LMFDB - Embedded newform 170.2.h.b.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(21,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("170.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.h (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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.23045668864.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 237x^{4} + 892x^{2} + 1156 $ x^8 + 26x^6 + 237x^4 + 892*x^2 + 1156
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.3
Root			$-2.26843i$ of defining polynomial
Character	$\chi$	$=$	170.81
Dual form			170.2.h.b.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.60402 + 1.60402i) q^{3} -1.00000 q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.60402 + 1.60402i) q^{6} +(2.26843 - 2.26843i) q^{7} -1.00000i q^{8} +2.14578i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.60402 + 1.60402i) q^{3} -1.00000 q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.60402 + 1.60402i) q^{6} +(2.26843 - 2.26843i) q^{7} -1.00000i q^{8} +2.14578i q^{9} +(-0.707107 + 0.707107i) q^{10} +(-1.82843 + 1.82843i) q^{11} +(-1.60402 - 1.60402i) q^{12} -5.68265 q^{13} +(2.26843 + 2.26843i) q^{14} +2.26843i q^{15} +1.00000 q^{16} +(0.604023 - 4.07862i) q^{17} -2.14578 q^{18} -4.35383i q^{19} +(-0.707107 - 0.707107i) q^{20} +7.27723 q^{21} +(-1.82843 - 1.82843i) q^{22} +(-3.41421 + 3.41421i) q^{23} +(1.60402 - 1.60402i) q^{24} +1.00000i q^{25} -5.68265i q^{26} +(1.37019 - 1.37019i) q^{27} +(-2.26843 + 2.26843i) q^{28} +(6.01824 + 6.01824i) q^{29} -2.26843 q^{30} +(-1.16402 - 1.16402i) q^{31} +1.00000i q^{32} -5.86568 q^{33} +(4.07862 + 0.604023i) q^{34} +3.20805 q^{35} -2.14578i q^{36} +(3.09686 + 3.09686i) q^{37} +4.35383 q^{38} +(-9.11510 - 9.11510i) q^{39} +(0.707107 - 0.707107i) q^{40} +(5.53686 - 5.53686i) q^{41} +7.27723i q^{42} -7.20805i q^{43} +(1.82843 - 1.82843i) q^{44} +(-1.51730 + 1.51730i) q^{45} +(-3.41421 - 3.41421i) q^{46} -4.89069 q^{47} +(1.60402 + 1.60402i) q^{48} -3.29156i q^{49} -1.00000 q^{50} +(7.51107 - 5.57334i) q^{51} +5.68265 q^{52} +1.14578i q^{53} +(1.37019 + 1.37019i) q^{54} -2.58579 q^{55} +(-2.26843 - 2.26843i) q^{56} +(6.98364 - 6.98364i) q^{57} +(-6.01824 + 6.01824i) q^{58} +8.01068i q^{59} -2.26843i q^{60} +(-4.51863 + 4.51863i) q^{61} +(1.16402 - 1.16402i) q^{62} +(4.86756 + 4.86756i) q^{63} -1.00000 q^{64} +(-4.01824 - 4.01824i) q^{65} -5.86568i q^{66} -14.0729 q^{67} +(-0.604023 + 4.07862i) q^{68} -10.9530 q^{69} +3.20805i q^{70} +(-4.37207 - 4.37207i) q^{71} +2.14578 q^{72} +(3.62981 + 3.62981i) q^{73} +(-3.09686 + 3.09686i) q^{74} +(-1.60402 + 1.60402i) q^{75} +4.35383i q^{76} +8.29532i q^{77} +(9.11510 - 9.11510i) q^{78} +(-1.29344 + 1.29344i) q^{79} +(0.707107 + 0.707107i) q^{80} +10.8330 q^{81} +(5.53686 + 5.53686i) q^{82} +12.1572i q^{83} -7.27723 q^{84} +(3.31113 - 2.45691i) q^{85} +7.20805 q^{86} +19.3068i q^{87} +(1.82843 + 1.82843i) q^{88} +16.2925 q^{89} +(-1.51730 - 1.51730i) q^{90} +(-12.8907 + 12.8907i) q^{91} +(3.41421 - 3.41421i) q^{92} -3.73423i q^{93} -4.89069i q^{94} +(3.07862 - 3.07862i) q^{95} +(-1.60402 + 1.60402i) q^{96} +(-12.5312 - 12.5312i) q^{97} +3.29156 q^{98} +(-3.92341 - 3.92341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 4 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 - 4 * q^7	$ 8 q - 8 q^{4} - 4 q^{7} + 8 q^{11} - 12 q^{13} - 4 q^{14} + 8 q^{16} - 8 q^{17} - 28 q^{18} + 16 q^{21} + 8 q^{22} - 16 q^{23} + 12 q^{27} + 4 q^{28} + 24 q^{29} + 4 q^{30} + 4 q^{31} + 16 q^{33} + 12 q^{34} - 20 q^{37} + 20 q^{38} - 4 q^{39} - 8 q^{44} - 8 q^{45} - 16 q^{46} + 20 q^{47} - 8 q^{50} + 4 q^{51} + 12 q^{52} + 12 q^{54} - 32 q^{55} + 4 q^{56} + 40 q^{57} - 24 q^{58} - 16 q^{61} - 4 q^{62} - 64 q^{63} - 8 q^{64} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 8 q^{69} + 4 q^{71} + 28 q^{72} + 28 q^{73} + 20 q^{74} + 4 q^{78} + 8 q^{79} - 8 q^{81} - 16 q^{84} + 8 q^{85} + 32 q^{86} - 8 q^{88} - 44 q^{89} - 8 q^{90} - 44 q^{91} + 16 q^{92} + 4 q^{95} + 20 q^{97} + 48 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 4 * q^7 + 8 * q^11 - 12 * q^13 - 4 * q^14 + 8 * q^16 - 8 * q^17 - 28 * q^18 + 16 * q^21 + 8 * q^22 - 16 * q^23 + 12 * q^27 + 4 * q^28 + 24 * q^29 + 4 * q^30 + 4 * q^31 + 16 * q^33 + 12 * q^34 - 20 * q^37 + 20 * q^38 - 4 * q^39 - 8 * q^44 - 8 * q^45 - 16 * q^46 + 20 * q^47 - 8 * q^50 + 4 * q^51 + 12 * q^52 + 12 * q^54 - 32 * q^55 + 4 * q^56 + 40 * q^57 - 24 * q^58 - 16 * q^61 - 4 * q^62 - 64 * q^63 - 8 * q^64 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 8 * q^69 + 4 * q^71 + 28 * q^72 + 28 * q^73 + 20 * q^74 + 4 * q^78 + 8 * q^79 - 8 * q^81 - 16 * q^84 + 8 * q^85 + 32 * q^86 - 8 * q^88 - 44 * q^89 - 8 * q^90 - 44 * q^91 + 16 * q^92 + 4 * q^95 + 20 * q^97 + 48 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.60402	+	1.60402i	0.926083	+	0.926083i	0.997450	−	0.0713668i	$-0.0227361\pi$
$3$	1.60402	+	1.60402i	0.926083	+	0.926083i	−0.0713668	+	0.997450i	$0.522736\pi$
$4$	−1.00000			−0.500000
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	−1.60402	+	1.60402i	−0.654840	+	0.654840i
$7$	2.26843	−	2.26843i	0.857387	−	0.857387i	−0.133643	−	0.991030i	$-0.542668\pi$
$7$	2.26843	−	2.26843i	0.857387	−	0.857387i	0.991030	+	0.133643i	$0.0426675\pi$
$8$		−	1.00000i		−	0.353553i
$9$			2.14578i			0.715261i
$10$	−0.707107	+	0.707107i	−0.223607	+	0.223607i
$11$	−1.82843	+	1.82843i	−0.551292	+	0.551292i	−0.926813	−	0.375522i	$-0.877463\pi$
$11$	−1.82843	+	1.82843i	−0.551292	+	0.551292i	0.375522	+	0.926813i	$0.377463\pi$
$12$	−1.60402	−	1.60402i	−0.463042	−	0.463042i
$13$	−5.68265			−1.57608			−0.788041	−	0.615623i	$-0.788905\pi$
$13$	−5.68265			−1.57608			−0.788041	+	0.615623i	$0.788905\pi$
$14$	2.26843	+	2.26843i	0.606264	+	0.606264i
$15$			2.26843i			0.585707i
$16$	1.00000			0.250000
$17$	0.604023	−	4.07862i	0.146497	−	0.989211i
$17$	0.604023	−	4.07862i	0.146497	−	0.989211i
$18$	−2.14578			−0.505766
$19$		−	4.35383i		−	0.998837i	−0.866361	−	0.499418i	$-0.833547\pi$
$19$		−	4.35383i		−	0.998837i	0.866361	−	0.499418i	$-0.166453\pi$
$20$	−0.707107	−	0.707107i	−0.158114	−	0.158114i
$21$	7.27723			1.58802
$22$	−1.82843	−	1.82843i	−0.389822	−	0.389822i
$23$	−3.41421	+	3.41421i	−0.711913	+	0.711913i	−0.966935	−	0.255022i	$-0.917917\pi$
$23$	−3.41421	+	3.41421i	−0.711913	+	0.711913i	0.255022	+	0.966935i	$0.417917\pi$
$24$	1.60402	−	1.60402i	0.327420	−	0.327420i
$25$			1.00000i			0.200000i
$26$		−	5.68265i		−	1.11446i
$27$	1.37019	−	1.37019i	0.263692	−	0.263692i
$28$	−2.26843	+	2.26843i	−0.428693	+	0.428693i
$29$	6.01824	+	6.01824i	1.11756	+	1.11756i	0.992099	+	0.125460i	$0.0400406\pi$
$29$	6.01824	+	6.01824i	1.11756	+	1.11756i	0.125460	+	0.992099i	$0.459959\pi$
$30$	−2.26843			−0.414157
$31$	−1.16402	−	1.16402i	−0.209064	−	0.209064i	0.594806	−	0.803870i	$-0.297229\pi$
$31$	−1.16402	−	1.16402i	−0.209064	−	0.209064i	−0.803870	+	0.594806i	$0.797229\pi$
$32$			1.00000i			0.176777i
$33$	−5.86568			−1.02108
$34$	4.07862	+	0.604023i	0.699478	+	0.103589i
$35$	3.20805			0.542259
$36$		−	2.14578i		−	0.357630i
$37$	3.09686	+	3.09686i	0.509120	+	0.509120i	0.914256	−	0.405136i	$-0.132776\pi$
$37$	3.09686	+	3.09686i	0.509120	+	0.509120i	−0.405136	+	0.914256i	$0.632776\pi$
$38$	4.35383			0.706284
$39$	−9.11510	−	9.11510i	−1.45958	−	1.45958i
$40$	0.707107	−	0.707107i	0.111803	−	0.111803i
$41$	5.53686	−	5.53686i	0.864713	−	0.864713i	−0.127168	−	0.991881i	$-0.540589\pi$
$41$	5.53686	−	5.53686i	0.864713	−	0.864713i	0.991881	+	0.127168i	$0.0405889\pi$
$42$			7.27723i			1.12290i
$43$		−	7.20805i		−	1.09922i	−0.835422	−	0.549608i	$-0.814777\pi$
$43$		−	7.20805i		−	1.09922i	0.835422	−	0.549608i	$-0.185223\pi$
$44$	1.82843	−	1.82843i	0.275646	−	0.275646i
$45$	−1.51730	+	1.51730i	−0.226185	+	0.226185i
$46$	−3.41421	−	3.41421i	−0.503398	−	0.503398i
$47$	−4.89069			−0.713381			−0.356690	−	0.934223i	$-0.616095\pi$
$47$	−4.89069			−0.713381			−0.356690	+	0.934223i	$0.616095\pi$
$48$	1.60402	+	1.60402i	0.231521	+	0.231521i
$49$		−	3.29156i		−	0.470223i
$50$	−1.00000			−0.141421
$51$	7.51107	−	5.57334i	1.05176	−	0.780423i
$52$	5.68265			0.788041
$53$			1.14578i			0.157385i	0.996899	+	0.0786926i	$0.0250746\pi$
$53$			1.14578i			0.157385i	−0.996899	+	0.0786926i	$0.974925\pi$
$54$	1.37019	+	1.37019i	0.186459	+	0.186459i
$55$	−2.58579			−0.348667
$56$	−2.26843	−	2.26843i	−0.303132	−	0.303132i
$57$	6.98364	−	6.98364i	0.925006	−	0.925006i
