LMFDB - Embedded newform 260.2.bg.c.23.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(23,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("260.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bg (of order $12$, degree $4$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.20
Character	$\chi$	$=$	260.23
Dual form			260.2.bg.c.147.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0281072 - 1.41393i) q^{2} +(-1.77624 - 0.475943i) q^{3} +(-1.99842 + 0.0794833i) q^{4} +(1.35785 + 1.77658i) q^{5} +(-0.623027 + 2.52487i) q^{6} +(0.755969 + 2.82131i) q^{7} +(0.168554 + 2.82340i) q^{8} +(0.330446 + 0.190783i) q^{9} +O(q^{10})$	\(q+(-0.0281072 - 1.41393i) q^{2} +(-1.77624 - 0.475943i) q^{3} +(-1.99842 + 0.0794833i) q^{4} +(1.35785 + 1.77658i) q^{5} +(-0.623027 + 2.52487i) q^{6} +(0.755969 + 2.82131i) q^{7} +(0.168554 + 2.82340i) q^{8} +(0.330446 + 0.190783i) q^{9} +(2.47380 - 1.96985i) q^{10} +(0.371450 + 0.643371i) q^{11} +(3.58751 + 0.809953i) q^{12} +(3.09439 + 1.85060i) q^{13} +(3.96791 - 1.14819i) q^{14} +(-1.56633 - 3.80190i) q^{15} +(3.98736 - 0.317682i) q^{16} +(0.511256 + 1.90803i) q^{17} +(0.260467 - 0.472591i) q^{18} +(-5.10854 - 2.94942i) q^{19} +(-2.85477 - 3.44243i) q^{20} -5.37114i q^{21} +(0.899244 - 0.543290i) q^{22} +(5.69929 + 1.52712i) q^{23} +(1.04439 - 5.09527i) q^{24} +(-1.31248 + 4.82467i) q^{25} +(2.52965 - 4.42729i) q^{26} +(3.40475 + 3.40475i) q^{27} +(-1.73499 - 5.57808i) q^{28} +(-3.52008 + 2.03232i) q^{29} +(-5.33161 + 2.32154i) q^{30} +6.21684 q^{31} +(-0.561255 - 5.62894i) q^{32} +(-0.353579 - 1.31957i) q^{33} +(2.68346 - 0.776511i) q^{34} +(-3.98580 + 5.17397i) q^{35} +(-0.675533 - 0.354999i) q^{36} +(-0.837565 + 3.12584i) q^{37} +(-4.02670 + 7.30604i) q^{38} +(-4.61562 - 4.75987i) q^{39} +(-4.78713 + 4.13321i) q^{40} +(-6.93331 + 4.00295i) q^{41} +(-7.59444 + 0.150968i) q^{42} +(0.547962 + 2.04502i) q^{43} +(-0.793451 - 1.25620i) q^{44} +(0.109755 + 0.846118i) q^{45} +(1.99906 - 8.10134i) q^{46} +(-2.37644 + 2.37644i) q^{47} +(-7.23373 - 1.33348i) q^{48} +(-1.32615 + 0.765653i) q^{49} +(6.85865 + 1.72015i) q^{50} -3.63246i q^{51} +(-6.33099 - 3.45232i) q^{52} +(0.529690 + 0.529690i) q^{53} +(4.71840 - 4.90979i) q^{54} +(-0.638626 + 1.53351i) q^{55} +(-7.83828 + 2.60995i) q^{56} +(7.67026 + 7.67026i) q^{57} +(2.97250 + 4.92003i) q^{58} +(0.918361 + 0.530216i) q^{59} +(3.43236 + 7.47330i) q^{60} +(6.10528 - 10.5747i) q^{61} +(-0.174738 - 8.79020i) q^{62} +(-0.288452 + 1.07652i) q^{63} +(-7.94318 + 0.951791i) q^{64} +(0.913989 + 8.01028i) q^{65} +(-1.85585 + 0.537026i) q^{66} +(-12.0928 - 3.24025i) q^{67} +(-1.17336 - 3.77241i) q^{68} +(-9.39651 - 5.42508i) q^{69} +(7.42768 + 5.49023i) q^{70} +(-3.73044 + 6.46131i) q^{71} +(-0.482958 + 0.965138i) q^{72} +(4.65282 - 4.65282i) q^{73} +(4.44327 + 1.09640i) q^{74} +(4.62755 - 7.94512i) q^{75} +(10.4434 + 5.48813i) q^{76} +(-1.53435 + 1.53435i) q^{77} +(-6.60042 + 6.65997i) q^{78} +16.1634 q^{79} +(5.97864 + 6.65251i) q^{80} +(-4.99955 - 8.65948i) q^{81} +(5.85478 + 9.69073i) q^{82} +(-10.6691 - 10.6691i) q^{83} +(0.426916 + 10.7338i) q^{84} +(-2.69556 + 3.49911i) q^{85} +(2.87612 - 0.832261i) q^{86} +(7.21978 - 1.93454i) q^{87} +(-1.75388 + 1.15720i) q^{88} +(-0.514730 - 0.891538i) q^{89} +(1.19327 - 0.178969i) q^{90} +(-2.88186 + 10.1293i) q^{91} +(-11.5110 - 2.59883i) q^{92} +(-11.0426 - 2.95886i) q^{93} +(3.42692 + 3.29333i) q^{94} +(-1.69677 - 13.0806i) q^{95} +(-1.68213 + 10.2655i) q^{96} +(17.0667 - 4.57301i) q^{97} +(1.11986 + 1.85357i) q^{98} +0.283466i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 12 q^{6}+O(q^{10}) $ 144 * q - 6 * q^2 - 12 * q^6	$ 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38} + 76 q^{40} - 72 q^{41} + 40 q^{42} - 120 q^{45} - 12 q^{46} - 40 q^{48} + 120 q^{50} - 10 q^{52} + 8 q^{53} - 20 q^{56} + 126 q^{58} + 16 q^{61} - 44 q^{62} + 32 q^{65} + 96 q^{66} - 64 q^{68} - 54 q^{72} - 12 q^{76} + 40 q^{77} - 100 q^{78} - 24 q^{80} - 32 q^{81} - 78 q^{82} - 24 q^{85} - 10 q^{88} - 8 q^{90} + 100 q^{92} - 48 q^{93} - 12 q^{97} - 162 q^{98}+O(q^{100}) $ 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.0281072	−	1.41393i	−0.0198748	−	0.999802i
$2$	−0.0281072	−	1.41393i	−0.0198748	−	0.999802i
$3$	−1.77624	−	0.475943i	−1.02552	−	0.274786i	−0.293417	−	0.955985i	$-0.594792\pi$
$3$	−1.77624	−	0.475943i	−1.02552	−	0.274786i	−0.732099	+	0.681199i	$0.761459\pi$
$4$	−1.99842	+	0.0794833i	−0.999210	+	0.0397417i
$5$	1.35785	+	1.77658i	0.607250	+	0.794511i
$5$	1.35785	+	1.77658i	0.607250	+	0.794511i
$6$	−0.623027	+	2.52487i	−0.254350	+	1.03077i
$7$	0.755969	+	2.82131i	0.285729	+	1.06636i	0.948305	+	0.317361i	$0.102797\pi$
$7$	0.755969	+	2.82131i	0.285729	+	1.06636i	−0.662575	+	0.748995i	$0.730537\pi$
$8$	0.168554	+	2.82340i	0.0595929	+	0.998223i
$9$	0.330446	+	0.190783i	0.110149	+	0.0635943i
$10$	2.47380	−	1.96985i	0.782285	−	0.622921i
$11$	0.371450	+	0.643371i	0.111997	+	0.193984i	0.916575	−	0.399862i	$-0.130942\pi$
$11$	0.371450	+	0.643371i	0.111997	+	0.193984i	−0.804579	+	0.593846i	$0.797609\pi$
$12$	3.58751	+	0.809953i	1.03563	+	0.233813i
$13$	3.09439	+	1.85060i	0.858231	+	0.513264i
$13$	3.09439	+	1.85060i	0.858231	+	0.513264i
$14$	3.96791	−	1.14819i	1.06047	−	0.306867i
$15$	−1.56633	−	3.80190i	−0.404423	−	0.981647i
$16$	3.98736	−	0.317682i	0.996841	−	0.0794205i
$17$	0.511256	+	1.90803i	0.123998	+	0.462766i	0.999802	−	0.0199008i	$-0.00633503\pi$
$17$	0.511256	+	1.90803i	0.123998	+	0.462766i	−0.875804	+	0.482666i	$0.839668\pi$
$18$	0.260467	−	0.472591i	0.0613926	−	0.111391i
$19$	−5.10854	−	2.94942i	−1.17198	−	0.676643i	−0.217835	−	0.975986i	$-0.569899\pi$
$19$	−5.10854	−	2.94942i	−1.17198	−	0.676643i	−0.954146	+	0.299343i	$0.903233\pi$
$20$	−2.85477	−	3.44243i	−0.638345	−	0.769750i
$21$		−	5.37114i		−	1.17208i
$22$	0.899244	−	0.543290i	0.191719	−	0.115830i
$23$	5.69929	+	1.52712i	1.18838	+	0.318426i	0.798247	−	0.602330i	$-0.205761\pi$
$23$	5.69929	+	1.52712i	1.18838	+	0.318426i	0.390137	+	0.920757i	$0.372428\pi$
$24$	1.04439	−	5.09527i	0.213184	−	1.04007i
$25$	−1.31248	+	4.82467i	−0.262495	+	0.964933i
$26$	2.52965	−	4.42729i	0.496106	−	0.868262i
$27$	3.40475	+	3.40475i	0.655245	+	0.655245i
$28$	−1.73499	−	5.57808i	−0.327882	−	1.05416i
$29$	−3.52008	+	2.03232i	−0.653662	+	0.377392i	−0.789858	−	0.613290i	$-0.789846\pi$
$29$	−3.52008	+	2.03232i	−0.653662	+	0.377392i	0.136196	+	0.990682i	$0.456512\pi$
$30$	−5.33161	+	2.32154i	−0.973415	+	0.423854i
$31$	6.21684			1.11658			0.558289	−	0.829647i	$-0.311458\pi$
$31$	6.21684			1.11658			0.558289	+	0.829647i	$0.311458\pi$
$32$	−0.561255	−	5.62894i	−0.0992168	−	0.995066i
$33$	−0.353579	−	1.31957i	−0.0615501	−	0.229708i
$34$	2.68346	−	0.776511i	0.460210	−	0.133171i
$35$	−3.98580	+	5.17397i	−0.673723	+	0.874560i
$36$	−0.675533	−	0.354999i	−0.112589	−	0.0591666i
$37$	−0.837565	+	3.12584i	−0.137695	+	0.513884i	0.862277	+	0.506436i	$0.169037\pi$
$37$	−0.837565	+	3.12584i	−0.137695	+	0.513884i	−0.999972	+	0.00744798i	$0.997629\pi$
$38$	−4.02670	+	7.30604i	−0.653217	+	1.18520i
$39$	−4.61562	−	4.75987i	−0.739091	−	0.762190i
$40$	−4.78713	+	4.13321i	−0.756911	+	0.653518i
$41$	−6.93331	+	4.00295i	−1.08280	+	0.625155i	−0.931650	−	0.363356i	$-0.881631\pi$
$41$	−6.93331	+	4.00295i	−1.08280	+	0.625155i	−0.151150	+	0.988511i	$0.548298\pi$
$42$	−7.59444	+	0.150968i	−1.17185	+	0.0232948i
$43$	0.547962	+	2.04502i	0.0835634	+	0.311863i	0.995038	−	0.0994930i	$-0.0317221\pi$
$43$	0.547962	+	2.04502i	0.0835634	+	0.311863i	−0.911475	+	0.411356i	$0.865055\pi$
$44$	−0.793451	−	1.25620i	−0.119617	−	0.189379i
$45$	0.109755	+	0.846118i	0.0163613	+	0.126132i
$46$	1.99906	−	8.10134i	0.294745	−	1.19448i
$47$	−2.37644	+	2.37644i	−0.346639	+	0.346639i	−0.858856	−	0.512217i	$-0.828824\pi$
$47$	−2.37644	+	2.37644i	−0.346639	+	0.346639i	0.512217	+	0.858856i	$0.328824\pi$
$48$	−7.23373	−	1.33348i	−1.04410	−	0.192471i
$49$	−1.32615	+	0.765653i	−0.189450	+	0.109379i
$50$	6.85865	+	1.72015i	0.969960	+	0.243266i
$51$		−	3.63246i		−	0.508646i
$52$	−6.33099	−	3.45232i	−0.877951	−	0.478751i
$53$	0.529690	+	0.529690i	0.0727585	+	0.0727585i	0.742550	−	0.669791i	$-0.233616\pi$
$53$	0.529690	+	0.529690i	0.0727585	+	0.0727585i	−0.669791	+	0.742550i	$0.733616\pi$
$54$	4.71840	−	4.90979i	0.642093	−	0.668138i
$55$	−0.638626	+	1.53351i	−0.0861123	+	0.206779i
$56$	−7.83828	+	2.60995i	−1.04743	+	0.348769i
$57$	7.67026	+	7.67026i	1.01595	+	1.01595i
$58$	2.97250	+	4.92003i	0.390309	+	0.646032i
$59$	0.918361	+	0.530216i	0.119560	+	0.0690283i	0.558588	−	0.829446i	$-0.311343\pi$
$59$	0.918361	+	0.530216i	0.119560	+	0.0690283i	−0.439027	+	0.898474i	$0.644677\pi$
$60$	3.43236	+	7.47330i	0.443116	+	0.964799i
$61$	6.10528	−	10.5747i	0.781701	−	1.35395i	−0.149249	−	0.988800i	$-0.547686\pi$
$61$	6.10528	−	10.5747i	0.781701	−	1.35395i	0.930950	−	0.365146i	$-0.118981\pi$
$62$	−0.174738	−	8.79020i	−0.0221917	−	1.11636i
$63$	−0.288452	+	1.07652i	−0.0363415	+	0.135628i
$64$	−7.94318	+	0.951791i	−0.992897	+	0.118974i
$65$	0.913989	+	8.01028i	0.113366	+	0.993553i
$66$	−1.85585	+	0.537026i	−0.228440	+	0.0661034i
$67$	−12.0928	−	3.24025i	−1.47737	−	0.395859i	−0.571917	−	0.820312i	$-0.693800\pi$
$67$	−12.0928	−	3.24025i	−1.47737	−	0.395859i	−0.905450	+	0.424452i	$0.860467\pi$
$68$	−1.17336	−	3.77241i	−0.142291	−	0.457472i
$69$	−9.39651	−	5.42508i	−1.13121	−	0.653102i
$70$	7.42768	+	5.49023i	0.887777	+	0.656208i
