LMFDB - Embedded newform 637.2.k.i.459.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(459,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("637.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (of order $6$, degree $2$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			459.1
Root			$1.32725 - 0.488273i$ of defining polynomial
Character	$\chi$	$=$	637.459
Dual form			637.2.k.i.569.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58860i q^{2} +(0.259233 + 0.449005i) q^{3} -4.70085 q^{4} +(1.39608 - 0.806027i) q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +O(q^{10})$	\(q-2.58860i q^{2} +(0.259233 + 0.449005i) q^{3} -4.70085 q^{4} +(1.39608 - 0.806027i) q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +(-2.08648 - 3.61389i) q^{10} +(2.34256 - 1.35248i) q^{11} +(-1.21862 - 2.11070i) q^{12} +(-2.36840 - 2.71858i) q^{13} +(0.723819 + 0.417897i) q^{15} +8.69632 q^{16} +3.12661 q^{17} +(-6.12277 - 3.53498i) q^{18} +(-3.18828 - 1.84075i) q^{19} +(-6.56276 + 3.78901i) q^{20} +(-3.50103 - 6.06396i) q^{22} -1.98604 q^{23} +(-3.13918 + 1.81241i) q^{24} +(-1.20064 + 2.07957i) q^{25} +(-7.03732 + 6.13084i) q^{26} +2.97143 q^{27} +(2.68636 - 4.65290i) q^{29} +(1.08177 - 1.87368i) q^{30} +(-9.07425 - 5.23902i) q^{31} -8.52843i q^{32} +(1.21454 + 0.701214i) q^{33} -8.09354i q^{34} +(-6.41947 + 11.1188i) q^{36} +5.95346i q^{37} +(-4.76497 + 8.25317i) q^{38} +(0.606687 - 1.76817i) q^{39} +(5.63528 + 9.76059i) q^{40} +(6.66970 + 3.85075i) q^{41} +(-1.67800 - 2.90638i) q^{43} +(-11.0120 + 6.35780i) q^{44} -4.40283i q^{45} +5.14106i q^{46} +(-0.913730 + 0.527542i) q^{47} +(2.25437 + 3.90469i) q^{48} +(5.38318 + 3.10798i) q^{50} +(0.810520 + 1.40386i) q^{51} +(11.1335 + 12.7796i) q^{52} +(-3.63284 + 6.29226i) q^{53} -7.69184i q^{54} +(2.18027 - 3.77633i) q^{55} -1.90873i q^{57} +(-12.0445 - 6.95390i) q^{58} -11.4241i q^{59} +(-3.40257 - 1.96447i) q^{60} +(-1.46254 + 2.53319i) q^{61} +(-13.5617 + 23.4896i) q^{62} -4.68406 q^{64} +(-5.49772 - 1.88636i) q^{65} +(1.81516 - 3.14395i) q^{66} +(11.7622 - 6.79091i) q^{67} -14.6977 q^{68} +(-0.514846 - 0.891740i) q^{69} +(1.17009 - 0.675554i) q^{71} +(16.5367 + 9.54747i) q^{72} +(7.88374 + 4.55168i) q^{73} +15.4111 q^{74} -1.24498 q^{75} +(14.9876 + 8.65311i) q^{76} +(-4.57708 - 1.57047i) q^{78} +(3.10289 + 5.37436i) q^{79} +(12.1407 - 7.00946i) q^{80} +(-3.32650 - 5.76166i) q^{81} +(9.96806 - 17.2652i) q^{82} -2.69672i q^{83} +(4.36499 - 2.52013i) q^{85} +(-7.52346 + 4.34367i) q^{86} +2.78557 q^{87} +(9.45576 + 16.3779i) q^{88} -1.75988i q^{89} -11.3972 q^{90} +9.33607 q^{92} -5.43251i q^{93} +(1.36560 + 2.36528i) q^{94} -5.93478 q^{95} +(3.82930 - 2.21085i) q^{96} +(13.4078 - 7.74102i) q^{97} -7.38776i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9	$ 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9} - 12 q^{10} + 12 q^{11} + q^{12} + 2 q^{13} - 12 q^{15} + 16 q^{16} + 34 q^{17} + 3 q^{18} - 9 q^{19} + 3 q^{20} - 15 q^{22} - 6 q^{23} - 15 q^{24} - 5 q^{25} + 6 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{31} + 6 q^{33} - 13 q^{36} - 19 q^{38} - 4 q^{39} + q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} + 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{55} - 24 q^{58} - 30 q^{60} - 5 q^{61} - 41 q^{62} + 2 q^{64} + 21 q^{65} + 34 q^{66} + 15 q^{67} - 22 q^{68} - 7 q^{69} + 30 q^{71} + 57 q^{72} - 42 q^{73} + 66 q^{74} + 2 q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} + 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 57 q^{86} + 20 q^{87} - 14 q^{88} - 66 q^{92} - q^{94} - 4 q^{95} - 21 q^{96} + 3 q^{97}+O(q^{100}) $ 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9 - 12 * q^10 + 12 * q^11 + q^12 + 2 * q^13 - 12 * q^15 + 16 * q^16 + 34 * q^17 + 3 * q^18 - 9 * q^19 + 3 * q^20 - 15 * q^22 - 6 * q^23 - 15 * q^24 - 5 * q^25 + 6 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^31 + 6 * q^33 - 13 * q^36 - 19 * q^38 - 4 * q^39 + q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 + 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 + 7 * q^52 - 8 * q^53 + 15 * q^55 - 24 * q^58 - 30 * q^60 - 5 * q^61 - 41 * q^62 + 2 * q^64 + 21 * q^65 + 34 * q^66 + 15 * q^67 - 22 * q^68 - 7 * q^69 + 30 * q^71 + 57 * q^72 - 42 * q^73 + 66 * q^74 + 2 * q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 + 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 57 * q^86 + 20 * q^87 - 14 * q^88 - 66 * q^92 - q^94 - 4 * q^95 - 21 * q^96 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	2.58860i		−	1.83042i	−0.402981	−	0.915209i	$-0.632026\pi$
$2$		−	2.58860i		−	1.83042i	0.402981	−	0.915209i	$-0.367974\pi$
$3$	0.259233	+	0.449005i	0.149668	+	0.259233i	0.931105	−	0.364752i	$-0.118846\pi$
$3$	0.259233	+	0.449005i	0.149668	+	0.259233i	−0.781437	+	0.623985i	$0.785513\pi$
$4$	−4.70085			−2.35043
$5$	1.39608	−	0.806027i	0.624346	−	0.360466i	−0.154213	−	0.988038i	$-0.549284\pi$
$5$	1.39608	−	0.806027i	0.624346	−	0.360466i	0.778559	+	0.627571i	$0.215951\pi$
$6$	1.16229	−	0.671051i	0.474504	−	0.273955i
$7$		0			0
$7$		0			0
$8$			6.99143i			2.47184i
$9$	1.36560	−	2.36528i	0.455199	−	0.788428i
$10$	−2.08648	−	3.61389i	−0.659803	−	1.14281i
$11$	2.34256	−	1.35248i	0.706309	−	0.407788i	−0.103384	−	0.994642i	$-0.532967\pi$
$11$	2.34256	−	1.35248i	0.706309	−	0.407788i	0.809693	+	0.586854i	$0.199634\pi$
$12$	−1.21862	−	2.11070i	−0.351784	−	0.609308i
$13$	−2.36840	−	2.71858i	−0.656876	−	0.753998i
$13$	−2.36840	−	2.71858i	−0.656876	−	0.753998i
$14$		0			0
$15$	0.723819	+	0.417897i	0.186889	+	0.107901i
$16$	8.69632			2.17408
$17$	3.12661			0.758314			0.379157	−	0.925332i	$-0.376214\pi$
$17$	3.12661			0.758314			0.379157	+	0.925332i	$0.376214\pi$
$18$	−6.12277	−	3.53498i	−1.44315	−	0.833204i
$19$	−3.18828	−	1.84075i	−0.731441	−	0.422297i	0.0875083	−	0.996164i	$-0.472110\pi$
$19$	−3.18828	−	1.84075i	−0.731441	−	0.422297i	−0.818949	+	0.573866i	$0.805443\pi$
$20$	−6.56276	+	3.78901i	−1.46748	+	0.847249i
$21$		0			0
$22$	−3.50103	−	6.06396i	−0.746421	−	1.29284i
$23$	−1.98604			−0.414117			−0.207059	−	0.978329i	$-0.566389\pi$
$23$	−1.98604			−0.414117			−0.207059	+	0.978329i	$0.566389\pi$
$24$	−3.13918	+	1.81241i	−0.640783	+	0.369956i
$25$	−1.20064	+	2.07957i	−0.240128	+	0.415914i
$26$	−7.03732	+	6.13084i	−1.38013	+	1.20236i
$27$	2.97143			0.571852
$28$		0			0
$29$	2.68636	−	4.65290i	0.498844	−	0.864023i	−0.501155	−	0.865357i	$-0.667092\pi$
$29$	2.68636	−	4.65290i	0.498844	−	0.864023i	0.999999	+	0.00133469i	$0.000424845\pi$
$30$	1.08177	−	1.87368i	0.197503	−	0.342086i
$31$	−9.07425	−	5.23902i	−1.62978	−	0.940956i	−0.984156	−	0.177303i	$-0.943263\pi$
$31$	−9.07425	−	5.23902i	−1.62978	−	0.940956i	−0.645627	−	0.763653i	$-0.723404\pi$
$32$		−	8.52843i		−	1.50763i
$33$	1.21454	+	0.701214i	0.211424	+	0.122066i
$34$		−	8.09354i		−	1.38803i
$35$		0			0
$36$	−6.41947	+	11.1188i	−1.06991	+	1.85314i
$37$			5.95346i			0.978743i	0.872075	+	0.489371i	$0.162774\pi$
$37$			5.95346i			0.978743i	−0.872075	+	0.489371i	$0.837226\pi$
$38$	−4.76497	+	8.25317i	−0.772981	+	1.33884i
$39$	0.606687	−	1.76817i	0.0971477	−	0.283134i
$40$	5.63528	+	9.76059i	0.891016	+	1.54329i
$41$	6.66970	+	3.85075i	1.04163	+	0.601386i	0.920295	−	0.391225i	$-0.127949\pi$
$41$	6.66970	+	3.85075i	1.04163	+	0.601386i	0.121337	+	0.992611i	$0.461282\pi$
$42$		0			0
$43$	−1.67800	−	2.90638i	−0.255892	−	0.443219i	0.709245	−	0.704962i	$-0.249036\pi$
$43$	−1.67800	−	2.90638i	−0.255892	−	0.443219i	−0.965138	+	0.261743i	$0.915703\pi$
$44$	−11.0120	+	6.35780i	−1.66013	+	0.958475i
$45$		−	4.40283i		−	0.656335i
$46$			5.14106i			0.758008i
$47$	−0.913730	+	0.527542i	−0.133281	+	0.0769500i	−0.565158	−	0.824983i	$-0.691185\pi$
$47$	−0.913730	+	0.527542i	−0.133281	+	0.0769500i	0.431877	+	0.901933i	$0.357852\pi$
$48$	2.25437	+	3.90469i	0.325390	+	0.563593i
$49$		0			0
$50$	5.38318	+	3.10798i	0.761297	+	0.439535i
$51$	0.810520	+	1.40386i	0.113495	+	0.196580i
$52$	11.1335	+	12.7796i	1.54394	+	1.77222i
$53$	−3.63284	+	6.29226i	−0.499009	+	0.864308i	−0.999999	−	0.00114437i	$-0.999636\pi$
$53$	−3.63284	+	6.29226i	−0.499009	+	0.864308i	0.500991	+	0.865453i	$0.332969\pi$
$54$		−	7.69184i		−	1.04673i
$55$	2.18027	−	3.77633i	0.293987	−	0.509201i
$56$		0			0
$57$		−	1.90873i		−	0.252818i
$58$	−12.0445	−	6.95390i	−1.58152	−	0.913092i
$59$		−	11.4241i		−	1.48729i	−0.668577	−	0.743643i	$-0.733096\pi$
