LMFDB - Embedded newform 460.2.e.a.91.13

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			91.13
Root			$0.0786378 - 1.41203i$ of defining polynomial
Character	$\chi$	$=$	460.91
Dual form			460.2.e.a.91.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35760 - 0.396143i) q^{2} -0.679463i q^{3} +(1.68614 - 1.07561i) q^{4} -1.00000i q^{5} +(-0.269165 - 0.922437i) q^{6} +1.16300 q^{7} +(1.86301 - 2.12819i) q^{8} +2.53833 q^{9} +O(q^{10})$	\(q+(1.35760 - 0.396143i) q^{2} -0.679463i q^{3} +(1.68614 - 1.07561i) q^{4} -1.00000i q^{5} +(-0.269165 - 0.922437i) q^{6} +1.16300 q^{7} +(1.86301 - 2.12819i) q^{8} +2.53833 q^{9} +(-0.396143 - 1.35760i) q^{10} -3.53986 q^{11} +(-0.730835 - 1.14567i) q^{12} -2.38665 q^{13} +(1.57888 - 0.460714i) q^{14} -0.679463 q^{15} +(1.68614 - 3.62725i) q^{16} +3.19542i q^{17} +(3.44603 - 1.00554i) q^{18} -1.16300 q^{19} +(-1.07561 - 1.68614i) q^{20} -0.790214i q^{21} +(-4.80570 + 1.40229i) q^{22} +(4.70285 + 0.939764i) q^{23} +(-1.44603 - 1.26584i) q^{24} -1.00000 q^{25} +(-3.24011 + 0.945456i) q^{26} -3.76309i q^{27} +(1.96098 - 1.25093i) q^{28} -0.284805 q^{29} +(-0.922437 + 0.269165i) q^{30} +4.43358i q^{31} +(0.852189 - 5.59230i) q^{32} +2.40520i q^{33} +(1.26584 + 4.33809i) q^{34} -1.16300i q^{35} +(4.27998 - 2.73024i) q^{36} -8.93580i q^{37} +(-1.57888 + 0.460714i) q^{38} +1.62164i q^{39} +(-2.12819 - 1.86301i) q^{40} -2.51978 q^{41} +(-0.313038 - 1.07279i) q^{42} +6.07154 q^{43} +(-5.96870 + 3.80749i) q^{44} -2.53833i q^{45} +(6.75686 - 0.587185i) q^{46} +13.2344i q^{47} +(-2.46458 - 1.14567i) q^{48} -5.64744 q^{49} +(-1.35760 + 0.396143i) q^{50} +2.17117 q^{51} +(-4.02423 + 2.56710i) q^{52} +7.45202i q^{53} +(-1.49072 - 5.10876i) q^{54} +3.53986i q^{55} +(2.16667 - 2.47508i) q^{56} +0.790214i q^{57} +(-0.386651 + 0.112824i) q^{58} +8.51278i q^{59} +(-1.14567 + 0.730835i) q^{60} +7.71164i q^{61} +(1.75634 + 6.01902i) q^{62} +2.95207 q^{63} +(-1.05842 - 7.92967i) q^{64} +2.38665i q^{65} +(0.952806 + 3.26530i) q^{66} -11.4005 q^{67} +(3.43701 + 5.38792i) q^{68} +(0.638535 - 3.19542i) q^{69} +(-0.460714 - 1.57888i) q^{70} +1.46199i q^{71} +(4.72892 - 5.40206i) q^{72} +4.88851 q^{73} +(-3.53986 - 12.1312i) q^{74} +0.679463i q^{75} +(-1.96098 + 1.25093i) q^{76} -4.11684 q^{77} +(0.642403 + 2.20154i) q^{78} -5.08495 q^{79} +(-3.62725 - 1.68614i) q^{80} +5.05811 q^{81} +(-3.42084 + 0.998194i) q^{82} +15.1460 q^{83} +(-0.849959 - 1.33241i) q^{84} +3.19542 q^{85} +(8.24271 - 2.40520i) q^{86} +0.193515i q^{87} +(-6.59477 + 7.53351i) q^{88} -3.06420i q^{89} +(-1.00554 - 3.44603i) q^{90} -2.77567 q^{91} +(8.94049 - 3.47385i) q^{92} +3.01246 q^{93} +(5.24271 + 17.9669i) q^{94} +1.16300i q^{95} +(-3.79976 - 0.579031i) q^{96} -13.5832i q^{97} +(-7.66695 + 2.23720i) q^{98} -8.98533 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
$3$		−	0.679463i		−	0.392288i	−0.980575	−	0.196144i	$-0.937158\pi$
$3$		−	0.679463i		−	0.392288i	0.980575	−	0.196144i	$-0.0628420\pi$
$4$	1.68614	−	1.07561i	0.843070	−	0.537803i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.269165	−	0.922437i	−0.109886	−	0.376583i
$7$	1.16300			0.439572			0.219786	−	0.975548i	$-0.429464\pi$
$7$	1.16300			0.439572			0.219786	+	0.975548i	$0.429464\pi$
$8$	1.86301	−	2.12819i	0.658672	−	0.752430i
$9$	2.53833			0.846110
$10$	−0.396143	−	1.35760i	−0.125272	−	0.429310i
$11$	−3.53986			−1.06731			−0.533654	−	0.845703i	$-0.679181\pi$
$11$	−3.53986			−1.06731			−0.533654	+	0.845703i	$0.679181\pi$
$12$	−0.730835	−	1.14567i	−0.210974	−	0.330727i
$13$	−2.38665			−0.661938			−0.330969	−	0.943642i	$-0.607376\pi$
$13$	−2.38665			−0.661938			−0.330969	+	0.943642i	$0.607376\pi$
$14$	1.57888	−	0.460714i	0.421974	−	0.123131i
$15$	−0.679463			−0.175437
$16$	1.68614	−	3.62725i	0.421535	−	0.906812i
$17$			3.19542i			0.775002i	0.921869	+	0.387501i	$0.126662\pi$
$17$			3.19542i			0.775002i	−0.921869	+	0.387501i	$0.873338\pi$
$18$	3.44603	−	1.00554i	0.812237	−	0.237009i
$19$	−1.16300			−0.266810			−0.133405	−	0.991062i	$-0.542591\pi$
$19$	−1.16300			−0.266810			−0.133405	+	0.991062i	$0.542591\pi$
$20$	−1.07561	−	1.68614i	−0.240513	−	0.377033i
$21$		−	0.790214i		−	0.172439i
$22$	−4.80570	+	1.40229i	−1.02458	+	0.298970i
$23$	4.70285	+	0.939764i	0.980613	+	0.195954i
$23$	4.70285	+	0.939764i	0.980613	+	0.195954i
$24$	−1.44603	−	1.26584i	−0.295170	−	0.258389i
$25$	−1.00000			−0.200000
$26$	−3.24011	+	0.945456i	−0.635438	+	0.185419i
$27$		−	3.76309i		−	0.724207i
$28$	1.96098	−	1.25093i	0.370590	−	0.236403i
$29$	−0.284805			−0.0528870			−0.0264435	−	0.999650i	$-0.508418\pi$
$29$	−0.284805			−0.0528870			−0.0264435	+	0.999650i	$0.508418\pi$
$30$	−0.922437	+	0.269165i	−0.168413	+	0.0491426i
$31$			4.43358i			0.796295i	0.917321	+	0.398148i	$0.130347\pi$
$31$			4.43358i			0.796295i	−0.917321	+	0.398148i	$0.869653\pi$
$32$	0.852189	−	5.59230i	0.150647	−	0.988588i
$33$			2.40520i			0.418692i
$34$	1.26584	+	4.33809i	0.217090	+	0.743976i
$35$		−	1.16300i		−	0.196582i
$36$	4.27998	−	2.73024i	0.713330	−	0.455041i
$37$		−	8.93580i		−	1.46904i	−0.678589	−	0.734518i	$-0.737408\pi$
$37$		−	8.93580i		−	1.46904i	0.678589	−	0.734518i	$-0.262592\pi$
$38$	−1.57888	+	0.460714i	−0.256128	+	0.0747376i
$39$			1.62164i			0.259670i
$40$	−2.12819	−	1.86301i	−0.336497	−	0.294567i
$41$	−2.51978			−0.393523			−0.196762	−	0.980451i	$-0.563042\pi$
$41$	−2.51978			−0.393523			−0.196762	+	0.980451i	$0.563042\pi$
$42$	−0.313038	−	1.07279i	−0.0483028	−	0.165535i
$43$	6.07154			0.925902			0.462951	−	0.886384i	$-0.346791\pi$
$43$	6.07154			0.925902			0.462951	+	0.886384i	$0.346791\pi$
$44$	−5.96870	+	3.80749i	−0.899815	+	0.574001i
$45$		−	2.53833i		−	0.378392i
$46$	6.75686	−	0.587185i	0.996245	−	0.0865756i
$47$			13.2344i			1.93043i	0.261456	+	0.965215i	$0.415797\pi$
$47$			13.2344i			1.93043i	−0.261456	+	0.965215i	$0.584203\pi$
$48$	−2.46458	−	1.14567i	−0.355732	−	0.165363i
$49$	−5.64744			−0.806777
$50$	−1.35760	+	0.396143i	−0.191993	+	0.0560232i
$51$	2.17117			0.304024
$52$	−4.02423	+	2.56710i	−0.558060	+	0.355992i
$53$			7.45202i			1.02361i	0.859100	+	0.511807i	$0.171024\pi$
$53$			7.45202i			1.02361i	−0.859100	+	0.511807i	$0.828976\pi$
$54$	−1.49072	−	5.10876i	−0.202862	−	0.695214i
$55$			3.53986i			0.477314i
$56$	2.16667	−	2.47508i	0.289533	−	0.330747i
$57$			0.790214i			0.104666i
$58$	−0.386651	+	0.112824i	−0.0507698	+	0.0148145i
$59$			8.51278i			1.10827i	0.832427	+	0.554135i	$0.186951\pi$
$59$			8.51278i			1.10827i	−0.832427	+	0.554135i	$0.813049\pi$
$60$	−1.14567	+	0.730835i	−0.147905	+	0.0943504i
$61$			7.71164i			0.987374i	0.869640	+	0.493687i	$0.164351\pi$
$61$			7.71164i			0.987374i	−0.869640	+	0.493687i	$0.835649\pi$
$62$	1.75634	+	6.01902i	0.223055	+	0.764416i
$63$	2.95207			0.371926
$64$	−1.05842	−	7.92967i	−0.132303	−	0.991209i
$65$			2.38665i			0.296028i
$66$	0.952806	+	3.26530i	0.117282	+	0.401930i
$67$	−11.4005			−1.39279			−0.696395	−	0.717659i	$-0.745214\pi$
$67$	−11.4005			−1.39279			−0.696395	+	0.717659i	$0.745214\pi$
$68$	3.43701	+	5.38792i	0.416799	+	0.653382i
$69$	0.638535	−	3.19542i	0.0768706	−	0.384683i
$70$	−0.460714	−	1.57888i	−0.0550658	−	0.188712i
$71$			1.46199i			0.173506i	0.996230	+	0.0867529i	$0.0276491\pi$
$71$			1.46199i			0.173506i	−0.996230	+	0.0867529i	$0.972351\pi$
$72$	4.72892	−	5.40206i	0.557309	−	0.636639i
$73$	4.88851			0.572156			0.286078	−	0.958206i	$-0.407648\pi$
$73$	4.88851			0.572156			0.286078	+	0.958206i	$0.407648\pi$
$74$	−3.53986	−	12.1312i	−0.411500	−	1.41022i
$75$			0.679463i			0.0784576i
$76$	−1.96098	+	1.25093i	−0.224939	+	0.143491i
$77$	−4.11684			−0.469158
$78$	0.642403	+	2.20154i	0.0727378	+	0.249275i
