LMFDB - Embedded newform 637.2.u.i.30.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (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:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.6
Root			$-1.12906 - 0.851598i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.i.361.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.34104 - 1.35160i) q^{2} +0.345949 q^{3} +(2.65363 - 4.59623i) q^{4} +(2.82162 + 1.62906i) q^{5} +(0.809880 - 0.467584i) q^{6} -8.94020i q^{8} -2.88032 q^{9} +O(q^{10})$	\(q+(2.34104 - 1.35160i) q^{2} +0.345949 q^{3} +(2.65363 - 4.59623i) q^{4} +(2.82162 + 1.62906i) q^{5} +(0.809880 - 0.467584i) q^{6} -8.94020i q^{8} -2.88032 q^{9} +8.80735 q^{10} +1.84603i q^{11} +(0.918023 - 1.59006i) q^{12} +(-3.60550 + 0.0186461i) q^{13} +(0.976136 + 0.563573i) q^{15} +(-6.77628 - 11.7369i) q^{16} +(-1.07657 + 1.86467i) q^{17} +(-6.74293 + 3.89303i) q^{18} +2.40096i q^{19} +(14.9751 - 8.64587i) q^{20} +(2.49509 + 4.32162i) q^{22} +(0.906314 + 1.56978i) q^{23} -3.09285i q^{24} +(2.80769 + 4.86305i) q^{25} +(-8.41541 + 4.91684i) q^{26} -2.03429 q^{27} +(1.36703 - 2.36777i) q^{29} +3.04689 q^{30} +(-1.50893 + 0.871180i) q^{31} +(-16.2422 - 9.37743i) q^{32} +0.638632i q^{33} +5.82036i q^{34} +(-7.64331 + 13.2386i) q^{36} +(5.14042 - 2.96783i) q^{37} +(3.24513 + 5.62072i) q^{38} +(-1.24732 + 0.00645062i) q^{39} +(14.5641 - 25.2258i) q^{40} +(-3.65577 - 2.11066i) q^{41} +(-4.34111 - 7.51903i) q^{43} +(8.48477 + 4.89868i) q^{44} +(-8.12716 - 4.69222i) q^{45} +(4.24343 + 2.44994i) q^{46} +(-5.09027 - 2.93887i) q^{47} +(-2.34425 - 4.06036i) q^{48} +(13.1458 + 7.58972i) q^{50} +(-0.372438 + 0.645082i) q^{51} +(-9.48199 + 16.6212i) q^{52} +(4.65314 + 8.05947i) q^{53} +(-4.76235 + 2.74954i) q^{54} +(-3.00729 + 5.20878i) q^{55} +0.830609i q^{57} -7.39071i q^{58} +(9.31173 + 5.37613i) q^{59} +(5.18062 - 2.99103i) q^{60} -10.1101 q^{61} +(-2.35497 + 4.07893i) q^{62} -23.5929 q^{64} +(-10.2037 - 5.82098i) q^{65} +(0.863173 + 1.49506i) q^{66} -0.826916i q^{67} +(5.71365 + 9.89633i) q^{68} +(0.313538 + 0.543065i) q^{69} +(-2.03884 + 1.17712i) q^{71} +25.7506i q^{72} +(2.76680 - 1.59741i) q^{73} +(8.02261 - 13.8956i) q^{74} +(0.971316 + 1.68237i) q^{75} +(11.0353 + 6.37126i) q^{76} +(-2.91130 + 1.70098i) q^{78} +(-0.400955 + 0.694475i) q^{79} -44.1559i q^{80} +7.93720 q^{81} -11.4110 q^{82} -9.97031i q^{83} +(-6.07534 + 3.50760i) q^{85} +(-20.3254 - 11.7349i) q^{86} +(0.472923 - 0.819127i) q^{87} +16.5039 q^{88} +(13.0886 - 7.55674i) q^{89} -25.3680 q^{90} +9.62010 q^{92} +(-0.522012 + 0.301384i) q^{93} -15.8887 q^{94} +(-3.91130 + 6.77458i) q^{95} +(-5.61897 - 3.24411i) q^{96} +(-7.99489 + 4.61585i) q^{97} -5.31715i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9	$ 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9} + 24 q^{10} - 2 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} - 12 q^{18} + 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} - 24 q^{26} - 12 q^{27} + 8 q^{29} - 16 q^{30} - 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} + 2 q^{38} - 10 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} - 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} - 26 q^{52} + 22 q^{53} + 12 q^{54} + 6 q^{55} + 18 q^{59} + 66 q^{60} + 28 q^{61} + 4 q^{62} - 52 q^{64} - 42 q^{65} - 26 q^{66} + 8 q^{68} - 4 q^{69} - 24 q^{71} - 30 q^{73} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} + 28 q^{82} - 48 q^{85} - 60 q^{86} + 2 q^{87} + 28 q^{88} - 12 q^{89} - 24 q^{90} + 24 q^{92} + 18 q^{93} + 8 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9 + 24 * q^10 - 2 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 - 12 * q^18 + 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 12 * q^27 + 8 * q^29 - 16 * q^30 - 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 + 2 * q^38 - 10 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 - 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 - 26 * q^52 + 22 * q^53 + 12 * q^54 + 6 * q^55 + 18 * q^59 + 66 * q^60 + 28 * q^61 + 4 * q^62 - 52 * q^64 - 42 * q^65 - 26 * q^66 + 8 * q^68 - 4 * q^69 - 24 * q^71 - 30 * q^73 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 + 28 * q^82 - 48 * q^85 - 60 * q^86 + 2 * q^87 + 28 * q^88 - 12 * q^89 - 24 * q^90 + 24 * q^92 + 18 * q^93 + 8 * q^94 - 22 * q^95 - 6 * q^96 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.34104	−	1.35160i	1.65536	−	0.955724i	0.680549	−	0.732702i	$-0.261741\pi$
$2$	2.34104	−	1.35160i	1.65536	−	0.955724i	0.974813	−	0.223022i	$-0.0715921\pi$
$3$	0.345949			0.199734			0.0998669	−	0.995001i	$-0.468158\pi$
$3$	0.345949			0.199734			0.0998669	+	0.995001i	$0.468158\pi$
$4$	2.65363	−	4.59623i	1.32682	−	2.29811i
$5$	2.82162	+	1.62906i	1.26187	+	0.728539i	0.973435	−	0.228962i	$-0.0735332\pi$
$5$	2.82162	+	1.62906i	1.26187	+	0.728539i	0.288431	+	0.957501i	$0.406867\pi$
$6$	0.809880	−	0.467584i	0.330632	−	0.190890i
$7$		0			0
$7$		0			0
$8$		−	8.94020i		−	3.16084i
$9$	−2.88032			−0.960106
$10$	8.80735			2.78513
$11$			1.84603i			0.556598i	0.960494	+	0.278299i	$0.0897707\pi$
$11$			1.84603i			0.556598i	−0.960494	+	0.278299i	$0.910229\pi$
$12$	0.918023	−	1.59006i	0.265010	−	0.459011i
$13$	−3.60550	+	0.0186461i	−0.999987	+	0.00517151i
$13$	−3.60550	+	0.0186461i	−0.999987	+	0.00517151i
$14$		0			0
$15$	0.976136	+	0.563573i	0.252037	+	0.145514i
$16$	−6.77628	−	11.7369i	−1.69407	−	2.93422i
$17$	−1.07657	+	1.86467i	−0.261107	+	0.452250i	−0.966536	−	0.256530i	$-0.917421\pi$
$17$	−1.07657	+	1.86467i	−0.261107	+	0.452250i	0.705430	+	0.708780i	$0.250754\pi$
$18$	−6.74293	+	3.89303i	−1.58932	+	0.917597i
$19$			2.40096i			0.550817i	0.961327	+	0.275408i	$0.0888131\pi$
$19$			2.40096i			0.550817i	−0.961327	+	0.275408i	$0.911187\pi$
$20$	14.9751	−	8.64587i	3.34853	−	1.93328i
$21$		0			0
$22$	2.49509	+	4.32162i	0.531954	+	0.921372i
$23$	0.906314	+	1.56978i	0.188979	+	0.327322i	0.944910	−	0.327329i	$-0.106149\pi$
$23$	0.906314	+	1.56978i	0.188979	+	0.327322i	−0.755931	+	0.654652i	$0.772815\pi$
$24$		−	3.09285i		−	0.631326i
$25$	2.80769	+	4.86305i	0.561537	+	0.972611i
$26$	−8.41541	+	4.91684i	−1.65040	+	0.964272i
$27$	−2.03429			−0.391500
$28$		0			0
$29$	1.36703	−	2.36777i	0.253851	−	0.439683i	−0.710732	−	0.703463i	$-0.751636\pi$
$29$	1.36703	−	2.36777i	0.253851	−	0.439683i	0.964583	+	0.263780i	$0.0849693\pi$
$30$	3.04689			0.556284
$31$	−1.50893	+	0.871180i	−0.271011	+	0.156468i	−0.629347	−	0.777124i	$-0.716678\pi$
$31$	−1.50893	+	0.871180i	−0.271011	+	0.156468i	0.358336	+	0.933593i	$0.383344\pi$
$32$	−16.2422	−	9.37743i	−2.87124	−	1.65771i
$33$			0.638632i			0.111172i
$34$			5.82036i			0.998183i
$35$		0			0
$36$	−7.64331	+	13.2386i	−1.27389	+	2.20643i
$37$	5.14042	−	2.96783i	0.845081	−	0.487908i	−0.0139073	−	0.999903i	$-0.504427\pi$
$37$	5.14042	−	2.96783i	0.845081	−	0.487908i	0.858988	+	0.511996i	$0.171094\pi$
$38$	3.24513	+	5.62072i	0.526429	+	0.911802i
$39$	−1.24732	+	0.00645062i	−0.199731	+	0.00103293i
$40$	14.5641	−	25.2258i	2.30279	−	3.98855i
$41$	−3.65577	−	2.11066i	−0.570935	−	0.329629i	0.186588	−	0.982438i	$-0.440257\pi$
$41$	−3.65577	−	2.11066i	−0.570935	−	0.329629i	−0.757523	+	0.652809i	$0.773590\pi$
$42$		0			0
$43$	−4.34111	−	7.51903i	−0.662014	−	1.14664i	−0.980086	−	0.198575i	$-0.936369\pi$
$43$	−4.34111	−	7.51903i	−0.662014	−	1.14664i	0.318072	−	0.948067i	$-0.396965\pi$
$44$	8.48477	+	4.89868i	1.27913	+	0.738504i
$45$	−8.12716	−	4.69222i	−1.21153	−	0.699475i
$46$	4.24343	+	2.44994i	0.625659	+	0.361224i
$47$	−5.09027	−	2.93887i	−0.742493	−	0.428678i	0.0804822	−	0.996756i	$-0.474354\pi$
$47$	−5.09027	−	2.93887i	−0.742493	−	0.428678i	−0.822975	+	0.568078i	$0.807687\pi$
$48$	−2.34425	−	4.06036i	−0.338363	−	0.586062i
$49$		0			0
$50$	13.1458	+	7.58972i	1.85910	+	1.07335i
$51$	−0.372438	+	0.645082i	−0.0521518	+	0.0903296i
$52$	−9.48199	+	16.6212i	−1.31491	+	2.30495i
$53$	4.65314	+	8.05947i	0.639158	+	1.10705i	0.985618	+	0.168989i	$0.0540503\pi$
$53$	4.65314	+	8.05947i	0.639158	+	1.10705i	−0.346460	+	0.938065i	$0.612616\pi$
$54$	−4.76235	+	2.74954i	−0.648074	+	0.374166i
$55$	−3.00729	+	5.20878i	−0.405503	+	0.702352i
$56$		0			0
$57$			0.830609i			0.110017i
$58$		−	7.39071i		−	0.970447i
$59$	9.31173	+	5.37613i	1.21228	+	0.699912i	0.963256	−	0.268584i	$-0.0865557\pi$
$59$	9.31173	+	5.37613i	1.21228	+	0.699912i	0.249028	+	0.968496i	$0.419889\pi$