$58$	−6.01824	+	6.01824i	−0.790233	+	0.790233i
$59$			8.01068i			1.04290i	0.853281	+	0.521451i	$0.174609\pi$
$59$			8.01068i			1.04290i	−0.853281	+	0.521451i	$0.825391\pi$
$60$		−	2.26843i		−	0.292853i
$61$	−4.51863	+	4.51863i	−0.578551	+	0.578551i	−0.934504	−	0.355953i	$-0.884156\pi$
$61$	−4.51863	+	4.51863i	−0.578551	+	0.578551i	0.355953	+	0.934504i	$0.384156\pi$
$62$	1.16402	−	1.16402i	0.147831	−	0.147831i
$63$	4.86756	+	4.86756i	0.613255	+	0.613255i
$64$	−1.00000			−0.125000
$65$	−4.01824	−	4.01824i	−0.498401	−	0.498401i
$66$		−	5.86568i		−	0.722015i
$67$	−14.0729			−1.71928			−0.859642	−	0.510897i	$-0.829313\pi$
$67$	−14.0729			−1.71928			−0.859642	+	0.510897i	$0.829313\pi$
$68$	−0.604023	+	4.07862i	−0.0732486	+	0.494606i
$69$	−10.9530			−1.31858
$70$			3.20805i			0.383435i
$71$	−4.37207	−	4.37207i	−0.518869	−	0.518869i	0.398360	−	0.917229i	$-0.369579\pi$
$71$	−4.37207	−	4.37207i	−0.518869	−	0.518869i	−0.917229	+	0.398360i	$0.869579\pi$
$72$	2.14578			0.252883
$73$	3.62981	+	3.62981i	0.424838	+	0.424838i	0.886865	−	0.462028i	$-0.152878\pi$
$73$	3.62981	+	3.62981i	0.424838	+	0.424838i	−0.462028	+	0.886865i	$0.652878\pi$
$74$	−3.09686	+	3.09686i	−0.360003	+	0.360003i
$75$	−1.60402	+	1.60402i	−0.185217	+	0.185217i
$76$			4.35383i			0.499418i
$77$			8.29532i			0.945340i
$78$	9.11510	−	9.11510i	1.03208	−	1.03208i
$79$	−1.29344	+	1.29344i	−0.145524	+	0.145524i	−0.776115	−	0.630591i	$-0.782812\pi$
$79$	−1.29344	+	1.29344i	−0.145524	+	0.145524i	0.630591	+	0.776115i	$0.282812\pi$
$80$	0.707107	+	0.707107i	0.0790569	+	0.0790569i
$81$	10.8330			1.20366
$82$	5.53686	+	5.53686i	0.611444	+	0.611444i
$83$			12.1572i			1.33443i	0.744865	+	0.667215i	$0.232514\pi$
$83$			12.1572i			1.33443i	−0.744865	+	0.667215i	$0.767486\pi$
$84$	−7.27723			−0.794011
$85$	3.31113	−	2.45691i	0.359142	−	0.266490i
$86$	7.20805			0.777264
$87$			19.3068i			2.06990i
$88$	1.82843	+	1.82843i	0.194911	+	0.194911i
$89$	16.2925			1.72700			0.863498	−	0.504351i	$-0.168268\pi$
$89$	16.2925			1.72700			0.863498	+	0.504351i	$0.168268\pi$
$90$	−1.51730	−	1.51730i	−0.159937	−	0.159937i
$91$	−12.8907	+	12.8907i	−1.35131	+	1.35131i
$92$	3.41421	−	3.41421i	0.355956	−	0.355956i
$93$		−	3.73423i		−	0.387221i
$94$		−	4.89069i		−	0.504436i
$95$	3.07862	−	3.07862i	0.315860	−	0.315860i
$96$	−1.60402	+	1.60402i	−0.163710	+	0.163710i
$97$	−12.5312	−	12.5312i	−1.27235	−	1.27235i	−0.944852	−	0.327497i	$-0.893795\pi$
$97$	−12.5312	−	12.5312i	−1.27235	−	1.27235i	−0.327497	−	0.944852i	$-0.606205\pi$
$98$	3.29156			0.332498
$99$	−3.92341	−	3.92341i	−0.394317	−	0.394317i
$100$		−	1.00000i		−	0.100000i
$101$	7.65685			0.761885			0.380943	−	0.924599i	$-0.375599\pi$
$101$	7.65685			0.761885			0.380943	+	0.924599i	$0.375599\pi$
$102$	5.57334	+	7.51107i	0.551843	+	0.743707i
$103$	−7.58767			−0.747635			−0.373817	−	0.927502i	$-0.621951\pi$
$103$	−7.58767			−0.747635			−0.373817	+	0.927502i	$0.621951\pi$
$104$			5.68265i			0.557229i
$105$	5.14578	+	5.14578i	0.502177	+	0.502177i
$106$	−1.14578			−0.111288
$107$	−3.85422	−	3.85422i	−0.372601	−	0.372601i	0.495823	−	0.868424i	$-0.334867\pi$
$107$	−3.85422	−	3.85422i	−0.372601	−	0.372601i	−0.868424	+	0.495823i	$0.834867\pi$
$108$	−1.37019	+	1.37019i	−0.131846	+	0.131846i
$109$	−6.01824	+	6.01824i	−0.576443	+	0.576443i	−0.933921	−	0.357479i	$-0.883636\pi$
$109$	−6.01824	+	6.01824i	−0.576443	+	0.576443i	0.357479	+	0.933921i	$0.383636\pi$
$110$		−	2.58579i		−	0.246545i
$111$			9.93487i			0.942976i
$112$	2.26843	−	2.26843i	0.214347	−	0.214347i
$113$	−5.57823	+	5.57823i	−0.524756	+	0.524756i	−0.919004	−	0.394248i	$-0.871005\pi$
$113$	−5.57823	+	5.57823i	−0.524756	+	0.524756i	0.394248	+	0.919004i	$0.371005\pi$
$114$	6.98364	+	6.98364i	0.654078	+	0.654078i
$115$	−4.82843			−0.450253
$116$	−6.01824	−	6.01824i	−0.558779	−	0.558779i
$117$		−	12.1937i		−	1.12731i
$118$	−8.01068			−0.737443
$119$	−7.88189	−	10.6223i	−0.722532	−	0.973741i
$120$	2.26843			0.207079
$121$			4.31371i			0.392155i
$122$	−4.51863	−	4.51863i	−0.409097	−	0.409097i
$123$	17.7625			1.60159
$124$	1.16402	+	1.16402i	0.104532	+	0.104532i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−4.86756	+	4.86756i	−0.433637	+	0.433637i
$127$		−	6.76992i		−	0.600733i	−0.953824	−	0.300367i	$-0.902891\pi$
$127$		−	6.76992i		−	0.600733i	0.953824	−	0.300367i	$-0.0971091\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	11.5619	−	11.5619i	1.01797	−	1.01797i
$130$	4.01824	−	4.01824i	0.352423	−	0.352423i
$131$	7.32804	+	7.32804i	0.640254	+	0.640254i	0.950618	−	0.310364i	$-0.100451\pi$
$131$	7.32804	+	7.32804i	0.640254	+	0.640254i	−0.310364	+	0.950618i	$0.600451\pi$
$132$	5.86568			0.510542
$133$	−9.87636	−	9.87636i	−0.856389	−	0.856389i
$134$		−	14.0729i		−	1.21572i
$135$	1.93774			0.166774
$136$	−4.07862	−	0.604023i	−0.349739	−	0.0517946i
$137$	−1.74115			−0.148756			−0.0743782	−	0.997230i	$-0.523697\pi$
$137$	−1.74115			−0.148756			−0.0743782	+	0.997230i	$0.523697\pi$
$138$		−	10.9530i		−	0.932378i
$139$	0.587666	+	0.587666i	0.0498452	+	0.0498452i	0.731590	−	0.681745i	$-0.238779\pi$
$139$	0.587666	+	0.587666i	0.0498452	+	0.0498452i	−0.681745	+	0.731590i	$0.738779\pi$
$140$	−3.20805			−0.271129
$141$	−7.84478	−	7.84478i	−0.660650	−	0.660650i
$142$	4.37207	−	4.37207i	0.366896	−	0.366896i
$143$	10.3903	−	10.3903i	0.868881	−	0.868881i
$144$			2.14578i			0.178815i
$145$			8.51107i			0.706806i
$146$	−3.62981	+	3.62981i	−0.300406	+	0.300406i
$147$	5.27975	−	5.27975i	0.435466	−	0.435466i
$148$	−3.09686	−	3.09686i	−0.254560	−	0.254560i
$149$	−2.44881			−0.200614			−0.100307	−	0.994957i	$-0.531983\pi$
$149$	−2.44881			−0.200614			−0.100307	+	0.994957i	$0.531983\pi$
$150$	−1.60402	−	1.60402i	−0.130968	−	0.130968i
$151$			4.53686i			0.369205i	0.982813	+	0.184602i	$0.0590997\pi$
$151$			4.53686i			0.369205i	−0.982813	+	0.184602i	$0.940900\pi$
$152$	−4.35383			−0.353142
$153$	8.75183	+	1.29610i	0.707544	+	0.104784i
$154$	−8.29532			−0.668456
$155$		−	1.64617i		−	0.132224i
$156$	9.11510	+	9.11510i	0.729792	+	0.729792i
$157$	23.5074			1.87610			0.938048	−	0.346504i	$-0.112631\pi$
$157$	23.5074			1.87610			0.938048	+	0.346504i	$0.112631\pi$
$158$	−1.29344	−	1.29344i	−0.102901	−	0.102901i
$159$	−1.83786	+	1.83786i	−0.145752	+	0.145752i
$160$	−0.707107	+	0.707107i	−0.0559017	+	0.0559017i
$161$			15.4898i			1.22077i
$162$			10.8330i			0.851118i
$163$	16.0479	−	16.0479i	1.25697	−	1.25697i	0.304440	−	0.952532i	$-0.401531\pi$
$163$	16.0479	−	16.0479i	1.25697	−	1.25697i	0.952532	−	0.304440i	$-0.0984692\pi$
$164$	−5.53686	+	5.53686i	−0.432356	+	0.432356i
$165$	−4.14766	−	4.14766i	−0.322895	−	0.322895i
$166$	−12.1572			−0.943585
$167$	−14.4364	−	14.4364i	−1.11712	−	1.11712i	−0.992162	−	0.124957i	$-0.960121\pi$
$167$	−14.4364	−	14.4364i	−1.11712	−	1.11712i	−0.124957	−	0.992162i	$-0.539879\pi$
$168$		−	7.27723i		−	0.561451i
$169$	19.2925			1.48404
$170$	2.45691	+	3.31113i	0.188437	+	0.253952i
$171$	9.34237			0.714429
$172$			7.20805i			0.549608i
$173$	−6.65873	−	6.65873i	−0.506254	−	0.506254i	0.407120	−	0.913375i	$-0.366533\pi$
$173$	−6.65873	−	6.65873i	−0.506254	−	0.506254i	−0.913375	+	0.407120i	$0.866533\pi$
$174$	−19.3068			−1.46364
$175$	2.26843	+	2.26843i	0.171477	+	0.171477i
$176$	−1.82843	+	1.82843i	−0.137823	+	0.137823i
$177$	−12.8493	+	12.8493i	−0.965814	+	0.965814i
$178$			16.2925i			1.22117i
$179$			6.65763i			0.497615i	0.968553	+	0.248807i	$0.0800386\pi$
$179$			6.65763i			0.497615i	−0.968553	+	0.248807i	$0.919961\pi$
$180$	1.51730	−	1.51730i	0.113093	−	0.113093i
$181$	0.0853971	−	0.0853971i	0.00634752	−	0.00634752i	−0.703926	−	0.710273i	$-0.748571\pi$
$181$	0.0853971	−	0.0853971i	0.00634752	−	0.00634752i	0.710273	+	0.703926i	$0.248571\pi$
$182$	−12.8907	−	12.8907i	−0.955522	−	0.955522i
$183$	−14.4960			−1.07157
$184$	3.41421	+	3.41421i	0.251699	+	0.251699i
$185$			4.37962i			0.321996i
$186$	3.73423			0.273807
$187$	6.35305	+	8.56188i	0.464581	+	0.626106i
$188$	4.89069			0.356690
$189$		−	6.21635i		−	0.452173i
$190$	3.07862	+	3.07862i	0.223347	+	0.223347i
$191$	−9.52253			−0.689026			−0.344513	−	0.938781i	$-0.611956\pi$
$191$	−9.52253			−0.689026			−0.344513	+	0.938781i	$0.611956\pi$
$192$	−1.60402	−	1.60402i	−0.115760	−	0.115760i
$193$	11.6318	−	11.6318i	0.837278	−	0.837278i	−0.151222	−	0.988500i	$-0.548321\pi$
$193$	11.6318	−	11.6318i	0.837278	−	0.837278i	0.988500	+	0.151222i	$0.0483207\pi$
$194$	12.5312	−	12.5312i	0.899687	−	0.899687i
