LMFDB - Embedded newform 845.2.f.e.408.4

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			408.4
Root			$-1.58474i$ of defining polynomial
Character	$\chi$	$=$	845.408
Dual form			845.2.f.e.437.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.58474i q^{2} +(-0.139520 - 0.139520i) q^{3} -0.511395 q^{4} +(-2.23506 - 0.0672627i) q^{5} +(-0.221103 + 0.221103i) q^{6} -0.548328 q^{7} -2.35905i q^{8} -2.96107i q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.58474i		−	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	0.665683	−	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
$5$	−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	$-0.533044\pi$
$7$	−0.548328			−0.207248			−0.103624	+	0.994617i	$0.533044\pi$
$8$		−	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	$-0.257350\pi$
$11$	−0.108291	−	0.108291i	−0.0326509	−	0.0326509i	−0.723244	+	0.690593i	$0.757350\pi$
$12$	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	0.923247	−	0.384207i	$-0.125525\pi$
$17$	2.22252	+	2.22252i	0.539041	+	0.539041i	−0.384207	+	0.923247i	$0.625525\pi$
$18$	−4.69252			−1.10604
$19$	−3.22599	−	3.22599i	−0.740092	−	0.740092i	0.232503	−	0.972596i	$-0.425308\pi$
$19$	−3.22599	−	3.22599i	−0.740092	−	0.740092i	−0.972596	+	0.232503i	$0.925308\pi$
$20$	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	−0.918123	−	0.396297i	$-0.870295\pi$
$23$	−2.50259	+	2.50259i	−0.521826	+	0.521826i	0.396297	+	0.918123i	$0.370295\pi$
$24$	−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	$-0.930207\pi$
$29$		−	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	−0.209350	+	0.977841i	$0.567135\pi$
$31$	−6.61000	+	6.61000i	−1.18719	+	1.18719i	−0.977841	+	0.209350i	$0.932865\pi$
$32$			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	$-0.688998\pi$
$37$	−6.80635			−1.11896			−0.559478	+	0.828845i	$0.688998\pi$
$38$	−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	$-0.659865\pi$
$41$	2.53005	−	2.53005i	0.395128	−	0.395128i	0.876511	+	0.481382i	$0.159865\pi$
$42$	0.121237	−	0.121237i	0.0187072	−	0.0187072i
$43$	−5.02761	+	5.02761i	−0.766703	+	0.766703i	−0.977524	−	0.210822i	$-0.932386\pi$
$43$	−5.02761	+	5.02761i	−0.766703	+	0.766703i	0.210822	+	0.977524i	$0.432386\pi$
$44$	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	$-0.732239\pi$
$47$	−9.13956			−1.33314			−0.666571	+	0.745442i	$0.732239\pi$
$48$	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	0.404844	−	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
$57$			0.900179i			0.119232i
$58$	−3.71246			−0.487469
$59$	2.69196	−	2.69196i	0.350463	−	0.350463i	−0.509819	−	0.860282i	$-0.670288\pi$
$59$	2.69196	−	2.69196i	0.350463	−	0.350463i	0.860282	+	0.509819i	$0.170288\pi$
$60$	−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	0.392513	−	0.919747i	$-0.371606\pi$
$71$	11.0573	−	11.0573i	1.31226	−	1.31226i	0.919747	−	0.392513i	$-0.128394\pi$
$72$	−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	$-0.784430\pi$
$79$		−	11.1394i		−	1.25328i	0.779309	−	0.626640i	$-0.215570\pi$
$80$	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	$-0.236337\pi$
$83$	13.4251			1.47360			0.736798	+	0.676113i	$0.236337\pi$
$84$	−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	$-0.589916\pi$
$89$	6.43047	−	6.43047i	0.681629	−	0.681629i	0.960367	+	0.278738i	$0.0899162\pi$