$71$	−3.73044	+	6.46131i	−0.442722	+	0.766817i	−0.997890	−	0.0649212i	$-0.979320\pi$
$71$	−3.73044	+	6.46131i	−0.442722	+	0.766817i	0.555169	+	0.831738i	$0.312654\pi$
$72$	−0.482958	+	0.965138i	−0.0569172	+	0.113743i
$73$	4.65282	−	4.65282i	0.544572	−	0.544572i	−0.380294	−	0.924866i	$-0.624177\pi$
$73$	4.65282	−	4.65282i	0.544572	−	0.544572i	0.924866	+	0.380294i	$0.124177\pi$
$74$	4.44327	+	1.09640i	0.516519	+	0.127454i
$75$	4.62755	−	7.94512i	0.534343	−	0.917424i
$76$	10.4434	+	5.48813i	1.19795	+	0.629532i
$77$	−1.53435	+	1.53435i	−0.174855	+	0.174855i
$78$	−6.60042	+	6.65997i	−0.747350	+	0.754093i
$79$	16.1634			1.81852			0.909259	−	0.416230i	$-0.136649\pi$
$79$	16.1634			1.81852			0.909259	+	0.416230i	$0.136649\pi$
$80$	5.97864	+	6.65251i	0.668432	+	0.743773i
$81$	−4.99955	−	8.65948i	−0.555506	−	0.962164i
$82$	5.85478	+	9.69073i	0.646552	+	1.07016i
$83$	−10.6691	−	10.6691i	−1.17108	−	1.17108i	−0.981952	−	0.189131i	$-0.939433\pi$
$83$	−10.6691	−	10.6691i	−1.17108	−	1.17108i	−0.189131	−	0.981952i	$-0.560567\pi$
$84$	0.426916	+	10.7338i	0.0465804	+	1.17115i
$85$	−2.69556	+	3.49911i	−0.292375	+	0.379532i
$86$	2.87612	−	0.832261i	0.310140	−	0.0897451i
$87$	7.21978	−	1.93454i	0.774042	−	0.207404i
$88$	−1.75388	+	1.15720i	−0.186965	+	0.123358i
$89$	−0.514730	−	0.891538i	−0.0545612	−	0.0945028i	0.837455	−	0.546507i	$-0.184043\pi$
$89$	−0.514730	−	0.891538i	−0.0545612	−	0.0945028i	−0.892016	+	0.452004i	$0.850709\pi$
$90$	1.19327	−	0.178969i	0.125782	−	0.0188649i
$91$	−2.88186	+	10.1293i	−0.302101	+	1.06183i
$92$	−11.5110	−	2.59883i	−1.20010	−	0.270947i
$93$	−11.0426	−	2.95886i	−1.14507	−	0.306820i
$94$	3.42692	+	3.29333i	0.353460	+	0.339681i
$95$	−1.69677	−	13.0806i	−0.174085	−	1.34204i
$96$	−1.68213	+	10.2655i	−0.171682	+	1.04772i
$97$	17.0667	−	4.57301i	1.73286	−	0.464318i	0.752021	−	0.659139i	$-0.229079\pi$
$97$	17.0667	−	4.57301i	1.73286	−	0.464318i	0.980839	+	0.194821i	$0.0624126\pi$
$98$	1.11986	+	1.85357i	0.113123	+	0.187239i
$99$			0.283466i			0.0284894i
$100$	2.23940	−	9.74603i	0.223940	−	0.974603i
$101$	−4.67940	−	8.10495i	−0.465617	−	0.806473i	0.533612	−	0.845730i	$-0.320834\pi$
$101$	−4.67940	−	8.10495i	−0.465617	−	0.806473i	−0.999229	+	0.0392565i	$0.987501\pi$
$102$	−5.13606	+	0.102098i	−0.508546	+	0.0101092i
$103$	0.630443	−	0.630443i	0.0621194	−	0.0621194i	−0.675365	−	0.737484i	$-0.736014\pi$
$103$	0.630443	−	0.630443i	0.0621194	−	0.0621194i	0.737484	+	0.675365i	$0.236014\pi$
$104$	−4.70341	+	9.04864i	−0.461208	+	0.887292i
$105$	9.54227	−	7.29322i	0.931230	−	0.711745i
$106$	0.734059	−	0.763835i	0.0712981	−	0.0741902i
$107$	3.28479	−	12.2590i	0.317552	−	1.18512i	−0.604037	−	0.796956i	$-0.706442\pi$
$107$	3.28479	−	12.2590i	0.317552	−	1.18512i	0.921590	−	0.388165i	$-0.126891\pi$
$108$	−7.07475	−	6.53351i	−0.680768	−	0.628687i
$109$	−5.47759			−0.524658			−0.262329	−	0.964978i	$-0.584491\pi$
$109$	−5.47759			−0.524658			−0.262329	+	0.964978i	$0.584491\pi$
$110$	2.18624	+	0.859872i	0.208450	+	0.0819856i
$111$	2.97544	−	5.15361i	0.282416	−	0.489159i
$112$	3.91061	+	11.0095i	0.369517	+	1.04030i
$113$	−9.70764	+	2.60115i	−0.913218	+	0.244696i	−0.684684	−	0.728840i	$-0.740060\pi$
$113$	−9.70764	+	2.60115i	−0.913218	+	0.244696i	−0.228534	+	0.973536i	$0.573393\pi$
$114$	10.6297	−	11.0608i	0.995559	−	1.03594i
$115$	5.02574	+	12.1988i	0.468653	+	1.13755i
$116$	6.87306	−	4.34121i	0.638147	−	0.403071i
$117$	0.669466	+	1.20188i	0.0618922	+	0.111114i
$118$	0.723878	−	1.31341i	0.0666384	−	0.120909i
$119$	−4.99666	+	2.88483i	−0.458043	+	0.264452i
$120$	10.4703	−	5.06319i	0.955801	−	0.462204i
$121$	5.22405	−	9.04832i	0.474914	−	0.822574i
$122$	−15.1235	−	8.33524i	−1.36921	−	0.754637i
$123$	14.2204	−	3.81035i	1.28221	−	0.343568i
$124$	−12.4239	+	0.494135i	−1.11570	+	0.0443746i
$125$	−10.3536	+	4.21946i	−0.926050	+	0.377400i
$126$	1.53023	+	0.377594i	0.136324	+	0.0336388i
$127$	−4.89419	+	18.2654i	−0.434289	+	1.62079i	0.308472	+	0.951234i	$0.400183\pi$
$127$	−4.89419	+	18.2654i	−0.434289	+	1.62079i	−0.742761	+	0.669557i	$0.766484\pi$
$128$	1.56903	+	11.2044i	0.138684	+	0.990337i
$129$		−	3.89325i		−	0.342782i
$130$	11.3003	−	1.51747i	0.991104	−	0.133091i
$131$		−	3.94889i		−	0.345016i	−0.985008	−	0.172508i	$-0.944813\pi$
$131$		−	3.94889i		−	0.345016i	0.985008	−	0.172508i	$-0.0551871\pi$
$132$	0.811483	+	2.60896i	0.0706305	+	0.227081i
$133$	4.45934	−	16.6425i	0.386674	−	1.44309i
$134$	−4.24160	+	17.1895i	−0.366419	+	1.48494i
$135$	−1.42567	+	10.6720i	−0.122702	+	0.918497i
$136$	−5.30096	+	1.76509i	−0.454554	+	0.151355i
$137$	15.2066	−	4.07459i	1.29919	−	0.348116i	0.458044	−	0.888930i	$-0.348550\pi$
$137$	15.2066	−	4.07459i	1.29919	−	0.348116i	0.841142	+	0.540814i	$0.181884\pi$
$138$	−7.40659	+	13.4385i	−0.630491	+	1.14396i
$139$	−2.81428	+	4.87448i	−0.238704	+	0.413448i	−0.960343	−	0.278822i	$-0.910056\pi$
$139$	−2.81428	+	4.87448i	−0.238704	+	0.413448i	0.721638	+	0.692270i	$0.243389\pi$
$140$	7.55406	−	10.6566i	0.638434	−	0.900644i
$141$	5.35218	−	3.09008i	0.450735	−	0.260232i
$142$	9.24072	+	5.09299i	0.775464	+	0.427394i
$143$	−0.0412086	+	2.67825i	−0.00344603	+	0.223967i
$144$	1.37822	+	0.655744i	0.114851	+	0.0546454i
$145$	−8.39032	−	3.49411i	−0.696778	−	0.290170i
$146$	−6.70956	−	6.44801i	−0.555287	−	0.533641i
$147$	2.71997	−	0.728815i	0.224340	−	0.0601116i
$148$	1.42536	−	6.31331i	0.117163	−	0.518951i
$149$	4.85387	−	8.40715i	0.397645	−	0.688741i	−0.595790	−	0.803140i	$-0.703161\pi$
$149$	4.85387	−	8.40715i	0.397645	−	0.688741i	0.993435	+	0.114399i	$0.0364944\pi$
$150$	−11.3639	−	6.31973i	−0.927862	−	0.516004i
$151$	14.1000			1.14744			0.573721	−	0.819051i	$-0.305499\pi$
$151$	14.1000			1.14744			0.573721	+	0.819051i	$0.305499\pi$
$152$	7.46632	−	14.9206i	0.605599	−	1.21022i
$153$	−0.195078	+	0.728040i	−0.0157711	+	0.0588585i
$154$	2.21259	+	2.12634i	0.178296	+	0.171345i
$155$	8.44155	+	11.0447i	0.678041	+	0.887133i
$156$	9.60228	+	9.14536i	0.768797	+	0.732215i
$157$	7.11530	−	7.11530i	0.567863	−	0.567863i	−0.363666	−	0.931529i	$-0.618475\pi$
$157$	7.11530	−	7.11530i	0.567863	−	0.567863i	0.931529	+	0.363666i	$0.118475\pi$
$158$	−0.454306	−	22.8539i	−0.0361426	−	1.81816i
$159$	−0.688757	−	1.19296i	−0.0546220	−	0.0946080i
$160$	9.23817	−	8.64039i	0.730341	−	0.683082i
$161$			17.2339i			1.35822i
$162$	−12.1034	+	7.31243i	−0.950934	+	0.574519i
$163$	6.54590	−	1.75397i	0.512715	−	0.137381i	0.00681999	−	0.999977i	$-0.497829\pi$
$163$	6.54590	−	1.75397i	0.512715	−	0.137381i	0.505895	+	0.862595i	$0.331162\pi$
$164$	13.5375	−	8.55065i	1.05710	−	0.667694i
$165$	1.86422	−	2.41995i	0.145129	−	0.188393i
$166$	−14.7855	+	15.3852i	−1.14758	+	1.19413i
$167$	−7.27515	−	1.94937i	−0.562968	−	0.150847i	−0.0338983	−	0.999425i	$-0.510792\pi$
$167$	−7.27515	−	1.94937i	−0.562968	−	0.150847i	−0.529069	+	0.848579i	$0.677459\pi$
$168$	15.1649	−	0.905328i	1.17000	−	0.0698476i
$169$	6.15056	+	11.4530i	0.473120	+	0.880998i
$170$	5.02328	+	3.71300i	0.385268	+	0.284774i
$171$	−1.12540	−	1.94925i	−0.0860613	−	0.149062i
$172$	−1.25760	−	4.04326i	−0.0958913	−	0.308295i
$173$	−7.21717	+	1.93384i	−0.548712	+	0.147027i	−0.522515	−	0.852630i	$-0.675006\pi$
$173$	−7.21717	+	1.93384i	−0.548712	+	0.147027i	−0.0261964	+	0.999657i	$0.508340\pi$
$174$	−2.93823	−	10.1539i	−0.222747	−	0.769767i
$175$	−14.6041	−	0.0556094i	−1.10397	−	0.00420367i
$176$	1.68550	+	2.44735i	0.127049	+	0.184476i
$177$	−1.37888	−	1.37888i	−0.103643	−	0.103643i
$178$	−1.24611	+	0.752853i	−0.0933998	+	0.0564287i
$179$	5.48498	+	9.50027i	0.409967	+	0.710083i	0.994886	−	0.101008i	$-0.0322069\pi$
$179$	5.48498	+	9.50027i	0.409967	+	0.710083i	−0.584919	+	0.811092i	$0.698874\pi$
$180$	−0.286589	−	1.68218i	−0.0213611	−	0.125382i
$181$	−3.11272			−0.231367			−0.115683	−	0.993286i	$-0.536906\pi$
$181$	−3.11272			−0.231367			−0.115683	+	0.993286i	$0.536906\pi$
$182$	14.4031	+	3.79006i	1.06763	+	0.280938i
$183$	−15.8774	+	15.8774i	−1.17369	+	1.17369i
$184$	−3.35103	+	16.3488i	−0.247041	+	1.20525i
$185$	−6.69059	+	2.75642i	−0.491902	+	0.202656i
$186$	−3.87326	+	15.6967i	−0.284001	+	1.15094i
$187$	−1.03767	+	1.03767i	−0.0758817	+	0.0758817i
$188$	4.56023	−	4.93801i	0.332589	−	0.360141i
$189$	−7.03199	+	12.1798i	−0.511502	+	0.885948i
$190$	−18.4474	+	2.76677i	−1.33832	+	0.200723i
$191$	−10.0423	−	5.79793i	−0.726635	−	0.419523i	0.0905546	−	0.995891i	$-0.471136\pi$
$191$	−10.0423	−	5.79793i	−0.726635	−	0.419523i	−0.817190	+	0.576368i	$0.804469\pi$
$192$	14.5620	+	2.08989i	1.05092	+	0.150825i
$193$	14.9578	+	4.00793i	1.07669	+	0.288497i	0.753238	−	0.657748i	$-0.228491\pi$
$193$	14.9578	+	4.00793i	1.07669	+	0.288497i	0.323449	+	0.946246i	$0.395158\pi$
$194$	−6.94562	−	24.0026i	−0.498667	−	1.72329i
$195$	2.18897	−	14.6632i	0.156756	−	1.05006i
$196$	2.58935	−	1.63550i	0.184953	−	0.116822i
$197$	−5.46820	+	20.4076i	−0.389593	+	1.45398i	0.441204	+	0.897407i	$0.354551\pi$
$197$	−5.46820	+	20.4076i	−0.389593	+	1.45398i	−0.830797	+	0.556575i	$0.812115\pi$
$198$	0.400802	−	0.00796741i	0.0284837	−	0.000566219i
$199$	6.70365	−	11.6111i	0.475209	−	0.823086i	−0.524388	−	0.851480i	$-0.675706\pi$
$199$	6.70365	−	11.6111i	0.475209	−	0.823086i	0.999597	+	0.0283933i	$0.00903908\pi$
$200$	−13.8432	−	2.89243i	−0.978861	−	0.204526i
$201$	19.9375	+	11.5109i	1.40629	+	0.811919i
$202$	−11.3283	+	6.84417i	−0.797060	+	0.481554i
$203$	−8.39488	−	8.39488i	−0.589205	−	0.589205i