$195$		−	12.8907i		−	0.923122i
$196$			3.29156i			0.235112i
$197$	−16.3414	+	16.3414i	−1.16428	+	1.16428i	−0.180745	+	0.983530i	$0.557851\pi$
$197$	−16.3414	+	16.3414i	−1.16428	+	1.16428i	−0.983530	+	0.180745i	$0.942149\pi$
$198$	3.92341	−	3.92341i	0.278824	−	0.278824i
$199$	−6.99322	−	6.99322i	−0.495737	−	0.495737i	0.414371	−	0.910108i	$-0.364001\pi$
$199$	−6.99322	−	6.99322i	−0.495737	−	0.495737i	−0.910108	+	0.414371i	$0.864001\pi$
$200$	1.00000			0.0707107
$201$	−22.5733	−	22.5733i	−1.59220	−	1.59220i
$202$			7.65685i			0.538734i
$203$	27.3039			1.91636
$204$	−7.51107	+	5.57334i	−0.525880	+	0.390212i
$205$	7.83031			0.546892
$206$		−	7.58767i		−	0.528658i
$207$	−7.32616	−	7.32616i	−0.509203	−	0.509203i
$208$	−5.68265			−0.394021
$209$	7.96066	+	7.96066i	0.550650	+	0.550650i
$210$	−5.14578	+	5.14578i	−0.355093	+	0.355093i
$211$	11.8907	−	11.8907i	0.818589	−	0.818589i	−0.167315	−	0.985904i	$-0.553510\pi$
$211$	11.8907	−	11.8907i	0.818589	−	0.818589i	0.985904	+	0.167315i	$0.0535096\pi$
$212$		−	1.14578i		−	0.0786926i
$213$		−	14.0258i		−	0.961031i
$214$	3.85422	−	3.85422i	0.263469	−	0.263469i
$215$	5.09686	−	5.09686i	0.347603	−	0.347603i
$216$	−1.37019	−	1.37019i	−0.0932293	−	0.0932293i
$217$	−5.28099			−0.358497
$218$	−6.01824	−	6.01824i	−0.407606	−	0.407606i
$219$			11.6446i			0.786870i
$220$	2.58579			0.174334
$221$	−3.43245	+	23.1774i	−0.230892	+	1.55908i
$222$	−9.93487			−0.666785
$223$			9.25144i			0.619522i	0.950814	+	0.309761i	$0.100249\pi$
$223$			9.25144i			0.619522i	−0.950814	+	0.309761i	$0.899751\pi$
$224$	2.26843	+	2.26843i	0.151566	+	0.151566i
$225$	−2.14578			−0.143052
$226$	−5.57823	−	5.57823i	−0.371059	−	0.371059i
$227$	14.5205	−	14.5205i	0.963760	−	0.963760i	−0.0356061	−	0.999366i	$-0.511336\pi$
$227$	14.5205	−	14.5205i	0.963760	−	0.963760i	0.999366	+	0.0356061i	$0.0113362\pi$
$228$	−6.98364	+	6.98364i	−0.462503	+	0.462503i
$229$			15.1618i			1.00192i	0.865471	+	0.500959i	$0.167019\pi$
$229$			15.1618i			1.00192i	−0.865471	+	0.500959i	$0.832981\pi$
$230$		−	4.82843i		−	0.318377i
$231$	−13.3059	+	13.3059i	−0.875463	+	0.875463i
$232$	6.01824	−	6.01824i	0.395117	−	0.395117i
$233$	−6.28745	−	6.28745i	−0.411904	−	0.411904i	0.470497	−	0.882402i	$-0.344075\pi$
$233$	−6.28745	−	6.28745i	−0.411904	−	0.411904i	−0.882402	+	0.470497i	$0.844075\pi$
$234$	12.1937			0.797128
$235$	−3.45824	−	3.45824i	−0.225591	−	0.225591i
$236$		−	8.01068i		−	0.521451i
$237$	−4.14943			−0.269534
$238$	10.6223	−	7.88189i	0.688539	−	0.510907i
$239$	−0.0827385			−0.00535191			−0.00267595	−	0.999996i	$-0.500852\pi$
$239$	−0.0827385			−0.00535191			−0.00267595	+	0.999996i	$0.500852\pi$
$240$			2.26843i			0.146427i
$241$	−0.829206	−	0.829206i	−0.0534138	−	0.0534138i	0.679895	−	0.733309i	$-0.262025\pi$
$241$	−0.829206	−	0.829206i	−0.0534138	−	0.0534138i	−0.733309	+	0.679895i	$0.762025\pi$
$242$	−4.31371			−0.277296
$243$	13.2658	+	13.2658i	0.851000	+	0.851000i
$244$	4.51863	−	4.51863i	0.289275	−	0.289275i
$245$	2.32749	−	2.32749i	0.148698	−	0.148698i
$246$			17.7625i			1.13250i
$247$			24.7413i			1.57425i
$248$	−1.16402	+	1.16402i	−0.0739153	+	0.0739153i
$249$	−19.5005	+	19.5005i	−1.23579	+	1.23579i
$250$	−0.707107	−	0.707107i	−0.0447214	−	0.0447214i
$251$	−18.1245			−1.14401			−0.572005	−	0.820250i	$-0.693834\pi$
$251$	−18.1245			−1.14401			−0.572005	+	0.820250i	$0.693834\pi$
$252$	−4.86756	−	4.86756i	−0.306627	−	0.306627i
$253$		−	12.4853i		−	0.784943i
$254$	6.76992			0.424783
$255$	9.25207	+	1.37019i	0.579387	+	0.0858044i
$256$	1.00000			0.0625000
$257$			25.3539i			1.58154i	0.612116	+	0.790768i	$0.290318\pi$
$257$			25.3539i			1.58154i	−0.612116	+	0.790768i	$0.709682\pi$
$258$	11.5619	+	11.5619i	0.719811	+	0.719811i
$259$	14.0500			0.873026
$260$	4.01824	+	4.01824i	0.249200	+	0.249200i
$261$	−12.9138	+	12.9138i	−0.799346	+	0.799346i
$262$	−7.32804	+	7.32804i	−0.452728	+	0.452728i
$263$			2.11385i			0.130345i	0.997874	+	0.0651727i	$0.0207598\pi$
$263$			2.11385i			0.130345i	−0.997874	+	0.0651727i	$0.979240\pi$
$264$			5.86568i			0.361008i
$265$	−0.810190	+	0.810190i	−0.0497696	+	0.0497696i
$266$	9.87636	−	9.87636i	0.605559	−	0.605559i
$267$	26.1335	+	26.1335i	1.59934	+	1.59934i
$268$	14.0729			0.859642
$269$	15.1898	+	15.1898i	0.926139	+	0.926139i	0.997454	−	0.0713148i	$-0.0227195\pi$
$269$	15.1898	+	15.1898i	0.926139	+	0.926139i	−0.0713148	+	0.997454i	$0.522719\pi$
$270$			1.93774i			0.117927i
$271$	22.5922			1.37238			0.686189	−	0.727423i	$-0.259282\pi$
$271$	22.5922			1.37238			0.686189	+	0.727423i	$0.259282\pi$
$272$	0.604023	−	4.07862i	0.0366243	−	0.247303i
$273$	−41.3539			−2.50285
$274$		−	1.74115i		−	0.105187i
$275$	−1.82843	−	1.82843i	−0.110258	−	0.110258i
$276$	10.9530			0.659291
$277$	18.0756	+	18.0756i	1.08606	+	1.08606i	0.995930	+	0.0901277i	$0.0287275\pi$
$277$	18.0756	+	18.0756i	1.08606	+	1.08606i	0.0901277	+	0.995930i	$0.471272\pi$
$278$	−0.587666	+	0.587666i	−0.0352459	+	0.0352459i
$279$	2.49773	−	2.49773i	0.149535	−	0.149535i
$280$		−	3.20805i		−	0.191717i
$281$		−	15.8248i		−	0.944027i	−0.881591	−	0.472014i	$-0.843527\pi$
$281$		−	15.8248i		−	0.944027i	0.881591	−	0.472014i	$-0.156473\pi$
$282$	7.84478	−	7.84478i	0.467150	−	0.467150i
$283$	−12.4325	+	12.4325i	−0.739032	+	0.739032i	−0.972391	−	0.233358i	$-0.925028\pi$
$283$	−12.4325	+	12.4325i	−0.739032	+	0.739032i	0.233358	+	0.972391i	$0.425028\pi$
$284$	4.37207	+	4.37207i	0.259434	+	0.259434i
$285$	9.87636			0.585025
$286$	10.3903	+	10.3903i	0.614391	+	0.614391i
$287$		−	25.1200i		−	1.48279i
$288$	−2.14578			−0.126441
$289$	−16.2703	−	4.92717i	−0.957077	−	0.289833i
$290$	−8.51107			−0.499787
$291$		−	40.2006i		−	2.35660i
$292$	−3.62981	−	3.62981i	−0.212419	−	0.212419i
$293$	−29.6524			−1.73231			−0.866157	−	0.499773i	$-0.833417\pi$
$293$	−29.6524			−1.73231			−0.866157	+	0.499773i	$0.833417\pi$
$294$	5.27975	+	5.27975i	0.307921	+	0.307921i
$295$	−5.66441	+	5.66441i	−0.329795	+	0.329795i
$296$	3.09686	−	3.09686i	0.180001	−	0.180001i
$297$			5.01057i			0.290743i
$298$		−	2.44881i		−	0.141856i
$299$	19.4018	−	19.4018i	1.12203	−	1.12203i
$300$	1.60402	−	1.60402i	0.0926083	−	0.0926083i
$301$	−16.3510	−	16.3510i	−0.942454	−	0.942454i
$302$	−4.53686			−0.261067
$303$	12.2818	+	12.2818i	0.705569	+	0.705569i
$304$		−	4.35383i		−	0.249709i
$305$	−6.39030			−0.365908
$306$	−1.29610	+	8.75183i	−0.0740932	+	0.500309i
$307$	32.0116			1.82700			0.913499	−	0.406842i	$-0.133370\pi$
$307$	32.0116			1.82700			0.913499	+	0.406842i	$0.133370\pi$
$308$		−	8.29532i		−	0.472670i
$309$	−12.1708	−	12.1708i	−0.692372	−	0.692372i
$310$	1.64617			0.0934962
$311$	8.72792	+	8.72792i	0.494915	+	0.494915i	0.909851	−	0.414936i	$-0.136196\pi$
$311$	8.72792	+	8.72792i	0.494915	+	0.494915i	−0.414936	+	0.909851i	$0.636196\pi$
$312$	−9.11510	+	9.11510i	−0.516041	+	0.516041i
$313$	1.39030	−	1.39030i	0.0785845	−	0.0785845i	−0.666722	−	0.745307i	$-0.732303\pi$
$313$	1.39030	−	1.39030i	0.0785845	−	0.0785845i	0.745307	+	0.666722i	$0.232303\pi$
$314$			23.5074i			1.32660i
$315$			6.88377i			0.387856i
$316$	1.29344	−	1.29344i	0.0727619	−	0.0727619i
$317$	8.08540	−	8.08540i	0.454121	−	0.454121i	−0.442599	−	0.896720i	$-0.645943\pi$
$317$	8.08540	−	8.08540i	0.454121	−	0.454121i	0.896720	+	0.442599i	$0.145943\pi$
$318$	−1.83786	−	1.83786i	−0.103062	−	0.103062i
$319$	−22.0078			−1.23220
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$		−	12.3645i		−	0.690120i
$322$	−15.4898			−0.863214
$323$	−17.7576	−	2.62981i	−0.988060	−	0.146327i
$324$	−10.8330			−0.601831
$325$		−	5.68265i		−	0.315216i
$326$	16.0479	+	16.0479i	0.888813	+	0.888813i
$327$	−19.3068			−1.06767
$328$	−5.53686	−	5.53686i	−0.305722	−	0.305722i
$329$	−11.0942	+	11.0942i	−0.611643	+	0.611643i
$330$	4.14766	−	4.14766i	0.228321	−	0.228321i
$331$		−	18.4784i		−	1.01566i	−0.861457	−	0.507831i	$-0.830447\pi$
$331$		−	18.4784i		−	1.01566i	0.861457	−	0.507831i	$-0.169553\pi$
$332$		−	12.1572i		−	0.667215i
$333$	−6.64518	+	6.64518i	−0.364154	+	0.364154i
$334$	14.4364	−	14.4364i	0.789922	−	0.789922i
$335$	−9.95108	−	9.95108i	−0.543685	−	0.543685i
$336$	7.27723			0.397006
$337$	−1.83708	−	1.83708i	−0.100072	−	0.100072i	0.655298	−	0.755370i	$-0.272543\pi$
$337$	−1.83708	−	1.83708i	−0.100072	−	0.100072i	−0.755370	+	0.655298i	$0.772543\pi$
$338$			19.2925i			1.04937i
$339$	−17.8952			−0.971936
$340$	−3.31113	+	2.45691i	−0.179571	+	0.133245i
$341$	4.25665			0.230510
$342$			9.34237i			0.505177i