$79$	−5.08495			−0.572102			−0.286051	−	0.958214i	$-0.592343\pi$
$79$	−5.08495			−0.572102			−0.286051	+	0.958214i	$0.592343\pi$
$80$	−3.62725	−	1.68614i	−0.405539	−	0.188516i
$81$	5.05811			0.562012
$82$	−3.42084	+	0.998194i	−0.377769	+	0.110232i
$83$	15.1460			1.66249			0.831246	−	0.555904i	$-0.187628\pi$
$83$	15.1460			1.66249			0.831246	+	0.555904i	$0.187628\pi$
$84$	−0.849959	−	1.33241i	−0.0927381	−	0.145378i
$85$	3.19542			0.346592
$86$	8.24271	−	2.40520i	0.888835	−	0.259360i
$87$			0.193515i			0.0207470i
$88$	−6.59477	+	7.53351i	−0.703005	+	0.803074i
$89$		−	3.06420i		−	0.324805i	−0.986725	−	0.162402i	$-0.948076\pi$
$89$		−	3.06420i		−	0.324805i	0.986725	−	0.162402i	$-0.0519243\pi$
$90$	−1.00554	−	3.44603i	−0.105994	−	0.363243i
$91$	−2.77567			−0.290969
$92$	8.94049	−	3.47385i	0.932111	−	0.362174i
$93$	3.01246			0.312377
$94$	5.24271	+	17.9669i	0.540744	+	1.85315i
$95$			1.16300i			0.119321i
$96$	−3.79976	−	0.579031i	−0.387811	−	0.0590971i
$97$		−	13.5832i		−	1.37917i	−0.724205	−	0.689584i	$-0.757793\pi$
$97$		−	13.5832i		−	1.37917i	0.724205	−	0.689584i	$-0.242207\pi$
$98$	−7.66695	+	2.23720i	−0.774479	+	0.225991i
$99$	−8.98533			−0.903059
$100$	−1.68614	+	1.07561i	−0.168614	+	0.107561i
$101$	−13.8429			−1.37742			−0.688708	−	0.725039i	$-0.741822\pi$
$101$	−13.8429			−1.37742			−0.688708	+	0.725039i	$0.741822\pi$
$102$	2.94757	−	0.860094i	0.291853	−	0.0851620i
$103$	11.3622			1.11955			0.559775	−	0.828645i	$-0.310888\pi$
$103$	11.3622			1.11955			0.559775	+	0.828645i	$0.310888\pi$
$104$	−4.44634	+	5.07926i	−0.436000	+	0.498062i
$105$	−0.790214			−0.0771169
$106$	2.95207	+	10.1168i	0.286730	+	0.982635i
$107$	−6.07154			−0.586958			−0.293479	−	0.955965i	$-0.594813\pi$
$107$	−6.07154			−0.586958			−0.293479	+	0.955965i	$0.594813\pi$
$108$	−4.04761	−	6.34510i	−0.389481	−	0.610558i
$109$			8.01437i			0.767637i	0.923408	+	0.383819i	$0.125391\pi$
$109$			8.01437i			0.767637i	−0.923408	+	0.383819i	$0.874609\pi$
$110$	1.40229	+	4.80570i	0.133703	+	0.458206i
$111$	−6.07154			−0.576286
$112$	1.96098	−	4.21848i	0.185295	−	0.398609i
$113$			4.90706i			0.461617i	0.972999	+	0.230809i	$0.0741371\pi$
$113$			4.90706i			0.461617i	−0.972999	+	0.230809i	$0.925863\pi$
$114$	0.313038	+	1.07279i	0.0293187	+	0.100476i
$115$	0.939764	−	4.70285i	0.0876334	−	0.438543i
$116$	−0.480222	+	0.306339i	−0.0445875	+	0.0284428i
$117$	−6.05811			−0.560072
$118$	3.37228	+	11.5569i	0.310444	+	1.06390i
$119$			3.71626i			0.340669i
$120$	−1.26584	+	1.44603i	−0.115555	+	0.132004i
$121$	1.53059			0.139145
$122$	3.05492	+	10.4693i	0.276579	+	0.947846i
$123$			1.71210i			0.154375i
$124$	4.76879	+	7.47565i	0.428250	+	0.671333i
$125$			1.00000i			0.0894427i
$126$	4.00772	−	1.16944i	0.357036	−	0.104182i
$127$		−	5.02137i		−	0.445575i	−0.974867	−	0.222787i	$-0.928484\pi$
$127$		−	5.02137i		−	0.445575i	0.974867	−	0.222787i	$-0.0715156\pi$
$128$	−4.57820	−	10.3460i	−0.404660	−	0.914467i
$129$		−	4.12539i		−	0.363220i
$130$	0.945456	+	3.24011i	0.0829220	+	0.284177i
$131$			2.24289i			0.195962i	0.995188	+	0.0979810i	$0.0312385\pi$
$131$			2.24289i			0.195962i	−0.995188	+	0.0979810i	$0.968762\pi$
$132$	2.58705	+	4.05551i	0.225174	+	0.352987i
$133$	−1.35256			−0.117282
$134$	−15.4773	+	4.51622i	−1.33703	+	0.390142i
$135$	−3.76309			−0.323875
$136$	6.80047	+	5.95308i	0.583135	+	0.510472i
$137$		−	5.46941i		−	0.467283i	−0.972323	−	0.233641i	$-0.924936\pi$
$137$		−	5.46941i		−	0.467283i	0.972323	−	0.233641i	$-0.0750642\pi$
$138$	−0.398970	−	4.59104i	−0.0339626	−	0.390815i
$139$		−	16.1962i		−	1.37374i	−0.726779	−	0.686872i	$-0.758983\pi$
$139$		−	16.1962i		−	1.37374i	0.726779	−	0.686872i	$-0.241017\pi$
$140$	−1.25093	−	1.96098i	−0.105723	−	0.165733i
$141$	8.99226			0.757285
$142$	0.579156	+	1.98479i	0.0486017	+	0.166560i
$143$	8.44841			0.706491
$144$	4.27998	−	9.20715i	0.356665	−	0.767263i
$145$			0.284805i			0.0236518i
$146$	6.63662	−	1.93655i	0.549251	−	0.160270i
$147$			3.83723i			0.316489i
$148$	−9.61140	−	15.0670i	−0.790052	−	1.23850i
$149$		−	17.2126i		−	1.41011i	−0.709152	−	0.705055i	$-0.750922\pi$
$149$		−	17.2126i		−	1.41011i	0.709152	−	0.705055i	$-0.249078\pi$
$150$	0.269165	+	0.922437i	0.0219772	+	0.0753167i
$151$		−	3.80751i		−	0.309851i	−0.987926	−	0.154925i	$-0.950486\pi$
$151$		−	3.80751i		−	0.309851i	0.987926	−	0.154925i	$-0.0495137\pi$
$152$	−2.16667	+	2.47508i	−0.175740	+	0.200756i
$153$			8.11102i			0.655737i
$154$	−5.58902	+	1.63086i	−0.450376	+	0.131419i
$155$	4.43358			0.356114
$156$	1.74425	+	2.73432i	0.139652	+	0.218920i
$157$			16.7787i			1.33908i	0.742775	+	0.669541i	$0.233509\pi$
$157$			16.7787i			1.33908i	−0.742775	+	0.669541i	$0.766491\pi$
$158$	−6.90331	+	2.01437i	−0.549198	+	0.160255i
$159$	5.06337			0.401552
$160$	−5.59230	−	0.852189i	−0.442110	−	0.0673715i
$161$	5.46941	+	1.09294i	0.431050	+	0.0861359i
$162$	6.86687	−	2.00374i	0.539513	−	0.157428i
$163$		−	15.8341i		−	1.24022i	−0.784515	−	0.620110i	$-0.787088\pi$
$163$		−	15.8341i		−	1.24022i	0.784515	−	0.620110i	$-0.212912\pi$
$164$	−4.24870	+	2.71029i	−0.331768	+	0.211638i
$165$	2.40520			0.187245
$166$	20.5622	−	6.00000i	1.59594	−	0.465690i
$167$		−	8.51278i		−	0.658738i	−0.944201	−	0.329369i	$-0.893164\pi$
$167$		−	8.51278i		−	0.658738i	0.944201	−	0.329369i	$-0.106836\pi$
$168$	−1.68173	−	1.47217i	−0.129748	−	0.113581i
$169$	−7.30390			−0.561838
$170$	4.33809	−	1.26584i	0.332716	−	0.0970858i
$171$	−2.95207			−0.225750
$172$	10.2375	−	6.53059i	0.780600	−	0.497953i
$173$	−3.19542			−0.242943			−0.121472	−	0.992595i	$-0.538761\pi$
$173$	−3.19542			−0.242943			−0.121472	+	0.992595i	$0.538761\pi$
$174$	0.0766596	+	0.262715i	0.00581155	+	0.0199164i
$175$	−1.16300			−0.0879143
$176$	−5.96870	+	12.8399i	−0.449908	+	0.967847i
$177$	5.78412			0.434761
$178$	−1.21386	−	4.15995i	−0.0909830	−	0.311802i
$179$		−	2.24289i		−	0.167641i	−0.996481	−	0.0838207i	$-0.973288\pi$
$179$		−	2.24289i		−	0.167641i	0.996481	−	0.0838207i	$-0.0267123\pi$
$180$	−2.73024	−	4.27998i	−0.203500	−	0.319011i
$181$			0.433943i			0.0322547i	0.999870	+	0.0161274i	$0.00513372\pi$
$181$			0.433943i			0.0322547i	−0.999870	+	0.0161274i	$0.994866\pi$
$182$	−3.76824	+	1.09956i	−0.279320	+	0.0815050i
$183$	5.23978			0.387335
$184$	10.7614	−	8.25780i	0.793344	−	0.608773i
$185$	−8.93580			−0.656973
$186$	4.08970	−	1.19337i	0.299872	−	0.0875018i
$187$		−	11.3113i		−	0.827166i
$188$	14.2350	+	22.3150i	1.03819	+	1.62749i
$189$		−	4.37646i		−	0.318341i
$190$	0.460714	+	1.57888i	0.0334237	+	0.114544i
$191$	−15.1460			−1.09593			−0.547964	−	0.836502i	$-0.684597\pi$
$191$	−15.1460			−1.09593			−0.547964	+	0.836502i	$0.684597\pi$
$192$	−5.38792	+	0.719159i	−0.388840	+	0.0519008i
$193$	12.1152			0.872071			0.436036	−	0.899929i	$-0.356382\pi$
$193$	12.1152			0.872071			0.436036	+	0.899929i	$0.356382\pi$
$194$	−5.38091	−	18.4406i	−0.386327	−	1.32396i
$195$	1.62164			0.116128
$196$	−9.52238	+	6.07442i	−0.680170	+	0.433887i
$197$	12.0252			0.856759			0.428380	−	0.903599i	$-0.359085\pi$
$197$	12.0252			0.856759			0.428380	+	0.903599i	$0.359085\pi$
$198$	−12.1985	+	3.55948i	−0.866906	+	0.252961i
$199$	−26.5465			−1.88183			−0.940916	−	0.338641i	$-0.890033\pi$
$199$	−26.5465			−1.88183			−0.940916	+	0.338641i	$0.890033\pi$
$200$	−1.86301	+	2.12819i	−0.131734	+	0.150486i
$201$			7.74620i			0.546375i
$202$	−18.7930	+	5.48376i	−1.32227	+	0.385836i
$203$	−0.331228			−0.0232476
$204$	3.66089	−	2.33532i	0.256314	−	0.163505i
$205$			2.51978i			0.175989i
$206$	15.4253	−	4.50106i	1.07473	−	0.313603i
$207$	11.9374	+	2.38543i	0.829706	+	0.165799i
$208$	−4.02423	+	8.65698i	−0.279030	+	0.600253i
$209$	4.11684			0.284768
$210$	−1.07279	+	0.313038i	−0.0740297	+	0.0216017i
