LMFDB - Embedded newform 845.2.k.e.268.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(268,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.268"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			268.7
Root			$1.58474i$ of defining polynomial
Character	$\chi$	$=$	845.268
Dual form			845.2.k.e.577.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.58474 q^{2} +(-0.139520 - 0.139520i) q^{3} +0.511395 q^{4} +(0.0672627 - 2.23506i) q^{5} +(-0.221103 - 0.221103i) q^{6} +0.548328i q^{7} -2.35905 q^{8} -2.96107i q^{9} +(0.106594 - 3.54198i) q^{10} +(-0.108291 + 0.108291i) q^{11} +(-0.0713497 - 0.0713497i) q^{12} +0.868956i q^{14} +(-0.321219 + 0.302450i) q^{15} -4.76126 q^{16} +(-2.22252 - 2.22252i) q^{17} -4.69252i q^{18} +(3.22599 - 3.22599i) q^{19} +(0.0343978 - 1.14300i) q^{20} +(0.0765027 - 0.0765027i) q^{21} +(-0.171613 + 0.171613i) q^{22} +(2.50259 - 2.50259i) q^{23} +(0.329134 + 0.329134i) q^{24} +(-4.99095 - 0.300672i) q^{25} +(-0.831688 + 0.831688i) q^{27} +0.280412i q^{28} -2.34263i q^{29} +(-0.509048 + 0.479305i) q^{30} +(-6.61000 - 6.61000i) q^{31} -2.82726 q^{32} +0.0302175 q^{33} +(-3.52211 - 3.52211i) q^{34} +(1.22554 + 0.0368820i) q^{35} -1.51427i q^{36} +6.80635i q^{37} +(5.11234 - 5.11234i) q^{38} +(-0.158676 + 5.27261i) q^{40} +(2.53005 + 2.53005i) q^{41} +(0.121237 - 0.121237i) q^{42} +(5.02761 - 5.02761i) q^{43} +(-0.0553794 + 0.0553794i) q^{44} +(-6.61815 - 0.199169i) q^{45} +(3.96595 - 3.96595i) q^{46} +9.13956i q^{47} +(0.664291 + 0.664291i) q^{48} +6.69934 q^{49} +(-7.90935 - 0.476486i) q^{50} +0.620172i q^{51} +(-3.70952 - 3.70952i) q^{53} +(-1.31801 + 1.31801i) q^{54} +(0.234752 + 0.249320i) q^{55} -1.29353i q^{56} -0.900179 q^{57} -3.71246i q^{58} +(-2.69196 - 2.69196i) q^{59} +(-0.164270 + 0.154672i) q^{60} +7.84971 q^{61} +(-10.4751 - 10.4751i) q^{62} +1.62364 q^{63} +5.04207 q^{64} +0.0478868 q^{66} +4.89032 q^{67} +(-1.13659 - 1.13659i) q^{68} -0.698322 q^{69} +(1.94217 + 0.0584483i) q^{70} +(11.0573 + 11.0573i) q^{71} +6.98531i q^{72} +3.91807 q^{73} +10.7863i q^{74} +(0.654387 + 0.738287i) q^{75} +(1.64975 - 1.64975i) q^{76} +(-0.0593789 - 0.0593789i) q^{77} -11.1394i q^{79} +(-0.320255 + 10.6417i) q^{80} -8.65113 q^{81} +(4.00947 + 4.00947i) q^{82} +13.4251i q^{83} +(0.0391231 - 0.0391231i) q^{84} +(-5.11695 + 4.81797i) q^{85} +(7.96744 - 7.96744i) q^{86} +(-0.326844 + 0.326844i) q^{87} +(0.255464 - 0.255464i) q^{88} +(-6.43047 - 6.43047i) q^{89} +(-10.4880 - 0.315631i) q^{90} +(1.27981 - 1.27981i) q^{92} +1.84445i q^{93} +14.4838i q^{94} +(-6.99327 - 7.42725i) q^{95} +(0.394459 + 0.394459i) q^{96} -7.57101 q^{97} +10.6167 q^{98} +(0.320657 + 0.320657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{2} + 4 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 8 q^{10} + 8 q^{11} + 24 q^{12} - 24 q^{15} + 4 q^{16} + 14 q^{17} - 4 q^{19} - 22 q^{20} + 4 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 8 * q^2 + 4 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 8 * q^10 + 8 * q^11 + 24 * q^12 - 24 * q^15 + 4 * q^16 + 14 * q^17 - 4 * q^19 - 22 * q^20 + 4 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 + 12 * q^32 + 36 * q^33 - 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 + 32 * q^43 + 36 * q^44 - 20 * q^45 + 4 * q^46 + 28 * q^48 + 36 * q^49 - 52 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^59 - 92 * q^60 + 32 * q^61 - 4 * q^62 + 64 * q^63 - 20 * q^64 - 32 * q^66 + 116 * q^67 - 50 * q^68 - 32 * q^69 + 32 * q^70 - 40 * q^71 + 72 * q^73 - 4 * q^75 - 16 * q^76 + 28 * q^77 - 34 * q^80 + 28 * q^81 + 34 * q^82 - 8 * q^84 + 60 * q^86 - 28 * q^87 + 32 * q^88 - 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 + 56 * q^96 + 44 * q^97 - 8 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.58474			1.12058			0.560290	−	0.828297i	$-0.310690\pi$
$2$	1.58474			1.12058			0.560290	+	0.828297i	$0.310690\pi$
$3$	−0.139520	−	0.139520i	−0.0805519	−	0.0805519i	0.665683	−	0.746235i	$-0.268140\pi$
$3$	−0.139520	−	0.139520i	−0.0805519	−	0.0805519i	−0.746235	+	0.665683i	$0.768140\pi$
$4$	0.511395			0.255697
$5$	0.0672627	−	2.23506i	0.0300808	−	0.999547i
$5$	0.0672627	−	2.23506i	0.0300808	−	0.999547i
$6$	−0.221103	−	0.221103i	−0.0902647	−	0.0902647i
$7$			0.548328i			0.207248i	0.994617	+	0.103624i	$0.0330439\pi$
$7$			0.548328i			0.207248i	−0.994617	+	0.103624i	$0.966956\pi$
$8$	−2.35905			−0.834050
$9$		−	2.96107i		−	0.987023i
$10$	0.106594	−	3.54198i	0.0337079	−	1.12007i
$11$	−0.108291	+	0.108291i	−0.0326509	+	0.0326509i	−0.723244	−	0.690593i	$-0.757350\pi$
$11$	−0.108291	+	0.108291i	−0.0326509	+	0.0326509i	0.690593	+	0.723244i	$0.257350\pi$
$12$	−0.0713497	−	0.0713497i	−0.0205969	−	0.0205969i
$13$		0			0
$13$		0			0
$14$			0.868956i			0.232238i
$15$	−0.321219	+	0.302450i	−0.0829385	+	0.0780923i
$16$	−4.76126			−1.19032
$17$	−2.22252	−	2.22252i	−0.539041	−	0.539041i	0.384207	−	0.923247i	$-0.374475\pi$
$17$	−2.22252	−	2.22252i	−0.539041	−	0.539041i	−0.923247	+	0.384207i	$0.874475\pi$
$18$		−	4.69252i		−	1.10604i
$19$	3.22599	−	3.22599i	0.740092	−	0.740092i	−0.232503	−	0.972596i	$-0.574692\pi$
$19$	3.22599	−	3.22599i	0.740092	−	0.740092i	0.972596	+	0.232503i	$0.0746917\pi$
$20$	0.0343978	−	1.14300i	0.00769158	−	0.255582i
$21$	0.0765027	−	0.0765027i	0.0166942	−	0.0166942i
$22$	−0.171613	+	0.171613i	−0.0365880	+	0.0365880i
$23$	2.50259	−	2.50259i	0.521826	−	0.521826i	−0.396297	−	0.918123i	$-0.629705\pi$
$23$	2.50259	−	2.50259i	0.521826	−	0.521826i	0.918123	+	0.396297i	$0.129705\pi$
$24$	0.329134	+	0.329134i	0.0671843	+	0.0671843i
$25$	−4.99095	−	0.300672i	−0.998190	−	0.0601343i
$26$		0			0
$27$	−0.831688	+	0.831688i	−0.160058	+	0.160058i
$28$			0.280412i			0.0529929i
$29$		−	2.34263i		−	0.435016i	−0.976059	−	0.217508i	$-0.930207\pi$
$29$		−	2.34263i		−	0.435016i	0.976059	−	0.217508i	$-0.0697927\pi$
$30$	−0.509048	+	0.479305i	−0.0929391	+	0.0875086i
$31$	−6.61000	−	6.61000i	−1.18719	−	1.18719i	−0.977841	−	0.209350i	$-0.932865\pi$
$31$	−6.61000	−	6.61000i	−1.18719	−	1.18719i	−0.209350	−	0.977841i	$-0.567135\pi$
$32$	−2.82726			−0.499793
$33$	0.0302175			0.00526019
$34$	−3.52211	−	3.52211i	−0.604038	−	0.604038i
$35$	1.22554	+	0.0368820i	0.207155	+	0.00623420i
$36$		−	1.51427i		−	0.252379i
$37$			6.80635i			1.11896i	0.828845	+	0.559478i	$0.188998\pi$
$37$			6.80635i			1.11896i	−0.828845	+	0.559478i	$0.811002\pi$
$38$	5.11234	−	5.11234i	0.829332	−	0.829332i
$39$		0			0
$40$	−0.158676	+	5.27261i	−0.0250889	+	0.833672i
$41$	2.53005	+	2.53005i	0.395128	+	0.395128i	0.876511	−	0.481382i	$-0.159865\pi$
$41$	2.53005	+	2.53005i	0.395128	+	0.395128i	−0.481382	+	0.876511i	$0.659865\pi$
$42$	0.121237	−	0.121237i	0.0187072	−	0.0187072i
$43$	5.02761	−	5.02761i	0.766703	−	0.766703i	−0.210822	−	0.977524i	$-0.567614\pi$
$43$	5.02761	−	5.02761i	0.766703	−	0.766703i	0.977524	+	0.210822i	$0.0676140\pi$
$44$	−0.0553794	+	0.0553794i	−0.00834876	+	0.00834876i
$45$	−6.61815	−	0.199169i	−0.986576	−	0.0296904i
$46$	3.96595	−	3.96595i	0.584747	−	0.584747i
$47$			9.13956i			1.33314i	0.745442	+	0.666571i	$0.232239\pi$
$47$			9.13956i			1.33314i	−0.745442	+	0.666571i	$0.767761\pi$
$48$	0.664291	+	0.664291i	0.0958822	+	0.0958822i
$49$	6.69934			0.957048
$50$	−7.90935	−	0.476486i	−1.11855	−	0.0673853i
$51$			0.620172i			0.0868415i
$52$		0			0
$53$	−3.70952	−	3.70952i	−0.509541	−	0.509541i	0.404844	−	0.914386i	$-0.367326\pi$
$53$	−3.70952	−	3.70952i	−0.509541	−	0.509541i	−0.914386	+	0.404844i	$0.867326\pi$
$54$	−1.31801	+	1.31801i	−0.179358	+	0.179358i
$55$	0.234752	+	0.249320i	0.0316540	+	0.0336183i
$56$		−	1.29353i		−	0.172856i
$57$	−0.900179			−0.119232
$58$		−	3.71246i		−	0.487469i
$59$	−2.69196	−	2.69196i	−0.350463	−	0.350463i	0.509819	−	0.860282i	$-0.329712\pi$
$59$	−2.69196	−	2.69196i	−0.350463	−	0.350463i	−0.860282	+	0.509819i	$0.829712\pi$
$60$	−0.164270	+	0.154672i	−0.0212071	+	0.0199680i
$61$	7.84971			1.00505			0.502526	−	0.864562i	$-0.332404\pi$
$61$	7.84971			1.00505			0.502526	+	0.864562i	$0.332404\pi$
$62$	−10.4751	−	10.4751i	−1.33034	−	1.33034i
$63$	1.62364			0.204559
$64$	5.04207			0.630258
$65$		0			0
$66$	0.0478868			0.00589446
$67$	4.89032			0.597448			0.298724	−	0.954340i	$-0.403439\pi$
$67$	4.89032			0.597448			0.298724	+	0.954340i	$0.403439\pi$
$68$	−1.13659	−	1.13659i	−0.137831	−	0.137831i
$69$	−0.698322			−0.0840681
