LMFDB - Embedded newform 845.2.f.d.437.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(408,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 3]))

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

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

chi := DirichletCharacter("845.408");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.f (of order $4$, degree $2$, 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:	$6.74735897080$
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			437.4
Root			$-1.58474i$ of defining polynomial
Character	$\chi$	$=$	845.437
Dual form			845.2.f.d.408.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.58474i q^{2} +(-0.139520 + 0.139520i) q^{3} -0.511395 q^{4} +(2.23506 - 0.0672627i) q^{5} +(0.221103 + 0.221103i) q^{6} +0.548328 q^{7} -2.35905i 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} +(-0.302450 + 0.321219i) q^{15} -4.76126 q^{16} +(2.22252 - 2.22252i) q^{17} +4.69252 q^{18} +(3.22599 - 3.22599i) q^{19} +(-1.14300 + 0.0343978i) 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} -0.280412 q^{28} +2.34263i q^{29} +(0.509048 + 0.479305i) q^{30} +(6.61000 + 6.61000i) q^{31} +2.82726i q^{32} +0.0302175i q^{33} +(-3.52211 - 3.52211i) q^{34} +(1.22554 - 0.0368820i) q^{35} -1.51427i q^{36} +6.80635 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} +(0.199169 + 6.61815i) q^{45} +(-3.96595 + 3.96595i) q^{46} +9.13956 q^{47} +(0.664291 - 0.664291i) q^{48} -6.69934 q^{49} +(-0.476486 - 7.90935i) 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} +0.900179i q^{57} +3.71246 q^{58} +(-2.69196 - 2.69196i) q^{59} +(0.154672 - 0.164270i) q^{60} +7.84971 q^{61} +(10.4751 - 10.4751i) q^{62} +1.62364i q^{63} -5.04207 q^{64} +0.0478868 q^{66} -4.89032i q^{67} +(-1.13659 + 1.13659i) q^{68} +0.698322 q^{69} +(-0.0584483 - 1.94217i) q^{70} +(-11.0573 - 11.0573i) q^{71} +6.98531 q^{72} +3.91807i 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} +(-10.6417 + 0.320255i) q^{80} -8.65113 q^{81} +(-4.00947 + 4.00947i) q^{82} -13.4251 q^{83} +(0.0391231 - 0.0391231i) q^{84} +(4.81797 - 5.11695i) 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} -1.84445 q^{93} -14.4838i q^{94} +(6.99327 - 7.42725i) q^{95} +(-0.394459 - 0.394459i) q^{96} +7.57101i q^{97} +10.6167i q^{98} +(0.320657 + 0.320657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7} - 8 q^{10} - 8 q^{11} - 24 q^{12} - 28 q^{15} + 4 q^{16} - 14 q^{17} - 4 q^{19} + 12 q^{20} - 4 q^{21} - 32 q^{22} + 8 q^{23} + 4 q^{24} + 18 q^{25} + 4 q^{27}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7 - 8 * q^10 - 8 * q^11 - 24 * q^12 - 28 * q^15 + 4 * q^16 - 14 * q^17 - 4 * q^19 + 12 * q^20 - 4 * q^21 - 32 * q^22 + 8 * q^23 + 4 * q^24 + 18 * q^25 + 4 * q^27 + 36 * q^28 + 40 * q^30 - 2 * q^34 - 20 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 - 32 * q^43 + 36 * q^44 + 6 * q^45 - 4 * q^46 + 40 * q^47 + 28 * q^48 - 36 * q^49 - 42 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 8 * q^59 - 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 + 12 * q^70 + 40 * q^71 + 8 * q^72 + 4 * q^75 + 16 * q^76 - 28 * q^77 - 112 * q^80 + 28 * q^81 - 34 * q^82 - 48 * q^83 - 8 * q^84 + 2 * q^85 - 60 * q^86 - 28 * q^87 - 32 * q^88 - 12 * q^89 + 46 * q^90 - 8 * q^92 + 64 * q^93 + 40 * q^95 - 56 * q^96 - 60 * q^99

Character values

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

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

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 $

$2$		−	1.58474i		−	1.12058i	−0.828297	−	0.560290i	$-0.810690\pi$
$2$		−	1.58474i		−	1.12058i	0.828297	−	0.560290i	$-0.189310\pi$
$3$	−0.139520	+	0.139520i	−0.0805519	+	0.0805519i	−0.746235	−	0.665683i	$-0.768140\pi$
$3$	−0.139520	+	0.139520i	−0.0805519	+	0.0805519i	0.665683	+	0.746235i	$0.268140\pi$
$4$	−0.511395			−0.255697
$5$	2.23506	−	0.0672627i	0.999547	−	0.0300808i
$5$	2.23506	−	0.0672627i	0.999547	−	0.0300808i
$6$	0.221103	+	0.221103i	0.0902647	+	0.0902647i
$7$	0.548328			0.207248			0.103624	−	0.994617i	$-0.466956\pi$
$7$	0.548328			0.207248			0.103624	+	0.994617i	$0.466956\pi$
$8$		−	2.35905i		−	0.834050i
$9$			2.96107i			0.987023i
$10$	−0.106594	−	3.54198i	−0.0337079	−	1.12007i
$11$	0.108291	−	0.108291i	0.0326509	−	0.0326509i	−0.690593	−	0.723244i	$-0.742650\pi$
$11$	0.108291	−	0.108291i	0.0326509	−	0.0326509i	0.723244	+	0.690593i	$0.242650\pi$
$12$	0.0713497	−	0.0713497i	0.0205969	−	0.0205969i
$13$		0			0
$13$		0			0
$14$		−	0.868956i		−	0.232238i
$15$	−0.302450	+	0.321219i	−0.0780923	+	0.0829385i
$16$	−4.76126			−1.19032
$17$	2.22252	−	2.22252i	0.539041	−	0.539041i	−0.384207	−	0.923247i	$-0.625525\pi$
$17$	2.22252	−	2.22252i	0.539041	−	0.539041i	0.923247	+	0.384207i	$0.125525\pi$
$18$	4.69252			1.10604
$19$	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	$0.0746917\pi$
$20$	−1.14300	+	0.0343978i	−0.255582	+	0.00769158i
$21$	−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	$-0.370295\pi$
$23$	−2.50259	−	2.50259i	−0.521826	−	0.521826i	−0.918123	+	0.396297i	$0.870295\pi$
$24$	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
$28$	−0.280412			−0.0529929
$29$			2.34263i			0.435016i	0.976059	+	0.217508i	$0.0697927\pi$
$29$			2.34263i			0.435016i	−0.976059	+	0.217508i	$0.930207\pi$
$30$	0.509048	+	0.479305i	0.0929391	+	0.0875086i
$31$	6.61000	+	6.61000i	1.18719	+	1.18719i	0.977841	+	0.209350i	$0.0671347\pi$
$31$	6.61000	+	6.61000i	1.18719	+	1.18719i	0.209350	+	0.977841i	$0.432865\pi$
$32$			2.82726i			0.499793i
$33$			0.0302175i			0.00526019i
$34$	−3.52211	−	3.52211i	−0.604038	−	0.604038i
$35$	1.22554	−	0.0368820i	0.207155	−	0.00623420i
$36$		−	1.51427i		−	0.252379i
$37$	6.80635			1.11896			0.559478	−	0.828845i	$-0.311002\pi$
$37$	6.80635			1.11896			0.559478	+	0.828845i	$0.311002\pi$
$38$	−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	0.481382	−	0.876511i	$-0.340135\pi$
$41$	−2.53005	−	2.53005i	−0.395128	−	0.395128i	−0.876511	+	0.481382i	$0.840135\pi$
$42$	0.121237	+	0.121237i	0.0187072	+	0.0187072i
$43$	−5.02761	−	5.02761i	−0.766703	−	0.766703i	0.210822	−	0.977524i	$-0.432386\pi$
$43$	−5.02761	−	5.02761i	−0.766703	−	0.766703i	−0.977524	+	0.210822i	$0.932386\pi$
$44$	−0.0553794	+	0.0553794i	−0.00834876	+	0.00834876i
$45$	0.199169	+	6.61815i	0.0296904	+	0.986576i
$46$	−3.96595	+	3.96595i	−0.584747	+	0.584747i
$47$	9.13956			1.33314			0.666571	−	0.745442i	$-0.267761\pi$
$47$	9.13956			1.33314			0.666571	+	0.745442i	$0.267761\pi$
