LMFDB - Embedded newform 460.2.e.a.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(91,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("460.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.e (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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.7465802011608416256.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + x^{12} + 8x^{10} - 20x^{8} + 32x^{6} + 16x^{4} - 64x^{2} + 256 $ x^16 - x^14 + x^12 + 8x^10 - 20x^8 + 32x^6 + 16x^4 - 64*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.4
Root			$1.18353 + 0.774115i$ of defining polynomial
Character	$\chi$	$=$	460.91
Dual form			460.2.e.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35760 + 0.396143i) q^{2} -1.47175i q^{3} +(1.68614 - 1.07561i) q^{4} +1.00000i q^{5} +(0.583024 + 1.99804i) q^{6} -3.53986 q^{7} +(-1.86301 + 2.12819i) q^{8} +0.833952 q^{9} +O(q^{10})$	\(q+(-1.35760 + 0.396143i) q^{2} -1.47175i q^{3} +(1.68614 - 1.07561i) q^{4} +1.00000i q^{5} +(0.583024 + 1.99804i) q^{6} -3.53986 q^{7} +(-1.86301 + 2.12819i) q^{8} +0.833952 q^{9} +(-0.396143 - 1.35760i) q^{10} +1.16300 q^{11} +(-1.58302 - 2.48158i) q^{12} +5.75893 q^{13} +(4.80570 - 1.40229i) q^{14} +1.47175 q^{15} +(1.68614 - 3.62725i) q^{16} -6.92143i q^{17} +(-1.13217 + 0.330364i) q^{18} +3.53986 q^{19} +(1.07561 + 1.68614i) q^{20} +5.20979i q^{21} +(-1.57888 + 0.460714i) q^{22} +(-4.70285 - 0.939764i) q^{23} +(3.13217 + 2.74188i) q^{24} -1.00000 q^{25} +(-7.81831 + 2.28136i) q^{26} -5.64262i q^{27} +(-5.96870 + 3.80749i) q^{28} -5.71519 q^{29} +(-1.99804 + 0.583024i) q^{30} -8.33558i q^{31} +(-0.852189 + 5.59230i) q^{32} -1.71164i q^{33} +(2.74188 + 9.39651i) q^{34} -3.53986i q^{35} +(1.40616 - 0.897004i) q^{36} -2.93580i q^{37} +(-4.80570 + 1.40229i) q^{38} -8.47571i q^{39} +(-2.12819 - 1.86301i) q^{40} +6.63662 q^{41} +(-2.06382 - 7.07279i) q^{42} +4.32076 q^{43} +(1.96098 - 1.25093i) q^{44} +0.833952i q^{45} +(6.75686 - 0.587185i) q^{46} -0.327086i q^{47} +(-5.33840 - 2.48158i) q^{48} +5.53059 q^{49} +(1.35760 - 0.396143i) q^{50} -10.1866 q^{51} +(9.71037 - 6.19435i) q^{52} +7.45202i q^{53} +(2.23529 + 7.66040i) q^{54} +1.16300i q^{55} +(6.59477 - 7.53351i) q^{56} -5.20979i q^{57} +(7.75893 - 2.26404i) q^{58} -8.51278i q^{59} +(2.48158 - 1.58302i) q^{60} -8.40520i q^{61} +(3.30209 + 11.3164i) q^{62} -2.95207 q^{63} +(-1.05842 - 7.92967i) q^{64} +5.75893i q^{65} +(0.678055 + 2.32372i) q^{66} -3.74555 q^{67} +(-7.44473 - 11.6705i) q^{68} +(-1.38310 + 6.92143i) q^{69} +(1.40229 + 4.80570i) q^{70} +12.6466i q^{71} +(-1.55366 + 1.77481i) q^{72} +1.85606 q^{73} +(1.16300 + 3.98563i) q^{74} +1.47175i q^{75} +(5.96870 - 3.80749i) q^{76} -4.11684 q^{77} +(3.35760 + 11.5066i) q^{78} +15.4773 q^{79} +(3.62725 + 1.68614i) q^{80} -5.80267 q^{81} +(-9.00986 + 2.62905i) q^{82} +15.1460 q^{83} +(5.60368 + 8.78443i) q^{84} +6.92143 q^{85} +(-5.86585 + 1.71164i) q^{86} +8.41134i q^{87} +(-2.16667 + 2.47508i) q^{88} +14.9358i q^{89} +(-0.330364 - 1.13217i) q^{90} -20.3858 q^{91} +(-8.94049 + 3.47385i) q^{92} -12.2679 q^{93} +(0.129573 + 0.444052i) q^{94} +3.53986i q^{95} +(8.23046 + 1.25421i) q^{96} -9.46639i q^{97} +(-7.50832 + 2.19091i) q^{98} +0.969883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9} - 30 q^{12} + 4 q^{13} + 4 q^{16} + 30 q^{18} + 2 q^{24} - 16 q^{25} - 54 q^{26} - 48 q^{29} + 34 q^{36} - 36 q^{41} - 40 q^{46} + 18 q^{48} + 68 q^{49} + 34 q^{52} - 40 q^{54} + 36 q^{58} + 6 q^{62} + 52 q^{64} + 40 q^{69} + 42 q^{70} - 78 q^{72} + 8 q^{73} + 72 q^{77} + 32 q^{78} + 40 q^{81} - 42 q^{82} + 12 q^{85} - 120 q^{93} + 20 q^{94} - 22 q^{96} - 18 q^{98}+O(q^{100}) $ 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9 - 30 * q^12 + 4 * q^13 + 4 * q^16 + 30 * q^18 + 2 * q^24 - 16 * q^25 - 54 * q^26 - 48 * q^29 + 34 * q^36 - 36 * q^41 - 40 * q^46 + 18 * q^48 + 68 * q^49 + 34 * q^52 - 40 * q^54 + 36 * q^58 + 6 * q^62 + 52 * q^64 + 40 * q^69 + 42 * q^70 - 78 * q^72 + 8 * q^73 + 72 * q^77 + 32 * q^78 + 40 * q^81 - 42 * q^82 + 12 * q^85 - 120 * q^93 + 20 * q^94 - 22 * q^96 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.35760	+	0.396143i	−0.959966	+	0.280116i
$2$	−1.35760	+	0.396143i	−0.959966	+	0.280116i
$3$		−	1.47175i		−	0.849715i	−0.905260	−	0.424858i	$-0.860324\pi$
$3$		−	1.47175i		−	0.849715i	0.905260	−	0.424858i	$-0.139676\pi$
$4$	1.68614	−	1.07561i	0.843070	−	0.537803i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.583024	+	1.99804i	0.238019	+	0.815698i
$7$	−3.53986			−1.33794			−0.668970	−	0.743289i	$-0.733265\pi$
$7$	−3.53986			−1.33794			−0.668970	+	0.743289i	$0.733265\pi$
$8$	−1.86301	+	2.12819i	−0.658672	+	0.752430i
$9$	0.833952			0.277984
$10$	−0.396143	−	1.35760i	−0.125272	−	0.429310i
$11$	1.16300			0.350657			0.175328	−	0.984510i	$-0.443901\pi$
$11$	1.16300			0.350657			0.175328	+	0.984510i	$0.443901\pi$
$12$	−1.58302	−	2.48158i	−0.456980	−	0.716370i
$13$	5.75893			1.59724			0.798620	−	0.601835i	$-0.205564\pi$
$13$	5.75893			1.59724			0.798620	+	0.601835i	$0.205564\pi$
$14$	4.80570	−	1.40229i	1.28438	−	0.374778i
$15$	1.47175			0.380004
$16$	1.68614	−	3.62725i	0.421535	−	0.906812i
$17$		−	6.92143i		−	1.67869i	−0.543597	−	0.839346i	$-0.682938\pi$
$17$		−	6.92143i		−	1.67869i	0.543597	−	0.839346i	$-0.317062\pi$
$18$	−1.13217	+	0.330364i	−0.266855	+	0.0778677i
$19$	3.53986			0.812099			0.406050	−	0.913851i	$-0.366906\pi$
$19$	3.53986			0.812099			0.406050	+	0.913851i	$0.366906\pi$
$20$	1.07561	+	1.68614i	0.240513	+	0.377033i
$21$			5.20979i			1.13687i
$22$	−1.57888	+	0.460714i	−0.336619	+	0.0982245i
$23$	−4.70285	−	0.939764i	−0.980613	−	0.195954i
$23$	−4.70285	−	0.939764i	−0.980613	−	0.195954i
$24$	3.13217	+	2.74188i	0.639352	+	0.559684i
$25$	−1.00000			−0.200000
$26$	−7.81831	+	2.28136i	−1.53330	+	0.447412i
$27$		−	5.64262i		−	1.08592i
$28$	−5.96870	+	3.80749i	−1.12798	+	0.719549i
$29$	−5.71519			−1.06128			−0.530642	−	0.847596i	$-0.678049\pi$
$29$	−5.71519			−1.06128			−0.530642	+	0.847596i	$0.678049\pi$
$30$	−1.99804	+	0.583024i	−0.364791	+	0.106445i
$31$		−	8.33558i		−	1.49711i	−0.663070	−	0.748557i	$-0.730747\pi$
$31$		−	8.33558i		−	1.49711i	0.663070	−	0.748557i	$-0.269253\pi$
$32$	−0.852189	+	5.59230i	−0.150647	+	0.988588i
$33$		−	1.71164i		−	0.297958i
$34$	2.74188	+	9.39651i	0.470228	+	1.61149i
$35$		−	3.53986i		−	0.598345i
$36$	1.40616	−	0.897004i	0.234360	−	0.149501i
$37$		−	2.93580i		−	0.482642i	−0.970445	−	0.241321i	$-0.922419\pi$
$37$		−	2.93580i		−	0.482642i	0.970445	−	0.241321i	$-0.0775807\pi$
$38$	−4.80570	+	1.40229i	−0.779588	+	0.227482i
$39$		−	8.47571i		−	1.35720i
$40$	−2.12819	−	1.86301i	−0.336497	−	0.294567i
$41$	6.63662			1.03647			0.518233	−	0.855239i	$-0.326590\pi$
$41$	6.63662			1.03647			0.518233	+	0.855239i	$0.326590\pi$
$42$	−2.06382	−	7.07279i	−0.318455	−	1.09136i
$43$	4.32076			0.658910			0.329455	−	0.944171i	$-0.393135\pi$
$43$	4.32076			0.658910			0.329455	+	0.944171i	$0.393135\pi$
$44$	1.96098	−	1.25093i	0.295628	−	0.188584i
$45$			0.833952i			0.124318i
$46$	6.75686	−	0.587185i	0.996245	−	0.0865756i
$47$		−	0.327086i		−	0.0477105i	−0.999715	−	0.0238552i	$-0.992406\pi$
$47$		−	0.327086i		−	0.0477105i	0.999715	−	0.0238552i	$-0.00759408\pi$
$48$	−5.33840	−	2.48158i	−0.770532	−	0.358185i
$49$	5.53059			0.790085
$50$	1.35760	−	0.396143i	0.191993	−	0.0560232i
$51$	−10.1866			−1.42641
$52$	9.71037	−	6.19435i	1.34659	−	0.859001i
$53$			7.45202i			1.02361i	0.859100	+	0.511807i	$0.171024\pi$
$53$			7.45202i			1.02361i	−0.859100	+	0.511807i	$0.828976\pi$
$54$	2.23529	+	7.66040i	0.304184	+	1.04245i
$55$			1.16300i			0.156818i
$56$	6.59477	−	7.53351i	0.881264	−	1.00671i
$57$		−	5.20979i		−	0.690053i
$58$	7.75893	−	2.26404i	1.01880	−	0.297283i
$59$		−	8.51278i		−	1.10827i	−0.832427	−	0.554135i	$-0.813049\pi$
$59$		−	8.51278i		−	1.10827i	0.832427	−	0.554135i	$-0.186951\pi$
$60$	2.48158	−	1.58302i	0.320370	−	0.204368i
