LMFDB - Embedded newform 1450.2.e.i.307.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(307,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("1450.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.e (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:	$11.5783082931$
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} + 36 x^{18} + 534 x^{16} + 4248 x^{14} + 19701 x^{12} + 54104 x^{10} + 85176 x^{8} + 70068 x^{6} + \cdots + 100 $ x^20 + 36x^18 + 534x^16 + 4248x^14 + 19701x^12 + 54104x^10 + 85176x^8 + 70068x^6 + 24828x^4 + 3384*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.10
Root			$2.46836i$ of defining polynomial
Character	$\chi$	$=$	1450.307
Dual form			1450.2.e.i.1143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.46836i q^{3} +1.00000 q^{4} -2.46836i q^{6} +(-1.24550 - 1.24550i) q^{7} -1.00000 q^{8} -3.09281 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.46836i q^{3} +1.00000 q^{4} -2.46836i q^{6} +(-1.24550 - 1.24550i) q^{7} -1.00000 q^{8} -3.09281 q^{9} +(2.22310 - 2.22310i) q^{11} +2.46836i q^{12} +(0.155168 + 0.155168i) q^{13} +(1.24550 + 1.24550i) q^{14} +1.00000 q^{16} -3.18401 q^{17} +3.09281 q^{18} +(-2.73832 - 2.73832i) q^{19} +(3.07435 - 3.07435i) q^{21} +(-2.22310 + 2.22310i) q^{22} +(0.904884 - 0.904884i) q^{23} -2.46836i q^{24} +(-0.155168 - 0.155168i) q^{26} -0.229088i q^{27} +(-1.24550 - 1.24550i) q^{28} +(2.96020 - 4.49858i) q^{29} +(3.35927 - 3.35927i) q^{31} -1.00000 q^{32} +(5.48741 + 5.48741i) q^{33} +3.18401 q^{34} -3.09281 q^{36} -4.43526i q^{37} +(2.73832 + 2.73832i) q^{38} +(-0.383011 + 0.383011i) q^{39} +(-3.27500 - 3.27500i) q^{41} +(-3.07435 + 3.07435i) q^{42} -0.610251i q^{43} +(2.22310 - 2.22310i) q^{44} +(-0.904884 + 0.904884i) q^{46} -5.52744i q^{47} +2.46836i q^{48} -3.89745i q^{49} -7.85928i q^{51} +(0.155168 + 0.155168i) q^{52} +(3.95662 - 3.95662i) q^{53} +0.229088i q^{54} +(1.24550 + 1.24550i) q^{56} +(6.75915 - 6.75915i) q^{57} +(-2.96020 + 4.49858i) q^{58} -1.49159i q^{59} +(0.227003 - 0.227003i) q^{61} +(-3.35927 + 3.35927i) q^{62} +(3.85210 + 3.85210i) q^{63} +1.00000 q^{64} +(-5.48741 - 5.48741i) q^{66} +(3.77437 - 3.77437i) q^{67} -3.18401 q^{68} +(2.23358 + 2.23358i) q^{69} -2.38823i q^{71} +3.09281 q^{72} +10.9231 q^{73} +4.43526i q^{74} +(-2.73832 - 2.73832i) q^{76} -5.53774 q^{77} +(0.383011 - 0.383011i) q^{78} +(11.4789 + 11.4789i) q^{79} -8.71296 q^{81} +(3.27500 + 3.27500i) q^{82} +(-10.2678 + 10.2678i) q^{83} +(3.07435 - 3.07435i) q^{84} +0.610251i q^{86} +(11.1041 + 7.30685i) q^{87} +(-2.22310 + 2.22310i) q^{88} +(1.40133 + 1.40133i) q^{89} -0.386524i q^{91} +(0.904884 - 0.904884i) q^{92} +(8.29188 + 8.29188i) q^{93} +5.52744i q^{94} -2.46836i q^{96} -13.7691i q^{97} +3.89745i q^{98} +(-6.87562 + 6.87562i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 20 q^{4} - 8 q^{7} - 20 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 20 * q^4 - 8 * q^7 - 20 * q^8 - 12 * q^9	$ 20 q - 20 q^{2} + 20 q^{4} - 8 q^{7} - 20 q^{8} - 12 q^{9} - 8 q^{11} - 4 q^{13} + 8 q^{14} + 20 q^{16} + 16 q^{17} + 12 q^{18} - 4 q^{19} + 4 q^{21} + 8 q^{22} + 12 q^{23} + 4 q^{26} - 8 q^{28} + 8 q^{29} + 28 q^{31} - 20 q^{32} - 16 q^{34} - 12 q^{36} + 4 q^{38} - 24 q^{39} + 24 q^{41} - 4 q^{42} - 8 q^{44} - 12 q^{46} - 4 q^{52} + 8 q^{56} - 8 q^{57} - 8 q^{58} + 24 q^{61} - 28 q^{62} + 20 q^{63} + 20 q^{64} + 12 q^{67} + 16 q^{68} - 28 q^{69} + 12 q^{72} - 16 q^{73} - 4 q^{76} + 16 q^{77} + 24 q^{78} + 32 q^{79} - 12 q^{81} - 24 q^{82} - 20 q^{83} + 4 q^{84} + 44 q^{87} + 8 q^{88} + 4 q^{89} + 12 q^{92} + 12 q^{93} + 8 q^{99}+O(q^{100}) $ 20 * q - 20 * q^2 + 20 * q^4 - 8 * q^7 - 20 * q^8 - 12 * q^9 - 8 * q^11 - 4 * q^13 + 8 * q^14 + 20 * q^16 + 16 * q^17 + 12 * q^18 - 4 * q^19 + 4 * q^21 + 8 * q^22 + 12 * q^23 + 4 * q^26 - 8 * q^28 + 8 * q^29 + 28 * q^31 - 20 * q^32 - 16 * q^34 - 12 * q^36 + 4 * q^38 - 24 * q^39 + 24 * q^41 - 4 * q^42 - 8 * q^44 - 12 * q^46 - 4 * q^52 + 8 * q^56 - 8 * q^57 - 8 * q^58 + 24 * q^61 - 28 * q^62 + 20 * q^63 + 20 * q^64 + 12 * q^67 + 16 * q^68 - 28 * q^69 + 12 * q^72 - 16 * q^73 - 4 * q^76 + 16 * q^77 + 24 * q^78 + 32 * q^79 - 12 * q^81 - 24 * q^82 - 20 * q^83 + 4 * q^84 + 44 * q^87 + 8 * q^88 + 4 * q^89 + 12 * q^92 + 12 * q^93 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			2.46836i			1.42511i	0.701617	+	0.712555i	$0.252462\pi$
$3$			2.46836i			1.42511i	−0.701617	+	0.712555i	$0.747538\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$		−	2.46836i		−	1.00770i
$7$	−1.24550	−	1.24550i	−0.470755	−	0.470755i	0.431404	−	0.902159i	$-0.358018\pi$
$7$	−1.24550	−	1.24550i	−0.470755	−	0.470755i	−0.902159	+	0.431404i	$0.858018\pi$
$8$	−1.00000			−0.353553
$9$	−3.09281			−1.03094
$10$		0			0
$11$	2.22310	−	2.22310i	0.670289	−	0.670289i	−0.287493	−	0.957783i	$-0.592822\pi$
$11$	2.22310	−	2.22310i	0.670289	−	0.670289i	0.957783	+	0.287493i	$0.0928219\pi$
$12$			2.46836i			0.712555i
$13$	0.155168	+	0.155168i	0.0430359	+	0.0430359i	0.728297	−	0.685261i	$-0.240312\pi$
$13$	0.155168	+	0.155168i	0.0430359	+	0.0430359i	−0.685261	+	0.728297i	$0.740312\pi$
$14$	1.24550	+	1.24550i	0.332874	+	0.332874i
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.18401			−0.772235			−0.386118	−	0.922450i	$-0.626184\pi$
$17$	−3.18401			−0.772235			−0.386118	+	0.922450i	$0.626184\pi$
$18$	3.09281			0.728982
$19$	−2.73832	−	2.73832i	−0.628213	−	0.628213i	0.319406	−	0.947618i	$-0.396517\pi$
$19$	−2.73832	−	2.73832i	−0.628213	−	0.628213i	−0.947618	+	0.319406i	$0.896517\pi$
$20$		0			0
$21$	3.07435	−	3.07435i	0.670878	−	0.670878i
$22$	−2.22310	+	2.22310i	−0.473966	+	0.473966i
$23$	0.904884	−	0.904884i	0.188681	−	0.188681i	−0.606444	−	0.795126i	$-0.707405\pi$
$23$	0.904884	−	0.904884i	0.188681	−	0.188681i	0.795126	+	0.606444i	$0.207405\pi$
$24$		−	2.46836i		−	0.503852i
$25$		0			0
$26$	−0.155168	−	0.155168i	−0.0304310	−	0.0304310i
$27$		−	0.229088i		−	0.0440881i
$28$	−1.24550	−	1.24550i	−0.235378	−	0.235378i
$29$	2.96020	−	4.49858i	0.549695	−	0.835365i
$29$	2.96020	−	4.49858i	0.549695	−	0.835365i
$30$		0			0
$31$	3.35927	−	3.35927i	0.603342	−	0.603342i	−0.337856	−	0.941198i	$-0.609702\pi$
$31$	3.35927	−	3.35927i	0.603342	−	0.603342i	0.941198	+	0.337856i	$0.109702\pi$
$32$	−1.00000			−0.176777
$33$	5.48741	+	5.48741i	0.955236	+	0.955236i
$34$	3.18401			0.546053
$35$		0			0
$36$	−3.09281			−0.515468
$37$		−	4.43526i		−	0.729152i	−0.931174	−	0.364576i	$-0.881214\pi$
$37$		−	4.43526i		−	0.729152i	0.931174	−	0.364576i	$-0.118786\pi$
$38$	2.73832	+	2.73832i	0.444213	+	0.444213i
$39$	−0.383011	+	0.383011i	−0.0613309	+	0.0613309i
$40$		0			0
$41$	−3.27500	−	3.27500i	−0.511469	−	0.511469i	0.403507	−	0.914976i	$-0.367791\pi$
$41$	−3.27500	−	3.27500i	−0.511469	−	0.511469i	−0.914976	+	0.403507i	$0.867791\pi$
$42$	−3.07435	+	3.07435i	−0.474382	+	0.474382i
$43$		−	0.610251i		−	0.0930624i	−0.998917	−	0.0465312i	$-0.985183\pi$
$43$		−	0.610251i		−	0.0930624i	0.998917	−	0.0465312i	$-0.0148167\pi$
$44$	2.22310	−	2.22310i	0.335145	−	0.335145i
$45$		0			0
$46$	−0.904884	+	0.904884i	−0.133418	+	0.133418i
$47$		−	5.52744i		−	0.806261i	−0.915143	−	0.403130i	$-0.867922\pi$
$47$		−	5.52744i		−	0.806261i	0.915143	−	0.403130i	$-0.132078\pi$
$48$			2.46836i			0.356277i
$49$		−	3.89745i		−	0.556779i
$50$		0			0
$51$		−	7.85928i		−	1.10052i
$52$	0.155168	+	0.155168i	0.0215180	+	0.0215180i
$53$	3.95662	−	3.95662i	0.543484	−	0.543484i	−0.381065	−	0.924548i	$-0.624442\pi$
$53$	3.95662	−	3.95662i	0.543484	−	0.543484i	0.924548	+	0.381065i	$0.124442\pi$
$54$			0.229088i			0.0311750i
$55$		0			0
$56$	1.24550	+	1.24550i	0.166437	+	0.166437i