$48$	0.664291	−	0.664291i	0.0958822	−	0.0958822i
$49$	−6.69934			−0.957048
$50$	−0.476486	−	7.90935i	−0.0673853	−	1.11855i
$51$			0.620172i			0.0868415i
$52$		0			0
$53$	−3.70952	+	3.70952i	−0.509541	+	0.509541i	−0.914386	−	0.404844i	$-0.867326\pi$
$53$	−3.70952	+	3.70952i	−0.509541	+	0.509541i	0.404844	+	0.914386i	$0.367326\pi$
$54$	−1.31801	+	1.31801i	−0.179358	+	0.179358i
$55$	0.234752	−	0.249320i	0.0316540	−	0.0336183i
$56$		−	1.29353i		−	0.172856i
$57$			0.900179i			0.119232i
$58$	3.71246			0.487469
$59$	−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	$0.829712\pi$
$60$	0.154672	−	0.164270i	0.0199680	−	0.0212071i
$61$	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
$63$			1.62364i			0.204559i
$64$	−5.04207			−0.630258
$65$		0			0
$66$	0.0478868			0.00589446
$67$		−	4.89032i		−	0.597448i	−0.954340	−	0.298724i	$-0.903439\pi$
$67$		−	4.89032i		−	0.597448i	0.954340	−	0.298724i	$-0.0965610\pi$
$68$	−1.13659	+	1.13659i	−0.137831	+	0.137831i
$69$	0.698322			0.0840681
$70$	−0.0584483	−	1.94217i	−0.00698591	−	0.232133i
$71$	−11.0573	−	11.0573i	−1.31226	−	1.31226i	−0.919747	−	0.392513i	$-0.871606\pi$
$71$	−11.0573	−	11.0573i	−1.31226	−	1.31226i	−0.392513	−	0.919747i	$-0.628394\pi$
$72$	6.98531			0.823226
$73$			3.91807i			0.458575i	0.973359	+	0.229288i	$0.0736396\pi$
$73$			3.91807i			0.458575i	−0.973359	+	0.229288i	$0.926360\pi$
$74$		−	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	$0.215570\pi$
$79$			11.1394i			1.25328i	−0.779309	+	0.626640i	$0.784430\pi$
$80$	−10.6417	+	0.320255i	−1.18978	+	0.0358056i
$81$	−8.65113			−0.961237
$82$	−4.00947	+	4.00947i	−0.442772	+	0.442772i
$83$	−13.4251			−1.47360			−0.736798	−	0.676113i	$-0.763663\pi$
$83$	−13.4251			−1.47360			−0.736798	+	0.676113i	$0.763663\pi$
$84$	0.0391231	−	0.0391231i	0.00426868	−	0.00426868i
$85$	4.81797	−	5.11695i	0.522582	−	0.555011i
$86$	−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
$93$	−1.84445			−0.191261
$94$		−	14.4838i		−	1.49389i
$95$	6.99327	−	7.42725i	0.717495	−	0.762020i
$96$	−0.394459	−	0.394459i	−0.0402593	−	0.0402593i
$97$			7.57101i			0.768719i	0.923183	+	0.384360i	$0.125578\pi$
$97$			7.57101i			0.768719i	−0.923183	+	0.384360i	$0.874422\pi$
$98$			10.6167i			1.07245i
$99$	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	$0.764833\pi$
$102$	0.982810			0.0973127
$103$	−10.3566	−	10.3566i	−1.02046	−	1.02046i	−0.999786	−	0.0206759i	$-0.993418\pi$
$103$	−10.3566	−	10.3566i	−1.02046	−	1.02046i	−0.0206759	−	0.999786i	$-0.506582\pi$
$104$		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	0.994535	+	0.104399i	$0.0332920\pi$
$107$	11.3675	+	11.3675i	1.09893	+	1.09893i	0.104399	+	0.994535i	$0.466708\pi$
$108$	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	$0.437638\pi$
$110$	−0.395107	−	0.372021i	−0.0376720	−	0.0354708i
$111$	−0.949621	+	0.949621i	−0.0901340	+	0.0901340i
$112$	−2.61073			−0.246691
$113$	3.22285	−	3.22285i	0.303180	−	0.303180i	−0.539077	−	0.842257i	$-0.681227\pi$
$113$	3.22285	−	3.22285i	0.303180	−	0.303180i	0.842257	+	0.539077i	$0.181227\pi$
$114$	1.42655			0.133608
$115$	−5.76176	−	5.42510i	−0.537287	−	0.505893i
$116$		−	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
$122$		−	12.4397i		−	1.12624i
$123$	0.705986			0.0636566
$124$	−3.38032	−	3.38032i	−0.303561	−	0.303561i
$125$	11.1348	−	1.00772i	0.995930	−	0.0901335i
$126$	2.57304			0.229224
$127$	−1.71992	+	1.71992i	−0.152618	+	0.152618i	−0.779286	−	0.626668i	$-0.784418\pi$
$127$	−1.71992	+	1.71992i	−0.152618	+	0.152618i	0.626668	+	0.779286i	$0.284418\pi$
$128$			13.6449i			1.20605i
$129$	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	$0.406800\pi$
$132$		−	0.0154531i		−	0.00134502i
$133$	1.76890	−	1.76890i	0.153383	−	0.153383i
$134$	−7.74988			−0.669487
$135$	−1.91481	−	1.80293i	−0.164801	−	0.155171i
$136$	−5.24304	−	5.24304i	−0.449587	−	0.449587i
$137$	−4.05549			−0.346484			−0.173242	−	0.984879i	$-0.555424\pi$
$137$	−4.05549			−0.346484			−0.173242	+	0.984879i	$0.555424\pi$
$138$		−	1.10666i		−	0.0942050i
$139$			12.8232i			1.08765i	0.839199	+	0.543825i	$0.183024\pi$
$139$			12.8232i			1.08765i	−0.839199	+	0.543825i	$0.816976\pi$
$140$	−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
$145$	0.157572	+	5.23591i	0.0130856	+	0.434819i
$146$	6.20911			0.513870
$147$	0.934691	−	0.934691i	0.0770920	−	0.0770920i
$148$	−3.48073			−0.286114
$149$	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	$0.194239\pi$
$150$	1.16999	+	1.03703i	0.0955294	+	0.0846734i
$151$	−4.89430	+	4.89430i	−0.398293	+	0.398293i	−0.877630	−	0.479338i	$-0.840877\pi$
$151$	−4.89430	+	4.89430i	−0.398293	+	0.398293i	0.479338	+	0.877630i	$0.340877\pi$
$152$	−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	0.792866	−	0.609396i	$-0.208588\pi$
$157$	2.29887	+	2.29887i	0.183470	+	0.183470i	−0.609396	+	0.792866i	$0.708588\pi$
$158$	17.6530			1.40440
$159$		−	1.03510i		−	0.0820890i
$160$	0.190169	+	6.31908i	0.0150342	+	0.499567i
$161$	−1.37224	−	1.37224i	−0.108148	−	0.108148i
$162$			13.7098i			1.07714i
$163$		−	10.8685i		−	0.851283i	−0.904892	−	0.425642i	$-0.860048\pi$
$163$		−	10.8685i		−	0.851283i	0.904892	−	0.425642i	$-0.139952\pi$
$164$	1.29386	+	1.29386i	0.101033	+	0.101033i
$165$	0.00203251	+	0.0675378i	0.000158231	+	0.00525781i
$166$			21.2753i			1.65128i
$167$	16.3588			1.26588			0.632942	−	0.774199i	$-0.281847\pi$
$167$	16.3588			1.26588			0.632942	+	0.774199i	$0.281847\pi$
$168$	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	$-0.166350\pi$
$173$	4.83220	+	4.83220i	0.367385	+	0.367385i	−0.499137	+	0.866523i	$0.666350\pi$
$174$	−0.517961	+	0.517961i	−0.0392666	+	0.0392666i
$175$	2.73668	−	0.164867i	0.206873	−	0.0124628i
$176$	−0.515602	+	0.515602i	−0.0388649	+	0.0388649i
$177$	0.751164			0.0564609
$178$	−10.1906	+	10.1906i	−0.763819	+	0.763819i
$179$	−5.67392			−0.424089			−0.212044	−	0.977260i	$-0.568012\pi$
$179$	−5.67392			−0.424089			−0.212044	+	0.977260i	$0.568012\pi$
$180$	−0.101854	−	3.38449i	−0.00759176	−	0.252265i
$181$			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
$187$		−	0.481358i		−	0.0352004i
$188$	−4.67392			−0.340881
$189$	−0.456038	−	0.456038i	−0.0331719	−	0.0331719i
$190$	−11.7702	−	11.0825i	−0.853903	−	0.804009i
$191$	−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
$193$			15.8378i			1.14003i	0.821634	+	0.570016i	$0.193063\pi$
$193$			15.8378i			1.14003i	−0.821634	+	0.570016i	$0.806937\pi$
$194$	11.9981			0.861411
$195$		0			0
