LMFDB - Embedded newform 731.2.f.c.259.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.11
Character	$\chi$	$=$	731.259
Dual form			731.2.f.c.302.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.21542i q^{2} +(0.483456 - 0.483456i) q^{3} +0.522759 q^{4} +(1.73874 - 1.73874i) q^{5} +(-0.587601 - 0.587601i) q^{6} +(3.36984 + 3.36984i) q^{7} -3.06621i q^{8} +2.53254i q^{9} +O(q^{10})$	\(q-1.21542i q^{2} +(0.483456 - 0.483456i) q^{3} +0.522759 q^{4} +(1.73874 - 1.73874i) q^{5} +(-0.587601 - 0.587601i) q^{6} +(3.36984 + 3.36984i) q^{7} -3.06621i q^{8} +2.53254i q^{9} +(-2.11330 - 2.11330i) q^{10} +(-2.85520 - 2.85520i) q^{11} +(0.252731 - 0.252731i) q^{12} +1.80782 q^{13} +(4.09576 - 4.09576i) q^{14} -1.68121i q^{15} -2.68120 q^{16} +(-2.02982 + 3.58885i) q^{17} +3.07810 q^{18} -5.40632i q^{19} +(0.908944 - 0.908944i) q^{20} +3.25833 q^{21} +(-3.47026 + 3.47026i) q^{22} +(4.51634 + 4.51634i) q^{23} +(-1.48238 - 1.48238i) q^{24} -1.04645i q^{25} -2.19726i q^{26} +(2.67474 + 2.67474i) q^{27} +(1.76161 + 1.76161i) q^{28} +(0.891866 - 0.891866i) q^{29} -2.04337 q^{30} +(-1.13305 + 1.13305i) q^{31} -2.87363i q^{32} -2.76073 q^{33} +(4.36195 + 2.46708i) q^{34} +11.7186 q^{35} +1.32391i q^{36} +(-5.12555 + 5.12555i) q^{37} -6.57094 q^{38} +(0.874001 - 0.874001i) q^{39} +(-5.33134 - 5.33134i) q^{40} +(-7.90564 - 7.90564i) q^{41} -3.96024i q^{42} +1.00000i q^{43} +(-1.49258 - 1.49258i) q^{44} +(4.40344 + 4.40344i) q^{45} +(5.48924 - 5.48924i) q^{46} -9.62086 q^{47} +(-1.29624 + 1.29624i) q^{48} +15.7116i q^{49} -1.27187 q^{50} +(0.753724 + 2.71638i) q^{51} +0.945055 q^{52} -12.5051i q^{53} +(3.25093 - 3.25093i) q^{54} -9.92891 q^{55} +(10.3326 - 10.3326i) q^{56} +(-2.61372 - 2.61372i) q^{57} +(-1.08399 - 1.08399i) q^{58} +4.98600i q^{59} -0.878869i q^{60} +(-5.30958 - 5.30958i) q^{61} +(1.37713 + 1.37713i) q^{62} +(-8.53425 + 8.53425i) q^{63} -8.85507 q^{64} +(3.14333 - 3.14333i) q^{65} +3.35544i q^{66} -3.09545 q^{67} +(-1.06111 + 1.87610i) q^{68} +4.36690 q^{69} -14.2429i q^{70} +(7.00748 - 7.00748i) q^{71} +7.76529 q^{72} +(3.01422 - 3.01422i) q^{73} +(6.22968 + 6.22968i) q^{74} +(-0.505913 - 0.505913i) q^{75} -2.82620i q^{76} -19.2431i q^{77} +(-1.06228 - 1.06228i) q^{78} +(-1.43827 - 1.43827i) q^{79} +(-4.66192 + 4.66192i) q^{80} -5.01139 q^{81} +(-9.60865 + 9.60865i) q^{82} +7.59900i q^{83} +1.70332 q^{84} +(2.71076 + 9.76941i) q^{85} +1.21542 q^{86} -0.862356i q^{87} +(-8.75463 + 8.75463i) q^{88} +9.20655 q^{89} +(5.35202 - 5.35202i) q^{90} +(6.09206 + 6.09206i) q^{91} +(2.36096 + 2.36096i) q^{92} +1.09556i q^{93} +11.6934i q^{94} +(-9.40020 - 9.40020i) q^{95} +(-1.38927 - 1.38927i) q^{96} +(-8.71703 + 8.71703i) q^{97} +19.0962 q^{98} +(7.23091 - 7.23091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		−	1.21542i		−	0.859430i	−0.902965	−	0.429715i	$-0.858614\pi$
$2$		−	1.21542i		−	0.859430i	0.902965	−	0.429715i	$-0.141386\pi$
$3$	0.483456	−	0.483456i	0.279123	−	0.279123i	−0.553636	−	0.832759i	$-0.686760\pi$
$3$	0.483456	−	0.483456i	0.279123	−	0.279123i	0.832759	+	0.553636i	$0.186760\pi$
$4$	0.522759			0.261380
$5$	1.73874	−	1.73874i	0.777589	−	0.777589i	−0.201831	−	0.979420i	$-0.564689\pi$
$5$	1.73874	−	1.73874i	0.777589	−	0.777589i	0.979420	+	0.201831i	$0.0646892\pi$
$6$	−0.587601	−	0.587601i	−0.239887	−	0.239887i
$7$	3.36984	+	3.36984i	1.27368	+	1.27368i	0.944143	+	0.329535i	$0.106892\pi$
$7$	3.36984	+	3.36984i	1.27368	+	1.27368i	0.329535	+	0.944143i	$0.393108\pi$
$8$		−	3.06621i		−	1.08407i
$9$			2.53254i			0.844180i
$10$	−2.11330	−	2.11330i	−0.668284	−	0.668284i
$11$	−2.85520	−	2.85520i	−0.860875	−	0.860875i	0.130565	−	0.991440i	$-0.458321\pi$
$11$	−2.85520	−	2.85520i	−0.860875	−	0.860875i	−0.991440	+	0.130565i	$0.958321\pi$
$12$	0.252731	−	0.252731i	0.0729572	−	0.0729572i
$13$	1.80782			0.501399			0.250700	−	0.968065i	$-0.419339\pi$
$13$	1.80782			0.501399			0.250700	+	0.968065i	$0.419339\pi$
$14$	4.09576	−	4.09576i	1.09464	−	1.09464i
$15$		−	1.68121i		−	0.434087i
$16$	−2.68120			−0.670301
$17$	−2.02982	+	3.58885i	−0.492303	+	0.870424i
$17$	−2.02982	+	3.58885i	−0.492303	+	0.870424i
$18$	3.07810			0.725514
$19$		−	5.40632i		−	1.24029i	−0.784485	−	0.620147i	$-0.787073\pi$
$19$		−	5.40632i		−	1.24029i	0.784485	−	0.620147i	$-0.212927\pi$
$20$	0.908944	−	0.908944i	0.203246	−	0.203246i
$21$	3.25833			0.711027
$22$	−3.47026	+	3.47026i	−0.739862	+	0.739862i
$23$	4.51634	+	4.51634i	0.941722	+	0.941722i	0.998393	−	0.0566712i	$-0.0180487\pi$
$23$	4.51634	+	4.51634i	0.941722	+	0.941722i	−0.0566712	+	0.998393i	$0.518049\pi$
$24$	−1.48238	−	1.48238i	−0.302589	−	0.302589i
$25$		−	1.04645i		−	0.209290i
$26$		−	2.19726i		−	0.430918i
$27$	2.67474	+	2.67474i	0.514754	+	0.514754i
$28$	1.76161	+	1.76161i	0.332914	+	0.332914i
$29$	0.891866	−	0.891866i	0.165615	−	0.165615i	−0.619434	−	0.785049i	$-0.712638\pi$
$29$	0.891866	−	0.891866i	0.165615	−	0.165615i	0.785049	+	0.619434i	$0.212638\pi$
$30$	−2.04337			−0.373067
$31$	−1.13305	+	1.13305i	−0.203502	+	0.203502i	−0.801499	−	0.597996i	$-0.795964\pi$
$31$	−1.13305	+	1.13305i	−0.203502	+	0.203502i	0.597996	+	0.801499i	$0.295964\pi$
$32$		−	2.87363i		−	0.507991i
$33$	−2.76073			−0.480581
$34$	4.36195	+	2.46708i	0.748069	+	0.423100i
$35$	11.7186			1.98080
$36$			1.32391i			0.220652i
$37$	−5.12555	+	5.12555i	−0.842634	+	0.842634i	−0.989201	−	0.146566i	$-0.953178\pi$
$37$	−5.12555	+	5.12555i	−0.842634	+	0.842634i	0.146566	+	0.989201i	$0.453178\pi$
$38$	−6.57094			−1.06595
$39$	0.874001	−	0.874001i	0.139952	−	0.139952i
$40$	−5.33134	−	5.33134i	−0.842960	−	0.842960i
$41$	−7.90564	−	7.90564i	−1.23465	−	1.23465i	−0.962157	−	0.272496i	$-0.912151\pi$
$41$	−7.90564	−	7.90564i	−1.23465	−	1.23465i	−0.272496	−	0.962157i	$-0.587849\pi$
$42$		−	3.96024i		−	0.611078i
$43$			1.00000i			0.152499i
$43$			1.00000i			0.152499i
$44$	−1.49258	−	1.49258i	−0.225015	−	0.225015i
$45$	4.40344	+	4.40344i	0.656426	+	0.656426i
$46$	5.48924	−	5.48924i	0.809344	−	0.809344i
$47$	−9.62086			−1.40335			−0.701673	−	0.712499i	$-0.747563\pi$
$47$	−9.62086			−1.40335			−0.701673	+	0.712499i	$0.747563\pi$
$48$	−1.29624	+	1.29624i	−0.187097	+	0.187097i
$49$			15.7116i			2.24451i
$50$	−1.27187			−0.179870
$51$	0.753724	+	2.71638i	0.105542	+	0.380369i
$52$	0.945055			0.131056
$53$		−	12.5051i		−	1.71771i	−0.512220	−	0.858855i	$-0.671177\pi$
$53$		−	12.5051i		−	1.71771i	0.512220	−	0.858855i	$-0.328823\pi$
$54$	3.25093	−	3.25093i	0.442395	−	0.442395i
$55$	−9.92891			−1.33881
$56$	10.3326	−	10.3326i	1.38075	−	1.38075i
$57$	−2.61372	−	2.61372i	−0.346195	−	0.346195i
$58$	−1.08399	−	1.08399i	−0.142335	−	0.142335i
$59$			4.98600i			0.649121i	0.945865	+	0.324561i	$0.105216\pi$
$59$			4.98600i			0.649121i	−0.945865	+	0.324561i	$0.894784\pi$
$60$		−	0.878869i		−	0.113461i
$61$	−5.30958	−	5.30958i	−0.679822	−	0.679822i	0.280138	−	0.959960i	$-0.409620\pi$
$61$	−5.30958	−	5.30958i	−0.679822	−	0.679822i	−0.959960	+	0.280138i	$0.909620\pi$
$62$	1.37713	+	1.37713i	0.174896	+	0.174896i
$63$	−8.53425	+	8.53425i	−1.07521	+	1.07521i
$64$	−8.85507			−1.10688
$65$	3.14333	−	3.14333i	0.389883	−	0.389883i
$66$			3.35544i			0.413026i
$67$	−3.09545			−0.378170			−0.189085	−	0.981961i	$-0.560552\pi$
$67$	−3.09545			−0.378170			−0.189085	+	0.981961i	$0.560552\pi$
$68$	−1.06111	+	1.87610i	−0.128678	+	0.227511i
$69$	4.36690			0.525713
$70$		−	14.2429i		−	1.70236i
$71$	7.00748	−	7.00748i	0.831635	−	0.831635i	−0.156105	−	0.987740i	$-0.549894\pi$
$71$	7.00748	−	7.00748i	0.831635	−	0.831635i	0.987740	+	0.156105i	$0.0498940\pi$
$72$	7.76529			0.915149
$73$	3.01422	−	3.01422i	0.352787	−	0.352787i	−0.508358	−	0.861146i	$-0.669747\pi$
$73$	3.01422	−	3.01422i	0.352787	−	0.352787i	0.861146	+	0.508358i	$0.169747\pi$
$74$	6.22968	+	6.22968i	0.724186	+	0.724186i
$75$	−0.505913	−	0.505913i	−0.0584178	−	0.0584178i
$76$		−	2.82620i		−	0.324188i
$77$		−	19.2431i		−	2.19296i