$57$	6.75915	−	6.75915i	0.895272	−	0.895272i
$58$	−2.96020	+	4.49858i	−0.388693	+	0.590692i
$59$		−	1.49159i		−	0.194188i	−0.995275	−	0.0970939i	$-0.969045\pi$
$59$		−	1.49159i		−	0.194188i	0.995275	−	0.0970939i	$-0.0309547\pi$
$60$		0			0
$61$	0.227003	−	0.227003i	0.0290648	−	0.0290648i	−0.692425	−	0.721490i	$-0.743458\pi$
$61$	0.227003	−	0.227003i	0.0290648	−	0.0290648i	0.721490	+	0.692425i	$0.243458\pi$
$62$	−3.35927	+	3.35927i	−0.426627	+	0.426627i
$63$	3.85210	+	3.85210i	0.485319	+	0.485319i
$64$	1.00000			0.125000
$65$		0			0
$66$	−5.48741	−	5.48741i	−0.675454	−	0.675454i
$67$	3.77437	−	3.77437i	0.461113	−	0.461113i	−0.437907	−	0.899020i	$-0.644280\pi$
$67$	3.77437	−	3.77437i	0.461113	−	0.461113i	0.899020	+	0.437907i	$0.144280\pi$
$68$	−3.18401			−0.386118
$69$	2.23358	+	2.23358i	0.268892	+	0.268892i
$70$		0			0
$71$		−	2.38823i		−	0.283431i	−0.989907	−	0.141716i	$-0.954738\pi$
$71$		−	2.38823i		−	0.283431i	0.989907	−	0.141716i	$-0.0452618\pi$
$72$	3.09281			0.364491
$73$	10.9231			1.27846			0.639228	−	0.769017i	$-0.279254\pi$
$73$	10.9231			1.27846			0.639228	+	0.769017i	$0.279254\pi$
$74$			4.43526i			0.515589i
$75$		0			0
$76$	−2.73832	−	2.73832i	−0.314106	−	0.314106i
$77$	−5.53774			−0.631084
$78$	0.383011	−	0.383011i	0.0433675	−	0.0433675i
$79$	11.4789	+	11.4789i	1.29147	+	1.29147i	0.933876	+	0.357598i	$0.116404\pi$
$79$	11.4789	+	11.4789i	1.29147	+	1.29147i	0.357598	+	0.933876i	$0.383596\pi$
$80$		0			0
$81$	−8.71296			−0.968106
$82$	3.27500	+	3.27500i	0.361663	+	0.361663i
$83$	−10.2678	+	10.2678i	−1.12704	+	1.12704i	−0.136385	+	0.990656i	$0.543548\pi$
$83$	−10.2678	+	10.2678i	−1.12704	+	1.12704i	−0.990656	+	0.136385i	$0.956452\pi$
$84$	3.07435	−	3.07435i	0.335439	−	0.335439i
$85$		0			0
$86$			0.610251i			0.0658051i
$87$	11.1041	+	7.30685i	1.19049	+	0.783376i
$88$	−2.22310	+	2.22310i	−0.236983	+	0.236983i
$89$	1.40133	+	1.40133i	0.148540	+	0.148540i	0.777466	−	0.628925i	$-0.216505\pi$
$89$	1.40133	+	1.40133i	0.148540	+	0.148540i	−0.628925	+	0.777466i	$0.716505\pi$
$90$		0			0
$91$		−	0.386524i		−	0.0405188i
$92$	0.904884	−	0.904884i	0.0943407	−	0.0943407i
$93$	8.29188	+	8.29188i	0.859828	+	0.859828i
$94$			5.52744i			0.570112i
$95$		0			0
$96$		−	2.46836i		−	0.251926i
$97$		−	13.7691i		−	1.39804i	−0.715104	−	0.699018i	$-0.753621\pi$
$97$		−	13.7691i		−	1.39804i	0.715104	−	0.699018i	$-0.246379\pi$
$98$			3.89745i			0.393702i
$99$	−6.87562	+	6.87562i	−0.691026	+	0.691026i
$100$		0			0
$101$	−12.5924	+	12.5924i	−1.25299	+	1.25299i	−0.298613	+	0.954374i	$0.596524\pi$
$101$	−12.5924	+	12.5924i	−1.25299	+	1.25299i	−0.954374	+	0.298613i	$0.903476\pi$
$102$			7.85928i			0.778185i
$103$	−4.38747	+	4.38747i	−0.432311	+	0.432311i	−0.889414	−	0.457103i	$-0.848887\pi$
$103$	−4.38747	+	4.38747i	−0.432311	+	0.432311i	0.457103	+	0.889414i	$0.348887\pi$
$104$	−0.155168	−	0.155168i	−0.0152155	−	0.0152155i
$105$		0			0
$106$	−3.95662	+	3.95662i	−0.384301	+	0.384301i
$107$	−1.51987	−	1.51987i	−0.146932	−	0.146932i	0.629814	−	0.776746i	$-0.283131\pi$
$107$	−1.51987	−	1.51987i	−0.146932	−	0.146932i	−0.776746	+	0.629814i	$0.783131\pi$
$108$		−	0.229088i		−	0.0220440i
$109$	3.60614			0.345406			0.172703	−	0.984974i	$-0.444750\pi$
$109$	3.60614			0.345406			0.172703	+	0.984974i	$0.444750\pi$
$110$		0			0
$111$	10.9478			1.03912
$112$	−1.24550	−	1.24550i	−0.117689	−	0.117689i
$113$	5.89874			0.554907			0.277454	−	0.960739i	$-0.410510\pi$
$113$	5.89874			0.554907			0.277454	+	0.960739i	$0.410510\pi$
$114$	−6.75915	+	6.75915i	−0.633053	+	0.633053i
$115$		0			0
$116$	2.96020	−	4.49858i	0.274848	−	0.417683i
$117$	−0.479906	−	0.479906i	−0.0443673	−	0.0443673i
$118$			1.49159i			0.137312i
$119$	3.96569	+	3.96569i	0.363534	+	0.363534i
$120$		0			0
$121$			1.11567i			0.101424i
$122$	−0.227003	+	0.227003i	−0.0205519	+	0.0205519i
$123$	8.08388	−	8.08388i	0.728899	−	0.728899i
$124$	3.35927	−	3.35927i	0.301671	−	0.301671i
$125$		0			0
$126$	−3.85210	−	3.85210i	−0.343172	−	0.343172i
$127$	14.3872			1.27666			0.638329	−	0.769764i	$-0.279626\pi$
$127$	14.3872			1.27666			0.638329	+	0.769764i	$0.279626\pi$
$128$	−1.00000			−0.0883883
$129$	1.50632			0.132624
$130$		0			0
$131$	7.38622	+	7.38622i	0.645337	+	0.645337i	0.951862	−	0.306525i	$-0.0991664\pi$
$131$	7.38622	+	7.38622i	0.645337	+	0.645337i	−0.306525	+	0.951862i	$0.599166\pi$
$132$	5.48741	+	5.48741i	0.477618	+	0.477618i
$133$			6.82115i			0.591469i
$134$	−3.77437	+	3.77437i	−0.326056	+	0.326056i
$135$		0			0
$136$	3.18401			0.273026
$137$	0.355629			0.0303834			0.0151917	−	0.999885i	$-0.495164\pi$
$137$	0.355629			0.0303834			0.0151917	+	0.999885i	$0.495164\pi$
$138$	−2.23358	−	2.23358i	−0.190135	−	0.190135i
$139$		−	16.1832i		−	1.37264i	−0.727297	−	0.686322i	$-0.759224\pi$
$139$		−	16.1832i		−	1.37264i	0.727297	−	0.686322i	$-0.240776\pi$
$140$		0			0
$141$	13.6437			1.14901
$142$			2.38823i			0.200416i
$143$	0.689908			0.0576930
$144$	−3.09281			−0.257734
$145$		0			0
$146$	−10.9231			−0.904005
$147$	9.62032			0.793471
$148$		−	4.43526i		−	0.364576i
$149$	1.37362			0.112532			0.0562658	−	0.998416i	$-0.482081\pi$
$149$	1.37362			0.112532			0.0562658	+	0.998416i	$0.482081\pi$
$150$		0			0
$151$			4.66500i			0.379632i	0.981820	+	0.189816i	$0.0607891\pi$
$151$			4.66500i			0.379632i	−0.981820	+	0.189816i	$0.939211\pi$
$152$	2.73832	+	2.73832i	0.222107	+	0.222107i
$153$	9.84753			0.796126
$154$	5.53774			0.446244
$155$		0			0
$156$	−0.383011	+	0.383011i	−0.0306654	+	0.0306654i
$157$			8.41067i			0.671245i	0.941997	+	0.335622i	$0.108947\pi$
$157$			8.41067i			0.671245i	−0.941997	+	0.335622i	$0.891053\pi$
$158$	−11.4789	−	11.4789i	−0.913210	−	0.913210i
$159$	9.76638	+	9.76638i	0.774524	+	0.774524i
$160$		0			0
$161$	−2.25407			−0.177645
$162$	8.71296			0.684555
$163$	0.0455185			0.00356529			0.00178264	−	0.999998i	$-0.499433\pi$
$163$	0.0455185			0.00356529			0.00178264	+	0.999998i	$0.499433\pi$
$164$	−3.27500	−	3.27500i	−0.255734	−	0.255734i
$165$		0			0
$166$	10.2678	−	10.2678i	0.796938	−	0.796938i
$167$	2.61867	−	2.61867i	0.202639	−	0.202639i	−0.598491	−	0.801130i	$-0.704233\pi$
$167$	2.61867	−	2.61867i	0.202639	−	0.202639i	0.801130	+	0.598491i	$0.204233\pi$
$168$	−3.07435	+	3.07435i	−0.237191	+	0.237191i
$169$		−	12.9518i		−	0.996296i
$170$		0			0
$171$	8.46909	+	8.46909i	0.647647	+	0.647647i
$172$		−	0.610251i		−	0.0465312i
$173$	−17.5607	−	17.5607i	−1.33511	−	1.33511i	−0.900727	−	0.434385i	$-0.856966\pi$
$173$	−17.5607	−	17.5607i	−1.33511	−	1.33511i	−0.434385	−	0.900727i	$-0.643034\pi$
$174$	−11.1041	−	7.30685i	−0.841801	−	0.553931i
$175$		0			0
$176$	2.22310	−	2.22310i	0.167572	−	0.167572i
$177$	3.68177			0.276739
$178$	−1.40133	−	1.40133i	−0.105034	−	0.105034i
$179$	20.9854			1.56852			0.784260	−	0.620433i	$-0.213043\pi$
$179$	20.9854			1.56852			0.784260	+	0.620433i	$0.213043\pi$
$180$		0			0
$181$	−10.8048			−0.803114			−0.401557	−	0.915834i	$-0.631531\pi$
$181$	−10.8048			−0.803114			−0.401557	+	0.915834i	$0.631531\pi$
$182$			0.386524i			0.0286511i
$183$	0.560327	+	0.560327i	0.0414205	+	0.0414205i
$184$	−0.904884	+	0.904884i	−0.0667089	+	0.0667089i
$185$		0			0
$186$	−8.29188	−	8.29188i	−0.607990	−	0.607990i
$187$	−7.07836	+	7.07836i	−0.517621	+	0.517621i
$188$		−	5.52744i		−	0.403130i
$189$	−0.285330	+	0.285330i	−0.0207547	+	0.0207547i
$190$		0			0
$191$	5.05827	−	5.05827i	0.366004	−	0.366004i	−0.500014	−	0.866017i	$-0.666672\pi$
$191$	5.05827	−	5.05827i	0.366004	−	0.366004i	0.866017	+	0.500014i	$0.166672\pi$
$192$			2.46836i			0.178139i
$193$		−	12.7572i		−	0.918280i	−0.888364	−	0.459140i	$-0.848158\pi$