$204$	0.288720	+	7.25918i	0.0202144	+	0.508244i
$205$	−16.5260	−	6.88217i	−1.15422	−	0.480671i
$206$	−0.909125	−	0.873685i	−0.0633417	−	0.0608725i
$207$	1.59196	+	1.59196i	0.110649	+	0.110649i
$208$	12.9264	+	6.39599i	0.896283	+	0.443482i
$209$		−	4.38225i		−	0.303127i
$210$	−10.5803	−	13.2871i	−0.730112	−	0.916900i
$211$	18.4262	−	10.6384i	1.26851	−	0.732376i	0.293806	−	0.955865i	$-0.405078\pi$
$211$	18.4262	−	10.6384i	1.26851	−	0.732376i	0.974706	+	0.223489i	$0.0717446\pi$
$212$	−1.10064	−	1.01644i	−0.0755926	−	0.0698095i
$213$	9.70139	−	9.70139i	0.664728	−	0.664728i
$214$	−17.4257	−	4.29991i	−1.19120	−	0.293936i
$215$	−2.88909	+	3.75033i	−0.197034	+	0.255771i
$216$	−9.03910	+	10.1869i	−0.615033	+	0.693128i
$217$	4.69974	+	17.5397i	0.319039	+	1.19067i
$218$	0.153959	+	7.74495i	0.0104275	+	0.524554i
$219$	−10.4790	+	6.05007i	−0.708107	+	0.408826i
$220$	1.15435	−	3.11537i	0.0778265	−	0.210038i
$221$	−1.94898	+	6.85033i	−0.131102	+	0.460803i
$222$	−7.37050	−	4.06222i	−0.494676	−	0.272639i
$223$	−0.397266	+	1.48262i	−0.0266029	+	0.0992833i	−0.977951	−	0.208835i	$-0.933033\pi$
$223$	−0.397266	+	1.48262i	−0.0266029	+	0.0992833i	0.951348	+	0.308119i	$0.0996994\pi$
$224$	15.4567	−	5.83878i	1.03275	−	0.390120i
$225$	−1.35417	+	1.34389i	−0.0902777	+	0.0895928i
$226$	3.95071	+	13.6528i	0.262798	+	0.908174i
$227$	4.12272	+	15.3862i	0.273634	+	1.02122i	0.956751	+	0.290908i	$0.0939575\pi$
$227$	4.12272	+	15.3862i	0.273634	+	1.02122i	−0.683116	+	0.730309i	$0.739376\pi$
$228$	−15.9381	−	14.7188i	−1.05552	−	0.974773i
$229$	−8.14461			−0.538211			−0.269106	−	0.963111i	$-0.586728\pi$
$229$	−8.14461			−0.538211			−0.269106	+	0.963111i	$0.586728\pi$
$230$	17.1071	−	7.44894i	1.12801	−	0.491168i
$231$	3.45564	−	1.99511i	0.227364	−	0.131269i
$232$	−6.33137	−	9.59603i	−0.415675	−	0.630010i
$233$	1.22509	+	1.22509i	0.0802581	+	0.0802581i	0.746096	−	0.665838i	$-0.231926\pi$
$233$	1.22509	+	1.22509i	0.0802581	+	0.0802581i	−0.665838	+	0.746096i	$0.731926\pi$
$234$	1.68056	−	0.980363i	0.109862	−	0.0640883i
$235$	−7.44878	−	0.995082i	−0.485905	−	0.0649120i
$236$	−1.87741	−	0.986600i	−0.122209	−	0.0642222i
$237$	−28.7101	−	7.69284i	−1.86492	−	0.499703i
$238$	4.21940	+	6.98387i	0.273503	+	0.452697i
$239$		−	13.7413i		−	0.888849i	−0.895816	−	0.444424i	$-0.853408\pi$
$239$		−	13.7413i		−	0.888849i	0.895816	−	0.444424i	$-0.146592\pi$
$240$	−7.45331	−	14.6620i	−0.481109	−	0.946426i
$241$	−26.0624	−	15.0472i	−1.67883	−	0.969272i	−0.962410	−	0.271602i	$-0.912446\pi$
$241$	−26.0624	−	15.0472i	−1.67883	−	0.969272i	−0.716419	−	0.697670i	$-0.754220\pi$
$242$	−12.9406	−	7.13214i	−0.831851	−	0.458471i
$243$	1.02033	+	3.80792i	0.0654541	+	0.244278i
$244$	−11.3604	+	21.6179i	−0.727275	+	1.38394i
$245$	−3.16096	−	1.31637i	−0.201946	−	0.0840997i
$246$	−5.78728	−	19.9996i	−0.368983	−	1.27513i
$247$	−10.3497	−	18.5805i	−0.658533	−	1.18225i
$248$	1.04787	+	17.5526i	0.0665401	+	1.11459i
$249$	13.8730	+	24.0287i	0.879166	+	1.52276i
$250$	6.25705	+	14.5207i	0.395731	+	0.918367i
$251$	3.59935	+	2.07809i	0.227189	+	0.131168i	0.609275	−	0.792959i	$-0.291461\pi$
$251$	3.59935	+	2.07809i	0.227189	+	0.131168i	−0.382086	+	0.924127i	$0.624794\pi$
$252$	0.490883	−	2.17426i	0.0309227	−	0.136966i
$253$	1.13450	+	4.23401i	0.0713253	+	0.266190i
$254$	25.9636	+	6.40668i	1.62910	+	0.401991i
$255$	6.45336	−	4.93234i	0.404125	−	0.308875i
$256$	15.7982	−	2.53343i	0.987385	−	0.158339i
$257$	−11.1250	−	2.98092i	−0.693956	−	0.185945i	−0.105434	−	0.994426i	$-0.533623\pi$
$257$	−11.1250	−	2.98092i	−0.693956	−	0.185945i	−0.588522	+	0.808481i	$0.700290\pi$
$258$	−5.50481	+	0.109428i	−0.342714	+	0.00681271i
$259$	−9.45214			−0.587327
$260$	−2.46322	−	15.9353i	−0.152762	−	0.988263i
$261$	−1.55093			−0.0959999
$262$	−5.58347	+	0.110992i	−0.344948	+	0.00685712i
$263$	16.6868	+	4.47122i	1.02895	+	0.275707i	0.733529	−	0.679658i	$-0.237872\pi$
$263$	16.6868	+	4.47122i	1.02895	+	0.275707i	0.295425	+	0.955366i	$0.404539\pi$
$264$	3.66609	−	1.22071i	0.225632	−	0.0751297i
$265$	−0.221796	+	1.66028i	−0.0136248	+	0.101990i
$266$	−23.6567	−	5.83744i	−1.45049	−	0.357916i
$267$	0.489964	+	1.82857i	0.0299853	+	0.111907i
$268$	24.4240	+	5.51420i	1.49193	+	0.336834i
$269$	17.3550	+	10.0199i	1.05815	+	0.610926i	0.924921	−	0.380159i	$-0.124131\pi$
$269$	17.3550	+	10.0199i	1.05815	+	0.610926i	0.133234	+	0.991085i	$0.457464\pi$
$270$	15.1295	+	1.71584i	0.920754	+	0.104423i
$271$	−13.2015	−	22.8657i	−0.801936	−	1.38899i	−0.918340	−	0.395792i	$-0.870470\pi$
$271$	−13.2015	−	22.8657i	−0.801936	−	1.38899i	0.116404	−	0.993202i	$-0.462863\pi$
$272$	2.64471	+	7.44560i	0.160359	+	0.451456i
$273$	9.93984	−	16.6204i	0.601586	−	1.00591i
$274$	−6.18862	−	21.3866i	−0.373868	−	1.29201i
$275$	−3.59157	+	0.947715i	−0.216580	+	0.0571494i
$276$	19.2094	+	10.0947i	1.15627	+	0.607630i
$277$	−4.28671	−	15.9982i	−0.257564	−	0.961241i	−0.966646	−	0.256115i	$-0.917557\pi$
$277$	−4.28671	−	15.9982i	−0.257564	−	0.961241i	0.709083	−	0.705125i	$-0.249109\pi$
$278$	6.97130	+	3.84220i	0.418111	+	0.230440i
$279$	2.05433	+	1.18607i	0.122989	+	0.0710079i
$280$	−15.2800	−	10.3814i	−0.913155	−	0.620408i
$281$			9.98320i			0.595548i	0.954636	+	0.297774i	$0.0962442\pi$
$281$			9.98320i			0.595548i	−0.954636	+	0.297774i	$0.903756\pi$
$282$	−4.51961	−	7.48078i	−0.269139	−	0.445474i
$283$	−9.38884	−	2.51573i	−0.558109	−	0.149545i	−0.0312715	−	0.999511i	$-0.509956\pi$
$283$	−9.38884	−	2.51573i	−0.558109	−	0.149545i	−0.526837	+	0.849966i	$0.676622\pi$
$284$	6.94142	−	13.2089i	0.411897	−	0.783805i
$285$	−3.21176	+	24.0419i	−0.190248	+	1.42412i
$286$	3.78803	−	0.0170118i	0.223991	−	0.00100593i
$287$	−16.5349	−	16.5349i	−0.976026	−	0.976026i
$288$	0.888441	−	1.96714i	0.0523519	−	0.115915i
$289$	11.3432	−	6.54902i	0.667249	−	0.385236i
$290$	−4.70462	+	11.9616i	−0.276265	+	0.702407i
$291$	−32.4911			−1.90466
$292$	−8.92847	+	9.66812i	−0.522499	+	0.565784i
$293$	1.50870	+	5.63053i	0.0881389	+	0.328939i	0.995890	−	0.0905701i	$-0.0288689\pi$
$293$	1.50870	+	5.63053i	0.0881389	+	0.328939i	−0.907751	+	0.419509i	$0.862202\pi$
$294$	−1.10695	−	3.82538i	−0.0645584	−	0.223101i
$295$	0.305027	+	2.35150i	0.0177594	+	0.136909i
$296$	−8.96666	−	1.83791i	−0.521177	−	0.106826i
$297$	−0.925822	+	3.45522i	−0.0537217	+	0.200492i
$298$	−12.0236	−	6.62675i	−0.696508	−	0.383877i
$299$	14.8098	+	15.2726i	0.856470	+	0.883238i
$300$	−8.61627	+	16.2455i	−0.497461	+	0.937935i
$301$	−5.35540	+	3.09194i	−0.308680	+	0.178217i
$302$	−0.396311	−	19.9365i	−0.0228051	−	1.14722i
$303$	4.45426	+	16.6235i	0.255890	+	0.954996i
$304$	−21.3066	−	10.1375i	−1.22202	−	0.581426i
$305$	27.0768	−	3.51230i	1.55041	−	0.201113i
$306$	1.03488	+	0.255364i	0.0591603	+	0.0145982i
$307$	5.68452	−	5.68452i	0.324433	−	0.324433i	−0.526032	−	0.850465i	$-0.676321\pi$
$307$	5.68452	−	5.68452i	0.324433	−	0.324433i	0.850465	+	0.526032i	$0.176321\pi$
$308$	2.94431	−	3.18822i	0.167768	−	0.181666i
$309$	−1.41988	+	0.819765i	−0.0807739	+	0.0466348i
$310$	15.3792	−	12.2462i	0.873482	−	0.695539i
$311$			0.730792i			0.0414394i	0.999785	+	0.0207197i	$0.00659576\pi$
$311$			0.730792i			0.0414394i	−0.999785	+	0.0207197i	$0.993404\pi$
$312$	12.6611	−	13.8340i	0.716791	−	0.783198i
$313$	19.5148	+	19.5148i	1.10304	+	1.10304i	0.994042	+	0.109001i	$0.0347650\pi$
$313$	19.5148	+	19.5148i	1.10304	+	1.10304i	0.109001	+	0.994042i	$0.465235\pi$
$314$	−10.2606	−	9.86058i	−0.579037	−	0.556465i
$315$	−2.30419	+	0.949293i	−0.129827	+	0.0534866i
$316$	−32.3012	+	1.28472i	−1.81708	+	0.0722710i
$317$	2.29455	+	2.29455i	0.128875	+	0.128875i	0.768602	−	0.639727i	$-0.220953\pi$
$317$	2.29455	+	2.29455i	0.128875	+	0.128875i	−0.639727	+	0.768602i	$0.720953\pi$
$318$	−1.66741	+	1.00739i	−0.0935037	+	0.0564915i
$319$	−2.61507	−	1.50981i	−0.146416	−	0.0845331i
$320$	−12.4766	−	12.8193i	−0.697463	−	0.716621i
$321$	−11.6692	+	20.2116i	−0.651309	+	1.12810i
$322$	24.3677	−	0.484397i	1.35796	−	0.0269944i
$323$	3.01581	−	11.2552i	0.167804	−	0.626254i
$324$	10.6795	+	16.9079i	0.593305	+	0.939327i
$325$	−12.9898	+	12.5006i	−0.720547	+	0.693406i
$326$	−2.66398	−	9.20618i	−0.147544	−	0.509883i
$327$	9.72954	+	2.60702i	0.538045	+	0.144169i
$328$	−12.4706	−	18.9008i	−0.688571	−	1.04362i
$329$	−8.50119	−	4.90816i	−0.468686	−	0.270596i
$330$	−3.47404	−	2.56787i	−0.191240	−	0.141356i
$331$	−8.02831	+	13.9054i	−0.441276	+	0.764312i	−0.997784	−	0.0665297i	$-0.978807\pi$
$331$	−8.02831	+	13.9054i	−0.441276	+	0.764312i	0.556509	+	0.830842i	$0.312141\pi$
$332$	22.1693	+	20.4733i	1.21670	+	1.12362i
$333$	−0.873126	+	0.873126i	−0.0478470	+	0.0478470i
$334$	−2.55180	+	10.3414i	−0.139628	+	0.565855i
$335$	−10.6636	−	25.8836i	−0.582616	−	1.41417i
$336$	−1.70632	−	21.4167i	−0.0930872	−	1.16838i
$337$	2.68226	−	2.68226i	0.146112	−	0.146112i	−0.630267	−	0.776379i	$-0.717054\pi$
$337$	2.68226	−	2.68226i	0.146112	−	0.146112i	0.776379	+	0.630267i	$0.217054\pi$
$338$	16.0209	−	9.01839i	0.871421	−	0.490536i
$339$	18.4811			1.00376
$340$	5.10874	−	7.20695i	0.277061	−	0.390852i
$341$	2.30925	+	3.99973i	0.125053	+	0.216598i
$342$	−2.72447	+	1.64603i	−0.147323	+	0.0890069i
$343$	11.2947	+	11.2947i	0.609859	+	0.609859i
$344$	−5.68155	+	1.89181i	−0.306329	+	0.102000i
$345$	−3.12098	−	24.0601i	−0.168028	−	1.29535i
$346$	2.93717	+	10.1503i	0.157903	+	0.545681i
$347$	32.2027	−	8.62869i	1.72873	−	0.463212i	0.748842	−	0.662749i	$-0.230610\pi$