$61$		−	8.40520i		−	1.07618i	−0.842889	−	0.538088i	$-0.819147\pi$
$61$		−	8.40520i		−	1.07618i	0.842889	−	0.538088i	$-0.180853\pi$
$62$	3.30209	+	11.3164i	0.419365	+	1.43718i
$63$	−2.95207			−0.371926
$64$	−1.05842	−	7.92967i	−0.132303	−	0.991209i
$65$			5.75893i			0.714308i
$66$	0.678055	+	2.32372i	0.0834629	+	0.286030i
$67$	−3.74555			−0.457592			−0.228796	−	0.973474i	$-0.573479\pi$
$67$	−3.74555			−0.457592			−0.228796	+	0.973474i	$0.573479\pi$
$68$	−7.44473	−	11.6705i	−0.902807	−	1.41526i
$69$	−1.38310	+	6.92143i	−0.166505	+	0.833242i
$70$	1.40229	+	4.80570i	0.167606	+	0.574391i
$71$			12.6466i			1.50087i	0.660943	+	0.750436i	$0.270157\pi$
$71$			12.6466i			1.50087i	−0.660943	+	0.750436i	$0.729843\pi$
$72$	−1.55366	+	1.77481i	−0.183100	+	0.209163i
$73$	1.85606			0.217235			0.108618	−	0.994084i	$-0.465358\pi$
$73$	1.85606			0.217235			0.108618	+	0.994084i	$0.465358\pi$
$74$	1.16300	+	3.98563i	0.135196	+	0.463320i
$75$			1.47175i			0.169943i
$76$	5.96870	−	3.80749i	0.684657	−	0.436750i
$77$	−4.11684			−0.469158
$78$	3.35760	+	11.5066i	0.380173	+	1.30287i
$79$	15.4773			1.74133			0.870664	−	0.491879i	$-0.163690\pi$
$79$	15.4773			1.74133			0.870664	+	0.491879i	$0.163690\pi$
$80$	3.62725	+	1.68614i	0.405539	+	0.188516i
$81$	−5.80267			−0.644741
$82$	−9.00986	+	2.62905i	−0.994973	+	0.290331i
$83$	15.1460			1.66249			0.831246	−	0.555904i	$-0.187628\pi$
$83$	15.1460			1.66249			0.831246	+	0.555904i	$0.187628\pi$
$84$	5.60368	+	8.78443i	0.611412	+	0.958460i
$85$	6.92143			0.750734
$86$	−5.86585	+	1.71164i	−0.632531	+	0.184571i
$87$			8.41134i			0.901790i
$88$	−2.16667	+	2.47508i	−0.230968	+	0.263845i
$89$			14.9358i			1.58319i	0.611045	+	0.791596i	$0.290749\pi$
$89$			14.9358i			1.58319i	−0.611045	+	0.791596i	$0.709251\pi$
$90$	−0.330364	−	1.13217i	−0.0348235	−	0.119341i
$91$	−20.3858			−2.13701
$92$	−8.94049	+	3.47385i	−0.932111	+	0.362174i
$93$	−12.2679			−1.27212
$94$	0.129573	+	0.444052i	0.0133645	+	0.0458004i
$95$			3.53986i			0.363182i
$96$	8.23046	+	1.25421i	0.840018	+	0.128007i
$97$		−	9.46639i		−	0.961166i	−0.876949	−	0.480583i	$-0.840425\pi$
$97$		−	9.46639i		−	0.961166i	0.876949	−	0.480583i	$-0.159575\pi$
$98$	−7.50832	+	2.19091i	−0.758455	+	0.221315i
$99$	0.969883			0.0974769
$100$	−1.68614	+	1.07561i	−0.168614	+	0.107561i
$101$	−6.39083			−0.635912			−0.317956	−	0.948106i	$-0.602996\pi$
$101$	−6.39083			−0.635912			−0.317956	+	0.948106i	$0.602996\pi$
$102$	13.8293	−	4.03536i	1.36931	−	0.399560i
$103$	1.40698			0.138634			0.0693168	−	0.997595i	$-0.477918\pi$
$103$	1.40698			0.138634			0.0693168	+	0.997595i	$0.477918\pi$
$104$	−10.7289	+	12.2561i	−1.05206	+	1.20181i
$105$	−5.20979			−0.508423
$106$	−2.95207	−	10.1168i	−0.286730	−	0.982635i
$107$	−4.32076			−0.417704			−0.208852	−	0.977947i	$-0.566973\pi$
$107$	−4.32076			−0.417704			−0.208852	+	0.977947i	$0.566973\pi$
$108$	−6.06924	−	9.51425i	−0.584013	−	0.915509i
$109$			0.131214i			0.0125680i	0.999980	+	0.00628400i	$0.00200027\pi$
$109$			0.131214i			0.0125680i	−0.999980	+	0.00628400i	$0.998000\pi$
$110$	−0.460714	−	1.57888i	−0.0439273	−	0.150540i
$111$	−4.32076			−0.410108
$112$	−5.96870	+	12.8399i	−0.563989	+	1.21326i
$113$		−	9.32663i		−	0.877376i	−0.898640	−	0.438688i	$-0.855443\pi$
$113$		−	9.32663i		−	0.877376i	0.898640	−	0.438688i	$-0.144557\pi$
$114$	2.06382	+	7.07279i	0.193295	+	0.662428i
$115$	0.939764	−	4.70285i	0.0876334	−	0.438543i
$116$	−9.63662	+	6.14730i	−0.894738	+	0.570763i
$117$	4.80267			0.444007
$118$	3.37228	+	11.5569i	0.310444	+	1.06390i
$119$			24.5009i			2.24599i
$120$	−2.74188	+	3.13217i	−0.250298	+	0.285927i
$121$	−9.64744			−0.877040
$122$	3.32967	+	11.4109i	0.301454	+	1.03309i
$123$		−	9.76745i		−	0.880701i
$124$	−8.96581	−	14.0550i	−0.805153	−	1.26217i
$125$		−	1.00000i		−	0.0894427i
$126$	4.00772	−	1.16944i	0.357036	−	0.104182i
$127$			10.1247i			0.898418i	0.893427	+	0.449209i	$0.148294\pi$
$127$			10.1247i			0.898418i	−0.893427	+	0.449209i	$0.851706\pi$
$128$	4.57820	+	10.3460i	0.404660	+	0.914467i
$129$		−	6.35908i		−	0.559886i
$130$	−2.28136	−	7.81831i	−0.200089	−	0.685711i
$131$			5.41204i			0.472852i	0.971650	+	0.236426i	$0.0759761\pi$
$131$			5.41204i			0.472852i	−0.971650	+	0.236426i	$0.924024\pi$
$132$	−1.84105	−	2.88607i	−0.160243	−	0.251200i
$133$	−12.5306			−1.08654
$134$	5.08495	−	1.48378i	0.439273	−	0.128179i
$135$	5.64262			0.485639
$136$	14.7301	+	12.8947i	1.26310	+	1.10571i
$137$			16.6474i			1.42229i	0.703047	+	0.711143i	$0.251822\pi$
$137$			16.6474i			1.42229i	−0.703047	+	0.711143i	$0.748178\pi$
$138$	−0.864189	−	9.94442i	−0.0735647	−	0.846525i
$139$			9.34213i			0.792389i	0.918167	+	0.396195i	$0.129669\pi$
$139$			9.34213i			0.792389i	−0.918167	+	0.396195i	$0.870331\pi$
$140$	−3.80749	−	5.96870i	−0.321792	−	0.504447i
$141$	−0.481390			−0.0405403
$142$	−5.00986	−	17.1690i	−0.420418	−	1.44079i
$143$	6.69762			0.560083
$144$	1.40616	−	3.02495i	0.117180	−	0.252079i
$145$		−	5.71519i		−	0.474621i
$146$	−2.51978	+	0.735265i	−0.208538	+	0.0608510i
$147$		−	8.13965i		−	0.671347i
$148$	−3.15776	−	4.95017i	−0.259567	−	0.406901i
$149$		−	19.0958i		−	1.56438i	−0.623037	−	0.782192i	$-0.714101\pi$
$149$		−	19.0958i		−	1.56438i	0.623037	−	0.782192i	$-0.285899\pi$
$150$	−0.583024	−	1.99804i	−0.0476037	−	0.163140i
$151$			4.20794i			0.342437i	0.985233	+	0.171218i	$0.0547704\pi$
$151$			4.20794i			0.342437i	−0.985233	+	0.171218i	$0.945230\pi$
$152$	−6.59477	+	7.53351i	−0.534907	+	0.611048i
$153$		−	5.77213i		−	0.466649i
$154$	5.58902	−	1.63086i	0.450376	−	0.131419i
$155$	8.33558			0.669530
$156$	−9.11653	−	14.2912i	−0.729907	−	1.14421i
$157$			2.54496i			0.203110i	0.994830	+	0.101555i	$0.0323818\pi$
$157$			2.54496i			0.203110i	−0.994830	+	0.101555i	$0.967618\pi$
$158$	−21.0119	+	6.13121i	−1.67162	+	0.487773i
$159$	10.9675			0.869780
$160$	−5.59230	−	0.852189i	−0.442110	−	0.0673715i
$161$	16.6474	+	3.32663i	1.31200	+	0.262175i
$162$	7.87769	−	2.29869i	0.618930	−	0.180602i
$163$			12.0811i			0.946267i	0.880991	+	0.473134i	$0.156877\pi$
$163$			12.0811i			0.946267i	−0.880991	+	0.473134i	$0.843123\pi$
$164$	11.1903	−	7.13839i	0.873814	−	0.557415i
$165$	1.71164			0.133251
$166$	−20.5622	+	6.00000i	−1.59594	+	0.465690i
$167$			8.51278i			0.658738i	0.944201	+	0.329369i	$0.106836\pi$
$167$			8.51278i			0.658738i	−0.944201	+	0.329369i	$0.893164\pi$
$168$	−11.0874	−	9.70586i	−0.855414	−	0.748823i
$169$	20.1653			1.55118
$170$	−9.39651	+	2.74188i	−0.720679	+	0.210292i
$171$	2.95207			0.225750
$172$	7.28541	−	4.64744i	0.555507	−	0.354364i
$173$	−6.92143			−0.526226			−0.263113	−	0.964765i	$-0.584749\pi$
$173$	−6.92143			−0.526226			−0.263113	+	0.964765i	$0.584749\pi$
$174$	−3.33210	−	11.4192i	−0.252606	−	0.865688i
$175$	3.53986			0.267588
$176$	1.96098	−	4.21848i	0.147814	−	0.317980i
$177$	−12.5287			−0.941713
$178$	−5.91672	−	20.2768i	−0.443477	−	1.51981i
$179$		−	5.41204i		−	0.404515i	−0.979332	−	0.202257i	$-0.935172\pi$
$179$		−	5.41204i		−	0.404515i	0.979332	−	0.202257i	$-0.0648277\pi$
$180$	0.897004	+	1.40616i	0.0668587	+	0.104809i
$181$			16.5508i			1.23021i	0.788445	+	0.615105i	$0.210886\pi$
$181$			16.5508i			1.23021i	−0.788445	+	0.615105i	$0.789114\pi$
$182$	27.6757	−	8.07570i	2.05146	−	0.598611i
$183$	−12.3704			−0.914443
$184$	10.7614	−	8.25780i	0.793344	−	0.608773i
$185$	2.93580			0.215844
$186$	16.6549	−	4.85985i	1.22119	−	0.356341i
$187$		−	8.04960i		−	0.588645i
$188$	−0.351816	−	0.551514i	−0.0256588	−	0.0402233i
$189$			19.9741i			1.45290i
$190$	−1.40229	−	4.80570i	−0.101733	−	0.348642i
$191$	−15.1460			−1.09593			−0.547964	−	0.836502i	$-0.684597\pi$
$191$	−15.1460			−1.09593			−0.547964	+	0.836502i	$0.684597\pi$
$192$	−11.6705	+	1.55773i	−0.842246	+	0.112420i
$193$	25.3739			1.82645			0.913227	−	0.407450i	$-0.133582\pi$
$193$	25.3739			1.82645			0.913227	+	0.407450i	$0.133582\pi$
$194$	3.75005	+	12.8515i	0.269238	+	0.922687i
$195$	8.47571			0.606958
$196$	9.32536	−	5.94874i	0.666097	−	0.424910i