$193$		−	12.7572i		−	0.918280i	0.888364	−	0.459140i	$-0.151842\pi$
$194$			13.7691i			0.988560i
$195$		0			0
$196$		−	3.89745i		−	0.278389i
$197$	−15.6497	−	15.6497i	−1.11500	−	1.11500i	−0.992464	−	0.122534i	$-0.960898\pi$
$197$	−15.6497	−	15.6497i	−1.11500	−	1.11500i	−0.122534	−	0.992464i	$-0.539102\pi$
$198$	6.87562	−	6.87562i	0.488629	−	0.488629i
$199$		−	5.37482i		−	0.381011i	−0.981686	−	0.190506i	$-0.938987\pi$
$199$		−	5.37482i		−	0.381011i	0.981686	−	0.190506i	$-0.0610127\pi$
$200$		0			0
$201$	9.31651	+	9.31651i	0.657136	+	0.657136i
$202$	12.5924	−	12.5924i	0.885996	−	0.885996i
$203$	−9.28992	+	1.91605i	−0.652025	+	0.134480i
$204$		−	7.85928i		−	0.550260i
$205$		0			0
$206$	4.38747	−	4.38747i	0.305690	−	0.305690i
$207$	−2.79863	+	2.79863i	−0.194518	+	0.194518i
$208$	0.155168	+	0.155168i	0.0107590	+	0.0107590i
$209$	−12.1751			−0.842168
$210$		0			0
$211$	14.5064	+	14.5064i	0.998664	+	0.998664i	0.999999	−	0.00133492i	$-0.000424917\pi$
$211$	14.5064	+	14.5064i	0.998664	+	0.998664i	−0.00133492	+	0.999999i	$0.500425\pi$
$212$	3.95662	−	3.95662i	0.271742	−	0.271742i
$213$	5.89502			0.403920
$214$	1.51987	+	1.51987i	0.103896	+	0.103896i
$215$		0			0
$216$			0.229088i			0.0155875i
$217$	−8.36794			−0.568053
$218$	−3.60614			−0.244239
$219$			26.9622i			1.82194i
$220$		0			0
$221$	−0.494057	−	0.494057i	−0.0332338	−	0.0332338i
$222$	−10.9478			−0.734770
$223$	11.6303	−	11.6303i	0.778823	−	0.778823i	−0.200808	−	0.979631i	$-0.564357\pi$
$223$	11.6303	−	11.6303i	0.778823	−	0.778823i	0.979631	+	0.200808i	$0.0643567\pi$
$224$	1.24550	+	1.24550i	0.0832186	+	0.0832186i
$225$		0			0
$226$	−5.89874			−0.392379
$227$	−13.5021	−	13.5021i	−0.896168	−	0.896168i	0.0989263	−	0.995095i	$-0.468459\pi$
$227$	−13.5021	−	13.5021i	−0.896168	−	0.896168i	−0.995095	+	0.0989263i	$0.968459\pi$
$228$	6.75915	−	6.75915i	0.447636	−	0.447636i
$229$	19.8544	−	19.8544i	1.31201	−	1.31201i	0.392084	−	0.919929i	$-0.371754\pi$
$229$	19.8544	−	19.8544i	1.31201	−	1.31201i	0.919929	−	0.392084i	$-0.128246\pi$
$230$		0			0
$231$		−	13.6692i		−	0.899364i
$232$	−2.96020	+	4.49858i	−0.194347	+	0.295346i
$233$	−16.3466	+	16.3466i	−1.07090	+	1.07090i	−0.0736172	+	0.997287i	$0.523454\pi$
$233$	−16.3466	+	16.3466i	−1.07090	+	1.07090i	−0.997287	+	0.0736172i	$0.976546\pi$
$234$	0.479906	+	0.479906i	0.0313724	+	0.0313724i
$235$		0			0
$236$		−	1.49159i		−	0.0970939i
$237$	−28.3340	+	28.3340i	−1.84049	+	1.84049i
$238$	−3.96569	−	3.96569i	−0.257057	−	0.257057i
$239$			10.5937i			0.685251i	0.939472	+	0.342625i	$0.111316\pi$
$239$			10.5937i			0.685251i	−0.939472	+	0.342625i	$0.888684\pi$
$240$		0			0
$241$		−	5.78154i		−	0.372422i	−0.982510	−	0.186211i	$-0.940379\pi$
$241$		−	5.78154i		−	0.372422i	0.982510	−	0.186211i	$-0.0596208\pi$
$242$		−	1.11567i		−	0.0717179i
$243$		−	22.1940i		−	1.42375i
$244$	0.227003	−	0.227003i	0.0145324	−	0.0145324i
$245$		0			0
$246$	−8.08388	+	8.08388i	−0.515409	+	0.515409i
$247$		−	0.849799i		−	0.0540714i
$248$	−3.35927	+	3.35927i	−0.213314	+	0.213314i
$249$	−25.3447	−	25.3447i	−1.60616	−	1.60616i
$250$		0			0
$251$	−13.6847	+	13.6847i	−0.863772	+	0.863772i	−0.991774	−	0.128002i	$-0.959144\pi$
$251$	−13.6847	+	13.6847i	−0.863772	+	0.863772i	0.128002	+	0.991774i	$0.459144\pi$
$252$	3.85210	+	3.85210i	0.242659	+	0.242659i
$253$		−	4.02329i		−	0.252942i
$254$	−14.3872			−0.902733
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.22077	−	5.22077i	−0.325662	−	0.325662i	0.525272	−	0.850934i	$-0.323964\pi$
$257$	−5.22077	−	5.22077i	−0.325662	−	0.325662i	−0.850934	+	0.525272i	$0.823964\pi$
$258$	−1.50632			−0.0937794
$259$	−5.52412	+	5.52412i	−0.343252	+	0.343252i
$260$		0			0
$261$	−9.15534	+	13.9132i	−0.566701	+	0.861208i
$262$	−7.38622	−	7.38622i	−0.456322	−	0.456322i
$263$		−	28.6554i		−	1.76697i	−0.468462	−	0.883484i	$-0.655192\pi$
$263$		−	28.6554i		−	1.76697i	0.468462	−	0.883484i	$-0.344808\pi$
$264$	−5.48741	−	5.48741i	−0.337727	−	0.337727i
$265$		0			0
$266$		−	6.82115i		−	0.418232i
$267$	−3.45898	+	3.45898i	−0.211686	+	0.211686i
$268$	3.77437	−	3.77437i	0.230556	−	0.230556i
$269$	−9.98191	+	9.98191i	−0.608608	+	0.608608i	−0.942582	−	0.333974i	$-0.891610\pi$
$269$	−9.98191	+	9.98191i	−0.608608	+	0.608608i	0.333974	+	0.942582i	$0.391610\pi$
$270$		0			0
$271$	12.6886	+	12.6886i	0.770775	+	0.770775i	0.978242	−	0.207467i	$-0.0665220\pi$
$271$	12.6886	+	12.6886i	0.770775	+	0.770775i	−0.207467	+	0.978242i	$0.566522\pi$
$272$	−3.18401			−0.193059
$273$	0.954082			0.0577437
$274$	−0.355629			−0.0214843
$275$		0			0
$276$	2.23358	+	2.23358i	0.134446	+	0.134446i
$277$	2.51465	+	2.51465i	0.151090	+	0.151090i	0.778605	−	0.627514i	$-0.215928\pi$
$277$	2.51465	+	2.51465i	0.151090	+	0.151090i	−0.627514	+	0.778605i	$0.715928\pi$
$278$			16.1832i			0.970606i
$279$	−10.3896	+	10.3896i	−0.622007	+	0.622007i
$280$		0			0
$281$	−28.0826			−1.67527			−0.837634	−	0.546232i	$-0.816062\pi$
$281$	−28.0826			−1.67527			−0.837634	+	0.546232i	$0.816062\pi$
$282$	−13.6437			−0.812472
$283$	7.54066	+	7.54066i	0.448246	+	0.448246i	0.894771	−	0.446525i	$-0.147339\pi$
$283$	7.54066	+	7.54066i	0.448246	+	0.448246i	−0.446525	+	0.894771i	$0.647339\pi$
$284$		−	2.38823i		−	0.141716i
$285$		0			0
$286$	−0.689908			−0.0407951
$287$			8.15803i			0.481553i
$288$	3.09281			0.182246
$289$	−6.86210			−0.403653
$290$		0			0
$291$	33.9870			1.99235
$292$	10.9231			0.639228
$293$		−	6.66687i		−	0.389483i	−0.980855	−	0.194741i	$-0.937613\pi$
$293$		−	6.66687i		−	0.389483i	0.980855	−	0.194741i	$-0.0623868\pi$
$294$	−9.62032			−0.561069
$295$		0			0
$296$			4.43526i			0.257794i
$297$	−0.509286	−	0.509286i	−0.0295518	−	0.0295518i
$298$	−1.37362			−0.0795719
$299$	0.280818			0.0162401
$300$		0			0
$301$	−0.760068	+	0.760068i	−0.0438096	+	0.0438096i
$302$		−	4.66500i		−	0.268440i
$303$	−31.0825	−	31.0825i	−1.78564	−	1.78564i
$304$	−2.73832	−	2.73832i	−0.157053	−	0.157053i
$305$		0			0
$306$	−9.84753			−0.562946
$307$	−18.3698			−1.04842			−0.524209	−	0.851590i	$-0.675639\pi$
$307$	−18.3698			−1.04842			−0.524209	+	0.851590i	$0.675639\pi$
$308$	−5.53774			−0.315542
$309$	−10.8299	−	10.8299i	−0.616090	−	0.616090i
$310$		0			0
$311$	−5.27939	+	5.27939i	−0.299367	+	0.299367i	−0.840766	−	0.541399i	$-0.817895\pi$
$311$	−5.27939	+	5.27939i	−0.299367	+	0.299367i	0.541399	+	0.840766i	$0.317895\pi$
$312$	0.383011	−	0.383011i	0.0216837	−	0.0216837i
$313$	−3.76536	+	3.76536i	−0.212830	+	0.212830i	−0.805469	−	0.592638i	$-0.798086\pi$
$313$	−3.76536	+	3.76536i	−0.212830	+	0.212830i	0.592638	+	0.805469i	$0.298086\pi$
$314$		−	8.41067i		−	0.474642i
$315$		0			0
$316$	11.4789	+	11.4789i	0.645737	+	0.645737i
$317$			20.2929i			1.13976i	0.821727	+	0.569881i	$0.193011\pi$
$317$			20.2929i			1.13976i	−0.821727	+	0.569881i	$0.806989\pi$
$318$	−9.76638	−	9.76638i	−0.547671	−	0.547671i
$319$	−3.41997	−	16.5816i	−0.191481	−	0.928391i
$320$		0			0
$321$	3.75160	−	3.75160i	0.209394	−	0.209394i
$322$	2.25407			0.125614
$323$	8.71881	+	8.71881i	0.485128	+	0.485128i
$324$	−8.71296			−0.484053
$325$		0			0
$326$	−0.0455185			−0.00252104
$327$			8.90126i			0.492241i
$328$	3.27500	+	3.27500i	0.180832	+	0.180832i
$329$	−6.88444	+	6.88444i	−0.379551	+	0.379551i
$330$		0			0
$331$	8.71548	+	8.71548i	0.479046	+	0.479046i	0.904827	−	0.425780i	$-0.140000\pi$
$331$	8.71548	+	8.71548i	0.479046	+	0.479046i	−0.425780	+	0.904827i	$0.640000\pi$
$332$	−10.2678	+	10.2678i	−0.563520	+	0.563520i
$333$			13.7174i			0.751710i
$334$	−2.61867	+	2.61867i	−0.143287	+	0.143287i
$335$		0			0
$336$	3.07435	−	3.07435i	0.167719	−	0.167719i
$337$		−	19.8857i		−	1.08324i	−0.840623	−	0.541620i	$-0.817811\pi$
