LMFDB - Embedded newform 637.2.u.h.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$-1.08105 - 0.911778i$ of defining polynomial
Character	$\chi$	$=$	637.361
Dual form			637.2.u.h.30.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.713220 - 0.411778i) q^{2} +2.66029 q^{3} +(-0.660878 - 1.14467i) q^{4} +(-2.73845 + 1.58105i) q^{5} +(-1.89737 - 1.09545i) q^{6} +2.73565i q^{8} +4.07715 q^{9} +O(q^{10})$	\(q+(-0.713220 - 0.411778i) q^{2} +2.66029 q^{3} +(-0.660878 - 1.14467i) q^{4} +(-2.73845 + 1.58105i) q^{5} +(-1.89737 - 1.09545i) q^{6} +2.73565i q^{8} +4.07715 q^{9} +2.60416 q^{10} +5.94270i q^{11} +(-1.75813 - 3.04517i) q^{12} +(-0.0766193 + 3.60474i) q^{13} +(-7.28508 + 4.20604i) q^{15} +(-0.195274 + 0.338225i) q^{16} +(-1.34982 - 2.33796i) q^{17} +(-2.90791 - 1.67888i) q^{18} -1.95705i q^{19} +(3.61956 + 2.08976i) q^{20} +(2.44707 - 4.23845i) q^{22} +(-1.36471 + 2.36374i) q^{23} +7.27763i q^{24} +(2.49941 - 4.32911i) q^{25} +(1.53900 - 2.53942i) q^{26} +2.86554 q^{27} +(2.99923 + 5.19481i) q^{29} +6.92783 q^{30} +(0.997270 + 0.575774i) q^{31} +(5.01684 - 2.89647i) q^{32} +15.8093i q^{33} +2.22331i q^{34} +(-2.69450 - 4.66701i) q^{36} +(5.63310 + 3.25227i) q^{37} +(-0.805869 + 1.39581i) q^{38} +(-0.203830 + 9.58965i) q^{39} +(-4.32519 - 7.49145i) q^{40} +(-3.23351 + 1.86687i) q^{41} +(3.49562 - 6.05460i) q^{43} +(6.80245 - 3.92740i) q^{44} +(-11.1651 + 6.44617i) q^{45} +(1.94667 - 1.12391i) q^{46} +(0.394969 - 0.228035i) q^{47} +(-0.519487 + 0.899778i) q^{48} +(-3.56527 + 2.05841i) q^{50} +(-3.59092 - 6.21965i) q^{51} +(4.17688 - 2.29459i) q^{52} +(-0.199643 + 0.345792i) q^{53} +(-2.04376 - 1.17997i) q^{54} +(-9.39568 - 16.2738i) q^{55} -5.20632i q^{57} -4.94006i q^{58} +(-4.16200 + 2.40293i) q^{59} +(9.62910 + 5.55936i) q^{60} -1.15703 q^{61} +(-0.474182 - 0.821308i) q^{62} -3.98971 q^{64} +(-5.48944 - 9.99254i) q^{65} +(6.50993 - 11.2755i) q^{66} -6.27918i q^{67} +(-1.78413 + 3.09021i) q^{68} +(-3.63052 + 6.28825i) q^{69} +(3.90335 + 2.25360i) q^{71} +11.1537i q^{72} +(-7.19299 - 4.15288i) q^{73} +(-2.67843 - 4.63917i) q^{74} +(6.64917 - 11.5167i) q^{75} +(-2.24018 + 1.29337i) q^{76} +(4.09418 - 6.75560i) q^{78} +(3.95705 + 6.85381i) q^{79} -1.23495i q^{80} -4.60828 q^{81} +3.07494 q^{82} +6.19795i q^{83} +(7.39284 + 4.26826i) q^{85} +(-4.98630 + 2.87884i) q^{86} +(7.97882 + 13.8197i) q^{87} -16.2571 q^{88} +(-3.08423 - 1.78068i) q^{89} +10.6176 q^{90} +3.60762 q^{92} +(2.65303 + 1.53173i) q^{93} -0.375600 q^{94} +(3.09418 + 5.35928i) q^{95} +(13.3462 - 7.70546i) q^{96} +(-2.96831 - 1.71375i) q^{97} +24.2293i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 - 6 * q^5 - 18 * q^6 + 8 * q^9	$ 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29} - 16 q^{30} + 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} - 