LMFDB - Embedded newform 637.2.k.i.459.5

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			459.5
Root			$0.874681 - 1.11128i$ of defining polynomial
Character	$\chi$	$=$	637.459
Dual form			637.2.k.i.569.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.34523i q^{2} +(1.02505 + 1.77544i) q^{3} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.38837 + 1.37893i) q^{6} +2.94654i q^{8} +(-0.601462 + 1.04176i) q^{9} +O(q^{10})$	\(q+1.34523i q^{2} +(1.02505 + 1.77544i) q^{3} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.38837 + 1.37893i) q^{6} +2.94654i q^{8} +(-0.601462 + 1.04176i) q^{9} +(-2.39973 - 4.15646i) q^{10} +(-1.10736 + 0.639336i) q^{11} +(0.195135 + 0.337984i) q^{12} +(-3.57420 - 0.474474i) q^{13} +(-6.33438 - 3.65716i) q^{15} -3.58303 q^{16} +7.73920 q^{17} +(-1.40141 - 0.809103i) q^{18} +(-0.817422 - 0.471939i) q^{19} +(-0.588191 + 0.339592i) q^{20} +(-0.860052 - 1.48965i) q^{22} -1.64727 q^{23} +(-5.23141 + 3.02035i) q^{24} +(3.86451 - 6.69354i) q^{25} +(0.638275 - 4.80810i) q^{26} +3.68419 q^{27} +(-2.02242 + 3.50293i) q^{29} +(4.91970 - 8.52117i) q^{30} +(-4.46193 - 2.57610i) q^{31} +1.07309i q^{32} +(-2.27021 - 1.31071i) q^{33} +10.4110i q^{34} +(-0.114498 + 0.198317i) q^{36} +1.05608i q^{37} +(0.634865 - 1.09962i) q^{38} +(-2.82133 - 6.83214i) q^{39} +(-5.25629 - 9.10417i) q^{40} +(3.63629 + 2.09941i) q^{41} +(1.91532 + 3.31744i) q^{43} +(-0.210805 + 0.121708i) q^{44} -4.29176i q^{45} -2.21596i q^{46} +(-0.774415 + 0.447109i) q^{47} +(-3.67279 - 6.36146i) q^{48} +(9.00432 + 5.19865i) q^{50} +(7.93308 + 13.7405i) q^{51} +(-0.680407 - 0.0903239i) q^{52} +(0.0399961 - 0.0692754i) q^{53} +4.95607i q^{54} +(2.28101 - 3.95082i) q^{55} -1.93505i q^{57} +(-4.71224 - 2.72061i) q^{58} +11.1847i q^{59} +(-1.20585 - 0.696200i) q^{60} +(-3.81196 + 6.60251i) q^{61} +(3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(11.8899 - 4.90994i) q^{65} +(1.76319 - 3.05394i) q^{66} +(5.47418 - 3.16052i) q^{67} +1.47328 q^{68} +(-1.68854 - 2.92464i) q^{69} +(9.89346 - 5.71199i) q^{71} +(-3.06959 - 1.77223i) q^{72} +(-0.658617 - 0.380253i) q^{73} -1.42067 q^{74} +15.8453 q^{75} +(-0.155610 - 0.0898413i) q^{76} +(9.19077 - 3.79533i) q^{78} +(1.42765 + 2.47277i) q^{79} +(11.0708 - 6.39172i) q^{80} +(5.58087 + 9.66636i) q^{81} +(-2.82418 + 4.89163i) q^{82} +2.32483i q^{83} +(-23.9125 + 13.8059i) q^{85} +(-4.46270 + 2.57654i) q^{86} -8.29233 q^{87} +(-1.88383 - 3.26289i) q^{88} -7.57626i q^{89} +5.77339 q^{90} -0.313586 q^{92} -10.5625i q^{93} +(-0.601462 - 1.04176i) q^{94} +3.36755 q^{95} +(-1.90522 + 1.09998i) q^{96} +(0.414443 - 0.239279i) q^{97} -1.53815i 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 $

$2$			1.34523i			0.951219i	0.879657	+	0.475609i	$0.157772\pi$
$2$			1.34523i			0.951219i	−0.879657	+	0.475609i	$0.842228\pi$
$3$	1.02505	+	1.77544i	0.591814	+	1.02505i	0.993988	+	0.109489i	$0.0349213\pi$
$3$	1.02505	+	1.77544i	0.591814	+	1.02505i	−0.402174	+	0.915563i	$0.631745\pi$
$4$	0.190366			0.0951832
$5$	−3.08979	+	1.78389i	−1.38179	+	0.797779i	−0.992372	−	0.123280i	$-0.960659\pi$
$5$	−3.08979	+	1.78389i	−1.38179	+	0.797779i	−0.389422	+	0.921059i	$0.627325\pi$
$6$	−2.38837	+	1.37893i	−0.975048	+	0.562944i
$7$		0			0
$7$		0			0
$8$			2.94654i			1.04176i
$9$	−0.601462	+	1.04176i	−0.200487	+	0.347254i
$10$	−2.39973	−	4.15646i	−0.758862	−	1.31439i
$11$	−1.10736	+	0.639336i	−0.333882	+	0.192767i	−0.657563	−	0.753399i	$-0.728413\pi$
$11$	−1.10736	+	0.639336i	−0.333882	+	0.192767i	0.323681	+	0.946166i	$0.395080\pi$
$12$	0.195135	+	0.337984i	0.0563307	+	0.0975677i
$13$	−3.57420	−	0.474474i	−0.991304	−	0.131595i
$13$	−3.57420	−	0.474474i	−0.991304	−	0.131595i
$14$		0			0
$15$	−6.33438	−	3.65716i	−1.63553	−	0.944273i
$16$	−3.58303			−0.895757
$17$	7.73920			1.87703			0.938515	−	0.345238i	$-0.112202\pi$
$17$	7.73920			1.87703			0.938515	+	0.345238i	$0.112202\pi$
$18$	−1.40141	−	0.809103i	−0.330315	−	0.190707i
$19$	−0.817422	−	0.471939i	−0.187530	−	0.108270i	0.403296	−	0.915070i	$-0.367865\pi$
$19$	−0.817422	−	0.471939i	−0.187530	−	0.108270i	−0.590826	+	0.806799i	$0.701198\pi$
$20$	−0.588191	+	0.339592i	−0.131524	+	0.0759352i
$21$		0			0
$22$	−0.860052	−	1.48965i	−0.183364	−	0.317595i
$23$	−1.64727			−0.343481			−0.171740	−	0.985142i	$-0.554939\pi$
$23$	−1.64727			−0.343481			−0.171740	+	0.985142i	$0.554939\pi$
$24$	−5.23141	+	3.02035i	−1.06786	+	0.616527i
$25$	3.86451	−	6.69354i	0.772903	−	1.33871i
$26$	0.638275	−	4.80810i	0.125176	−	0.942946i
$27$	3.68419			0.709023
$28$		0			0
$29$	−2.02242	+	3.50293i	−0.375554	+	0.650478i	−0.990410	−	0.138161i	$-0.955881\pi$
$29$	−2.02242	+	3.50293i	−0.375554	+	0.650478i	0.614856	+	0.788639i	$0.289214\pi$
$30$	4.91970	−	8.52117i	0.898210	−	1.55575i
$31$	−4.46193	−	2.57610i	−0.801387	−	0.462681i	0.0425691	−	0.999094i	$-0.486446\pi$
$31$	−4.46193	−	2.57610i	−0.801387	−	0.462681i	−0.843956	+	0.536413i	$0.819779\pi$
$32$			1.07309i			0.189698i
$33$	−2.27021	−	1.31071i	−0.395192	−	0.228164i
$34$			10.4110i			1.78547i
$35$		0			0
$36$	−0.114498	+	0.198317i	−0.0190830	+	0.0330528i
$37$			1.05608i			0.173619i	0.996225	+	0.0868094i	$0.0276671\pi$
$37$			1.05608i			0.173619i	−0.996225	+	0.0868094i	$0.972333\pi$
$38$	0.634865	−	1.09962i	0.102989	−	0.178382i
$39$	−2.82133	−	6.83214i	−0.451775	−	1.09402i
$40$	−5.25629	−	9.10417i	−0.831093	−	1.43950i
$41$	3.63629	+	2.09941i	0.567893	+	0.327873i	0.756307	−	0.654217i	$-0.227002\pi$
$41$	3.63629	+	2.09941i	0.567893	+	0.327873i	−0.188415	+	0.982090i	$0.560335\pi$
$42$		0			0
$43$	1.91532	+	3.31744i	0.292084	+	0.505904i	0.974302	−	0.225244i	$-0.0723180\pi$
$43$	1.91532	+	3.31744i	0.292084	+	0.505904i	−0.682218	+	0.731148i	$0.738985\pi$
$44$	−0.210805	+	0.121708i	−0.0317800	+	0.0183482i
$45$		−	4.29176i		−	0.639778i
$46$		−	2.21596i		−	0.326725i
$47$	−0.774415	+	0.447109i	−0.112960	+	0.0652175i	−0.555416	−	0.831573i	$-0.687441\pi$
$47$	−0.774415	+	0.447109i	−0.112960	+	0.0652175i	0.442456	+	0.896790i	$0.354107\pi$
$48$	−3.67279	−	6.36146i	−0.530121	−	0.918197i
$49$		0			0
$50$	9.00432	+	5.19865i	1.27340	+	0.735200i
$51$	7.93308	+	13.7405i	1.11085	+	1.92405i
$52$	−0.680407	−	0.0903239i	−0.0943554	−	0.0125257i
$53$	0.0399961	−	0.0692754i	0.00549389	−	0.00951570i	−0.863265	−	0.504750i	$-0.831585\pi$
$53$	0.0399961	−	0.0692754i	0.00549389	−	0.00951570i	0.868759	+	0.495235i	$0.164918\pi$
$54$			4.95607i			0.674436i
$55$	2.28101	−	3.95082i	0.307571	−	0.532729i
$56$		0			0
$57$		−	1.93505i		−	0.256303i
$58$	−4.71224	−	2.72061i	−0.618747	−	0.357234i
$59$			11.1847i			1.45613i	0.685509	+	0.728064i	$0.259580\pi$
$59$			11.1847i			1.45613i	−0.685509	+	0.728064i	$0.740420\pi$
$60$	−1.20585	−	0.696200i	−0.155675	−	0.0898790i
$61$	−3.81196	+	6.60251i	−0.488072	+	0.845365i	−0.999906	−	0.0137195i	$-0.995633\pi$
$61$	−3.81196	+	6.60251i	−0.488072	+	0.845365i	0.511834	+	0.859084i	$0.328966\pi$
$62$	3.46543	−	6.00231i	0.440111	−	0.762294i
$63$		0			0
$64$	−8.60961			−1.07620
$65$	11.8899	−	4.90994i	1.47476	−	0.609003i
$66$	1.76319	−	3.05394i	0.217034	−	0.375914i
$67$	5.47418	−	3.16052i	0.668777	−	0.386119i	−0.126836	−	0.991924i	$-0.540482\pi$
$67$	5.47418	−	3.16052i	0.668777	−	0.386119i	0.795613	+	0.605805i	$0.207149\pi$
$68$	1.47328			0.178662
$69$	−1.68854	−	2.92464i	−0.203277	−	0.352085i
$70$		0			0
$71$	9.89346	−	5.71199i	1.17414	−	0.677889i	0.219487	−	0.975616i	$-0.429562\pi$
$71$	9.89346	−	5.71199i	1.17414	−	0.677889i	0.954651	+	0.297727i	$0.0962285\pi$
$72$	−3.06959	−	1.77223i	−0.361755	−	0.208859i
$73$	−0.658617	−	0.380253i	−0.0770853	−	0.0445052i	0.460962	−	0.887420i	$-0.347504\pi$
$73$	−0.658617	−	0.380253i	−0.0770853	−	0.0445052i	−0.538047	+	0.842915i	$0.680838\pi$
$74$	−1.42067			−0.165149
$75$	15.8453			1.82966
$76$	−0.155610	−	0.0898413i	−0.0178497	−	0.0103055i
$77$		0			0
$78$	9.19077	−	3.79533i	1.04065	−	0.429737i
$79$	1.42765	+	2.47277i	0.160624	+	0.278208i	0.935093	−	0.354404i	$-0.115316\pi$
$79$	1.42765	+	2.47277i	0.160624	+	0.278208i	−0.774469	+	0.632612i	$0.781983\pi$