$78$	−1.06228	−	1.06228i	−0.120279	−	0.120279i
$79$	−1.43827	−	1.43827i	−0.161818	−	0.161818i	0.621554	−	0.783371i	$-0.286502\pi$
$79$	−1.43827	−	1.43827i	−0.161818	−	0.161818i	−0.783371	+	0.621554i	$0.786502\pi$
$80$	−4.66192	+	4.66192i	−0.521219	+	0.521219i
$81$	−5.01139			−0.556821
$82$	−9.60865	+	9.60865i	−1.06110	+	1.06110i
$83$			7.59900i			0.834099i	0.908884	+	0.417049i	$0.136936\pi$
$83$			7.59900i			0.834099i	−0.908884	+	0.417049i	$0.863064\pi$
$84$	1.70332			0.185848
$85$	2.71076	+	9.76941i	0.294023	+	1.05964i
$86$	1.21542			0.131062
$87$		−	0.862356i		−	0.0924543i
$88$	−8.75463	+	8.75463i	−0.933247	+	0.933247i
$89$	9.20655			0.975893			0.487946	−	0.872874i	$-0.337746\pi$
$89$	9.20655			0.975893			0.487946	+	0.872874i	$0.337746\pi$
$90$	5.35202	−	5.35202i	0.564152	−	0.564152i
$91$	6.09206	+	6.09206i	0.638621	+	0.638621i
$92$	2.36096	+	2.36096i	0.246147	+	0.246147i
$93$			1.09556i			0.113605i
$94$			11.6934i			1.20608i
$95$	−9.40020	−	9.40020i	−0.964440	−	0.964440i
$96$	−1.38927	−	1.38927i	−0.141792	−	0.141792i
$97$	−8.71703	+	8.71703i	−0.885080	+	0.885080i	−0.994046	−	0.108965i	$-0.965246\pi$
$97$	−8.71703	+	8.71703i	−0.885080	+	0.885080i	0.108965	+	0.994046i	$0.465246\pi$
$98$	19.0962			1.92900
$99$	7.23091	−	7.23091i	0.726734	−	0.726734i
$100$		−	0.547042i		−	0.0547042i
$101$	0.813281			0.0809245			0.0404622	−	0.999181i	$-0.487117\pi$
$101$	0.813281			0.0809245			0.0404622	+	0.999181i	$0.487117\pi$
$102$	3.30153	−	0.916090i	0.326901	−	0.0907064i
$103$	−0.438416			−0.0431984			−0.0215992	−	0.999767i	$-0.506876\pi$
$103$	−0.438416			−0.0431984			−0.0215992	+	0.999767i	$0.506876\pi$
$104$		−	5.54315i		−	0.543551i
$105$	5.66540	−	5.66540i	0.552887	−	0.552887i
$106$	−15.1989			−1.47625
$107$	−9.04569	+	9.04569i	−0.874480	+	0.874480i	−0.992957	−	0.118477i	$-0.962199\pi$
$107$	−9.04569	+	9.04569i	−0.874480	+	0.874480i	0.118477	+	0.992957i	$0.462199\pi$
$108$	1.39824	+	1.39824i	0.134546	+	0.134546i
$109$	3.81774	+	3.81774i	0.365673	+	0.365673i	0.865896	−	0.500223i	$-0.166749\pi$
$109$	3.81774	+	3.81774i	0.365673	+	0.365673i	−0.500223	+	0.865896i	$0.666749\pi$
$110$			12.0678i			1.15062i
$111$			4.95595i			0.470398i
$112$	−9.03522	−	9.03522i	−0.853748	−	0.853748i
$113$	−9.56128	−	9.56128i	−0.899449	−	0.899449i	0.0959381	−	0.995387i	$-0.469415\pi$
$113$	−9.56128	−	9.56128i	−0.899449	−	0.899449i	−0.995387	+	0.0959381i	$0.969415\pi$
$114$	−3.17676	+	3.17676i	−0.297531	+	0.297531i
$115$	15.7055			1.46455
$116$	0.466231	−	0.466231i	0.0432885	−	0.0432885i
$117$			4.57838i			0.423271i
$118$	6.06007			0.557875
$119$	−18.9340	+	5.25369i	−1.73568	+	0.481605i
$120$	−5.15494			−0.470579
$121$			5.30433i			0.482212i
$122$	−6.45336	+	6.45336i	−0.584260	+	0.584260i
$123$	−7.64405			−0.689241
$124$	−0.592314	+	0.592314i	−0.0531914	+	0.0531914i
$125$	6.87420	+	6.87420i	0.614847	+	0.614847i
$126$	10.3727	+	10.3727i	0.924072	+	0.924072i
$127$			9.00021i			0.798640i	0.916812	+	0.399320i	$0.130754\pi$
$127$			9.00021i			0.798640i	−0.916812	+	0.399320i	$0.869246\pi$
$128$			5.01535i			0.443298i
$129$	0.483456	+	0.483456i	0.0425659	+	0.0425659i
$130$	−3.82046	−	3.82046i	−0.335077	−	0.335077i
$131$	−12.0648	+	12.0648i	−1.05410	+	1.05410i	−0.0556539	+	0.998450i	$0.517724\pi$
$131$	−12.0648	+	12.0648i	−1.05410	+	1.05410i	−0.998450	+	0.0556539i	$0.982276\pi$
$132$	−1.44320			−0.125614
$133$	18.2184	−	18.2184i	1.57974	−	1.57974i
$134$			3.76227i			0.325010i
$135$	9.30137			0.800534
$136$	11.0042	+	6.22384i	0.943599	+	0.533690i
$137$	17.4842			1.49377			0.746887	−	0.664951i	$-0.231548\pi$
$137$	17.4842			1.49377			0.746887	+	0.664951i	$0.231548\pi$
$138$		−	5.30761i		−	0.451814i
$139$	−4.08422	+	4.08422i	−0.346419	+	0.346419i	−0.858774	−	0.512355i	$-0.828773\pi$
$139$	−4.08422	+	4.08422i	−0.346419	+	0.346419i	0.512355	+	0.858774i	$0.328773\pi$
$140$	6.12598			0.517740
$141$	−4.65126	+	4.65126i	−0.391707	+	0.391707i
$142$	−8.51702	−	8.51702i	−0.714732	−	0.714732i
$143$	−5.16169	−	5.16169i	−0.431642	−	0.431642i
$144$		−	6.79026i		−	0.565855i
$145$		−	3.10145i		−	0.257562i
$146$	−3.66353	−	3.66353i	−0.303196	−	0.303196i
$147$	7.59586	+	7.59586i	0.626496	+	0.626496i
$148$	−2.67943	+	2.67943i	−0.220248	+	0.220248i
$149$	−9.37030			−0.767645			−0.383822	−	0.923407i	$-0.625393\pi$
$149$	−9.37030			−0.767645			−0.383822	+	0.923407i	$0.625393\pi$
$150$	−0.614895	+	0.614895i	−0.0502060	+	0.0502060i
$151$		−	22.0692i		−	1.79596i	−0.440032	−	0.897982i	$-0.645033\pi$
$151$		−	22.0692i		−	1.79596i	0.440032	−	0.897982i	$-0.354967\pi$
$152$	−16.5769			−1.34456
$153$	−9.08891	−	5.14059i	−0.734795	−	0.415592i
$154$	−23.3884			−1.88469
$155$			3.94017i			0.316482i
$156$	0.456892	−	0.456892i	0.0365807	−	0.0365807i
$157$	14.4114			1.15015			0.575076	−	0.818100i	$-0.304972\pi$
$157$	14.4114			1.15015			0.575076	+	0.818100i	$0.304972\pi$
$158$	−1.74809	+	1.74809i	−0.139071	+	0.139071i
$159$	−6.04567	−	6.04567i	−0.479453	−	0.479453i
$160$	−4.99650	−	4.99650i	−0.395008	−	0.395008i
$161$			30.4386i			2.39890i
$162$			6.09093i			0.478548i
$163$	1.63679	+	1.63679i	0.128204	+	0.128204i	0.768297	−	0.640093i	$-0.221104\pi$
$163$	1.63679	+	1.63679i	0.128204	+	0.128204i	−0.640093	+	0.768297i	$0.721104\pi$
$164$	−4.13275	−	4.13275i	−0.322713	−	0.322713i
$165$	−4.80019	+	4.80019i	−0.373694	+	0.373694i
$166$	9.23596			0.716850
$167$	6.60358	−	6.60358i	0.511001	−	0.511001i	−0.403832	−	0.914833i	$-0.632322\pi$
$167$	6.60358	−	6.60358i	0.511001	−	0.511001i	0.914833	+	0.403832i	$0.132322\pi$
$168$		−	9.99073i		−	0.770801i
$169$	−9.73179			−0.748599
$170$	11.8739	−	3.29470i	0.910688	−	0.252692i
$171$	13.6917			1.04703
$172$			0.522759i			0.0398600i
$173$	15.0499	−	15.0499i	1.14423	−	1.14423i	0.156556	−	0.987669i	$-0.449961\pi$
$173$	15.0499	−	15.0499i	1.14423	−	1.14423i	0.987669	−	0.156556i	$-0.0500392\pi$
$174$	−1.04812			−0.0794580
$175$	3.52637	−	3.52637i	0.266568	−	0.266568i
$176$	7.65537	+	7.65537i	0.577045	+	0.577045i
$177$	2.41051	+	2.41051i	0.181185	+	0.181185i
$178$		−	11.1898i		−	0.838712i
$179$			10.5708i			0.790095i	0.918661	+	0.395048i	$0.129272\pi$
$179$			10.5708i			0.790095i	−0.918661	+	0.395048i	$0.870728\pi$
$180$	2.30194	+	2.30194i	0.171576	+	0.171576i
$181$	13.1676	+	13.1676i	0.978739	+	0.978739i	0.999779	−	0.0210397i	$-0.00669764\pi$
$181$	13.1676	+	13.1676i	0.978739	+	0.978739i	−0.0210397	+	0.999779i	$0.506698\pi$
$182$	7.40440	−	7.40440i	0.548850	−	0.548850i
$183$	−5.13390			−0.379508
$184$	13.8480	−	13.8480i	1.02089	−	1.02089i
$185$			17.8240i			1.31045i
$186$	1.33157			0.0976352
$187$	16.0424	−	4.45135i	1.17314	−	0.325515i
$188$	−5.02940			−0.366806
$189$			18.0269i			1.31126i
$190$	−11.4252	+	11.4252i	−0.828869	+	0.828869i
$191$	−3.98704			−0.288492			−0.144246	−	0.989542i	$-0.546076\pi$
$191$	−3.98704			−0.288492			−0.144246	+	0.989542i	$0.546076\pi$
$192$	−4.28104	+	4.28104i	−0.308957	+	0.308957i
$193$	13.8282	+	13.8282i	0.995377	+	0.995377i	0.999989	−	0.00461236i	$-0.00146816\pi$
$193$	13.8282	+	13.8282i	0.995377	+	0.995377i	−0.00461236	+	0.999989i	$0.501468\pi$
$194$	10.5948	+	10.5948i	0.760665	+	0.760665i
$195$		−	3.03933i		−	0.217651i
$196$			8.21338i			0.586670i
$197$	6.61664	+	6.61664i	0.471416	+	0.471416i	0.902373	−	0.430957i	$-0.141824\pi$
$197$	6.61664	+	6.61664i	0.471416	+	0.471416i	−0.430957	+	0.902373i	$0.641824\pi$
$198$	−8.78858	−	8.78858i	−0.624577	−	0.624577i
$199$	−4.50000	+	4.50000i	−0.318996	+	0.318996i	−0.848382	−	0.529385i	$-0.822423\pi$
$199$	−4.50000	+	4.50000i	−0.318996	+	0.318996i	0.529385	+	0.848382i	$0.322423\pi$
$200$	−3.20863			−0.226885
$201$	−1.49651	+	1.49651i	−0.105556	+	0.105556i
$202$		−	0.988476i		−	0.0695489i
$203$	6.01089			0.421882
$204$	0.394016	+	1.42001i	0.0275867	+	0.0994207i
$205$	−27.4917			−1.92011
$206$			0.532859i			0.0371260i
$207$	−11.4378	+	11.4378i	−0.794983	+	0.794983i
$208$	−4.84713			−0.336088