$211$		−	14.7346i		−	1.01437i	−0.861836	−	0.507187i	$-0.830685\pi$
$211$		−	14.7346i		−	1.01437i	0.861836	−	0.507187i	$-0.169315\pi$
$212$	8.01544	+	12.5652i	0.550503	+	0.862978i
$213$	0.993366			0.0680643
$214$	−8.24271	+	2.40520i	−0.563460	+	0.164416i
$215$		−	6.07154i		−	0.414076i
$216$	−8.00859	−	7.01066i	−0.544915	−	0.477015i
$217$			5.15624i			0.350029i
$218$	3.17484	+	10.8803i	0.215027	+	0.736906i
$219$		−	3.32156i		−	0.224450i
$220$	3.80749	+	5.96870i	0.256701	+	0.402410i
$221$		−	7.62634i		−	0.513003i
$222$	−8.24271	+	2.40520i	−0.553215	+	0.161427i
$223$		−	8.64152i		−	0.578679i	−0.957227	−	0.289339i	$-0.906564\pi$
$223$		−	8.64152i		−	0.578679i	0.957227	−	0.289339i	$-0.0934356\pi$
$224$	0.991093	−	6.50382i	0.0662202	−	0.434555i
$225$	−2.53833			−0.169222
$226$	1.94390	+	6.66181i	0.129306	+	0.443137i
$227$	−3.55657			−0.236058			−0.118029	−	0.993010i	$-0.537658\pi$
$227$	−3.55657			−0.236058			−0.118029	+	0.993010i	$0.537658\pi$
$228$	0.849959	+	1.33241i	0.0562899	+	0.0882411i
$229$			7.09294i			0.468715i	0.972151	+	0.234357i	$0.0752986\pi$
$229$			7.09294i			0.468715i	−0.972151	+	0.234357i	$0.924701\pi$
$230$	−0.587185	−	6.75686i	−0.0387178	−	0.445534i
$231$			2.79724i			0.184045i
$232$	−0.530594	+	0.606121i	−0.0348352	+	0.0397938i
$233$	3.48303			0.228181			0.114090	−	0.993470i	$-0.463605\pi$
$233$	3.48303			0.228181			0.114090	+	0.993470i	$0.463605\pi$
$234$	−8.22447	+	2.39988i	−0.537650	+	0.156885i
$235$	13.2344			0.863315
$236$	9.15640	+	14.3537i	0.596031	+	0.934349i
$237$			3.45504i			0.224429i
$238$	1.47217	+	5.04518i	0.0954267	+	0.327031i
$239$			4.98027i			0.322147i	0.986942	+	0.161073i	$0.0514956\pi$
$239$			4.98027i			0.322147i	−0.986942	+	0.161073i	$0.948504\pi$
$240$	−1.14567	+	2.46458i	−0.0739527	+	0.159088i
$241$		−	25.7144i		−	1.65641i	−0.560423	−	0.828207i	$-0.689361\pi$
$241$		−	25.7144i		−	1.65641i	0.560423	−	0.828207i	$-0.310639\pi$
$242$	2.07793	−	0.606335i	0.133574	−	0.0389767i
$243$		−	14.7261i		−	0.944678i
$244$	8.29469	+	13.0029i	0.531013	+	0.832426i
$245$			5.64744i			0.360802i
$246$	0.678236	+	2.32434i	0.0432427	+	0.148194i
$247$	2.77567			0.176612
$248$	9.43553	+	8.25979i	0.599157	+	0.524497i
$249$		−	10.2912i		−	0.652176i
$250$	0.396143	+	1.35760i	0.0250543	+	0.0858620i
$251$	−19.0680			−1.20356			−0.601780	−	0.798662i	$-0.705542\pi$
$251$	−19.0680			−1.20356			−0.601780	+	0.798662i	$0.705542\pi$
$252$	4.97760	−	3.17527i	0.313560	−	0.200023i
$253$	−16.6474	−	3.32663i	−1.04662	−	0.209143i
$254$	−1.98918	−	6.81700i	−0.124812	−	0.427737i
$255$		−	2.17117i		−	0.135964i
$256$	−10.3139	−	12.2321i	−0.644616	−	0.764506i
$257$	−13.6402			−0.850851			−0.425425	−	0.904994i	$-0.639876\pi$
$257$	−13.6402			−0.850851			−0.425425	+	0.904994i	$0.639876\pi$
$258$	−1.63425	−	5.60062i	−0.101744	−	0.348679i
$259$		−	10.3923i		−	0.645746i
$260$	2.56710	+	4.02423i	0.159205	+	0.249572i
$261$	−0.722930			−0.0447483
$262$	0.888506	+	3.04494i	0.0548921	+	0.188117i
$263$	17.2448			1.06336			0.531678	−	0.846946i	$-0.321561\pi$
$263$	17.2448			1.06336			0.531678	+	0.846946i	$0.321561\pi$
$264$	5.11874	+	4.48091i	0.315037	+	0.275781i
$265$	7.45202			0.457774
$266$	−1.83623	+	0.535809i	−0.112587	+	0.0328525i
$267$	−2.08201			−0.127417
$268$	−19.2228	+	12.2624i	−1.17422	+	0.749047i
$269$	5.32436			0.324632			0.162316	−	0.986739i	$-0.448104\pi$
$269$	5.32436			0.324632			0.162316	+	0.986739i	$0.448104\pi$
$270$	−5.10876	+	1.49072i	−0.310909	+	0.0907226i
$271$		−	2.58255i		−	0.156879i	−0.996919	−	0.0784395i	$-0.975006\pi$
$271$		−	2.58255i		−	0.156879i	0.996919	−	0.0784395i	$-0.0249937\pi$
$272$	11.5906	+	5.38792i	0.702781	+	0.326691i
$273$			1.88596i			0.114144i
$274$	−2.16667	−	7.42525i	−0.130893	−	0.448576i
$275$	3.53986			0.213461
$276$	−2.36035	−	6.07473i	−0.142076	−	0.365656i
$277$	29.1509			1.75151			0.875755	−	0.482756i	$-0.160364\pi$
$277$	29.1509			1.75151			0.875755	+	0.482756i	$0.160364\pi$
$278$	−6.41602	−	21.9879i	−0.384807	−	1.31875i
$279$			11.2539i			0.673753i
$280$	−2.47508	−	2.16667i	−0.147915	−	0.129483i
$281$		−	23.7749i		−	1.41829i	−0.705061	−	0.709147i	$-0.749080\pi$
$281$		−	23.7749i		−	1.41829i	0.705061	−	0.709147i	$-0.250920\pi$
$282$	12.2079	−	3.56223i	0.726968	−	0.212128i
$283$	−4.07678			−0.242339			−0.121170	−	0.992632i	$-0.538665\pi$
$283$	−4.07678			−0.242339			−0.121170	+	0.992632i	$0.538665\pi$
$284$	1.57252	+	2.46511i	0.0933120	+	0.146278i
$285$	0.790214			0.0468082
$286$	11.4695	−	3.34678i	0.678208	−	0.197899i
$287$	−2.93049			−0.172982
$288$	2.16314	−	14.1951i	0.127464	−	0.836454i
$289$	6.78931			0.399371
$290$	0.112824	+	0.386651i	0.00662524	+	0.0227049i
$291$	−9.22931			−0.541032
$292$	8.24271	−	5.25811i	0.482368	−	0.307708i
$293$			22.6820i			1.32510i	0.749019	+	0.662548i	$0.230525\pi$
$293$			22.6820i			1.32510i	−0.749019	+	0.662548i	$0.769475\pi$
$294$	1.52009	+	5.20941i	0.0886536	+	0.303819i
$295$	8.51278			0.495633
$296$	−19.0171	−	16.6474i	−1.10535	−	0.967613i
$297$			13.3208i			0.772952i
$298$	−6.81866	−	23.3678i	−0.394994	−	1.35366i
$299$	−11.2241	−	2.24289i	−0.649105	−	0.129710i
$300$	0.730835	+	1.14567i	0.0421948	+	0.0661453i
$301$	7.06119			0.407000
$302$	−1.50832	−	5.16906i	−0.0867940	−	0.297446i
$303$			9.40571i			0.540344i
$304$	−1.96098	+	4.21848i	−0.112470	+	0.241946i
$305$	7.71164			0.441567
$306$	3.21313	+	11.0115i	0.183682	+	0.629486i
$307$		−	12.3488i		−	0.704782i	−0.935853	−	0.352391i	$-0.885369\pi$
$307$		−	12.3488i		−	0.704782i	0.935853	−	0.352391i	$-0.114631\pi$
$308$	−6.94158	+	4.42810i	−0.395533	+	0.252315i
$309$		−	7.72019i		−	0.439186i
$310$	6.01902	−	1.75634i	0.341857	−	0.0997531i
$311$			23.9579i			1.35853i	0.733894	+	0.679264i	$0.237701\pi$
$311$			23.9579i			1.35853i	−0.733894	+	0.679264i	$0.762299\pi$
$312$	3.45117	+	3.02113i	0.195384	+	0.171038i
$313$			5.46941i			0.309149i	0.987981	+	0.154575i	$0.0494007\pi$
$313$			5.46941i			0.309149i	−0.987981	+	0.154575i	$0.950599\pi$
$314$	6.64675	+	22.7787i	0.375098	+	1.28547i
$315$		−	2.95207i		−	0.166330i
$316$	−8.57394	+	5.46941i	−0.482322	+	0.307678i
$317$	−8.76428			−0.492251			−0.246126	−	0.969238i	$-0.579158\pi$
$317$	−8.76428			−0.492251			−0.246126	+	0.969238i	$0.579158\pi$
$318$	6.87402	−	2.00582i	0.385476	−	0.112481i
$319$	1.00817			0.0564467
$320$	−7.92967	+	1.05842i	−0.443282	+	0.0591676i
$321$			4.12539i			0.230257i
$322$	7.85821	−	0.682894i	0.437921	−	0.0380562i
$323$		−	3.71626i		−	0.206778i
$324$	8.52868	−	5.44053i	0.473816	−	0.302252i
$325$	2.38665			0.132388
$326$	−6.27256	−	21.4963i	−0.347405	−	1.19057i
$327$	5.44547			0.301135
$328$	−4.69436	+	5.36258i	−0.259203	+	0.296099i
$329$			15.3915i			0.848562i
$330$	3.26530	−	0.952806i	0.179749	−	0.0524502i
$331$		−	32.3321i		−	1.77713i	−0.458750	−	0.888565i	$-0.651703\pi$
$331$		−	32.3321i		−	1.77713i	0.458750	−	0.888565i	$-0.348297\pi$
$332$	25.5383	−	16.2912i	1.40160	−	0.894094i
$333$		−	22.6820i		−	1.24297i
$334$	−3.37228	−	11.5569i	−0.184523	−	0.632367i
$335$			11.4005i			0.622875i
$336$	−2.86630	−	1.33241i	−0.156370	−	0.0726890i
$337$			15.3380i			0.835513i	0.908559	+	0.417757i	$0.137184\pi$
$337$			15.3380i			0.835513i	−0.908559	+	0.417757i	$0.862816\pi$
$338$	−9.91575	+	2.89339i	−0.539346	+	0.157380i
$339$	3.33416			0.181087
$340$	5.38792	−	3.43701i	0.292201	−	0.186398i
$341$		−	15.6943i		−	0.849892i
$342$	−4.00772	+	1.16944i	−0.216713	+	0.0632362i
$343$	−14.7089			−0.794208
$344$	11.3113	−	12.9214i	0.609866	−	0.696677i
$345$	−3.19542	−	0.638535i	−0.172035	−	0.0343776i
$346$	−4.33809	+	1.26584i	−0.233217	+	0.0680522i
$347$			0.463178i			0.0248647i	0.999923	+	0.0124324i	$0.00395744\pi$
$347$			0.463178i			0.0248647i	−0.999923	+	0.0124324i	$0.996043\pi$