$90$	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	$-0.764833\pi$
$101$		−	13.5352i		−	1.34680i	0.739279	−	0.673400i	$-0.235167\pi$
$102$	−0.982810			−0.0973127
$103$	−10.3566	+	10.3566i	−1.02046	+	1.02046i	−0.0206759	+	0.999786i	$0.506582\pi$
$103$	−10.3566	+	10.3566i	−1.02046	+	1.02046i	−0.999786	+	0.0206759i	$0.993418\pi$
$104$		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	$-0.0623623\pi$
$109$	8.20821	+	8.20821i	0.786203	+	0.786203i	−0.194666	+	0.980870i	$0.562362\pi$
$110$	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	0.842257	−	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
$115$	5.76176	−	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	0.626668	−	0.779286i	$-0.284418\pi$
$127$	−1.71992	−	1.71992i	−0.152618	−	0.152618i	−0.779286	+	0.626668i	$0.784418\pi$
$128$			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	$-0.444576\pi$
$137$	4.05549			0.346484			0.173242	+	0.984879i	$0.444576\pi$
$138$		−	1.10666i		−	0.0942050i
$139$		−	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
$145$	−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	$-0.305761\pi$
$149$	−3.00860	−	3.00860i	−0.246474	−	0.246474i	−0.819522	+	0.573048i	$0.805761\pi$
$150$	−1.16999	+	1.03703i	−0.0955294	+	0.0846734i
$151$	4.89430	+	4.89430i	0.398293	+	0.398293i	0.877630	−	0.479338i	$-0.159123\pi$
$151$	4.89430	+	4.89430i	0.398293	+	0.398293i	−0.479338	+	0.877630i	$0.659123\pi$
$152$	−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	$0.208588\pi$
$158$	−17.6530			−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	$-0.718153\pi$
$167$	−16.3588			−1.26588			−0.632942	+	0.774199i	$0.718153\pi$
$168$	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	−0.499137	−	0.866523i	$-0.666350\pi$
$173$	4.83220	−	4.83220i	0.367385	−	0.367385i	0.866523	+	0.499137i	$0.166350\pi$
$174$	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	$-0.957390\pi$
$181$		−	3.59115i		−	0.266928i	0.991054	−	0.133464i	$-0.0426101\pi$
$182$		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	$-0.713561\pi$
$223$	−18.5682			−1.24342			−0.621708	+	0.783249i	$0.713561\pi$
$224$		−	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	$-0.576169\pi$
$229$	11.1149	−	11.1149i	0.734491	−	0.734491i	0.971506	+	0.237015i	$0.0761691\pi$
$230$	−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	−0.488623	−	0.872495i	$-0.662500\pi$
$233$	5.85956	−	5.85956i	0.383873	−	0.383873i	0.872495	+	0.488623i	$0.162500\pi$
$234$		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	$-0.467588\pi$
$239$	−13.8081	−	13.8081i	−0.893170	−	0.893170i	−0.994820	+	0.101650i	$0.967588\pi$
$240$	−1.44005	−	1.52941i	−0.0929546	−	0.0987230i
$241$	12.1149	+	12.1149i	0.780391	+	0.780391i	0.979897	−	0.199505i	$-0.0639336\pi$
$241$	12.1149	+	12.1149i	0.780391	+	0.780391i	−0.199505	+	0.979897i	$0.563934\pi$
$242$	−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	$0.101708\pi$
$251$			9.95304i			0.628230i	−0.949385	+	0.314115i	$0.898292\pi$
$252$		−	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	0.765177	−	0.643820i	$-0.222651\pi$
$257$	1.94551	+	1.94551i	0.121357	+	0.121357i	−0.643820	+	0.765177i	$0.722651\pi$
$258$		−	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	0.559491	−	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
