LMFDB - Embedded newform 637.2.k.g.569.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("637.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
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:	$\Z[a_1, \ldots, a_{5}]$
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			569.1
Root			$-1.12906 - 0.851598i$ of defining polynomial
Character	$\chi$	$=$	637.569
Dual form			637.2.k.g.459.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70320i q^{2} +(-0.172975 + 0.299601i) q^{3} -5.30727 q^{4} +(-2.82162 - 1.62906i) q^{5} +(0.809880 + 0.467584i) q^{6} +8.94020i q^{8} +(1.44016 + 2.49443i) q^{9} +O(q^{10})$	\(q-2.70320i q^{2} +(-0.172975 + 0.299601i) q^{3} -5.30727 q^{4} +(-2.82162 - 1.62906i) q^{5} +(0.809880 + 0.467584i) q^{6} +8.94020i q^{8} +(1.44016 + 2.49443i) q^{9} +(-4.40367 + 7.62739i) q^{10} +(1.59871 + 0.923014i) q^{11} +(0.918023 - 1.59006i) q^{12} +(-3.60550 - 0.0186461i) q^{13} +(0.976136 - 0.563573i) q^{15} +13.5526 q^{16} +2.15314 q^{17} +(6.74293 - 3.89303i) q^{18} +(-2.07929 + 1.20048i) q^{19} +(14.9751 + 8.64587i) q^{20} +(2.49509 - 4.32162i) q^{22} -1.81263 q^{23} +(-2.67849 - 1.54643i) q^{24} +(2.80769 + 4.86305i) q^{25} +(-0.0504042 + 9.74638i) q^{26} -2.03429 q^{27} +(1.36703 + 2.36777i) q^{29} +(-1.52345 - 2.63869i) q^{30} +(1.50893 - 0.871180i) q^{31} -18.7549i q^{32} +(-0.553071 + 0.319316i) q^{33} -5.82036i q^{34} +(-7.64331 - 13.2386i) q^{36} -5.93565i q^{37} +(3.24513 + 5.62072i) q^{38} +(0.629247 - 1.07699i) 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} -9.38444i q^{45} +4.89989i 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} +(19.1354 + 0.0989601i) q^{52} +(4.65314 + 8.05947i) q^{53} +5.49909i q^{54} +(-3.00729 - 5.20878i) q^{55} -0.830609i q^{57} +(6.40054 - 3.69535i) q^{58} +10.7523i q^{59} +(-5.18062 + 2.99103i) q^{60} +(5.05504 + 8.75558i) q^{61} +(-2.35497 - 4.07893i) q^{62} -23.5929 q^{64} +(10.1430 + 5.92620i) q^{65} +(0.863173 + 1.49506i) q^{66} +(-0.716130 - 0.413458i) q^{67} -11.4273 q^{68} +(0.313538 - 0.543065i) q^{69} +(-2.03884 - 1.17712i) q^{71} +(-22.3007 + 12.8753i) q^{72} +(-2.76680 + 1.59741i) q^{73} -16.0452 q^{74} -1.94263 q^{75} +(11.0353 - 6.37126i) q^{76} +(-2.91130 - 1.70098i) q^{78} +(-0.400955 + 0.694475i) q^{79} +(-38.2402 - 22.0780i) q^{80} +(-3.96860 + 6.87381i) q^{81} +(5.70552 + 9.88225i) q^{82} +9.97031i q^{83} +(-6.07534 - 3.50760i) q^{85} +(20.3254 + 11.7349i) q^{86} -0.945847 q^{87} +(-8.25193 + 14.2928i) q^{88} -15.1135i q^{89} -25.3680 q^{90} +9.62010 q^{92} +0.602768i q^{93} +(7.94435 - 13.7600i) q^{94} +7.82261 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 - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9	$ 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9} - 12 q^{10} - 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{15} + 16 q^{16} - 8 q^{17} + 12 q^{18} + 12 q^{20} + 6 q^{22} + 24 q^{23} + 12 q^{24} + 10 q^{25} - 18 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 18 q^{31} - 30 q^{33} - 10 q^{36} + 2 q^{38} + 14 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} - 24 q^{44} + 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} + 28 q^{52} + 22 q^{53} + 6 q^{55} + 12 q^{58} - 66 q^{60} - 14 q^{61} + 4 q^{62} - 52 q^{64} - 18 q^{65} - 26 q^{66} + 24 q^{67} - 16 q^{68} - 4 q^{69} - 24 q^{71} - 60 q^{72} + 30 q^{73} - 12 q^{74} + 92 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 60 q^{86} - 4 q^{87} - 14 q^{88} - 24 q^{90} + 24 q^{92} - 4 q^{94} + 44 q^{95} + 6 q^{96} - 6 q^{97}+O(q^{100}) $ 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9 - 12 * q^10 - 6 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^15 + 16 * q^16 - 8 * q^17 + 12 * q^18 + 12 * q^20 + 6 * q^22 + 24 * q^23 + 12 * q^24 + 10 * q^25 - 18 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 18 * q^31 - 30 * q^33 - 10 * q^36 + 2 * q^38 + 14 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 - 24 * q^44 + 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 + 28 * q^52 + 22 * q^53 + 6 * q^55 + 12 * q^58 - 66 * q^60 - 14 * q^61 + 4 * q^62 - 52 * q^64 - 18 * q^65 - 26 * q^66 + 24 * q^67 - 16 * q^68 - 4 * q^69 - 24 * q^71 - 60 * q^72 + 30 * q^73 - 12 * q^74 + 92 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 60 * q^86 - 4 * q^87 - 14 * q^88 - 24 * q^90 + 24 * q^92 - 4 * q^94 + 44 * q^95 + 6 * q^96 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	2.70320i		−	1.91145i	−0.294264	−	0.955724i	$-0.595075\pi$
$2$		−	2.70320i		−	1.91145i	0.294264	−	0.955724i	$-0.404925\pi$
$3$	−0.172975	+	0.299601i	−0.0998669	+	0.172975i	−0.911629	−	0.411013i	$-0.865175\pi$
$3$	−0.172975	+	0.299601i	−0.0998669	+	0.172975i	0.811763	+	0.583988i	$0.198508\pi$
$4$	−5.30727			−2.65363
$5$	−2.82162	−	1.62906i	−1.26187	−	0.728539i	−0.288431	−	0.957501i	$-0.593133\pi$
$5$	−2.82162	−	1.62906i	−1.26187	−	0.728539i	−0.973435	+	0.228962i	$0.926467\pi$
$6$	0.809880	+	0.467584i	0.330632	+	0.190890i
$7$		0			0
$7$		0			0
$8$			8.94020i			3.16084i
$9$	1.44016	+	2.49443i	0.480053	+	0.831477i
$10$	−4.40367	+	7.62739i	−1.39256	+	2.41199i
$11$	1.59871	+	0.923014i	0.482028	+	0.278299i	0.721261	−	0.692663i	$-0.243563\pi$
$11$	1.59871	+	0.923014i	0.482028	+	0.278299i	−0.239233	+	0.970962i	$0.576896\pi$
$12$	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
$16$	13.5526			3.38814
$17$	2.15314			0.522213			0.261107	−	0.965310i	$-0.415913\pi$
$17$	2.15314			0.522213			0.261107	+	0.965310i	$0.415913\pi$
$18$	6.74293	−	3.89303i	1.58932	−	0.917597i
$19$	−2.07929	+	1.20048i	−0.477021	+	0.275408i	−0.719174	−	0.694830i	$-0.755480\pi$
$19$	−2.07929	+	1.20048i	−0.477021	+	0.275408i	0.242153	+	0.970238i	$0.422146\pi$
$20$	14.9751	+	8.64587i	3.34853	+	1.93328i
$21$		0			0
$22$	2.49509	−	4.32162i	0.531954	−	0.921372i
$23$	−1.81263			−0.377959			−0.188979	−	0.981981i	$-0.560518\pi$
$23$	−1.81263			−0.377959			−0.188979	+	0.981981i	$0.560518\pi$
$24$	−2.67849	−	1.54643i	−0.546744	−	0.315663i
$25$	2.80769	+	4.86305i	0.561537	+	0.972611i
$26$	−0.0504042	+	9.74638i	−0.00988507	+	1.91142i
$27$	−2.03429			−0.391500
$28$		0			0
$29$	1.36703	+	2.36777i	0.253851	+	0.439683i	0.964583	−	0.263780i	$-0.0849693\pi$
$29$	1.36703	+	2.36777i	0.253851	+	0.439683i	−0.710732	+	0.703463i	$0.751636\pi$
$30$	−1.52345	−	2.63869i	−0.278142	−	0.481756i
$31$	1.50893	−	0.871180i	0.271011	−	0.156468i	−0.358336	−	0.933593i	$-0.616656\pi$
$31$	1.50893	−	0.871180i	0.271011	−	0.156468i	0.629347	+	0.777124i	$0.283322\pi$
$32$		−	18.7549i		−	3.31542i
$33$	−0.553071	+	0.319316i	−0.0962774	+	0.0555858i
$34$		−	5.82036i		−	0.998183i
$35$		0			0
$36$	−7.64331	−	13.2386i	−1.27389	−	2.20643i
$37$		−	5.93565i		−	0.975815i	−0.872895	−	0.487908i	$-0.837760\pi$
$37$		−	5.93565i		−	0.975815i	0.872895	−	0.487908i	$-0.162240\pi$
$38$	3.24513	+	5.62072i	0.526429	+	0.911802i
$39$	0.629247	−	1.07699i	0.100760	−	0.172456i
$40$	14.5641	−	25.2258i	2.30279	−	3.98855i
$41$	−3.65577	+	2.11066i	−0.570935	+	0.329629i	−0.757523	−	0.652809i	$-0.773590\pi$
$41$	−3.65577	+	2.11066i	−0.570935	+	0.329629i	0.186588	+	0.982438i	$0.440257\pi$
$42$		0			0
$43$	−4.34111	+	7.51903i	−0.662014	+	1.14664i	0.318072	+	0.948067i	$0.396965\pi$
$43$	−4.34111	+	7.51903i	−0.662014	+	1.14664i	−0.980086	+	0.198575i	$0.936369\pi$
$44$	−8.48477	−	4.89868i	−1.27913	−	0.738504i
$45$		−	9.38444i		−	1.39895i
$46$			4.89989i			0.722449i