$197$	1.85797			0.132375			0.0661874	−	0.997807i	$-0.478916\pi$
$197$	1.85797			0.132375			0.0661874	+	0.997807i	$0.478916\pi$
$198$	−1.31671	+	0.384213i	−0.0935745	+	0.0273048i
$199$	−18.8916			−1.33919			−0.669594	−	0.742727i	$-0.733532\pi$
$199$	−18.8916			−1.33919			−0.669594	+	0.742727i	$0.733532\pi$
$200$	1.86301	−	2.12819i	0.131734	−	0.150486i
$201$			5.51252i			0.388823i
$202$	8.67618	−	2.53169i	0.610454	−	0.178129i
$203$	20.2310			1.41994
$204$	−17.1761	+	10.9568i	−1.20256	+	0.767129i
$205$			6.63662i			0.463522i
$206$	−1.91011	+	0.557365i	−0.133084	+	0.0388335i
$207$	−3.92195	−	0.783717i	−0.272595	−	0.0544721i
$208$	9.71037	−	20.8891i	0.673293	−	1.44840i
$209$	4.11684			0.284768
$210$	7.07279	−	2.06382i	0.488069	−	0.142417i
$211$		−	9.98092i		−	0.687115i	−0.939132	−	0.343557i	$-0.888368\pi$
$211$		−	9.98092i		−	0.687115i	0.939132	−	0.343557i	$-0.111632\pi$
$212$	8.01544	+	12.5652i	0.550503	+	0.862978i
$213$	18.6126			1.27531
$214$	5.86585	−	1.71164i	0.400981	−	0.117005i
$215$			4.32076i			0.294673i
$216$	12.0086	+	10.5122i	0.817081	+	0.715267i
$217$			29.5068i			2.00305i
$218$	−0.0519795	−	0.178135i	−0.00352049	−	0.0120649i
$219$		−	2.73165i		−	0.184588i
$220$	1.25093	+	1.96098i	0.0843375	+	0.132209i
$221$		−	39.8600i		−	2.68128i
$222$	5.86585	−	1.71164i	0.393690	−	0.114878i
$223$			12.1431i			0.813161i	0.913615	+	0.406581i	$0.133279\pi$
$223$			12.1431i			0.813161i	−0.913615	+	0.406581i	$0.866721\pi$
$224$	3.01663	−	19.7959i	0.201557	−	1.32267i
$225$	−0.833952			−0.0555968
$226$	3.69468	+	12.6618i	0.245767	+	0.842251i
$227$	−27.6203			−1.83323			−0.916613	−	0.399775i	$-0.869088\pi$
$227$	−27.6203			−1.83323			−0.916613	+	0.399775i	$0.869088\pi$
$228$	−5.60368	−	8.78443i	−0.371113	−	0.581763i
$229$		−	2.67337i		−	0.176661i	−0.996091	−	0.0883306i	$-0.971847\pi$
$229$		−	2.67337i		−	0.176661i	0.996091	−	0.0883306i	$-0.0281532\pi$
$230$	0.587185	+	6.75686i	0.0387178	+	0.445534i
$231$			6.05897i			0.398651i
$232$	10.6474	−	12.1630i	0.699039	−	0.798543i
$233$	−19.2493			−1.26107			−0.630533	−	0.776162i	$-0.717164\pi$
$233$	−19.2493			−1.26107			−0.630533	+	0.776162i	$0.717164\pi$
$234$	−6.52009	+	1.90255i	−0.426232	+	0.124373i
$235$	0.327086			0.0213368
$236$	−9.15640	−	14.3537i	−0.596031	−	0.934349i
$237$		−	22.7787i		−	1.47963i
$238$	−9.70586	−	33.2623i	−0.629137	−	2.15608i
$239$		−	12.6352i		−	0.817303i	−0.912691	−	0.408651i	$-0.865999\pi$
$239$		−	12.6352i		−	0.817303i	0.912691	−	0.408651i	$-0.134001\pi$
$240$	2.48158	−	5.33840i	0.160185	−	0.344592i
$241$		−	5.48076i		−	0.353047i	−0.984296	−	0.176523i	$-0.943515\pi$
$241$		−	5.48076i		−	0.353047i	0.984296	−	0.176523i	$-0.0564851\pi$
$242$	13.0973	−	3.82177i	0.841929	−	0.245673i
$243$		−	8.38778i		−	0.538076i
$244$	−9.04069	−	14.1724i	−0.578771	−	0.907292i
$245$			5.53059i			0.353337i
$246$	3.86931	+	13.2603i	0.246698	+	0.845443i
$247$	20.3858			1.29712
$248$	17.7397	+	15.5292i	1.12647	+	0.986107i
$249$		−	22.2912i		−	1.41265i
$250$	0.396143	+	1.35760i	0.0250543	+	0.0858620i
$251$	−3.20863			−0.202527			−0.101263	−	0.994860i	$-0.532289\pi$
$251$	−3.20863			−0.202527			−0.101263	+	0.994860i	$0.532289\pi$
$252$	−4.97760	+	3.17527i	−0.313560	+	0.200023i
$253$	−5.46941	−	1.09294i	−0.343859	−	0.0687127i
$254$	−4.01082	−	13.7452i	−0.251661	−	0.862451i
$255$		−	10.1866i		−	0.637910i
$256$	−10.3139	−	12.2321i	−0.644616	−	0.764506i
$257$	1.64018			0.102311			0.0511557	−	0.998691i	$-0.483710\pi$
$257$	1.64018			0.102311			0.0511557	+	0.998691i	$0.483710\pi$
$258$	2.51911	+	8.63307i	0.156833	+	0.537471i
$259$			10.3923i			0.645746i
$260$	6.19435	+	9.71037i	0.384157	+	0.602212i
$261$	−4.76620			−0.295020
$262$	−2.14394	−	7.34737i	−0.132453	−	0.453922i
$263$	21.9476			1.35335			0.676674	−	0.736283i	$-0.263421\pi$
$263$	21.9476			1.35335			0.676674	+	0.736283i	$0.263421\pi$
$264$	3.64270	+	3.18880i	0.224193	+	0.196257i
$265$	−7.45202			−0.457774
$266$	17.0115	−	4.96391i	1.04304	−	0.304357i
$267$	21.9818			1.34526
$268$	−6.31553	+	4.02874i	−0.385782	+	0.246094i
$269$	−7.55805			−0.460822			−0.230411	−	0.973093i	$-0.574007\pi$
$269$	−7.55805			−0.460822			−0.230411	+	0.973093i	$0.574007\pi$
$270$	−7.66040	+	2.23529i	−0.466197	+	0.136035i
$271$			14.9403i			0.907561i	0.891114	+	0.453780i	$0.149925\pi$
$271$			14.9403i			0.907561i	−0.891114	+	0.453780i	$0.850075\pi$
$272$	−25.1057	−	11.6705i	−1.52226	−	0.707628i
$273$			30.0028i			1.81585i
$274$	−6.59477	−	22.6005i	−0.398405	−	1.36535i
$275$	−1.16300			−0.0701314
$276$	5.11264	+	13.1582i	0.307745	+	0.792029i
$277$	9.82732			0.590466			0.295233	−	0.955425i	$-0.404603\pi$
$277$	9.82732			0.590466			0.295233	+	0.955425i	$0.404603\pi$
$278$	−3.70082	−	12.6829i	−0.221961	−	0.760667i
$279$		−	6.95147i		−	0.416174i
$280$	7.53351	+	6.59477i	0.450213	+	0.394113i
$281$		−	5.77494i		−	0.344504i	−0.985053	−	0.172252i	$-0.944896\pi$
$281$		−	5.77494i		−	0.344504i	0.985053	−	0.172252i	$-0.0551044\pi$
$282$	0.653533	−	0.190699i	0.0389173	−	0.0113560i
$283$	8.83050			0.524919			0.262459	−	0.964943i	$-0.415466\pi$
$283$	8.83050			0.524919			0.262459	+	0.964943i	$0.415466\pi$
$284$	13.6027	+	21.3239i	0.807174	+	1.26534i
$285$	5.20979			0.308601
$286$	−9.09267	+	2.65322i	−0.537661	+	0.156888i
$287$	−23.4927			−1.38673
$288$	−0.710684	+	4.66370i	−0.0418775	+	0.274811i
$289$	−30.9062			−1.81801
$290$	2.26404	+	7.75893i	0.132949	+	0.455620i
$291$	−13.9322			−0.816718
$292$	3.12957	−	1.99639i	0.183144	−	0.116830i
$293$			2.44831i			0.143032i	0.997439	+	0.0715160i	$0.0227837\pi$
$293$			2.44831i			0.143032i	−0.997439	+	0.0715160i	$0.977216\pi$
$294$	3.22447	+	11.0504i	0.188055	+	0.644471i
$295$	8.51278			0.495633
$296$	6.24795	+	5.46941i	0.363155	+	0.317903i
$297$		−	6.56235i		−	0.380786i
$298$	7.56466	+	25.9243i	0.438209	+	1.50176i
$299$	−27.0834	−	5.41204i	−1.56627	−	0.312986i
$300$	1.58302	+	2.48158i	0.0913959	+	0.143274i
$301$	−15.2949			−0.881582
$302$	−1.66695	−	5.71268i	−0.0959220	−	0.328728i
$303$			9.40571i			0.540344i
$304$	5.96870	−	12.8399i	0.342328	−	0.736421i
$305$	8.40520			0.481281
$306$	2.28659	+	7.83623i	0.130716	+	0.447968i
$307$			21.2050i			1.21023i	0.796137	+	0.605116i	$0.206873\pi$
$307$			21.2050i			1.21023i	−0.796137	+	0.605116i	$0.793127\pi$
$308$	−6.94158	+	4.42810i	−0.395533	+	0.252315i
$309$		−	2.07072i		−	0.117799i
$310$	−11.3164	+	3.30209i	−0.642726	+	0.187546i
$311$			9.51159i			0.539353i	0.962951	+	0.269676i	$0.0869167\pi$
$311$			9.51159i			0.539353i	−0.962951	+	0.269676i	$0.913083\pi$
$312$	18.0380	+	15.7903i	1.02120	+	0.893949i
$313$		−	16.6474i		−	0.940969i	−0.882408	−	0.470484i	$-0.844079\pi$
$313$		−	16.6474i		−	0.940969i	0.882408	−	0.470484i	$-0.155921\pi$
$314$	−1.00817	−	3.45504i	−0.0568944	−	0.194979i
$315$		−	2.95207i		−	0.166330i
$316$	26.0968	−	16.6474i	1.46806	−	0.936492i
$317$	2.41375			0.135570			0.0677849	−	0.997700i	$-0.478407\pi$
$317$	2.41375			0.135570			0.0677849	+	0.997700i	$0.478407\pi$
$318$	−14.8895	+	4.34471i	−0.834960	+	0.243639i
$319$	−6.64675			−0.372147
$320$	7.92967	−	1.05842i	0.443282	−	0.0591676i
$321$			6.35908i			0.354929i
$322$	−23.9183	+	2.07855i	−1.33292	+	0.115833i
$323$		−	24.5009i		−	1.36326i
$324$	−9.78412	+	6.24139i	−0.543562	+	0.346744i
$325$	−5.75893			−0.319448
$326$	−4.78586	−	16.4013i	−0.265064	−	0.908385i
$327$	0.193114			0.0106792
$328$	−12.3641	+	14.1240i	−0.682691	+	0.779869i
$329$			1.15784i			0.0638338i
$330$	−2.32372	+	0.678055i	−0.127917	+	0.0373257i
$331$			7.46743i			0.410447i	0.978715	+	0.205224i	$0.0657922\pi$
$331$			7.46743i			0.410447i	−0.978715	+	0.205224i	$0.934208\pi$
$332$	25.5383	−	16.2912i	1.40160	−	0.894094i
$333$		−	2.44831i		−	0.134167i
$334$	−3.37228	−	11.5569i	−0.184523	−	0.632367i
$335$		−	3.74555i		−	0.204641i
$336$	18.8972	+	8.78443i	1.03093	+	0.479230i
$337$			31.4548i			1.71345i	0.515770	+	0.856727i	$0.327506\pi$
$337$			31.4548i			1.71345i	−0.515770	+	0.856727i	$0.672494\pi$