2 q^{38} - 10 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} + 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} + 26 q^{52} + 22 q^{53} - 12 q^{54} - 6 q^{55} - 18 q^{59} + 66 q^{60} - 28 q^{61} - 4 q^{62} - 52 q^{64} - 42 q^{65} + 26 q^{66} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 30 q^{73} + 6 q^{74} + 46 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} - 28 q^{82} - 48 q^{85} - 60 q^{86} - 2 q^{87} + 28 q^{88} + 12 q^{89} + 24 q^{90} + 24 q^{92} + 18 q^{93} - 8 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 - 6 * q^5 - 18 * q^6 + 8 * q^9 - 24 * q^10 + 2 * q^12 + 4 * q^13 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^18 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 + 24 * q^26 + 12 * q^27 + 8 * q^29 - 16 * q^30 + 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 - 2 * q^38 - 10 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 + 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 + 26 * q^52 + 22 * q^53 - 12 * q^54 - 6 * q^55 - 18 * q^59 + 66 * q^60 - 28 * q^61 - 4 * q^62 - 52 * q^64 - 42 * q^65 + 26 * q^66 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 30 * q^73 + 6 * q^74 + 46 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 - 28 * q^82 - 48 * q^85 - 60 * q^86 - 2 * q^87 + 28 * q^88 + 12 * q^89 + 24 * q^90 + 24 * q^92 + 18 * q^93 - 8 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.713220	−	0.411778i	−0.504323	−	0.291171i	0.226174	−	0.974087i	$-0.427378\pi$
$2$	−0.713220	−	0.411778i	−0.504323	−	0.291171i	−0.730497	+	0.682916i	$0.760712\pi$
$3$	2.66029			1.53592			0.767960	−	0.640498i	$-0.221272\pi$
$3$	2.66029			1.53592			0.767960	+	0.640498i	$0.221272\pi$
$4$	−0.660878	−	1.14467i	−0.330439	−	0.572337i
$5$	−2.73845	+	1.58105i	−1.22467	+	0.707065i	−0.965911	−	0.258876i	$-0.916648\pi$
$5$	−2.73845	+	1.58105i	−1.22467	+	0.707065i	−0.258762	+	0.965941i	$0.583315\pi$
$6$	−1.89737	−	1.09545i	−0.774600	−	0.447215i
$7$		0			0
$7$		0			0
$8$			2.73565i			0.967199i
$9$	4.07715			1.35905
$10$	2.60416			0.823508
$11$			5.94270i			1.79179i	0.444265	+	0.895895i	$0.353465\pi$
$11$			5.94270i			1.79179i	−0.444265	+	0.895895i	$0.646535\pi$
$12$	−1.75813	−	3.04517i	−0.507528	−	0.879064i
$13$	−0.0766193	+	3.60474i	−0.0212504	+	0.999774i
$13$	−0.0766193	+	3.60474i	−0.0212504	+	0.999774i
$14$		0			0
$15$	−7.28508	+	4.20604i	−1.88100	+	1.08600i
$16$	−0.195274	+	0.338225i	−0.0488186	+	0.0845563i
$17$	−1.34982	−	2.33796i	−0.327380	−	0.567038i	0.654611	−	0.755966i	$-0.272832\pi$
$17$	−1.34982	−	2.33796i	−0.327380	−	0.567038i	−0.981991	+	0.188927i	$0.939499\pi$
$18$	−2.90791	−	1.67888i	−0.685401	−	0.395716i
$19$		−	1.95705i		−	0.448978i	−0.974477	−	0.224489i	$-0.927929\pi$
$19$		−	1.95705i		−	0.448978i	0.974477	−	0.224489i	$-0.0720712\pi$
