.55533	+	1.34728i	0.336781	+	0.0474853i
$806$	−19.0695	−	19.8218i	−0.671694	−	0.698192i
$807$			10.9893i			0.386843i
$808$	−17.4508	−	19.6031i	−0.613915	−	0.689636i
$809$	−32.0587			−1.12712			−0.563562	−	0.826074i	$-0.690569\pi$
$809$	−32.0587			−1.12712			−0.563562	+	0.826074i	$0.690569\pi$
$810$	−0.980473	−	1.01915i	−0.0344503	−	0.0358094i
$811$			0.119991i			0.00421346i	0.999998	+	0.00210673i	$0.000670593\pi$
$811$			0.119991i			0.00421346i	−0.999998	+	0.00210673i	$0.999329\pi$
$812$	−0.319445	+	8.25419i	−0.0112103	+	0.289665i
$813$	−14.7411			−0.516992
$814$	3.01820	+	3.13727i	0.105788	+	0.109961i
$815$	9.32869			0.326770
$816$	13.8406	+	1.07289i	0.484517	+	0.0375588i
$817$	27.6840			0.968541
$818$	39.2591	−	37.7691i	1.37266	−	1.32057i
$819$	6.14467			0.214712
$820$	−5.58714	−	0.216228i	−0.195111	−	0.00755099i
$821$	−17.9135			−0.625187			−0.312594	−	0.949887i	$-0.601198\pi$
$821$	−17.9135			−0.625187			−0.312594	+	0.949887i	$0.601198\pi$
$822$	−2.49444	+	2.39977i	−0.0870036	+	0.0837016i
$823$			29.6276i			1.03275i	0.856362	+	0.516376i	$0.172719\pi$
$823$			29.6276i			1.03275i	−0.856362	+	0.516376i	$0.827281\pi$
$824$	−23.6782	−	26.5986i	−0.824868	−	0.926607i
$825$			0.838109i			0.0291792i
$826$	4.37314	+	4.54566i	0.152161	+	0.158164i
$827$	−7.41677			−0.257906			−0.128953	−	0.991651i	$-0.541162\pi$
$827$	−7.41677			−0.257906			−0.128953	+	0.991651i	$0.541162\pi$
$828$	−9.43883	−	1.70545i	−0.328022	−	0.0592685i
$829$	−48.0998			−1.67057			−0.835287	−	0.549813i	$-0.814699\pi$
$829$	−48.0998			−1.67057			−0.835287	+	0.549813i	$0.814699\pi$
$830$	8.45732	+	8.79096i	0.293558	+	0.305139i
$831$			22.5583i			0.782538i
$832$	−2.82867	+	24.2662i	−0.0980666	+	0.841278i
$833$			10.2427i			0.354887i
$834$	−9.49703	+	9.13660i	−0.328855	+	0.316375i
$835$	12.3005			0.425675
$836$	−0.478427	+	12.3622i	−0.0165467	+	0.427554i
$837$	−6.36885			−0.220140
$838$	−11.0816	+	10.6611i	−0.382809	+	0.368280i
$839$	35.8021			1.23602			0.618012	−	0.786169i	$-0.287938\pi$
$839$	35.8021			1.23602			0.618012	+	0.786169i	$0.287938\pi$
$840$	−3.78412	−	4.25086i	−0.130565	−	0.146668i
$841$	−24.7867			−0.854712
$842$	36.9430	+	38.4004i	1.27314	+	1.32336i
$843$	33.3197			1.14759
$844$	−9.12497	−	0.353145i	−0.314094	−	0.0121557i
$845$		−	3.67424i		−	0.126398i
$846$	−10.6624	−	11.0831i	−0.366582	−	0.381043i
$847$	20.7201			0.711950
$848$	1.04702	−	13.5068i	0.0359549	−	0.463826i
$849$			16.5981i			0.569647i
$850$	−3.40276	−	3.53699i	−0.116714	−	0.121318i
$851$	17.4422	+	2.45931i	0.597911	+	0.0843040i
$852$	0.761184	−	19.6684i	0.0260777	−	0.673827i
$853$	22.6277			0.774756			0.387378	−	0.921921i	$-0.373381\pi$
$853$	22.6277			0.774756			0.387378	+	0.921921i	$0.373381\pi$