$59$		−	11.4241i		−	1.48729i	0.668577	−	0.743643i	$-0.266904\pi$
$60$	−3.40257	−	1.96447i	−0.439270	−	0.253613i
$61$	−1.46254	+	2.53319i	−0.187259	+	0.324341i	−0.944335	−	0.328985i	$-0.893294\pi$
$61$	−1.46254	+	2.53319i	−0.187259	+	0.324341i	0.757077	+	0.653326i	$0.226627\pi$
$62$	−13.5617	+	23.4896i	−1.72234	+	2.98318i
$63$		0			0
$64$	−4.68406			−0.585507
$65$	−5.49772	−	1.88636i	−0.681909	−	0.233974i
$66$	1.81516	−	3.14395i	0.223431	−	0.386994i
$67$	11.7622	−	6.79091i	1.43698	−	0.829642i	0.439343	−	0.898320i	$-0.355211\pi$
$67$	11.7622	−	6.79091i	1.43698	−	0.829642i	0.997639	+	0.0686778i	$0.0218780\pi$
$68$	−14.6977			−1.78236
$69$	−0.514846	−	0.891740i	−0.0619802	−	0.107353i
$70$		0			0
$71$	1.17009	−	0.675554i	0.138865	−	0.0801736i	−0.428958	−	0.903324i	$-0.641119\pi$
$71$	1.17009	−	0.675554i	0.138865	−	0.0801736i	0.567823	+	0.823151i	$0.307786\pi$
$72$	16.5367	+	9.54747i	1.94887	+	1.12518i
$73$	7.88374	+	4.55168i	0.922721	+	0.532733i	0.884502	−	0.466536i	$-0.154498\pi$
$73$	7.88374	+	4.55168i	0.922721	+	0.532733i	0.0382192	+	0.999269i	$0.487831\pi$
$74$	15.4111			1.79151
$75$	−1.24498			−0.143758
$76$	14.9876	+	8.65311i	1.71920	+	0.992579i
$77$		0			0
$78$	−4.57708	−	1.57047i	−0.518252	−	0.177821i
$79$	3.10289	+	5.37436i	0.349102	+	0.604663i	0.986090	−	0.166211i	$-0.0531532\pi$
$79$	3.10289	+	5.37436i	0.349102	+	0.604663i	−0.636988	+	0.770874i	$0.719820\pi$
$80$	12.1407	−	7.00946i	1.35738	−	0.783682i
$81$	−3.32650	−	5.76166i	−0.369611	−	0.640185i
$82$	9.96806	−	17.2652i	1.10079	−	1.90662i
$83$		−	2.69672i		−	0.296003i	−0.988987	−	0.148002i	$-0.952716\pi$
$83$		−	2.69672i		−	0.296003i	0.988987	−	0.148002i	$-0.0472841\pi$
$84$		0			0
$85$	4.36499	−	2.52013i	0.473450	−	0.273346i
$86$	−7.52346	+	4.34367i	−0.811275	+	0.468390i
$87$	2.78557			0.298644
$88$	9.45576	+	16.3779i	1.00799	+	1.74589i
$89$		−	1.75988i		−	0.186546i	−0.995641	−	0.0932732i	$-0.970267\pi$
$89$		−	1.75988i		−	0.186546i	0.995641	−	0.0932732i	$-0.0297330\pi$
$90$	−11.3972			−1.20137
$91$		0			0
$92$	9.33607			0.973353
$93$		−	5.43251i		−	0.563325i
$94$	1.36560	+	2.36528i	0.140851	+	0.243960i
$95$	−5.93478			−0.608896
$96$	3.82930	−	2.21085i	0.390827	−	0.225644i
$97$	13.4078	−	7.74102i	1.36136	−	0.785981i	0.371555	−	0.928411i	$-0.378825\pi$
$97$	13.4078	−	7.74102i	1.36136	−	0.785981i	0.989805	+	0.142430i	$0.0454915\pi$
$98$		0			0
$99$		−	7.38776i		−	0.742498i
$100$	5.64404	−	9.77576i	0.564404	−	0.977576i
$101$	0.639651	+	1.10791i	0.0636477	+	0.110241i	0.896093	−	0.443866i	$-0.146393\pi$
$101$	0.639651	+	1.10791i	0.0636477	+	0.110241i	−0.832446	+	0.554107i	$0.813060\pi$
$102$	3.63404	−	2.09811i	0.359823	−	0.207744i
$103$	5.73367	+	9.93101i	0.564956	+	0.978532i	0.997054	+	0.0767054i	$0.0244401\pi$
$103$	5.73367	+	9.93101i	0.564956	+	0.978532i	−0.432098	+	0.901827i	$0.642227\pi$
$104$	19.0068	−	16.5585i	1.86377	−	1.62370i
$105$		0			0
$106$	16.2881	+	9.40397i	1.58204	+	0.913394i
$107$	−5.13525			−0.496444			−0.248222	−	0.968703i	$-0.579846\pi$
$107$	−5.13525			−0.496444			−0.248222	+	0.968703i	$0.579846\pi$
$108$	−13.9682			−1.34410
$109$	1.49635	+	0.863916i	0.143324	+	0.0827481i	0.569947	−	0.821681i	$-0.306964\pi$
$109$	1.49635	+	0.863916i	0.143324	+	0.0827481i	−0.426623	+	0.904429i	$0.640297\pi$
$110$	−9.77542	−	5.64384i	−0.932050	−	0.538119i
$111$	−2.67313	+	1.54333i	−0.253722	+	0.146487i
$112$		0			0
$113$	4.29556	+	7.44014i	0.404093	+	0.699909i	0.994215	−	0.107404i	$-0.0342540\pi$
$113$	4.29556	+	7.44014i	0.404093	+	0.699909i	−0.590123	+	0.807314i	$0.700921\pi$
$114$	−4.94095			−0.462762
$115$	−2.77267	+	1.60080i	−0.258552	+	0.149275i
$116$	−12.6282	+	21.8726i	−1.17250	+	2.03082i
$117$	−9.66449	+	1.88945i	−0.893482	+	0.174680i
$118$	−29.5723			−2.72235
$119$		0			0
$120$	−2.92170	+	5.06053i	−0.266714	+	0.461961i
$121$	−1.84160	+	3.18975i	−0.167419	+	0.289977i
$122$	6.55741	+	3.78592i	0.593680	+	0.342761i
$123$			3.99297i			0.360034i
$124$	42.6567	+	24.6279i	3.83069	+	2.21165i
$125$			11.9313i			1.06716i
$126$		0			0
$127$	−1.56206	+	2.70556i	−0.138610	+	0.240080i	−0.926971	−	0.375133i	$-0.877597\pi$
$127$	−1.56206	+	2.70556i	−0.138610	+	0.240080i	0.788361	+	0.615214i	$0.210930\pi$
$128$		−	4.93170i		−	0.435904i
$129$	0.869985	−	1.50686i	0.0765979	−	0.132671i
$130$	−4.88303	+	14.2314i	−0.428270	+	1.24818i
$131$	5.10460	+	8.84142i	0.445991	+	0.772479i	0.998121	−	0.0612793i	$-0.0195180\pi$
$131$	5.10460	+	8.84142i	0.445991	+	0.772479i	−0.552130	+	0.833758i	$0.686185\pi$
$132$	−5.70937	−	3.29630i	−0.496936	−	0.286906i
$133$		0			0
$134$	−17.5790	−	30.4476i	−1.51859	−	2.63028i
$135$	4.14835	−	2.39505i	0.357033	−	0.206133i
$136$			21.8595i			1.87443i
$137$		−	9.99261i		−	0.853726i	−0.904316	−	0.426863i	$-0.859619\pi$
$137$		−	9.99261i		−	0.853726i	0.904316	−	0.426863i	$-0.140381\pi$
$138$	−2.30836	+	1.33273i	−0.196501	+	0.113450i
$139$	−0.832100	−	1.44124i	−0.0705778	−	0.122244i	0.828577	−	0.559875i	$-0.189151\pi$
$139$	−0.832100	−	1.44124i	−0.0705778	−	0.122244i	−0.899155	+	0.437631i	$0.855818\pi$
$140$		0			0
$141$	−0.473738	−	0.273513i	−0.0398959	−	0.0230339i
$142$	−1.74874	−	3.02891i	−0.146751	−	0.254180i
$143$	−9.22495	−	3.16523i	−0.771429	−	0.264690i
$144$	11.8757	−	20.5692i	0.989638	−	1.71410i
$145$		−	8.66110i		−	0.719265i
$146$	11.7825	−	20.4078i	0.975124	−	1.68897i
$147$		0			0
$148$		−	27.9863i		−	2.30046i
$149$	17.1456	+	9.89902i	1.40462	+	0.810959i	0.994863	−	0.101234i	$-0.0322792\pi$
$149$	17.1456	+	9.89902i	1.40462	+	0.810959i	0.409760	+	0.912193i	$0.365613\pi$
$150$			3.22276i			0.263138i
$151$	−6.52544	−	3.76746i	−0.531033	−	0.306592i	0.210404	−	0.977614i	$-0.432522\pi$
$151$	−6.52544	−	3.76746i	−0.531033	−	0.306592i	−0.741437	+	0.671023i	$0.765855\pi$
$152$	12.8695	−	22.2906i	1.04385	−	1.80801i
$153$	4.26968	−	7.39531i	0.345183	−	0.597875i
$154$		0			0
$155$	−16.8912			−1.35673
$156$	−2.85195	+	8.31190i	−0.228339	+	0.665485i
$157$	7.00223	−	12.1282i	0.558839	−	0.967938i	−0.438755	−	0.898607i	$-0.644580\pi$
$157$	7.00223	−	12.1282i	0.558839	−	0.967938i	0.997594	−	0.0693309i	$-0.0220864\pi$
$158$	13.9121	−	8.03214i	1.10679	−	0.639003i
$159$	−3.76700			−0.298743
$160$	−6.87414	−	11.9064i	−0.543448	−	0.941280i
$161$		0			0
$162$	−14.9146	+	8.61097i	−1.17181	+	0.676542i
$163$	6.20936	+	3.58498i	0.486355	+	0.280797i	0.723061	−	0.690784i	$-0.242735\pi$
$163$	6.20936	+	3.58498i	0.486355	+	0.280797i	−0.236706	+	0.971581i	$0.576068\pi$
$164$	−31.3533	−	18.1018i	−2.44828	−	1.41351i
$165$	2.26079			0.176002
$166$	−6.98072			−0.541809
$167$	−15.5716	−	8.99027i	−1.20497	−	0.695688i	−0.243312	−	0.969948i	$-0.578234\pi$
$167$	−15.5716	−	8.99027i	−1.20497	−	0.695688i	−0.961656	+	0.274260i	$0.911567\pi$
$168$		0			0
$169$	−1.78135	+	12.8774i	−0.137027	+	0.990567i
$170$	−6.52361	−	11.2992i	−0.500338	−	0.866611i
$171$	−8.70780	+	5.02745i	−0.665902	+	0.384459i
$172$	7.88803	+	13.6625i	0.601456	+	1.04175i
$173$	6.40579	−	11.0952i	0.487023	−	0.843549i	−0.512865	−	0.858469i	$-0.671416\pi$
$173$	6.40579	−	11.0952i	0.487023	−	0.843549i	0.999889	+	0.0149198i	$0.00474930\pi$
$174$		−	7.21072i		−	0.546643i
$175$		0			0
$176$	20.3717	−	11.7616i	1.53557	−	0.886562i
$177$	5.12945	−	2.96149i	0.385553	−	0.222599i
$178$	−4.55561			−0.341458
$179$	0.920110	+	1.59368i	0.0687723	+	0.119117i	0.898361	−	0.439258i	$-0.144758\pi$
$179$	0.920110	+	1.59368i	0.0687723	+	0.119117i	−0.829589	+	0.558375i	$0.811425\pi$
$180$			20.6971i			1.54267i
$181$	3.29928			0.245234			0.122617	−	0.992454i	$-0.460871\pi$
$181$	3.29928			0.245234			0.122617	+	0.992454i	$0.460871\pi$
$182$		0			0
$183$	−1.51655			−0.112107
$184$		−	13.8852i		−	1.02363i
$185$	4.79865	+	8.31150i	0.352804	+	0.611074i
$186$	−14.0626			−1.03112
$187$	7.32427	−	4.22867i	0.535604	−	0.309231i
$188$	4.29531	−	2.47990i	0.313268	−	0.180865i
$189$		0			0
$190$			15.3628i			1.11453i
$191$	−2.44807	+	4.24018i	−0.177136	+	0.306809i	−0.940898	−	0.338689i	$-0.890017\pi$
$191$	−2.44807	+	4.24018i	−0.177136	+	0.306809i	0.763762	+	0.645498i	$0.223350\pi$
$192$	−1.21426	−	2.10316i	−0.0876318	−	0.151783i
$193$	2.61462	−	1.50955i	0.188204	−	0.108660i	−0.402937	−	0.915228i	$-0.632011\pi$
$193$	2.61462	−	1.50955i	0.188204	−	0.108660i	0.591142	+	0.806568i	$0.298677\pi$
$194$	−20.0384	−	34.7075i	−1.43867	−	2.49186i
$195$	−0.578207	−	2.95751i	−0.0414063	−	0.211792i
$196$		0			0
$197$	4.02694	+	2.32496i	0.286908	+	0.165646i	0.636546	−	0.771238i	$-0.280362\pi$