$20$	3.61956	+	2.08976i	0.809359	+	0.467284i
$21$		0			0
$22$	2.44707	−	4.23845i	0.521717	−	0.903641i
$23$	−1.36471	+	2.36374i	−0.284561	+	0.492874i	−0.972503	−	0.232892i	$-0.925181\pi$
$23$	−1.36471	+	2.36374i	−0.284561	+	0.492874i	0.687941	+	0.725766i	$0.258515\pi$
$24$			7.27763i			1.48554i
$25$	2.49941	−	4.32911i	0.499883	−	0.865822i
$26$	1.53900	−	2.53942i	0.301822	−	0.498022i
$27$	2.86554			0.551474
$28$		0			0
$29$	2.99923	+	5.19481i	0.556942	+	0.964652i	0.997750	+	0.0670505i	$0.0213589\pi$
$29$	2.99923	+	5.19481i	0.556942	+	0.964652i	−0.440807	+	0.897602i	$0.645308\pi$
$30$	6.92783			1.26484
$31$	0.997270	+	0.575774i	0.179115	+	0.103412i	0.586877	−	0.809676i	$-0.300357\pi$
$31$	0.997270	+	0.575774i	0.179115	+	0.103412i	−0.407762	+	0.913088i	$0.633691\pi$
$32$	5.01684	−	2.89647i	0.886860	−	0.512029i
$33$			15.8093i			2.75205i
$34$			2.22331i			0.381294i
$35$		0			0
$36$	−2.69450	−	4.66701i	−0.449083	−	0.777835i
$37$	5.63310	+	3.25227i	0.926075	+	0.534670i	0.885568	−	0.464509i	$-0.153769\pi$
$37$	5.63310	+	3.25227i	0.926075	+	0.534670i	0.0405072	+	0.999179i	$0.487103\pi$
$38$	−0.805869	+	1.39581i	−0.130729	+	0.226430i
$39$	−0.203830	+	9.58965i	−0.0326389	+	1.53557i
$40$	−4.32519	−	7.49145i	−0.683873	−	1.18450i
$41$	−3.23351	+	1.86687i	−0.504990	+	0.291556i	−0.730772	−	0.682622i	$-0.760840\pi$
$41$	−3.23351	+	1.86687i	−0.504990	+	0.291556i	0.225782	+	0.974178i	$0.427506\pi$
$42$		0			0
$43$	3.49562	−	6.05460i	0.533078	−	0.923318i	−0.466176	−	0.884692i	$-0.654369\pi$
$43$	3.49562	−	6.05460i	0.533078	−	0.923318i	0.999254	−	0.0386258i	$-0.0122980\pi$
$44$	6.80245	−	3.92740i	1.02551	−	0.592077i
$45$	−11.1651	+	6.44617i	−1.66439	+	0.960938i
$46$	1.94667	−	1.12391i	0.287021	−	0.165712i
$47$	0.394969	−	0.228035i	0.0576121	−	0.0332624i	−0.470917	−	0.882177i	$-0.656077\pi$
$47$	0.394969	−	0.228035i	0.0576121	−	0.0332624i	0.528529	+	0.848915i	$0.322744\pi$
$48$	−0.519487	+	0.899778i	−0.0749815	+	0.129872i
$49$		0			0
$50$	−3.56527	+	2.05841i	−0.504205	+	0.291103i
$51$	−3.59092	−	6.21965i	−0.502829	−	0.870926i
$52$	4.17688	−	2.29459i	0.579230	−	0.318202i
$53$	−0.199643	+	0.345792i	−0.0274231	+	0.0474982i	−0.879411	−	0.476063i	$-0.842063\pi$
$53$	−0.199643	+	0.345792i	−0.0274231	+	0.0474982i	0.851988	+	0.523561i	$0.175397\pi$
$54$	−2.04376	−	1.17997i	−0.278121	−	0.160573i
$55$	−9.39568	−	16.2738i	−1.26691	−	2.19436i
$56$		0			0
$57$		−	5.20632i		−	0.689594i
$58$		−	4.94006i		−	0.648662i
$59$	−4.16200	+	2.40293i	−0.541846	+	0.312835i	−0.745827	−	0.666140i	$-0.767945\pi$
$59$	−4.16200	+	2.40293i	−0.541846	+	0.312835i	0.203981	+	0.978975i	$0.434612\pi$
$60$	9.62910	+	5.55936i	1.24311	+	0.717711i
$61$	−1.15703			−0.148142			−0.0740711	−	0.997253i	$-0.523599\pi$
$61$	−1.15703			−0.148142			−0.0740711	+	0.997253i	$0.523599\pi$