$196$	3.42601			0.244715
$197$		−	5.71277i		−	0.407018i	−0.979073	−	0.203509i	$-0.934765\pi$
$197$		−	5.71277i		−	0.407018i	0.979073	−	0.203509i	$-0.0652346\pi$
$198$	0.508157	−	0.508157i	0.0361132	−	0.0361132i
$199$	9.30312			0.659481			0.329740	−	0.944072i	$-0.393039\pi$
$199$	9.30312			0.659481			0.329740	+	0.944072i	$0.393039\pi$
$200$	−0.709299	−	11.7739i	−0.0501550	−	0.832541i
$201$	0.682297	+	0.682297i	0.0481255	+	0.0481255i
$202$	21.4497			1.50919
$203$			1.28453i			0.0901563i
$204$		−	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
$210$	0.279125	+	0.262816i	0.0192615	+	0.0181360i
$211$	−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
$213$	3.08543			0.211410
$214$	18.0145	−	18.0145i	1.23144	−	1.23144i
$215$	−11.5752	−	10.8988i	−0.789419	−	0.743293i
$216$	−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
$223$	18.5682			1.24342			0.621708	−	0.783249i	$-0.286439\pi$
$223$	18.5682			1.24342			0.621708	+	0.783249i	$0.286439\pi$
$224$			1.55026i			0.103581i
$225$	0.890310	+	14.7785i	0.0593540	+	0.985237i
$226$	−5.10737	−	5.10737i	−0.339737	−	0.339737i
$227$		−	6.38666i		−	0.423898i	−0.977281	−	0.211949i	$-0.932019\pi$
$227$		−	6.38666i		−	0.423898i	0.977281	−	0.211949i	$-0.0679810\pi$
$228$		−	0.460347i		−	0.0304872i
$229$	−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
$232$	5.52638			0.362825
$233$	5.85956	+	5.85956i	0.383873	+	0.383873i	0.872495	−	0.488623i	$-0.162500\pi$
$233$	5.85956	+	5.85956i	0.383873	+	0.383873i	−0.488623	+	0.872495i	$0.662500\pi$
$234$		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	$0.0324123\pi$
$240$	1.44005	−	1.52941i	0.0929546	−	0.0987230i
$241$	−12.1149	+	12.1149i	−0.780391	+	0.780391i	−0.979897	−	0.199505i	$-0.936066\pi$
$241$	−12.1149	+	12.1149i	−0.780391	+	0.780391i	0.199505	+	0.979897i	$0.436066\pi$
$242$	17.3950			1.11819
$243$	3.70207	−	3.70207i	0.237488	−	0.237488i
$244$	−4.01430			−0.256989
$245$	−14.9734	+	0.450615i	−0.956615	+	0.0287888i
$246$		−	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	$-0.101708\pi$
$252$		−	0.830319i		−	0.0523052i
$253$	−0.542016			−0.0340762
$254$	2.72562	+	2.72562i	0.171020	+	0.171020i
$255$	0.0417144	+	1.38612i	0.00261226	+	0.0868022i
$256$	11.5394			0.721213
$257$	1.94551	−	1.94551i	0.121357	−	0.121357i	−0.643820	−	0.765177i	$-0.722651\pi$
$257$	1.94551	−	1.94551i	0.121357	−	0.121357i	0.765177	+	0.643820i	$0.222651\pi$
$258$		−	2.22323i		−	0.138412i
$259$	3.73211			0.231902
$260$		0			0
$261$	−6.93669			−0.429370
$262$		−	10.4704i		−	0.646866i
$263$	−4.36804	+	4.36804i	−0.269345	+	0.269345i	−0.828836	−	0.559491i	$-0.810997\pi$
$263$	−4.36804	+	4.36804i	−0.269345	+	0.269345i	0.559491	+	0.828836i	$0.310997\pi$
$264$	0.0712845			0.00438726
$265$	−8.04147	+	8.54049i	−0.493983	+	0.524638i
$266$	−2.80324	−	2.80324i	−0.171878	−	0.171878i
$267$	1.79436			0.109813
$268$			2.50088i			0.152766i
$269$			21.2230i			1.29399i	0.762495	+	0.646994i	$0.223974\pi$
$269$			21.2230i			1.29399i	−0.762495	+	0.646994i	$0.776026\pi$
$270$	−2.85717	+	3.03447i	−0.173882	+	0.184672i
$271$	−9.11094	+	9.11094i	−0.553450	+	0.553450i	−0.927435	−	0.373985i	$-0.877991\pi$
$271$	−9.11094	+	9.11094i	−0.553450	+	0.553450i	0.373985	+	0.927435i	$0.377991\pi$
$272$	−10.5820	+	10.5820i	−0.641629	+	0.641629i
$273$		0			0
$274$			6.42690i			0.388263i
$275$	0.507915	−	0.573035i	0.0306284	−	0.0345553i
$276$	−0.357118			−0.0214960
$277$	−15.0447	+	15.0447i	−0.903948	+	0.903948i	−0.995775	−	0.0918270i	$-0.970729\pi$
$277$	−15.0447	+	15.0447i	−0.903948	+	0.903948i	0.0918270	+	0.995775i	$0.470729\pi$
$278$	20.3214			1.21880
$279$	−19.5727	+	19.5727i	−1.17178	+	1.17178i
$280$	−0.0870065	−	2.89112i	−0.00519963	−	0.172777i
$281$	4.22655	−	4.22655i	0.252135	−	0.252135i	−0.569711	−	0.821845i	$-0.692945\pi$
$281$	4.22655	−	4.22655i	0.252135	−	0.252135i	0.821845	+	0.569711i	$0.192945\pi$
$282$	2.02078	+	2.02078i	0.120336	+	0.120336i
$283$	−1.08748	−	1.08748i	−0.0646437	−	0.0646437i	0.674046	−	0.738690i	$-0.264555\pi$
$283$	−1.08748	−	1.08748i	−0.0646437	−	0.0646437i	−0.738690	+	0.674046i	$0.764555\pi$
$284$	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
$288$	−8.37171			−0.493308
$289$			7.12080i			0.418870i
$290$	8.29755	−	0.249710i	0.487249	−	0.0146635i
$291$	−1.05631	−	1.05631i	−0.0619218	−	0.0619218i
$292$		−	2.00368i		−	0.117256i
$293$			2.79186i			0.163102i	0.996669	+	0.0815512i	$0.0259874\pi$
$293$			2.79186i			0.163102i	−0.996669	+	0.0815512i	$0.974013\pi$
$294$	−1.48124	−	1.48124i	−0.0863877	−	0.0863877i
$295$	−6.19775	−	5.83561i	−0.360847	−	0.339762i
$296$		−	16.0565i		−	0.933265i
$297$	−0.180128			−0.0104521
$298$	−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
$305$	17.5445	−	0.527993i	1.00460	−	0.0302328i
$306$	10.4292	−	10.4292i	0.596199	−	0.596199i
$307$	−2.12112			−0.121058			−0.0605292	−	0.998166i	$-0.519279\pi$
$307$	−2.12112			−0.121058			−0.0605292	+	0.998166i	$0.519279\pi$
$308$	−0.0303661	+	0.0303661i	−0.00173027	+	0.00173027i
$309$	2.88989			0.164400
$310$	22.7079	−	24.1171i	1.28972	−	1.36976i
$311$		−	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	−0.984941	−	0.172891i	$-0.944689\pi$
$313$	−14.3666	+	14.3666i	−0.812050	+	0.812050i	0.172891	+	0.984941i	$0.444689\pi$
$314$	3.64310	−	3.64310i	0.205592	−	0.205592i
$315$	0.109210	+	3.62892i	0.00615329	+	0.204466i
$316$		−	5.69663i		−	0.320460i
$317$		−	8.78989i		−	0.493689i	−0.969055	−	0.246845i	$-0.920606\pi$
$317$		−	8.78989i		−	0.493689i	0.969055	−	0.246845i	$-0.0793937\pi$
$318$	−1.64037			−0.0919872
$319$	0.253686	+	0.253686i	0.0142037	+	0.0142037i
$320$	−11.2693	+	0.339143i	−0.629973	+	0.0189587i
$321$	−3.17198			−0.177042
$322$	−2.17464	+	2.17464i	−0.121188	+	0.121188i
$323$		−	14.3396i		−	0.797879i
$324$	4.42414			0.245786
$325$		0			0
$326$	−17.2237			−0.953930
$327$		−	2.29042i		−	0.126660i
$328$	−5.96852	+	5.96852i	−0.329557	+	0.329557i
$329$	5.01147			0.276291
$330$	0.107030	−	0.00322099i	0.00589179	−	0.000177310i
$331$	12.8491	+	12.8491i	0.706250	+	0.706250i	0.965745	−	0.259494i	$-0.0835558\pi$
$331$	12.8491	+	12.8491i	0.706250	+	0.706250i	−0.259494	+	0.965745i	$0.583556\pi$
$332$	6.86552			0.376794
$333$			20.1541i			1.10444i
$334$		−	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	$-0.981368\pi$
$337$	−17.2522	+	17.2522i	−0.939788	+	0.939788i	0.0584999	+	0.998287i	$0.481368\pi$
$338$		0			0
$339$			0.899302i			0.0488434i
$340$	−2.46388	+	2.61678i	−0.133623	+	0.141915i
$341$	1.43161			0.0775258