$197$	4.02694	+	2.32496i	0.286908	+	0.165646i	−0.349639	+	0.936885i	$0.613696\pi$
$198$	−19.1240			−1.35908
$199$	0.410721			0.0291152			0.0145576	−	0.999894i	$-0.495366\pi$
$199$	0.410721			0.0291152			0.0145576	+	0.999894i	$0.495366\pi$
$200$	−14.5392	−	8.39420i	−1.02808	−	0.593560i
$201$	6.09830	+	3.52085i	0.430141	+	0.248342i
$202$	2.86793	−	1.65580i	0.201787	−	0.116502i
$203$		0			0
$204$	−3.81013	−	6.59934i	−0.266763	−	0.462047i
$205$	12.4152			0.867118
$206$	25.7074	−	14.8422i	1.79112	−	1.03410i
$207$	−2.71213	+	4.69754i	−0.188506	+	0.326502i
$208$	−20.5964	−	23.6416i	−1.42810	−	1.63925i
$209$	−9.95831			−0.688831
$210$		0			0
$211$	3.75800	−	6.50905i	0.258711	−	0.448101i	−0.707186	−	0.707028i	$-0.750035\pi$
$211$	3.75800	−	6.50905i	0.258711	−	0.448101i	0.965897	+	0.258927i	$0.0833688\pi$
$212$	17.0774	−	29.5790i	1.17288	−	2.03149i
$213$	0.606654	+	0.350252i	0.0415672	+	0.0239989i
$214$			13.2931i			0.908699i
$215$	−4.68524	−	2.70502i	−0.319531	−	0.184481i
$216$			20.7745i			1.41353i
$217$		0			0
$218$	2.23633	−	3.87344i	0.151464	−	0.262343i
$219$			4.71978i			0.318933i
$220$	−10.2491	+	17.7520i	−0.690996	+	1.19684i
$221$	−7.40506	−	8.49993i	−0.498118	−	0.571767i
$222$	3.99507	+	6.91967i	0.268132	+	0.464418i
$223$	19.5544	+	11.2897i	1.30946	+	0.756016i	0.982006	−	0.188852i	$-0.0604766\pi$
$223$	19.5544	+	11.2897i	1.30946	+	0.756016i	0.327452	+	0.944868i	$0.393810\pi$
$224$		0			0
$225$	3.27918	+	5.67971i	0.218612	+	0.378648i
$226$	19.2595	−	11.1195i	1.28113	−	0.739658i
$227$			13.6717i			0.907424i	0.891148	+	0.453712i	$0.149901\pi$
$227$			13.6717i			0.907424i	−0.891148	+	0.453712i	$0.850099\pi$
$228$			8.97268i			0.594230i
$229$	−6.86832	+	3.96543i	−0.453872	+	0.262043i	−0.709464	−	0.704742i	$-0.751063\pi$
$229$	−6.86832	+	3.96543i	−0.453872	+	0.262043i	0.255592	+	0.966785i	$0.417730\pi$
$230$	4.14383	+	7.17733i	0.273236	+	0.473259i
$231$		0			0
$232$	32.5305	+	18.7815i	2.13573	+	1.23306i
$233$	−3.28585	−	5.69127i	−0.215263	−	0.372847i	0.738091	−	0.674702i	$-0.235728\pi$
$233$	−3.28585	−	5.69127i	−0.215263	−	0.372847i	−0.953354	+	0.301854i	$0.902394\pi$
$234$	4.89104	+	25.0175i	0.319738	+	1.63545i
$235$	−0.850427	+	1.47298i	−0.0554757	+	0.0960868i
$236$			53.7028i			3.49576i
$237$	−1.60874	+	2.78642i	−0.104499	+	0.180998i
$238$		0			0
$239$			9.39284i			0.607572i	0.952740	+	0.303786i	$0.0982508\pi$
$239$			9.39284i			0.607572i	−0.952740	+	0.303786i	$0.901749\pi$
$240$	6.29456	+	3.63417i	0.406312	+	0.234584i
$241$			10.0858i			0.649686i	0.945768	+	0.324843i	$0.105311\pi$
$241$			10.0858i			0.649686i	−0.945768	+	0.324843i	$0.894689\pi$
$242$	8.25699	+	4.76718i	0.530780	+	0.306446i
$243$	6.18182	−	10.7072i	0.396564	−	0.686869i
$244$	6.87517	−	11.9081i	0.440137	−	0.762340i
$245$		0			0
$246$	10.3362			0.659012
$247$	2.54689	+	13.0272i	0.162054	+	0.828902i
$248$	36.6282	−	63.4420i	2.32590	−	4.02857i
$249$	1.21084	−	0.699078i	0.0767337	−	0.0443022i
$250$	30.8853			1.95336
$251$	5.17427	+	8.96209i	0.326597	+	0.565682i	0.981834	−	0.189741i	$-0.0607648\pi$
$251$	5.17427	+	8.96209i	0.326597	+	0.565682i	−0.655237	+	0.755423i	$0.727431\pi$
$252$		0			0
$253$	−4.65242	+	2.68607i	−0.292495	+	0.168872i
$254$	7.00363	+	4.04355i	0.439447	+	0.253715i
$255$	2.26310	+	1.30660i	0.141721	+	0.0818225i
$256$	−22.1343			−1.38339
$257$	7.98658			0.498189			0.249095	−	0.968479i	$-0.419867\pi$
$257$	7.98658			0.498189			0.249095	+	0.968479i	$0.419867\pi$
$258$	−3.90065	−	2.25204i	−0.242844	−	0.140206i
$259$		0			0
$260$	25.8440	+	8.86749i	1.60278	+	0.549939i
$261$	−7.33696	−	12.7080i	−0.454146	−	0.786604i
$262$	22.8869	−	13.2138i	1.41396	−	0.816349i
$263$	−2.52967	−	4.38152i	−0.155986	−	0.270176i	0.777431	−	0.628968i	$-0.216522\pi$
$263$	−2.52967	−	4.38152i	−0.155986	−	0.270176i	−0.933418	+	0.358792i	$0.883189\pi$
$264$	−4.90249	+	8.49136i	−0.301727	+	0.522607i
$265$			11.7127i			0.719503i
$266$		0			0
$267$	0.790192	−	0.456218i	0.0483590	−	0.0279201i
$268$	−55.2924	+	31.9231i	−3.37752	+	1.95001i
$269$	−13.8902			−0.846902			−0.423451	−	0.905919i	$-0.639181\pi$
$269$	−13.8902			−0.846902			−0.423451	+	0.905919i	$0.639181\pi$
$270$	−6.19983	−	10.7384i	−0.377310	−	0.653519i
$271$			8.32721i			0.505842i	0.967487	+	0.252921i	$0.0813913\pi$
$271$			8.32721i			0.505842i	−0.967487	+	0.252921i	$0.918609\pi$
$272$	27.1900			1.64863
$273$		0			0
$274$	−25.8669			−1.56267
$275$			6.49537i			0.391685i
$276$	2.42022	+	4.19194i	0.145680	+	0.252325i
$277$	23.2116			1.39465			0.697325	−	0.716755i	$-0.254374\pi$
$277$	23.2116			1.39465			0.697325	+	0.716755i	$0.254374\pi$
$278$	−3.73080	+	2.15398i	−0.223758	+	0.129187i
$279$	−24.7835	+	14.3088i	−1.48375	+	0.856644i
$280$		0			0
$281$			27.1595i			1.62020i	0.586292	+	0.810100i	$0.300587\pi$
$281$			27.1595i			1.62020i	−0.586292	+	0.810100i	$0.699413\pi$
$282$	−0.708015	+	1.22632i	−0.0421617	+	0.0730262i
$283$	8.07563	+	13.9874i	0.480046	+	0.831464i	0.999738	−	0.0228894i	$-0.00728654\pi$
$283$	8.07563	+	13.9874i	0.480046	+	0.831464i	−0.519692	+	0.854354i	$0.673953\pi$
$284$	−5.50044	+	3.17568i	−0.326391	+	0.188442i
$285$	−1.53849	−	2.66474i	−0.0911323	−	0.157846i
$286$	−8.19351	+	23.8797i	−0.484493	+	1.41204i
$287$		0			0
$288$	−20.1721	−	11.6464i	−1.18865	−	0.686270i
$289$	−7.22433			−0.424960
$290$	−22.4201			−1.31656
$291$	6.95151	+	4.01345i	0.407504	+	0.235273i
$292$	−37.0603	−	21.3968i	−2.16879	−	1.25215i
$293$	12.6831	−	7.32260i	0.740956	−	0.427791i	−0.0814609	−	0.996677i	$-0.525959\pi$
$293$	12.6831	−	7.32260i	0.740956	−	0.427791i	0.822417	+	0.568885i	$0.192625\pi$
$294$		0			0
$295$	−9.20810	−	15.9489i	−0.536116	−	0.928580i
$296$	−41.6232			−2.41930
$297$	6.96075	−	4.01879i	0.403904	−	0.233194i
$298$	25.6246	−	44.3831i	1.48439	−	2.57104i
$299$	4.70373	+	5.39920i	0.272024	+	0.312244i
$300$	5.85248			0.337893
$301$		0			0
$302$	−9.75246	+	16.8918i	−0.561191	+	0.972011i
$303$	−0.331637	+	0.574412i	−0.0190521	+	0.0329991i
$304$	−27.7263	−	16.0078i	−1.59021	−	0.918108i
$305$			4.71537i			0.270001i
$306$	−19.1435	−	11.0525i	−1.09436	−	0.631830i
$307$			8.97844i			0.512427i	0.966620	+	0.256213i	$0.0824750\pi$
$307$			8.97844i			0.512427i	−0.966620	+	0.256213i	$0.917525\pi$
$308$		0			0
$309$	−2.97271	+	5.14889i	−0.169112	+	0.292910i
$310$			43.7245i			2.48338i
$311$	−6.09080	+	10.5496i	−0.345378	+	0.598212i	−0.985422	−	0.170126i	$-0.945583\pi$
$311$	−6.09080	+	10.5496i	−0.345378	+	0.598212i	0.640045	+	0.768338i	$0.278916\pi$
$312$	12.3620	+	4.24161i	0.699862	+	0.240134i
$313$	6.56198	+	11.3657i	0.370905	+	0.642427i	0.989705	−	0.143122i	$-0.0457141\pi$
$313$	6.56198	+	11.3657i	0.370905	+	0.642427i	−0.618800	+	0.785549i	$0.712381\pi$
$314$	−31.3951	−	18.1260i	−1.77173	−	1.02291i
$315$		0			0
$316$	−14.5862	−	25.2641i	−0.820540	−	1.42122i
$317$	14.4761	−	8.35775i	0.813056	−	0.469418i	−0.0349599	−	0.999389i	$-0.511130\pi$
$317$	14.4761	−	8.35775i	0.813056	−	0.469418i	0.848016	+	0.529971i	$0.177797\pi$
$318$			9.75127i			0.546824i
$319$		−	14.5330i		−	0.813689i
$320$	−6.53932	+	3.77548i	−0.365559	+	0.211056i
$321$	−1.33123	−	2.30575i	−0.0743018	−	0.128695i
$322$		0			0
$323$	−9.96849	−	5.75531i	−0.554661	−	0.320234i
$324$	15.6374	+	27.0847i	0.868743	+	1.50471i
$325$	8.49708	−	1.66122i	0.471333	−	0.0921480i
$326$	9.28007	−	16.0736i	0.513976	−	0.890232i
$327$			0.895821i			0.0495390i
$328$	−26.9223	+	46.6307i	−1.48653	+	2.57475i
$329$		0			0
$330$		−	5.85228i		−	0.322157i
$331$	−3.43522	−	1.98332i	−0.188817	−	0.109013i	0.402612	−	0.915371i	$-0.368102\pi$
$331$	−3.43522	−	1.98332i	−0.188817	−	0.109013i	−0.591428	+	0.806357i	$0.701436\pi$
$332$			12.6769i			0.695733i
$333$	14.0816	+	8.13002i	0.771668	+	0.445523i
$334$	−23.2722	+	40.3087i	−1.27340	+	2.20559i
$335$	10.9473	−	18.9613i	0.598116	−	1.03597i
$336$		0			0
$337$	−13.7032			−0.746461			−0.373230	−	0.927739i	$-0.621750\pi$
$337$	−13.7032			−0.746461			−0.373230	+	0.927739i	$0.621750\pi$
$338$	33.3344	+	4.61121i	1.81315	+	0.250817i
$339$	−2.22710	+	3.85746i	−0.120960	+	0.209508i
$340$	−20.5192	+	11.8468i	−1.11281	+	0.642481i
$341$	−28.3426			−1.53484
$342$	13.0141	+	22.5410i	0.703720	+	1.21888i
$343$		0			0
$344$	20.3197	−	11.7316i	1.09557	−	0.632526i
$345$	−1.43753	−	0.829960i	−0.0773942	−	0.0446835i
$346$	−28.7209	−	16.5820i	−1.54405	−	0.891456i
$347$	−26.3979			−1.41711			−0.708556	−	0.705655i	$-0.750653\pi$