$347$	32.2027	−	8.62869i	1.72873	−	0.463212i	0.979890	+	0.199537i	$0.0639437\pi$
$348$	−14.2744	+	4.43987i	−0.765188	+	0.238002i
$349$	−4.92642	−	8.53282i	−0.263705	−	0.456751i	0.703518	−	0.710677i	$-0.251611\pi$
$349$	−4.92642	−	8.53282i	−0.263705	−	0.456751i	−0.967224	+	0.253926i	$0.918278\pi$
$350$	0.331851	+	20.6508i	0.0177382	+	1.10383i
$351$	4.23481	+	16.8365i	0.226038	+	0.898665i
$352$	3.41302	−	2.45197i	0.181915	−	0.130690i
$353$	3.46411	+	0.928206i	0.184376	+	0.0494034i	0.349826	−	0.936815i	$-0.386241\pi$
$353$	3.46411	+	0.928206i	0.184376	+	0.0494034i	−0.165450	+	0.986218i	$0.552908\pi$
$354$	−1.91089	+	1.98840i	−0.101563	+	0.105682i
$355$	−16.5444	+	2.14608i	−0.878087	+	0.113902i
$356$	1.09951	+	1.74075i	0.0582738	+	0.0922598i
$357$	10.2483	−	2.74603i	0.542398	−	0.145335i
$358$	13.2786	−	8.02243i	0.701795	−	0.423999i
$359$			11.8440i			0.625103i	0.949901	+	0.312552i	$0.101184\pi$
$359$			11.8440i			0.625103i	−0.949901	+	0.312552i	$0.898816\pi$
$360$	−2.37043	+	0.452499i	−0.124933	+	0.0238488i
$361$	7.89814	+	13.6800i	0.415692	+	0.719999i
$362$	0.0874898	+	4.40119i	0.00459836	+	0.231321i
$363$	−13.5857	+	13.5857i	−0.713063	+	0.713063i
$364$	4.95406	−	20.4716i	0.259663	−	1.07300i
$365$	14.5840	+	1.94827i	0.763359	+	0.101977i
$366$	22.8959	+	22.0033i	1.19679	+	1.15013i
$367$	−2.92552	+	10.9182i	−0.152711	+	0.569924i	0.846580	+	0.532262i	$0.178658\pi$
$367$	−2.92552	+	10.9182i	−0.152711	+	0.569924i	−0.999291	+	0.0376622i	$0.988009\pi$
$368$	23.2103	+	4.27862i	1.20992	+	0.223039i
$369$	−3.05477			−0.159025
$370$	4.08545	+	9.38258i	0.212392	+	0.487777i
$371$	−1.09399	+	1.89485i	−0.0567973	+	0.0983758i
$372$	22.3030	+	5.03535i	1.15636	+	0.261071i
$373$	1.81338	−	0.485894i	0.0938932	−	0.0251586i	−0.211567	−	0.977364i	$-0.567857\pi$
$373$	1.81338	−	0.485894i	0.0938932	−	0.0251586i	0.305460	+	0.952205i	$0.401190\pi$
$374$	1.49636	+	1.43803i	0.0773748	+	0.0743585i
$375$	20.3987	−	2.56709i	1.05338	−	0.132564i
$376$	−7.11019	−	6.30908i	−0.366680	−	0.325366i
$377$	−14.6535	−	0.225464i	−0.754694	−	0.0116120i
$378$	17.4190	+	9.60044i	0.895939	+	0.493793i
$379$	6.81451	−	3.93436i	0.350038	−	0.202094i	−0.314664	−	0.949203i	$-0.601892\pi$
$379$	6.81451	−	3.93436i	0.350038	−	0.202094i	0.664702	+	0.747109i	$0.268559\pi$
$380$	4.43054	+	26.0057i	0.227282	+	1.33406i
$381$	17.3866	−	30.1144i	0.890741	−	1.54281i
$382$	−7.91562	+	14.3621i	−0.404999	+	0.734830i
$383$	8.49414	−	2.27600i	0.434031	−	0.116298i	−0.0351870	−	0.999381i	$-0.511203\pi$
$383$	8.49414	−	2.27600i	0.434031	−	0.116298i	0.469218	+	0.883083i	$0.344536\pi$
$384$	2.54567	−	20.6485i	0.129908	−	1.05371i
$385$	−4.80931	−	0.642475i	−0.245105	−	0.0327435i
$386$	5.24653	−	21.2620i	0.267041	−	1.08221i
$387$	−0.209083	+	0.780310i	−0.0106283	+	0.0396654i
$388$	−33.7429	+	10.4953i	−1.71304	+	0.532818i
$389$		−	17.3518i		−	0.879773i	−0.898053	−	0.439886i	$-0.855019\pi$
$389$		−	17.3518i		−	0.879773i	0.898053	−	0.439886i	$-0.144981\pi$
$390$	−20.7944	−	2.68292i	−1.05296	−	0.135855i
$391$			11.6552i			0.589427i
$392$	−2.38527	−	3.61520i	−0.120474	−	0.182595i
$393$	−1.87945	+	7.01420i	−0.0948056	+	0.353819i
$394$	29.0087	+	7.15808i	1.46144	+	0.360619i
$395$	21.9474	+	28.7155i	1.10430	+	1.44483i
$396$	−0.0225308	−	0.566483i	−0.00113221	−	0.0284668i
$397$	20.0082	−	5.36118i	1.00418	−	0.269070i	0.280986	−	0.959712i	$-0.409338\pi$
$397$	20.0082	−	5.36118i	1.00418	−	0.269070i	0.723197	+	0.690642i	$0.242672\pi$
$398$	−16.6057	−	9.15217i	−0.832368	−	0.458757i
$399$	−15.8417	+	27.4387i	−0.793079	+	1.37365i
$400$	−3.70061	+	19.6547i	−0.185030	+	0.982733i
$401$	−11.5829	+	6.68738i	−0.578422	+	0.333952i	−0.760506	−	0.649331i	$-0.775049\pi$
$401$	−11.5829	+	6.68738i	−0.578422	+	0.333952i	0.182084	+	0.983283i	$0.441716\pi$
$402$	15.7153	−	28.5139i	0.783809	−	1.42214i
$403$	19.2374	+	11.5049i	0.958281	+	0.573099i
$404$	9.99561	+	15.8252i	0.497300	+	0.787332i
$405$	8.59561	−	20.6404i	0.427119	−	1.02563i
$406$	−11.6338	+	12.1058i	−0.577378	+	0.600799i
$407$	−2.32219	+	0.622228i	−0.115106	+	0.0308427i
$408$	10.2559	−	0.612266i	0.507742	−	0.0303117i
$409$	−3.35983	+	5.81940i	−0.166133	+	0.287751i	−0.937057	−	0.349176i	$-0.886461\pi$
$409$	−3.35983	+	5.81940i	−0.166133	+	0.287751i	0.770924	+	0.636927i	$0.219795\pi$
$410$	−9.26643	+	23.5601i	−0.457637	+	1.16355i
$411$	−28.9499			−1.42799
$412$	−1.20978	+	1.31000i	−0.0596016	+	0.0645390i
$413$	−0.801654	+	2.99181i	−0.0394468	+	0.147218i
$414$	2.20618	−	2.29567i	0.108428	−	0.112826i
$415$	4.46744	−	33.4415i	0.219298	−	1.64158i
$416$	8.68018	−	18.4568i	0.425581	−	0.904920i
$417$	7.31883	−	7.31883i	0.358405	−	0.358405i
$418$	−6.19622	+	0.123173i	−0.303067	+	0.00602457i
$419$	−9.19228	−	15.9215i	−0.449072	−	0.777816i	0.549254	−	0.835656i	$-0.314912\pi$
$419$	−9.19228	−	15.9215i	−0.449072	−	0.777816i	−0.998326	+	0.0578398i	$0.981579\pi$
$420$	−18.4898	+	15.3334i	−0.902208	+	0.748191i
$421$			13.8793i			0.676438i	0.941068	+	0.338219i	$0.109824\pi$
$421$			13.8793i			0.676438i	−0.941068	+	0.338219i	$0.890176\pi$
$422$	−15.5599	−	25.7544i	−0.757443	−	1.25371i
$423$	−1.23867	+	0.331900i	−0.0602260	+	0.0161375i
$424$	−1.40625	+	1.58481i	−0.0682933	+	0.0769651i
$425$	−9.87663	−	0.0376082i	−0.479087	−	0.00182426i
$426$	−13.9898	−	13.4444i	−0.677808	−	0.651386i
$427$	34.4498	+	9.23081i	1.66714	+	0.446710i
$428$	−5.59000	+	24.7597i	−0.270203	+	1.19681i
$429$	1.34789	−	4.73761i	0.0650768	−	0.228734i
$430$	5.38393	+	3.97958i	0.259636	+	0.191912i
$431$	11.8879	+	20.5905i	0.572621	+	0.991808i	0.996296	+	0.0859938i	$0.0274065\pi$
$431$	11.8879	+	20.5905i	0.572621	+	0.991808i	−0.423675	+	0.905814i	$0.639260\pi$
$432$	14.6576	+	12.4944i	0.705215	+	0.601135i
$433$	−12.5807	+	3.37099i	−0.604590	+	0.161999i	−0.548113	−	0.836405i	$-0.684653\pi$
$433$	−12.5807	+	3.37099i	−0.604590	+	0.161999i	−0.0564772	+	0.998404i	$0.517987\pi$
$434$	24.6678	−	7.13811i	1.18409	−	0.342640i
$435$	13.2403	+	10.1997i	0.634822	+	0.489039i
$436$	10.9465	−	0.435377i	0.524243	−	0.0208508i
$437$	−24.6109	−	24.6109i	−1.17730	−	1.17730i
$438$	8.84894	+	14.6466i	0.422819	+	0.699842i
$439$	−19.5851	−	33.9224i	−0.934747	−	1.61903i	−0.775085	−	0.631857i	$-0.782293\pi$
$439$	−19.5851	−	33.9224i	−0.934747	−	1.61903i	−0.159662	−	0.987172i	$-0.551040\pi$
$440$	−4.43737	−	1.54462i	−0.211543	−	0.0736367i
$441$	−0.584294			−0.0278235
$442$	9.74070	+	2.56318i	0.463318	+	0.121918i
$443$	−9.85855	+	9.85855i	−0.468394	+	0.468394i	−0.901394	−	0.433000i	$-0.857455\pi$
$443$	−9.85855	+	9.85855i	−0.468394	+	0.468394i	0.433000	+	0.901394i	$0.357455\pi$
$444$	−5.53655	+	10.5356i	−0.262753	+	0.499997i
$445$	0.884962	−	2.12504i	0.0419512	−	0.100736i
$446$	2.10749	+	0.520036i	0.0997924	+	0.0246244i
$447$	−12.6230	+	12.6230i	−0.597047	+	0.597047i
$448$	−8.69010	−	21.6907i	−0.410569	−	1.02479i
$449$	10.9484	−	18.9632i	0.516688	−	0.894929i	−0.483125	−	0.875552i	$-0.660498\pi$
$449$	10.9484	−	18.9632i	0.516688	−	0.894929i	0.999812	−	0.0193777i	$-0.00616849\pi$
$450$	1.93824	+	1.87693i	0.0913694	+	0.0884792i
$451$	−5.15076	−	2.97379i	−0.242540	−	0.140030i
$452$	19.1932	−	5.96979i	0.902772	−	0.280795i
$453$	−25.0451	−	6.71080i	−1.17672	−	0.315301i
$454$	21.6392	−	6.26172i	1.01558	−	0.293877i
$455$	−21.9086	+	8.63418i	−1.02709	+	0.404776i
$456$	−20.3634	+	22.9491i	−0.953602	+	1.07469i
$457$	2.93021	−	10.9357i	0.137069	−	0.511550i	−0.862911	−	0.505355i	$-0.831361\pi$
$457$	2.93021	−	10.9357i	0.137069	−	0.511550i	0.999981	−	0.00619471i	$-0.00197185\pi$
$458$	0.228922	+	11.5159i	0.0106968	+	0.538105i
$459$	−4.75568	+	8.23707i	−0.221976	+	0.384474i
$460$	−11.0131	−	23.9790i	−0.513490	−	1.11802i
$461$	27.0810	+	15.6352i	1.26129	+	0.728204i	0.973323	−	0.229438i	$-0.0736888\pi$
$461$	27.0810	+	15.6352i	1.26129	+	0.728204i	0.287963	+	0.957642i	$0.407022\pi$
$462$	−2.91809	−	4.82997i	−0.135762	−	0.224710i
$463$	−21.4921	−	21.4921i	−0.998822	−	0.998822i	0.00117715	−	0.999999i	$-0.499625\pi$
$463$	−21.4921	−	21.4921i	−0.998822	−	0.998822i	−0.999999	+	0.00117715i	$0.999625\pi$
$464$	−13.3902	+	9.22186i	−0.621624	+	0.428114i
$465$	−9.73759	−	23.6358i	−0.451570	−	1.09608i
$466$	1.69776	−	1.76662i	0.0786471	−	0.0818373i
$467$	−16.0622	−	16.0622i	−0.743269	−	0.743269i	0.229937	−	0.973206i	$-0.426148\pi$
$467$	−16.0622	−	16.0622i	−0.743269	−	0.743269i	−0.973206	+	0.229937i	$0.926148\pi$
$468$	−1.43340	−	2.34865i	−0.0662591	−	0.108566i
$469$		−	36.5670i		−	1.68851i
$470$	−1.19762	+	10.5601i	−0.0552419	+	0.487099i
$471$	−16.0250	+	9.25203i	−0.738393	+	0.426311i
$472$	−1.34222	+	2.68227i	−0.0617806	+	0.123462i
$473$	−1.11217	+	1.11217i	−0.0511375	+	0.0511375i
$474$	−10.0702	+	40.8104i	−0.462540	+	1.87448i
$475$	20.9348	−	20.7760i	0.960555	−	0.953267i
$476$	9.75614	−	6.16224i	0.447172	−	0.282446i
$477$	0.0739780	+	0.276090i	0.00338722	+	0.0126413i
$478$	−19.4293	+	0.386228i	−0.888673	+	0.0176657i
$479$	−4.81730	+	2.78127i	−0.220108	+	0.127080i	−0.606000	−	0.795464i	$-0.707227\pi$
$479$	−4.81730	+	2.78127i	−0.220108	+	0.127080i	0.385892	+	0.922544i	$0.373894\pi$
$480$	−20.5216	+	10.9506i	−0.936677	+	0.499824i
$481$	−8.37643	+	8.12257i	−0.381932	+	0.370357i
$482$	−20.5431	+	37.2735i	−0.935715	+	1.69776i
$483$	8.20238	−	30.6117i	0.373221	−	1.39288i
$484$	−9.72065	+	18.4976i	−0.441848	+	0.840798i
$485$	31.2983	+	24.1109i	1.42118	+	1.09482i
$486$	5.35546	−	1.54971i	0.242929	−	0.0702961i
$487$	2.56039	+	9.55552i	0.116022	+	0.433002i	0.999361	−	0.0357331i	$-0.0113766\pi$