$80$	11.0708	−	6.39172i	1.23775	−	0.714616i
$81$	5.58087	+	9.66636i	0.620097	+	1.07404i
$82$	−2.82418	+	4.89163i	−0.311879	+	0.540190i
$83$			2.32483i			0.255183i	0.991827	+	0.127591i	$0.0407246\pi$
$83$			2.32483i			0.255183i	−0.991827	+	0.127591i	$0.959275\pi$
$84$		0			0
$85$	−23.9125	+	13.8059i	−2.59367	+	1.49746i
$86$	−4.46270	+	2.57654i	−0.481226	+	0.277836i
$87$	−8.29233			−0.889032
$88$	−1.88383	−	3.26289i	−0.200817	−	0.347825i
$89$		−	7.57626i		−	0.803082i	−0.915841	−	0.401541i	$-0.868475\pi$
$89$		−	7.57626i		−	0.803082i	0.915841	−	0.401541i	$-0.131525\pi$
$90$	5.77339			0.608569
$91$		0			0
$92$	−0.313586			−0.0326936
$93$		−	10.5625i		−	1.09528i
$94$	−0.601462	−	1.04176i	−0.0620361	−	0.107450i
$95$	3.36755			0.345503
$96$	−1.90522	+	1.09998i	−0.194450	+	0.112266i
$97$	0.414443	−	0.239279i	0.0420803	−	0.0242951i	−0.478812	−	0.877917i	$-0.658933\pi$
$97$	0.414443	−	0.239279i	0.0420803	−	0.0242951i	0.520893	+	0.853622i	$0.325599\pi$
$98$		0			0
$99$		−	1.53815i		−	0.154589i
$100$	0.735674	−	1.27422i	0.0735674	−	0.127422i
$101$	−1.43918	−	2.49273i	−0.143204	−	0.248036i	0.785498	−	0.618865i	$-0.212407\pi$
$101$	−1.43918	−	2.49273i	−0.143204	−	0.248036i	−0.928701	+	0.370829i	$0.879074\pi$
$102$	−18.4841	+	10.6718i	−1.83020	+	1.05666i
$103$	5.66755	+	9.81649i	0.558441	+	0.967248i	0.997627	+	0.0688516i	$0.0219335\pi$
$103$	5.66755	+	9.81649i	0.558441	+	0.967248i	−0.439186	+	0.898396i	$0.644733\pi$
$104$	1.39806	−	10.5315i	0.137091	−	1.03270i
$105$		0			0
$106$	0.0931910	+	0.0538039i	0.00905151	+	0.00522589i
$107$	−6.57206			−0.635345			−0.317673	−	0.948200i	$-0.602901\pi$
$107$	−6.57206			−0.635345			−0.317673	+	0.948200i	$0.602901\pi$
$108$	0.701346			0.0674871
$109$	−5.05684	−	2.91957i	−0.484358	−	0.279644i	0.237873	−	0.971296i	$-0.423550\pi$
$109$	−5.05684	−	2.91957i	−0.484358	−	0.279644i	−0.722231	+	0.691652i	$0.756883\pi$
$110$	5.31475	+	3.06847i	0.506741	+	0.292567i
$111$	−1.87501	+	1.08254i	−0.177968	+	0.102750i
$112$		0			0
$113$	−3.26617	−	5.65717i	−0.307255	−	0.532181i	0.670506	−	0.741904i	$-0.266077\pi$
$113$	−3.26617	−	5.65717i	−0.307255	−	0.532181i	−0.977761	+	0.209723i	$0.932744\pi$
$114$	2.60308			0.243800
$115$	5.08973	−	2.93855i	0.474619	−	0.274022i
$116$	−0.385001	+	0.666841i	−0.0357464	+	0.0619146i
$117$	2.64403	−	3.43809i	0.244441	−	0.317851i
$118$	−15.0460			−1.38510
$119$		0			0
$120$	10.7759	−	18.6645i	0.983705	−	1.70383i
$121$	−4.68250	+	8.11033i	−0.425682	+	0.737302i
$122$	−8.88187	−	5.12795i	−0.804127	−	0.464263i
$123$			8.60802i			0.776159i
$124$	−0.849402	−	0.490402i	−0.0762786	−	0.0440394i
$125$			9.73656i			0.870865i
$126$		0			0
$127$	7.35818	−	12.7447i	0.652932	−	1.13091i	−0.329475	−	0.944164i	$-0.606872\pi$
$127$	7.35818	−	12.7447i	0.652932	−	1.13091i	0.982408	−	0.186748i	$-0.0597948\pi$
$128$		−	9.43568i		−	0.834005i
$129$	−3.92661	+	6.80109i	−0.345719	+	0.598802i
$130$	6.60498	+	15.9946i	0.579295	+	1.40282i
$131$	5.59335	+	9.68796i	0.488693	+	0.846441i	0.999915	−	0.0130074i	$-0.00414049\pi$
$131$	5.59335	+	9.68796i	0.488693	+	0.846441i	−0.511222	+	0.859448i	$0.670807\pi$
$132$	−0.432171	−	0.249514i	−0.0376157	−	0.0217174i
$133$		0			0
$134$	4.25161	+	7.36400i	0.367283	+	0.636153i
$135$	−11.3834	+	6.57219i	−0.979724	+	0.565644i
$136$			22.8038i			1.95541i
$137$			17.6308i			1.50630i	0.657848	+	0.753151i	$0.271467\pi$
$137$			17.6308i			1.50630i	−0.657848	+	0.753151i	$0.728533\pi$
$138$	3.93430	−	2.27147i	0.334910	−	0.193360i
$139$	−2.92855	−	5.07240i	−0.248396	−	0.430235i	0.714685	−	0.699447i	$-0.246570\pi$
$139$	−2.92855	−	5.07240i	−0.248396	−	0.430235i	−0.963081	+	0.269212i	$0.913237\pi$
$140$		0			0
$141$	−1.58763	−	0.916619i	−0.133703	−	0.0771932i
$142$	7.68392	+	13.3089i	0.644820	+	1.11686i
$143$	4.26128	−	1.75970i	0.356346	−	0.147153i
$144$	2.15506	−	3.73267i	0.179588	−	0.311055i
$145$		−	14.4311i		−	1.19844i
$146$	0.511526	−	0.885989i	0.0423342	−	0.0733250i
$147$		0			0
$148$			0.201043i			0.0165256i
$149$	9.07505	+	5.23948i	0.743457	+	0.429235i	0.823325	−	0.567570i	$-0.192116\pi$
$149$	9.07505	+	5.23948i	0.743457	+	0.429235i	−0.0798677	+	0.996805i	$0.525450\pi$
$150$			21.3155i			1.74041i
$151$	−4.08249	−	2.35703i	−0.332229	−	0.191812i	0.324602	−	0.945851i	$-0.394770\pi$
$151$	−4.08249	−	2.35703i	−0.332229	−	0.191812i	−0.656830	+	0.754039i	$0.728103\pi$
$152$	1.39059	−	2.40857i	0.112791	−	0.195361i
$153$	−4.65483	+	8.06241i	−0.376321	+	0.651807i
$154$		0			0
$155$	18.3819			1.47647
$156$	−0.537087	−	1.30061i	−0.0430014	−	0.104132i
$157$	4.50105	−	7.79604i	0.359223	−	0.622192i	−0.628608	−	0.777722i	$-0.716375\pi$
$157$	4.50105	−	7.79604i	0.359223	−	0.622192i	0.987831	+	0.155530i	$0.0497085\pi$
$158$	−3.32643	+	1.92052i	−0.264637	+	0.152788i
$159$	0.163992			0.0130054
$160$	−1.91428	−	3.31563i	−0.151337	−	0.262123i
$161$		0			0
$162$	−13.0034	+	7.50754i	−1.02165	+	0.589848i
$163$	10.4203	+	6.01619i	0.816185	+	0.471224i	0.849099	−	0.528234i	$-0.177146\pi$
$163$	10.4203	+	6.01619i	0.816185	+	0.471224i	−0.0329144	+	0.999458i	$0.510479\pi$
$164$	0.692227	+	0.399657i	0.0540538	+	0.0312080i
$165$	9.35261			0.728099
$166$	−3.12742			−0.242735
$167$	16.8199	+	9.71099i	1.30157	+	0.751459i	0.980672	−	0.195657i	$-0.0626838\pi$
$167$	16.8199	+	9.71099i	1.30157	+	0.751459i	0.320893	+	0.947116i	$0.396017\pi$
$168$		0			0
$169$	12.5497	+	3.39173i	0.965365	+	0.260902i
$170$	−18.5720	−	32.1677i	−1.42441	−	2.46715i
$171$	0.983297	−	0.567707i	0.0751946	−	0.0434136i
$172$	0.364613	+	0.631528i	0.0278015	+	0.0481536i
$173$	−7.18976	+	12.4530i	−0.546627	+	0.946786i	0.451875	+	0.892081i	$0.350755\pi$
$173$	−7.18976	+	12.4530i	−0.546627	+	0.946786i	−0.998503	+	0.0547049i	$0.982578\pi$
$174$		−	11.1551i		−	0.845663i
$175$		0			0
$176$	3.96771	−	2.29076i	0.299077	−	0.172672i
$177$	−19.8578	+	11.4649i	−1.49261	+	0.861757i
$178$	10.1918			0.763907
$179$	2.71303	+	4.69911i	0.202781	+	0.351228i	0.949424	−	0.313998i	$-0.101669\pi$
$179$	2.71303	+	4.69911i	0.202781	+	0.351228i	−0.746642	+	0.665226i	$0.768335\pi$
$180$		−	0.817008i		−	0.0608962i
$181$	15.4902			1.15138			0.575688	−	0.817669i	$-0.304734\pi$
$181$	15.4902			1.15138			0.575688	+	0.817669i	$0.304734\pi$
$182$		0			0
$183$	−15.6298			−1.15539
$184$		−	4.85376i		−	0.357824i
$185$	−1.88393	−	3.26307i	−0.138509	−	0.239905i
$186$	14.2090			1.04185
$187$	−8.57010	+	4.94795i	−0.626707	+	0.361830i
$188$	−0.147423	+	0.0851144i	−0.0107519	+	0.00620761i
$189$		0			0
$190$			4.53011i			0.328649i
$191$	−2.37311	+	4.11035i	−0.171712	+	0.297414i	−0.939019	−	0.343866i	$-0.888263\pi$
$191$	−2.37311	+	4.11035i	−0.171712	+	0.297414i	0.767306	+	0.641281i	$0.221597\pi$
$192$	−8.82529	−	15.2859i	−0.636911	−	1.10316i
$193$	18.2204	−	10.5196i	1.31154	−	0.757215i	0.329185	−	0.944266i	$-0.393226\pi$
$193$	18.2204	−	10.5196i	1.31154	−	0.757215i	0.982350	+	0.187050i	$0.0598928\pi$
$194$	0.321884	+	0.557519i	0.0231099	+	0.0400276i
$195$	20.9051	+	16.0769i	1.49704	+	1.15129i
$196$		0			0
$197$	5.03342	+	2.90604i	0.358616	+	0.207047i	0.668474	−	0.743736i	$-0.266948\pi$
$197$	5.03342	+	2.90604i	0.358616	+	0.207047i	−0.309857	+	0.950783i	$0.600281\pi$
$198$	2.06915			0.147048
$199$	10.6182			0.752703			0.376352	−	0.926477i	$-0.377179\pi$
$199$	10.6182			0.752703			0.376352	+	0.926477i	$0.377179\pi$
$200$	19.7228	+	11.3869i	1.39461	+	0.805178i
$201$	11.2226	+	6.47939i	0.791583	+	0.457021i
$202$	3.35329	−	1.93602i	0.235936	−	0.136218i
$203$		0			0
$204$	1.51019	+	2.61573i	0.105735	+	0.183138i
$205$	−14.9805			−1.04628
$206$	−13.2054	+	7.62414i	−0.920064	+	0.531199i
$207$	0.990773	−	1.71607i	0.0688635	−	0.119275i
$208$	12.8064	+	1.70005i	0.887967	+	0.117877i
$209$	1.20691			0.0834837
$210$		0			0
$211$	2.33275	−	4.04043i	0.160593	−	0.278155i	−0.774489	−	0.632588i	$-0.781993\pi$
$211$	2.33275	−	4.04043i	0.160593	−	0.278155i	0.935081	+	0.354433i	$0.115326\pi$
$212$	0.00761392	−	0.0131877i	0.000522926	−	0.000905735i
$213$	20.2826	+	11.7102i	1.38974	+	0.802368i
