LMFDB - Embedded newform 637.2.q.h.491.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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([0, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
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			491.1
Root			$-1.12906 - 0.851598i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.h.589.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.34104 + 1.35160i) q^{2} +(-0.172975 - 0.299601i) q^{3} +(2.65363 - 4.59623i) q^{4} +3.25812i q^{5} +(0.809880 + 0.467584i) q^{6} +8.94020i q^{8} +(1.44016 - 2.49443i) q^{9} +O(q^{10})$	\(q+(-2.34104 + 1.35160i) q^{2} +(-0.172975 - 0.299601i) q^{3} +(2.65363 - 4.59623i) q^{4} +3.25812i 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} -1.83605 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} +7.78607i q^{18} +(2.07929 + 1.20048i) q^{19} +(14.9751 + 8.64587i) q^{20} +(2.49509 - 4.32162i) q^{22} +(0.906314 + 1.56978i) q^{23} +(2.67849 - 1.54643i) q^{24} -5.61537 q^{25} +(8.46582 - 4.82954i) q^{26} -2.03429 q^{27} +(1.36703 + 2.36777i) q^{29} +(-1.52345 + 2.63869i) q^{30} +1.74236i q^{31} +(16.2422 + 9.37743i) q^{32} +(0.553071 + 0.319316i) q^{33} -5.82036i q^{34} +(-7.64331 - 13.2386i) q^{36} +(-5.14042 + 2.96783i) q^{37} -6.49025 q^{38} +(0.618074 + 1.08344i) q^{39} -29.1283 q^{40} +(-3.65577 + 2.11066i) q^{41} +(-4.34111 + 7.51903i) q^{43} +9.79737i q^{44} +(8.12716 + 4.69222i) q^{45} +(-4.24343 - 2.44994i) q^{46} -5.87774i q^{47} +(-2.34425 + 4.06036i) q^{48} +(13.1458 - 7.58972i) q^{50} +0.744877 q^{51} +(-9.65339 + 16.5222i) q^{52} -9.30628 q^{53} +(4.76235 - 2.74954i) q^{54} +(-3.00729 - 5.20878i) q^{55} -0.830609i q^{57} +(-6.40054 - 3.69535i) q^{58} +(-9.31173 - 5.37613i) q^{59} -5.98206i q^{60} +(5.05504 - 8.75558i) q^{61} +(-2.35497 - 4.07893i) q^{62} -23.5929 q^{64} +(0.0607514 - 11.7472i) q^{65} -1.72635 q^{66} +(0.716130 - 0.413458i) q^{67} +(5.71365 + 9.89633i) q^{68} +(0.313538 - 0.543065i) q^{69} +(-2.03884 - 1.17712i) q^{71} +(22.3007 + 12.8753i) q^{72} -3.19482i 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} +0.801911 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} -23.4698i q^{86} +(0.472923 - 0.819127i) q^{87} +(-8.25193 - 14.2928i) q^{88} +(-13.0886 + 7.55674i) q^{89} -25.3680 q^{90} +9.62010 q^{92} +(0.522012 - 0.301384i) q^{93} +(7.94435 + 13.7600i) q^{94} +(-3.91130 + 6.77458i) q^{95} -6.48823i q^{96} +(-7.99489 - 4.61585i) q^{97} +5.31715i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9	$ 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.34104	+	1.35160i	−1.65536	+	0.955724i	−0.680549	+	0.732702i	$0.738259\pi$
$2$	−2.34104	+	1.35160i	−1.65536	+	0.955724i	−0.974813	+	0.223022i	$0.928408\pi$
$3$	−0.172975	−	0.299601i	−0.0998669	−	0.172975i	0.811763	−	0.583988i	$-0.198508\pi$
$3$	−0.172975	−	0.299601i	−0.0998669	−	0.172975i	−0.911629	+	0.411013i	$0.865175\pi$
$4$	2.65363	−	4.59623i	1.32682	−	2.29811i
$5$			3.25812i			1.45708i	0.685005	+	0.728539i	$0.259800\pi$
$5$			3.25812i			1.45708i	−0.685005	+	0.728539i	$0.740200\pi$
$6$	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	$-0.756437\pi$
$11$	−1.59871	+	0.923014i	−0.482028	+	0.278299i	0.239233	+	0.970962i	$0.423104\pi$
$12$	−1.83605			−0.530021
$13$	−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	$0.250754\pi$
$18$			7.78607i			1.83519i
$19$	2.07929	+	1.20048i	0.477021	+	0.275408i	0.719174	−	0.694830i	$-0.244520\pi$
$19$	2.07929	+	1.20048i	0.477021	+	0.275408i	−0.242153	+	0.970238i	$0.577854\pi$
$20$	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	$0.772815\pi$
$24$	2.67849	−	1.54643i	0.546744	−	0.315663i
$25$	−5.61537			−1.12307
$26$	8.46582	−	4.82954i	1.66028	−	0.947151i
$27$	−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
$31$			1.74236i			0.312937i	0.987683	+	0.156468i	$0.0500110\pi$
$31$			1.74236i			0.312937i	−0.987683	+	0.156468i	$0.949989\pi$
$32$	16.2422	+	9.37743i	2.87124	+	1.65771i
$33$	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
$37$	−5.14042	+	2.96783i	−0.845081	+	0.487908i	−0.858988	−	0.511996i	$-0.828906\pi$
$37$	−5.14042	+	2.96783i	−0.845081	+	0.487908i	0.0139073	+	0.999903i	$0.495573\pi$
$38$	−6.49025			−1.05286
$39$	0.618074	+	1.08344i	0.0989710	+	0.173489i
$40$	−29.1283			−4.60558
$41$	−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	$0.936369\pi$
$44$			9.79737i			1.47701i
$45$	8.12716	+	4.69222i	1.21153	+	0.699475i
$46$	−4.24343	−	2.44994i	−0.625659	−	0.361224i
$47$		−	5.87774i		−	0.857357i	−0.903457	−	0.428678i	$-0.858979\pi$
$47$		−	5.87774i		−	0.857357i	0.903457	−	0.428678i	$-0.141021\pi$
$48$	−2.34425	+	4.06036i	−0.338363	+	0.586062i
$49$		0			0
$50$	13.1458	−	7.58972i	1.85910	−	1.07335i
$51$	0.744877			0.104304
$52$	−9.65339	+	16.5222i	−1.33868	+	2.29122i
$53$	−9.30628			−1.27832			−0.639158	−	0.769076i	$-0.720717\pi$
$53$	−9.30628			−1.27832			−0.639158	+	0.769076i	$0.720717\pi$
$54$	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
$58$	−6.40054	−	3.69535i	−0.840432	−	0.485224i
$59$	−9.31173	−	5.37613i	−1.21228	−	0.699912i	−0.249028	−	0.968496i	$-0.580111\pi$
$59$	−9.31173	−	5.37613i	−1.21228	−	0.699912i	−0.963256	+	0.268584i	$0.913444\pi$
$60$		−	5.98206i		−	0.772281i
$61$	5.05504	−	8.75558i	0.647231	−	1.12104i	−0.336550	−	0.941665i	$-0.609260\pi$
$61$	5.05504	−	8.75558i	0.647231	−	1.12104i	0.983781	−	0.179371i	$-0.0574064\pi$
$62$	−2.35497	−	4.07893i	−0.299081	−	0.518024i