$347$	−26.3979			−1.41711			−0.708556	+	0.705655i	$0.750653\pi$
$348$	−13.0945			−0.701941
$349$	4.23507	+	2.44512i	0.226698	+	0.130884i	0.609048	−	0.793133i	$-0.291552\pi$
$349$	4.23507	+	2.44512i	0.226698	+	0.130884i	−0.382350	+	0.924018i	$0.624885\pi$
$350$		0			0
$351$	−7.03753	−	8.07806i	−0.375636	−	0.431175i
$352$	−11.5345	−	19.9784i	−0.614792	−	1.06485i
$353$	11.7413	−	6.77886i	0.624928	−	0.360802i	−0.153857	−	0.988093i	$-0.549170\pi$
$353$	11.7413	−	6.77886i	0.624928	−	0.360802i	0.778785	+	0.627291i	$0.215836\pi$
$354$	−7.66612	−	13.2781i	−0.407450	−	0.705724i
$355$	1.08903	−	1.88626i	0.0577997	−	0.100112i
$356$			8.27291i			0.438464i
$357$		0			0
$358$	4.12540	−	2.38180i	0.218034	−	0.125882i
$359$	7.43541	−	4.29284i	0.392426	−	0.226567i	−0.290785	−	0.956789i	$-0.593916\pi$
$359$	7.43541	−	4.29284i	0.392426	−	0.226567i	0.683211	+	0.730221i	$0.260583\pi$
$360$	30.7821			1.62236
$361$	−2.72326	−	4.71683i	−0.143330	−	0.248254i
$362$		−	8.54053i		−	0.448880i
$363$	−1.90962			−0.100229
$364$		0			0
$365$	14.6751			0.768130
$366$			3.92574i			0.205202i
$367$	−0.831612	−	1.44039i	−0.0434098	−	0.0751880i	0.843504	−	0.537123i	$-0.180489\pi$
$367$	−0.831612	−	1.44039i	−0.0434098	−	0.0751880i	−0.886914	+	0.461935i	$0.847155\pi$
$368$	−17.2712			−0.900324
$369$	18.2162	−	10.5171i	0.948299	−	0.547501i
$370$	21.5152	−	12.4218i	1.11852	−	0.645778i
$371$		0			0
$372$			25.5374i			1.32405i
$373$	−6.98174	+	12.0927i	−0.361501	+	0.626138i	−0.988208	−	0.153117i	$-0.951069\pi$
$373$	−6.98174	+	12.0927i	−0.361501	+	0.626138i	0.626707	+	0.779255i	$0.284402\pi$
$374$	−10.9463	−	18.9596i	−0.566022	−	0.980378i
$375$	−5.35719	+	3.09298i	−0.276644	+	0.159721i
$376$	−3.68828	−	6.38828i	−0.190208	−	0.329450i
$377$	−19.0117	+	3.71687i	−0.979150	+	0.191429i
$378$		0			0
$379$	−27.3454	−	15.7879i	−1.40464	−	0.810969i	−0.409775	−	0.912187i	$-0.634393\pi$
$379$	−27.3454	−	15.7879i	−1.40464	−	0.810969i	−0.994864	+	0.101218i	$0.967726\pi$
$380$	27.8985			1.43116
$381$	−1.61975			−0.0829822
$382$	10.9761	+	6.33707i	0.561588	+	0.324233i
$383$	27.6333	+	15.9541i	1.41200	+	0.815217i	0.995576	−	0.0939554i	$-0.0299511\pi$
$383$	27.6333	+	15.9541i	1.41200	+	0.815217i	0.416420	+	0.909172i	$0.363284\pi$
$384$	2.21435	−	1.27846i	0.113001	−	0.0652410i
$385$		0			0
$386$	−3.90762	−	6.76820i	−0.198893	−	0.344492i
$387$	−9.16588			−0.465928
$388$	−63.0283	+	36.3894i	−3.19978	+	1.84739i
$389$	−12.7075	+	22.0100i	−0.644296	+	1.11595i	0.340168	+	0.940365i	$0.389516\pi$
$389$	−12.7075	+	22.0100i	−0.644296	+	1.11595i	−0.984464	+	0.175589i	$0.943817\pi$
$390$	−7.65581	+	1.49675i	−0.387667	+	0.0757908i
$391$	−6.20956			−0.314031
$392$		0			0
$393$	−2.64656	+	4.58398i	−0.133501	+	0.231231i
$394$	6.01838	−	10.4241i	0.303202	−	0.525161i
$395$	8.66376	+	5.00203i	0.435921	+	0.251679i
$396$			34.7288i			1.74519i
$397$	3.60178	+	2.07949i	0.180768	+	0.104366i	0.587653	−	0.809113i	$-0.300052\pi$
$397$	3.60178	+	2.07949i	0.180768	+	0.104366i	−0.406885	+	0.913479i	$0.633385\pi$
$398$		−	1.06319i		−	0.0532930i
$399$		0			0
$400$	−10.4412	+	18.0846i	−0.522058	+	0.904231i
$401$		−	19.6013i		−	0.978844i	−0.872047	−	0.489422i	$-0.837208\pi$
$401$		−	19.6013i		−	0.978844i	0.872047	−	0.489422i	$-0.162792\pi$
$402$	9.11409	−	15.7861i	0.454569	−	0.787337i
$403$	7.24877	+	37.0772i	0.361087	+	1.84695i
$404$	−3.00691	−	5.20811i	−0.149599	−	0.259113i
$405$	−9.28811	−	5.36249i	−0.461530	−	0.266464i
$406$		0			0
$407$	8.05193	+	13.9463i	0.399119	+	0.691295i
$408$	−9.81500	+	5.66669i	−0.485915	+	0.280543i
$409$		−	17.6337i		−	0.871930i	−0.899964	−	0.435965i	$-0.856407\pi$
$409$		−	17.6337i		−	0.871930i	0.899964	−	0.435965i	$-0.143593\pi$
$410$		−	32.1381i		−	1.58719i
$411$	4.48673	−	2.59041i	0.221314	−	0.127776i
$412$	−26.9532	−	46.6842i	−1.32789	−	2.29997i
$413$		0			0
$414$	12.1601	+	7.02061i	0.597634	+	0.345044i
$415$	−2.17363	−	3.76483i	−0.106699	−	0.184808i
$416$	−23.1852	+	20.1987i	−1.13675	+	0.990324i
$417$	0.431416	−	0.747234i	0.0211265	−	0.0365922i
$418$			25.7781i			1.26085i
$419$	14.9455	−	25.8864i	0.730137	−	1.26463i	−0.226688	−	0.973968i	$-0.572790\pi$
$419$	14.9455	−	25.8864i	0.730137	−	1.26463i	0.956824	−	0.290666i	$-0.0938770\pi$
$420$		0			0
$421$			12.8528i			0.626407i	0.949686	+	0.313203i	$0.101402\pi$
$421$			12.8528i			0.626407i	−0.949686	+	0.313203i	$0.898598\pi$
$422$	−16.8493	−	9.72796i	−0.820212	−	0.473550i
$423$			2.88164i			0.140110i
$424$	−43.9919	−	25.3987i	−2.13644	−	1.23347i
$425$	−3.75393	+	6.50200i	−0.182093	+	0.315394i
$426$	0.906662	−	1.57038i	0.0439279	−	0.0760854i
$427$		0			0
$428$	24.1401			1.16685
$429$	−0.970207	−	4.96257i	−0.0468421	−	0.239595i
$430$	−7.00223	+	12.1282i	−0.337677	+	0.584874i
$431$	7.76876	−	4.48530i	0.374208	−	0.216049i	−0.301087	−	0.953597i	$-0.597350\pi$
$431$	7.76876	−	4.48530i	0.374208	−	0.216049i	0.675295	+	0.737547i	$0.264016\pi$
$432$	25.8405			1.24325
$433$	1.72531	+	2.98833i	0.0829132	+	0.143610i	0.904500	−	0.426473i	$-0.140244\pi$
$433$	1.72531	+	2.98833i	0.0829132	+	0.143610i	−0.821587	+	0.570083i	$0.806911\pi$
$434$		0			0
$435$	3.88887	−	2.24524i	0.186457	−	0.107651i
$436$	−7.03410	−	4.06114i	−0.336872	−	0.194493i
$437$	6.33204	+	3.65580i	0.302902	+	0.174881i
$438$	12.2176			0.583780
$439$	−38.5144			−1.83819			−0.919096	−	0.394034i	$-0.871079\pi$
$439$	−38.5144			−1.83819			−0.919096	+	0.394034i	$0.871079\pi$
$440$	26.4020	+	15.2432i	1.25867	+	0.726691i
$441$		0			0
$442$	−22.0029	+	19.1687i	−1.04657	+	0.911764i
$443$	7.51997	+	13.0250i	0.357284	+	0.618835i	0.987506	−	0.157580i	$-0.0503693\pi$
$443$	7.51997	+	13.0250i	0.357284	+	0.618835i	−0.630222	+	0.776415i	$0.717036\pi$
$444$	12.5660	−	7.25498i	0.596356	−	0.344306i
$445$	−1.41851	−	2.45693i	−0.0672437	−	0.116469i
$446$	29.2246	−	50.6185i	1.38382	−	2.39685i
$447$			10.2646i			0.485499i
$448$		0			0
$449$	33.7087	−	19.4617i	1.59081	−	0.918456i	0.597646	−	0.801760i	$-0.296103\pi$
$449$	33.7087	−	19.4617i	1.59081	−	0.918456i	0.993168	−	0.116696i	$-0.0372304\pi$
$450$	14.7025	−	8.48850i	0.693083	−	0.400152i
$451$	20.8322			0.980952
$452$	−20.1928	−	34.9750i	−0.949790	−	1.64509i
$453$		−	3.90660i		−	0.183548i
$454$	35.3906			1.66097
$455$		0			0
$456$	13.3448			0.624927
$457$		−	13.9396i		−	0.652069i	−0.945358	−	0.326034i	$-0.894287\pi$
$457$		−	13.9396i		−	0.652069i	0.945358	−	0.326034i	$-0.105713\pi$
$458$	10.2649	+	17.7793i	0.479648	+	0.830774i
$459$	9.29049			0.433643
$460$	13.0339	−	7.52512i	0.607709	−	0.350861i
$461$	−32.4443	+	18.7317i	−1.51108	+	0.872424i	−0.511167	+	0.859481i	$0.670787\pi$
$461$	−32.4443	+	18.7317i	−1.51108	+	0.872424i	−0.999916	+	0.0129430i	$0.995880\pi$
$462$		0			0
$463$		−	6.75275i		−	0.313827i	−0.987612	−	0.156913i	$-0.949846\pi$
$463$		−	6.75275i		−	0.313827i	0.987612	−	0.156913i	$-0.0501544\pi$
$464$	23.3614	−	40.4631i	1.08453	−	1.87845i
$465$	−4.37875	−	7.58421i	−0.203059	−	0.351709i
$466$	−14.7324	+	8.50576i	−0.682466	+	0.394022i
$467$	−2.52516	−	4.37371i	−0.116851	−	0.202391i	0.801667	−	0.597770i	$-0.203947\pi$
$467$	−2.52516	−	4.37371i	−0.116851	−	0.202391i	−0.918518	+	0.395379i	$0.870613\pi$
$468$	45.4314	−	8.88205i	2.10006	−	0.410573i
$469$		0			0
$470$	3.81296	+	2.20141i	0.175879	+	0.101544i
$471$	7.26084			0.334562
$472$	79.8705			3.67634
$473$	−7.86163	−	4.53892i	−0.361478	−	0.208700i
$474$	7.21294	+	4.16439i	0.331301	+	0.191277i
$475$	7.65595	−	4.42017i	0.351279	−	0.202811i
$476$		0			0
$477$	9.92198	+	17.1854i	0.454296	+	0.786864i
$478$	24.3143			1.11211
$479$	−8.18670	+	4.72659i	−0.374060	+	0.215964i	−0.675231	−	0.737607i	$-0.735956\pi$
$479$	−8.18670	+	4.72659i	−0.374060	+	0.215964i	0.301171	+	0.953570i	$0.402623\pi$
$480$	3.56401	−	6.17304i	0.162674	−	0.281759i
$481$	16.1850	−	14.1002i	0.737971	−	0.642913i
$482$	26.1082			1.18920
$483$		0			0
$484$	8.65711	−	14.9946i	0.393505	−	0.681571i
$485$	12.4789	−	21.6142i	0.566639	−	0.981448i
$486$	−27.7167	−	16.0023i	−1.25726	−	0.725877i
$487$		−	39.9996i		−	1.81255i	−0.422684	−	0.906277i	$-0.638912\pi$
$487$		−	39.9996i		−	1.81255i	0.422684	−	0.906277i	$-0.361088\pi$
$488$	−17.7106	−	10.2252i	−0.801721	−	0.462874i
$489$			3.71737i			0.168105i
$490$		0			0
$491$	−3.38049	+	5.85517i	−0.152559	+	0.264240i	−0.932168	−	0.362027i	$-0.882085\pi$
$491$	−3.38049	+	5.85517i	−0.152559	+	0.264240i	0.779608	+	0.626267i	$0.215418\pi$
$492$		−	18.7704i		−	0.846233i