$343$	8.41233	+	8.41233i	0.454223	+	0.454223i
$344$	−7.20805			−0.388632
$345$	−7.74491	−	7.74491i	−0.416972	−	0.416972i
$346$	6.65873	−	6.65873i	0.357976	−	0.357976i
$347$	−9.15522	+	9.15522i	−0.491478	+	0.491478i	−0.908772	−	0.417294i	$-0.862979\pi$
$347$	−9.15522	+	9.15522i	−0.491478	+	0.491478i	0.417294	+	0.908772i	$0.362979\pi$
$348$		−	19.3068i		−	1.03495i
$349$		−	20.3698i		−	1.09037i	−0.838315	−	0.545186i	$-0.816459\pi$
$349$		−	20.3698i		−	1.09037i	0.838315	−	0.545186i	$-0.183541\pi$
$350$	−2.26843	+	2.26843i	−0.121253	+	0.121253i
$351$	−7.78628	+	7.78628i	−0.415601	+	0.415601i
$352$	−1.82843	−	1.82843i	−0.0974555	−	0.0974555i
$353$	33.1680			1.76536			0.882678	−	0.469978i	$-0.155738\pi$
$353$	33.1680			1.76536			0.882678	+	0.469978i	$0.155738\pi$
$354$	−12.8493	−	12.8493i	−0.682934	−	0.682934i
$355$		−	6.18303i		−	0.328161i
$356$	−16.2925			−0.863498
$357$	4.39562	−	29.6811i	0.232641	−	1.57089i
$358$	−6.65763			−0.351867
$359$			17.2272i			0.909217i	0.890691	+	0.454609i	$0.150221\pi$
$359$			17.2272i			0.909217i	−0.890691	+	0.454609i	$0.849779\pi$
$360$	1.51730	+	1.51730i	0.0799686	+	0.0799686i
$361$	0.0441757			0.00232503
$362$	0.0853971	+	0.0853971i	0.00448837	+	0.00448837i
$363$	−6.91929	+	6.91929i	−0.363169	+	0.363169i
$364$	12.8907	−	12.8907i	0.675656	−	0.675656i
$365$			5.13333i			0.268691i
$366$		−	14.4960i		−	0.757716i
$367$	16.4879	−	16.4879i	0.860663	−	0.860663i	−0.130752	−	0.991415i	$-0.541739\pi$
$367$	16.4879	−	16.4879i	0.860663	−	0.860663i	0.991415	+	0.130752i	$0.0417391\pi$
$368$	−3.41421	+	3.41421i	−0.177978	+	0.177978i
$369$	11.8809	+	11.8809i	0.618495	+	0.618495i
$370$	−4.37962			−0.227686
$371$	2.59913	+	2.59913i	0.134940	+	0.134940i
$372$			3.73423i			0.193611i
$373$	10.6098			0.549355			0.274678	−	0.961536i	$-0.411429\pi$
$373$	10.6098			0.549355			0.274678	+	0.961536i	$0.411429\pi$
$374$	−8.56188	+	6.35305i	−0.442724	+	0.328508i
$375$	−2.26843			−0.117141
$376$			4.89069i			0.252218i
$377$	−34.1995	−	34.1995i	−1.76136	−	1.76136i
$378$	6.21635			0.319734
$379$	−19.6872	−	19.6872i	−1.01126	−	1.01126i	−0.999936	−	0.0113269i	$-0.996394\pi$
$379$	−19.6872	−	19.6872i	−1.01126	−	1.01126i	−0.0113269	−	0.999936i	$-0.503606\pi$
$380$	−3.07862	+	3.07862i	−0.157930	+	0.157930i
$381$	10.8591	−	10.8591i	0.556329	−	0.556329i
$382$		−	9.52253i		−	0.487215i
$383$		−	0.426776i		−	0.0218073i	−0.999941	−	0.0109036i	$-0.996529\pi$
$383$		−	0.426776i		−	0.0218073i	0.999941	−	0.0109036i	$-0.00347080\pi$
$384$	1.60402	−	1.60402i	0.0818550	−	0.0818550i
$385$	−5.86568	+	5.86568i	−0.298943	+	0.298943i
$386$	11.6318	+	11.6318i	0.592045	+	0.592045i
$387$	15.4669			0.786227
$388$	12.5312	+	12.5312i	0.636175	+	0.636175i
$389$			0.807061i			0.0409196i	0.999791	+	0.0204598i	$0.00651302\pi$
$389$			0.807061i			0.0409196i	−0.999791	+	0.0204598i	$0.993487\pi$
$390$	12.8907			0.652746
$391$	11.8630	+	15.9876i	0.599939	+	0.808525i
$392$	−3.29156			−0.166249
$393$			23.5087i			1.18586i
$394$	−16.3414	−	16.3414i	−0.823267	−	0.823267i
$395$	−1.82921			−0.0920373
$396$	3.92341	+	3.92341i	0.197159	+	0.197159i
$397$	18.9138	−	18.9138i	0.949258	−	0.949258i	−0.0495157	−	0.998773i	$-0.515768\pi$
$397$	18.9138	−	18.9138i	0.949258	−	0.949258i	0.998773	+	0.0495157i	$0.0157678\pi$
$398$	6.99322	−	6.99322i	0.350539	−	0.350539i
$399$		−	31.6838i		−	1.58618i
$400$			1.00000i			0.0500000i
$401$	−10.9226	+	10.9226i	−0.545450	+	0.545450i	−0.925121	−	0.379671i	$-0.876037\pi$
$401$	−10.9226	+	10.9226i	−0.545450	+	0.545450i	0.379671	+	0.925121i	$0.376037\pi$
$402$	22.5733	−	22.5733i	1.12586	−	1.12586i
$403$	6.61471	+	6.61471i	0.329502	+	0.329502i
$404$	−7.65685			−0.380943
$405$	7.66006	+	7.66006i	0.380632	+	0.380632i
$406$			27.3039i			1.35507i
$407$	−11.3248			−0.561348
$408$	−5.57334	−	7.51107i	−0.275921	−	0.371853i
$409$	9.19581			0.454703			0.227352	−	0.973813i	$-0.426993\pi$
$409$	9.19581			0.454703			0.227352	+	0.973813i	$0.426993\pi$
$410$			7.83031i			0.386711i
$411$	−2.79285	−	2.79285i	−0.137761	−	0.137761i
$412$	7.58767			0.373817
$413$	18.1717	+	18.1717i	0.894170	+	0.894170i
$414$	7.32616	−	7.32616i	0.360061	−	0.360061i
$415$	−8.59647	+	8.59647i	−0.421984	+	0.421984i
$416$		−	5.68265i		−	0.278615i
$417$			1.88526i			0.0923216i
$418$	−7.96066	+	7.96066i	−0.389369	+	0.389369i
$419$	6.93774	−	6.93774i	0.338931	−	0.338931i	−0.517034	−	0.855965i	$-0.672964\pi$
$419$	6.93774	−	6.93774i	0.338931	−	0.338931i	0.855965	+	0.517034i	$0.172964\pi$
$420$	−5.14578	−	5.14578i	−0.251088	−	0.251088i
$421$	−17.0410			−0.830528			−0.415264	−	0.909701i	$-0.636311\pi$
$421$	−17.0410			−0.830528			−0.415264	+	0.909701i	$0.636311\pi$
$422$	11.8907	+	11.8907i	0.578830	+	0.578830i
$423$		−	10.4944i		−	0.510253i
$424$	1.14578			0.0556441
$425$	4.07862	+	0.604023i	0.197842	+	0.0292994i
$426$	14.0258			0.679552
$427$			20.5004i			0.992083i
$428$	3.85422	+	3.85422i	0.186301	+	0.186301i
$429$	33.3326			1.60931
$430$	5.09686	+	5.09686i	0.245792	+	0.245792i
$431$	13.8152	−	13.8152i	0.665455	−	0.665455i	−0.291206	−	0.956660i	$-0.594056\pi$
$431$	13.8152	−	13.8152i	0.665455	−	0.665455i	0.956660	+	0.291206i	$0.0940564\pi$
$432$	1.37019	−	1.37019i	0.0659231	−	0.0659231i
$433$		−	16.7404i		−	0.804491i	−0.915532	−	0.402245i	$-0.868230\pi$
$433$		−	16.7404i		−	0.804491i	0.915532	−	0.402245i	$-0.131770\pi$
$434$		−	5.28099i		−	0.253496i
$435$	−13.6520	+	13.6520i	−0.654561	+	0.654561i
$436$	6.01824	−	6.01824i	0.288221	−	0.288221i
$437$	14.8649	+	14.8649i	0.711085	+	0.711085i
$438$	−11.6446			−0.556401
$439$	7.98755	+	7.98755i	0.381225	+	0.381225i	0.871543	−	0.490318i	$-0.163120\pi$
$439$	7.98755	+	7.98755i	0.381225	+	0.381225i	−0.490318	+	0.871543i	$0.663120\pi$
$440$			2.58579i			0.123273i
$441$	7.06298			0.336332
$442$	−23.1774	−	3.43245i	−1.10243	−	0.163265i
$443$	−19.7084			−0.936376			−0.468188	−	0.883629i	$-0.655093\pi$
$443$	−19.7084			−0.936376			−0.468188	+	0.883629i	$0.655093\pi$
$444$		−	9.93487i		−	0.471488i
$445$	11.5205	+	11.5205i	0.546124	+	0.546124i
$446$	−9.25144			−0.438069
$447$	−3.92794	−	3.92794i	−0.185785	−	0.185785i
$448$	−2.26843	+	2.26843i	−0.107173	+	0.107173i
$449$	−6.43042	+	6.43042i	−0.303470	+	0.303470i	−0.842370	−	0.538900i	$-0.818840\pi$
$449$	−6.43042	+	6.43042i	−0.303470	+	0.303470i	0.538900	+	0.842370i	$0.318840\pi$
$450$		−	2.14578i		−	0.101153i
$451$			20.2475i			0.953418i
$452$	5.57823	−	5.57823i	0.262378	−	0.262378i
$453$	−7.27723	+	7.27723i	−0.341914	+	0.341914i
$454$	14.5205	+	14.5205i	0.681481	+	0.681481i
$455$	−18.2302			−0.854645
$456$	−6.98364	−	6.98364i	−0.327039	−	0.327039i
$457$			7.73959i			0.362043i	0.983479	+	0.181021i	$0.0579403\pi$
$457$			7.73959i			0.362043i	−0.983479	+	0.181021i	$0.942060\pi$
$458$	−15.1618			−0.708464
$459$	−4.76085	−	6.41609i	−0.222217	−	0.299478i
$460$	4.82843			0.225127
$461$		−	25.0045i		−	1.16458i	−0.812982	−	0.582289i	$-0.802157\pi$
$461$		−	25.0045i		−	1.16458i	0.812982	−	0.582289i	$-0.197843\pi$
$462$	−13.3059	−	13.3059i	−0.619046	−	0.619046i
$463$	−29.7745			−1.38374			−0.691868	−	0.722024i	$-0.743212\pi$
$463$	−29.7745			−1.38374			−0.691868	+	0.722024i	$0.743212\pi$
$464$	6.01824	+	6.01824i	0.279390	+	0.279390i
$465$	2.64050	−	2.64050i	0.122450	−	0.122450i
$466$	6.28745	−	6.28745i	0.291260	−	0.291260i
$467$			12.3104i			0.569659i	0.958578	+	0.284829i	$0.0919370\pi$
$467$			12.3104i			0.569659i	−0.958578	+	0.284829i	$0.908063\pi$
$468$			12.1937i			0.563655i
$469$	−31.9235	+	31.9235i	−1.47409	+	1.47409i
$470$	3.45824	−	3.45824i	0.159517	−	0.159517i
$471$	37.7065	+	37.7065i	1.73742	+	1.73742i
$472$	8.01068			0.368722
$473$	13.1794	+	13.1794i	0.605989	+	0.605989i
$474$		−	4.14943i		−	0.190590i
$475$	4.35383			0.199767
$476$	7.88189	+	10.6223i	0.361266	+	0.486871i
$477$	−2.45860			−0.112571
$478$		−	0.0827385i		−	0.00378437i
$479$	−4.61361	−	4.61361i	−0.210801	−	0.210801i	0.593807	−	0.804608i	$-0.297624\pi$
$479$	−4.61361	−	4.61361i	−0.210801	−	0.210801i	−0.804608	+	0.593807i	$0.797624\pi$
$480$	−2.26843			−0.103539
$481$	−17.5983	−	17.5983i	−0.802416	−	0.802416i
$482$	0.829206	−	0.829206i	0.0377693	−	0.0377693i
$483$	−24.8460	+	24.8460i	−1.13053	+	1.13053i
$484$		−	4.31371i		−	0.196078i
$485$		−	17.7218i		−	0.804704i
$486$	−13.2658	+	13.2658i	−0.601748	+	0.601748i
$487$	−9.85234	+	9.85234i	−0.446452	+	0.446452i	−0.894173	−	0.447721i	$-0.852236\pi$
$487$	−9.85234	+	9.85234i	−0.446452	+	0.446452i	0.447721	+	0.894173i	$0.352236\pi$