$63$		0			0
$64$	−23.5929			−2.94911
$65$	0.0607514	−	11.7472i	0.00753529	−	1.45706i
$66$	−1.72635			−0.212499
$67$	0.716130	−	0.413458i	0.0874892	−	0.0505119i	−0.455617	−	0.890176i	$-0.650581\pi$
$67$	0.716130	−	0.413458i	0.0874892	−	0.0505119i	0.543106	+	0.839664i	$0.317248\pi$
$68$	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	0.374114	−	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
$73$		−	3.19482i		−	0.373925i	−0.982367	−	0.186963i	$-0.940136\pi$
$73$		−	3.19482i		−	0.373925i	0.982367	−	0.186963i	$-0.0598644\pi$
$74$	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
$79$	0.801911			0.0902220			0.0451110	−	0.998982i	$-0.485636\pi$
$79$	0.801911			0.0902220			0.0451110	+	0.998982i	$0.485636\pi$
$80$	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
$86$		−	23.4698i		−	2.53081i
$87$	0.472923	−	0.819127i	0.0507027	−	0.0878196i
$88$	−8.25193	−	14.2928i	−0.879658	−	1.52361i
$89$	−13.0886	+	7.55674i	−1.38739	+	0.801012i	−0.993021	−	0.117938i	$-0.962372\pi$
$89$	−13.0886	+	7.55674i	−1.38739	+	0.801012i	−0.394373	+	0.918950i	$0.629038\pi$
$90$	−25.3680			−2.67402
$91$		0			0
$92$	9.62010			1.00296
$93$	0.522012	−	0.301384i	0.0541301	−	0.0312520i
$94$	7.94435	+	13.7600i	0.819397	+	1.41924i
$95$	−3.91130	+	6.77458i	−0.401291	+	0.695057i
$96$		−	6.48823i		−	0.662202i
$97$	−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	−0.953622	−	0.301007i	$-0.902677\pi$
$101$	−7.41169	−	12.8374i	−0.737491	−	1.27737i	0.216131	−	0.976364i	$-0.430656\pi$
$102$	−1.74378	+	1.00677i	−0.172660	+	0.0996855i
$103$	−4.28286			−0.422003			−0.211001	−	0.977486i	$-0.567672\pi$
$103$	−4.28286			−0.422003			−0.211001	+	0.977486i	$0.567672\pi$
$104$	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
$109$		−	4.27153i		−	0.409139i	−0.978852	−	0.204569i	$-0.934421\pi$
$109$		−	4.27153i		−	0.409139i	0.978852	−	0.204569i	$-0.0655794\pi$
$110$	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	$0.207952\pi$
$114$	1.12265	+	1.94448i	0.105146	+	0.182118i
$115$	−5.11454	+	2.95288i	−0.476934	+	0.275358i
$116$	14.5104			1.34726
$117$	−5.23901	+	8.96682i	−0.484347	+	0.828983i
$118$	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
$122$			27.3295i			2.47430i
$123$	1.26471	+	0.730180i	0.114035	+	0.0658381i
$124$	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	$0.975488\pi$
$128$	22.7475	−	13.1333i	2.01061	−	1.16083i
$129$	3.00361			0.264453
$130$	15.7352	+	27.5827i	1.38007	+	2.41916i
$131$	18.6615			1.63046			0.815230	−	0.579138i	$-0.196611\pi$
$131$	18.6615			1.63046			0.815230	+	0.579138i	$0.196611\pi$
$132$	2.93530	−	1.69470i	0.255485	−	0.147504i
$133$		0			0
$134$	−1.11766	+	1.93584i	−0.0965509	+	0.167231i
$135$		−	6.62797i		−	0.570445i
$136$	−16.6706	−	9.62475i	−1.42949	−	0.825315i
$137$	−7.29328	−	4.21078i	−0.623107	−	0.359751i	0.154971	−	0.987919i	$-0.450472\pi$
$137$	−7.29328	−	4.21078i	−0.623107	−	0.359751i	−0.778078	+	0.628168i	$0.783805\pi$
$138$			1.69511i			0.144298i
$139$	−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
$142$	6.36399			0.534054
$143$	5.78135	−	3.29812i	0.483461	−	0.275803i
$144$	−39.0357			−3.25298
$145$	−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
$149$	−3.48232	−	2.01052i	−0.285283	−	0.164708i	0.350530	−	0.936552i	$-0.386002\pi$
$149$	−3.48232	−	2.01052i	−0.285283	−	0.164708i	−0.635813	+	0.771843i	$0.719335\pi$
$150$	−4.54777	−	2.62566i	−0.371324	−	0.214384i
$151$			18.9010i			1.53814i	0.639165	+	0.769069i	$0.279280\pi$
$151$			18.9010i			1.53814i	−0.639165	+	0.769069i	$0.720720\pi$
$152$	−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
$156$	6.61987	+	0.0342352i	0.530014	+	0.00274101i
$157$	11.5735			0.923670			0.461835	−	0.886966i	$-0.347191\pi$
$157$	11.5735			0.923670			0.461835	+	0.886966i	$0.347191\pi$
$158$	−1.87730	+	1.08386i	−0.149350	+	0.0862273i
$159$	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
$163$	−3.81520	−	2.20271i	−0.298830	−	0.172529i	0.343087	−	0.939304i	$-0.388527\pi$
$163$	−3.81520	−	2.20271i	−0.298830	−	0.172529i	−0.641917	+	0.766774i	$0.721861\pi$
$164$			22.4037i			1.74943i
$165$	−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	−0.166362	−	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
$170$	18.9635			1.45443
$171$	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	−0.958274	−	0.285851i	$-0.907724\pi$
$173$	−3.04600	+	5.27583i	−0.231583	+	0.401114i	0.726691	+	0.686964i	$0.241057\pi$
$174$			2.55681i			0.193831i
$175$		0			0
$176$	21.6666	+	12.5092i	1.63318	+	0.942917i
$177$			3.71974i			0.279592i
$178$	20.4273	−	35.3812i	1.53109	−	2.65193i
$179$	1.93982	+	3.35987i	0.144989	+	0.251128i	0.929369	−	0.369152i	$-0.120352\pi$
$179$	1.93982	+	3.35987i	0.144989	+	0.251128i	−0.784380	+	0.620281i	$0.787019\pi$
$180$	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
$185$	−9.66954	−	16.7481i	−0.710919	−	1.23135i
$186$	−0.814700	+	1.41110i	−0.0597367	+	0.103467i
$187$		−	3.97476i		−	0.290663i
$188$	−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	−0.502777	−	0.864416i	$-0.667688\pi$
$191$	6.87168	−	11.9021i	0.497218	−	0.861206i	0.999995	+	0.00320983i	$0.00102172\pi$
$192$	4.08097	+	7.06845i	0.294519	+	0.510122i
$193$	19.7047	−	11.3765i	1.41838	−	0.818899i	0.422219	−	0.906494i	$-0.361251\pi$
$193$	19.7047	−	11.3765i	1.41838	−	0.818899i	0.996156	+	0.0875946i	$0.0279180\pi$
$194$	24.9551			1.79167
$195$	−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	$0.506474\pi$