$493$	8.39918	−	14.5478i	0.378280	−	0.655200i
$494$	33.7223	−	6.59287i	1.51724	−	0.296627i
$495$	−5.95473	−	10.3139i	−0.267645	−	0.463575i
$496$	−78.9125	−	45.5602i	−3.54328	−	2.04571i
$497$		0			0
$498$	−1.80963	−	3.13438i	−0.0810916	−	0.140455i
$499$	−9.83591	+	5.67877i	−0.440316	+	0.254217i	−0.703732	−	0.710466i	$-0.748484\pi$
$499$	−9.83591	+	5.67877i	−0.440316	+	0.254217i	0.263416	+	0.964682i	$0.415151\pi$
$500$		−	56.0871i		−	2.50829i
$501$		−	9.32230i		−	0.416490i
$502$	23.1993	−	13.3941i	1.03543	−	0.597808i
$503$	−6.96423	−	12.0624i	−0.310520	−	0.537836i	0.667955	−	0.744202i	$-0.267170\pi$
$503$	−6.96423	−	12.0624i	−0.310520	−	0.537836i	−0.978475	+	0.206365i	$0.933836\pi$
$504$		0			0
$505$	1.78601	+	1.03115i	0.0794763	+	0.0458857i
$506$	6.95317	+	12.0432i	0.309106	+	0.535388i
$507$	−6.24379	+	2.53840i	−0.277296	+	0.112734i
$508$	7.34301	−	12.7185i	0.325793	−	0.564290i
$509$		−	19.8149i		−	0.878281i	−0.898418	−	0.439141i	$-0.855283\pi$
$509$		−	19.8149i		−	0.878281i	0.898418	−	0.439141i	$-0.144717\pi$
$510$	3.38227	−	5.85826i	0.149769	−	0.259408i
$511$		0			0
$512$			47.4335i			2.09628i
$513$	−9.47373	−	5.46966i	−0.418276	−	0.241491i
$514$		−	20.6741i		−	0.911894i
$515$	16.0093	+	9.24299i	0.705455	+	0.407295i
$516$	−4.08967	+	7.08352i	−0.180038	+	0.311835i
$517$	−1.42698	+	2.47160i	−0.0627585	+	0.108701i
$518$		0			0
$519$	6.64237			0.291568
$520$	13.1883	−	38.4370i	0.578347	−	1.68557i
$521$	−15.5476	+	26.9292i	−0.681151	+	1.17979i	0.293479	+	0.955966i	$0.405187\pi$
$521$	−15.5476	+	26.9292i	−0.681151	+	1.17979i	−0.974630	+	0.223823i	$0.928146\pi$
$522$	−32.8959	+	18.9924i	−1.43981	+	0.831277i
$523$	−22.7202			−0.993485			−0.496742	−	0.867898i	$-0.665471\pi$
$523$	−22.7202			−0.993485			−0.496742	+	0.867898i	$0.665471\pi$
$524$	−23.9960	−	41.5622i	−1.04827	−	1.81565i
$525$		0			0
$526$	−11.3420	+	6.54831i	−0.494535	+	0.285520i
$527$	−28.3716	−	16.3804i	−1.23589	−	0.713540i
$528$	10.5620	+	6.09798i	0.459652	+	0.265380i
$529$	−19.0557			−0.828507
$530$	30.3194			1.31699
$531$	−27.0211	−	15.6007i	−1.17262	−	0.677011i
$532$		0			0
$533$	−5.32794	−	27.2522i	−0.230779	−	1.18043i
$534$	−1.18097	−	2.04549i	−0.0511054	−	0.0885171i
$535$	−7.16922	+	4.13915i	−0.309952	+	0.178951i
$536$	47.4782	+	82.2346i	2.05074	+	3.55199i
$537$	−0.477046	+	0.826267i	−0.0205860	+	0.0356561i
$538$			35.9563i			1.55018i
$539$		0			0
$540$	−19.5008	+	11.2588i	−0.839180	+	0.484501i
$541$	1.81754	−	1.04936i	0.0781423	−	0.0451155i	−0.460420	−	0.887701i	$-0.652301\pi$
$541$	1.81754	−	1.04936i	0.0781423	−	0.0451155i	0.538562	+	0.842586i	$0.318968\pi$
$542$	21.5558			0.925902
$543$	0.855283	+	1.48139i	0.0367037	+	0.0635727i
$544$		−	26.6650i		−	1.14325i
$545$	2.78536			0.119312
$546$		0			0
$547$	25.3770			1.08504			0.542521	−	0.840042i	$-0.317470\pi$
$547$	25.3770			1.08504			0.542521	+	0.840042i	$0.317470\pi$
$548$			46.9738i			2.00662i
$549$	3.99447	+	6.91862i	0.170480	+	0.295280i
$550$	16.8139			0.716948
$551$	−17.1297	+	9.88983i	−0.729749	+	0.421321i
$552$	6.23454	−	3.59951i	0.265360	−	0.153205i
$553$		0			0
$554$		−	60.0855i		−	2.55279i
$555$	−2.48794	+	4.30923i	−0.105607	+	0.182917i
$556$	3.91158	+	6.77506i	0.165888	+	0.287327i
$557$	−38.3219	+	22.1252i	−1.62375	+	0.937473i	−0.637846	+	0.770164i	$0.720174\pi$
$557$	−38.3219	+	22.1252i	−1.62375	+	0.937473i	−0.985904	+	0.167309i	$0.946492\pi$
$558$	37.0397	+	64.1547i	1.56802	+	2.71588i
$559$	−3.92705	+	11.4452i	−0.166097	+	0.484082i
$560$		0			0
$561$	3.79738	+	2.19242i	0.160326	+	0.0925641i
$562$	70.3051			2.96564
$563$	−38.8907			−1.63905			−0.819523	−	0.573046i	$-0.805762\pi$
$563$	−38.8907			−1.63905			−0.819523	+	0.573046i	$0.805762\pi$
$564$	2.22697	+	1.28574i	0.0937725	+	0.0541396i
$565$	11.9939	+	6.92468i	0.504587	+	0.291324i
$566$	36.2078	−	20.9046i	1.52193	−	0.878685i
$567$		0			0
$568$	4.72309	+	8.18063i	0.198177	+	0.343252i
$569$	−46.1579			−1.93504			−0.967520	−	0.252796i	$-0.918650\pi$
$569$	−46.1579			−1.93504			−0.967520	+	0.252796i	$0.918650\pi$
$570$	−6.89796	+	3.98254i	−0.288924	+	0.166810i
$571$	10.5684	−	18.3050i	0.442274	−	0.766041i	−0.555584	−	0.831461i	$-0.687505\pi$
$571$	10.5684	−	18.3050i	0.442274	−	0.766041i	0.997858	+	0.0654194i	$0.0208385\pi$
$572$	43.3651	+	14.8793i	1.81319	+	0.622134i
$573$	−2.53848			−0.106047
$574$		0			0
$575$	2.38452	−	4.13011i	0.0994413	−	0.172237i
$576$	−6.39653	+	11.0791i	−0.266522	+	0.461630i
$577$	−21.9368	−	12.6652i	−0.913239	−	0.527259i	−0.0317671	−	0.999495i	$-0.510113\pi$
$577$	−21.9368	−	12.6652i	−0.913239	−	0.527259i	−0.881472	+	0.472237i	$0.843447\pi$
$578$			18.7009i			0.777855i
$579$	1.35559	+	0.782650i	0.0563364	+	0.0325258i
$580$			40.7146i			1.69058i
$581$		0			0
$582$	10.3892	−	17.9947i	0.430647	−	0.745903i
$583$			19.6533i			0.813958i
$584$	−31.8227	+	55.1186i	−1.31683	+	2.28082i
$585$	−11.9694	+	10.4277i	−0.494876	+	0.431131i
$586$	−18.9553	−	32.8315i	−0.783036	−	1.35626i
$587$	−3.08554	−	1.78144i	−0.127354	−	0.0735278i	0.434970	−	0.900445i	$-0.356759\pi$
$587$	−3.08554	−	1.78144i	−0.127354	−	0.0735278i	−0.562324	+	0.826917i	$0.690092\pi$
$588$		0			0
$589$	19.2875	+	33.4069i	0.794727	+	1.37651i
$590$	−41.2853	+	23.8361i	−1.69969	+	0.981316i
$591$			2.41082i			0.0991679i
$592$			51.7732i			2.12786i
$593$	−21.9568	+	12.6768i	−0.901659	+	0.520573i	−0.877738	−	0.479141i	$-0.840948\pi$
$593$	−21.9568	+	12.6768i	−0.901659	+	0.520573i	−0.0239212	+	0.999714i	$0.507615\pi$
$594$	−10.4030	−	18.0186i	−0.426842	−	0.739312i
$595$		0			0
$596$	−80.5990	−	46.5338i	−3.30146	−	1.90610i
$597$	0.106472	+	0.184415i	0.00435762	+	0.00754762i
$598$	13.9764	−	12.1761i	0.571537	−	0.497917i
$599$	−5.46078	+	9.45835i	−0.223122	+	0.386458i	−0.955754	−	0.294166i	$-0.904958\pi$
$599$	−5.46078	+	9.45835i	−0.223122	+	0.386458i	0.732633	+	0.680624i	$0.238291\pi$
$600$		−	8.70421i		−	0.355348i
$601$	12.1282	−	21.0067i	0.494720	−	0.856880i	−0.505262	−	0.862966i	$-0.668604\pi$
$601$	12.1282	−	21.0067i	0.494720	−	0.856880i	0.999981	+	0.00608649i	$0.00193740\pi$
$602$		0			0
$603$		−	37.0946i		−	1.51061i
$604$	30.6751	+	17.7103i	1.24815	+	0.720621i
$605$			5.93753i			0.241395i
$606$	1.48692	+	0.858476i	0.0604022	+	0.0348732i
$607$	−4.92724	+	8.53422i	−0.199990	+	0.346393i	−0.948525	−	0.316702i	$-0.897424\pi$
$607$	−4.92724	+	8.53422i	−0.199990	+	0.346393i	0.748535	+	0.663096i	$0.230758\pi$
$608$	−15.6987	+	27.1910i	−0.636667	+	1.10274i
$609$		0			0
$610$	12.2062			0.494215
$611$	3.59825	+	1.23462i	0.145569	+	0.0499472i
$612$	−20.0712	+	34.7643i	−0.811328	+	1.40526i
$613$	−3.18428	+	1.83844i	−0.128612	+	0.0742540i	−0.562926	−	0.826508i	$-0.690324\pi$
$613$	−3.18428	+	1.83844i	−0.128612	+	0.0742540i	0.434314	+	0.900762i	$0.356991\pi$
$614$	23.2416			0.937955
$615$	3.21844	+	5.57450i	0.129780	+	0.224785i
$616$		0			0
$617$	16.2352	−	9.37341i	0.653605	−	0.377359i	−0.136231	−	0.990677i	$-0.543499\pi$
$617$	16.2352	−	9.37341i	0.653605	−	0.377359i	0.789836	+	0.613318i	$0.210166\pi$
$618$	13.3284	+	7.69517i	0.536148	+	0.309545i
$619$	−13.7650	−	7.94725i	−0.553264	−	0.319427i	0.197174	−	0.980369i	$-0.436824\pi$
$619$	−13.7650	−	7.94725i	−0.553264	−	0.319427i	−0.750437	+	0.660942i	$0.770157\pi$
$620$	79.4029			3.18890
$621$	−5.90137			−0.236814
$622$	27.3086	+	15.7667i	1.09498	+	0.632185i
$623$		0			0
$624$	5.27594	−	15.3765i	0.211207	−	0.615555i
$625$	3.61371	+	6.25913i	0.144549	+	0.250365i
$626$	29.4212	−	16.9864i	1.17591	−	0.678911i
$627$	−2.58152	−	4.47133i	−0.103096	−	0.178568i
$628$	−32.9165	+	57.0130i	−1.31351	+	2.27507i
$629$			18.6141i			0.742194i
$630$		0			0
$631$	−17.0998	+	9.87255i	−0.680731	+	0.393020i	−0.800130	−	0.599826i	$-0.795236\pi$
$631$	−17.0998	+	9.87255i	−0.680731	+	0.393020i	0.119400	+	0.992846i	$0.461903\pi$
$632$	−37.5745	+	21.6936i	−1.49463	+	0.862927i
$633$	3.89679			0.154883
$634$	−21.6349	−	37.4727i	−0.859231	−	1.48823i
$635$			5.03624i			0.199857i
$636$	17.7081			0.702173
$637$		0			0
$638$	−37.6200			−1.48939
$639$		−	3.69014i		−	0.145980i
$640$	−3.97508	−	6.88504i	−0.157129	−	0.272155i
$641$	29.7786			1.17618			0.588092	−	0.808794i	$-0.299879\pi$
$641$	29.7786			1.17618			0.588092	+	0.808794i	$0.299879\pi$
$642$	−5.96867	+	3.44601i	−0.235565	+	0.136003i
$643$	−10.0220	+	5.78623i	−0.395231	+	0.228187i	−0.684424	−	0.729084i	$-0.739946\pi$
$643$	−10.0220	+	5.78623i	−0.395231	+	0.228187i	0.289193	+	0.957271i	$0.406613\pi$
$644$		0			0