$348$	0.208146	+	0.326293i	0.0111578	+	0.0174912i
$349$	3.91889			0.209773			0.104887	−	0.994484i	$-0.466552\pi$
$349$	3.91889			0.209773			0.104887	+	0.994484i	$0.466552\pi$
$350$	−1.57888	+	0.460714i	−0.0843948	+	0.0246262i
$351$			8.98119i			0.479380i
$352$	−3.01663	+	19.7959i	−0.160787	+	1.05513i
$353$	7.58980			0.403964			0.201982	−	0.979389i	$-0.435262\pi$
$353$	7.58980			0.403964			0.201982	+	0.979389i	$0.435262\pi$
$354$	7.85250	−	2.29134i	0.417356	−	0.121783i
$355$	1.46199			0.0775942
$356$	−3.29588	−	5.16668i	−0.174681	−	0.273833i
$357$	2.52506			0.133640
$358$	−0.888506	−	3.04494i	−0.0469590	−	0.160930i
$359$	−3.83280			−0.202287			−0.101144	−	0.994872i	$-0.532250\pi$
$359$	−3.83280			−0.202287			−0.101144	+	0.994872i	$0.532250\pi$
$360$	−5.40206	−	4.72892i	−0.284714	−	0.249236i
$361$	−17.6474			−0.928813
$362$	0.171904	+	0.589119i	0.00903505	+	0.0309634i
$363$		−	1.03998i		−	0.0545849i
$364$	−4.68017	+	2.98553i	−0.245307	+	0.156484i
$365$		−	4.88851i		−	0.255876i
$366$	7.11351	−	2.07570i	0.371829	−	0.108499i
$367$	−11.9207			−0.622255			−0.311127	−	0.950368i	$-0.600707\pi$
$367$	−11.9207			−0.622255			−0.311127	+	0.950368i	$0.600707\pi$
$368$	11.3384	−	15.4738i	0.591057	−	0.806630i
$369$	−6.39603			−0.332964
$370$	−12.1312	+	3.53986i	−0.630672	+	0.184028i
$371$			8.66668i			0.449952i
$372$	5.07943	−	3.24022i	0.263356	−	0.167998i
$373$		−	30.2624i		−	1.56693i	−0.621436	−	0.783465i	$-0.713451\pi$
$373$		−	30.2624i		−	1.56693i	0.621436	−	0.783465i	$-0.286549\pi$
$374$	−4.48091	−	15.3562i	−0.231702	−	0.794051i
$375$	0.679463			0.0350873
$376$	28.1653	+	24.6557i	1.45251	+	1.27152i
$377$	0.679731			0.0350079
$378$	−1.73371	−	5.94147i	−0.0891723	−	0.305596i
$379$	17.4553			0.896619			0.448309	−	0.893878i	$-0.352026\pi$
$379$	17.4553			0.896619			0.448309	+	0.893878i	$0.352026\pi$
$380$	1.25093	+	1.96098i	0.0641712	+	0.100596i
$381$	−3.41184			−0.174794
$382$	−20.5622	+	6.00000i	−1.05205	+	0.306987i
$383$	13.1513			0.671998			0.335999	−	0.941862i	$-0.390926\pi$
$383$	13.1513			0.671998			0.335999	+	0.941862i	$0.390926\pi$
$384$	−7.02974	+	3.11072i	−0.358735	+	0.158743i
$385$			4.11684i			0.209814i
$386$	16.4476	−	4.79936i	0.837159	−	0.244281i
$387$	15.4116			0.783415
$388$	−14.6102	−	22.9032i	−0.741721	−	1.16274i
$389$			34.7815i			1.76349i	0.471726	+	0.881745i	$0.343631\pi$
$389$			34.7815i			1.76349i	−0.471726	+	0.881745i	$0.656369\pi$
$390$	2.20154	−	0.642403i	0.111479	−	0.0325293i
$391$	−3.00294	+	15.0276i	−0.151865	+	0.759977i
$392$	−10.5212	+	12.0188i	−0.531401	+	0.607043i
$393$	1.52396			0.0768736
$394$	16.3254	−	4.76370i	0.822460	−	0.239992i
$395$			5.08495i			0.255852i
$396$	−15.1505	+	9.66468i	−0.761343	+	0.485668i
$397$	−14.7914			−0.742358			−0.371179	−	0.928561i	$-0.621046\pi$
$397$	−14.7914			−0.742358			−0.371179	+	0.928561i	$0.621046\pi$
$398$	−36.0395	+	10.5162i	−1.80649	+	0.527131i
$399$			0.919016i			0.0460083i
$400$	−1.68614	+	3.62725i	−0.0843070	+	0.181362i
$401$			16.6820i			0.833059i	0.909122	+	0.416530i	$0.136754\pi$
$401$			16.6820i			0.833059i	−0.909122	+	0.416530i	$0.863246\pi$
$402$	3.06861	+	10.5162i	0.153048	+	0.524502i
$403$		−	10.5814i		−	0.527098i
$404$	−23.3410	+	14.8895i	−1.16126	+	0.740779i
$405$		−	5.05811i		−	0.251339i
$406$	−0.449674	+	0.131214i	−0.0223170	+	0.00651203i
$407$			31.6315i			1.56791i
$408$	4.04490	−	4.62067i	0.200252	−	0.228757i
$409$	30.4207			1.50421			0.752104	−	0.659044i	$-0.229039\pi$
$409$	30.4207			1.50421			0.752104	+	0.659044i	$0.229039\pi$
$410$	0.998194	+	3.42084i	0.0492973	+	0.168943i
$411$	−3.71626			−0.183310
$412$	19.1582	−	12.2212i	0.943859	−	0.602098i
$413$			9.90033i			0.487164i
$414$	17.1511	−	1.49047i	0.842933	−	0.0732525i
$415$		−	15.1460i		−	0.743489i
$416$	−2.03388	+	13.3469i	−0.0997191	+	0.654384i
$417$	−11.0047			−0.538904
$418$	5.58902	−	1.63086i	0.273368	−	0.0797680i
$419$	31.7989			1.55348			0.776738	−	0.629824i	$-0.216873\pi$
$419$	31.7989			1.55348			0.776738	+	0.629824i	$0.216873\pi$
$420$	−1.33241	+	0.849959i	−0.0650150	+	0.0414738i
$421$			13.4089i			0.653510i	0.945109	+	0.326755i	$0.105955\pi$
$421$			13.4089i			0.653510i	−0.945109	+	0.326755i	$0.894045\pi$
$422$	−5.83703	−	20.0037i	−0.284142	−	0.973765i
$423$			33.5932i			1.63336i
$424$	15.8593	+	13.8832i	0.770198	+	0.674226i
$425$		−	3.19542i		−	0.155000i
$426$	1.34859	−	0.393515i	0.0653394	−	0.0190659i
$427$			8.96861i			0.434022i
$428$	−10.2375	+	6.53059i	−0.494847	+	0.315668i
$429$		−	5.74038i		−	0.277148i
$430$	−2.40520	−	8.24271i	−0.115989	−	0.397499i
$431$	−15.6662			−0.754616			−0.377308	−	0.926088i	$-0.623150\pi$
$431$	−15.6662			−0.754616			−0.377308	+	0.926088i	$0.623150\pi$
$432$	−13.6497	−	6.34510i	−0.656720	−	0.305279i
$433$		−	14.9789i		−	0.719840i	−0.932983	−	0.359920i	$-0.882804\pi$
$433$		−	14.9789i		−	0.719840i	0.932983	−	0.359920i	$-0.117196\pi$
$434$	2.04261	+	7.00010i	0.0980485	+	0.336016i
$435$	0.193515			0.00927833
$436$	8.62031	+	13.5134i	0.412838	+	0.647172i
$437$	−5.46941	−	1.09294i	−0.261637	−	0.0522825i
$438$	−1.31581	−	4.50934i	−0.0628720	−	0.215465i
$439$			23.2450i			1.10942i	0.832043	+	0.554712i	$0.187171\pi$
$439$			23.2450i			1.10942i	−0.832043	+	0.554712i	$0.812829\pi$
$440$	7.53351	+	6.59477i	0.359146	+	0.314394i
$441$	−14.3351			−0.682622
$442$	−3.02113	−	10.3535i	−0.143700	−	0.492466i
$443$			37.3633i			1.77519i	0.460629	+	0.887593i	$0.347624\pi$
$443$			37.3633i			1.77519i	−0.460629	+	0.887593i	$0.652376\pi$
$444$	−10.2375	+	6.53059i	−0.485849	+	0.309928i
$445$	−3.06420			−0.145257
$446$	−3.42328	−	11.7317i	−0.162097	−	0.555512i
$447$	−11.6953			−0.553170
$448$	−1.23094	−	9.22219i	−0.0581565	−	0.435707i
$449$	−32.3734			−1.52780			−0.763899	−	0.645336i	$-0.776717\pi$
$449$	−32.3734			−1.52780			−0.763899	+	0.645336i	$0.776717\pi$
$450$	−3.44603	+	1.00554i	−0.162447	+	0.0474017i
$451$	8.91966			0.420010
$452$	5.27806	+	8.27399i	0.248259	+	0.389176i
$453$	−2.58706			−0.121551
$454$	−4.82839	+	1.40891i	−0.226608	+	0.0661235i
$455$			2.77567i			0.130125i
$456$	1.68173	+	1.47217i	0.0787541	+	0.0689408i
$457$		−	12.6533i		−	0.591895i	−0.955204	−	0.295947i	$-0.904365\pi$
$457$		−	12.6533i		−	0.591895i	0.955204	−	0.295947i	$-0.0956353\pi$
$458$	2.80982	+	9.62936i	0.131294	+	0.449950i
$459$	12.0246			0.561262
$460$	−3.47385	−	8.94049i	−0.161969	−	0.416853i
$461$	−26.8817			−1.25200			−0.626002	−	0.779821i	$-0.715310\pi$
$461$	−26.8817			−1.25200			−0.626002	+	0.779821i	$0.715310\pi$
$462$	1.10811	+	3.79753i	0.0515539	+	0.176677i
$463$			11.3203i			0.526100i	0.964782	+	0.263050i	$0.0847284\pi$
$463$			11.3203i			0.526100i	−0.964782	+	0.263050i	$0.915272\pi$
$464$	−0.480222	+	1.03306i	−0.0222938	+	0.0479586i
$465$		−	3.01246i		−	0.139699i
$466$	4.72855	−	1.37978i	0.219046	−	0.0639171i
$467$	−29.8807			−1.38271			−0.691356	−	0.722514i	$-0.742986\pi$
$467$	−29.8807			−1.38271			−0.691356	+	0.722514i	$0.742986\pi$
$468$	−10.2148	+	6.51614i	−0.472180	+	0.301209i
$469$	−13.2587			−0.612231
$470$	17.9669	−	5.24271i	0.828753	−	0.241828i
$471$	11.4005			0.525306
$472$	18.1168	+	15.8593i	0.833895	+	0.729986i
$473$	−21.4924			−0.988222
$474$	1.36869	+	4.69055i	0.0628660	+	0.215444i
$475$	1.16300			0.0533620
$476$	3.99723	+	6.26614i	0.183213	+	0.287208i
$477$			18.9157i			0.866090i
$478$	1.97290	+	6.76120i	0.0902384	+	0.309250i
$479$	28.0533			1.28179			0.640894	−	0.767629i	$-0.278564\pi$
$479$	28.0533			1.28179			0.640894	+	0.767629i	$0.278564\pi$
$480$	−0.579031	+	3.79976i	−0.0264290	+	0.173434i
$481$			21.3266i			0.972411i
$482$	−10.1866	−	34.9099i	−0.463987	−	1.59010i
$483$	0.742614	−	3.71626i	0.0337901	−	0.169096i
$484$	2.58080	−	1.64632i	0.117309	−	0.0748326i