$854$	28.2150	+	29.3280i	0.965496	+	1.00358i
$855$			7.38055i			0.252409i
$856$	−3.59411	−	4.03741i	−0.122844	−	0.137996i
$857$	12.7193			0.434484			0.217242	−	0.976118i	$-0.430294\pi$
$857$	12.7193			0.434484			0.217242	+	0.976118i	$0.430294\pi$
$858$	2.50945	+	2.60844i	0.0856711	+	0.0890508i
$859$		−	26.6909i		−	0.910683i	−0.890317	−	0.455342i	$-0.849517\pi$
$859$		−	26.6909i		−	0.910683i	0.890317	−	0.455342i	$-0.150483\pi$
$860$	−7.49627	−	0.290113i	−0.255621	−	0.00989276i
$861$		−	5.62524i		−	0.191708i
$862$	−12.2147	+	11.7512i	−0.416036	+	0.400246i
$863$			21.6963i			0.738550i	0.929320	+	0.369275i	$0.120394\pi$
$863$			21.6963i			0.738550i	−0.929320	+	0.369275i	$0.879606\pi$
$864$	3.59510	+	4.36752i	0.122308	+	0.148586i
$865$		−	11.5739i		−	0.393525i
$866$	−34.4238	−	35.7818i	−1.16977	−	1.21592i
$867$		−	4.95547i		−	0.168297i
$868$	−25.6107	−	0.991159i	−0.869285	−	0.0336421i
$869$	−10.4752			−0.355348
$870$	−2.09196	+	2.01256i	−0.0709240	+	0.0682322i
$871$	−18.1705			−0.615683
$872$	−14.7446	+	13.1257i	−0.499315	+	0.444491i
$873$		−	17.4142i		−	0.589380i
$874$	29.3283	+	40.5658i	0.992044	+	1.37216i
$875$			2.01213i			0.0680224i
$876$	−4.66500	−	0.180540i	−0.157616	−	0.00609988i
$877$	−31.0482			−1.04842			−0.524212	−	0.851588i	$-0.675640\pi$
$877$	−31.0482			−1.04842			−0.524212	+	0.851588i	$0.675640\pi$
$878$	−3.46275	−	3.59935i	−0.116862	−	0.121472i
$879$	−7.44141			−0.250993
$880$	0.259097	−	3.34241i	0.00873414	−	0.112673i
$881$			12.9916i			0.437699i	0.975759	+	0.218850i	$0.0702304\pi$
$881$			12.9916i			0.437699i	−0.975759	+	0.218850i	$0.929770\pi$
$882$	−3.00786	+	2.89370i	−0.101280	+	0.0974360i
$883$			52.5758i			1.76932i	0.466239	+	0.884659i	$0.345609\pi$
$883$			52.5758i			1.76932i	−0.466239	+	0.884659i	$0.654391\pi$
$884$	−21.1808	−	0.819716i	−0.712387	−	0.0275700i
$885$			2.21667i			0.0745126i
$886$	12.2693	+	12.7533i	0.412194	+	0.428455i
$887$		−	36.7678i		−	1.23454i	−0.786751	−	0.617270i	$-0.788239\pi$
$887$		−	36.7678i		−	1.23454i	0.786751	−	0.617270i	$-0.211761\pi$
$888$	−6.90750	−	7.75947i	−0.231800	−	0.260391i
$889$			20.3923i			0.683936i
$890$	−4.00579	+	3.85376i	−0.134274	+	0.129178i
$891$	0.838109			0.0280777
$892$	29.8114	+	1.15373i	0.998160	+	0.0386297i
$893$			80.2618i			2.68586i
$894$	5.71605	−	5.49911i	0.191173	−	0.183918i
$895$	4.53328			0.151531
$896$	13.7771	+	18.1224i	0.460260	+	0.605427i
$897$	14.5021	+	2.04476i	0.484212	+	0.0682727i
$898$	37.2853	−	35.8702i	1.24423	−	1.19700i
$899$			13.0730i			0.436008i
$900$	0.0773439	−	1.99850i	0.00257813	−	0.0666168i
$901$	11.7541			0.391586
$902$	2.38795	−	2.29732i	0.0795099	−	0.0764923i
$903$		−	7.54738i		−	0.251161i
$904$	−0.0924726	+	0.0823194i	−0.00307559	+	0.00273790i
$905$	21.5833			0.717455
