LMFDB - Embedded newform 572.2.e.b.131.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(131,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("572.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.5
Character	$\chi$	$=$	572.131
Dual form			572.2.e.b.131.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39939 - 0.204204i) q^{2} -3.30990i q^{3} +(1.91660 + 0.571522i) q^{4} +3.38816 q^{5} +(-0.675895 + 4.63186i) q^{6} +3.64850 q^{7} +(-2.56537 - 1.19116i) q^{8} -7.95546 q^{9} +O(q^{10})$	\(q+(-1.39939 - 0.204204i) q^{2} -3.30990i q^{3} +(1.91660 + 0.571522i) q^{4} +3.38816 q^{5} +(-0.675895 + 4.63186i) q^{6} +3.64850 q^{7} +(-2.56537 - 1.19116i) q^{8} -7.95546 q^{9} +(-4.74137 - 0.691875i) q^{10} +(-3.04826 - 1.30695i) q^{11} +(1.89168 - 6.34377i) q^{12} +1.00000i q^{13} +(-5.10568 - 0.745036i) q^{14} -11.2145i q^{15} +(3.34672 + 2.19076i) q^{16} -2.46031i q^{17} +(11.1328 + 1.62454i) q^{18} +2.27167 q^{19} +(6.49376 + 1.93641i) q^{20} -12.0762i q^{21} +(3.99883 + 2.45141i) q^{22} +3.66413i q^{23} +(-3.94263 + 8.49114i) q^{24} +6.47965 q^{25} +(0.204204 - 1.39939i) q^{26} +16.4021i q^{27} +(6.99271 + 2.08520i) q^{28} -5.42789i q^{29} +(-2.29004 + 15.6935i) q^{30} -8.06247i q^{31} +(-4.23602 - 3.74915i) q^{32} +(-4.32589 + 10.0894i) q^{33} +(-0.502404 + 3.44294i) q^{34} +12.3617 q^{35} +(-15.2475 - 4.54673i) q^{36} -1.66138 q^{37} +(-3.17896 - 0.463884i) q^{38} +3.30990 q^{39} +(-8.69190 - 4.03585i) q^{40} -4.13884i q^{41} +(-2.46600 + 16.8993i) q^{42} +0.268482 q^{43} +(-5.09534 - 4.24706i) q^{44} -26.9544 q^{45} +(0.748229 - 5.12756i) q^{46} -1.47252i q^{47} +(7.25121 - 11.0773i) q^{48} +6.31152 q^{49} +(-9.06758 - 1.32317i) q^{50} -8.14339 q^{51} +(-0.571522 + 1.91660i) q^{52} +0.462704 q^{53} +(3.34937 - 22.9530i) q^{54} +(-10.3280 - 4.42817i) q^{55} +(-9.35975 - 4.34595i) q^{56} -7.51902i q^{57} +(-1.10840 + 7.59576i) q^{58} +12.1193i q^{59} +(6.40933 - 21.4937i) q^{60} +13.0200i q^{61} +(-1.64639 + 11.2826i) q^{62} -29.0255 q^{63} +(5.16227 + 6.11155i) q^{64} +3.38816i q^{65} +(8.11392 - 13.2357i) q^{66} +3.80684i q^{67} +(1.40612 - 4.71543i) q^{68} +12.1279 q^{69} +(-17.2989 - 2.52430i) q^{70} +3.16290i q^{71} +(20.4087 + 9.47624i) q^{72} +4.95698i q^{73} +(2.32493 + 0.339261i) q^{74} -21.4470i q^{75} +(4.35389 + 1.29831i) q^{76} +(-11.1216 - 4.76841i) q^{77} +(-4.63186 - 0.675895i) q^{78} +8.18019 q^{79} +(11.3392 + 7.42266i) q^{80} +30.4230 q^{81} +(-0.845166 + 5.79186i) q^{82} -7.49670 q^{83} +(6.90180 - 23.1452i) q^{84} -8.33593i q^{85} +(-0.375712 - 0.0548250i) q^{86} -17.9658 q^{87} +(6.26312 + 6.98379i) q^{88} +11.1692 q^{89} +(37.7198 + 5.50419i) q^{90} +3.64850i q^{91} +(-2.09413 + 7.02268i) q^{92} -26.6860 q^{93} +(-0.300694 + 2.06063i) q^{94} +7.69680 q^{95} +(-12.4093 + 14.0208i) q^{96} -2.07823 q^{97} +(-8.83229 - 1.28883i) q^{98} +(24.2503 + 10.3974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.39939	−	0.204204i	−0.989520	−	0.144394i
$2$	−1.39939	−	0.204204i	−0.989520	−	0.144394i
$3$		−	3.30990i		−	1.91097i	−0.295033	−	0.955487i	$-0.595331\pi$
$3$		−	3.30990i		−	1.91097i	0.295033	−	0.955487i	$-0.404669\pi$
$4$	1.91660	+	0.571522i	0.958301	+	0.285761i
$5$	3.38816			1.51523			0.757616	−	0.652700i	$-0.226364\pi$
$5$	3.38816			1.51523			0.757616	+	0.652700i	$0.226364\pi$
$6$	−0.675895	+	4.63186i	−0.275933	+	1.89095i
$7$	3.64850			1.37900			0.689501	−	0.724285i	$-0.257830\pi$
$7$	3.64850			1.37900			0.689501	+	0.724285i	$0.257830\pi$
$8$	−2.56537	−	1.19116i	−0.906996	−	0.421139i
$9$	−7.95546			−2.65182
$10$	−4.74137	−	0.691875i	−1.49935	−	0.218790i
$11$	−3.04826	−	1.30695i	−0.919084	−	0.394061i
$11$	−3.04826	−	1.30695i	−0.919084	−	0.394061i
$12$	1.89168	−	6.34377i	0.546082	−	1.83129i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−5.10568	−	0.745036i	−1.36455	−	0.199119i
$15$		−	11.2145i		−	2.89557i
$16$	3.34672	+	2.19076i	0.836681	+	0.547690i
$17$		−	2.46031i		−	0.596713i	−0.954455	−	0.298356i	$-0.903562\pi$
$17$		−	2.46031i		−	0.596713i	0.954455	−	0.298356i	$-0.0964384\pi$
$18$	11.1328	+	1.62454i	2.62403	+	0.382907i
$19$	2.27167			0.521158			0.260579	−	0.965453i	$-0.416087\pi$
$19$	2.27167			0.521158			0.260579	+	0.965453i	$0.416087\pi$
$20$	6.49376	+	1.93641i	1.45205	+	0.432995i
$21$		−	12.0762i		−	2.63524i
$22$	3.99883	+	2.45141i	0.852552	+	0.522642i
$23$			3.66413i			0.764024i	0.924157	+	0.382012i	$0.124769\pi$
$23$			3.66413i			0.764024i	−0.924157	+	0.382012i	$0.875231\pi$
$24$	−3.94263	+	8.49114i	−0.804786	+	1.73325i
$25$	6.47965			1.29593
$26$	0.204204	−	1.39939i	0.0400476	−	0.274444i
$27$			16.4021i			3.15659i
$28$	6.99271	+	2.08520i	1.32150	+	0.394065i
$29$		−	5.42789i		−	1.00793i	−0.863723	−	0.503967i	$-0.831873\pi$
$29$		−	5.42789i		−	1.00793i	0.863723	−	0.503967i	$-0.168127\pi$
$30$	−2.29004	+	15.6935i	−0.418102	+	2.86523i
$31$		−	8.06247i		−	1.44806i	−0.689767	−	0.724031i	$-0.742287\pi$
$31$		−	8.06247i		−	1.44806i	0.689767	−	0.724031i	$-0.257713\pi$
$32$	−4.23602	−	3.74915i	−0.748830	−	0.662762i
$33$	−4.32589	+	10.0894i	−0.753041	+	1.75635i
$34$	−0.502404	+	3.44294i	−0.0861616	+	0.590459i
$35$	12.3617			2.08951
$36$	−15.2475	−	4.54673i	−2.54124	−	0.757788i
$37$	−1.66138			−0.273130			−0.136565	−	0.990631i	$-0.543606\pi$
$37$	−1.66138			−0.273130			−0.136565	+	0.990631i	$0.543606\pi$
$38$	−3.17896	−	0.463884i	−0.515696	−	0.0752519i
$39$	3.30990			0.530009
$40$	−8.69190	−	4.03585i	−1.37431	−	0.638124i
$41$		−	4.13884i		−	0.646378i	−0.946334	−	0.323189i	$-0.895245\pi$
$41$		−	4.13884i		−	0.646378i	0.946334	−	0.323189i	$-0.104755\pi$
$42$	−2.46600	+	16.8993i	−0.380512	+	2.60762i
$43$	0.268482			0.0409431			0.0204716	−	0.999790i	$-0.493483\pi$
$43$	0.268482			0.0409431			0.0204716	+	0.999790i	$0.493483\pi$
$44$	−5.09534	−	4.24706i	−0.768152	−	0.640268i
$45$	−26.9544			−4.01813
$46$	0.748229	−	5.12756i	0.110320	−	0.756018i
$47$		−	1.47252i		−	0.214789i	−0.994216	−	0.107395i	$-0.965749\pi$
$47$		−	1.47252i		−	0.214789i	0.994216	−	0.107395i	$-0.0342508\pi$
$48$	7.25121	−	11.0773i	1.04662	−	1.59888i
$49$	6.31152			0.901645
$50$	−9.06758	−	1.32317i	−1.28235	−	0.187124i
$51$	−8.14339			−1.14030
$52$	−0.571522	+	1.91660i	−0.0792559	+	0.265785i
$53$	0.462704			0.0635573			0.0317786	−	0.999495i	$-0.489883\pi$
$53$	0.462704			0.0635573			0.0317786	+	0.999495i	$0.489883\pi$
$54$	3.34937	−	22.9530i	0.455792	−	3.12351i
$55$	−10.3280	−	4.42817i	−1.39263	−	0.597094i
$56$	−9.35975	−	4.34595i	−1.25075	−	0.580752i
$57$		−	7.51902i		−	0.995919i
$58$	−1.10840	+	7.59576i	−0.145539	+	0.997371i
$59$			12.1193i			1.57780i	0.614523	+	0.788899i	$0.289349\pi$
$59$			12.1193i			1.57780i	−0.614523	+	0.788899i	$0.710651\pi$
$60$	6.40933	−	21.4937i	0.827442	−	2.77483i
$61$			13.0200i			1.66705i	0.552484	+	0.833523i	$0.313680\pi$
$61$			13.0200i			1.66705i	−0.552484	+	0.833523i	$0.686320\pi$
$62$	−1.64639	+	11.2826i	−0.209091	+	1.43289i
$63$	−29.0255			−3.65687
$64$	5.16227	+	6.11155i	0.645284	+	0.763943i
$65$			3.38816i			0.420250i
$66$	8.11392	−	13.2357i	0.998755	−	1.62921i
$67$			3.80684i			0.465079i	0.972587	+	0.232539i	$0.0747035\pi$
$67$			3.80684i			0.465079i	−0.972587	+	0.232539i	$0.925297\pi$
$68$	1.40612	−	4.71543i	0.170517	−	0.571830i
$69$	12.1279			1.46003
$70$	−17.2989	−	2.52430i	−2.06761	−	0.301712i
$71$			3.16290i			0.375367i	0.982230	+	0.187683i	$0.0600979\pi$
$71$			3.16290i			0.375367i	−0.982230	+	0.187683i	$0.939902\pi$
$72$	20.4087	+	9.47624i	2.40519	+	1.11679i
$73$			4.95698i			0.580171i	0.957001	+	0.290086i	$0.0936838\pi$
$73$			4.95698i			0.580171i	−0.957001	+	0.290086i	$0.906316\pi$
$74$	2.32493	+	0.339261i	0.270268	+	0.0394383i
$75$		−	21.4470i		−	2.47649i
$76$	4.35389	+	1.29831i	0.499426	+	0.148927i