$487$	2.56039	+	9.55552i	0.116022	+	0.433002i	−0.883339	+	0.468735i	$0.844710\pi$
$488$	30.8856	+	15.4552i	1.39812	+	0.699626i
$489$	−12.4619			−0.563547
$490$	−1.77241	+	4.50639i	−0.0800695	+	0.203578i
$491$	24.5107	−	14.1513i	1.10615	−	0.638637i	0.168322	−	0.985732i	$-0.446165\pi$
$491$	24.5107	−	14.1513i	1.10615	−	0.638637i	0.937830	+	0.347095i	$0.112832\pi$
$492$	−28.1155	+	8.74497i	−1.26755	+	0.394253i
$493$	−5.67738	−	5.67738i	−0.255697	−	0.255697i
$494$	−25.9808	+	15.1560i	−1.16893	+	0.681899i
$495$	−0.503599	+	0.384904i	−0.0226351	+	0.0173002i
$496$	24.7888	−	1.97498i	1.11305	−	0.0886792i
$497$	−21.0495	−	5.64019i	−0.944199	−	0.252997i
$498$	33.5851	−	20.2909i	1.50499	−	0.909257i
$499$		−	12.0868i		−	0.541079i	−0.962709	−	0.270539i	$-0.912798\pi$
$499$		−	12.0868i		−	0.541079i	0.962709	−	0.270539i	$-0.0872020\pi$
$500$	20.3554	−	9.25520i	0.910320	−	0.413905i
$501$	11.9946	+	6.92511i	0.535881	+	0.309391i
$502$	2.83711	−	5.14765i	0.126626	−	0.229751i
$503$	−10.6214	−	39.6396i	−0.473585	−	1.76744i	−0.626727	−	0.779239i	$-0.715606\pi$
$503$	−10.6214	−	39.6396i	−0.473585	−	1.76744i	0.153142	−	0.988204i	$-0.451061\pi$
$504$	−3.08806	−	0.632964i	−0.137553	−	0.0281944i
$505$	8.04517	−	19.3187i	0.358006	−	0.859669i
$506$	5.95472	−	1.72311i	0.264720	−	0.0766017i
$507$	−5.47392	−	23.2706i	−0.243105	−	1.03348i
$508$	8.32886	−	36.8909i	0.369533	−	1.63677i
$509$	17.7791	+	30.7944i	0.788046	+	1.36494i	0.927162	+	0.374660i	$0.122241\pi$
$509$	17.7791	+	30.7944i	0.788046	+	1.36494i	−0.139116	+	0.990276i	$0.544426\pi$
$510$	−7.15539	−	8.98599i	−0.316846	−	0.397906i
$511$	16.6445	+	9.60969i	0.736308	+	0.425108i
$512$	−4.02614	−	22.2663i	−0.177932	−	0.984043i
$513$	−7.35129	−	27.4354i	−0.324567	−	1.21130i
$514$	−3.90214	+	15.8137i	−0.172116	+	0.697514i
$515$	1.97608	+	0.263984i	0.0870765	+	0.0116325i
$516$	0.309449	+	7.78036i	0.0136227	+	0.342511i
$517$	−2.41166	−	0.646202i	−0.106065	−	0.0284199i
$518$	0.265673	+	13.3647i	0.0116730	+	0.587211i
$519$	13.7399			0.603113
$520$	−22.4622	+	3.93072i	−0.985032	+	0.172374i
$521$	−37.4245			−1.63960			−0.819800	−	0.572651i	$-0.805915\pi$
$521$	−37.4245			−1.63960			−0.819800	+	0.572651i	$0.805915\pi$
$522$	0.0435921	+	2.19291i	0.00190797	+	0.0959809i
$523$	−9.46456	−	2.53602i	−0.413856	−	0.110892i	0.0458821	−	0.998947i	$-0.485390\pi$
$523$	−9.46456	−	2.53602i	−0.413856	−	0.110892i	−0.459738	+	0.888054i	$0.652057\pi$
$524$	0.313871	+	7.89155i	0.0137115	+	0.344744i
$525$	25.9140	+	7.04950i	1.13098	+	0.307665i
$526$	5.85300	−	23.7198i	0.255203	−	1.03423i
$527$	3.17839	+	11.8619i	0.138453	+	0.516714i
$528$	−1.82905	−	5.14929i	−0.0795993	−	0.224094i
$529$	10.2312	+	5.90699i	0.444835	+	0.256826i
$530$	2.35376	+	0.266940i	0.102241	+	0.0115951i
$531$	0.202312	+	0.350415i	0.00877961	+	0.0152067i
$532$	−7.58883	+	33.6131i	−0.329018	+	1.45731i
$533$	−28.8622	−	0.444085i	−1.25016	−	0.0192355i
$534$	2.57171	−	0.744173i	0.111289	−	0.0322035i
$535$	26.2393	−	10.8102i	1.13443	−	0.467366i
$536$	7.11023	−	34.6889i	0.307115	−	1.49833i
$537$	−5.22108	−	19.4853i	−0.225306	−	0.840854i
$538$	13.6797	−	24.8205i	0.589775	−	1.07009i
$539$	−0.985198	−	0.568804i	−0.0424355	−	0.0245001i
$540$	2.00084	−	21.4404i	0.0861023	−	0.922647i
$541$		−	12.1521i		−	0.522459i	−0.965277	−	0.261230i	$-0.915872\pi$
$541$		−	12.1521i		−	0.522459i	0.965277	−	0.261230i	$-0.0841280\pi$
$542$	−31.9596	+	19.3088i	−1.37278	+	0.829384i
$543$	5.52896	+	1.48148i	0.237270	+	0.0635764i
$544$	10.4533	−	3.94872i	0.448180	−	0.169300i
$545$	−7.43776	−	9.73138i	−0.318598	−	0.416846i
$546$	−23.7796	−	13.5871i	−1.01767	−	0.581475i
$547$	21.9944	+	21.9944i	0.940414	+	0.940414i	0.998322	−	0.0579077i	$-0.0184429\pi$
$547$	21.9944	+	21.9944i	0.940414	+	0.940414i	−0.0579077	+	0.998322i	$0.518443\pi$
$548$	−30.0653	+	9.35142i	−1.28433	+	0.399473i
$549$	4.03493	−	2.32957i	0.172206	−	0.0994235i
$550$	1.44096	+	5.05161i	0.0614426	+	0.215401i
$551$	23.9766			1.02144
$552$	13.7333	−	27.4445i	0.584530	−	1.16812i
$553$	12.2190	+	45.6019i	0.519604	+	1.93919i
$554$	−22.5000	+	6.51080i	−0.955932	+	0.276617i
$555$	13.1960	−	1.71174i	0.560140	−	0.0726591i
$556$	5.23668	−	9.96495i	0.222085	−	0.422608i
$557$	−7.36329	+	27.4802i	−0.311993	+	1.16437i	0.614764	+	0.788711i	$0.289251\pi$
$557$	−7.36329	+	27.4802i	−0.311993	+	1.16437i	−0.926757	+	0.375661i	$0.877416\pi$
$558$	1.61928	−	2.93802i	0.0685495	−	0.124376i
$559$	−2.08891	+	7.34216i	−0.0883513	+	0.310540i
$560$	−14.2492	+	21.8967i	−0.602137	+	0.925305i
$561$	2.33702	−	1.34928i	0.0986690	−	0.0569666i
$562$	14.1156	−	0.280599i	0.595430	−	0.0118364i
$563$	1.84191	+	6.87409i	0.0776271	+	0.289708i	0.993816	−	0.111038i	$-0.0354175\pi$
$563$	1.84191	+	6.87409i	0.0776271	+	0.289708i	−0.916189	+	0.400746i	$0.868751\pi$
$564$	−10.4503	+	6.60069i	−0.440037	+	0.277939i
$565$	−17.8027	−	13.7144i	−0.748965	−	0.576970i
$566$	−3.29319	+	13.3459i	−0.138423	+	0.560971i
$567$	20.6516	−	20.6516i	0.867286	−	0.867286i
$568$	−18.8716	−	9.44344i	−0.791837	−	0.396238i
$569$	14.7552	−	8.51892i	0.618570	−	0.357132i	−0.157742	−	0.987480i	$-0.550421\pi$
$569$	14.7552	−	8.51892i	0.618570	−	0.357132i	0.776312	+	0.630349i	$0.217088\pi$
$570$	34.0840	+	3.86546i	1.42762	+	0.161906i
$571$		−	7.62927i		−	0.319275i	−0.987176	−	0.159638i	$-0.948967\pi$
$571$		−	7.62927i		−	0.319275i	0.987176	−	0.159638i	$-0.0510326\pi$
$572$	−0.130524	−	5.35554i	−0.00545749	−	0.223927i
$573$	15.0781	+	15.0781i	0.629897	+	0.629897i
$574$	−22.9146	+	23.8441i	−0.956435	+	0.995232i
$575$	−14.8480	+	25.4929i	−0.619205	+	1.06313i
$576$	−2.80637	−	1.20091i	−0.116932	−	0.0500378i
$577$	−6.70392	−	6.70392i	−0.279088	−	0.279088i	0.553657	−	0.832745i	$-0.313232\pi$
$577$	−6.70392	−	6.70392i	−0.279088	−	0.279088i	−0.832745	+	0.553657i	$0.813232\pi$
$578$	−9.57870	−	15.8545i	−0.398422	−	0.659461i
$579$	−24.6612	−	14.2381i	−1.02488	−	0.591717i
$580$	17.0451	+	6.31582i	0.707759	+	0.262250i
$581$	22.0353	−	38.1663i	0.914179	−	1.58340i
$582$	0.913232	+	45.9403i	0.0378547	+	1.90429i
$583$	−0.144034	+	0.537541i	−0.00596526	+	0.0222627i
$584$	13.9210	+	12.3525i	0.576057	+	0.511151i
$585$	−1.22620	+	2.82134i	−0.0506972	+	0.116648i
$586$	7.91879	−	2.29145i	0.327122	−	0.0946591i
$587$	−29.7861	−	7.98116i	−1.22940	−	0.329418i	−0.415056	−	0.909796i	$-0.636238\pi$
$587$	−29.7861	−	7.98116i	−1.22940	−	0.329418i	−0.814347	+	0.580378i	$0.802905\pi$
$588$	−5.37772	+	1.67267i	−0.221773	+	0.0689798i
$589$	−31.7590	−	18.3361i	−1.30861	−	0.755524i
$590$	3.31629	−	0.497382i	0.136529	−	0.0204769i
$591$	19.4257	−	33.6463i	0.799068	−	1.38403i
$592$	−2.34666	+	12.7299i	−0.0964470	+	0.523197i
$593$	8.29602	−	8.29602i	0.340677	−	0.340677i	−0.515945	−	0.856622i	$-0.672559\pi$
$593$	8.29602	−	8.29602i	0.340677	−	0.340677i	0.856622	+	0.515945i	$0.172559\pi$
$594$	4.91147	+	1.21194i	0.201520	+	0.0497263i
$595$	−11.9099	−	4.95981i	−0.488256	−	0.203332i
$596$	−9.03184	+	17.1868i	−0.369959	+	0.704000i
$597$	−17.4335	+	17.4335i	−0.713507	+	0.713507i
$598$	21.1782	−	21.3693i	0.866042	−	0.873855i
$599$	−16.2031			−0.662039			−0.331019	−	0.943624i	$-0.607393\pi$
$599$	−16.2031			−0.662039			−0.331019	+	0.943624i	$0.607393\pi$
$600$	23.2123	+	11.7262i	0.947636	+	0.478721i
$601$	7.99537	+	13.8484i	0.326138	+	0.564887i	0.981742	−	0.190217i	$-0.0609193\pi$
$601$	7.99537	+	13.8484i	0.326138	+	0.564887i	−0.655604	+	0.755105i	$0.727586\pi$
$602$	4.52233	+	7.48528i	0.184316	+	0.305077i
$603$	−3.37782	−	3.37782i	−0.137555	−	0.137555i
$604$	−28.1777	+	1.12072i	−1.14654	+	0.0456013i
$605$	23.1686	−	3.00533i	0.941936	−	0.122184i
$606$	23.3793	−	6.76526i	0.949721	−	0.274820i
$607$	−26.0647	+	6.98402i	−1.05793	+	0.283473i	−0.745527	−	0.666475i	$-0.767802\pi$
$607$	−26.0647	+	6.98402i	−1.05793	+	0.283473i	−0.312408	+	0.949948i	$0.601136\pi$
$608$	−13.7349	+	30.4111i	−0.557024	+	1.23333i
$609$	10.9159	+	18.9068i	0.442333	+	0.766144i
$610$	−5.72721	−	38.1861i	−0.231888	−	1.54611i
$611$	−11.7515	+	2.95580i	−0.475414	+	0.119579i
$612$	0.331980	−	1.47043i	0.0134195	−	0.0594388i
$613$	−33.8062	−	9.05834i	−1.36542	−	0.365863i	−0.499615	−	0.866247i	$-0.666525\pi$
$613$	−33.8062	−	9.05834i	−1.36542	−	0.365863i	−0.865803	+	0.500385i	$0.833192\pi$
$614$	−8.19731	−	7.87776i	−0.330816	−	0.317920i
$615$	26.0786	+	20.0898i	1.05159	+	0.810100i
$616$	−4.59070	−	4.07346i	−0.184964	−	0.164124i
$617$	−22.9735	+	6.15572i	−0.924877	+	0.247820i	−0.689669	−	0.724125i	$-0.742244\pi$
$617$	−22.9735	+	6.15572i	−0.924877	+	0.247820i	−0.235208	+	0.971945i	$0.575577\pi$
$618$	1.19900	+	1.98457i	0.0482310	+	0.0798311i
$619$			18.0359i			0.724925i	0.931998	+	0.362463i	$0.118064\pi$
$619$			18.0359i			0.724925i	−0.931998	+	0.362463i	$0.881936\pi$
$620$	−17.7476	−	21.4010i	−0.712762	−	0.859486i
$621$	14.2052	+	24.6041i	0.570035	+	0.987330i
$622$	1.03329	−	0.0205405i	0.0414312	−	0.000823598i
$623$	2.12619	−	2.12619i	0.0851840	−	0.0851840i
$624$	−19.9163	−	17.5131i	−0.797290	−	0.701083i
$625$	−21.5548	−	12.6645i	−0.862193	−	0.506581i
$626$	27.0442	−	28.1412i	1.08090	−	1.12475i
$627$	−2.08570	+	7.78395i	−0.0832949	+	0.310861i
$628$	−13.6538	+	14.7849i	−0.544846	+	0.589982i
$629$	−6.39240			−0.254882
$630$	1.40700	+	3.23130i	0.0560563	+	0.128738i
$631$	−14.5180	+	25.1460i	−0.577954	+	1.00105i	0.417760	+	0.908557i	$0.362815\pi$
$631$	−14.5180	+	25.1460i	−0.577954	+	1.00105i	−0.995714	+	0.0924878i	$0.970518\pi$