$342$	15.1380	−	15.1380i	0.818569	−	0.818569i
$343$	−7.51173			−0.405595
$344$	−11.8604	+	11.8604i	−0.639468	+	0.639468i
$345$	1.56079	−	0.0469710i	0.0840301	−	0.00252884i
$346$	7.65777	−	7.65777i	0.411684	−	0.411684i
$347$	−5.49531	−	5.49531i	−0.295004	−	0.295004i	0.544049	−	0.839053i	$-0.316890\pi$
$347$	−5.49531	−	5.49531i	−0.295004	−	0.295004i	−0.839053	+	0.544049i	$0.816890\pi$
$348$	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
$353$	−25.6178			−1.36350			−0.681749	−	0.731586i	$-0.738780\pi$
$353$	−25.6178			−1.36350			−0.681749	+	0.731586i	$0.738780\pi$
$354$		−	1.19040i		−	0.0632689i
$355$	−25.4574	−	23.9699i	−1.35114	−	1.27219i
$356$	3.28851	+	3.28851i	0.174291	+	0.174291i
$357$			0.340058i			0.0179978i
$358$			8.99168i			0.475225i
$359$	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
$362$	5.69103			0.299114
$363$	−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	0.230376	−	0.973102i	$-0.426005\pi$
$367$	−14.2286	−	14.2286i	−0.742726	−	0.742726i	−0.973102	+	0.230376i	$0.926005\pi$
$368$	11.9155	+	11.9155i	0.621138	+	0.621138i
$369$	7.49167	−	7.49167i	0.390001	−	0.390001i
$370$	−0.725514	−	24.1079i	−0.0377177	−	1.25331i
$371$	−2.03403	+	2.03403i	−0.105602	+	0.105602i
$372$	0.943243			0.0489049
$373$	18.5300	−	18.5300i	0.959447	−	0.959447i	−0.0397619	−	0.999209i	$-0.512660\pi$
$373$	18.5300	−	18.5300i	0.959447	−	0.959447i	0.999209	+	0.0397619i	$0.0126600\pi$
$374$	−0.762826			−0.0394448
$375$	−1.41293	+	1.69413i	−0.0729636	+	0.0874844i
$376$		−	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
$382$			37.2130i			1.90398i
$383$	−24.1261			−1.23278			−0.616392	−	0.787440i	$-0.711406\pi$
$383$	−24.1261			−1.23278			−0.616392	+	0.787440i	$0.711406\pi$
$384$	−1.90373	−	1.90373i	−0.0971494	−	0.0971494i
$385$	0.128721	−	0.136709i	0.00656024	−	0.00696735i
$386$	25.0988			1.27750
$387$	14.8871	−	14.8871i	0.756753	−	0.756753i
$388$		−	3.87177i		−	0.196559i
$389$	14.3262			0.726365			0.363183	−	0.931718i	$-0.381690\pi$
$389$	14.3262			0.726365			0.363183	+	0.931718i	$0.381690\pi$
$390$		0			0
$391$	−11.1241			−0.562571
$392$			15.8041i			0.798226i
$393$	−0.921815	+	0.921815i	−0.0464994	+	0.0464994i
$394$	−9.05325			−0.456096
$395$	0.749265	+	24.8972i	0.0376996	+	1.25271i
$396$	−0.163982	−	0.163982i	−0.00824042	−	0.00824042i
$397$	−33.4931			−1.68097			−0.840484	−	0.541836i	$-0.817729\pi$
$397$	−33.4931			−1.68097			−0.840484	+	0.541836i	$0.817729\pi$
$398$		−	14.7430i		−	0.739000i
$399$			0.493593i			0.0247106i
$400$	−23.7632	+	1.43158i	−1.18816	+	0.0715789i
$401$	13.1161	−	13.1161i	0.654989	−	0.654989i	−0.299201	−	0.954190i	$-0.596720\pi$
$401$	13.1161	−	13.1161i	0.654989	−	0.654989i	0.954190	+	0.299201i	$0.0967202\pi$
$402$	1.08126	−	1.08126i	0.0539285	−	0.0539285i
$403$		0			0
$404$		−	6.92181i		−	0.344373i
$405$	−19.3358	+	0.581898i	−0.960802	+	0.0289148i
$406$	2.03564			0.101027
$407$	0.737066	−	0.737066i	0.0365350	−	0.0365350i
$408$	1.46302			0.0724301
$409$	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	$0.209182\pi$
$410$	−8.69171	+	9.23109i	−0.429253	+	0.455891i
$411$	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
$418$	−1.10724			−0.0541569
$419$		−	1.00695i		−	0.0491929i	−0.999697	−	0.0245965i	$-0.992170\pi$
$419$		−	1.00695i		−	0.0491929i	0.999697	−	0.0245965i	$-0.00783009\pi$
$420$	0.0848107	−	0.0900737i	0.00413834	−	0.00439515i
$421$	−0.294746	−	0.294746i	−0.0143650	−	0.0143650i	0.699888	−	0.714253i	$-0.253233\pi$
$421$	−0.294746	−	0.294746i	−0.0143650	−	0.0143650i	−0.714253	+	0.699888i	$0.753233\pi$
$422$			8.67736i			0.422407i
$423$			27.0628i			1.31584i
$424$	8.75094	+	8.75094i	0.424983	+	0.424983i
$425$	10.4242	−	11.7607i	0.505650	−	0.570480i
$426$		−	4.88959i		−	0.236901i
$427$	4.30421			0.208296
$428$	−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	0.774264	−	0.632863i	$-0.218120\pi$
$431$	2.93555	+	2.93555i	0.141401	+	0.141401i	−0.632863	+	0.774264i	$0.718120\pi$
$432$	3.95989	+	3.95989i	0.190520	+	0.190520i
$433$	−10.6032	−	10.6032i	−0.509556	−	0.509556i	0.404834	−	0.914390i	$-0.367329\pi$
$433$	−10.6032	−	10.6032i	−0.509556	−	0.509556i	−0.914390	+	0.404834i	$0.867329\pi$
$434$	5.74380	−	5.74380i	0.275711	−	0.275711i
$435$	−0.752498	−	0.708529i	−0.0360795	−	0.0339714i
$436$	4.19763	−	4.19763i	0.201030	−	0.201030i
$437$	−16.1466			−0.772399
$438$	−0.866294	+	0.866294i	−0.0413932	+	0.0413932i
$439$	13.8820			0.662550			0.331275	−	0.943534i	$-0.392521\pi$
$439$	13.8820			0.662550			0.331275	+	0.943534i	$0.392521\pi$
$440$	−0.588159	−	0.553792i	−0.0280394	−	0.0264010i
$441$		−	19.8372i		−	0.944628i
$442$		0			0
$443$	10.0594	−	10.0594i	0.477938	−	0.477938i	−0.426533	−	0.904472i	$-0.640265\pi$
$443$	10.0594	−	10.0594i	0.477938	−	0.477938i	0.904472	+	0.426533i	$0.140265\pi$
$444$	0.485631	−	0.485631i	0.0230470	−	0.0230470i
$445$	−14.8050	−	13.9399i	−0.701824	−	0.660816i
$446$		−	29.4257i		−	1.39335i
$447$			0.839520i			0.0397079i
$448$	−2.76470			−0.130620
$449$	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	$0.699797\pi$
$450$	23.4201	−	1.41091i	1.10404	−	0.0665108i
$451$	−0.547964			−0.0258026
$452$	−1.64815	+	1.64815i	−0.0775223	+	0.0775223i
$453$		−	1.36571i		−	0.0641664i
$454$	−10.1212			−0.475011
$455$		0			0
$456$	2.12357			0.0994451
$457$		−	36.9587i		−	1.72885i	−0.502759	−	0.864426i	$-0.667682\pi$
$457$		−	36.9587i		−	1.72885i	0.502759	−	0.864426i	$-0.332318\pi$
$458$	−17.6141	+	17.6141i	−0.823055	+	0.823055i
$459$	−3.69689			−0.172556
$460$	2.94653	+	2.77437i	0.137383	+	0.129355i
$461$	18.1916	+	18.1916i	0.847269	+	0.847269i	0.989792	−	0.142523i	$-0.0455214\pi$
$461$	18.1916	+	18.1916i	0.847269	+	0.847269i	−0.142523	+	0.989792i	$0.545521\pi$
$462$	0.0262577			0.00122162
$463$			15.9580i			0.741632i	0.928706	+	0.370816i	$0.120922\pi$
$463$			15.9580i			0.741632i	−0.928706	+	0.370816i	$0.879078\pi$
$464$		−	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	$-0.541388\pi$
$467$	18.6259	−	18.6259i	0.861902	−	0.861902i	0.991559	+	0.129657i	$0.0413877\pi$
$468$		0			0
$469$		−	2.68150i		−	0.123820i
$470$	−0.974219	−	32.3721i	−0.0449374	−	1.49321i
$471$	−0.641475			−0.0295576
$472$	−6.35046	+	6.35046i	−0.292304	+	0.292304i
$473$	−1.08889			−0.0500671
$474$	−2.46295	+	2.46295i	−0.113127	+	0.113127i
$475$	15.1308	−	17.0707i	0.694248	−	0.783258i
$476$	−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
$483$	0.382910			0.0174230
$484$		−	5.61335i		−	0.255152i
$485$	0.509246	+	16.9216i	0.0231237	+	0.768371i