$70$	1.94217	+	0.0584483i	0.232133	+	0.00698591i
$71$	11.0573	+	11.0573i	1.31226	+	1.31226i	0.919747	+	0.392513i	$0.128394\pi$
$71$	11.0573	+	11.0573i	1.31226	+	1.31226i	0.392513	+	0.919747i	$0.371606\pi$
$72$			6.98531i			0.823226i
$73$	3.91807			0.458575			0.229288	−	0.973359i	$-0.426360\pi$
$73$	3.91807			0.458575			0.229288	+	0.973359i	$0.426360\pi$
$74$			10.7863i			1.25388i
$75$	0.654387	+	0.738287i	0.0755622	+	0.0852500i
$76$	1.64975	−	1.64975i	0.189240	−	0.189240i
$77$	−0.0593789	−	0.0593789i	−0.00676686	−	0.00676686i
$78$		0			0
$79$		−	11.1394i		−	1.25328i	−0.779309	−	0.626640i	$-0.784430\pi$
$79$		−	11.1394i		−	1.25328i	0.779309	−	0.626640i	$-0.215570\pi$
$80$	−0.320255	+	10.6417i	−0.0358056	+	1.18978i
$81$	−8.65113			−0.961237
$82$	4.00947	+	4.00947i	0.442772	+	0.442772i
$83$			13.4251i			1.47360i	0.676113	+	0.736798i	$0.263663\pi$
$83$			13.4251i			1.47360i	−0.676113	+	0.736798i	$0.736337\pi$
$84$	0.0391231	−	0.0391231i	0.00426868	−	0.00426868i
$85$	−5.11695	+	4.81797i	−0.555011	+	0.522582i
$86$	7.96744	−	7.96744i	0.859151	−	0.859151i
$87$	−0.326844	+	0.326844i	−0.0350413	+	0.0350413i
$88$	0.255464	−	0.255464i	0.0272325	−	0.0272325i
$89$	−6.43047	−	6.43047i	−0.681629	−	0.681629i	0.278738	−	0.960367i	$-0.410084\pi$
$89$	−6.43047	−	6.43047i	−0.681629	−	0.681629i	−0.960367	+	0.278738i	$0.910084\pi$
$90$	−10.4880	−	0.315631i	−1.10554	−	0.0332705i
$91$		0			0
$92$	1.27981	−	1.27981i	0.133430	−	0.133430i
$93$			1.84445i			0.191261i
$94$			14.4838i			1.49389i
$95$	−6.99327	−	7.42725i	−0.717495	−	0.762020i
$96$	0.394459	+	0.394459i	0.0402593	+	0.0402593i
$97$	−7.57101			−0.768719			−0.384360	−	0.923183i	$-0.625578\pi$
$97$	−7.57101			−0.768719			−0.384360	+	0.923183i	$0.625578\pi$
$98$	10.6167			1.07245
$99$	0.320657	+	0.320657i	0.0322272	+	0.0322272i
$100$	−2.55235	−	0.153762i	−0.255235	−	0.0153762i
$101$			13.5352i			1.34680i	0.739279	+	0.673400i	$0.235167\pi$
$101$			13.5352i			1.34680i	−0.739279	+	0.673400i	$0.764833\pi$
$102$			0.982810i			0.0973127i
$103$	10.3566	−	10.3566i	1.02046	−	1.02046i	0.0206759	−	0.999786i	$-0.493418\pi$
$103$	10.3566	−	10.3566i	1.02046	−	1.02046i	0.999786	−	0.0206759i	$-0.00658183\pi$
$104$		0			0
$105$	−0.165842	−	0.176134i	−0.0161845	−	0.0171889i
$106$	−5.87861	−	5.87861i	−0.570981	−	0.570981i
$107$	11.3675	−	11.3675i	1.09893	−	1.09893i	0.104399	−	0.994535i	$-0.466708\pi$
$107$	11.3675	−	11.3675i	1.09893	−	1.09893i	0.994535	−	0.104399i	$-0.0332920\pi$
$108$	−0.425321	+	0.425321i	−0.0409265	+	0.0409265i
$109$	−8.20821	+	8.20821i	−0.786203	+	0.786203i	−0.980870	−	0.194666i	$-0.937638\pi$
$109$	−8.20821	+	8.20821i	−0.786203	+	0.786203i	0.194666	+	0.980870i	$0.437638\pi$
$110$	0.372021	+	0.395107i	0.0354708	+	0.0376720i
$111$	0.949621	−	0.949621i	0.0901340	−	0.0901340i
$112$		−	2.61073i		−	0.246691i
$113$	3.22285	+	3.22285i	0.303180	+	0.303180i	0.842257	−	0.539077i	$-0.181227\pi$
$113$	3.22285	+	3.22285i	0.303180	+	0.303180i	−0.539077	+	0.842257i	$0.681227\pi$
$114$	−1.42655			−0.133608
$115$	−5.42510	−	5.76176i	−0.505893	−	0.537287i
$116$		−	1.19801i		−	0.111232i
$117$		0			0
$118$	−4.26605	−	4.26605i	−0.392722	−	0.392722i
$119$	1.21867	−	1.21867i	0.111715	−	0.111715i
$120$	0.757772	−	0.713495i	0.0691748	−	0.0651329i
$121$			10.9765i			0.997868i
$122$	12.4397			1.12624
$123$		−	0.705986i		−	0.0636566i
$124$	−3.38032	−	3.38032i	−0.303561	−	0.303561i
$125$	−1.00772	+	11.1348i	−0.0901335	+	0.995930i
$126$	2.57304			0.229224
$127$	1.71992	+	1.71992i	0.152618	+	0.152618i	0.779286	−	0.626668i	$-0.215582\pi$
$127$	1.71992	+	1.71992i	0.152618	+	0.152618i	−0.626668	+	0.779286i	$0.715582\pi$
$128$	13.6449			1.20605
$129$	−1.40290			−0.123519
$130$		0			0
$131$	6.60705			0.577260			0.288630	−	0.957441i	$-0.406800\pi$
$131$	6.60705			0.577260			0.288630	+	0.957441i	$0.406800\pi$
$132$	0.0154531			0.00134502
$133$	1.76890	+	1.76890i	0.153383	+	0.153383i
$134$	7.74988			0.669487
$135$	1.80293	+	1.91481i	0.155171	+	0.164801i
$136$	5.24304	+	5.24304i	0.449587	+	0.449587i
$137$		−	4.05549i		−	0.346484i	−0.984879	−	0.173242i	$-0.944576\pi$
$137$		−	4.05549i		−	0.346484i	0.984879	−	0.173242i	$-0.0554243\pi$
$138$	−1.10666			−0.0942050
$139$		−	12.8232i		−	1.08765i	−0.839199	−	0.543825i	$-0.816976\pi$
$139$		−	12.8232i		−	1.08765i	0.839199	−	0.543825i	$-0.183024\pi$
$140$	0.626737	+	0.0188613i	0.0529689	+	0.00159407i
$141$	1.27515	−	1.27515i	0.107387	−	0.107387i
$142$	17.5229	+	17.5229i	1.47049	+	1.47049i
$143$		0			0
$144$			14.0984i			1.17487i
$145$	−5.23591	−	0.157572i	−0.434819	−	0.0130856i
$146$	6.20911			0.513870
$147$	−0.934691	−	0.934691i	−0.0770920	−	0.0770920i
$148$			3.48073i			0.286114i
$149$	3.00860	−	3.00860i	0.246474	−	0.246474i	−0.573048	−	0.819522i	$-0.694239\pi$
$149$	3.00860	−	3.00860i	0.246474	−	0.246474i	0.819522	+	0.573048i	$0.194239\pi$
$150$	1.03703	+	1.16999i	0.0846734	+	0.0955294i
$151$	4.89430	−	4.89430i	0.398293	−	0.398293i	−0.479338	−	0.877630i	$-0.659123\pi$
$151$	4.89430	−	4.89430i	0.398293	−	0.398293i	0.877630	+	0.479338i	$0.159123\pi$
$152$	−7.61026	+	7.61026i	−0.617274	+	0.617274i
$153$	−6.58104	+	6.58104i	−0.532045	+	0.532045i
$154$	−0.0941001	−	0.0941001i	−0.00758280	−	0.00758280i
$155$	−15.2183	+	14.3291i	−1.22236	+	1.15094i
$156$		0			0
$157$	2.29887	−	2.29887i	0.183470	−	0.183470i	−0.609396	−	0.792866i	$-0.708588\pi$
$157$	2.29887	−	2.29887i	0.183470	−	0.183470i	0.792866	+	0.609396i	$0.208588\pi$
$158$		−	17.6530i		−	1.40440i
$159$			1.03510i			0.0820890i
$160$	−0.190169	+	6.31908i	−0.0150342	+	0.499567i
$161$	1.37224	+	1.37224i	0.108148	+	0.108148i
$162$	−13.7098			−1.07714
$163$	−10.8685			−0.851283			−0.425642	−	0.904892i	$-0.639952\pi$
$163$	−10.8685			−0.851283			−0.425642	+	0.904892i	$0.639952\pi$
$164$	1.29386	+	1.29386i	0.101033	+	0.101033i
$165$	0.00203251	−	0.0675378i	0.000158231	−	0.00525781i
$166$			21.2753i			1.65128i
$167$			16.3588i			1.26588i	0.774199	+	0.632942i	$0.218153\pi$
$167$			16.3588i			1.26588i	−0.774199	+	0.632942i	$0.781847\pi$
$168$	−0.180474	+	0.180474i	−0.0139238	+	0.0139238i
$169$		0			0
$170$	−8.10903	+	7.63522i	−0.621934	+	0.585594i
$171$	−9.55237	−	9.55237i	−0.730488	−	0.730488i
$172$	2.57109	−	2.57109i	0.196044	−	0.196044i
$173$	−4.83220	+	4.83220i	−0.367385	+	0.367385i	−0.866523	−	0.499137i	$-0.833650\pi$
$173$	−4.83220	+	4.83220i	−0.367385	+	0.367385i	0.499137	+	0.866523i	$0.333650\pi$
$174$	−0.517961	+	0.517961i	−0.0392666	+	0.0392666i
$175$	0.164867	−	2.73668i	0.0124628	−	0.206873i
$176$	0.515602	−	0.515602i	0.0388649	−	0.0388649i
$177$			0.751164i			0.0564609i
$178$	−10.1906	−	10.1906i	−0.763819	−	0.763819i
$179$	5.67392			0.424089			0.212044	−	0.977260i	$-0.431988\pi$
$179$	5.67392			0.424089			0.212044	+	0.977260i	$0.431988\pi$
$180$	−3.38449	−	0.101854i	−0.252265	−	0.00759176i
$181$			3.59115i			0.266928i	0.991054	+	0.133464i	$0.0426101\pi$
$181$			3.59115i			0.266928i	−0.991054	+	0.133464i	$0.957390\pi$
$182$		0			0
$183$	−1.09519	−	1.09519i	−0.0809588	−	0.0809588i
$184$	−5.90373	+	5.90373i	−0.435229	+	0.435229i
$185$	15.2126	+	0.457813i	1.11845	+	0.0336591i
$186$			2.92297i			0.214323i
$187$	0.481358			0.0352004
$188$			4.67392i			0.340881i
$189$	−0.456038	−	0.456038i	−0.0331719	−	0.0331719i
$190$	−11.0825	−	11.7702i	−0.804009	−	0.853903i
$191$	−23.4821			−1.69911			−0.849553	−	0.527504i	$-0.823128\pi$
$191$	−23.4821			−1.69911			−0.849553	+	0.527504i	$0.823128\pi$
$192$	−0.703469	−	0.703469i	−0.0507685	−	0.0507685i
$193$	15.8378			1.14003			0.570016	−	0.821634i	$-0.306937\pi$
$193$	15.8378			1.14003			0.570016	+	0.821634i	$0.306937\pi$
$194$	−11.9981			−0.861411
$195$		0			0
$196$	3.42601			0.244715
$197$	5.71277			0.407018			0.203509	−	0.979073i	$-0.434765\pi$
$197$	5.71277			0.407018			0.203509	+	0.979073i	$0.434765\pi$
$198$	0.508157	+	0.508157i	0.0361132	+	0.0361132i
$199$	−9.30312			−0.659481			−0.329740	−	0.944072i	$-0.606961\pi$
$199$	−9.30312			−0.659481			−0.329740	+	0.944072i	$0.606961\pi$
$200$	11.7739	+	0.709299i	0.832541	+	0.0501550i
$201$	−0.682297	−	0.682297i	−0.0481255	−	0.0481255i
$202$			21.4497i			1.50919i
$203$	1.28453			0.0901563
$204$			0.317153i			0.0222051i
$205$	5.82499	−	5.48464i	0.406835	−	0.383064i
$206$	16.4124	−	16.4124i	1.14351	−	1.14351i
$207$	−7.41034	−	7.41034i	−0.515054	−	0.515054i
$208$		0			0
$209$			0.698690i			0.0483294i
$210$	−0.262816	−	0.279125i	−0.0181360	−	0.0192615i