$485$	−13.5832			−0.616783
$486$	−5.83364	−	19.9921i	−0.264619	−	0.906859i
$487$			31.1349i			1.41086i	0.708781	+	0.705429i	$0.249246\pi$
$487$			31.1349i			1.41086i	−0.708781	+	0.705429i	$0.750754\pi$
$488$	16.4119	+	14.3668i	0.742930	+	0.650356i
$489$	−10.7587			−0.486523
$490$	2.23720	+	7.66695i	0.101066	+	0.346357i
$491$			30.9504i			1.39677i	0.715722	+	0.698385i	$0.246098\pi$
$491$			30.9504i			1.39677i	−0.715722	+	0.698385i	$0.753902\pi$
$492$	1.84154	+	2.88684i	0.0830231	+	0.130149i
$493$		−	0.910072i		−	0.0409876i
$494$	3.76824	−	1.09956i	0.169541	−	0.0494717i
$495$			8.98533i			0.403860i
$496$	16.0817	+	7.47565i	0.722090	+	0.335666i
$497$			1.70029i			0.0762682i
$498$	−4.07678	−	13.9713i	−0.182685	−	0.626067i
$499$		−	6.56809i		−	0.294028i	−0.989134	−	0.147014i	$-0.953034\pi$
$499$		−	6.56809i		−	0.294028i	0.989134	−	0.147014i	$-0.0469662\pi$
$500$	1.07561	+	1.68614i	0.0481026	+	0.0754065i
$501$	−5.78412			−0.258415
$502$	−25.8866	+	7.55366i	−1.15538	+	0.337136i
$503$	24.3969			1.08780			0.543902	−	0.839149i	$-0.316946\pi$
$503$	24.3969			1.08780			0.543902	+	0.839149i	$0.316946\pi$
$504$	5.49972	−	6.28258i	0.244977	−	0.279848i
$505$			13.8429i			0.615999i
$506$	−23.9183	+	2.07855i	−1.06330	+	0.0924028i
$507$			4.96273i			0.220403i
$508$	−5.40102	−	8.46674i	−0.239632	−	0.375651i
$509$	−12.1922			−0.540412			−0.270206	−	0.962803i	$-0.587092\pi$
$509$	−12.1922			−0.540412			−0.270206	+	0.962803i	$0.587092\pi$
$510$	−0.860094	−	2.94757i	−0.0380856	−	0.130521i
$511$	5.68532			0.251504
$512$	−18.8477	−	12.5205i	−0.832960	−	0.553333i
$513$			4.37646i			0.193226i
$514$	−18.5179	+	5.40347i	−0.816788	+	0.238337i
$515$		−	11.3622i		−	0.500678i
$516$	−4.43730	−	6.95599i	−0.195341	−	0.306220i
$517$		−	46.8478i		−	2.06036i
$518$	−4.11684	−	14.1086i	−0.180884	−	0.619895i
$519$			2.17117i			0.0953037i
$520$	5.07926	+	4.44634i	0.222740	+	0.194985i
$521$		−	15.2300i		−	0.667237i	−0.942708	−	0.333619i	$-0.891730\pi$
$521$		−	15.2300i		−	0.667237i	0.942708	−	0.333619i	$-0.108270\pi$
$522$	−0.981448	+	0.286384i	−0.0429568	+	0.0125347i
$523$	−37.2916			−1.63065			−0.815324	−	0.579005i	$-0.803441\pi$
$523$	−37.2916			−1.63065			−0.815324	+	0.579005i	$0.803441\pi$
$524$	2.41247	+	3.78183i	0.105389	+	0.165210i
$525$			0.790214i			0.0344877i
$526$	23.4114	−	6.83140i	1.02079	−	0.297863i
$527$	−14.1671			−0.617131
$528$	8.72427	+	4.05551i	0.379675	+	0.176493i
$529$	21.2337	+	8.83915i	0.923204	+	0.384311i
$530$	10.1168	−	2.95207i	0.439448	−	0.128230i
$531$			21.6082i			0.937718i
$532$	−2.28061	+	1.45482i	−0.0988770	+	0.0630746i
$533$	6.01383			0.260488
$534$	−2.82654	+	0.824776i	−0.122316	+	0.0356915i
$535$			6.07154i			0.262496i
$536$	−21.2391	+	24.2624i	−0.917391	+	1.04798i
$537$	−1.52396			−0.0657637
$538$	7.22834	−	2.10921i	0.311636	−	0.0909345i
$539$	19.9911			0.861079
$540$	−6.34510	+	4.04761i	−0.273050	+	0.174181i
$541$	45.1850			1.94266			0.971328	−	0.237744i	$-0.0764078\pi$
$541$	45.1850			1.94266			0.971328	+	0.237744i	$0.0764078\pi$
$542$	−1.02306	−	3.50607i	−0.0439443	−	0.150599i
$543$	0.294848			0.0126531
$544$	17.8697	+	2.72310i	0.766158	+	0.116752i
$545$	8.01437			0.343298
$546$	0.747112	+	2.56038i	0.0319735	+	0.109574i
$547$		−	16.1869i		−	0.692100i	−0.938216	−	0.346050i	$-0.887523\pi$
$547$		−	16.1869i		−	0.692100i	0.938216	−	0.346050i	$-0.112477\pi$
$548$	−5.88293	−	9.22219i	−0.251306	−	0.393952i
$549$			19.5747i			0.835427i
$550$	4.80570	−	1.40229i	0.204916	−	0.0597939i
$551$	0.331228			0.0141108
$552$	−5.61087	−	7.31200i	−0.238815	−	0.311220i
$553$	−5.91378			−0.251480
$554$	39.5752	−	11.5480i	1.68139	−	0.490625i
$555$			6.07154i			0.257723i
$556$	−17.4207	−	27.3091i	−0.738804	−	1.15816i
$557$		−	30.6215i		−	1.29747i	−0.761012	−	0.648737i	$-0.775297\pi$
$557$		−	30.6215i		−	1.29747i	0.761012	−	0.648737i	$-0.224703\pi$
$558$	4.45816	+	15.2783i	0.188729	+	0.646780i
$559$	−14.4907			−0.612890
$560$	−4.21848	−	1.96098i	−0.178263	−	0.0828664i
$561$	−7.68563			−0.324487
$562$	−9.41829	−	32.2768i	−0.397287	−	1.36151i
$563$	−12.1431			−0.511770			−0.255885	−	0.966707i	$-0.582367\pi$
$563$	−12.1431			−0.511770			−0.255885	+	0.966707i	$0.582367\pi$
$564$	15.1622	−	9.67214i	0.638445	−	0.407271i
$565$	4.90706			0.206441
$566$	−5.53462	+	1.61499i	−0.232638	+	0.0678831i
$567$	5.88256			0.247044
$568$	3.11139	+	2.72369i	0.130551	+	0.114283i
$569$			37.5211i			1.57297i	0.617610	+	0.786484i	$0.288101\pi$
$569$			37.5211i			1.57297i	−0.617610	+	0.786484i	$0.711899\pi$
$570$	1.07279	−	0.313038i	0.0449343	−	0.0131117i
$571$	−10.9508			−0.458277			−0.229138	−	0.973394i	$-0.573591\pi$
$571$	−10.9508			−0.458277			−0.229138	+	0.973394i	$0.573591\pi$
$572$	14.2452	−	9.08716i	0.595622	−	0.379953i
$573$			10.2912i			0.429920i
$574$	−3.97843	+	1.16090i	−0.166056	+	0.0484549i
$575$	−4.70285	−	0.939764i	−0.196123	−	0.0391909i
$576$	−2.68662	−	20.1281i	−0.111943	−	0.838672i
$577$	−19.1222			−0.796067			−0.398034	−	0.917371i	$-0.630307\pi$
$577$	−19.1222			−0.796067			−0.398034	+	0.917371i	$0.630307\pi$
$578$	9.21715	−	2.68954i	0.383383	−	0.111870i
$579$		−	8.23183i		−	0.342103i
$580$	0.306339	+	0.480222i	0.0127200	+	0.0199401i
$581$	17.6148			0.730784
$582$	−12.5297	+	3.65613i	−0.519372	+	0.151551i
$583$		−	26.3791i		−	1.09251i
$584$	9.10731	−	10.4037i	0.376863	−	0.430508i
$585$			6.05811i			0.250472i
$586$	8.98533	+	30.7930i	0.371180	+	1.27205i
$587$			15.3774i			0.634695i	0.948309	+	0.317347i	$0.102792\pi$
$587$			15.3774i			0.634695i	−0.948309	+	0.317347i	$0.897208\pi$
$588$	4.12735	+	6.47010i	0.170209	+	0.266823i
$589$		−	5.15624i		−	0.212459i
$590$	11.5569	−	3.37228i	0.475791	−	0.138835i
$591$		−	8.17067i		−	0.336096i
$592$	−32.4124	−	15.0670i	−1.33214	−	0.619250i
$593$	−9.29488			−0.381695			−0.190847	−	0.981620i	$-0.561124\pi$
$593$	−9.29488			−0.381695			−0.190847	+	0.981620i	$0.561124\pi$
$594$	5.27695	+	18.0843i	0.216516	+	0.742007i
$595$	3.71626			0.152352
$596$	−18.5140	−	29.0229i	−0.758362	−	1.18882i
$597$			18.0374i			0.738220i
$598$	−16.1263	+	1.40140i	−0.659453	+	0.0573077i
$599$			25.4614i			1.04032i	0.854068	+	0.520162i	$0.174128\pi$
$599$			25.4614i			1.04032i	−0.854068	+	0.520162i	$0.825872\pi$
$600$	1.44603	+	1.26584i	0.0590339	+	0.0516778i
$601$	12.1583			0.495948			0.247974	−	0.968767i	$-0.420235\pi$
$601$	12.1583			0.495948			0.247974	+	0.968767i	$0.420235\pi$
$602$	9.58625	−	2.79724i	0.390706	−	0.114007i
$603$	−28.9382			−1.17845
$604$	−4.09538	−	6.41999i	−0.166639	−	0.261226i
$605$		−	1.53059i		−	0.0622275i
$606$	3.72601	+	12.7692i	0.151359	+	0.518712i
$607$		−	37.2700i		−	1.51274i	−0.654142	−	0.756372i	$-0.726970\pi$
$607$		−	37.2700i		−	1.51274i	0.654142	−	0.756372i	$-0.273030\pi$
$608$	−0.991093	+	6.50382i	−0.0401941	+	0.263765i
$609$			0.225057i			0.00911978i
$610$	10.4693	−	3.05492i	0.423890	−	0.123690i
$611$		−	31.5858i		−	1.27783i
$612$	8.72427	+	13.6763i	0.352658	+	0.552833i
$613$		−	10.4845i		−	0.423464i	−0.977328	−	0.211732i	$-0.932090\pi$
$613$		−	10.4845i		−	0.423464i	0.977328	−	0.211732i	$-0.0679104\pi$
$614$	−4.89189	−	16.7647i	−0.197421	−	0.676567i
$615$	1.71210			0.0690384
$616$	−7.66970	+	8.76144i	−0.309021	+	0.353009i
$617$		−	47.6120i		−	1.91679i	−0.285452	−	0.958393i	$-0.592144\pi$
$617$		−	47.6120i		−	1.91679i	0.285452	−	0.958393i	$-0.407856\pi$
$618$	−3.05830	−	10.4809i	−0.123023	−	0.421604i
$619$	27.8733			1.12032			0.560162	−	0.828383i	$-0.310739\pi$
$619$	27.8733			1.12032			0.560162	+	0.828383i	$0.310739\pi$
$620$	7.47565	−	4.76879i	0.300229	−	0.191519i
$621$	3.53642	−	17.6973i	0.141912	−	0.710167i
$622$	9.49077	+	32.5252i	0.380545	+	1.30414i
$623$		−	3.56366i		−	0.142775i
$624$	5.88210	+	2.73432i	0.235472	+	0.109460i