$488$	4.51863	+	4.51863i	0.204549	+	0.204549i
$489$	51.4825			2.32812
$490$	2.32749	+	2.32749i	0.105145	+	0.105145i
$491$			0.302247i			0.0136402i	0.999977	+	0.00682010i	$0.00217092\pi$
$491$			0.302247i			0.0136402i	−0.999977	+	0.00682010i	$0.997829\pi$
$492$	−17.7625			−0.800796
$493$	28.1813	−	20.9110i	1.26922	−	0.941782i
$494$	−24.7413			−1.11316
$495$		−	5.54853i		−	0.249388i
$496$	−1.16402	−	1.16402i	−0.0522660	−	0.0522660i
$497$	−19.8355			−0.889742
$498$	−19.5005	−	19.5005i	−0.873838	−	0.873838i
$499$	11.6941	−	11.6941i	0.523500	−	0.523500i	−0.395127	−	0.918627i	$-0.629299\pi$
$499$	11.6941	−	11.6941i	0.523500	−	0.523500i	0.918627	+	0.395127i	$0.129299\pi$
$500$	0.707107	−	0.707107i	0.0316228	−	0.0316228i
$501$		−	46.3125i		−	2.06909i
$502$		−	18.1245i		−	0.808937i
$503$	−0.399884	+	0.399884i	−0.0178300	+	0.0178300i	−0.715966	−	0.698136i	$-0.754013\pi$
$503$	−0.399884	+	0.399884i	−0.0178300	+	0.0178300i	0.698136	+	0.715966i	$0.254013\pi$
$504$	4.86756	−	4.86756i	0.216818	−	0.216818i
$505$	5.41421	+	5.41421i	0.240929	+	0.240929i
$506$	12.4853			0.555038
$507$	30.9456	+	30.9456i	1.37434	+	1.37434i
$508$			6.76992i			0.300367i
$509$	9.94842			0.440956			0.220478	−	0.975392i	$-0.429238\pi$
$509$	9.94842			0.440956			0.220478	+	0.975392i	$0.429238\pi$
$510$	−1.37019	+	9.25207i	−0.0606728	+	0.409689i
$511$	16.4680			0.728500
$512$			1.00000i			0.0441942i
$513$	−5.96555	−	5.96555i	−0.263386	−	0.263386i
$514$	−25.3539			−1.11831
$515$	−5.36529	−	5.36529i	−0.236423	−	0.236423i
$516$	−11.5619	+	11.5619i	−0.508983	+	0.508983i
$517$	8.94227	−	8.94227i	0.393281	−	0.393281i
$518$			14.0500i			0.617323i
$519$		−	21.3615i		−	0.937667i
$520$	−4.01824	+	4.01824i	−0.176211	+	0.176211i
$521$	−8.68265	+	8.68265i	−0.380394	+	0.380394i	−0.871244	−	0.490850i	$-0.836686\pi$
$521$	−8.68265	+	8.68265i	−0.380394	+	0.380394i	0.490850	+	0.871244i	$0.336686\pi$
$522$	−12.9138	−	12.9138i	−0.565223	−	0.565223i
$523$	13.1024			0.572927			0.286464	−	0.958091i	$-0.407520\pi$
$523$	13.1024			0.572927			0.286464	+	0.958091i	$0.407520\pi$
$524$	−7.32804	−	7.32804i	−0.320127	−	0.320127i
$525$			7.27723i			0.317605i
$526$	−2.11385			−0.0921681
$527$	−5.45069	+	4.04450i	−0.237436	+	0.176181i
$528$	−5.86568			−0.255271
$529$		−	0.313708i		−	0.0136395i
$530$	−0.810190	−	0.810190i	−0.0351924	−	0.0351924i
$531$	−17.1892			−0.745947
$532$	9.87636	+	9.87636i	0.428195	+	0.428195i
$533$	−31.4640	+	31.4640i	−1.36286	+	1.36286i
$534$	−26.1335	+	26.1335i	−1.13091	+	1.13091i
$535$		−	5.45069i		−	0.235654i
$536$			14.0729i			0.607859i
$537$	−10.6790	+	10.6790i	−0.460833	+	0.460833i
$538$	−15.1898	+	15.1898i	−0.654879	+	0.654879i
$539$	6.01838	+	6.01838i	0.259230	+	0.259230i
$540$	−1.93774			−0.0833868
$541$	7.74601	+	7.74601i	0.333027	+	0.333027i	0.853735	−	0.520708i	$-0.174332\pi$
$541$	7.74601	+	7.74601i	0.333027	+	0.333027i	−0.520708	+	0.853735i	$0.674332\pi$
$542$			22.5922i			0.970418i
$543$	0.273958			0.0117567
$544$	4.07862	+	0.604023i	0.174869	+	0.0258973i
$545$	−8.51107			−0.364574
$546$		−	41.3539i		−	1.76979i
$547$	10.2981	+	10.2981i	0.440316	+	0.440316i	0.892118	−	0.451802i	$-0.149219\pi$
$547$	10.2981	+	10.2981i	0.440316	+	0.440316i	−0.451802	+	0.892118i	$0.649219\pi$
$548$	1.74115			0.0743782
$549$	−9.69599	−	9.69599i	−0.413815	−	0.413815i
$550$	1.82843	−	1.82843i	0.0779644	−	0.0779644i
$551$	26.2024	−	26.2024i	1.11626	−	1.11626i
$552$			10.9530i			0.466189i
$553$			5.86818i			0.249540i
$554$	−18.0756	+	18.0756i	−0.767959	+	0.767959i
$555$	−7.02501	+	7.02501i	−0.298195	+	0.298195i
$556$	−0.587666	−	0.587666i	−0.0249226	−	0.0249226i
$557$	−5.85876			−0.248243			−0.124122	−	0.992267i	$-0.539611\pi$
$557$	−5.85876			−0.248243			−0.124122	+	0.992267i	$0.539611\pi$
$558$	2.49773	+	2.49773i	0.105737	+	0.105737i
$559$			40.9608i			1.73246i
$560$	3.20805			0.135565
$561$	−3.54301	+	23.9239i	−0.149586	+	1.01007i
$562$	15.8248			0.667528
$563$			15.8330i			0.667280i	0.942701	+	0.333640i	$0.108277\pi$
$563$			15.8330i			0.667280i	−0.942701	+	0.333640i	$0.891723\pi$
$564$	7.84478	+	7.84478i	0.330325	+	0.330325i
$565$	−7.88881			−0.331885
$566$	−12.4325	−	12.4325i	−0.522575	−	0.522575i
$567$	24.5738	−	24.5738i	1.03200	−	1.03200i
$568$	−4.37207	+	4.37207i	−0.183448	+	0.183448i
$569$		−	15.0288i		−	0.630039i	−0.949085	−	0.315019i	$-0.897989\pi$
$569$		−	15.0288i		−	0.630039i	0.949085	−	0.315019i	$-0.102011\pi$
$570$			9.87636i			0.413675i
$571$	4.81410	−	4.81410i	0.201464	−	0.201464i	−0.599163	−	0.800627i	$-0.704500\pi$
$571$	4.81410	−	4.81410i	0.201464	−	0.201464i	0.800627	+	0.599163i	$0.204500\pi$
$572$	−10.3903	+	10.3903i	−0.434440	+	0.434440i
$573$	−15.2744	−	15.2744i	−0.638096	−	0.638096i
$574$	25.1200			1.04849
$575$	−3.41421	−	3.41421i	−0.142383	−	0.142383i
$576$		−	2.14578i		−	0.0894076i
$577$	−22.6806			−0.944204			−0.472102	−	0.881544i	$-0.656505\pi$
$577$	−22.6806			−0.944204			−0.472102	+	0.881544i	$0.656505\pi$
$578$	4.92717	−	16.2703i	0.204943	−	0.676756i
$579$	37.3155			1.55078
$580$		−	8.51107i		−	0.353403i
$581$	27.5779	+	27.5779i	1.14412	+	1.14412i
$582$	40.2006			1.66637
$583$	−2.09498	−	2.09498i	−0.0867652	−	0.0867652i
$584$	3.62981	−	3.62981i	0.150203	−	0.150203i
$585$	8.62226	−	8.62226i	0.356487	−	0.356487i
$586$		−	29.6524i		−	1.22493i
$587$		−	40.9919i		−	1.69192i	−0.533248	−	0.845959i	$-0.679029\pi$
$587$		−	40.9919i		−	1.69192i	0.533248	−	0.845959i	$-0.320971\pi$
$588$	−5.27975	+	5.27975i	−0.217733	+	0.217733i
$589$	−5.06794	+	5.06794i	−0.208821	+	0.208821i
$590$	−5.66441	−	5.66441i	−0.233200	−	0.233200i
$591$	−52.4239			−2.15643
$592$	3.09686	+	3.09686i	0.127280	+	0.127280i
$593$		−	12.4390i		−	0.510809i	−0.966834	−	0.255405i	$-0.917791\pi$
$593$		−	12.4390i		−	0.510809i	0.966834	−	0.255405i	$-0.0822087\pi$
$594$	−5.01057			−0.205586
$595$	1.93774	−	13.0844i	0.0794394	−	0.536408i
$596$	2.44881			0.100307
$597$		−	22.4346i		−	0.918187i
$598$	19.4018	+	19.4018i	0.793397	+	0.793397i
$599$	−15.4382			−0.630789			−0.315395	−	0.948961i	$-0.602137\pi$
$599$	−15.4382			−0.630789			−0.315395	+	0.948961i	$0.602137\pi$
$600$	1.60402	+	1.60402i	0.0654840	+	0.0654840i
$601$	1.63560	−	1.63560i	0.0667176	−	0.0667176i	−0.672961	−	0.739678i	$-0.734978\pi$
$601$	1.63560	−	1.63560i	0.0667176	−	0.0667176i	0.739678	+	0.672961i	$0.234978\pi$
$602$	16.3510	−	16.3510i	0.666415	−	0.666415i
$603$		−	30.1975i		−	1.22974i
$604$		−	4.53686i		−	0.184602i
$605$	−3.05025	+	3.05025i	−0.124010	+	0.124010i
$606$	−12.2818	+	12.2818i	−0.498913	+	0.498913i
$607$	−18.4798	−	18.4798i	−0.750070	−	0.750070i	0.224422	−	0.974492i	$-0.427951\pi$
$607$	−18.4798	−	18.4798i	−0.750070	−	0.750070i	−0.974492	+	0.224422i	$0.927951\pi$
$608$	4.35383			0.176571
$609$	43.7961	+	43.7961i	1.77471	+	1.77471i
$610$		−	6.39030i		−	0.258736i
$611$	27.7921			1.12435
$612$	−8.75183	−	1.29610i	−0.353772	−	0.0523918i
$613$	41.1938			1.66380			0.831902	−	0.554923i	$-0.187252\pi$
$613$	41.1938			1.66380			0.831902	+	0.554923i	$0.187252\pi$
$614$			32.0116i			1.29188i
$615$	12.5600	+	12.5600i	0.506468	+	0.506468i
$616$	8.29532			0.334228
$617$	26.9435	+	26.9435i	1.08471	+	1.08471i	0.996064	+	0.0886418i	$0.0282526\pi$
$617$	26.9435	+	26.9435i	1.08471	+	1.08471i	0.0886418	+	0.996064i	$0.471747\pi$
$618$	12.1708	−	12.1708i	0.489581	−	0.489581i
$619$	−24.1574	+	24.1574i	−0.970966	+	0.970966i	−0.999590	−	0.0286241i	$-0.990887\pi$
$619$	−24.1574	+	24.1574i	−0.970966	+	0.970966i	0.0286241	+	0.999590i	$0.490887\pi$
$620$			1.64617i			0.0661118i
$621$			9.35621i			0.375452i
$622$	−8.72792	+	8.72792i	−0.349958	+	0.349958i
$623$	36.9583	−	36.9583i	1.48070	−	1.48070i
$624$	−9.11510	−	9.11510i	−0.364896	−	0.364896i
$625$	−1.00000			−0.0400000
$626$	1.39030	+	1.39030i	0.0555677	+	0.0555677i
$627$			25.5382i			1.01990i
$628$	−23.5074			−0.938048
$629$	14.5015	−	10.7603i	0.578212	−	0.429043i
$630$	−6.88377			−0.274256
$631$		−	31.9751i		−	1.27291i	−0.771314	−	0.636454i	$-0.780400\pi$
$631$		−	31.9751i		−	1.27291i	0.771314	−	0.636454i	$-0.219600\pi$
$632$	1.29344	+	1.29344i	0.0514504	+	0.0514504i
$633$	38.1459			1.51616
$634$	8.08540	+	8.08540i	0.321112	+	0.321112i
$635$	4.78706	−	4.78706i	0.189969	−	0.189969i
$636$	1.83786	−	1.83786i	0.0728759	−	0.0728759i
$637$			18.7048i			0.741111i
$638$		−	22.0078i		−	0.871298i
$639$	9.38150	−	9.38150i	0.371126	−	0.371126i
$640$	0.707107	−	0.707107i	0.0279508	−	0.0279508i
$641$	−32.0152	−	32.0152i	−1.26453	−	1.26453i	−0.948876	−	0.315649i	$-0.897778\pi$