$209$	−15.4361	+	15.4361i	−1.06774	+	1.06774i
$210$	−6.88583	−	6.88583i	−0.475168	−	0.475168i
$211$	19.9826	+	19.9826i	1.37566	+	1.37566i	0.851811	+	0.523849i	$0.175504\pi$
$211$	19.9826	+	19.9826i	1.37566	+	1.37566i	0.523849	+	0.851811i	$0.324496\pi$
$212$		−	6.53716i		−	0.448974i
$213$		−	6.77562i		−	0.464258i
$214$	10.9943	+	10.9943i	0.751554	+	0.751554i
$215$	1.73874	+	1.73874i	0.118581	+	0.118581i
$216$	8.20130	−	8.20130i	0.558028	−	0.558028i
$217$	−7.63641			−0.518393
$218$	4.64015	−	4.64015i	0.314271	−	0.314271i
$219$		−	2.91448i		−	0.196942i
$220$	−5.19043			−0.349939
$221$	−3.66954	+	6.48800i	−0.246840	+	0.436430i
$222$	6.02355			0.404274
$223$		−	8.70574i		−	0.582980i	−0.956574	−	0.291490i	$-0.905849\pi$
$223$		−	8.70574i		−	0.582980i	0.956574	−	0.291490i	$-0.0941509\pi$
$224$	9.68366	−	9.68366i	0.647017	−	0.647017i
$225$	2.65018			0.176679
$226$	−11.6209	+	11.6209i	−0.773014	+	0.773014i
$227$	14.8247	+	14.8247i	0.983948	+	0.983948i	0.999873	−	0.0159255i	$-0.00506946\pi$
$227$	14.8247	+	14.8247i	0.983948	+	0.983948i	−0.0159255	+	0.999873i	$0.505069\pi$
$228$	−1.36634	−	1.36634i	−0.0904884	−	0.0904884i
$229$		−	6.61684i		−	0.437253i	−0.975809	−	0.218627i	$-0.929842\pi$
$229$		−	6.61684i		−	0.437253i	0.975809	−	0.218627i	$-0.0701577\pi$
$230$		−	19.0887i		−	1.25867i
$231$	−9.30320	−	9.30320i	−0.612105	−	0.612105i
$232$	−2.73465	−	2.73465i	−0.179538	−	0.179538i
$233$	20.9045	−	20.9045i	1.36950	−	1.36950i	0.508349	−	0.861151i	$-0.330256\pi$
$233$	20.9045	−	20.9045i	1.36950	−	1.36950i	0.861151	−	0.508349i	$-0.169744\pi$
$234$	5.56464			0.363772
$235$	−16.7282	+	16.7282i	−1.09123	+	1.09123i
$236$			2.60648i			0.169667i
$237$	−1.39068			−0.0903341
$238$	6.38543	+	23.0127i	0.413906	+	1.49169i
$239$	−4.81677			−0.311571			−0.155786	−	0.987791i	$-0.549791\pi$
$239$	−4.81677			−0.311571			−0.155786	+	0.987791i	$0.549791\pi$
$240$			4.50767i			0.290969i
$241$	21.3942	−	21.3942i	1.37812	−	1.37812i	0.530328	−	0.847792i	$-0.322069\pi$
$241$	21.3942	−	21.3942i	1.37812	−	1.37812i	0.847792	−	0.530328i	$-0.177931\pi$
$242$	6.44698			0.414427
$243$	−10.4470	+	10.4470i	−0.670175	+	0.670175i
$244$	−2.77563	−	2.77563i	−0.177692	−	0.177692i
$245$	27.3184	+	27.3184i	1.74531	+	1.74531i
$246$			9.29072i			0.592355i
$247$		−	9.77365i		−	0.621883i
$248$	3.47417	+	3.47417i	0.220610	+	0.220610i
$249$	3.67378	+	3.67378i	0.232816	+	0.232816i
$250$	8.35503	−	8.35503i	0.528419	−	0.528419i
$251$	−19.7330			−1.24553			−0.622767	−	0.782408i	$-0.713991\pi$
$251$	−19.7330			−1.24553			−0.622767	+	0.782408i	$0.713991\pi$
$252$	−4.46136	+	4.46136i	−0.281039	+	0.281039i
$253$		−	25.7901i		−	1.62141i
$254$	10.9390			0.686375
$255$	6.03361	+	3.41255i	0.377839	+	0.213702i
$256$	−11.6144			−0.725900
$257$			11.8508i			0.739230i	0.929185	+	0.369615i	$0.120510\pi$
$257$			11.8508i			0.739230i	−0.929185	+	0.369615i	$0.879490\pi$
$258$	0.587601	−	0.587601i	0.0365824	−	0.0365824i
$259$	−34.5445			−2.14649
$260$	1.64321	−	1.64321i	0.101907	−	0.101907i
$261$	2.25869	+	2.25869i	0.139809	+	0.139809i
$262$	14.6637	+	14.6637i	0.905929	+	0.905929i
$263$			7.38345i			0.455283i	0.973745	+	0.227642i	$0.0731014\pi$
$263$			7.38345i			0.455283i	−0.973745	+	0.227642i	$0.926899\pi$
$264$			8.46496i			0.520982i
$265$	−21.7432	−	21.7432i	−1.33567	−	1.33567i
$266$	−22.1430	−	22.1430i	−1.35767	−	1.35767i
$267$	4.45096	−	4.45096i	0.272394	−	0.272394i
$268$	−1.61818			−0.0988458
$269$	−1.61902	+	1.61902i	−0.0987132	+	0.0987132i	−0.754739	−	0.656026i	$-0.772236\pi$
$269$	−1.61902	+	1.61902i	−0.0987132	+	0.0987132i	0.656026	+	0.754739i	$0.272236\pi$
$270$		−	11.3050i		−	0.688003i
$271$	−6.77323			−0.411445			−0.205722	−	0.978610i	$-0.565954\pi$
$271$	−6.77323			−0.411445			−0.205722	+	0.978610i	$0.565954\pi$
$272$	5.44235	−	9.62244i	0.329991	−	0.583446i
$273$	5.89048			0.356508
$274$		−	21.2506i		−	1.28379i
$275$	−2.98783	+	2.98783i	−0.180173	+	0.180173i
$276$	2.28284			0.137411
$277$	18.2711	−	18.2711i	1.09781	−	1.09781i	0.103139	−	0.994667i	$-0.467112\pi$
$277$	18.2711	−	18.2711i	1.09781	−	1.09781i	0.994667	−	0.103139i	$-0.0328885\pi$
$278$	4.96404	+	4.96404i	0.297723	+	0.297723i
$279$	−2.86950	−	2.86950i	−0.171793	−	0.171793i
$280$		−	35.9315i		−	2.14732i
$281$		−	6.16166i		−	0.367574i	−0.982966	−	0.183787i	$-0.941164\pi$
$281$		−	6.16166i		−	0.367574i	0.982966	−	0.183787i	$-0.0588357\pi$
$282$	5.65323	+	5.65323i	0.336645	+	0.336645i
$283$	−6.32272	−	6.32272i	−0.375847	−	0.375847i	0.493755	−	0.869601i	$-0.335624\pi$
$283$	−6.32272	−	6.32272i	−0.375847	−	0.375847i	−0.869601	+	0.493755i	$0.835624\pi$
$284$	3.66323	−	3.66323i	0.217372	−	0.217372i
$285$	−9.08916			−0.538395
$286$	−6.27361	+	6.27361i	−0.370966	+	0.370966i
$287$		−	53.2814i		−	3.14510i
$288$	7.27759			0.428836
$289$	−8.75969	−	14.5694i	−0.515276	−	0.857024i
$290$	−3.76956			−0.221356
$291$			8.42860i			0.494093i
$292$	1.57571	−	1.57571i	0.0922114	−	0.0922114i
$293$	1.14484			0.0668822			0.0334411	−	0.999441i	$-0.489353\pi$
$293$	1.14484			0.0668822			0.0334411	+	0.999441i	$0.489353\pi$
$294$	9.23215	−	9.23215i	0.538430	−	0.538430i
$295$	8.66936	+	8.66936i	0.504750	+	0.504750i
$296$	15.7160	+	15.7160i	0.913473	+	0.913473i
$297$		−	15.2738i		−	0.886277i
$298$			11.3888i			0.659737i
$299$	8.16473	+	8.16473i	0.472178	+	0.472178i
$300$	−0.264471	−	0.264471i	−0.0152692	−	0.0152692i
$301$	−3.36984	+	3.36984i	−0.194234	+	0.194234i
$302$	−26.8233			−1.54351
$303$	0.393185	−	0.393185i	0.0225879	−	0.0225879i
$304$			14.4954i			0.831371i
$305$	−18.4640			−1.05724
$306$	−6.24797	+	11.0468i	−0.357173	+	0.631505i
$307$	2.49660			0.142489			0.0712443	−	0.997459i	$-0.477303\pi$
$307$	2.49660			0.142489			0.0712443	+	0.997459i	$0.477303\pi$
$308$		−	10.0595i		−	0.573194i
$309$	−0.211955	+	0.211955i	−0.0120577	+	0.0120577i
$310$	4.78896			0.271995
$311$	4.05433	−	4.05433i	0.229900	−	0.229900i	−0.582751	−	0.812651i	$-0.698024\pi$
$311$	4.05433	−	4.05433i	0.229900	−	0.229900i	0.812651	+	0.582751i	$0.198024\pi$
$312$	−2.67987	−	2.67987i	−0.151718	−	0.151718i
$313$	−9.94190	−	9.94190i	−0.561950	−	0.561950i	0.367911	−	0.929861i	$-0.380073\pi$
$313$	−9.94190	−	9.94190i	−0.561950	−	0.561950i	−0.929861	+	0.367911i	$0.880073\pi$
$314$		−	17.5158i		−	0.988476i
$315$			29.6777i			1.67215i
$316$	−0.751867	−	0.751867i	−0.0422958	−	0.0422958i
$317$	−14.2981	−	14.2981i	−0.803063	−	0.803063i	0.180510	−	0.983573i	$-0.442225\pi$
$317$	−14.2981	−	14.2981i	−0.803063	−	0.803063i	−0.983573	+	0.180510i	$0.942225\pi$
$318$	−7.34801	+	7.34801i	−0.412056	+	0.412056i
$319$	−5.09291			−0.285148
$320$	−15.3967	+	15.3967i	−0.860701	+	0.860701i
$321$			8.74638i			0.488176i
$322$	36.9957			2.06169
$323$	19.4025	+	10.9738i	1.07958	+	0.610601i
$324$	−2.61975			−0.145542
$325$		−	1.89179i		−	0.104938i
$326$	1.98939	−	1.98939i	0.110182	−	0.110182i
$327$	3.69142			0.204136
$328$	−24.2403	+	24.2403i	−1.33845	+	1.33845i
$329$	−32.4207	−	32.4207i	−1.78741	−	1.78741i
$330$	5.83424	+	5.83424i	0.321164	+	0.321164i
$331$			16.2295i			0.892056i	0.895019	+	0.446028i	$0.147162\pi$
$331$			16.2295i			0.892056i	−0.895019	+	0.446028i	$0.852838\pi$
$332$			3.97245i			0.218016i
$333$	−12.9807	−	12.9807i	−0.711335	−	0.711335i
$334$	−8.02611	−	8.02611i	−0.439169	−	0.439169i
$335$	−5.38219	+	5.38219i	−0.294061	+	0.294061i
$336$	−8.73626			−0.476602
$337$	−7.87796	+	7.87796i	−0.429140	+	0.429140i	−0.888335	−	0.459195i	$-0.848138\pi$
$337$	−7.87796	+	7.87796i	−0.429140	+	0.429140i	0.459195	+	0.888335i	$0.348138\pi$
$338$			11.8282i			0.643369i
$339$	−9.24491			−0.502115
$340$	1.41707	+	5.10705i	0.0768516	+	0.276969i
$341$	6.47019			0.350380
$342$		−	16.6412i		−	0.899851i
$343$	−29.3567	+	29.3567i	−1.58511	+	1.58511i
$344$	3.06621			0.165319
$345$	7.59292	−	7.59292i	0.408789	−	0.408789i
$346$	−18.2920	−	18.2920i	−0.983382	−	0.983382i
$347$	6.30019	+	6.30019i	0.338212	+	0.338212i	0.855694	−	0.517482i	$-0.173131\pi$