$62$	−0.474182	−	0.821308i	−0.0602212	−	0.104306i
$63$		0			0
$64$	−3.98971			−0.498714
$65$	−5.48944	−	9.99254i	−0.680881	−	1.23942i
$66$	6.50993	−	11.2755i	0.801316	−	1.38792i
$67$		−	6.27918i		−	0.767124i	−0.923515	−	0.383562i	$-0.874697\pi$
$67$		−	6.27918i		−	0.767124i	0.923515	−	0.383562i	$-0.125303\pi$
$68$	−1.78413	+	3.09021i	−0.216358	+	0.374743i
$69$	−3.63052	+	6.28825i	−0.437063	+	0.757016i
$70$		0			0
$71$	3.90335	+	2.25360i	0.463242	+	0.267453i	0.713406	−	0.700751i	$-0.247151\pi$
$71$	3.90335	+	2.25360i	0.463242	+	0.267453i	−0.250165	+	0.968203i	$0.580485\pi$
$72$			11.1537i			1.31447i
$73$	−7.19299	−	4.15288i	−0.841876	−	0.486057i	0.0160254	−	0.999872i	$-0.494899\pi$
$73$	−7.19299	−	4.15288i	−0.841876	−	0.486057i	−0.857901	+	0.513814i	$0.828232\pi$
$74$	−2.67843	−	4.63917i	−0.311361	−	0.539293i
$75$	6.64917	−	11.5167i	0.767780	−	1.32983i
$76$	−2.24018	+	1.29337i	−0.256966	+	0.148360i
$77$		0			0
$78$	4.09418	−	6.75560i	0.463575	−	0.764921i
$79$	3.95705	+	6.85381i	0.445203	+	0.771114i	0.998066	−	0.0621581i	$-0.0197983\pi$
$79$	3.95705	+	6.85381i	0.445203	+	0.771114i	−0.552864	+	0.833272i	$0.686465\pi$
$80$		−	1.23495i		−	0.138072i
$81$	−4.60828			−0.512031
$82$	3.07494			0.339571
$83$			6.19795i			0.680313i	0.940369	+	0.340156i	$0.110480\pi$
$83$			6.19795i			0.680313i	−0.940369	+	0.340156i	$0.889520\pi$
$84$		0			0
$85$	7.39284	+	4.26826i	0.801866	+	0.462958i
$86$	−4.98630	+	2.87884i	−0.537687	+	0.310434i
$87$	7.97882	+	13.8197i	0.855419	+	1.48163i
$88$	−16.2571			−1.73302
$89$	−3.08423	−	1.78068i	−0.326928	−	0.188752i	0.327549	−	0.944834i	$-0.393778\pi$
$89$	−3.08423	−	1.78068i	−0.326928	−	0.188752i	−0.654476	+	0.756083i	$0.727111\pi$
$90$	10.6176			1.11919
$91$		0			0
$92$	3.60762			0.376120
$93$	2.65303	+	1.53173i	0.275106	+	0.158833i
$94$	−0.375600			−0.0387402
$95$	3.09418	+	5.35928i	0.317457	+	0.549851i
$96$	13.3462	−	7.70546i	1.36215	−	0.786435i
$97$	−2.96831	−	1.71375i	−0.301386	−	0.174005i	0.341679	−	0.939817i	$-0.389004\pi$
$97$	−2.96831	−	1.71375i	−0.301386	−	0.174005i	−0.643065	+	0.765811i	$0.722338\pi$
$98$		0			0
$99$			24.2293i			2.43513i
$100$	−6.60723			−0.660723
$101$	13.3295			1.32633			0.663167	−	0.748472i	$-0.269212\pi$
$101$	13.3295			1.32633			0.663167	+	0.748472i	$0.269212\pi$
$102$			5.91465i			0.585637i
$103$	5.82248	+	10.0848i	0.573706	+	0.993688i	0.996181	+	0.0873131i	$0.0278281\pi$
$103$	5.82248	+	10.0848i	0.573706	+	0.993688i	−0.422475	+	0.906375i	$0.638839\pi$
$104$	−9.86130	−	0.209604i	−0.966981	−	0.0205533i
$105$		0			0
$106$	0.284779	−	0.164417i	0.0276602	−	0.0159696i
$107$	−1.96483	+	3.40318i	−0.189947	+	0.328998i	−0.945232	−	0.326398i	$-0.894165\pi$
$107$	−1.96483	+	3.40318i	−0.189947	+	0.328998i	0.755285	+	0.655396i	$0.227498\pi$
$108$	−1.89377	−	3.28011i	−0.182228	−	0.315629i