$211$	−5.47558			−0.376955			−0.188477	−	0.982078i	$-0.560355\pi$
$211$	−5.47558			−0.376955			−0.188477	+	0.982078i	$0.560355\pi$
$212$	−1.89703	−	1.89703i	−0.130288	−	0.130288i
$213$		−	3.08543i		−	0.211410i
$214$	18.0145	−	18.0145i	1.23144	−	1.23144i
$215$	−10.8988	−	11.5752i	−0.743293	−	0.789419i
$216$	1.96199	−	1.96199i	0.133497	−	0.133497i
$217$	3.62445	−	3.62445i	0.246043	−	0.246043i
$218$	−13.0079	+	13.0079i	−0.881003	+	0.881003i
$219$	−0.546648	−	0.546648i	−0.0369391	−	0.0369391i
$220$	0.120051	+	0.127501i	0.00809385	+	0.00859612i
$221$		0			0
$222$	1.50490	−	1.50490i	0.101002	−	0.101002i
$223$		−	18.5682i		−	1.24342i	−0.783249	−	0.621708i	$-0.786439\pi$
$223$		−	18.5682i		−	1.24342i	0.783249	−	0.621708i	$-0.213561\pi$
$224$		−	1.55026i		−	0.103581i
$225$	−0.890310	+	14.7785i	−0.0593540	+	0.985237i
$226$	5.10737	+	5.10737i	0.339737	+	0.339737i
$227$	6.38666			0.423898			0.211949	−	0.977281i	$-0.432019\pi$
$227$	6.38666			0.423898			0.211949	+	0.977281i	$0.432019\pi$
$228$	−0.460347			−0.0304872
$229$	−11.1149	−	11.1149i	−0.734491	−	0.734491i	0.237015	−	0.971506i	$-0.423831\pi$
$229$	−11.1149	−	11.1149i	−0.734491	−	0.734491i	−0.971506	+	0.237015i	$0.923831\pi$
$230$	−8.59736	−	9.13088i	−0.566893	−	0.602072i
$231$			0.0165691i			0.00109017i
$232$			5.52638i			0.362825i
$233$	−5.85956	+	5.85956i	−0.383873	+	0.383873i	−0.872495	−	0.488623i	$-0.837500\pi$
$233$	−5.85956	+	5.85956i	−0.383873	+	0.383873i	0.488623	+	0.872495i	$0.337500\pi$
$234$		0			0
$235$	20.4274	+	0.614751i	1.33254	+	0.0401019i
$236$	−1.37665	−	1.37665i	−0.0896125	−	0.0896125i
$237$	−1.55417	+	1.55417i	−0.100954	+	0.100954i
$238$	1.93127	−	1.93127i	0.125186	−	0.125186i
$239$	13.8081	−	13.8081i	0.893170	−	0.893170i	−0.101650	−	0.994820i	$-0.532412\pi$
$239$	13.8081	−	13.8081i	0.893170	−	0.893170i	0.994820	+	0.101650i	$0.0324123\pi$
$240$	1.52941	−	1.44005i	0.0987230	−	0.0929546i
$241$	12.1149	−	12.1149i	0.780391	−	0.780391i	−0.199505	−	0.979897i	$-0.563934\pi$
$241$	12.1149	−	12.1149i	0.780391	−	0.780391i	0.979897	+	0.199505i	$0.0639336\pi$
$242$			17.3950i			1.11819i
$243$	3.70207	+	3.70207i	0.237488	+	0.237488i
$244$	4.01430			0.256989
$245$	0.450615	−	14.9734i	0.0287888	−	0.956615i
$246$		−	1.11880i		−	0.0713323i
$247$		0			0
$248$	15.5933	+	15.5933i	0.990176	+	0.990176i
$249$	1.87307	−	1.87307i	0.118701	−	0.118701i
$250$	−1.59698	+	17.6458i	−0.101002	+	1.11602i
$251$		−	9.95304i		−	0.628230i	−0.949385	−	0.314115i	$-0.898292\pi$
$251$		−	9.95304i		−	0.628230i	0.949385	−	0.314115i	$-0.101708\pi$
$252$	0.830319			0.0523052
$253$			0.542016i			0.0340762i
$254$	2.72562	+	2.72562i	0.171020	+	0.171020i
$255$	1.38612	+	0.0417144i	0.0868022	+	0.00261226i
$256$	11.5394			0.721213
$257$	−1.94551	−	1.94551i	−0.121357	−	0.121357i	0.643820	−	0.765177i	$-0.277349\pi$
$257$	−1.94551	−	1.94551i	−0.121357	−	0.121357i	−0.765177	+	0.643820i	$0.777349\pi$
$258$	−2.22323			−0.138412
$259$	−3.73211			−0.231902
$260$		0			0
$261$	−6.93669			−0.429370
$262$	10.4704			0.646866
$263$	−4.36804	−	4.36804i	−0.269345	−	0.269345i	0.559491	−	0.828836i	$-0.310997\pi$
$263$	−4.36804	−	4.36804i	−0.269345	−	0.269345i	−0.828836	+	0.559491i	$0.810997\pi$
$264$	−0.0712845			−0.00438726
$265$	−8.54049	+	8.04147i	−0.524638	+	0.493983i
$266$	2.80324	+	2.80324i	0.171878	+	0.171878i
$267$			1.79436i			0.109813i
$268$	2.50088			0.152766
$269$		−	21.2230i		−	1.29399i	−0.762495	−	0.646994i	$-0.776026\pi$
$269$		−	21.2230i		−	1.29399i	0.762495	−	0.646994i	$-0.223974\pi$
$270$	2.85717	+	3.03447i	0.173882	+	0.184672i
$271$	9.11094	−	9.11094i	0.553450	−	0.553450i	−0.373985	−	0.927435i	$-0.622009\pi$
$271$	9.11094	−	9.11094i	0.553450	−	0.553450i	0.927435	+	0.373985i	$0.122009\pi$
$272$	10.5820	+	10.5820i	0.641629	+	0.641629i
$273$		0			0
$274$		−	6.42690i		−	0.388263i
$275$	0.573035	−	0.507915i	0.0345553	−	0.0306284i
$276$	−0.357118			−0.0214960
$277$	15.0447	+	15.0447i	0.903948	+	0.903948i	0.995775	−	0.0918270i	$-0.0292707\pi$
$277$	15.0447	+	15.0447i	0.903948	+	0.903948i	−0.0918270	+	0.995775i	$0.529271\pi$
$278$		−	20.3214i		−	1.21880i
$279$	−19.5727	+	19.5727i	−1.17178	+	1.17178i
$280$	−2.89112	−	0.0870065i	−0.172777	−	0.00519963i
$281$	−4.22655	+	4.22655i	−0.252135	+	0.252135i	−0.821845	−	0.569711i	$-0.807055\pi$
$281$	−4.22655	+	4.22655i	−0.252135	+	0.252135i	0.569711	+	0.821845i	$0.307055\pi$
$282$	2.02078	−	2.02078i	0.120336	−	0.120336i
$283$	1.08748	−	1.08748i	0.0646437	−	0.0646437i	−0.674046	−	0.738690i	$-0.735445\pi$
$283$	1.08748	−	1.08748i	0.0646437	−	0.0646437i	0.738690	+	0.674046i	$0.235445\pi$
$284$	5.65464	+	5.65464i	0.335541	+	0.335541i
$285$	−0.0605484	+	2.01195i	−0.00358658	+	0.119178i
$286$		0			0
$287$	−1.38730	+	1.38730i	−0.0818897	+	0.0818897i
$288$			8.37171i			0.493308i
$289$		−	7.12080i		−	0.418870i
$290$	−8.29755	−	0.249710i	−0.487249	−	0.0146635i
$291$	1.05631	+	1.05631i	0.0619218	+	0.0619218i
$292$	2.00368			0.117256
$293$	2.79186			0.163102			0.0815512	−	0.996669i	$-0.474013\pi$
$293$	2.79186			0.163102			0.0815512	+	0.996669i	$0.474013\pi$
$294$	−1.48124	−	1.48124i	−0.0863877	−	0.0863877i
$295$	−6.19775	+	5.83561i	−0.360847	+	0.339762i
$296$		−	16.0565i		−	0.933265i
$297$		−	0.180128i		−	0.0104521i
$298$	4.76785	−	4.76785i	0.276194	−	0.276194i
$299$		0			0
$300$	0.334650	+	0.377556i	0.0193210	+	0.0217982i
$301$	2.75678	+	2.75678i	0.158898	+	0.158898i
$302$	7.75619	−	7.75619i	0.446318	−	0.446318i
$303$	1.88843	−	1.88843i	0.108487	−	0.108487i
$304$	−15.3598	+	15.3598i	−0.880944	+	0.880944i
$305$	0.527993	−	17.5445i	0.0302328	−	1.00460i
$306$	−10.4292	+	10.4292i	−0.596199	+	0.596199i
$307$		−	2.12112i		−	0.121058i	−0.998166	−	0.0605292i	$-0.980721\pi$
$307$		−	2.12112i		−	0.121058i	0.998166	−	0.0605292i	$-0.0192788\pi$
$308$	−0.0303661	−	0.0303661i	−0.00173027	−	0.00173027i
$309$	−2.88989			−0.164400
$310$	−24.1171	+	22.7079i	−1.36976	+	1.28972i
$311$		−	21.2656i		−	1.20586i	−0.797794	−	0.602931i	$-0.794000\pi$
$311$		−	21.2656i		−	1.20586i	0.797794	−	0.602931i	$-0.206000\pi$
$312$		0			0
$313$	−14.3666	−	14.3666i	−0.812050	−	0.812050i	0.172891	−	0.984941i	$-0.444689\pi$
$313$	−14.3666	−	14.3666i	−0.812050	−	0.812050i	−0.984941	+	0.172891i	$0.944689\pi$
$314$	3.64310	−	3.64310i	0.205592	−	0.205592i
$315$	0.109210	−	3.62892i	0.00615329	−	0.204466i
$316$		−	5.69663i		−	0.320460i
$317$	8.78989			0.493689			0.246845	−	0.969055i	$-0.420606\pi$
$317$	8.78989			0.493689			0.246845	+	0.969055i	$0.420606\pi$
$318$			1.64037i			0.0919872i
$319$	0.253686	+	0.253686i	0.0142037	+	0.0142037i
$320$	0.339143	−	11.2693i	0.0189587	−	0.629973i
$321$	−3.17198			−0.177042
$322$	2.17464	+	2.17464i	0.121188	+	0.121188i
$323$	−14.3396			−0.797879
$324$	−4.42414			−0.245786
$325$		0			0
$326$	−17.2237			−0.953930
$327$	2.29042			0.126660
$328$	−5.96852	−	5.96852i	−0.329557	−	0.329557i
$329$	−5.01147			−0.276291
$330$	0.00322099	−	0.107030i	0.000177310	−	0.00589179i
$331$	−12.8491	−	12.8491i	−0.706250	−	0.706250i	0.259494	−	0.965745i	$-0.416444\pi$
$331$	−12.8491	−	12.8491i	−0.706250	−	0.706250i	−0.965745	+	0.259494i	$0.916444\pi$
$332$			6.86552i			0.376794i
$333$	20.1541			1.10444
$334$			25.9245i			1.41852i
$335$	0.328936	−	10.9301i	0.0179717	−	0.597177i
$336$	−0.364249	+	0.364249i	−0.0198714	+	0.0198714i
$337$	17.2522	+	17.2522i	0.939788	+	0.939788i	0.998287	−	0.0584999i	$-0.0186317\pi$
$337$	17.2522	+	17.2522i	0.939788	+	0.939788i	−0.0584999	+	0.998287i	$0.518632\pi$
$338$		0			0
$339$		−	0.899302i		−	0.0488434i
$340$	−2.61678	+	2.46388i	−0.141915	+	0.133623i
$341$	1.43161			0.0775258
$342$	−15.1380	−	15.1380i	−0.818569	−	0.818569i
$343$			7.51173i			0.405595i
$344$	−11.8604	+	11.8604i	−0.639468	+	0.639468i
$345$	−0.0469710	+	1.56079i	−0.00252884	+	0.0840301i
$346$	−7.65777	+	7.65777i	−0.411684	+	0.411684i
$347$	−5.49531	+	5.49531i	−0.295004	+	0.295004i	−0.839053	−	0.544049i	$-0.816890\pi$
$347$	−5.49531	+	5.49531i	−0.295004	+	0.295004i	0.544049	+	0.839053i	$0.316890\pi$
$348$	−0.167146	+	0.167146i	−0.00895997	+	0.00895997i
$349$	−3.58556	−	3.58556i	−0.191931	−	0.191931i	0.604599	−	0.796530i	$-0.293333\pi$
$349$	−3.58556	−	3.58556i	−0.191931	−	0.191931i	−0.796530	+	0.604599i	$0.793333\pi$
$350$	0.261271	−	4.33692i	0.0139655	−	0.231818i
$351$		0			0
$352$	0.306166	−	0.306166i	0.0163187	−	0.0163187i
$353$			25.6178i			1.36350i	0.731586	+	0.681749i	$0.238780\pi$