$47$	5.09027	+	2.93887i	0.742493	+	0.428678i	0.822975	−	0.568078i	$-0.192313\pi$
$47$	5.09027	+	2.93887i	0.742493	+	0.428678i	−0.0804822	+	0.996756i	$0.525646\pi$
$48$	−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
$52$	19.1354	+	0.0989601i	2.65360	+	0.0137233i
$53$	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	$0.612616\pi$
$54$			5.49909i			0.748331i
$55$	−3.00729	−	5.20878i	−0.405503	−	0.702352i
$56$		0			0
$57$		−	0.830609i		−	0.110017i
$58$	6.40054	−	3.69535i	0.840432	−	0.485224i
$59$			10.7523i			1.39982i	0.714229	+	0.699912i	$0.246778\pi$
$59$			10.7523i			1.39982i	−0.714229	+	0.699912i	$0.753222\pi$
$60$	−5.18062	+	2.99103i	−0.668815	+	0.386141i
$61$	5.05504	+	8.75558i	0.647231	+	1.12104i	0.983781	+	0.179371i	$0.0574064\pi$
$61$	5.05504	+	8.75558i	0.647231	+	1.12104i	−0.336550	+	0.941665i	$0.609260\pi$
$62$	−2.35497	−	4.07893i	−0.299081	−	0.518024i
$63$		0			0
$64$	−23.5929			−2.94911
$65$	10.1430	+	5.92620i	1.25808	+	0.735055i
$66$	0.863173	+	1.49506i	0.106249	+	0.184029i
$67$	−0.716130	−	0.413458i	−0.0874892	−	0.0505119i	0.455617	−	0.890176i	$-0.349419\pi$
$67$	−0.716130	−	0.413458i	−0.0874892	−	0.0505119i	−0.543106	+	0.839664i	$0.682752\pi$
$68$	−11.4273			−1.38576
$69$	0.313538	−	0.543065i	0.0377456	−	0.0653773i
$70$		0			0
$71$	−2.03884	−	1.17712i	−0.241965	−	0.139699i	0.374114	−	0.927383i	$-0.377947\pi$
$71$	−2.03884	−	1.17712i	−0.241965	−	0.139699i	−0.616080	+	0.787684i	$0.711280\pi$
$72$	−22.3007	+	12.8753i	−2.62816	+	1.51737i
$73$	−2.76680	+	1.59741i	−0.323829	+	0.186963i	−0.653098	−	0.757273i	$-0.726531\pi$
$73$	−2.76680	+	1.59741i	−0.323829	+	0.186963i	0.329269	+	0.944236i	$0.393198\pi$
$74$	−16.0452			−1.86522
$75$	−1.94263			−0.224316
$76$	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	$0.181031\pi$
$80$	−38.2402	−	22.0780i	−4.27538	−	2.46839i
$81$	−3.96860	+	6.87381i	−0.440955	+	0.763757i
$82$	5.70552	+	9.88225i	0.630069	+	1.09131i
$83$			9.97031i			1.09438i	0.837007	+	0.547192i	$0.184303\pi$
$83$			9.97031i			1.09438i	−0.837007	+	0.547192i	$0.815697\pi$
$84$		0			0
$85$	−6.07534	−	3.50760i	−0.658963	−	0.380452i
$86$	20.3254	+	11.7349i	2.19175	+	1.26541i
$87$	−0.945847			−0.101405
$88$	−8.25193	+	14.2928i	−0.879658	+	1.52361i
$89$		−	15.1135i		−	1.60202i	−0.598648	−	0.801012i	$-0.704295\pi$
$89$		−	15.1135i		−	1.60202i	0.598648	−	0.801012i	$-0.295705\pi$
$90$	−25.3680			−2.67402
$91$		0			0
$92$	9.62010			1.00296
$93$			0.602768i			0.0625041i
$94$	7.94435	−	13.7600i	0.819397	−	1.41924i
$95$	7.82261			0.802583
$96$	5.61897	+	3.24411i	0.573484	+	0.331101i
$97$	−7.99489	−	4.61585i	−0.811758	−	0.468669i	0.0358079	−	0.999359i	$-0.488600\pi$
$97$	−7.99489	−	4.61585i	−0.811758	−	0.468669i	−0.847566	+	0.530690i	$0.821933\pi$
$98$		0			0
$99$			5.31715i			0.534394i
$100$	−14.9011	−	25.8095i	−1.49011	−	2.58095i
$101$	−7.41169	+	12.8374i	−0.737491	+	1.27737i	0.216131	+	0.976364i	$0.430656\pi$
$101$	−7.41169	+	12.8374i	−0.737491	+	1.27737i	−0.953622	+	0.301007i	$0.902677\pi$
$102$	1.74378	+	1.00677i	0.172660	+	0.0996855i
$103$	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
$107$	−19.1258			−1.84896			−0.924479	−	0.381233i	$-0.875500\pi$
$107$	−19.1258			−1.84896			−0.924479	+	0.381233i	$0.875500\pi$
$108$	10.7965			1.03890
$109$	−3.69925	+	2.13577i	−0.354324	+	0.204569i	−0.666588	−	0.745426i	$-0.732246\pi$
$109$	−3.69925	+	2.13577i	−0.354324	+	0.204569i	0.312264	+	0.949995i	$0.398913\pi$
$110$	−14.0804	+	8.12930i	−1.34251	+	0.775099i
$111$	1.77833	+	1.02672i	0.168791	+	0.0974516i
$112$		0			0
$113$	−1.37488	+	2.38137i	−0.129338	+	0.224020i	−0.923420	−	0.383790i	$-0.874619\pi$
$113$	−1.37488	+	2.38137i	−0.129338	+	0.224020i	0.794082	+	0.607810i	$0.207952\pi$
$114$	−2.24530			−0.210291
$115$	5.11454	+	2.95288i	0.476934	+	0.275358i
$116$	−7.25520	−	12.5664i	−0.673629	−	1.16676i
$117$	−5.14599	−	9.02053i	−0.475747	−	0.833948i
$118$	29.0655			2.67569
$119$		0			0
$120$	5.03845	+	8.72685i	0.459945	+	0.796649i
$121$	−3.79609	−	6.57502i	−0.345099	−	0.597729i
$122$	23.6680	−	13.6648i	2.14280	−	1.23715i
$123$		−	1.46036i		−	0.131676i
$124$	−8.00828	+	4.62358i	−0.719165	+	0.415210i
$125$		−	2.00495i		−	0.179329i
$126$		0			0
$127$	−4.86719	−	8.43022i	−0.431893	−	0.748061i	0.565143	−	0.824993i	$-0.308821\pi$
$127$	−4.86719	−	8.43022i	−0.431893	−	0.748061i	−0.997036	+	0.0769320i	$0.975488\pi$
$128$			26.2666i			2.32166i
$129$	−1.50181	−	2.60120i	−0.132227	−	0.229023i
$130$	16.0197	−	27.4185i	1.40502	−	2.40476i
$131$	−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
$136$			19.2495i			1.65063i
$137$			8.42156i			0.719502i	0.933048	+	0.359751i	$0.117138\pi$
$137$			8.42156i			0.719502i	−0.933048	+	0.359751i	$0.882862\pi$
$138$	−1.46801	−	0.847556i	−0.124965	−	0.0721488i
$139$	−8.81809	+	15.2734i	−0.747941	+	1.29547i	0.200867	+	0.979619i	$0.435624\pi$
$139$	−8.81809	+	15.2734i	−0.747941	+	1.29547i	−0.948808	+	0.315853i	$0.897709\pi$
$140$		0			0
$141$	−1.76098	+	1.01670i	−0.148301	+	0.0856216i
$142$	−3.18199	+	5.51138i	−0.267027	+	0.462504i
$143$	−5.74693	−	3.35774i	−0.480583	−	0.280788i
$144$	19.5179	+	33.8059i	1.62649	+	2.81716i
$145$		−	8.90791i		−	0.739762i
$146$	4.31811	+	7.47919i	0.357370	+	0.618982i
$147$		0			0
$148$			31.5021i			2.58946i
$149$	3.48232	−	2.01052i	0.285283	−	0.164708i	−0.350530	−	0.936552i	$-0.613998\pi$
$149$	3.48232	−	2.01052i	0.285283	−	0.164708i	0.635813	+	0.771843i	$0.280665\pi$
$150$			5.25132i			0.428768i
$151$	16.3687	−	9.45048i	1.33207	−	0.769069i	0.346451	−	0.938068i	$-0.387387\pi$
$151$	16.3687	−	9.45048i	1.33207	−	0.769069i	0.985616	+	0.168999i	$0.0540534\pi$
$152$	−10.7325	−	18.5892i	−0.870521	−	1.50779i
$153$	3.10086	+	5.37086i	0.250690	+	0.434208i
$154$		0			0
$155$	−5.67682			−0.455973
$156$	−3.33958	+	5.71586i	−0.267381	+	0.457635i
$157$	−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	$0.986142\pi$
$158$	1.87730	+	1.08386i	0.149350	+	0.0862273i
$159$	−3.21950			−0.255323
$160$	−30.5528	+	52.9190i	−2.41541	+	4.18362i
$161$		0			0
$162$	18.5813	+	10.7279i	1.45988	+	0.842863i
$163$	3.81520	−	2.20271i	0.298830	−	0.172529i	−0.343087	−	0.939304i	$-0.611473\pi$
$163$	3.81520	−	2.20271i	0.298830	−	0.172529i	0.641917	+	0.766774i	$0.278139\pi$
$164$	19.4021	−	11.2018i	1.51505	−	0.874716i
$165$	2.08074			0.161985
$166$	26.9517			2.09186
$167$	7.81076	−	4.50954i	0.604415	−	0.348959i	−0.166362	−	0.986065i	$-0.553202\pi$
$167$	7.81076	−	4.50954i	0.604415	−	0.348959i	0.770776	+	0.637106i	$0.219869\pi$
$168$		0			0
$169$	12.9993	+	0.134457i	0.999947	+	0.0103429i
$170$	−9.48173	+	16.4228i	−0.727215	+	1.25957i
$171$	−5.98901	−	3.45776i	−0.457991	−	0.264421i
$172$	23.0395	−	39.9055i	1.75674	−	3.04277i
$173$	−3.04600	−	5.27583i	−0.231583	−	0.401114i	0.726691	−	0.686964i	$-0.241057\pi$
$173$	−3.04600	−	5.27583i	−0.231583	−	0.401114i	−0.958274	+	0.285851i	$0.907724\pi$
$174$			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
$178$	−40.8547			−3.06219
$179$	1.93982	−	3.35987i	0.144989	−	0.251128i	−0.784380	−	0.620281i	$-0.787019\pi$
$179$	1.93982	−	3.35987i	0.144989	−	0.251128i	0.929369	+	0.369152i	$0.120352\pi$
$180$			49.8057i			3.71230i
$181$	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
$184$		−	16.2052i		−	1.19467i
$185$	−9.66954	+	16.7481i	−0.710919	+	1.23135i
$186$	1.62940			0.119473
$187$	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
$191$	6.87168	+	11.9021i	0.497218	+	0.861206i	0.999995	−	0.00320983i	$-0.00102172\pi$