$109$	−9.74566	−	5.62666i	−0.933465	−	0.538936i	−0.0455595	−	0.998962i	$-0.514507\pi$
$109$	−9.74566	−	5.62666i	−0.933465	−	0.538936i	−0.887906	+	0.460025i	$0.847840\pi$
$110$			15.4757i			1.47555i
$111$	14.9857	+	8.65199i	1.42238	+	0.821210i
$112$		0			0
$113$	2.88709	−	5.00059i	0.271595	−	0.470416i	−0.697676	−	0.716414i	$-0.745782\pi$
$113$	2.88709	−	5.00059i	0.271595	−	0.470416i	0.969270	+	0.245998i	$0.0791157\pi$
$114$	−2.14385	+	3.71325i	−0.200790	+	0.347778i
$115$		−	8.63066i		−	0.804813i
$116$	3.96424	−	6.86627i	0.368071	−	0.637517i
$117$	−0.312389	+	14.6971i	−0.0288803	+	1.35874i
$118$	3.95790			0.364354
$119$		0			0
$120$	−11.5063	−	19.9294i	−1.05037	−	1.81930i
$121$	−24.3156			−2.21051
$122$	0.825215	+	0.476438i	0.0747115	+	0.0431347i
$123$	−8.60209	+	4.96642i	−0.775625	+	0.447807i
$124$		−	1.52207i		−	0.136686i
$125$		−	0.00370455i		−	0.000331345i
$126$		0			0
$127$	3.06558	+	5.30975i	0.272027	+	0.471164i	0.969381	−	0.245563i	$-0.0789728\pi$
$127$	3.06558	+	5.30975i	0.272027	+	0.471164i	−0.697354	+	0.716727i	$0.745639\pi$
$128$	−7.18812	−	4.15007i	−0.635346	−	0.366817i
$129$	9.29938	−	16.1070i	0.818765	−	1.41814i
$130$	−0.199529	+	9.38731i	−0.0174998	+	0.823322i
$131$	−5.11084	−	8.85224i	−0.446537	−	0.773424i	0.551621	−	0.834095i	$-0.314009\pi$
$131$	−5.11084	−	8.85224i	−0.446537	−	0.773424i	−0.998158	+	0.0606707i	$0.980676\pi$
$132$	18.0965	−	10.4480i	1.57510	−	0.909383i
$133$		0			0
$134$	−2.58563	+	4.47844i	−0.223364	+	0.386878i
$135$	−7.84715	+	4.53056i	−0.675375	+	0.389928i
$136$	6.39584	−	3.69264i	0.548439	−	0.316641i
$137$	17.2751	−	9.97376i	1.47591	−	0.852116i	0.476278	−	0.879295i	$-0.341986\pi$
$137$	17.2751	−	9.97376i	1.47591	−	0.852116i	0.999631	+	0.0271788i	$0.00865233\pi$
$138$	5.17872	−	2.98994i	0.440842	−	0.254520i
$139$	10.1637	−	17.6041i	0.862077	−	1.49316i	−0.00784365	−	0.999969i	$-0.502497\pi$
$139$	10.1637	−	17.6041i	0.862077	−	1.49316i	0.869921	−	0.493192i	$-0.164170\pi$
$140$		0			0
$141$	1.05073	−	0.606641i	0.0884877	−	0.0510884i
$142$	−1.85596	−	3.21462i	−0.155749	−	0.269765i
$143$	−21.4219	−	0.455325i	−1.79139	−	0.0380762i
$144$	−0.796164	+	1.37900i	−0.0663470	+	0.114916i
$145$	−16.4265	−	9.48383i	−1.36414	−	0.787589i
$146$	3.42013	+	5.92383i	0.283052	+	0.490260i
$147$		0			0
$148$		−	8.59741i		−	0.706703i
$149$			10.7162i			0.877901i	0.898511	+	0.438951i	$0.144650\pi$
$149$			10.7162i			0.877901i	−0.898511	+	0.438951i	$0.855350\pi$
$150$	−9.48465	+	5.47597i	−0.774418	+	0.447111i
$151$	7.57267	+	4.37208i	0.616255	+	0.355795i	0.775409	−	0.631459i	$-0.217544\pi$
$151$	7.57267	+	4.37208i	0.616255	+	0.355795i	−0.159155	+	0.987254i	$0.550877\pi$
$152$	5.35380			0.434251
$153$	−5.50343	−	9.53222i	−0.444926	−	0.770634i
$154$		0			0
$155$	−3.64130			−0.292476
$156$	11.1117	−	6.10427i	0.889651	−	0.488733i