$77$	−11.1216	−	4.76841i	−1.26742	−	0.543411i
$78$	−4.63186	−	0.675895i	−0.524454	−	0.0765300i
$79$	8.18019			0.920343			0.460171	−	0.887830i	$-0.347788\pi$
$79$	8.18019			0.920343			0.460171	+	0.887830i	$0.347788\pi$
$80$	11.3392	+	7.42266i	1.26777	+	0.829878i
$81$	30.4230			3.38034
$82$	−0.845166	+	5.79186i	−0.0933329	+	0.639604i
$83$	−7.49670			−0.822869			−0.411435	−	0.911439i	$-0.634972\pi$
$83$	−7.49670			−0.822869			−0.411435	+	0.911439i	$0.634972\pi$
$84$	6.90180	−	23.1452i	0.753048	−	2.52535i
$85$		−	8.33593i		−	0.904159i
$86$	−0.375712	−	0.0548250i	−0.0405140	−	0.00591193i
$87$	−17.9658			−1.92614
$88$	6.26312	+	6.98379i	0.667651	+	0.744474i
$89$	11.1692			1.18394			0.591968	−	0.805961i	$-0.298351\pi$
$89$	11.1692			1.18394			0.591968	+	0.805961i	$0.298351\pi$
$90$	37.7198	+	5.50419i	3.97602	+	0.580193i
$91$			3.64850i			0.382466i
$92$	−2.09413	+	7.02268i	−0.218329	+	0.732165i
$93$	−26.6860			−2.76721
$94$	−0.300694	+	2.06063i	−0.0310142	+	0.212538i
$95$	7.69680			0.789675
$96$	−12.4093	+	14.0208i	−1.26652	+	1.43099i
$97$	−2.07823			−0.211012			−0.105506	−	0.994419i	$-0.533646\pi$
$97$	−2.07823			−0.211012			−0.105506	+	0.994419i	$0.533646\pi$
$98$	−8.83229	−	1.28883i	−0.892196	−	0.130192i
$99$	24.2503	+	10.3974i	2.43725	+	1.04498i
$100$	12.4189	+	3.70327i	1.24189	+	0.370327i
$101$		−	3.48082i		−	0.346354i	−0.984891	−	0.173177i	$-0.944597\pi$
$101$		−	3.48082i		−	0.346354i	0.984891	−	0.173177i	$-0.0554033\pi$
$102$	11.3958	+	1.66291i	1.12835	+	0.164653i
$103$		−	0.786469i		−	0.0774931i	−0.999249	−	0.0387465i	$-0.987664\pi$
$103$		−	0.786469i		−	0.0774931i	0.999249	−	0.0387465i	$-0.0123365\pi$
$104$	1.19116	−	2.56537i	0.116803	−	0.251555i
$105$		−	40.9160i		−	3.99300i
$106$	−0.647504	−	0.0944858i	−0.0628912	−	0.00917727i
$107$	5.01242			0.484569			0.242285	−	0.970205i	$-0.422103\pi$
$107$	5.01242			0.484569			0.242285	+	0.970205i	$0.422103\pi$
$108$	−9.37417	+	31.4363i	−0.902030	+	3.02496i
$109$			4.68963i			0.449185i	0.974453	+	0.224593i	$0.0721051\pi$
$109$			4.68963i			0.449185i	−0.974453	+	0.224593i	$0.927895\pi$
$110$	13.5487	+	8.30577i	1.29182	+	0.791924i
$111$			5.49902i			0.521944i
$112$	12.2105	+	7.99298i	1.15378	+	0.755266i
$113$	−0.503468			−0.0473623			−0.0236811	−	0.999720i	$-0.507539\pi$
$113$	−0.503468			−0.0473623			−0.0236811	+	0.999720i	$0.507539\pi$
$114$	−1.53541	+	10.5221i	−0.143805	+	0.985482i
$115$			12.4147i			1.15767i
$116$	3.10216	−	10.4031i	0.288029	−	0.965904i
$117$		−	7.95546i		−	0.735483i
$118$	2.47480	−	16.9597i	0.227824	−	1.56126i
$119$		−	8.97643i		−	0.822868i
$120$	−13.3583	+	28.7694i	−1.21944	+	2.62627i
$121$	7.58375	+	7.96786i	0.689431	+	0.724351i
$122$	2.65874	−	18.2202i	0.240711	−	1.64958i
$123$	−13.6992			−1.23521
$124$	4.60788	−	15.4526i	0.413800	−	1.38768i
$125$	5.01330			0.448403
$126$	40.6180	+	5.92711i	3.61854	+	0.528029i
$127$	15.7562			1.39814			0.699070	−	0.715053i	$-0.253597\pi$
$127$	15.7562			1.39814			0.699070	+	0.715053i	$0.253597\pi$
$128$	−5.97604	−	9.60661i	−0.528213	−	0.849112i
$129$		−	0.888649i		−	0.0782412i
$130$	0.691875	−	4.74137i	0.0606815	−	0.415846i
$131$	−18.4648			−1.61328			−0.806640	−	0.591044i	$-0.798716\pi$
$131$	−18.4648			−1.61328			−0.806640	+	0.591044i	$0.798716\pi$
$132$	−14.0573	+	16.8651i	−1.22354	+	1.46792i
$133$	8.28819			0.718677
$134$	0.777370	−	5.32726i	0.0671545	−	0.460205i
$135$			55.5730i			4.78297i
$136$	−2.93063	+	6.31161i	−0.251299	+	0.541216i
$137$	−10.6968			−0.913893			−0.456947	−	0.889494i	$-0.651057\pi$
$137$	−10.6968			−0.913893			−0.456947	+	0.889494i	$0.651057\pi$
$138$	−16.9717	−	2.47657i	−1.44473	−	0.210819i
$139$	4.88465			0.414311			0.207155	−	0.978308i	$-0.433579\pi$
$139$	4.88465			0.414311			0.207155	+	0.978308i	$0.433579\pi$
$140$	23.6924	+	7.06499i	2.00238	+	0.597100i
$141$	−4.87390			−0.410456
$142$	0.645875	−	4.42613i	0.0542006	−	0.371433i
$143$	1.30695	−	3.04826i	0.109293	−	0.254908i
$144$	−26.6247	−	17.4285i	−2.21873	−	1.45238i
$145$		−	18.3906i		−	1.52726i
$146$	1.01223	−	6.93677i	0.0837731	−	0.574091i
$147$		−	20.8905i		−	1.72302i
$148$	−3.18421	−	0.949518i	−0.261741	−	0.0780499i
$149$		−	6.42574i		−	0.526417i	−0.964739	−	0.263209i	$-0.915219\pi$
$149$		−	6.42574i		−	0.526417i	0.964739	−	0.263209i	$-0.0847807\pi$
$150$	−4.37956	+	30.0128i	−0.357590	+	2.45054i
$151$	−1.34645			−0.109572			−0.0547862	−	0.998498i	$-0.517448\pi$
$151$	−1.34645			−0.109572			−0.0547862	+	0.998498i	$0.517448\pi$
$152$	−5.82769	−	2.70593i	−0.472688	−	0.219480i
$153$			19.5729i			1.58238i
$154$	14.5897	+	8.94394i	1.17567	+	0.720724i
$155$		−	27.3170i		−	2.19415i
$156$	6.34377	+	1.89168i	0.507908	+	0.151456i
$157$	−0.284135			−0.0226765			−0.0113382	−	0.999936i	$-0.503609\pi$
$157$	−0.284135			−0.0226765			−0.0113382	+	0.999936i	$0.503609\pi$
$158$	−11.4473	−	1.67042i	−0.910698	−	0.132892i
$159$		−	1.53151i		−	0.121456i
$160$	−14.3523	−	12.7027i	−1.13465	−	1.00424i
$161$			13.3686i			1.05359i
$162$	−42.5738	−	6.21249i	−3.34491	−	0.488100i
$163$			22.6394i			1.77326i	0.462482	+	0.886629i	$0.346959\pi$
$163$			22.6394i			1.77326i	−0.462482	+	0.886629i	$0.653041\pi$
$164$	2.36544	−	7.93250i	0.184710	−	0.619424i
$165$	−14.6568	+	34.1847i	−1.14103	+	2.66127i
$166$	10.4908	+	1.53085i	0.814246	+	0.118817i
$167$	22.6967			1.75633			0.878163	−	0.478361i	$-0.158769\pi$
$167$	22.6967			1.75633			0.878163	+	0.478361i	$0.158769\pi$
$168$	−14.3847	+	30.9799i	−1.10980	+	2.39015i
$169$	−1.00000			−0.0769231
$170$	−1.70223	+	11.6652i	−0.130555	+	0.894683i
$171$	−18.0722			−1.38202
$172$	0.514573	+	0.153443i	0.0392358	+	0.0117000i
$173$			13.4534i			1.02284i	0.859331	+	0.511421i	$0.170881\pi$
$173$			13.4534i			1.02284i	−0.859331	+	0.511421i	$0.829119\pi$
$174$	25.1412	+	3.66868i	1.90595	+	0.278122i
$175$	23.6410			1.78709
$176$	−7.33845	−	11.0520i	−0.553157	−	0.833077i
$177$	40.1137			3.01513
$178$	−15.6302	−	2.28080i	−1.17153	−	0.170953i
$179$			0.860764i			0.0643365i	0.999482	+	0.0321682i	$0.0102412\pi$
$179$			0.860764i			0.0643365i	−0.999482	+	0.0321682i	$0.989759\pi$
$180$	−51.6609	−	15.4051i	−3.85057	−	1.14822i
$181$	0.970978			0.0721722			0.0360861	−	0.999349i	$-0.488511\pi$
$181$	0.970978			0.0721722			0.0360861	+	0.999349i	$0.488511\pi$
$182$	0.745036	−	5.10568i	0.0552257	−	0.378458i
$183$	43.0951			3.18568
$184$	4.36457	−	9.39986i	0.321761	−	0.692967i
$185$	−5.62904			−0.413855
$186$	37.3442	+	5.44938i	2.73821	+	0.399568i
$187$	−3.21551	+	7.49966i	−0.235141	+	0.548429i
$188$	0.841578	−	2.82223i	0.0613784	−	0.205833i
$189$			59.8430i			4.35294i
$190$	−10.7709	−	1.57172i	−0.781400	−	0.114024i
$191$			4.91996i			0.355996i	0.984031	+	0.177998i	$0.0569620\pi$
$191$			4.91996i			0.355996i	−0.984031	+	0.177998i	$0.943038\pi$
$192$	20.2286	−	17.0866i	1.45988	−	1.23312i
$193$			18.3240i			1.31899i	0.751709	+	0.659495i	$0.229230\pi$
$193$			18.3240i			1.31899i	−0.751709	+	0.659495i	$0.770770\pi$
$194$	2.90826	+	0.424382i	0.208801	+	0.0304688i
$195$	11.2145			0.803087
$196$	12.0967	+	3.60717i	0.864047	+	0.257655i
$197$			8.55064i			0.609208i	0.952479	+	0.304604i	$0.0985241\pi$
$197$			8.55064i			0.609208i	−0.952479	+	0.304604i	$0.901476\pi$
$198$	−31.8125	−	19.5021i	−2.26082	−	1.38595i
$199$		−	10.0993i		−	0.715921i	−0.933737	−	0.357960i	$-0.883472\pi$
$199$		−	10.0993i		−	0.715921i	0.933737	−	0.357960i	$-0.116528\pi$
$200$	−16.6227	−	7.71831i	−1.17540	−	0.545767i
$201$	12.6003			0.888754
$202$	−0.710796	+	4.87103i	−0.0500114	+	0.342725i
$203$		−	19.8036i		−	1.38994i
$204$	−15.6076	−	4.65413i	−1.09275	−	0.325854i
$205$		−	14.0231i		−	0.979413i
$206$	−0.160600	+	1.10058i	−0.0111895	+	0.0766810i
$207$		−	29.1499i		−	2.02606i
$208$	−2.19076	+	3.34672i	−0.151902	+	0.232054i
$209$	−6.92465	−	2.96897i	−0.478988	−	0.205368i