$632$	2.72440	+	45.6356i	0.108371	+	1.81529i
$633$	−37.7927	+	10.1265i	−1.50213	+	0.402493i
$634$	3.17985	−	3.30884i	0.126288	−	0.131411i
$635$	−39.0955	+	16.1068i	−1.55146	+	0.639177i
$636$	1.47125	+	2.32929i	0.0583387	+	0.0923625i
$637$	−5.52055	−	0.0849412i	−0.218732	−	0.00336549i
$638$	−2.06127	+	3.73997i	−0.0816065	+	0.148067i
$639$	−2.46542	+	1.42341i	−0.0975303	+	0.0563092i
$640$	−17.7750	+	18.0014i	−0.702617	+	0.711568i
$641$	13.4570	−	23.3081i	0.531518	−	0.920616i	−0.467805	−	0.883832i	$-0.654955\pi$
$641$	13.4570	−	23.3081i	0.531518	−	0.920616i	0.999323	−	0.0367845i	$-0.0117115\pi$
$642$	28.9058	+	15.9313i	1.14082	+	0.628760i
$643$	3.49374	−	0.936146i	0.137780	−	0.0369180i	−0.189270	−	0.981925i	$-0.560612\pi$
$643$	3.49374	−	0.936146i	0.137780	−	0.0369180i	0.327050	+	0.945007i	$0.393945\pi$
$644$	−1.36981	−	34.4407i	−0.0539781	−	1.35715i
$645$	6.91668	−	5.28646i	0.272344	−	0.208154i
$646$	−15.9988	−	3.94781i	−0.629466	−	0.155325i
$647$	−6.85446	+	25.5812i	−0.269477	+	1.00570i	0.689976	+	0.723832i	$0.257621\pi$
$647$	−6.85446	+	25.5812i	−0.269477	+	1.00570i	−0.959453	+	0.281869i	$0.909046\pi$
$648$	23.6065	−	15.5753i	0.927350	−	0.611857i
$649$			0.787796i			0.0309237i
$650$	18.0401	+	18.0154i	0.707590	+	0.706624i
$651$		−	33.3915i		−	1.30872i
$652$	−12.9421	+	4.02546i	−0.506850	+	0.157649i
$653$	−6.00112	+	22.3965i	−0.234842	+	0.876443i	0.743378	+	0.668872i	$0.233222\pi$
$653$	−6.00112	+	22.3965i	−0.234842	+	0.876443i	−0.978220	+	0.207571i	$0.933444\pi$
$654$	3.41269	−	13.8302i	0.133447	−	0.540804i
$655$	7.01553	−	5.36201i	0.274119	−	0.209511i
$656$	−26.3740	+	18.1638i	−1.02973	+	0.709177i
$657$	2.42518	−	0.649826i	0.0946155	−	0.0253521i
$658$	−6.70088	+	12.1581i	−0.261227	+	0.473971i
$659$	5.06989	−	8.78131i	0.197495	−	0.342071i	−0.750221	−	0.661188i	$-0.770053\pi$
$659$	5.06989	−	8.78131i	0.197495	−	0.342071i	0.947716	+	0.319116i	$0.103386\pi$
$660$	−3.53315	+	4.98424i	−0.137528	+	0.194011i
$661$	−22.7406	+	13.1293i	−0.884505	+	0.510669i	−0.872141	−	0.489254i	$-0.837269\pi$
$661$	−22.7406	+	13.1293i	−0.884505	+	0.510669i	−0.0123639	+	0.999924i	$0.503936\pi$
$662$	19.8870	+	10.9607i	0.772931	+	0.425998i
$663$	6.72223	−	11.2403i	0.261070	−	0.436536i
$664$	28.3247	−	31.9214i	1.09921	−	1.23879i
$665$	35.6218	−	14.6756i	1.38135	−	0.569097i
$666$	1.25908	+	1.21000i	0.0487885	+	0.0468866i
$667$	−23.1655	+	6.20718i	−0.896973	+	0.240343i
$668$	14.6937	+	3.31741i	0.568518	+	0.128354i
$669$	1.41128	−	2.44441i	0.0545633	−	0.0945064i
$670$	−36.2979	+	15.8052i	−1.40231	+	0.610608i
$671$	9.07124			0.350191
$672$	−30.2339	+	3.01458i	−1.16630	+	0.116290i
$673$	−11.5728	+	43.1904i	−0.446100	+	1.66487i	0.266917	+	0.963719i	$0.413995\pi$
$673$	−11.5728	+	43.1904i	−0.446100	+	1.66487i	−0.713017	+	0.701147i	$0.752672\pi$
$674$	−3.86793	−	3.71715i	−0.148987	−	0.143179i
$675$	−20.8955	+	11.9581i	−0.804266	+	0.460269i
$676$	−13.2017	−	22.3990i	−0.507758	−	0.861500i
$677$	−6.23481	+	6.23481i	−0.239623	+	0.239623i	−0.816694	−	0.577071i	$-0.804196\pi$
$677$	−6.23481	+	6.23481i	−0.239623	+	0.239623i	0.577071	+	0.816694i	$0.304196\pi$
$678$	−0.519452	−	26.1311i	−0.0199494	−	1.00356i
$679$	25.8038	+	44.6934i	0.990258	+	1.71518i
$680$	−10.3337	−	7.02086i	−0.396281	−	0.269238i
$681$		−	29.2918i		−	1.12247i
$682$	5.59046	−	3.37755i	0.214070	−	0.129333i
$683$	−46.5408	+	12.4706i	−1.78083	+	0.477173i	−0.990735	−	0.135808i	$-0.956637\pi$
$683$	−46.5408	+	12.4706i	−1.78083	+	0.477173i	−0.790098	+	0.612981i	$0.789970\pi$
$684$	2.40395	+	3.80596i	0.0919173	+	0.145525i
$685$	27.8871	+	21.4830i	1.06551	+	0.820824i
$686$	15.6526	−	16.2875i	0.597618	−	0.621859i
$687$	14.4668	+	3.87637i	0.551944	+	0.147893i
$688$	2.83459	+	7.98017i	0.108068	+	0.304241i
$689$	0.658825	+	2.61932i	0.0250993	+	0.0997880i
$690$	−33.9317	+	5.08912i	−1.29176	+	0.193740i
$691$	10.0626	+	17.4290i	0.382800	+	0.663029i	0.991461	−	0.130401i	$-0.0416266\pi$
$691$	10.0626	+	17.4290i	0.382800	+	0.663029i	−0.608661	+	0.793430i	$0.708293\pi$
$692$	14.2692	−	4.43826i	0.542435	−	0.168717i
$693$	−0.799745	+	0.214291i	−0.0303798	+	0.00814025i
$694$	−13.1055	−	45.2900i	−0.497479	−	1.71918i
$695$	−12.4813	+	1.61902i	−0.473442	+	0.0614131i
$696$	6.67889	+	20.0583i	0.253163	+	0.760307i
$697$	−11.1824	−	11.1824i	−0.423565	−	0.423565i
$698$	−11.9264	+	7.20547i	−0.451420	+	0.272731i
$699$	−1.59298	−	2.75912i	−0.0602521	−	0.104360i
$700$	29.1895	−	1.04965i	1.10326	−	0.0396731i
$701$	22.5793			0.852807			0.426404	−	0.904533i	$-0.359780\pi$
$701$	22.5793			0.852807			0.426404	+	0.904533i	$0.359780\pi$
$702$	23.6867	−	6.46097i	0.893995	−	0.243854i
$703$	13.4981	−	13.4981i	0.509092	−	0.509092i
$704$	−3.56285	−	4.75687i	−0.134280	−	0.179281i
$705$	12.7573	+	5.31271i	0.480466	+	0.200088i
$706$	1.21506	−	4.92411i	0.0457292	−	0.185321i
$707$	19.3291	−	19.3291i	0.726947	−	0.726947i
$708$	2.86518	+	2.64599i	0.107680	+	0.0994422i
$709$	−4.67963	+	8.10535i	−0.175747	+	0.304403i	−0.940420	−	0.340016i	$-0.889567\pi$
$709$	−4.67963	+	8.10535i	−0.175747	+	0.304403i	0.764672	+	0.644419i	$0.222901\pi$
$710$	3.49943	+	23.3324i	0.131331	+	0.875650i
$711$	5.34111	+	3.08369i	0.200307	+	0.115647i
$712$	2.43041	−	1.60356i	0.0910834	−	0.0600960i
$713$	35.4316	+	9.49386i	1.32692	+	0.355548i
$714$	−4.17075	−	14.4133i	−0.156086	−	0.539402i
$715$	−4.81408	+	3.56346i	−0.180036	+	0.133266i
$716$	−11.7164	−	18.5496i	−0.437863	−	0.693230i
$717$	−6.54006	+	24.4079i	−0.244243	+	0.911528i
$718$	16.7467	−	0.332902i	0.624980	−	0.0124238i
$719$	16.5880	−	28.7312i	0.618626	−	1.07149i	−0.371110	−	0.928589i	$-0.621023\pi$
$719$	16.5880	−	28.7312i	0.618626	−	1.07149i	0.989737	−	0.142903i	$-0.0456438\pi$
$720$	0.706430	+	3.33891i	0.0263271	+	0.124434i
$721$	2.25527	+	1.30208i	0.0839907	+	0.0484921i
$722$	19.1206	−	11.5520i	0.711595	−	0.429919i
$723$	39.1317	+	39.1317i	1.45532	+	1.45532i
$724$	6.22053	−	0.247410i	0.231184	−	0.00919491i
$725$	−5.18524	−	19.6506i	−0.192575	−	0.729804i
$726$	19.5911	+	18.8274i	0.727094	+	0.698750i
$727$	−10.0654	−	10.0654i	−0.373304	−	0.373304i	0.495375	−	0.868679i	$-0.335031\pi$
$727$	−10.0654	−	10.0654i	−0.373304	−	0.373304i	−0.868679	+	0.495375i	$0.835031\pi$
$728$	−29.0847	−	6.42932i	−1.07795	−	0.238286i
$729$			22.7479i			0.842515i
$730$	2.34481	−	20.6755i	0.0867854	−	0.765235i
$731$	−3.62182	+	2.09106i	−0.133958	+	0.0773405i
$732$	30.4677	−	32.9917i	1.12612	−	1.21941i
$733$	−14.0986	+	14.0986i	−0.520743	+	0.520743i	−0.917796	−	0.397053i	$-0.870033\pi$
$733$	−14.0986	+	14.0986i	−0.520743	+	0.520743i	0.397053	+	0.917796i	$0.370033\pi$
$734$	15.5198	+	3.82961i	0.572846	+	0.141353i
$735$	4.98812	+	3.84263i	0.183990	+	0.141738i
$736$	5.39731	−	32.9381i	0.198948	−	1.21411i
$737$	−2.40718	−	8.98373i	−0.0886697	−	0.330920i
$738$	0.0858610	+	4.31925i	0.00316059	+	0.158994i
$739$	7.96409	−	4.59807i	0.292964	−	0.169143i	−0.346314	−	0.938119i	$-0.612567\pi$
$739$	7.96409	−	4.59807i	0.292964	−	0.169143i	0.639278	+	0.768976i	$0.279233\pi$
$740$	13.1515	−	6.04028i	0.483459	−	0.222045i
$741$	9.54023	+	37.9294i	0.350469	+	1.39337i
$742$	2.70995	+	1.49358i	0.0994852	+	0.0548309i
$743$	−4.90862	+	18.3192i	−0.180080	+	0.672067i	0.815551	+	0.578686i	$0.196434\pi$
$743$	−4.90862	+	18.3192i	−0.180080	+	0.672067i	−0.995630	+	0.0933813i	$0.970232\pi$
$744$	6.49277	−	31.6765i	0.238037	−	1.16132i
$745$	21.5268	−	2.79237i	0.788682	−	0.102305i
$746$	−0.737991	−	2.55034i	−0.0270198	−	0.0933747i
$747$	−1.49007	−	5.56102i	−0.0545189	−	0.203467i
$748$	1.99122	−	2.15617i	0.0728061	−	0.0788374i
$749$	37.0697			1.35450
$750$	−4.20305	−	28.7702i	−0.153474	−	1.05054i
$751$	0.353432	−	0.204054i	0.0128969	−	0.00744604i	−0.493538	−	0.869724i	$-0.664296\pi$
$751$	0.353432	−	0.204054i	0.0128969	−	0.00744604i	0.506435	+	0.862278i	$0.330963\pi$
$752$	−8.72077	+	10.2307i	−0.318014	+	0.373074i
$753$	−5.40428	−	5.40428i	−0.196943	−	0.196943i
$754$	0.0930767	+	20.7254i	0.00338965	+	0.754776i
$755$	19.1457	+	25.0498i	0.696784	+	0.911655i
$756$	13.0848	−	24.8992i	0.475889	−	0.905576i
$757$	51.3303	+	13.7539i	1.86563	+	0.499895i	1.00000		0.000784346i	$-0.000249665\pi$
$757$	51.3303	+	13.7539i	1.86563	+	0.499895i	0.865633	+	0.500679i	$0.166916\pi$
$758$	−5.75446	−	9.52468i	−0.209011	−	0.345952i
$759$		−	8.06059i		−	0.292581i
$760$	36.6458	−	6.99544i	1.32928	−	0.253751i
$761$	−26.9462	−	15.5574i	−0.976798	−	0.563955i	−0.0754964	−	0.997146i	$-0.524054\pi$
$761$	−26.9462	−	15.5574i	−0.976798	−	0.563955i	−0.901302	+	0.433191i	$0.857387\pi$
$762$	−43.0685	−	23.7370i	−1.56021	−	0.859902i
$763$	−4.14089	−	15.4540i	−0.149910	−	0.559473i
$764$	20.5296	+	10.7885i	0.742734	+	0.390314i
$765$	−1.55831	+	0.641999i	−0.0563407	+	0.0232115i
$766$	−3.45686	−	11.9462i	−0.124901	−	0.431633i
$767$	1.86055	+	3.34022i	0.0671807	+	0.120608i
$768$	−29.2672	−	3.01904i	−1.05609	−	0.108940i
$769$	4.77787	+	8.27552i	0.172294	+	0.298423i	0.939222	−	0.343311i	$-0.111549\pi$
$769$	4.77787	+	8.27552i	0.172294	+	0.298423i	−0.766927	+	0.641734i	$0.778215\pi$
$770$	−0.773241	+	6.81810i	−0.0278657	+	0.245707i
$771$	18.3419	+	10.5897i	0.660567	+	0.381379i
$772$	−30.2106	−	6.82064i	−1.08730	−	0.245480i
$773$	−11.4690	−	42.8029i	−0.412511	−	1.53951i	−0.789769	−	0.613404i	$-0.789800\pi$
$773$	−11.4690	−	42.8029i	−0.412511	−	1.53951i	0.377258	−	0.926108i	$-0.376867\pi$
$774$	1.10918	+	0.273698i	0.0398688	+	0.00983787i
$775$	−8.15945	+	29.9942i	−0.293096	+	1.07742i