$60$	5.18062	−	2.99103i	0.668815	−	0.386141i
$61$	−10.1101			−1.29446			−0.647231	−	0.762294i	$-0.724073\pi$
$61$	−10.1101			−1.29446			−0.647231	+	0.762294i	$0.724073\pi$
$62$	−2.35497	+	4.07893i	−0.299081	+	0.518024i
$63$		0			0
$64$	−23.5929			−2.94911
$65$	−10.2037	−	5.82098i	−1.26562	−	0.722003i
$66$	0.863173	+	1.49506i	0.106249	+	0.184029i
$67$		−	0.826916i		−	0.101024i	−0.998723	−	0.0505119i	$-0.983915\pi$
$67$		−	0.826916i		−	0.101024i	0.998723	−	0.0505119i	$-0.0160853\pi$
$68$	5.71365	+	9.89633i	0.692881	+	1.20011i
$69$	0.313538	+	0.543065i	0.0377456	+	0.0653773i
$70$		0			0
$71$	−2.03884	+	1.17712i	−0.241965	+	0.139699i	−0.616080	−	0.787684i	$-0.711280\pi$
$71$	−2.03884	+	1.17712i	−0.241965	+	0.139699i	0.374114	+	0.927383i	$0.377947\pi$
$72$			25.7506i			3.03474i
$73$	2.76680	−	1.59741i	0.323829	−	0.186963i	−0.329269	−	0.944236i	$-0.606802\pi$
$73$	2.76680	−	1.59741i	0.323829	−	0.186963i	0.653098	+	0.757273i	$0.273469\pi$
$74$	8.02261	−	13.8956i	0.932610	−	1.61533i
$75$	0.971316	+	1.68237i	0.112158	+	0.194263i
$76$	11.0353	+	6.37126i	1.26584	+	0.730833i
$77$		0			0
$78$	−2.91130	+	1.70098i	−0.329640	+	0.192598i
$79$	−0.400955	+	0.694475i	−0.0451110	+	0.0781345i	−0.887699	−	0.460424i	$-0.847697\pi$
$79$	−0.400955	+	0.694475i	−0.0451110	+	0.0781345i	0.842588	+	0.538558i	$0.181031\pi$
$80$		−	44.1559i		−	4.93678i
$81$	7.93720			0.881911
$82$	−11.4110			−1.26014
$83$		−	9.97031i		−	1.09438i	−0.837007	−	0.547192i	$-0.815697\pi$
$83$		−	9.97031i		−	1.09438i	0.837007	−	0.547192i	$-0.184303\pi$
$84$		0			0
$85$	−6.07534	+	3.50760i	−0.658963	+	0.380452i
$86$	−20.3254	−	11.7349i	−2.19175	−	1.26541i
$87$	0.472923	−	0.819127i	0.0507027	−	0.0878196i
$88$	16.5039			1.75932
$89$	13.0886	−	7.55674i	1.38739	−	0.801012i	0.394373	−	0.918950i	$-0.370962\pi$
$89$	13.0886	−	7.55674i	1.38739	−	0.801012i	0.993021	+	0.117938i	$0.0376284\pi$
$90$	−25.3680			−2.67402
$91$		0			0
$92$	9.62010			1.00296
$93$	−0.522012	+	0.301384i	−0.0541301	+	0.0312520i
$94$	−15.8887			−1.63879
$95$	−3.91130	+	6.77458i	−0.401291	+	0.695057i
$96$	−5.61897	−	3.24411i	−0.573484	−	0.331101i
$97$	−7.99489	+	4.61585i	−0.811758	+	0.468669i	−0.847566	−	0.530690i	$-0.821933\pi$
$97$	−7.99489	+	4.61585i	−0.811758	+	0.468669i	0.0358079	+	0.999359i	$0.488600\pi$
$98$		0			0
$99$		−	5.31715i		−	0.534394i
$100$	29.8023			2.98023
$101$	14.8234			1.47498			0.737491	−	0.675357i	$-0.236011\pi$
$101$	14.8234			1.47498			0.737491	+	0.675357i	$0.236011\pi$
$102$			2.01355i			0.199371i
$103$	2.14143	−	3.70907i	0.211001	−	0.365465i	−0.741027	−	0.671475i	$-0.765661\pi$
$103$	2.14143	−	3.70907i	0.211001	−	0.365465i	0.952028	+	0.306010i	$0.0989942\pi$
$104$	0.166700	+	32.2339i	0.0163463	+	3.16079i
$105$		0			0
$106$	21.7863	+	12.5783i	2.11608	+	1.22172i
$107$	9.56289	+	16.5634i	0.924479	+	1.60124i	0.792397	+	0.610006i	$0.208833\pi$
$107$	9.56289	+	16.5634i	0.924479	+	1.60124i	0.132082	+	0.991239i	$0.457834\pi$
$108$	−5.39827	+	9.35007i	−0.519448	+	0.899711i
$109$	3.69925	−	2.13577i	0.354324	−	0.204569i	−0.312264	−	0.949995i	$-0.601087\pi$
$109$	3.69925	−	2.13577i	0.354324	−	0.204569i	0.666588	+	0.745426i	$0.267754\pi$
$110$			16.2586i			1.55020i
$111$	1.77833	−	1.02672i	0.168791	−	0.0974516i
$112$		0			0
$113$	−1.37488	−	2.38137i	−0.129338	−	0.224020i	0.794082	−	0.607810i	$-0.207952\pi$
$113$	−1.37488	−	2.38137i	−0.129338	−	0.224020i	−0.923420	+	0.383790i	$0.874619\pi$
$114$	1.12265	+	1.94448i	0.105146	+	0.182118i
$115$			5.90576i			0.550715i
$116$	−7.25520	−	12.5664i	−0.673629	−	1.16676i
$117$	10.3850	−	0.0537068i	0.960094	−	0.00496520i
$118$	29.0655			2.67569
$119$		0			0
$120$	5.03845	−	8.72685i	0.459945	−	0.796649i
$121$	7.59218			0.690198
$122$	−23.6680	+	13.6648i	−2.14280	+	1.23715i
$123$	−1.26471	−	0.730180i	−0.114035	−	0.0658381i
$124$			9.24717i			0.830420i
$125$			2.00495i			0.179329i
$126$		0			0
$127$	−4.86719	+	8.43022i	−0.431893	+	0.748061i	−0.997036	−	0.0769320i	$-0.975488\pi$
$127$	−4.86719	+	8.43022i	−0.431893	+	0.748061i	0.565143	+	0.824993i	$0.308821\pi$
$128$	−22.7475	+	13.1333i	−2.01061	+	1.16083i
$129$	−1.50181	−	2.60120i	−0.132227	−	0.229023i
$130$	−31.7549	+	0.164223i	−2.78509	+	0.0144033i
$131$	−9.33073	+	16.1613i	−0.815230	+	1.41202i	0.0939330	+	0.995579i	$0.470056\pi$
$131$	−9.33073	+	16.1613i	−0.815230	+	1.41202i	−0.909163	+	0.416441i	$0.863277\pi$
$132$	2.93530	+	1.69470i	0.255485	+	0.147504i
$133$		0			0
$134$	−1.11766	−	1.93584i	−0.0965509	−	0.167231i
$135$	−5.73999	−	3.31399i	−0.494020	−	0.285223i
$136$	16.6706	+	9.62475i	1.42949	+	0.825315i
$137$	7.29328	+	4.21078i	0.623107	+	0.359751i	0.778078	−	0.628168i	$-0.216195\pi$
$137$	7.29328	+	4.21078i	0.623107	+	0.359751i	−0.154971	+	0.987919i	$0.549528\pi$
$138$	1.46801	+	0.847556i	0.124965	+	0.0721488i
$139$	−8.81809	−	15.2734i	−0.747941	−	1.29547i	−0.948808	−	0.315853i	$-0.897709\pi$
$139$	−8.81809	−	15.2734i	−0.747941	−	1.29547i	0.200867	−	0.979619i	$-0.435624\pi$
$140$		0			0
$141$	−1.76098	−	1.01670i	−0.148301	−	0.0856216i
$142$	−3.18199	+	5.51138i	−0.267027	+	0.462504i
$143$	−0.0344213	−	6.65586i	−0.00287845	−	0.556591i
$144$	19.5179	+	33.8059i	1.62649	+	2.81716i
$145$	7.71448	−	4.45396i	0.640653	−	0.369881i
$146$	4.31811	−	7.47919i	0.357370	−	0.618982i
$147$		0			0
$148$		−	31.5021i		−	2.58946i
$149$		−	4.02104i		−	0.329416i	−0.986342	−	0.164708i	$-0.947332\pi$
$149$		−	4.02104i		−	0.329416i	0.986342	−	0.164708i	$-0.0526683\pi$
$150$	4.54777	+	2.62566i	0.371324	+	0.214384i
$151$	−16.3687	+	9.45048i	−1.33207	+	0.769069i	−0.985616	−	0.168999i	$-0.945947\pi$
$151$	−16.3687	+	9.45048i	−1.33207	+	0.769069i	−0.346451	+	0.938068i	$0.612613\pi$
$152$	21.4650			1.74104
$153$	3.10086	−	5.37086i	0.250690	−	0.434208i
$154$		0			0
$155$	−5.67682			−0.455973
$156$	−3.28029	+	5.75009i	−0.262633	+	0.460376i
$157$	−5.78677	−	10.0230i	−0.461835	−	0.799922i	0.537218	−	0.843444i	$-0.319475\pi$
$157$	−5.78677	−	10.0230i	−0.461835	−	0.799922i	−0.999052	+	0.0435222i	$0.986142\pi$
$158$			2.16772i			0.172455i
$159$	1.60975	+	2.78817i	0.127661	+	0.221116i
$160$	−30.5528	−	52.9190i	−2.41541	−	4.18362i
$161$		0			0
$162$	18.5813	−	10.7279i	1.45988	−	0.842863i
$163$		−	4.40542i		−	0.345059i	−0.985004	−	0.172529i	$-0.944806\pi$
$163$		−	4.40542i		−	0.345059i	0.985004	−	0.172529i	$-0.0551940\pi$
$164$	−19.4021	+	11.2018i	−1.51505	+	0.874716i
$165$	−1.04037	+	1.80197i	−0.0809927	+	0.140284i
$166$	−13.4759	−	23.3409i	−1.04593	−	1.81160i
$167$	7.81076	+	4.50954i	0.604415	+	0.348959i	0.770776	−	0.637106i	$-0.219869\pi$
$167$	7.81076	+	4.50954i	0.604415	+	0.348959i	−0.166362	+	0.986065i	$0.553202\pi$
$168$		0			0
$169$	12.9993	−	0.134457i	0.999947	−	0.0103429i
$170$	−9.48173	+	16.4228i	−0.727215	+	1.25957i
$171$		−	6.91552i		−	0.528843i
$172$	−46.0789			−3.51349
$173$	6.09200			0.463166			0.231583	−	0.972815i	$-0.425609\pi$
$173$	6.09200			0.463166			0.231583	+	0.972815i	$0.425609\pi$
$174$		−	2.55681i		−	0.193831i
$175$		0			0
$176$	21.6666	−	12.5092i	1.63318	−	0.942917i
$177$	3.22139	+	1.85987i	0.242134	+	0.139796i
$178$	20.4273	−	35.3812i	1.53109	−	2.65193i
$179$	−3.87964			−0.289978			−0.144989	−	0.989433i	$-0.546315\pi$
$179$	−3.87964			−0.289978			−0.144989	+	0.989433i	$0.546315\pi$
$180$	−43.1330	+	24.9029i	−3.21495	+	1.85615i
$181$	6.58392			0.489379			0.244690	−	0.969601i	$-0.421314\pi$
$181$	6.58392			0.489379			0.244690	+	0.969601i	$0.421314\pi$
$182$		0			0
$183$	−3.49757			−0.258548
$184$	14.0342	−	8.10262i	1.03461	−	0.597333i
$185$	19.3391			1.42184
$186$	−0.814700	+	1.41110i	−0.0597367	+	0.103467i
$187$	−3.44224	−	1.98738i	−0.251721	−	0.145331i
$188$	−27.0155	+	15.5974i	−1.97030	+	1.13756i
$189$		0			0
$190$			21.1460i			1.53410i
$191$	−13.7434			−0.994435			−0.497218	−	0.867626i	$-0.665645\pi$
$191$	−13.7434			−0.994435			−0.497218	+	0.867626i	$0.665645\pi$
$192$	−8.16195			−0.589038
$193$		−	22.7530i		−	1.63780i	−0.573937	−	0.818899i	$-0.694585\pi$
$193$		−	22.7530i		−	1.63780i	0.573937	−	0.818899i	$-0.305415\pi$
$194$	−12.4776	+	21.6118i	−0.895836	+	1.55163i
$195$	−3.52997	−	2.01376i	−0.252786	−	0.144208i
$196$		0			0
$197$	−12.5809	−	7.26358i	−0.896352	−	0.517509i	−0.0203371	−	0.999793i	$-0.506474\pi$
$197$	−12.5809	−	7.26358i	−0.896352	−	0.517509i	−0.876015	+	0.482284i	$0.839807\pi$
$198$	−7.18665	−	12.4476i	−0.510733	−	0.884615i