$353$			25.6178i			1.36350i	−0.731586	+	0.681749i	$0.761220\pi$
$354$			1.19040i			0.0632689i
$355$	25.4574	−	23.9699i	1.35114	−	1.27219i
$356$	−3.28851	−	3.28851i	−0.174291	−	0.174291i
$357$	−0.340058			−0.0179978
$358$	8.99168			0.475225
$359$	10.0443	+	10.0443i	0.530117	+	0.530117i	0.920607	−	0.390490i	$-0.127694\pi$
$359$	10.0443	+	10.0443i	0.530117	+	0.530117i	−0.390490	+	0.920607i	$0.627694\pi$
$360$	15.6126	+	0.469850i	0.822854	+	0.0247633i
$361$		−	1.81398i		−	0.0954726i
$362$			5.69103i			0.299114i
$363$	1.53145	−	1.53145i	0.0803801	−	0.0803801i
$364$		0			0
$365$	0.263540	−	8.75710i	0.0137943	−	0.458368i
$366$	−1.73559	−	1.73559i	−0.0907208	−	0.0907208i
$367$	−14.2286	+	14.2286i	−0.742726	+	0.742726i	−0.973102	−	0.230376i	$-0.926005\pi$
$367$	−14.2286	+	14.2286i	−0.742726	+	0.742726i	0.230376	+	0.973102i	$0.426005\pi$
$368$	−11.9155	+	11.9155i	−0.621138	+	0.621138i
$369$	7.49167	−	7.49167i	0.390001	−	0.390001i
$370$	24.1079	+	0.725514i	1.25331	+	0.0377177i
$371$	2.03403	−	2.03403i	0.105602	−	0.105602i
$372$			0.943243i			0.0489049i
$373$	18.5300	+	18.5300i	0.959447	+	0.959447i	0.999209	−	0.0397619i	$-0.0126600\pi$
$373$	18.5300	+	18.5300i	0.959447	+	0.959447i	−0.0397619	+	0.999209i	$0.512660\pi$
$374$	0.762826			0.0394448
$375$	1.69413	−	1.41293i	0.0874844	−	0.0729636i
$376$		−	21.5607i		−	1.11191i
$377$		0			0
$378$	−0.722700	−	0.722700i	−0.0371717	−	0.0371717i
$379$	−15.9314	+	15.9314i	−0.818341	+	0.818341i	−0.985868	−	0.167526i	$-0.946422\pi$
$379$	−15.9314	+	15.9314i	−0.818341	+	0.818341i	0.167526	+	0.985868i	$0.446422\pi$
$380$	−3.57632	−	3.79826i	−0.183461	−	0.194846i
$381$		−	0.479925i		−	0.0245873i
$382$	−37.2130			−1.90398
$383$			24.1261i			1.23278i	0.787440	+	0.616392i	$0.211406\pi$
$383$			24.1261i			1.23278i	−0.787440	+	0.616392i	$0.788594\pi$
$384$	−1.90373	−	1.90373i	−0.0971494	−	0.0971494i
$385$	−0.136709	+	0.128721i	−0.00696735	+	0.00656024i
$386$	25.0988			1.27750
$387$	−14.8871	−	14.8871i	−0.756753	−	0.756753i
$388$	−3.87177			−0.196559
$389$	−14.3262			−0.726365			−0.363183	−	0.931718i	$-0.618310\pi$
$389$	−14.3262			−0.726365			−0.363183	+	0.931718i	$0.618310\pi$
$390$		0			0
$391$	−11.1241			−0.562571
$392$	−15.8041			−0.798226
$393$	−0.921815	−	0.921815i	−0.0464994	−	0.0464994i
$394$	9.05325			0.456096
$395$	−24.8972	−	0.749265i	−1.25271	−	0.0376996i
$396$	0.163982	+	0.163982i	0.00824042	+	0.00824042i
$397$		−	33.4931i		−	1.68097i	−0.541836	−	0.840484i	$-0.682271\pi$
$397$		−	33.4931i		−	1.68097i	0.541836	−	0.840484i	$-0.317729\pi$
$398$	−14.7430			−0.739000
$399$		−	0.493593i		−	0.0247106i
$400$	23.7632	+	1.43158i	1.18816	+	0.0715789i
$401$	−13.1161	+	13.1161i	−0.654989	+	0.654989i	−0.954190	−	0.299201i	$-0.903280\pi$
$401$	−13.1161	+	13.1161i	−0.654989	+	0.654989i	0.299201	+	0.954190i	$0.403280\pi$
$402$	−1.08126	−	1.08126i	−0.0539285	−	0.0539285i
$403$		0			0
$404$			6.92181i			0.344373i
$405$	−0.581898	+	19.3358i	−0.0289148	+	0.960802i
$406$	2.03564			0.101027
$407$	−0.737066	−	0.737066i	−0.0365350	−	0.0365350i
$408$		−	1.46302i		−	0.0724301i
$409$	3.65748	−	3.65748i	0.180851	−	0.180851i	−0.610876	−	0.791727i	$-0.709182\pi$
$409$	3.65748	−	3.65748i	0.180851	−	0.180851i	0.791727	+	0.610876i	$0.209182\pi$
$410$	9.23109	−	8.69171i	0.455891	−	0.429253i
$411$	−0.565822	+	0.565822i	−0.0279099	+	0.0279099i
$412$	5.29629	−	5.29629i	0.260929	−	0.260929i
$413$	1.47608	−	1.47608i	0.0726329	−	0.0726329i
$414$	−11.7434	−	11.7434i	−0.577159	−	0.577159i
$415$	30.0058	+	0.903008i	1.47293	+	0.0443269i
$416$		0			0
$417$	−1.78909	+	1.78909i	−0.0876122	+	0.0876122i
$418$			1.10724i			0.0541569i
$419$			1.00695i			0.0491929i	0.999697	+	0.0245965i	$0.00783009\pi$
$419$			1.00695i			0.0491929i	−0.999697	+	0.0245965i	$0.992170\pi$
$420$	−0.0848107	−	0.0900737i	−0.00413834	−	0.00439515i
$421$	0.294746	+	0.294746i	0.0143650	+	0.0143650i	0.714253	−	0.699888i	$-0.246767\pi$
$421$	0.294746	+	0.294746i	0.0143650	+	0.0143650i	−0.699888	+	0.714253i	$0.746767\pi$
$422$	−8.67736			−0.422407
$423$	27.0628			1.31584
$424$	8.75094	+	8.75094i	0.424983	+	0.424983i
$425$	10.4242	+	11.7607i	0.505650	+	0.570480i
$426$		−	4.88959i		−	0.236901i
$427$			4.30421i			0.208296i
$428$	5.81326	−	5.81326i	0.280995	−	0.280995i
$429$		0			0
$430$	−17.2718	−	18.3436i	−0.832918	−	0.884606i
$431$	−2.93555	−	2.93555i	−0.141401	−	0.141401i	0.632863	−	0.774264i	$-0.281880\pi$
$431$	−2.93555	−	2.93555i	−0.141401	−	0.141401i	−0.774264	+	0.632863i	$0.781880\pi$
$432$	3.95989	−	3.95989i	0.190520	−	0.190520i
$433$	10.6032	−	10.6032i	0.509556	−	0.509556i	−0.404834	−	0.914390i	$-0.632671\pi$
$433$	10.6032	−	10.6032i	0.509556	−	0.509556i	0.914390	+	0.404834i	$0.132671\pi$
$434$	5.74380	−	5.74380i	0.275711	−	0.275711i
$435$	0.708529	+	0.752498i	0.0339714	+	0.0360795i
$436$	−4.19763	+	4.19763i	−0.201030	+	0.201030i
$437$		−	16.1466i		−	0.772399i
$438$	−0.866294	−	0.866294i	−0.0413932	−	0.0413932i
$439$	−13.8820			−0.662550			−0.331275	−	0.943534i	$-0.607479\pi$
$439$	−13.8820			−0.662550			−0.331275	+	0.943534i	$0.607479\pi$
$440$	−0.553792	−	0.588159i	−0.0264010	−	0.0280394i
$441$		−	19.8372i		−	0.944628i
$442$		0			0
$443$	10.0594	+	10.0594i	0.477938	+	0.477938i	0.904472	−	0.426533i	$-0.140265\pi$
$443$	10.0594	+	10.0594i	0.477938	+	0.477938i	−0.426533	+	0.904472i	$0.640265\pi$
$444$	0.485631	−	0.485631i	0.0230470	−	0.0230470i
$445$	−14.8050	+	13.9399i	−0.701824	+	0.660816i
$446$		−	29.4257i		−	1.39335i
$447$	−0.839520			−0.0397079
$448$			2.76470i			0.130620i
$449$	4.70669	+	4.70669i	0.222122	+	0.222122i	0.809392	−	0.587269i	$-0.199797\pi$
$449$	4.70669	+	4.70669i	0.222122	+	0.222122i	−0.587269	+	0.809392i	$0.699797\pi$
$450$	−1.41091	+	23.4201i	−0.0665108	+	1.10404i
$451$	−0.547964			−0.0258026
$452$	1.64815	+	1.64815i	0.0775223	+	0.0775223i
$453$	−1.36571			−0.0641664
$454$	10.1212			0.475011
$455$		0			0
$456$	2.12357			0.0994451
$457$	36.9587			1.72885			0.864426	−	0.502759i	$-0.167682\pi$
$457$	36.9587			1.72885			0.864426	+	0.502759i	$0.167682\pi$
$458$	−17.6141	−	17.6141i	−0.823055	−	0.823055i
$459$	3.69689			0.172556
$460$	−2.77437	−	2.94653i	−0.129355	−	0.137383i
$461$	−18.1916	−	18.1916i	−0.847269	−	0.847269i	0.142523	−	0.989792i	$-0.454479\pi$
$461$	−18.1916	−	18.1916i	−0.847269	−	0.847269i	−0.989792	+	0.142523i	$0.954479\pi$
$462$			0.0262577i			0.00122162i
$463$	15.9580			0.741632			0.370816	−	0.928706i	$-0.379078\pi$
$463$	15.9580			0.741632			0.370816	+	0.928706i	$0.379078\pi$
$464$			11.1539i			0.517806i
$465$	4.12245	+	0.124063i	0.191174	+	0.00575328i
$466$	−9.28587	+	9.28587i	−0.430160	+	0.430160i
$467$	−18.6259	−	18.6259i	−0.861902	−	0.861902i	0.129657	−	0.991559i	$-0.458612\pi$
$467$	−18.6259	−	18.6259i	−0.861902	−	0.861902i	−0.991559	+	0.129657i	$0.958612\pi$
$468$		0			0
$469$			2.68150i			0.123820i
$470$	32.3721	+	0.974219i	1.49321	+	0.0449374i
$471$	−0.641475			−0.0295576
$472$	6.35046	+	6.35046i	0.292304	+	0.292304i
$473$			1.08889i			0.0500671i
$474$	−2.46295	+	2.46295i	−0.113127	+	0.113127i
$475$	−17.0707	+	15.1308i	−0.783258	+	0.694248i
$476$	0.623222	−	0.623222i	0.0285653	−	0.0285653i
$477$	−10.9841	+	10.9841i	−0.502929	+	0.502929i
$478$	21.8822	−	21.8822i	1.00087	−	1.00087i
$479$	−11.7379	−	11.7379i	−0.536320	−	0.536320i	0.386126	−	0.922446i	$-0.373813\pi$
$479$	−11.7379	−	11.7379i	−0.536320	−	0.536320i	−0.922446	+	0.386126i	$0.873813\pi$
$480$	0.908170	−	0.855105i	0.0414521	−	0.0390300i
$481$		0			0
$482$	19.1990	−	19.1990i	0.874490	−	0.874490i
$483$		−	0.382910i		−	0.0174230i
$484$			5.61335i			0.255152i
$485$	−0.509246	+	16.9216i	−0.0231237	+	0.768371i
$486$	5.86681	+	5.86681i	0.266124	+	0.266124i
$487$	26.2798			1.19085			0.595425	−	0.803411i	$-0.296984\pi$
$487$	26.2798			1.19085			0.595425	+	0.803411i	$0.296984\pi$
$488$	−18.5179			−0.838264
$489$	1.51637	+	1.51637i	0.0685724	+	0.0685724i
$490$	0.714107	−	23.7289i	0.0322601	−	1.07196i
$491$		−	41.6040i		−	1.87756i	−0.344513	−	0.938781i	$-0.611956\pi$
$491$		−	41.6040i		−	1.87756i	0.344513	−	0.938781i	$-0.388044\pi$
$492$		−	0.361038i		−	0.0162768i
$493$	−5.20655	+	5.20655i	−0.234491	+	0.234491i
$494$		0			0
$495$	0.738254	−	0.695118i	0.0331821	−	0.0312432i
$496$	31.4719	+	31.4719i	1.41313	+	1.41313i
$497$	−6.06302	+	6.06302i	−0.271964	+	0.271964i
$498$	2.96832	−	2.96832i	0.133014	−	0.133014i