$198$	−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	$0.846266\pi$
$200$		−	50.2025i		−	3.54985i
$201$	−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
$205$	−6.87678	−	11.9109i	−0.480295	−	0.831896i
$206$	10.0263	−	5.78871i	0.698568	−	0.403318i
$207$	5.22095			0.362881
$208$	24.2131	+	42.4437i	1.67887	+	2.94294i
$209$	−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
$213$			0.814450i			0.0558052i
$214$	−44.7741	−	25.8504i	−3.06070	−	1.76709i
$215$	−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
$219$	−0.957171	+	0.552623i	−0.0646796	+	0.0373428i
$220$	−31.9210			−2.15212
$221$	3.91635	−	6.70301i	0.263442	−	0.450893i
$222$	−5.55083			−0.372548
$223$	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
$226$		−	7.43315i		−	0.494446i
$227$	23.1427	+	13.3614i	1.53603	+	0.886829i	0.999065	+	0.0432270i	$0.0137639\pi$
$227$	23.1427	+	13.3614i	1.53603	+	0.886829i	0.536968	+	0.843602i	$0.319569\pi$
$228$	−3.81767	−	2.20413i	−0.252831	−	0.145972i
$229$			3.00670i			0.198688i	0.995053	+	0.0993442i	$0.0316745\pi$
$229$			3.00670i			0.198688i	−0.995053	+	0.0993442i	$0.968326\pi$
$230$	7.98222	−	13.8256i	0.526332	−	0.911634i
$231$		0			0
$232$	−21.1683	+	12.2215i	−1.38977	+	0.802383i
$233$	11.7148			0.767462			0.383731	−	0.923445i	$-0.374639\pi$
$233$	11.7148			0.767462			0.383731	+	0.923445i	$0.374639\pi$
$234$	0.145180	−	28.0727i	0.00949072	−	1.83517i
$235$	19.1504			1.24924
$236$	−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	$0.0147060\pi$
$239$			1.42797i			0.0923677i	−0.998933	+	0.0461838i	$0.985294\pi$
$240$	−13.2292	−	7.63786i	−0.853938	−	0.493021i
$241$	2.32068	+	1.33984i	0.149488	+	0.0863069i	0.572878	−	0.819640i	$-0.305827\pi$
$241$	2.32068	+	1.33984i	0.149488	+	0.0863069i	−0.423390	+	0.905947i	$0.639160\pi$
$242$		−	20.5232i		−	1.31928i
$243$	−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
$247$	−7.47450	−	4.36710i	−0.475591	−	0.277872i
$248$	−15.5770			−0.989143
$249$	2.98711	−	1.72461i	0.189301	−	0.109293i
$250$	2.70989	+	4.69367i	0.171389	+	0.296854i
$251$	−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
$255$			2.42690i			0.151978i
$256$	−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
$261$	7.87497			0.487448
$262$	−43.6872	+	25.2228i	−2.69900	+	1.55827i
$263$	−2.02680	−	3.51052i	−0.124978	−	0.216468i	0.796747	−	0.604314i	$-0.206553\pi$
$263$	−2.02680	−	3.51052i	−0.124978	−	0.216468i	−0.921724	+	0.387846i	$0.873219\pi$
$264$	−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
$268$		−	4.38866i		−	0.268080i
$269$	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	$0.127752\pi$
$270$	8.95836	+	15.5163i	0.545188	+	0.944294i
$271$	2.41189	−	1.39251i	0.146512	−	0.0845888i	−0.424952	−	0.905216i	$-0.639709\pi$
$271$	2.41189	−	1.39251i	0.146512	−	0.0845888i	0.571464	+	0.820627i	$0.306376\pi$
$272$	29.1806			1.76933
$273$		0			0
$274$	22.7651			1.37529
$275$	8.97733	−	5.18306i	0.541353	−	0.312551i
$276$	−1.66403	−	2.88219i	−0.100163	−	0.173487i
$277$	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	$-0.000541901\pi$
$278$		−	47.6741i		−	2.85930i
$279$	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	0.997380	+	0.0723362i	$0.0230455\pi$
$283$	9.44312	+	16.3560i	0.561335	+	0.972261i	−0.436045	+	0.899925i	$0.643621\pi$
$284$	−10.8207	+	6.24731i	−0.642088	+	0.370710i
$285$	2.70623			0.160303
$286$	−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
$291$			3.19370i			0.187218i
$292$	−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
$296$	−26.5329	−	45.9564i	−1.54220	−	2.67116i
$297$	3.25224	−	1.87768i	0.188714	−	0.108954i
$298$	10.8697			0.629663
$299$	−3.23845	−	5.67675i	−0.187284	−	0.328295i
$300$	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
$304$		−	32.5391i		−	1.86625i
$305$	28.5268	+	16.4699i	1.63344	+	0.943066i
$306$	−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
$310$	13.2896	−	7.67278i	0.754801	−	0.435785i
$311$	23.6979			1.34378			0.671891	−	0.740650i	$-0.265482\pi$
$311$	23.6979			1.34378			0.671891	+	0.740650i	$0.265482\pi$
$312$	−9.68614	+	5.52570i	−0.548370	+	0.312831i
$313$	5.18025			0.292805			0.146403	−	0.989225i	$-0.453231\pi$
$313$	5.18025			0.292805			0.146403	+	0.989225i	$0.453231\pi$
$314$	−27.0941	+	15.6428i	−1.52901	+	0.882774i
$315$		0			0
$316$	2.12798	−	3.68577i	0.119708	−	0.207341i
$317$		−	6.06537i		−	0.340665i	−0.985387	−	0.170332i	$-0.945516\pi$
$317$		−	6.06537i		−	0.340665i	0.985387	−	0.170332i	$-0.0544842\pi$
$318$	−7.53697	−	4.35147i	−0.422652	−	0.244018i
$319$	−4.37096	−	2.52358i	−0.244727	−	0.141293i
$320$		−	76.8686i		−	4.29709i
$321$	3.30827	−	5.73010i	0.184650	−	0.319823i
$322$		0			0
$323$	−4.47700	+	2.58480i	−0.249107	+	0.143822i
$324$	−42.1248			−2.34027
$325$	20.2462	+	0.104705i	1.12306	+	0.00580799i
$326$	11.9087			0.659562
$327$	−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
$331$	14.9605	+	8.63743i	0.822301	+	0.474756i	0.851209	−	0.524826i	$-0.175870\pi$
$331$	14.9605	+	8.63743i	0.822301	+	0.474756i	−0.0289082	+	0.999582i	$0.509203\pi$
$332$	45.8258	+	26.4576i	2.51502	+	1.45205i
$333$			17.0966i			0.936886i
$334$	−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	$0.573073\pi$
$338$	−30.6136	+	17.2551i	−1.66516	+	0.938552i
$339$	0.951279			0.0516664
$340$	−32.2435	+	18.6158i	−1.74865	+	1.00958i
$341$	−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