$199$	−11.9202	+	20.6464i	−0.845001	+	1.46358i	0.0406192	+	0.999175i	$0.487067\pi$
$199$	−11.9202	+	20.6464i	−0.845001	+	1.46358i	−0.885620	+	0.464410i	$0.846266\pi$
$200$	43.4767	−	25.1013i	3.07426	−	1.77493i
$201$		−	0.286071i		−	0.0201779i
$202$	34.7021	−	20.0353i	2.44163	−	1.40968i
$203$		0			0
$204$	1.97663	+	3.42363i	0.138392	+	0.239702i
$205$	−6.87678	−	11.9109i	−0.480295	−	0.831896i
$206$		−	11.5774i		−	0.806637i
$207$	−2.61047	−	4.52147i	−0.181440	−	0.314264i
$208$	24.6508	+	42.1910i	1.70922	+	2.92542i
$209$	−4.43223			−0.306584
$210$		0			0
$211$	−2.15764	+	3.73714i	−0.148538	+	0.257275i	−0.930687	−	0.365816i	$-0.880790\pi$
$211$	−2.15764	+	3.73714i	−0.148538	+	0.257275i	0.782149	+	0.623091i	$0.214123\pi$
$212$	49.3909			3.39218
$213$	−0.705334	+	0.407225i	−0.0483287	+	0.0279026i
$214$	44.7741	+	25.8504i	3.06070	+	1.76709i
$215$		−	28.2878i		−	1.92921i
$216$			18.1870i			1.23747i
$217$		0			0
$218$	5.77339	−	9.99981i	0.391024	−	0.677273i
$219$	0.957171	−	0.552623i	0.0646796	−	0.0373428i
$220$	15.9605	+	27.6444i	1.07606	+	1.86379i
$221$	3.84681	−	6.74316i	0.258764	−	0.453594i
$222$	2.77542	−	4.80716i	0.186274	−	0.322636i
$223$	20.2604	+	11.6973i	1.35674	+	0.783312i	0.989182	−	0.146691i	$-0.0468623\pi$
$223$	20.2604	+	11.6973i	1.35674	+	0.783312i	0.367553	+	0.930003i	$0.380196\pi$
$224$		0			0
$225$	−8.08703	−	14.0071i	−0.539135	−	0.933810i
$226$	−6.43730	−	3.71658i	−0.428203	−	0.247223i
$227$	−23.1427	−	13.3614i	−1.53603	−	0.886829i	−0.999065	−	0.0432270i	$-0.986236\pi$
$227$	−23.1427	−	13.3614i	−1.53603	−	0.886829i	−0.536968	−	0.843602i	$-0.680431\pi$
$228$	3.81767	+	2.20413i	0.252831	+	0.145972i
$229$	2.60388	+	1.50335i	0.172069	+	0.0993442i	0.583561	−	0.812069i	$-0.301659\pi$
$229$	2.60388	+	1.50335i	0.172069	+	0.0993442i	−0.411492	+	0.911413i	$0.634992\pi$
$230$	7.98222	+	13.8256i	0.526332	+	0.911634i
$231$		0			0
$232$	−21.1683	−	12.2215i	−1.38977	−	0.802383i
$233$	−5.85740	+	10.1453i	−0.383731	+	0.664641i	−0.991592	−	0.129402i	$-0.958694\pi$
$233$	−5.85740	+	10.1453i	−0.383731	+	0.664641i	0.607861	+	0.794043i	$0.292028\pi$
$234$	24.2391	−	14.1621i	1.58456	−	0.925804i
$235$	−9.57521	−	16.5847i	−0.624618	−	1.08187i
$236$	49.4199	−	28.5326i	3.21696	−	1.85731i
$237$	−0.138710	+	0.240253i	−0.00901019	+	0.0156061i
$238$		0			0
$239$		−	1.42797i		−	0.0923677i	−0.998933	−	0.0461838i	$-0.985294\pi$
$239$		−	1.42797i		−	0.0923677i	0.998933	−	0.0461838i	$-0.0147060\pi$
$240$		−	15.2757i		−	0.986043i
$241$	−2.32068	−	1.33984i	−0.149488	−	0.0863069i	0.423390	−	0.905947i	$-0.360840\pi$
$241$	−2.32068	−	1.33984i	−0.149488	−	0.0863069i	−0.572878	+	0.819640i	$0.694173\pi$
$242$	17.7736	−	10.2616i	1.14253	−	0.659639i
$243$	8.84874			0.567647
$244$	−26.8284	+	46.4682i	−1.71751	+	2.97482i
$245$		0			0
$246$	−3.94764			−0.251692
$247$	−0.0447686	−	8.65665i	−0.00284856	−	0.550810i
$248$	7.78852	+	13.4901i	0.494571	+	0.856623i
$249$		−	3.44922i		−	0.218586i
$250$	2.70989	+	4.69367i	0.171389	+	0.296854i
$251$	−5.46696	−	9.46906i	−0.345072	−	0.597681i	0.640295	−	0.768129i	$-0.278812\pi$
$251$	−5.46696	−	9.46906i	−0.345072	−	0.597681i	−0.985367	+	0.170447i	$0.945479\pi$
$252$		0			0
$253$	−2.89786	+	1.67308i	−0.182187	+	0.105186i
$254$			26.3139i			1.65108i
$255$	−2.10176	+	1.21345i	−0.131617	+	0.0759892i
$256$	−11.9089	+	20.6268i	−0.744307	+	1.28918i
$257$	−2.07569	−	3.59520i	−0.129478	−	0.224262i	0.793996	−	0.607922i	$-0.207997\pi$
$257$	−2.07569	−	3.59520i	−0.129478	−	0.224262i	−0.923474	+	0.383660i	$0.874663\pi$
$258$	−7.03156	−	4.05967i	−0.437766	−	0.252744i
$259$		0			0
$260$	−53.8315	+	31.4519i	−3.33849	+	1.95057i
$261$	−3.93749	+	6.81993i	−0.243724	+	0.422143i
$262$			50.4456i			3.11654i
$263$	4.05360			0.249955			0.124978	−	0.992160i	$-0.460114\pi$
$263$	4.05360			0.249955			0.124978	+	0.992160i	$0.460114\pi$
$264$	5.70949			0.351395
$265$			30.3210i			1.86260i
$266$		0			0
$267$	4.52801	−	2.61425i	0.277110	−	0.159989i
$268$	−3.80069	−	2.19433i	−0.232164	−	0.134040i
$269$	2.00011	−	3.46430i	0.121949	−	0.211222i	−0.798587	−	0.601879i	$-0.794419\pi$
$269$	2.00011	−	3.46430i	0.121949	−	0.211222i	0.920536	+	0.390657i	$0.127752\pi$
$270$	−17.9167			−1.09038
$271$	−2.41189	+	1.39251i	−0.146512	+	0.0845888i	−0.571464	−	0.820627i	$-0.693624\pi$
$271$	−2.41189	+	1.39251i	−0.146512	+	0.0845888i	0.424952	+	0.905216i	$0.360291\pi$
$272$	29.1806			1.76933
$273$		0			0
$274$	22.7651			1.37529
$275$	−8.97733	+	5.18306i	−0.541353	+	0.312551i
$276$	3.32807			0.200326
$277$	8.34618	−	14.4560i	0.501474	−	0.868578i	−0.498525	−	0.866875i	$-0.666125\pi$
$277$	8.34618	−	14.4560i	0.501474	−	0.868578i	0.999999	−	0.00170243i	$-0.000541901\pi$
$278$	−41.2870	−	23.8370i	−2.47623	−	1.42965i
$279$	4.34619	−	2.50928i	0.260200	−	0.150226i
$280$		0			0
$281$		−	13.3731i		−	0.797774i	−0.917000	−	0.398887i	$-0.869397\pi$
$281$		−	13.3731i		−	0.797774i	0.917000	−	0.398887i	$-0.130603\pi$
$282$	−5.49668			−0.327322
$283$	−18.8862			−1.12267			−0.561335	−	0.827589i	$-0.689712\pi$
$283$	−18.8862			−1.12267			−0.561335	+	0.827589i	$0.689712\pi$
$284$			12.4946i			0.741419i
$285$	−1.35311	+	2.34366i	−0.0801515	+	0.138826i
$286$	−9.07663	−	15.5351i	−0.536712	−	0.918609i
$287$		0			0
$288$	46.7827	+	27.0100i	2.75669	+	1.59158i
$289$	6.18199	+	10.7075i	0.363647	+	0.629855i
$290$	12.0399	−	20.8537i	0.707008	−	1.22457i
$291$	−2.76583	+	1.59685i	−0.162136	+	0.0936090i
$292$		−	16.9558i		−	0.992262i
$293$	2.95999	−	1.70895i	0.172925	−	0.0998380i	−0.411040	−	0.911617i	$-0.634834\pi$
$293$	2.95999	−	1.70895i	0.172925	−	0.0998380i	0.583964	+	0.811779i	$0.301501\pi$
$294$		0			0
$295$	17.5161	+	30.3388i	1.01983	+	1.76639i
$296$	−26.5329	−	45.9564i	−1.54220	−	2.67116i
$297$		−	3.75536i		−	0.217908i
$298$	−5.43483	−	9.41340i	−0.314831	−	0.545304i
$299$	−3.29699	−	5.64295i	−0.190670	−	0.326340i
$300$	10.3101			0.595252
$301$		0			0
$302$	−25.5465	+	44.2479i	−1.47004	+	2.54618i
$303$	5.12814			0.294604
$304$	28.1797	−	16.2696i	1.61622	−	0.933123i
$305$	−28.5268	−	16.4699i	−1.63344	−	0.943066i
$306$		−	16.7645i		−	0.958362i
$307$		−	16.3679i		−	0.934165i	−0.884214	−	0.467083i	$-0.845305\pi$
$307$		−	16.3679i		−	0.934165i	0.884214	−	0.467083i	$-0.154695\pi$
$308$		0			0
$309$	0.740826	−	1.28315i	0.0421441	−	0.0729958i
$310$	−13.2896	+	7.67278i	−0.754801	+	0.435785i
$311$	−11.8489	−	20.5230i	−0.671891	−	1.16375i	−0.977367	−	0.211550i	$-0.932149\pi$
$311$	−11.8489	−	20.5230i	−0.671891	−	1.16375i	0.305476	−	0.952200i	$-0.401184\pi$
$312$	0.0576698	+	11.1513i	0.00326491	+	0.631318i
$313$	−2.59013	+	4.48623i	−0.146403	+	0.253577i	−0.929895	−	0.367824i	$-0.880103\pi$
$313$	−2.59013	+	4.48623i	−0.146403	+	0.253577i	0.783493	+	0.621401i	$0.213436\pi$
$314$	−27.0941	−	15.6428i	−1.52901	−	0.882774i
$315$		0			0
$316$	2.12798	+	3.68577i	0.119708	+	0.207341i
$317$	−5.25276	−	3.03268i	−0.295024	−	0.170332i	0.345181	−	0.938536i	$-0.387817\pi$
$317$	−5.25276	−	3.03268i	−0.295024	−	0.170332i	−0.640206	+	0.768204i	$0.721151\pi$
$318$	7.53697	+	4.35147i	0.422652	+	0.244018i
$319$	4.37096	+	2.52358i	0.244727	+	0.141293i
$320$	−66.5702	−	38.4343i	−3.72139	−	2.14854i
$321$	3.30827	+	5.73010i	0.184650	+	0.319823i
$322$		0			0
$323$	−4.47700	−	2.58480i	−0.249107	−	0.143822i
$324$	21.0624	−	36.4812i	1.17013	−	2.02673i
$325$	−10.2138	−	17.4814i	−0.566559	−	0.969694i
$326$	−5.95435	−	10.3132i	−0.329781	−	0.571198i
$327$	1.27975	−	0.738866i	0.0707706	−	0.0408594i
$328$	−18.8697	+	32.6833i	−1.04190	+	1.80463i
$329$		0			0
$330$			5.62465i			0.309627i
$331$			17.2749i			0.949512i	0.880118	+	0.474756i	$0.157464\pi$
$331$			17.2749i			0.949512i	−0.880118	+	0.474756i	$0.842536\pi$
$332$	−45.8258	−	26.4576i	−2.51502	−	1.45205i
$333$	−14.8061	+	8.54829i	−0.811367	+	0.468443i
$334$	24.3804			1.33403
$335$	1.34710	−	2.33324i	0.0735998	−	0.127479i
$336$		0			0
$337$	−8.35464			−0.455106			−0.227553	−	0.973766i	$-0.573073\pi$
$337$	−8.35464			−0.455106			−0.227553	+	0.973766i	$0.573073\pi$
$338$	30.2501	−	17.8846i	1.64539	−	0.972794i
$339$	−0.475639	−	0.823832i	−0.0258332	−	0.0447444i
$340$			37.2315i			2.01916i
$341$	−1.60822	−	2.78552i	−0.0870901	−	0.150844i
$342$	−9.34700	−	16.1895i	−0.505428	−	0.875427i
$343$		0			0
$344$	−67.2216	+	38.8104i	−3.62435	+	2.09252i
$345$			2.04309i			0.109997i
$346$	14.2616	−	8.23394i	0.766708	−	0.442659i