$210$	−8.35520	+	57.2576i	−0.576564	+	3.95115i
$211$	13.2949			0.915260			0.457630	−	0.889143i	$-0.348698\pi$
$211$	13.2949			0.915260			0.457630	+	0.889143i	$0.348698\pi$
$212$	0.886819	+	0.264446i	0.0609070	+	0.0181622i
$213$	10.4689			0.717316
$214$	−7.01435	−	1.02356i	−0.479491	−	0.0699688i
$215$	0.909661			0.0620383
$216$	19.5376	−	42.0775i	1.32936	−	2.86301i
$217$		−	29.4159i		−	1.99688i
$218$	0.957640	−	6.56264i	0.0648595	−	0.444478i
$219$	16.4071			1.10869
$220$	−17.2639	−	14.3897i	−1.16393	−	0.970155i
$221$	2.46031			0.165498
$222$	1.12292	−	7.69529i	0.0753655	−	0.516474i
$223$		−	13.9178i		−	0.932005i	−0.884783	−	0.466002i	$-0.845694\pi$
$223$		−	13.9178i		−	0.932005i	0.884783	−	0.466002i	$-0.154306\pi$
$224$	−15.4551	−	13.6788i	−1.03264	−	0.913950i
$225$	−51.5486			−3.43658
$226$	0.704550	+	0.102810i	0.0468659	+	0.00683882i
$227$	−18.3127			−1.21546			−0.607728	−	0.794145i	$-0.707919\pi$
$227$	−18.3127			−1.21546			−0.607728	+	0.794145i	$0.707919\pi$
$228$	4.29729	−	14.4110i	0.284595	−	0.954390i
$229$	−17.5457			−1.15946			−0.579728	−	0.814810i	$-0.696841\pi$
$229$	−17.5457			−1.15946			−0.579728	+	0.814810i	$0.696841\pi$
$230$	2.53512	−	17.3730i	0.167161	−	1.14554i
$231$	−15.7830	+	36.8113i	−1.03844	+	2.42200i
$232$	−6.46550	+	13.9246i	−0.424481	+	0.914192i
$233$			21.7862i			1.42726i	0.700521	+	0.713632i	$0.252951\pi$
$233$			21.7862i			1.42726i	−0.700521	+	0.713632i	$0.747049\pi$
$234$	−1.62454	+	11.1328i	−0.106199	+	0.727775i
$235$		−	4.98914i		−	0.325456i
$236$	−6.92645	+	23.2279i	−0.450873	+	1.51201i
$237$		−	27.0756i		−	1.75875i
$238$	−1.83302	+	12.5616i	−0.118817	+	0.814244i
$239$	2.91796			0.188747			0.0943737	−	0.995537i	$-0.469915\pi$
$239$	2.91796			0.188747			0.0943737	+	0.995537i	$0.469915\pi$
$240$	24.5683	−	37.5318i	1.58588	−	2.42267i
$241$		−	24.7077i		−	1.59156i	−0.605585	−	0.795780i	$-0.707061\pi$
$241$		−	24.7077i		−	1.59156i	0.605585	−	0.795780i	$-0.292939\pi$
$242$	−8.98558	−	12.6988i	−0.577615	−	0.816310i
$243$		−	51.4910i		−	3.30315i
$244$	−7.44125	+	24.9542i	−0.476377	+	1.59753i
$245$	21.3844			1.36620
$246$	19.1705	+	2.79742i	1.22227	+	0.178357i
$247$			2.27167i			0.144543i
$248$	−9.60371	+	20.6832i	−0.609836	+	1.31339i
$249$			24.8133i			1.57248i
$250$	−7.01557	−	1.02373i	−0.443704	−	0.0647466i
$251$		−	25.9522i		−	1.63809i	−0.573732	−	0.819043i	$-0.694505\pi$
$251$		−	25.9522i		−	1.63809i	0.573732	−	0.819043i	$-0.305495\pi$
$252$	−55.6303	−	16.5887i	−3.50438	−	1.04499i
$253$	4.78885	−	11.1692i	0.301072	−	0.702203i
$254$	−22.0492	−	3.21748i	−1.38349	−	0.201883i
$255$	−27.5911			−1.72782
$256$	6.40113	+	14.6637i	0.400071	+	0.916484i
$257$	−1.66514			−0.103868			−0.0519342	−	0.998651i	$-0.516539\pi$
$257$	−1.66514			−0.103868			−0.0519342	+	0.998651i	$0.516539\pi$
$258$	−0.181465	+	1.24357i	−0.0112975	+	0.0774213i
$259$	−6.06155			−0.376646
$260$	−1.93641	+	6.49376i	−0.120091	+	0.402726i
$261$			43.1814i			2.67286i
$262$	25.8395	+	3.77058i	1.59637	+	0.232947i
$263$	6.26154			0.386103			0.193051	−	0.981189i	$-0.438162\pi$
$263$	6.26154			0.386103			0.193051	+	0.981189i	$0.438162\pi$
$264$	23.1157	−	20.7303i	1.42267	−	1.27586i
$265$	1.56772			0.0963040
$266$	−11.5984	−	1.69248i	−0.711146	−	0.103773i
$267$		−	36.9691i		−	2.26247i
$268$	−2.17569	+	7.29619i	−0.132902	+	0.445686i
$269$	30.9237			1.88545			0.942725	−	0.333572i	$-0.108254\pi$
$269$	30.9237			1.88545			0.942725	+	0.333572i	$0.108254\pi$
$270$	11.3482	−	77.7685i	0.690631	−	4.73284i
$271$	4.30761			0.261669			0.130834	−	0.991404i	$-0.458234\pi$
$271$	4.30761			0.261669			0.130834	+	0.991404i	$0.458234\pi$
$272$	5.38995	−	8.23398i	0.326814	−	0.499258i
$273$	12.0762			0.730883
$274$	14.9691	+	2.18434i	0.904316	+	0.131961i
$275$	−19.7516	−	8.46860i	−1.19107	−	0.510676i
$276$	23.2444	+	6.93138i	1.39915	+	0.417220i
$277$			16.8748i			1.01391i	0.861973	+	0.506954i	$0.169228\pi$
$277$			16.8748i			1.01391i	−0.861973	+	0.506954i	$0.830772\pi$
$278$	−6.83555	−	0.997464i	−0.409969	−	0.0598239i
$279$			64.1407i			3.84000i
$280$	−31.7124	−	14.7248i	−1.89518	−	0.879974i
$281$		−	21.3762i		−	1.27520i	−0.770369	−	0.637598i	$-0.779928\pi$
$281$		−	21.3762i		−	1.27520i	0.770369	−	0.637598i	$-0.220072\pi$
$282$	6.82050	+	0.995268i	0.406155	+	0.0592674i
$283$	15.8967			0.944961			0.472481	−	0.881341i	$-0.343359\pi$
$283$	15.8967			0.944961			0.472481	+	0.881341i	$0.343359\pi$
$284$	−1.80767	+	6.06201i	−0.107265	+	0.359714i
$285$		−	25.4757i		−	1.50905i
$286$	−2.45141	+	3.99883i	−0.144955	+	0.236456i
$287$		−	15.1005i		−	0.891356i
$288$	33.6995	+	29.8262i	1.98576	+	1.75753i
$289$	10.9469			0.643934
$290$	−3.75542	+	25.7357i	−0.220526	+	1.51125i
$291$			6.87873i			0.403238i
$292$	−2.83303	+	9.50056i	−0.165790	+	0.555979i
$293$		−	24.3974i		−	1.42531i	−0.701513	−	0.712657i	$-0.747492\pi$
$293$		−	24.3974i		−	1.42531i	0.701513	−	0.712657i	$-0.252508\pi$
$294$	−4.26592	+	29.2340i	−0.248793	+	1.70496i
$295$			41.0622i			2.39073i
$296$	4.26207	+	1.97898i	0.247728	+	0.115026i
$297$	21.4368	−	49.9979i	1.24389	−	2.90117i
$298$	−1.31216	+	8.99214i	−0.0760114	+	0.520900i
$299$	−3.66413			−0.211902
$300$	12.2575	−	41.1054i	0.707684	−	2.37322i
$301$	0.979555			0.0564606
$302$	1.88421	+	0.274950i	0.108424	+	0.0158216i
$303$	−11.5212			−0.661874
$304$	7.60267	+	4.97670i	0.436043	+	0.285433i
$305$			44.1141i			2.52596i
$306$	3.99686	−	27.3902i	0.228485	−	1.56579i
$307$	−4.97498			−0.283937			−0.141969	−	0.989871i	$-0.545343\pi$
$307$	−4.97498			−0.283937			−0.141969	+	0.989871i	$0.545343\pi$
$308$	−18.5903	−	15.4954i	−1.05928	−	0.882930i
$309$	−2.60314			−0.148087
$310$	−5.57823	+	38.2272i	−0.316822	+	2.17116i
$311$			20.9744i			1.18935i	0.803966	+	0.594675i	$0.202719\pi$
$311$			20.9744i			1.18935i	−0.803966	+	0.594675i	$0.797281\pi$
$312$	−8.49114	−	3.94263i	−0.480716	−	0.223207i
$313$	−13.9454			−0.788239			−0.394119	−	0.919059i	$-0.628950\pi$
$313$	−13.9454			−0.788239			−0.394119	+	0.919059i	$0.628950\pi$
$314$	0.397617	+	0.0580215i	0.0224388	+	0.00327434i
$315$	−98.3430			−5.54100
$316$	15.6782	+	4.67516i	0.881965	+	0.262998i
$317$	−30.2567			−1.69939			−0.849694	−	0.527277i	$-0.823213\pi$
$317$	−30.2567			−1.69939			−0.849694	+	0.527277i	$0.823213\pi$
$318$	−0.312739	+	2.14318i	−0.0175375	+	0.120183i
$319$	−7.09400	+	16.5456i	−0.397188	+	0.926377i
$320$	17.4906	+	20.7069i	0.977755	+	1.15755i
$321$		−	16.5906i		−	0.925999i
$322$	2.72991	−	18.7079i	0.152132	−	1.04255i
$323$		−	5.58902i		−	0.310981i
$324$	58.3088	+	17.3874i	3.23938	+	0.965969i
$325$			6.47965i			0.359426i
$326$	4.62306	−	31.6815i	0.256047	−	1.75467i
$327$	15.5222			0.858381
$328$	−4.93002	+	10.6177i	−0.272215	+	0.586262i
$329$		−	5.37248i		−	0.296195i
$330$	27.4913	−	44.8448i	1.51335	−	2.46863i
$331$		−	13.7221i		−	0.754232i	−0.926166	−	0.377116i	$-0.876916\pi$
$331$		−	13.7221i		−	0.754232i	0.926166	−	0.377116i	$-0.123084\pi$
$332$	−14.3682	−	4.28453i	−0.788556	−	0.235144i
$333$	13.2171			0.724292
$334$	−31.7617	−	4.63476i	−1.73792	−	0.253603i
$335$			12.8982i			0.704703i
$336$	26.4560	−	40.4156i	1.44329	−	2.20485i
$337$			22.8260i			1.24341i	0.783252	+	0.621705i	$0.213560\pi$
$337$			22.8260i			1.24341i	−0.783252	+	0.621705i	$0.786440\pi$
$338$	1.39939	+	0.204204i	0.0761169	+	0.0111072i
$339$			1.66643i			0.0905081i
$340$	4.76417	−	15.9767i	0.258373	−	0.866456i
$341$	−10.5373	+	24.5765i	−0.570625	+	1.33089i
$342$	25.2901	+	3.69041i	1.36753	+	0.199555i
$343$	−2.51193			−0.135632
$344$	−0.688756	−	0.319805i	−0.0371352	−	0.0172427i
$345$	41.0914			2.21229
$346$	2.74723	−	18.8266i	0.147692	−	1.01212i
$347$	26.5720			1.42646			0.713230	−	0.700930i	$-0.247231\pi$
$347$	26.5720			1.42646			0.713230	+	0.700930i	$0.247231\pi$