$191$	6.87168	+	11.9021i	0.497218	+	0.861206i	−0.502777	+	0.864416i	$0.667688\pi$
$192$	4.08097	−	7.06845i	0.294519	−	0.510122i
$193$	−19.7047	−	11.3765i	−1.41838	−	0.818899i	−0.422219	−	0.906494i	$-0.638749\pi$
$193$	−19.7047	−	11.3765i	−1.41838	−	0.818899i	−0.996156	+	0.0875946i	$0.972082\pi$
$194$	−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	−0.876015	−	0.482284i	$-0.839807\pi$
$197$	−12.5809	+	7.26358i	−0.896352	+	0.517509i	−0.0203371	+	0.999793i	$0.506474\pi$
$198$	14.3733			1.02147
$199$	23.8404			1.69000			0.845001	−	0.534765i	$-0.179600\pi$
$199$	23.8404			1.69000			0.845001	+	0.534765i	$0.179600\pi$
$200$	−43.4767	+	25.1013i	−3.07426	+	1.77493i
$201$	0.247745	−	0.143035i	0.0174746	−	0.0100889i
$202$	34.7021	+	20.0353i	2.44163	+	1.40968i
$203$		0			0
$204$	1.97663	−	3.42363i	0.138392	−	0.239702i
$205$	13.7536			0.960591
$206$	−10.0263	−	5.78871i	−0.698568	−	0.403318i
$207$	−2.61047	−	4.52147i	−0.181440	−	0.314264i
$208$	−48.8638	−	0.252703i	−3.38810	−	0.0175218i
$209$	−4.43223			−0.306584
$210$		0			0
$211$	−2.15764	−	3.73714i	−0.148538	−	0.257275i	0.782149	−	0.623091i	$-0.214123\pi$
$211$	−2.15764	−	3.73714i	−0.148538	−	0.257275i	−0.930687	+	0.365816i	$0.880790\pi$
$212$	−24.6955	−	42.7738i	−1.69609	−	2.93772i
$213$	0.705334	−	0.407225i	0.0483287	−	0.0279026i
$214$			51.7007i			3.53419i
$215$	24.4979	−	14.1439i	1.67075	−	0.964605i
$216$		−	18.1870i		−	1.23747i
$217$		0			0
$218$	5.77339	+	9.99981i	0.391024	+	0.677273i
$219$		−	1.10525i		−	0.0746856i
$220$	15.9605	+	27.6444i	1.07606	+	1.86379i
$221$	−7.76315	−	0.0401478i	−0.522206	−	0.00270063i
$222$	2.77542	−	4.80716i	0.186274	−	0.322636i
$223$	20.2604	−	11.6973i	1.35674	−	0.783312i	0.367553	−	0.930003i	$-0.380196\pi$
$223$	20.2604	−	11.6973i	1.35674	−	0.783312i	0.989182	+	0.146691i	$0.0468623\pi$
$224$		0			0
$225$	−8.08703	+	14.0071i	−0.539135	+	0.933810i
$226$	6.43730	+	3.71658i	0.428203	+	0.247223i
$227$		−	26.7229i		−	1.77366i	−0.462097	−	0.886829i	$-0.652903\pi$
$227$		−	26.7229i		−	1.77366i	0.462097	−	0.886829i	$-0.347097\pi$
$228$			4.40826i			0.291944i
$229$	−2.60388	−	1.50335i	−0.172069	−	0.0993442i	0.411492	−	0.911413i	$-0.365008\pi$
$229$	−2.60388	−	1.50335i	−0.172069	−	0.0993442i	−0.583561	+	0.812069i	$0.698341\pi$
$230$	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	$0.292028\pi$
$234$	−24.3843	+	13.9106i	−1.59405	+	0.909365i
$235$	−9.57521	−	16.5847i	−0.624618	−	1.08187i
$236$		−	57.0651i		−	3.71462i
$237$	−0.138710	−	0.240253i	−0.00901019	−	0.0156061i
$238$		0			0
$239$			1.42797i			0.0923677i	0.998933	+	0.0461838i	$0.0147060\pi$
$239$			1.42797i			0.0923677i	−0.998933	+	0.0461838i	$0.985294\pi$
$240$	13.2292	−	7.63786i	0.853938	−	0.493021i
$241$		−	2.67969i		−	0.172614i	−0.996269	−	0.0863069i	$-0.972493\pi$
$241$		−	2.67969i		−	0.172614i	0.996269	−	0.0863069i	$-0.0275065\pi$
$242$	−17.7736	+	10.2616i	−1.14253	+	0.659639i
$243$	−4.42437	−	7.66323i	−0.283824	−	0.491597i
$244$	−26.8284	−	46.4682i	−1.71751	−	2.97482i
$245$		0			0
$246$	−3.94764			−0.251692
$247$	7.51926	−	4.28956i	0.478439	−	0.272938i
$248$	7.78852	+	13.4901i	0.494571	+	0.856623i
$249$	−2.98711	−	1.72461i	−0.189301	−	0.109293i
$250$	−5.41978			−0.342777
$251$	−5.46696	+	9.46906i	−0.345072	+	0.597681i	−0.985367	−	0.170447i	$-0.945479\pi$
$251$	−5.46696	+	9.46906i	−0.345072	+	0.597681i	0.640295	+	0.768129i	$0.278812\pi$
$252$		0			0
$253$	−2.89786	−	1.67308i	−0.182187	−	0.105186i
$254$	−22.7885	+	13.1570i	−1.42988	+	0.825541i
$255$	2.10176	−	1.21345i	0.131617	−	0.0759892i
$256$	23.8178			1.48861
$257$	4.15138			0.258956			0.129478	−	0.991582i	$-0.458670\pi$
$257$	4.15138			0.258956			0.129478	+	0.991582i	$0.458670\pi$
$258$	−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
$262$	43.6872	+	25.2228i	2.69900	+	1.55827i
$263$	−2.02680	+	3.51052i	−0.124978	+	0.216468i	−0.921724	−	0.387846i	$-0.873219\pi$
$263$	−2.02680	+	3.51052i	−0.124978	+	0.216468i	0.796747	+	0.604314i	$0.206553\pi$
$264$	−2.85475	−	4.94457i	−0.175698	−	0.304317i
$265$		−	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
$269$	−4.00022			−0.243898			−0.121949	−	0.992536i	$-0.538914\pi$
$269$	−4.00022			−0.243898			−0.121949	+	0.992536i	$0.538914\pi$
$270$	8.95836	−	15.5163i	0.545188	−	0.944294i
$271$			2.78502i			0.169178i	0.996416	+	0.0845888i	$0.0269577\pi$
$271$			2.78502i			0.169178i	−0.996416	+	0.0845888i	$0.973042\pi$
$272$	29.1806			1.76933
$273$		0			0
$274$	22.7651			1.37529
$275$			10.3661i			0.625101i
$276$	−1.66403	+	2.88219i	−0.100163	+	0.173487i
$277$	−16.6924			−1.00295			−0.501474	−	0.865173i	$-0.667209\pi$
$277$	−16.6924			−1.00295			−0.501474	+	0.865173i	$0.667209\pi$
$278$	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	$0.130603\pi$
$281$			13.3731i			0.797774i	−0.917000	+	0.398887i	$0.869397\pi$
$282$	2.74834	+	4.76026i	0.163661	+	0.283470i
$283$	9.44312	−	16.3560i	0.561335	−	0.972261i	−0.436045	−	0.899925i	$-0.643621\pi$
$283$	9.44312	−	16.3560i	0.561335	−	0.972261i	0.997380	−	0.0723362i	$-0.0230455\pi$
$284$	10.8207	+	6.24731i	0.642088	+	0.370710i
$285$	−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
$289$	−12.3640			−0.727293
$290$	−24.0798			−1.41402
$291$	2.76583	−	1.59685i	0.162136	−	0.0936090i
$292$	14.6841	−	8.47789i	0.859324	−	0.496131i
$293$	2.95999	+	1.70895i	0.172925	+	0.0998380i	0.583964	−	0.811779i	$-0.301501\pi$
$293$	2.95999	+	1.70895i	0.172925	+	0.0998380i	−0.411040	+	0.911617i	$0.634834\pi$
$294$		0			0
$295$	17.5161	−	30.3388i	1.01983	−	1.76639i
$296$	53.0659			3.08439
$297$	−3.25224	−	1.87768i	−0.188714	−	0.108954i
$298$	−5.43483	−	9.41340i	−0.314831	−	0.545304i
$299$	6.53543	+	0.0337985i	0.377954	+	0.00195462i
$300$	10.3101			0.595252
$301$		0			0
$302$	−25.5465	−	44.2479i	−1.47004	−	2.54618i
$303$	−2.56407	−	4.44110i	−0.147302	−	0.255134i
$304$	−28.1797	+	16.2696i	−1.61622	+	0.933123i
$305$		−	32.9399i		−	1.88613i
$306$	14.5185	−	8.38225i	0.829966	−	0.479181i
$307$			16.3679i			0.934165i	0.884214	+	0.467083i	$0.154695\pi$
$307$			16.3679i			0.934165i	−0.884214	+	0.467083i	$0.845305\pi$
$308$		0			0
$309$	0.740826	+	1.28315i	0.0421441	+	0.0729958i
$310$			15.3456i			0.871569i
$311$	−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	$-0.401184\pi$
$312$	9.62847	+	5.62559i	0.545105	+	0.318486i
$313$	−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	0.640206	−	0.768204i	$-0.278849\pi$
$317$	5.25276	+	3.03268i	0.295024	+	0.170332i	−0.345181	+	0.938536i	$0.612183\pi$
$318$			8.70294i			0.488037i
$319$			5.04715i			0.282586i
$320$	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
$325$	−10.0324	−	17.5861i	−0.556500	−	0.975502i
$326$	−5.95435	−	10.3132i	−0.329781	−	0.571198i
$327$		−	1.47773i		−	0.0817188i
$328$	−18.8697	−	32.6833i	−1.04190	−	1.80463i
$329$		0			0
$330$		−	5.62465i		−	0.309627i
$331$	−14.9605	+	8.63743i	−0.822301	+	0.474756i	−0.851209	−	0.524826i	$-0.824130\pi$
$331$	−14.9605	+	8.63743i	−0.822301	+	0.474756i	0.0289082	+	0.999582i	$0.490797\pi$
$332$		−	52.9151i		−	2.90410i
$333$	14.8061	−	8.54829i	0.811367	−	0.468443i
$334$	−12.1902	−	21.1140i	−0.667017	−	1.15531i
$335$	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	$0.573073\pi$
$338$	0.363465	−	35.1397i	0.0197699	−	1.91135i
$339$	−0.475639	−	0.823832i	−0.0258332	−	0.0447444i
$340$	32.2435	+	18.6158i	1.74865	+	1.00958i
$341$	3.21644			0.174180