$641$	−32.0152	−	32.0152i	−1.26453	−	1.26453i	−0.315649	−	0.948876i	$-0.602222\pi$
$642$	12.3645			0.487988
$643$	−24.9629	−	24.9629i	−0.984439	−	0.984439i	0.0154416	−	0.999881i	$-0.495085\pi$
$643$	−24.9629	−	24.9629i	−0.984439	−	0.984439i	−0.999881	+	0.0154416i	$0.995085\pi$
$644$		−	15.4898i		−	0.610384i
$645$	16.3510			0.643818
$646$	2.62981	−	17.7576i	0.103469	−	0.698664i
$647$	−24.6950			−0.970861			−0.485430	−	0.874275i	$-0.661337\pi$
$647$	−24.6950			−0.970861			−0.485430	+	0.874275i	$0.661337\pi$
$648$		−	10.8330i		−	0.425559i
$649$	−14.6469	−	14.6469i	−0.574943	−	0.574943i
$650$	5.68265			0.222892
$651$	−8.47084	−	8.47084i	−0.331998	−	0.331998i
$652$	−16.0479	+	16.0479i	−0.628486	+	0.628486i
$653$	11.2541	−	11.2541i	0.440407	−	0.440407i	−0.451742	−	0.892149i	$-0.649197\pi$
$653$	11.2541	−	11.2541i	0.440407	−	0.440407i	0.892149	+	0.451742i	$0.149197\pi$
$654$		−	19.3068i		−	0.754955i
$655$			10.3634i			0.404932i
$656$	5.53686	−	5.53686i	0.216178	−	0.216178i
$657$	−7.78879	+	7.78879i	−0.303870	+	0.303870i
$658$	−11.0942	−	11.0942i	−0.432497	−	0.432497i
$659$	2.52086			0.0981989			0.0490994	−	0.998794i	$-0.484365\pi$
$659$	2.52086			0.0981989			0.0490994	+	0.998794i	$0.484365\pi$
$660$	4.14766	+	4.14766i	0.161448	+	0.161448i
$661$			12.1208i			0.471443i	0.971821	+	0.235722i	$0.0757454\pi$
$661$			12.1208i			0.471443i	−0.971821	+	0.235722i	$0.924255\pi$
$662$	18.4784			0.718182
$663$	−42.6828	+	31.6713i	−1.65766	+	1.23001i
$664$	12.1572			0.471793
$665$		−	13.9673i		−	0.541628i
$666$	−6.64518	−	6.64518i	−0.257496	−	0.257496i
$667$	−41.0951			−1.59121
$668$	14.4364	+	14.4364i	0.558559	+	0.558559i
$669$	−14.8395	+	14.8395i	−0.573729	+	0.573729i
$670$	9.95108	−	9.95108i	0.384444	−	0.384444i
$671$		−	16.5240i		−	0.637900i
$672$			7.27723i			0.280725i
$673$	−16.4469	+	16.4469i	−0.633981	+	0.633981i	−0.949064	−	0.315083i	$-0.897968\pi$
$673$	−16.4469	+	16.4469i	−0.633981	+	0.633981i	0.315083	+	0.949064i	$0.397968\pi$
$674$	1.83708	−	1.83708i	0.0707618	−	0.0707618i
$675$	1.37019	+	1.37019i	0.0527385	+	0.0527385i
$676$	−19.2925			−0.742018
$677$	−1.45511	−	1.45511i	−0.0559245	−	0.0559245i	0.678591	−	0.734516i	$-0.262591\pi$
$677$	−1.45511	−	1.45511i	−0.0559245	−	0.0559245i	−0.734516	+	0.678591i	$0.762591\pi$
$678$		−	17.8952i		−	0.687262i
$679$	−56.8523			−2.18179
$680$	−2.45691	−	3.31113i	−0.0942183	−	0.126976i
$681$	46.5825			1.78504
$682$			4.25665i			0.162995i
$683$	−9.73834	−	9.73834i	−0.372627	−	0.372627i	0.495806	−	0.868433i	$-0.334873\pi$
$683$	−9.73834	−	9.73834i	−0.372627	−	0.372627i	−0.868433	+	0.495806i	$0.834873\pi$
$684$	−9.34237			−0.357214
$685$	−1.23118	−	1.23118i	−0.0470409	−	0.0470409i
$686$	−8.41233	+	8.41233i	−0.321184	+	0.321184i
$687$	−24.3199	+	24.3199i	−0.927860	+	0.927860i
$688$		−	7.20805i		−	0.274804i
$689$		−	6.51107i		−	0.248052i
$690$	7.74491	−	7.74491i	0.294844	−	0.294844i
$691$	14.3615	−	14.3615i	0.546338	−	0.546338i	−0.379041	−	0.925380i	$-0.623746\pi$
$691$	14.3615	−	14.3615i	0.546338	−	0.546338i	0.925380	+	0.379041i	$0.123746\pi$
$692$	6.65873	+	6.65873i	0.253127	+	0.253127i
$693$	−17.8000			−0.676164
$694$	−9.15522	−	9.15522i	−0.347527	−	0.347527i
$695$			0.831086i			0.0315249i
$696$	19.3068			0.731822
$697$	−19.2384	−	25.9272i	−0.728705	−	0.982061i
$698$	20.3698			0.771009
$699$		−	20.1704i		−	0.762916i
$700$	−2.26843	−	2.26843i	−0.0857387	−	0.0857387i
$701$	−41.7527			−1.57698			−0.788489	−	0.615048i	$-0.789136\pi$
$701$	−41.7527			−1.57698			−0.788489	+	0.615048i	$0.789136\pi$
$702$	−7.78628	−	7.78628i	−0.293874	−	0.293874i
$703$	13.4832	−	13.4832i	0.508528	−	0.508528i
$704$	1.82843	−	1.82843i	0.0689114	−	0.0689114i
$705$		−	11.0942i		−	0.417832i
$706$			33.1680i			1.24830i
$707$	17.3691	−	17.3691i	0.653230	−	0.653230i
$708$	12.8493	−	12.8493i	0.482907	−	0.482907i
$709$	−36.3578	−	36.3578i	−1.36545	−	1.36545i	−0.866811	−	0.498637i	$-0.833834\pi$
$709$	−36.3578	−	36.3578i	−1.36545	−	1.36545i	−0.498637	−	0.866811i	$-0.666166\pi$
$710$	6.18303			0.232045
$711$	−2.77545	−	2.77545i	−0.104087	−	0.104087i
$712$		−	16.2925i		−	0.610586i
$713$	7.94842			0.297671
$714$	29.6811	+	4.39562i	1.11079	+	0.164502i
$715$	14.6941			0.549528
$716$		−	6.65763i		−	0.248807i
$717$	−0.132714	−	0.132714i	−0.00495631	−	0.00495631i
$718$	−17.2272			−0.642914
$719$	31.1026	+	31.1026i	1.15993	+	1.15993i	0.984490	+	0.175443i	$0.0561359\pi$
$719$	31.1026	+	31.1026i	1.15993	+	1.15993i	0.175443	+	0.984490i	$0.443864\pi$
$720$	−1.51730	+	1.51730i	−0.0565463	+	0.0565463i
$721$	−17.2121	+	17.2121i	−0.641012	+	0.641012i
$722$			0.0441757i			0.00164405i
$723$		−	2.66013i		−	0.0989313i
$724$	−0.0853971	+	0.0853971i	−0.00317376	+	0.00317376i
$725$	−6.01824	+	6.01824i	−0.223512	+	0.223512i
$726$	−6.91929	−	6.91929i	−0.256799	−	0.256799i
$727$	34.1619			1.26699			0.633497	−	0.773745i	$-0.281619\pi$
$727$	34.1619			1.26699			0.633497	+	0.773745i	$0.281619\pi$
$728$	12.8907	+	12.8907i	0.477761	+	0.477761i
$729$			10.0583i			0.372530i
$730$	−5.13333			−0.189993
$731$	−29.3989	−	4.35383i	−1.08736	−	0.161032i
$732$	14.4960			0.535786
$733$			9.63393i			0.355837i	0.984045	+	0.177919i	$0.0569364\pi$
$733$			9.63393i			0.355837i	−0.984045	+	0.177919i	$0.943064\pi$
$734$	16.4879	+	16.4879i	0.608581	+	0.608581i
$735$	7.46669			0.275413
$736$	−3.41421	−	3.41421i	−0.125850	−	0.125850i
$737$	25.7314	−	25.7314i	0.947827	−	0.947827i
$738$	−11.8809	+	11.8809i	−0.437342	+	0.437342i
$739$			34.3768i			1.26457i	0.774736	+	0.632285i	$0.217883\pi$
$739$			34.3768i			1.26457i	−0.774736	+	0.632285i	$0.782117\pi$
$740$		−	4.37962i		−	0.160998i
$741$	−39.6856	+	39.6856i	−1.45789	+	1.45789i
$742$	−2.59913	+	2.59913i	−0.0954170	+	0.0954170i
$743$	10.4068	+	10.4068i	0.381789	+	0.381789i	0.871746	−	0.489958i	$-0.162988\pi$
$743$	10.4068	+	10.4068i	0.381789	+	0.381789i	−0.489958	+	0.871746i	$0.662988\pi$
$744$	−3.73423			−0.136903
$745$	−1.73157	−	1.73157i	−0.0634398	−	0.0634398i
$746$			10.6098i			0.388453i
$747$	−26.0868			−0.954466
$748$	−6.35305	−	8.56188i	−0.232291	−	0.313053i
$749$	−17.4861			−0.638927
$750$		−	2.26843i		−	0.0828314i
$751$	−2.95895	−	2.95895i	−0.107974	−	0.107974i	0.651056	−	0.759030i	$-0.274326\pi$
$751$	−2.95895	−	2.95895i	−0.107974	−	0.107974i	−0.759030	+	0.651056i	$0.774326\pi$
$752$	−4.89069			−0.178345
$753$	−29.0722	−	29.0722i	−1.05945	−	1.05945i
$754$	34.1995	−	34.1995i	1.24547	−	1.24547i
$755$	−3.20805	+	3.20805i	−0.116753	+	0.116753i
$756$			6.21635i			0.226086i
$757$			23.3964i			0.850357i	0.905110	+	0.425178i	$0.139789\pi$
$757$			23.3964i			0.850357i	−0.905110	+	0.425178i	$0.860211\pi$
$758$	19.6872	−	19.6872i	0.715071	−	0.715071i
$759$	20.0267	−	20.0267i	0.726923	−	0.726923i
$760$	−3.07862	−	3.07862i	−0.111673	−	0.111673i
$761$	26.2704			0.952302			0.476151	−	0.879363i	$-0.342032\pi$
$761$	26.2704			0.952302			0.476151	+	0.879363i	$0.342032\pi$
$762$	10.8591	+	10.8591i	0.393384	+	0.393384i
$763$			27.3039i			0.988468i
$764$	9.52253			0.344513
$765$	5.27200	+	7.10496i	0.190609	+	0.256880i
$766$	0.426776			0.0154201
$767$		−	45.5219i		−	1.64370i
$768$	1.60402	+	1.60402i	0.0578802	+	0.0578802i
$769$	27.1033			0.977369			0.488685	−	0.872461i	$-0.337477\pi$
$769$	27.1033			0.977369			0.488685	+	0.872461i	$0.337477\pi$
$770$	−5.86568	−	5.86568i	−0.211384	−	0.211384i
$771$	−40.6683	+	40.6683i	−1.46463	+	1.46463i
$772$	−11.6318	+	11.6318i	−0.418639	+	0.418639i
$773$		−	31.6782i		−	1.13939i	−0.821857	−	0.569693i	$-0.807062\pi$
$773$		−	31.6782i		−	1.13939i	0.821857	−	0.569693i	$-0.192938\pi$
$774$			15.4669i			0.555946i
$775$	1.16402	−	1.16402i	0.0418128	−	0.0418128i
$776$	−12.5312	+	12.5312i	−0.449843	+	0.449843i
$777$	22.5366	+	22.5366i	0.808495	+	0.808495i
$778$	−0.807061			−0.0289345
$779$	−24.1066	−	24.1066i	−0.863707	−	0.863707i
$780$			12.8907i			0.461561i
$781$	15.9880			0.572096
$782$	−15.9876	+	11.8630i	−0.571714	+	0.424221i
$783$	16.4922			0.589383
$784$		−	3.29156i		−	0.117556i
$785$	16.6223	+	16.6223i	0.593274	+	0.593274i
$786$	−23.5087			−0.838527
$787$	−12.3579	−	12.3579i	−0.440513	−	0.440513i	0.451671	−	0.892184i	$-0.350828\pi$
$787$	−12.3579	−	12.3579i	−0.440513	−	0.440513i	−0.892184	+	0.451671i	$0.850828\pi$
$788$	16.3414	−	16.3414i	0.582138	−	0.582138i
$789$	−3.39066	+	3.39066i	−0.120711	+	0.120711i
$790$		−	1.82921i		−	0.0650802i
$791$			25.3077i			0.899837i
$792$	−3.92341	+	3.92341i	−0.139412	+	0.139412i