$345$	1.76937	+	1.02155i	0.0952598	+	0.0549983i
$346$		−	16.4679i		−	0.885318i
$347$	−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	−0.203054	−	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
$352$	−34.6220			−1.84536
$353$	−15.4466	+	8.91811i	−0.822141	+	0.474663i	−0.851154	−	0.524916i	$-0.824097\pi$
$353$	−15.4466	+	8.91811i	−0.822141	+	0.474663i	0.0290134	+	0.999579i	$0.490763\pi$
$354$	−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
$359$		−	5.68162i		−	0.299864i	−0.988696	−	0.149932i	$-0.952094\pi$
$359$		−	5.68162i		−	0.299864i	0.988696	−	0.149932i	$-0.0479055\pi$
$360$	−41.9494	+	72.6584i	−2.21093	+	3.82943i
$361$	−6.61771	−	11.4622i	−0.348300	−	0.603274i
$362$	−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
$367$	−9.81580	−	17.0015i	−0.512381	−	0.887469i	−0.999897	−	0.0143554i	$-0.995430\pi$
$367$	−9.81580	−	17.0015i	−0.512381	−	0.887469i	0.487516	−	0.873114i	$-0.337903\pi$
$368$	12.2829	−	21.2746i	0.640289	−	1.10901i
$369$			12.1587i			0.632958i
$370$	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	0.0678240	+	0.997697i	$0.478394\pi$
$373$	−16.0323	+	27.7687i	−0.830119	+	1.43781i	−0.897943	+	0.440111i	$0.854939\pi$
$374$	5.37227	+	9.30505i	0.277794	+	0.481153i
$375$	−0.600686	+	0.346806i	−0.0310193	+	0.0179090i
$376$	52.5482			2.70997
$377$	−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	$0.495816\pi$
$380$	20.7583	+	35.9545i	1.06488	+	1.84443i
$381$	−1.68380	+	2.91643i	−0.0862637	+	0.149413i
$382$			37.1510i			1.90081i
$383$	−0.606070	−	0.349915i	−0.0309687	−	0.0178798i	0.484436	−	0.874827i	$-0.339025\pi$
$383$	−0.606070	−	0.349915i	−0.0309687	−	0.0178798i	−0.515404	+	0.856947i	$0.672358\pi$
$384$	−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
$388$	−42.4310	+	24.4976i	−2.15411	+	1.24368i
$389$	20.0547			1.01681			0.508407	−	0.861117i	$-0.330235\pi$
$389$	20.0547			1.01681			0.508407	+	0.861117i	$0.330235\pi$
$390$	5.54200	−	9.48539i	0.280630	−	0.480311i
$391$	−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
$395$			2.61272i			0.131460i
$396$	24.4388	+	14.1098i	1.22810	+	0.709043i
$397$	19.2953	+	11.1401i	0.968403	+	0.559108i	0.898749	−	0.438463i	$-0.144477\pi$
$397$	19.2953	+	11.1401i	0.968403	+	0.559108i	0.0696541	+	0.997571i	$0.477810\pi$
$398$		−	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	−0.600340	−	0.799745i	$-0.704968\pi$
$401$	−4.16341	+	2.40374i	−0.207911	+	0.120037i	0.392429	+	0.919782i	$0.371635\pi$
$402$	0.773306			0.0385690
$403$	0.0324883	−	6.28208i	0.00161836	−	0.312933i
$404$	−78.6717			−3.91406
$405$	22.3957	−	12.9302i	1.11285	−	0.642506i
$406$		0			0
$407$	5.47869	−	9.48937i	0.271568	−	0.470370i
$408$			6.65935i			0.329687i
$409$	−31.8727	−	18.4017i	−1.57601	−	0.909907i	−0.995409	−	0.0957164i	$-0.969486\pi$
$409$	−31.8727	−	18.4017i	−1.57601	−	0.909907i	−0.580597	−	0.814191i	$-0.697181\pi$
$410$	32.1976	+	18.5893i	1.59013	+	0.918060i
$411$			2.91343i			0.143709i
$412$	−11.3651	+	19.6850i	−0.559921	+	0.969811i
$413$		0			0
$414$	−12.2224	+	7.05662i	−0.600699	+	0.346814i
$415$	−32.4845			−1.59460
$416$	−58.3864	−	34.1132i	−2.86263	−	1.67254i
$417$	6.10122			0.298778
$418$	10.3760	−	5.99059i	0.507507	−	0.293009i
$419$	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
$423$	−14.6616	−	8.46489i	−0.712872	−	0.411577i
$424$		−	83.2000i		−	4.04055i
$425$	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
$429$	−1.98815	−	1.16161i	−0.0959886	−	0.0560829i
$430$	76.4674			3.68759
$431$	−27.0426	+	15.6131i	−1.30260	+	0.752055i	−0.980849	−	0.194771i	$-0.937604\pi$
$431$	−27.0426	+	15.6131i	−1.30260	+	0.752055i	−0.321748	+	0.946825i	$0.604270\pi$
$432$	13.7849	+	23.8762i	0.663228	+	1.14874i
$433$	−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
$437$			4.35204i			0.208186i
$438$	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
$443$	−35.8813			−1.70477			−0.852385	−	0.522915i	$-0.824845\pi$
$443$	−35.8813			−1.70477			−0.852385	+	0.522915i	$0.824845\pi$
$444$	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	$0.636614\pi$
$450$		−	43.7217i		−	2.06106i
$451$	3.89633	−	6.74864i	0.183471	−	0.317781i
$452$	7.29687	+	12.6386i	0.343216	+	0.594467i
$453$	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	$-0.252160\pi$
$457$	35.6995	−	20.6111i	1.66995	−	0.964147i	0.967660	−	0.252257i	$-0.0811729\pi$
$458$	−4.06385	−	7.03880i	−0.189891	−	0.328901i
$459$	2.19006	−	3.79329i	0.102223	−	0.177056i
$460$			31.3435i			1.46140i
$461$	−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
$467$	−4.44860			−0.205857			−0.102928	−	0.994689i	$-0.532821\pi$
$467$	−4.44860			−0.205857			−0.102928	+	0.994689i	$0.532821\pi$
$468$	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
$473$		−	16.0276i		−	0.736951i
$474$	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
$478$	−1.93004	−	3.34293i	−0.0882780	−	0.152902i
$479$	27.4328	−	15.8383i	1.25343	−	0.723671i	0.281645	−	0.959519i	$-0.409120\pi$
$479$	27.4328	−	15.8383i	1.25343	−	0.723671i	0.971790	+	0.235848i	$0.0757868\pi$
$480$	21.1394			0.964879
$481$	18.5892	−	10.6047i	0.847593	−	0.483531i
$482$	−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
$486$		−	23.9199i		−	1.08503i
$487$	23.3096	+	13.4578i	1.05626	+	0.609832i	0.924395	−	0.381436i	$-0.124570\pi$
$487$	23.3096	+	13.4578i	1.05626	+	0.609832i	0.131864	+	0.991268i	$0.457904\pi$
$488$	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	$0.762894\pi$