$337$		−	19.8857i		−	1.08324i	0.840623	−	0.541620i	$-0.182189\pi$
$338$			12.9518i			0.704488i
$339$			14.5602i			0.790803i
$340$		0			0
$341$		−	14.9360i		−	0.808827i
$342$	−8.46909	−	8.46909i	−0.457956	−	0.457956i
$343$	−13.5728	+	13.5728i	−0.732862	+	0.732862i
$344$			0.610251i			0.0329025i
$345$		0			0
$346$	17.5607	+	17.5607i	0.944067	+	0.944067i
$347$	22.1013	−	22.1013i	1.18646	−	1.18646i	0.208422	−	0.978039i	$-0.433167\pi$
$347$	22.1013	−	22.1013i	1.18646	−	1.18646i	0.978039	−	0.208422i	$-0.0668326\pi$
$348$	11.1041	+	7.30685i	0.595243	+	0.391688i
$349$		−	32.2595i		−	1.72681i	−0.504511	−	0.863405i	$-0.668327\pi$
$349$		−	32.2595i		−	1.72681i	0.504511	−	0.863405i	$-0.331673\pi$
$350$		0			0
$351$	0.0355472	−	0.0355472i	0.00189737	−	0.00189737i
$352$	−2.22310	+	2.22310i	−0.118492	+	0.118492i
$353$	1.91301	+	1.91301i	0.101819	+	0.101819i	0.756181	−	0.654362i	$-0.227063\pi$
$353$	1.91301	+	1.91301i	0.101819	+	0.101819i	−0.654362	+	0.756181i	$0.727063\pi$
$354$	−3.68177			−0.195684
$355$		0			0
$356$	1.40133	+	1.40133i	0.0742702	+	0.0742702i
$357$	−9.78875	+	9.78875i	−0.518075	+	0.518075i
$358$	−20.9854			−1.10911
$359$	22.6067	+	22.6067i	1.19314	+	1.19314i	0.976181	+	0.216956i	$0.0696129\pi$
$359$	22.6067	+	22.6067i	1.19314	+	1.19314i	0.216956	+	0.976181i	$0.430387\pi$
$360$		0			0
$361$		−	4.00326i		−	0.210698i
$362$	10.8048			0.567888
$363$	−2.75387			−0.144541
$364$		−	0.386524i		−	0.0202594i
$365$		0			0
$366$	−0.560327	−	0.560327i	−0.0292887	−	0.0292887i
$367$	10.2287			0.533935			0.266967	−	0.963706i	$-0.413978\pi$
$367$	10.2287			0.533935			0.266967	+	0.963706i	$0.413978\pi$
$368$	0.904884	−	0.904884i	0.0471703	−	0.0471703i
$369$	10.1289	+	10.1289i	0.527292	+	0.527292i
$370$		0			0
$371$	−9.85596			−0.511696
$372$	8.29188	+	8.29188i	0.429914	+	0.429914i
$373$	−19.1443	+	19.1443i	−0.991255	+	0.991255i	−0.999962	−	0.00870748i	$-0.997228\pi$
$373$	−19.1443	+	19.1443i	−0.991255	+	0.991255i	0.00870748	+	0.999962i	$0.497228\pi$
$374$	7.07836	−	7.07836i	0.366013	−	0.366013i
$375$		0			0
$376$			5.52744i			0.285056i
$377$	1.15737	−	0.238707i	0.0596073	−	0.0122941i
$378$	0.285330	−	0.285330i	0.0146758	−	0.0146758i
$379$	1.76015	+	1.76015i	0.0904129	+	0.0904129i	0.750867	−	0.660454i	$-0.229636\pi$
$379$	1.76015	+	1.76015i	0.0904129	+	0.0904129i	−0.660454	+	0.750867i	$0.729636\pi$
$380$		0			0
$381$			35.5128i			1.81938i
$382$	−5.05827	+	5.05827i	−0.258804	+	0.258804i
$383$	0.210447	+	0.210447i	0.0107533	+	0.0107533i	0.712463	−	0.701710i	$-0.247580\pi$
$383$	0.210447	+	0.210447i	0.0107533	+	0.0107533i	−0.701710	+	0.712463i	$0.747580\pi$
$384$		−	2.46836i		−	0.125963i
$385$		0			0
$386$			12.7572i			0.649322i
$387$			1.88739i			0.0959414i
$388$		−	13.7691i		−	0.699018i
$389$	−11.2901	+	11.2901i	−0.572430	+	0.572430i	−0.932807	−	0.360377i	$-0.882648\pi$
$389$	−11.2901	+	11.2901i	−0.572430	+	0.572430i	0.360377	+	0.932807i	$0.382648\pi$
$390$		0			0
$391$	−2.88116	+	2.88116i	−0.145706	+	0.145706i
$392$			3.89745i			0.196851i
$393$	−18.2319	+	18.2319i	−0.919676	+	0.919676i
$394$	15.6497	+	15.6497i	0.788423	+	0.788423i
$395$		0			0
$396$	−6.87562	+	6.87562i	−0.345513	+	0.345513i
$397$	3.60226	+	3.60226i	0.180792	+	0.180792i	0.791701	−	0.610909i	$-0.209196\pi$
$397$	3.60226	+	3.60226i	0.180792	+	0.180792i	−0.610909	+	0.791701i	$0.709196\pi$
$398$			5.37482i			0.269415i
$399$	−16.8371			−0.842908
$400$		0			0
$401$	−11.4735			−0.572957			−0.286479	−	0.958087i	$-0.592485\pi$
$401$	−11.4735			−0.572957			−0.286479	+	0.958087i	$0.592485\pi$
$402$	−9.31651	−	9.31651i	−0.464665	−	0.464665i
$403$	1.04250			0.0519307
$404$	−12.5924	+	12.5924i	−0.626494	+	0.626494i
$405$		0			0
$406$	9.28992	−	1.91605i	0.461051	−	0.0950921i
$407$	−9.86002	−	9.86002i	−0.488743	−	0.488743i
$408$			7.85928i			0.389092i
$409$	−28.0128	−	28.0128i	−1.38514	−	1.38514i	−0.835207	−	0.549935i	$-0.814652\pi$
$409$	−28.0128	−	28.0128i	−1.38514	−	1.38514i	−0.549935	−	0.835207i	$-0.685348\pi$
$410$		0			0
$411$			0.877820i			0.0432997i
$412$	−4.38747	+	4.38747i	−0.216155	+	0.216155i
$413$	−1.85777	+	1.85777i	−0.0914150	+	0.0914150i
$414$	2.79863	−	2.79863i	0.137545	−	0.137545i
$415$		0			0
$416$	−0.155168	−	0.155168i	−0.00760775	−	0.00760775i
$417$	39.9461			1.95617
$418$	12.1751			0.595503
$419$	12.8383			0.627192			0.313596	−	0.949557i	$-0.398466\pi$
$419$	12.8383			0.627192			0.313596	+	0.949557i	$0.398466\pi$
$420$		0			0
$421$	12.9907	+	12.9907i	0.633130	+	0.633130i	0.948852	−	0.315722i	$-0.102247\pi$
$421$	12.9907	+	12.9907i	0.633130	+	0.633130i	−0.315722	+	0.948852i	$0.602247\pi$
$422$	−14.5064	−	14.5064i	−0.706162	−	0.706162i
$423$			17.0953i			0.831204i
$424$	−3.95662	+	3.95662i	−0.192151	+	0.192151i
$425$		0			0
$426$	−5.89502			−0.285615
$427$	−0.565466			−0.0273648
$428$	−1.51987	−	1.51987i	−0.0734659	−	0.0734659i
$429$			1.70294i			0.0822189i
$430$		0			0
$431$	−20.6050			−0.992510			−0.496255	−	0.868177i	$-0.665292\pi$
$431$	−20.6050			−0.992510			−0.496255	+	0.868177i	$0.665292\pi$
$432$		−	0.229088i		−	0.0110220i
$433$	36.2040			1.73985			0.869927	−	0.493180i	$-0.164166\pi$
$433$	36.2040			1.73985			0.869927	+	0.493180i	$0.164166\pi$
$434$	8.36794			0.401674
$435$		0			0
$436$	3.60614			0.172703
$437$	−4.95571			−0.237064
$438$		−	26.9622i		−	1.28831i
$439$	−7.87262			−0.375740			−0.187870	−	0.982194i	$-0.560158\pi$
$439$	−7.87262			−0.375740			−0.187870	+	0.982194i	$0.560158\pi$
$440$		0			0
$441$			12.0541i			0.574004i
$442$	0.494057	+	0.494057i	0.0234999	+	0.0234999i
$443$	14.2317			0.676169			0.338085	−	0.941116i	$-0.390221\pi$
$443$	14.2317			0.676169			0.338085	+	0.941116i	$0.390221\pi$
$444$	10.9478			0.519561
$445$		0			0
$446$	−11.6303	+	11.6303i	−0.550711	+	0.550711i
$447$			3.39060i			0.160370i
$448$	−1.24550	−	1.24550i	−0.0588444	−	0.0588444i
$449$	−9.81094	−	9.81094i	−0.463007	−	0.463007i	0.436633	−	0.899640i	$-0.356171\pi$
$449$	−9.81094	−	9.81094i	−0.463007	−	0.463007i	−0.899640	+	0.436633i	$0.856171\pi$
$450$		0			0
$451$	−14.5613			−0.685664
$452$	5.89874			0.277454
$453$	−11.5149			−0.541017
$454$	13.5021	+	13.5021i	0.633687	+	0.633687i
$455$		0			0
$456$	−6.75915	+	6.75915i	−0.316526	+	0.316526i
$457$	27.0893	−	27.0893i	1.26718	−	1.26718i	0.319647	−	0.947537i	$-0.396436\pi$
$457$	27.0893	−	27.0893i	1.26718	−	1.26718i	0.947537	−	0.319647i	$-0.103564\pi$
$458$	−19.8544	+	19.8544i	−0.927734	+	0.927734i
$459$			0.729419i			0.0340464i
$460$		0			0
$461$	−14.8907	−	14.8907i	−0.693531	−	0.693531i	0.269476	−	0.963007i	$-0.413149\pi$
$461$	−14.8907	−	14.8907i	−0.693531	−	0.693531i	−0.963007	+	0.269476i	$0.913149\pi$
$462$			13.6692i			0.635947i
$463$	−4.96124	−	4.96124i	−0.230568	−	0.230568i	0.582362	−	0.812930i	$-0.302129\pi$
$463$	−4.96124	−	4.96124i	−0.230568	−	0.230568i	−0.812930	+	0.582362i	$0.802129\pi$
$464$	2.96020	−	4.49858i	0.137424	−	0.208841i
$465$		0			0
$466$	16.3466	−	16.3466i	0.757243	−	0.757243i
$467$	11.2622			0.521153			0.260577	−	0.965453i	$-0.416087\pi$
$467$	11.2622			0.521153			0.260577	+	0.965453i	$0.416087\pi$
$468$	−0.479906	−	0.479906i	−0.0221836	−	0.0221836i
$469$	−9.40197			−0.434143
$470$		0			0
$471$	−20.7606			−0.956597
$472$			1.49159i			0.0686558i
$473$	−1.35665	−	1.35665i	−0.0623787	−	0.0623787i
$474$	28.3340	−	28.3340i	1.30142	−	1.30142i
$475$		0			0
$476$	3.96569	+	3.96569i	0.181767	+	0.181767i
$477$	−12.2371	+	12.2371i	−0.560297	+	0.560297i
$478$		−	10.5937i		−	0.484546i
$479$	−13.3645	+	13.3645i	−0.610640	+	0.610640i	−0.943113	−	0.332473i	$-0.892117\pi$
$479$	−13.3645	+	13.3645i	−0.610640	+	0.610640i	0.332473	+	0.943113i	$0.392117\pi$