$347$	−14.4110	+	24.9606i	−0.773623	+	1.33995i	0.161942	+	0.986800i	$0.448224\pi$
$347$	−14.4110	+	24.9606i	−0.773623	+	1.33995i	−0.935565	+	0.353154i	$0.885109\pi$
$348$	−2.50993	−	4.34733i	−0.134546	−	0.233041i
$349$	10.1516	+	5.86103i	0.543403	+	0.313734i	0.746457	−	0.665434i	$-0.231753\pi$
$349$	10.1516	+	5.86103i	0.543403	+	0.313734i	−0.203054	+	0.979167i	$0.565087\pi$
$350$		0			0
$351$	7.33464	−	0.0379317i	0.391494	−	0.00202464i
$352$	17.3110	−	29.9835i	0.922679	−	1.59813i
$353$			17.8362i			0.949326i	0.880168	+	0.474663i	$0.157430\pi$
$353$			17.8362i			0.949326i	−0.880168	+	0.474663i	$0.842570\pi$
$354$	10.0552			0.534426
$355$	−7.67043			−0.407104
$356$		−	80.2113i		−	4.25119i
$357$		0			0
$358$	−9.08239	+	5.24372i	−0.480019	+	0.277139i
$359$	−4.92042	−	2.84081i	−0.259690	−	0.149932i	0.364503	−	0.931202i	$-0.381239\pi$
$359$	−4.92042	−	2.84081i	−0.259690	−	0.149932i	−0.624193	+	0.781270i	$0.714572\pi$
$360$	−41.9494	+	72.6584i	−2.21093	+	3.82943i
$361$	13.2354			0.696601
$362$	15.4132	−	8.89882i	0.810100	−	0.467712i
$363$	2.62651			0.137856
$364$		0			0
$365$	10.4091			0.544838
$366$	−8.18794	+	4.72731i	−0.427991	+	0.247100i
$367$	19.6316			1.02476			0.512381	−	0.858758i	$-0.328764\pi$
$367$	19.6316			1.02476			0.512381	+	0.858758i	$0.328764\pi$
$368$	12.2829	−	21.2746i	0.640289	−	1.10901i
$369$	10.5298	+	6.07937i	0.548158	+	0.316479i
$370$	45.2735	−	26.1387i	2.35366	−	1.35888i
$371$		0			0
$372$			3.19905i			0.165863i
$373$	32.0645			1.66024			0.830119	−	0.557586i	$-0.188272\pi$
$373$	32.0645			1.66024			0.830119	+	0.557586i	$0.188272\pi$
$374$	−10.7445			−0.555587
$375$			0.693612i			0.0358180i
$376$	−26.2741	+	45.5081i	−1.35498	+	2.34690i
$377$	−4.88468	+	8.56248i	−0.251574	+	0.440990i
$378$		0			0
$379$	−16.4745	−	9.51154i	−0.846237	−	0.488575i	0.0131425	−	0.999914i	$-0.495816\pi$
$379$	−16.4745	−	9.51154i	−0.846237	−	0.488575i	−0.859379	+	0.511339i	$0.829150\pi$
$380$	20.7583	+	35.9545i	1.06488	+	1.84443i
$381$	−1.68380	+	2.91643i	−0.0862637	+	0.149413i
$382$	−32.1737	+	18.5755i	−1.64615	+	0.950406i
$383$		−	0.699829i		−	0.0357596i	−0.999840	−	0.0178798i	$-0.994308\pi$
$383$		−	0.699829i		−	0.0357596i	0.999840	−	0.0178798i	$-0.00569162\pi$
$384$	−7.86948	+	4.54345i	−0.401588	+	0.231857i
$385$		0			0
$386$	−30.7529	−	53.2657i	−1.56528	−	2.71115i
$387$	12.5038	+	21.6572i	0.635604	+	1.10090i
$388$			48.9951i			2.48735i
$389$	−10.0274	−	17.3679i	−0.508407	−	0.880587i	−0.999953	−	0.00973506i	$-0.996901\pi$
$389$	−10.0274	−	17.3679i	−0.508407	−	0.880587i	0.491545	−	0.870852i	$-0.336432\pi$
$390$	−10.9856	+	0.0568128i	−0.556277	+	0.00287683i
$391$	−3.90284			−0.197375
$392$		0			0
$393$	−3.22796	+	5.59099i	−0.162829	+	0.282028i
$394$	−39.2698			−1.97838
$395$	−2.26269	+	1.30636i	−0.113848	+	0.0657302i
$396$	−24.4388	−	14.1098i	−1.22810	−	0.709043i
$397$			22.2803i			1.11822i	0.829095	+	0.559108i	$0.188856\pi$
$397$			22.2803i			1.11822i	−0.829095	+	0.559108i	$0.811144\pi$
$398$			64.4453i			3.23035i
$399$		0			0
$400$	38.0513	−	65.9069i	1.90257	−	3.29534i
$401$	4.16341	−	2.40374i	0.207911	−	0.120037i	−0.392429	−	0.919782i	$-0.628365\pi$
$401$	4.16341	−	2.40374i	0.207911	−	0.120037i	0.600340	+	0.799745i	$0.295032\pi$
$402$	−0.386653	−	0.669702i	−0.0192845	−	0.0334017i
$403$	5.42420	−	3.16918i	0.270199	−	0.157868i
$404$	39.3358	−	68.1317i	1.95703	−	3.38968i
$405$	22.3957	+	12.9302i	1.11285	+	0.642506i
$406$		0			0
$407$	5.47869	+	9.48937i	0.271568	+	0.470370i
$408$	5.76716	+	3.32967i	0.285517	+	0.164843i
$409$	31.8727	+	18.4017i	1.57601	+	0.909907i	0.995409	+	0.0957164i	$0.0305142\pi$
$409$	31.8727	+	18.4017i	1.57601	+	0.909907i	0.580597	+	0.814191i	$0.302819\pi$
$410$	−32.1976	−	18.5893i	−1.59013	−	0.918060i
$411$	2.52310	+	1.45672i	0.124456	+	0.0718545i
$412$	−11.3651	−	19.6850i	−0.559921	−	0.969811i
$413$		0			0
$414$	−12.2224	−	7.05662i	−0.600699	−	0.346814i
$415$	16.2423	−	28.1324i	0.797301	−	1.38097i
$416$	58.7361	+	33.5075i	2.87977	+	1.64284i
$417$	−3.05061	−	5.28382i	−0.149389	−	0.258750i
$418$	−10.3760	+	5.99059i	−0.507507	+	0.293009i
$419$	14.6334	−	25.3457i	0.714887	−	1.23822i	−0.248116	−	0.968730i	$-0.579812\pi$
$419$	14.6334	−	25.3457i	0.714887	−	1.23822i	0.963003	−	0.269490i	$-0.0868552\pi$
$420$		0			0
$421$			7.53862i			0.367410i	0.982981	+	0.183705i	$0.0588091\pi$
$421$			7.53862i			0.367410i	−0.982981	+	0.183705i	$0.941191\pi$
$422$			11.6650i			0.567845i
$423$	14.6616	+	8.46489i	0.712872	+	0.411577i
$424$	72.0533	−	41.6000i	3.49922	−	2.02027i
$425$	−12.0907			−0.586484
$426$	−1.10081	+	1.90666i	−0.0533343	+	0.0923778i
$427$		0			0
$428$	101.506			4.90646
$429$	−0.0119080	−	2.30259i	−0.000574925	−	0.111170i
$430$	−38.2337	−	66.2227i	−1.84379	−	3.19354i
$431$			31.2261i			1.50411i	0.659101	+	0.752055i	$0.270937\pi$
$431$			31.2261i			1.50411i	−0.659101	+	0.752055i	$0.729063\pi$
$432$	13.7849	+	23.8762i	0.663228	+	1.14874i
$433$	−2.94202	−	5.09573i	−0.141384	−	0.244885i	0.786634	−	0.617420i	$-0.211822\pi$
$433$	−2.94202	−	5.09573i	−0.141384	−	0.244885i	−0.928018	+	0.372535i	$0.878489\pi$
$434$		0			0
$435$	2.66882	−	1.54084i	0.127960	−	0.0738777i
$436$		−	22.6702i		−	1.08570i
$437$	−3.76898	+	2.17602i	−0.180295	+	0.104093i
$438$	1.49385	−	2.58742i	0.0713788	−	0.123632i
$439$	4.97821	+	8.62251i	0.237597	+	0.411530i	0.960024	−	0.279917i	$-0.0903069\pi$
$439$	4.97821	+	8.62251i	0.237597	+	0.411530i	−0.722427	+	0.691447i	$0.756974\pi$
$440$	46.5676	+	26.8858i	2.22002	+	1.28173i
$441$		0			0
$442$	−0.108527	−	20.9853i	−0.00516212	−	0.998170i
$443$	17.9406	−	31.0741i	0.852385	−	1.47637i	−0.0266653	−	0.999644i	$-0.508489\pi$
$443$	17.9406	−	31.0741i	0.852385	−	1.47637i	0.879050	−	0.476729i	$-0.158178\pi$
$444$		−	10.8981i		−	0.517202i
$445$	49.2416			2.33427
$446$	63.2404			2.99452
$447$		−	1.39108i		−	0.0657956i
$448$		0			0
$449$	3.46001	−	1.99764i	0.163288	−	0.0942744i	−0.416129	−	0.909306i	$-0.636614\pi$
$449$	3.46001	−	1.99764i	0.163288	−	0.0942744i	0.579417	+	0.815031i	$0.303280\pi$
$450$	−37.8641	−	21.8608i	−1.78493	−	1.03053i
$451$	3.89633	−	6.74864i	0.183471	−	0.317781i
$452$	−14.5937			−0.686432
$453$	−5.66274	+	3.26939i	−0.266059	+	0.153609i
$454$	−72.2371			−3.39026
$455$		0			0
$456$	7.42580			0.347745
$457$	−35.6995	+	20.6111i	−1.66995	+	0.964147i	−0.702291	+	0.711890i	$0.747840\pi$
$457$	−35.6995	+	20.6111i	−1.66995	+	0.964147i	−0.967660	+	0.252257i	$0.918827\pi$
$458$	8.12770			0.379783
$459$	2.19006	−	3.79329i	0.102223	−	0.177056i
$460$	27.1443	+	15.6717i	1.26561	+	0.730699i
$461$	−21.4139	+	12.3633i	−0.997343	+	0.575816i	−0.907461	−	0.420136i	$-0.861982\pi$
$461$	−21.4139	+	12.3633i	−0.997343	+	0.575816i	−0.0898818	+	0.995952i	$0.528649\pi$
$462$		0			0
$463$			24.4057i			1.13423i	0.823639	+	0.567115i	$0.191940\pi$
$463$			24.4057i			1.13423i	−0.823639	+	0.567115i	$0.808060\pi$
$464$	−37.0536			−1.72017
$465$	−1.96389			−0.0910733
$466$			31.6674i			1.46696i
$467$	2.22430	−	3.85260i	0.102928	−	0.178277i	−0.809962	−	0.586483i	$-0.800512\pi$
$467$	2.22430	−	3.85260i	0.102928	−	0.178277i	0.912890	+	0.408206i	$0.133845\pi$
$468$	27.3111	−	47.8744i	1.26246	−	2.21299i
$469$		0			0
$470$	−44.8318	−	25.8837i	−2.06794	−	1.19392i
$471$	−2.00193	−	3.46744i	−0.0922441	−	0.159771i
$472$	48.0637	−	83.2487i	2.21231	−	3.83183i
$473$	13.8803	−	8.01382i	0.638219	−	0.368476i
$474$			0.749922i			0.0344450i
$475$	−11.6760	+	6.74113i	−0.535730	+	0.309304i
$476$		0			0
$477$	−13.4025	−	23.2139i	−0.613660	−	1.06289i
$478$	−1.93004	−	3.34293i	−0.0882780	−	0.152902i
$479$		−	31.6766i		−	1.44734i	−0.690145	−	0.723671i	$-0.742453\pi$
$479$		−	31.6766i		−	1.44734i	0.690145	−	0.723671i	$-0.257547\pi$
$480$	−10.5697	−	18.3073i	−0.482440	−	0.835610i
$481$	−18.4785	+	10.7964i	−0.842546	+	0.492271i
$482$	−7.24372			−0.329942
$483$		0			0
$484$	20.1469	−	34.8954i	0.915767	−	1.58616i
$485$	−30.0780			−1.36577
$486$	20.7152	−	11.9599i	0.939662	−	0.542514i
$487$	−23.3096	−	13.4578i	−1.05626	−	0.609832i	−0.131864	−	0.991268i	$-0.542096\pi$
$487$	−23.3096	−	13.4578i	−1.05626	−	0.609832i	−0.924395	+	0.381436i	$0.875430\pi$
$488$			90.3860i			4.09158i
$489$		−	1.52405i		−	0.0689200i
$490$		0			0
$491$	4.86358	−	8.42396i	0.219490	−	0.380168i	−0.735162	−	0.677891i	$-0.762894\pi$
$491$	4.86358	−	8.42396i	0.219490	−	0.380168i	0.954652	+	0.297723i	$0.0962273\pi$
$492$	−6.71215	+	3.87526i	−0.302607	+	0.174710i