$645$		−	2.80493i		−	0.110444i
$646$	−14.8982	+	25.8044i	−0.586162	+	1.01526i
$647$	−12.7533	−	22.0893i	−0.501382	−	0.868420i	−0.999999	−	0.00159698i	$-0.999492\pi$
$647$	−12.7533	−	22.0893i	−0.501382	−	0.868420i	0.498616	−	0.866823i	$-0.333842\pi$
$648$	40.2823	−	23.2570i	1.58244	−	0.913620i
$649$	−15.4508	−	26.7616i	−0.606497	−	1.05048i
$650$	−4.30024	−	21.9956i	−0.168669	−	0.862737i
$651$		0			0
$652$	−29.1893	−	16.8524i	−1.14314	−	0.659993i
$653$	−44.8293			−1.75430			−0.877152	−	0.480212i	$-0.840560\pi$
$653$	−44.8293			−1.75430			−0.877152	+	0.480212i	$0.840560\pi$
$654$	2.31892			0.0906771
$655$	14.2529	+	8.22889i	0.556905	+	0.321529i
$656$	58.0018	+	33.4874i	2.26459	+	1.30746i
$657$	21.5320	−	12.4315i	0.840043	−	0.484999i
$658$		0			0
$659$	−20.5867	−	35.6572i	−0.801944	−	1.38901i	−0.918335	−	0.395805i	$-0.870466\pi$
$659$	−20.5867	−	35.6572i	−0.801944	−	1.38901i	0.116390	−	0.993204i	$-0.462868\pi$
$660$	−10.6276			−0.413680
$661$	18.9606	−	10.9469i	0.737481	−	0.425785i	−0.0836719	−	0.996493i	$-0.526665\pi$
$661$	18.9606	−	10.9469i	0.737481	−	0.425785i	0.821153	+	0.570709i	$0.193331\pi$
$662$	−5.13404	+	8.89241i	−0.199540	+	0.345613i
$663$	1.89687	−	5.52837i	0.0736684	−	0.214704i
$664$	18.8539			0.731673
$665$		0			0
$666$	21.0454	−	36.4517i	0.815492	−	1.41247i
$667$	−5.33520	+	9.24084i	−0.206580	+	0.357807i
$668$	73.1999	+	42.2620i	2.83219	+	1.63516i
$669$			11.7067i			0.452606i
$670$	−49.0832	−	28.3382i	−1.89625	−	1.09480i
$671$			7.91219i			0.305447i
$672$		0			0
$673$	17.8344	−	30.8901i	0.687466	−	1.19073i	−0.285189	−	0.958471i	$-0.592056\pi$
$673$	17.8344	−	30.8901i	0.687466	−	1.19073i	0.972655	−	0.232254i	$-0.0746102\pi$
$674$			35.4721i			1.36633i
$675$	−3.56762	+	6.17930i	−0.137318	+	0.237841i
$676$	8.37388	−	60.5347i	0.322072	−	2.32826i
$677$	1.27766	+	2.21297i	0.0491044	+	0.0850514i	0.889533	−	0.456871i	$-0.151030\pi$
$677$	1.27766	+	2.21297i	0.0491044	+	0.0850514i	−0.840428	+	0.541923i	$0.817697\pi$
$678$	9.98541	+	5.76508i	0.383488	+	0.221407i
$679$		0			0
$680$	17.6193	+	30.5175i	0.675670	+	1.17029i
$681$	−6.13867	+	3.54416i	−0.235234	+	0.135813i
$682$			73.3678i			2.80940i
$683$			35.7399i			1.36755i	0.729693	+	0.683775i	$0.239663\pi$
$683$			35.7399i			1.36755i	−0.729693	+	0.683775i	$0.760337\pi$
$684$	40.9341	−	23.6333i	1.56515	−	0.903642i
$685$	−8.05431	−	13.9505i	−0.307739	−	0.533020i
$686$		0			0
$687$	−3.56099	−	2.05594i	−0.135860	−	0.0784390i
$688$	−14.5924	−	25.2748i	−0.556330	−	0.963592i
$689$	25.7100	−	5.02643i	0.979474	−	0.191492i
$690$	−2.14843	+	3.72120i	−0.0817895	+	0.141664i
$691$		−	26.0292i		−	0.990197i	−0.868837	−	0.495099i	$-0.835132\pi$
$691$		−	26.0292i		−	0.990197i	0.868837	−	0.495099i	$-0.164868\pi$
$692$	−30.1127	+	52.1567i	−1.14471	+	1.98270i
$693$		0			0
$694$			68.3335i			2.59391i
$695$	−2.32336	−	1.34139i	−0.0881299	−	0.0508818i
$696$			19.4751i			0.738202i
$697$	20.8535	+	12.0398i	0.789884	+	0.456040i
$698$	6.32944	−	10.9629i	0.239573	−	0.414952i
$699$	1.70360	−	2.95073i	0.0644362	−	0.111607i
$700$		0			0
$701$	−1.12731			−0.0425779			−0.0212890	−	0.999773i	$-0.506777\pi$
$701$	−1.12731			−0.0425779			−0.0212890	+	0.999773i	$0.506777\pi$
$702$	−20.9109	+	18.2174i	−0.789230	+	0.687570i
$703$	10.9588	−	18.9813i	0.413321	−	0.715892i
$704$	−10.9727	+	6.33509i	−0.413549	+	0.238763i
$705$	−0.881834			−0.0332118
$706$	−17.5478	−	30.3936i	−0.660419	−	1.14388i
$707$		0			0
$708$	−24.1128	+	13.9215i	−0.906215	+	0.523203i
$709$	−5.23972	−	3.02515i	−0.196782	−	0.113612i	0.398372	−	0.917224i	$-0.369575\pi$
$709$	−5.23972	−	3.02515i	−0.196782	−	0.113612i	−0.595153	+	0.803612i	$0.702909\pi$
$710$	−4.88276	−	2.81906i	−0.183247	−	0.105798i
$711$	16.9492			0.635644
$712$	12.3040			0.461114
$713$	18.0218	+	10.4049i	0.674922	+	0.389666i
$714$		0			0
$715$	−15.4300	+	3.01664i	−0.577050	+	0.112816i
$716$	−4.32530	−	7.49164i	−0.161644	−	0.279976i
$717$	−4.21743	+	2.43493i	−0.157503	+	0.0909342i
$718$	−11.1124	−	19.2473i	−0.414713	−	0.718304i
$719$	−23.5589	+	40.8052i	−0.878597	+	1.52178i	−0.0257170	+	0.999669i	$0.508187\pi$
$719$	−23.5589	+	40.8052i	−0.878597	+	1.52178i	−0.852880	+	0.522106i	$0.825146\pi$
$720$		−	38.2884i		−	1.42692i
$721$		0			0
$722$	−12.2100	+	7.04944i	−0.454409	+	0.262353i
$723$	−4.52859	+	2.61458i	−0.168420	+	0.0972374i
$724$	−15.5095			−0.576404
$725$	6.45070	+	11.1729i	0.239573	+	0.414953i
$726$			4.94324i			0.183461i
$727$	−17.9215			−0.664671			−0.332335	−	0.943161i	$-0.607837\pi$
$727$	−17.9215			−0.664671			−0.332335	+	0.943161i	$0.607837\pi$
$728$		0			0
$729$	−13.5489			−0.501810
$730$		−	37.9880i		−	1.40600i
$731$	−5.24644	−	9.08711i	−0.194047	−	0.336099i
$732$	7.12908			0.263498
$733$	39.2037	−	22.6343i	1.44802	−	0.836016i	0.449658	−	0.893201i	$-0.351546\pi$
$733$	39.2037	−	22.6343i	1.44802	−	0.836016i	0.998364	+	0.0571848i	$0.0182124\pi$
$734$	−3.72861	+	2.15271i	−0.137625	+	0.0794581i
$735$		0			0
$736$			16.9378i			0.624335i
$737$	18.3691	−	31.8163i	0.676635	−	1.17197i
$738$	−27.2247	−	47.1546i	−1.00215	−	1.73578i
$739$	16.6808	−	9.63066i	0.613613	−	0.354270i	−0.160765	−	0.986993i	$-0.551396\pi$
$739$	16.6808	−	9.63066i	0.613613	−	0.354270i	0.774378	+	0.632723i	$0.218063\pi$
$740$	−22.5577	−	39.0712i	−0.829239	−	1.43628i
$741$	−5.18905	+	4.52065i	−0.190624	+	0.166070i
$742$		0			0
$743$	30.2115	+	17.4426i	1.10835	+	0.639908i	0.938402	−	0.345545i	$-0.112306\pi$
$743$	30.2115	+	17.4426i	1.10835	+	0.639908i	0.169951	+	0.985453i	$0.445639\pi$
$744$	37.9810			1.39245
$745$	31.9155			1.16929
$746$	31.3032	+	18.0729i	1.14609	+	0.661697i
$747$	−6.37850	−	3.68263i	−0.233377	−	0.134740i
$748$	−34.4303	+	19.8784i	−1.25890	+	0.726825i
$749$		0			0
$750$	8.00648	+	13.8676i	0.292355	+	0.506374i
$751$	24.9668			0.911051			0.455526	−	0.890223i	$-0.349451\pi$
$751$	24.9668			0.911051			0.455526	+	0.890223i	$0.349451\pi$
$752$	−7.94609	+	4.58767i	−0.289764	+	0.167295i
$753$	−2.68268	+	4.64654i	−0.0977623	+	0.169329i
$754$	9.62150	+	49.2136i	0.350394	+	1.79225i
$755$	−12.1467			−0.442064
$756$		0			0
$757$	5.30243	−	9.18408i	0.192720	−	0.333801i	−0.753431	−	0.657527i	$-0.771602\pi$
$757$	5.30243	−	9.18408i	0.192720	−	0.333801i	0.946151	+	0.323726i	$0.104936\pi$
$758$	−40.8685	+	70.7863i	−1.48441	+	2.57108i
$759$	−2.41212	−	1.39264i	−0.0875543	−	0.0505495i
$760$		−	41.4926i		−	1.50510i
$761$	−28.2660	−	16.3194i	−1.02464	−	0.591578i	−0.109198	−	0.994020i	$-0.534828\pi$
$761$	−28.2660	−	16.3194i	−1.02464	−	0.591578i	−0.915446	+	0.402442i	$0.868162\pi$
$762$			4.19288i			0.151892i
$763$		0			0
$764$	11.5080	−	19.9325i	0.416345	−	0.721131i
$765$		−	13.7659i		−	0.497708i
$766$	41.2988	−	71.5316i	1.49219	−	2.58454i
$767$	−31.0572	+	27.0568i	−1.12141	+	0.976963i
$768$	−5.73794	−	9.93841i	−0.207050	−	0.358621i
$769$	45.1851	+	26.0876i	1.62942	+	0.940744i	0.984267	+	0.176686i	$0.0565378\pi$
$769$	45.1851	+	26.0876i	1.62942	+	0.940744i	0.645148	+	0.764057i	$0.276796\pi$
$770$		0			0
$771$	2.07039	+	3.58601i	0.0745631	+	0.129147i
$772$	−12.2909	+	7.09618i	−0.442360	+	0.255397i
$773$		−	35.7057i		−	1.28425i	−0.766602	−	0.642123i	$-0.778054\pi$
$773$		−	35.7057i		−	1.28425i	0.766602	−	0.642123i	$-0.221946\pi$
$774$			23.7268i			0.852842i
$775$	21.7898	−	12.5804i	0.782714	−	0.451900i
$776$	54.1208	+	93.7400i	1.94282	+	3.36507i
$777$		0			0
$778$	56.9752	+	32.8947i	2.04266	+	1.17933i
$779$	−14.1766	−	24.5545i	−0.507928	−	0.879757i
$780$	2.71807	+	13.9028i	0.0973225	+	0.497801i
$781$	1.82735	−	3.16506i	0.0653876	−	0.113255i
$782$			16.0741i			0.574808i
$783$	7.98231	−	13.8258i	0.285265	−	0.494093i
$784$		0			0
$785$		−	22.5760i		−	0.805770i
$786$	11.8661	+	6.85089i	0.423249	+	0.244363i
$787$			6.10621i			0.217663i	0.994060	+	0.108831i	$0.0347109\pi$
$787$			6.10621i			0.217663i	−0.994060	+	0.108831i	$0.965289\pi$
$788$	−18.9301	−	10.9293i	−0.674356	−	0.389339i
$789$	1.31155	−	2.27167i	0.0466923	−	0.0808735i
$790$	12.9482	−	22.4270i	0.460678	−	0.797918i
$791$		0			0
$792$	51.6510			1.83534
$793$	10.3505	−	2.02358i	0.367559	−	0.0718595i
$794$	5.38296	−	9.32356i	0.191034	−	0.330881i
$795$	−5.25904	+	3.03631i	−0.186519	+	0.107687i
$796$	−1.93074			−0.0684332
$797$	23.1149	+	40.0363i	0.818773	+	1.41816i	0.906586	+	0.422020i	$0.138679\pi$
$797$	23.1149	+	40.0363i	0.818773	+	1.41816i	−0.0878129	+	0.996137i	$0.527988\pi$
$798$		0			0
$799$	−2.85688	+	1.64942i	−0.101069	+	0.0583522i