$492$	6.71215	−	3.87526i	0.302607	−	0.174710i
$493$	−5.88682			−0.265129
$494$	23.4006	+	0.121018i	1.05284	+	0.00544487i
$495$	−17.3239			−0.778653
$496$	20.4498	−	11.8067i	0.918225	−	0.530137i
$497$		0			0
$498$	−4.66196	+	8.07475i	−0.208907	+	0.361838i
$499$			7.87525i			0.352545i	0.984341	+	0.176272i	$0.0564039\pi$
$499$			7.87525i			0.352545i	−0.984341	+	0.176272i	$0.943596\pi$
$500$	−9.21523	−	5.32042i	−0.412118	−	0.237936i
$501$	−2.70213	−	1.56007i	−0.120722	−	0.0696989i
$502$		−	29.5565i		−	1.31917i
$503$	−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
$506$	9.04533			0.402114
$507$	−2.20827	−	3.91786i	−0.0980725	−	0.173998i
$508$	−51.6630			−2.29217
$509$	19.9407	−	11.5128i	0.883857	−	0.510295i	0.0119288	−	0.999929i	$-0.496203\pi$
$509$	19.9407	−	11.5128i	0.883857	−	0.510295i	0.871928	+	0.489634i	$0.162870\pi$
$510$	−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
$514$	9.71853	+	5.61100i	0.428666	+	0.247490i
$515$		−	13.9541i		−	0.614891i
$516$	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
$520$	105.022	+	0.543130i	4.60552	+	0.0238178i
$521$	−0.486481			−0.0213131			−0.0106566	−	0.999943i	$-0.503392\pi$
$521$	−0.486481			−0.0213131			−0.0106566	+	0.999943i	$0.503392\pi$
$522$	−18.4356	+	10.6438i	−0.806904	+	0.465866i
$523$	−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
$527$	−3.24893	−	1.87577i	−0.141526	−	0.0817099i
$528$		−	8.65510i		−	0.376665i
$529$	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
$534$	−14.1336			−0.611622
$535$	−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
$541$			22.5384i			0.969002i	0.874791	+	0.484501i	$0.160999\pi$
$541$			22.5384i			0.969002i	−0.874791	+	0.484501i	$0.839001\pi$
$542$	−3.76422	+	6.51982i	−0.161687	+	0.280050i
$543$	−1.13885	−	1.97255i	−0.0488728	−	0.0846502i
$544$	−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
$549$	−14.5601	−	25.2189i	−0.621411	−	1.07631i
$550$	−14.0108	+	24.2675i	−0.597424	+	1.03477i
$551$			6.56436i			0.279651i
$552$	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	$-0.661764\pi$
$557$	0.629579	−	0.363487i	0.0266761	−	0.0154015i	0.513279	+	0.858222i	$0.328431\pi$
$558$	−13.5661			−0.574300
$559$	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	$0.826355\pi$
$564$			10.7918i			0.454417i
$565$	−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
$569$	−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	$-0.345292\pi$
$570$	−6.33537	+	3.65773i	−0.265360	+	0.153205i
$571$	−16.9992			−0.711393			−0.355697	−	0.934602i	$-0.615756\pi$
$571$	−16.9992			−0.711393			−0.355697	+	0.934602i	$0.615756\pi$
$572$	0.182683	−	35.3244i	0.00763836	−	1.47699i
$573$	−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
$577$			15.9759i			0.665084i	0.943088	+	0.332542i	$0.107906\pi$
$577$			15.9759i			0.665084i	−0.943088	+	0.332542i	$0.892094\pi$
$578$	−28.9445	−	16.7111i	−1.20393	−	0.695092i
$579$	−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
$583$	14.8780	−	8.58982i	0.616184	−	0.355754i
$584$	28.5623			1.18192
$585$	−29.2150	−	17.0693i	−1.20789	−	0.705731i
$586$	−9.23926			−0.381670
$587$	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
$590$			94.6989i			3.89869i
$591$	4.35235	+	2.51283i	0.179032	+	0.103364i
$592$	69.6660	+	40.2217i	2.86325	+	1.65310i
$593$			29.0532i			1.19307i	0.802586	+	0.596536i	$0.203457\pi$
$593$			29.0532i			1.19307i	−0.802586	+	0.596536i	$0.796543\pi$
$594$	−5.07574	+	8.79143i	−0.208260	+	0.360717i
$595$		0			0
$596$	−18.4816	+	10.6704i	−0.757037	+	0.437075i
$597$	8.24757			0.337551
$598$	15.2540	+	8.91240i	0.623783	+	0.364455i
$599$	3.45554			0.141190			0.0705948	−	0.997505i	$-0.477510\pi$
$599$	3.45554			0.141190			0.0705948	+	0.997505i	$0.477510\pi$
$600$	−15.0407	+	8.68376i	−0.614035	+	0.354513i
$601$	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
$605$	−21.4222	−	12.3681i	−0.870938	−	0.502836i
$606$		−	13.8624i		−	0.563120i
$607$	7.73922	−	13.4047i	0.314125	−	0.544081i	−0.665126	−	0.746731i	$-0.731622\pi$
$607$	7.73922	−	13.4047i	0.314125	−	0.544081i	0.979251	+	0.202650i	$0.0649555\pi$
$608$	22.5148	+	38.9967i	0.913095	+	1.58153i
$609$		0			0
$610$	−89.0429			−3.60524
$611$	−0.109597	+	21.1922i	−0.00443383	+	0.857345i
$612$	32.9142			1.33048
$613$	−6.17669	+	3.56611i	−0.249474	+	0.144034i	−0.619523	−	0.784978i	$-0.712674\pi$
$613$	−6.17669	+	3.56611i	−0.249474	+	0.144034i	0.370049	+	0.929012i	$0.379341\pi$
$614$	−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	0.410911	−	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
$619$			42.3570i			1.70247i	0.524784	+	0.851235i	$0.324146\pi$
$619$			42.3570i			1.70247i	−0.524784	+	0.851235i	$0.675854\pi$
$620$	−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
$625$	−21.5445			−0.861779
$626$	−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	$0.706482\pi$
$632$			7.16924i			0.285177i
$633$	−0.746432	+	1.29286i	−0.0296680	+	0.0513865i
$634$	8.19794	+	14.1992i	0.325582	+	0.563924i
$635$	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
$640$	42.7898	+	74.1142i	1.69142	+	2.92962i
$641$	−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	$0.952440\pi$
$642$			17.8858i			0.705897i
$643$	−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	0.545901	−	0.837850i	$-0.316188\pi$
$647$	−11.5137	−	19.9423i	−0.452649	−	0.784011i	−0.998550	+	0.0538387i	$0.982854\pi$
$648$	61.4532	−	35.4800i	2.41411	−	1.39379i
$649$	19.8490			0.779140