$342$	−9.34700	+	16.1895i	−0.505428	+	0.875427i
$343$		0			0
$344$	−67.2216	−	38.8104i	−3.62435	−	2.09252i
$345$	−1.76937	+	1.02155i	−0.0952598	+	0.0549983i
$346$	−14.2616	+	8.23394i	−0.766708	+	0.442659i
$347$	28.8220			1.54725			0.773623	−	0.633646i	$-0.218443\pi$
$347$	28.8220			1.54725			0.773623	+	0.633646i	$0.218443\pi$
$348$	5.01986			0.269093
$349$	10.1516	−	5.86103i	0.543403	−	0.313734i	−0.203054	−	0.979167i	$-0.565087\pi$
$349$	10.1516	−	5.86103i	0.543403	−	0.313734i	0.746457	+	0.665434i	$0.231753\pi$
$350$		0			0
$351$	7.33464	+	0.0379317i	0.391494	+	0.00202464i
$352$	17.3110	−	29.9835i	0.922679	−	1.59813i
$353$	15.4466	+	8.91811i	0.822141	+	0.474663i	0.851154	−	0.524916i	$-0.175903\pi$
$353$	15.4466	+	8.91811i	0.822141	+	0.474663i	−0.0290134	+	0.999579i	$0.509237\pi$
$354$	−5.02759	+	8.70804i	−0.267213	+	0.462827i
$355$	3.83521	+	6.64278i	0.203552	+	0.352562i
$356$			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	0.624193	−	0.781270i	$-0.285428\pi$
$359$	4.92042	+	2.84081i	0.259690	+	0.149932i	−0.364503	+	0.931202i	$0.618761\pi$
$360$	83.8987			4.42185
$361$	−6.61771	+	11.4622i	−0.348300	+	0.603274i
$362$		−	17.7976i		−	0.935423i
$363$	2.62651			0.137856
$364$		0			0
$365$	10.4091			0.544838
$366$			9.45462i			0.494201i
$367$	−9.81580	+	17.0015i	−0.512381	+	0.887469i	0.487516	+	0.873114i	$0.337903\pi$
$367$	−9.81580	+	17.0015i	−0.512381	+	0.887469i	−0.999897	+	0.0143554i	$0.995430\pi$
$368$	−24.5658			−1.28058
$369$	−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
$373$	−16.0323	−	27.7687i	−0.830119	−	1.43781i	−0.897943	−	0.440111i	$-0.854939\pi$
$373$	−16.0323	−	27.7687i	−0.830119	−	1.43781i	0.0678240	−	0.997697i	$-0.478394\pi$
$374$	5.37227	−	9.30505i	0.277794	−	0.481153i
$375$	0.600686	+	0.346806i	0.0310193	+	0.0179090i
$376$	−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	−0.859379	−	0.511339i	$-0.829150\pi$
$379$	−16.4745	+	9.51154i	−0.846237	+	0.488575i	0.0131425	+	0.999914i	$0.495816\pi$
$380$	−41.5167			−2.12976
$381$	3.36760			0.172527
$382$	32.1737	−	18.5755i	1.64615	−	0.950406i
$383$	0.606070	−	0.349915i	0.0309687	−	0.0178798i	−0.484436	−	0.874827i	$-0.660975\pi$
$383$	0.606070	−	0.349915i	0.0309687	−	0.0178798i	0.515404	+	0.856947i	$0.327642\pi$
$384$	−7.86948	−	4.54345i	−0.401588	−	0.231857i
$385$		0			0
$386$	−30.7529	+	53.2657i	−1.56528	+	2.71115i
$387$	−25.0076			−1.27121
$388$	42.4310	+	24.4976i	2.15411	+	1.24368i
$389$	−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	$-0.336432\pi$
$390$	5.44359	+	9.54220i	0.275647	+	0.483188i
$391$	−3.90284			−0.197375
$392$		0			0
$393$	−3.22796	−	5.59099i	−0.162829	−	0.282028i
$394$	19.6349	+	34.0086i	0.989192	+	1.71333i
$395$	2.26269	−	1.30636i	0.113848	−	0.0657302i
$396$		−	28.2195i		−	1.41809i
$397$	−19.2953	+	11.1401i	−0.968403	+	0.559108i	−0.898749	−	0.438463i	$-0.855523\pi$
$397$	−19.2953	+	11.1401i	−0.968403	+	0.559108i	−0.0696541	+	0.997571i	$0.522190\pi$
$398$		−	64.4453i		−	3.23035i
$399$		0			0
$400$	38.0513	+	65.9069i	1.90257	+	3.29534i
$401$		−	4.80749i		−	0.240074i	−0.992769	−	0.120037i	$-0.961699\pi$
$401$		−	4.80749i		−	0.240074i	0.992769	−	0.120037i	$-0.0383014\pi$
$402$	−0.386653	−	0.669702i	−0.0192845	−	0.0334017i
$403$	−5.45669	+	3.11290i	−0.271817	+	0.155065i
$404$	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
$409$			36.8035i			1.81981i	0.414811	+	0.909907i	$0.363848\pi$
$409$			36.8035i			1.81981i	−0.414811	+	0.909907i	$0.636152\pi$
$410$		−	37.1786i		−	1.83612i
$411$	−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
$416$	−0.349706	+	67.6207i	−0.0171457	+	3.31538i
$417$	−3.05061	−	5.28382i	−0.149389	−	0.258750i
$418$			11.9812i			0.586019i
$419$	14.6334	+	25.3457i	0.714887	+	1.23822i	0.963003	+	0.269490i	$0.0868552\pi$
$419$	14.6334	+	25.3457i	0.714887	+	1.23822i	−0.248116	+	0.968730i	$0.579812\pi$
$420$		0			0
$421$		−	7.53862i		−	0.367410i	−0.982981	−	0.183705i	$-0.941191\pi$
$421$		−	7.53862i		−	0.367410i	0.982981	−	0.183705i	$-0.0588091\pi$
$422$	−10.1022	+	5.83251i	−0.491768	+	0.283922i
$423$			16.9298i			0.823154i
$424$	−72.0533	+	41.6000i	−3.49922	+	2.02027i
$425$	6.04534	+	10.4708i	0.293242	+	0.507910i
$426$	−1.10081	−	1.90666i	−0.0533343	−	0.0923778i
$427$		0			0
$428$	101.506			4.90646
$429$	2.00005	−	1.14098i	0.0965635	−	0.0550871i
$430$	−38.2337	−	66.2227i	−1.84379	−	3.19354i
$431$	27.0426	+	15.6131i	1.30260	+	0.752055i	0.980849	−	0.194771i	$-0.0623963\pi$
$431$	27.0426	+	15.6131i	1.30260	+	0.752055i	0.321748	+	0.946825i	$0.395730\pi$
$432$	−27.5699			−1.32646
$433$	−2.94202	+	5.09573i	−0.141384	+	0.244885i	−0.928018	−	0.372535i	$-0.878489\pi$
$433$	−2.94202	+	5.09573i	−0.141384	+	0.244885i	0.786634	+	0.617420i	$0.211822\pi$
$434$		0			0
$435$	2.66882	+	1.54084i	0.127960	+	0.0738777i
$436$	19.6329	−	11.3351i	0.940247	−	0.542852i
$437$	3.76898	−	2.17602i	0.180295	−	0.104093i
$438$	−2.98770			−0.142758
$439$	−9.95642			−0.475194			−0.237597	−	0.971364i	$-0.576360\pi$
$439$	−9.95642			−0.475194			−0.237597	+	0.971364i	$0.576360\pi$
$440$	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	$-0.158178\pi$
$444$	−9.43805	−	5.44906i	−0.447910	−	0.258601i
$445$	−24.6208	+	42.6444i	−1.16714	+	2.02154i
$446$	−31.6202	−	54.7678i	−1.49726	−	2.59333i
$447$			1.39108i			0.0657956i
$448$		0			0
$449$	3.46001	+	1.99764i	0.163288	+	0.0942744i	0.579417	−	0.815031i	$-0.303280\pi$
$449$	3.46001	+	1.99764i	0.163288	+	0.0942744i	−0.416129	+	0.909306i	$0.636614\pi$
$450$	37.8641	+	21.8608i	1.78493	+	1.03053i
$451$	−7.79266			−0.366942
$452$	7.29687	−	12.6386i	0.343216	−	0.594467i
$453$			6.53877i			0.307218i
$454$	−72.2371			−3.39026
$455$		0			0
$456$	7.42580			0.347745
$457$			41.2222i			1.92829i	0.265369	+	0.964147i	$0.414506\pi$
$457$			41.2222i			1.92829i	−0.265369	+	0.964147i	$0.585494\pi$
$458$	−4.06385	+	7.03880i	−0.189891	+	0.328901i
$459$	−4.38011			−0.204446
$460$	−27.1443	−	15.6717i	−1.26561	−	0.730699i
$461$	−21.4139	−	12.3633i	−0.997343	−	0.575816i	−0.0898818	−	0.995952i	$-0.528649\pi$
$461$	−21.4139	−	12.3633i	−0.997343	−	0.575816i	−0.907461	+	0.420136i	$0.861982\pi$
$462$		0			0
$463$		−	24.4057i		−	1.13423i	−0.823639	−	0.567115i	$-0.808060\pi$
$463$		−	24.4057i		−	1.13423i	0.823639	−	0.567115i	$-0.191940\pi$
$464$	18.5268	+	32.0893i	0.860084	+	1.48971i
$465$	0.981946	−	1.70078i	0.0455366	−	0.0788718i
$466$	27.4248	+	15.8337i	1.27043	+	0.733482i
$467$	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
$471$	4.00386			0.184488
$472$	−96.1273			−4.42462
$473$	−13.8803	+	8.01382i	−0.638219	+	0.368476i
$474$	−0.649451	+	0.374961i	−0.0298303	+	0.0172225i
$475$	−11.6760	−	6.74113i	−0.535730	−	0.309304i
$476$		0			0
$477$	−13.4025	+	23.2139i	−0.613660	+	1.06289i
$478$	3.86008			0.176556
$479$	−27.4328	−	15.8383i	−1.25343	−	0.723671i	−0.281645	−	0.959519i	$-0.590880\pi$
$479$	−27.4328	−	15.8383i	−1.25343	−	0.723671i	−0.971790	+	0.235848i	$0.924213\pi$
$480$	−10.5697	−	18.3073i	−0.482440	−	0.835610i
$481$	−0.110677	+	21.4010i	−0.00504644	+	0.975802i
$482$	−7.24372			−0.329942
$483$		0			0
$484$	20.1469	+	34.8954i	0.915767	+	1.58616i
$485$	15.0390	+	26.0483i	0.682887	+	1.18279i
$486$	−20.7152	+	11.9599i	−0.939662	+	0.542514i
$487$		−	26.9156i		−	1.21966i	−0.792531	−	0.609832i	$-0.791237\pi$
$487$		−	26.9156i		−	1.21966i	0.792531	−	0.609832i	$-0.208763\pi$
$488$	−78.2766	+	45.1930i	−3.54341	+	2.04579i
$489$			1.52405i			0.0689200i
$490$		0			0