$265$	8.04147	+	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	$-0.776026\pi$
$269$		−	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	0.927435	−	0.373985i	$-0.122009\pi$
$271$	9.11094	+	9.11094i	0.553450	+	0.553450i	−0.373985	+	0.927435i	$0.622009\pi$
$272$	−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	0.0918270	−	0.995775i	$-0.470729\pi$
$277$	−15.0447	−	15.0447i	−0.903948	−	0.903948i	−0.995775	+	0.0918270i	$0.970729\pi$
$278$	−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	$-0.307055\pi$
$281$	−4.22655	−	4.22655i	−0.252135	−	0.252135i	−0.821845	+	0.569711i	$0.807055\pi$
$282$	2.02078	−	2.02078i	0.120336	−	0.120336i
$283$	−1.08748	+	1.08748i	−0.0646437	+	0.0646437i	−0.738690	−	0.674046i	$-0.764555\pi$
$283$	−1.08748	+	1.08748i	−0.0646437	+	0.0646437i	0.674046	+	0.738690i	$0.264555\pi$
$284$	−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	$-0.480721\pi$
$307$	2.12112			0.121058			0.0605292	+	0.998166i	$0.480721\pi$
$308$	−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	$0.206000\pi$
$311$			21.2656i			1.20586i	−0.797794	+	0.602931i	$0.794000\pi$
$312$		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
$317$		−	8.78989i		−	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	$-0.916444\pi$
$331$	−12.8491	+	12.8491i	−0.706250	+	0.706250i	0.259494	+	0.965745i	$0.416444\pi$
$332$	−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	0.0584999	−	0.998287i	$-0.481368\pi$
$337$	−17.2522	−	17.2522i	−0.939788	−	0.939788i	−0.998287	+	0.0584999i	$0.981368\pi$
$338$		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	−0.839053	−	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	$-0.706667\pi$
$349$	3.58556	−	3.58556i	0.191931	−	0.191931i	0.796530	+	0.604599i	$0.206667\pi$
$350$	−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	$-0.261220\pi$
$353$	25.6178			1.36350			0.681749	+	0.731586i	$0.261220\pi$
$354$			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	$-0.872306\pi$
$359$	−10.0443	+	10.0443i	−0.530117	+	0.530117i	0.390490	+	0.920607i	$0.372306\pi$
$360$	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	−0.973102	−	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
$370$	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	0.999209	−	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
$375$	1.41293	+	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	$-0.0535779\pi$
$379$	15.9314	+	15.9314i	0.818341	+	0.818341i	−0.167526	+	0.985868i	$0.553578\pi$
$380$	−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	$-0.288594\pi$
$383$	24.1261			1.23278			0.616392	+	0.787440i	$0.288594\pi$
$384$	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	$-0.182271\pi$
$397$	33.4931			1.68097			0.840484	+	0.541836i	$0.182271\pi$
$398$		−	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	$-0.403280\pi$
$401$	−13.1161	−	13.1161i	−0.654989	−	0.654989i	−0.954190	+	0.299201i	$0.903280\pi$
$402$	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	$-0.290818\pi$
$409$	−3.65748	−	3.65748i	−0.180851	−	0.180851i	−0.791727	+	0.610876i	$0.790818\pi$
$410$	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	$0.00783009\pi$
$419$			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	−0.699888	−	0.714253i	$-0.746767\pi$
$421$	0.294746	−	0.294746i	0.0143650	−	0.0143650i	0.714253	+	0.699888i	$0.246767\pi$