$486$	−5.86681	−	5.86681i	−0.266124	−	0.266124i
$487$		−	26.2798i		−	1.19085i	−0.803411	−	0.595425i	$-0.796984\pi$
$487$		−	26.2798i		−	1.19085i	0.803411	−	0.595425i	$-0.203016\pi$
$488$		−	18.5179i		−	0.838264i
$489$	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	$-0.388044\pi$
$492$	−0.361038			−0.0162768
$493$	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	$0.165204\pi$
$500$	−5.69429	+	0.515344i	−0.254657	+	0.0230469i
$501$	−2.28238	+	2.28238i	−0.101969	+	0.101969i
$502$	−15.7730			−0.703982
$503$	7.54802	−	7.54802i	0.336550	−	0.336550i	−0.518517	−	0.855067i	$-0.673516\pi$
$503$	7.54802	−	7.54802i	0.336550	−	0.336550i	0.855067	+	0.518517i	$0.173516\pi$
$504$	3.83024			0.170612
$505$	0.910411	+	30.2519i	0.0405128	+	1.34619i
$506$			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
$512$			9.00279i			0.397871i
$513$	−5.36603			−0.236916
$514$	−3.08312	−	3.08312i	−0.135991	−	0.135991i
$515$	−23.8441	−	22.4509i	−1.05070	−	0.989304i
$516$	−0.717437			−0.0315834
$517$	0.989731	−	0.989731i	0.0435283	−	0.0435283i
$518$		−	5.91442i		−	0.259864i
$519$	−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	$0.540888\pi$
$522$			10.9928i			0.481143i
$523$	2.09684	−	2.09684i	0.0916884	−	0.0916884i	−0.659775	−	0.751463i	$-0.729348\pi$
$523$	2.09684	−	2.09684i	0.0916884	−	0.0916884i	0.751463	+	0.659775i	$0.229348\pi$
$524$	−3.37881			−0.147604
$525$	−0.358819	+	0.404823i	−0.0156601	+	0.0176679i
$526$	6.92220	+	6.92220i	0.301822	+	0.301822i
$527$	29.3817			1.27989
$528$		−	0.143873i		−	0.00626129i
$529$		−	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
$535$	26.1715	+	24.6423i	1.13149	+	1.06538i
$536$	−11.5365			−0.498301
$537$	0.791625	−	0.791625i	0.0341611	−	0.0341611i
$538$	33.6329			1.45002
$539$	−0.725477	+	0.725477i	−0.0312485	+	0.0312485i
$540$	0.979224	+	0.922007i	0.0421391	+	0.0396769i
$541$	15.4678	−	15.4678i	0.665013	−	0.665013i	−0.291544	−	0.956557i	$-0.594169\pi$
$541$	15.4678	−	15.4678i	0.665013	−	0.665013i	0.956557	+	0.291544i	$0.0941691\pi$
$542$	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	0.743931	−	0.668256i	$-0.232959\pi$
$547$	1.76989	+	1.76989i	0.0756751	+	0.0756751i	−0.668256	+	0.743931i	$0.732959\pi$
$548$	2.07396			0.0885951
$549$			23.2435i			0.992010i
$550$	−0.908110	−	0.804912i	−0.0387219	−	0.0343216i
$551$	7.55729	+	7.55729i	0.321952	+	0.321952i
$552$		−	1.64738i		−	0.0701170i
$553$			6.10804i			0.259740i
$554$	23.8419	+	23.8419i	1.01295	+	1.01295i
$555$	−2.05858	+	2.18633i	−0.0873819	+	0.0928045i
$556$		−	6.55772i		−	0.278109i
$557$	9.43469			0.399761			0.199880	−	0.979820i	$-0.435945\pi$
$557$	9.43469			0.399761			0.199880	+	0.979820i	$0.435945\pi$
$558$	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	$-0.183842\pi$
$563$	6.92420	+	6.92420i	0.291820	+	0.291820i	−0.545979	+	0.837799i	$0.683842\pi$
$564$	0.652105	−	0.652105i	0.0274586	−	0.0274586i
$565$	6.98646	−	7.42002i	0.293923	−	0.312163i
$566$	−1.72336	+	1.72336i	−0.0724384	+	0.0724384i
$567$	−4.74366			−0.199215
$568$	−26.0847	+	26.0847i	−1.09449	+	1.09449i
$569$	6.41861			0.269082			0.134541	−	0.990908i	$-0.457044\pi$
$569$	6.41861			0.269082			0.134541	+	0.990908i	$0.457044\pi$
$570$	3.18841	−	0.0959534i	0.133548	−	0.00401905i
$571$		−	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
$577$		−	24.8642i		−	1.03511i	−0.855650	−	0.517554i	$-0.826843\pi$
$577$		−	24.8642i		−	1.03511i	0.855650	−	0.517554i	$-0.173157\pi$
$578$	11.2846			0.469377
$579$	−2.20969	−	2.20969i	−0.0918316	−	0.0918316i
$580$	−0.0805813	−	2.67762i	−0.00334596	−	0.111182i
$581$	−7.36135			−0.305400
$582$	−1.67397	+	1.67397i	−0.0693882	+	0.0693882i
$583$			0.803414i			0.0332740i
$584$	9.24291			0.382474
$585$		0			0
$586$	4.42437			0.182769
$587$			26.7672i			1.10480i	0.833579	+	0.552400i	$0.186288\pi$
$587$			26.7672i			1.10480i	−0.833579	+	0.552400i	$0.813712\pi$
$588$	−0.477996	+	0.477996i	−0.0197122	+	0.0197122i
$589$	42.6475			1.75726
$590$	−9.24791	+	9.82180i	−0.380731	+	0.404357i
$591$	0.797046	+	0.797046i	0.0327861	+	0.0327861i
$592$	−32.4068			−1.33191
$593$		−	19.8452i		−	0.814944i	−0.913218	−	0.407472i	$-0.866410\pi$
$593$		−	19.8452i		−	0.814944i	0.913218	−	0.407472i	$-0.133590\pi$
$594$			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	$-0.731849\pi$
$599$		−	36.5285i		−	1.49252i	0.665657	−	0.746258i	$-0.268151\pi$
$600$	1.74166	+	1.54373i	0.0711028	+	0.0630226i
$601$	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
$603$	14.4806			0.589695
$604$	2.50292	−	2.50292i	0.101842	−	0.101842i
$605$	0.738312	+	24.5332i	0.0300166	+	0.997416i
$606$	−2.99266	+	2.99266i	−0.121568	+	0.121568i
$607$	12.6350	+	12.6350i	0.512841	+	0.512841i	0.915396	−	0.402555i	$-0.131878\pi$
$607$	12.6350	+	12.6350i	0.512841	+	0.512841i	−0.402555	+	0.915396i	$0.631878\pi$
$608$	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
$613$	−15.3746			−0.620973			−0.310487	−	0.950578i	$-0.600492\pi$
$613$	−15.3746			−0.620973			−0.310487	+	0.950578i	$0.600492\pi$
$614$			3.36141i			0.135656i
$615$	1.57792	−	0.0474865i	0.0636278	−	0.00191484i
$616$	−0.140078	−	0.140078i	−0.00564390	−	0.00564390i
$617$		−	1.24370i		−	0.0500694i	−0.999687	−	0.0250347i	$-0.992030\pi$
$617$		−	1.24370i		−	0.0500694i	0.999687	−	0.0250347i	$-0.00796963\pi$
$618$		−	4.57972i		−	0.184223i
$619$	−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
$622$	−33.7004			−1.35126
$623$	−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
$630$	5.75089	−	0.173069i	0.229121	−	0.00689525i
$631$	14.6542	−	14.6542i	0.583374	−	0.583374i	−0.352455	−	0.935829i	$-0.614653\pi$
$631$	14.6542	−	14.6542i	0.583374	−	0.583374i	0.935829	+	0.352455i	$0.114653\pi$
$632$	26.2784			1.04530
$633$	0.763953	−	0.763953i	0.0303644	−	0.0303644i
$634$	−13.9297			−0.553218
$635$	−3.72842	+	3.95979i	−0.147958	+	0.157140i
$636$			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	$0.886500\pi$
$642$			5.02675i			0.198390i
$643$	2.66903			0.105256			0.0526282	−	0.998614i	$-0.483240\pi$
$643$	2.66903			0.105256			0.0526282	+	0.998614i	$0.483240\pi$
$644$	0.701756	+	0.701756i	0.0276531	+	0.0276531i
$645$	3.13556	−	0.0943630i	0.123463	−	0.00371554i
$646$	−22.7246			−0.894087
$647$	−29.8183	+	29.8183i	−1.17228	+	1.17228i	−0.190615	+	0.981665i	$0.561048\pi$
$647$	−29.8183	+	29.8183i	−1.17228	+	1.17228i	−0.981665	+	0.190615i	$0.938952\pi$
$648$			20.4084i			0.801719i
$649$	−0.583029			−0.0228859
$650$		0			0
$651$	−1.01136			−0.0396385