$491$	4.86358	+	8.42396i	0.219490	+	0.380168i	0.954652	−	0.297723i	$-0.0962273\pi$
$491$	4.86358	+	8.42396i	0.219490	+	0.380168i	−0.735162	+	0.677891i	$0.762894\pi$
$492$			7.75052i			0.349421i
$493$	2.94341	+	5.09813i	0.132564	+	0.229608i
$494$	−11.5955	−	20.3260i	−0.521707	−	0.914512i
$495$	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	0.339514	−	0.940601i	$-0.389737\pi$
$499$	−6.82017	−	3.93763i	−0.305313	−	0.176272i	−0.644827	+	0.764329i	$0.723071\pi$
$500$			10.6408i			0.475872i
$501$			3.12015i			0.139398i
$502$	25.5967	+	14.7783i	1.14244	+	0.659586i
$503$	−4.87603	+	8.44553i	−0.217411	+	0.376568i	−0.954016	−	0.299756i	$-0.903095\pi$
$503$	−4.87603	+	8.44553i	−0.217411	+	0.376568i	0.736604	+	0.676324i	$0.236428\pi$
$504$		0			0
$505$	41.8259	−	24.1482i	1.86123	−	1.07458i
$506$	−4.52266	+	7.83348i	−0.201057	+	0.348241i
$507$	−2.28883	+	3.87134i	−0.101651	+	0.171932i
$508$	25.8315	+	44.7414i	1.14609	+	1.98508i
$509$			23.0256i			1.02059i	0.859999	+	0.510295i	$0.170464\pi$
$509$			23.0256i			1.02059i	−0.859999	+	0.510295i	$0.829536\pi$
$510$	−3.28019	−	5.68146i	−0.145249	−	0.251579i
$511$		0			0
$512$		−	11.8512i		−	0.523752i
$513$	4.22988	−	2.44212i	0.186754	−	0.107822i
$514$		−	11.2220i		−	0.494981i
$515$	−12.0846	+	6.97705i	−0.532511	+	0.307445i
$516$	7.97048	+	13.8053i	0.350881	+	0.607744i
$517$	5.42524	+	9.39679i	0.238602	+	0.413270i
$518$		0			0
$519$	2.10752			0.0925100
$520$	−52.9814	+	90.6802i	−2.32339	+	3.97659i
$521$	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	$0.829941\pi$
$522$	18.4356	+	10.6438i	0.806904	+	0.465866i
$523$	34.6270			1.51413			0.757065	−	0.653339i	$-0.226632\pi$
$523$	34.6270			1.51413			0.757065	+	0.653339i	$0.226632\pi$
$524$	49.5207	−	85.7724i	2.16332	−	3.74698i
$525$		0			0
$526$	9.48962	+	5.47883i	0.413767	+	0.238888i
$527$	3.24893	−	1.87577i	0.141526	−	0.0817099i
$528$	−7.49554	+	4.32755i	−0.326201	+	0.188332i
$529$	−19.7144			−0.857147
$530$	−81.9636			−3.56027
$531$	−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
$535$	53.9656	+	31.1571i	2.33314	+	1.34704i
$536$	3.69639	−	6.40234i	0.159660	−	0.276539i
$537$	0.671080	+	1.16234i	0.0289592	+	0.0501589i
$538$			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	0.0178050	−	0.999841i	$-0.494332\pi$
$541$	−19.5188	−	11.2692i	−0.839181	−	0.484501i	−0.856986	+	0.515340i	$0.827666\pi$
$542$	7.52844			0.323374
$543$	−1.13885	+	1.97255i	−0.0488728	+	0.0846502i
$544$		−	40.3818i		−	1.73136i
$545$	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	$0.181553\pi$
$548$		−	44.6955i		−	1.90930i
$549$	−14.5601	+	25.2189i	−0.621411	+	1.07631i
$550$	28.0217			1.19485
$551$	−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
$555$	−3.34517	−	5.79401i	−0.141995	−	0.245942i
$556$	46.8000	−	81.0600i	1.98476	−	3.43771i
$557$	−0.629579	−	0.363487i	−0.0266761	−	0.0154015i	0.486603	−	0.873623i	$-0.338236\pi$
$557$	−0.629579	−	0.363487i	−0.0266761	−	0.0154015i	−0.513279	+	0.858222i	$0.671569\pi$
$558$	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
$562$	36.1502			1.52490
$563$	41.6077			1.75355			0.876777	−	0.480897i	$-0.159689\pi$
$563$	41.6077			1.75355			0.876777	+	0.480897i	$0.159689\pi$
$564$	9.34597	−	5.39590i	0.393537	−	0.227208i
$565$	7.75879	−	4.47954i	0.326415	−	0.188456i
$566$	−44.2134	−	25.5266i	−1.85843	−	1.07296i
$567$		0			0
$568$	10.5237	−	18.2276i	0.441565	−	0.764813i
$569$	25.3888			1.06435			0.532177	−	0.846633i	$-0.321374\pi$
$569$	25.3888			1.06435			0.532177	+	0.846633i	$0.321374\pi$
$570$	6.33537	+	3.65773i	0.265360	+	0.153205i
$571$	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	$0.717577\pi$
$572$	30.5005	+	17.8204i	1.27529	+	0.745109i
$573$	−4.75451			−0.198622
$574$		0			0
$575$	−5.08929	−	8.81490i	−0.212238	−	0.367607i
$576$	−33.9776	−	58.8508i	−1.41573	−	2.45212i
$577$	13.8355	−	7.98794i	0.575980	−	0.332542i	−0.183554	−	0.983010i	$-0.558760\pi$
$577$	13.8355	−	7.98794i	0.575980	−	0.332542i	0.759534	+	0.650467i	$0.225427\pi$
$578$			33.4223i			1.39018i
$579$	6.81682	−	3.93570i	0.283298	−	0.163562i
$580$			47.2767i			1.96306i
$581$		0			0
$582$	−4.31660	−	7.47657i	−0.178929	−	0.309914i
$583$			17.1796i			0.711508i
$584$	−14.2812	−	24.7357i	−0.590959	−	1.02357i
$585$	−0.174984	+	33.8356i	−0.00723468	+	1.39893i
$586$	4.61963	−	8.00144i	0.190835	−	0.330536i
$587$	13.8404	−	7.99075i	0.571254	−	0.329814i	−0.186396	−	0.982475i	$-0.559681\pi$
$587$	13.8404	−	7.99075i	0.571254	−	0.329814i	0.757650	+	0.652661i	$0.226347\pi$
$588$		0			0
$589$	−2.09166	+	3.62287i	−0.0861855	+	0.149278i
$590$	−82.0116	−	47.3494i	−3.37637	−	1.94935i
$591$		−	5.02566i		−	0.206728i
$592$		−	80.4433i		−	3.30620i
$593$	−25.1608	−	14.5266i	−1.03323	−	0.596536i	−0.115322	−	0.993328i	$-0.536790\pi$
$593$	−25.1608	−	14.5266i	−1.03323	−	0.596536i	−0.917908	+	0.396792i	$0.870123\pi$
$594$	−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
$598$	0.0913640	−	17.6666i	0.00373615	−	0.722439i
$599$	−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	$0.855823\pi$
$600$		−	17.3675i		−	0.709026i
$601$	7.76518	+	13.4497i	0.316748	+	0.548624i	0.979808	−	0.199943i	$-0.0640756\pi$
$601$	7.76518	+	13.4497i	0.316748	+	0.548624i	−0.663059	+	0.748567i	$0.730742\pi$
$602$		0			0
$603$		−	2.38178i		−	0.0969936i
$604$	−86.8732	+	50.1563i	−3.53482	+	2.04083i
$605$			24.7363i			1.00567i
$606$	−12.0052	+	6.93118i	−0.487676	+	0.281560i
$607$	7.73922	+	13.4047i	0.314125	+	0.544081i	0.979251	−	0.202650i	$-0.0649555\pi$
$607$	7.73922	+	13.4047i	0.314125	+	0.544081i	−0.665126	+	0.746731i	$0.731622\pi$
$608$	22.5148	+	38.9967i	0.913095	+	1.58153i
$609$		0			0
$610$	−89.0429			−3.60524
$611$	−18.2982	−	10.6910i	−0.740266	−	0.432513i
$612$	−16.4571	−	28.5046i	−0.665240	−	1.15223i
$613$	6.17669	+	3.56611i	0.249474	+	0.144034i	0.619523	−	0.784978i	$-0.287326\pi$
$613$	6.17669	+	3.56611i	0.249474	+	0.144034i	−0.370049	+	0.929012i	$0.620659\pi$
$614$	44.2456			1.78561
$615$	−2.37902	+	4.12058i	−0.0959312	+	0.166158i
$616$		0			0
$617$	−4.30142	−	2.48342i	−0.173168	−	0.0999789i	0.410911	−	0.911676i	$-0.365211\pi$
$617$	−4.30142	−	2.48342i	−0.173168	−	0.0999789i	−0.584079	+	0.811697i	$0.698544\pi$
$618$	3.46860	−	2.00260i	0.139528	−	0.0805563i
$619$	36.6822	−	21.1785i	1.47438	−	0.851235i	0.474799	−	0.880094i	$-0.342521\pi$
$619$	36.6822	−	21.1785i	1.47438	−	0.851235i	0.999583	+	0.0288589i	$0.00918734\pi$
$620$	30.1284			1.20999
$621$	3.68741			0.147971
$622$	−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
$626$	12.1272	+	7.00162i	0.484699	+	0.279841i
$627$	0.766663	−	1.32790i	0.0306176	−	0.0530312i
$628$	30.7120	+	53.1947i	1.22554	+	2.12270i
$629$		−	12.7803i		−	0.509583i
$630$		0			0
$631$	−5.42803	−	3.13387i	−0.216086	−	0.124758i	0.388050	−	0.921638i	$-0.373149\pi$
$631$	−5.42803	−	3.13387i	−0.216086	−	0.124758i	−0.604137	+	0.796881i	$0.706482\pi$
$632$	−6.20874	−	3.58462i	−0.246971	−	0.142589i
$633$	1.49286			0.0593361
$634$	8.19794	−	14.1992i	0.325582	−	0.563924i
$635$			31.7158i			1.25860i
$636$	17.0868			0.677534
$637$		0			0
$638$	13.6434			0.540149
$639$		−	6.78098i		−	0.268251i
$640$	42.7898	−	74.1142i	1.69142	−	2.92962i
$641$	31.5637			1.24669			0.623345	−	0.781947i	$-0.285773\pi$
$641$	31.5637			1.24669			0.623345	+	0.781947i	$0.285773\pi$
$642$	−15.4896	−	8.94291i	−0.611325	−	0.352949i
$643$	−15.8053	−	9.12520i	−0.623300	−	0.359863i	0.154852	−	0.987938i	$-0.450510\pi$