$625$	1.00000			0.0400000
$626$	2.16667	+	7.42525i	0.0865975	+	0.296773i
$627$		−	2.79724i		−	0.111711i
$628$	18.0472	+	28.2912i	0.720163	+	1.12894i
$629$	28.5536			1.13851
$630$	−1.16944	−	4.00772i	−0.0465917	−	0.159671i
$631$	37.1899			1.48051			0.740253	−	0.672329i	$-0.234706\pi$
$631$	37.1899			1.48051			0.740253	+	0.672329i	$0.234706\pi$
$632$	−9.47329	+	10.8218i	−0.376827	+	0.430467i
$633$	−10.0116			−0.397927
$634$	−11.8984	+	3.47191i	−0.472544	+	0.137887i
$635$	−5.02137			−0.199267
$636$	8.53756	−	5.44620i	0.338536	−	0.215956i
$637$	13.4785			0.534036
$638$	1.36869	−	0.399380i	0.0541870	−	0.0158116i
$639$			3.71100i			0.146805i
$640$	−10.3460	+	4.57820i	−0.408962	+	0.180969i
$641$		−	12.8783i		−	0.508663i	−0.967117	−	0.254331i	$-0.918145\pi$
$641$		−	12.8783i		−	0.508663i	0.967117	−	0.254331i	$-0.0818554\pi$
$642$	1.63425	+	5.60062i	0.0644986	+	0.221039i
$643$	−26.8777			−1.05995			−0.529977	−	0.848012i	$-0.677799\pi$
$643$	−26.8777			−1.05995			−0.529977	+	0.848012i	$0.677799\pi$
$644$	10.3978	−	4.04007i	0.409729	−	0.159201i
$645$	−4.12539			−0.162437
$646$	−1.47217	−	5.04518i	−0.0579218	−	0.198500i
$647$		−	0.572262i		−	0.0224979i	−0.999937	−	0.0112490i	$-0.996419\pi$
$647$		−	0.572262i		−	0.0224979i	0.999937	−	0.0112490i	$-0.00358073\pi$
$648$	9.42328	−	10.7646i	0.370181	−	0.422875i
$649$		−	30.1340i		−	1.18286i
$650$	3.24011	−	0.945456i	0.127088	−	0.0370838i
$651$	3.50348			0.137312
$652$	−17.0312	−	26.6985i	−0.666994	−	1.04559i
$653$	32.2544			1.26221			0.631106	−	0.775696i	$-0.282601\pi$
$653$	32.2544			1.26221			0.631106	+	0.775696i	$0.282601\pi$
$654$	7.39275	−	2.15719i	0.289080	−	0.0843527i
$655$	2.24289			0.0876369
$656$	−4.24870	+	9.13986i	−0.165884	+	0.356852i
$657$	12.4086			0.484107
$658$	6.09725	+	20.8955i	0.237696	+	0.814591i
$659$	12.4086			0.483372			0.241686	−	0.970354i	$-0.422300\pi$
$659$	12.4086			0.483372			0.241686	+	0.970354i	$0.422300\pi$
$660$	4.05551	−	2.58705i	0.157861	−	0.100701i
$661$			43.3582i			1.68644i	0.537570	+	0.843219i	$0.319342\pi$
$661$			43.3582i			1.68644i	−0.537570	+	0.843219i	$0.680658\pi$
$662$	−12.8081	−	43.8939i	−0.497802	−	1.70599i
$663$	−5.18182			−0.201245
$664$	28.2171	−	32.2337i	1.09504	−	1.25091i
$665$			1.35256i			0.0524501i
$666$	−8.98533	−	30.7930i	−0.348174	−	1.19321i
$667$	−1.33940	−	0.267650i	−0.0518617	−	0.0103634i
$668$	−9.15640	−	14.3537i	−0.354272	−	0.555363i
$669$	−5.87159			−0.227009
$670$	4.51622	+	15.4773i	0.174477	+	0.597939i
$671$		−	27.2981i		−	1.05383i
$672$	−4.41911	−	0.673411i	−0.170471	−	0.0259774i
$673$	17.4027			0.670823			0.335412	−	0.942072i	$-0.391125\pi$
$673$	17.4027			0.670823			0.335412	+	0.942072i	$0.391125\pi$
$674$	6.07604	+	20.8228i	0.234040	+	0.802065i
$675$			3.76309i			0.144841i
$676$	−12.3154	+	7.85612i	−0.473669	+	0.302158i
$677$			29.6092i			1.13797i	0.822347	+	0.568986i	$0.192664\pi$
$677$			29.6092i			1.13797i	−0.822347	+	0.568986i	$0.807336\pi$
$678$	4.52645	−	1.32081i	0.173837	−	0.0507253i
$679$		−	15.7973i		−	0.606243i
$680$	5.95308	−	6.80047i	0.228290	−	0.260786i
$681$			2.41656i			0.0926027i
$682$	−6.21718	−	21.3065i	−0.238068	−	0.815867i
$683$		−	25.8996i		−	0.991020i	−0.868602	−	0.495510i	$-0.834981\pi$
$683$		−	25.8996i		−	0.991020i	0.868602	−	0.495510i	$-0.165019\pi$
$684$	−4.97760	+	3.17527i	−0.190323	+	0.121409i
$685$	−5.46941			−0.208975
$686$	−19.9688	+	5.82685i	−0.762413	+	0.222470i
$687$	4.81939			0.183871
$688$	10.2375	−	22.0230i	0.390300	−	0.839619i
$689$		−	17.7854i		−	0.677569i
$690$	−4.59104	+	0.398970i	−0.174778	+	0.0151885i
$691$		−	22.5354i		−	0.857287i	−0.903474	−	0.428643i	$-0.858992\pi$
$691$		−	22.5354i		−	0.857287i	0.903474	−	0.428643i	$-0.141008\pi$
$692$	−5.38792	+	3.43701i	−0.204818	+	0.130656i
$693$	−10.4499			−0.396959
$694$	0.183485	+	0.628810i	0.00696500	+	0.0238693i
$695$	−16.1962			−0.614357
$696$	0.411837	+	0.360519i	0.0156106	+	0.0136654i
$697$		−	8.05174i		−	0.304981i
$698$	5.32027	−	1.55244i	0.201375	−	0.0587608i
$699$		−	2.36659i		−	0.0895127i
$700$	−1.96098	+	1.25093i	−0.0741179	+	0.0472806i
$701$			5.43765i			0.205377i	0.994714	+	0.102689i	$0.0327445\pi$
$701$			5.43765i			0.205377i	−0.994714	+	0.102689i	$0.967255\pi$
$702$	3.55784	+	12.1928i	0.134282	+	0.460189i
$703$			10.3923i			0.391953i
$704$	3.74666	+	28.0699i	0.141208	+	1.05793i
$705$		−	8.99226i		−	0.338668i
$706$	10.3039	−	3.00665i	0.387792	−	0.113157i
$707$	−16.0992			−0.605473
$708$	9.75284	−	6.22144i	0.366534	−	0.233816i
$709$			2.31710i			0.0870205i	0.999053	+	0.0435102i	$0.0138541\pi$
$709$			2.31710i			0.0870205i	−0.999053	+	0.0435102i	$0.986146\pi$
$710$	1.98479	−	0.579156i	0.0744878	−	0.0217354i
$711$	−12.9073			−0.484061
$712$	−6.52122	−	5.70863i	−0.244393	−	0.213940i
$713$	−4.16652	+	20.8505i	−0.156037	+	0.780857i
$714$	3.42802	−	1.00029i	0.128290	−	0.0374348i
$715$		−	8.44841i		−	0.315952i
$716$	−2.41247	−	3.78183i	−0.0901581	−	0.141333i
$717$	3.38391			0.126374
$718$	−5.20340	+	1.51834i	−0.194189	+	0.0566639i
$719$		−	50.9154i		−	1.89882i	−0.314032	−	0.949412i	$-0.601680\pi$
$719$		−	50.9154i		−	1.89882i	0.314032	−	0.949412i	$-0.398320\pi$
$720$	−9.20715	−	4.27998i	−0.343130	−	0.159505i
$721$	13.2142			0.492122
$722$	−23.9581	+	6.99092i	−0.891629	+	0.260175i
$723$	−17.4720			−0.649791
$724$	0.466752	+	0.731688i	0.0173467	+	0.0271930i
$725$	0.284805			0.0105774
$726$	−0.411982	−	1.41188i	−0.0152901	−	0.0523997i
$727$	10.2883			0.381574			0.190787	−	0.981631i	$-0.438896\pi$
$727$	10.2883			0.381574			0.190787	+	0.981631i	$0.438896\pi$
$728$	−5.17108	+	5.90716i	−0.191653	+	0.218934i
$729$	5.16850			0.191426
$730$	−1.93655	−	6.63662i	−0.0716749	−	0.245632i
$731$			19.4011i			0.717576i
$732$	8.83500	−	5.63594i	0.326551	−	0.208310i
$733$			13.1896i			0.487169i	0.969880	+	0.243584i	$0.0783233\pi$
$733$			13.1896i			0.487169i	−0.969880	+	0.243584i	$0.921677\pi$
$734$	−16.1835	+	4.72230i	−0.597343	+	0.174303i
$735$	3.83723			0.141538
$736$	9.26316	−	25.4989i	0.341445	−	0.939902i
$737$	40.3561			1.48653
$738$	−8.68323	+	2.53374i	−0.319634	+	0.0932684i
$739$		−	36.6567i		−	1.34844i	−0.738532	−	0.674219i	$-0.764481\pi$
$739$		−	36.6567i		−	1.34844i	0.738532	−	0.674219i	$-0.235519\pi$
$740$	−15.0670	+	9.61140i	−0.553874	+	0.353322i
$741$		−	1.88596i		−	0.0692826i
$742$	3.43325	+	11.7659i	0.126039	+	0.431938i
$743$	−6.92489			−0.254050			−0.127025	−	0.991900i	$-0.540543\pi$
$743$	−6.92489			−0.254050			−0.127025	+	0.991900i	$0.540543\pi$
$744$	5.61222	−	6.41109i	0.205754	−	0.235042i
$745$	−17.2126			−0.630621
$746$	−11.9883	−	41.0842i	−0.438922	−	1.50420i
$747$	38.4456			1.40665
$748$	−12.1665	−	19.0725i	−0.444852	−	0.697359i
$749$	−7.06119			−0.258010
$750$	0.922437	−	0.269165i	0.0336826	−	0.00982851i
$751$	30.6233			1.11746			0.558730	−	0.829350i	$-0.311289\pi$
$751$	30.6233			1.11746			0.558730	+	0.829350i	$0.311289\pi$
$752$	48.0043	+	22.3150i	1.75054	+	0.813744i
$753$			12.9560i			0.472143i
$754$	0.922801	−	0.269271i	0.0336064	−	0.00980628i
$755$	−3.80751			−0.138569
$756$	−4.70735	−	7.37933i	−0.171205	−	0.268384i
$757$			14.3517i			0.521620i	0.965390	+	0.260810i	$0.0839896\pi$
$757$			14.3517i			0.521620i	−0.965390	+	0.260810i	$0.916010\pi$
$758$	23.6973	−	6.91481i	0.860724	−	0.251157i
$759$	−2.26032	+	11.3113i	−0.0820445	+	0.410575i
$760$	2.47508	+	2.16667i	0.0897807	+	0.0785934i
$761$	22.3858			0.811486			0.405743	−	0.913987i	$-0.367013\pi$
$761$	22.3858			0.811486			0.405743	+	0.913987i	$0.367013\pi$
$762$	−4.63190	+	1.35158i	−0.167796	+	0.0489625i
$763$			9.32069i			0.337432i
$764$	−25.5383	+	16.2912i	−0.923944	+	0.589394i
$765$	8.11102			0.293255
$766$	17.8541	−	5.20979i	0.645095	−	0.188237i