$348$	−34.4333	−	10.2679i	−1.84582	−	0.550415i
$349$		−	7.59546i		−	0.406575i	−0.979119	−	0.203288i	$-0.934837\pi$
$349$		−	7.59546i		−	0.406575i	0.979119	−	0.203288i	$-0.0651627\pi$
$350$	−33.0830	−	4.82757i	−1.76836	−	0.258045i
$351$	−16.4021			−0.875480
$352$	8.01252	+	16.9647i	0.427069	+	0.904219i
$353$	−18.8949			−1.00567			−0.502836	−	0.864382i	$-0.667710\pi$
$353$	−18.8949			−1.00567			−0.502836	+	0.864382i	$0.667710\pi$
$354$	−56.1348	−	8.19137i	−2.98353	−	0.435366i
$355$			10.7164i			0.568768i
$356$	21.4070	+	6.38347i	1.13457	+	0.338323i
$357$	−29.7111			−1.57248
$358$	0.175771	−	1.20455i	0.00928979	−	0.0636623i
$359$	26.7350			1.41102			0.705510	−	0.708700i	$-0.250718\pi$
$359$	26.7350			1.41102			0.705510	+	0.708700i	$0.250718\pi$
$360$	69.1481	+	32.1071i	3.64443	+	1.69219i
$361$	−13.8395			−0.728395
$362$	−1.35878	−	0.198277i	−0.0714159	−	0.0104212i
$363$	26.3729	−	25.1015i	1.38422	−	1.31749i
$364$	−2.08520	+	6.99271i	−0.109294	+	0.366518i
$365$			16.7951i			0.879094i
$366$	−60.3070	−	8.80018i	−3.15230	−	0.459993i
$367$		−	21.4052i		−	1.11734i	−0.829389	−	0.558672i	$-0.811311\pi$
$367$		−	21.4052i		−	1.11734i	0.829389	−	0.558672i	$-0.188689\pi$
$368$	−8.02724	+	12.2628i	−0.418449	+	0.639245i
$369$			32.9264i			1.71408i
$370$	7.87724	+	1.14947i	0.409518	+	0.0597581i
$371$	1.68817			0.0876456
$372$	−51.1465	−	15.2517i	−2.65182	−	0.790761i
$373$		−	1.40274i		−	0.0726311i	−0.999340	−	0.0363155i	$-0.988438\pi$
$373$		−	1.40274i		−	0.0726311i	0.999340	−	0.0363155i	$-0.0115621\pi$
$374$	6.03122	−	9.83835i	0.311867	−	0.508729i
$375$		−	16.5935i		−	0.856886i
$376$	−1.75401	+	3.77756i	−0.0904561	+	0.194813i
$377$	5.42789			0.279551
$378$	12.2202	−	83.7439i	0.628537	−	4.30732i
$379$		−	28.5798i		−	1.46804i	−0.679125	−	0.734022i	$-0.737641\pi$
$379$		−	28.5798i		−	1.46804i	0.679125	−	0.734022i	$-0.262359\pi$
$380$	14.7517	+	4.39889i	0.756746	+	0.225659i
$381$		−	52.1517i		−	2.67181i
$382$	1.00467	−	6.88495i	0.0514035	−	0.352265i
$383$		−	4.13836i		−	0.211460i	−0.994395	−	0.105730i	$-0.966282\pi$
$383$		−	4.13836i		−	0.211460i	0.994395	−	0.105730i	$-0.0337180\pi$
$384$	−31.7969	+	19.7801i	−1.62263	+	1.00940i
$385$	−37.6816	−	16.1562i	−1.92043	−	0.823394i
$386$	3.74183	−	25.6425i	0.190454	−	1.30517i
$387$	−2.13590			−0.108574
$388$	−3.98313	−	1.18775i	−0.202213	−	0.0602990i
$389$	8.97124			0.454860			0.227430	−	0.973794i	$-0.426968\pi$
$389$	8.97124			0.454860			0.227430	+	0.973794i	$0.426968\pi$
$390$	−15.6935	−	2.29004i	−0.794671	−	0.115961i
$391$	9.01490			0.455903
$392$	−16.1914	−	7.51803i	−0.817789	−	0.379718i
$393$			61.1168i			3.08293i
$394$	1.74607	−	11.9657i	0.0879659	−	0.602824i
$395$	27.7158			1.39453
$396$	40.5358	+	33.7873i	2.03700	+	1.69788i
$397$	−32.2239			−1.61727			−0.808636	−	0.588309i	$-0.799794\pi$
$397$	−32.2239			−1.61727			−0.808636	+	0.588309i	$0.799794\pi$
$398$	−2.06231	+	14.1329i	−0.103375	+	0.708418i
$399$		−	27.4331i		−	1.37337i
$400$	21.6856	+	14.1954i	1.08428	+	0.709768i
$401$	11.9891			0.598706			0.299353	−	0.954142i	$-0.403229\pi$
$401$	11.9891			0.598706			0.299353	+	0.954142i	$0.403229\pi$
$402$	−17.6327	−	2.57302i	−0.879440	−	0.128331i
$403$	8.06247			0.401620
$404$	1.98936	−	6.67134i	0.0989746	−	0.331912i
$405$	103.078			5.12200
$406$	−4.04398	+	27.7131i	−0.200699	+	1.37538i
$407$	5.06433	+	2.17135i	0.251029	+	0.107630i
$408$	20.8908	+	9.70009i	1.03425	+	0.480226i
$409$		−	7.91270i		−	0.391258i	−0.980678	−	0.195629i	$-0.937325\pi$
$409$		−	7.91270i		−	0.391258i	0.980678	−	0.195629i	$-0.0626748\pi$
$410$	−2.86356	+	19.6238i	−0.141421	+	0.969149i
$411$			35.4055i			1.74643i
$412$	0.449485	−	1.50735i	0.0221445	−	0.0742617i
$413$			44.2172i			2.17579i
$414$	−5.95251	+	40.7921i	−0.292550	+	2.00482i
$415$	−25.4000			−1.24684
$416$	3.74915	−	4.23602i	0.183817	−	0.207688i
$417$		−	16.1677i		−	0.791737i
$418$	9.08403	+	5.56880i	0.444314	+	0.272379i
$419$			8.99176i			0.439276i	0.975581	+	0.219638i	$0.0704876\pi$
$419$			8.99176i			0.439276i	−0.975581	+	0.219638i	$0.929512\pi$
$420$	23.3844	−	78.4197i	1.14104	−	3.82649i
$421$	0.804120			0.0391904			0.0195952	−	0.999808i	$-0.493762\pi$
$421$	0.804120			0.0391904			0.0195952	+	0.999808i	$0.493762\pi$
$422$	−18.6048	−	2.71487i	−0.905668	−	0.132158i
$423$			11.7146i			0.569583i
$424$	−1.18701	−	0.551155i	−0.0576462	−	0.0267665i
$425$		−	15.9419i		−	0.773298i
$426$	−14.6501	−	2.13778i	−0.709799	−	0.103576i
$427$			47.5036i			2.29886i
$428$	9.60682	+	2.86471i	0.464363	+	0.138471i
$429$	−10.0894	−	4.32589i	−0.487123	−	0.208856i
$430$	−1.27297	−	0.185756i	−0.0613882	−	0.00895795i
$431$	−33.8112			−1.62863			−0.814314	−	0.580424i	$-0.802887\pi$
$431$	−33.8112			−1.62863			−0.814314	+	0.580424i	$0.802887\pi$
$432$	−35.9331	+	54.8934i	−1.72883	+	2.64106i
$433$	−30.1294			−1.44793			−0.723964	−	0.689838i	$-0.757682\pi$
$433$	−30.1294			−1.44793			−0.723964	+	0.689838i	$0.757682\pi$
$434$	−6.00683	+	41.1644i	−0.288337	+	1.97595i
$435$	−60.8711			−2.91854
$436$	−2.68023	+	8.98815i	−0.128360	+	0.430454i
$437$			8.32371i			0.398177i
$438$	−22.9600	−	3.35040i	−1.09707	−	0.160088i
$439$	−26.3144			−1.25592			−0.627960	−	0.778246i	$-0.716110\pi$
$439$	−26.3144			−1.25592			−0.627960	+	0.778246i	$0.716110\pi$
$440$	21.2205	+	23.6622i	1.01165	+	1.12805i
$441$	−50.2110			−2.39100
$442$	−3.44294	−	0.502404i	−0.163764	−	0.0238969i
$443$			14.9454i			0.710080i	0.934851	+	0.355040i	$0.115533\pi$
$443$			14.9454i			0.710080i	−0.934851	+	0.355040i	$0.884467\pi$
$444$	−3.14281	+	10.5394i	−0.149151	+	0.500179i
$445$	37.8432			1.79394
$446$	−2.84207	+	19.4765i	−0.134576	+	0.922238i
$447$	−21.2686			−1.00597
$448$	18.8345	+	22.2979i	0.889847	+	1.05348i
$449$	−10.3204			−0.487052			−0.243526	−	0.969894i	$-0.578304\pi$
$449$	−10.3204			−0.487052			−0.243526	+	0.969894i	$0.578304\pi$
$450$	72.1368	+	10.5264i	3.40056	+	0.496220i
$451$	−5.40927	+	12.6162i	−0.254712	+	0.594076i
$452$	−0.964948	−	0.287743i	−0.0453873	−	0.0135343i
$453$			4.45661i			0.209390i
$454$	25.6267	+	3.73952i	1.20272	+	0.175504i
$455$			12.3617i			0.579525i
$456$	−8.95637	+	19.2891i	−0.419420	+	0.903294i
$457$		−	14.7674i		−	0.690788i	−0.938458	−	0.345394i	$-0.887745\pi$
$457$		−	14.7674i		−	0.690788i	0.938458	−	0.345394i	$-0.112255\pi$
$458$	24.5534	+	3.58291i	1.14730	+	0.167418i
$459$	40.3543			1.88358
$460$	−7.09527	+	23.7940i	−0.330818	+	1.10940i
$461$			21.2808i			0.991148i	0.868566	+	0.495574i	$0.165042\pi$
$461$			21.2808i			0.991148i	−0.868566	+	0.495574i	$0.834958\pi$
$462$	29.6036	−	48.2905i	1.37728	−	2.24668i
$463$			16.7667i			0.779217i	0.920981	+	0.389608i	$0.127390\pi$
$463$			16.7667i			0.779217i	−0.920981	+	0.389608i	$0.872610\pi$
$464$	11.8912	−	18.1657i	0.552036	−	0.843320i
$465$	−90.4166			−4.19297
$466$	4.44883	−	30.4875i	0.206088	−	1.41231i
$467$		−	19.2629i		−	0.891383i	−0.895187	−	0.445691i	$-0.852958\pi$
$467$		−	19.2629i		−	0.891383i	0.895187	−	0.445691i	$-0.147042\pi$
$468$	4.54673	−	15.2475i	0.210172	−	0.704814i
$469$			13.8892i			0.641345i
$470$	−1.01880	+	6.98177i	−0.0469938	+	0.322045i
$471$			0.940460i			0.0433341i
$472$	14.4360	−	31.0905i	0.664473	−	1.43106i
$473$	−0.818402	−	0.350893i	−0.0376302	−	0.0161341i
$474$	−5.52894	+	37.8895i	−0.253953	+	1.74032i
$475$	14.7197			0.675384
$476$	5.13023	−	17.2042i	0.235144	−	0.788555i
$477$	−3.68102			−0.168543
$478$	−4.08338	−	0.595859i	−0.186769	−	0.0272539i
$479$	−25.7851			−1.17815			−0.589077	−	0.808077i	$-0.700508\pi$
$479$	−25.7851			−1.17815			−0.589077	+	0.808077i	$0.700508\pi$
$480$	−42.0448	+	47.5048i	−1.91907	+	2.16829i
$481$		−	1.66138i		−	0.0757526i
$482$	−5.04540	+	34.5757i	−0.229812	+	1.57488i
$483$	44.2487			2.01338
$484$	9.98121	+	19.6055i	0.453691	+	0.891159i
$485$	−7.04137			−0.319732