$493$	2.94341	+	5.09813i	0.132564	+	0.229608i
$494$	−11.8051	−	20.2050i	−0.531137	−	0.909067i
$495$	8.66196	−	15.0030i	0.389326	−	0.674333i
$496$	20.4498	+	11.8067i	0.918225	+	0.530137i
$497$		0			0
$498$	−4.66196	−	8.07475i	−0.208907	−	0.361838i
$499$	6.82017	+	3.93763i	0.305313	+	0.176272i	0.644827	−	0.764329i	$-0.276929\pi$
$499$	6.82017	+	3.93763i	0.305313	+	0.176272i	−0.339514	+	0.940601i	$0.610263\pi$
$500$	9.21523	+	5.32042i	0.412118	+	0.237936i
$501$	2.70213	+	1.56007i	0.120722	+	0.0696989i
$502$	−25.5967	−	14.7783i	−1.14244	−	0.659586i
$503$	−4.87603	−	8.44553i	−0.217411	−	0.376568i	0.736604	−	0.676324i	$-0.236428\pi$
$503$	−4.87603	−	8.44553i	−0.217411	−	0.376568i	−0.954016	+	0.299756i	$0.903095\pi$
$504$		0			0
$505$	41.8259	+	24.1482i	1.86123	+	1.07458i
$506$	−4.52266	+	7.83348i	−0.201057	+	0.348241i
$507$	4.49710	−	0.0465154i	0.199723	−	0.00206582i
$508$	25.8315	+	44.7414i	1.14609	+	1.98508i
$509$	−19.9407	+	11.5128i	−0.883857	+	0.510295i	−0.871928	−	0.489634i	$-0.837130\pi$
$509$	−19.9407	+	11.5128i	−0.883857	+	0.510295i	−0.0119288	+	0.999929i	$0.503797\pi$
$510$	−3.28019	+	5.68146i	−0.145249	+	0.251579i
$511$		0			0
$512$			11.8512i			0.523752i
$513$		−	4.88424i		−	0.215645i
$514$	−9.71853	−	5.61100i	−0.428666	−	0.247490i
$515$	12.0846	−	6.97705i	0.532511	−	0.307445i
$516$	−15.9410			−0.701762
$517$	5.42524	−	9.39679i	0.238602	−	0.413270i
$518$		0			0
$519$	2.10752			0.0925100
$520$	−52.0407	+	91.2233i	−2.28213	+	4.00041i
$521$	0.243241	+	0.421305i	0.0106566	+	0.0184577i	0.871305	−	0.490743i	$-0.163275\pi$
$521$	0.243241	+	0.421305i	0.0106566	+	0.0184577i	−0.860648	+	0.509200i	$0.829941\pi$
$522$			21.2876i			0.931733i
$523$	−17.3135	−	29.9878i	−0.757065	−	1.31128i	−0.944341	−	0.328968i	$-0.893299\pi$
$523$	−17.3135	−	29.9878i	−0.757065	−	1.31128i	0.187275	−	0.982307i	$-0.440034\pi$
$524$	49.5207	+	85.7724i	2.16332	+	3.74698i
$525$		0			0
$526$	9.48962	−	5.47883i	0.413767	−	0.238888i
$527$		−	3.75154i		−	0.163420i
$528$	7.49554	−	4.32755i	0.326201	−	0.188332i
$529$	9.85719	−	17.0732i	0.428574	−	0.742311i
$530$	40.9818	+	70.9826i	1.78014	+	3.08329i
$531$	−26.8208	−	15.4850i	−1.16392	−	0.671990i
$532$		0			0
$533$	13.2202	+	7.54182i	0.572632	+	0.326672i
$534$	7.06682	−	12.2401i	0.305811	−	0.529681i
$535$			62.3141i			2.69408i
$536$	−7.39279			−0.319320
$537$	−1.34216			−0.0579185
$538$		−	10.8134i		−	0.466198i
$539$		0			0
$540$	−30.4637	+	17.5882i	−1.31095	+	0.756876i
$541$	19.5188	+	11.2692i	0.839181	+	0.484501i	0.856986	−	0.515340i	$-0.172334\pi$
$541$	19.5188	+	11.2692i	0.839181	+	0.484501i	−0.0178050	+	0.999841i	$0.505668\pi$
$542$	−3.76422	+	6.51982i	−0.161687	+	0.280050i
$543$	2.27770			0.0977456
$544$	34.9717	−	20.1909i	1.49940	−	0.865678i
$545$	13.9172			0.596146
$546$		0			0
$547$	39.3716			1.68341			0.841704	−	0.539940i	$-0.181553\pi$
$547$	39.3716			1.68341			0.841704	+	0.539940i	$0.181553\pi$
$548$	38.7074	−	22.3477i	1.65350	−	0.954648i
$549$	29.1202			1.24282
$550$	−14.0108	+	24.2675i	−0.597424	+	1.03477i
$551$	5.68490	+	3.28218i	0.242185	+	0.139826i
$552$	4.85510	−	2.80310i	0.206647	−	0.119308i
$553$		0			0
$554$		−	45.1227i		−	1.91708i
$555$	6.69034			0.283989
$556$	−93.6000			−3.96952
$557$		−	0.726975i		−	0.0308029i	−0.999881	−	0.0154015i	$-0.995097\pi$
$557$		−	0.726975i		−	0.0308029i	0.999881	−	0.0154015i	$-0.00490263\pi$
$558$	6.78306	−	11.7486i	0.287150	−	0.497358i
$559$	15.7921	+	27.0289i	0.667935	+	1.14320i
$560$		0			0
$561$	−1.19084	−	0.687532i	−0.0502773	−	0.0290276i
$562$	−18.0751	−	31.3070i	−0.762452	−	1.32061i
$563$	−20.8038	+	36.0333i	−0.876777	+	1.51862i	−0.0219200	+	0.999760i	$0.506978\pi$
$563$	−20.8038	+	36.0333i	−0.876777	+	1.51862i	−0.854857	+	0.518863i	$0.826355\pi$
$564$	−9.34597	+	5.39590i	−0.393537	+	0.227208i
$565$		−	8.95907i		−	0.376911i
$566$	−44.2134	+	25.5266i	−1.85843	+	1.07296i
$567$		0			0
$568$	10.5237	+	18.2276i	0.441565	+	0.764813i
$569$	−12.6944	−	21.9873i	−0.532177	−	0.921757i	−0.999294	−	0.0375618i	$-0.988041\pi$
$569$	−12.6944	−	21.9873i	−0.532177	−	0.921757i	0.467118	−	0.884195i	$-0.345292\pi$
$570$			7.31546i			0.306411i
$571$	8.49958	+	14.7217i	0.355697	+	0.616084i	0.987237	−	0.159259i	$-0.0509103\pi$
$571$	8.49958	+	14.7217i	0.355697	+	0.616084i	−0.631540	+	0.775343i	$0.717577\pi$
$572$	−30.6832	−	17.5040i	−1.28293	−	0.731879i
$573$	−4.75451			−0.198622
$574$		0			0
$575$	−5.08929	+	8.81490i	−0.212238	+	0.367607i
$576$	67.9551			2.83146
$577$	−13.8355	+	7.98794i	−0.575980	+	0.332542i	−0.759534	−	0.650467i	$-0.774573\pi$
$577$	−13.8355	+	7.98794i	−0.575980	+	0.332542i	0.183554	+	0.983010i	$0.441240\pi$
$578$	28.9445	+	16.7111i	1.20393	+	0.695092i
$579$		−	7.87139i		−	0.327124i
$580$		−	47.2767i		−	1.96306i
$581$		0			0
$582$	−4.31660	+	7.47657i	−0.178929	+	0.309914i
$583$	−14.8780	+	8.58982i	−0.616184	+	0.355754i
$584$	−14.2812	−	24.7357i	−0.590959	−	1.02357i
$585$	29.3900	+	16.7663i	1.21513	+	0.693200i
$586$	4.61963	−	8.00144i	0.190835	−	0.330536i
$587$	13.8404	+	7.99075i	0.571254	+	0.329814i	0.757650	−	0.652661i	$-0.226347\pi$
$587$	13.8404	+	7.99075i	0.571254	+	0.329814i	−0.186396	+	0.982475i	$0.559681\pi$
$588$		0			0
$589$	−2.09166	−	3.62287i	−0.0861855	−	0.149278i
$590$	82.0116	+	47.3494i	3.37637	+	1.94935i
$591$	−4.35235	−	2.51283i	−0.179032	−	0.103364i
$592$	−69.6660	−	40.2217i	−2.86325	−	1.65310i
$593$	25.1608	+	14.5266i	1.03323	+	0.596536i	0.917908	−	0.396792i	$-0.129877\pi$
$593$	25.1608	+	14.5266i	1.03323	+	0.596536i	0.115322	+	0.993328i	$0.463210\pi$
$594$	−5.07574	−	8.79143i	−0.208260	−	0.360717i
$595$		0			0
$596$	−18.4816	−	10.6704i	−0.757037	−	0.437075i
$597$	−4.12379	+	7.14261i	−0.168775	+	0.292327i
$598$	−15.3454	−	8.75416i	−0.627519	−	0.357984i
$599$	−1.72777	−	2.99259i	−0.0705948	−	0.122274i	0.828567	−	0.559889i	$-0.189156\pi$
$599$	−1.72777	−	2.99259i	−0.0705948	−	0.122274i	−0.899162	+	0.437616i	$0.855823\pi$
$600$	15.0407	−	8.68376i	0.614035	−	0.354513i
$601$	7.76518	−	13.4497i	0.316748	−	0.548624i	−0.663059	−	0.748567i	$-0.730742\pi$
$601$	7.76518	−	13.4497i	0.316748	−	0.548624i	0.979808	+	0.199943i	$0.0640756\pi$
$602$		0			0
$603$			2.38178i			0.0969936i
$604$			100.313i			4.08166i
$605$	21.4222	+	12.3681i	0.870938	+	0.502836i
$606$	12.0052	−	6.93118i	0.487676	−	0.281560i
$607$	−15.4784			−0.628250			−0.314125	−	0.949382i	$-0.601711\pi$
$607$	−15.4784			−0.628250			−0.314125	+	0.949382i	$0.601711\pi$
$608$	22.5148	−	38.9967i	0.913095	−	1.58153i
$609$		0			0
$610$	−89.0429			−3.60524
$611$	18.4078	+	10.5012i	0.744700	+	0.424833i
$612$	−16.4571	−	28.5046i	−0.665240	−	1.15223i
$613$			7.13223i			0.288068i	0.989573	+	0.144034i	$0.0460075\pi$
$613$			7.13223i			0.288068i	−0.989573	+	0.144034i	$0.953993\pi$
$614$	−22.1228	−	38.3178i	−0.892804	−	1.54638i
$615$	−2.37902	−	4.12058i	−0.0959312	−	0.166158i
$616$		0			0
$617$	−4.30142	+	2.48342i	−0.173168	+	0.0999789i	−0.584079	−	0.811697i	$-0.698544\pi$
$617$	−4.30142	+	2.48342i	−0.173168	+	0.0999789i	0.410911	+	0.911676i	$0.365211\pi$
$618$		−	4.00520i		−	0.161113i
$619$	−36.6822	+	21.1785i	−1.47438	+	0.851235i	−0.999583	−	0.0288589i	$-0.990813\pi$
$619$	−36.6822	+	21.1785i	−1.47438	+	0.851235i	−0.474799	+	0.880094i	$0.657479\pi$
$620$	−15.0642	+	26.0920i	−0.604993	+	1.04788i
$621$	−1.84371	−	3.19339i	−0.0739854	−	0.128146i
$622$	−55.4776	−	32.0300i	−2.22445	−	1.28429i
$623$		0			0
$624$	8.52791	+	14.5959i	0.341390	+	0.584305i
$625$	10.7722	−	18.6581i	0.430889	−	0.746322i
$626$			14.0032i			0.559682i
$627$	−1.53333			−0.0612352
$628$	−61.4239			−2.45108
$629$			12.7803i			0.509583i
$630$		0			0
$631$	−5.42803	+	3.13387i	−0.216086	+	0.124758i	−0.604137	−	0.796881i	$-0.706482\pi$
$631$	−5.42803	+	3.13387i	−0.216086	+	0.124758i	0.388050	+	0.921638i	$0.373149\pi$
$632$	6.20874	+	3.58462i	0.246971	+	0.142589i
$633$	−0.746432	+	1.29286i	−0.0296680	+	0.0513865i
$634$	−16.3959			−0.651163
$635$	−27.4667	+	15.8579i	−1.08998	+	0.629302i
$636$	17.0868			0.677534
$637$		0			0
$638$	13.6434			0.540149
$639$	5.87250	−	3.39049i	0.232313	−	0.134126i
$640$	−85.5797			−3.38283
$641$	−15.7818	+	27.3350i	−0.623345	+	1.07967i	0.365513	+	0.930806i	$0.380894\pi$
$641$	−15.7818	+	27.3350i	−0.623345	+	1.07967i	−0.988858	+	0.148860i	$0.952440\pi$
$642$	15.4896	+	8.94291i	0.611325	+	0.352949i
$643$	−15.8053	+	9.12520i	−0.623300	+	0.359863i	−0.778153	−	0.628075i	$-0.783843\pi$