$643$	−15.8053	−	9.12520i	−0.623300	−	0.359863i	−0.778153	+	0.628075i	$0.783843\pi$
$644$		0			0
$645$			9.78613i			0.385329i
$646$	6.98721	+	12.1022i	0.274908	+	0.476155i
$647$	−11.5137	+	19.9423i	−0.452649	+	0.784011i	−0.998550	−	0.0538387i	$-0.982854\pi$
$647$	−11.5137	+	19.9423i	−0.452649	+	0.784011i	0.545901	+	0.837850i	$0.316188\pi$
$648$	−61.4532	−	35.4800i	−2.41411	−	1.39379i
$649$	−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
$653$	28.8124			1.12752			0.563759	−	0.825939i	$-0.309355\pi$
$653$	28.8124			1.12752			0.563759	+	0.825939i	$0.309355\pi$
$654$	−3.99460			−0.156201
$655$	52.6555	−	30.4007i	2.05742	−	1.18785i
$656$	−49.5450	+	28.6048i	−1.93441	+	1.11683i
$657$	−7.96926	−	4.60105i	−0.310910	−	0.179504i
$658$		0			0
$659$	15.6114	−	27.0397i	0.608134	−	1.05332i	−0.383414	−	0.923577i	$-0.625252\pi$
$659$	15.6114	−	27.0397i	0.608134	−	1.05332i	0.991548	−	0.129742i	$-0.0414149\pi$
$660$	−11.0431			−0.429850
$661$	−23.0000	−	13.2791i	−0.894598	−	0.516496i	−0.0191541	−	0.999817i	$-0.506097\pi$
$661$	−23.0000	−	13.2791i	−0.894598	−	0.516496i	−0.875444	+	0.483320i	$0.839431\pi$
$662$	23.3487	+	40.4411i	0.907471	+	1.57179i
$663$	1.35486	−	2.31890i	0.0526183	−	0.0900587i
$664$	−89.1366			−3.45917
$665$		0			0
$666$	−23.1077	−	40.0237i	−0.895405	−	1.55089i
$667$	−2.47792	−	4.29188i	−0.0959454	−	0.166182i
$668$	−41.4538	+	23.9334i	−1.60390	+	0.926010i
$669$			8.09337i			0.312908i
$670$	6.30721	−	3.64147i	0.243669	−	0.140682i
$671$			18.6635i			0.720495i
$672$		0			0
$673$	−9.86930	−	17.0941i	−0.380434	−	0.658930i	0.610691	−	0.791869i	$-0.290892\pi$
$673$	−9.86930	−	17.0941i	−0.380434	−	0.658930i	−0.991124	+	0.132939i	$0.957559\pi$
$674$			22.5842i			0.869912i
$675$	−5.71165	−	9.89287i	−0.219842	−	0.380777i
$676$	−68.9908	−	0.713602i	−2.65349	−	0.0274462i
$677$	−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
$682$		−	8.69468i		−	0.332936i
$683$			6.76255i			0.258762i	0.991595	+	0.129381i	$0.0412990\pi$
$683$			6.76255i			0.258762i	−0.991595	+	0.129381i	$0.958701\pi$
$684$	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
$689$	−16.6266	−	29.1452i	−0.633424	−	1.11034i
$690$	2.76144	+	4.78296i	0.105126	+	0.182084i
$691$		−	9.17090i		−	0.348877i	−0.984668	−	0.174439i	$-0.944189\pi$
$691$		−	9.17090i		−	0.348877i	0.984668	−	0.174439i	$-0.0558111\pi$
$692$	16.1659	+	28.0002i	0.614537	+	1.06441i
$693$		0			0
$694$		−	77.9115i		−	2.95748i
$695$	49.7626	−	28.7304i	1.88760	−	1.08981i
$696$		−	8.45605i		−	0.320526i
$697$	−7.87137	+	4.54454i	−0.298150	+	0.172137i
$698$	−15.8435	−	27.4418i	−0.599686	−	1.03869i
$699$	−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	$0.146131\pi$
$702$	0.102537	−	19.8270i	0.00387000	−	0.748321i
$703$	7.12562	+	12.3419i	0.268748	+	0.465485i
$704$	−37.7181	−	21.7766i	−1.42156	−	0.820736i
$705$	6.62507			0.249515
$706$	24.1074	−	41.7552i	0.907294	−	1.57148i
$707$		0			0
$708$	17.0968	+	9.87082i	0.642535	+	0.370968i
$709$	−30.2866	+	17.4860i	−1.13744	+	0.656699i	−0.945795	−	0.324766i	$-0.894715\pi$
$709$	−30.2866	+	17.4860i	−1.13744	+	0.656699i	−0.191642	+	0.981465i	$0.561381\pi$
$710$	17.9567	−	10.3673i	0.673905	−	0.389079i
$711$	−2.30976			−0.0866227
$712$	135.117			5.06374
$713$	−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
$717$	−0.427821	−	0.247002i	−0.0159773	−	0.00922448i
$718$	7.67926	−	13.3009i	0.286588	−	0.496384i
$719$	4.18051	+	7.24085i	0.155907	+	0.270038i	0.933389	−	0.358867i	$-0.116837\pi$
$719$	4.18051	+	7.24085i	0.155907	+	0.270038i	−0.777482	+	0.628905i	$0.783503\pi$
$720$		−	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
$724$	−34.9427			−1.29863
$725$	−7.67639	+	13.2959i	−0.285094	+	0.493797i
$726$		−	7.09997i		−	0.263505i
$727$	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
$730$		−	28.1379i		−	1.04143i
$731$	−9.34703	+	16.1895i	−0.345712	+	0.598791i
$732$	18.5625			0.686092
$733$	−10.5282	−	6.07846i	−0.388868	−	0.224513i	0.292802	−	0.956173i	$-0.405412\pi$
$733$	−10.5282	−	6.07846i	−0.388868	−	0.224513i	−0.681670	+	0.731660i	$0.738746\pi$
$734$	45.9583	+	26.5340i	1.69635	+	0.979389i
$735$		0			0
$736$			33.9956i			1.25309i
$737$	−0.763255	−	1.32200i	−0.0281148	−	0.0486963i
$738$	−16.4337	+	28.4640i	−0.604934	+	1.04778i
$739$	41.9537	+	24.2220i	1.54329	+	0.891019i	0.998628	+	0.0523634i	$0.0166754\pi$
$739$	41.9537	+	24.2220i	1.54329	+	0.891019i	0.544662	+	0.838656i	$0.316658\pi$
$740$	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	−0.745004	−	0.667060i	$-0.767553\pi$
$743$	−14.7143	+	8.49532i	−0.539816	+	0.311663i	0.205188	+	0.978722i	$0.434219\pi$
$744$	−5.38886			−0.197565
$745$	−13.1010			−0.479985
$746$	−75.0642	+	43.3384i	−2.74830	+	1.58673i
$747$	−24.8702	+	14.3588i	−0.909955	+	0.525363i
$748$	−18.2689	−	10.5475i	−0.667977	−	0.385657i
$749$		0			0
$750$	0.937485	−	1.62377i	0.0342321	−	0.0592917i
$751$	−43.0323			−1.57027			−0.785136	−	0.619323i	$-0.787407\pi$
$751$	−43.0323			−1.57027			−0.785136	+	0.619323i	$0.787407\pi$
$752$	68.9863	+	39.8292i	2.51567	+	1.45242i
$753$	−1.89129	−	3.27581i	−0.0689225	−	0.119377i
$754$	−23.1461	+	13.2043i	−0.842930	+	0.480871i
$755$	−61.5817			−2.24119
$756$		0			0
$757$	−14.5892	−	25.2693i	−0.530255	−	0.918428i	−0.999377	−	0.0352949i	$-0.988763\pi$
$757$	−14.5892	−	25.2693i	−0.530255	−	0.918428i	0.469122	−	0.883133i	$-0.344570\pi$
$758$	25.7116	+	44.5337i	0.933886	+	1.61754i
$759$	1.00251	−	0.578801i	0.0363889	−	0.0210091i
$760$			69.9357i			2.53683i
$761$	−25.4829	+	14.7126i	−0.923754	+	0.533330i	−0.884831	−	0.465912i	$-0.845726\pi$
$761$	−25.4829	+	14.7126i	−0.923754	+	0.533330i	−0.0389234	+	0.999242i	$0.512393\pi$
$762$		−	9.10328i		−	0.329777i
$763$		0			0
$764$	−36.4699	−	63.1677i	−1.31943	−	2.28533i
$765$		−	20.2060i		−	0.730550i
$766$	−0.945888	−	1.63833i	−0.0341763	−	0.0591951i
$767$	0.200488	−	38.7673i	0.00723921	−	1.39981i
$768$	−4.11988	+	7.13584i	−0.148663	+	0.257492i
$769$	−14.8839	+	8.59322i	−0.536727	+	0.309879i	−0.743751	−	0.668456i	$-0.766955\pi$
$769$	−14.8839	+	8.59322i	−0.536727	+	0.309879i	0.207024	+	0.978336i	$0.433622\pi$
$770$		0			0
$771$	−0.718083	+	1.24376i	−0.0258611	+	0.0447928i
$772$	104.578	+	60.3782i	3.76385	+	2.17306i
$773$			21.9601i			0.789851i	0.918713	+	0.394926i	$0.129230\pi$
$773$			21.9601i			0.789851i	−0.918713	+	0.394926i	$0.870770\pi$
$774$			67.6004i			2.42985i
$775$	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
$780$	18.7345	−	10.6876i	0.670803	−	0.382677i
$781$	−2.17300	−	3.76375i	−0.0777561	−	0.134678i
$782$			10.5501i			0.377272i
$783$	−2.78094	−	4.81673i	−0.0993827	−	0.172136i
$784$		0			0
$785$			37.7081i			1.34586i
$786$	−15.1135	+	8.72581i	−0.539082	+	0.311239i
$787$		−	2.33567i		−	0.0832578i	−0.999133	−	0.0416289i	$-0.986745\pi$
$787$		−	2.33567i		−	0.0832578i	0.999133	−	0.0416289i	$-0.0132547\pi$
$788$	66.7702	−	38.5498i	2.37859	−	1.37328i
$789$	−0.701169	−	1.21446i	−0.0249623	−	0.0432359i
$790$	−3.53135	−	6.11648i	−0.125640	−	0.217615i
$791$		0			0
$792$	−47.5364			−1.68913
$793$	−18.0627	−	31.6625i	−0.641425	−	1.12437i
$794$	30.1140	+	52.1590i	1.06871	+	1.85105i
$795$	9.08420	+	5.24476i	0.322183	+	0.186013i
$796$	−126.527			−4.48465
$797$	−13.9020	+	24.0790i	−0.492434	+	0.852921i	−0.999962	−	0.00871411i	$-0.997226\pi$
$797$	−13.9020	+	24.0790i	−0.492434	+	0.852921i	0.507528	+	0.861635i	$0.330560\pi$
$798$		0			0
$799$	10.9601	+	6.32780i	0.387739	+	0.223861i