$776$	15.7881	+	47.4153i	0.566759	+	1.70211i
$777$	16.7893	+	4.49868i	0.602313	+	0.161389i
$778$	−24.5344	+	0.487711i	−0.879599	+	0.0174853i
$779$	47.2255			1.69203
$780$	−3.20900	+	29.4773i	−0.114901	+	1.05546i
$781$	−5.54269			−0.198333
$782$	16.4796	−	0.327594i	0.589311	−	0.0117147i
$783$	−18.9045	−	5.06545i	−0.675593	−	0.181025i
$784$	−5.04461	+	3.47423i	−0.180165	+	0.124080i
$785$	22.3024	+	2.97938i	0.796008	+	0.106339i
$786$	9.97044	+	2.46027i	0.355634	+	0.0877548i
$787$	−10.7604	−	40.1584i	−0.383567	−	1.43149i	−0.840413	−	0.541946i	$-0.817688\pi$
$787$	−10.7604	−	40.1584i	−0.383567	−	1.43149i	0.456846	−	0.889546i	$-0.348979\pi$
$788$	9.30570	−	41.2176i	0.331502	−	1.46832i
$789$	−27.5118	−	15.8840i	−0.979447	−	0.565484i
$790$	39.9849	−	31.8393i	1.42260	−	1.13279i
$791$	−14.6773	−	25.4219i	−0.521866	−	0.903899i
$792$	−0.800337	+	0.0477793i	−0.0284387	+	0.00169776i
$793$	38.4616	−	21.4237i	1.36581	−	0.760779i
$794$	−8.14274	−	28.1396i	−0.288975	−	0.998637i
$795$	1.18416	−	2.84350i	0.0419979	−	0.100848i
$796$	−12.4738	+	23.7366i	−0.442123	+	0.841322i
$797$	−1.57365	−	5.87293i	−0.0557414	−	0.208030i	0.932438	−	0.361329i	$-0.117677\pi$
$797$	−1.57365	−	5.87293i	−0.0557414	−	0.208030i	−0.988180	+	0.153299i	$0.951010\pi$
$798$	39.2418	+	21.6280i	1.38914	+	0.765622i
$799$	−5.74928	−	3.31935i	−0.203395	−	0.117430i
$800$	27.8944	+	4.67998i	0.986216	+	0.165462i
$801$		−	0.392806i		−	0.0138791i
$802$	9.78108	+	16.1895i	0.345382	+	0.571670i
$803$	4.72179	+	1.26520i	0.166628	+	0.0446479i
$804$	−40.7585	−	21.4190i	−1.43744	−	0.755390i
$805$	−30.6175	+	23.4011i	−1.07912	+	0.824782i
$806$	15.7264	−	27.5237i	0.553940	−	0.969482i
$807$	−26.0579	−	26.0579i	−0.917280	−	0.917280i
$808$	22.0948	−	14.5779i	0.777292	−	0.512850i
$809$	−40.2858	+	23.2590i	−1.41637	+	0.817744i	−0.995978	−	0.0895963i	$-0.971442\pi$
$809$	−40.2858	+	23.2590i	−1.41637	+	0.817744i	−0.420396	+	0.907341i	$0.638109\pi$
$810$	−29.4258	−	11.5735i	−1.03392	−	0.406651i
$811$	−11.3333			−0.397964			−0.198982	−	0.980003i	$-0.563764\pi$
$811$	−11.3333			−0.397964			−0.198982	+	0.980003i	$0.563764\pi$
$812$	17.4437	+	16.1092i	0.612155	+	0.565323i
$813$	12.5664	+	46.8983i	0.440722	+	1.64480i
$814$	0.945059	+	3.26593i	0.0331243	+	0.114471i
$815$	12.0044	+	9.24769i	0.420497	+	0.323932i
$816$	−1.15397	−	14.4839i	−0.0403969	−	0.507039i
$817$	3.23234	−	12.0632i	0.113085	−	0.422039i
$818$	8.32268	+	4.58702i	0.290996	+	0.160381i
$819$	−2.88479	+	2.79736i	−0.100803	+	0.0977476i
$820$	33.5728	+	12.4399i	1.17241	+	0.434421i
$821$	23.1416	−	13.3608i	0.807648	−	0.466296i	−0.0384908	−	0.999259i	$-0.512255\pi$
$821$	23.1416	−	13.3608i	0.807648	−	0.466296i	0.846138	+	0.532963i	$0.178922\pi$
$822$	0.813699	+	40.9332i	0.0283810	+	1.42771i
$823$	−6.73837	−	25.1480i	−0.234885	−	0.876603i	−0.978201	−	0.207662i	$-0.933415\pi$
$823$	−6.73837	−	25.1480i	−0.234885	−	0.876603i	0.743316	−	0.668941i	$-0.233252\pi$
$824$	1.88626	+	1.67373i	0.0657108	+	0.0583071i
$825$	6.83056	+	0.0260094i	0.237810	+	0.000905530i
$826$	4.25276	+	1.04939i	0.147972	+	0.0365131i
$827$	1.43947	−	1.43947i	0.0500553	−	0.0500553i	−0.681636	−	0.731691i	$-0.738731\pi$
$827$	1.43947	−	1.43947i	0.0500553	−	0.0500553i	0.731691	+	0.681636i	$0.238731\pi$
$828$	−3.30793	−	3.05486i	−0.114959	−	0.106164i
$829$	36.5548	−	21.1049i	1.26960	−	0.733004i	0.294687	−	0.955594i	$-0.404784\pi$
$829$	36.5548	−	21.1049i	1.26960	−	0.733004i	0.974912	+	0.222590i	$0.0714511\pi$
$830$	−47.4096	−	5.37673i	−1.64561	−	0.186629i
$831$			30.4570i			1.05654i
$832$	−26.3407	−	11.7544i	−0.913200	−	0.407512i
$833$	−2.13889	−	2.13889i	−0.0741082	−	0.0741082i
$834$	−10.5541	−	10.1426i	−0.365457	−	0.351211i
$835$	−6.41536	−	15.5718i	−0.222013	−	0.538886i
$836$	0.348316	+	8.75758i	0.0120468	+	0.302887i
$837$	21.1668	+	21.1668i	0.731632	+	0.731632i
$838$	−22.2536	+	13.4448i	−0.768737	+	0.464442i
$839$	37.3832	+	21.5832i	1.29061	+	0.745135i	0.978763	−	0.204996i	$-0.0657181\pi$
$839$	37.3832	+	21.5832i	1.29061	+	0.745135i	0.311850	+	0.950131i	$0.399051\pi$
$840$	22.2001	+	25.7123i	0.765975	+	0.887160i
$841$	−6.23937	+	10.8069i	−0.215151	+	0.372652i
$842$	19.6245	−	0.390109i	0.676304	−	0.0134440i
$843$	4.75144	−	17.7326i	0.163648	−	0.610744i
$844$	−35.9777	+	22.7245i	−1.23840	+	0.782210i
$845$	−11.9956	+	26.4784i	−0.412661	+	0.910885i
$846$	0.504100	+	1.74206i	0.0173313	+	0.0598934i
$847$	29.4774	+	7.89844i	1.01285	+	0.271394i
$848$	2.28034	+	1.94379i	0.0783072	+	0.0667502i
$849$	15.4795	+	8.93711i	0.531256	+	0.306721i
$850$	0.224428	+	13.9660i	0.00769783	+	0.479028i
$851$	−9.54705	+	16.5360i	−0.327269	+	0.566846i
$852$	−18.6164	+	20.1586i	−0.637786	+	0.690621i
$853$	16.7372	−	16.7372i	0.573071	−	0.573071i	−0.359914	−	0.932985i	$-0.617194\pi$
$853$	16.7372	−	16.7372i	0.573071	−	0.573071i	0.932985	+	0.359914i	$0.117194\pi$
$854$	12.0835	−	48.9693i	0.413488	−	1.67569i
$855$	1.93487	−	4.64614i	0.0661711	−	0.158895i
$856$	35.1657	+	7.20796i	1.20194	+	0.246363i
$857$	−5.13406	+	5.13406i	−0.175376	+	0.175376i	−0.789337	−	0.613960i	$-0.789575\pi$
$857$	−5.13406	+	5.13406i	−0.175376	+	0.175376i	0.613960	+	0.789337i	$0.289575\pi$
$858$	−6.73656	−	1.77267i	−0.229982	−	0.0605179i
$859$	−3.35602			−0.114506			−0.0572530	−	0.998360i	$-0.518234\pi$
$859$	−3.35602			−0.114506			−0.0572530	+	0.998360i	$0.518234\pi$
$860$	5.47553	−	7.72438i	0.186714	−	0.263399i
$861$	21.5004	+	37.2398i	0.732731	+	1.26913i
$862$	28.7794	−	17.3875i	0.980231	−	0.592219i
$863$	10.8195	+	10.8195i	0.368298	+	0.368298i	0.866856	−	0.498558i	$-0.166137\pi$
$863$	10.8195	+	10.8195i	0.368298	+	0.368298i	−0.498558	+	0.866856i	$0.666137\pi$
$864$	17.2542	−	21.0761i	0.587001	−	0.717023i
$865$	−13.2355	−	10.1960i	−0.450019	−	0.346675i
$866$	5.11996	+	17.6935i	0.173983	+	0.601251i
$867$	−23.2653	+	6.23392i	−0.790131	+	0.211715i
$868$	−10.7862	−	34.6781i	−0.366106	−	1.17705i
$869$	6.00388	+	10.3990i	0.203668	+	0.352763i
$870$	14.0496	−	19.0075i	0.476325	−	0.644416i
$871$	−31.4234	−	32.4055i	−1.06474	−	1.09802i
$872$	−0.923270	−	15.4654i	−0.0312659	−	0.523726i
$873$	6.51206	+	1.74490i	0.220400	+	0.0590560i
$874$	−34.1065	+	35.4900i	−1.15367	+	1.20047i
$875$	−19.7314	−	26.0209i	−0.667043	−	0.879665i
$876$	20.4606	−	12.9235i	0.691300	−	0.436644i
$877$	−55.4155	+	14.8485i	−1.87125	+	0.501400i	−0.871306	+	0.490739i	$0.836727\pi$
$877$	−55.4155	+	14.8485i	−1.87125	+	0.501400i	−0.999943	+	0.0106605i	$0.996607\pi$
$878$	−47.4136	+	28.6455i	−1.60013	+	0.966740i
$879$		−	10.7192i		−	0.361551i
$880$	−2.05926	+	6.31756i	−0.0694177	+	0.212965i
$881$	−14.6187	−	25.3203i	−0.492515	−	0.853062i	0.507448	−	0.861683i	$-0.330589\pi$
$881$	−14.6187	−	25.3203i	−0.492515	−	0.853062i	−0.999963	+	0.00862111i	$0.997256\pi$
$882$	0.0164228	+	0.826153i	0.000552986	+	0.0278180i
$883$	−25.3420	+	25.3420i	−0.852825	+	0.852825i	−0.990480	−	0.137655i	$-0.956043\pi$
$883$	−25.3420	+	25.3420i	−0.852825	+	0.852825i	0.137655	+	0.990480i	$0.456043\pi$
$884$	3.35039	−	13.8448i	0.112686	−	0.465649i
$885$	0.577377	−	4.32201i	0.0194083	−	0.145283i
$886$	14.2164	+	13.6622i	0.477611	+	0.458992i
$887$	8.80524	−	32.8616i	0.295651	−	1.10339i	−0.645048	−	0.764142i	$-0.723162\pi$
$887$	8.80524	−	32.8616i	0.295651	−	1.10339i	0.940699	−	0.339243i	$-0.110171\pi$
$888$	15.0522	+	7.53220i	0.505120	+	0.252764i
$889$	−55.2322			−1.85243
$890$	−3.02953	−	1.19155i	−0.101550	−	0.0399408i
$891$	3.71417	−	6.43313i	0.124429	−	0.215518i
$892$	0.676061	−	2.99447i	0.0226362	−	0.100262i
$893$	19.1492	−	5.13102i	0.640805	−	0.171703i
$894$	18.2029	+	17.4933i	0.608795	+	0.585063i
$895$	−9.43020	+	22.6445i	−0.315217	+	0.756921i
$896$	−30.4249	+	12.8969i	−1.01643	+	0.430855i
$897$	−19.0368	−	34.1765i	−0.635622	−	1.14112i
$898$	−27.1205	−	14.9473i	−0.905022	−	0.498799i
$899$	−21.8838	+	12.6346i	−0.729864	+	0.421387i
$900$	2.59937	−	2.79329i	0.0866458	−	0.0931098i
$901$	−0.739859	+	1.28147i	−0.0246483	+	0.0426920i
$902$	−4.05997	+	7.36642i	−0.135182	+	0.245275i
$903$	10.9841	−	2.94318i	0.365528	−	0.0979429i
$904$	−8.98036	−	26.9701i	−0.298682	−	0.897013i
$905$	−4.22662	−	5.53000i	−0.140498	−	0.183824i
$906$	−8.78469	+	35.6007i	−0.291852	+	1.18275i
$907$	−5.87734	+	21.9345i	−0.195154	+	0.728324i	0.797073	+	0.603883i	$0.206381\pi$
$907$	−5.87734	+	21.9345i	−0.195154	+	0.728324i	−0.992227	+	0.124441i	$0.960286\pi$
$908$	−9.46187	−	30.4204i	−0.314003	−	1.00954i
$909$		−	3.57100i		−	0.118442i
$910$	12.8239	+	30.7346i	0.425110	+	1.01884i
$911$		−	12.6026i		−	0.417542i	−0.977965	−	0.208771i	$-0.933054\pi$
$911$		−	12.6026i		−	0.417542i	0.977965	−	0.208771i	$-0.0669463\pi$
$912$	33.0209	+	28.1474i	1.09343	+	0.932055i
$913$	2.90114	−	10.8272i	0.0960137	−	0.358328i
$914$	−15.5447	−	3.83575i	−0.514173	−	0.126875i
$915$	−49.7667	−	6.64832i	−1.64523	−	0.219787i
$916$	16.2764	−	0.647361i	0.537786	−	0.0213894i
$917$	11.1411	−	2.98524i	0.367911	−	0.0985813i
$918$	11.7804	+	6.49269i	0.388810	+	0.214291i
$919$	5.71455	−	9.89789i	0.188506	−	0.326501i	−0.756247	−	0.654287i	$-0.772969\pi$
$919$	5.71455	−	9.89789i	0.188506	−	0.326501i	0.944752	+	0.327785i	$0.106302\pi$
$920$	−33.5951	+	16.2458i	−1.10760	+	0.535609i
$921$	−12.8026	+	7.39158i	−0.421860	+	0.243561i
$922$	21.3460	−	38.7302i	0.702992	−	1.27551i
$923$	−23.5008	+	13.0903i	−0.773537	+	0.430872i
$924$	−6.74724	+	4.26174i	−0.221968	+	0.140201i
$925$	−13.9818	−	8.14356i	−0.459720	−	0.267759i