$338$	−27.3764	+	7.98835i	−1.48908	+	0.434509i
$339$	−13.7265			−0.745519
$340$	11.6705	−	7.44473i	0.632922	−	0.403747i
$341$		−	9.69426i		−	0.524973i
$342$	−4.00772	+	1.16944i	−0.216713	+	0.0632362i
$343$	5.20149			0.280854
$344$	−8.04960	+	9.19542i	−0.434005	+	0.495784i
$345$	−6.92143	−	1.38310i	−0.372637	−	0.0744635i
$346$	9.39651	−	2.74188i	0.505160	−	0.147404i
$347$		−	19.8241i		−	1.06421i	−0.846677	−	0.532107i	$-0.821401\pi$
$347$		−	19.8241i		−	1.06421i	0.846677	−	0.532107i	$-0.178599\pi$
$348$	9.04729	+	14.1827i	0.484986	+	0.760273i
$349$	−28.6634			−1.53432			−0.767160	−	0.641456i	$-0.778331\pi$
$349$	−28.6634			−1.53432			−0.767160	+	0.641456i	$0.778331\pi$
$350$	−4.80570	+	1.40229i	−0.256876	+	0.0749556i
$351$		−	32.4955i		−	1.73448i
$352$	−0.991093	+	6.50382i	−0.0528255	+	0.346655i
$353$	12.6439			0.672966			0.336483	−	0.941690i	$-0.390763\pi$
$353$	12.6439			0.672966			0.336483	+	0.941690i	$0.390763\pi$
$354$	17.0089	−	4.96316i	0.904013	−	0.263789i
$355$	−12.6466			−0.671211
$356$	16.0650	+	25.1839i	0.851446	+	1.33474i
$357$	36.0592			1.90845
$358$	2.14394	+	7.34737i	0.113311	+	0.388320i
$359$	23.7325			1.25256			0.626278	−	0.779600i	$-0.284578\pi$
$359$	23.7325			1.25256			0.626278	+	0.779600i	$0.284578\pi$
$360$	−1.77481	−	1.55366i	−0.0935407	−	0.0818849i
$361$	−6.46941			−0.340495
$362$	−6.55649	−	22.4693i	−0.344601	−	1.18096i
$363$			14.1986i			0.745234i
$364$	−34.3733	+	21.9271i	−1.80165	+	1.14929i
$365$			1.85606i			0.0971505i
$366$	16.7940	−	4.90044i	0.877835	−	0.256150i
$367$	32.7053			1.70720			0.853601	−	0.520927i	$-0.174414\pi$
$367$	32.7053			1.70720			0.853601	+	0.520927i	$0.174414\pi$
$368$	−11.3384	+	15.4738i	−0.591057	+	0.806630i
$369$	5.53462			0.288121
$370$	−3.98563	+	1.16300i	−0.207203	+	0.0604613i
$371$		−	26.3791i		−	1.36953i
$372$	−20.6854	+	13.1954i	−1.07249	+	0.684151i
$373$			13.9713i			0.723404i	0.932294	+	0.361702i	$0.117804\pi$
$373$			13.9713i			0.723404i	−0.932294	+	0.361702i	$0.882196\pi$
$374$	3.18880	+	10.9281i	0.164889	+	0.565079i
$375$	−1.47175			−0.0760009
$376$	0.696104	+	0.609364i	0.0358988	+	0.0314255i
$377$	−32.9134			−1.69513
$378$	−7.91260	−	27.1167i	−0.406980	−	1.39473i
$379$	−20.7170			−1.06416			−0.532081	−	0.846693i	$-0.678590\pi$
$379$	−20.7170			−1.06416			−0.532081	+	0.846693i	$0.678590\pi$
$380$	3.80749	+	5.96870i	0.195320	+	0.306188i
$381$	14.9010			0.763399
$382$	20.5622	−	6.00000i	1.05205	−	0.306987i
$383$	1.99477			0.101928			0.0509639	−	0.998700i	$-0.483771\pi$
$383$	1.99477			0.101928			0.0509639	+	0.998700i	$0.483771\pi$
$384$	15.2268	−	6.73797i	0.777037	−	0.343845i
$385$		−	4.11684i		−	0.209814i
$386$	−34.4476	+	10.0517i	−1.75333	+	0.511619i
$387$	3.60330			0.183166
$388$	−10.1821	−	15.9617i	−0.516918	−	0.810331i
$389$			16.4309i			0.833081i	0.909117	+	0.416541i	$0.136758\pi$
$389$			16.4309i			0.833081i	−0.909117	+	0.416541i	$0.863242\pi$
$390$	−11.5066	+	3.35760i	−0.582659	+	0.170019i
$391$	−6.50451	+	32.5505i	−0.328947	+	1.64615i
$392$	−10.3035	+	11.7702i	−0.520407	+	0.594484i
$393$	7.96517			0.401789
$394$	−2.52238	+	0.736023i	−0.127075	+	0.0370803i
$395$			15.4773i			0.778745i
$396$	1.63536	−	1.04321i	0.0821799	−	0.0524234i
$397$	−0.580900			−0.0291545			−0.0145773	−	0.999894i	$-0.504640\pi$
$397$	−0.580900			−0.0291545			−0.0145773	+	0.999894i	$0.504640\pi$
$398$	25.6472	−	7.48378i	1.28558	−	0.375128i
$399$			18.4419i			0.923250i
$400$	−1.68614	+	3.62725i	−0.0843070	+	0.181362i
$401$			8.44831i			0.421889i	0.977498	+	0.210944i	$0.0676539\pi$
$401$			8.44831i			0.421889i	−0.977498	+	0.210944i	$0.932346\pi$
$402$	−2.18375	−	7.48378i	−0.108915	−	0.373257i
$403$		−	48.0041i		−	2.39125i
$404$	−10.7758	+	6.87402i	−0.536118	+	0.341995i
$405$		−	5.80267i		−	0.288337i
$406$	−27.4655	+	8.01437i	−1.36309	+	0.397746i
$407$		−	3.41432i		−	0.169242i
$408$	18.9777	−	21.6791i	0.939537	−	1.07327i
$409$	2.95154			0.145944			0.0729722	−	0.997334i	$-0.476752\pi$
$409$	2.95154			0.145944			0.0729722	+	0.997334i	$0.476752\pi$
$410$	−2.62905	−	9.00986i	−0.129840	−	0.444965i
$411$	24.5009			1.20854
$412$	2.37236	−	1.51335i	0.116878	−	0.0745576i
$413$			30.1340i			1.48280i
$414$	5.63490	−	0.489683i	0.276940	−	0.0240666i
$415$			15.1460i			0.743489i
$416$	−4.90770	+	32.2057i	−0.240620	+	1.57901i
$417$	13.7493			0.673305
$418$	−5.58902	+	1.63086i	−0.273368	+	0.0797680i
$419$	13.6392			0.666320			0.333160	−	0.942870i	$-0.391885\pi$
$419$	13.6392			0.666320			0.333160	+	0.942870i	$0.391885\pi$
$420$	−8.78443	+	5.60368i	−0.428636	+	0.273432i
$421$		−	22.9416i		−	1.11811i	−0.829132	−	0.559053i	$-0.811165\pi$
$421$		−	22.9416i		−	1.11811i	0.829132	−	0.559053i	$-0.188835\pi$
$422$	3.95388	+	13.5501i	0.192472	+	0.659607i
$423$		−	0.272774i		−	0.0132627i
$424$	−15.8593	−	13.8832i	−0.770198	−	0.674226i
$425$			6.92143i			0.335739i
$426$	−25.2684	+	7.37326i	−1.22426	+	0.357236i
$427$			29.7532i			1.43986i
$428$	−7.28541	+	4.64744i	−0.352154	+	0.224642i
$429$		−	9.85722i		−	0.475911i
$430$	−1.71164	−	5.86585i	−0.0825427	−	0.282876i
$431$	21.3048			1.02622			0.513109	−	0.858324i	$-0.328494\pi$
$431$	21.3048			1.02622			0.513109	+	0.858324i	$0.328494\pi$
$432$	−20.4672	−	9.51425i	−0.984728	−	0.457755i
$433$		−	21.3294i		−	1.02503i	−0.858679	−	0.512514i	$-0.828714\pi$
$433$		−	21.3294i		−	1.02503i	0.858679	−	0.512514i	$-0.171286\pi$
$434$	−11.6889	−	40.0583i	−0.561086	−	1.92286i
$435$	−8.41134			−0.403293
$436$	0.141134	+	0.221245i	0.00675911	+	0.0105957i
$437$	−16.6474	−	3.32663i	−0.796355	−	0.159134i
$438$	1.08213	+	3.70848i	0.0517060	+	0.177198i
$439$			10.4758i			0.499984i	0.968248	+	0.249992i	$0.0804281\pi$
$439$			10.4758i			0.499984i	−0.968248	+	0.249992i	$0.919572\pi$
$440$	−2.47508	−	2.16667i	−0.117995	−	0.103292i
$441$	4.61225			0.219631
$442$	15.7903	+	54.1139i	0.751068	+	2.57393i
$443$			12.6173i			0.599465i	0.954023	+	0.299733i	$0.0968975\pi$
$443$			12.6173i			0.599465i	−0.954023	+	0.299733i	$0.903103\pi$
$444$	−7.28541	+	4.64744i	−0.345750	+	0.220558i
$445$	−14.9358			−0.708025
$446$	−4.81041	−	16.4854i	−0.227779	−	0.780608i
$447$	−28.1042			−1.32928
$448$	3.74666	+	28.0699i	0.177013	+	1.32618i
$449$	−13.7434			−0.648591			−0.324295	−	0.945956i	$-0.605127\pi$
$449$	−13.7434			−0.648591			−0.324295	+	0.945956i	$0.605127\pi$
$450$	1.13217	−	0.330364i	0.0533710	−	0.0155735i
$451$	7.71837			0.363444
$452$	−10.0318	−	15.7260i	−0.471856	−	0.739689i
$453$	6.19303			0.290974
$454$	37.4973	−	10.9416i	1.75984	−	0.513516i
$455$		−	20.3858i		−	0.955701i
$456$	11.0874	+	9.70586i	0.519217	+	0.454519i
$457$			3.81412i			0.178417i	0.996013	+	0.0892084i	$0.0284337\pi$
$457$			3.81412i			0.178417i	−0.996013	+	0.0892084i	$0.971566\pi$
$458$	1.05904	+	3.62936i	0.0494856	+	0.169589i
$459$	−39.0550			−1.82293
$460$	−3.47385	−	8.94049i	−0.161969	−	0.416853i
$461$	24.6480			1.14797			0.573985	−	0.818866i	$-0.305397\pi$
$461$	24.6480			1.14797			0.573985	+	0.818866i	$0.305397\pi$
$462$	−2.40022	−	8.22564i	−0.111668	−	0.382691i
$463$			41.6124i			1.93389i	0.254983	+	0.966945i	$0.417930\pi$
$463$			41.6124i			1.93389i	−0.254983	+	0.966945i	$0.582070\pi$
$464$	−9.63662	+	20.7304i	−0.447369	+	0.962386i
$465$		−	12.2679i		−	0.568910i
$466$	26.1329	−	7.62550i	1.21058	−	0.353245i
$467$	−5.16511			−0.239013			−0.119506	−	0.992833i	$-0.538131\pi$
$467$	−5.16511			−0.239013			−0.119506	+	0.992833i	$0.538131\pi$
$468$	8.09798	−	5.16578i	0.374329	−	0.238788i
$469$	13.2587			0.612231
$470$	−0.444052	+	0.129573i	−0.0204826	+	0.00597677i
$471$	3.74555			0.172586
$472$	18.1168	+	15.8593i	0.833895	+	0.729986i
$473$	5.02503			0.231051
$474$	9.02361	+	30.9242i	0.414468	+	1.42040i
$475$	−3.53986			−0.162420
$476$	26.3533	+	41.3119i	1.20790	+	1.89353i
$477$			6.21462i			0.284548i
$478$	5.00535	+	17.1535i	0.228939	+	0.784583i
$479$	2.23875			0.102291			0.0511455	−	0.998691i	$-0.483713\pi$
$479$	2.23875			0.102291			0.0511455	+	0.998691i	$0.483713\pi$
$480$	−1.25421	+	8.23046i	−0.0572466	+	0.375667i