$347$	6.30019	+	6.30019i	0.338212	+	0.338212i	−0.517482	+	0.855694i	$0.673131\pi$
$348$		−	0.450805i		−	0.0241657i
$349$			0.778233i			0.0416578i	0.999783	+	0.0208289i	$0.00663053\pi$
$349$			0.778233i			0.0416578i	−0.999783	+	0.0208289i	$0.993369\pi$
$350$	−4.28601	−	4.28601i	−0.229097	−	0.229097i
$351$	4.83545	+	4.83545i	0.258097	+	0.258097i
$352$	−8.20479	+	8.20479i	−0.437317	+	0.437317i
$353$	−35.1052			−1.86846			−0.934232	−	0.356666i	$-0.883913\pi$
$353$	−35.1052			−1.86846			−0.934232	+	0.356666i	$0.883913\pi$
$354$	2.92978	−	2.92978i	0.155716	−	0.155716i
$355$		−	24.3684i		−	1.29334i
$356$	4.81281			0.255079
$357$	−6.61382	+	11.6937i	−0.350041	+	0.618895i
$358$	12.8479			0.679032
$359$			35.7138i			1.88490i	0.334343	+	0.942451i	$0.391486\pi$
$359$			35.7138i			1.88490i	−0.334343	+	0.942451i	$0.608514\pi$
$360$	13.5018	−	13.5018i	0.711610	−	0.711610i
$361$	−10.2283			−0.538331
$362$	16.0041	−	16.0041i	0.841158	−	0.841158i
$363$	2.56441	+	2.56441i	0.134597	+	0.134597i
$364$	3.18468	+	3.18468i	0.166923	+	0.166923i
$365$		−	10.4819i		−	0.548647i
$366$			6.23983i			0.326161i
$367$	−1.42804	−	1.42804i	−0.0745431	−	0.0745431i	0.668852	−	0.743395i	$-0.266786\pi$
$367$	−1.42804	−	1.42804i	−0.0745431	−	0.0745431i	−0.743395	+	0.668852i	$0.766786\pi$
$368$	−12.1092	−	12.1092i	−0.631237	−	0.631237i
$369$	20.0214	−	20.0214i	1.04227	−	1.04227i
$370$	21.6636			1.12624
$371$	42.1402	−	42.1402i	2.18781	−	2.18781i
$372$			0.572715i			0.0296939i
$373$	1.37509			0.0711997			0.0355998	−	0.999366i	$-0.488666\pi$
$373$	1.37509			0.0711997			0.0355998	+	0.999366i	$0.488666\pi$
$374$	−5.41025	−	19.4982i	−0.279758	−	1.00823i
$375$	6.64675			0.343237
$376$			29.4996i			1.52132i
$377$	1.61233	−	1.61233i	0.0830394	−	0.0830394i
$378$	21.9102			1.12694
$379$	12.3540	−	12.3540i	0.634584	−	0.634584i	−0.314631	−	0.949214i	$-0.601881\pi$
$379$	12.3540	−	12.3540i	0.634584	−	0.634584i	0.949214	+	0.314631i	$0.101881\pi$
$380$	−4.91404	−	4.91404i	−0.252085	−	0.252085i
$381$	4.35120	+	4.35120i	0.222919	+	0.222919i
$382$			4.84592i			0.247939i
$383$		−	1.33735i		−	0.0683353i	−0.999416	−	0.0341677i	$-0.989122\pi$
$383$		−	1.33735i		−	0.0683353i	0.999416	−	0.0341677i	$-0.0108780\pi$
$384$	2.42470	+	2.42470i	0.123735	+	0.123735i
$385$	−33.4588	−	33.4588i	−1.70522	−	1.70522i
$386$	16.8071	−	16.8071i	0.855457	−	0.855457i
$387$	−2.53254			−0.128736
$388$	−4.55691	+	4.55691i	−0.231342	+	0.231342i
$389$		−	13.3499i		−	0.676865i	−0.940991	−	0.338433i	$-0.890103\pi$
$389$		−	13.3499i		−	0.676865i	0.940991	−	0.338433i	$-0.109897\pi$
$390$	−3.69405			−0.187056
$391$	−25.3758	+	7.04112i	−1.28331	+	0.356085i
$392$	48.1750			2.43321
$393$			11.6656i			0.588450i
$394$	8.04198	−	8.04198i	0.405149	−	0.405149i
$395$	−5.00155			−0.251655
$396$	3.78003	−	3.78003i	0.189953	−	0.189953i
$397$	1.11820	+	1.11820i	0.0561209	+	0.0561209i	0.734610	−	0.678489i	$-0.237365\pi$
$397$	1.11820	+	1.11820i	0.0561209	+	0.0561209i	−0.678489	+	0.734610i	$0.737365\pi$
$398$	5.46938	+	5.46938i	0.274155	+	0.274155i
$399$		−	17.6156i		−	0.881883i
$400$			2.80575i			0.140287i
$401$	−6.14818	−	6.14818i	−0.307025	−	0.307025i	0.536729	−	0.843755i	$-0.319660\pi$
$401$	−6.14818	−	6.14818i	−0.307025	−	0.307025i	−0.843755	+	0.536729i	$0.819660\pi$
$402$	1.81889	+	1.81889i	0.0907180	+	0.0907180i
$403$	−2.04836	+	2.04836i	−0.102036	+	0.102036i
$404$	0.425150			0.0211520
$405$	−8.71351	+	8.71351i	−0.432978	+	0.432978i
$406$		−	7.30574i		−	0.362578i
$407$	29.2689			1.45081
$408$	8.32897	−	2.31107i	0.412346	−	0.114415i
$409$	−27.7180			−1.37057			−0.685285	−	0.728275i	$-0.740322\pi$
$409$	−27.7180			−1.37057			−0.685285	+	0.728275i	$0.740322\pi$
$410$			33.4139i			1.65020i
$411$	8.45282	−	8.45282i	0.416947	−	0.416947i
$412$	−0.229186			−0.0112912
$413$	−16.8020	+	16.8020i	−0.826772	+	0.826772i
$414$	13.9017	+	13.9017i	0.683232	+	0.683232i
$415$	13.2127	+	13.2127i	0.648586	+	0.648586i
$416$		−	5.19501i		−	0.254706i
$417$			3.94908i			0.193387i
$418$	18.7613	+	18.7613i	0.917647	+	0.917647i
$419$	12.1163	+	12.1163i	0.591918	+	0.591918i	0.938149	−	0.346231i	$-0.112539\pi$
$419$	12.1163	+	12.1163i	0.591918	+	0.591918i	−0.346231	+	0.938149i	$0.612539\pi$
$420$	2.96164	−	2.96164i	0.144513	−	0.144513i
$421$	1.21007			0.0589751			0.0294876	−	0.999565i	$-0.490612\pi$
$421$	1.21007			0.0589751			0.0294876	+	0.999565i	$0.490612\pi$
$422$	24.2872	−	24.2872i	1.18228	−	1.18228i
$423$		−	24.3652i		−	1.18468i
$424$	−38.3433			−1.86211
$425$	3.75555	+	2.12410i	0.182171	+	0.103034i
$426$	−8.23520			−0.398997
$427$		−	35.7848i		−	1.73175i
$428$	−4.72872	+	4.72872i	−0.228571	+	0.228571i
$429$	−4.99090			−0.240963
$430$	2.11330	−	2.11330i	0.101912	−	0.101912i
$431$	19.0030	+	19.0030i	0.915340	+	0.915340i	0.996686	−	0.0813457i	$-0.0259218\pi$
$431$	19.0030	+	19.0030i	0.915340	+	0.915340i	−0.0813457	+	0.996686i	$0.525922\pi$
$432$	−7.17152	−	7.17152i	−0.345040	−	0.345040i
$433$		−	18.6170i		−	0.894675i	−0.894365	−	0.447338i	$-0.852372\pi$
$433$		−	18.6170i		−	0.894675i	0.894365	−	0.447338i	$-0.147628\pi$
$434$			9.28143i			0.445523i
$435$	−1.49941	−	1.49941i	−0.0718914	−	0.0718914i
$436$	1.99576	+	1.99576i	0.0955795	+	0.0955795i
$437$	24.4168	−	24.4168i	1.16801	−	1.16801i
$438$	−3.54231			−0.169258
$439$	8.33712	−	8.33712i	0.397909	−	0.397909i	−0.479586	−	0.877495i	$-0.659213\pi$
$439$	8.33712	−	8.33712i	0.397909	−	0.397909i	0.877495	+	0.479586i	$0.159213\pi$
$440$			30.4441i			1.45137i
$441$	−39.7903			−1.89477
$442$	7.88563	+	4.46003i	0.375081	+	0.212142i
$443$	−24.5635			−1.16705			−0.583524	−	0.812096i	$-0.698327\pi$
$443$	−24.5635			−1.16705			−0.583524	+	0.812096i	$0.698327\pi$
$444$			2.59077i			0.122952i
$445$	16.0078	−	16.0078i	0.758844	−	0.758844i
$446$	−10.5811			−0.501030
$447$	−4.53013	+	4.53013i	−0.214268	+	0.214268i
$448$	−29.8401	−	29.8401i	−1.40981	−	1.40981i
$449$	3.11493	+	3.11493i	0.147003	+	0.147003i	0.776778	−	0.629775i	$-0.216853\pi$
$449$	3.11493	+	3.11493i	0.147003	+	0.147003i	−0.629775	+	0.776778i	$0.716853\pi$
$450$		−	3.22108i		−	0.151843i
$451$			45.1444i			2.12576i
$452$	−4.99825	−	4.99825i	−0.235098	−	0.235098i
$453$	−10.6695	−	10.6695i	−0.501296	−	0.501296i
$454$	18.0182	−	18.0182i	0.845634	−	0.845634i
$455$	21.1850			0.993170
$456$	−8.01420	+	8.01420i	−0.375299	+	0.375299i
$457$		−	20.1409i		−	0.942153i	−0.882092	−	0.471076i	$-0.843866\pi$
$457$		−	20.1409i		−	0.942153i	0.882092	−	0.471076i	$-0.156134\pi$
$458$	−8.04223			−0.375789
$459$	−15.0285	+	4.17001i	−0.701469	+	0.194639i
$460$	8.21020			0.382802
$461$		−	25.1970i		−	1.17354i	−0.809753	−	0.586771i	$-0.800399\pi$
$461$		−	25.1970i		−	1.17354i	0.809753	−	0.586771i	$-0.199601\pi$
$462$	−11.3073	+	11.3073i	−0.526062	+	0.526062i
$463$	−18.9118			−0.878905			−0.439452	−	0.898266i	$-0.644827\pi$
$463$	−18.9118			−0.878905			−0.439452	+	0.898266i	$0.644827\pi$
$464$	−2.39128	+	2.39128i	−0.111012	+	0.111012i
$465$	1.90490	+	1.90490i	0.0883377	+	0.0883377i
$466$	−25.4077	−	25.4077i	−1.17699	−	1.17699i
$467$			3.24354i			0.150093i	0.997180	+	0.0750466i	$0.0239105\pi$
$467$			3.24354i			0.150093i	−0.997180	+	0.0750466i	$0.976089\pi$
$468$			2.39339i			0.110635i
$469$	−10.4312	−	10.4312i	−0.481666	−	0.481666i
$470$	20.3318	+	20.3318i	0.937834	+	0.937834i
$471$	6.96726	−	6.96726i	0.321034	−	0.321034i
$472$	15.2881			0.703692
$473$	2.85520	−	2.85520i	0.131282	−	0.131282i
$474$			1.69025i			0.0776359i
$475$	−5.65745			−0.259581
$476$	−9.89792	+	2.74641i	−0.453670	+	0.125882i
$477$	31.6697			1.45006
$478$			5.85439i			0.267774i
$479$	12.5145	−	12.5145i	0.571800	−	0.571800i	−0.360831	−	0.932631i	$-0.617507\pi$
$479$	12.5145	−	12.5145i	0.571800	−	0.571800i	0.932631	+	0.360831i	$0.117507\pi$
$480$	−4.83118			−0.220512
$481$	−9.26607	+	9.26607i	−0.422496	+	0.422496i
$482$	−26.0029	−	26.0029i	−1.18440	−	1.18440i