$906$	−5.98790	+	5.76065i	−0.198935	+	0.191385i
$907$	54.1710			1.79872			0.899360	−	0.437209i	$-0.144033\pi$
$907$	54.1710			1.79872			0.899360	+	0.437209i	$0.144033\pi$
$908$	1.03525	−	26.7501i	0.0343561	−	0.887734i
$909$	9.27908			0.307768
$910$	6.02468	+	6.26235i	0.199716	+	0.207595i
$911$	33.7358			1.11772			0.558859	−	0.829263i	$-0.311239\pi$
$911$	33.7358			1.11772			0.558859	+	0.829263i	$0.311239\pi$
$912$	2.28166	−	29.4339i	0.0755532	−	0.974654i
$913$	−7.22932			−0.239256
$914$	20.4526	+	21.2595i	0.676513	+	0.703201i
$915$			14.3017i			0.472800i
$916$	−4.72283	−	0.182778i	−0.156047	−	0.00603915i
$917$		−	36.1501i		−	1.19378i
$918$	−3.53699	+	3.40276i	−0.116738	+	0.112308i
$919$	44.0943			1.45454			0.727268	−	0.686354i	$-0.240790\pi$
$919$	44.0943			1.45454			0.727268	+	0.686354i	$0.240790\pi$
$920$	−7.51640	−	11.2918i	−0.247809	−	0.372278i
$921$	−5.60524			−0.184699
$922$	−34.6898	+	33.3732i	−1.14245	+	1.09909i
$923$			30.0542i			0.989247i
$924$	3.37025	+	0.130432i	0.110873	+	0.00429089i
$925$			3.67292i			0.120765i
$926$	−0.303641	−	0.315620i	−0.00997827	−	0.0103719i
$927$	12.5904			0.413522
$928$	8.96497	−	7.37945i	0.294289	−	0.242242i
$929$	0.745966			0.0244744			0.0122372	−	0.999925i	$-0.496105\pi$
$929$	0.745966			0.0244744			0.0122372	+	0.999925i	$0.496105\pi$
$930$	−6.24449	−	6.49083i	−0.204765	−	0.212843i
$931$	21.7824			0.713891
$932$	1.06263	−	27.4575i	0.0348076	−	0.899400i
$933$	24.6632			0.807437
$934$	37.1197	−	35.7110i	1.21460	−	1.16850i
$935$	2.90868			0.0951239
$936$	−5.74316	−	6.45152i	−0.187721	−	0.210875i
$937$			42.1627i			1.37739i	0.725049	+	0.688697i	$0.241817\pi$
$937$			42.1627i			1.37739i	−0.725049	+	0.688697i	$0.758183\pi$
$938$	−12.2017	+	11.7386i	−0.398399	+	0.383279i
$939$	−10.8619			−0.354466
$940$	0.841098	−	21.7333i	0.0274336	−	0.708861i
$941$			5.37120i			0.175096i	0.996160	+	0.0875481i	$0.0279031\pi$
$941$			5.37120i			0.175096i	−0.996160	+	0.0875481i	$0.972097\pi$
$942$	−4.00973	+	3.85755i	−0.130644	+	0.125686i
$943$	1.87191	−	13.2762i	0.0609579	−	0.432333i
$944$	0.685271	−	8.84016i	0.0223037	−	0.287723i
$945$	2.01213			0.0654546
$946$	3.20391	−	3.08231i	0.104168	−	0.100215i
$947$			43.7437i			1.42148i	0.703455	+	0.710740i	$0.251640\pi$
$947$			43.7437i			1.42148i	−0.703455	+	0.710740i	$0.748360\pi$
$948$	24.9786	+	0.966695i	0.811267	+	0.0313968i
$949$	7.12835			0.231396
$950$	−7.52191	+	7.23643i	−0.244043	+	0.234781i
$951$		−	19.0344i		−	0.617233i
$952$	−14.7527	+	13.1329i	−0.478138	+	0.425639i
$953$		−	19.6200i		−	0.635554i	−0.948165	−	0.317777i	$-0.897064\pi$
$953$		−	19.6200i		−	0.635554i	0.948165	−	0.317777i	$-0.102936\pi$
$954$	3.32070	+	3.45170i	0.107512	+	0.111753i
$955$		−	24.4980i		−	0.792737i