$480$		0			0
$481$	0.688211	−	0.688211i	0.0313797	−	0.0313797i
$482$			5.78154i			0.263342i
$483$		−	5.56386i		−	0.253164i
$484$			1.11567i			0.0507122i
$485$		0			0
$486$			22.1940i			1.00674i
$487$	6.98259	+	6.98259i	0.316412	+	0.316412i	0.847387	−	0.530976i	$-0.178174\pi$
$487$	6.98259	+	6.98259i	0.316412	+	0.316412i	−0.530976	+	0.847387i	$0.678174\pi$
$488$	−0.227003	+	0.227003i	−0.0102760	+	0.0102760i
$489$			0.112356i			0.00508092i
$490$		0			0
$491$	−18.5807	−	18.5807i	−0.838534	−	0.838534i	0.150132	−	0.988666i	$-0.452030\pi$
$491$	−18.5807	−	18.5807i	−0.838534	−	0.838534i	−0.988666	+	0.150132i	$0.952030\pi$
$492$	8.08388	−	8.08388i	0.364450	−	0.364450i
$493$	−9.42530	+	14.3235i	−0.424494	+	0.645098i
$494$			0.849799i			0.0382343i
$495$		0			0
$496$	3.35927	−	3.35927i	0.150836	−	0.150836i
$497$	−2.97455	+	2.97455i	−0.133427	+	0.133427i
$498$	25.3447	+	25.3447i	1.13572	+	1.13572i
$499$	−35.5843			−1.59297			−0.796486	−	0.604657i	$-0.793310\pi$
$499$	−35.5843			−1.59297			−0.796486	+	0.604657i	$0.793310\pi$
$500$		0			0
$501$	6.46383	+	6.46383i	0.288783	+	0.288783i
$502$	13.6847	−	13.6847i	0.610779	−	0.610779i
$503$	−26.7341			−1.19201			−0.596006	−	0.802980i	$-0.703247\pi$
$503$	−26.7341			−1.19201			−0.596006	+	0.802980i	$0.703247\pi$
$504$	−3.85210	−	3.85210i	−0.171586	−	0.171586i
$505$		0			0
$506$			4.02329i			0.178857i
$507$	31.9698			1.41983
$508$	14.3872			0.638329
$509$			19.1760i			0.849963i	0.905202	+	0.424981i	$0.139719\pi$
$509$			19.1760i			0.849963i	−0.905202	+	0.424981i	$0.860281\pi$
$510$		0			0
$511$	−13.6048	−	13.6048i	−0.601840	−	0.601840i
$512$	−1.00000			−0.0441942
$513$	−0.627316	+	0.627316i	−0.0276967	+	0.0276967i
$514$	5.22077	+	5.22077i	0.230278	+	0.230278i
$515$		0			0
$516$	1.50632			0.0663121
$517$	−12.2881	−	12.2881i	−0.540428	−	0.540428i
$518$	5.52412	−	5.52412i	0.242716	−	0.242716i
$519$	43.3461	−	43.3461i	1.90268	−	1.90268i
$520$		0			0
$521$		−	25.5356i		−	1.11874i	−0.828919	−	0.559368i	$-0.811044\pi$
$521$		−	25.5356i		−	1.11874i	0.828919	−	0.559368i	$-0.188956\pi$
$522$	9.15534	−	13.9132i	0.400718	−	0.608966i
$523$	−3.17640	+	3.17640i	−0.138894	+	0.138894i	−0.773135	−	0.634241i	$-0.781313\pi$
$523$	−3.17640	+	3.17640i	−0.138894	+	0.138894i	0.634241	+	0.773135i	$0.281313\pi$
$524$	7.38622	+	7.38622i	0.322669	+	0.322669i
$525$		0			0
$526$			28.6554i			1.24943i
$527$	−10.6959	+	10.6959i	−0.465922	+	0.465922i
$528$	5.48741	+	5.48741i	0.238809	+	0.238809i
$529$			21.3624i			0.928799i
$530$		0			0
$531$			4.61319i			0.200195i
$532$			6.82115i			0.295734i
$533$		−	1.01635i		−	0.0440231i
$534$	3.45898	−	3.45898i	0.149685	−	0.149685i
$535$		0			0
$536$	−3.77437	+	3.77437i	−0.163028	+	0.163028i
$537$			51.7995i			2.23531i
$538$	9.98191	−	9.98191i	0.430351	−	0.430351i
$539$	−8.66442	−	8.66442i	−0.373203	−	0.373203i
$540$		0			0
$541$	−1.06380	+	1.06380i	−0.0457362	+	0.0457362i	−0.729605	−	0.683869i	$-0.760296\pi$
$541$	−1.06380	+	1.06380i	−0.0457362	+	0.0457362i	0.683869	+	0.729605i	$0.260296\pi$
$542$	−12.6886	−	12.6886i	−0.545020	−	0.545020i
$543$		−	26.6701i		−	1.14453i
$544$	3.18401			0.136513
$545$		0			0
$546$	−0.954082			−0.0408309
$547$	−0.0958715	−	0.0958715i	−0.00409917	−	0.00409917i	0.705054	−	0.709153i	$-0.250923\pi$
$547$	−0.0958715	−	0.0958715i	−0.00409917	−	0.00409917i	−0.709153	+	0.705054i	$0.750923\pi$
$548$	0.355629			0.0151917
$549$	−0.702078	+	0.702078i	−0.0299640	+	0.0299640i
$550$		0			0
$551$	−20.4245	+	4.21256i	−0.870112	+	0.179461i
$552$	−2.23358	−	2.23358i	−0.0950675	−	0.0950675i
$553$		−	28.5939i		−	1.21594i
$554$	−2.51465	−	2.51465i	−0.106837	−	0.106837i
$555$		0			0
$556$		−	16.1832i		−	0.686322i
$557$	−4.25579	+	4.25579i	−0.180324	+	0.180324i	−0.791497	−	0.611173i	$-0.790698\pi$
$557$	−4.25579	+	4.25579i	−0.180324	+	0.180324i	0.611173	+	0.791497i	$0.290698\pi$
$558$	10.3896	−	10.3896i	0.439826	−	0.439826i
$559$	0.0946915	−	0.0946915i	0.00400503	−	0.00400503i
$560$		0			0
$561$	−17.4720	−	17.4720i	−0.737667	−	0.737667i
$562$	28.0826			1.18459
$563$	23.4558			0.988545			0.494273	−	0.869307i	$-0.335434\pi$
$563$	23.4558			0.988545			0.494273	+	0.869307i	$0.335434\pi$
$564$	13.6437			0.574505
$565$		0			0
$566$	−7.54066	−	7.54066i	−0.316958	−	0.316958i
$567$	10.8520	+	10.8520i	0.455741	+	0.455741i
$568$			2.38823i			0.100208i
$569$	−15.0833	+	15.0833i	−0.632325	+	0.632325i	−0.948651	−	0.316325i	$-0.897551\pi$
$569$	−15.0833	+	15.0833i	−0.632325	+	0.632325i	0.316325	+	0.948651i	$0.397551\pi$
$570$		0			0
$571$	−15.2167			−0.636801			−0.318400	−	0.947956i	$-0.603146\pi$
$571$	−15.2167			−0.636801			−0.318400	+	0.947956i	$0.603146\pi$
$572$	0.689908			0.0288465
$573$	12.4856	+	12.4856i	0.521595	+	0.521595i
$574$		−	8.15803i		−	0.340510i
$575$		0			0
$576$	−3.09281			−0.128867
$577$		−	7.53694i		−	0.313767i	−0.987617	−	0.156883i	$-0.949855\pi$
$577$		−	7.53694i		−	0.313767i	0.987617	−	0.156883i	$-0.0501447\pi$
$578$	6.86210			0.285426
$579$	31.4893			1.30865
$580$		0			0
$581$	25.5772			1.06112
$582$	−33.9870			−1.40881
$583$		−	17.5919i		−	0.728583i
$584$	−10.9231			−0.452003
$585$		0			0
$586$			6.66687i			0.275406i
$587$	−1.50704	−	1.50704i	−0.0622024	−	0.0622024i	0.675321	−	0.737524i	$-0.264005\pi$
$587$	−1.50704	−	1.50704i	−0.0622024	−	0.0622024i	−0.737524	+	0.675321i	$0.764005\pi$
$588$	9.62032			0.396735
$589$	−18.3975			−0.758054
$590$		0			0
$591$	38.6292	−	38.6292i	1.58899	−	1.58899i
$592$		−	4.43526i		−	0.182288i
$593$	−19.5271	−	19.5271i	−0.801881	−	0.801881i	0.181508	−	0.983389i	$-0.441902\pi$
$593$	−19.5271	−	19.5271i	−0.801881	−	0.801881i	−0.983389	+	0.181508i	$0.941902\pi$
$594$	0.509286	+	0.509286i	0.0208962	+	0.0208962i
$595$		0			0
$596$	1.37362			0.0562658
$597$	13.2670			0.542982
$598$	−0.280818			−0.0114835
$599$	−4.79824	−	4.79824i	−0.196051	−	0.196051i	0.602254	−	0.798305i	$-0.294270\pi$
$599$	−4.79824	−	4.79824i	−0.196051	−	0.196051i	−0.798305	+	0.602254i	$0.794270\pi$
$600$		0			0
$601$	−3.83941	+	3.83941i	−0.156613	+	0.156613i	−0.781064	−	0.624451i	$-0.785323\pi$
$601$	−3.83941	+	3.83941i	−0.156613	+	0.156613i	0.624451	+	0.781064i	$0.285323\pi$
$602$	0.760068	−	0.760068i	0.0309781	−	0.0309781i
$603$	−11.6734	+	11.6734i	−0.475378	+	0.475378i
$604$			4.66500i			0.189816i
$605$		0			0
$606$	31.0825	+	31.0825i	1.26264	+	1.26264i
$607$			29.2903i			1.18886i	0.804149	+	0.594428i	$0.202621\pi$
$607$			29.2903i			1.18886i	−0.804149	+	0.594428i	$0.797379\pi$
$608$	2.73832	+	2.73832i	0.111053	+	0.111053i
$609$	−4.72951	−	22.9309i	−0.191649	−	0.929206i
$610$		0			0
$611$	0.857684	−	0.857684i	0.0346982	−	0.0346982i
$612$	9.84753			0.398063
$613$	28.4824	+	28.4824i	1.15040	+	1.15040i	0.986473	+	0.163922i	$0.0524145\pi$
$613$	28.4824	+	28.4824i	1.15040	+	1.15040i	0.163922	+	0.986473i	$0.447585\pi$
$614$	18.3698			0.741343
$615$		0			0
$616$	5.53774			0.223122
$617$		−	30.0616i		−	1.21024i	−0.796136	−	0.605118i	$-0.793126\pi$
$617$		−	30.0616i		−	1.21024i	0.796136	−	0.605118i	$-0.206874\pi$
$618$	10.8299	+	10.8299i	0.435641	+	0.435641i
$619$	34.4317	−	34.4317i	1.38393	−	1.38393i	0.546406	−	0.837521i	$-0.315996\pi$
$619$	34.4317	−	34.4317i	1.38393	−	1.38393i	0.837521	−	0.546406i	$-0.184004\pi$
$620$		0			0
$621$	−0.207298	−	0.207298i	−0.00831859	−	0.00831859i
$622$	5.27939	−	5.27939i	0.211684	−	0.211684i
$623$		−	3.49071i		−	0.139852i
$624$	−0.383011	+	0.383011i	−0.0153327	+	0.0153327i
$625$		0			0
$626$	3.76536	−	3.76536i	0.150494	−	0.150494i
$627$		−	30.0525i		−	1.20018i
$628$			8.41067i			0.335622i
$629$			14.1219i			0.563077i
$630$		0			0
$631$		−	25.0953i		−	0.999027i	−0.866306	−	0.499514i	$-0.833512\pi$