$483$	14.7157	+	14.7157i	0.669589	+	0.669589i
$484$			2.77289i			0.126040i
$485$			30.3133i			1.37646i
$486$	12.6975	+	12.6975i	0.575969	+	0.575969i
$487$	7.31263	+	7.31263i	0.331367	+	0.331367i	0.853105	−	0.521739i	$-0.174716\pi$
$487$	7.31263	+	7.31263i	0.331367	+	0.331367i	−0.521739	+	0.853105i	$0.674716\pi$
$488$	−16.2803	+	16.2803i	−0.736973	+	0.736973i
$489$	1.58264			0.0715693
$490$	33.2033	−	33.2033i	1.49997	−	1.49997i
$491$		−	9.52477i		−	0.429847i	−0.976631	−	0.214923i	$-0.931050\pi$
$491$		−	9.52477i		−	0.429847i	0.976631	−	0.214923i	$-0.0689502\pi$
$492$	−3.99600			−0.180154
$493$	1.39045	+	5.01110i	0.0626227	+	0.225689i
$494$	−11.8791			−0.534465
$495$		−	25.1454i		−	1.13020i
$496$	3.03795	−	3.03795i	0.136408	−	0.136408i
$497$	47.2281			2.11847
$498$	4.46518	−	4.46518i	0.200089	−	0.200089i
$499$	3.81699	+	3.81699i	0.170872	+	0.170872i	0.787362	−	0.616491i	$-0.211446\pi$
$499$	3.81699	+	3.81699i	0.170872	+	0.170872i	−0.616491	+	0.787362i	$0.711446\pi$
$500$	3.59355	+	3.59355i	0.160709	+	0.160709i
$501$		−	6.38508i		−	0.285264i
$502$			23.9838i			1.07045i
$503$	11.6717	+	11.6717i	0.520413	+	0.520413i	0.917696	−	0.397283i	$-0.130047\pi$
$503$	11.6717	+	11.6717i	0.520413	+	0.520413i	−0.397283	+	0.917696i	$0.630047\pi$
$504$	26.1678	+	26.1678i	1.16561	+	1.16561i
$505$	1.41409	−	1.41409i	0.0629260	−	0.0629260i
$506$	−31.3457			−1.39349
$507$	−4.70489	+	4.70489i	−0.208951	+	0.208951i
$508$			4.70494i			0.208748i
$509$	−12.6334			−0.559965			−0.279982	−	0.960005i	$-0.590329\pi$
$509$	−12.6334			−0.559965			−0.279982	+	0.960005i	$0.590329\pi$
$510$	4.14767	−	7.33336i	0.183662	−	0.324727i
$511$	20.3148			0.898675
$512$			24.1470i			1.06716i
$513$	14.4605	−	14.4605i	0.638446	−	0.638446i
$514$	14.4036			0.635317
$515$	−0.762293	+	0.762293i	−0.0335906	+	0.0335906i
$516$	0.252731	+	0.252731i	0.0111259	+	0.0111259i
$517$	27.4695	+	27.4695i	1.20811	+	1.20811i
$518$			41.9860i			1.84476i
$519$		−	14.5520i		−	0.638760i
$520$	−9.63811	−	9.63811i	−0.422659	−	0.422659i
$521$	−21.7805	−	21.7805i	−0.954219	−	0.954219i	0.0447780	−	0.998997i	$-0.485742\pi$
$521$	−21.7805	−	21.7805i	−0.954219	−	0.954219i	−0.998997	+	0.0447780i	$0.985742\pi$
$522$	2.74525	−	2.74525i	0.120156	−	0.120156i
$523$	−18.2715			−0.798957			−0.399478	−	0.916743i	$-0.630809\pi$
$523$	−18.2715			−0.798957			−0.399478	+	0.916743i	$0.630809\pi$
$524$	−6.30697	+	6.30697i	−0.275521	+	0.275521i
$525$		−	3.40969i		−	0.148811i
$526$	8.97398			0.391284
$527$	−1.76647	−	6.36625i	−0.0769485	−	0.277318i
$528$	7.40207			0.322134
$529$			17.7946i			0.773679i
$530$	−26.4270	+	26.4270i	−1.14792	+	1.14792i
$531$	−12.6272			−0.547976
$532$	9.52384	−	9.52384i	0.412911	−	0.412911i
$533$	−14.2920	−	14.2920i	−0.619054	−	0.619054i
$534$	−5.40978	−	5.40978i	−0.234104	−	0.234104i
$535$			31.4563i			1.35997i
$536$			9.49129i			0.409961i
$537$	5.11049	+	5.11049i	0.220534	+	0.220534i
$538$	1.96778	+	1.96778i	0.0848371	+	0.0848371i
$539$	44.8597	−	44.8597i	1.93225	−	1.93225i
$540$	4.86238			0.209243
$541$	2.82297	−	2.82297i	0.121369	−	0.121369i	−0.643813	−	0.765183i	$-0.722649\pi$
$541$	2.82297	−	2.82297i	0.121369	−	0.121369i	0.765183	+	0.643813i	$0.222649\pi$
$542$			8.23231i			0.353608i
$543$	12.7319			0.546378
$544$	10.3130	+	5.83294i	0.442167	+	0.250085i
$545$	13.2761			0.568687
$546$		−	7.15940i		−	0.306394i
$547$	6.70862	−	6.70862i	0.286840	−	0.286840i	−0.548989	−	0.835829i	$-0.684987\pi$
$547$	6.70862	−	6.70862i	0.286840	−	0.286840i	0.835829	+	0.548989i	$0.184987\pi$
$548$	9.14001			0.390442
$549$	13.4467	−	13.4467i	0.573892	−	0.573892i
$550$	3.63146	+	3.63146i	0.154846	+	0.154846i
$551$	−4.82171	−	4.82171i	−0.205412	−	0.205412i
$552$		−	13.3898i		−	0.569909i
$553$		−	9.69344i		−	0.412207i
$554$	−22.2071	−	22.2071i	−0.943487	−	0.943487i
$555$	8.61712	+	8.61712i	0.365776	+	0.365776i
$556$	−2.13506	+	2.13506i	−0.0905469	+	0.0905469i
$557$	−12.8775			−0.545639			−0.272820	−	0.962065i	$-0.587956\pi$
$557$	−12.8775			−0.545639			−0.272820	+	0.962065i	$0.587956\pi$
$558$	−3.48765	+	3.48765i	−0.147644	+	0.147644i
$559$			1.80782i			0.0764627i
$560$	−31.4198			−1.32773
$561$	5.60377	−	9.90783i	0.236591	−	0.418309i
$562$	−7.48900			−0.315904
$563$		−	28.5671i		−	1.20396i	−0.798512	−	0.601979i	$-0.794379\pi$
$563$		−	28.5671i		−	1.20396i	0.798512	−	0.601979i	$-0.205621\pi$
$564$	−2.43149	+	2.43149i	−0.102384	+	0.102384i
$565$	−33.2492			−1.39880
$566$	−7.68475	+	7.68475i	−0.323014	+	0.323014i
$567$	−16.8876	−	16.8876i	−0.709210	−	0.709210i
$568$	−21.4864	−	21.4864i	−0.901549	−	0.901549i
$569$			25.4605i			1.06736i	0.845686	+	0.533680i	$0.179191\pi$
$569$			25.4605i			1.06736i	−0.845686	+	0.533680i	$0.820809\pi$
$570$			11.0471i			0.462713i
$571$	2.16827	+	2.16827i	0.0907392	+	0.0907392i	0.751019	−	0.660280i	$-0.229562\pi$
$571$	2.16827	+	2.16827i	0.0907392	+	0.0907392i	−0.660280	+	0.751019i	$0.729562\pi$
$572$	−2.69832	−	2.69832i	−0.112822	−	0.112822i
$573$	−1.92756	+	1.92756i	−0.0805249	+	0.0805249i
$574$	−64.7592			−2.70300
$575$	4.72613	−	4.72613i	0.197093	−	0.197093i
$576$		−	22.4258i		−	0.934409i
$577$	36.0826			1.50214			0.751070	−	0.660223i	$-0.229538\pi$
$577$	36.0826			1.50214			0.751070	+	0.660223i	$0.229538\pi$
$578$	−17.7079	+	10.6467i	−0.736553	+	0.442844i
$579$	13.3707			0.555666
$580$		−	1.62131i		−	0.0673213i
$581$	−25.6074	+	25.6074i	−1.06237	+	1.06237i
$582$	10.2443			0.424639
$583$	−35.7046	+	35.7046i	−1.47873	+	1.47873i
$584$	−9.24221	−	9.24221i	−0.382445	−	0.382445i
$585$	7.96062	+	7.96062i	0.329131	+	0.329131i
$586$		−	1.39146i		−	0.0574806i
$587$		−	2.78509i		−	0.114953i	−0.998347	−	0.0574765i	$-0.981695\pi$
$587$		−	2.78509i		−	0.114953i	0.998347	−	0.0574765i	$-0.0183054\pi$
$588$	3.97081	+	3.97081i	0.163753	+	0.163753i
$589$	6.12565	+	6.12565i	0.252403	+	0.252403i
$590$	10.5369	−	10.5369i	0.433797	−	0.433797i
$591$	6.39771			0.263166
$592$	13.7426	−	13.7426i	0.564819	−	0.564819i
$593$			39.7577i			1.63265i	0.577590	+	0.816327i	$0.303993\pi$
$593$			39.7577i			1.63265i	−0.577590	+	0.816327i	$0.696007\pi$
$594$	−18.5641			−0.761694
$595$	−23.7865	+	42.0561i	−0.975152	+	1.72413i
$596$	−4.89841			−0.200647
$597$			4.35110i			0.178079i
$598$	9.92356	−	9.92356i	0.405804	−	0.405804i
$599$	10.9563			0.447661			0.223831	−	0.974628i	$-0.428144\pi$
$599$	10.9563			0.447661			0.223831	+	0.974628i	$0.428144\pi$
$600$	−1.55123	+	1.55123i	−0.0633288	+	0.0633288i
$601$	−15.6538	−	15.6538i	−0.638531	−	0.638531i	0.311662	−	0.950193i	$-0.399114\pi$
$601$	−15.6538	−	15.6538i	−0.638531	−	0.638531i	−0.950193	+	0.311662i	$0.899114\pi$
$602$	4.09576	+	4.09576i	0.166931	+	0.166931i
$603$		−	7.83936i		−	0.319243i
$604$		−	11.5369i		−	0.469428i
$605$	9.22286	+	9.22286i	0.374963	+	0.374963i
$606$	−0.477884	−	0.477884i	−0.0194127	−	0.0194127i
$607$	−10.7895	+	10.7895i	−0.437930	+	0.437930i	−0.891315	−	0.453385i	$-0.850216\pi$
$607$	−10.7895	+	10.7895i	−0.437930	+	0.437930i	0.453385	+	0.891315i	$0.350216\pi$
$608$	−15.5358			−0.630058
$609$	2.90600	−	2.90600i	0.117757	−	0.117757i
$610$			22.4415i			0.908628i
$611$	−17.3928			−0.703637
$612$	−4.75131	−	2.68729i	−0.192060	−	0.108627i
$613$	20.6711			0.834898			0.417449	−	0.908700i	$-0.362924\pi$
$613$	20.6711			0.834898			0.417449	+	0.908700i	$0.362924\pi$
$614$		−	3.03441i		−	0.122459i
$615$	−13.2910	+	13.2910i	−0.535947	+	0.535947i
$616$	−59.0034			−2.37731
$617$	27.1168	−	27.1168i	1.09168	−	1.09168i	0.0963324	−	0.995349i	$-0.469289\pi$
$617$	27.1168	−	27.1168i	1.09168	−	1.09168i	0.995349	−	0.0963324i	$-0.0307112\pi$
$618$	0.257614	+	0.257614i	0.0103627	+	0.0103627i
$619$	19.7823	+	19.7823i	0.795119	+	0.795119i	0.982321	−	0.187202i	$-0.0599420\pi$
$619$	19.7823	+	19.7823i	0.795119	+	0.795119i	−0.187202	+	0.982321i	$0.559942\pi$
$620$			2.05976i			0.0827221i
$621$			24.1601i			0.969510i
$622$	−4.92770	−	4.92770i	−0.197583	−	0.197583i