$767$		−	20.3170i		−	0.733605i
$768$	−8.31126	+	7.00789i	−0.299907	+	0.252875i
$769$			32.6472i			1.17729i	0.808392	+	0.588645i	$0.200338\pi$
$769$			32.6472i			1.17729i	−0.808392	+	0.588645i	$0.799662\pi$
$770$	1.63086	+	5.58902i	0.0587721	+	0.201414i
$771$			9.26800i			0.333779i
$772$	20.4279	−	13.0312i	0.735218	−	0.469003i
$773$		−	36.9053i		−	1.32739i	−0.748003	−	0.663695i	$-0.768987\pi$
$773$		−	36.9053i		−	1.32739i	0.748003	−	0.663695i	$-0.231013\pi$
$774$	20.9227	−	6.10520i	0.752052	−	0.219447i
$775$		−	4.43358i		−	0.159259i
$776$	−28.9078	−	25.3056i	−1.03773	−	0.908420i
$777$	−7.06119			−0.253319
$778$	13.7784	+	47.2192i	0.493981	+	1.69289i
$779$	2.93049			0.104996
$780$	2.73432	−	1.74425i	0.0979042	−	0.0624541i
$781$		−	5.17522i		−	0.185184i
$782$	1.87630	+	21.5910i	0.0670963	+	0.772092i
$783$			1.07175i			0.0383012i
$784$	−9.52238	+	20.4847i	−0.340085	+	0.731595i
$785$	16.7787			0.598856
$786$	2.06892	−	0.603707i	0.0737961	−	0.0215335i
$787$	0.865924			0.0308669			0.0154334	−	0.999881i	$-0.495087\pi$
$787$	0.865924			0.0308669			0.0154334	+	0.999881i	$0.495087\pi$
$788$	20.2762	−	12.9344i	0.722308	−	0.460768i
$789$		−	11.7172i		−	0.417142i
$790$	2.01437	+	6.90331i	0.0716681	+	0.245609i
$791$			5.70689i			0.202914i
$792$	−16.7397	+	19.1225i	−0.594820	+	0.679489i
$793$		−	18.4050i		−	0.653581i
$794$	−20.0807	+	5.85951i	−0.712639	+	0.207946i
$795$		−	5.06337i		−	0.179579i
$796$	−44.7611	+	28.5536i	−1.58652	+	1.01206i
$797$		−	4.60244i		−	0.163027i	−0.996672	−	0.0815135i	$-0.974025\pi$
$797$		−	4.60244i		−	0.163027i	0.996672	−	0.0815135i	$-0.0259754\pi$
$798$	0.364062	+	1.24765i	0.0128877	+	0.0441665i
$799$	−42.2893			−1.49609
$800$	−0.852189	+	5.59230i	−0.0301294	+	0.197718i
$801$		−	7.77796i		−	0.274821i
$802$	6.60847	+	22.6474i	0.233353	+	0.799709i
$803$	−17.3046			−0.610667
$804$	8.33187	+	13.0612i	0.293842	+	0.460633i
$805$	1.09294	−	5.46941i	0.0385212	−	0.192771i
$806$	−4.19176	−	14.3653i	−0.147648	−	0.505996i
$807$		−	3.61771i		−	0.127349i
$808$	−25.7893	+	29.4603i	−0.907265	+	1.03641i
$809$	35.0439			1.23208			0.616039	−	0.787716i	$-0.288736\pi$
$809$	35.0439			1.23208			0.616039	+	0.787716i	$0.288736\pi$
$810$	−2.00374	−	6.86687i	−0.0704041	−	0.241277i
$811$			10.0046i			0.351309i	0.984452	+	0.175654i	$0.0562041\pi$
$811$			10.0046i			0.351309i	−0.984452	+	0.175654i	$0.943796\pi$
$812$	−0.558497	+	0.356271i	−0.0195994	+	0.0125027i
$813$	−1.75475			−0.0615418
$814$	12.5306	+	42.9428i	0.439197	+	1.50514i
$815$	−15.8341			−0.554643
$816$	3.66089	−	7.87536i	0.128157	−	0.275693i
$817$	−7.06119			−0.247040
$818$	41.2991	−	12.0510i	1.44399	−	0.421353i
$819$	−7.04556			−0.246192
$820$	2.71029	+	4.24870i	0.0946474	+	0.148371i
$821$	−26.7107			−0.932211			−0.466106	−	0.884729i	$-0.654343\pi$
$821$	−26.7107			−0.932211			−0.466106	+	0.884729i	$0.654343\pi$
$822$	−5.04518	+	1.47217i	−0.175971	+	0.0513479i
$823$			19.0791i			0.665055i	0.943094	+	0.332527i	$0.107901\pi$
$823$			19.0791i			0.665055i	−0.943094	+	0.332527i	$0.892099\pi$
$824$	21.1678	−	24.1809i	0.737416	−	0.842383i
$825$		−	2.40520i		−	0.0837384i
$826$	3.92195	+	13.4407i	0.136462	+	0.467661i
$827$	38.3439			1.33335			0.666674	−	0.745350i	$-0.267717\pi$
$827$	38.3439			1.33335			0.666674	+	0.745350i	$0.267717\pi$
$828$	22.6939	−	8.81777i	0.788668	−	0.306439i
$829$	−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
$831$		−	19.8070i		−	0.687097i
$832$	2.52608	+	18.9254i	0.0875762	+	0.656119i
$833$		−	18.0459i		−	0.625254i
$834$	−14.9400	+	4.35945i	−0.517329	+	0.150955i
$835$	−8.51278			−0.294597
$836$	6.94158	−	4.42810i	0.240079	−	0.153149i
$837$	16.6840			0.576683
$838$	43.1700	−	12.5969i	1.49128	−	0.435153i
$839$	−15.0659			−0.520132			−0.260066	−	0.965591i	$-0.583744\pi$
$839$	−15.0659			−0.520132			−0.260066	+	0.965591i	$0.583744\pi$
$840$	−1.47217	+	1.68173i	−0.0507948	+	0.0580251i
$841$	−28.9189			−0.997203
$842$	5.31185	+	18.2039i	0.183059	+	0.627348i
$843$	−16.1542			−0.556380
$844$	−15.8487	−	24.8447i	−0.545534	−	0.855189i
$845$			7.30390i			0.251262i
$846$	13.3077	+	45.6060i	0.457529	+	1.56797i
$847$	1.78008			0.0611641
$848$	27.0303	+	12.5652i	0.928225	+	0.431489i
$849$			2.77002i			0.0950669i
$850$	−1.26584	−	4.33809i	−0.0434181	−	0.148795i
$851$	8.39754	−	42.0238i	0.287864	−	1.44056i
$852$	1.67495	−	1.06847i	0.0573830	−	0.0366052i
$853$	40.8505			1.39869			0.699347	−	0.714782i	$-0.253474\pi$
$853$	40.8505			1.39869			0.699347	+	0.714782i	$0.253474\pi$
$854$	3.55286	+	12.1758i	0.121576	+	0.416646i
$855$			2.95207i			0.100959i
$856$	−11.3113	+	12.9214i	−0.386613	+	0.441645i
$857$	−17.2146			−0.588039			−0.294019	−	0.955799i	$-0.594993\pi$
$857$	−17.2146			−0.588039			−0.294019	+	0.955799i	$0.594993\pi$
$858$	−2.27401	−	7.79312i	−0.0776336	−	0.266053i
$859$			23.8177i			0.812649i	0.913729	+	0.406325i	$0.133190\pi$
$859$			23.8177i			0.812649i	−0.913729	+	0.406325i	$0.866810\pi$
$860$	−6.53059	−	10.2375i	−0.222691	−	0.349095i
$861$			1.99116i			0.0678586i
$862$	−21.2684	+	6.20608i	−0.724406	+	0.211380i
$863$		−	47.1128i		−	1.60374i	−0.597499	−	0.801870i	$-0.703839\pi$
$863$		−	47.1128i		−	1.60374i	0.597499	−	0.801870i	$-0.296161\pi$
$864$	−21.0443	−	3.20687i	−0.715942	−	0.109100i
$865$			3.19542i			0.108647i
$866$	−5.93380	−	20.3353i	−0.201639	−	0.691022i
$867$		−	4.61309i		−	0.156669i
$868$	5.54609	+	8.69415i	0.188247	+	0.295099i
$869$	18.0000			0.610608
$870$	0.262715	−	0.0766596i	0.00890688	−	0.00259901i
$871$	27.2090			0.921940
$872$	17.0561	+	14.9308i	0.577594	+	0.505621i
$873$		−	34.4787i		−	1.16693i
$874$	−7.85821	+	0.682894i	−0.265808	+	0.0230992i
$875$			1.16300i			0.0393165i
$876$	−3.57269	−	5.60062i	−0.120710	−	0.189227i
$877$	−13.5862			−0.458775			−0.229388	−	0.973335i	$-0.573672\pi$
$877$	−13.5862			−0.458775			−0.229388	+	0.973335i	$0.573672\pi$
$878$	9.20836	+	31.5574i	0.310767	+	1.06501i
$879$	15.4116			0.519820
$880$	12.8399	+	5.96870i	0.432834	+	0.201205i
$881$		−	0.390833i		−	0.0131675i	−0.999978	−	0.00658375i	$-0.997904\pi$
$881$		−	0.390833i		−	0.0131675i	0.999978	−	0.00658375i	$-0.00209569\pi$
$882$	−19.4612	+	5.67874i	−0.655294	+	0.191213i
$883$			41.1920i			1.38622i	0.720831	+	0.693110i	$0.243760\pi$
$883$			41.1920i			1.38622i	−0.720831	+	0.693110i	$0.756240\pi$
$884$	−8.20295	−	12.8591i	−0.275895	−	0.432498i
$885$		−	5.78412i		−	0.194431i
$886$	14.8012	+	50.7244i	0.497257	+	1.70412i
$887$		−	28.5670i		−	0.959186i	−0.877491	−	0.479593i	$-0.840784\pi$
$887$		−	28.5670i		−	0.959186i	0.877491	−	0.479593i	$-0.159216\pi$
$888$	−11.3113	+	12.9214i	−0.379583	+	0.433615i
$889$		−	5.83984i		−	0.195862i
$890$	−4.15995	+	1.21386i	−0.139442	+	0.0406888i
$891$	−17.9050			−0.599839
$892$	−9.29488	−	14.5708i	−0.311215	−	0.487867i
$893$		−	15.3915i		−	0.515058i
$894$	−15.8775	+	4.63303i	−0.531024	+	0.154952i
$895$	−2.24289			−0.0749715
$896$	−5.32443	−	12.0324i	−0.177877	−	0.401974i
$897$	−1.52396	+	7.62634i	−0.0508835	+	0.254636i
$898$	−43.9501	+	12.8245i	−1.46663	+	0.427960i
$899$		−	1.26271i		−	0.0421137i
$900$	−4.27998	+	2.73024i	−0.142666	+	0.0910081i
$901$	−23.8123			−0.793303
$902$	12.1093	−	3.53346i	0.403196	−	0.117651i
$903$		−	4.79782i		−	0.159661i
$904$	10.4432	+	9.14187i	0.347335	+	0.304054i
$905$	0.433943			0.0144247
$906$	−3.51219	+	1.02485i	−0.116685	+	0.0340483i
$907$	−11.2367			−0.373107			−0.186553	−	0.982445i	$-0.559732\pi$
$907$	−11.2367			−0.373107			−0.186553	+	0.982445i	$0.559732\pi$
$908$	−5.99688	+	3.82547i	−0.199013	+	0.126953i
$909$	−35.1377			−1.16544
$910$	1.09956	+	3.76824i	0.0364502	+	0.124916i
$911$	11.5022			0.381085			0.190543	−	0.981679i	$-0.438975\pi$
$911$	11.5022			0.381085			0.190543	+	0.981679i	$0.438975\pi$