$486$	−10.5146	+	72.0561i	−0.476954	+	3.26853i
$487$		−	39.7733i		−	1.80230i	−0.433505	−	0.901151i	$-0.642723\pi$
$487$		−	39.7733i		−	1.80230i	0.433505	−	0.901151i	$-0.357277\pi$
$488$	15.5090	−	33.4013i	0.702059	−	1.51200i
$489$	74.9344			3.38865
$490$	−29.9252	−	4.36678i	−1.35188	−	0.197271i
$491$	−20.7840			−0.937969			−0.468984	−	0.883206i	$-0.655380\pi$
$491$	−20.7840			−0.937969			−0.468984	+	0.883206i	$0.655380\pi$
$492$	−26.2558	−	7.82937i	−1.18370	−	0.352975i
$493$	−13.3543			−0.601447
$494$	0.463884	−	3.17896i	0.0208711	−	0.143028i
$495$	82.1640	+	35.2282i	3.69300	+	1.58339i
$496$	17.6630	−	26.9829i	0.793090	−	1.21157i
$497$			11.5398i			0.517631i
$498$	5.06698	−	34.7236i	0.227057	−	1.55600i
$499$			8.26104i			0.369815i	0.982756	+	0.184907i	$0.0591985\pi$
$499$			8.26104i			0.369815i	−0.982756	+	0.184907i	$0.940801\pi$
$500$	9.60850	+	2.86521i	0.429705	+	0.128136i
$501$		−	75.1241i		−	3.35630i
$502$	−5.29953	+	36.3173i	−0.236529	+	1.62092i
$503$	11.5844			0.516525			0.258262	−	0.966075i	$-0.416850\pi$
$503$	11.5844			0.516525			0.258262	+	0.966075i	$0.416850\pi$
$504$	74.4611	+	34.5740i	3.31676	+	1.54005i
$505$		−	11.7936i		−	0.524807i
$506$	−8.98228	+	14.6522i	−0.399311	+	0.651371i
$507$			3.30990i			0.146998i
$508$	30.1985	+	9.00505i	1.33984	+	0.399534i
$509$	27.8518			1.23451			0.617255	−	0.786763i	$-0.288245\pi$
$509$	27.8518			1.23451			0.617255	+	0.786763i	$0.288245\pi$
$510$	38.6108	+	5.63421i	1.70972	+	0.249487i
$511$			18.0855i			0.800057i
$512$	−5.96330	−	21.8275i	−0.263543	−	0.964648i
$513$			37.2603i			1.64508i
$514$	2.33018	+	0.340027i	0.102780	+	0.0149980i
$515$		−	2.66469i		−	0.117420i
$516$	0.507883	−	1.70319i	0.0223583	−	0.0749786i
$517$	−1.92452	+	4.48862i	−0.0846401	+	0.197409i
$518$	8.48249	+	1.23779i	0.372699	+	0.0543854i
$519$	44.5294			1.95462
$520$	4.03585	−	8.69190i	0.176984	−	0.381165i
$521$	33.9509			1.48742			0.743708	−	0.668505i	$-0.233065\pi$
$521$	33.9509			1.48742			0.743708	+	0.668505i	$0.233065\pi$
$522$	8.81780	−	60.4278i	0.385945	−	2.64485i
$523$	−26.6616			−1.16583			−0.582916	−	0.812533i	$-0.698088\pi$
$523$	−26.6616			−1.16583			−0.582916	+	0.812533i	$0.698088\pi$
$524$	−35.3897	−	10.5531i	−1.54601	−	0.461013i
$525$		−	78.2494i		−	3.41508i
$526$	−8.76235	−	1.27863i	−0.382057	−	0.0557509i
$527$	−19.8362			−0.864078
$528$	−36.5811	+	24.2896i	−1.59199	+	1.05707i
$529$	9.57413			0.416267
$530$	−2.19385	−	0.320133i	−0.0952948	−	0.0139057i
$531$		−	96.4146i		−	4.18404i
$532$	15.8852	+	4.73689i	0.688709	+	0.205370i
$533$	4.13884			0.179273
$534$	−7.54923	+	51.7343i	−0.326687	+	2.23876i
$535$	16.9829			0.734235
$536$	4.53456	−	9.76595i	0.195863	−	0.421825i
$537$	2.84905			0.122945
$538$	−43.2744	−	6.31473i	−1.86569	−	0.272247i
$539$	−19.2391	−	8.24886i	−0.828688	−	0.355303i
$540$	−31.7612	+	106.511i	−1.36679	+	4.58352i
$541$		−	2.26817i		−	0.0975161i	−0.998811	−	0.0487580i	$-0.984474\pi$
$541$		−	2.26817i		−	0.0975161i	0.998811	−	0.0487580i	$-0.0155263\pi$
$542$	−6.02804	−	0.879630i	−0.258927	−	0.0377833i
$543$		−	3.21384i		−	0.137919i
$544$	−9.22407	+	10.4219i	−0.395479	+	0.446836i
$545$			15.8892i			0.680620i
$546$	−16.8993	−	2.46600i	−0.723224	−	0.105535i
$547$	6.31707			0.270098			0.135049	−	0.990839i	$-0.456881\pi$
$547$	6.31707			0.270098			0.135049	+	0.990839i	$0.456881\pi$
$548$	−20.5016	−	6.11349i	−0.875785	−	0.261155i
$549$		−	103.581i		−	4.42071i
$550$	25.9110	+	15.8843i	1.10485	+	0.677307i
$551$		−	12.3304i		−	0.525293i
$552$	−31.1126	−	14.4463i	−1.32424	−	0.614876i
$553$	29.8454			1.26915
$554$	3.44589	−	23.6144i	0.146402	−	1.00328i
$555$			18.6316i			0.790867i
$556$	9.36193	+	2.79169i	0.397034	+	0.118394i
$557$			27.1008i			1.14830i	0.818752	+	0.574148i	$0.194667\pi$
$557$			27.1008i			1.14830i	−0.818752	+	0.574148i	$0.805333\pi$
$558$	13.0978	−	89.7581i	0.554473	−	3.79976i
$559$			0.268482i			0.0113556i
$560$	41.3712	+	27.0815i	1.74825	+	1.14440i
$561$	24.8231	+	10.6430i	1.04803	+	0.449349i
$562$	−4.36509	+	29.9137i	−0.184130	+	1.26183i
$563$	−17.6243			−0.742777			−0.371389	−	0.928477i	$-0.621118\pi$
$563$	−17.6243			−0.742777			−0.371389	+	0.928477i	$0.621118\pi$
$564$	−9.34133	−	2.78554i	−0.393341	−	0.117293i
$565$	−1.70583			−0.0717649
$566$	−22.2457	−	3.24617i	−0.935058	−	0.136447i
$567$	110.998			4.66149
$568$	3.76752	−	8.11400i	0.158082	−	0.340456i
$569$			12.6178i			0.528966i	0.964390	+	0.264483i	$0.0852013\pi$
$569$			12.6178i			0.528966i	−0.964390	+	0.264483i	$0.914799\pi$
$570$	−5.20223	+	35.6505i	−0.217897	+	1.49323i
$571$	−22.1407			−0.926560			−0.463280	−	0.886212i	$-0.653328\pi$
$571$	−22.1407			−0.926560			−0.463280	+	0.886212i	$0.653328\pi$
$572$	4.24706	−	5.09534i	0.177578	−	0.213047i
$573$	16.2846			0.680298
$574$	−3.08358	+	21.1316i	−0.128706	+	0.882015i
$575$			23.7423i			0.990122i
$576$	−41.0682	−	48.6202i	−1.71118	−	2.02584i
$577$	11.8129			0.491779			0.245889	−	0.969298i	$-0.420920\pi$
$577$	11.8129			0.491779			0.245889	+	0.969298i	$0.420920\pi$
$578$	−15.3190	−	2.23539i	−0.637186	−	0.0929800i
$579$	60.6506			2.52055
$580$	10.5106	−	35.2474i	0.436430	−	1.46357i
$581$	−27.3517			−1.13474
$582$	1.40466	−	9.62605i	0.0582251	−	0.399013i
$583$	−1.41044	−	0.604732i	−0.0584145	−	0.0250455i
$584$	5.90457	−	12.7165i	0.244333	−	0.526213i
$585$		−	26.9544i		−	1.11443i
$586$	−4.98205	+	34.1416i	−0.205806	+	1.41038i
$587$			27.8673i			1.15021i	0.818081	+	0.575103i	$0.195038\pi$
$587$			27.8673i			1.15021i	−0.818081	+	0.575103i	$0.804962\pi$
$588$	11.9394	−	40.0388i	0.492372	−	1.65117i
$589$		−	18.3153i		−	0.754669i
$590$	8.38504	−	57.4621i	0.345207	−	2.36568i
$591$	28.3018			1.16418
$592$	−5.56019	−	3.63970i	−0.228523	−	0.149591i
$593$			18.2908i			0.751113i	0.926799	+	0.375557i	$0.122548\pi$
$593$			18.2908i			0.751113i	−0.926799	+	0.375557i	$0.877452\pi$
$594$	−40.2082	+	65.5892i	−1.64976	+	2.69116i
$595$		−	30.4136i		−	1.24684i
$596$	3.67245	−	12.3156i	0.150430	−	0.504466i
$597$	−33.4277			−1.36811
$598$	5.12756	+	0.748229i	0.209682	+	0.0305974i
$599$			21.6501i			0.884601i	0.896867	+	0.442300i	$0.145837\pi$
$599$			21.6501i			0.884601i	−0.896867	+	0.442300i	$0.854163\pi$
$600$	−25.5469	+	55.0196i	−1.04295	+	2.24617i
$601$		−	5.66018i		−	0.230884i	−0.993314	−	0.115442i	$-0.963172\pi$
$601$		−	5.66018i		−	0.230884i	0.993314	−	0.115442i	$-0.0368284\pi$
$602$	−1.37078	−	0.200029i	−0.0558689	−	0.00815256i
$603$		−	30.2851i		−	1.23331i
$604$	−2.58061	−	0.769525i	−0.105003	−	0.0313115i
$605$	25.6950	+	26.9964i	1.04465	+	1.09756i
$606$	16.1226	+	2.35267i	0.654938	+	0.0955705i
$607$	−33.0850			−1.34288			−0.671439	−	0.741059i	$-0.734324\pi$
$607$	−33.0850			−1.34288			−0.671439	+	0.741059i	$0.734324\pi$
$608$	−9.62286	−	8.51685i	−0.390258	−	0.345404i
$609$	−65.5481			−2.65614
$610$	9.00825	−	61.7329i	0.364733	−	2.49949i
$611$	1.47252			0.0595718
$612$	−11.1864	+	37.5135i	−0.452182	+	1.51639i
$613$		−	47.3563i		−	1.91270i	−0.292221	−	0.956351i	$-0.594394\pi$
$613$		−	47.3563i		−	1.91270i	0.292221	−	0.956351i	$-0.405606\pi$
$614$	6.96195	+	1.01591i	0.280962	+	0.0409988i
$615$	−46.4150			−1.87163
$616$	22.8510	+	25.4803i	0.920692	+	1.02663i
$617$	−3.03586			−0.122219			−0.0611095	−	0.998131i	$-0.519464\pi$
$617$	−3.03586			−0.122219			−0.0611095	+	0.998131i	$0.519464\pi$
$618$	3.64281	+	0.531570i	0.146535	+	0.0213829i
$619$		−	8.34589i		−	0.335449i	−0.985834	−	0.167725i	$-0.946358\pi$
$619$		−	8.34589i		−	0.335449i	0.985834	−	0.167725i	$-0.0536420\pi$
$620$	15.6123	−	52.3558i	0.627004	−	2.10266i
$621$	−60.0995			−2.41171
$622$	4.28305	−	29.3514i	0.171735	−	1.17689i
$623$	40.7509			1.63265
$624$	11.0773	+	7.25121i	0.443448	+	0.290281i
$625$	−15.4124			−0.616495
$626$	19.5151	+	2.84770i	0.779978	+	0.113817i