$623$	31.0246	+	31.0246i	1.24297	+	1.24297i
$624$	−2.34338	+	2.34338i	−0.0938101	+	0.0938101i
$625$	29.1372			1.16549
$626$	−12.0836	+	12.0836i	−0.482957	+	0.482957i
$627$			14.9254i			0.596062i
$628$	7.53368			0.300626
$629$	−7.99090	−	28.7987i	−0.318618	−	1.14828i
$630$	36.0708			1.43710
$631$			10.7340i			0.427312i	0.976909	+	0.213656i	$0.0685372\pi$
$631$			10.7340i			0.427312i	−0.976909	+	0.213656i	$0.931463\pi$
$632$	−4.41002	+	4.41002i	−0.175421	+	0.175421i
$633$	19.3214			0.767958
$634$	−17.3782	+	17.3782i	−0.690177	+	0.690177i
$635$	15.6490	+	15.6490i	0.621014	+	0.621014i
$636$	−3.16043	−	3.16043i	−0.125319	−	0.125319i
$637$			28.4037i			1.12540i
$638$			6.19002i			0.245065i
$639$	17.7467	+	17.7467i	0.702050	+	0.702050i
$640$	8.72040	+	8.72040i	0.344704	+	0.344704i
$641$	−15.9156	+	15.9156i	−0.628627	+	0.628627i	−0.947722	−	0.319096i	$-0.896621\pi$
$641$	−15.9156	+	15.9156i	−0.628627	+	0.628627i	0.319096	+	0.947722i	$0.396621\pi$
$642$	10.6305			0.419553
$643$	20.1288	−	20.1288i	0.793804	−	0.793804i	−0.188307	−	0.982110i	$-0.560300\pi$
$643$	20.1288	−	20.1288i	0.793804	−	0.793804i	0.982110	+	0.188307i	$0.0602999\pi$
$644$			15.9121i			0.627024i
$645$	1.68121			0.0661976
$646$	13.3378	−	23.5821i	0.524769	−	0.927826i
$647$	−47.7353			−1.87667			−0.938334	−	0.345731i	$-0.887631\pi$
$647$	−47.7353			−1.87667			−0.938334	+	0.345731i	$0.887631\pi$
$648$			15.3659i			0.603631i
$649$	14.2360	−	14.2360i	0.558812	−	0.558812i
$650$	−2.29932			−0.0901868
$651$	−3.69187	+	3.69187i	−0.144696	+	0.144696i
$652$	0.855650	+	0.855650i	0.0335098	+	0.0335098i
$653$	−26.5238	−	26.5238i	−1.03796	−	1.03796i	−0.999251	−	0.0387066i	$-0.987676\pi$
$653$	−26.5238	−	26.5238i	−1.03796	−	1.03796i	−0.0387066	−	0.999251i	$-0.512324\pi$
$654$		−	4.48661i		−	0.175441i
$655$			41.9551i			1.63932i
$656$	21.1966	+	21.1966i	0.827589	+	0.827589i
$657$	7.63363	+	7.63363i	0.297816	+	0.297816i
$658$	−39.4047	+	39.4047i	−1.53616	+	1.53616i
$659$	14.4560			0.563128			0.281564	−	0.959542i	$-0.409147\pi$
$659$	14.4560			0.563128			0.281564	+	0.959542i	$0.409147\pi$
$660$	−2.50935	+	2.50935i	−0.0976761	+	0.0976761i
$661$		−	4.14391i		−	0.161180i	−0.996747	−	0.0805898i	$-0.974320\pi$
$661$		−	4.14391i		−	0.161180i	0.996747	−	0.0805898i	$-0.0256804\pi$
$662$	19.7257			0.766660
$663$	1.36260	+	4.91072i	0.0529189	+	0.190717i
$664$	23.3001			0.904220
$665$		−	63.3542i		−	2.45677i
$666$	−15.7769	+	15.7769i	−0.611343	+	0.611343i
$667$	8.05594			0.311927
$668$	3.45208	−	3.45208i	0.133565	−	0.133565i
$669$	−4.20884	−	4.20884i	−0.162723	−	0.162723i
$670$	6.54161	+	6.54161i	0.252725	+	0.252725i
$671$			30.3198i			1.17048i
$672$		−	9.36325i		−	0.361195i
$673$	6.16566	+	6.16566i	0.237669	+	0.237669i	0.815884	−	0.578215i	$-0.196251\pi$
$673$	6.16566	+	6.16566i	0.237669	+	0.237669i	−0.578215	+	0.815884i	$0.696251\pi$
$674$	9.57501	+	9.57501i	0.368816	+	0.368816i
$675$	2.79898	−	2.79898i	0.107733	−	0.107733i
$676$	−5.08738			−0.195669
$677$	−18.5058	+	18.5058i	−0.711234	+	0.711234i	−0.966793	−	0.255560i	$-0.917740\pi$
$677$	−18.5058	+	18.5058i	−0.711234	+	0.711234i	0.255560	+	0.966793i	$0.417740\pi$
$678$			11.2364i			0.431532i
$679$	−58.7499			−2.25462
$680$	29.9550	−	8.31174i	1.14872	−	0.318741i
$681$	14.3341			0.549286
$682$		−	7.86398i		−	0.301127i
$683$	27.8278	−	27.8278i	1.06480	−	1.06480i	0.0670502	−	0.997750i	$-0.478641\pi$
$683$	27.8278	−	27.8278i	1.06480	−	1.06480i	0.997750	−	0.0670502i	$-0.0213588\pi$
$684$	7.15748			0.273673
$685$	30.4005	−	30.4005i	1.16154	−	1.16154i
$686$	35.6806	+	35.6806i	1.36229	+	1.36229i
$687$	−3.19895	−	3.19895i	−0.122048	−	0.122048i
$688$		−	2.68120i		−	0.102220i
$689$		−	22.6070i		−	0.861258i
$690$	−9.22857	−	9.22857i	−0.351325	−	0.351325i
$691$	−23.1141	−	23.1141i	−0.879303	−	0.879303i	0.114160	−	0.993462i	$-0.463582\pi$
$691$	−23.1141	−	23.1141i	−0.879303	−	0.879303i	−0.993462	+	0.114160i	$0.963582\pi$
$692$	7.86749	−	7.86749i	0.299077	−	0.299077i
$693$	48.7340			1.85125
$694$	7.65736	−	7.65736i	0.290670	−	0.290670i
$695$			14.2028i			0.538744i
$696$	−2.64416			−0.100227
$697$	44.4191	−	12.3252i	1.68250	−	0.466849i
$698$	0.945878			0.0358020
$699$		−	20.2128i		−	0.764519i
$700$	1.84344	−	1.84344i	0.0696755	−	0.0696755i
$701$	10.7998			0.407904			0.203952	−	0.978981i	$-0.434621\pi$
$701$	10.7998			0.407904			0.203952	+	0.978981i	$0.434621\pi$
$702$	5.87709	−	5.87709i	0.221816	−	0.221816i
$703$	27.7103	+	27.7103i	1.04512	+	1.04512i
$704$	25.2830	+	25.2830i	0.952889	+	0.952889i
$705$			16.1747i			0.609174i
$706$			42.6675i			1.60581i
$707$	2.74062	+	2.74062i	0.103072	+	0.103072i
$708$	1.26012	+	1.26012i	0.0473581	+	0.0473581i
$709$	−6.88714	+	6.88714i	−0.258652	+	0.258652i	−0.824506	−	0.565854i	$-0.808547\pi$
$709$	−6.88714	+	6.88714i	−0.258652	+	0.258652i	0.565854	+	0.824506i	$0.308547\pi$
$710$	−29.6178			−1.11154
$711$	3.64247	−	3.64247i	0.136603	−	0.136603i
$712$		−	28.2292i		−	1.05793i
$713$	−10.2345			−0.383285
$714$	14.2127	+	8.03856i	0.531897	+	0.300835i
$715$	−17.9497			−0.671280
$716$			5.52596i			0.206515i
$717$	−2.32870	+	2.32870i	−0.0869668	+	0.0869668i
$718$	43.4072			1.61994
$719$	−21.9954	+	21.9954i	−0.820291	+	0.820291i	−0.986150	−	0.165858i	$-0.946961\pi$
$719$	−21.9954	+	21.9954i	−0.820291	+	0.820291i	0.165858	+	0.986150i	$0.446961\pi$
$720$	−11.8065	−	11.8065i	−0.440003	−	0.440003i
$721$	−1.47739	−	1.47739i	−0.0550209	−	0.0550209i
$722$			12.4316i			0.462658i
$723$		−	20.6863i		−	0.769331i
$724$	6.88348	+	6.88348i	0.255822	+	0.255822i
$725$	−0.933294	−	0.933294i	−0.0346617	−	0.0346617i
$726$	3.11683	−	3.11683i	0.115676	−	0.115676i
$727$	−9.01645			−0.334402			−0.167201	−	0.985923i	$-0.553473\pi$
$727$	−9.01645			−0.334402			−0.167201	+	0.985923i	$0.553473\pi$
$728$	18.6795	−	18.6795i	0.692309	−	0.692309i
$729$		−	4.93283i		−	0.182697i
$730$	−12.7399			−0.471524
$731$	−3.58885	−	2.02982i	−0.132738	−	0.0750755i
$732$	−2.68379			−0.0991958
$733$			7.87371i			0.290822i	0.989371	+	0.145411i	$0.0464505\pi$
$733$			7.87371i			0.290822i	−0.989371	+	0.145411i	$0.953550\pi$
$734$	−1.73567	+	1.73567i	−0.0640646	+	0.0640646i
$735$	26.4145			0.974313
$736$	12.9783	−	12.9783i	0.478386	−	0.478386i
$737$	8.83813	+	8.83813i	0.325557	+	0.325557i
$738$	−24.3343	−	24.3343i	−0.895758	−	0.895758i
$739$		−	40.6451i		−	1.49515i	−0.664176	−	0.747577i	$-0.731217\pi$
$739$		−	40.6451i		−	1.49515i	0.664176	−	0.747577i	$-0.268783\pi$
$740$			9.31767i			0.342524i
$741$	−4.72513	−	4.72513i	−0.173582	−	0.173582i
$742$	−51.2179	−	51.2179i	−1.88027	−	1.88027i
$743$	10.0068	−	10.0068i	0.367114	−	0.367114i	−0.499310	−	0.866423i	$-0.666413\pi$
$743$	10.0068	−	10.0068i	0.367114	−	0.367114i	0.866423	+	0.499310i	$0.166413\pi$
$744$	3.35922			0.123155
$745$	−16.2925	+	16.2925i	−0.596912	+	0.596912i
$746$		−	1.67131i		−	0.0611912i
$747$	−19.2448			−0.704130
$748$	8.38632	−	2.32699i	0.306634	−	0.0850830i
$749$	−60.9650			−2.22761
$750$		−	8.07858i		−	0.294988i
$751$	−2.29416	+	2.29416i	−0.0837153	+	0.0837153i	−0.747724	−	0.664009i	$-0.768854\pi$
$751$	−2.29416	+	2.29416i	−0.0837153	+	0.0837153i	0.664009	+	0.747724i	$0.268854\pi$
$752$	25.7955			0.940665
$753$	−9.54001	+	9.54001i	−0.347657	+	0.347657i
$754$	−1.95966	−	1.95966i	−0.0713666	−	0.0713666i
$755$	−38.3726	−	38.3726i	−1.39652	−	1.39652i
$756$			9.42371i			0.342737i
$757$		−	21.4476i		−	0.779527i	−0.920915	−	0.389763i	$-0.872557\pi$
$757$		−	21.4476i		−	0.779527i	0.920915	−	0.389763i	$-0.127443\pi$
$758$	−15.0153	−	15.0153i	−0.545380	−	0.545380i
$759$	−12.4684	−	12.4684i	−0.452573	−	0.452573i
$760$	−28.8229	+	28.8229i	−1.04552	+	1.04552i
$761$	−1.84773			−0.0669802			−0.0334901	−	0.999439i	$-0.510662\pi$
$761$	−1.84773			−0.0669802			−0.0334901	+	0.999439i	$0.510662\pi$
$762$	5.28853	−	5.28853i	0.191583	−	0.191583i
$763$			25.7303i			0.931500i
$764$	−2.08426			−0.0754060
$765$	−24.7414	+	6.86511i	−0.894529	+	0.248208i