$800$	17.7355	+	10.2396i	0.627044	+	0.362024i
$801$	−4.16260	−	2.40328i	−0.147078	−	0.0849157i
$802$	−50.7400			−1.79169
$803$	24.6242			0.868968
$804$	−28.6672	−	16.5510i	−1.01101	−	0.583710i
$805$		0			0
$806$	95.9780	−	18.7642i	3.38068	−	0.660939i
$807$	−3.60080	−	6.23678i	−0.126754	−	0.219545i
$808$	−7.74586	+	4.47208i	−0.272498	+	0.157327i
$809$	−19.6439	−	34.0243i	−0.690644	−	1.19623i	−0.971627	−	0.236518i	$-0.923994\pi$
$809$	−19.6439	−	34.0243i	−0.690644	−	1.19623i	0.280983	−	0.959713i	$-0.409339\pi$
$810$	−13.8814	+	24.0432i	−0.487741	+	0.844792i
$811$		−	6.90664i		−	0.242525i	−0.992620	−	0.121262i	$-0.961306\pi$
$811$		−	6.90664i		−	0.242525i	0.992620	−	0.121262i	$-0.0386943\pi$
$812$		0			0
$813$	−3.73896	+	2.15869i	−0.131131	+	0.0757085i
$814$	36.1015	−	20.8432i	1.26536	−	0.730555i
$815$	11.5583			0.404871
$816$	7.04853	+	12.2084i	0.246748	+	0.427380i
$817$			12.3551i			0.432251i
$818$	−45.6466			−1.59600
$819$		0			0
$820$	−58.3622			−2.03810
$821$		−	1.91049i		−	0.0666765i	−0.999444	−	0.0333382i	$-0.989386\pi$
$821$		−	1.91049i		−	0.0666765i	0.999444	−	0.0333382i	$-0.0106139\pi$
$822$	−6.70554	−	11.6143i	−0.233883	−	0.405097i
$823$	−1.57969			−0.0550645			−0.0275322	−	0.999621i	$-0.508765\pi$
$823$	−1.57969			−0.0550645			−0.0275322	+	0.999621i	$0.508765\pi$
$824$	−69.4320	+	40.0866i	−2.41878	+	1.39648i
$825$	−2.91645	+	1.68381i	−0.101538	+	0.0586228i
$826$		0			0
$827$			32.5050i			1.13031i	0.824985	+	0.565155i	$0.191184\pi$
$827$			32.5050i			1.13031i	−0.824985	+	0.565155i	$0.808816\pi$
$828$	12.7493	−	22.0824i	0.443069	−	0.767418i
$829$	17.5269	+	30.3575i	0.608735	+	1.05436i	0.991449	+	0.130493i	$0.0416561\pi$
$829$	17.5269	+	30.3575i	0.608735	+	1.05436i	−0.382714	+	0.923867i	$0.625011\pi$
$830$	−9.74564	+	5.62665i	−0.338276	+	0.195304i
$831$	6.01721	+	10.4221i	0.208735	+	0.361539i
$832$	11.0937	+	12.7340i	0.384606	+	0.441472i
$833$		0			0
$834$	−1.93429	−	1.11676i	−0.0669790	−	0.0386703i
$835$	−28.9856			−1.00309
$836$	46.8126			1.61905
$837$	−26.9635	−	15.5674i	−0.931994	−	0.538087i
$838$	−67.0096	−	38.6880i	−2.31481	−	1.33645i
$839$	−4.63746	+	2.67744i	−0.160103	+	0.0924354i	−0.577911	−	0.816100i	$-0.696132\pi$
$839$	−4.63746	+	2.67744i	−0.160103	+	0.0924354i	0.417808	+	0.908535i	$0.362798\pi$
$840$		0			0
$841$	0.0669890	+	0.116028i	0.00230997	+	0.00400098i
$842$	33.2708			1.14659
$843$	−12.1947	+	7.04064i	−0.420009	+	0.242492i
$844$	−17.6658	+	30.5981i	−0.608082	+	1.05323i
$845$	7.89260	+	19.4137i	0.271514	+	0.667850i
$846$	7.45942			0.256460
$847$		0			0
$848$	−31.5923	+	54.7195i	−1.08488	+	1.87907i
$849$	−4.18694	+	7.25199i	−0.143695	+	0.248888i
$850$	16.8311	+	9.71744i	0.577302	+	0.333305i
$851$		−	11.8238i		−	0.405314i
$852$	−2.85179	−	1.64648i	−0.0977008	−	0.0564076i
$853$		−	49.6270i		−	1.69920i	−0.527431	−	0.849598i	$-0.676845\pi$
$853$		−	49.6270i		−	1.69920i	0.527431	−	0.849598i	$-0.323155\pi$
$854$		0			0
$855$	−8.10452	+	14.0374i	−0.277169	+	0.480070i
$856$		−	35.9028i		−	1.22713i
$857$	−2.94196	+	5.09563i	−0.100496	+	0.174063i	−0.911889	−	0.410437i	$-0.865376\pi$
$857$	−2.94196	+	5.09563i	−0.100496	+	0.174063i	0.811393	+	0.584500i	$0.198709\pi$
$858$	−12.8461	+	2.51148i	−0.438559	+	0.0857405i
$859$	21.6931	+	37.5735i	0.740159	+	1.28199i	0.952423	+	0.304780i	$0.0985830\pi$
$859$	21.6931	+	37.5735i	0.740159	+	1.28199i	−0.212264	+	0.977212i	$0.568084\pi$
$860$	22.0246	+	12.7159i	0.751033	+	0.433609i
$861$		0			0
$862$	−11.6106	−	20.1102i	−0.395460	−	0.684957i
$863$	26.9570	−	15.5636i	0.917626	−	0.529792i	0.0347490	−	0.999396i	$-0.488937\pi$
$863$	26.9570	−	15.5636i	0.917626	−	0.529792i	0.882877	+	0.469604i	$0.155603\pi$
$864$		−	25.3416i		−	0.862139i
$865$		−	20.6530i		−	0.702222i
$866$	7.73558	−	4.46614i	0.262866	−	0.151766i
$867$	−1.87278	−	3.24376i	−0.0636031	−	0.110164i
$868$		0			0
$869$	14.5374	+	8.39318i	0.493148	+	0.284719i
$870$	−5.81203	−	10.0667i	−0.197046	−	0.341294i
$871$	−46.3192	−	15.8929i	−1.56947	−	0.538510i
$872$	−6.04001	+	10.4616i	−0.204540	+	0.354274i
$873$		−	42.2844i		−	1.43111i
$874$	9.46341	−	16.3911i	0.320105	−	0.554438i
$875$		0			0
$876$		−	22.1870i		−	0.749629i
$877$	25.9033	+	14.9553i	0.874693	+	0.505004i	0.868905	−	0.494979i	$-0.164824\pi$
$877$	25.9033	+	14.9553i	0.874693	+	0.505004i	0.00578807	+	0.999983i	$0.498158\pi$
$878$			99.6984i			3.36466i
$879$	6.57576	+	3.79652i	0.221795	+	0.128053i
$880$	18.9603	−	32.8402i	0.639152	−	1.10704i
$881$	−7.28477	+	12.6176i	−0.245430	+	0.425097i	−0.962252	−	0.272159i	$-0.912262\pi$
$881$	−7.28477	+	12.6176i	−0.245430	+	0.425097i	0.716822	+	0.697256i	$0.245596\pi$
$882$		0			0
$883$	48.9296			1.64661			0.823307	−	0.567597i	$-0.192127\pi$
$883$	48.9296			1.64661			0.823307	+	0.567597i	$0.192127\pi$
$884$	34.8101	+	39.9569i	1.17079	+	1.34390i
$885$	4.77408	−	8.26896i	0.160479	−	0.277958i
$886$	33.7164	−	19.4662i	1.13273	−	0.653980i
$887$	−54.5902			−1.83296			−0.916480	−	0.400080i	$-0.868982\pi$
$887$	−54.5902			−1.83296			−0.916480	+	0.400080i	$0.868982\pi$
$888$	−10.7901	−	18.6890i	−0.362092	−	0.627162i
$889$		0			0
$890$	−6.36000	+	3.67195i	−0.213188	+	0.123084i
$891$	−15.5851	−	8.99803i	−0.522119	−	0.301445i
$892$	−91.9222	−	53.0713i	−3.07778	−	1.77696i
$893$	3.88430			0.129983
$894$	26.5710			0.888666
$895$	2.56909	+	1.48327i	0.0858753	+	0.0495801i
$896$		0			0
$897$	−1.20490	+	3.51165i	−0.0402306	+	0.117251i
$898$	−50.3787	−	87.2584i	−1.68116	−	2.91185i
$899$	−48.7533	+	28.1477i	−1.62601	+	0.938780i
$900$	−15.4150	−	26.6995i	−0.513832	−	0.889983i
$901$	−11.3585	+	19.6734i	−0.378405	+	0.655417i
$902$		−	53.9263i		−	1.79555i
$903$		0			0
$904$	−52.0172	+	30.0321i	−1.73007	+	0.998854i
$905$	4.60606	−	2.65931i	0.153111	−	0.0883985i
$906$	−10.1126			−0.335970
$907$	11.3628	+	19.6809i	0.377295	+	0.653494i	0.990668	−	0.136300i	$-0.0435211\pi$
$907$	11.3628	+	19.6809i	0.377295	+	0.653494i	−0.613373	+	0.789793i	$0.710188\pi$
$908$		−	64.2688i		−	2.13283i
$909$	3.49402			0.115889
$910$		0			0
$911$	−42.2359			−1.39934			−0.699669	−	0.714467i	$-0.746669\pi$
$911$	−42.2359			−1.39934			−0.699669	+	0.714467i	$0.746669\pi$
$912$		−	16.5990i		−	0.549646i
$913$	−3.64725	−	6.31722i	−0.120706	−	0.209070i
$914$	−36.0842			−1.19356
$915$	−2.11722	+	1.22238i	−0.0699933	+	0.0404106i
$916$	32.2870	−	18.6409i	1.06679	−	0.615912i
$917$		0			0
$918$		−	24.0494i		−	0.793747i
$919$	−15.3470	+	26.5818i	−0.506251	+	0.876853i	0.493722	+	0.869620i	$0.335636\pi$
$919$	−15.3470	+	26.5818i	−0.506251	+	0.876853i	−0.999974	+	0.00723365i	$0.997697\pi$
$920$	−11.1919	−	19.3849i	−0.368985	−	0.639101i
$921$	−4.03136	+	2.32751i	−0.132838	+	0.0766940i
$922$	48.4890	+	83.9854i	1.59690	+	2.76591i
$923$	−4.60780	−	1.58101i	−0.151668	−	0.0520396i
$924$		0			0
$925$	−12.3806	−	7.14797i	−0.407073	−	0.235024i
$926$	−17.4802			−0.574434
$927$	31.3195			1.02867
$928$	−39.6819	−	22.9104i	−1.30262	−	0.752070i
$929$	32.4110	+	18.7125i	1.06337	+	0.613936i	0.926362	−	0.376634i	$-0.122918\pi$
$929$	32.4110	+	18.7125i	1.06337	+	0.613936i	0.137007	+	0.990570i	$0.456252\pi$
$930$	−19.6325	+	11.3348i	−0.643775	+	0.371684i
$931$		0			0
$932$	15.4463	+	26.7538i	0.505961	+	0.876350i
$933$	−6.31574			−0.206768
$934$	−11.3218	+	6.53663i	−0.370460	+	0.213885i
$935$	6.81684	−	11.8071i	0.222935	−	0.386134i
$936$	−13.2100	−	67.5686i	−0.431782	−	2.20855i
$937$	−44.3386			−1.44848			−0.724239	−	0.689549i	$-0.757809\pi$
$937$	−44.3386			−1.44848			−0.724239	+	0.689549i	$0.757809\pi$
$938$		0			0
$939$	−3.40216	+	5.89272i	−0.111025	+	0.192302i
$940$	3.99773	−	6.92427i	0.130392	−	0.225845i
$941$	23.8202	+	13.7526i	0.776518	+	0.448323i	0.835195	−	0.549954i	$-0.185355\pi$
$941$	23.8202	+	13.7526i	0.776518	+	0.448323i	−0.0586770	+	0.998277i	$0.518688\pi$
$942$		−	18.7954i		−	0.612388i
$943$	−13.2463	−	7.64774i	−0.431358	−	0.249045i
$944$		−	99.3472i		−	3.23348i
$945$		0			0
$946$	−11.7494	+	20.3506i	−0.382007	+	0.661656i
$947$			5.08330i			0.165185i	0.996583	+	0.0825925i	$0.0263200\pi$
$947$			5.08330i			0.165185i	−0.996583	+	0.0825925i	$0.973680\pi$
$948$	7.56246	−	13.0986i	0.245617	−	0.425422i
$949$	−6.29775	−	32.2128i	−0.204434	−	1.04567i
$950$	−11.4420	−	19.8182i	−0.371229	−	0.642987i
$951$	7.50534	+	4.33321i	0.243377	+	0.140514i
$952$		0			0
$953$	4.90718	+	8.49949i	0.158959	+	0.275326i	0.934494	−	0.355980i	$-0.115853\pi$
$953$	4.90718	+	8.49949i	0.158959	+	0.275326i	−0.775534	+	0.631305i	$0.782519\pi$