$481$		−	16.9071i		−	0.770895i
$482$	2.17117	+	7.44067i	0.0988940	+	0.338913i
$483$	4.89597	−	24.5009i	0.222774	−	1.11483i
$484$	−16.2669	+	10.3768i	−0.739406	+	0.471675i
$485$	9.46639			0.429847
$486$	3.32276	+	11.3872i	0.150724	+	0.516535i
$487$		−	30.3341i		−	1.37457i	−0.726389	−	0.687284i	$-0.758803\pi$
$487$		−	30.3341i		−	1.37457i	0.726389	−	0.687284i	$-0.241197\pi$
$488$	17.8879	+	15.6589i	0.809747	+	0.708847i
$489$	17.7804			0.804058
$490$	−2.19091	−	7.50832i	−0.0989752	−	0.339191i
$491$		−	23.2954i		−	1.05131i	−0.850698	−	0.525654i	$-0.823821\pi$
$491$		−	23.2954i		−	1.05131i	0.850698	−	0.525654i	$-0.176179\pi$
$492$	−10.5059	−	16.4693i	−0.473644	−	0.742493i
$493$			39.5573i			1.78157i
$494$	−27.6757	+	8.07570i	−1.24519	+	0.363343i
$495$			0.969883i			0.0435930i
$496$	−30.2352	−	14.0550i	−1.35760	−	0.631087i
$497$		−	44.7671i		−	2.00808i
$498$	8.83050	+	30.2624i	0.395704	+	1.35609i
$499$		−	22.5990i		−	1.01167i	−0.862631	−	0.505834i	$-0.831185\pi$
$499$		−	22.5990i		−	1.01167i	0.862631	−	0.505834i	$-0.168815\pi$
$500$	−1.07561	−	1.68614i	−0.0481026	−	0.0754065i
$501$	12.5287			0.559740
$502$	4.35603	−	1.27108i	0.194419	−	0.0567310i
$503$	2.63342			0.117418			0.0587092	−	0.998275i	$-0.481302\pi$
$503$	2.63342			0.117418			0.0587092	+	0.998275i	$0.481302\pi$
$504$	5.49972	−	6.28258i	0.244977	−	0.279848i
$505$		−	6.39083i		−	0.284388i
$506$	7.85821	−	0.682894i	0.349340	−	0.0303583i
$507$		−	29.6783i		−	1.31806i
$508$	10.8901	+	17.0716i	0.483172	+	0.757429i
$509$	34.6596			1.53626			0.768130	−	0.640293i	$-0.221187\pi$
$509$	34.6596			1.53626			0.768130	+	0.640293i	$0.221187\pi$
$510$	4.03536	+	13.8293i	0.178689	+	0.612372i
$511$	−6.57018			−0.290648
$512$	18.8477	+	12.5205i	0.832960	+	0.553333i
$513$		−	19.9741i		−	0.881877i
$514$	−2.22670	+	0.649745i	−0.0982154	+	0.0286590i
$515$			1.40698i			0.0619989i
$516$	−6.83987	−	10.7223i	−0.301108	−	0.472023i
$517$		−	0.380401i		−	0.0167300i
$518$	−4.11684	−	14.1086i	−0.180884	−	0.619895i
$519$			10.1866i			0.447143i
$520$	−12.2561	−	10.7289i	−0.537467	−	0.470494i
$521$			5.00371i			0.219216i	0.993975	+	0.109608i	$0.0349596\pi$
$521$			5.00371i			0.219216i	−0.993975	+	0.109608i	$0.965040\pi$
$522$	6.47057	−	1.88810i	0.283209	−	0.0826398i
$523$	17.3919			0.760493			0.380247	−	0.924885i	$-0.375839\pi$
$523$	17.3919			0.760493			0.380247	+	0.924885i	$0.375839\pi$
$524$	5.82122	+	9.12545i	0.254301	+	0.398647i
$525$		−	5.20979i		−	0.227374i
$526$	−29.7960	+	8.69440i	−1.29917	+	0.379094i
$527$	−57.6941			−2.51320
$528$	−6.20855	−	2.88607i	−0.270192	−	0.125600i
$529$	21.2337	+	8.83915i	0.923204	+	0.384311i
$530$	10.1168	−	2.95207i	0.439448	−	0.128230i
$531$		−	7.09924i		−	0.308081i
$532$	−21.1283	+	13.4780i	−0.916030	+	0.584345i
$533$	38.2199			1.65549
$534$	−29.8424	+	8.70793i	−1.29141	+	0.376829i
$535$		−	4.32076i		−	0.186803i
$536$	6.97798	−	7.97126i	0.301403	−	0.344306i
$537$	−7.96517			−0.343722
$538$	10.2608	−	2.99407i	0.442374	−	0.129084i
$539$	6.43206			0.277049
$540$	9.51425	−	6.06924i	0.409428	−	0.261178i
$541$	6.53779			0.281082			0.140541	−	0.990075i	$-0.455116\pi$
$541$	6.53779			0.281082			0.140541	+	0.990075i	$0.455116\pi$
$542$	−5.91852	−	20.2830i	−0.254222	−	0.871228i
$543$	24.3586			1.04533
$544$	38.7067	+	5.89837i	1.65953	+	0.252890i
$545$	−0.131214			−0.00562058
$546$	−11.8854	−	40.7317i	−0.508649	−	1.74316i
$547$		−	34.5946i		−	1.47916i	−0.673069	−	0.739579i	$-0.735024\pi$
$547$		−	34.5946i		−	1.47916i	0.673069	−	0.739579i	$-0.264976\pi$
$548$	17.9061	+	28.0699i	0.764910	+	1.19909i
$549$		−	7.00953i		−	0.299160i
$550$	1.57888	−	0.460714i	0.0673237	−	0.0196449i
$551$	−20.2310			−0.861869
$552$	−12.1534	−	15.8382i	−0.517284	−	0.674117i
$553$	−54.7873			−2.32979
$554$	−13.3415	+	3.89303i	−0.566828	+	0.165399i
$555$		−	4.32076i		−	0.183406i
$556$	10.0485	+	15.7521i	0.426150	+	0.668040i
$557$			3.84587i			0.162955i	0.996675	+	0.0814774i	$0.0259638\pi$
$557$			3.84587i			0.162955i	−0.996675	+	0.0814774i	$0.974036\pi$
$558$	2.75378	+	9.43730i	0.116577	+	0.399513i
$559$	24.8830			1.05244
$560$	−12.8399	−	5.96870i	−0.542587	−	0.252224i
$561$	−11.8470			−0.500181
$562$	2.28771	+	7.84005i	0.0965011	+	0.330712i
$563$	−8.64152			−0.364197			−0.182098	−	0.983280i	$-0.558289\pi$
$563$	−8.64152			−0.364197			−0.182098	+	0.983280i	$0.558289\pi$
$564$	−0.811691	+	0.517786i	−0.0341783	+	0.0218027i
$565$	9.32663			0.392374
$566$	−11.9883	+	3.49815i	−0.503904	+	0.147038i
$567$	20.5406			0.862625
$568$	−26.9144	−	23.5606i	−1.12930	−	0.988583i
$569$			5.28746i			0.221662i	0.993839	+	0.110831i	$0.0353512\pi$
$569$			5.28746i			0.221662i	−0.993839	+	0.110831i	$0.964649\pi$
$570$	−7.07279	+	2.06382i	−0.296247	+	0.0864440i
$571$	23.7200			0.992650			0.496325	−	0.868137i	$-0.334682\pi$
$571$	23.7200			0.992650			0.496325	+	0.868137i	$0.334682\pi$
$572$	11.2931	−	7.20401i	0.472190	−	0.301215i
$573$			22.2912i			0.931227i
$574$	31.8936	−	9.30648i	1.33121	−	0.388445i
$575$	4.70285	+	0.939764i	0.196123	+	0.0391909i
$576$	−0.882673	−	6.61296i	−0.0367780	−	0.275540i
$577$	−16.0897			−0.669825			−0.334912	−	0.942249i	$-0.608707\pi$
$577$	−16.0897			−0.669825			−0.334912	+	0.942249i	$0.608707\pi$
$578$	41.9581	−	12.2433i	1.74523	−	0.509253i
$579$		−	37.3441i		−	1.55197i
$580$	−6.14730	−	9.63662i	−0.255253	−	0.400139i
$581$	−53.6148			−2.22432
$582$	18.9143	−	5.51914i	0.784022	−	0.228776i
$583$			8.66668i			0.358937i
$584$	−3.45784	+	3.95005i	−0.143087	+	0.163454i
$585$			4.80267i			0.198566i
$586$	−0.969883	−	3.32382i	−0.0400655	−	0.137306i
$587$			32.2006i			1.32906i	0.747261	+	0.664531i	$0.231369\pi$
$587$			32.2006i			1.32906i	−0.747261	+	0.664531i	$0.768631\pi$
$588$	−8.75506	−	13.7246i	−0.361053	−	0.565993i
$589$		−	29.5068i		−	1.21581i
$590$	−11.5569	+	3.37228i	−0.475791	+	0.138835i
$591$		−	2.73447i		−	0.112481i
$592$	−10.6489	−	4.95017i	−0.437666	−	0.203451i
$593$	13.0612			0.536359			0.268179	−	0.963369i	$-0.413578\pi$
$593$	13.0612			0.536359			0.268179	+	0.963369i	$0.413578\pi$
$594$	2.59963	+	8.90903i	0.106664	+	0.365542i
$595$	−24.5009			−1.00444
$596$	−20.5395	−	32.1981i	−0.841331	−	1.31889i
$597$			27.8037i			1.13793i
$598$	38.9123	−	3.38156i	1.59124	−	0.138282i
$599$		−	16.6052i		−	0.678469i	−0.940702	−	0.339234i	$-0.889832\pi$
$599$		−	16.6052i		−	0.678469i	0.940702	−	0.339234i	$-0.110168\pi$
$600$	−3.13217	−	2.74188i	−0.127870	−	0.111937i
$601$	0.980281			0.0399865			0.0199932	−	0.999800i	$-0.493636\pi$
$601$	0.980281			0.0399865			0.0199932	+	0.999800i	$0.493636\pi$
$602$	20.7643	−	6.05897i	0.846289	−	0.246945i
$603$	−3.12361			−0.127203
$604$	4.52608	+	7.09517i	0.184164	+	0.288698i
$605$		−	9.64744i		−	0.392224i
$606$	−3.72601	−	12.7692i	−0.151359	−	0.518712i
$607$			9.05291i			0.367446i	0.982978	+	0.183723i	$0.0588150\pi$
$607$			9.05291i			0.367446i	−0.982978	+	0.183723i	$0.941185\pi$
$608$	−3.01663	+	19.7959i	−0.122340	+	0.802831i
$609$		−	29.7749i		−	1.20654i
$610$	−11.4109	+	3.32967i	−0.462013	+	0.134814i
$611$		−	1.88367i		−	0.0762051i
$612$	−6.20855	−	9.73263i	−0.250966	−	0.393418i
$613$		−	10.4845i		−	0.423464i	−0.977328	−	0.211732i	$-0.932090\pi$
$613$		−	10.4845i		−	0.423464i	0.977328	−	0.211732i	$-0.0679104\pi$
$614$	−8.40022	−	28.7878i	−0.339005	−	1.16178i
$615$	9.76745			0.393862
$616$	7.66970	−	8.76144i	0.309021	−	0.353009i
$617$			8.27118i			0.332985i	0.986043	+	0.166493i	$0.0532442\pi$
$617$			8.27118i			0.332985i	−0.986043	+	0.166493i	$0.946756\pi$
$618$	0.820302	+	2.81120i	0.0329974	+	0.113083i
$619$	−15.1042			−0.607087			−0.303544	−	0.952818i	$-0.598170\pi$
$619$	−15.1042			−0.607087			−0.303544	+	0.952818i	$0.598170\pi$
$620$	14.0550	−	8.96581i	0.564461	−	0.360075i
$621$	−5.30273	+	26.5364i	−0.212791	+	1.06487i
$622$	−3.76795	−	12.9129i	−0.151081	−	0.517760i
$623$		−	52.8706i		−	2.11822i
$624$	−30.7435	−	14.2912i	−1.23073	−	0.572107i
$625$	1.00000			0.0400000
$626$	6.59477	+	22.6005i	0.263580	+	0.903298i