$766$	−1.62544			−0.0587294
$767$			9.01379i			0.325469i
$768$	−5.61505	+	5.61505i	−0.202616	+	0.202616i
$769$	−5.38463			−0.194175			−0.0970874	−	0.995276i	$-0.530953\pi$
$769$	−5.38463			−0.194175			−0.0970874	+	0.995276i	$0.530953\pi$
$770$	−40.6664	+	40.6664i	−1.46552	+	1.46552i
$771$	5.72932	+	5.72932i	0.206336	+	0.206336i
$772$	7.22883	+	7.22883i	0.260171	+	0.260171i
$773$		−	22.5701i		−	0.811790i	−0.913920	−	0.405895i	$-0.866960\pi$
$773$		−	22.5701i		−	0.811790i	0.913920	−	0.405895i	$-0.133040\pi$
$774$			3.07810i			0.110640i
$775$	1.18568	+	1.18568i	0.0425910	+	0.0425910i
$776$	26.7282	+	26.7282i	0.959487	+	0.959487i
$777$	−16.7007	+	16.7007i	−0.599136	+	0.599136i
$778$	−16.2257			−0.581719
$779$	−42.7404	+	42.7404i	−1.53133	+	1.53133i
$780$		−	1.58884i		−	0.0568895i
$781$	−40.0155			−1.43187
$782$	8.55791	+	30.8422i	0.306030	+	1.10291i
$783$	4.77102			0.170502
$784$		−	42.1260i		−	1.50450i
$785$	25.0577	−	25.0577i	0.894346	−	0.894346i
$786$	14.1785			0.505732
$787$	3.01138	−	3.01138i	0.107344	−	0.107344i	−0.651395	−	0.758739i	$-0.725816\pi$
$787$	3.01138	−	3.01138i	0.107344	−	0.107344i	0.758739	+	0.651395i	$0.225816\pi$
$788$	3.45891	+	3.45891i	0.123219	+	0.123219i
$789$	3.56957	+	3.56957i	0.127080	+	0.127080i
$790$			6.07897i			0.216280i
$791$		−	64.4399i		−	2.29122i
$792$	−22.1715	−	22.1715i	−0.787829	−	0.787829i
$793$	−9.59877	−	9.59877i	−0.340862	−	0.340862i
$794$	1.35908	−	1.35908i	0.0482320	−	0.0482320i
$795$	−21.0237			−0.745635
$796$	−2.35242	+	2.35242i	−0.0833792	+	0.0833792i
$797$		−	18.9496i		−	0.671230i	−0.941999	−	0.335615i	$-0.891056\pi$
$797$		−	18.9496i		−	0.671230i	0.941999	−	0.335615i	$-0.108944\pi$
$798$	−21.4103			−0.757917
$799$	19.5286	−	34.5278i	0.690872	−	1.22151i
$800$	−3.00711			−0.106317
$801$			23.3160i			0.823829i
$802$	−7.47261	+	7.47261i	−0.263867	+	0.263867i
$803$	−17.2124			−0.607412
$804$	−0.782317	+	0.782317i	−0.0275902	+	0.0275902i
$805$	52.9250	+	52.9250i	1.86536	+	1.86536i
$806$	2.48961	+	2.48961i	0.0876927	+	0.0876927i
$807$			1.56545i			0.0551063i
$808$		−	2.49369i		−	0.0877276i
$809$	24.8617	+	24.8617i	0.874090	+	0.874090i	0.992915	−	0.118825i	$-0.0379128\pi$
$809$	24.8617	+	24.8617i	0.874090	+	0.874090i	−0.118825	+	0.992915i	$0.537913\pi$
$810$	10.5906	+	10.5906i	0.372114	+	0.372114i
$811$	19.2622	−	19.2622i	0.676386	−	0.676386i	−0.282794	−	0.959181i	$-0.591261\pi$
$811$	19.2622	−	19.2622i	0.676386	−	0.676386i	0.959181	+	0.282794i	$0.0912614\pi$
$812$	3.14225			0.110271
$813$	−3.27456	+	3.27456i	−0.114844	+	0.114844i
$814$		−	35.5740i		−	1.24687i
$815$	5.69193			0.199380
$816$	−2.02089	−	7.28316i	−0.0707452	−	0.254962i
$817$	5.40632			0.189143
$818$			33.6890i			1.17791i
$819$	−15.4284	+	15.4284i	−0.539111	+	0.539111i
$820$	−14.3716			−0.501877
$821$	3.37884	−	3.37884i	0.117922	−	0.117922i	−0.645683	−	0.763605i	$-0.723427\pi$
$821$	3.37884	−	3.37884i	0.117922	−	0.117922i	0.763605	+	0.645683i	$0.223427\pi$
$822$	−10.2737	−	10.2737i	−0.358337	−	0.358337i
$823$	18.9356	+	18.9356i	0.660053	+	0.660053i	0.955392	−	0.295339i	$-0.0954327\pi$
$823$	18.9356	+	18.9356i	0.660053	+	0.660053i	−0.295339	+	0.955392i	$0.595433\pi$
$824$			1.34427i			0.0468300i
$825$			2.88896i			0.100581i
$826$	20.4214	+	20.4214i	0.710553	+	0.710553i
$827$	−12.1563	−	12.1563i	−0.422717	−	0.422717i	0.463421	−	0.886138i	$-0.346622\pi$
$827$	−12.1563	−	12.1563i	−0.422717	−	0.422717i	−0.886138	+	0.463421i	$0.846622\pi$
$828$	−5.97922	+	5.97922i	−0.207792	+	0.207792i
$829$	−14.3562			−0.498613			−0.249306	−	0.968425i	$-0.580203\pi$
$829$	−14.3562			−0.498613			−0.249306	+	0.968425i	$0.580203\pi$
$830$	16.0590	−	16.0590i	0.557415	−	0.557415i
$831$		−	17.6666i		−	0.612846i
$832$	−16.0084			−0.554991
$833$	−56.3866	−	31.8917i	−1.95368	−	1.10498i
$834$	4.79978			0.166203
$835$		−	22.9639i		−	0.794697i
$836$	−8.06938	+	8.06938i	−0.279085	+	0.279085i
$837$	−6.06124			−0.209507
$838$	14.7263	−	14.7263i	0.508712	−	0.508712i
$839$	8.78334	+	8.78334i	0.303235	+	0.303235i	0.842278	−	0.539043i	$-0.181214\pi$
$839$	8.78334	+	8.78334i	0.303235	+	0.303235i	−0.539043	+	0.842278i	$0.681214\pi$
$840$	−17.3713	−	17.3713i	−0.599367	−	0.599367i
$841$			27.4091i			0.945143i
$842$		−	1.47074i		−	0.0506850i
$843$	−2.97889	−	2.97889i	−0.102599	−	0.102599i
$844$	10.4461	+	10.4461i	0.359570	+	0.359570i
$845$	−16.9211	+	16.9211i	−0.582102	+	0.582102i
$846$	−29.6139			−1.01815
$847$	−17.8747	+	17.8747i	−0.614183	+	0.614183i
$848$			33.5288i			1.15138i
$849$	−6.11351			−0.209815
$850$	2.58167	−	4.56457i	0.0885506	−	0.156563i
$851$	−46.2974			−1.58705
$852$		−	3.54202i		−	0.121347i
$853$	30.2204	−	30.2204i	1.03473	−	1.03473i	0.0353528	−	0.999375i	$-0.488745\pi$
$853$	30.2204	−	30.2204i	1.03473	−	1.03473i	0.999375	−	0.0353528i	$-0.0112555\pi$
$854$	−43.4935			−1.48832
$855$	23.8064	−	23.8064i	0.814161	−	0.814161i
$856$	27.7360	+	27.7360i	0.947995	+	0.947995i
$857$	−4.30875	−	4.30875i	−0.147184	−	0.147184i	0.629675	−	0.776859i	$-0.283188\pi$
$857$	−4.30875	−	4.30875i	−0.147184	−	0.147184i	−0.776859	+	0.629675i	$0.783188\pi$
$858$			6.06602i			0.207091i
$859$			0.982420i			0.0335197i	0.999860	+	0.0167599i	$0.00533508\pi$
$859$			0.982420i			0.0335197i	−0.999860	+	0.0167599i	$0.994665\pi$
$860$	0.908944	+	0.908944i	0.0309947	+	0.0309947i
$861$	−25.7592	−	25.7592i	−0.877872	−	0.877872i
$862$	23.0965	−	23.0965i	0.786671	−	0.786671i
$863$	−17.4232			−0.593091			−0.296546	−	0.955019i	$-0.595835\pi$
$863$	−17.4232			−0.593091			−0.296546	+	0.955019i	$0.595835\pi$
$864$	7.68621	−	7.68621i	0.261490	−	0.261490i
$865$		−	52.3359i		−	1.77947i
$866$	−22.6274			−0.768911
$867$	−11.2786	−	2.80874i	−0.383041	−	0.0953900i
$868$	−3.99200			−0.135497
$869$			8.21307i			0.278609i
$870$	−1.82242	+	1.82242i	−0.0617857	+	0.0617857i
$871$	−5.59602			−0.189614
$872$	11.7060	−	11.7060i	0.396414	−	0.396414i
$873$	−22.0762	−	22.0762i	−0.747167	−	0.747167i
$874$	−29.6766	−	29.6766i	−1.00383	−	1.00383i
$875$			46.3299i			1.56624i
$876$		−	1.52357i		−	0.0514767i
$877$	26.7378	+	26.7378i	0.902871	+	0.902871i	0.995684	−	0.0928124i	$-0.0295857\pi$
$877$	26.7378	+	26.7378i	0.902871	+	0.902871i	−0.0928124	+	0.995684i	$0.529586\pi$
$878$	−10.1331	−	10.1331i	−0.341975	−	0.341975i
$879$	0.553479	−	0.553479i	0.0186684	−	0.0186684i
$880$	26.6214			0.897409
$881$	29.6482	−	29.6482i	0.998873	−	0.998873i	−0.00112631	−	0.999999i	$-0.500359\pi$
$881$	29.6482	−	29.6482i	0.998873	−	0.998873i	0.999999	+	0.00112631i	$0.000358514\pi$
$882$			48.3618i			1.62843i
$883$	21.3346			0.717966			0.358983	−	0.933344i	$-0.383124\pi$
$883$	21.3346			0.717966			0.358983	+	0.933344i	$0.383124\pi$
$884$	−1.91829	+	3.39166i	−0.0645190	+	0.114074i
$885$	8.38251			0.281775
$886$			29.8550i			1.00300i
$887$	−25.3177	+	25.3177i	−0.850086	+	0.850086i	−0.990143	−	0.140057i	$-0.955271\pi$
$887$	−25.3177	+	25.3177i	−0.850086	+	0.850086i	0.140057	+	0.990143i	$0.455271\pi$
$888$	15.1960			0.509943
$889$	−30.3292	+	30.3292i	−1.01721	+	1.01721i
$890$	−19.4562	−	19.4562i	−0.652173	−	0.652173i
$891$	14.3085	+	14.3085i	0.479353	+	0.479353i
$892$		−	4.55101i		−	0.152379i
$893$			52.0134i			1.74056i
$894$	5.50600	+	5.50600i	0.184148	+	0.184148i
$895$	18.3798	+	18.3798i	0.614370	+	0.614370i
$896$	−16.9009	+	16.9009i	−0.564620	+	0.564620i
$897$	7.89457			0.263592
$898$	3.78594	−	3.78594i	0.126339	−	0.126339i
$899$			2.02106i			0.0674062i
$900$	1.38541			0.0461802
$901$	44.8790	+	25.3831i	1.49514	+	0.845633i
$902$	54.8693			1.82695
$903$			3.25833i			0.108431i
$904$	−29.3169	+	29.3169i	−0.975064	+	0.975064i
$905$	45.7901			1.52211
$906$	−12.9679	+	12.9679i	−0.430829	+	0.430829i
$907$	18.4995	+	18.4995i	0.614267	+	0.614267i	0.944055	−	0.329788i	$-0.106977\pi$
$907$	18.4995	+	18.4995i	0.614267	+	0.614267i	−0.329788	+	0.944055i	$0.606977\pi$
$908$	7.74973	+	7.74973i	0.257184	+	0.257184i
$909$			2.05967i			0.0683148i