$650$	−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
$655$			60.8014i			2.37571i
$656$	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	$-0.0414149\pi$
$660$	5.52153	+	9.56356i	0.214925	+	0.372261i
$661$	23.0000	−	13.2791i	0.894598	−	0.516496i	0.0191541	−	0.999817i	$-0.493903\pi$
$661$	23.0000	−	13.2791i	0.894598	−	0.516496i	0.875444	+	0.483320i	$0.160569\pi$
$662$	−46.6973			−1.81494
$663$	−2.68566	−	0.0138891i	−0.104302	−	0.000539407i
$664$	−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
$668$		−	47.8667i		−	1.85202i
$669$	−7.00906	−	4.04668i	−0.270986	−	0.156454i
$670$	−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	$0.957559\pi$
$674$	19.5585	−	11.2921i	0.753366	−	0.434956i
$675$	11.4233			0.439683
$676$	35.1134	−	59.3910i	1.35052	−	2.28427i
$677$	13.1440			0.505163			0.252582	−	0.967576i	$-0.418720\pi$
$677$	13.1440			0.505163			0.252582	+	0.967576i	$0.418720\pi$
$678$	−2.22698	+	1.28575i	−0.0855266	+	0.0493788i
$679$		0			0
$680$	31.3586	−	54.3147i	1.20255	−	2.08287i
$681$		−	9.24475i		−	0.354260i
$682$	7.52981	+	4.34734i	0.288331	+	0.166468i
$683$	−5.85654	−	3.38128i	−0.224094	−	0.129381i	0.383750	−	0.923437i	$-0.374632\pi$
$683$	−5.85654	−	3.38128i	−0.224094	−	0.129381i	−0.607845	+	0.794056i	$0.707966\pi$
$684$		−	36.7025i		−	1.40336i
$685$	13.7192	−	23.7624i	0.524185	−	0.907915i
$686$		0			0
$687$	0.900810	−	0.520083i	0.0343681	−	0.0198424i
$688$	117.666			4.48599
$689$	33.5538	+	0.173526i	1.27830	+	0.00661082i
$690$	−5.52288			−0.210253
$691$	−7.94223	+	4.58545i	−0.302137	+	0.174439i	−0.643402	−	0.765528i	$-0.722478\pi$
$691$	−7.94223	+	4.58545i	−0.302137	+	0.174439i	0.341266	+	0.939967i	$0.389144\pi$
$692$	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
$696$	7.32316	+	4.22803i	0.277584	+	0.160263i
$697$		−	9.08908i		−	0.344273i
$698$	−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	$0.146131\pi$
$702$	−17.2219	+	9.82469i	−0.650000	+	0.370809i
$703$	−14.2512			−0.537495
$704$	37.7181	−	21.7766i	1.42156	−	0.820736i
$705$	−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
$709$	30.2866	+	17.4860i	1.13744	+	0.656699i	0.945795	−	0.324766i	$-0.105285\pi$
$709$	30.2866	+	17.4860i	1.13744	+	0.656699i	0.191642	+	0.981465i	$0.438619\pi$
$710$			20.7347i			0.778158i
$711$	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
$716$	20.5903			0.769496
$717$	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	−0.777482	−	0.628905i	$-0.783503\pi$
$719$	4.18051	−	7.24085i	0.155907	−	0.270038i	0.933389	+	0.358867i	$0.116837\pi$
$720$		−	127.183i		−	4.73984i
$721$		0			0
$722$	30.9846	+	17.8890i	1.15313	+	0.665758i
$723$		−	0.927035i		−	0.0344768i
$724$	17.4713	−	30.2612i	0.649317	−	1.12465i
$725$	−7.67639	−	13.2959i	−0.285094	−	0.493797i
$726$	−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
$731$	−9.34703	−	16.1895i	−0.345712	−	0.598791i
$732$	−9.28127	+	16.0756i	−0.343046	+	0.594173i
$733$			12.1569i			0.449026i	0.974471	+	0.224513i	$0.0720792\pi$
$733$			12.1569i			0.449026i	−0.974471	+	0.224513i	$0.927921\pi$
$734$	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	−0.544662	+	0.838656i	$0.683342\pi$
$739$	−41.9537	+	24.2220i	−1.54329	+	0.891019i	−0.998628	+	0.0523634i	$0.983325\pi$
$740$	−102.638			−3.77304
$741$	−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	$0.434219\pi$
$744$	2.69443	+	4.66689i	0.0987826	+	0.171097i
$745$	6.55052	−	11.3458i	0.239993	−	0.415679i
$746$		−	86.6767i		−	3.17346i
$747$	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
$751$	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	$0.545926\pi$
$752$	−68.9863	+	39.8292i	−2.51567	+	1.45242i
$753$	3.78258			0.137845
$754$	23.0083	+	13.4430i	0.837911	+	0.489563i
$755$	−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
$759$			1.15760i			0.0420183i
$760$	−60.5661	−	34.9678i	−2.19696	−	1.26842i
$761$	25.4829	+	14.7126i	0.923754	+	0.533330i	0.884831	−	0.465912i	$-0.154274\pi$
$761$	25.4829	+	14.7126i	0.923754	+	0.533330i	0.0389234	+	0.999242i	$0.487607\pi$
$762$		−	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
$766$	1.89178			0.0683526
$767$	33.4732	+	19.5573i	1.20865	+	0.706172i
$768$	8.23976			0.297327
$769$	−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
$772$		−	120.756i		−	4.34612i
$773$	−19.0180	−	10.9801i	−0.684031	−	0.394926i	0.117341	−	0.993092i	$-0.462563\pi$
$773$	−19.0180	−	10.9801i	−0.684031	−	0.394926i	−0.801372	+	0.598166i	$0.795896\pi$
$774$	−58.5437	−	33.8002i	−2.10431	−	1.21492i
$775$		−	9.78399i		−	0.351451i
$776$	41.2666	−	71.4759i	1.48139	−	2.56584i
$777$		0			0
$778$	−46.9488	+	27.1059i	−1.68320	+	0.971794i
$779$	−10.1352			−0.363131
$780$	−0.111542	+	21.5683i	−0.00399386	+	0.772271i
$781$	4.34600			0.155512
$782$	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
$786$	15.1135	+	8.72581i	0.539082	+	0.311239i
$787$	2.02275	+	1.16784i	0.0721033	+	0.0416289i	0.535618	−	0.844460i	$-0.320079\pi$
$787$	2.02275	+	1.16784i	0.0721033	+	0.0416289i	−0.463515	+	0.886089i	$0.653412\pi$
$788$			77.0996i			2.74656i
$789$	−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
$793$	−18.3892	+	31.4740i	−0.653020	+	1.11767i
$794$	−60.2280			−2.13741
$795$	−9.08420	+	5.24476i	−0.322183	+	0.186013i
$796$	63.2637	+	109.576i	2.24232	+	3.88382i
$797$	−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
$801$			43.5316i			1.53811i
$802$	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