$627$		−	6.05897i		−	0.241972i
$628$	2.73738	+	4.29117i	0.109233	+	0.171236i
$629$	−20.3199			−0.810208
$630$	1.16944	+	4.00772i	0.0465917	+	0.159671i
$631$	−36.3050			−1.44528			−0.722640	−	0.691225i	$-0.757072\pi$
$631$	−36.3050			−1.44528			−0.722640	+	0.691225i	$0.757072\pi$
$632$	−28.8342	+	32.9386i	−1.14696	+	1.31023i
$633$	−14.6894			−0.583852
$634$	−3.27690	+	0.956191i	−0.130142	+	0.0379752i
$635$	−10.1247			−0.401785
$636$	18.4928	−	11.7967i	0.733286	−	0.467771i
$637$	31.8503			1.26196
$638$	9.02361	−	2.63307i	0.357248	−	0.104244i
$639$			10.5466i			0.417218i
$640$	−10.3460	+	4.57820i	−0.408962	+	0.180969i
$641$			33.5891i			1.32669i	0.748315	+	0.663344i	$0.230863\pi$
$641$			33.5891i			1.32669i	−0.748315	+	0.663344i	$0.769137\pi$
$642$	−2.51911	−	8.63307i	−0.0994213	−	0.340720i
$643$	1.33940			0.0528207			0.0264104	−	0.999651i	$-0.491592\pi$
$643$	1.33940			0.0528207			0.0264104	+	0.999651i	$0.491592\pi$
$644$	31.6481	−	12.2969i	1.24711	−	0.484567i
$645$	6.35908			0.250388
$646$	9.70586	+	33.2623i	0.381872	+	1.30869i
$647$			41.6967i			1.63927i	0.572889	+	0.819633i	$0.305822\pi$
$647$			41.6967i			1.63927i	−0.572889	+	0.819633i	$0.694178\pi$
$648$	10.8104	−	12.3492i	0.424673	−	0.485123i
$649$		−	9.90033i		−	0.388622i
$650$	7.81831	−	2.28136i	0.306659	−	0.0894824i
$651$	43.4266			1.70202
$652$	12.9945	+	20.3705i	0.508906	+	0.797770i
$653$	−13.9039			−0.544101			−0.272051	−	0.962283i	$-0.587702\pi$
$653$	−13.9039			−0.544101			−0.272051	+	0.962283i	$0.587702\pi$
$654$	−0.262171	+	0.0765008i	−0.0102517	+	0.00299142i
$655$	−5.41204			−0.211466
$656$	11.1903	−	24.0727i	0.436907	−	0.939880i
$657$	1.54786			0.0603878
$658$	−0.458671	−	1.57188i	−0.0178808	−	0.0612783i
$659$	−2.90120			−0.113015			−0.0565074	−	0.998402i	$-0.517996\pi$
$659$	−2.90120			−0.113015			−0.0565074	+	0.998402i	$0.517996\pi$
$660$	2.88607	−	1.84105i	0.112340	−	0.0716629i
$661$			9.24133i			0.359446i	0.983717	+	0.179723i	$0.0575202\pi$
$661$			9.24133i			0.359446i	−0.983717	+	0.179723i	$0.942480\pi$
$662$	−2.95818	−	10.1378i	−0.114973	−	0.394015i
$663$	−58.6640			−2.27832
$664$	−28.2171	+	32.2337i	−1.09504	+	1.25091i
$665$		−	12.5306i		−	0.485916i
$666$	0.969883	+	3.32382i	0.0375822	+	0.128795i
$667$	26.8777	+	5.37093i	1.04071	+	0.207963i
$668$	9.15640	+	14.3537i	0.354272	+	0.555363i
$669$	17.8716			0.690956
$670$	1.48378	+	5.08495i	0.0573233	+	0.196449i
$671$		−	9.77523i		−	0.377368i
$672$	−29.1347	−	4.43972i	−1.12389	−	0.171266i
$673$	−12.1472			−0.468241			−0.234121	−	0.972208i	$-0.575221\pi$
$673$	−12.1472			−0.468241			−0.234121	+	0.972208i	$0.575221\pi$
$674$	−12.4606	−	42.7030i	−0.479965	−	1.64486i
$675$			5.64262i			0.217184i
$676$	34.0015	−	21.6899i	1.30775	−	0.834228i
$677$		−	22.1571i		−	0.851568i	−0.904825	−	0.425784i	$-0.859998\pi$
$677$		−	22.1571i		−	0.851568i	0.904825	−	0.425784i	$-0.140002\pi$
$678$	18.6350	−	5.43765i	0.715674	−	0.208832i
$679$			33.5097i			1.28598i
$680$	−12.8947	+	14.7301i	−0.494487	+	0.564875i
$681$			40.6502i			1.55772i
$682$	3.84032	+	13.1609i	0.147053	+	0.503957i
$683$			19.4459i			0.744078i	0.928217	+	0.372039i	$0.121341\pi$
$683$			19.4459i			0.744078i	−0.928217	+	0.372039i	$0.878659\pi$
$684$	4.97760	−	3.17527i	0.190323	−	0.121409i
$685$	−16.6474			−0.636066
$686$	−7.06153	+	2.06054i	−0.269610	+	0.0786716i
$687$	−3.93453			−0.150112
$688$	7.28541	−	15.6725i	0.277754	−	0.597507i
$689$			42.9157i			1.63496i
$690$	9.94442	−	0.864189i	0.378577	−	0.0328991i
$691$			19.0338i			0.724081i	0.932162	+	0.362040i	$0.117920\pi$
$691$			19.0338i			0.724081i	−0.932162	+	0.362040i	$0.882080\pi$
$692$	−11.6705	+	7.44473i	−0.443646	+	0.283006i
$693$	−3.43325			−0.130418
$694$	7.85319	+	26.9131i	0.298103	+	1.02161i
$695$	−9.34213			−0.354367
$696$	−17.9010	−	15.6704i	−0.678534	−	0.593984i
$697$		−	45.9349i		−	1.73991i
$698$	38.9134	−	11.3548i	1.47289	−	0.429787i
$699$			28.3302i			1.07155i
$700$	5.96870	−	3.80749i	0.225596	−	0.143910i
$701$			1.32081i			0.0498862i	0.999689	+	0.0249431i	$0.00794046\pi$
$701$			1.32081i			0.0498862i	−0.999689	+	0.0249431i	$0.992060\pi$
$702$	12.8729	+	44.1157i	0.485855	+	1.66504i
$703$		−	10.3923i		−	0.391953i
$704$	−1.23094	−	9.22219i	−0.0463929	−	0.347574i
$705$		−	0.481390i		−	0.0181302i
$706$	−17.1653	+	5.00879i	−0.646025	+	0.188508i
$707$	22.6226			0.850812
$708$	−21.1251	+	13.4759i	−0.793931	+	0.506457i
$709$			14.6676i			0.550854i	0.961322	+	0.275427i	$0.0888193\pi$
$709$			14.6676i			0.550854i	−0.961322	+	0.275427i	$0.911181\pi$
$710$	17.1690	−	5.00986i	0.644340	−	0.188017i
$711$	12.9073			0.484061
$712$	−31.7863	−	27.8255i	−1.19124	−	1.04280i
$713$	−7.83348	+	39.2010i	−0.293366	+	1.46809i
$714$	−48.9538	+	14.2846i	−1.83205	+	0.534588i
$715$			6.69762i			0.250477i
$716$	−5.82122	−	9.12545i	−0.217549	−	0.341034i
$717$	−18.5958			−0.694475
$718$	−32.2192	+	9.40149i	−1.20241	+	0.350861i
$719$		−	24.8798i		−	0.927858i	−0.885872	−	0.463929i	$-0.846439\pi$
$719$		−	24.8798i		−	0.927858i	0.885872	−	0.463929i	$-0.153561\pi$
$720$	3.02495	+	1.40616i	0.112733	+	0.0524045i
$721$	−4.98050			−0.185484
$722$	8.78285	−	2.56281i	0.326864	−	0.0953780i
$723$	−8.06631			−0.299989
$724$	17.8021	+	27.9070i	0.661611	+	1.03715i
$725$	5.71519			0.212257
$726$	−5.62469	−	19.2760i	−0.208752	−	0.715400i
$727$	16.7420			0.620926			0.310463	−	0.950585i	$-0.399516\pi$
$727$	16.7420			0.620926			0.310463	+	0.950585i	$0.399516\pi$
$728$	37.9789	−	43.3849i	1.40759	−	1.60795i
$729$	−29.7527			−1.10195
$730$	−0.735265	−	2.51978i	−0.0272134	−	0.0932612i
$731$		−	29.9058i		−	1.10611i
$732$	−20.8582	+	13.3056i	−0.770940	+	0.491791i
$733$		−	14.5767i		−	0.538403i	−0.963084	−	0.269202i	$-0.913240\pi$
$733$		−	14.5767i		−	0.538403i	0.963084	−	0.269202i	$-0.0867598\pi$
$734$	−44.4006	+	12.9560i	−1.63886	+	0.478214i
$735$	8.13965			0.300236
$736$	9.26316	−	25.4989i	0.341445	−	0.939902i
$737$	−4.35606			−0.160458
$738$	−7.51379	+	2.19250i	−0.276586	+	0.0807072i
$739$		−	30.1332i		−	1.10847i	−0.832361	−	0.554234i	$-0.813011\pi$
$739$		−	30.1332i		−	1.10847i	0.832361	−	0.554234i	$-0.186989\pi$
$740$	4.95017	−	3.15776i	0.181972	−	0.116082i
$741$		−	30.0028i		−	1.10218i
$742$	10.4499	+	35.8122i	0.383628	+	1.31471i
$743$	5.43289			0.199313			0.0996567	−	0.995022i	$-0.468226\pi$
$743$	5.43289			0.199313			0.0996567	+	0.995022i	$0.468226\pi$
$744$	22.8552	−	26.1085i	0.837911	−	0.957183i
$745$	19.0958			0.699614
$746$	−5.53462	−	18.9673i	−0.202637	−	0.694444i
$747$	12.6311			0.462146
$748$	−8.65820	−	13.5728i	−0.316575	−	0.496269i
$749$	15.2949			0.558863
$750$	1.99804	−	0.583024i	0.0729583	−	0.0212890i
$751$	10.0611			0.367134			0.183567	−	0.983007i	$-0.441236\pi$
$751$	10.0611			0.367134			0.183567	+	0.983007i	$0.441236\pi$
$752$	−1.18642	−	0.551514i	−0.0432644	−	0.0201116i
$753$			4.72230i			0.172090i
$754$	44.6832	−	13.0384i	1.62726	−	0.474832i
$755$	−4.20794			−0.153142
$756$	21.4842	+	33.6791i	0.781374	+	1.22490i
$757$			16.5853i			0.602805i	0.953497	+	0.301402i	$0.0974547\pi$
$757$			16.5853i			0.602805i	−0.953497	+	0.301402i	$0.902545\pi$
$758$	28.1254	−	8.20692i	1.02156	−	0.298089i
$759$	−1.60854	+	8.04960i	−0.0583862	+	0.292182i
$760$	−7.53351	−	6.59477i	−0.273269	−	0.239218i
$761$	34.1984			1.23969			0.619845	−	0.784724i	$-0.287195\pi$
$761$	34.1984			1.23969			0.619845	+	0.784724i	$0.287195\pi$
$762$	−20.2295	+	5.90292i	−0.732838	+	0.213840i
$763$		−	0.464478i		−	0.0168152i
$764$	−25.5383	+	16.2912i	−0.923944	+	0.589394i
$765$	5.77213			0.208692
$766$	−2.70809	+	0.790214i	−0.0978472	+	0.0285516i
$767$		−	49.0245i		−	1.77017i
$768$	−18.0026	+	15.1794i	−0.649613	+	0.547740i
$769$			44.6472i			1.61002i	0.593261	+	0.805010i	$0.297840\pi$
$769$			44.6472i			1.61002i	−0.593261	+	0.805010i	$0.702160\pi$
$770$	1.63086	+	5.58902i	0.0587721	+	0.201414i
$771$		−	2.41393i		−	0.0869355i
$772$	42.7840	−	27.2924i	1.53983	−	0.982274i
$773$		−	42.9053i		−	1.54319i	−0.636111	−	0.771597i	$-0.719458\pi$