$793$	25.6777	−	25.6777i	0.911844	−	0.911844i
$794$	18.9138	+	18.9138i	0.671227	+	0.671227i
$795$	−2.59913			−0.0921816
$796$	6.99322	+	6.99322i	0.247868	+	0.247868i
$797$		−	14.1900i		−	0.502634i	−0.967905	−	0.251317i	$-0.919136\pi$
$797$		−	14.1900i		−	0.502634i	0.967905	−	0.251317i	$-0.0808637\pi$
$798$	31.6838			1.12160
$799$	−2.95409	+	19.9473i	−0.104508	+	0.705684i
$800$	−1.00000			−0.0353553
$801$			34.9601i			1.23525i
$802$	−10.9226	−	10.9226i	−0.385691	−	0.385691i
$803$	−13.2737			−0.468419
$804$	22.5733	+	22.5733i	0.796100	+	0.796100i
$805$	−10.9530	+	10.9530i	−0.386041	+	0.386041i
$806$	−6.61471	+	6.61471i	−0.232993	+	0.232993i
$807$			48.7296i			1.71536i
$808$		−	7.65685i		−	0.269367i
$809$	17.2453	−	17.2453i	0.606312	−	0.606312i	−0.335668	−	0.941980i	$-0.608962\pi$
$809$	17.2453	−	17.2453i	0.606312	−	0.606312i	0.941980	+	0.335668i	$0.108962\pi$
$810$	−7.66006	+	7.66006i	−0.269147	+	0.269147i
$811$	−9.10566	−	9.10566i	−0.319743	−	0.319743i	0.528925	−	0.848668i	$-0.322595\pi$
$811$	−9.10566	−	9.10566i	−0.319743	−	0.319743i	−0.848668	+	0.528925i	$0.822595\pi$
$812$	−27.3039			−0.958180
$813$	36.2384	+	36.2384i	1.27094	+	1.27094i
$814$		−	11.3248i		−	0.396933i
$815$	22.6952			0.794978
$816$	7.51107	−	5.57334i	0.262940	−	0.195106i
$817$	−31.3826			−1.09794
$818$			9.19581i			0.321524i
$819$	−27.6606	−	27.6606i	−0.966540	−	0.966540i
$820$	−7.83031			−0.273446
$821$	13.4527	+	13.4527i	0.469503	+	0.469503i	0.901754	−	0.432251i	$-0.142280\pi$
$821$	13.4527	+	13.4527i	0.469503	+	0.469503i	−0.432251	+	0.901754i	$0.642280\pi$
$822$	2.79285	−	2.79285i	0.0974117	−	0.0974117i
$823$	−11.4872	+	11.4872i	−0.400417	+	0.400417i	−0.878380	−	0.477963i	$-0.841375\pi$
$823$	−11.4872	+	11.4872i	−0.400417	+	0.400417i	0.477963	+	0.878380i	$0.341375\pi$
$824$			7.58767i			0.264329i
$825$		−	5.86568i		−	0.204217i
$826$	−18.1717	+	18.1717i	−0.632274	+	0.632274i
$827$	−12.4889	+	12.4889i	−0.434283	+	0.434283i	−0.890082	−	0.455800i	$-0.849353\pi$
$827$	−12.4889	+	12.4889i	−0.434283	+	0.434283i	0.455800	+	0.890082i	$0.349353\pi$
$828$	7.32616	+	7.32616i	0.254602	+	0.254602i
$829$	−1.81004			−0.0628654			−0.0314327	−	0.999506i	$-0.510007\pi$
$829$	−1.81004			−0.0628654			−0.0314327	+	0.999506i	$0.510007\pi$
$830$	−8.59647	−	8.59647i	−0.298388	−	0.298388i
$831$			57.9874i			2.01156i
$832$	5.68265			0.197010
$833$	−13.4250	−	1.98818i	−0.465150	−	0.0688864i
$834$	−1.88526			−0.0652813
$835$		−	20.4161i		−	0.706528i
$836$	−7.96066	−	7.96066i	−0.275325	−	0.275325i
$837$	−3.18984			−0.110257
$838$	6.93774	+	6.93774i	0.239660	+	0.239660i
$839$	19.0797	−	19.0797i	0.658705	−	0.658705i	−0.296368	−	0.955074i	$-0.595776\pi$
$839$	19.0797	−	19.0797i	0.658705	−	0.658705i	0.955074	+	0.296368i	$0.0957756\pi$
$840$	5.14578	−	5.14578i	0.177546	−	0.177546i
$841$			43.4384i			1.49787i
$842$		−	17.0410i		−	0.587272i
$843$	25.3833	−	25.3833i	0.874248	−	0.874248i
$844$	−11.8907	+	11.8907i	−0.409294	+	0.409294i
$845$	13.6418	+	13.6418i	0.469293	+	0.469293i
$846$	10.4944			0.360803
$847$	9.78535	+	9.78535i	0.336229	+	0.336229i
$848$			1.14578i			0.0393463i
$849$	−39.8839			−1.36881
$850$	−0.604023	+	4.07862i	−0.0207178	+	0.139896i
$851$	−21.1467			−0.724899
$852$			14.0258i			0.480516i
$853$	−12.8918	−	12.8918i	−0.441407	−	0.441407i	0.451078	−	0.892485i	$-0.351040\pi$
$853$	−12.8918	−	12.8918i	−0.441407	−	0.441407i	−0.892485	+	0.451078i	$0.851040\pi$
$854$	−20.5004			−0.701509
$855$	6.60605	+	6.60605i	0.225922	+	0.225922i
$856$	−3.85422	+	3.85422i	−0.131734	+	0.131734i
$857$	−7.32470	+	7.32470i	−0.250207	+	0.250207i	−0.821055	−	0.570848i	$-0.806614\pi$
$857$	−7.32470	+	7.32470i	−0.250207	+	0.250207i	0.570848	+	0.821055i	$0.306614\pi$
$858$			33.3326i			1.13796i
$859$			54.5456i			1.86107i	0.366202	+	0.930535i	$0.380658\pi$
$859$			54.5456i			1.86107i	−0.366202	+	0.930535i	$0.619342\pi$
$860$	−5.09686	+	5.09686i	−0.173801	+	0.173801i
$861$	40.2931	−	40.2931i	1.37318	−	1.37318i
$862$	13.8152	+	13.8152i	0.470548	+	0.470548i
$863$	1.42063			0.0483589			0.0241794	−	0.999708i	$-0.492303\pi$
$863$	1.42063			0.0483589			0.0241794	+	0.999708i	$0.492303\pi$
$864$	1.37019	+	1.37019i	0.0466147	+	0.0466147i
$865$		−	9.41687i		−	0.320183i
$866$	16.7404			0.568861
$867$	−18.1947	−	34.0012i	−0.617923	−	1.15474i
$868$	5.28099			0.179249
$869$		−	4.72994i		−	0.160452i
$870$	−13.6520	−	13.6520i	−0.462845	−	0.462845i
$871$	79.9716			2.70973
$872$	6.01824	+	6.01824i	0.203803	+	0.203803i
$873$	26.8892	−	26.8892i	0.910062	−	0.910062i
$874$	−14.8649	+	14.8649i	−0.502813	+	0.502813i
$875$			3.20805i			0.108452i
$876$		−	11.6446i		−	0.393435i
$877$	20.4621	−	20.4621i	0.690958	−	0.690958i	−0.271485	−	0.962443i	$-0.587515\pi$
$877$	20.4621	−	20.4621i	0.690958	−	0.690958i	0.962443	+	0.271485i	$0.0875147\pi$
$878$	−7.98755	+	7.98755i	−0.269567	+	0.269567i
$879$	−47.5632	−	47.5632i	−1.60427	−	1.60427i
$880$	−2.58579			−0.0871668
$881$	13.0607	+	13.0607i	0.440026	+	0.440026i	0.892021	−	0.451994i	$-0.149287\pi$
$881$	13.0607	+	13.0607i	0.440026	+	0.440026i	−0.451994	+	0.892021i	$0.649287\pi$
$882$			7.06298i			0.237823i
$883$	13.7927			0.464162			0.232081	−	0.972696i	$-0.425446\pi$
$883$	13.7927			0.464162			0.232081	+	0.972696i	$0.425446\pi$
$884$	3.43245	−	23.1774i	0.115446	−	0.779539i
$885$	−18.1717			−0.610835
$886$		−	19.7084i		−	0.662118i
$887$	−14.8015	−	14.8015i	−0.496987	−	0.496987i	0.413512	−	0.910499i	$-0.364302\pi$
$887$	−14.8015	−	14.8015i	−0.496987	−	0.496987i	−0.910499	+	0.413512i	$0.864302\pi$
$888$	9.93487			0.333392
$889$	−15.3571	−	15.3571i	−0.515061	−	0.515061i
$890$	−11.5205	+	11.5205i	−0.386168	+	0.386168i
$891$	−19.8073	+	19.8073i	−0.663569	+	0.663569i
$892$		−	9.25144i		−	0.309761i
$893$			21.2932i			0.712551i
$894$	3.92794	−	3.92794i	0.131370	−	0.131370i
$895$	−4.70766	+	4.70766i	−0.157360	+	0.157360i
$896$	−2.26843	−	2.26843i	−0.0757830	−	0.0757830i
$897$	62.2418			2.07819
$898$	−6.43042	−	6.43042i	−0.214586	−	0.214586i
$899$		−	14.0107i		−	0.467282i
$900$	2.14578			0.0715261
$901$	4.67321	+	0.692079i	0.155687	+	0.0230565i
$902$	−20.2475			−0.674168
$903$		−	52.4546i		−	1.74558i
$904$	5.57823	+	5.57823i	0.185529	+	0.185529i
$905$	0.120770			0.00401452
$906$	−7.27723	−	7.27723i	−0.241770	−	0.241770i
$907$	−20.0606	+	20.0606i	−0.666103	+	0.666103i	−0.956812	−	0.290709i	$-0.906109\pi$
$907$	−20.0606	+	20.0606i	−0.666103	+	0.666103i	0.290709	+	0.956812i	$0.406109\pi$
$908$	−14.5205	+	14.5205i	−0.481880	+	0.481880i
$909$			16.4299i			0.544947i
$910$		−	18.2302i		−	0.604325i
$911$	−19.9375	+	19.9375i	−0.660560	+	0.660560i	−0.955512	−	0.294952i	$-0.904696\pi$
$911$	−19.9375	+	19.9375i	−0.660560	+	0.660560i	0.294952	+	0.955512i	$0.404696\pi$
$912$	6.98364	−	6.98364i	0.231252	−	0.231252i
$913$	−22.2286	−	22.2286i	−0.735660	−	0.735660i
$914$	−7.73959			−0.256003
$915$	−10.2502	−	10.2502i	−0.338861	−	0.338861i
$916$		−	15.1618i		−	0.500959i
$917$	33.2463			1.09789
$918$	6.41609	−	4.76085i	0.211763	−	0.157131i
$919$	5.49805			0.181364			0.0906820	−	0.995880i	$-0.471095\pi$
$919$	5.49805			0.181364			0.0906820	+	0.995880i	$0.471095\pi$
$920$			4.82843i			0.159189i
$921$	51.3473	+	51.3473i	1.69195	+	1.69195i
$922$	25.0045			0.823481
$923$	24.8449	+	24.8449i	0.817780	+	0.817780i
$924$	13.3059	−	13.3059i	0.437732	−	0.437732i
$925$	−3.09686	+	3.09686i	−0.101824	+	0.101824i
$926$		−	29.7745i		−	0.978449i
$927$		−	16.2815i		−	0.534754i
$928$	−6.01824	+	6.01824i	−0.197558	+	0.197558i
$929$	7.24530	−	7.24530i	0.237711	−	0.237711i	−0.578191	−	0.815901i	$-0.696241\pi$
$929$	7.24530	−	7.24530i	0.237711	−	0.237711i	0.815901	+	0.578191i	$0.196241\pi$
$930$	2.64050	+	2.64050i	0.0865853	+	0.0865853i
$931$	−14.3309			−0.469676
$932$	6.28745	+	6.28745i	0.205952	+	0.205952i
$933$			27.9996i			0.916665i
$934$	−12.3104			−0.402810
$935$	−1.56188	+	10.5464i	−0.0510788	+	0.344906i
$936$	−12.1937			−0.398564
$937$			18.3456i			0.599326i	0.954045	+	0.299663i	$0.0968743\pi$
$937$			18.3456i			0.599326i	−0.954045	+	0.299663i	$0.903126\pi$
$938$	−31.9235	−	31.9235i	−1.04234	−	1.04234i
$939$	4.46016			0.145552
$940$	3.45824	+	3.45824i	0.112795	+	0.112795i
$941$	−0.741002	+	0.741002i	−0.0241560	+	0.0241560i	−0.719082	−	0.694926i	$-0.755437\pi$
$941$	−0.741002	+	0.741002i	−0.0241560	+	0.0241560i	0.694926	+	0.719082i	$0.255437\pi$
$942$	−37.7065	+	37.7065i	−1.22854	+	1.22854i
$943$			37.8081i			1.23120i
$944$			8.01068i			0.260726i
$945$	4.39562	−	4.39562i	0.142990	−	0.142990i