$157$	−3.25367	+	5.63552i	−0.259671	+	0.449763i	−0.966154	−	0.257967i	$-0.916947\pi$
$157$	−3.25367	+	5.63552i	−0.259671	+	0.449763i	0.706483	+	0.707730i	$0.250281\pi$
$158$		−	6.51770i		−	0.518520i
$159$	−0.531109	+	0.919907i	−0.0421197	+	0.0729534i
$160$	−9.15891	+	15.8637i	−0.724075	+	1.25414i
$161$		0			0
$162$	3.28672	+	1.89759i	0.258229	+	0.149089i
$163$		−	2.61267i		−	0.204640i	−0.994752	−	0.102320i	$-0.967373\pi$
$163$		−	2.61267i		−	0.204640i	0.994752	−	0.102320i	$-0.0326266\pi$
$164$	4.27392	+	2.46755i	0.333737	+	0.192683i
$165$	−24.9952	−	43.2930i	−1.94588	−	3.37036i
$166$	2.55218	−	4.42050i	0.198087	−	0.343097i
$167$	−3.36558	+	1.94312i	−0.260436	+	0.150363i	−0.624534	−	0.780998i	$-0.714711\pi$
$167$	−3.36558	+	1.94312i	−0.260436	+	0.150363i	0.364097	+	0.931361i	$0.381378\pi$
$168$		0			0
$169$	−12.9883	−	0.552385i	−0.999097	−	0.0424911i
$170$	−3.51515	−	6.08842i	−0.269600	−	0.466961i
$171$		−	7.97919i		−	0.610184i
$172$	−9.24072			−0.704599
$173$	−13.9768			−1.06263			−0.531317	−	0.847173i	$-0.678303\pi$
$173$	−13.9768			−1.06263			−0.531317	+	0.847173i	$0.678303\pi$
$174$		−	13.1420i		−	0.996293i
$175$		0			0
$176$	−2.00997	−	1.16046i	−0.151507	−	0.0874727i
$177$	−11.0721	+	6.39250i	−0.832232	+	0.480490i
$178$	1.46649	+	2.54004i	0.109918	+	0.190384i
$179$	25.2843			1.88984			0.944919	−	0.327305i	$-0.106140\pi$
$179$	25.2843			1.88984			0.944919	+	0.327305i	$0.106140\pi$
$180$	14.7575	+	8.52026i	1.09996	+	0.635063i
$181$	−0.864474			−0.0642559			−0.0321279	−	0.999484i	$-0.510228\pi$
$181$	−0.864474			−0.0642559			−0.0321279	+	0.999484i	$0.510228\pi$
$182$		0			0
$183$	−3.07803			−0.227535
$184$	−6.46638	−	3.73336i	−0.476708	−	0.275227i
$185$	−20.5680			−1.51219
$186$	−1.26146	−	2.18492i	−0.0924950	−	0.160206i
$187$	13.8938	−	8.02158i	1.01601	−	0.586596i
$188$	−0.522052	−	0.301407i	−0.0380746	−	0.0219824i
$189$		0			0
$190$		−	5.09647i		−	0.369737i
$191$	14.6676			1.06131			0.530657	−	0.847587i	$-0.321945\pi$
$191$	14.6676			1.06131			0.530657	+	0.847587i	$0.321945\pi$
$192$	−10.6138			−0.765985
$193$			16.4959i			1.18740i	0.804686	+	0.593700i	$0.202333\pi$
$193$			16.4959i			1.18740i	−0.804686	+	0.593700i	$0.797667\pi$
$194$	1.41137	+	2.44457i	0.101331	+	0.175510i
$195$	−14.6035	−	26.5831i	−1.04578	−	1.90365i
$196$		0			0
$197$	9.53510	−	5.50509i	0.679348	−	0.392222i	−0.120262	−	0.992742i	$-0.538373\pi$
$197$	9.53510	−	5.50509i	0.679348	−	0.392222i	0.799609	+	0.600521i	$0.205040\pi$
$198$	9.97709	−	17.2808i	0.709041	−	1.22809i
$199$	−10.6059	−	18.3699i	−0.751829	−	1.30221i	−0.946935	−	0.321425i	$-0.895838\pi$
$199$	−10.6059	−	18.3699i	−0.751829	−	1.30221i	0.195106	−	0.980782i	$-0.437495\pi$
$200$	11.8429	+	6.83753i	0.837423	+	0.483486i
$201$		−	16.7045i		−	1.17824i