$773$		−	42.9053i		−	1.54319i	0.636111	−	0.771597i	$-0.280542\pi$
$774$	−4.89184	+	1.42743i	−0.175833	+	0.0513078i
$775$			8.33558i			0.299423i
$776$	20.1463	+	17.6359i	0.723211	+	0.633093i
$777$	15.2949			0.548701
$778$	−6.50901	−	22.3066i	−0.233359	−	0.799730i
$779$	23.4927			0.841713
$780$	14.2912	−	9.11653i	0.511708	−	0.326424i
$781$			14.7079i			0.526291i
$782$	−4.06416	−	46.7671i	−0.145334	−	1.67239i
$783$			32.2487i			1.15247i
$784$	9.32536	−	20.0608i	0.333049	−	0.716458i
$785$	−2.54496			−0.0908337
$786$	−10.8135	+	3.15535i	−0.385704	+	0.112548i
$787$	−2.63565			−0.0939506			−0.0469753	−	0.998896i	$-0.514958\pi$
$787$	−2.63565			−0.0939506			−0.0469753	+	0.998896i	$0.514958\pi$
$788$	3.13280	−	1.99844i	0.111601	−	0.0711917i
$789$		−	32.3014i		−	1.14996i
$790$	−6.13121	−	21.0119i	−0.218139	−	0.747569i
$791$			33.0149i			1.17388i
$792$	−1.80690	+	2.06410i	−0.0642053	+	0.0733446i
$793$		−	48.4050i		−	1.71891i
$794$	0.788629	−	0.230120i	0.0279874	−	0.00816665i
$795$			10.9675i			0.388978i
$796$	−31.8539	+	20.3199i	−1.12903	+	0.720220i
$797$		−	47.3035i		−	1.67558i	−0.545996	−	0.837788i	$-0.683848\pi$
$797$		−	47.3035i		−	1.67558i	0.545996	−	0.837788i	$-0.316152\pi$
$798$	−7.30564	−	25.0367i	−0.258617	−	0.886289i
$799$	−2.26391			−0.0800912
$800$	0.852189	−	5.59230i	0.0301294	−	0.197718i
$801$			12.4557i			0.440102i
$802$	−3.34674	−	11.4694i	−0.118178	−	0.404999i
$803$	2.15859			0.0761749
$804$	5.92930	+	9.29488i	0.209110	+	0.327805i
$805$	−3.32663	+	16.6474i	−0.117248	+	0.586745i
$806$	19.0165	+	65.1702i	0.669827	+	2.29552i
$807$			11.1236i			0.391568i
$808$	11.9062	−	13.6009i	0.418857	−	0.478479i
$809$	−32.4597			−1.14122			−0.570611	−	0.821221i	$-0.693293\pi$
$809$	−32.4597			−1.14122			−0.570611	+	0.821221i	$0.693293\pi$
$810$	2.29869	+	7.87769i	0.0807677	+	0.276794i
$811$			24.2658i			0.852086i	0.904703	+	0.426043i	$0.140093\pi$
$811$			24.2658i			0.852086i	−0.904703	+	0.426043i	$0.859907\pi$
$812$	34.1123	−	21.7606i	1.19711	−	0.763646i
$813$	21.9884			0.771168
$814$	1.35256	+	4.63528i	0.0474073	+	0.162466i
$815$	−12.0811			−0.423184
$816$	−17.1761	+	36.9494i	−0.601282	+	1.29349i
$817$	15.2949			0.535100
$818$	−4.00700	+	1.16923i	−0.140102	+	0.0408813i
$819$	−17.0008			−0.594055
$820$	7.13839	+	11.1903i	0.249284	+	0.390781i
$821$	14.7107			0.513408			0.256704	−	0.966490i	$-0.417363\pi$
$821$	14.7107			0.513408			0.256704	+	0.966490i	$0.417363\pi$
$822$	−33.2623	+	9.70586i	−1.16016	+	0.338531i
$823$			13.4405i			0.468506i	0.972176	+	0.234253i	$0.0752644\pi$
$823$			13.4405i			0.468506i	−0.972176	+	0.234253i	$0.924736\pi$
$824$	−2.62121	+	2.99432i	−0.0913141	+	0.104312i
$825$			1.71164i			0.0595917i
$826$	−11.9374	−	40.9099i	−0.415355	−	1.42344i
$827$	−6.28210			−0.218450			−0.109225	−	0.994017i	$-0.534837\pi$
$827$	−6.28210			−0.218450			−0.109225	+	0.994017i	$0.534837\pi$
$828$	−7.45594	+	2.89702i	−0.259112	+	0.100678i
$829$	−28.2337			−0.980597			−0.490298	−	0.871555i	$-0.663112\pi$
$829$	−28.2337			−0.980597			−0.490298	+	0.871555i	$0.663112\pi$
$830$	−6.00000	−	20.5622i	−0.208263	−	0.713725i
$831$		−	14.4634i		−	0.501728i
$832$	−6.09538	−	45.6665i	−0.211319	−	1.58320i
$833$		−	38.2796i		−	1.32631i
$834$	−18.6660	+	5.44669i	−0.646350	+	0.188603i
$835$	−8.51278			−0.294597
$836$	6.94158	−	4.42810i	0.240079	−	0.153149i
$837$	−47.0345			−1.62575
$838$	−18.5166	+	5.40309i	−0.639644	+	0.186647i
$839$	30.2119			1.04303			0.521515	−	0.853242i	$-0.325367\pi$
$839$	30.2119			1.04303			0.521515	+	0.853242i	$0.325367\pi$
$840$	9.70586	−	11.0874i	0.334884	−	0.382553i
$841$	3.66345			0.126326
$842$	9.08817	+	31.1455i	0.313199	+	1.07334i
$843$	−8.49927			−0.292731
$844$	−10.7355	−	16.8292i	−0.369533	−	0.579286i
$845$			20.1653i			0.693708i
$846$	0.108058	+	0.370318i	0.00371510	+	0.0127318i
$847$	34.1506			1.17343
$848$	27.0303	+	12.5652i	0.928225	+	0.431489i
$849$		−	12.9963i		−	0.446032i
$850$	−2.74188	−	9.39651i	−0.0940457	−	0.322298i
$851$	−2.75896	+	13.8066i	−0.0945758	+	0.473285i
$852$	31.3835	−	20.0198i	1.07518	−	0.685868i
$853$	−19.2010			−0.657431			−0.328715	−	0.944429i	$-0.606616\pi$
$853$	−19.2010			−0.657431			−0.328715	+	0.944429i	$0.606616\pi$
$854$	−11.7865	−	40.3929i	−0.403327	−	1.38222i
$855$			2.95207i			0.100959i
$856$	8.04960	−	9.19542i	0.275130	−	0.314293i
$857$	57.6819			1.97038			0.985189	−	0.171472i	$-0.0548524\pi$
$857$	57.6819			1.97038			0.985189	+	0.171472i	$0.0548524\pi$
$858$	3.90488	+	13.3821i	0.133310	+	0.456859i
$859$			55.8795i			1.90658i	0.302052	+	0.953292i	$0.402328\pi$
$859$			55.8795i			1.90658i	−0.302052	+	0.953292i	$0.597672\pi$
$860$	4.64744	+	7.28541i	0.158476	+	0.248430i
$861$			34.5754i			1.17833i
$862$	−28.9234	+	8.43977i	−0.985134	+	0.287460i
$863$		−	35.1360i		−	1.19604i	−0.801480	−	0.598021i	$-0.795954\pi$
$863$		−	35.1360i		−	1.19604i	0.801480	−	0.598021i	$-0.204046\pi$
$864$	31.5552	+	4.80858i	1.07353	+	0.163591i
$865$		−	6.92143i		−	0.235336i
$866$	8.44952	+	28.9568i	0.287126	+	0.983992i
$867$			45.4861i			1.54479i
$868$	31.7377	+	49.7526i	1.07725	+	1.68871i
$869$	18.0000			0.610608
$870$	11.4192	−	3.33210i	0.387147	−	0.112969i
$871$	−21.5704			−0.730884
$872$	−0.279248	−	0.244452i	−0.00945654	−	0.00827819i
$873$		−	7.89451i		−	0.267189i
$874$	23.9183	−	2.07855i	0.809050	−	0.0703080i
$875$			3.53986i			0.119669i
$876$	−2.93818	−	4.60595i	−0.0992720	−	0.155621i
$877$	−24.7643			−0.836230			−0.418115	−	0.908394i	$-0.637309\pi$
$877$	−24.7643			−0.836230			−0.418115	+	0.908394i	$0.637309\pi$
$878$	−4.14993	−	14.2220i	−0.140054	−	0.479968i
$879$	3.60330			0.121536
$880$	4.21848	+	1.96098i	0.142205	+	0.0661045i
$881$			7.84285i			0.264232i	0.991234	+	0.132116i	$0.0421772\pi$
$881$			7.84285i			0.264232i	−0.991234	+	0.132116i	$0.957823\pi$
$882$	−6.26157	+	1.82711i	−0.210838	+	0.0615221i
$883$			2.88449i			0.0970708i	0.998821	+	0.0485354i	$0.0154554\pi$
$883$			2.88449i			0.0970708i	−0.998821	+	0.0485354i	$0.984545\pi$
$884$	−42.8737	−	67.2096i	−1.44200	−	2.26050i
$885$		−	12.5287i		−	0.421147i
$886$	−4.99826	−	17.1292i	−0.167920	−	0.575467i
$887$		−	27.8673i		−	0.935691i	−0.883810	−	0.467846i	$-0.845030\pi$
$887$		−	27.8673i		−	0.935691i	0.883810	−	0.467846i	$-0.154970\pi$
$888$	8.04960	−	9.19542i	0.270127	−	0.308578i
$889$		−	35.8398i		−	1.20203i
$890$	20.2768	−	5.91672i	0.679680	−	0.198329i
$891$	−6.74849			−0.226083
$892$	13.0612	+	20.4750i	0.437321	+	0.685552i
$893$		−	1.15784i		−	0.0387456i
$894$	38.1541	−	11.1333i	1.27607	−	0.372353i
$895$	5.41204			0.180904
$896$	−16.2062	−	36.6234i	−0.541410	−	1.22350i
$897$	−7.96517	+	39.8600i	−0.265949	+	1.33089i
$898$	18.6580	−	5.44436i	0.622625	−	0.181681i
$899$			47.6395i			1.58887i
$900$	−1.40616	+	0.897004i	−0.0468720	+	0.0299001i
$901$	51.5786			1.71833
$902$	−10.4784	+	3.05758i	−0.348894	+	0.101806i
$903$			22.5102i			0.749094i
$904$	19.8489	+	17.3756i	0.660164	+	0.577903i
$905$	−16.5508			−0.550167
$906$	−8.40764	+	2.45333i	−0.279325	+	0.0815064i
$907$	−34.2014			−1.13564			−0.567820	−	0.823153i	$-0.692213\pi$
$907$	−34.2014			−1.13564			−0.567820	+	0.823153i	$0.692213\pi$
$908$	−46.5718	+	29.7086i	−1.54554	+	0.985915i
$909$	−5.32964			−0.176773
$910$	8.07570	+	27.6757i	0.267707	+	0.917441i
$911$	22.6587			0.750716			0.375358	−	0.926880i	$-0.377520\pi$
$911$	22.6587			0.750716			0.375358	+	0.926880i	$0.377520\pi$
$912$	−18.8972	−	8.78443i	−0.625748	−	0.290882i
$913$	17.6148			0.582964
$914$	−1.51094	−	5.17803i	−0.0499774	−	0.171274i
$915$		−	12.3704i		−	0.408951i
$916$	−2.87549	−	4.50768i	−0.0950090	−	0.148938i
$917$		−	19.1578i		−	0.632648i
$918$	53.0209	−	15.4714i	1.74995	−	0.510631i
$919$	16.5070			0.544516			0.272258	−	0.962224i	$-0.412230\pi$
$919$	16.5070			0.544516			0.272258	+	0.962224i	$0.412230\pi$
$920$	8.25780	+	10.7614i	0.272252	+	0.354794i
$921$	31.2085			1.02835
$922$	−33.4620	+	9.76414i	−1.10201	+	0.321565i
$923$			72.8308i			2.39725i