$627$	−9.82701	+	22.9199i	−0.392453	+	0.915333i
$628$	−0.544574	−	0.162390i	−0.0217309	−	0.00648005i
$629$			4.08752i			0.162980i
$630$	137.621	+	20.0820i	5.48293	+	0.800086i
$631$			5.91858i			0.235615i	0.993036	+	0.117808i	$0.0375866\pi$
$631$			5.91858i			0.235615i	−0.993036	+	0.117808i	$0.962413\pi$
$632$	−20.9852	−	9.74392i	−0.834747	−	0.387592i
$633$		−	44.0049i		−	1.74904i
$634$	42.3411	+	6.17854i	1.68158	+	0.245381i
$635$	53.3847			2.11851
$636$	0.875289	−	2.93529i	0.0347075	−	0.116392i
$637$			6.31152i			0.250071i
$638$	13.3060	−	21.7052i	0.526788	−	0.859317i
$639$		−	25.1623i		−	0.995405i
$640$	−20.2478	−	32.5488i	−0.800365	−	1.28660i
$641$	31.0384			1.22594			0.612972	−	0.790105i	$-0.289974\pi$
$641$	31.0384			1.22594			0.612972	+	0.790105i	$0.289974\pi$
$642$	−3.38787	+	23.2168i	−0.133709	+	0.916295i
$643$			21.3963i			0.843786i	0.906646	+	0.421893i	$0.138634\pi$
$643$			21.3963i			0.843786i	−0.906646	+	0.421893i	$0.861366\pi$
$644$	−7.64044	+	25.6222i	−0.301075	+	1.00966i
$645$		−	3.01089i		−	0.118554i
$646$	−1.14130	+	7.82124i	−0.0449038	+	0.307723i
$647$			10.1571i			0.399317i	0.979866	+	0.199658i	$0.0639832\pi$
$647$			10.1571i			0.399317i	−0.979866	+	0.199658i	$0.936017\pi$
$648$	−78.0464	−	36.2387i	−3.06595	−	1.42359i
$649$	15.8394	−	36.9427i	0.621749	−	1.45013i
$650$	1.32317	−	9.06758i	0.0518989	−	0.355660i
$651$	−97.3638			−3.81599
$652$	−12.9389	+	43.3908i	−0.506728	+	1.69931i
$653$	−13.1760			−0.515617			−0.257809	−	0.966196i	$-0.583000\pi$
$653$	−13.1760			−0.515617			−0.257809	+	0.966196i	$0.583000\pi$
$654$	−21.7217	−	3.16969i	−0.849385	−	0.123945i
$655$	−62.5618			−2.44449
$656$	9.06721	−	13.8515i	0.354015	−	0.540812i
$657$		−	39.4351i		−	1.53851i
$658$	−1.09708	+	7.51822i	−0.0427687	+	0.293091i
$659$	−1.29334			−0.0503815			−0.0251907	−	0.999683i	$-0.508019\pi$
$659$	−1.29334			−0.0503815			−0.0251907	+	0.999683i	$0.508019\pi$
$660$	−47.6286	+	57.1417i	−1.85394	+	2.22424i
$661$	2.67377			0.103997			0.0519987	−	0.998647i	$-0.483441\pi$
$661$	2.67377			0.103997			0.0519987	+	0.998647i	$0.483441\pi$
$662$	−2.80209	+	19.2025i	−0.108906	+	0.746328i
$663$		−	8.14339i		−	0.316263i
$664$	19.2318	+	8.92978i	0.746339	+	0.346542i
$665$	28.0817			1.08896
$666$	−18.4959	−	2.69898i	−0.716701	−	0.104583i
$667$	19.8885			0.770086
$668$	43.5006	+	12.9717i	1.68309	+	0.501890i
$669$	−46.0666			−1.78104
$670$	2.63386	−	18.0496i	0.101755	−	0.697318i
$671$	17.0166	−	39.6885i	0.656918	−	1.53216i
$672$	−45.2754	+	51.1549i	−1.74654	+	1.97334i
$673$		−	46.4120i		−	1.78905i	−0.447016	−	0.894526i	$-0.647513\pi$
$673$		−	46.4120i		−	1.78905i	0.447016	−	0.894526i	$-0.352487\pi$
$674$	4.66114	−	31.9425i	0.179541	−	1.23038i
$675$			106.280i			4.09072i
$676$	−1.91660	−	0.571522i	−0.0737155	−	0.0219816i
$677$			33.1432i			1.27380i	0.770948	+	0.636898i	$0.219783\pi$
$677$			33.1432i			1.27380i	−0.770948	+	0.636898i	$0.780217\pi$
$678$	0.340291	−	2.33199i	0.0130688	−	0.0895596i
$679$	−7.58240			−0.290986
$680$	−9.92944	+	21.3848i	−0.380777	+	0.820068i
$681$			60.6132i			2.32270i
$682$	19.7644	−	32.2404i	0.756818	−	1.23455i
$683$			11.2715i			0.431293i	0.976471	+	0.215647i	$0.0691859\pi$
$683$			11.2715i			0.431293i	−0.976471	+	0.215647i	$0.930814\pi$
$684$	−34.6373	−	10.3287i	−1.32439	−	0.394927i
$685$	−36.2427			−1.38476
$686$	3.51518	+	0.512945i	0.134210	+	0.0195843i
$687$			58.0747i			2.21569i
$688$	0.898535	+	0.588180i	0.0342563	+	0.0224241i
$689$			0.462704i			0.0176276i
$690$	−57.5030	−	8.39101i	−2.18910	−	0.319440i
$691$		−	12.0248i		−	0.457446i	−0.973492	−	0.228723i	$-0.926545\pi$
$691$		−	12.0248i		−	0.457446i	0.973492	−	0.228723i	$-0.0734550\pi$
$692$	−7.68890	+	25.7848i	−0.292288	+	0.980189i
$693$	88.4771	+	37.9349i	3.36097	+	1.44103i
$694$	−37.1847	−	5.42610i	−1.41151	−	0.205972i
$695$	16.5500			0.627777
$696$	46.0890	+	21.4002i	1.74700	+	0.811171i
$697$	−10.1828			−0.385702
$698$	−1.55102	+	10.6290i	−0.0587070	+	0.402315i
$699$	72.1103			2.72746
$700$	45.3103	+	13.5113i	1.71257	+	0.510681i
$701$			4.98845i			0.188411i	0.995553	+	0.0942056i	$0.0300311\pi$
$701$			4.98845i			0.188411i	−0.995553	+	0.0942056i	$0.969969\pi$
$702$	22.9530	+	3.34937i	0.866305	+	0.126414i
$703$	−3.77412			−0.142344
$704$	−7.74842	−	25.3764i	−0.292030	−	0.956409i
$705$	−16.5136			−0.621937
$706$	26.4414	+	3.85840i	0.995134	+	0.145213i
$707$		−	12.6997i		−	0.477623i
$708$	76.8820	+	22.9259i	2.88940	+	0.861607i
$709$	4.82025			0.181028			0.0905141	−	0.995895i	$-0.471149\pi$
$709$	4.82025			0.181028			0.0905141	+	0.995895i	$0.471149\pi$
$710$	2.18833	−	14.9965i	0.0821265	−	0.562807i
$711$	−65.0772			−2.44059
$712$	−28.6533	−	13.3044i	−1.07383	−	0.498602i
$713$	29.5420			1.10636
$714$	41.5775	+	6.06712i	1.55600	+	0.227056i
$715$	4.42817	−	10.3280i	0.165604	−	0.386245i
$716$	−0.491946	+	1.64974i	−0.0183849	+	0.0616537i
$717$		−	9.65818i		−	0.360691i
$718$	−37.4128	−	5.45939i	−1.39623	−	0.203743i
$719$			47.2849i			1.76343i	0.471784	+	0.881714i	$0.343610\pi$
$719$			47.2849i			1.76343i	−0.471784	+	0.881714i	$0.656390\pi$
$720$	−90.2090	−	59.0507i	−3.36189	−	2.20069i
$721$		−	2.86943i		−	0.106863i
$722$	19.3669	+	2.82608i	0.720761	+	0.105176i
$723$	−81.7800			−3.04143
$724$	1.86098	+	0.554936i	0.0691627	+	0.0206240i
$725$		−	35.1708i		−	1.30621i
$726$	−42.0318	+	29.7414i	−1.55995	+	1.10381i
$727$			22.9216i			0.850117i	0.905166	+	0.425058i	$0.139746\pi$
$727$			22.9216i			0.850117i	−0.905166	+	0.425058i	$0.860254\pi$
$728$	4.34595	−	9.35975i	0.161072	−	0.346895i
$729$	−79.1611			−2.93189
$730$	3.42962	−	23.5029i	0.126936	−	0.869882i
$731$		−	0.660549i		−	0.0244313i
$732$	82.5962	+	24.6298i	3.05284	+	0.910344i
$733$		−	32.5604i		−	1.20265i	−0.799006	−	0.601323i	$-0.794640\pi$
$733$		−	32.5604i		−	1.20265i	0.799006	−	0.601323i	$-0.205360\pi$
$734$	−4.37102	+	29.9543i	−0.161337	+	1.10563i
$735$		−	70.7805i		−	2.61078i
$736$	13.7374	−	15.5213i	0.506367	−	0.572124i
$737$	4.97536	−	11.6042i	0.183270	−	0.427447i
$738$	6.72369	−	46.0769i	0.247502	−	1.69612i
$739$	−38.4469			−1.41429			−0.707146	−	0.707068i	$-0.750018\pi$
$739$	−38.4469			−1.41429			−0.707146	+	0.707068i	$0.750018\pi$
$740$	−10.7886	−	3.21712i	−0.396598	−	0.118264i
$741$	7.51902			0.276218
$742$	−2.36242	−	0.344731i	−0.0867271	−	0.0126555i
$743$	−38.2393			−1.40286			−0.701432	−	0.712737i	$-0.747455\pi$
$743$	−38.2393			−1.40286			−0.701432	+	0.712737i	$0.747455\pi$
$744$	68.4596	+	31.7874i	2.50985	+	1.16538i
$745$		−	21.7715i		−	0.797644i
$746$	−0.286444	+	1.96298i	−0.0104875	+	0.0718699i
$747$	59.6397			2.18210
$748$	−10.4491	+	12.5361i	−0.382056	+	0.458366i
$749$	18.2878			0.668222
$750$	−3.38846	+	23.2209i	−0.123729	+	0.847907i
$751$		−	17.9107i		−	0.653571i	−0.945098	−	0.326786i	$-0.894034\pi$
$751$		−	17.9107i		−	0.653571i	0.945098	−	0.326786i	$-0.105966\pi$
$752$	3.22594	−	4.92812i	0.117638	−	0.179710i
$753$	−85.8992			−3.13034
$754$	−7.59576	−	1.10840i	−0.276621	−	0.0403654i
$755$	−4.56199			−0.166028
$756$	−34.2016	+	114.695i	−1.24390	+	4.17143i
$757$	25.8674			0.940168			0.470084	−	0.882622i	$-0.344224\pi$
$757$	25.8674			0.940168			0.470084	+	0.882622i	$0.344224\pi$
$758$	−5.83610	+	39.9943i	−0.211977	+	1.45266i
$759$	−36.9690	−	15.8506i	−1.34189	−	0.575342i
$760$	−19.7452	−	9.16813i	−0.716232	−	0.332563i
$761$			22.3556i			0.810392i	0.914230	+	0.405196i	$0.132797\pi$
$761$			22.3556i			0.810392i	−0.914230	+	0.405196i	$0.867203\pi$
$762$	−10.6496	+	72.9807i	−0.385793	+	2.64381i
$763$			17.1101i			0.619427i
$764$	−2.81186	+	9.42960i	−0.101730	+	0.341151i
$765$			66.3162i			2.39767i
$766$	−0.845068	+	5.79119i	−0.0305336	+	0.209244i
$767$	−12.1193			−0.437602
$768$	48.5356	−	21.1871i	1.75138	−	0.764524i