$910$		−	25.7487i		−	0.853560i
$911$	−37.1367	−	37.1367i	−1.23039	−	1.23039i	−0.963813	−	0.266579i	$-0.914107\pi$
$911$	−37.1367	−	37.1367i	−1.23039	−	1.23039i	−0.266579	−	0.963813i	$-0.585893\pi$
$912$	7.00791	+	7.00791i	0.232055	+	0.232055i
$913$	21.6967	−	21.6967i	0.718055	−	0.718055i
$914$	−24.4796			−0.809715
$915$	−8.92652	+	8.92652i	−0.295102	+	0.295102i
$916$		−	3.45902i		−	0.114289i
$917$	−81.3126			−2.68518
$918$	5.06830	+	18.2659i	0.167279	+	0.602864i
$919$	0.614850			0.0202820			0.0101410	−	0.999949i	$-0.496772\pi$
$919$	0.614850			0.0202820			0.0101410	+	0.999949i	$0.496772\pi$
$920$		−	48.1563i		−	1.58767i
$921$	1.20700	−	1.20700i	0.0397719	−	0.0397719i
$922$	−30.6249			−1.00858
$923$	12.6683	−	12.6683i	0.416981	−	0.416981i
$924$	−4.86333	−	4.86333i	−0.159992	−	0.159992i
$925$	5.36363	+	5.36363i	0.176355	+	0.176355i
$926$			22.9857i			0.755357i
$927$		−	1.11031i		−	0.0364673i
$928$	−2.56289	−	2.56289i	−0.0841311	−	0.0841311i
$929$	13.8330	+	13.8330i	0.453845	+	0.453845i	0.896628	−	0.442784i	$-0.146009\pi$
$929$	13.8330	+	13.8330i	0.453845	+	0.453845i	−0.442784	+	0.896628i	$0.646009\pi$
$930$	2.31525	−	2.31525i	0.0759200	−	0.0759200i
$931$	84.9419			2.78386
$932$	10.9280	−	10.9280i	0.357959	−	0.357959i
$933$		−	3.92018i		−	0.128341i
$934$	3.94226			0.128995
$935$	20.1539	−	35.6334i	0.659102	−	1.16534i
$936$	14.0383			0.458855
$937$		−	26.8354i		−	0.876676i	−0.898810	−	0.438338i	$-0.855567\pi$
$937$		−	26.8354i		−	0.876676i	0.898810	−	0.438338i	$-0.144433\pi$
$938$	−12.6782	+	12.6782i	−0.413959	+	0.413959i
$939$	−9.61294			−0.313707
$940$	−8.74482	+	8.74482i	−0.285225	+	0.285225i
$941$	3.20036	+	3.20036i	0.104329	+	0.104329i	0.757344	−	0.653016i	$-0.226496\pi$
$941$	3.20036	+	3.20036i	0.104329	+	0.104329i	−0.653016	+	0.757344i	$0.726496\pi$
$942$	−8.46813	−	8.46813i	−0.275907	−	0.275907i
$943$		−	71.4091i		−	2.32540i
$944$		−	13.3685i		−	0.435107i
$945$	31.3441	+	31.3441i	1.01962	+	1.01962i
$946$	−3.47026	−	3.47026i	−0.112828	−	0.112828i
$947$	19.0999	−	19.0999i	0.620663	−	0.620663i	−0.325038	−	0.945701i	$-0.605377\pi$
$947$	19.0999	−	19.0999i	0.620663	−	0.620663i	0.945701	+	0.325038i	$0.105377\pi$
$948$	−0.726989			−0.0236115
$949$	5.44916	−	5.44916i	0.176887	−	0.176887i
$950$			6.87616i			0.223092i
$951$	−13.8250			−0.448307
$952$	16.1089	+	58.0555i	0.522092	+	1.88159i
$953$	19.6179			0.635487			0.317743	−	0.948177i	$-0.397075\pi$
$953$	19.6179			0.635487			0.317743	+	0.948177i	$0.397075\pi$
$954$		−	38.4919i		−	1.24622i
$955$	−6.93244	+	6.93244i	−0.224328	+	0.224328i
$956$	−2.51801			−0.0814384
$957$	−2.46220	+	2.46220i	−0.0795916	+	0.0795916i
$958$	−15.2103	−	15.2103i	−0.491423	−	0.491423i
$959$	58.9188	+	58.9188i	1.90259	+	1.90259i
$960$			14.8872i			0.480483i
$961$			28.4324i			0.917174i
$962$	11.2621	+	11.2621i	0.363106	+	0.363106i
$963$	−22.9086	−	22.9086i	−0.738219	−	0.738219i
$964$	11.1840	−	11.1840i	0.360213	−	0.360213i
$965$	48.0874			1.54799
$966$	17.8858	−	17.8858i	0.575465	−	0.575465i
$967$			3.20171i			0.102960i	0.998674	+	0.0514800i	$0.0163939\pi$
$967$			3.20171i			0.102960i	−0.998674	+	0.0514800i	$0.983606\pi$
$968$	16.2642			0.522750
$969$	14.6856	−	4.07487i	0.471770	−	0.130904i
$970$	36.8434			1.18297
$971$		−	19.0434i		−	0.611132i	−0.952171	−	0.305566i	$-0.901154\pi$
$971$		−	19.0434i		−	0.611132i	0.952171	−	0.305566i	$-0.0988457\pi$
$972$	−5.46127	+	5.46127i	−0.175170	+	0.175170i
$973$	−27.5263			−0.882453
$974$	8.88790	−	8.88790i	0.284787	−	0.284787i
$975$	−0.914599	−	0.914599i	−0.0292906	−	0.0292906i
$976$	14.2361	+	14.2361i	0.455685	+	0.455685i
$977$			52.4337i			1.67750i	0.544514	+	0.838752i	$0.316714\pi$
$977$			52.4337i			1.67750i	−0.544514	+	0.838752i	$0.683286\pi$
$978$		−	1.92356i		−	0.0615088i
$979$	−26.2865	−	26.2865i	−0.840122	−	0.840122i
$980$	14.2810	+	14.2810i	0.456188	+	0.456188i
$981$	−9.66858	+	9.66858i	−0.308694	+	0.308694i
$982$	−11.5766			−0.369423
$983$	9.74990	−	9.74990i	0.310973	−	0.310973i	−0.534313	−	0.845287i	$-0.679430\pi$
$983$	9.74990	−	9.74990i	0.310973	−	0.310973i	0.845287	+	0.534313i	$0.179430\pi$
$984$			23.4383i			0.747184i
$985$	23.0093			0.733136
$986$	6.09058	−	1.68998i	0.193964	−	0.0538198i
$987$	−31.3480			−0.997817
$988$		−	5.10927i		−	0.162547i
$989$	−4.51634	+	4.51634i	−0.143611	+	0.143611i
$990$	−30.5621			−0.971329
$991$	−3.94301	+	3.94301i	−0.125254	+	0.125254i	−0.766955	−	0.641701i	$-0.778229\pi$
$991$	−3.94301	+	3.94301i	−0.125254	+	0.125254i	0.641701	+	0.766955i	$0.278229\pi$
$992$	3.25598	+	3.25598i	0.103377	+	0.103377i
$993$	7.84626	+	7.84626i	0.248994	+	0.248994i
$994$		−	57.4019i		−	1.82068i
$995$			15.6487i			0.496096i
$996$	1.92050	+	1.92050i	0.0608535	+	0.0608535i
$997$	28.2291	+	28.2291i	0.894025	+	0.894025i	0.994899	−	0.100874i	$-0.0321640\pi$
$997$	28.2291	+	28.2291i	0.894025	+	0.894025i	−0.100874	+	0.994899i	$0.532164\pi$
$998$	4.63923	−	4.63923i	0.146852	−	0.146852i
$999$	−27.4190			−0.867499

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.c.259.11	✓	56
17.13	even	4	inner	731.2.f.c.302.18	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.c.259.11	✓	56	1.1	even	1	trivial
731.2.f.c.302.18	yes	56	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.21542i q^{2} +(0.483456 - 0.483456i) q^{3} +0.522759 q^{4} +(1.73874 - 1.73874i) q^{5} +(-0.587601 - 0.587601i) q^{6} +(3.36984 + 3.36984i) q^{7} -3.06621i q^{8} +2.53254i q^{9} +O(q^{10})\)	\(q-1.21542i q^{2} +(0.483456 - 0.483456i) q^{3} +0.522759 q^{4} +(1.73874 - 1.73874i) q^{5} +(-0.587601 - 0.587601i) q^{6} +(3.36984 + 3.36984i) q^{7} -3.06621i q^{8} +2.53254i q^{9} +(-2.11330 - 2.11330i) q^{10} +(-2.85520 - 2.85520i) q^{11} +(0.252731 - 0.252731i) q^{12} +1.80782 q^{13} +(4.09576 - 4.09576i) q^{14} -1.68121i q^{15} -2.68120 q^{16} +(-2.02982 + 3.58885i) q^{17} +3.07810 q^{18} -5.40632i q^{19} +(0.908944 - 0.908944i) q^{20} +3.25833 q^{21} +(-3.47026 + 3.47026i) q^{22} +(4.51634 + 4.51634i) q^{23} +(-1.48238 - 1.48238i) q^{24} -1.04645i q^{25} -2.19726i q^{26} +(2.67474 + 2.67474i) q^{27} +(1.76161 + 1.76161i) q^{28} +(0.891866 - 0.891866i) q^{29} -2.04337 q^{30} +(-1.13305 + 1.13305i) q^{31} -2.87363i q^{32} -2.76073 q^{33} +(4.36195 + 2.46708i) q^{34} +11.7186 q^{35} +1.32391i q^{36} +(-5.12555 + 5.12555i) q^{37} -6.57094 q^{38} +(0.874001 - 0.874001i) q^{39} +(-5.33134 - 5.33134i) q^{40} +(-7.90564 - 7.90564i) q^{41} -3.96024i q^{42} +1.00000i q^{43} +(-1.49258 - 1.49258i) q^{44} +(4.40344 + 4.40344i) q^{45} +(5.48924 - 5.48924i) q^{46} -9.62086 q^{47} +(-1.29624 + 1.29624i) q^{48} +15.7116i q^{49} -1.27187 q^{50} +(0.753724 + 2.71638i) q^{51} +0.945055 q^{52} -12.5051i q^{53} +(3.25093 - 3.25093i) q^{54} -9.92891 q^{55} +(10.3326 - 10.3326i) q^{56} +(-2.61372 - 2.61372i) q^{57} +(-1.08399 - 1.08399i) q^{58} +4.98600i q^{59} -0.878869i q^{60} +(-5.30958 - 5.30958i) q^{61} +(1.37713 + 1.37713i) q^{62} +(-8.53425 + 8.53425i) q^{63} -8.85507 q^{64} +(3.14333 - 3.14333i) q^{65} +3.35544i q^{66} -3.09545 q^{67} +(-1.06111 + 1.87610i) q^{68} +4.36690 q^{69} -14.2429i q^{70} +(7.00748 - 7.00748i) q^{71} +7.76529 q^{72} +(3.01422 - 3.01422i) q^{73} +(6.22968 + 6.22968i) q^{74} +(-0.505913 - 0.505913i) q^{75} -2.82620i q^{76} -19.2431i q^{77} +(-1.06228 - 1.06228i) q^{78} +(-1.43827 - 1.43827i) q^{79} +(-4.66192 + 4.66192i) q^{80} -5.01139 q^{81} +(-9.60865 + 9.60865i) q^{82} +7.59900i q^{83} +1.70332 q^{84} +(2.71076 + 9.76941i) q^{85} +1.21542 q^{86} -0.862356i q^{87} +(-8.75463 + 8.75463i) q^{88} +9.20655 q^{89} +(5.35202 - 5.35202i) q^{90} +(6.09206 + 6.09206i) q^{91} +(2.36096 + 2.36096i) q^{92} +1.09556i q^{93} +11.6934i q^{94} +(-9.40020 - 9.40020i) q^{95} +(-1.38927 - 1.38927i) q^{96} +(-8.71703 + 8.71703i) q^{97} +19.0962 q^{98} +(7.23091 - 7.23091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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