$652$			5.55807i			0.217671i
$653$	17.8654	−	17.8654i	0.699125	−	0.699125i	−0.265096	−	0.964222i	$-0.585404\pi$
$653$	17.8654	−	17.8654i	0.699125	−	0.699125i	0.964222	+	0.265096i	$0.0854038\pi$
$654$	−3.62971			−0.141933
$655$	14.7671	−	0.444408i	0.576999	−	0.0173644i
$656$	12.0463	+	12.0463i	0.470328	+	0.470328i
$657$	−11.6017			−0.452624
$658$		−	7.94187i		−	0.309606i
$659$			37.8224i			1.47335i	0.676247	+	0.736675i	$0.263605\pi$
$659$			37.8224i			1.47335i	−0.676247	+	0.736675i	$0.736395\pi$
$660$	−0.00103941	−	0.0345385i	−4.04591e−5	−	0.00134441i
$661$	−12.1671	+	12.1671i	−0.473244	+	0.473244i	−0.902963	−	0.429719i	$-0.858613\pi$
$661$	−12.1671	+	12.1671i	−0.473244	+	0.473244i	0.429719	+	0.902963i	$0.358613\pi$
$662$	20.3625	−	20.3625i	0.791409	−	0.791409i
$663$		0			0
$664$			31.6705i			1.22905i
$665$	3.83461	−	4.07257i	0.148700	−	0.157927i
$666$	31.9389			1.23761
$667$	5.86264	−	5.86264i	0.227002	−	0.227002i
$668$	−8.36582			−0.323683
$669$	−2.59063	+	2.59063i	−0.100159	+	0.100159i
$670$	−17.3214	+	0.521278i	−0.669184	+	0.0201387i
$671$	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	$-0.0426113\pi$
$673$	22.2477	+	22.2477i	0.857585	+	0.857585i	−0.133468	+	0.991053i	$0.542611\pi$
$674$	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	−0.993191	−	0.116494i	$-0.962835\pi$
$677$	−28.8731	−	28.8731i	−1.10968	−	1.10968i	−0.116494	−	0.993191i	$-0.537165\pi$
$678$	1.42516			0.0547329
$679$			4.15139i			0.159316i
$680$	−12.0711	−	11.3658i	−0.462907	−	0.435859i
$681$	0.891066	+	0.891066i	0.0341457	+	0.0341457i
$682$		−	2.26872i		−	0.0868738i
$683$		−	31.7791i		−	1.21600i	−0.793939	−	0.607998i	$-0.791973\pi$
$683$		−	31.7791i		−	1.21600i	0.793939	−	0.607998i	$-0.208027\pi$
$684$	−4.88503	−	4.88503i	−0.186784	−	0.186784i
$685$	−9.06426	+	0.272783i	−0.346327	+	0.0104225i
$686$			11.9041i			0.454501i
$687$	3.10149			0.118329
$688$	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	0.969023	−	0.246971i	$-0.0794351\pi$
$691$	18.9805	+	18.9805i	0.722052	+	0.722052i	−0.246971	+	0.969023i	$0.579435\pi$
$692$	−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
$695$	0.862523	+	28.6606i	0.0327174	+	1.08716i
$696$	−0.771040	+	0.771040i	−0.0292262	+	0.0292262i
$697$	−11.2462			−0.425980
$698$	−5.68217	+	5.68217i	−0.215073	+	0.215073i
$699$	−1.63505			−0.0618433
$700$	−1.39952	+	0.0843120i	−0.0528970	+	0.00318669i
$701$			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
$707$			7.42171i			0.279122i
$708$	−0.384141			−0.0144369
$709$	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	$0.501243\pi$
$710$	−37.9861	+	40.3433i	−1.42559	+	1.51406i
$711$	−32.9845			−1.23702
$712$	−15.1698	+	15.1698i	−0.568512	+	0.568512i
$713$		−	33.0842i		−	1.23901i
$714$	0.538902			0.0201679
$715$		0			0
$716$	2.90161			0.108438
$717$			3.85300i			0.143893i
$718$	15.9176	−	15.9176i	0.594038	−	0.594038i
$719$	−29.1155			−1.08583			−0.542913	−	0.839789i	$-0.682679\pi$
$719$	−29.1155			−1.08583			−0.542913	+	0.839789i	$0.682679\pi$
$720$	−0.948298	−	31.5108i	−0.0353410	−	1.17434i
$721$	−5.67879	−	5.67879i	−0.211489	−	0.211489i
$722$	−2.87468			−0.106985
$723$		−	3.38055i		−	0.125724i
$724$		−	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	$-0.884210\pi$
$727$	−15.6053	+	15.6053i	−0.578768	+	0.578768i	0.355796	+	0.934564i	$0.384210\pi$
$728$		0			0
$729$		−	24.9204i		−	0.922977i
$730$	13.8777	−	0.417641i	0.513637	−	0.0154576i
$731$	−22.3479			−0.826568
$732$	0.560075	−	0.560075i	0.0207010	−	0.0207010i
$733$	−34.8651			−1.28777			−0.643886	−	0.765121i	$-0.722679\pi$
$733$	−34.8651			−1.28777			−0.643886	+	0.765121i	$0.722679\pi$
$734$	−22.5486	+	22.5486i	−0.832283	+	0.832283i
$735$	2.02622	−	2.15196i	0.0747381	−	0.0793761i
$736$	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
$743$	3.12911			0.114796			0.0573980	−	0.998351i	$-0.481720\pi$
$743$	3.12911			0.114796			0.0573980	+	0.998351i	$0.481720\pi$
$744$			4.35115i			0.159521i
$745$	6.52203	−	6.92677i	0.238949	−	0.253777i
$746$	−29.3652	−	29.3652i	−1.07514	−	1.07514i
$747$		−	39.7526i		−	1.45447i
$748$			0.246164i			0.00900064i
$749$	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	$0.957748\pi$
$752$	−43.5158			−1.58686
$753$	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	0.886965	−	0.461836i	$-0.152809\pi$
$757$	11.6968	+	11.6968i	0.425129	+	0.425129i	−0.461836	+	0.886965i	$0.652809\pi$
$758$	25.2471	+	25.2471i	0.917016	+	0.917016i
$759$	0.0756220	−	0.0756220i	0.00274490	−	0.00274490i
$760$	−17.5212	−	16.4975i	−0.635563	−	0.598426i
$761$	16.3741	−	16.3741i	0.593559	−	0.593559i	−0.345032	−	0.938591i	$-0.612132\pi$
$761$	16.3741	−	16.3741i	0.593559	−	0.593559i	0.938591	+	0.345032i	$0.112132\pi$
$762$	−0.760555			−0.0275520
$763$	−4.50079	+	4.50079i	−0.162939	+	0.162939i
$764$	12.0086			0.434457
$765$	15.1516	+	14.2663i	0.547809	+	0.515800i
$766$			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
$772$		−	8.09938i		−	0.291503i
$773$	8.08997			0.290976			0.145488	−	0.989360i	$-0.453525\pi$
$773$	8.08997			0.290976			0.145488	+	0.989360i	$0.453525\pi$
$774$	−23.5921	−	23.5921i	−0.848001	−	0.848001i
$775$	34.9776	+	31.0027i	1.25643	+	1.11365i
$776$	17.8604			0.641150
$777$	−0.520704	+	0.520704i	−0.0186801	+	0.0186801i
$778$		−	22.7032i		−	0.813950i
$779$	−16.3238			−0.584863
$780$		0			0
$781$	−2.39481			−0.0856930
$782$			17.6288i			0.630405i
$783$	1.94834	−	1.94834i	0.0696279	−	0.0696279i
$784$	31.8973			1.13919
$785$	5.29272	+	4.98347i	0.188905	+	0.177868i
$786$	1.46083	+	1.46083i	0.0521063	+	0.0521063i
$787$	16.2116			0.577882			0.288941	−	0.957347i	$-0.406697\pi$
$787$	16.2116			0.577882			0.288941	+	0.957347i	$0.406697\pi$
$788$			2.92148i			0.104073i
$789$		−	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
$795$	−0.0696238	−	2.31351i	−0.00246930	−	0.0820519i
$796$	−4.75757			−0.168627
$797$	−11.7874	+	11.7874i	−0.417531	+	0.417531i	−0.884352	−	0.466821i	$-0.845399\pi$
$797$	−11.7874	+	11.7874i	−0.417531	+	0.417531i	0.466821	+	0.884352i	$0.345399\pi$
$798$	0.782216			0.0276901
$799$	20.3129	−	20.3129i	0.718617	−	0.718617i
$800$	0.850077	+	14.1107i	0.0300548	+	0.498889i
$801$	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
$808$	31.9301			1.12330
$809$		−	24.1266i		−	0.848247i	−0.905604	−	0.424123i	$-0.860582\pi$
$809$		−	24.1266i		−	0.848247i	0.905604	−	0.424123i	$-0.139418\pi$
$810$	0.922156	+	30.6421i	0.0324013	+	1.07665i
$811$	−17.7808	−	17.7808i	−0.624369	−	0.624369i	0.322276	−	0.946646i	$-0.395552\pi$