$214$		−	8.84091i		−	0.604352i
$215$	−11.8359	−	6.83344i	−0.807200	−	0.466037i
$216$			10.8556i			0.738631i
$217$		0			0
$218$	3.92748	−	6.80260i	0.266003	−	0.460730i
$219$		−	1.55912i		−	0.105355i
$220$	0.434227	−	0.752104i	0.0292756	−	0.0507068i
$221$	−27.6614	−	3.67205i	−1.86071	−	0.247009i
$222$	−1.45626	−	2.52232i	−0.0977377	−	0.169287i
$223$	−20.9798	−	12.1127i	−1.40491	−	0.811126i	−0.410020	−	0.912076i	$-0.634478\pi$
$223$	−20.9798	−	12.1127i	−1.40491	−	0.811126i	−0.994891	+	0.100950i	$0.967812\pi$
$224$		0			0
$225$	4.64872	+	8.05182i	0.309915	+	0.536788i
$226$	7.61017	−	4.39373i	0.506221	−	0.292267i
$227$		−	15.3753i		−	1.02049i	−0.860028	−	0.510247i	$-0.829554\pi$
$227$		−	15.3753i		−	1.02049i	0.860028	−	0.510247i	$-0.170446\pi$
$228$		−	0.368368i		−	0.0243958i
$229$	14.1608	−	8.17573i	0.935771	−	0.540268i	0.0471389	−	0.998888i	$-0.484990\pi$
$229$	14.1608	−	8.17573i	0.935771	−	0.540268i	0.888632	+	0.458621i	$0.151656\pi$
$230$	3.95302	+	6.84683i	0.260654	+	0.451467i
$231$		0			0
$232$	−10.3215	−	5.95913i	−0.677641	−	0.391236i
$233$	−14.5554	−	25.2106i	−0.953554	−	1.65160i	−0.737643	−	0.675191i	$-0.764061\pi$
$233$	−14.5554	−	25.2106i	−0.953554	−	1.65160i	−0.215911	−	0.976413i	$-0.569272\pi$
$234$	4.62500	+	3.55682i	0.302346	+	0.232517i
$235$	1.59518	−	2.76294i	0.104058	−	0.180234i
$236$			2.12920i			0.138599i
$237$	−2.92684	+	5.06943i	−0.190119	+	0.329295i
$238$		0			0
$239$			8.65409i			0.559787i	0.960031	+	0.279893i	$0.0902991\pi$
$239$			8.65409i			0.559787i	−0.960031	+	0.279893i	$0.909701\pi$
$240$	22.6963	+	13.1037i	1.46504	+	0.845840i
$241$			18.1982i			1.17225i	0.810222	+	0.586124i	$0.199347\pi$
$241$			18.1982i			1.17225i	−0.810222	+	0.586124i	$0.800653\pi$
$242$	−10.9102	−	6.29902i	−0.701336	−	0.404916i
$243$	−5.91508	+	10.2452i	−0.379453	+	0.657231i
$244$	−0.725669	+	1.25690i	−0.0464562	+	0.0804645i
$245$		0			0
$246$	−11.5797			−0.738297
$247$	2.69770	+	2.07465i	0.171651	+	0.132007i
$248$	7.59057	−	13.1473i	0.482002	−	0.834851i
$249$	−4.12759	+	2.38307i	−0.261576	+	0.151021i
$250$	−13.0979			−0.828383
$251$	−7.93598	−	13.7455i	−0.500915	−	0.867610i	−0.999999	−	0.00105678i	$-0.999664\pi$
$251$	−7.93598	−	13.7455i	−0.500915	−	0.867610i	0.499085	−	0.866553i	$-0.333670\pi$
$252$		0			0
$253$	1.82413	−	1.05316i	0.114682	−	0.0662117i
$254$	17.1446	+	9.89841i	1.07574	+	0.621082i
$255$	−49.0230	−	28.3034i	−3.06994	−	1.77243i
$256$	−4.52609			−0.282880
$257$	−24.3267			−1.51746			−0.758730	−	0.651406i	$-0.774180\pi$
$257$	−24.3267			−1.51746			−0.758730	+	0.651406i	$0.774180\pi$
$258$	−9.14900	−	5.28218i	−0.569592	−	0.328854i
$259$		0			0
$260$	2.26344	−	0.934688i	0.140372	−	0.0579669i
$261$	−2.43282	−	4.21376i	−0.150588	−	0.260825i
$262$	−13.0325	+	7.52432i	−0.805150	+	0.464854i
$263$	−7.71727	−	13.3667i	−0.475867	−	0.824226i	0.523751	−	0.851872i	$-0.324532\pi$
$263$	−7.71727	−	13.3667i	−0.475867	−	0.824226i	−0.999618	+	0.0276456i	$0.991199\pi$
$264$	3.86204	−	6.68925i	0.237692	−	0.411695i
$265$			0.285395i			0.0175317i
$266$		0			0
$267$	13.4512	−	7.76606i	0.823201	−	0.475275i
$268$	1.04210	−	0.601656i	0.0636563	−	0.0367520i
$269$	13.0407			0.795106			0.397553	−	0.917579i	$-0.369859\pi$
$269$	13.0407			0.795106			0.397553	+	0.917579i	$0.369859\pi$
$270$	−8.84108	−	15.3132i	−0.538051	−	0.931931i
$271$		−	26.9706i		−	1.63835i	−0.573544	−	0.819174i	$-0.694432\pi$
$271$		−	26.9706i		−	1.63835i	0.573544	−	0.819174i	$-0.305568\pi$
$272$	−27.7298			−1.68136
$273$		0			0
$274$	−23.7174			−1.43282
$275$			9.88289i			0.595961i
$276$	−0.321442	−	0.556753i	−0.0193485	−	0.0335126i
$277$	−12.7015			−0.763156			−0.381578	−	0.924337i	$-0.624619\pi$
$277$	−12.7015			−0.763156			−0.381578	+	0.924337i	$0.624619\pi$
$278$	6.82352	−	3.93956i	0.409248	−	0.236279i
$279$	5.36737	−	3.09885i	0.321336	−	0.185523i
$280$		0			0
$281$			26.7216i			1.59408i	0.603930	+	0.797038i	$0.293601\pi$
$281$			26.7216i			1.59408i	−0.603930	+	0.797038i	$0.706399\pi$
$282$	1.23306	−	2.13572i	0.0734276	−	0.127180i
$283$	−7.37113	−	12.7672i	−0.438168	−	0.758929i	0.559380	−	0.828911i	$-0.311039\pi$
$283$	−7.37113	−	12.7672i	−0.438168	−	0.758929i	−0.997548	+	0.0699819i	$0.977706\pi$
$284$	1.88338	−	1.08737i	0.111758	−	0.0645236i
$285$	3.45191	+	5.97888i	0.204473	+	0.354158i
$286$	2.36719	+	5.73238i	0.139975	+	0.338963i
$287$		0			0
$288$	−1.11791	−	0.645425i	−0.0658734	−	0.0380320i
$289$	42.8952			2.52324
$290$	19.4131			1.13997
$291$	0.849651	+	0.490546i	0.0498074	+	0.0287563i
$292$	−0.125379	−	0.0723874i	−0.00733723	−	0.00423615i
$293$	10.0312	−	5.79153i	0.586030	−	0.338345i	−0.177496	−	0.984121i	$-0.556800\pi$
$293$	10.0312	−	5.79153i	0.586030	−	0.338345i	0.763526	+	0.645777i	$0.223466\pi$
$294$		0			0
$295$	−19.9523	−	34.5584i	−1.16167	−	2.01207i
$296$	−3.11179			−0.180869
$297$	−4.07974	+	2.35544i	−0.236730	+	0.136676i
$298$	−7.04829	+	12.2080i	−0.408297	+	0.707190i
$299$	5.88768	+	0.781589i	0.340493	+	0.0452005i
$300$	3.01641			0.174153
$301$		0			0
$302$	3.17074	−	5.49188i	0.182455	−	0.316022i
$303$	2.95047	−	5.11036i	0.169500	−	0.293582i
$304$	2.92885	+	1.69097i	0.167981	+	0.0969838i
$305$		−	27.2004i		−	1.55749i
$306$	−10.8458	−	6.26180i	−0.620011	−	0.357963i
$307$		−	29.3335i		−	1.67415i	−0.547086	−	0.837076i	$-0.684263\pi$
$307$		−	29.3335i		−	1.67415i	0.547086	−	0.837076i	$-0.315737\pi$
$308$		0			0
$309$	−11.6191	+	20.1248i	−0.660986	+	1.14486i
$310$			24.7278i			1.40444i
$311$	0.0753271	−	0.130470i	0.00427141	−	0.00739830i	−0.863882	−	0.503695i	$-0.831974\pi$
$311$	0.0753271	−	0.130470i	0.00427141	−	0.00739830i	0.868153	+	0.496296i	$0.165307\pi$
$312$	20.1312	−	8.31317i	1.13970	−	0.470641i
$313$	−5.26057	−	9.11157i	−0.297345	−	0.515016i	0.678183	−	0.734893i	$-0.262768\pi$
$313$	−5.26057	−	9.11157i	−0.297345	−	0.515016i	−0.975528	+	0.219877i	$0.929434\pi$
$314$	10.4874	+	6.05493i	0.591841	+	0.341699i
$315$		0			0
$316$	0.271777	+	0.470732i	0.0152887	+	0.0264808i
$317$	1.30489	−	0.753380i	0.0732901	−	0.0423140i	−0.462907	−	0.886407i	$-0.653194\pi$
$317$	1.30489	−	0.753380i	0.0732901	−	0.0423140i	0.536197	+	0.844093i	$0.319860\pi$
$318$			0.220607i			0.0123710i
$319$		−	5.17202i		−	0.289578i
$320$	26.6018	−	15.3586i	1.48709	−	0.858571i
$321$	−6.73671	−	11.6683i	−0.376006	−	0.651262i
$322$		0			0
$323$	−6.32619	−	3.65243i	−0.351999	−	0.203227i
$324$	1.06241	+	1.84015i	0.0590228	+	0.102231i
$325$	−16.9884	+	22.0904i	−0.942349	+	1.22535i
$326$	−8.09314	+	14.0177i	−0.448237	+	0.776370i
$327$		−	11.9708i		−	0.661989i
$328$	−6.18600	+	10.7145i	−0.341565	+	0.591607i
$329$		0			0
$330$			12.5814i			0.692582i
$331$	−21.8679	−	12.6254i	−1.20197	−	0.693957i	−0.240976	−	0.970531i	$-0.577467\pi$
$331$	−21.8679	−	12.6254i	−1.20197	−	0.693957i	−0.960993	+	0.276574i	$0.910801\pi$
$332$			0.442569i			0.0242891i
$333$	−1.10019	−	0.635193i	−0.0602899	−	0.0348084i
$334$	−13.0635	+	22.6266i	−0.714802	+	1.23807i
$335$	−11.2760	+	19.5306i	−0.616075	+	1.06707i
$336$		0			0
$337$	32.1811			1.75302			0.876509	−	0.481386i	$-0.159866\pi$
$337$	32.1811			1.75302			0.876509	+	0.481386i	$0.159866\pi$
$338$	−4.56264	+	16.8823i	−0.248175	+	0.918273i
$339$	6.69598	−	11.5978i	0.363676	−	0.629905i
$340$	−4.55213	+	2.62817i	−0.246874	+	0.142533i
$341$	6.58797			0.356759
$342$	0.763694	+	1.32276i	0.0412959	+	0.0715265i
$343$		0			0
$344$	−9.77495	+	5.64357i	−0.527030	+	0.304281i
$345$	10.4345	+	6.02434i	0.561773	+	0.324340i
$346$	−16.7521	−	9.67185i	−0.900600	−	0.519962i
$347$	24.7638			1.32939			0.664695	−	0.747115i	$-0.268562\pi$
$347$	24.7638			1.32939			0.664695	+	0.747115i	$0.268562\pi$
$348$	−1.57858			−0.0846209
$349$	10.0075	+	5.77782i	0.535688	+	0.309280i	0.743330	−	0.668925i	$-0.233245\pi$
$349$	10.0075	+	5.77782i	0.535688	+	0.309280i	−0.207642	+	0.978205i	$0.566579\pi$
$350$		0			0
$351$	−13.1680	−	1.74805i	−0.702857	−	0.0933042i
$352$	−0.686067	−	1.18830i	−0.0365675	−	0.0633368i
$353$	17.3971	−	10.0442i	0.925953	−	0.534599i	0.0404237	−	0.999183i	$-0.487129\pi$