$807$	−1.38387			−0.0487147
$808$	114.769	−	66.2620i	4.03756	−	2.33109i
$809$	−7.51017	−	13.0080i	−0.264043	−	0.457337i	0.703269	−	0.710924i	$-0.251723\pi$
$809$	−7.51017	−	13.0080i	−0.264043	−	0.457337i	−0.967313	+	0.253587i	$0.918390\pi$
$810$	−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
$814$			29.6199i			1.03818i
$815$	7.17670	−	12.4304i	0.251389	−	0.435418i
$816$	−5.04750	−	8.74252i	−0.176698	−	0.306049i
$817$	−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	−0.201412	−	0.979507i	$-0.564553\pi$
$821$	15.6492	−	9.03506i	0.546160	−	0.315326i	0.747572	+	0.664181i	$0.231220\pi$
$822$	−3.93779	−	6.82045i	−0.137346	−	0.237890i
$823$	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	$0.141924\pi$
$824$		−	38.2896i		−	1.33388i
$825$	−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	0.895117	−	0.445832i	$-0.147092\pi$
$829$	1.76947	+	3.06482i	0.0614563	+	0.106445i	−0.833660	+	0.552278i	$0.813759\pi$
$830$	76.0474	−	43.9060i	2.63964	−	1.52400i
$831$	−5.77471			−0.200323
$832$	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
$837$		−	3.54447i		−	0.122515i
$838$	−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
$842$	10.1892	+	17.6482i	0.351143	+	0.608197i
$843$	4.00660	−	2.31321i	0.137995	−	0.0796713i
$844$	−22.9023			−0.788330
$845$	−0.438079	+	42.3533i	−0.0150704	+	1.45700i
$846$	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
$850$			32.6835i			1.12103i
$851$	−9.31768	−	5.37956i	−0.319406	−	0.184409i
$852$	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
$856$	−148.080	+	85.4941i	−5.06127	+	2.92213i
$857$	−6.89363			−0.235482			−0.117741	−	0.993044i	$-0.537565\pi$
$857$	−6.89363			−0.235482			−0.117741	+	0.993044i	$0.537565\pi$
$858$	6.22435	+	0.0321897i	0.212496	+	0.00109894i
$859$	37.4834			1.27892			0.639459	−	0.768825i	$-0.279158\pi$
$859$	37.4834			1.27892			0.639459	+	0.768825i	$0.279158\pi$
$860$	−130.017	+	75.0654i	−4.43355	+	2.55971i
$861$		0			0
$862$	42.2052	−	73.1015i	1.43751	−	2.48985i
$863$		−	17.5248i		−	0.596552i	−0.954480	−	0.298276i	$-0.903588\pi$
$863$		−	17.5248i		−	0.596552i	0.954480	−	0.298276i	$-0.0964115\pi$
$864$	−33.0413	−	19.0764i	−1.12409	−	0.648993i
$865$	−17.1893	−	9.92425i	−0.584454	−	0.337435i
$866$		−	15.9057i		−	0.540498i
$867$	2.13866	−	3.70426i	0.0726326	−	0.125803i
$868$		0			0
$869$	−1.28202	+	0.740175i	−0.0434896	+	0.0251087i
$870$	−8.33040			−0.282427
$871$	−2.58972	+	1.47737i	−0.0877493	+	0.0500588i
$872$	38.1883			1.29322
$873$	−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
$877$	−40.4859	−	23.3745i	−1.36711	−	0.789302i	−0.376553	−	0.926395i	$-0.622891\pi$
$877$	−40.4859	−	23.3745i	−1.36711	−	0.789302i	−0.990558	+	0.137093i	$0.956224\pi$
$878$	−23.3083	−	13.4571i	−0.786618	−	0.454154i
$879$		−	1.18242i		−	0.0398821i
$880$	−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	$0.340491\pi$
$884$	−20.4160	−	35.7878i	−0.686666	−	1.20367i
$885$	−12.1194			−0.407388
$886$	83.9993	−	48.4970i	2.82201	−	1.62929i
$887$	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
$891$	12.6892	+	7.32614i	0.425106	+	0.245435i
$892$		−	124.162i		−	4.15725i
$893$	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
$898$	−10.8000			−0.360401
$899$	−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
$905$			21.4512i			0.713063i
$906$	−8.83779	+	15.3075i	−0.293616	+	0.508558i
$907$	−11.2142	−	19.4236i	−0.372361	−	0.644949i	0.617567	−	0.786518i	$-0.288118\pi$
$907$	−11.2142	−	19.4236i	−0.372361	−	0.644949i	−0.989928	+	0.141570i	$0.954785\pi$
$908$	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
$913$	−9.20274	−	15.9396i	−0.304566	−	0.527524i
$914$	−55.7159	+	96.5027i	−1.84292	+	3.19203i
$915$		−	11.3955i		−	0.376724i
$916$	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	−0.772981	−	0.634429i	$-0.781235\pi$
$919$	4.93957	−	8.55558i	0.162941	−	0.282223i	0.935922	+	0.352207i	$0.114569\pi$
$920$	−26.3993	−	45.7250i	−0.870361	−	1.50751i
$921$	4.90383	−	2.83123i	0.161587	−	0.0932922i
$922$	66.8408			2.20129
$923$	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
$928$			51.2769i			1.68325i
$929$	−25.9060	−	14.9568i	−0.849947	−	0.490717i	0.0106859	−	0.999943i	$-0.496599\pi$
$929$	−25.9060	−	14.9568i	−0.849947	−	0.490717i	−0.860633	+	0.509226i	$0.829932\pi$
$930$	−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
$934$	10.4143	−	6.01273i	0.340768	−	0.196742i
$935$	12.9502			0.423518
$936$	−80.1651	−	46.8378i	−2.62028	−	1.53094i
$937$	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
$941$			42.0885i			1.37205i	0.727580	+	0.686023i	$0.240645\pi$
$941$			42.0885i			1.37205i	−0.727580	+	0.686023i	$0.759355\pi$
$942$	9.37318	+	5.41161i	0.305395	+	0.176320i
$943$	−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
$947$	52.2540	−	30.1689i	1.69803	−	0.980357i	0.750397	−	0.660988i	$-0.229862\pi$
$947$	52.2540	−	30.1689i	1.69803	−	0.980357i	0.947630	−	0.319369i	$-0.103471\pi$
$948$	−1.47234			−0.0478195
$949$	−0.0595711	+	11.5189i	−0.00193376	+	0.373920i
$950$	36.4452			1.18244
$951$	−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	$0.257473\pi$
$954$		−	72.4593i		−	2.34596i
$955$	38.7785	+	22.3888i	1.25484	+	0.724484i
$956$	6.56328	+	3.78931i	0.212272	+	0.122555i
$957$			1.74606i			0.0564421i
$958$	−42.8140	+	74.1561i	−1.38326	+	2.39588i
$959$		0			0
$960$	−23.0299	+	13.2963i	−0.743287	+	0.429137i
$961$	27.9642			0.902070
$962$	−29.1847	+	49.9510i	−0.940951	+	1.61048i