$769$			33.3904i			1.20409i	0.798463	+	0.602044i	$0.205647\pi$
$769$			33.3904i			1.20409i	−0.798463	+	0.602044i	$0.794353\pi$
$770$	49.4323	+	30.3035i	1.78142	+	1.09206i
$771$			5.51145i			0.198490i
$772$	−10.4726	+	35.1198i	−0.376916	+	1.26399i
$773$	−28.6201			−1.02939			−0.514696	−	0.857373i	$-0.672095\pi$
$773$	−28.6201			−1.02939			−0.514696	+	0.857373i	$0.672095\pi$
$774$	2.98896	+	0.436158i	0.107436	+	0.0156774i
$775$		−	52.2420i		−	1.87659i
$776$	5.33143	+	2.47550i	0.191387	+	0.0888654i
$777$			20.0632i			0.719762i
$778$	−12.5543	−	1.83196i	−0.450093	−	0.0656789i
$779$		−	9.40209i		−	0.336865i
$780$	21.4937	+	6.40933i	0.769599	+	0.229491i
$781$	4.13376	−	9.64132i	0.147917	−	0.344994i
$782$	−12.6154	−	1.84088i	−0.451125	−	0.0658296i
$783$	89.0289			3.18163
$784$	21.1229	+	13.8270i	0.754389	+	0.493822i
$785$	−0.962697			−0.0343601
$786$	12.4803	−	85.5264i	0.445157	−	3.05063i
$787$	−33.4844			−1.19359			−0.596795	−	0.802394i	$-0.703559\pi$
$787$	−33.4844			−1.19359			−0.596795	+	0.802394i	$0.703559\pi$
$788$	−4.88688	+	16.3882i	−0.174088	+	0.583805i
$789$		−	20.7251i		−	0.737833i
$790$	−38.7853	−	5.65967i	−1.37992	−	0.201362i
$791$	−1.83690			−0.0653127
$792$	−49.8260	−	55.5593i	−1.77049	−	1.97421i
$793$	−13.0200			−0.462355
$794$	45.0939	+	6.58024i	1.60032	+	0.233524i
$795$		−	5.18899i		−	0.184035i
$796$	5.77198	−	19.3563i	0.204582	−	0.686067i
$797$	14.4788			0.512867			0.256433	−	0.966562i	$-0.417453\pi$
$797$	14.4788			0.512867			0.256433	+	0.966562i	$0.417453\pi$
$798$	−5.60194	+	38.3897i	−0.198307	+	1.35898i
$799$	−3.62286			−0.128167
$800$	−27.4479	−	24.2932i	−0.970431	−	0.858894i
$801$	−88.8565			−3.13959
$802$	−16.7774	−	2.44821i	−0.592431	−	0.0864494i
$803$	6.47855	−	15.1102i	0.228623	−	0.533226i
$804$	24.1497	+	7.20133i	0.851694	+	0.253971i
$805$			45.2949i			1.59644i
$806$	−11.2826	−	1.64639i	−0.397412	−	0.0579915i
$807$		−	102.354i		−	3.60304i
$808$	−4.14622	+	8.92959i	−0.145863	+	0.314142i
$809$		−	5.77857i		−	0.203164i	−0.994827	−	0.101582i	$-0.967610\pi$
$809$		−	5.77857i		−	0.203164i	0.994827	−	0.101582i	$-0.0323904\pi$
$810$	−144.247	−	21.0489i	−5.06832	−	0.739584i
$811$	−24.0975			−0.846178			−0.423089	−	0.906088i	$-0.639054\pi$
$811$	−24.0975			−0.846178			−0.423089	+	0.906088i	$0.639054\pi$
$812$	11.3182	−	37.9557i	0.397192	−	1.33198i
$813$		−	14.2578i		−	0.500042i
$814$	−6.64359	−	4.07273i	−0.232858	−	0.142749i
$815$			76.7061i			2.68690i
$816$	−27.2537	−	17.8402i	−0.954070	−	0.624533i
$817$	0.609903			0.0213378
$818$	−1.61580	+	11.0730i	−0.0564952	+	0.387158i
$819$		−	29.0255i		−	1.01423i
$820$	8.01449	−	26.8766i	0.279878	−	0.938572i
$821$		−	40.1363i		−	1.40077i	−0.713767	−	0.700383i	$-0.753013\pi$
$821$		−	40.1363i		−	1.40077i	0.713767	−	0.700383i	$-0.246987\pi$
$822$	7.22994	−	49.5463i	0.252173	−	1.72812i
$823$		−	38.6066i		−	1.34574i	−0.739759	−	0.672871i	$-0.765061\pi$
$823$		−	38.6066i		−	1.34574i	0.739759	−	0.672871i	$-0.234939\pi$
$824$	−0.936812	+	2.01759i	−0.0326354	+	0.0702859i
$825$	−28.0303	+	65.3760i	−0.975888	+	2.27610i
$826$	9.02931	−	61.8772i	0.314170	−	2.15298i
$827$	−2.93825			−0.102173			−0.0510865	−	0.998694i	$-0.516268\pi$
$827$	−2.93825			−0.102173			−0.0510865	+	0.998694i	$0.516268\pi$
$828$	16.6598	−	55.8687i	0.578968	−	1.94157i
$829$	−3.99161			−0.138634			−0.0693172	−	0.997595i	$-0.522082\pi$
$829$	−3.99161			−0.138634			−0.0693172	+	0.997595i	$0.522082\pi$
$830$	35.5446	+	5.18678i	1.23377	+	0.180036i
$831$	55.8539			1.93755
$832$	−6.11155	+	5.16227i	−0.211880	+	0.178969i
$833$		−	15.5283i		−	0.538023i
$834$	−3.30151	+	22.6250i	−0.114322	+	0.783440i
$835$	76.9003			2.66124
$836$	−11.5750	−	9.64793i	−0.400328	−	0.333681i
$837$	132.242			4.57094
$838$	1.83615	−	12.5830i	0.0634287	−	0.434673i
$839$			51.7240i			1.78571i	0.450345	+	0.892855i	$0.351301\pi$
$839$			51.7240i			1.78571i	−0.450345	+	0.892855i	$0.648699\pi$
$840$	−48.7376	+	104.965i	−1.68161	+	3.62163i
$841$	−0.462017			−0.0159316
$842$	−1.12528	−	0.164204i	−0.0387797	−	0.00565885i
$843$	−70.7531			−2.43687
$844$	25.4811	+	7.59834i	0.877094	+	0.261546i
$845$	−3.38816			−0.116556
$846$	2.39216	−	16.3933i	0.0822442	−	0.563613i
$847$	27.6693	+	29.0707i	0.950727	+	0.998881i
$848$	1.54854	+	1.01367i	0.0531772	+	0.0348097i
$849$		−	52.6166i		−	1.80580i
$850$	−3.25540	+	22.3091i	−0.111659	+	0.765194i
$851$		−	6.08753i		−	0.208678i
$852$	20.0647	+	5.98320i	0.687404	+	0.204981i
$853$			10.3548i			0.354542i	0.984162	+	0.177271i	$0.0567269\pi$
$853$			10.3548i			0.354542i	−0.984162	+	0.177271i	$0.943273\pi$
$854$	9.70041	−	66.4762i	0.331941	−	2.27477i
$855$	−61.2316			−2.09408
$856$	−12.8587	−	5.97061i	−0.439502	−	0.204071i
$857$		−	19.2916i		−	0.658988i	−0.944158	−	0.329494i	$-0.893122\pi$
$857$		−	19.2916i		−	0.658988i	0.944158	−	0.329494i	$-0.106878\pi$
$858$	13.2357	+	8.11392i	0.451860	+	0.277005i
$859$		−	6.88893i		−	0.235047i	−0.993070	−	0.117524i	$-0.962504\pi$
$859$		−	6.88893i		−	0.235047i	0.993070	−	0.117524i	$-0.0374956\pi$
$860$	1.74346	+	0.519891i	0.0594514	+	0.0177281i
$861$	−49.9813			−1.70336
$862$	47.3152	+	6.90437i	1.61156	+	0.235164i
$863$		−	48.8191i		−	1.66182i	−0.556405	−	0.830911i	$-0.687820\pi$
$863$		−	48.8191i		−	1.66182i	0.556405	−	0.830911i	$-0.312180\pi$
$864$	61.4940	−	69.4797i	2.09207	−	2.36375i
$865$			45.5822i			1.54984i
$866$	42.1629	+	6.15254i	1.43275	+	0.209072i
$867$		−	36.2331i		−	1.23054i
$868$	16.8118	−	56.3786i	0.570631	−	1.91361i
$869$	−24.9353	−	10.6911i	−0.845873	−	0.362671i
$870$	85.1826	+	12.4301i	2.88796	+	0.421420i
$871$	−3.80684			−0.128990
$872$	5.58611	−	12.0306i	0.189169	−	0.407409i
$873$	16.5333			0.559566
$874$	1.69973	−	11.6481i	0.0574943	−	0.394004i
$875$	18.2910			0.618348
$876$	31.4460	+	9.37705i	1.06246	+	0.316821i
$877$			18.5633i			0.626838i	0.949615	+	0.313419i	$0.101475\pi$
$877$			18.5633i			0.626838i	−0.949615	+	0.313419i	$0.898525\pi$
$878$	36.8242	+	5.37350i	1.24276	+	0.181347i
$879$	−80.7532			−2.72374
$880$	−24.8639	−	37.4460i	−0.838161	−	1.26231i
$881$	11.4335			0.385204			0.192602	−	0.981277i	$-0.438307\pi$
$881$	11.4335			0.385204			0.192602	+	0.981277i	$0.438307\pi$
$882$	70.2650	+	10.2533i	2.36595	+	0.345246i
$883$			11.9040i			0.400601i	0.979734	+	0.200301i	$0.0641919\pi$
$883$			11.9040i			0.400601i	−0.979734	+	0.200301i	$0.935808\pi$
$884$	4.71543	+	1.40612i	0.158597	+	0.0472930i
$885$	135.912			4.56863
$886$	3.05191	−	20.9146i	0.102531	−	0.702638i
$887$	−25.6648			−0.861740			−0.430870	−	0.902414i	$-0.641793\pi$
$887$	−25.6648			−0.861740			−0.430870	+	0.902414i	$0.641793\pi$
$888$	6.55022	−	14.1070i	0.219811	−	0.473401i
$889$	57.4866			1.92804
$890$	−52.9575	−	7.72772i	−1.77514	−	0.259034i
$891$	−92.7372	−	39.7615i	−3.10681	−	1.33206i
$892$	7.95433	−	26.6749i	0.266331	−	0.893141i
$893$		−	3.34509i		−	0.111939i
$894$	29.7631	+	4.34312i	0.995427	+	0.145256i
$895$			2.91641i			0.0974848i
$896$	−21.8036	−	35.0497i	−0.728406	−	1.17093i
$897$			12.1279i			0.404940i
$898$	14.4424	+	2.10747i	0.481948	+	0.0703272i
$899$	−43.7622			−1.45955
$900$	−98.7982	−	29.4612i	−3.29327	−	0.982040i
$901$		−	1.13839i		−	0.0379254i
$902$	10.1460	−	16.5505i	0.337824	−	0.551071i
$903$		−	3.24223i		−	0.107895i
$904$	1.29158	+	0.599712i	0.0429574	+	0.0199461i
$905$	3.28983			0.109358
$906$	0.910057	−	6.23656i	0.0302346	−	0.207196i
$907$			51.3966i			1.70660i	0.521424	+	0.853298i	$0.325401\pi$
$907$			51.3966i			1.70660i	−0.521424	+	0.853298i	$0.674599\pi$
$908$	−35.0981	−	10.4661i	−1.16477	−	0.347330i
$909$			27.6915i			0.918470i
$910$	2.52430	−	17.2989i	0.0836799	−	0.573452i
$911$		−	16.2748i		−	0.539208i	−0.962971	−	0.269604i	$-0.913107\pi$
$911$		−	16.2748i		−	0.539208i	0.962971	−	0.269604i	$-0.0868928\pi$