$643$	−15.8053	+	9.12520i	−0.623300	+	0.359863i	0.154852	+	0.987938i	$0.450510\pi$
$644$		0			0
$645$		−	9.78613i		−	0.385329i
$646$	−13.9744			−0.549816
$647$	23.0273			0.905298			0.452649	−	0.891689i	$-0.350479\pi$
$647$	23.0273			0.905298			0.452649	+	0.891689i	$0.350479\pi$
$648$		−	70.9601i		−	2.78758i
$649$	−9.92448	+	17.1897i	−0.389570	+	0.674755i
$650$	−47.5387	−	27.1197i	−1.86462	−	1.06372i
$651$		0			0
$652$	−20.2483	−	11.6904i	−0.792985	−	0.457830i
$653$	−14.4062	−	24.9523i	−0.563759	−	0.976459i	−0.997164	−	0.0752597i	$-0.976021\pi$
$653$	−14.4062	−	24.9523i	−0.563759	−	0.976459i	0.433405	−	0.901199i	$-0.357312\pi$
$654$	1.99730	−	3.45943i	0.0781006	−	0.135274i
$655$	−52.6555	+	30.4007i	−2.05742	+	1.18785i
$656$			57.2096i			2.23366i
$657$	−7.96926	+	4.60105i	−0.310910	+	0.179504i
$658$		0			0
$659$	15.6114	+	27.0397i	0.608134	+	1.05332i	0.991548	+	0.129742i	$0.0414149\pi$
$659$	15.6114	+	27.0397i	0.608134	+	1.05332i	−0.383414	+	0.923577i	$0.625252\pi$
$660$	5.52153	+	9.56356i	0.214925	+	0.372261i
$661$		−	26.5582i		−	1.03299i	−0.856289	−	0.516496i	$-0.827236\pi$
$661$		−	26.5582i		−	1.03299i	0.856289	−	0.516496i	$-0.172764\pi$
$662$	23.3487	+	40.4411i	0.907471	+	1.57179i
$663$	1.33080	−	2.33279i	0.0516840	−	0.0905981i
$664$	−89.1366			−3.45917
$665$		0			0
$666$	−23.1077	+	40.0237i	−0.895405	+	1.55089i
$667$	4.95584			0.191891
$668$	41.4538	−	23.9334i	1.60390	−	0.926010i
$669$	7.00906	+	4.04668i	0.270986	+	0.156454i
$670$		−	7.28293i		−	0.281364i
$671$		−	18.6635i		−	0.720495i
$672$		0			0
$673$	−9.86930	+	17.0941i	−0.380434	+	0.658930i	−0.991124	−	0.132939i	$-0.957559\pi$
$673$	−9.86930	+	17.0941i	−0.380434	+	0.658930i	0.610691	+	0.791869i	$0.290892\pi$
$674$	−19.5585	+	11.2921i	−0.753366	+	0.434956i
$675$	−5.71165	−	9.89287i	−0.219842	−	0.380777i
$676$	33.8774	−	60.1046i	1.30298	−	2.31172i
$677$	−6.57198	+	11.3830i	−0.252582	+	0.437484i	−0.964236	−	0.265046i	$-0.914613\pi$
$677$	−6.57198	+	11.3830i	−0.252582	+	0.437484i	0.711654	+	0.702530i	$0.247946\pi$
$678$	−2.22698	−	1.28575i	−0.0855266	−	0.0493788i
$679$		0			0
$680$	31.3586	+	54.3147i	1.20255	+	2.08287i
$681$	−8.00619	−	4.62238i	−0.306798	−	0.177130i
$682$	−7.52981	−	4.34734i	−0.288331	−	0.166468i
$683$	5.85654	+	3.38128i	0.224094	+	0.129381i	0.607845	−	0.794056i	$-0.292034\pi$
$683$	5.85654	+	3.38128i	0.224094	+	0.129381i	−0.383750	+	0.923437i	$0.625368\pi$
$684$	−31.7853	−	18.3513i	−1.21534	−	0.701678i
$685$	13.7192	+	23.7624i	0.524185	+	0.907915i
$686$		0			0
$687$	0.900810	+	0.520083i	0.0343681	+	0.0198424i
$688$	−58.8332	+	101.902i	−2.24300	+	3.88498i
$689$	−16.9272	−	28.9717i	−0.644874	−	1.10373i
$690$	2.76144	+	4.78296i	0.105126	+	0.182084i
$691$	7.94223	−	4.58545i	0.302137	−	0.174439i	−0.341266	−	0.939967i	$-0.610856\pi$
$691$	7.94223	−	4.58545i	0.302137	−	0.174439i	0.643402	+	0.765528i	$0.277522\pi$
$692$	16.1659	−	28.0002i	0.614537	−	1.06441i
$693$		0			0
$694$			77.9115i			2.95748i
$695$		−	57.4609i		−	2.17962i
$696$	−7.32316	−	4.22803i	−0.277584	−	0.160263i
$697$	7.87137	−	4.54454i	0.298150	−	0.172137i
$698$	31.6870			1.19937
$699$	−2.02636	+	3.50976i	−0.0766440	+	0.132751i
$700$		0			0
$701$	47.4700			1.79292			0.896459	−	0.443127i	$-0.146131\pi$
$701$	47.4700			1.79292			0.896459	+	0.443127i	$0.146131\pi$
$702$	17.1194	−	10.0023i	0.646130	−	0.377512i
$703$	7.12562	+	12.3419i	0.268748	+	0.465485i
$704$		−	43.5532i		−	1.64147i
$705$	−3.31253	−	5.73748i	−0.124757	−	0.216086i
$706$	24.1074	+	41.7552i	0.907294	+	1.57148i
$707$		0			0
$708$	17.0968	−	9.87082i	0.642535	−	0.370968i
$709$			34.9719i			1.31340i	0.754153	+	0.656699i	$0.228048\pi$
$709$			34.9719i			1.31340i	−0.754153	+	0.656699i	$0.771952\pi$
$710$	−17.9567	+	10.3673i	−0.673905	+	0.389079i
$711$	1.15488	−	2.00031i	0.0433114	−	0.0750175i
$712$	−67.5587	−	117.015i	−2.53187	−	4.38533i
$713$	−2.73512	−	1.57912i	−0.102431	−	0.0591387i
$714$		0			0
$715$	10.7457	−	18.8364i	0.401866	−	0.704440i
$716$	−10.2952	+	17.8317i	−0.384748	+	0.666403i
$717$		−	0.494005i		−	0.0184490i
$718$	−15.3585			−0.573175
$719$	−8.36101			−0.311813			−0.155907	−	0.987772i	$-0.549830\pi$
$719$	−8.36101			−0.311813			−0.155907	+	0.987772i	$0.549830\pi$
$720$			127.183i			4.73984i
$721$		0			0
$722$	30.9846	−	17.8890i	1.15313	−	0.665758i
$723$	−0.802836	−	0.463517i	−0.0298578	−	0.0172384i
$724$	17.4713	−	30.2612i	0.649317	−	1.12465i
$725$	15.3528			0.570188
$726$	6.14875	−	3.54998i	0.228202	−	0.131752i
$727$	27.4014			1.01626			0.508131	−	0.861280i	$-0.330337\pi$
$727$	27.4014			1.01626			0.508131	+	0.861280i	$0.330337\pi$
$728$		0			0
$729$	−20.7504			−0.768532
$730$	24.3681	−	14.0689i	0.901905	−	0.520715i
$731$	18.6941			0.691425
$732$	−9.28127	+	16.0756i	−0.343046	+	0.594173i
$733$	10.5282	+	6.07846i	0.388868	+	0.224513i	0.681670	−	0.731660i	$-0.261254\pi$
$733$	10.5282	+	6.07846i	0.388868	+	0.224513i	−0.292802	+	0.956173i	$0.594588\pi$
$734$	45.9583	−	26.5340i	1.69635	−	0.979389i
$735$		0			0
$736$		−	33.9956i		−	1.25309i
$737$	1.52651			0.0562297
$738$	32.8674			1.20987
$739$			48.4439i			1.78204i	0.453966	+	0.891019i	$0.350009\pi$
$739$			48.4439i			1.78204i	−0.453966	+	0.891019i	$0.649991\pi$
$740$	51.3189	−	88.8869i	1.88652	−	3.26755i
$741$	−0.0154876	−	2.99476i	−0.000568953	−	0.110015i
$742$		0			0
$743$	−14.7143	−	8.49532i	−0.539816	−	0.311663i	0.205188	−	0.978722i	$-0.434219\pi$
$743$	−14.7143	−	8.49532i	−0.539816	−	0.311663i	−0.745004	+	0.667060i	$0.767553\pi$
$744$	2.69443	+	4.66689i	0.0987826	+	0.171097i
$745$	6.55052	−	11.3458i	0.239993	−	0.415679i
$746$	75.0642	−	43.3384i	2.74830	−	1.58673i
$747$			28.7177i			1.05073i
$748$	−18.2689	+	10.5475i	−0.667977	+	0.385657i
$749$		0			0
$750$	0.937485	+	1.62377i	0.0342321	+	0.0592917i
$751$	21.5162	+	37.2671i	0.785136	+	1.35990i	0.928918	+	0.370287i	$0.120741\pi$
$751$	21.5162	+	37.2671i	0.785136	+	1.35990i	−0.143781	+	0.989610i	$0.545926\pi$
$752$			79.6585i			2.90485i
$753$	−1.89129	−	3.27581i	−0.0689225	−	0.119377i
$754$	0.137808	+	26.6472i	0.00501868	+	0.970434i
$755$	−61.5817			−2.24119
$756$		0			0
$757$	−14.5892	+	25.2693i	−0.530255	+	0.918428i	0.469122	+	0.883133i	$0.344570\pi$
$757$	−14.5892	+	25.2693i	−0.530255	+	0.918428i	−0.999377	+	0.0352949i	$0.988763\pi$
$758$	−51.4231			−1.86777
$759$	−1.00251	+	0.578801i	−0.0363889	+	0.0210091i
$760$	60.5661	+	34.9678i	2.19696	+	1.26842i
$761$			29.4251i			1.06666i	0.845907	+	0.533330i	$0.179059\pi$
$761$			29.4251i			1.06666i	−0.845907	+	0.533330i	$0.820941\pi$
$762$			9.10328i			0.329777i
$763$		0			0
$764$	−36.4699	+	63.1677i	−1.31943	+	2.28533i
$765$	17.4989	−	10.1030i	0.632675	−	0.365275i
$766$	−0.945888	−	1.63833i	−0.0341763	−	0.0591951i
$767$	−33.6737	−	19.2100i	−1.21589	−	0.693634i
$768$	−4.11988	+	7.13584i	−0.148663	+	0.257492i
$769$	−14.8839	−	8.59322i	−0.536727	−	0.309879i	0.207024	−	0.978336i	$-0.433622\pi$
$769$	−14.8839	−	8.59322i	−0.536727	−	0.309879i	−0.743751	+	0.668456i	$0.766955\pi$
$770$		0			0
$771$	−0.718083	−	1.24376i	−0.0258611	−	0.0447928i
$772$	−104.578	−	60.3782i	−3.76385	−	2.17306i
$773$	19.0180	+	10.9801i	0.684031	+	0.394926i	0.801372	−	0.598166i	$-0.204104\pi$
$773$	19.0180	+	10.9801i	0.684031	+	0.394926i	−0.117341	+	0.993092i	$0.537437\pi$
$774$	58.5437	+	33.8002i	2.10431	+	1.21492i
$775$	−8.47319	−	4.89200i	−0.304366	−	0.175726i
$776$	41.2666	+	71.4759i	1.48139	+	2.56584i
$777$		0			0
$778$	−46.9488	−	27.1059i	−1.68320	−	0.971794i
$779$	5.06759	−	8.77733i	0.181565	−	0.314480i
$780$	−18.6230	+	10.8808i	−0.666809	+	0.389594i
$781$	−2.17300	−	3.76375i	−0.0777561	−	0.134678i
$782$	−9.13669	+	5.27507i	−0.326727	+	0.188636i
$783$	−2.78094	+	4.81673i	−0.0993827	+	0.172136i
$784$		0			0
$785$		−	37.7081i		−	1.34586i
$786$			17.4516i			0.622478i
$787$	−2.02275	−	1.16784i	−0.0721033	−	0.0416289i	0.463515	−	0.886089i	$-0.346588\pi$
$787$	−2.02275	−	1.16784i	−0.0721033	−	0.0416289i	−0.535618	+	0.844460i	$0.679921\pi$
$788$	−66.7702	+	38.5498i	−2.37859	+	1.37328i
$789$	1.40234			0.0499246
$790$	−3.53135	+	6.11648i	−0.125640	+	0.217615i
$791$		0			0
$792$	−47.5364			−1.68913
$793$	36.4519	−	0.188514i	1.29444	−	0.00669432i
$794$	30.1140	+	52.1590i	1.06871	+	1.85105i
$795$			10.4895i			0.372025i
$796$	63.2637	+	109.576i	2.24232	+	3.88382i
$797$	−13.9020	−	24.0790i	−0.492434	−	0.852921i	0.507528	−	0.861635i	$-0.330560\pi$