$499$	8.31651	−	8.31651i	0.372298	−	0.372298i	−0.496015	−	0.868314i	$-0.665204\pi$
$499$	8.31651	−	8.31651i	0.372298	−	0.372298i	0.868314	+	0.496015i	$0.165204\pi$
$500$	−0.515344	+	5.69429i	−0.0230469	+	0.254657i
$501$	2.28238	−	2.28238i	0.101969	−	0.101969i
$502$		−	15.7730i		−	0.703982i
$503$	7.54802	+	7.54802i	0.336550	+	0.336550i	0.855067	−	0.518517i	$-0.173516\pi$
$503$	7.54802	+	7.54802i	0.336550	+	0.336550i	−0.518517	+	0.855067i	$0.673516\pi$
$504$	−3.83024			−0.170612
$505$	30.2519	+	0.910411i	1.34619	+	0.0405128i
$506$			0.858953i			0.0381851i
$507$		0			0
$508$	0.879556	+	0.879556i	0.0390240	+	0.0390240i
$509$	2.13171	−	2.13171i	0.0944864	−	0.0944864i	−0.658284	−	0.752770i	$-0.728717\pi$
$509$	2.13171	−	2.13171i	0.0944864	−	0.0944864i	0.752770	+	0.658284i	$0.228717\pi$
$510$	2.19664	+	0.0661064i	0.0972687	+	0.00292724i
$511$			2.14839i			0.0950390i
$512$	−9.00279			−0.397871
$513$			5.36603i			0.236916i
$514$	−3.08312	−	3.08312i	−0.135991	−	0.135991i
$515$	−22.4509	−	23.8441i	−0.989304	−	1.05070i
$516$	−0.717437			−0.0315834
$517$	−0.989731	−	0.989731i	−0.0435283	−	0.0435283i
$518$	−5.91442			−0.259864
$519$	1.34838			0.0591871
$520$		0			0
$521$	−5.84796			−0.256204			−0.128102	−	0.991761i	$-0.540888\pi$
$521$	−5.84796			−0.256204			−0.128102	+	0.991761i	$0.540888\pi$
$522$	−10.9928			−0.481143
$523$	2.09684	+	2.09684i	0.0916884	+	0.0916884i	0.751463	−	0.659775i	$-0.229348\pi$
$523$	2.09684	+	2.09684i	0.0916884	+	0.0916884i	−0.659775	+	0.751463i	$0.729348\pi$
$524$	3.37881			0.147604
$525$	−0.404823	+	0.358819i	−0.0176679	+	0.0156601i
$526$	−6.92220	−	6.92220i	−0.301822	−	0.301822i
$527$			29.3817i			1.27989i
$528$	−0.143873			−0.00626129
$529$			10.4741i			0.455395i
$530$	−13.5344	+	12.7436i	−0.587899	+	0.553548i
$531$	−7.97107	+	7.97107i	−0.345915	+	0.345915i
$532$	0.904605	+	0.904605i	0.0392196	+	0.0392196i
$533$		0			0
$534$			2.84359i			0.123054i
$535$	−24.6423	−	26.1715i	−1.06538	−	1.13149i
$536$	−11.5365			−0.498301
$537$	−0.791625	−	0.791625i	−0.0341611	−	0.0341611i
$538$		−	33.6329i		−	1.45002i
$539$	−0.725477	+	0.725477i	−0.0312485	+	0.0312485i
$540$	0.922007	+	0.979224i	0.0396769	+	0.0421391i
$541$	−15.4678	+	15.4678i	−0.665013	+	0.665013i	−0.956557	−	0.291544i	$-0.905831\pi$
$541$	−15.4678	+	15.4678i	−0.665013	+	0.665013i	0.291544	+	0.956557i	$0.405831\pi$
$542$	14.4385	−	14.4385i	0.620185	−	0.620185i
$543$	0.501037	−	0.501037i	0.0215015	−	0.0215015i
$544$	6.28364	+	6.28364i	0.269409	+	0.269409i
$545$	17.7937	+	18.8979i	0.762198	+	0.809497i
$546$		0			0
$547$	1.76989	−	1.76989i	0.0756751	−	0.0756751i	−0.668256	−	0.743931i	$-0.732959\pi$
$547$	1.76989	−	1.76989i	0.0756751	−	0.0756751i	0.743931	+	0.668256i	$0.232959\pi$
$548$		−	2.07396i		−	0.0885951i
$549$		−	23.2435i		−	0.992010i
$550$	0.908110	−	0.804912i	0.0387219	−	0.0343216i
$551$	−7.55729	−	7.55729i	−0.321952	−	0.321952i
$552$	1.64738			0.0701170
$553$	6.10804			0.259740
$554$	23.8419	+	23.8419i	1.01295	+	1.01295i
$555$	−2.05858	−	2.18633i	−0.0873819	−	0.0928045i
$556$		−	6.55772i		−	0.278109i
$557$			9.43469i			0.399761i	0.979820	+	0.199880i	$0.0640553\pi$
$557$			9.43469i			0.399761i	−0.979820	+	0.199880i	$0.935945\pi$
$558$	−31.0175	+	31.0175i	−1.31308	+	1.31308i
$559$		0			0
$560$	−5.83514	−	0.175605i	−0.246580	−	0.00742067i
$561$	−0.0671590	−	0.0671590i	−0.00283546	−	0.00283546i
$562$	−6.69798	+	6.69798i	−0.282537	+	0.282537i
$563$	−6.92420	+	6.92420i	−0.291820	+	0.291820i	−0.837799	−	0.545979i	$-0.816158\pi$
$563$	−6.92420	+	6.92420i	−0.291820	+	0.291820i	0.545979	+	0.837799i	$0.316158\pi$
$564$	0.652105	−	0.652105i	0.0274586	−	0.0274586i
$565$	7.42002	−	6.98646i	0.312163	−	0.293923i
$566$	1.72336	−	1.72336i	0.0724384	−	0.0724384i
$567$		−	4.74366i		−	0.199215i
$568$	−26.0847	−	26.0847i	−1.09449	−	1.09449i
$569$	−6.41861			−0.269082			−0.134541	−	0.990908i	$-0.542956\pi$
$569$	−6.41861			−0.269082			−0.134541	+	0.990908i	$0.542956\pi$
$570$	−0.0959534	+	3.18841i	−0.00401905	+	0.133548i
$571$		−	1.72174i		−	0.0720527i	−0.999351	−	0.0360264i	$-0.988530\pi$
$571$		−	1.72174i		−	0.0720527i	0.999351	−	0.0360264i	$-0.0114700\pi$
$572$		0			0
$573$	3.27622	+	3.27622i	0.136866	+	0.136866i
$574$	−2.19851	+	2.19851i	−0.0917639	+	0.0917639i
$575$	−13.2428	+	11.7378i	−0.552261	+	0.489502i
$576$		−	14.9299i		−	0.622079i
$577$	24.8642			1.03511			0.517554	−	0.855650i	$-0.326843\pi$
$577$	24.8642			1.03511			0.517554	+	0.855650i	$0.326843\pi$
$578$		−	11.2846i		−	0.469377i
$579$	−2.20969	−	2.20969i	−0.0918316	−	0.0918316i
$580$	−2.67762	−	0.0805813i	−0.111182	−	0.00334596i
$581$	−7.36135			−0.305400
$582$	1.67397	+	1.67397i	0.0693882	+	0.0693882i
$583$	0.803414			0.0332740
$584$	−9.24291			−0.382474
$585$		0			0
$586$	4.42437			0.182769
$587$	−26.7672			−1.10480			−0.552400	−	0.833579i	$-0.686288\pi$
$587$	−26.7672			−1.10480			−0.552400	+	0.833579i	$0.686288\pi$
$588$	−0.477996	−	0.477996i	−0.0197122	−	0.0197122i
$589$	−42.6475			−1.75726
$590$	−9.82180	+	9.24791i	−0.404357	+	0.380731i
$591$	−0.797046	−	0.797046i	−0.0327861	−	0.0327861i
$592$		−	32.4068i		−	1.33191i
$593$	−19.8452			−0.814944			−0.407472	−	0.913218i	$-0.633590\pi$
$593$	−19.8452			−0.814944			−0.407472	+	0.913218i	$0.633590\pi$
$594$		−	0.285456i		−	0.0117124i
$595$	−2.64183	−	2.80577i	−0.108304	−	0.115025i
$596$	1.53858	−	1.53858i	0.0630229	−	0.0630229i
$597$	1.29797	+	1.29797i	0.0531224	+	0.0531224i
$598$		0			0
$599$			36.5285i			1.49252i	0.665657	+	0.746258i	$0.268151\pi$
$599$			36.5285i			1.49252i	−0.665657	+	0.746258i	$0.731849\pi$
$600$	−1.54373	−	1.74166i	−0.0630226	−	0.0711028i
$601$	29.8955			1.21946			0.609732	−	0.792608i	$-0.291277\pi$
$601$	29.8955			1.21946			0.609732	+	0.792608i	$0.291277\pi$
$602$	4.36877	+	4.36877i	0.178058	+	0.178058i
$603$		−	14.4806i		−	0.589695i
$604$	2.50292	−	2.50292i	0.101842	−	0.101842i
$605$	24.5332	+	0.738312i	0.997416	+	0.0300166i
$606$	2.99266	−	2.99266i	0.121568	−	0.121568i
$607$	12.6350	−	12.6350i	0.512841	−	0.512841i	−0.402555	−	0.915396i	$-0.631878\pi$
$607$	12.6350	−	12.6350i	0.512841	−	0.512841i	0.915396	+	0.402555i	$0.131878\pi$
$608$	−9.12070	+	9.12070i	−0.369893	+	0.369893i
$609$	−0.179217	−	0.179217i	−0.00726226	−	0.00726226i
$610$	0.836730	−	27.8035i	0.0338782	−	1.12573i
$611$		0			0
$612$	−3.36551	+	3.36551i	−0.136043	+	0.136043i
$613$			15.3746i			0.620973i	0.950578	+	0.310487i	$0.100492\pi$
$613$			15.3746i			0.620973i	−0.950578	+	0.310487i	$0.899508\pi$
$614$		−	3.36141i		−	0.135656i
$615$	−1.57792	−	0.0474865i	−0.0636278	−	0.00191484i
$616$	0.140078	+	0.140078i	0.00564390	+	0.00564390i
$617$	1.24370			0.0500694			0.0250347	−	0.999687i	$-0.492030\pi$
$617$	1.24370			0.0500694			0.0250347	+	0.999687i	$0.492030\pi$
$618$	−4.57972			−0.184223
$619$	−28.7865	−	28.7865i	−1.15703	−	1.15703i	−0.985112	−	0.171915i	$-0.945005\pi$
$619$	−28.7865	−	28.7865i	−1.15703	−	1.15703i	−0.171915	−	0.985112i	$-0.554995\pi$
$620$	−7.78257	+	7.32783i	−0.312555	+	0.294293i
$621$			4.16275i			0.167045i
$622$		−	33.7004i		−	1.35126i
$623$	3.52601	−	3.52601i	0.141266	−	0.141266i
$624$		0			0
$625$	24.8192	+	3.00128i	0.992768	+	0.120051i
$626$	−22.7674	−	22.7674i	−0.909966	−	0.909966i
$627$	0.0974812	−	0.0974812i	0.00389302	−	0.00389302i
$628$	1.17563	−	1.17563i	0.0469127	−	0.0469127i
$629$	15.1272	−	15.1272i	0.603163	−	0.603163i
$630$	0.173069	−	5.75089i	0.00689525	−	0.229121i
$631$	−14.6542	+	14.6542i	−0.583374	+	0.583374i	−0.935829	−	0.352455i	$-0.885347\pi$
$631$	−14.6542	+	14.6542i	−0.583374	+	0.583374i	0.352455	+	0.935829i	$0.385347\pi$
$632$			26.2784i			1.04530i
$633$	0.763953	+	0.763953i	0.0303644	+	0.0303644i
$634$	13.9297			0.553218
$635$	3.95979	−	3.72842i	0.157140	−	0.147958i
$636$			0.529346i			0.0209899i
$637$		0			0
$638$	0.402025	+	0.402025i	0.0159163	+	0.0159163i
$639$	32.7414	−	32.7414i	1.29523	−	1.29523i
$640$	0.917791	−	30.4971i	0.0362789	−	1.20550i
$641$			17.6751i			0.698123i	0.937100	+	0.349061i	$0.113500\pi$
$641$			17.6751i			0.698123i	−0.937100	+	0.349061i	$0.886500\pi$
$642$	−5.02675			−0.198390
$643$		−	2.66903i		−	0.105256i	−0.998614	−	0.0526282i	$-0.983240\pi$
$643$		−	2.66903i		−	0.105256i	0.998614	−	0.0526282i	$-0.0167598\pi$
$644$	0.701756	+	0.701756i	0.0276531	+	0.0276531i
$645$	−0.0943630	+	3.13556i	−0.00371554	+	0.123463i
$646$	−22.7246			−0.894087
$647$	29.8183	+	29.8183i	1.17228	+	1.17228i	0.981665	+	0.190615i	$0.0610481\pi$