$912$	2.86630	+	1.33241i	0.0949127	+	0.0441205i
$913$	−53.6148			−1.77439
$914$	−5.01251	−	17.1780i	−0.165799	−	0.568199i
$915$		−	5.23978i		−	0.173222i
$916$	7.62922	+	11.9597i	0.252076	+	0.395160i
$917$			2.60847i			0.0861393i
$918$	16.3246	−	4.76348i	0.538793	−	0.157218i
$919$	−38.1765			−1.25933			−0.629663	−	0.776869i	$-0.716807\pi$
$919$	−38.1765			−1.25933			−0.629663	+	0.776869i	$0.716807\pi$
$920$	−8.25780	−	10.7614i	−0.272252	−	0.354794i
$921$	−8.39054			−0.276478
$922$	−36.4945	+	10.6490i	−1.20188	+	0.350706i
$923$		−	3.48925i		−	0.114850i
$924$	3.00873	+	4.71655i	0.0989801	+	0.155163i
$925$			8.93580i			0.293807i
$926$	4.48447	+	15.3684i	0.147369	+	0.505038i
$927$	28.8410			0.947262
$928$	−0.242708	+	1.59272i	−0.00796728	+	0.0522835i
$929$	−8.03510			−0.263623			−0.131812	−	0.991275i	$-0.542079\pi$
$929$	−8.03510			−0.263623			−0.131812	+	0.991275i	$0.542079\pi$
$930$	−1.19337	−	4.08970i	−0.0391320	−	0.134107i
$931$	6.56795			0.215256
$932$	5.87288	−	3.74637i	0.192373	−	0.122716i
$933$	16.2785			0.532934
$934$	−40.5659	+	11.8370i	−1.32736	+	0.387320i
$935$	−11.3113			−0.369920
$936$	−11.2863	+	12.8928i	−0.368904	+	0.421415i
$937$			36.5045i			1.19255i	0.802781	+	0.596274i	$0.203353\pi$
$937$			36.5045i			1.19255i	−0.802781	+	0.596274i	$0.796647\pi$
$938$	−18.0000	+	5.25236i	−0.587721	+	0.171495i
$939$	3.71626			0.121276
$940$	22.3150	−	14.2350i	0.727835	−	0.464294i
$941$			17.5802i			0.573099i	0.958065	+	0.286549i	$0.0925083\pi$
$941$			17.5802i			0.573099i	−0.958065	+	0.286549i	$0.907492\pi$
$942$	15.4773	−	4.51622i	0.504276	−	0.147147i
$943$	−11.8501	−	2.36800i	−0.385894	−	0.0771126i
$944$	30.8780	+	14.3537i	1.00499	+	0.467174i
$945$	−4.37646			−0.142366
$946$	−29.1780	+	8.51408i	−0.948660	+	0.276817i
$947$		−	46.1938i		−	1.50110i	−0.660815	−	0.750549i	$-0.729789\pi$
$947$		−	46.1938i		−	1.50110i	0.660815	−	0.750549i	$-0.270211\pi$
$948$	3.71626	+	5.82568i	0.120699	+	0.189209i
$949$	−11.6672			−0.378732
$950$	1.57888	−	0.460714i	0.0512257	−	0.0149475i
$951$			5.95501i			0.193104i
$952$	7.90892	+	6.92341i	0.256330	+	0.224389i
$953$			52.9790i			1.71616i	0.513518	+	0.858079i	$0.328342\pi$
$953$			52.9790i			1.71616i	−0.513518	+	0.858079i	$0.671658\pi$
$954$	7.49333	+	25.6799i	0.242605	+	0.831417i
$955$			15.1460i			0.490114i
$956$	5.35681	+	8.39743i	0.173252	+	0.271592i
$957$		−	0.685015i		−	0.0221434i
$958$	38.0851	−	11.1131i	1.23047	−	0.359049i
$959$		−	6.36090i		−	0.205404i
$960$	0.719159	+	5.38792i	0.0232107	+	0.173894i
$961$	11.3433			0.365914
$962$	8.44841	+	28.9530i	0.272388	+	0.933481i
$963$	−15.4116			−0.496631
$964$	−27.6586	−	43.3582i	−0.890825	−	1.39647i
$965$		−	12.1152i		−	0.390002i
$966$	−0.464001	−	5.33937i	−0.0149290	−	0.171791i
$967$			51.8494i			1.66737i	0.552244	+	0.833683i	$0.313772\pi$
$967$			51.8494i			1.66737i	−0.552244	+	0.833683i	$0.686228\pi$
$968$	2.85151	−	3.25740i	0.0916508	−	0.104697i
$969$	−2.52506			−0.0811167
$970$	−18.4406	+	5.38091i	−0.592091	+	0.172771i
$971$	8.84721			0.283921			0.141960	−	0.989872i	$-0.454659\pi$
$971$	8.84721			0.283921			0.141960	+	0.989872i	$0.454659\pi$
$972$	−15.8395	−	24.8302i	−0.508051	−	0.796430i
$973$		−	18.8361i		−	0.603859i
$974$	12.3339	+	42.2687i	0.395203	+	1.35438i
$975$		−	1.62164i		−	0.0519341i
$976$	27.9720	+	13.0029i	0.895363	+	0.416213i
$977$			27.4493i			0.878181i	0.898443	+	0.439090i	$0.144699\pi$
$977$			27.4493i			0.878181i	−0.898443	+	0.439090i	$0.855301\pi$
$978$	−14.6059	+	4.26197i	−0.467046	+	0.136283i
$979$			10.8468i			0.346667i
$980$	6.07442	+	9.52238i	0.194040	+	0.304181i
$981$			20.3431i			0.649506i
$982$	12.2608	+	42.0181i	0.391257	+	1.34085i
$983$	−6.62295			−0.211239			−0.105620	−	0.994407i	$-0.533683\pi$
$983$	−6.62295			−0.211239			−0.105620	+	0.994407i	$0.533683\pi$
$984$	3.64367	+	3.18964i	0.116156	+	0.101682i
$985$		−	12.0252i		−	0.383154i
$986$	−0.360519	−	1.23551i	−0.0114813	−	0.0393467i
$987$	10.4580			0.332881
$988$	4.68017	−	2.98553i	0.148896	−	0.0949823i
$989$	28.5536	+	5.70582i	0.907951	+	0.181434i
$990$	3.55948	+	12.1985i	0.113128	+	0.387692i
$991$		−	26.6720i		−	0.847265i	−0.905834	−	0.423633i	$-0.860755\pi$
$991$		−	26.6720i		−	0.847265i	0.905834	−	0.423633i	$-0.139245\pi$
$992$	24.7939	+	3.77825i	0.787208	+	0.119960i
$993$	−21.9684			−0.697148
$994$	0.673557	+	2.30830i	0.0213639	+	0.0732149i
$995$			26.5465i			0.841581i
$996$	−11.0692	−	17.3524i	−0.350743	−	0.549830i
$997$	−56.5898			−1.79222			−0.896108	−	0.443837i	$-0.853617\pi$
$997$	−56.5898			−1.79222			−0.896108	+	0.443837i	$0.853617\pi$
$998$	−2.60190	−	8.91681i	−0.0823618	−	0.282257i
$999$	−33.6262			−1.06389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.e.a.91.13	✓	16
4.3	odd	2	inner	460.2.e.a.91.15	yes	16
23.22	odd	2	inner	460.2.e.a.91.14	yes	16
92.91	even	2	inner	460.2.e.a.91.16	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.e.a.91.13	✓	16	1.1	even	1	trivial
460.2.e.a.91.14	yes	16	23.22	odd	2	inner
460.2.e.a.91.15	yes	16	4.3	odd	2	inner
460.2.e.a.91.16	yes	16	92.91	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35760 - 0.396143i) q^{2} -0.679463i q^{3} +(1.68614 - 1.07561i) q^{4} -1.00000i q^{5} +(-0.269165 - 0.922437i) q^{6} +1.16300 q^{7} +(1.86301 - 2.12819i) q^{8} +2.53833 q^{9} +O(q^{10})\)	\(q+(1.35760 - 0.396143i) q^{2} -0.679463i q^{3} +(1.68614 - 1.07561i) q^{4} -1.00000i q^{5} +(-0.269165 - 0.922437i) q^{6} +1.16300 q^{7} +(1.86301 - 2.12819i) q^{8} +2.53833 q^{9} +(-0.396143 - 1.35760i) q^{10} -3.53986 q^{11} +(-0.730835 - 1.14567i) q^{12} -2.38665 q^{13} +(1.57888 - 0.460714i) q^{14} -0.679463 q^{15} +(1.68614 - 3.62725i) q^{16} +3.19542i q^{17} +(3.44603 - 1.00554i) q^{18} -1.16300 q^{19} +(-1.07561 - 1.68614i) q^{20} -0.790214i q^{21} +(-4.80570 + 1.40229i) q^{22} +(4.70285 + 0.939764i) q^{23} +(-1.44603 - 1.26584i) q^{24} -1.00000 q^{25} +(-3.24011 + 0.945456i) q^{26} -3.76309i q^{27} +(1.96098 - 1.25093i) q^{28} -0.284805 q^{29} +(-0.922437 + 0.269165i) q^{30} +4.43358i q^{31} +(0.852189 - 5.59230i) q^{32} +2.40520i q^{33} +(1.26584 + 4.33809i) q^{34} -1.16300i q^{35} +(4.27998 - 2.73024i) q^{36} -8.93580i q^{37} +(-1.57888 + 0.460714i) q^{38} +1.62164i q^{39} +(-2.12819 - 1.86301i) q^{40} -2.51978 q^{41} +(-0.313038 - 1.07279i) q^{42} +6.07154 q^{43} +(-5.96870 + 3.80749i) q^{44} -2.53833i q^{45} +(6.75686 - 0.587185i) q^{46} +13.2344i q^{47} +(-2.46458 - 1.14567i) q^{48} -5.64744 q^{49} +(-1.35760 + 0.396143i) q^{50} +2.17117 q^{51} +(-4.02423 + 2.56710i) q^{52} +7.45202i q^{53} +(-1.49072 - 5.10876i) q^{54} +3.53986i q^{55} +(2.16667 - 2.47508i) q^{56} +0.790214i q^{57} +(-0.386651 + 0.112824i) q^{58} +8.51278i q^{59} +(-1.14567 + 0.730835i) q^{60} +7.71164i q^{61} +(1.75634 + 6.01902i) q^{62} +2.95207 q^{63} +(-1.05842 - 7.92967i) q^{64} +2.38665i q^{65} +(0.952806 + 3.26530i) q^{66} -11.4005 q^{67} +(3.43701 + 5.38792i) q^{68} +(0.638535 - 3.19542i) q^{69} +(-0.460714 - 1.57888i) q^{70} +1.46199i q^{71} +(4.72892 - 5.40206i) q^{72} +4.88851 q^{73} +(-3.53986 - 12.1312i) q^{74} +0.679463i q^{75} +(-1.96098 + 1.25093i) q^{76} -4.11684 q^{77} +(0.642403 + 2.20154i) q^{78} -5.08495 q^{79} +(-3.62725 - 1.68614i) q^{80} +5.05811 q^{81} +(-3.42084 + 0.998194i) q^{82} +15.1460 q^{83} +(-0.849959 - 1.33241i) q^{84} +3.19542 q^{85} +(8.24271 - 2.40520i) q^{86} +0.193515i q^{87} +(-6.59477 + 7.53351i) q^{88} -3.06420i q^{89} +(-1.00554 - 3.44603i) q^{90} -2.77567 q^{91} +(8.94049 - 3.47385i) q^{92} +3.01246 q^{93} +(5.24271 + 17.9669i) q^{94} +1.16300i q^{95} +(-3.79976 - 0.579031i) q^{96} -13.5832i q^{97} +(-7.66695 + 2.23720i) q^{98} -8.98533 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