$353$	17.3971	−	10.0442i	0.925953	−	0.534599i	0.885529	+	0.464583i	$0.153796\pi$
$354$	−15.4229	−	26.7133i	−0.819719	−	1.41980i
$355$	−20.3791	+	35.2977i	−1.08161	+	1.87340i
$356$		−	1.44227i		−	0.0764399i
$357$		0			0
$358$	−6.32136	+	3.64964i	−0.334094	+	0.192890i
$359$	13.0346	−	7.52551i	0.687938	−	0.397181i	−0.114901	−	0.993377i	$-0.536655\pi$
$359$	13.0346	−	7.52551i	0.687938	−	0.397181i	0.802839	+	0.596196i	$0.203322\pi$
$360$	12.6458			0.666495
$361$	−9.05455	−	15.6829i	−0.476555	−	0.825418i
$362$			20.8378i			1.09521i
$363$	−19.1992			−1.00770
$364$		0			0
$365$	2.71331			0.142021
$366$		−	21.0257i		−	1.09903i
$367$	4.50178	+	7.79731i	0.234991	+	0.407016i	0.959270	−	0.282491i	$-0.0911607\pi$
$367$	4.50178	+	7.79731i	0.234991	+	0.407016i	−0.724279	+	0.689507i	$0.757827\pi$
$368$	5.90223			0.307675
$369$	−4.37418	+	2.52543i	−0.227711	+	0.131469i
$370$	4.38956	−	2.53431i	0.228202	−	0.131753i
$371$		0			0
$372$		−	2.01075i		−	0.104253i
$373$	8.06953	−	13.9768i	0.417824	−	0.723693i	−0.577896	−	0.816110i	$-0.696126\pi$
$373$	8.06953	−	13.9768i	0.417824	−	0.723693i	0.995720	+	0.0924174i	$0.0294594\pi$
$374$	−6.65611	−	11.5287i	−0.344179	−	0.596136i
$375$	−17.2867	+	9.98048i	−0.892681	+	0.515390i
$376$	−1.31742	−	2.28184i	−0.0679409	−	0.117677i
$377$	8.89057	−	11.5606i	0.457888	−	0.595400i
$378$		0			0
$379$	−13.5668	−	7.83277i	−0.696878	−	0.402342i	0.109306	−	0.994008i	$-0.465137\pi$
$379$	−13.5668	−	7.83277i	−0.696878	−	0.402342i	−0.806183	+	0.591666i	$0.798471\pi$
$380$	0.641068			0.0328861
$381$	30.1700			1.54566
$382$	−5.52935	−	3.19237i	−0.282906	−	0.163336i
$383$	−21.3327	−	12.3164i	−1.09005	−	0.629339i	−0.156459	−	0.987685i	$-0.550008\pi$
$383$	−21.3327	−	12.3164i	−1.09005	−	0.629339i	−0.933589	+	0.358345i	$0.883341\pi$
$384$	16.7525	−	9.67207i	0.854898	−	0.493576i
$385$		0			0
$386$	14.1512	+	24.5106i	0.720277	+	1.24756i
$387$	−4.60798			−0.234237
$388$	0.0788960	−	0.0455506i	0.00400534	−	0.00231248i
$389$	−9.42834	+	16.3304i	−0.478036	+	0.827982i	−0.999683	−	0.0251791i	$-0.991984\pi$
$389$	−9.42834	+	16.3304i	−0.478036	+	0.827982i	0.521647	+	0.853161i	$0.325318\pi$
$390$	−21.6270	+	28.1221i	−1.09513	+	1.42402i
$391$	−12.7486			−0.644724
$392$		0			0
$393$	−11.4669	+	19.8613i	−0.578431	+	1.00187i
$394$	−3.90929	+	6.77108i	−0.196947	+	0.341122i
$395$	−8.82229	−	5.09355i	−0.443897	−	0.256284i
$396$		−	0.292811i		−	0.0147143i
$397$	12.5600	+	7.25149i	0.630366	+	0.363942i	0.780894	−	0.624664i	$-0.214764\pi$
$397$	12.5600	+	7.25149i	0.630366	+	0.363942i	−0.150528	+	0.988606i	$0.548097\pi$
$398$			14.2839i			0.715985i
$399$		0			0
$400$	−13.8467	+	23.9831i	−0.692333	+	1.19916i
$401$			20.9889i			1.04814i	0.851676	+	0.524069i	$0.175587\pi$
$401$			20.9889i			1.04814i	−0.851676	+	0.524069i	$0.824413\pi$
$402$	−8.71624	+	15.0970i	−0.434727	+	0.752968i
$403$	14.7255	+	11.3245i	0.733531	+	0.564116i
$404$	−0.273971	−	0.474532i	−0.0136306	−	0.0236089i
$405$	−34.4874	−	19.9113i	−1.71369	−	0.989401i
$406$		0			0
$407$	−0.675191	−	1.16947i	−0.0334680	−	0.0579683i
$408$	−40.4869	+	23.3751i	−2.00440	+	1.15724i
$409$		−	21.4276i		−	1.05953i	−0.848146	−	0.529763i	$-0.822281\pi$
$409$		−	21.4276i		−	1.05953i	0.848146	−	0.529763i	$-0.177719\pi$
$410$		−	20.1521i		−	0.995242i
$411$	−31.3025	+	18.0725i	−1.54404	+	0.891451i
$412$	1.07891	+	1.86873i	0.0531542	+	0.0920657i
$413$		0			0
$414$	2.30850	+	1.33281i	0.113457	+	0.0655043i
$415$	−4.14723	−	7.18321i	−0.203580	−	0.352610i
$416$	0.509155	−	3.83545i	0.0249634	−	0.188048i
$417$	6.00383	−	10.3989i	0.294009	−	0.509238i
$418$			1.62357i			0.0794113i
$419$	3.98203	−	6.89708i	0.194535	−	0.336944i	−0.752213	−	0.658920i	$-0.771014\pi$
$419$	3.98203	−	6.89708i	0.194535	−	0.336944i	0.946748	+	0.321976i	$0.104347\pi$
$420$		0			0
$421$		−	2.81786i		−	0.137334i	−0.997640	−	0.0686670i	$-0.978125\pi$
$421$		−	2.81786i		−	0.137334i	0.997640	−	0.0686670i	$-0.0218746\pi$
$422$	5.43530	+	3.13807i	0.264586	+	0.152759i
$423$		−	1.07568i		−	0.0523011i
$424$	0.204122	+	0.117850i	0.00991306	+	0.00572331i
$425$	29.9082	−	51.8026i	1.45076	−	2.51279i
$426$	−15.7528	+	27.2847i	−0.763227	+	1.32195i
$427$		0			0
$428$	−1.25110			−0.0604742
$429$	7.49227	+	5.76187i	0.361730	+	0.278186i
$430$	9.19253	−	15.9219i	0.443303	−	0.767823i
$431$	4.96775	−	2.86813i	0.239288	−	0.138153i	−0.375561	−	0.926797i	$-0.622550\pi$
$431$	4.96775	−	2.86813i	0.239288	−	0.138153i	0.614849	+	0.788645i	$0.289217\pi$
$432$	−13.2006			−0.635112
$433$	12.2628	+	21.2398i	0.589314	+	1.02072i	0.994322	+	0.106409i	$0.0339351\pi$
$433$	12.2628	+	21.2398i	0.589314	+	1.02072i	−0.405009	+	0.914313i	$0.632732\pi$
$434$		0			0
$435$	25.6215	−	14.7926i	1.22846	−	0.709251i
$436$	−0.962653	−	0.555788i	−0.0461027	−	0.0266174i
$437$	1.34652	+	0.777413i	0.0644128	+	0.0371887i
$438$	2.09736			0.100216
$439$	36.6423			1.74884			0.874420	−	0.485169i	$-0.161242\pi$
$439$	36.6423			1.74884			0.874420	+	0.485169i	$0.161242\pi$
$440$	11.6412	+	6.72108i	0.554975	+	0.320415i
$441$		0			0
$442$	4.93973	−	37.2108i	0.234959	−	1.76994i
$443$	−13.5467	−	23.4635i	−0.643622	−	1.11479i	−0.984618	−	0.174721i	$-0.944098\pi$
$443$	−13.5467	−	23.4635i	−0.643622	−	1.11479i	0.340996	−	0.940065i	$-0.389236\pi$
$444$	−0.356939	+	0.206079i	−0.0169396	+	0.00978008i
$445$	13.5152	+	23.4090i	0.640682	+	1.10969i
$446$	16.2943	−	28.2226i	0.771558	−	1.33638i
$447$			21.4830i			1.01611i
$448$		0			0
$449$	23.7571	−	13.7162i	1.12117	−	0.647307i	0.179470	−	0.983764i	$-0.442562\pi$
$449$	23.7571	−	13.7162i	1.12117	−	0.647307i	0.941699	+	0.336456i	$0.109228\pi$
$450$	−10.8315	+	6.25358i	−0.510602	+	0.294796i
$451$	−5.36892			−0.252812
$452$	−0.621768	−	1.07693i	−0.0292455	−	0.0506547i
$453$		−	9.66431i		−	0.454069i
$454$	20.6832			0.970712
$455$		0			0
$456$	5.70169			0.267006
$457$		−	39.6639i		−	1.85540i	−0.373327	−	0.927700i	$-0.621783\pi$
$457$		−	39.6639i		−	1.85540i	0.373327	−	0.927700i	$-0.378217\pi$
$458$	10.9982	+	19.0495i	0.513913	+	0.890123i
$459$	28.5127			1.33086
$460$	0.968913	−	0.559402i	0.0451758	−	0.0260823i
$461$	4.23988	−	2.44790i	0.197471	−	0.114010i	−0.398004	−	0.917384i	$-0.630297\pi$
$461$	4.23988	−	2.44790i	0.197471	−	0.114010i	0.595475	+	0.803374i	$0.296964\pi$
$462$		0			0
$463$			4.71193i			0.218982i	0.993988	+	0.109491i	$0.0349221\pi$
$463$			4.71193i			0.218982i	−0.993988	+	0.109491i	$0.965078\pi$
$464$	7.24638	−	12.5511i	0.336405	−	0.582670i
$465$	18.8424	+	32.6360i	0.873794	+	1.51346i
$466$	33.9140	−	19.5803i	1.57104	−	0.907038i
$467$	−16.0081	−	27.7268i	−0.740765	−	1.28304i	−0.952147	−	0.305639i	$-0.901130\pi$
$467$	−16.0081	−	27.7268i	−0.740765	−	1.28304i	0.211383	−	0.977403i	$-0.432203\pi$
$468$	0.503335	−	0.654496i	0.0232667	−	0.0302541i
$469$		0			0
$470$	3.71678	+	2.14588i	0.171442	+	0.0989822i
$471$	18.4552			0.850372
$472$	−32.9563			−1.51693
$473$	−4.24191	−	2.44907i	−0.195043	−	0.112608i
$474$	−6.81953	−	3.93726i	−0.313232	−	0.180844i
$475$	−6.31788	+	3.64763i	−0.289884	+	0.167365i
$476$		0			0
$477$	0.0481123	+	0.0833330i	0.00220291	+	0.00381556i
$478$	−11.6417			−0.532480
$479$	−15.6097	+	9.01224i	−0.713224	+	0.411780i	−0.812254	−	0.583305i	$-0.801759\pi$
$479$	−15.6097	+	9.01224i	−0.713224	+	0.411780i	0.0990298	+	0.995084i	$0.468426\pi$
$480$	3.92447	−	6.79738i	0.179127	−	0.310257i
$481$	0.501083	−	3.77464i	0.0228474	−	0.172109i
$482$	−24.4807			−1.11506
$483$		0			0
$484$	−0.891390	+	1.54393i	−0.0405177	+	0.0701788i
$485$	−0.853693	+	1.47864i	−0.0387642	+	0.0671416i
$486$	−13.7821	−	7.95712i	−0.625170	−	0.360942i
$487$			17.6004i			0.797550i	0.917049	+	0.398775i	$0.130565\pi$
$487$			17.6004i			0.797550i	−0.917049	+	0.398775i	$0.869435\pi$
$488$	−19.4545	−	11.2321i	−0.880666	−	0.508453i
$489$			24.6676i			1.11551i
$490$		0			0
$491$	1.93180	−	3.34598i	0.0871810	−	0.151002i	−0.819138	−	0.573597i	$-0.805547\pi$
$491$	1.93180	−	3.34598i	0.0871810	−	0.151002i	0.906318	+	0.422595i	$0.138881\pi$
$492$			1.63868i			0.0738773i
$493$	−15.6519	+	27.1099i	−0.704926	+	1.22097i