$797$	−13.9020	−	24.0790i	−0.492434	−	0.852921i	−0.999962	+	0.00871411i	$0.997226\pi$
$798$		0			0
$799$	10.9601	−	6.32780i	0.387739	−	0.223861i
$800$		−	105.315i		−	3.72346i
$801$	−37.6995	+	21.7658i	−1.33205	+	0.769057i
$802$	6.49779	−	11.2545i	0.229445	−	0.397410i
$803$	2.94886	+	5.10758i	0.104063	+	0.180243i
$804$	−1.31485	−	0.759127i	−0.0463711	−	0.0267724i
$805$		0			0
$806$	8.41479	−	14.7505i	0.296398	−	0.519564i
$807$	0.691937	−	1.19847i	0.0243573	−	0.0421882i
$808$		−	132.524i		−	4.66218i
$809$	15.0203			0.528087			0.264043	−	0.964511i	$-0.414944\pi$
$809$	15.0203			0.528087			0.264043	+	0.964511i	$0.414944\pi$
$810$	69.9056			2.45623
$811$			43.6933i			1.53428i	0.641481	+	0.767139i	$0.278320\pi$
$811$			43.6933i			1.53428i	−0.641481	+	0.767139i	$0.721680\pi$
$812$		0			0
$813$	−0.834393	+	0.481737i	−0.0292634	+	0.0168953i
$814$	25.6516	+	14.8100i	0.899089	+	0.519089i
$815$	7.17670	−	12.4304i	0.251389	−	0.435418i
$816$	10.0950			0.353395
$817$	18.0529	−	10.4228i	0.631590	−	0.364648i
$818$	99.4870			3.47848
$819$		0			0
$820$	−72.9939			−2.54906
$821$	−15.6492	+	9.03506i	−0.546160	+	0.315326i	−0.747572	−	0.664181i	$-0.768780\pi$
$821$	−15.6492	+	9.03506i	−0.546160	+	0.315326i	0.201412	+	0.979507i	$0.435447\pi$
$822$	7.87557			0.274692
$823$	2.22775	−	3.85857i	0.0776544	−	0.134501i	−0.824583	−	0.565741i	$-0.808590\pi$
$823$	2.22775	−	3.85857i	0.0776544	−	0.134501i	0.902238	+	0.431239i	$0.141924\pi$
$824$	−33.1598	−	19.1448i	−1.15518	−	0.666941i
$825$	−3.10570	+	1.79308i	−0.108127	+	0.0624269i
$826$		0			0
$827$		−	11.8352i		−	0.411549i	−0.978599	−	0.205774i	$-0.934029\pi$
$827$		−	11.8352i		−	0.411549i	0.978599	−	0.205774i	$-0.0659713\pi$
$828$	−27.7090			−0.962953
$829$	−3.53894			−0.122913			−0.0614563	−	0.998110i	$-0.519574\pi$
$829$	−3.53894			−0.122913			−0.0614563	+	0.998110i	$0.519574\pi$
$830$		−	87.8120i		−	3.04800i
$831$	2.88736	−	5.00105i	0.100161	−	0.173484i
$832$	85.0643	−	0.439917i	2.94907	−	0.0152514i
$833$		0			0
$834$	−14.2832	−	8.24640i	−0.494586	−	0.285550i
$835$	14.6927	+	25.4484i	0.508460	+	0.880679i
$836$	−11.7615	+	20.3715i	−0.406781	+	0.704565i
$837$	3.06960	−	1.77223i	0.106101	−	0.0612573i
$838$		−	79.1137i		−	2.73294i
$839$	28.9991	−	16.7426i	1.00116	−	0.578020i	0.0925687	−	0.995706i	$-0.470492\pi$
$839$	28.9991	−	16.7426i	1.00116	−	0.578020i	0.908591	+	0.417686i	$0.137159\pi$
$840$		0			0
$841$	10.7625	+	18.6411i	0.371119	+	0.642797i
$842$	10.1892	+	17.6482i	0.351143	+	0.608197i
$843$		−	4.62642i		−	0.159343i
$844$	11.4512	+	19.8340i	0.394165	+	0.682714i
$845$	36.8981	+	20.7973i	1.26933	+	0.715448i
$846$	45.7645			1.57342
$847$		0			0
$848$	63.0620	−	109.227i	2.16556	−	3.75086i
$849$	−6.53368			−0.224235
$850$	−28.3047	+	16.3417i	−0.970844	+	0.560517i
$851$	9.31768	+	5.37956i	0.319406	+	0.184409i
$852$			4.32250i			0.148087i
$853$			22.0871i			0.756248i	0.925755	+	0.378124i	$0.123431\pi$
$853$			22.0871i			0.756248i	−0.925755	+	0.378124i	$0.876569\pi$
$854$		0			0
$855$	11.2658	−	19.5129i	0.385282	−	0.667329i
$856$	148.080	−	85.4941i	5.06127	−	2.92213i
$857$	3.44682	+	5.97006i	0.117741	+	0.203933i	0.918872	−	0.394555i	$-0.129101\pi$
$857$	3.44682	+	5.97006i	0.117741	+	0.203933i	−0.801131	+	0.598489i	$0.795768\pi$
$858$	−3.14005	−	5.37435i	−0.107200	−	0.183477i
$859$	−18.7417	+	32.4616i	−0.639459	+	1.10758i	0.346093	+	0.938200i	$0.387508\pi$
$859$	−18.7417	+	32.4616i	−0.639459	+	1.10758i	−0.985552	+	0.169375i	$0.945825\pi$
$860$	−130.017	−	75.0654i	−4.43355	−	2.55971i
$861$		0			0
$862$	42.2052	+	73.1015i	1.43751	+	2.48985i
$863$	−15.1769	−	8.76241i	−0.516629	−	0.298276i	0.218925	−	0.975742i	$-0.429745\pi$
$863$	−15.1769	−	8.76241i	−0.516629	−	0.298276i	−0.735554	+	0.677466i	$0.763078\pi$
$864$	33.0413	+	19.0764i	1.12409	+	0.648993i
$865$	17.1893	+	9.92425i	0.584454	+	0.337435i
$866$	−13.7747	−	7.95285i	−0.468085	−	0.270249i
$867$	2.13866	+	3.70426i	0.0726326	+	0.125803i
$868$		0			0
$869$	−1.28202	−	0.740175i	−0.0434896	−	0.0251087i
$870$	4.16520	−	7.21434i	0.141213	−	0.244589i
$871$	0.0154188	+	2.98145i	0.000522446	+	0.101022i
$872$	−19.0942	−	33.0721i	−0.646610	−	1.11996i
$873$	23.0278	−	13.2951i	0.779374	−	0.449972i
$874$	−5.88221	+	10.1883i	−0.198969	+	0.344624i
$875$		0			0
$876$		−	5.86584i		−	0.198188i
$877$		−	46.7491i		−	1.57860i	−0.614005	−	0.789302i	$-0.710443\pi$
$877$		−	46.7491i		−	1.57860i	0.614005	−	0.789302i	$-0.289557\pi$
$878$	23.3083	+	13.4571i	0.786618	+	0.454154i
$879$	1.02401	−	0.591210i	0.0345389	−	0.0199410i
$880$	81.5131			2.74781
$881$	1.45937	−	2.52771i	0.0491675	−	0.0851606i	−0.840394	−	0.541976i	$-0.817677\pi$
$881$	1.45937	−	2.52771i	0.0491675	−	0.0851606i	0.889562	+	0.456815i	$0.151010\pi$
$882$		0			0
$883$	28.5505			0.960801			0.480400	−	0.877049i	$-0.340491\pi$
$883$	28.5505			0.960801			0.480400	+	0.877049i	$0.340491\pi$
$884$	−20.7851	−	35.5747i	−0.699078	−	1.19651i
$885$	6.05968	+	10.4957i	0.203694	+	0.352808i
$886$		−	96.9941i		−	3.25858i
$887$	0.211457	+	0.366254i	0.00710004	+	0.0122976i	0.869554	−	0.493839i	$-0.164407\pi$
$887$	0.211457	+	0.366254i	0.00710004	+	0.0122976i	−0.862454	+	0.506136i	$0.831073\pi$
$888$	−9.17905	−	15.8986i	−0.308029	−	0.533521i
$889$		0			0
$890$	115.276	−	66.5548i	3.86407	−	2.23092i
$891$			14.6523i			0.490870i
$892$	107.527	−	62.0809i	3.60028	−	2.07862i
$893$	7.05610	−	12.2215i	0.236123	−	0.408978i
$894$	−1.88018	−	3.25656i	−0.0628825	−	0.108916i
$895$	−10.9469	−	6.32018i	−0.365914	−	0.211260i
$896$		0			0
$897$	−1.14059	−	1.95217i	−0.0380832	−	0.0651812i
$898$	5.40001	−	9.35309i	0.180201	−	0.312117i
$899$			4.76372i			0.158879i
$900$	−85.8401			−2.86134
$901$	−20.0377			−0.667553
$902$		−	21.0651i		−	0.701391i
$903$		0			0
$904$	−21.2899	+	12.2917i	−0.708091	+	0.408816i
$905$	18.5773	+	10.7256i	0.617531	+	0.356532i
$906$	−8.83779	+	15.3075i	−0.293616	+	0.508558i
$907$	22.4284			0.744723			0.372361	−	0.928088i	$-0.378548\pi$
$907$	22.4284			0.744723			0.372361	+	0.928088i	$0.378548\pi$
$908$	−122.824	+	70.9127i	−4.07607	+	2.35332i
$909$	−42.6961			−1.41614
$910$		0			0
$911$	−32.5788			−1.07938			−0.539692	−	0.841863i	$-0.681459\pi$
$911$	−32.5788			−1.07938			−0.539692	+	0.841863i	$0.681459\pi$
$912$	9.74874	−	5.62844i	0.322813	−	0.186376i
$913$	18.4055			0.609132
$914$	−55.7159	+	96.5027i	−1.84292	+	3.19203i
$915$	−9.86881	−	5.69776i	−0.326253	−	0.188362i
$916$	13.8195	−	7.97869i	0.456609	−	0.263623i
$917$		0			0
$918$		−	11.8403i		−	0.390788i
$919$	−9.87913			−0.325883			−0.162941	−	0.986636i	$-0.552098\pi$
$919$	−9.87913			−0.325883			−0.162941	+	0.986636i	$0.552098\pi$
$920$	52.7987			1.74072
$921$		−	5.66246i		−	0.186584i
$922$	−33.4204	+	57.8859i	−1.10064	+	1.90637i
$923$	7.32908	−	4.28214i	0.241240	−	0.140948i
$924$		0			0
$925$	28.8654	+	16.6654i	0.949088	+	0.547956i
$926$	32.9867	+	57.1346i	1.08401	+	1.87756i
$927$	−6.16800	+	10.6833i	−0.202584	+	0.350886i
$928$	−44.4071	+	25.6385i	−1.45774	+	0.841624i
$929$		−	29.9136i		−	0.981434i	−0.871319	−	0.490717i	$-0.836735\pi$
$929$		−	29.9136i		−	0.981434i	0.871319	−	0.490717i	$-0.163265\pi$
$930$	−4.59754	+	2.65439i	−0.150759	+	0.0870409i
$931$		0			0
$932$	31.0868	+	53.8439i	1.01828	+	1.76371i
$933$	−4.09913	−	7.09990i	−0.134199	−	0.232440i
$934$		−	12.0255i		−	0.393485i
$935$	−6.47512	−	11.2152i	−0.211759	−	0.366778i
$936$	−0.480150	−	92.8439i	−0.0156942	−	3.03470i
$937$	31.8296			1.03983			0.519914	−	0.854219i	$-0.325964\pi$
$937$	31.8296			1.03983			0.519914	+	0.854219i	$0.325964\pi$
$938$		0			0
$939$	−0.896052	+	1.55201i	−0.0292416	+	0.0506479i
$940$	−101.636			−3.31501
$941$	−36.4497	+	21.0443i	−1.18823	+	0.686023i	−0.957903	−	0.287091i	$-0.907312\pi$
$941$	−36.4497	+	21.0443i	−1.18823	+	0.686023i	−0.230324	+	0.973114i	$0.573979\pi$
$942$	−9.37318	−	5.41161i	−0.305395	−	0.176320i
$943$		−	7.65167i		−	0.249173i
$944$		−	145.721i		−	4.74280i
$945$		0			0
$946$	21.6629	−	37.5213i	0.704322	−	1.21992i
$947$	−52.2540	+	30.1689i	−1.69803	+	0.980357i	−0.750397	+	0.660988i	$0.770138\pi$
$947$	−52.2540	+	30.1689i	−1.69803	+	0.980357i	−0.947630	+	0.319369i	$0.896529\pi$
$948$	0.736172	+	1.27509i	0.0239098	+	0.0414129i
$949$	−9.94591	+	5.81106i	−0.322858	+	0.188635i
$950$	−18.2226	+	31.5624i	−0.591219	+	1.02402i
$951$	−1.81719	−	1.04915i	−0.0589264	−	0.0340212i
$952$		0			0