$647$	29.8183	+	29.8183i	1.17228	+	1.17228i	0.190615	+	0.981665i	$0.438952\pi$
$648$	20.4084			0.801719
$649$	0.583029			0.0228859
$650$		0			0
$651$	−1.01136			−0.0396385
$652$	−5.55807			−0.217671
$653$	17.8654	+	17.8654i	0.699125	+	0.699125i	0.964222	−	0.265096i	$-0.0854038\pi$
$653$	17.8654	+	17.8654i	0.699125	+	0.699125i	−0.265096	+	0.964222i	$0.585404\pi$
$654$	3.62971			0.141933
$655$	0.444408	−	14.7671i	0.0173644	−	0.576999i
$656$	−12.0463	−	12.0463i	−0.470328	−	0.470328i
$657$		−	11.6017i		−	0.452624i
$658$	−7.94187			−0.309606
$659$		−	37.8224i		−	1.47335i	−0.676247	−	0.736675i	$-0.736395\pi$
$659$		−	37.8224i		−	1.47335i	0.676247	−	0.736675i	$-0.263605\pi$
$660$	0.00103941	−	0.0345385i	4.04591e−5	−	0.00134441i
$661$	12.1671	−	12.1671i	0.473244	−	0.473244i	−0.429719	−	0.902963i	$-0.641387\pi$
$661$	12.1671	−	12.1671i	0.473244	−	0.473244i	0.902963	+	0.429719i	$0.141387\pi$
$662$	−20.3625	−	20.3625i	−0.791409	−	0.791409i
$663$		0			0
$664$		−	31.6705i		−	1.22905i
$665$	4.07257	−	3.83461i	0.157927	−	0.148700i
$666$	31.9389			1.23761
$667$	−5.86264	−	5.86264i	−0.227002	−	0.227002i
$668$			8.36582i			0.323683i
$669$	−2.59063	+	2.59063i	−0.100159	+	0.100159i
$670$	0.521278	−	17.3214i	0.0201387	−	0.669184i
$671$	−0.850052	+	0.850052i	−0.0328159	+	0.0328159i
$672$	−0.216293	+	0.216293i	−0.00834368	+	0.00834368i
$673$	−22.2477	+	22.2477i	−0.857585	+	0.857585i	−0.991053	−	0.133468i	$-0.957389\pi$
$673$	−22.2477	+	22.2477i	−0.857585	+	0.857585i	0.133468	+	0.991053i	$0.457389\pi$
$674$	27.3402	+	27.3402i	1.05311	+	1.05311i
$675$	4.40098	−	3.90085i	0.169394	−	0.150144i
$676$		0			0
$677$	−28.8731	+	28.8731i	−1.10968	+	1.10968i	−0.116494	+	0.993191i	$0.537165\pi$
$677$	−28.8731	+	28.8731i	−1.10968	+	1.10968i	−0.993191	+	0.116494i	$0.962835\pi$
$678$		−	1.42516i		−	0.0547329i
$679$		−	4.15139i		−	0.159316i
$680$	12.0711	−	11.3658i	0.462907	−	0.435859i
$681$	−0.891066	−	0.891066i	−0.0341457	−	0.0341457i
$682$	2.26872			0.0868738
$683$	−31.7791			−1.21600			−0.607998	−	0.793939i	$-0.708027\pi$
$683$	−31.7791			−1.21600			−0.607998	+	0.793939i	$0.708027\pi$
$684$	−4.88503	−	4.88503i	−0.186784	−	0.186784i
$685$	−9.06426	−	0.272783i	−0.346327	−	0.0104225i
$686$			11.9041i			0.454501i
$687$			3.10149i			0.118329i
$688$	−23.9378	+	23.9378i	−0.912619	+	0.912619i
$689$		0			0
$690$	−0.0744368	+	2.47344i	−0.00283376	+	0.0941623i
$691$	−18.9805	−	18.9805i	−0.722052	−	0.722052i	0.246971	−	0.969023i	$-0.420565\pi$
$691$	−18.9805	−	18.9805i	−0.722052	−	0.722052i	−0.969023	+	0.246971i	$0.920565\pi$
$692$	−2.47116	+	2.47116i	−0.0939395	+	0.0939395i
$693$	−0.175825	+	0.175825i	−0.00667904	+	0.00667904i
$694$	−8.70863	+	8.70863i	−0.330575	+	0.330575i
$695$	−28.6606	−	0.862523i	−1.08716	−	0.0327174i
$696$	0.771040	−	0.771040i	0.0292262	−	0.0292262i
$697$		−	11.2462i		−	0.425980i
$698$	−5.68217	−	5.68217i	−0.215073	−	0.215073i
$699$	1.63505			0.0618433
$700$	0.0843120	−	1.39952i	0.00318669	−	0.0528970i
$701$			39.3253i			1.48530i	0.669681	+	0.742649i	$0.266431\pi$
$701$			39.3253i			1.48530i	−0.669681	+	0.742649i	$0.733569\pi$
$702$		0			0
$703$	21.9572	+	21.9572i	0.828131	+	0.828131i
$704$	−0.546010	+	0.546010i	−0.0205785	+	0.0205785i
$705$	−2.76426	−	2.93580i	−0.104108	−	0.110569i
$706$			40.5975i			1.52791i
$707$	−7.42171			−0.279122
$708$			0.384141i			0.0144369i
$709$	26.5229	+	26.5229i	0.996087	+	0.996087i	0.999992	−	0.00390546i	$-0.00124315\pi$
$709$	26.5229	+	26.5229i	0.996087	+	0.996087i	−0.00390546	+	0.999992i	$0.501243\pi$
$710$	40.3433	−	37.9861i	1.51406	−	1.42559i
$711$	−32.9845			−1.23702
$712$	15.1698	+	15.1698i	0.568512	+	0.568512i
$713$	−33.0842			−1.23901
$714$	−0.538902			−0.0201679
$715$		0			0
$716$	2.90161			0.108438
$717$	−3.85300			−0.143893
$718$	15.9176	+	15.9176i	0.594038	+	0.594038i
$719$	29.1155			1.08583			0.542913	−	0.839789i	$-0.317321\pi$
$719$	29.1155			1.08583			0.542913	+	0.839789i	$0.317321\pi$
$720$	31.5108	+	0.948298i	1.17434	+	0.0353410i
$721$	5.67879	+	5.67879i	0.211489	+	0.211489i
$722$		−	2.87468i		−	0.106985i
$723$	−3.38055			−0.125724
$724$			1.83649i			0.0682528i
$725$	−0.704363	+	11.6920i	−0.0261594	+	0.434228i
$726$	2.42694	−	2.42694i	0.0900723	−	0.0900723i
$727$	15.6053	+	15.6053i	0.578768	+	0.578768i	0.934564	−	0.355796i	$-0.115790\pi$
$727$	15.6053	+	15.6053i	0.578768	+	0.578768i	−0.355796	+	0.934564i	$0.615790\pi$
$728$		0			0
$729$			24.9204i			0.922977i
$730$	0.417641	−	13.8777i	0.0154576	−	0.513637i
$731$	−22.3479			−0.826568
$732$	−0.560075	−	0.560075i	−0.0207010	−	0.0207010i
$733$			34.8651i			1.28777i	0.765121	+	0.643886i	$0.222679\pi$
$733$			34.8651i			1.28777i	−0.765121	+	0.643886i	$0.777321\pi$
$734$	−22.5486	+	22.5486i	−0.832283	+	0.832283i
$735$	−2.15196	+	2.02622i	−0.0793761	+	0.0747381i
$736$	−7.07547	+	7.07547i	−0.260805	+	0.260805i
$737$	−0.529577	+	0.529577i	−0.0195072	+	0.0195072i
$738$	11.8723	−	11.8723i	0.437026	−	0.437026i
$739$	24.1959	+	24.1959i	0.890060	+	0.890060i	0.994528	−	0.104468i	$-0.0333140\pi$
$739$	24.1959	+	24.1959i	0.890060	+	0.890060i	−0.104468	+	0.994528i	$0.533314\pi$
$740$	7.77962	+	0.234123i	0.285985	+	0.00860654i
$741$		0			0
$742$	3.22341	−	3.22341i	0.118335	−	0.118335i
$743$		−	3.12911i		−	0.114796i	−0.998351	−	0.0573980i	$-0.981720\pi$
$743$		−	3.12911i		−	0.114796i	0.998351	−	0.0573980i	$-0.0182804\pi$
$744$		−	4.35115i		−	0.159521i
$745$	−6.52203	−	6.92677i	−0.238949	−	0.253777i
$746$	29.3652	+	29.3652i	1.07514	+	1.07514i
$747$	39.7526			1.45447
$748$	0.246164			0.00900064
$749$	6.23310	+	6.23310i	0.227753	+	0.227753i
$750$	2.68475	−	2.23913i	0.0980332	−	0.0817614i
$751$			7.25382i			0.264696i	0.991203	+	0.132348i	$0.0422516\pi$
$751$			7.25382i			0.264696i	−0.991203	+	0.132348i	$0.957748\pi$
$752$		−	43.5158i		−	1.58686i
$753$	−1.38865	+	1.38865i	−0.0506051	+	0.0506051i
$754$		0			0
$755$	−10.6098	−	11.2682i	−0.386131	−	0.410093i
$756$	−0.233215	−	0.233215i	−0.00848196	−	0.00848196i
$757$	11.6968	−	11.6968i	0.425129	−	0.425129i	−0.461836	−	0.886965i	$-0.652809\pi$
$757$	11.6968	−	11.6968i	0.425129	−	0.425129i	0.886965	+	0.461836i	$0.152809\pi$
$758$	−25.2471	+	25.2471i	−0.917016	+	0.917016i
$759$	0.0756220	−	0.0756220i	0.00274490	−	0.00274490i
$760$	16.4975	+	17.5212i	0.598426	+	0.635563i
$761$	−16.3741	+	16.3741i	−0.593559	+	0.593559i	−0.938591	−	0.345032i	$-0.887868\pi$
$761$	−16.3741	+	16.3741i	−0.593559	+	0.593559i	0.345032	+	0.938591i	$0.387868\pi$
$762$		−	0.760555i		−	0.0275520i
$763$	−4.50079	−	4.50079i	−0.162939	−	0.162939i
$764$	−12.0086			−0.434457
$765$	14.2663	+	15.1516i	0.515800	+	0.547809i
$766$			38.2335i			1.38143i
$767$		0			0
$768$	−1.60998	−	1.60998i	−0.0580951	−	0.0580951i
$769$	−4.16667	+	4.16667i	−0.150254	+	0.150254i	−0.778231	−	0.627978i	$-0.783883\pi$
$769$	−4.16667	+	4.16667i	−0.150254	+	0.150254i	0.627978	+	0.778231i	$0.283883\pi$
$770$	−0.216648	+	0.203990i	−0.00780746	+	0.00735127i
$771$			0.542874i			0.0195511i
$772$	8.09938			0.291503
$773$		−	8.08997i		−	0.290976i	−0.989360	−	0.145488i	$-0.953525\pi$
$773$		−	8.08997i		−	0.290976i	0.989360	−	0.145488i	$-0.0464752\pi$
$774$	−23.5921	−	23.5921i	−0.848001	−	0.848001i
$775$	31.0027	+	34.9776i	1.11365	+	1.25643i
$776$	17.8604			0.641150
$777$	0.520704	+	0.520704i	0.0186801	+	0.0186801i
$778$	−22.7032			−0.813950
$779$	16.3238			0.584863
$780$		0			0
$781$	−2.39481			−0.0856930
$782$	−17.6288			−0.630405
$783$	1.94834	+	1.94834i	0.0696279	+	0.0696279i
$784$	−31.8973			−1.13919
$785$	−4.98347	−	5.29272i	−0.177868	−	0.188905i
$786$	−1.46083	−	1.46083i	−0.0521063	−	0.0521063i
$787$			16.2116i			0.577882i	0.957347	+	0.288941i	$0.0933032\pi$
$787$			16.2116i			0.577882i	−0.957347	+	0.288941i	$0.906697\pi$
$788$	2.92148			0.104073
$789$			1.21886i			0.0433925i
$790$	−39.4555	−	1.18739i	−1.40376	−	0.0422454i
$791$	−1.76718	+	1.76718i	−0.0628336	+	0.0628336i
$792$	−0.756445	−	0.756445i	−0.0268791	−	0.0268791i
$793$		0			0
$794$		−	53.0777i		−	1.88366i
$795$	2.31351	+	0.0696238i	0.0820519	+	0.00246930i
$796$	−4.75757			−0.168627
$797$	11.7874	+	11.7874i	0.417531	+	0.417531i	0.884352	−	0.466821i	$-0.154601\pi$
$797$	11.7874	+	11.7874i	0.417531	+	0.417531i	−0.466821	+	0.884352i	$0.654601\pi$
$798$		−	0.782216i		−	0.0276901i
$799$	20.3129	−	20.3129i	0.718617	−	0.718617i
$800$	14.1107	+	0.850077i	0.498889	+	0.0300548i