$422$			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	$-0.781880\pi$
$431$	−2.93555	+	2.93555i	−0.141401	+	0.141401i	0.632863	+	0.774264i	$0.281880\pi$
$432$	3.95989	−	3.95989i	0.190520	−	0.190520i
$433$	−10.6032	+	10.6032i	−0.509556	+	0.509556i	−0.914390	−	0.404834i	$-0.867329\pi$
$433$	−10.6032	+	10.6032i	−0.509556	+	0.509556i	0.404834	+	0.914390i	$0.367329\pi$
$434$	−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	0.904472	−	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
$447$			0.839520i			0.0397079i
$448$	2.76470			0.130620
$449$	−4.70669	+	4.70669i	−0.222122	+	0.222122i	−0.809392	−	0.587269i	$-0.800203\pi$
$449$	−4.70669	+	4.70669i	−0.222122	+	0.222122i	0.587269	+	0.809392i	$0.300203\pi$
$450$	−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	$-0.954479\pi$
$461$	−18.1916	+	18.1916i	−0.847269	+	0.847269i	0.142523	+	0.989792i	$0.454479\pi$
$462$	−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	0.991559	−	0.129657i	$-0.0413877\pi$
$467$	18.6259	+	18.6259i	0.861902	+	0.861902i	−0.129657	+	0.991559i	$0.541388\pi$
$468$		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	$-0.626187\pi$
$479$	11.7379	−	11.7379i	0.536320	−	0.536320i	0.922446	+	0.386126i	$0.126187\pi$
$480$	−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	$0.388044\pi$
$491$			41.6040i			1.87756i	−0.344513	+	0.938781i	$0.611956\pi$
$492$	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	$-0.334796\pi$
$499$	−8.31651	−	8.31651i	−0.372298	−	0.372298i	−0.868314	+	0.496015i	$0.834796\pi$
$500$	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	0.855067	−	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
$505$	−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	$-0.271283\pi$
$509$	−2.13171	−	2.13171i	−0.0944864	−	0.0944864i	−0.752770	+	0.658284i	$0.771283\pi$
$510$	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	0.751463	−	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
$525$	0.358819	+	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	$-0.405831\pi$
$541$	−15.4678	−	15.4678i	−0.665013	−	0.665013i	−0.956557	+	0.291544i	$0.905831\pi$
$542$	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	$0.232959\pi$
$548$	−2.07396			−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	$-0.564055\pi$
$557$	−9.43469			−0.399761			−0.199880	+	0.979820i	$0.564055\pi$
$558$	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	−0.545979	−	0.837799i	$-0.683842\pi$
$563$	6.92420	−	6.92420i	0.291820	−	0.291820i	0.837799	+	0.545979i	$0.183842\pi$
$564$	−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	$0.0114700\pi$
$571$			1.72174i			0.0720527i	−0.999351	+	0.0360264i	$0.988530\pi$
$572$		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	$0.268151\pi$
$599$			36.5285i			1.49252i	−0.665657	+	0.746258i	$0.731849\pi$
$600$	−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	−0.402555	−	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
$613$	15.3746			0.620973			0.310487	−	0.950578i	$-0.399508\pi$
$613$	15.3746			0.620973			0.310487	+	0.950578i	$0.399508\pi$
$614$		−	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	0.171915	−	0.985112i	$-0.445005\pi$
$619$	28.7865	−	28.7865i	1.15703	−	1.15703i	0.985112	−	0.171915i	$-0.0549954\pi$
$620$	−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	$-0.385347\pi$