$924$	6.51706	+	10.2163i	0.214396	+	0.336091i
$925$			2.93580i			0.0965284i
$926$	−16.4845	−	56.4928i	−0.541713	−	1.85647i
$927$	1.17335			0.0385379
$928$	4.87043	−	31.9611i	0.159880	−	1.04917i
$929$	46.2688			1.51803			0.759015	−	0.651073i	$-0.225681\pi$
$929$	46.2688			1.51803			0.759015	+	0.651073i	$0.225681\pi$
$930$	4.85985	+	16.6549i	0.159361	+	0.546134i
$931$	19.5775			0.641627
$932$	−32.4571	+	20.7047i	−1.06317	+	0.678206i
$933$	13.9987			0.458296
$934$	7.01214	−	2.04612i	0.229444	−	0.0669512i
$935$	8.04960			0.263250
$936$	−8.94740	+	10.2210i	−0.292455	+	0.334084i
$937$			56.3876i			1.84210i	0.389441	+	0.921051i	$0.372668\pi$
$937$			56.3876i			1.84210i	−0.389441	+	0.921051i	$0.627332\pi$
$938$	−18.0000	+	5.25236i	−0.587721	+	0.171495i
$939$	−24.5009			−0.799556
$940$	0.551514	−	0.351816i	0.0179884	−	0.0114750i
$941$			39.6971i			1.29409i	0.762453	+	0.647044i	$0.223995\pi$
$941$			39.6971i			1.29409i	−0.762453	+	0.647044i	$0.776005\pi$
$942$	−5.08495	+	1.48378i	−0.165677	+	0.0483440i
$943$	−31.2111	−	6.23686i	−1.01637	−	0.203100i
$944$	−30.8780	−	14.3537i	−1.00499	−	0.467174i
$945$	−19.9741			−0.649756
$946$	−6.82197	+	1.99063i	−0.221801	+	0.0647211i
$947$		−	16.6941i		−	0.542484i	−0.962511	−	0.271242i	$-0.912566\pi$
$947$		−	16.6941i		−	0.542484i	0.962511	−	0.271242i	$-0.0874344\pi$
$948$	−24.5009	−	38.4080i	−0.795751	−	1.24743i
$949$	10.6889			0.346977
$950$	4.80570	−	1.40229i	0.155918	−	0.0454964i
$951$		−	3.55244i		−	0.115196i
$952$	−52.1426	−	45.6453i	−1.68995	−	1.47937i
$953$			2.39477i			0.0775742i	0.999247	+	0.0387871i	$0.0123494\pi$
$953$			2.39477i			0.0775742i	−0.999247	+	0.0387871i	$0.987651\pi$
$954$	−2.46188	−	8.43696i	−0.0797064	−	0.273157i
$955$		−	15.1460i		−	0.490114i
$956$	−13.5905	−	21.3047i	−0.439548	−	0.689044i
$957$			9.78236i			0.316219i
$958$	−3.03932	+	0.886865i	−0.0981959	+	0.0286533i
$959$		−	58.9296i		−	1.90293i
$960$	−1.55773	−	11.6705i	−0.0502756	−	0.376664i
$961$	−38.4819			−1.24135
$962$	6.69762	+	22.9530i	0.215940	+	0.740034i
$963$	−3.60330			−0.116115
$964$	−5.89514	−	9.24133i	−0.189870	−	0.297643i
$965$			25.3739i			0.816815i
$966$	3.05911	+	35.2018i	0.0984251	+	1.13260i
$967$			27.1960i			0.874563i	0.899325	+	0.437282i	$0.144059\pi$
$967$			27.1960i			0.874563i	−0.899325	+	0.437282i	$0.855941\pi$
$968$	17.9732	−	20.5316i	0.577681	−	0.659911i
$969$	−36.0592			−1.15839
$970$	−12.8515	+	3.75005i	−0.412638	+	0.120407i
$971$	24.7066			0.792871			0.396436	−	0.918063i	$-0.370247\pi$
$971$	24.7066			0.792871			0.396436	+	0.918063i	$0.370247\pi$
$972$	−9.02195	−	14.1430i	−0.289379	−	0.453636i
$973$		−	33.0698i		−	1.06017i
$974$	12.0166	+	41.1814i	0.385038	+	1.31954i
$975$			8.47571i			0.271440i
$976$	−30.4878	−	14.1724i	−0.975889	−	0.453646i
$977$		−	25.3686i		−	0.811614i	−0.913959	−	0.405807i	$-0.866991\pi$
$977$		−	25.3686i		−	0.811614i	0.913959	−	0.405807i	$-0.133009\pi$
$978$	−24.1386	+	7.04359i	−0.771868	+	0.225229i
$979$			17.3703i			0.555157i
$980$	5.94874	+	9.32536i	0.190026	+	0.297888i
$981$			0.109426i			0.00349370i
$982$	9.22834	+	31.6258i	0.294488	+	1.00922i
$983$	−50.6994			−1.61706			−0.808530	−	0.588454i	$-0.799737\pi$
$983$	−50.6994			−1.61706			−0.808530	+	0.588454i	$0.799737\pi$
$984$	20.7870	+	18.1968i	0.662666	+	0.580093i
$985$			1.85797i			0.0591998i
$986$	−15.6704	−	53.7029i	−0.499046	−	1.71025i
$987$	1.70405			0.0542405
$988$	34.3733	−	21.9271i	1.09356	−	0.697594i
$989$	−20.3199	−	4.06049i	−0.646135	−	0.129116i
$990$	−0.384213	−	1.31671i	−0.0122111	−	0.0418478i
$991$		−	13.9029i		−	0.441639i	−0.975315	−	0.220820i	$-0.929127\pi$
$991$		−	13.9029i		−	0.441639i	0.975315	−	0.220820i	$-0.0708732\pi$
$992$	46.6150	+	7.10349i	1.48003	+	0.225536i
$993$	10.9902			0.348763
$994$	17.7342	+	60.7757i	0.562494	+	1.92769i
$995$		−	18.8916i		−	0.598903i
$996$	−23.9765	−	37.5860i	−0.759725	−	1.19096i
$997$	−11.8776			−0.376168			−0.188084	−	0.982153i	$-0.560228\pi$
$997$	−11.8776			−0.376168			−0.188084	+	0.982153i	$0.560228\pi$
$998$	8.95244	+	30.6803i	0.283384	+	0.971168i
$999$	−16.5656			−0.524112

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.e.a.91.4	yes	16
4.3	odd	2	inner	460.2.e.a.91.2	yes	16
23.22	odd	2	inner	460.2.e.a.91.3	yes	16
92.91	even	2	inner	460.2.e.a.91.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.e.a.91.1	✓	16	92.91	even	2	inner
460.2.e.a.91.2	yes	16	4.3	odd	2	inner
460.2.e.a.91.3	yes	16	23.22	odd	2	inner
460.2.e.a.91.4	yes	16	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35760 + 0.396143i) q^{2} -1.47175i q^{3} +(1.68614 - 1.07561i) q^{4} +1.00000i q^{5} +(0.583024 + 1.99804i) q^{6} -3.53986 q^{7} +(-1.86301 + 2.12819i) q^{8} +0.833952 q^{9} +O(q^{10})\)	\(q+(-1.35760 + 0.396143i) q^{2} -1.47175i q^{3} +(1.68614 - 1.07561i) q^{4} +1.00000i q^{5} +(0.583024 + 1.99804i) q^{6} -3.53986 q^{7} +(-1.86301 + 2.12819i) q^{8} +0.833952 q^{9} +(-0.396143 - 1.35760i) q^{10} +1.16300 q^{11} +(-1.58302 - 2.48158i) q^{12} +5.75893 q^{13} +(4.80570 - 1.40229i) q^{14} +1.47175 q^{15} +(1.68614 - 3.62725i) q^{16} -6.92143i q^{17} +(-1.13217 + 0.330364i) q^{18} +3.53986 q^{19} +(1.07561 + 1.68614i) q^{20} +5.20979i q^{21} +(-1.57888 + 0.460714i) q^{22} +(-4.70285 - 0.939764i) q^{23} +(3.13217 + 2.74188i) q^{24} -1.00000 q^{25} +(-7.81831 + 2.28136i) q^{26} -5.64262i q^{27} +(-5.96870 + 3.80749i) q^{28} -5.71519 q^{29} +(-1.99804 + 0.583024i) q^{30} -8.33558i q^{31} +(-0.852189 + 5.59230i) q^{32} -1.71164i q^{33} +(2.74188 + 9.39651i) q^{34} -3.53986i q^{35} +(1.40616 - 0.897004i) q^{36} -2.93580i q^{37} +(-4.80570 + 1.40229i) q^{38} -8.47571i q^{39} +(-2.12819 - 1.86301i) q^{40} +6.63662 q^{41} +(-2.06382 - 7.07279i) q^{42} +4.32076 q^{43} +(1.96098 - 1.25093i) q^{44} +0.833952i q^{45} +(6.75686 - 0.587185i) q^{46} -0.327086i q^{47} +(-5.33840 - 2.48158i) q^{48} +5.53059 q^{49} +(1.35760 - 0.396143i) q^{50} -10.1866 q^{51} +(9.71037 - 6.19435i) q^{52} +7.45202i q^{53} +(2.23529 + 7.66040i) q^{54} +1.16300i q^{55} +(6.59477 - 7.53351i) q^{56} -5.20979i q^{57} +(7.75893 - 2.26404i) q^{58} -8.51278i q^{59} +(2.48158 - 1.58302i) q^{60} -8.40520i q^{61} +(3.30209 + 11.3164i) q^{62} -2.95207 q^{63} +(-1.05842 - 7.92967i) q^{64} +5.75893i q^{65} +(0.678055 + 2.32372i) q^{66} -3.74555 q^{67} +(-7.44473 - 11.6705i) q^{68} +(-1.38310 + 6.92143i) q^{69} +(1.40229 + 4.80570i) q^{70} +12.6466i q^{71} +(-1.55366 + 1.77481i) q^{72} +1.85606 q^{73} +(1.16300 + 3.98563i) q^{74} +1.47175i q^{75} +(5.96870 - 3.80749i) q^{76} -4.11684 q^{77} +(3.35760 + 11.5066i) q^{78} +15.4773 q^{79} +(3.62725 + 1.68614i) q^{80} -5.80267 q^{81} +(-9.00986 + 2.62905i) q^{82} +15.1460 q^{83} +(5.60368 + 8.78443i) q^{84} +6.92143 q^{85} +(-5.86585 + 1.71164i) q^{86} +8.41134i q^{87} +(-2.16667 + 2.47508i) q^{88} +14.9358i q^{89} +(-0.330364 - 1.13217i) q^{90} -20.3858 q^{91} +(-8.94049 + 3.47385i) q^{92} -12.2679 q^{93} +(0.129573 + 0.444052i) q^{94} +3.53986i q^{95} +(8.23046 + 1.25421i) q^{96} -9.46639i q^{97} +(-7.50832 + 2.19091i) q^{98} +0.969883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9} - 30 q^{12} + 4 q^{13} + 4 q^{16} + 30 q^{18} + 2 q^{24} - 16 q^{25} - 54 q^{26} - 48 q^{29} + 34 q^{36} - 36 q^{41} - 40 q^{46} + 18 q^{48} + 68 q^{49} + 34 q^{52} - 40 q^{54} + 36 q^{58} + 6 q^{62} + 52 q^{64} + 40 q^{69} + 42 q^{70} - 78 q^{72} + 8 q^{73} + 72 q^{77} + 32 q^{78} + 40 q^{81} - 42 q^{82} + 12 q^{85} - 120 q^{93} + 20 q^{94} - 22 q^{96} - 18 q^{98}+O(q^{100}) \) 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9 - 30 * q^12 + 4 * q^13 + 4 * q^16 + 30 * q^18 + 2 * q^24 - 16 * q^25 - 54 * q^26 - 48 * q^29 + 34 * q^36 - 36 * q^41 - 40 * q^46 + 18 * q^48 + 68 * q^49 + 34 * q^52 - 40 * q^54 + 36 * q^58 + 6 * q^62 + 52 * q^64 + 40 * q^69 + 42 * q^70 - 78 * q^72 + 8 * q^73 + 72 * q^77 + 32 * q^78 + 40 * q^81 - 42 * q^82 + 12 * q^85 - 120 * q^93 + 20 * q^94 - 22 * q^96 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more