$811$	−17.7808	−	17.7808i	−0.624369	−	0.624369i	−0.946646	+	0.322276i	$0.895552\pi$
$812$		−	0.656902i		−	0.0230527i
$813$		−	2.54232i		−	0.0891629i
$814$	−1.16806	−	1.16806i	−0.0409403	−	0.0409403i
$815$	−0.731041	−	24.2916i	−0.0256073	−	0.850898i
$816$		−	2.95280i		−	0.103369i
$817$	−32.4380			−1.13486
$818$	−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	0.0218363	−	0.999762i	$-0.493049\pi$
$821$	−28.0206	−	28.0206i	−0.977925	−	0.977925i	−0.999762	+	0.0218363i	$0.993049\pi$
$822$	−0.896680	−	0.896680i	−0.0312753	−	0.0312753i
$823$	−28.2448	−	28.2448i	−0.984551	−	0.984551i	0.0153317	−	0.999882i	$-0.495120\pi$
$823$	−28.2448	−	28.2448i	−0.984551	−	0.984551i	−0.999882	+	0.0153317i	$0.995120\pi$
$824$	−24.4316	+	24.4316i	−0.851116	+	0.851116i
$825$	0.00908554	+	0.150814i	0.000316318	+	0.00525067i
$826$	−2.33919	+	2.33919i	−0.0813910	+	0.0813910i
$827$	−25.6019			−0.890264			−0.445132	−	0.895465i	$-0.646843\pi$
$827$	−25.6019			−0.890264			−0.445132	+	0.895465i	$0.646843\pi$
$828$	−3.78961	+	3.78961i	−0.131698	+	0.131698i
$829$	18.8337			0.654121			0.327060	−	0.945003i	$-0.393942\pi$
$829$	18.8337			0.654121			0.327060	+	0.945003i	$0.393942\pi$
$830$	1.43103	+	47.5514i	0.0496718	+	1.65053i
$831$		−	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
$837$		−	10.9949i		−	0.380040i
$838$	−1.59576			−0.0551246
$839$	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	$0.608361\pi$
$840$	0.415508	+	0.391229i	0.0143364	+	0.0134987i
$841$	23.5121			0.810761
$842$	−0.467095	+	0.467095i	−0.0160971	+	0.0160971i
$843$			1.17938i			0.0406199i
$844$	2.80018			0.0963863
$845$		0			0
$846$	42.8875			1.47450
$847$			6.01875i			0.206807i
$848$	17.6620	−	17.6620i	0.606515	−	0.606515i
$849$	0.303449			0.0104143
$850$	−18.6377	−	16.5197i	−0.639268	−	0.566621i
$851$	−17.0335	−	17.0335i	−0.583901	−	0.583901i
$852$	−1.57787			−0.0540569
$853$			2.14143i			0.0733210i	0.999328	+	0.0366605i	$0.0116720\pi$
$853$			2.14143i			0.0733210i	−0.999328	+	0.0366605i	$0.988328\pi$
$854$		−	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	0.286686	−	0.958025i	$-0.407446\pi$
$857$	36.4384	−	36.4384i	1.24471	−	1.24471i	0.958025	−	0.286686i	$-0.0925537\pi$
$858$		0			0
$859$			4.40721i			0.150372i	0.997170	+	0.0751861i	$0.0239551\pi$
$859$			4.40721i			0.150372i	−0.997170	+	0.0751861i	$0.976045\pi$
$860$	5.91947	+	5.57359i	0.201852	+	0.190058i
$861$	0.387112			0.0131927
$862$	4.65208	−	4.65208i	0.158451	−	0.158451i
$863$	−53.8912			−1.83448			−0.917239	−	0.398338i	$-0.869587\pi$
$863$	−53.8912			−1.83448			−0.917239	+	0.398338i	$0.869587\pi$
$864$	2.35140	−	2.35140i	0.0799961	−	0.0799961i
$865$	11.1253	+	10.4752i	0.378270	+	0.356168i
$866$	−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
$873$	−22.4183			−0.758743
$874$			25.5882i			0.865534i
$875$	6.10554	−	0.552563i	0.206405	−	0.0186800i
$876$	0.279553	+	0.279553i	0.00944522	+	0.00944522i
$877$			13.1339i			0.443501i	0.975103	+	0.221750i	$0.0711770\pi$
$877$			13.1339i			0.443501i	−0.975103	+	0.221750i	$0.928823\pi$
$878$		−	21.9993i		−	0.742440i
$879$	−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	$0.788467\pi$
$882$	−31.4368			−1.05853
$883$	−7.40474	−	7.40474i	−0.249189	−	0.249189i	0.571449	−	0.820638i	$-0.306382\pi$
$883$	−7.40474	−	7.40474i	−0.249189	−	0.249189i	−0.820638	+	0.571449i	$0.806382\pi$
$884$		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	−0.930839	−	0.365429i	$-0.880922\pi$
$887$	−38.6062	−	38.6062i	−1.29627	−	1.29627i	−0.365429	−	0.930839i	$-0.619078\pi$
$888$	2.24020	+	2.24020i	0.0751763	+	0.0751763i
$889$	−0.943078	+	0.943078i	−0.0316298	+	0.0316298i
$890$	−22.0911	+	23.4620i	−0.740497	+	0.786449i
$891$	−0.936839	+	0.936839i	−0.0313853	+	0.0313853i
$892$	−9.49566			−0.317938
$893$	29.4841	−	29.4841i	0.986647	−	0.986647i
$894$	1.33042			0.0444959
$895$	−12.6815	+	0.381643i	−0.423897	+	0.0127569i
$896$			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
$902$			0.868379i			0.0289139i
$903$	0.769250			0.0255990
$904$	−7.60285	−	7.60285i	−0.252867	−	0.252867i
$905$	0.241550	+	8.02642i	0.00802940	+	0.266807i
$906$	−2.16429			−0.0719036
$907$	−28.9752	+	28.9752i	−0.962106	+	0.962106i	−0.999308	−	0.0372014i	$-0.988156\pi$
$907$	−28.9752	+	28.9752i	−0.962106	+	0.962106i	0.0372014	+	0.999308i	$0.488156\pi$
$908$			3.26610i			0.108389i
$909$	−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	$0.368567\pi$
$912$		−	4.28599i		−	0.141923i
$913$	−1.45382	+	1.45382i	−0.0481143	+	0.0481143i
$914$	−58.5698			−1.93732
$915$	−2.37415	+	2.52148i	−0.0784869	+	0.0833575i
$916$	5.68408	+	5.68408i	0.187807	+	0.187807i
$917$	3.62283			0.119636
$918$			5.85860i			0.193363i
$919$		−	34.8809i		−	1.15061i	−0.817938	−	0.575307i	$-0.804883\pi$
$919$		−	34.8809i		−	1.15061i	0.817938	−	0.575307i	$-0.195117\pi$
$920$	−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
$925$	33.9701	−	2.04648i	1.11693	−	0.0672877i
$926$	25.2893			0.831058
$927$	30.6665	−	30.6665i	1.00722	−	1.00722i
$928$	−6.62322			−0.217418
$929$	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	$0.204531\pi$
$930$	0.196607	+	6.53301i	0.00644700	+	0.214226i
$931$	−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	0.143757	−	0.989613i	$-0.454082\pi$
$937$	−25.8920	−	25.8920i	−0.845856	−	0.845856i	−0.989613	+	0.143757i	$0.954082\pi$
$938$	−4.24947			−0.138750
$939$		−	4.00886i		−	0.130824i
$940$	−10.4465	+	0.314380i	−0.340726	+	0.0102540i
$941$	20.9205	+	20.9205i	0.681989	+	0.681989i	0.960448	−	0.278459i	$-0.0898236\pi$
$941$	20.9205	+	20.9205i	0.681989	+	0.681989i	−0.278459	+	0.960448i	$0.589824\pi$
$942$			1.01657i			0.0331216i
$943$			12.6634i			0.412376i
$944$	12.8171	+	12.8171i	0.417162	+	0.417162i
$945$	−1.04994	−	0.988595i	−0.0341547	−	0.0321590i
$946$			1.72560i			0.0561042i
$947$	27.6047			0.897032			0.448516	−	0.893775i	$-0.351953\pi$
$947$	27.6047			0.897032			0.448516	+	0.893775i	$0.351953\pi$
$948$	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	$-0.0949559\pi$
$953$	20.4341	+	20.4341i	0.661926	+	0.661926i	−0.293908	+	0.955834i	$0.594956\pi$
$954$	−17.4070	+	17.4070i	−0.563572	+	0.563572i
$955$	−52.4838	+	1.57947i	−1.69834	+	0.0511104i
$956$	−7.06137	+	7.06137i	−0.228381	+	0.228381i
$957$	−0.0707884			−0.00228826
$958$	−18.6015	+	18.6015i	−0.600989	+	0.600989i
$959$	−2.22374			−0.0718083
$960$	1.52497	−	1.61961i	0.0492183	−	0.0522726i
$961$			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