$954$	44.4861	−	25.6840i	1.44029	−	0.831552i
$955$			7.89284i			0.255406i
$956$		−	44.1543i		−	1.42805i
$957$	6.52536	−	3.76742i	0.210935	−	0.121783i
$958$	12.2353	+	21.1921i	0.395303	+	0.684685i
$959$		0			0
$960$	−3.39041	−	1.95746i	−0.109425	−	0.0631766i
$961$	39.3947	+	68.2336i	1.27080	+	2.20108i
$962$	−36.4997	−	41.8964i	−1.17680	−	1.35079i
$963$	−7.01268	+	12.1463i	−0.225981	+	0.391410i
$964$		−	47.4121i		−	1.52704i
$965$	2.43348	−	4.21490i	0.0783364	−	0.135683i
$966$		0			0
$967$			2.69619i			0.0867036i	0.999060	+	0.0433518i	$0.0138036\pi$
$967$			2.69619i			0.0867036i	−0.999060	+	0.0433518i	$0.986196\pi$
$968$	−22.3009	−	12.8754i	−0.716779	−	0.413832i
$969$		−	5.96786i		−	0.191715i
$970$	−55.9504	−	32.3030i	−1.79646	−	1.03719i
$971$	12.4620	−	21.5848i	0.399925	−	0.692691i	−0.593791	−	0.804619i	$-0.702369\pi$
$971$	12.4620	−	21.5848i	0.399925	−	0.692691i	0.993716	+	0.111929i	$0.0357028\pi$
$972$	−29.0598	+	50.3331i	−0.932094	+	1.61443i
$973$		0			0
$974$	−103.543			−3.31773
$975$	2.94862	+	3.38459i	0.0944314	+	0.108394i
$976$	−12.7187	+	22.0294i	−0.407115	+	0.705144i
$977$	24.5197	−	14.1565i	0.784456	−	0.452906i	−0.0535514	−	0.998565i	$-0.517054\pi$
$977$	24.5197	−	14.1565i	0.784456	−	0.452906i	0.838007	+	0.545659i	$0.183721\pi$
$978$	9.62280			0.307703
$979$	−2.38019	−	4.12262i	−0.0760713	−	0.131759i
$980$		0			0
$981$	4.08681	−	2.35952i	0.130482	−	0.0753337i
$982$	15.1567	+	8.75073i	0.483670	+	0.279247i
$983$	32.7805	+	18.9258i	1.04554	+	0.603641i	0.921396	−	0.388624i	$-0.127049\pi$
$983$	32.7805	+	18.9258i	1.04554	+	0.603641i	0.124140	+	0.992265i	$0.460383\pi$
$984$	−27.9166			−0.889947
$985$	7.49591			0.238839
$986$	−37.6585	−	21.7421i	−1.19929	−	0.692410i
$987$		0			0
$988$	−11.9725	−	61.2391i	−0.380897	−	1.94827i
$989$	3.33257	+	5.77218i	0.105970	+	0.183545i
$990$	−26.6986	+	15.4144i	−0.848536	+	0.489903i
$991$	−29.2079	−	50.5896i	−0.927820	−	1.60703i	−0.786962	−	0.617001i	$-0.788347\pi$
$991$	−29.2079	−	50.5896i	−0.927820	−	1.60703i	−0.140858	−	0.990030i	$-0.544986\pi$
$992$	−44.6806	+	77.3891i	−1.41861	+	2.45711i
$993$		−	2.05657i		−	0.0652633i
$994$		0			0
$995$	0.573399	−	0.331052i	0.0181780	−	0.0104950i
$996$	−5.69197	+	3.28626i	−0.180357	+	0.104129i
$997$	−28.0588			−0.888632			−0.444316	−	0.895870i	$-0.646553\pi$
$997$	−28.0588			−0.888632			−0.444316	+	0.895870i	$0.646553\pi$
$998$	14.7001	+	25.4613i	0.465322	+	0.805962i
$999$			17.6903i			0.559696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.i.459.1		12
7.2	even	3		637.2.u.g.30.1		12
7.3	odd	6		637.2.q.g.589.6		12
7.4	even	3		637.2.q.i.589.6		12
7.5	odd	6		91.2.u.b.30.1	yes	12
7.6	odd	2		91.2.k.b.4.1	✓	12
13.10	even	6		637.2.u.g.361.1		12
21.5	even	6		819.2.do.e.667.6		12
21.20	even	2		819.2.bm.f.550.6		12
91.6	even	12		1183.2.e.j.508.12		24
91.10	odd	6		637.2.q.g.491.6		12
91.19	even	12		1183.2.e.j.170.12		24
91.20	even	12		1183.2.e.j.508.1		24
91.23	even	6	inner	637.2.k.i.569.6		12
91.32	odd	12		8281.2.a.co.1.1		12
91.33	even	12		1183.2.e.j.170.1		24
91.45	even	12		8281.2.a.cp.1.1		12
91.46	odd	12		8281.2.a.co.1.12		12
91.59	even	12		8281.2.a.cp.1.12		12
91.62	odd	6		91.2.u.b.88.1	yes	12
91.75	odd	6		91.2.k.b.23.6	yes	12
91.88	even	6		637.2.q.i.491.6		12
273.62	even	6		819.2.do.e.361.6		12
273.257	even	6		819.2.bm.f.478.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.1	✓	12	7.6	odd	2
91.2.k.b.23.6	yes	12	91.75	odd	6
91.2.u.b.30.1	yes	12	7.5	odd	6
91.2.u.b.88.1	yes	12	91.62	odd	6
637.2.k.i.459.1		12	1.1	even	1	trivial
637.2.k.i.569.6		12	91.23	even	6	inner
637.2.q.g.491.6		12	91.10	odd	6
637.2.q.g.589.6		12	7.3	odd	6
637.2.q.i.491.6		12	91.88	even	6
637.2.q.i.589.6		12	7.4	even	3
637.2.u.g.30.1		12	7.2	even	3
637.2.u.g.361.1		12	13.10	even	6
819.2.bm.f.478.1		12	273.257	even	6
819.2.bm.f.550.6		12	21.20	even	2
819.2.do.e.361.6		12	273.62	even	6
819.2.do.e.667.6		12	21.5	even	6
1183.2.e.j.170.1		24	91.33	even	12
1183.2.e.j.170.12		24	91.19	even	12
1183.2.e.j.508.1		24	91.20	even	12
1183.2.e.j.508.12		24	91.6	even	12
8281.2.a.co.1.1		12	91.32	odd	12
8281.2.a.co.1.12		12	91.46	odd	12
8281.2.a.cp.1.1		12	91.45	even	12
8281.2.a.cp.1.12		12	91.59	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.58860i q^{2} +(0.259233 + 0.449005i) q^{3} -4.70085 q^{4} +(1.39608 - 0.806027i) q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +O(q^{10})\)	\(q-2.58860i q^{2} +(0.259233 + 0.449005i) q^{3} -4.70085 q^{4} +(1.39608 - 0.806027i) q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +(-2.08648 - 3.61389i) q^{10} +(2.34256 - 1.35248i) q^{11} +(-1.21862 - 2.11070i) q^{12} +(-2.36840 - 2.71858i) q^{13} +(0.723819 + 0.417897i) q^{15} +8.69632 q^{16} +3.12661 q^{17} +(-6.12277 - 3.53498i) q^{18} +(-3.18828 - 1.84075i) q^{19} +(-6.56276 + 3.78901i) q^{20} +(-3.50103 - 6.06396i) q^{22} -1.98604 q^{23} +(-3.13918 + 1.81241i) q^{24} +(-1.20064 + 2.07957i) q^{25} +(-7.03732 + 6.13084i) q^{26} +2.97143 q^{27} +(2.68636 - 4.65290i) q^{29} +(1.08177 - 1.87368i) q^{30} +(-9.07425 - 5.23902i) q^{31} -8.52843i q^{32} +(1.21454 + 0.701214i) q^{33} -8.09354i q^{34} +(-6.41947 + 11.1188i) q^{36} +5.95346i q^{37} +(-4.76497 + 8.25317i) q^{38} +(0.606687 - 1.76817i) q^{39} +(5.63528 + 9.76059i) q^{40} +(6.66970 + 3.85075i) q^{41} +(-1.67800 - 2.90638i) q^{43} +(-11.0120 + 6.35780i) q^{44} -4.40283i q^{45} +5.14106i q^{46} +(-0.913730 + 0.527542i) q^{47} +(2.25437 + 3.90469i) q^{48} +(5.38318 + 3.10798i) q^{50} +(0.810520 + 1.40386i) q^{51} +(11.1335 + 12.7796i) q^{52} +(-3.63284 + 6.29226i) q^{53} -7.69184i q^{54} +(2.18027 - 3.77633i) q^{55} -1.90873i q^{57} +(-12.0445 - 6.95390i) q^{58} -11.4241i q^{59} +(-3.40257 - 1.96447i) q^{60} +(-1.46254 + 2.53319i) q^{61} +(-13.5617 + 23.4896i) q^{62} -4.68406 q^{64} +(-5.49772 - 1.88636i) q^{65} +(1.81516 - 3.14395i) q^{66} +(11.7622 - 6.79091i) q^{67} -14.6977 q^{68} +(-0.514846 - 0.891740i) q^{69} +(1.17009 - 0.675554i) q^{71} +(16.5367 + 9.54747i) q^{72} +(7.88374 + 4.55168i) q^{73} +15.4111 q^{74} -1.24498 q^{75} +(14.9876 + 8.65311i) q^{76} +(-4.57708 - 1.57047i) q^{78} +(3.10289 + 5.37436i) q^{79} +(12.1407 - 7.00946i) q^{80} +(-3.32650 - 5.76166i) q^{81} +(9.96806 - 17.2652i) q^{82} -2.69672i q^{83} +(4.36499 - 2.52013i) q^{85} +(-7.52346 + 4.34367i) q^{86} +2.78557 q^{87} +(9.45576 + 16.3779i) q^{88} -1.75988i q^{89} -11.3972 q^{90} +9.33607 q^{92} -5.43251i q^{93} +(1.36560 + 2.36528i) q^{94} -5.93478 q^{95} +(3.82930 - 2.21085i) q^{96} +(13.4078 - 7.74102i) q^{97} -7.38776i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9	\( 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9} - 12 q^{10} + 12 q^{11} + q^{12} + 2 q^{13} - 12 q^{15} + 16 q^{16} + 34 q^{17} + 3 q^{18} - 9 q^{19} + 3 q^{20} - 15 q^{22} - 6 q^{23} - 15 q^{24} - 5 q^{25} + 6 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{31} + 6 q^{33} - 13 q^{36} - 19 q^{38} - 4 q^{39} + q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} + 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{55} - 24 q^{58} - 30 q^{60} - 5 q^{61} - 41 q^{62} + 2 q^{64} + 21 q^{65} + 34 q^{66} + 15 q^{67} - 22 q^{68} - 7 q^{69} + 30 q^{71} + 57 q^{72} - 42 q^{73} + 66 q^{74} + 2 q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} + 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 57 q^{86} + 20 q^{87} - 14 q^{88} - 66 q^{92} - q^{94} - 4 q^{95} - 21 q^{96} + 3 q^{97}+O(q^{100}) \) 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9 - 12 * q^10 + 12 * q^11 + q^12 + 2 * q^13 - 12 * q^15 + 16 * q^16 + 34 * q^17 + 3 * q^18 - 9 * q^19 + 3 * q^20 - 15 * q^22 - 6 * q^23 - 15 * q^24 - 5 * q^25 + 6 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^31 + 6 * q^33 - 13 * q^36 - 19 * q^38 - 4 * q^39 + q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 + 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 + 7 * q^52 - 8 * q^53 + 15 * q^55 - 24 * q^58 - 30 * q^60 - 5 * q^61 - 41 * q^62 + 2 * q^64 + 21 * q^65 + 34 * q^66 + 15 * q^67 - 22 * q^68 - 7 * q^69 + 30 * q^71 + 57 * q^72 - 42 * q^73 + 66 * q^74 + 2 * q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 + 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 57 * q^86 + 20 * q^87 - 14 * q^88 - 66 * q^92 - q^94 - 4 * q^95 - 21 * q^96 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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