$801$	−19.0411	+	19.0411i	−0.672783	+	0.672783i
$802$	−20.7856	+	20.7856i	−0.733967	+	0.733967i
$803$	−0.424291	+	0.424291i	−0.0149729	+	0.0149729i
$804$	−0.348923	−	0.348923i	−0.0123056	−	0.0123056i
$805$	3.15933	−	2.97473i	0.111352	−	0.104846i
$806$		0			0
$807$	−2.96103	+	2.96103i	−0.104233	+	0.104233i
$808$		−	31.9301i		−	1.12330i
$809$			24.1266i			0.848247i	0.905604	+	0.424123i	$0.139418\pi$
$809$			24.1266i			0.848247i	−0.905604	+	0.424123i	$0.860582\pi$
$810$	−0.922156	+	30.6421i	−0.0324013	+	1.07665i
$811$	17.7808	+	17.7808i	0.624369	+	0.624369i	0.946646	−	0.322276i	$-0.104448\pi$
$811$	17.7808	+	17.7808i	0.624369	+	0.624369i	−0.322276	+	0.946646i	$0.604448\pi$
$812$	0.656902			0.0230527
$813$	−2.54232			−0.0891629
$814$	−1.16806	−	1.16806i	−0.0409403	−	0.0409403i
$815$	−0.731041	+	24.2916i	−0.0256073	+	0.850898i
$816$		−	2.95280i		−	0.103369i
$817$		−	32.4380i		−	1.13486i
$818$	5.79615	−	5.79615i	0.202658	−	0.202658i
$819$		0			0
$820$	2.97887	−	2.80481i	0.104027	−	0.0979484i
$821$	28.0206	+	28.0206i	0.977925	+	0.977925i	0.999762	−	0.0218363i	$-0.00695127\pi$
$821$	28.0206	+	28.0206i	0.977925	+	0.977925i	−0.0218363	+	0.999762i	$0.506951\pi$
$822$	−0.896680	+	0.896680i	−0.0312753	+	0.0312753i
$823$	28.2448	−	28.2448i	0.984551	−	0.984551i	−0.0153317	−	0.999882i	$-0.504880\pi$
$823$	28.2448	−	28.2448i	0.984551	−	0.984551i	0.999882	+	0.0153317i	$0.00488041\pi$
$824$	−24.4316	+	24.4316i	−0.851116	+	0.851116i
$825$	−0.150814	−	0.00908554i	−0.00525067	−	0.000316318i
$826$	2.33919	−	2.33919i	0.0813910	−	0.0813910i
$827$		−	25.6019i		−	0.890264i	−0.895465	−	0.445132i	$-0.853157\pi$
$827$		−	25.6019i		−	0.890264i	0.895465	−	0.445132i	$-0.146843\pi$
$828$	−3.78961	−	3.78961i	−0.131698	−	0.131698i
$829$	−18.8337			−0.654121			−0.327060	−	0.945003i	$-0.606058\pi$
$829$	−18.8337			−0.654121			−0.327060	+	0.945003i	$0.606058\pi$
$830$	47.5514	+	1.43103i	1.65053	+	0.0496718i
$831$		−	4.19807i		−	0.145629i
$832$		0			0
$833$	−14.8894	−	14.8894i	−0.515888	−	0.515888i
$834$	−2.83524	+	2.83524i	−0.0981764	+	0.0981764i
$835$	36.5629	+	1.10034i	1.26531	+	0.0380788i
$836$			0.357306i			0.0123577i
$837$	10.9949			0.380040
$838$			1.59576i			0.0551246i
$839$	17.6320	+	17.6320i	0.608723	+	0.608723i	0.942612	−	0.333890i	$-0.108361\pi$
$839$	17.6320	+	17.6320i	0.608723	+	0.608723i	−0.333890	+	0.942612i	$0.608361\pi$
$840$	0.391229	+	0.415508i	0.0134987	+	0.0143364i
$841$	23.5121			0.810761
$842$	0.467095	+	0.467095i	0.0160971	+	0.0160971i
$843$	1.17938			0.0406199
$844$	−2.80018			−0.0963863
$845$		0			0
$846$	42.8875			1.47450
$847$	−6.01875			−0.206807
$848$	17.6620	+	17.6620i	0.606515	+	0.606515i
$849$	−0.303449			−0.0104143
$850$	16.5197	+	18.6377i	0.566621	+	0.639268i
$851$	17.0335	+	17.0335i	0.583901	+	0.583901i
$852$		−	1.57787i		−	0.0540569i
$853$	2.14143			0.0733210			0.0366605	−	0.999328i	$-0.488328\pi$
$853$	2.14143			0.0733210			0.0366605	+	0.999328i	$0.488328\pi$
$854$			6.82105i			0.233412i
$855$	−21.9926	+	20.7076i	−0.752131	+	0.708184i
$856$	−26.8164	+	26.8164i	−0.916566	+	0.916566i
$857$	−36.4384	−	36.4384i	−1.24471	−	1.24471i	−0.958025	−	0.286686i	$-0.907446\pi$
$857$	−36.4384	−	36.4384i	−1.24471	−	1.24471i	−0.286686	−	0.958025i	$-0.592554\pi$
$858$		0			0
$859$		−	4.40721i		−	0.150372i	−0.997170	−	0.0751861i	$-0.976045\pi$
$859$		−	4.40721i		−	0.150372i	0.997170	−	0.0751861i	$-0.0239551\pi$
$860$	−5.57359	−	5.91947i	−0.190058	−	0.201852i
$861$	0.387112			0.0131927
$862$	−4.65208	−	4.65208i	−0.158451	−	0.158451i
$863$			53.8912i			1.83448i	0.398338	+	0.917239i	$0.369587\pi$
$863$			53.8912i			1.83448i	−0.398338	+	0.917239i	$0.630413\pi$
$864$	2.35140	−	2.35140i	0.0799961	−	0.0799961i
$865$	10.4752	+	11.1253i	0.356168	+	0.378270i
$866$	16.8033	−	16.8033i	0.570998	−	0.570998i
$867$	−0.993493	+	0.993493i	−0.0337408	+	0.0337408i
$868$	1.85352	−	1.85352i	0.0629126	−	0.0629126i
$869$	1.20630	+	1.20630i	0.0409208	+	0.0409208i
$870$	1.12283	+	1.19251i	0.0380676	+	0.0404300i
$871$		0			0
$872$	19.3636	−	19.3636i	0.655733	−	0.655733i
$873$			22.4183i			0.758743i
$874$		−	25.5882i		−	0.865534i
$875$	−6.10554	−	0.552563i	−0.206405	−	0.0186800i
$876$	−0.279553	−	0.279553i	−0.00944522	−	0.00944522i
$877$	−13.1339			−0.443501			−0.221750	−	0.975103i	$-0.571177\pi$
$877$	−13.1339			−0.443501			−0.221750	+	0.975103i	$0.571177\pi$
$878$	−21.9993			−0.742440
$879$	−0.389521	−	0.389521i	−0.0131382	−	0.0131382i
$880$	−1.11772	−	1.18708i	−0.0376783	−	0.0400165i
$881$			36.6097i			1.23341i	0.787193	+	0.616706i	$0.211533\pi$
$881$			36.6097i			1.23341i	−0.787193	+	0.616706i	$0.788467\pi$
$882$		−	31.4368i		−	1.05853i
$883$	7.40474	−	7.40474i	0.249189	−	0.249189i	−0.571449	−	0.820638i	$-0.693618\pi$
$883$	7.40474	−	7.40474i	0.249189	−	0.249189i	0.820638	+	0.571449i	$0.193618\pi$
$884$		0			0
$885$	1.67889	+	0.0505253i	0.0564354	+	0.00169839i
$886$	15.9416	+	15.9416i	0.535568	+	0.535568i
$887$	−38.6062	+	38.6062i	−1.29627	+	1.29627i	−0.365429	+	0.930839i	$0.619078\pi$
$887$	−38.6062	+	38.6062i	−1.29627	+	1.29627i	−0.930839	+	0.365429i	$0.880922\pi$
$888$	−2.24020	+	2.24020i	−0.0751763	+	0.0751763i
$889$	−0.943078	+	0.943078i	−0.0316298	+	0.0316298i
$890$	−23.4620	+	22.0911i	−0.786449	+	0.740497i
$891$	0.936839	−	0.936839i	0.0313853	−	0.0313853i
$892$		−	9.49566i		−	0.317938i
$893$	29.4841	+	29.4841i	0.986647	+	0.986647i
$894$	−1.33042			−0.0444959
$895$	0.381643	−	12.6815i	0.0127569	−	0.423897i
$896$			7.48186i			0.249951i
$897$		0			0
$898$	7.45887	+	7.45887i	0.248906	+	0.248906i
$899$	−15.4848	+	15.4848i	−0.516446	+	0.516446i
$900$	−0.455300	+	7.55767i	−0.0151767	+	0.251922i
$901$			16.4890i			0.549327i
$902$	−0.868379			−0.0289139
$903$		−	0.769250i		−	0.0255990i
$904$	−7.60285	−	7.60285i	−0.252867	−	0.252867i
$905$	8.02642	+	0.241550i	0.266807	+	0.00802940i
$906$	−2.16429			−0.0719036
$907$	28.9752	+	28.9752i	0.962106	+	0.962106i	0.999308	−	0.0372014i	$-0.0118443\pi$
$907$	28.9752	+	28.9752i	0.962106	+	0.962106i	−0.0372014	+	0.999308i	$0.511844\pi$
$908$	3.26610			0.108389
$909$	40.0785			1.32932
$910$		0			0
$911$	24.2232			0.802551			0.401276	−	0.915957i	$-0.368567\pi$
$911$	24.2232			0.802551			0.401276	+	0.915957i	$0.368567\pi$
$912$	4.28599			0.141923
$913$	−1.45382	−	1.45382i	−0.0481143	−	0.0481143i
$914$	58.5698			1.93732
$915$	−2.52148	+	2.37415i	−0.0833575	+	0.0784869i
$916$	−5.68408	−	5.68408i	−0.187807	−	0.187807i
$917$			3.62283i			0.119636i
$918$	5.85860			0.193363
$919$			34.8809i			1.15061i	0.817938	+	0.575307i	$0.195117\pi$
$919$			34.8809i			1.15061i	−0.817938	+	0.575307i	$0.804883\pi$
$920$	12.7981	+	13.5923i	0.421940	+	0.448124i
$921$	−0.295938	+	0.295938i	−0.00975148	+	0.00975148i
$922$	−28.8290	−	28.8290i	−0.949432	−	0.949432i
$923$		0			0
$924$			0.00847334i			0.000278753i
$925$	2.04648	−	33.9701i	0.0672877	−	1.11693i
$926$	25.2893			0.831058
$927$	−30.6665	−	30.6665i	−1.00722	−	1.00722i
$928$			6.62322i			0.217418i
$929$	6.13631	−	6.13631i	0.201326	−	0.201326i	−0.599242	−	0.800568i	$-0.704531\pi$
$929$	6.13631	−	6.13631i	0.201326	−	0.201326i	0.800568	+	0.599242i	$0.204531\pi$
$930$	6.53301	+	0.196607i	0.214226	+	0.00644700i
$931$	21.6120	−	21.6120i	0.708304	−	0.708304i
$932$	−2.99655	+	2.99655i	−0.0981553	+	0.0981553i
$933$	−2.96697	+	2.96697i	−0.0971343	+	0.0971343i
$934$	−29.5171	−	29.5171i	−0.965829	−	0.965829i
$935$	0.0323774	−	1.07586i	0.00105885	−	0.0351844i
$936$		0			0
$937$	−25.8920	+	25.8920i	−0.845856	+	0.845856i	−0.989613	−	0.143757i	$-0.954082\pi$
$937$	−25.8920	+	25.8920i	−0.845856	+	0.845856i	0.143757	+	0.989613i	$0.454082\pi$
$938$			4.24947i			0.138750i
$939$			4.00886i			0.130824i
$940$	10.4465	+	0.314380i	0.340726	+	0.0102540i
$941$	−20.9205	−	20.9205i	−0.681989	−	0.681989i	0.278459	−	0.960448i	$-0.410176\pi$
$941$	−20.9205	−	20.9205i	−0.681989	−	0.681989i	−0.960448	+	0.278459i	$0.910176\pi$
$942$	−1.01657			−0.0331216
$943$	12.6634			0.412376
$944$	12.8171	+	12.8171i	0.417162	+	0.417162i
$945$	−1.04994	+	0.988595i	−0.0341547	+	0.0321590i
$946$			1.72560i			0.0561042i
$947$			27.6047i			0.897032i	0.893775	+	0.448516i	$0.148047\pi$
$947$			27.6047i			0.897032i	−0.893775	+	0.448516i	$0.851953\pi$
$948$	−0.794793	+	0.794793i	−0.0258137	+	0.0258137i
$949$		0			0
$950$	−27.0526	+	23.9783i	−0.877702	+	0.777960i
$951$	−1.22636	−	1.22636i	−0.0397676	−	0.0397676i