$967$		−	4.31688i		−	0.138822i	−0.997588	−	0.0694108i	$-0.977888\pi$
$967$		−	4.31688i		−	0.138822i	0.997588	−	0.0694108i	$-0.0221119\pi$
$968$	25.8942			0.832272
$969$	2.00067	+	2.00067i	0.0642707	+	0.0642707i
$970$	26.8163	−	0.807022i	0.861021	−	0.0259119i
$971$	−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
$973$			7.03132i			0.225414i
$974$	−41.6466			−1.33444
$975$		0			0
$976$	−37.3745			−1.19633
$977$			47.6508i			1.52448i	0.647292	+	0.762242i	$0.275902\pi$
$977$			47.6508i			1.52448i	−0.647292	+	0.762242i	$0.724098\pi$
$978$	2.40304	−	2.40304i	0.0768408	−	0.0768408i
$979$	−1.39272			−0.0445116
$980$	7.65731	−	0.230442i	0.244604	−	0.00736121i
$981$	−24.3051	−	24.3051i	−0.776001	−	0.776001i
$982$	−65.9315			−2.10396
$983$			7.39039i			0.235717i	0.993030	+	0.117858i	$0.0376029\pi$
$983$			7.39039i			0.235717i	−0.993030	+	0.117858i	$0.962397\pi$
$984$		−	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
$990$	1.10158	−	1.16994i	0.0350105	−	0.0371831i
$991$	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
$993$	−3.58541			−0.113780
$994$	−9.60830	+	9.60830i	−0.304757	+	0.304757i
$995$	20.7930	−	0.625753i	0.659182	−	0.0198377i
$996$	−0.957877	+	0.957877i	−0.0303515	+	0.0303515i
$997$	23.9164	+	23.9164i	0.757441	+	0.757441i	0.975856	−	0.218415i	$-0.0700886\pi$
$997$	23.9164	+	23.9164i	0.757441	+	0.757441i	−0.218415	+	0.975856i	$0.570089\pi$
$998$	−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.f.d.437.4		20
5.3	odd	4		845.2.k.d.268.4		20
13.2	odd	12		845.2.o.g.357.4		20
13.3	even	3		845.2.t.e.657.4		20
13.4	even	6		65.2.t.a.37.4	yes	20
13.5	odd	4		845.2.k.d.577.4		20
13.6	odd	12		845.2.o.f.587.4		20
13.7	odd	12		845.2.o.e.587.2		20
13.8	odd	4		845.2.k.e.577.7		20
13.9	even	3		845.2.t.g.427.2		20
13.10	even	6		845.2.t.f.657.2		20
13.11	odd	12		65.2.o.a.32.2	✓	20
13.12	even	2		845.2.f.e.437.7		20
39.11	even	12		585.2.cf.a.487.4		20
39.17	odd	6		585.2.dp.a.37.2		20
65.3	odd	12		845.2.o.f.488.4		20
65.4	even	6		325.2.x.b.232.2		20
65.8	even	4		845.2.f.e.408.4		20
65.17	odd	12		325.2.s.b.193.4		20
65.18	even	4	inner	845.2.f.d.408.7		20
65.23	odd	12		845.2.o.e.488.2		20
65.24	odd	12		325.2.s.b.32.4		20
65.28	even	12		845.2.t.g.188.2		20
65.33	even	12		845.2.t.f.418.2		20
65.37	even	12		325.2.x.b.318.2		20
65.38	odd	4		845.2.k.e.268.7		20
65.43	odd	12		65.2.o.a.63.2	yes	20
65.48	odd	12		845.2.o.g.258.4		20
65.58	even	12		845.2.t.e.418.4		20
65.63	even	12		65.2.t.a.58.4	yes	20
195.128	odd	12		585.2.dp.a.253.2		20
195.173	even	12		585.2.cf.a.388.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.2	✓	20	13.11	odd	12
65.2.o.a.63.2	yes	20	65.43	odd	12
65.2.t.a.37.4	yes	20	13.4	even	6
65.2.t.a.58.4	yes	20	65.63	even	12
325.2.s.b.32.4		20	65.24	odd	12
325.2.s.b.193.4		20	65.17	odd	12
325.2.x.b.232.2		20	65.4	even	6
325.2.x.b.318.2		20	65.37	even	12
585.2.cf.a.388.4		20	195.173	even	12
585.2.cf.a.487.4		20	39.11	even	12
585.2.dp.a.37.2		20	39.17	odd	6
585.2.dp.a.253.2		20	195.128	odd	12
845.2.f.d.408.7		20	65.18	even	4	inner
845.2.f.d.437.4		20	1.1	even	1	trivial
845.2.f.e.408.4		20	65.8	even	4
845.2.f.e.437.7		20	13.12	even	2
845.2.k.d.268.4		20	5.3	odd	4
845.2.k.d.577.4		20	13.5	odd	4
845.2.k.e.268.7		20	65.38	odd	4
845.2.k.e.577.7		20	13.8	odd	4
845.2.o.e.488.2		20	65.23	odd	12
845.2.o.e.587.2		20	13.7	odd	12
845.2.o.f.488.4		20	65.3	odd	12
845.2.o.f.587.4		20	13.6	odd	12
845.2.o.g.258.4		20	65.48	odd	12
845.2.o.g.357.4		20	13.2	odd	12
845.2.t.e.418.4		20	65.58	even	12
845.2.t.e.657.4		20	13.3	even	3
845.2.t.f.418.2		20	65.33	even	12
845.2.t.f.657.2		20	13.10	even	6
845.2.t.g.188.2		20	65.28	even	12
845.2.t.g.427.2		20	13.9	even	3

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

\(f(q)\)	\(=\)	\(q-1.58474i q^{2} +(-0.139520 + 0.139520i) q^{3} -0.511395 q^{4} +(2.23506 - 0.0672627i) q^{5} +(0.221103 + 0.221103i) q^{6} +0.548328 q^{7} -2.35905i 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} +(-0.302450 + 0.321219i) q^{15} -4.76126 q^{16} +(2.22252 - 2.22252i) q^{17} +4.69252 q^{18} +(3.22599 - 3.22599i) q^{19} +(-1.14300 + 0.0343978i) 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} -0.280412 q^{28} +2.34263i q^{29} +(0.509048 + 0.479305i) q^{30} +(6.61000 + 6.61000i) q^{31} +2.82726i q^{32} +0.0302175i q^{33} +(-3.52211 - 3.52211i) q^{34} +(1.22554 - 0.0368820i) q^{35} -1.51427i q^{36} +6.80635 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} +(0.199169 + 6.61815i) q^{45} +(-3.96595 + 3.96595i) q^{46} +9.13956 q^{47} +(0.664291 - 0.664291i) q^{48} -6.69934 q^{49} +(-0.476486 - 7.90935i) 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} +0.900179i q^{57} +3.71246 q^{58} +(-2.69196 - 2.69196i) q^{59} +(0.154672 - 0.164270i) q^{60} +7.84971 q^{61} +(10.4751 - 10.4751i) q^{62} +1.62364i q^{63} -5.04207 q^{64} +0.0478868 q^{66} -4.89032i q^{67} +(-1.13659 + 1.13659i) q^{68} +0.698322 q^{69} +(-0.0584483 - 1.94217i) q^{70} +(-11.0573 - 11.0573i) q^{71} +6.98531 q^{72} +3.91807i 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} +(-10.6417 + 0.320255i) q^{80} -8.65113 q^{81} +(-4.00947 + 4.00947i) q^{82} -13.4251 q^{83} +(0.0391231 - 0.0391231i) q^{84} +(4.81797 - 5.11695i) 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} -1.84445 q^{93} -14.4838i q^{94} +(6.99327 - 7.42725i) q^{95} +(-0.394459 - 0.394459i) q^{96} +7.57101i q^{97} +10.6167i q^{98} +(0.320657 + 0.320657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7} - 8 q^{10} - 8 q^{11} - 24 q^{12} - 28 q^{15} + 4 q^{16} - 14 q^{17} - 4 q^{19} + 12 q^{20} - 4 q^{21} - 32 q^{22} + 8 q^{23} + 4 q^{24} + 18 q^{25} + 4 q^{27}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7 - 8 * q^10 - 8 * q^11 - 24 * q^12 - 28 * q^15 + 4 * q^16 - 14 * q^17 - 4 * q^19 + 12 * q^20 - 4 * q^21 - 32 * q^22 + 8 * q^23 + 4 * q^24 + 18 * q^25 + 4 * q^27 + 36 * q^28 + 40 * q^30 - 2 * q^34 - 20 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 - 32 * q^43 + 36 * q^44 + 6 * q^45 - 4 * q^46 + 40 * q^47 + 28 * q^48 - 36 * q^49 - 42 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 8 * q^59 - 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 + 12 * q^70 + 40 * q^71 + 8 * q^72 + 4 * q^75 + 16 * q^76 - 28 * q^77 - 112 * q^80 + 28 * q^81 - 34 * q^82 - 48 * q^83 - 8 * q^84 + 2 * q^85 - 60 * q^86 - 28 * q^87 - 32 * q^88 - 12 * q^89 + 46 * q^90 - 8 * q^92 + 64 * q^93 + 40 * q^95 - 56 * q^96 - 60 * q^99

Introduction

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