$631$		−	25.0953i		−	0.999027i	0.866306	−	0.499514i	$-0.166488\pi$
$632$	−11.4789	−	11.4789i	−0.456605	−	0.456605i
$633$	−35.8071	+	35.8071i	−1.42321	+	1.42321i
$634$		−	20.2929i		−	0.805934i
$635$		0			0
$636$	9.76638	+	9.76638i	0.387262	+	0.387262i
$637$	0.604761	−	0.604761i	0.0239615	−	0.0239615i
$638$	3.41997	+	16.5816i	0.135398	+	0.656472i
$639$			7.38635i			0.292200i
$640$		0			0
$641$	34.1928	−	34.1928i	1.35054	−	1.35054i	0.465474	−	0.885062i	$-0.345884\pi$
$641$	34.1928	−	34.1928i	1.35054	−	1.35054i	0.885062	−	0.465474i	$-0.154116\pi$
$642$	−3.75160	+	3.75160i	−0.148064	+	0.148064i
$643$	−18.2800	−	18.2800i	−0.720892	−	0.720892i	0.247895	−	0.968787i	$-0.420261\pi$
$643$	−18.2800	−	18.2800i	−0.720892	−	0.720892i	−0.968787	+	0.247895i	$0.920261\pi$
$644$	−2.25407			−0.0888227
$645$		0			0
$646$	−8.71881	−	8.71881i	−0.343037	−	0.343037i
$647$	−9.59951	+	9.59951i	−0.377396	+	0.377396i	−0.870162	−	0.492766i	$-0.835986\pi$
$647$	−9.59951	+	9.59951i	−0.377396	+	0.377396i	0.492766	+	0.870162i	$0.335986\pi$
$648$	8.71296			0.342277
$649$	−3.31594	−	3.31594i	−0.130162	−	0.130162i
$650$		0			0
$651$		−	20.6551i		−	0.809537i
$652$	0.0455185			0.00178264
$653$	7.63625			0.298829			0.149415	−	0.988775i	$-0.452261\pi$
$653$	7.63625			0.298829			0.149415	+	0.988775i	$0.452261\pi$
$654$		−	8.90126i		−	0.348067i
$655$		0			0
$656$	−3.27500	−	3.27500i	−0.127867	−	0.127867i
$657$	−33.7832			−1.31801
$658$	6.88444	−	6.88444i	0.268383	−	0.268383i
$659$	30.5055	+	30.5055i	1.18832	+	1.18832i	0.977531	+	0.210794i	$0.0676049\pi$
$659$	30.5055	+	30.5055i	1.18832	+	1.18832i	0.210794	+	0.977531i	$0.432395\pi$
$660$		0			0
$661$	22.3898			0.870860			0.435430	−	0.900222i	$-0.356596\pi$
$661$	22.3898			0.870860			0.435430	+	0.900222i	$0.356596\pi$
$662$	−8.71548	−	8.71548i	−0.338737	−	0.338737i
$663$	1.21951	−	1.21951i	0.0473619	−	0.0473619i
$664$	10.2678	−	10.2678i	0.398469	−	0.398469i
$665$		0			0
$666$		−	13.7174i		−	0.531539i
$667$	−1.39205	−	6.74933i	−0.0539005	−	0.261335i
$668$	2.61867	−	2.61867i	0.101319	−	0.101319i
$669$	28.7078	+	28.7078i	1.10991	+	1.10991i
$670$		0			0
$671$		−	1.00930i		−	0.0389637i
$672$	−3.07435	+	3.07435i	−0.118596	+	0.118596i
$673$	19.0774	+	19.0774i	0.735379	+	0.735379i	0.971680	−	0.236301i	$-0.0759351\pi$
$673$	19.0774	+	19.0774i	0.735379	+	0.735379i	−0.236301	+	0.971680i	$0.575935\pi$
$674$			19.8857i			0.765967i
$675$		0			0
$676$		−	12.9518i		−	0.498148i
$677$			18.3552i			0.705446i	0.935728	+	0.352723i	$0.114744\pi$
$677$			18.3552i			0.705446i	−0.935728	+	0.352723i	$0.885256\pi$
$678$		−	14.5602i		−	0.559182i
$679$	−17.1494	+	17.1494i	−0.658132	+	0.658132i
$680$		0			0
$681$	33.3282	−	33.3282i	1.27714	−	1.27714i
$682$			14.9360i			0.571927i
$683$	25.8310	−	25.8310i	0.988397	−	0.988397i	−0.0115366	−	0.999933i	$-0.503672\pi$
$683$	25.8310	−	25.8310i	0.988397	−	0.988397i	0.999933	+	0.0115366i	$0.00367230\pi$
$684$	8.46909	+	8.46909i	0.323824	+	0.323824i
$685$		0			0
$686$	13.5728	−	13.5728i	0.518212	−	0.518212i
$687$	49.0078	+	49.0078i	1.86976	+	1.86976i
$688$		−	0.610251i		−	0.0232656i
$689$	1.22788			0.0467787
$690$		0			0
$691$	16.2862			0.619554			0.309777	−	0.950809i	$-0.399746\pi$
$691$	16.2862			0.619554			0.309777	+	0.950809i	$0.399746\pi$
$692$	−17.5607	−	17.5607i	−0.667556	−	0.667556i
$693$	17.1272			0.650608
$694$	−22.1013	+	22.1013i	−0.838954	+	0.838954i
$695$		0			0
$696$	−11.1041	−	7.30685i	−0.420901	−	0.276965i
$697$	10.4276	+	10.4276i	0.394974	+	0.394974i
$698$			32.2595i			1.22104i
$699$	−40.3494	−	40.3494i	−1.52615	−	1.52615i
$700$		0			0
$701$			4.20886i			0.158966i	0.996836	+	0.0794831i	$0.0253270\pi$
$701$			4.20886i			0.158966i	−0.996836	+	0.0794831i	$0.974673\pi$
$702$	−0.0355472	+	0.0355472i	−0.00134164	+	0.00134164i
$703$	−12.1451	+	12.1451i	−0.458063	+	0.458063i
$704$	2.22310	−	2.22310i	0.0837862	−	0.0837862i
$705$		0			0
$706$	−1.91301	−	1.91301i	−0.0719971	−	0.0719971i
$707$	31.3676			1.17970
$708$	3.68177			0.138369
$709$	30.5767			1.14833			0.574167	−	0.818738i	$-0.305326\pi$
$709$	30.5767			1.14833			0.574167	+	0.818738i	$0.305326\pi$
$710$		0			0
$711$	−35.5020	−	35.5020i	−1.33143	−	1.33143i
$712$	−1.40133	−	1.40133i	−0.0525170	−	0.0525170i
$713$		−	6.07949i		−	0.227679i
$714$	9.78875	−	9.78875i	0.366335	−	0.366335i
$715$		0			0
$716$	20.9854			0.784260
$717$	−26.1491			−0.976557
$718$	−22.6067	−	22.6067i	−0.843676	−	0.843676i
$719$			34.2384i			1.27688i	0.769672	+	0.638439i	$0.220420\pi$
$719$			34.2384i			1.27688i	−0.769672	+	0.638439i	$0.779580\pi$
$720$		0			0
$721$	10.9292			0.407025
$722$			4.00326i			0.148986i
$723$	14.2709			0.530742
$724$	−10.8048			−0.401557
$725$		0			0
$726$	2.75387			0.102206
$727$	−33.9231			−1.25814			−0.629069	−	0.777350i	$-0.716564\pi$
$727$	−33.9231			−1.25814			−0.629069	+	0.777350i	$0.716564\pi$
$728$			0.386524i			0.0143255i
$729$	28.6439			1.06089
$730$		0			0
$731$			1.94304i			0.0718661i
$732$	0.560327	+	0.560327i	0.0207103	+	0.0207103i
$733$	21.3978			0.790347			0.395174	−	0.918606i	$-0.370684\pi$
$733$	21.3978			0.790347			0.395174	+	0.918606i	$0.370684\pi$
$734$	−10.2287			−0.377549
$735$		0			0
$736$	−0.904884	+	0.904884i	−0.0333545	+	0.0333545i
$737$		−	16.7816i		−	0.618158i
$738$	−10.1289	−	10.1289i	−0.372852	−	0.372852i
$739$	27.6151	+	27.6151i	1.01584	+	1.01584i	0.999873	+	0.0159671i	$0.00508269\pi$
$739$	27.6151	+	27.6151i	1.01584	+	1.01584i	0.0159671	+	0.999873i	$0.494917\pi$
$740$		0			0
$741$	2.09761			0.0770577
$742$	9.85596			0.361824
$743$	10.6341			0.390126			0.195063	−	0.980791i	$-0.437509\pi$
$743$	10.6341			0.390126			0.195063	+	0.980791i	$0.437509\pi$
$744$	−8.29188	−	8.29188i	−0.303995	−	0.303995i
$745$		0			0
$746$	19.1443	−	19.1443i	0.700923	−	0.700923i
$747$	31.7564	−	31.7564i	1.16191	−	1.16191i
$748$	−7.07836	+	7.07836i	−0.258811	+	0.258811i
$749$			3.78601i			0.138338i
$750$		0			0
$751$	−7.42613	−	7.42613i	−0.270983	−	0.270983i	0.558513	−	0.829496i	$-0.311372\pi$
$751$	−7.42613	−	7.42613i	−0.270983	−	0.270983i	−0.829496	+	0.558513i	$0.811372\pi$
$752$		−	5.52744i		−	0.201565i
$753$	−33.7788	−	33.7788i	−1.23097	−	1.23097i
$754$	−1.15737	+	0.238707i	−0.0421488	+	0.00869321i
$755$		0			0
$756$	−0.285330	+	0.285330i	−0.0103773	+	0.0103773i
$757$	−28.8090			−1.04708			−0.523541	−	0.852000i	$-0.675389\pi$
$757$	−28.8090			−1.04708			−0.523541	+	0.852000i	$0.675389\pi$
$758$	−1.76015	−	1.76015i	−0.0639316	−	0.0639316i
$759$	9.93094			0.360470
$760$		0			0
$761$	−7.88150			−0.285704			−0.142852	−	0.989744i	$-0.545627\pi$
$761$	−7.88150			−0.285704			−0.142852	+	0.989744i	$0.545627\pi$
$762$		−	35.5128i		−	1.28649i
$763$	−4.49146	−	4.49146i	−0.162602	−	0.162602i
$764$	5.05827	−	5.05827i	0.183002	−	0.183002i
$765$		0			0
$766$	−0.210447	−	0.210447i	−0.00760376	−	0.00760376i
$767$	0.231447	−	0.231447i	0.00835705	−	0.00835705i
$768$			2.46836i			0.0890693i
$769$	−27.2683	+	27.2683i	−0.983320	+	0.983320i	−0.999863	−	0.0165436i	$-0.994734\pi$
$769$	−27.2683	+	27.2683i	−0.983320	+	0.983320i	0.0165436	+	0.999863i	$0.494734\pi$
$770$		0			0
$771$	12.8867	−	12.8867i	0.464105	−	0.464105i
$772$		−	12.7572i		−	0.459140i
$773$			38.8898i			1.39877i	0.714746	+	0.699384i	$0.246542\pi$
$773$			38.8898i			1.39877i	−0.714746	+	0.699384i	$0.753458\pi$
$774$		−	1.88739i		−	0.0678408i
$775$		0			0
$776$			13.7691i			0.494280i
$777$	−13.6355	−	13.6355i	−0.489172	−	0.489172i
$778$	11.2901	−	11.2901i	0.404769	−	0.404769i
$779$			17.9360i			0.642622i
$780$		0			0
$781$	−5.30928	−	5.30928i	−0.189981	−	0.189981i
$782$	2.88116	−	2.88116i	0.103030	−	0.103030i