$631$	−14.6542	−	14.6542i	−0.583374	−	0.583374i	−0.935829	+	0.352455i	$0.885347\pi$
$632$	−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	$-0.886500\pi$
$641$		−	17.6751i		−	0.698123i	0.937100	−	0.349061i	$-0.113500\pi$
$642$			5.02675i			0.198390i
$643$	−2.66903			−0.105256			−0.0526282	−	0.998614i	$-0.516760\pi$
$643$	−2.66903			−0.105256			−0.0526282	+	0.998614i	$0.516760\pi$
$644$	−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	−0.981665	−	0.190615i	$-0.938952\pi$
$647$	−29.8183	−	29.8183i	−1.17228	−	1.17228i	−0.190615	−	0.981665i	$-0.561048\pi$
$648$			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	0.964222	−	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
$655$	−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	$-0.736395\pi$
$659$		−	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	0.902963	−	0.429719i	$-0.141387\pi$
$661$	12.1671	+	12.1671i	0.473244	+	0.473244i	−0.429719	+	0.902963i	$0.641387\pi$
$662$	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	−0.133468	−	0.991053i	$-0.542611\pi$
$673$	22.2477	−	22.2477i	0.857585	−	0.857585i	0.991053	+	0.133468i	$0.0426113\pi$
$674$	−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	$0.962835\pi$
$678$	−1.42516			−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	$-0.920565\pi$
$691$	−18.9805	+	18.9805i	−0.722052	+	0.722052i	0.246971	+	0.969023i	$0.420565\pi$
$692$	−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	$-0.733569\pi$
$701$		−	39.3253i		−	1.48530i	0.669681	−	0.742649i	$-0.266431\pi$
$702$		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	$-0.998757\pi$
$709$	−26.5229	+	26.5229i	−0.996087	+	0.996087i	0.00390546	+	0.999992i	$0.498757\pi$
$710$	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	0.355796	−	0.934564i	$-0.384210\pi$
$727$	−15.6053	−	15.6053i	−0.578768	−	0.578768i	−0.934564	+	0.355796i	$0.884210\pi$
$728$		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	$-0.277321\pi$
$733$	34.8651			1.28777			0.643886	+	0.765121i	$0.277321\pi$
$734$	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	$-0.966686\pi$
$739$	−24.1959	+	24.1959i	−0.890060	+	0.890060i	0.104468	+	0.994528i	$0.466686\pi$
$740$	−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	$-0.518280\pi$
$743$	−3.12911			−0.114796			−0.0573980	+	0.998351i	$0.518280\pi$
$744$		−	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	$-0.957748\pi$
$751$		−	7.25382i		−	0.264696i	0.991203	−	0.132348i	$-0.0422516\pi$
$752$	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	−0.461836	−	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
$760$	17.5212	−	16.4975i	0.635563	−	0.598426i
$761$	−16.3741	−	16.3741i	−0.593559	−	0.593559i	0.345032	−	0.938591i	$-0.387868\pi$
$761$	−16.3741	−	16.3741i	−0.593559	−	0.593559i	−0.938591	+	0.345032i	$0.887868\pi$
$762$	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	$-0.216117\pi$
$769$	4.16667	+	4.16667i	0.150254	+	0.150254i	−0.627978	+	0.778231i	$0.716117\pi$
$770$	−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	$-0.546475\pi$
$773$	−8.08997			−0.290976			−0.145488	+	0.989360i	$0.546475\pi$
$774$	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	$-0.593303\pi$
$787$	−16.2116			−0.577882			−0.288941	+	0.957347i	$0.593303\pi$