$494$	−2.79087	+	3.62902i	−0.125567	+	0.163277i
$495$	2.74388	+	4.75254i	0.123328	+	0.213611i
$496$	15.9872	+	9.23023i	0.717848	+	0.414450i
$497$		0			0
$498$	−3.20576	−	5.55255i	−0.143654	−	0.248816i
$499$	−10.9528	+	6.32363i	−0.490317	+	0.283084i	−0.724706	−	0.689058i	$-0.758024\pi$
$499$	−10.9528	+	6.32363i	−0.490317	+	0.283084i	0.234389	+	0.972143i	$0.424691\pi$
$500$			1.85351i			0.0828917i
$501$			39.8171i			1.77890i
$502$	18.4908	−	10.6757i	0.825287	−	0.476480i
$503$	11.0180	+	19.0837i	0.491268	+	0.850902i	0.999949	−	0.0100533i	$-0.00320011\pi$
$503$	11.0180	+	19.0837i	0.491268	+	0.850902i	−0.508681	+	0.860955i	$0.669867\pi$
$504$		0			0
$505$	8.89351	+	5.13467i	0.395756	+	0.228490i
$506$	1.41674	+	2.45387i	0.0629818	+	0.109088i
$507$	6.84233	+	25.7580i	0.303879	+	1.14395i
$508$	1.40075	−	2.42617i	0.0621482	−	0.107644i
$509$			15.6702i			0.694568i	0.937760	+	0.347284i	$0.112896\pi$
$509$			15.6702i			0.694568i	−0.937760	+	0.347284i	$0.887104\pi$
$510$	38.0745	−	65.9470i	1.68597	−	2.92018i
$511$		0			0
$512$		−	24.9600i		−	1.10309i
$513$	−3.01154	−	1.73871i	−0.132963	−	0.0767661i
$514$		−	32.7249i		−	1.44344i
$515$	−35.0230	−	20.2206i	−1.54330	−	0.891025i
$516$	−0.747495	+	1.29470i	−0.0329066	+	0.0569959i
$517$	0.571705	−	0.990222i	0.0251436	−	0.0435499i
$518$		0			0
$519$	−29.4795			−1.29401
$520$	14.4673	+	35.0341i	0.634435	+	1.53635i
$521$	−12.6207	+	21.8598i	−0.552925	+	0.957694i	0.445137	+	0.895463i	$0.353155\pi$
$521$	−12.6207	+	21.8598i	−0.552925	+	0.957694i	−0.998062	+	0.0622317i	$0.980178\pi$
$522$	5.66846	−	3.27269i	0.248102	−	0.143242i
$523$	13.2477			0.579279			0.289640	−	0.957136i	$-0.406465\pi$
$523$	13.2477			0.579279			0.289640	+	0.957136i	$0.406465\pi$
$524$	1.06479	+	1.84426i	0.0465154	+	0.0805670i
$525$		0			0
$526$	17.9812	−	10.3815i	0.784019	−	0.452654i
$527$	−34.5318	−	19.9369i	−1.50423	−	0.868466i
$528$	8.13422	+	4.69629i	0.353996	+	0.204380i
$529$	−20.2865			−0.882021
$530$	−0.383920			−0.0166764
$531$	−11.6518	−	6.72720i	−0.505647	−	0.291935i
$532$		0			0
$533$	−12.0007	−	9.22903i	−0.519807	−	0.399754i
$534$	10.4471	+	18.0949i	0.452091	+	0.783044i
$535$	20.3063	−	11.7238i	0.877916	−	0.506865i
$536$	9.31258	+	16.1299i	0.402242	+	0.696704i
$537$	−5.56200	+	9.63366i	−0.240018	+	0.415723i
$538$			17.5427i			0.756320i
$539$		0			0
$540$	−2.16701	+	1.25112i	−0.0932532	+	0.0538398i
$541$	−12.4737	+	7.20170i	−0.536287	+	0.309625i	−0.743573	−	0.668655i	$-0.766870\pi$
$541$	−12.4737	+	7.20170i	−0.536287	+	0.309625i	0.207286	+	0.978280i	$0.433537\pi$
$542$	36.2816			1.55843
$543$	15.8782	+	27.5019i	0.681401	+	1.18022i
$544$			8.30488i			0.356069i
$545$	20.8328			0.892377
$546$		0			0
$547$	2.00679			0.0858042			0.0429021	−	0.999079i	$-0.486340\pi$
$547$	2.00679			0.0858042			0.0429021	+	0.999079i	$0.486340\pi$
$548$			3.35631i			0.143375i
$549$	−4.58550	−	7.94232i	−0.195704	−	0.338970i
$550$	−13.2947			−0.566889
$551$	3.30634	−	1.90892i	0.140855	−	0.0813226i
$552$	8.61757	−	4.97535i	0.366788	−	0.211765i
$553$		0			0
$554$		−	17.0863i		−	0.725928i
$555$	3.86226	−	6.68962i	0.163944	−	0.283959i
$556$	−0.557497	−	0.965614i	−0.0236432	−	0.0409512i
$557$	−7.42977	+	4.28958i	−0.314810	+	0.181755i	−0.649077	−	0.760723i	$-0.724845\pi$
$557$	−7.42977	+	4.28958i	−0.314810	+	0.181755i	0.334267	+	0.942478i	$0.391511\pi$
$558$	4.16865	+	7.22032i	0.176473	+	0.305661i
$559$	−5.27170	−	12.7659i	−0.222969	−	0.539942i
$560$		0			0
$561$	−17.5696	−	10.1438i	−0.741788	−	0.428272i
$562$	−35.9466			−1.51631
$563$	−12.7744			−0.538375			−0.269188	−	0.963088i	$-0.586755\pi$
$563$	−12.7744			−0.538375			−0.269188	+	0.963088i	$0.586755\pi$
$564$	−0.302231	−	0.174493i	−0.0127262	−	0.00734750i
$565$	20.1835	+	11.6530i	0.849126	+	0.490243i
$566$	17.1747	−	9.91583i	0.721908	−	0.416794i
$567$		0			0
$568$	16.8306	+	29.1515i	0.706196	+	1.22317i
$569$	5.79116			0.242778			0.121389	−	0.992605i	$-0.461265\pi$
$569$	5.79116			0.242778			0.121389	+	0.992605i	$0.461265\pi$
$570$	−8.04295	+	4.64360i	−0.336882	+	0.194499i
$571$	−22.0666	+	38.2204i	−0.923458	+	1.59948i	−0.129435	+	0.991588i	$0.541316\pi$
$571$	−22.0666	+	38.2204i	−0.923458	+	1.59948i	−0.794023	+	0.607888i	$0.792017\pi$
$572$	0.811204	−	0.334987i	0.0339182	−	0.0140065i
$573$	−9.73025			−0.406487
$574$		0			0
$575$	−6.36592	+	11.0261i	−0.265477	+	0.459820i
$576$	5.17835	−	8.96917i	0.215765	−	0.373715i
$577$	−10.3343	−	5.96649i	−0.430221	−	0.248388i	0.269220	−	0.963079i	$-0.413234\pi$
$577$	−10.3343	−	5.96649i	−0.430221	−	0.248388i	−0.699441	+	0.714691i	$0.746568\pi$
$578$			57.7037i			2.40016i
$579$	37.3538	+	21.5662i	1.55237	+	0.896261i
$580$		−	2.74719i		−	0.114071i
$581$		0			0
$582$	−0.659895	+	1.14297i	−0.0273535	+	0.0473777i
$583$			0.102284i			0.00423617i
$584$	1.12043	−	1.94064i	0.0463637	−	0.0803043i
$585$	−2.03633	+	15.3396i	−0.0841919	+	0.634215i
$586$	7.79091	+	13.4943i	0.321840	+	0.557443i
$587$	−17.6250	−	10.1758i	−0.727462	−	0.420000i	0.0900312	−	0.995939i	$-0.471303\pi$
$587$	−17.6250	−	10.1758i	−0.727462	−	0.420000i	−0.817493	+	0.575939i	$0.804637\pi$
$588$		0			0
$589$	2.43152	+	4.21152i	0.100189	+	0.173533i
$590$	46.4889	−	26.8404i	1.91392	−	1.10500i
$591$			11.9154i			0.490133i
$592$		−	3.78397i		−	0.155520i
$593$	−15.7443	+	9.09000i	−0.646543	+	0.373282i	−0.787130	−	0.616787i	$-0.788434\pi$
$593$	−15.7443	+	9.09000i	−0.646543	+	0.373282i	0.140588	+	0.990068i	$0.455101\pi$
$594$	−3.16859	−	5.48817i	−0.130009	−	0.225182i
$595$		0			0
$596$	1.72759	+	0.997422i	0.0707646	+	0.0408560i
$597$	10.8842	+	18.8520i	0.445460	+	0.771560i
$598$	−1.05141	+	7.92026i	−0.0429955	+	0.323884i
$599$	19.1341	−	33.1412i	0.781797	−	1.35411i	−0.149096	−	0.988823i	$-0.547636\pi$
$599$	19.1341	−	33.1412i	0.781797	−	1.35411i	0.930894	−	0.365290i	$-0.119030\pi$
$600$			46.6888i			1.90606i
$601$	−13.4360	+	23.2718i	−0.548064	+	0.949275i	0.450343	+	0.892856i	$0.351302\pi$
$601$	−13.4360	+	23.2718i	−0.548064	+	0.949275i	−0.998407	+	0.0564195i	$0.982032\pi$
$602$		0			0
$603$			7.60372i			0.309648i
$604$	−0.777170	−	0.448699i	−0.0316226	−	0.0182573i
$605$		−	33.4122i		−	1.35840i
$606$	6.87459	+	3.96904i	0.279261	+	0.161231i
$607$	−4.70105	+	8.14245i	−0.190810	+	0.330492i	−0.945519	−	0.325568i	$-0.894445\pi$
$607$	−4.70105	+	8.14245i	−0.190810	+	0.330492i	0.754709	+	0.656059i	$0.227778\pi$
$608$	0.506435	−	0.877171i	0.0205386	−	0.0355740i
$609$		0			0
$610$	36.5908			1.48152
$611$	2.98005	−	1.23061i	0.120560	−	0.0497853i
$612$	−0.886124	+	1.53481i	−0.0358194	+	0.0620411i
$613$	11.5089	−	6.64469i	0.464842	−	0.268376i	−0.249236	−	0.968443i	$-0.580180\pi$
$613$	11.5089	−	6.64469i	0.464842	−	0.268376i	0.714078	+	0.700066i	$0.246846\pi$
$614$	39.4602			1.59248
$615$	−15.3557	−	26.5969i	−0.619204	−	1.07249i
$616$		0			0
$617$	−9.72211	+	5.61306i	−0.391397	+	0.225973i	−0.682765	−	0.730638i	$-0.739223\pi$
$617$	−9.72211	+	5.61306i	−0.391397	+	0.225973i	0.291368	+	0.956611i	$0.405890\pi$
$618$	−27.0724	−	15.6303i	−1.08901	−	0.628742i
$619$	8.04109	+	4.64253i	0.323199	+	0.186599i	0.652817	−	0.757515i	$-0.273587\pi$
$619$	8.04109	+	4.64253i	0.323199	+	0.186599i	−0.329619	+	0.944114i	$0.606920\pi$
$620$	3.49929			0.140535
$621$	−6.06888			−0.243536
$622$	0.175512	+	0.101332i	0.00703740	+	0.00406304i
$623$		0			0
$624$	10.1089	+	24.4797i	0.404681	+	0.979974i
$625$	1.95363	+	3.38379i	0.0781452	+	0.135351i
$626$	12.2571	−	7.07665i	0.489893	−	0.282840i
$627$	1.23715	+	2.14280i	0.0494068	+	0.0855752i
$628$	0.856848	−	1.48410i	0.0341920	−	0.0592222i
$629$			8.17322i			0.325888i
$630$		0			0
$631$	9.00894	−	5.20132i	0.358640	−	0.207061i	−0.309844	−	0.950787i	$-0.600277\pi$
$631$	9.00894	−	5.20132i	0.358640	−	0.207061i	0.668484	+	0.743726i	$0.266943\pi$
$632$	−7.28611	+	4.20664i	−0.289826	+	0.167331i
$633$	9.56474			0.380164
$634$	1.01347	+	1.75538i	0.0402499	+	0.0697149i
$635$			52.5046i			2.08358i
$636$	0.0312187			0.00123790
$637$		0			0
$638$	6.95754			0.275452
$639$			13.7422i			0.543632i
$640$	16.8322	+	29.1542i	0.665351	+	1.15242i