$926$	−29.7843	+	30.9925i	−0.978774	+	1.01848i
$927$	0.328605	−	0.0880494i	0.0107928	−	0.00289192i
$928$	13.4155	+	18.6737i	0.440384	+	0.612993i
$929$	−10.5791	+	18.3236i	−0.347091	+	0.601179i	−0.985731	−	0.168327i	$-0.946164\pi$
$929$	−10.5791	+	18.3236i	−0.347091	+	0.601179i	0.638641	+	0.769505i	$0.279497\pi$
$930$	−33.1458	+	14.4327i	−1.08689	+	0.473265i
$931$	9.03293			0.296042
$932$	−2.54561	−	2.35086i	−0.0833843	−	0.0770051i
$933$	0.347815	−	1.29806i	0.0113870	−	0.0424967i
$934$	−22.2594	+	23.1623i	−0.728350	+	0.757894i
$935$	−3.25249	−	0.434500i	−0.106368	−	0.0142097i
$936$	−3.28055	+	2.09275i	−0.107228	+	0.0684038i
$937$	18.1623	−	18.1623i	0.593338	−	0.593338i	−0.345194	−	0.938531i	$-0.612187\pi$
$937$	18.1623	−	18.1623i	0.593338	−	0.593338i	0.938531	+	0.345194i	$0.112187\pi$
$938$	−51.7034	+	1.02780i	−1.68818	+	0.0335587i
$939$	−25.3751	−	43.9510i	−0.828086	−	1.43429i
$940$	14.9649	+	1.39654i	0.488101	+	0.0455500i
$941$		−	50.8294i		−	1.65699i	−0.559995	−	0.828496i	$-0.689197\pi$
$941$		−	50.8294i		−	1.65699i	0.559995	−	0.828496i	$-0.310803\pi$
$942$	13.5322	+	22.3982i	0.440902	+	0.729774i
$943$	−45.6279	+	12.2260i	−1.48585	+	0.398132i
$944$	3.83028	+	1.82242i	0.124665	+	0.0593147i
$945$	−31.1867	+	4.04542i	−1.01450	+	0.131598i
$946$	1.60379	+	1.54127i	0.0521437	+	0.0501110i
$947$	−12.7418	−	3.41416i	−0.414054	−	0.110945i	0.0457775	−	0.998952i	$-0.485423\pi$
$947$	−12.7418	−	3.41416i	−0.414054	−	0.110945i	−0.459831	+	0.888006i	$0.652090\pi$
$948$	57.9862	+	13.0915i	1.88330	+	0.425194i
$949$	23.0082	−	5.78715i	0.746877	−	0.187859i
$950$	−29.9643	−	29.0165i	−0.972170	−	0.941419i
$951$	−2.98361	−	5.16776i	−0.0967501	−	0.167576i
$952$	−8.98723	−	13.6213i	−0.291278	−	0.441470i
$953$	−14.8681	+	3.98389i	−0.481624	+	0.129051i	−0.491459	−	0.870901i	$-0.663536\pi$
$953$	−14.8681	+	3.98389i	−0.481624	+	0.129051i	0.00983471	+	0.999952i	$0.496869\pi$
$954$	0.388293	−	0.112360i	0.0125715	−	0.00363779i
$955$	−3.33548	−	25.7137i	−0.107934	−	0.832075i
$956$	1.09220	+	27.4608i	0.0353243	+	0.888147i
$957$	3.92642	+	3.92642i	0.126923	+	0.126923i
$958$	4.06794	+	6.73318i	0.131429	+	0.217539i
$959$	22.9914	+	39.8223i	0.742432	+	1.28593i
$960$	16.0602	+	28.7084i	0.518341	+	0.926559i
$961$	7.64910			0.246745
$962$	11.7202	+	11.6154i	0.377875	+	0.374496i
$963$	3.42425	−	3.42425i	0.110345	−	0.110345i
$964$	53.2797	+	27.9990i	1.71602	+	0.901787i
$965$	13.1901	+	32.0159i	0.424604	+	1.03063i
$966$	−43.5135	−	10.7372i	−1.40002	−	0.345464i
$967$	8.47146	−	8.47146i	0.272424	−	0.272424i	−0.557652	−	0.830075i	$-0.688297\pi$
$967$	8.47146	−	8.47146i	0.272424	−	0.272424i	0.830075	+	0.557652i	$0.188297\pi$
$968$	26.4276	+	13.2245i	0.849414	+	0.425050i
$969$	−10.7136	+	18.5566i	−0.344172	+	0.596123i
$970$	33.2115	−	44.9315i	1.06636	−	1.44266i
$971$	32.4828	+	18.7540i	1.04242	+	0.601843i	0.920519	−	0.390699i	$-0.127767\pi$
$971$	32.4828	+	18.7540i	1.04242	+	0.601843i	0.121904	+	0.992542i	$0.461100\pi$
$972$	−2.34171	−	7.52872i	−0.0751104	−	0.241484i
$973$	−15.8800	−	4.25502i	−0.509088	−	0.136410i
$974$	13.4389	−	3.88881i	0.430610	−	0.124605i
$975$	29.0227	−	16.0216i	0.929470	−	0.513102i
$976$	20.9846	−	44.1046i	0.671701	−	1.41175i
$977$	11.5034	−	42.9312i	0.368026	−	1.37349i	−0.495246	−	0.868753i	$-0.664922\pi$
$977$	11.5034	−	42.9312i	0.368026	−	1.37349i	0.863272	−	0.504739i	$-0.168411\pi$
$978$	0.350269	+	17.6203i	0.0112004	+	0.563436i
$979$	0.382393	−	0.662324i	0.0122213	−	0.0211680i
$980$	6.42155	+	2.37941i	0.205129	+	0.0760076i
$981$	−1.81005	−	1.04503i	−0.0577903	−	0.0333653i
$982$	−20.6979	−	34.2588i	−0.660496	−	1.09324i
$983$	16.9723	+	16.9723i	0.541331	+	0.541331i	0.923919	−	0.382588i	$-0.124967\pi$
$983$	16.9723	+	16.9723i	0.541331	+	0.541331i	−0.382588	+	0.923919i	$0.624967\pi$
$984$	13.1551	+	39.5077i	0.419368	+	1.25946i
$985$	−43.6808	+	17.9958i	−1.39178	+	0.573394i
$986$	−7.86787	+	8.18702i	−0.250564	+	0.260728i
$987$	12.7642	+	12.7642i	0.406288	+	0.406288i
$988$	22.1598	+	36.3091i	0.704997	+	1.15515i
$989$			12.4920i			0.397221i
$990$	0.558384	+	0.701238i	0.0177466	+	0.0222868i
$991$	−4.47688	+	2.58473i	−0.142213	+	0.0821065i	−0.569418	−	0.822048i	$-0.692831\pi$
$991$	−4.47688	+	2.58473i	−0.142213	+	0.0821065i	0.427205	+	0.904155i	$0.359498\pi$
$992$	−3.48923	−	34.9942i	−0.110783	−	1.11107i
$993$	20.8784	−	20.8784i	0.662557	−	0.662557i
$994$	−7.38322	+	29.9211i	−0.234182	+	0.949040i
$995$	29.7305	−	3.85653i	0.942522	−	0.122260i
$996$	−29.6340	−	46.9169i	−0.938988	−	1.48662i
$997$	7.98534	+	29.8017i	0.252898	+	0.943829i	0.969248	+	0.246087i	$0.0791450\pi$
$997$	7.98534	+	29.8017i	0.252898	+	0.943829i	−0.716349	+	0.697742i	$0.754188\pi$
$998$	−17.0899	+	0.339725i	−0.540972	+	0.0107538i
$999$	−13.4944	+	7.79100i	−0.426944	+	0.246496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bg.c.23.20	✓	144
4.3	odd	2	inner	260.2.bg.c.23.24	yes	144
5.2	odd	4	inner	260.2.bg.c.127.36	yes	144
13.4	even	6	inner	260.2.bg.c.43.32	yes	144
20.7	even	4	inner	260.2.bg.c.127.32	yes	144
52.43	odd	6	inner	260.2.bg.c.43.36	yes	144
65.17	odd	12	inner	260.2.bg.c.147.24	yes	144
260.147	even	12	inner	260.2.bg.c.147.20	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bg.c.23.20	✓	144	1.1	even	1	trivial
260.2.bg.c.23.24	yes	144	4.3	odd	2	inner
260.2.bg.c.43.32	yes	144	13.4	even	6	inner
260.2.bg.c.43.36	yes	144	52.43	odd	6	inner
260.2.bg.c.127.32	yes	144	20.7	even	4	inner
260.2.bg.c.127.36	yes	144	5.2	odd	4	inner
260.2.bg.c.147.20	yes	144	260.147	even	12	inner
260.2.bg.c.147.24	yes	144	65.17	odd	12	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0281072 - 1.41393i) q^{2} +(-1.77624 - 0.475943i) q^{3} +(-1.99842 + 0.0794833i) q^{4} +(1.35785 + 1.77658i) q^{5} +(-0.623027 + 2.52487i) q^{6} +(0.755969 + 2.82131i) q^{7} +(0.168554 + 2.82340i) q^{8} +(0.330446 + 0.190783i) q^{9} +O(q^{10})\)	\(q+(-0.0281072 - 1.41393i) q^{2} +(-1.77624 - 0.475943i) q^{3} +(-1.99842 + 0.0794833i) q^{4} +(1.35785 + 1.77658i) q^{5} +(-0.623027 + 2.52487i) q^{6} +(0.755969 + 2.82131i) q^{7} +(0.168554 + 2.82340i) q^{8} +(0.330446 + 0.190783i) q^{9} +(2.47380 - 1.96985i) q^{10} +(0.371450 + 0.643371i) q^{11} +(3.58751 + 0.809953i) q^{12} +(3.09439 + 1.85060i) q^{13} +(3.96791 - 1.14819i) q^{14} +(-1.56633 - 3.80190i) q^{15} +(3.98736 - 0.317682i) q^{16} +(0.511256 + 1.90803i) q^{17} +(0.260467 - 0.472591i) q^{18} +(-5.10854 - 2.94942i) q^{19} +(-2.85477 - 3.44243i) q^{20} -5.37114i q^{21} +(0.899244 - 0.543290i) q^{22} +(5.69929 + 1.52712i) q^{23} +(1.04439 - 5.09527i) q^{24} +(-1.31248 + 4.82467i) q^{25} +(2.52965 - 4.42729i) q^{26} +(3.40475 + 3.40475i) q^{27} +(-1.73499 - 5.57808i) q^{28} +(-3.52008 + 2.03232i) q^{29} +(-5.33161 + 2.32154i) q^{30} +6.21684 q^{31} +(-0.561255 - 5.62894i) q^{32} +(-0.353579 - 1.31957i) q^{33} +(2.68346 - 0.776511i) q^{34} +(-3.98580 + 5.17397i) q^{35} +(-0.675533 - 0.354999i) q^{36} +(-0.837565 + 3.12584i) q^{37} +(-4.02670 + 7.30604i) q^{38} +(-4.61562 - 4.75987i) q^{39} +(-4.78713 + 4.13321i) q^{40} +(-6.93331 + 4.00295i) q^{41} +(-7.59444 + 0.150968i) q^{42} +(0.547962 + 2.04502i) q^{43} +(-0.793451 - 1.25620i) q^{44} +(0.109755 + 0.846118i) q^{45} +(1.99906 - 8.10134i) q^{46} +(-2.37644 + 2.37644i) q^{47} +(-7.23373 - 1.33348i) q^{48} +(-1.32615 + 0.765653i) q^{49} +(6.85865 + 1.72015i) q^{50} -3.63246i q^{51} +(-6.33099 - 3.45232i) q^{52} +(0.529690 + 0.529690i) q^{53} +(4.71840 - 4.90979i) q^{54} +(-0.638626 + 1.53351i) q^{55} +(-7.83828 + 2.60995i) q^{56} +(7.67026 + 7.67026i) q^{57} +(2.97250 + 4.92003i) q^{58} +(0.918361 + 0.530216i) q^{59} +(3.43236 + 7.47330i) q^{60} +(6.10528 - 10.5747i) q^{61} +(-0.174738 - 8.79020i) q^{62} +(-0.288452 + 1.07652i) q^{63} +(-7.94318 + 0.951791i) q^{64} +(0.913989 + 8.01028i) q^{65} +(-1.85585 + 0.537026i) q^{66} +(-12.0928 - 3.24025i) q^{67} +(-1.17336 - 3.77241i) q^{68} +(-9.39651 - 5.42508i) q^{69} +(7.42768 + 5.49023i) q^{70} +(-3.73044 + 6.46131i) q^{71} +(-0.482958 + 0.965138i) q^{72} +(4.65282 - 4.65282i) q^{73} +(4.44327 + 1.09640i) q^{74} +(4.62755 - 7.94512i) q^{75} +(10.4434 + 5.48813i) q^{76} +(-1.53435 + 1.53435i) q^{77} +(-6.60042 + 6.65997i) q^{78} +16.1634 q^{79} +(5.97864 + 6.65251i) q^{80} +(-4.99955 - 8.65948i) q^{81} +(5.85478 + 9.69073i) q^{82} +(-10.6691 - 10.6691i) q^{83} +(0.426916 + 10.7338i) q^{84} +(-2.69556 + 3.49911i) q^{85} +(2.87612 - 0.832261i) q^{86} +(7.21978 - 1.93454i) q^{87} +(-1.75388 + 1.15720i) q^{88} +(-0.514730 - 0.891538i) q^{89} +(1.19327 - 0.178969i) q^{90} +(-2.88186 + 10.1293i) q^{91} +(-11.5110 - 2.59883i) q^{92} +(-11.0426 - 2.95886i) q^{93} +(3.42692 + 3.29333i) q^{94} +(-1.69677 - 13.0806i) q^{95} +(-1.68213 + 10.2655i) q^{96} +(17.0667 - 4.57301i) q^{97} +(1.11986 + 1.85357i) q^{98} +0.283466i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 12 q^{6}+O(q^{10}) \) 144 * q - 6 * q^2 - 12 * q^6	\( 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38} + 76 q^{40} - 72 q^{41} + 40 q^{42} - 120 q^{45} - 12 q^{46} - 40 q^{48} + 120 q^{50} - 10 q^{52} + 8 q^{53} - 20 q^{56} + 126 q^{58} + 16 q^{61} - 44 q^{62} + 32 q^{65} + 96 q^{66} - 64 q^{68} - 54 q^{72} - 12 q^{76} + 40 q^{77} - 100 q^{78} - 24 q^{80} - 32 q^{81} - 78 q^{82} - 24 q^{85} - 10 q^{88} - 8 q^{90} + 100 q^{92} - 48 q^{93} - 12 q^{97} - 162 q^{98}+O(q^{100}) \) 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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