$963$	55.0883			1.77520
$964$	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	$0.0980874\pi$
$967$			18.8630i			0.606594i	−0.952896	+	0.303297i	$0.901913\pi$
$968$	−58.7820	−	33.9378i	−1.88932	−	1.09080i
$969$	1.54881	+	0.894208i	0.0497551	+	0.0287261i
$970$			81.3068i			2.61061i
$971$	−0.782231	+	1.35486i	−0.0251030	+	0.0434797i	−0.878304	−	0.478103i	$-0.841325\pi$
$971$	−0.782231	+	1.35486i	−0.0251030	+	0.0434797i	0.853201	+	0.521582i	$0.174658\pi$
$972$	23.4813	+	40.6708i	0.753164	+	1.30452i
$973$		0			0
$974$	−72.7582			−2.33132
$975$	−3.47071	−	6.08390i	−0.111152	−	0.194841i
$976$	−137.017			−4.38582
$977$	−24.1409	+	13.9378i	−0.772336	+	0.445909i	−0.833707	−	0.552206i	$-0.813786\pi$
$977$	−24.1409	+	13.9378i	−0.772336	+	0.445909i	0.0613710	+	0.998115i	$0.480453\pi$
$978$	−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
$982$	−22.7716	−	13.1472i	−0.726672	−	0.419544i
$983$		−	33.4239i		−	1.06606i	−0.846097	−	0.533029i	$-0.821054\pi$
$983$		−	33.4239i		−	1.06606i	0.846097	−	0.533029i	$-0.178946\pi$
$984$	−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
$989$	−15.7376			−0.500428
$990$	40.5559	−	23.4150i	1.28895	−	0.744177i
$991$	9.45548	+	16.3774i	0.300363	+	0.520244i	0.976218	−	0.216790i	$-0.0695588\pi$
$991$	9.45548	+	16.3774i	0.300363	+	0.520244i	−0.675855	+	0.737035i	$0.736225\pi$
$992$	−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
$996$		−	18.3059i		−	0.580046i
$997$	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	$-0.0757480\pi$
$998$	−10.6442	−	18.4363i	−0.336936	−	0.583589i
$999$	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.q.h.491.1		12
7.2	even	3		637.2.u.i.361.6		12
7.3	odd	6		637.2.k.h.569.1		12
7.4	even	3		637.2.k.g.569.1		12
7.5	odd	6		637.2.u.h.361.6		12
7.6	odd	2		91.2.q.a.36.1	✓	12
13.2	odd	12		8281.2.a.by.1.1		6
13.4	even	6	inner	637.2.q.h.589.1		12
13.11	odd	12		8281.2.a.ch.1.6		6
21.20	even	2		819.2.ct.a.127.6		12
28.27	even	2		1456.2.cc.c.673.4		12
91.4	even	6		637.2.u.i.30.6		12
91.17	odd	6		637.2.u.h.30.6		12
91.30	even	6		637.2.k.g.459.6		12
91.41	even	12		1183.2.a.m.1.1		6
91.55	odd	6		1183.2.c.i.337.1		12
91.62	odd	6		1183.2.c.i.337.12		12
91.69	odd	6		91.2.q.a.43.1	yes	12
91.76	even	12		1183.2.a.p.1.6		6
91.82	odd	6		637.2.k.h.459.6		12
273.251	even	6		819.2.ct.a.316.6		12
364.251	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	7.6	odd	2
91.2.q.a.43.1	yes	12	91.69	odd	6
637.2.k.g.459.6		12	91.30	even	6
637.2.k.g.569.1		12	7.4	even	3
637.2.k.h.459.6		12	91.82	odd	6
637.2.k.h.569.1		12	7.3	odd	6
637.2.q.h.491.1		12	1.1	even	1	trivial
637.2.q.h.589.1		12	13.4	even	6	inner
637.2.u.h.30.6		12	91.17	odd	6
637.2.u.h.361.6		12	7.5	odd	6
637.2.u.i.30.6		12	91.4	even	6
637.2.u.i.361.6		12	7.2	even	3
819.2.ct.a.127.6		12	21.20	even	2
819.2.ct.a.316.6		12	273.251	even	6
1183.2.a.m.1.1		6	91.41	even	12
1183.2.a.p.1.6		6	91.76	even	12
1183.2.c.i.337.1		12	91.55	odd	6
1183.2.c.i.337.12		12	91.62	odd	6
1456.2.cc.c.225.4		12	364.251	even	6
1456.2.cc.c.673.4		12	28.27	even	2
8281.2.a.by.1.1		6	13.2	odd	12
8281.2.a.ch.1.6		6	13.11	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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.34104 + 1.35160i) q^{2} +(-0.172975 - 0.299601i) q^{3} +(2.65363 - 4.59623i) q^{4} +3.25812i q^{5} +(0.809880 + 0.467584i) q^{6} +8.94020i q^{8} +(1.44016 - 2.49443i) q^{9} +O(q^{10})\)	\(q+(-2.34104 + 1.35160i) q^{2} +(-0.172975 - 0.299601i) q^{3} +(2.65363 - 4.59623i) q^{4} +3.25812i 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} -1.83605 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} +7.78607i q^{18} +(2.07929 + 1.20048i) q^{19} +(14.9751 + 8.64587i) q^{20} +(2.49509 - 4.32162i) q^{22} +(0.906314 + 1.56978i) q^{23} +(2.67849 - 1.54643i) q^{24} -5.61537 q^{25} +(8.46582 - 4.82954i) q^{26} -2.03429 q^{27} +(1.36703 + 2.36777i) q^{29} +(-1.52345 + 2.63869i) q^{30} +1.74236i q^{31} +(16.2422 + 9.37743i) q^{32} +(0.553071 + 0.319316i) q^{33} -5.82036i q^{34} +(-7.64331 - 13.2386i) q^{36} +(-5.14042 + 2.96783i) q^{37} -6.49025 q^{38} +(0.618074 + 1.08344i) q^{39} -29.1283 q^{40} +(-3.65577 + 2.11066i) q^{41} +(-4.34111 + 7.51903i) q^{43} +9.79737i q^{44} +(8.12716 + 4.69222i) q^{45} +(-4.24343 - 2.44994i) q^{46} -5.87774i q^{47} +(-2.34425 + 4.06036i) q^{48} +(13.1458 - 7.58972i) q^{50} +0.744877 q^{51} +(-9.65339 + 16.5222i) q^{52} -9.30628 q^{53} +(4.76235 - 2.74954i) q^{54} +(-3.00729 - 5.20878i) q^{55} -0.830609i q^{57} +(-6.40054 - 3.69535i) q^{58} +(-9.31173 - 5.37613i) q^{59} -5.98206i q^{60} +(5.05504 - 8.75558i) q^{61} +(-2.35497 - 4.07893i) q^{62} -23.5929 q^{64} +(0.0607514 - 11.7472i) q^{65} -1.72635 q^{66} +(0.716130 - 0.413458i) q^{67} +(5.71365 + 9.89633i) q^{68} +(0.313538 - 0.543065i) q^{69} +(-2.03884 - 1.17712i) q^{71} +(22.3007 + 12.8753i) q^{72} -3.19482i 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} +0.801911 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} -23.4698i q^{86} +(0.472923 - 0.819127i) q^{87} +(-8.25193 - 14.2928i) q^{88} +(-13.0886 + 7.55674i) q^{89} -25.3680 q^{90} +9.62010 q^{92} +(0.522012 - 0.301384i) q^{93} +(7.94435 + 13.7600i) q^{94} +(-3.91130 + 6.77458i) q^{95} -6.48823i q^{96} +(-7.99489 - 4.61585i) q^{97} +5.31715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9	\( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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