$641$	−14.8591			−0.586899			−0.293449	−	0.955975i	$-0.594803\pi$
$641$	−14.8591			−0.586899			−0.293449	+	0.955975i	$0.594803\pi$
$642$	15.6965	−	9.06239i	0.619492	−	0.357664i
$643$	−1.98945	+	1.14861i	−0.0784563	+	0.0452968i	−0.538715	−	0.842488i	$-0.681090\pi$
$643$	−1.98945	+	1.14861i	−0.0784563	+	0.0452968i	0.460259	+	0.887785i	$0.347757\pi$
$644$		0			0
$645$		−	28.0185i		−	1.10323i
$646$	4.91334	−	8.51016i	0.193313	−	0.334828i
$647$	−3.99932	−	6.92703i	−0.157230	−	0.272330i	0.776639	−	0.629946i	$-0.216923\pi$
$647$	−3.99932	−	6.92703i	−0.157230	−	0.272330i	−0.933869	+	0.357616i	$0.883590\pi$
$648$	−28.4823	+	16.4443i	−1.11889	+	0.645991i
$649$	−7.15081	−	12.3856i	−0.280694	−	0.486176i
$650$	−29.7166	−	22.8533i	−1.16558	−	0.896380i
$651$		0			0
$652$	1.98368	+	1.14528i	0.0776871	+	0.0448526i
$653$	3.98444			0.155923			0.0779615	−	0.996956i	$-0.475159\pi$
$653$	3.98444			0.155923			0.0779615	+	0.996956i	$0.475159\pi$
$654$	16.1035			0.629696
$655$	−34.5645	−	19.9558i	−1.35055	−	0.779738i
$656$	−13.0289	−	7.52225i	−0.508694	−	0.293695i
$657$	0.792267	−	0.457415i	0.0309093	−	0.0178455i
$658$		0			0
$659$	13.7501	+	23.8159i	0.535629	+	0.927737i	0.999133	+	0.0416417i	$0.0132588\pi$
$659$	13.7501	+	23.8159i	0.535629	+	0.927737i	−0.463504	+	0.886095i	$0.653408\pi$
$660$	1.78042			0.0693028
$661$	−6.05023	+	3.49310i	−0.235327	+	0.135866i	−0.613027	−	0.790062i	$-0.710048\pi$
$661$	−6.05023	+	3.49310i	−0.235327	+	0.135866i	0.377700	+	0.925928i	$0.376715\pi$
$662$	16.9841	−	29.4173i	0.660105	−	1.14333i
$663$	−21.8349	−	52.8752i	−0.847996	−	2.05350i
$664$	−6.85019			−0.265839
$665$		0			0
$666$	0.854479	−	1.48000i	0.0331104	−	0.0573488i
$667$	3.33148	−	5.77029i	0.128995	−	0.223427i
$668$	3.20195	+	1.84865i	0.123887	+	0.0715263i
$669$		−	49.6646i		−	1.92014i
$670$	−26.2731	−	15.1688i	−1.01502	−	0.586022i
$671$		−	9.74849i		−	0.376336i
$672$		0			0
$673$	2.72783	−	4.72474i	0.105150	−	0.182125i	−0.808649	−	0.588291i	$-0.799801\pi$
$673$	2.72783	−	4.72474i	0.105150	−	0.182125i	0.913800	+	0.406166i	$0.133134\pi$
$674$			43.2909i			1.66750i
$675$	14.2376	−	24.6603i	0.548006	−	0.949174i
$676$	2.38905	+	0.645671i	0.0918866	+	0.0248335i
$677$	16.8961	+	29.2649i	0.649371	+	1.12474i	0.983273	+	0.182135i	$0.0583009\pi$
$677$	16.8961	+	29.2649i	0.649371	+	1.12474i	−0.333903	+	0.942607i	$0.608366\pi$
$678$	15.6016	+	9.00761i	0.599177	+	0.345935i
$679$		0			0
$680$	−40.6795	−	70.4590i	−1.55999	−	2.70198i
$681$	27.2979	−	15.7605i	1.04606	−	0.603942i
$682$			8.86231i			0.339355i
$683$			12.2988i			0.470602i	0.971923	+	0.235301i	$0.0756076\pi$
$683$			12.2988i			0.470602i	−0.971923	+	0.235301i	$0.924392\pi$
$684$	0.187187	−	0.108072i	0.00715726	−	0.00413225i
$685$	−31.4514	−	54.4754i	−1.20170	−	2.08140i
$686$		0			0
$687$	29.0311	+	16.7611i	1.10760	+	0.639476i
$688$	−6.86265	−	11.8865i	−0.261636	−	0.453167i
$689$	−0.175823	+	0.228627i	−0.00669834	+	0.00870998i
$690$	−8.10410	+	14.0367i	−0.308518	+	0.534369i
$691$		−	11.0897i		−	0.421871i	−0.977500	−	0.210935i	$-0.932349\pi$
$691$		−	11.0897i		−	0.421871i	0.977500	−	0.210935i	$-0.0676509\pi$
$692$	−1.36869	+	2.37064i	−0.0520297	+	0.0901181i
$693$		0			0
$694$			33.3129i			1.26454i
$695$	18.0972	+	10.4484i	0.686465	+	0.396331i
$696$		−	24.4337i		−	0.926156i
$697$	28.1419	+	16.2478i	1.06595	+	0.615428i
$698$	−7.77247	+	13.4623i	−0.294193	+	0.509556i
$699$	29.8400	−	51.6844i	1.12865	−	1.95488i
$700$		0			0
$701$	10.6470			0.402133			0.201066	−	0.979578i	$-0.435559\pi$
$701$	10.6470			0.402133			0.201066	+	0.979578i	$0.435559\pi$
$702$	2.35153	−	17.7140i	0.0887526	−	0.668571i
$703$	0.498406	−	0.863265i	0.0187977	−	0.0325587i
$704$	9.53396	−	5.50443i	0.359325	−	0.207456i
$705$	6.54058			0.246333
$706$	13.5117	+	23.4030i	0.508521	+	0.880784i
$707$		0			0
$708$	−3.78027	+	2.18254i	−0.142071	+	0.0820248i
$709$	35.2532	+	20.3535i	1.32396	+	0.764391i	0.984358	−	0.176178i	$-0.0563733\pi$
$709$	35.2532	+	20.3535i	1.32396	+	0.764391i	0.339605	+	0.940568i	$0.389707\pi$
$710$	−47.4833	−	27.4145i	−1.78202	−	1.02885i
$711$	−3.43472			−0.128812
$712$	22.3237			0.836618
$713$	7.35003	+	4.24354i	0.275261	+	0.158922i
$714$		0			0
$715$	−10.0273	+	13.0387i	−0.375001	+	0.487621i
$716$	0.516470	+	0.894552i	0.0193014	+	0.0334310i
$717$	−15.3648	+	8.87089i	−0.573810	+	0.331290i
$718$	10.1235	+	17.5344i	0.377806	+	0.654380i
$719$	4.88769	−	8.46572i	0.182280	−	0.315718i	−0.760377	−	0.649482i	$-0.774986\pi$
$719$	4.88769	−	8.46572i	0.182280	−	0.315718i	0.942657	+	0.333764i	$0.108319\pi$
$720$			15.3775i			0.573086i
$721$		0			0
$722$	21.0971	−	12.1804i	0.785153	−	0.453308i
$723$	−32.3098	+	18.6541i	−1.20161	+	0.693752i
$724$	2.94881			0.109592
$725$	15.6313	+	27.0743i	0.580533	+	1.00551i
$726$		−	25.8273i		−	0.958540i
$727$	12.2091			0.452811			0.226406	−	0.974033i	$-0.427303\pi$
$727$	12.2091			0.452811			0.226406	+	0.974033i	$0.427303\pi$
$728$		0			0
$729$	9.23219			0.341933
$730$			3.65002i			0.135093i
$731$	14.8231	+	25.6743i	0.548251	+	0.949598i
$732$	−2.97539			−0.109974
$733$	19.3256	−	11.1577i	0.713809	−	0.412118i	−0.0986608	−	0.995121i	$-0.531456\pi$
$733$	19.3256	−	11.1577i	0.713809	−	0.412118i	0.812470	+	0.583003i	$0.198123\pi$
$734$	−10.4891	+	6.05591i	−0.387161	+	0.223528i
$735$		0			0
$736$		−	1.76768i		−	0.0651576i
$737$	−4.04126	+	6.99968i	−0.148862	+	0.257836i
$738$	−3.39728	−	5.88426i	−0.125056	−	0.216603i
$739$	−36.6960	+	21.1865i	−1.34989	+	0.779357i	−0.988233	−	0.152956i	$-0.951121\pi$
$739$	−36.6960	+	21.1865i	−1.34989	+	0.779357i	−0.361653	+	0.932313i	$0.617787\pi$
$740$	−0.358637	−	0.621178i	−0.0131838	−	0.0228350i
$741$	−0.918130	+	6.91624i	−0.0337283	+	0.254074i
$742$		0			0
$743$	−26.8296	−	15.4901i	−0.984282	−	0.568276i	−0.0807220	−	0.996737i	$-0.525723\pi$
$743$	−26.8296	−	15.4901i	−0.984282	−	0.568276i	−0.903560	+	0.428461i	$0.859056\pi$
$744$	31.1229			1.14102
$745$	−37.3866			−1.36974
$746$	18.8020	+	10.8553i	0.688390	+	0.397442i
$747$	−2.42192	−	1.39830i	−0.0886133	−	0.0511609i
$748$	−1.63146	+	0.941923i	−0.0596520	+	0.0344401i
$749$		0			0
$750$	−13.4260	−	23.2545i	−0.490248	−	0.849135i
$751$	−22.5660			−0.823444			−0.411722	−	0.911309i	$-0.635073\pi$
$751$	−22.5660			−0.823444			−0.411722	+	0.911309i	$0.635073\pi$
$752$	2.77475	−	1.60200i	0.101185	−	0.0584190i
$753$	16.2696	−	28.1798i	0.592897	−	1.02693i
$754$	15.5516	+	11.9598i	0.566356	+	0.435551i
$755$	16.8187			0.612095
$756$		0			0
$757$	−16.1404	+	27.9560i	−0.586633	+	1.01608i	0.408037	+	0.912965i	$0.366213\pi$
$757$	−16.1404	+	27.9560i	−0.586633	+	1.01608i	−0.994670	+	0.103112i	$0.967120\pi$
$758$	10.5368	−	18.2504i	0.382716	−	0.662883i
$759$	3.73966	+	2.15909i	0.135741	+	0.0783701i
$760$			9.92260i			0.359931i
$761$	25.7657	+	14.8758i	0.934006	+	0.539249i	0.888076	−	0.459696i	$-0.152042\pi$
$761$	25.7657	+	14.8758i	0.934006	+	0.539249i	0.0459296	+	0.998945i	$0.485375\pi$
$762$			40.5855i			1.47026i
$763$		0			0
$764$	−0.451761	+	0.782473i	−0.0163441	+	0.0283089i
$765$		−	33.2148i		−	1.20088i
$766$	16.5684	−	28.6972i	0.598639	−	1.03687i
$767$	5.30687	−	39.9764i	0.191620	−	1.44347i
$768$	−4.63947	−	8.03581i	−0.167413	−	0.289967i
$769$	36.2090	+	20.9053i	1.30573	+	0.753863i	0.981380	−	0.192075i	$-0.0615215\pi$
$769$	36.2090	+	20.9053i	1.30573	+	0.753863i	0.324349	+	0.945938i	$0.394855\pi$
$770$		0			0
$771$	−24.9361	−	43.1907i	−0.898053	−	1.55547i
$772$	3.46856	−	2.00257i	0.124836	−	0.0720742i
$773$			41.4336i			1.49026i	0.666917	+	0.745132i	$0.267613\pi$
$773$			41.4336i			1.49026i	−0.666917	+	0.745132i	$0.732387\pi$
$774$		−	6.19877i		−	0.222810i
$775$	−34.4864	+	19.9107i	−1.23879	+	0.715215i
$776$	0.705044	+	1.22117i	0.0253096	+	0.0438375i
$777$		0			0
$778$	−21.9680	−	12.6832i	−0.787592	−	0.454716i
$779$	−1.98159	−	3.43221i	−0.0709978	−	0.122972i
$780$	3.97963	+	3.06050i	0.142493	+	0.109583i
$781$	−7.30376	+	12.6505i	−0.261349	+	0.452670i
$782$		−	17.1497i		−	0.613273i
$783$	−7.45098	+	12.9055i	−0.266276	+	0.461204i