$202$	−9.50686	−	5.48879i	−0.668901	−	0.386190i
$203$		0			0
$204$	−4.74632	+	8.22086i	−0.332309	+	0.575576i
$205$	5.90322	−	10.2247i	0.412299	−	0.714122i
$206$		−	9.59027i		−	0.668186i
$207$	−5.56412	+	9.63734i	−0.386733	+	0.669842i
$208$	−1.20425	−	0.729828i	−0.0834998	−	0.0506044i
$209$	11.6301			0.804474
$210$		0			0
$211$	8.96788	+	15.5328i	0.617375	+	1.06932i	0.989963	+	0.141327i	$0.0451370\pi$
$211$	8.96788	+	15.5328i	0.617375	+	1.06932i	−0.372588	+	0.927997i	$0.621530\pi$
$212$	0.527759			0.0362466
$213$	10.3840	+	5.99523i	0.711503	+	0.410786i
$214$	2.80271	−	1.61815i	0.191589	−	0.110614i
$215$			22.1070i			1.50768i
$216$			7.83913i			0.533385i
$217$		0			0
$218$	4.63387	+	8.02610i	0.313845	+	0.543596i
$219$	−19.1355	−	11.0479i	−1.29305	−	0.746545i
$220$	−12.4188	+	21.5100i	−0.837275	+	1.45020i
$221$	8.53115	−	4.68662i	0.573867	−	0.315256i
$222$	−7.12540	−	12.3415i	−0.478225	−	0.828311i
$223$	−13.8834	+	8.01558i	−0.929700	+	0.536763i	−0.886717	−	0.462313i	$-0.847020\pi$
$223$	−13.8834	+	8.01558i	−0.929700	+	0.536763i	−0.0429835	+	0.999076i	$0.513686\pi$
$224$		0			0
$225$	10.1905	−	17.6505i	0.679366	−	1.17670i
$226$	−4.11826	+	2.37768i	−0.273943	+	0.158161i
$227$	14.1812	−	8.18751i	0.941239	−	0.543424i	0.0508902	−	0.998704i	$-0.483794\pi$
$227$	14.1812	−	8.18751i	0.941239	−	0.543424i	0.890348	+	0.455280i	$0.150461\pi$
$228$	−5.95954	+	3.44074i	−0.394680	+	0.227869i
$229$	23.3917	−	13.5052i	1.54577	−	0.892449i	0.547310	−	0.836930i	$-0.315652\pi$
$229$	23.3917	−	13.5052i	1.54577	−	0.892449i	0.998458	−	0.0555193i	$-0.0176814\pi$
$230$	−3.55392	+	6.15556i	−0.234338	+	0.405886i
$231$		0			0
$232$	−14.2112	+	8.20484i	−0.933011	+	0.538674i
$233$	5.78406	+	10.0183i	0.378926	+	0.656320i	0.990906	−	0.134554i	$-0.0429601\pi$
$233$	5.78406	+	10.0183i	0.378926	+	0.656320i	−0.611980	+	0.790873i	$0.709627\pi$
$234$	6.27473	−	10.3536i	0.410192	−	0.676837i
$235$	−0.721069	+	1.24893i	−0.0470374	+	0.0814711i
$236$	5.50114	+	3.17609i	0.358094	+	0.206746i
$237$	10.5269	+	18.2331i	0.683796	+	1.18437i
$238$		0			0
$239$		−	14.6731i		−	0.949122i	−0.880223	−	0.474561i	$-0.842607\pi$
$239$		−	14.6731i		−	0.949122i	0.880223	−	0.474561i	$-0.157393\pi$
$240$		−	3.28533i		−	0.212067i
$241$	−12.4246	+	7.17334i	−0.800338	+	0.462076i	−0.843589	−	0.536989i	$-0.819562\pi$
$241$	−12.4246	+	7.17334i	−0.800338	+	0.462076i	0.0432510	+	0.999064i	$0.486228\pi$
$242$	17.3424	+	10.0126i	1.11481	+	0.643637i
$243$	−20.8560			−1.33791
$244$	0.764654	+	1.32442i	0.0489519	+	0.0847872i
$245$		0			0
$246$	8.18025			0.521554
$247$	7.05464	+	0.149948i	0.448876	+	0.00954094i
$248$	−1.57512	+	2.72818i	−0.100020	+	0.173240i
$249$			16.4883i			1.04491i
$250$	−0.00152545	+	0.00264216i	−9.64781e−5	+	0.000167105i
$251$	4.30726	−	7.46040i	0.271872	−	0.470896i	−0.697469	−	0.716615i	$-0.745691\pi$