$956$	−53.7397	−	2.07978i	−1.73807	−	0.0672648i
$957$		−	1.72034i		−	0.0556106i
$958$	−12.3160	+	11.8486i	−0.397913	+	0.382811i
$959$		−	4.92482i		−	0.159031i
$960$	−0.926277	+	7.94619i	−0.0298955	+	0.256462i
$961$	−9.56223			−0.308459
$962$	10.9974	+	11.4312i	0.354570	+	0.368558i
$963$	1.91110			0.0615842
$964$	14.8611	+	0.575140i	0.478645	+	0.0185240i
$965$			3.78506i			0.121845i
$966$	11.0593	−	7.99566i	0.355827	−	0.257256i
$967$			6.85698i			0.220506i	0.993904	+	0.110253i	$0.0351661\pi$
$967$			6.85698i			0.220506i	−0.993904	+	0.110253i	$0.964834\pi$
$968$	−19.3662	−	21.7548i	−0.622453	−	0.699226i
$969$	25.6144			0.822852
$970$	17.7477	−	17.0741i	0.569844	−	0.548217i
$971$	−52.4035			−1.68171			−0.840855	−	0.541261i	$-0.817947\pi$
$971$	−52.4035			−1.68171			−0.840855	+	0.541261i	$0.817947\pi$
$972$	−1.99850	−	0.0773439i	−0.0641020	−	0.00248081i
$973$		−	18.7502i		−	0.601103i
$974$	−14.5945	−	15.1703i	−0.467639	−	0.486087i
$975$			3.05381i			0.0978002i
$976$	4.42129	−	57.0357i	0.141522	−	1.82567i
$977$			25.9457i			0.830078i	0.909804	+	0.415039i	$0.136232\pi$
$977$			25.9457i			0.830078i	−0.909804	+	0.415039i	$0.863768\pi$
$978$	9.50736	−	9.14654i	0.304012	−	0.292474i
$979$		−	3.29419i		−	0.105283i
$980$	−5.89824	−	0.228268i	−0.188413	−	0.00729174i
$981$		−	6.97931i		−	0.222832i
$982$	−10.3788	−	10.7883i	−0.331202	−	0.344268i
$983$	−21.2299			−0.677128			−0.338564	−	0.940943i	$-0.609941\pi$
$983$	−21.2299			−0.677128			−0.338564	+	0.940943i	$0.609941\pi$
$984$	−5.90616	+	5.25768i	−0.188281	+	0.167609i
$985$			18.0777i			0.576004i
$986$	6.98464	+	7.26018i	0.222436	+	0.231211i
$987$	21.8815			0.696495
$988$	−1.74324	+	45.0439i	−0.0554598	+	1.43304i
$989$	2.51155	−	17.8127i	0.0798625	−	0.566411i
$990$	0.821743	+	0.854161i	0.0261167	+	0.0271470i
$991$		−	30.7276i		−	0.976093i	−0.872818	−	0.488047i	$-0.837710\pi$
$991$		−	30.7276i		−	0.976093i	0.872818	−	0.488047i	$-0.162290\pi$
$992$	22.8966	+	27.8161i	0.726969	+	0.883162i
$993$	7.97792			0.253172
$994$	19.4158	+	20.1818i	0.615832	+	0.640126i
$995$			15.0594i			0.477416i
$996$	17.2386	+	0.667150i	0.546226	+	0.0211395i
$997$	−53.1913			−1.68459			−0.842293	−	0.539021i	$-0.818795\pi$
$997$	−53.1913			−1.68459			−0.842293	+	0.539021i	$0.818795\pi$
$998$	12.0719	+	12.5481i	0.382129	+	0.397204i
$999$	3.67292			0.116206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.p.b.91.14	yes	48
4.3	odd	2		1380.2.p.a.91.13	✓	48
23.22	odd	2		1380.2.p.a.91.14	yes	48
92.91	even	2	inner	1380.2.p.b.91.13	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.p.a.91.13	✓	48	4.3	odd	2
1380.2.p.a.91.14	yes	48	23.22	odd	2
1380.2.p.b.91.13	yes	48	92.91	even	2	inner