$788$			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	0.466821	−	0.884352i	$-0.345399\pi$
$797$	−11.7874	−	11.7874i	−0.417531	−	0.417531i	−0.884352	+	0.466821i	$0.845399\pi$
$798$	−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	$0.139418\pi$
$809$			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	−0.322276	−	0.946646i	$-0.604448\pi$
$811$	17.7808	−	17.7808i	0.624369	−	0.624369i	0.946646	+	0.322276i	$0.104448\pi$
$812$		−	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	$-0.506951\pi$
$821$	28.0206	−	28.0206i	0.977925	−	0.977925i	0.999762	+	0.0218363i	$0.00695127\pi$
$822$	−0.896680	+	0.896680i	−0.0312753	+	0.0312753i
$823$	−28.2448	+	28.2448i	−0.984551	+	0.984551i	−0.999882	−	0.0153317i	$-0.995120\pi$
$823$	−28.2448	+	28.2448i	−0.984551	+	0.984551i	0.0153317	+	0.999882i	$0.495120\pi$
$824$	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	$-0.353157\pi$
$827$	25.6019			0.890264			0.445132	+	0.895465i	$0.353157\pi$
$828$	−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	$-0.891639\pi$
$839$	−17.6320	+	17.6320i	−0.608723	+	0.608723i	0.333890	+	0.942612i	$0.391639\pi$
$840$	−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	0.958025	+	0.286686i	$0.0925537\pi$
$857$	36.4384	+	36.4384i	1.24471	+	1.24471i	0.286686	+	0.958025i	$0.407446\pi$
$858$		0			0
$859$		−	4.40721i		−	0.150372i	−0.997170	−	0.0751861i	$-0.976045\pi$
$859$		−	4.40721i		−	0.150372i	0.997170	−	0.0751861i	$-0.0239551\pi$
$860$	−5.91947	+	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	$-0.130413\pi$
$863$	53.8912			1.83448			0.917239	+	0.398338i	$0.130413\pi$
$864$	−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	$-0.788467\pi$
$881$		−	36.6097i		−	1.23341i	0.787193	−	0.616706i	$-0.211533\pi$
$882$	31.4368			1.05853
$883$	−7.40474	+	7.40474i	−0.249189	+	0.249189i	−0.820638	−	0.571449i	$-0.806382\pi$
$883$	−7.40474	+	7.40474i	−0.249189	+	0.249189i	0.571449	+	0.820638i	$0.306382\pi$
$884$		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
$890$	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	0.0372014	−	0.999308i	$-0.488156\pi$
$907$	−28.9752	−	28.9752i	−0.962106	−	0.962106i	−0.999308	+	0.0372014i	$0.988156\pi$
$908$			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	$0.195117\pi$
$919$			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
$925$	−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	$-0.295469\pi$
$929$	−6.13631	−	6.13631i	−0.201326	−	0.201326i	−0.800568	+	0.599242i	$0.795469\pi$
$930$	−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	−0.989613	−	0.143757i	$-0.954082\pi$
$937$	−25.8920	+	25.8920i	−0.845856	+	0.845856i	0.143757	+	0.989613i	$0.454082\pi$
$938$	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	$-0.910176\pi$
$941$	−20.9205	+	20.9205i	−0.681989	+	0.681989i	0.278459	+	0.960448i	$0.410176\pi$
$942$			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	$-0.648047\pi$
$947$	−27.6047			−0.897032			−0.448516	+	0.893775i	$0.648047\pi$
$948$	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	−0.293908	−	0.955834i	$-0.594956\pi$
$953$	20.4341	−	20.4341i	0.661926	−	0.661926i	0.955834	+	0.293908i	$0.0949559\pi$
$954$	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	−0.218415	−	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.f.e.408.4		20
5.2	odd	4		845.2.k.e.577.7		20
13.2	odd	12		845.2.o.f.488.4		20