$800$	91.2059	−	52.6577i	3.22461	−	1.86173i
$801$	37.6995	−	21.7658i	1.33205	−	0.769057i
$802$	−12.9956			−0.458890
$803$	−5.89773			−0.208126
$804$	−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
$808$	−114.769	−	66.2620i	−4.03756	−	2.33109i
$809$	−7.51017	+	13.0080i	−0.264043	+	0.457337i	−0.967313	−	0.253587i	$-0.918390\pi$
$809$	−7.51017	+	13.0080i	−0.264043	+	0.457337i	0.703269	+	0.710924i	$0.251723\pi$
$810$	−34.9528	−	60.5401i	−1.22812	−	2.12716i
$811$		−	43.6933i		−	1.53428i	−0.641481	−	0.767139i	$-0.721680\pi$
$811$		−	43.6933i		−	1.53428i	0.641481	−	0.767139i	$-0.278320\pi$
$812$		0			0
$813$	−0.834393	−	0.481737i	−0.0292634	−	0.0168953i
$814$	−25.6516	−	14.8100i	−0.899089	−	0.519089i
$815$	−14.3534			−0.502778
$816$	−5.04750	+	8.74252i	−0.176698	+	0.306049i
$817$		−	20.8456i		−	0.729297i
$818$	99.4870			3.47848
$819$		0			0
$820$	−72.9939			−2.54906
$821$			18.0701i			0.630651i	0.948984	+	0.315326i	$0.102114\pi$
$821$			18.0701i			0.630651i	−0.948984	+	0.315326i	$0.897886\pi$
$822$	−3.93779	+	6.82045i	−0.137346	+	0.237890i
$823$	−4.45550			−0.155309			−0.0776544	−	0.996980i	$-0.524743\pi$
$823$	−4.45550			−0.155309			−0.0776544	+	0.996980i	$0.524743\pi$
$824$	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	$0.0659713\pi$
$827$			11.8352i			0.411549i	−0.978599	+	0.205774i	$0.934029\pi$
$828$	13.8545	+	23.9967i	0.481477	+	0.833942i
$829$	1.76947	−	3.06482i	0.0614563	−	0.106445i	−0.833660	−	0.552278i	$-0.813759\pi$
$829$	1.76947	−	3.06482i	0.0614563	−	0.106445i	0.895117	+	0.445832i	$0.147092\pi$
$830$	−76.0474	−	43.9060i	−2.63964	−	1.52400i
$831$	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
$835$	−29.3853			−1.01692
$836$	23.5230			0.813561
$837$	−3.06960	+	1.77223i	−0.106101	+	0.0612573i
$838$	68.5145	−	39.5569i	2.36679	−	1.36647i
$839$	28.9991	+	16.7426i	1.00116	+	0.578020i	0.908591	−	0.417686i	$-0.137159\pi$
$839$	28.9991	+	16.7426i	1.00116	+	0.578020i	0.0925687	+	0.995706i	$0.470492\pi$
$840$		0			0
$841$	10.7625	−	18.6411i	0.371119	−	0.642797i
$842$	−20.3784			−0.702285
$843$	−4.00660	−	2.31321i	−0.137995	−	0.0796713i
$844$	11.4512	+	19.8340i	0.394165	+	0.682714i
$845$	−36.4600	−	21.5561i	−1.25426	−	0.741551i
$846$	45.7645			1.57342
$847$		0			0
$848$	63.0620	+	109.227i	2.16556	+	3.75086i
$849$	3.26684	+	5.65833i	0.112118	+	0.194193i
$850$	28.3047	−	16.3417i	0.970844	−	0.560517i
$851$			10.7591i			0.368818i
$852$	−3.74340	+	2.16125i	−0.128247	+	0.0740433i
$853$		−	22.0871i		−	0.756248i	−0.925755	−	0.378124i	$-0.876569\pi$
$853$		−	22.0871i		−	0.756248i	0.925755	−	0.378124i	$-0.123431\pi$
$854$		0			0
$855$	11.2658	+	19.5129i	0.385282	+	0.667329i
$856$		−	170.988i		−	5.84426i
$857$	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	$0.795768\pi$
$858$	−3.08430	−	5.40654i	−0.105296	−	0.184576i
$859$	−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	0.735554	−	0.677466i	$-0.236922\pi$
$863$	15.1769	+	8.76241i	0.516629	+	0.298276i	−0.218925	+	0.975742i	$0.570255\pi$
$864$			38.1528i			1.29799i
$865$			19.8485i			0.674869i
$866$	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
$871$	2.57430	+	1.50408i	0.0872268	+	0.0509637i
$872$	−19.0942	−	33.0721i	−0.646610	−	1.11996i
$873$		−	26.5903i		−	0.899944i
$874$	−5.88221	−	10.1883i	−0.198969	−	0.344624i
$875$		0			0
$876$			5.86584i			0.198188i
$877$	40.4859	−	23.3745i	1.36711	−	0.789302i	0.376553	−	0.926395i	$-0.377109\pi$
$877$	40.4859	−	23.3745i	1.36711	−	0.789302i	0.990558	+	0.137093i	$0.0437760\pi$
$878$			26.9142i			0.908309i
$879$	−1.02401	+	0.591210i	−0.0345389	+	0.0199410i
$880$	−40.7565	−	70.5924i	−1.37390	−	2.37967i
$881$	1.45937	+	2.52771i	0.0491675	+	0.0851606i	0.889562	−	0.456815i	$-0.151010\pi$
$881$	1.45937	+	2.52771i	0.0491675	+	0.0851606i	−0.840394	+	0.541976i	$0.817677\pi$
$882$		0			0
$883$	28.5505			0.960801			0.480400	−	0.877049i	$-0.340491\pi$
$883$	28.5505			0.960801			0.480400	+	0.877049i	$0.340491\pi$
$884$	41.2011	+	0.213075i	1.38574	+	0.00716649i
$885$	6.05968	+	10.4957i	0.203694	+	0.352808i
$886$	−83.9993	−	48.4970i	−2.82201	−	1.62929i
$887$	−0.422914			−0.0142001			−0.00710004	−	0.999975i	$-0.502260\pi$
$887$	−0.422914			−0.0142001			−0.00710004	+	0.999975i	$0.502260\pi$
$888$	−9.17905	+	15.8986i	−0.308029	+	0.533521i
$889$		0			0
$890$	115.276	+	66.5548i	3.86407	+	2.23092i
$891$	−12.6892	+	7.32614i	−0.425106	+	0.245435i
$892$	−107.527	+	62.0809i	−3.60028	+	2.07862i
$893$	−14.1122			−0.472247
$894$	3.76035			0.125765
$895$	−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
$899$	4.12550	+	2.38186i	0.137593	+	0.0794394i
$900$	42.9200	−	74.3397i	1.43067	−	2.47799i
$901$	10.0189	+	17.3532i	0.333777	+	0.578118i
$902$			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
$906$	17.6756			0.587232
$907$	−11.2142	+	19.4236i	−0.372361	+	0.644949i	−0.989928	−	0.141570i	$-0.954785\pi$
$907$	−11.2142	+	19.4236i	−0.372361	+	0.644949i	0.617567	+	0.786518i	$0.288118\pi$
$908$			141.825i			4.70664i
$909$	−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	$0.681459\pi$
$912$		−	11.2569i		−	0.372752i
$913$	−9.20274	+	15.9396i	−0.304566	+	0.527524i
$914$	111.432			3.68583
$915$	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
$919$	4.93957	+	8.55558i	0.162941	+	0.282223i	0.935922	−	0.352207i	$-0.114569\pi$
$919$	4.93957	+	8.55558i	0.162941	+	0.282223i	−0.772981	+	0.634429i	$0.781235\pi$
$920$	−26.3993	+	45.7250i	−0.870361	+	1.50751i
$921$	−4.90383	−	2.83123i	−0.161587	−	0.0932922i
$922$	−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
$926$	−65.9734			−2.16802
$927$	12.3360			0.405168
$928$	44.4071	−	25.6385i	1.45774	−	0.841624i
$929$	25.9060	−	14.9568i	0.849947	−	0.490717i	−0.0106859	−	0.999943i	$-0.503401\pi$
$929$	25.9060	−	14.9568i	0.849947	−	0.490717i	0.860633	+	0.509226i	$0.170068\pi$
$930$	−4.59754	−	2.65439i	−0.150759	−	0.0870409i
$931$		0			0
$932$	31.0868	−	53.8439i	1.01828	−	1.76371i
$933$	8.19826			0.268399
$934$	−10.4143	−	6.01273i	−0.340768	−	0.196742i
$935$	−6.47512	−	11.2152i	−0.211759	−	0.366778i
$936$	80.6453	−	46.0061i	2.63597	−	1.50376i
$937$	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
$940$	50.8182	+	88.0197i	1.65751	+	2.87089i
$941$	36.4497	−	21.0443i	1.18823	−	0.686023i	0.230324	−	0.973114i	$-0.426021\pi$
$941$	36.4497	−	21.0443i	1.18823	−	0.686023i	0.957903	+	0.287091i	$0.0926881\pi$
$942$		−	10.8232i		−	0.352640i
$943$	6.62654	−	3.82584i	0.215790	−	0.124586i
$944$			145.721i			4.74280i
$945$		0			0
$946$	21.6629	+	37.5213i	0.704322	+	1.21992i
$947$			60.3377i			1.96071i	0.197234	+	0.980357i	$0.436804\pi$
$947$			60.3377i			1.96071i	−0.197234	+	0.980357i	$0.563196\pi$
$948$	0.736172	+	1.27509i	0.0239098	+	0.0414129i
$949$	10.0055	−	5.70788i	0.324792	−	0.185286i
$950$	−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	−0.971735	−	0.236073i	$-0.924139\pi$
$953$	−8.68770	+	15.0475i	−0.281422	+	0.487438i	0.690313	+	0.723511i	$0.257473\pi$
$954$	62.7516	+	36.2297i	2.03166	+	1.17298i
$955$		−	44.7776i		−	1.44897i
$956$		−	7.57862i		−	0.245110i
$957$	−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
$962$	57.8511	+	0.299182i	1.86520	+	0.00964600i
$963$	−27.5442	−	47.7079i	−0.887598	−	1.53737i
$964$			14.2218i			0.458054i
$965$	37.0661	+	64.2003i	1.19320	+	2.06668i
$966$		0			0
$967$			18.8630i			0.606594i	0.952896	+	0.303297i	$0.0980874\pi$
$967$			18.8630i			0.606594i	−0.952896	+	0.303297i	$0.901913\pi$