$912$	16.4724	−	25.1641i	0.545455	−	0.833267i
$913$	22.8519	+	9.79783i	0.756286	+	0.324261i
$914$	−3.01555	+	20.6653i	−0.0997455	+	0.683549i
$915$	146.013			4.82705
$916$	−33.6282	−	10.0278i	−1.11111	−	0.331327i
$917$	−67.3688			−2.22471
$918$	−56.4715	−	8.24049i	−1.86384	−	0.271977i
$919$	−19.9121			−0.656840			−0.328420	−	0.944532i	$-0.606516\pi$
$919$	−19.9121			−0.656840			−0.328420	+	0.944532i	$0.606516\pi$
$920$	14.7879	−	31.8483i	0.487542	−	1.05001i
$921$			16.4667i			0.542596i
$922$	4.34563	−	29.7803i	0.143116	−	0.980761i
$923$	−3.16290			−0.104108
$924$	−51.2882	+	61.5322i	−1.68726	+	2.02426i
$925$	−10.7652			−0.353957
$926$	3.42383	−	23.4633i	0.112514	−	0.771051i
$927$			6.25673i			0.205498i
$928$	−20.3500	+	22.9927i	−0.668021	+	0.754771i
$929$	20.6217			0.676577			0.338288	−	0.941043i	$-0.390152\pi$
$929$	20.6217			0.676577			0.338288	+	0.941043i	$0.390152\pi$
$930$	126.528	+	18.4634i	4.14903	+	0.605439i
$931$	14.3377			0.469899
$932$	−12.4513	+	41.7555i	−0.407856	+	1.36775i
$933$	69.4233			2.27282
$934$	−3.93356	+	26.9564i	−0.128710	+	0.882041i
$935$	−10.8947	+	25.4101i	−0.356294	+	0.830998i
$936$	−9.47624	+	20.4087i	−0.309741	+	0.667080i
$937$			38.4363i			1.25566i	0.778351	+	0.627829i	$0.216056\pi$
$937$			38.4363i			1.25566i	−0.778351	+	0.627829i	$0.783944\pi$
$938$	2.83623	−	19.4365i	0.0926062	−	0.634623i
$939$			46.1578i			1.50630i
$940$	2.85140	−	9.56219i	0.0930026	−	0.311884i
$941$		−	35.4911i		−	1.15698i	−0.815690	−	0.578489i	$-0.803643\pi$
$941$		−	35.4911i		−	1.15698i	0.815690	−	0.578489i	$-0.196357\pi$
$942$	0.192045	−	1.31607i	0.00625718	−	0.0428800i
$943$	15.1652			0.493848
$944$	−26.5505	+	40.5599i	−0.864145	+	1.32011i
$945$			202.758i			6.59572i
$946$	1.07361	+	0.658158i	0.0349061	+	0.0213986i
$947$		−	7.04671i		−	0.228987i	−0.993424	−	0.114494i	$-0.963475\pi$
$947$		−	7.04671i		−	0.228987i	0.993424	−	0.114494i	$-0.0365246\pi$
$948$	15.4743	−	51.8932i	0.502583	−	1.68541i
$949$	−4.95698			−0.160911
$950$	−20.5986	−	3.00581i	−0.668306	−	0.0975213i
$951$			100.147i			3.24749i
$952$	−10.6924	+	23.0279i	−0.346542	+	0.746338i
$953$			36.6850i			1.18834i	0.804338	+	0.594171i	$0.202520\pi$
$953$			36.6850i			1.18834i	−0.804338	+	0.594171i	$0.797480\pi$
$954$	5.15120	+	0.751679i	0.166776	+	0.0243365i
$955$			16.6696i			0.539416i
$956$	5.59257	+	1.66768i	0.180877	+	0.0539367i
$957$	54.7644	+	23.4805i	1.77028	+	0.759016i
$958$	36.0835	+	5.26542i	1.16581	+	0.170118i
$959$	−39.0274			−1.26026
$960$	68.5379	−	57.8922i	2.21205	−	1.86846i
$961$	−34.0035			−1.09689
$962$	−0.339261	+	2.32493i	−0.0109382	+	0.0749587i
$963$	−39.8762			−1.28499
$964$	14.1210	−	47.3548i	0.454806	−	1.52519i
$965$			62.0847i			1.99858i
$966$	−61.9213	−	9.03574i	−1.99228	−	0.290720i
$967$	0.191793			0.00616763			0.00308382	−	0.999995i	$-0.499018\pi$
$967$	0.191793			0.00616763			0.00308382	+	0.999995i	$0.499018\pi$
$968$	−9.96412	−	29.4740i	−0.320259	−	0.947330i
$969$	−18.4991			−0.594278
$970$	9.85365	+	1.43787i	0.316382	+	0.0461674i
$971$		−	52.6104i		−	1.68835i	−0.536069	−	0.844174i	$-0.680091\pi$
$971$		−	52.6104i		−	1.68835i	0.536069	−	0.844174i	$-0.319909\pi$
$972$	29.4282	−	98.6877i	0.943911	−	3.16541i
$973$	17.8216			0.571335
$974$	−8.12186	+	55.6585i	−0.260241	+	1.78341i
$975$	21.4470			0.686854
$976$	−28.5238	+	43.5745i	−0.913025	+	1.39479i
$977$	37.7870			1.20891			0.604456	−	0.796639i	$-0.293391\pi$
$977$	37.7870			1.20891			0.604456	+	0.796639i	$0.293391\pi$
$978$	−104.863	−	15.3019i	−3.35314	−	0.489300i
$979$	−34.0467	−	14.5977i	−1.08814	−	0.466544i
$980$	40.9855	+	12.2217i	1.30923	+	0.390408i
$981$		−	37.3082i		−	1.19116i
$982$	29.0850	+	4.24417i	0.928139	+	0.135437i
$983$			23.2609i			0.741907i	0.928651	+	0.370953i	$0.120969\pi$
$983$			23.2609i			0.741907i	−0.928651	+	0.370953i	$0.879031\pi$
$984$	35.1434	+	16.3179i	1.12033	+	0.520196i
$985$			28.9710i			0.923092i
$986$	18.6879	+	2.72700i	0.595144	+	0.0868453i
$987$	−17.7824			−0.566020
$988$	−1.29831	+	4.35389i	−0.0413048	+	0.138516i
$989$			0.983753i			0.0312815i
$990$	−107.786	−	66.0762i	−3.42566	−	2.10004i
$991$			4.40605i			0.139963i	0.997548	+	0.0699815i	$0.0222940\pi$
$991$			4.40605i			0.139963i	−0.997548	+	0.0699815i	$0.977706\pi$
$992$	−30.2274	+	34.1528i	−0.959722	+	1.08435i
$993$	−45.4187			−1.44132
$994$	2.35647	−	16.1487i	0.0747427	−	0.512206i
$995$		−	34.2181i		−	1.08479i
$996$	−14.1814	+	47.5573i	−0.449354	+	1.50691i
$997$			36.5300i			1.15692i	0.815712	+	0.578458i	$0.196345\pi$
$997$			36.5300i			1.15692i	−0.815712	+	0.578458i	$0.803655\pi$
$998$	1.68693	−	11.5604i	0.0533990	−	0.365939i
$999$		−	27.2502i		−	0.862159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.b.131.5	✓	64
4.3	odd	2	inner	572.2.e.b.131.59	yes	64
11.10	odd	2	inner	572.2.e.b.131.60	yes	64
44.43	even	2	inner	572.2.e.b.131.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.b.131.5	✓	64	1.1	even	1	trivial
572.2.e.b.131.6	yes	64	44.43	even	2	inner
572.2.e.b.131.59	yes	64	4.3	odd	2	inner
572.2.e.b.131.60	yes	64	11.10	odd	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39939 - 0.204204i) q^{2} -3.30990i q^{3} +(1.91660 + 0.571522i) q^{4} +3.38816 q^{5} +(-0.675895 + 4.63186i) q^{6} +3.64850 q^{7} +(-2.56537 - 1.19116i) q^{8} -7.95546 q^{9} +O(q^{10})\)	\(q+(-1.39939 - 0.204204i) q^{2} -3.30990i q^{3} +(1.91660 + 0.571522i) q^{4} +3.38816 q^{5} +(-0.675895 + 4.63186i) q^{6} +3.64850 q^{7} +(-2.56537 - 1.19116i) q^{8} -7.95546 q^{9} +(-4.74137 - 0.691875i) q^{10} +(-3.04826 - 1.30695i) q^{11} +(1.89168 - 6.34377i) q^{12} +1.00000i q^{13} +(-5.10568 - 0.745036i) q^{14} -11.2145i q^{15} +(3.34672 + 2.19076i) q^{16} -2.46031i q^{17} +(11.1328 + 1.62454i) q^{18} +2.27167 q^{19} +(6.49376 + 1.93641i) q^{20} -12.0762i q^{21} +(3.99883 + 2.45141i) q^{22} +3.66413i q^{23} +(-3.94263 + 8.49114i) q^{24} +6.47965 q^{25} +(0.204204 - 1.39939i) q^{26} +16.4021i q^{27} +(6.99271 + 2.08520i) q^{28} -5.42789i q^{29} +(-2.29004 + 15.6935i) q^{30} -8.06247i q^{31} +(-4.23602 - 3.74915i) q^{32} +(-4.32589 + 10.0894i) q^{33} +(-0.502404 + 3.44294i) q^{34} +12.3617 q^{35} +(-15.2475 - 4.54673i) q^{36} -1.66138 q^{37} +(-3.17896 - 0.463884i) q^{38} +3.30990 q^{39} +(-8.69190 - 4.03585i) q^{40} -4.13884i q^{41} +(-2.46600 + 16.8993i) q^{42} +0.268482 q^{43} +(-5.09534 - 4.24706i) q^{44} -26.9544 q^{45} +(0.748229 - 5.12756i) q^{46} -1.47252i q^{47} +(7.25121 - 11.0773i) q^{48} +6.31152 q^{49} +(-9.06758 - 1.32317i) q^{50} -8.14339 q^{51} +(-0.571522 + 1.91660i) q^{52} +0.462704 q^{53} +(3.34937 - 22.9530i) q^{54} +(-10.3280 - 4.42817i) q^{55} +(-9.35975 - 4.34595i) q^{56} -7.51902i q^{57} +(-1.10840 + 7.59576i) q^{58} +12.1193i q^{59} +(6.40933 - 21.4937i) q^{60} +13.0200i q^{61} +(-1.64639 + 11.2826i) q^{62} -29.0255 q^{63} +(5.16227 + 6.11155i) q^{64} +3.38816i q^{65} +(8.11392 - 13.2357i) q^{66} +3.80684i q^{67} +(1.40612 - 4.71543i) q^{68} +12.1279 q^{69} +(-17.2989 - 2.52430i) q^{70} +3.16290i q^{71} +(20.4087 + 9.47624i) q^{72} +4.95698i q^{73} +(2.32493 + 0.339261i) q^{74} -21.4470i q^{75} +(4.35389 + 1.29831i) q^{76} +(-11.1216 - 4.76841i) q^{77} +(-4.63186 - 0.675895i) q^{78} +8.18019 q^{79} +(11.3392 + 7.42266i) q^{80} +30.4230 q^{81} +(-0.845166 + 5.79186i) q^{82} -7.49670 q^{83} +(6.90180 - 23.1452i) q^{84} -8.33593i q^{85} +(-0.375712 - 0.0548250i) q^{86} -17.9658 q^{87} +(6.26312 + 6.98379i) q^{88} +11.1692 q^{89} +(37.7198 + 5.50419i) q^{90} +3.64850i q^{91} +(-2.09413 + 7.02268i) q^{92} -26.6860 q^{93} +(-0.300694 + 2.06063i) q^{94} +7.69680 q^{95} +(-12.4093 + 14.0208i) q^{96} -2.07823 q^{97} +(-8.83229 - 1.28883i) q^{98} +(24.2503 + 10.3974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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