$783$	−1.03057	−	0.678147i	−0.0368296	−	0.0242350i
$784$		−	3.89745i		−	0.139195i
$785$		0			0
$786$	18.2319	−	18.2319i	0.650309	−	0.650309i
$787$	−35.0753	+	35.0753i	−1.25030	+	1.25030i	−0.294713	+	0.955586i	$0.595224\pi$
$787$	−35.0753	+	35.0753i	−1.25030	+	1.25030i	−0.955586	+	0.294713i	$0.904776\pi$
$788$	−15.6497	−	15.6497i	−0.557499	−	0.557499i
$789$	70.7319			2.51812
$790$		0			0
$791$	−7.34689	−	7.34689i	−0.261225	−	0.261225i
$792$	6.87562	−	6.87562i	0.244315	−	0.244315i
$793$	0.0704474			0.00250166
$794$	−3.60226	−	3.60226i	−0.127839	−	0.127839i
$795$		0			0
$796$		−	5.37482i		−	0.190506i
$797$	−14.8638			−0.526503			−0.263252	−	0.964727i	$-0.584795\pi$
$797$	−14.8638			−0.526503			−0.263252	+	0.964727i	$0.584795\pi$
$798$	16.8371			0.596026
$799$			17.5994i			0.622623i
$800$		0			0
$801$	−4.33404	−	4.33404i	−0.153136	−	0.153136i
$802$	11.4735			0.405142
$803$	24.2832	−	24.2832i	0.856936	−	0.856936i
$804$	9.31651	+	9.31651i	0.328568	+	0.328568i
$805$		0			0
$806$	−1.04250			−0.0367206
$807$	−24.6390	−	24.6390i	−0.867333	−	0.867333i
$808$	12.5924	−	12.5924i	0.442998	−	0.442998i
$809$	−8.19288	+	8.19288i	−0.288046	+	0.288046i	−0.836307	−	0.548261i	$-0.815290\pi$
$809$	−8.19288	+	8.19288i	−0.288046	+	0.288046i	0.548261	+	0.836307i	$0.315290\pi$
$810$		0			0
$811$		−	21.5729i		−	0.757527i	−0.925494	−	0.378763i	$-0.876349\pi$
$811$		−	21.5729i		−	0.757527i	0.925494	−	0.378763i	$-0.123651\pi$
$812$	−9.28992	+	1.91605i	−0.326012	+	0.0672402i
$813$	−31.3199	+	31.3199i	−1.09844	+	1.09844i
$814$	9.86002	+	9.86002i	0.345594	+	0.345594i
$815$		0			0
$816$		−	7.85928i		−	0.275130i
$817$	−1.67106	+	1.67106i	−0.0584630	+	0.0584630i
$818$	28.0128	+	28.0128i	0.979444	+	0.979444i
$819$			1.19545i			0.0417723i
$820$		0			0
$821$			49.0185i			1.71076i	0.518003	+	0.855379i	$0.326675\pi$
$821$			49.0185i			1.71076i	−0.518003	+	0.855379i	$0.673325\pi$
$822$		−	0.877820i		−	0.0306175i
$823$		−	49.5516i		−	1.72726i	−0.504126	−	0.863630i	$-0.668185\pi$
$823$		−	49.5516i		−	1.72726i	0.504126	−	0.863630i	$-0.331815\pi$
$824$	4.38747	−	4.38747i	0.152845	−	0.152845i
$825$		0			0
$826$	1.85777	−	1.85777i	0.0646401	−	0.0646401i
$827$			7.23122i			0.251454i	0.992065	+	0.125727i	$0.0401264\pi$
$827$			7.23122i			0.251454i	−0.992065	+	0.125727i	$0.959874\pi$
$828$	−2.79863	+	2.79863i	−0.0972592	+	0.0972592i
$829$	−28.5556	−	28.5556i	−0.991779	−	0.991779i	0.00818792	−	0.999966i	$-0.497394\pi$
$829$	−28.5556	−	28.5556i	−0.991779	−	0.991779i	−0.999966	+	0.00818792i	$0.997394\pi$
$830$		0			0
$831$	−6.20706	+	6.20706i	−0.215320	+	0.215320i
$832$	0.155168	+	0.155168i	0.00537949	+	0.00537949i
$833$			12.4095i			0.429964i
$834$	−39.9461			−1.38322
$835$		0			0
$836$	−12.1751			−0.421084
$837$	−0.769569	−	0.769569i	−0.0266002	−	0.0266002i
$838$	−12.8383			−0.443492
$839$	1.98872	−	1.98872i	0.0686581	−	0.0686581i	−0.671944	−	0.740602i	$-0.734540\pi$
$839$	1.98872	−	1.98872i	0.0686581	−	0.0686581i	0.740602	+	0.671944i	$0.234540\pi$
$840$		0			0
$841$	−11.4744	−	26.6334i	−0.395670	−	0.918393i
$842$	−12.9907	−	12.9907i	−0.447690	−	0.447690i
$843$		−	69.3180i		−	2.38744i
$844$	14.5064	+	14.5064i	0.499332	+	0.499332i
$845$		0			0
$846$		−	17.0953i		−	0.587750i
$847$	1.38957	−	1.38957i	0.0477461	−	0.0477461i
$848$	3.95662	−	3.95662i	0.135871	−	0.135871i
$849$	−18.6131	+	18.6131i	−0.638799	+	0.638799i
$850$		0			0
$851$	−4.01340	−	4.01340i	−0.137577	−	0.137577i
$852$	5.89502			0.201960
$853$	4.47961			0.153379			0.0766895	−	0.997055i	$-0.475565\pi$
$853$	4.47961			0.153379			0.0766895	+	0.997055i	$0.475565\pi$
$854$	0.565466			0.0193499
$855$		0			0
$856$	1.51987	+	1.51987i	0.0519482	+	0.0519482i
$857$	1.32833	+	1.32833i	0.0453750	+	0.0453750i	0.729430	−	0.684055i	$-0.239785\pi$
$857$	1.32833	+	1.32833i	0.0453750	+	0.0453750i	−0.684055	+	0.729430i	$0.739785\pi$
$858$		−	1.70294i		−	0.0581375i
$859$	19.9337	−	19.9337i	0.680128	−	0.680128i	−0.279901	−	0.960029i	$-0.590302\pi$
$859$	19.9337	−	19.9337i	0.680128	−	0.680128i	0.960029	+	0.279901i	$0.0903015\pi$
$860$		0			0
$861$	−20.1370			−0.686266
$862$	20.6050			0.701810
$863$	28.0463	+	28.0463i	0.954706	+	0.954706i	0.999018	−	0.0443116i	$-0.0141095\pi$
$863$	28.0463	+	28.0463i	0.954706	+	0.954706i	−0.0443116	+	0.999018i	$0.514109\pi$
$864$			0.229088i			0.00779374i
$865$		0			0
$866$	−36.2040			−1.23026
$867$		−	16.9381i		−	0.575249i
$868$	−8.36794			−0.284026
$869$	51.0373			1.73132
$870$		0			0
$871$	1.17132			0.0396888
$872$	−3.60614			−0.122119
$873$			42.5851i			1.44129i
$874$	4.95571			0.167630
$875$		0			0
$876$			26.9622i			0.910970i
$877$	22.5184	+	22.5184i	0.760393	+	0.760393i	0.976393	−	0.216000i	$-0.0693012\pi$
$877$	22.5184	+	22.5184i	0.760393	+	0.760393i	−0.216000	+	0.976393i	$0.569301\pi$
$878$	7.87262			0.265688
$879$	16.4563			0.555056
$880$		0			0
$881$	−1.42415	+	1.42415i	−0.0479809	+	0.0479809i	−0.730690	−	0.682709i	$-0.760802\pi$
$881$	−1.42415	+	1.42415i	−0.0479809	+	0.0479809i	0.682709	+	0.730690i	$0.260802\pi$
$882$		−	12.0541i		−	0.405882i
$883$	30.2243	+	30.2243i	1.01713	+	1.01713i	0.999851	+	0.0172779i	$0.00550000\pi$
$883$	30.2243	+	30.2243i	1.01713	+	1.01713i	0.0172779	+	0.999851i	$0.494500\pi$
$884$	−0.494057	−	0.494057i	−0.0166169	−	0.0166169i
$885$		0			0
$886$	−14.2317			−0.478124
$887$	−36.3183			−1.21945			−0.609725	−	0.792613i	$-0.708720\pi$
$887$	−36.3183			−1.21945			−0.609725	+	0.792613i	$0.708720\pi$
$888$	−10.9478			−0.367385
$889$	−17.9193	−	17.9193i	−0.600993	−	0.600993i
$890$		0			0
$891$	−19.3698	+	19.3698i	−0.648911	+	0.648911i
$892$	11.6303	−	11.6303i	0.389411	−	0.389411i
$893$	−15.1359	+	15.1359i	−0.506503	+	0.506503i
$894$		−	3.39060i		−	0.113399i
$895$		0			0
$896$	1.24550	+	1.24550i	0.0416093	+	0.0416093i
$897$			0.693161i			0.0231440i
$898$	9.81094	+	9.81094i	0.327395	+	0.327395i
$899$	−5.16782	−	25.0560i	−0.172356	−	0.835665i
$900$		0			0
$901$	−12.5979	+	12.5979i	−0.419697	+	0.419697i
$902$	14.5613			0.484838
$903$	−1.87612	−	1.87612i	−0.0624335	−	0.0624335i
$904$	−5.89874			−0.196189
$905$		0			0
$906$	11.5149			0.382557
$907$			26.9725i			0.895607i	0.894132	+	0.447804i	$0.147794\pi$
$907$			26.9725i			0.895607i	−0.894132	+	0.447804i	$0.852206\pi$
$908$	−13.5021	−	13.5021i	−0.448084	−	0.448084i
$909$	38.9458	−	38.9458i	1.29175	−	1.29175i
$910$		0			0
$911$	12.8986	+	12.8986i	0.427349	+	0.427349i	0.887724	−	0.460375i	$-0.152285\pi$
$911$	12.8986	+	12.8986i	0.427349	+	0.427349i	−0.460375	+	0.887724i	$0.652285\pi$
$912$	6.75915	−	6.75915i	0.223818	−	0.223818i
$913$			45.6528i			1.51089i
$914$	−27.0893	+	27.0893i	−0.896034	+	0.896034i
$915$		0			0
$916$	19.8544	−	19.8544i	0.656007	−	0.656007i
$917$		−	18.3991i		−	0.607592i
$918$		−	0.729419i		−	0.0240744i
$919$		−	20.9482i		−	0.691018i	−0.938415	−	0.345509i	$-0.887706\pi$
$919$		−	20.9482i		−	0.691018i	0.938415	−	0.345509i	$-0.112294\pi$
$920$		0			0
$921$		−	45.3432i		−	1.49411i
$922$	14.8907	+	14.8907i	0.490400	+	0.490400i
$923$	0.370578	−	0.370578i	0.0121977	−	0.0121977i
$924$		−	13.6692i		−	0.449682i
$925$		0			0
$926$	4.96124	+	4.96124i	0.163036	+	0.163036i
$927$	13.5696	−	13.5696i	0.445685	−	0.445685i
$928$	−2.96020	+	4.49858i	−0.0971734	+	0.147673i
$929$		−	32.5854i		−	1.06909i	−0.845139	−	0.534546i	$-0.820483\pi$
$929$		−	32.5854i		−	1.06909i	0.845139	−	0.534546i	$-0.179517\pi$
$930$		0			0
$931$	−10.6725	+	10.6725i	−0.349776	+	0.349776i
$932$	−16.3466	+	16.3466i	−0.535452	+	0.535452i
$933$	−13.0314	−	13.0314i	−0.426631	−	0.426631i
$934$	−11.2622			−0.368511
$935$		0			0
$936$	0.479906	+	0.479906i	0.0156862	+	0.0156862i
$937$	−20.8740	+	20.8740i	−0.681922	+	0.681922i	−0.960433	−	0.278511i	$-0.910159\pi$