$968$	58.7820	−	33.9378i	1.88932	−	1.09080i
$969$		−	1.78842i		−	0.0574522i
$970$	70.4138	−	40.6534i	2.26085	−	1.30530i
$971$	−0.782231	−	1.35486i	−0.0251030	−	0.0434797i	0.853201	−	0.521582i	$-0.174658\pi$
$971$	−0.782231	−	1.35486i	−0.0251030	−	0.0434797i	−0.878304	+	0.478103i	$0.841325\pi$
$972$	23.4813	+	40.6708i	0.753164	+	1.30452i
$973$		0			0
$974$	−72.7582			−2.33132
$975$	7.00417	+	0.0362226i	0.224313	+	0.00116005i
$976$	68.5087	+	118.661i	2.19291	+	3.79823i
$977$	24.1409	+	13.9378i	0.772336	+	0.445909i	0.833707	−	0.552206i	$-0.186214\pi$
$977$	24.1409	+	13.9378i	0.772336	+	0.445909i	−0.0613710	+	0.998115i	$0.519547\pi$
$978$	4.11981			0.131737
$979$	13.9499	−	24.1620i	0.445842	−	0.772221i
$980$		0			0
$981$	−10.6550	−	6.15169i	−0.340189	−	0.196408i
$982$	22.7716	−	13.1472i	0.726672	−	0.419544i
$983$	−28.9460	+	16.7120i	−0.923233	+	0.533029i	−0.884665	−	0.466227i	$-0.845613\pi$
$983$	−28.9460	+	16.7120i	−0.923233	+	0.533029i	−0.0385681	+	0.999256i	$0.512280\pi$
$984$	13.0559			0.416207
$985$	47.3313			1.50810
$986$	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
$990$	−40.5559	−	23.4150i	−1.28895	−	0.744177i
$991$	9.45548	−	16.3774i	0.300363	−	0.520244i	−0.675855	−	0.737035i	$-0.736225\pi$
$991$	9.45548	−	16.3774i	0.300363	−	0.520244i	0.976218	+	0.216790i	$0.0695588\pi$
$992$	−16.3388	−	28.2997i	−0.518759	−	0.898517i
$993$		−	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
$997$	−43.5775			−1.38011			−0.690057	−	0.723755i	$-0.742415\pi$
$997$	−43.5775			−1.38011			−0.690057	+	0.723755i	$0.742415\pi$
$998$	−10.6442	+	18.4363i	−0.336936	+	0.583589i
$999$			12.0748i			0.382031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.g.569.1		12
7.2	even	3		637.2.q.h.491.1		12
7.3	odd	6		637.2.u.h.361.6		12
7.4	even	3		637.2.u.i.361.6		12
7.5	odd	6		91.2.q.a.36.1	✓	12
7.6	odd	2		637.2.k.h.569.1		12
13.4	even	6		637.2.u.i.30.6		12
21.5	even	6		819.2.ct.a.127.6		12
28.19	even	6		1456.2.cc.c.673.4		12
91.2	odd	12		8281.2.a.by.1.1		6
91.4	even	6	inner	637.2.k.g.459.6		12
91.17	odd	6		637.2.k.h.459.6		12
91.30	even	6		637.2.q.h.589.1		12
91.37	odd	12		8281.2.a.ch.1.6		6
91.54	even	12		1183.2.a.m.1.1		6
91.68	odd	6		1183.2.c.i.337.1		12
91.69	odd	6		637.2.u.h.30.6		12
91.75	odd	6		1183.2.c.i.337.12		12
91.82	odd	6		91.2.q.a.43.1	yes	12
91.89	even	12		1183.2.a.p.1.6		6
273.173	even	6		819.2.ct.a.316.6		12
364.355	even	6		1456.2.cc.c.225.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.1	✓	12	7.5	odd	6
91.2.q.a.43.1	yes	12	91.82	odd	6
637.2.k.g.459.6		12	91.4	even	6	inner
637.2.k.g.569.1		12	1.1	even	1	trivial
637.2.k.h.459.6		12	91.17	odd	6
637.2.k.h.569.1		12	7.6	odd	2
637.2.q.h.491.1		12	7.2	even	3
637.2.q.h.589.1		12	91.30	even	6
637.2.u.h.30.6		12	91.69	odd	6
637.2.u.h.361.6		12	7.3	odd	6
637.2.u.i.30.6		12	13.4	even	6
637.2.u.i.361.6		12	7.4	even	3
819.2.ct.a.127.6		12	21.5	even	6
819.2.ct.a.316.6		12	273.173	even	6
1183.2.a.m.1.1		6	91.54	even	12
1183.2.a.p.1.6		6	91.89	even	12
1183.2.c.i.337.1		12	91.68	odd	6
1183.2.c.i.337.12		12	91.75	odd	6
1456.2.cc.c.225.4		12	364.355	even	6
1456.2.cc.c.673.4		12	28.19	even	6
8281.2.a.by.1.1		6	91.2	odd	12
8281.2.a.ch.1.6		6	91.37	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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.70320i q^{2} +(-0.172975 + 0.299601i) q^{3} -5.30727 q^{4} +(-2.82162 - 1.62906i) q^{5} +(0.809880 + 0.467584i) q^{6} +8.94020i q^{8} +(1.44016 + 2.49443i) q^{9} +O(q^{10})\)	\(q-2.70320i q^{2} +(-0.172975 + 0.299601i) q^{3} -5.30727 q^{4} +(-2.82162 - 1.62906i) q^{5} +(0.809880 + 0.467584i) q^{6} +8.94020i q^{8} +(1.44016 + 2.49443i) q^{9} +(-4.40367 + 7.62739i) q^{10} +(1.59871 + 0.923014i) q^{11} +(0.918023 - 1.59006i) q^{12} +(-3.60550 - 0.0186461i) q^{13} +(0.976136 - 0.563573i) q^{15} +13.5526 q^{16} +2.15314 q^{17} +(6.74293 - 3.89303i) q^{18} +(-2.07929 + 1.20048i) q^{19} +(14.9751 + 8.64587i) q^{20} +(2.49509 - 4.32162i) q^{22} -1.81263 q^{23} +(-2.67849 - 1.54643i) q^{24} +(2.80769 + 4.86305i) q^{25} +(-0.0504042 + 9.74638i) q^{26} -2.03429 q^{27} +(1.36703 + 2.36777i) q^{29} +(-1.52345 - 2.63869i) q^{30} +(1.50893 - 0.871180i) q^{31} -18.7549i q^{32} +(-0.553071 + 0.319316i) q^{33} -5.82036i q^{34} +(-7.64331 - 13.2386i) q^{36} -5.93565i q^{37} +(3.24513 + 5.62072i) q^{38} +(0.629247 - 1.07699i) 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} -9.38444i q^{45} +4.89989i 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} +(19.1354 + 0.0989601i) q^{52} +(4.65314 + 8.05947i) q^{53} +5.49909i q^{54} +(-3.00729 - 5.20878i) q^{55} -0.830609i q^{57} +(6.40054 - 3.69535i) q^{58} +10.7523i q^{59} +(-5.18062 + 2.99103i) q^{60} +(5.05504 + 8.75558i) q^{61} +(-2.35497 - 4.07893i) q^{62} -23.5929 q^{64} +(10.1430 + 5.92620i) q^{65} +(0.863173 + 1.49506i) q^{66} +(-0.716130 - 0.413458i) q^{67} -11.4273 q^{68} +(0.313538 - 0.543065i) q^{69} +(-2.03884 - 1.17712i) q^{71} +(-22.3007 + 12.8753i) q^{72} +(-2.76680 + 1.59741i) q^{73} -16.0452 q^{74} -1.94263 q^{75} +(11.0353 - 6.37126i) q^{76} +(-2.91130 - 1.70098i) q^{78} +(-0.400955 + 0.694475i) q^{79} +(-38.2402 - 22.0780i) q^{80} +(-3.96860 + 6.87381i) q^{81} +(5.70552 + 9.88225i) q^{82} +9.97031i q^{83} +(-6.07534 - 3.50760i) q^{85} +(20.3254 + 11.7349i) q^{86} -0.945847 q^{87} +(-8.25193 + 14.2928i) q^{88} -15.1135i q^{89} -25.3680 q^{90} +9.62010 q^{92} +0.602768i q^{93} +(7.94435 - 13.7600i) q^{94} +7.82261 q^{95} +(5.61897 + 3.24411i) q^{96} +(-7.99489 - 4.61585i) q^{97} +5.31715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9	\( 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9} - 12 q^{10} - 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{15} + 16 q^{16} - 8 q^{17} + 12 q^{18} + 12 q^{20} + 6 q^{22} + 24 q^{23} + 12 q^{24} + 10 q^{25} - 18 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 18 q^{31} - 30 q^{33} - 10 q^{36} + 2 q^{38} + 14 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} - 24 q^{44} + 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} + 28 q^{52} + 22 q^{53} + 6 q^{55} + 12 q^{58} - 66 q^{60} - 14 q^{61} + 4 q^{62} - 52 q^{64} - 18 q^{65} - 26 q^{66} + 24 q^{67} - 16 q^{68} - 4 q^{69} - 24 q^{71} - 60 q^{72} + 30 q^{73} - 12 q^{74} + 92 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 60 q^{86} - 4 q^{87} - 14 q^{88} - 24 q^{90} + 24 q^{92} - 4 q^{94} + 44 q^{95} + 6 q^{96} - 6 q^{97}+O(q^{100}) \) 12 * q - 8 * q^4 - 6 * q^5 + 18 * q^6 - 4 * q^9 - 12 * q^10 - 6 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^15 + 16 * q^16 - 8 * q^17 + 12 * q^18 + 12 * q^20 + 6 * q^22 + 24 * q^23 + 12 * q^24 + 10 * q^25 - 18 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 18 * q^31 - 30 * q^33 - 10 * q^36 + 2 * q^38 + 14 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 - 24 * q^44 + 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 + 28 * q^52 + 22 * q^53 + 6 * q^55 + 12 * q^58 - 66 * q^60 - 14 * q^61 + 4 * q^62 - 52 * q^64 - 18 * q^65 - 26 * q^66 + 24 * q^67 - 16 * q^68 - 4 * q^69 - 24 * q^71 - 60 * q^72 + 30 * q^73 - 12 * q^74 + 92 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 60 * q^86 - 4 * q^87 - 14 * q^88 - 24 * q^90 + 24 * q^92 - 4 * q^94 + 44 * q^95 + 6 * q^96 - 6 * q^97

Introduction

L-functions

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Database

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