13.3	even	3		65.2.t.a.58.4	yes	20
13.4	even	6		845.2.t.e.418.4		20
13.5	odd	4		845.2.k.d.268.4		20
13.6	odd	12		845.2.o.g.258.4		20
13.7	odd	12		65.2.o.a.63.2	yes	20
13.8	odd	4		845.2.k.e.268.7		20
13.9	even	3		845.2.t.f.418.2		20
13.10	even	6		845.2.t.g.188.2		20
13.11	odd	12		845.2.o.e.488.2		20
13.12	even	2		845.2.f.d.408.7		20
39.20	even	12		585.2.cf.a.388.4		20
39.29	odd	6		585.2.dp.a.253.2		20
65.2	even	12		845.2.t.e.657.4		20
65.3	odd	12		325.2.s.b.32.4		20
65.7	even	12		65.2.t.a.37.4	yes	20
65.12	odd	4		845.2.k.d.577.4		20
65.17	odd	12		845.2.o.f.587.4		20
65.22	odd	12		845.2.o.e.587.2		20
65.29	even	6		325.2.x.b.318.2		20
65.32	even	12		845.2.t.g.427.2		20
65.33	even	12		325.2.x.b.232.2		20
65.37	even	12		845.2.t.f.657.2		20
65.42	odd	12		65.2.o.a.32.2	✓	20
65.47	even	4	inner	845.2.f.e.437.7		20
65.57	even	4		845.2.f.d.437.4		20
65.59	odd	12		325.2.s.b.193.4		20
65.62	odd	12		845.2.o.g.357.4		20
195.107	even	12		585.2.cf.a.487.4		20
195.137	odd	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	65.42	odd	12
65.2.o.a.63.2	yes	20	13.7	odd	12
65.2.t.a.37.4	yes	20	65.7	even	12
65.2.t.a.58.4	yes	20	13.3	even	3
325.2.s.b.32.4		20	65.3	odd	12
325.2.s.b.193.4		20	65.59	odd	12
325.2.x.b.232.2		20	65.33	even	12
325.2.x.b.318.2		20	65.29	even	6
585.2.cf.a.388.4		20	39.20	even	12
585.2.cf.a.487.4		20	195.107	even	12
585.2.dp.a.37.2		20	195.137	odd	12
585.2.dp.a.253.2		20	39.29	odd	6
845.2.f.d.408.7		20	13.12	even	2
845.2.f.d.437.4		20	65.57	even	4
845.2.f.e.408.4		20	1.1	even	1	trivial
845.2.f.e.437.7		20	65.47	even	4	inner
845.2.k.d.268.4		20	13.5	odd	4
845.2.k.d.577.4		20	65.12	odd	4
845.2.k.e.268.7		20	13.8	odd	4
845.2.k.e.577.7		20	5.2	odd	4
845.2.o.e.488.2		20	13.11	odd	12
845.2.o.e.587.2		20	65.22	odd	12
845.2.o.f.488.4		20	13.2	odd	12
845.2.o.f.587.4		20	65.17	odd	12
845.2.o.g.258.4		20	13.6	odd	12
845.2.o.g.357.4		20	65.62	odd	12
845.2.t.e.418.4		20	13.4	even	6
845.2.t.e.657.4		20	65.2	even	12
845.2.t.f.418.2		20	13.9	even	3
845.2.t.f.657.2		20	65.37	even	12
845.2.t.g.188.2		20	13.10	even	6
845.2.t.g.427.2		20	65.32	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.58474i q^{2} +(-0.139520 - 0.139520i) q^{3} -0.511395 q^{4} +(-2.23506 - 0.0672627i) q^{5} +(-0.221103 + 0.221103i) q^{6} -0.548328 q^{7} -2.35905i q^{8} -2.96107i q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7	\( 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7} - 8 q^{10} + 8 q^{11} - 24 q^{12} + 28 q^{15} + 4 q^{16} - 14 q^{17} + 4 q^{19} - 12 q^{20} + 4 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{24} + 18 q^{25} + 4 q^{27} - 36 q^{28} + 40 q^{30} + 2 q^{34} - 20 q^{35} + 8 q^{37} - 8 q^{38} - 16 q^{40} - 38 q^{41} + 16 q^{42} - 32 q^{43} - 36 q^{44} - 6 q^{45} + 4 q^{46} - 40 q^{47} + 28 q^{48} - 36 q^{49} + 42 q^{50} - 10 q^{53} + 36 q^{54} - 16 q^{55} + 8 q^{59} + 28 q^{60} + 32 q^{61} + 4 q^{62} + 20 q^{64} - 32 q^{66} - 50 q^{68} + 32 q^{69} - 12 q^{70} - 40 q^{71} - 8 q^{72} + 4 q^{75} - 16 q^{76} - 28 q^{77} + 112 q^{80} + 28 q^{81} - 34 q^{82} + 48 q^{83} + 8 q^{84} - 2 q^{85} + 60 q^{86} - 28 q^{87} - 32 q^{88} + 12 q^{89} + 46 q^{90} - 8 q^{92} - 64 q^{93} + 40 q^{95} + 56 q^{96} + 60 q^{99}+O(q^{100}) \) 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

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