$937$	−20.8740	+	20.8740i	−0.681922	+	0.681922i	0.278511	+	0.960433i	$0.410159\pi$
$938$	9.40197			0.306985
$939$	−9.29426	−	9.29426i	−0.303307	−	0.303307i
$940$		0			0
$941$		−	27.8674i		−	0.908451i	−0.890887	−	0.454225i	$-0.849916\pi$
$941$		−	27.8674i		−	0.908451i	0.890887	−	0.454225i	$-0.150084\pi$
$942$	20.7606			0.676416
$943$	−5.92699			−0.193009
$944$		−	1.49159i		−	0.0485470i
$945$		0			0
$946$	1.35665	+	1.35665i	0.0441084	+	0.0441084i
$947$	22.0535			0.716644			0.358322	−	0.933598i	$-0.383349\pi$
$947$	22.0535			0.716644			0.358322	+	0.933598i	$0.383349\pi$
$948$	−28.3340	+	28.3340i	−0.920245	+	0.920245i
$949$	1.69492	+	1.69492i	0.0550195	+	0.0550195i
$950$		0			0
$951$	−50.0902			−1.62429
$952$	−3.96569	−	3.96569i	−0.128529	−	0.128529i
$953$	−17.5814	+	17.5814i	−0.569518	+	0.569518i	−0.931993	−	0.362476i	$-0.881932\pi$
$953$	−17.5814	+	17.5814i	−0.569518	+	0.569518i	0.362476	+	0.931993i	$0.381932\pi$
$954$	12.2371	−	12.2371i	0.396190	−	0.396190i
$955$		0			0
$956$			10.5937i			0.342625i
$957$	40.9294	−	8.44171i	1.32306	−	0.272882i
$958$	13.3645	−	13.3645i	0.431788	−	0.431788i
$959$	−0.442936	−	0.442936i	−0.0143031	−	0.0143031i
$960$		0			0
$961$			8.43066i			0.271957i
$962$	−0.688211	+	0.688211i	−0.0221888	+	0.0221888i
$963$	4.70068	+	4.70068i	0.151477	+	0.151477i
$964$		−	5.78154i		−	0.186211i
$965$		0			0
$966$			5.56386i			0.179014i
$967$			60.5614i			1.94752i	0.227568	+	0.973762i	$0.426922\pi$
$967$			60.5614i			1.94752i	−0.227568	+	0.973762i	$0.573078\pi$
$968$		−	1.11567i		−	0.0358589i
$969$	−21.5212	+	21.5212i	−0.691360	+	0.691360i
$970$		0			0
$971$	14.8425	−	14.8425i	0.476319	−	0.476319i	−0.427633	−	0.903952i	$-0.640653\pi$
$971$	14.8425	−	14.8425i	0.476319	−	0.476319i	0.903952	+	0.427633i	$0.140653\pi$
$972$		−	22.1940i		−	0.711873i
$973$	−20.1563	+	20.1563i	−0.646180	+	0.646180i
$974$	−6.98259	−	6.98259i	−0.223737	−	0.223737i
$975$		0			0
$976$	0.227003	−	0.227003i	0.00726620	−	0.00726620i
$977$	9.36059	+	9.36059i	0.299472	+	0.299472i	0.840807	−	0.541335i	$-0.182081\pi$
$977$	9.36059	+	9.36059i	0.299472	+	0.299472i	−0.541335	+	0.840807i	$0.682081\pi$
$978$		−	0.112356i		−	0.00359275i
$979$	6.23058			0.199130
$980$		0			0
$981$	−11.1531			−0.356091
$982$	18.5807	+	18.5807i	0.592933	+	0.592933i
$983$	47.0588			1.50094			0.750471	−	0.660903i	$-0.229827\pi$
$983$	47.0588			1.50094			0.750471	+	0.660903i	$0.229827\pi$
$984$	−8.08388	+	8.08388i	−0.257705	+	0.257705i
$985$		0			0
$986$	9.42530	−	14.3235i	0.300163	−	0.456153i
$987$	−16.9933	−	16.9933i	−0.540902	−	0.540902i
$988$		−	0.849799i		−	0.0270357i
$989$	−0.552206	−	0.552206i	−0.0175591	−	0.0175591i
$990$		0			0
$991$			16.6463i			0.528786i	0.964415	+	0.264393i	$0.0851717\pi$
$991$			16.6463i			0.528786i	−0.964415	+	0.264393i	$0.914828\pi$
$992$	−3.35927	+	3.35927i	−0.106657	+	0.106657i
$993$	−21.5130	+	21.5130i	−0.682693	+	0.682693i
$994$	2.97455	−	2.97455i	0.0943469	−	0.0943469i
$995$		0			0
$996$	−25.3447	−	25.3447i	−0.803078	−	0.803078i
$997$	35.4922			1.12405			0.562024	−	0.827121i	$-0.310023\pi$
$997$	35.4922			1.12405			0.562024	+	0.827121i	$0.310023\pi$
$998$	35.5843			1.12640
$999$	−1.01607			−0.0321469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.e.i.307.10	✓	20
5.2	odd	4		1450.2.j.i.1293.10	yes	20
5.3	odd	4		1450.2.j.j.1293.1	yes	20
5.4	even	2		1450.2.e.j.307.1	yes	20
29.12	odd	4		1450.2.j.j.157.1	yes	20
145.12	even	4		1450.2.e.j.1143.10	yes	20
145.99	odd	4		1450.2.j.i.157.10	yes	20
145.128	even	4	inner	1450.2.e.i.1143.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1450.2.e.i.307.10	✓	20	1.1	even	1	trivial
1450.2.e.i.1143.1	yes	20	145.128	even	4	inner
1450.2.e.j.307.1	yes	20	5.4	even	2
1450.2.e.j.1143.10	yes	20	145.12	even	4
1450.2.j.i.157.10	yes	20	145.99	odd	4
1450.2.j.i.1293.10	yes	20	5.2	odd	4
1450.2.j.j.157.1	yes	20	29.12	odd	4
1450.2.j.j.1293.1	yes	20	5.3	odd	4

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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.46836i q^{3} +1.00000 q^{4} -2.46836i q^{6} +(-1.24550 - 1.24550i) q^{7} -1.00000 q^{8} -3.09281 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.46836i q^{3} +1.00000 q^{4} -2.46836i q^{6} +(-1.24550 - 1.24550i) q^{7} -1.00000 q^{8} -3.09281 q^{9} +(2.22310 - 2.22310i) q^{11} +2.46836i q^{12} +(0.155168 + 0.155168i) q^{13} +(1.24550 + 1.24550i) q^{14} +1.00000 q^{16} -3.18401 q^{17} +3.09281 q^{18} +(-2.73832 - 2.73832i) q^{19} +(3.07435 - 3.07435i) q^{21} +(-2.22310 + 2.22310i) q^{22} +(0.904884 - 0.904884i) q^{23} -2.46836i q^{24} +(-0.155168 - 0.155168i) q^{26} -0.229088i q^{27} +(-1.24550 - 1.24550i) q^{28} +(2.96020 - 4.49858i) q^{29} +(3.35927 - 3.35927i) q^{31} -1.00000 q^{32} +(5.48741 + 5.48741i) q^{33} +3.18401 q^{34} -3.09281 q^{36} -4.43526i q^{37} +(2.73832 + 2.73832i) q^{38} +(-0.383011 + 0.383011i) q^{39} +(-3.27500 - 3.27500i) q^{41} +(-3.07435 + 3.07435i) q^{42} -0.610251i q^{43} +(2.22310 - 2.22310i) q^{44} +(-0.904884 + 0.904884i) q^{46} -5.52744i q^{47} +2.46836i q^{48} -3.89745i q^{49} -7.85928i q^{51} +(0.155168 + 0.155168i) q^{52} +(3.95662 - 3.95662i) q^{53} +0.229088i q^{54} +(1.24550 + 1.24550i) q^{56} +(6.75915 - 6.75915i) q^{57} +(-2.96020 + 4.49858i) q^{58} -1.49159i q^{59} +(0.227003 - 0.227003i) q^{61} +(-3.35927 + 3.35927i) q^{62} +(3.85210 + 3.85210i) q^{63} +1.00000 q^{64} +(-5.48741 - 5.48741i) q^{66} +(3.77437 - 3.77437i) q^{67} -3.18401 q^{68} +(2.23358 + 2.23358i) q^{69} -2.38823i q^{71} +3.09281 q^{72} +10.9231 q^{73} +4.43526i q^{74} +(-2.73832 - 2.73832i) q^{76} -5.53774 q^{77} +(0.383011 - 0.383011i) q^{78} +(11.4789 + 11.4789i) q^{79} -8.71296 q^{81} +(3.27500 + 3.27500i) q^{82} +(-10.2678 + 10.2678i) q^{83} +(3.07435 - 3.07435i) q^{84} +0.610251i q^{86} +(11.1041 + 7.30685i) q^{87} +(-2.22310 + 2.22310i) q^{88} +(1.40133 + 1.40133i) q^{89} -0.386524i q^{91} +(0.904884 - 0.904884i) q^{92} +(8.29188 + 8.29188i) q^{93} +5.52744i q^{94} -2.46836i q^{96} -13.7691i q^{97} +3.89745i q^{98} +(-6.87562 + 6.87562i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 20 q^{4} - 8 q^{7} - 20 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 20 * q^4 - 8 * q^7 - 20 * q^8 - 12 * q^9	\( 20 q - 20 q^{2} + 20 q^{4} - 8 q^{7} - 20 q^{8} - 12 q^{9} - 8 q^{11} - 4 q^{13} + 8 q^{14} + 20 q^{16} + 16 q^{17} + 12 q^{18} - 4 q^{19} + 4 q^{21} + 8 q^{22} + 12 q^{23} + 4 q^{26} - 8 q^{28} + 8 q^{29} + 28 q^{31} - 20 q^{32} - 16 q^{34} - 12 q^{36} + 4 q^{38} - 24 q^{39} + 24 q^{41} - 4 q^{42} - 8 q^{44} - 12 q^{46} - 4 q^{52} + 8 q^{56} - 8 q^{57} - 8 q^{58} + 24 q^{61} - 28 q^{62} + 20 q^{63} + 20 q^{64} + 12 q^{67} + 16 q^{68} - 28 q^{69} + 12 q^{72} - 16 q^{73} - 4 q^{76} + 16 q^{77} + 24 q^{78} + 32 q^{79} - 12 q^{81} - 24 q^{82} - 20 q^{83} + 4 q^{84} + 44 q^{87} + 8 q^{88} + 4 q^{89} + 12 q^{92} + 12 q^{93} + 8 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 20 * q^4 - 8 * q^7 - 20 * q^8 - 12 * q^9 - 8 * q^11 - 4 * q^13 + 8 * q^14 + 20 * q^16 + 16 * q^17 + 12 * q^18 - 4 * q^19 + 4 * q^21 + 8 * q^22 + 12 * q^23 + 4 * q^26 - 8 * q^28 + 8 * q^29 + 28 * q^31 - 20 * q^32 - 16 * q^34 - 12 * q^36 + 4 * q^38 - 24 * q^39 + 24 * q^41 - 4 * q^42 - 8 * q^44 - 12 * q^46 - 4 * q^52 + 8 * q^56 - 8 * q^57 - 8 * q^58 + 24 * q^61 - 28 * q^62 + 20 * q^63 + 20 * q^64 + 12 * q^67 + 16 * q^68 - 28 * q^69 + 12 * q^72 - 16 * q^73 - 4 * q^76 + 16 * q^77 + 24 * q^78 + 32 * q^79 - 12 * q^81 - 24 * q^82 - 20 * q^83 + 4 * q^84 + 44 * q^87 + 8 * q^88 + 4 * q^89 + 12 * q^92 + 12 * q^93 + 8 * q^99

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