$953$	−8.68770	−	15.0475i	−0.281422	−	0.487438i	0.690313	−	0.723511i	$-0.257473\pi$
$953$	−8.68770	−	15.0475i	−0.281422	−	0.487438i	−0.971735	+	0.236073i	$0.924139\pi$
$954$	−62.7516	−	36.2297i	−2.03166	−	1.17298i
$955$	−38.7785	−	22.3888i	−1.25484	−	0.724484i
$956$	−6.56328	−	3.78931i	−0.212272	−	0.122555i
$957$	1.51213	+	0.873029i	0.0488803	+	0.0282210i
$958$	−42.8140	−	74.1561i	−1.38326	−	2.39588i
$959$		0			0
$960$	−23.0299	−	13.2963i	−0.743287	−	0.429137i
$961$	−13.9821	+	24.2177i	−0.451035	+	0.781216i
$962$	−28.6665	+	50.2501i	−0.924244	+	1.62013i
$963$	−27.5442	−	47.7079i	−0.887598	−	1.53737i
$964$	−12.3165	+	7.11091i	−0.396686	+	0.229027i
$965$	37.0661	−	64.2003i	1.19320	−	2.06668i
$966$		0			0
$967$		−	18.8630i		−	0.606594i	−0.952896	−	0.303297i	$-0.901913\pi$
$967$		−	18.8630i		−	0.606594i	0.952896	−	0.303297i	$-0.0980874\pi$
$968$		−	67.8756i		−	2.18160i
$969$	−1.54881	−	0.894208i	−0.0497551	−	0.0287261i
$970$	−70.4138	+	40.6534i	−2.26085	+	1.30530i
$971$	1.56446			0.0502060			0.0251030	−	0.999685i	$-0.492009\pi$
$971$	1.56446			0.0502060			0.0251030	+	0.999685i	$0.492009\pi$
$972$	23.4813	−	40.6708i	0.753164	−	1.30452i
$973$		0			0
$974$	−72.7582			−2.33132
$975$	−3.53345	−	6.04768i	−0.113161	−	0.193681i
$976$	68.5087	+	118.661i	2.19291	+	3.79823i
$977$			27.8755i			0.891817i	0.895078	+	0.445909i	$0.147119\pi$
$977$			27.8755i			0.891817i	−0.895078	+	0.445909i	$0.852881\pi$
$978$	−2.05990	−	3.56786i	−0.0658685	−	0.114088i
$979$	13.9499	+	24.1620i	0.445842	+	0.772221i
$980$		0			0
$981$	−10.6550	+	6.15169i	−0.340189	+	0.196408i
$982$		−	26.2944i		−	0.839088i
$983$	28.9460	−	16.7120i	0.923233	−	0.533029i	0.0385681	−	0.999256i	$-0.487720\pi$
$983$	28.9460	−	16.7120i	0.923233	−	0.533029i	0.884665	+	0.466227i	$0.154387\pi$
$984$	−6.52795	+	11.3067i	−0.208104	+	0.360446i
$985$	−23.6657	−	40.9901i	−0.754051	−	1.30605i
$986$	13.7813	+	7.95661i	0.438885	+	0.253390i
$987$		0			0
$988$	−39.9068	−	22.7658i	−1.26960	−	0.724277i
$989$	7.86882	−	13.6292i	0.250214	−	0.433383i
$990$		−	46.8300i		−	1.48835i
$991$	−18.9110			−0.600726			−0.300363	−	0.953825i	$-0.597108\pi$
$991$	−18.9110			−0.600726			−0.300363	+	0.953825i	$0.597108\pi$
$992$	32.6777			1.03752
$993$			5.97622i			0.189650i
$994$		0			0
$995$	−67.2685	+	38.8375i	−2.13256	+	1.23123i
$996$	−15.8534	−	9.15297i	−0.502335	−	0.290023i
$997$	21.7888	−	37.7393i	0.690057	−	1.19521i	−0.281762	−	0.959484i	$-0.590919\pi$
$997$	21.7888	−	37.7393i	0.690057	−	1.19521i	0.971819	−	0.235730i	$-0.0757480\pi$
$998$	21.2884			0.673871
$999$	−10.4571	+	6.03742i	−0.330849	+	0.191016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.i.30.6		12
7.2	even	3		637.2.q.h.589.1		12
7.3	odd	6		637.2.k.h.459.6		12
7.4	even	3		637.2.k.g.459.6		12
7.5	odd	6		91.2.q.a.43.1	yes	12
7.6	odd	2		637.2.u.h.30.6		12
13.10	even	6		637.2.k.g.569.1		12
21.5	even	6		819.2.ct.a.316.6		12
28.19	even	6		1456.2.cc.c.225.4		12
91.10	odd	6		637.2.u.h.361.6		12
91.19	even	12		1183.2.a.p.1.6		6
91.23	even	6		637.2.q.h.491.1		12
91.33	even	12		1183.2.a.m.1.1		6
91.58	odd	12		8281.2.a.ch.1.6		6
91.61	odd	6		1183.2.c.i.337.12		12
91.62	odd	6		637.2.k.h.569.1		12
91.72	odd	12		8281.2.a.by.1.1		6
91.75	odd	6		91.2.q.a.36.1	✓	12
91.82	odd	6		1183.2.c.i.337.1		12
91.88	even	6	inner	637.2.u.i.361.6		12
273.257	even	6		819.2.ct.a.127.6		12
364.75	even	6		1456.2.cc.c.673.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.1	✓	12	91.75	odd	6
91.2.q.a.43.1	yes	12	7.5	odd	6
637.2.k.g.459.6		12	7.4	even	3
637.2.k.g.569.1		12	13.10	even	6
637.2.k.h.459.6		12	7.3	odd	6
637.2.k.h.569.1		12	91.62	odd	6
637.2.q.h.491.1		12	91.23	even	6
637.2.q.h.589.1		12	7.2	even	3
637.2.u.h.30.6		12	7.6	odd	2
637.2.u.h.361.6		12	91.10	odd	6
637.2.u.i.30.6		12	1.1	even	1	trivial
637.2.u.i.361.6		12	91.88	even	6	inner
819.2.ct.a.127.6		12	273.257	even	6
819.2.ct.a.316.6		12	21.5	even	6
1183.2.a.m.1.1		6	91.33	even	12
1183.2.a.p.1.6		6	91.19	even	12
1183.2.c.i.337.1		12	91.82	odd	6
1183.2.c.i.337.12		12	91.61	odd	6
1456.2.cc.c.225.4		12	28.19	even	6
1456.2.cc.c.673.4		12	364.75	even	6
8281.2.a.by.1.1		6	91.72	odd	12
8281.2.a.ch.1.6		6	91.58	odd	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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.34104 - 1.35160i) q^{2} +0.345949 q^{3} +(2.65363 - 4.59623i) q^{4} +(2.82162 + 1.62906i) q^{5} +(0.809880 - 0.467584i) q^{6} -8.94020i q^{8} -2.88032 q^{9} +O(q^{10})\)	\(q+(2.34104 - 1.35160i) q^{2} +0.345949 q^{3} +(2.65363 - 4.59623i) q^{4} +(2.82162 + 1.62906i) q^{5} +(0.809880 - 0.467584i) q^{6} -8.94020i q^{8} -2.88032 q^{9} +8.80735 q^{10} +1.84603i q^{11} +(0.918023 - 1.59006i) q^{12} +(-3.60550 + 0.0186461i) q^{13} +(0.976136 + 0.563573i) q^{15} +(-6.77628 - 11.7369i) q^{16} +(-1.07657 + 1.86467i) q^{17} +(-6.74293 + 3.89303i) q^{18} +2.40096i q^{19} +(14.9751 - 8.64587i) q^{20} +(2.49509 + 4.32162i) q^{22} +(0.906314 + 1.56978i) q^{23} -3.09285i q^{24} +(2.80769 + 4.86305i) q^{25} +(-8.41541 + 4.91684i) q^{26} -2.03429 q^{27} +(1.36703 - 2.36777i) q^{29} +3.04689 q^{30} +(-1.50893 + 0.871180i) q^{31} +(-16.2422 - 9.37743i) q^{32} +0.638632i q^{33} +5.82036i q^{34} +(-7.64331 + 13.2386i) q^{36} +(5.14042 - 2.96783i) q^{37} +(3.24513 + 5.62072i) q^{38} +(-1.24732 + 0.00645062i) q^{39} +(14.5641 - 25.2258i) q^{40} +(-3.65577 - 2.11066i) q^{41} +(-4.34111 - 7.51903i) q^{43} +(8.48477 + 4.89868i) q^{44} +(-8.12716 - 4.69222i) q^{45} +(4.24343 + 2.44994i) q^{46} +(-5.09027 - 2.93887i) q^{47} +(-2.34425 - 4.06036i) q^{48} +(13.1458 + 7.58972i) q^{50} +(-0.372438 + 0.645082i) q^{51} +(-9.48199 + 16.6212i) q^{52} +(4.65314 + 8.05947i) q^{53} +(-4.76235 + 2.74954i) q^{54} +(-3.00729 + 5.20878i) q^{55} +0.830609i q^{57} -7.39071i q^{58} +(9.31173 + 5.37613i) q^{59} +(5.18062 - 2.99103i) q^{60} -10.1101 q^{61} +(-2.35497 + 4.07893i) q^{62} -23.5929 q^{64} +(-10.2037 - 5.82098i) q^{65} +(0.863173 + 1.49506i) q^{66} -0.826916i q^{67} +(5.71365 + 9.89633i) q^{68} +(0.313538 + 0.543065i) q^{69} +(-2.03884 + 1.17712i) q^{71} +25.7506i q^{72} +(2.76680 - 1.59741i) q^{73} +(8.02261 - 13.8956i) q^{74} +(0.971316 + 1.68237i) q^{75} +(11.0353 + 6.37126i) q^{76} +(-2.91130 + 1.70098i) q^{78} +(-0.400955 + 0.694475i) q^{79} -44.1559i q^{80} +7.93720 q^{81} -11.4110 q^{82} -9.97031i q^{83} +(-6.07534 + 3.50760i) q^{85} +(-20.3254 - 11.7349i) q^{86} +(0.472923 - 0.819127i) q^{87} +16.5039 q^{88} +(13.0886 - 7.55674i) q^{89} -25.3680 q^{90} +9.62010 q^{92} +(-0.522012 + 0.301384i) q^{93} -15.8887 q^{94} +(-3.91130 + 6.77458i) q^{95} +(-5.61897 - 3.24411i) q^{96} +(-7.99489 + 4.61585i) q^{97} -5.31715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9	\( 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9} + 24 q^{10} - 2 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} - 12 q^{18} + 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} - 24 q^{26} - 12 q^{27} + 8 q^{29} - 16 q^{30} - 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} + 2 q^{38} - 10 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} - 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} - 26 q^{52} + 22 q^{53} + 12 q^{54} + 6 q^{55} + 18 q^{59} + 66 q^{60} + 28 q^{61} + 4 q^{62} - 52 q^{64} - 42 q^{65} - 26 q^{66} + 8 q^{68} - 4 q^{69} - 24 q^{71} - 30 q^{73} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} + 28 q^{82} - 48 q^{85} - 60 q^{86} + 2 q^{87} + 28 q^{88} - 12 q^{89} - 24 q^{90} + 24 q^{92} + 18 q^{93} + 8 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9 + 24 * q^10 - 2 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 - 12 * q^18 + 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 12 * q^27 + 8 * q^29 - 16 * q^30 - 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 + 2 * q^38 - 10 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 - 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 - 26 * q^52 + 22 * q^53 + 12 * q^54 + 6 * q^55 + 18 * q^59 + 66 * q^60 + 28 * q^61 + 4 * q^62 - 52 * q^64 - 42 * q^65 - 26 * q^66 + 8 * q^68 - 4 * q^69 - 24 * q^71 - 30 * q^73 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 + 28 * q^82 - 48 * q^85 - 60 * q^86 + 2 * q^87 + 28 * q^88 - 12 * q^89 - 24 * q^90 + 24 * q^92 + 18 * q^93 + 8 * q^94 - 22 * q^95 - 6 * q^96 - 6 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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