$784$		0			0
$785$			32.1175i			1.14632i
$786$	−26.7180	−	15.4256i	−0.952998	−	0.550214i
$787$			23.8627i			0.850612i	0.905050	+	0.425306i	$0.139833\pi$
$787$			23.8627i			0.850612i	−0.905050	+	0.425306i	$0.860167\pi$
$788$	0.958193	+	0.553213i	0.0341342	+	0.0197074i
$789$	15.8212	−	27.4031i	0.563250	−	0.975577i
$790$	6.85198	−	11.8680i	0.243782	−	0.422243i
$791$		0			0
$792$	4.53221			0.161045
$793$	16.7574	−	21.7900i	0.595073	−	0.773785i
$794$	−9.75490	+	16.8960i	−0.346188	+	0.599616i
$795$	−0.506701	+	0.292544i	−0.0179708	+	0.0103755i
$796$	2.02135			0.0716447
$797$	−25.4115	−	44.0141i	−0.900123	−	1.55906i	−0.827333	−	0.561712i	$-0.810143\pi$
$797$	−25.4115	−	44.0141i	−0.900123	−	1.55906i	−0.0727899	−	0.997347i	$-0.523190\pi$
$798$		0			0
$799$	−5.99335	+	3.46026i	−0.212029	+	0.122415i
$800$	7.18279	+	4.14699i	0.253950	+	0.146618i
$801$	7.89267	+	4.55683i	0.278874	+	0.161008i
$802$	−28.2349			−0.997008
$803$	0.972438			0.0343166
$804$	2.13641	+	1.23346i	0.0753454	+	0.0435007i
$805$		0			0
$806$	−15.2341	+	19.8092i	−0.536598	+	0.697748i
$807$	13.3674	+	23.1530i	0.470555	+	0.815025i
$808$	7.34493	−	4.24060i	0.258394	−	0.149184i
$809$	−2.20588	−	3.82070i	−0.0775547	−	0.134329i	0.824640	−	0.565658i	$-0.191378\pi$
$809$	−2.20588	−	3.82070i	−0.0775547	−	0.134329i	−0.902194	+	0.431330i	$0.858045\pi$
$810$	26.7852	−	46.3933i	0.941136	−	1.63010i
$811$		−	17.6493i		−	0.619750i	−0.950777	−	0.309875i	$-0.899713\pi$
$811$		−	17.6493i		−	0.619750i	0.950777	−	0.309875i	$-0.100287\pi$
$812$		0			0
$813$	47.8848	−	27.6463i	1.67939	−	0.969598i
$814$	1.57320	−	0.908285i	0.0551405	−	0.0318354i
$815$	−42.9288			−1.50373
$816$	−28.4244	−	49.2326i	−0.995054	−	1.72348i
$817$		−	3.61566i		−	0.126496i
$818$	28.8249			1.00784
$819$		0			0
$820$	−2.85178			−0.0995884
$821$			3.56043i			0.124260i	0.998068	+	0.0621299i	$0.0197893\pi$
$821$			3.56043i			0.124260i	−0.998068	+	0.0621299i	$0.980211\pi$
$822$	−24.3116	−	42.1089i	−0.847964	−	1.46872i
$823$	−21.8665			−0.762217			−0.381109	−	0.924530i	$-0.624458\pi$
$823$	−21.8665			−0.762217			−0.381109	+	0.924530i	$0.624458\pi$
$824$	−28.9247	+	16.6997i	−1.00764	+	0.581760i
$825$	−17.5465	+	10.1305i	−0.610891	+	0.352698i
$826$		0			0
$827$			18.1361i			0.630653i	0.948983	+	0.315327i	$0.102114\pi$
$827$			18.1361i			0.630653i	−0.948983	+	0.315327i	$0.897886\pi$
$828$	0.188610	−	0.326682i	0.00655465	−	0.0113530i
$829$	−15.4497	−	26.7596i	−0.536590	−	0.929401i	−0.999085	−	0.0427787i	$-0.986379\pi$
$829$	−15.4497	−	26.7596i	−0.536590	−	0.929401i	0.462495	−	0.886622i	$-0.346954\pi$
$830$	9.66305	−	5.57896i	0.335409	−	0.193649i
$831$	−13.0196	−	22.5507i	−0.451646	−	0.782275i
$832$	30.7724	+	4.08504i	1.06684	+	0.141623i
$833$		0			0
$834$	13.9889	+	8.07651i	0.484397	+	0.279667i
$835$	−69.2933			−2.39799
$836$	0.229755			0.00794625
$837$	−16.4386	−	9.49084i	−0.568202	−	0.328051i
$838$	9.27813	+	5.35673i	0.320508	+	0.185045i
$839$	13.3333	−	7.69796i	0.460315	−	0.265763i	−0.251862	−	0.967763i	$-0.581043\pi$
$839$	13.3333	−	7.69796i	0.460315	−	0.265763i	0.712177	+	0.702000i	$0.247709\pi$
$840$		0			0
$841$	6.31965	+	10.9459i	0.217919	+	0.377446i
$842$	3.79065			0.130635
$843$	−47.4426	+	27.3910i	−1.63401	+	0.943396i
$844$	0.444076	−	0.769163i	0.0152857	−	0.0264757i
$845$	−44.8265	+	11.9076i	−1.54208	+	0.409636i
$846$	1.44703			0.0497498
$847$		0			0
$848$	−0.143307	+	0.248216i	−0.00492119	+	0.00852376i
$849$	15.1116	−	26.1740i	0.518628	−	0.898290i
$850$	69.6862	+	40.2333i	2.39022	+	1.37999i
$851$		−	1.73966i		−	0.0596347i
$852$	3.86113	+	2.22922i	0.132280	+	0.0763719i
$853$			23.7772i			0.814116i	0.913402	+	0.407058i	$0.133445\pi$
$853$			23.7772i			0.814116i	−0.913402	+	0.407058i	$0.866555\pi$
$854$		0			0
$855$	−2.02545	+	3.50818i	−0.0692690	+	0.119977i
$856$		−	19.3648i		−	0.661877i
$857$	15.0525	−	26.0717i	0.514184	−	0.890592i	−0.485681	−	0.874136i	$-0.661428\pi$
$857$	15.0525	−	26.0717i	0.514184	−	0.890592i	0.999865	−	0.0164561i	$-0.00523837\pi$
$858$	−7.75102	+	10.0788i	−0.264615	+	0.344085i
$859$	−7.56717	−	13.1067i	−0.258188	−	0.447195i	0.707568	−	0.706645i	$-0.249792\pi$
$859$	−7.56717	−	13.1067i	−0.258188	−	0.447195i	−0.965757	+	0.259450i	$0.916459\pi$
$860$	−2.25315	−	1.30086i	−0.0768318	−	0.0443589i
$861$		0			0
$862$	3.85828	+	6.68274i	0.131414	+	0.227615i
$863$	15.8186	−	9.13287i	0.538471	−	0.310886i	−0.205988	−	0.978555i	$-0.566041\pi$
$863$	15.8186	−	9.13287i	0.538471	−	0.310886i	0.744459	+	0.667668i	$0.232707\pi$
$864$			3.95348i			0.134500i
$865$		−	51.3029i		−	1.74435i
$866$	−28.5724	+	16.4963i	−0.970929	+	0.560566i
$867$	43.9697	+	76.1578i	1.49329	+	2.58646i
$868$		0			0
$869$	−3.16186	−	1.82550i	−0.107259	−	0.0619259i
$870$	19.8994	+	34.4668i	0.674653	+	1.16853i
$871$	−21.0654	+	8.69895i	−0.713772	+	0.294753i
$872$	8.60263	−	14.9002i	0.291322	−	0.504584i
$873$			0.575668i			0.0194834i
$874$	−1.04580	+	1.81137i	−0.0353746	+	0.0612706i
$875$		0			0
$876$		−	0.296803i		−	0.0100281i
$877$	−6.05906	−	3.49820i	−0.204600	−	0.118126i	0.394199	−	0.919025i	$-0.371022\pi$
$877$	−6.05906	−	3.49820i	−0.204600	−	0.118126i	−0.598799	+	0.800899i	$0.704355\pi$
$878$			49.2922i			1.66353i
$879$	20.5650	+	11.8732i	0.693641	+	0.400474i
$880$	−8.17292	+	14.1559i	−0.275509	+	0.477195i
$881$	−12.8873	+	22.3215i	−0.434184	+	0.752029i	−0.997229	−	0.0743977i	$-0.976297\pi$
$881$	−12.8873	+	22.3215i	−0.434184	+	0.752029i	0.563045	+	0.826427i	$0.309630\pi$
$882$		0			0
$883$	−16.4526			−0.553674			−0.276837	−	0.960917i	$-0.589286\pi$
$883$	−16.4526			−0.553674			−0.276837	+	0.960917i	$0.589286\pi$
$884$	−5.26580	−	0.699034i	−0.177108	−	0.0235111i
$885$	40.9043	−	70.8484i	1.37498	−	2.38154i
$886$	31.5637	−	18.2233i	1.06040	−	0.612225i
$887$	−55.2455			−1.85496			−0.927481	−	0.373871i	$-0.878030\pi$
$887$	−55.2455			−1.85496			−0.927481	+	0.373871i	$0.878030\pi$
$888$	−3.18974	−	5.52479i	−0.107041	−	0.185400i
$889$		0			0
$890$	−31.4904	+	18.1810i	−1.05556	+	0.609429i
$891$	−12.3601	−	7.13611i	−0.414079	−	0.239069i
$892$	−3.99385	−	2.30585i	−0.133724	−	0.0772056i
$893$	0.844032			0.0282444
$894$	−28.8995			−0.966542
$895$	−16.7654	−	9.67949i	−0.560404	−	0.323550i
$896$		0			0
$897$	4.64751	+	11.2544i	0.155176	+	0.375774i
$898$	18.4514	+	31.9587i	0.615731	+	1.06648i
$899$	18.0478	−	10.4199i	0.601927	−	0.347523i
$900$	0.884960	+	1.53280i	0.0294987	+	0.0510932i
$901$	0.309538	−	0.536136i	0.0103122	−	0.0178613i
$902$		−	7.22241i		−	0.240480i
$903$		0			0
$904$	16.6691	−	9.62388i	0.554405	−	0.320086i
$905$	−47.8614	+	27.6328i	−1.59097	+	0.918544i
$906$	13.0007			0.431919
$907$	23.9212	+	41.4327i	0.794290	+	1.37575i	0.923289	+	0.384107i	$0.125490\pi$
$907$	23.9212	+	41.4327i	0.794290	+	1.37575i	−0.128998	+	0.991645i	$0.541176\pi$
$908$		−	2.92694i		−	0.0971338i
$909$	3.46245			0.114842
$910$		0			0
$911$	−23.0711			−0.764380			−0.382190	−	0.924084i	$-0.624830\pi$
$911$	−23.0711			−0.764380			−0.382190	+	0.924084i	$0.624830\pi$
$912$			6.93333i			0.229585i
$913$	−1.48635	−	2.57443i	−0.0491909	−	0.0852011i
$914$	53.3569			1.76489
$915$	48.2928	−	27.8819i	1.59651	−	0.921746i
$916$	2.69574	−	1.55638i	0.0890697	−	0.0514244i
$917$		0			0
$918$			38.3560i			1.26594i
$919$	21.7184	−	37.6174i	0.716424	−	1.24088i	−0.245984	−	0.969274i	$-0.579111\pi$
$919$	21.7184	−	37.6174i	0.716424	−	1.24088i	0.962408	−	0.271609i	$-0.0875557\pi$
$920$	8.65856	+	14.9971i	0.285464	+	0.494439i
$921$	52.0799	−	30.0684i	1.71609	−	0.990787i
$922$	3.29298	+	5.70360i	0.108448	+	0.187838i
$923$	−38.0714	+	15.7216i	−1.25313	+	0.517482i
$924$		0			0
$925$	7.06892	+	4.08124i	0.232425	+	0.134190i
$926$	−6.33861			−0.208300
$927$	−13.6353			−0.447841
$928$	−3.75897	−	2.17024i	−0.123394	−	0.0712418i
$929$	−11.0695	−	6.39095i	−0.363177	−	0.209680i	0.307296	−	0.951614i	$-0.400576\pi$
$929$	−11.0695	−	6.39095i	−0.363177	−	0.209680i	−0.670474	+	0.741933i	$0.733909\pi$
$930$	−43.9027	+	25.3473i	−1.43963	+	0.831169i
$931$		0			0
$932$	−2.77085	−	4.79926i	−0.0907623	−	0.157205i