1380.2.p.b.91.14	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01915 + 0.980473i) q^{2} -1.00000i q^{3} +(0.0773439 - 1.99850i) q^{4} +1.00000i q^{5} +(0.980473 + 1.01915i) q^{6} -2.01213 q^{7} +(1.88065 + 2.11261i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.01915 + 0.980473i) q^{2} -1.00000i q^{3} +(0.0773439 - 1.99850i) q^{4} +1.00000i q^{5} +(0.980473 + 1.01915i) q^{6} -2.01213 q^{7} +(1.88065 + 2.11261i) q^{8} -1.00000 q^{9} +(-0.980473 - 1.01915i) q^{10} +0.838109 q^{11} +(-1.99850 - 0.0773439i) q^{12} +3.05381 q^{13} +(2.05067 - 1.97284i) q^{14} +1.00000 q^{15} +(-3.98804 - 0.309144i) q^{16} -3.47052i q^{17} +(1.01915 - 0.980473i) q^{18} -7.38055 q^{19} +(1.99850 + 0.0773439i) q^{20} +2.01213i q^{21} +(-0.854161 + 0.821743i) q^{22} +(-0.669578 + 4.74886i) q^{23} +(2.11261 - 1.88065i) q^{24} -1.00000 q^{25} +(-3.11230 + 2.99418i) q^{26} +1.00000i q^{27} +(-0.155626 + 4.02125i) q^{28} +2.05264 q^{29} +(-1.01915 + 0.980473i) q^{30} +6.36885i q^{31} +(4.36752 - 3.59510i) q^{32} -0.838109i q^{33} +(3.40276 + 3.53699i) q^{34} -2.01213i q^{35} +(-0.0773439 + 1.99850i) q^{36} -3.67292i q^{37} +(7.52191 - 7.23643i) q^{38} -3.05381i q^{39} +(-2.11261 + 1.88065i) q^{40} -2.79566 q^{41} +(-1.97284 - 2.05067i) q^{42} -3.75094 q^{43} +(0.0648226 - 1.67496i) q^{44} -1.00000i q^{45} +(-3.97373 - 5.49632i) q^{46} -10.8748i q^{47} +(-0.309144 + 3.98804i) q^{48} -2.95133 q^{49} +(1.01915 - 0.980473i) q^{50} -3.47052 q^{51} +(0.236194 - 6.10305i) q^{52} +3.38684i q^{53} +(-0.980473 - 1.01915i) q^{54} +0.838109i q^{55} +(-3.78412 - 4.25086i) q^{56} +7.38055i q^{57} +(-2.09196 + 2.01256i) q^{58} +2.21667i q^{59} +(0.0773439 - 1.99850i) q^{60} +14.3017i q^{61} +(-6.24449 - 6.49083i) q^{62} +2.01213 q^{63} +(-0.926277 + 7.94619i) q^{64} +3.05381i q^{65} +(0.821743 + 0.854161i) q^{66} -5.95010 q^{67} +(-6.93585 - 0.268424i) q^{68} +(4.74886 + 0.669578i) q^{69} +(1.97284 + 2.05067i) q^{70} +9.84155i q^{71} +(-1.88065 - 2.11261i) q^{72} +2.33425 q^{73} +(3.60120 + 3.74327i) q^{74} +1.00000i q^{75} +(-0.570841 + 14.7501i) q^{76} -1.68638 q^{77} +(2.99418 + 3.11230i) q^{78} -12.4986 q^{79} +(0.309144 - 3.98804i) q^{80} +1.00000 q^{81} +(2.84921 - 2.74107i) q^{82} -8.62575 q^{83} +(4.02125 + 0.155626i) q^{84} +3.47052 q^{85} +(3.82278 - 3.67770i) q^{86} -2.05264i q^{87} +(1.57619 + 1.77060i) q^{88} -3.93051i q^{89} +(0.980473 + 1.01915i) q^{90} -6.14467 q^{91} +(9.43883 + 1.70545i) q^{92} +6.36885 q^{93} +(10.6624 + 11.0831i) q^{94} -7.38055i q^{95} +(-3.59510 - 4.36752i) q^{96} +17.4142i q^{97} +(3.00786 - 2.89370i) q^{98} -0.838109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Introduction

L-functions

Modular forms

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Database

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