$946$	−13.1794	+	13.1794i	−0.428499	+	0.428499i
$947$	25.4030	+	25.4030i	0.825487	+	0.825487i	0.986889	−	0.161402i	$-0.0516015\pi$
$947$	25.4030	+	25.4030i	0.825487	+	0.825487i	−0.161402	+	0.986889i	$0.551601\pi$
$948$	4.14943			0.134767
$949$	−20.6269	−	20.6269i	−0.669579	−	0.669579i
$950$			4.35383i			0.141257i
$951$	25.9383			0.841108
$952$	−10.6223	+	7.88189i	−0.344269	+	0.255453i
$953$	0.289066			0.00936376			0.00468188	−	0.999989i	$-0.498510\pi$
$953$	0.289066			0.00936376			0.00468188	+	0.999989i	$0.498510\pi$
$954$		−	2.45860i		−	0.0796001i
$955$	−6.73345	−	6.73345i	−0.217889	−	0.217889i
$956$	0.0827385			0.00267595
$957$	−35.3011	−	35.3011i	−1.14112	−	1.14112i
$958$	4.61361	−	4.61361i	0.149059	−	0.149059i
$959$	−3.94968	+	3.94968i	−0.127542	+	0.127542i
$960$		−	2.26843i		−	0.0732133i
$961$		−	28.2901i		−	0.912585i
$962$	17.5983	−	17.5983i	0.567394	−	0.567394i
$963$	8.27031	−	8.27031i	0.266507	−	0.266507i
$964$	0.829206	+	0.829206i	0.0267069	+	0.0267069i
$965$	16.4499			0.529541
$966$	−24.8460	−	24.8460i	−0.799408	−	0.799408i
$967$		−	31.1696i		−	1.00235i	−0.865347	−	0.501173i	$-0.832902\pi$
$967$		−	31.1696i		−	1.00235i	0.865347	−	0.501173i	$-0.167098\pi$
$968$	4.31371			0.138648
$969$	−24.2654	−	32.7019i	−0.779516	−	1.05054i
$970$	17.7218			0.569012
$971$			19.6962i			0.632081i	0.948746	+	0.316041i	$0.102354\pi$
$971$			19.6962i			0.632081i	−0.948746	+	0.316041i	$0.897646\pi$
$972$	−13.2658	−	13.2658i	−0.425500	−	0.425500i
$973$	2.66616			0.0854732
$974$	−9.85234	−	9.85234i	−0.315689	−	0.315689i
$975$	9.11510	−	9.11510i	0.291917	−	0.291917i
$976$	−4.51863	+	4.51863i	−0.144638	+	0.144638i
$977$		−	20.4047i		−	0.652806i	−0.945231	−	0.326403i	$-0.894163\pi$
$977$		−	20.4047i		−	0.652806i	0.945231	−	0.326403i	$-0.105837\pi$
$978$			51.4825i			1.64623i
$979$	−29.7896	+	29.7896i	−0.952079	+	0.952079i
$980$	−2.32749	+	2.32749i	−0.0743489	+	0.0743489i
$981$	−12.9138	−	12.9138i	−0.412307	−	0.412307i
$982$	−0.302247			−0.00964508
$983$	−16.9814	−	16.9814i	−0.541623	−	0.541623i	0.382382	−	0.924004i	$-0.375104\pi$
$983$	−16.9814	−	16.9814i	−0.541623	−	0.541623i	−0.924004	+	0.382382i	$0.875104\pi$
$984$		−	17.7625i		−	0.566248i
$985$	−23.1102			−0.736352
$986$	20.9110	+	28.1813i	0.665941	+	0.897474i
$987$	−35.5907			−1.13286
$988$		−	24.7413i		−	0.787124i
$989$	24.6098	+	24.6098i	0.782546	+	0.782546i
$990$	5.54853			0.176344
$991$	18.5907	+	18.5907i	0.590552	+	0.590552i	0.937781	−	0.347228i	$-0.112877\pi$
$991$	18.5907	+	18.5907i	0.590552	+	0.590552i	−0.347228	+	0.937781i	$0.612877\pi$
$992$	1.16402	−	1.16402i	0.0369576	−	0.0369576i
$993$	29.6397	−	29.6397i	0.940588	−	0.940588i
$994$		−	19.8355i		−	0.629143i
$995$		−	9.88991i		−	0.313531i
$996$	19.5005	−	19.5005i	0.617897	−	0.617897i
$997$	−23.5532	+	23.5532i	−0.745937	+	0.745937i	−0.973713	−	0.227777i	$-0.926854\pi$
$997$	−23.5532	+	23.5532i	−0.745937	+	0.745937i	0.227777	+	0.973713i	$0.426854\pi$
$998$	11.6941	+	11.6941i	0.370170	+	0.370170i
$999$	8.48654			0.268502

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.h.b.81.3	yes	8
3.2	odd	2		1530.2.q.g.1441.2		8
4.3	odd	2		1360.2.bt.b.81.2		8
5.2	odd	4		850.2.g.i.149.3		8
5.3	odd	4		850.2.g.l.149.2		8
5.4	even	2		850.2.h.n.251.2		8
17.2	even	8		2890.2.a.bd.1.4		4
17.4	even	4	inner	170.2.h.b.21.3	✓	8
17.8	even	8		2890.2.b.o.2311.3		8
17.9	even	8		2890.2.b.o.2311.6		8
17.15	even	8		2890.2.a.be.1.1		4
51.38	odd	4		1530.2.q.g.361.2		8
68.55	odd	4		1360.2.bt.b.1041.2		8
85.4	even	4		850.2.h.n.701.2		8
85.38	odd	4		850.2.g.i.599.3		8
85.72	odd	4		850.2.g.l.599.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.h.b.21.3	✓	8	17.4	even	4	inner
170.2.h.b.81.3	yes	8	1.1	even	1	trivial
850.2.g.i.149.3		8	5.2	odd	4
850.2.g.i.599.3		8	85.38	odd	4
850.2.g.l.149.2		8	5.3	odd	4
850.2.g.l.599.2		8	85.72	odd	4
850.2.h.n.251.2		8	5.4	even	2
850.2.h.n.701.2		8	85.4	even	4
1360.2.bt.b.81.2		8	4.3	odd	2
1360.2.bt.b.1041.2		8	68.55	odd	4
1530.2.q.g.361.2		8	51.38	odd	4
1530.2.q.g.1441.2		8	3.2	odd	2
2890.2.a.bd.1.4		4	17.2	even	8
2890.2.a.be.1.1		4	17.15	even	8
2890.2.b.o.2311.3		8	17.8	even	8
2890.2.b.o.2311.6		8	17.9	even	8

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.60402 + 1.60402i) q^{3} -1.00000 q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.60402 + 1.60402i) q^{6} +(2.26843 - 2.26843i) q^{7} -1.00000i q^{8} +2.14578i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.60402 + 1.60402i) q^{3} -1.00000 q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.60402 + 1.60402i) q^{6} +(2.26843 - 2.26843i) q^{7} -1.00000i q^{8} +2.14578i q^{9} +(-0.707107 + 0.707107i) q^{10} +(-1.82843 + 1.82843i) q^{11} +(-1.60402 - 1.60402i) q^{12} -5.68265 q^{13} +(2.26843 + 2.26843i) q^{14} +2.26843i q^{15} +1.00000 q^{16} +(0.604023 - 4.07862i) q^{17} -2.14578 q^{18} -4.35383i q^{19} +(-0.707107 - 0.707107i) q^{20} +7.27723 q^{21} +(-1.82843 - 1.82843i) q^{22} +(-3.41421 + 3.41421i) q^{23} +(1.60402 - 1.60402i) q^{24} +1.00000i q^{25} -5.68265i q^{26} +(1.37019 - 1.37019i) q^{27} +(-2.26843 + 2.26843i) q^{28} +(6.01824 + 6.01824i) q^{29} -2.26843 q^{30} +(-1.16402 - 1.16402i) q^{31} +1.00000i q^{32} -5.86568 q^{33} +(4.07862 + 0.604023i) q^{34} +3.20805 q^{35} -2.14578i q^{36} +(3.09686 + 3.09686i) q^{37} +4.35383 q^{38} +(-9.11510 - 9.11510i) q^{39} +(0.707107 - 0.707107i) q^{40} +(5.53686 - 5.53686i) q^{41} +7.27723i q^{42} -7.20805i q^{43} +(1.82843 - 1.82843i) q^{44} +(-1.51730 + 1.51730i) q^{45} +(-3.41421 - 3.41421i) q^{46} -4.89069 q^{47} +(1.60402 + 1.60402i) q^{48} -3.29156i q^{49} -1.00000 q^{50} +(7.51107 - 5.57334i) q^{51} +5.68265 q^{52} +1.14578i q^{53} +(1.37019 + 1.37019i) q^{54} -2.58579 q^{55} +(-2.26843 - 2.26843i) q^{56} +(6.98364 - 6.98364i) q^{57} +(-6.01824 + 6.01824i) q^{58} +8.01068i q^{59} -2.26843i q^{60} +(-4.51863 + 4.51863i) q^{61} +(1.16402 - 1.16402i) q^{62} +(4.86756 + 4.86756i) q^{63} -1.00000 q^{64} +(-4.01824 - 4.01824i) q^{65} -5.86568i q^{66} -14.0729 q^{67} +(-0.604023 + 4.07862i) q^{68} -10.9530 q^{69} +3.20805i q^{70} +(-4.37207 - 4.37207i) q^{71} +2.14578 q^{72} +(3.62981 + 3.62981i) q^{73} +(-3.09686 + 3.09686i) q^{74} +(-1.60402 + 1.60402i) q^{75} +4.35383i q^{76} +8.29532i q^{77} +(9.11510 - 9.11510i) q^{78} +(-1.29344 + 1.29344i) q^{79} +(0.707107 + 0.707107i) q^{80} +10.8330 q^{81} +(5.53686 + 5.53686i) q^{82} +12.1572i q^{83} -7.27723 q^{84} +(3.31113 - 2.45691i) q^{85} +7.20805 q^{86} +19.3068i q^{87} +(1.82843 + 1.82843i) q^{88} +16.2925 q^{89} +(-1.51730 - 1.51730i) q^{90} +(-12.8907 + 12.8907i) q^{91} +(3.41421 - 3.41421i) q^{92} -3.73423i q^{93} -4.89069i q^{94} +(3.07862 - 3.07862i) q^{95} +(-1.60402 + 1.60402i) q^{96} +(-12.5312 - 12.5312i) q^{97} +3.29156 q^{98} +(-3.92341 - 3.92341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 4 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 - 4 * q^7	\( 8 q - 8 q^{4} - 4 q^{7} + 8 q^{11} - 12 q^{13} - 4 q^{14} + 8 q^{16} - 8 q^{17} - 28 q^{18} + 16 q^{21} + 8 q^{22} - 16 q^{23} + 12 q^{27} + 4 q^{28} + 24 q^{29} + 4 q^{30} + 4 q^{31} + 16 q^{33} + 12 q^{34} - 20 q^{37} + 20 q^{38} - 4 q^{39} - 8 q^{44} - 8 q^{45} - 16 q^{46} + 20 q^{47} - 8 q^{50} + 4 q^{51} + 12 q^{52} + 12 q^{54} - 32 q^{55} + 4 q^{56} + 40 q^{57} - 24 q^{58} - 16 q^{61} - 4 q^{62} - 64 q^{63} - 8 q^{64} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 8 q^{69} + 4 q^{71} + 28 q^{72} + 28 q^{73} + 20 q^{74} + 4 q^{78} + 8 q^{79} - 8 q^{81} - 16 q^{84} + 8 q^{85} + 32 q^{86} - 8 q^{88} - 44 q^{89} - 8 q^{90} - 44 q^{91} + 16 q^{92} + 4 q^{95} + 20 q^{97} + 48 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 4 * q^7 + 8 * q^11 - 12 * q^13 - 4 * q^14 + 8 * q^16 - 8 * q^17 - 28 * q^18 + 16 * q^21 + 8 * q^22 - 16 * q^23 + 12 * q^27 + 4 * q^28 + 24 * q^29 + 4 * q^30 + 4 * q^31 + 16 * q^33 + 12 * q^34 - 20 * q^37 + 20 * q^38 - 4 * q^39 - 8 * q^44 - 8 * q^45 - 16 * q^46 + 20 * q^47 - 8 * q^50 + 4 * q^51 + 12 * q^52 + 12 * q^54 - 32 * q^55 + 4 * q^56 + 40 * q^57 - 24 * q^58 - 16 * q^61 - 4 * q^62 - 64 * q^63 - 8 * q^64 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 8 * q^69 + 4 * q^71 + 28 * q^72 + 28 * q^73 + 20 * q^74 + 4 * q^78 + 8 * q^79 - 8 * q^81 - 16 * q^84 + 8 * q^85 + 32 * q^86 - 8 * q^88 - 44 * q^89 - 8 * q^90 - 44 * q^91 + 16 * q^92 + 4 * q^95 + 20 * q^97 + 48 * q^98 - 4 * q^99

Introduction

L-functions

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