$933$	0.308857			0.0101115
$934$	37.2988	−	21.5345i	1.22045	−	0.704629i
$935$	17.6532	−	30.5762i	0.577320	−	0.999948i
$936$	10.1305	+	7.79074i	0.331124	+	0.254648i
$937$	−16.2533			−0.530971			−0.265486	−	0.964115i	$-0.585532\pi$
$937$	−16.2533			−0.530971			−0.265486	+	0.964115i	$0.585532\pi$
$938$		0			0
$939$	10.7847	−	18.6797i	0.351946	−	0.609588i
$940$	0.303669	−	0.525971i	0.00990460	−	0.0171553i
$941$	−39.1000	−	22.5744i	−1.27462	−	0.735905i	−0.298770	−	0.954325i	$-0.596576\pi$
$941$	−39.1000	−	22.5744i	−1.27462	−	0.735905i	−0.975855	+	0.218420i	$0.929910\pi$
$942$			24.8265i			0.808890i
$943$	−5.98997	−	3.45831i	−0.195060	−	0.112618i
$944$		−	40.0752i		−	1.30434i
$945$		0			0
$946$	3.29455	−	5.70633i	0.107115	−	0.185529i
$947$			19.8557i			0.645225i	0.946531	+	0.322612i	$0.104561\pi$
$947$			19.8557i			0.645225i	−0.946531	+	0.322612i	$0.895439\pi$
$948$	−0.557172	+	0.965050i	−0.0180961	+	0.0313434i
$949$	2.17361	+	1.67160i	0.0705583	+	0.0542623i
$950$	−4.90689	−	8.49898i	−0.159200	−	0.275743i
$951$	2.67516	+	1.54451i	0.0867482	+	0.0500841i
$952$		0			0
$953$	7.86433	+	13.6214i	0.254751	+	0.441241i	0.964828	−	0.262883i	$-0.0846733\pi$
$953$	7.86433	+	13.6214i	0.254751	+	0.441241i	−0.710077	+	0.704124i	$0.751340\pi$
$954$	−0.112102	+	0.0647220i	−0.00362943	+	0.00209545i
$955$		−	16.9335i		−	0.547954i
$956$			1.64745i			0.0532823i
$957$	9.18262	−	5.30159i	0.296832	−	0.171376i
$958$	−12.1235	−	20.9985i	−0.391693	−	0.678432i
$959$		0			0
$960$	54.5365	+	31.4867i	1.76016	+	1.01623i
$961$	−2.22744	−	3.85804i	−0.0718529	−	0.124453i
$962$	5.07775	+	0.674070i	0.163713	+	0.0217329i
$963$	3.95285	−	6.84653i	0.127379	−	0.220626i
$964$			3.46432i			0.111578i
$965$	−37.5315	+	65.0064i	−1.20818	+	2.09263i
$966$		0			0
$967$		−	52.1912i		−	1.67835i	−0.543858	−	0.839177i	$-0.683037\pi$
$967$		−	52.1912i		−	1.67835i	0.543858	−	0.839177i	$-0.316963\pi$
$968$	−23.8974	−	13.7972i	−0.768091	−	0.443458i
$969$		−	14.9757i		−	0.481089i
$970$	−1.98910	−	1.14841i	−0.0638663	−	0.0368732i
$971$	−11.2292	+	19.4495i	−0.360362	+	0.624165i	−0.988020	−	0.154324i	$-0.950680\pi$
$971$	−11.2292	+	19.4495i	−0.360362	+	0.624165i	0.627658	+	0.778489i	$0.284013\pi$
$972$	−1.12603	+	1.95035i	−0.0361175	+	0.0625574i
$973$		0			0
$974$	−23.6765			−0.758645
$975$	−56.6342	−	7.51819i	−1.81375	−	0.240775i
$976$	13.6584	−	23.6570i	0.437193	−	0.757241i
$977$	−35.5369	+	20.5172i	−1.13693	+	0.656405i	−0.945668	−	0.325135i	$-0.894590\pi$
$977$	−35.5369	+	20.5172i	−1.13693	+	0.656405i	−0.191259	+	0.981540i	$0.561257\pi$
$978$	−33.1835			−1.06109
$979$	4.84378	+	8.38967i	0.154808	+	0.268135i
$980$		0			0
$981$	6.08300	−	3.51202i	0.194215	−	0.112130i
$982$	4.50110	+	2.59871i	0.143636	+	0.0829282i
$983$	23.2379	+	13.4164i	0.741173	+	0.427916i	0.822496	−	0.568772i	$-0.192581\pi$
$983$	23.2379	+	13.4164i	0.741173	+	0.427916i	−0.0813229	+	0.996688i	$0.525915\pi$
$984$	−25.3639			−0.808571
$985$	−20.7362			−0.660711
$986$	−36.4689	−	21.0553i	−1.16141	−	0.670539i
$987$		0			0
$988$	0.513552	+	0.394943i	0.0163383	+	0.0125648i
$989$	−3.15506	−	5.46473i	−0.100325	−	0.173768i
$990$	−6.39324	+	3.69114i	−0.203191	+	0.117312i
$991$	−5.18755	−	8.98510i	−0.164788	−	0.285421i	0.771792	−	0.635875i	$-0.219361\pi$
$991$	−5.18755	−	8.98510i	−0.164788	−	0.285421i	−0.936580	+	0.350454i	$0.886027\pi$
$992$	2.76439	−	4.78807i	0.0877696	−	0.152021i
$993$		−	51.7669i		−	1.64277i
$994$		0			0
$995$	−32.8079	+	18.9417i	−1.04008	+	0.600491i
$996$	−0.785755	+	0.453656i	−0.0248976	+	0.0143746i
$997$	53.9097			1.70734			0.853669	−	0.520816i	$-0.174372\pi$
$997$	53.9097			1.70734			0.853669	+	0.520816i	$0.174372\pi$
$998$	−8.50671	−	14.7341i	−0.269275	−	0.466398i
$999$			3.89081i			0.123100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.i.459.5		12
7.2	even	3		637.2.u.g.30.5		12
7.3	odd	6		637.2.q.g.589.2		12
7.4	even	3		637.2.q.i.589.2		12
7.5	odd	6		91.2.u.b.30.5	yes	12
7.6	odd	2		91.2.k.b.4.5	✓	12
13.10	even	6		637.2.u.g.361.5		12
21.5	even	6		819.2.do.e.667.2		12
21.20	even	2		819.2.bm.f.550.2		12
91.6	even	12		1183.2.e.j.508.4		24
91.10	odd	6		637.2.q.g.491.2		12
91.19	even	12		1183.2.e.j.170.4		24
91.20	even	12		1183.2.e.j.508.9		24
91.23	even	6	inner	637.2.k.i.569.2		12
91.32	odd	12		8281.2.a.co.1.9		12
91.33	even	12		1183.2.e.j.170.9		24
91.45	even	12		8281.2.a.cp.1.9		12
91.46	odd	12		8281.2.a.co.1.4		12
91.59	even	12		8281.2.a.cp.1.4		12
91.62	odd	6		91.2.u.b.88.5	yes	12
91.75	odd	6		91.2.k.b.23.2	yes	12
91.88	even	6		637.2.q.i.491.2		12
273.62	even	6		819.2.do.e.361.2		12
273.257	even	6		819.2.bm.f.478.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.5	✓	12	7.6	odd	2
91.2.k.b.23.2	yes	12	91.75	odd	6
91.2.u.b.30.5	yes	12	7.5	odd	6
91.2.u.b.88.5	yes	12	91.62	odd	6
637.2.k.i.459.5		12	1.1	even	1	trivial
637.2.k.i.569.2		12	91.23	even	6	inner
637.2.q.g.491.2		12	91.10	odd	6
637.2.q.g.589.2		12	7.3	odd	6
637.2.q.i.491.2		12	91.88	even	6
637.2.q.i.589.2		12	7.4	even	3
637.2.u.g.30.5		12	7.2	even	3
637.2.u.g.361.5		12	13.10	even	6
819.2.bm.f.478.5		12	273.257	even	6
819.2.bm.f.550.2		12	21.20	even	2
819.2.do.e.361.2		12	273.62	even	6
819.2.do.e.667.2		12	21.5	even	6
1183.2.e.j.170.4		24	91.19	even	12
1183.2.e.j.170.9		24	91.33	even	12
1183.2.e.j.508.4		24	91.6	even	12
1183.2.e.j.508.9		24	91.20	even	12
8281.2.a.co.1.4		12	91.46	odd	12
8281.2.a.co.1.9		12	91.32	odd	12
8281.2.a.cp.1.4		12	91.59	even	12
8281.2.a.cp.1.9		12	91.45	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)

\(f(q)\)	\(=\)	\(q+1.34523i q^{2} +(1.02505 + 1.77544i) q^{3} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.38837 + 1.37893i) q^{6} +2.94654i q^{8} +(-0.601462 + 1.04176i) q^{9} +O(q^{10})\)	\(q+1.34523i q^{2} +(1.02505 + 1.77544i) q^{3} +0.190366 q^{4} +(-3.08979 + 1.78389i) q^{5} +(-2.38837 + 1.37893i) q^{6} +2.94654i q^{8} +(-0.601462 + 1.04176i) q^{9} +(-2.39973 - 4.15646i) q^{10} +(-1.10736 + 0.639336i) q^{11} +(0.195135 + 0.337984i) q^{12} +(-3.57420 - 0.474474i) q^{13} +(-6.33438 - 3.65716i) q^{15} -3.58303 q^{16} +7.73920 q^{17} +(-1.40141 - 0.809103i) q^{18} +(-0.817422 - 0.471939i) q^{19} +(-0.588191 + 0.339592i) q^{20} +(-0.860052 - 1.48965i) q^{22} -1.64727 q^{23} +(-5.23141 + 3.02035i) q^{24} +(3.86451 - 6.69354i) q^{25} +(0.638275 - 4.80810i) q^{26} +3.68419 q^{27} +(-2.02242 + 3.50293i) q^{29} +(4.91970 - 8.52117i) q^{30} +(-4.46193 - 2.57610i) q^{31} +1.07309i q^{32} +(-2.27021 - 1.31071i) q^{33} +10.4110i q^{34} +(-0.114498 + 0.198317i) q^{36} +1.05608i q^{37} +(0.634865 - 1.09962i) q^{38} +(-2.82133 - 6.83214i) q^{39} +(-5.25629 - 9.10417i) q^{40} +(3.63629 + 2.09941i) q^{41} +(1.91532 + 3.31744i) q^{43} +(-0.210805 + 0.121708i) q^{44} -4.29176i q^{45} -2.21596i q^{46} +(-0.774415 + 0.447109i) q^{47} +(-3.67279 - 6.36146i) q^{48} +(9.00432 + 5.19865i) q^{50} +(7.93308 + 13.7405i) q^{51} +(-0.680407 - 0.0903239i) q^{52} +(0.0399961 - 0.0692754i) q^{53} +4.95607i q^{54} +(2.28101 - 3.95082i) q^{55} -1.93505i q^{57} +(-4.71224 - 2.72061i) q^{58} +11.1847i q^{59} +(-1.20585 - 0.696200i) q^{60} +(-3.81196 + 6.60251i) q^{61} +(3.46543 - 6.00231i) q^{62} -8.60961 q^{64} +(11.8899 - 4.90994i) q^{65} +(1.76319 - 3.05394i) q^{66} +(5.47418 - 3.16052i) q^{67} +1.47328 q^{68} +(-1.68854 - 2.92464i) q^{69} +(9.89346 - 5.71199i) q^{71} +(-3.06959 - 1.77223i) q^{72} +(-0.658617 - 0.380253i) q^{73} -1.42067 q^{74} +15.8453 q^{75} +(-0.155610 - 0.0898413i) q^{76} +(9.19077 - 3.79533i) q^{78} +(1.42765 + 2.47277i) q^{79} +(11.0708 - 6.39172i) q^{80} +(5.58087 + 9.66636i) q^{81} +(-2.82418 + 4.89163i) q^{82} +2.32483i q^{83} +(-23.9125 + 13.8059i) q^{85} +(-4.46270 + 2.57654i) q^{86} -8.29233 q^{87} +(-1.88383 - 3.26289i) q^{88} -7.57626i q^{89} +5.77339 q^{90} -0.313586 q^{92} -10.5625i q^{93} +(-0.601462 - 1.04176i) q^{94} +3.36755 q^{95} +(-1.90522 + 1.09998i) q^{96} +(0.414443 - 0.239279i) q^{97} -1.53815i 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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