$952$	−2.87490	+	2.87490i	−0.0931762	+	0.0931762i
$953$	−20.4341	+	20.4341i	−0.661926	+	0.661926i	−0.955834	−	0.293908i	$-0.905044\pi$
$953$	−20.4341	+	20.4341i	−0.661926	+	0.661926i	0.293908	+	0.955834i	$0.405044\pi$
$954$	−17.4070	+	17.4070i	−0.563572	+	0.563572i
$955$	−1.57947	+	52.4838i	−0.0511104	+	1.69834i
$956$	7.06137	−	7.06137i	0.228381	−	0.228381i
$957$		−	0.0707884i		−	0.00228826i
$958$	−18.6015	−	18.6015i	−0.600989	−	0.600989i
$959$	2.22374			0.0718083
$960$	−1.61961	+	1.52497i	−0.0522726	+	0.0492183i
$961$			56.3841i			1.81884i
$962$		0			0
$963$	−33.6599	−	33.6599i	−1.08467	−	1.08467i
$964$	6.19551	−	6.19551i	0.199544	−	0.199544i
$965$	1.06529	−	35.3984i	0.0342930	−	1.13952i
$966$		−	0.606811i		−	0.0195238i
$967$	4.31688			0.138822			0.0694108	−	0.997588i	$-0.477888\pi$
$967$	4.31688			0.138822			0.0694108	+	0.997588i	$0.477888\pi$
$968$		−	25.8942i		−	0.832272i
$969$	2.00067	+	2.00067i	0.0642707	+	0.0642707i
$970$	−0.807022	+	26.8163i	−0.0259119	+	0.861021i
$971$	−13.5586			−0.435116			−0.217558	−	0.976047i	$-0.569809\pi$
$971$	−13.5586			−0.435116			−0.217558	+	0.976047i	$0.569809\pi$
$972$	1.89322	+	1.89322i	0.0607250	+	0.0607250i
$973$	7.03132			0.225414
$974$	41.6466			1.33444
$975$		0			0
$976$	−37.3745			−1.19633
$977$	−47.6508			−1.52448			−0.762242	−	0.647292i	$-0.775902\pi$
$977$	−47.6508			−1.52448			−0.762242	+	0.647292i	$0.775902\pi$
$978$	2.40304	+	2.40304i	0.0768408	+	0.0768408i
$979$	1.39272			0.0445116
$980$	0.230442	−	7.65731i	0.00736121	−	0.244604i
$981$	24.3051	+	24.3051i	0.776001	+	0.776001i
$982$		−	65.9315i		−	2.10396i
$983$	7.39039			0.235717			0.117858	−	0.993030i	$-0.462397\pi$
$983$	7.39039			0.235717			0.117858	+	0.993030i	$0.462397\pi$
$984$			1.66546i			0.0530928i
$985$	0.384256	−	12.7684i	0.0122434	−	0.406834i
$986$	−8.25101	+	8.25101i	−0.262766	+	0.262766i
$987$	0.699200	+	0.699200i	0.0222558	+	0.0222558i
$988$		0			0
$989$		−	25.1641i		−	0.800171i
$990$	1.16994	−	1.10158i	0.0371831	−	0.0350105i
$991$	20.0105			0.635654			0.317827	−	0.948149i	$-0.397047\pi$
$991$	20.0105			0.635654			0.317827	+	0.948149i	$0.397047\pi$
$992$	18.6882	+	18.6882i	0.593350	+	0.593350i
$993$			3.58541i			0.113780i
$994$	−9.60830	+	9.60830i	−0.304757	+	0.304757i
$995$	−0.625753	+	20.7930i	−0.0198377	+	0.659182i
$996$	0.957877	−	0.957877i	0.0303515	−	0.0303515i
$997$	23.9164	−	23.9164i	0.757441	−	0.757441i	−0.218415	−	0.975856i	$-0.570089\pi$
$997$	23.9164	−	23.9164i	0.757441	−	0.757441i	0.975856	+	0.218415i	$0.0700886\pi$
$998$	13.1795	−	13.1795i	0.417190	−	0.417190i
$999$	−5.66075	−	5.66075i	−0.179098	−	0.179098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.k.e.268.7		20
5.2	odd	4		845.2.f.e.437.7		20
13.2	odd	12		65.2.t.a.58.4	yes	20
13.3	even	3		845.2.o.e.488.2		20
13.4	even	6		845.2.o.g.258.4		20
13.5	odd	4		845.2.f.e.408.4		20
13.6	odd	12		845.2.t.f.418.2		20
13.7	odd	12		845.2.t.e.418.4		20
13.8	odd	4		845.2.f.d.408.7		20
13.9	even	3		65.2.o.a.63.2	yes	20
13.10	even	6		845.2.o.f.488.4		20
13.11	odd	12		845.2.t.g.188.2		20
13.12	even	2		845.2.k.d.268.4		20
39.2	even	12		585.2.dp.a.253.2		20
39.35	odd	6		585.2.cf.a.388.4		20
65.2	even	12		65.2.o.a.32.2	✓	20
65.7	even	12		845.2.o.f.587.4		20
65.9	even	6		325.2.s.b.193.4		20
65.12	odd	4		845.2.f.d.437.4		20
65.17	odd	12		845.2.t.g.427.2		20
65.22	odd	12		65.2.t.a.37.4	yes	20
65.28	even	12		325.2.s.b.32.4		20
65.32	even	12		845.2.o.e.587.2		20
65.37	even	12		845.2.o.g.357.4		20
65.42	odd	12		845.2.t.f.657.2		20
65.47	even	4		845.2.k.d.577.4		20
65.48	odd	12		325.2.x.b.232.2		20
65.54	odd	12		325.2.x.b.318.2		20
65.57	even	4	inner	845.2.k.e.577.7		20
65.62	odd	12		845.2.t.e.657.4		20
195.2	odd	12		585.2.cf.a.487.4		20
195.152	even	12		585.2.dp.a.37.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.2	✓	20	65.2	even	12
65.2.o.a.63.2	yes	20	13.9	even	3
65.2.t.a.37.4	yes	20	65.22	odd	12
65.2.t.a.58.4	yes	20	13.2	odd	12
325.2.s.b.32.4		20	65.28	even	12
325.2.s.b.193.4		20	65.9	even	6
325.2.x.b.232.2		20	65.48	odd	12
325.2.x.b.318.2		20	65.54	odd	12
585.2.cf.a.388.4		20	39.35	odd	6
585.2.cf.a.487.4		20	195.2	odd	12
585.2.dp.a.37.2		20	195.152	even	12
585.2.dp.a.253.2		20	39.2	even	12
845.2.f.d.408.7		20	13.8	odd	4
845.2.f.d.437.4		20	65.12	odd	4
845.2.f.e.408.4		20	13.5	odd	4
845.2.f.e.437.7		20	5.2	odd	4
845.2.k.d.268.4		20	13.12	even	2
845.2.k.d.577.4		20	65.47	even	4
845.2.k.e.268.7		20	1.1	even	1	trivial
845.2.k.e.577.7		20	65.57	even	4	inner
845.2.o.e.488.2		20	13.3	even	3
845.2.o.e.587.2		20	65.32	even	12
845.2.o.f.488.4		20	13.10	even	6
845.2.o.f.587.4		20	65.7	even	12
845.2.o.g.258.4		20	13.4	even	6
845.2.o.g.357.4		20	65.37	even	12
845.2.t.e.418.4		20	13.7	odd	12
845.2.t.e.657.4		20	65.62	odd	12
845.2.t.f.418.2		20	13.6	odd	12
845.2.t.f.657.2		20	65.42	odd	12
845.2.t.g.188.2		20	13.11	odd	12
845.2.t.g.427.2		20	65.17	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.58474 q^{2} +(-0.139520 - 0.139520i) q^{3} +0.511395 q^{4} +(0.0672627 - 2.23506i) q^{5} +(-0.221103 - 0.221103i) q^{6} +0.548328i q^{7} -2.35905 q^{8} -2.96107i q^{9} +(0.106594 - 3.54198i) q^{10} +(-0.108291 + 0.108291i) q^{11} +(-0.0713497 - 0.0713497i) q^{12} +0.868956i q^{14} +(-0.321219 + 0.302450i) q^{15} -4.76126 q^{16} +(-2.22252 - 2.22252i) q^{17} -4.69252i q^{18} +(3.22599 - 3.22599i) q^{19} +(0.0343978 - 1.14300i) q^{20} +(0.0765027 - 0.0765027i) q^{21} +(-0.171613 + 0.171613i) q^{22} +(2.50259 - 2.50259i) q^{23} +(0.329134 + 0.329134i) q^{24} +(-4.99095 - 0.300672i) q^{25} +(-0.831688 + 0.831688i) q^{27} +0.280412i q^{28} -2.34263i q^{29} +(-0.509048 + 0.479305i) q^{30} +(-6.61000 - 6.61000i) q^{31} -2.82726 q^{32} +0.0302175 q^{33} +(-3.52211 - 3.52211i) q^{34} +(1.22554 + 0.0368820i) q^{35} -1.51427i q^{36} +6.80635i q^{37} +(5.11234 - 5.11234i) q^{38} +(-0.158676 + 5.27261i) q^{40} +(2.53005 + 2.53005i) q^{41} +(0.121237 - 0.121237i) q^{42} +(5.02761 - 5.02761i) q^{43} +(-0.0553794 + 0.0553794i) q^{44} +(-6.61815 - 0.199169i) q^{45} +(3.96595 - 3.96595i) q^{46} +9.13956i q^{47} +(0.664291 + 0.664291i) q^{48} +6.69934 q^{49} +(-7.90935 - 0.476486i) q^{50} +0.620172i q^{51} +(-3.70952 - 3.70952i) q^{53} +(-1.31801 + 1.31801i) q^{54} +(0.234752 + 0.249320i) q^{55} -1.29353i q^{56} -0.900179 q^{57} -3.71246i q^{58} +(-2.69196 - 2.69196i) q^{59} +(-0.164270 + 0.154672i) q^{60} +7.84971 q^{61} +(-10.4751 - 10.4751i) q^{62} +1.62364 q^{63} +5.04207 q^{64} +0.0478868 q^{66} +4.89032 q^{67} +(-1.13659 - 1.13659i) q^{68} -0.698322 q^{69} +(1.94217 + 0.0584483i) q^{70} +(11.0573 + 11.0573i) q^{71} +6.98531i q^{72} +3.91807 q^{73} +10.7863i q^{74} +(0.654387 + 0.738287i) q^{75} +(1.64975 - 1.64975i) q^{76} +(-0.0593789 - 0.0593789i) q^{77} -11.1394i q^{79} +(-0.320255 + 10.6417i) q^{80} -8.65113 q^{81} +(4.00947 + 4.00947i) q^{82} +13.4251i q^{83} +(0.0391231 - 0.0391231i) q^{84} +(-5.11695 + 4.81797i) q^{85} +(7.96744 - 7.96744i) q^{86} +(-0.326844 + 0.326844i) q^{87} +(0.255464 - 0.255464i) q^{88} +(-6.43047 - 6.43047i) q^{89} +(-10.4880 - 0.315631i) q^{90} +(1.27981 - 1.27981i) q^{92} +1.84445i q^{93} +14.4838i q^{94} +(-6.99327 - 7.42725i) q^{95} +(0.394459 + 0.394459i) q^{96} -7.57101 q^{97} +10.6167 q^{98} +(0.320657 + 0.320657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{2} + 4 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 8 q^{10} + 8 q^{11} + 24 q^{12} - 24 q^{15} + 4 q^{16} + 14 q^{17} - 4 q^{19} - 22 q^{20} + 4 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 8 * q^2 + 4 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 8 * q^10 + 8 * q^11 + 24 * q^12 - 24 * q^15 + 4 * q^16 + 14 * q^17 - 4 * q^19 - 22 * q^20 + 4 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 + 12 * q^32 + 36 * q^33 - 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 + 32 * q^43 + 36 * q^44 - 20 * q^45 + 4 * q^46 + 28 * q^48 + 36 * q^49 - 52 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^59 - 92 * q^60 + 32 * q^61 - 4 * q^62 + 64 * q^63 - 20 * q^64 - 32 * q^66 + 116 * q^67 - 50 * q^68 - 32 * q^69 + 32 * q^70 - 40 * q^71 + 72 * q^73 - 4 * q^75 - 16 * q^76 + 28 * q^77 - 34 * q^80 + 28 * q^81 + 34 * q^82 - 8 * q^84 + 60 * q^86 - 28 * q^87 + 32 * q^88 - 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 + 56 * q^96 + 44 * q^97 - 8 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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