$251$	4.30726	−	7.46040i	0.271872	−	0.470896i	0.969341	+	0.245719i	$0.0790239\pi$
$252$		0			0
$253$	−14.0470	−	8.11004i	−0.883128	−	0.509874i
$254$		−	5.04936i		−	0.316825i
$255$	19.6671	+	11.3548i	1.23160	+	0.711066i
$256$	7.40753	+	12.8302i	0.462970	+	0.801888i
$257$	5.18197	−	8.97544i	0.323243	−	0.559873i	−0.657912	−	0.753094i	$-0.728560\pi$
$257$	5.18197	−	8.97544i	0.323243	−	0.559873i	0.981155	+	0.193222i	$0.0618936\pi$
$258$	−13.2650	+	7.65856i	−0.825844	+	0.476801i
$259$		0			0
$260$	−7.81035	+	12.8875i	−0.484377	+	0.799247i
$261$	12.2283	+	21.1800i	0.756913	+	1.31101i
$262$			8.41813i			0.520074i
$263$	−22.0826			−1.36167			−0.680835	−	0.732436i	$-0.738383\pi$
$263$	−22.0826			−1.36167			−0.680835	+	0.732436i	$0.738383\pi$
$264$	−43.2488			−2.66178
$265$		−	1.26258i		−	0.0775596i
$266$		0			0
$267$	−8.20495	−	4.73713i	−0.502135	−	0.289908i
$268$	−7.18761	+	4.14977i	−0.439053	+	0.253488i
$269$	−6.46995	−	11.2063i	−0.394480	−	0.683259i	0.598555	−	0.801082i	$-0.295742\pi$
$269$	−6.46995	−	11.2063i	−0.394480	−	0.683259i	−0.993035	+	0.117823i	$0.962409\pi$
$270$	7.46233			0.454143
$271$	15.3069	+	8.83745i	0.929829	+	0.536837i	0.886757	−	0.462235i	$-0.152952\pi$
$271$	15.3069	+	8.83745i	0.929829	+	0.536837i	0.0430712	+	0.999072i	$0.486286\pi$
$272$	1.05434			0.0639289
$273$		0			0
$274$	−16.4279			−0.992446
$275$	25.7266	+	14.8533i	1.55137	+	0.895685i
$276$	9.59732			0.577691
$277$	−9.00751	−	15.6015i	−0.541209	−	0.937401i	−0.998835	−	0.0482562i	$-0.984634\pi$
$277$	−9.00751	−	15.6015i	−0.541209	−	0.937401i	0.457626	−	0.889145i	$-0.348700\pi$
$278$	−14.4980	+	8.37041i	−0.869530	+	0.502024i
$279$	4.06602	+	2.34752i	0.243426	+	0.140542i
$280$		0			0
$281$			2.44178i			0.145665i	0.997344	+	0.0728323i	$0.0232038\pi$
$281$			2.44178i			0.145665i	−0.997344	+	0.0728323i	$0.976796\pi$
$282$	−0.999205			−0.0595018
$283$	28.7240			1.70746			0.853732	−	0.520713i	$-0.174334\pi$
$283$	28.7240			1.70746			0.853732	+	0.520713i	$0.174334\pi$
$284$		−	5.95741i		−	0.353507i
$285$	8.23143	+	14.2573i	0.487588	+	0.844527i
$286$	15.0910	+	9.14580i	0.892350	+	0.540802i
$287$		0			0
$288$	20.4544	−	11.8094i	1.20529	−	0.695873i
$289$	4.85596	−	8.41078i	0.285645	−	0.494752i
$290$	7.81046	+	13.5281i	0.458646	+	0.794399i
$291$	−7.89657	−	4.55909i	−0.462905	−	0.267258i
$292$			10.9782i			0.642449i
$293$	25.4013	+	14.6654i	1.48396	+	0.856763i	0.999834	−	0.0182359i	$-0.00580499\pi$
$293$	25.4013	+	14.6654i	1.48396	+	0.856763i	0.484124	+	0.874999i	$0.339138\pi$
$294$		0			0
$295$	7.59829	−	13.1606i	0.442390	−	0.766241i
$296$	−8.89708	+	15.4102i	−0.517132	+	0.895699i
$297$			17.0291i			0.988126i
$298$	4.41267	−	7.64298i	0.255619	−	0.442746i
$299$	−8.41611	−	5.10052i	−0.486716	−	0.294971i
$300$	−17.5772			−1.01482
$301$		0			0
$302$	−3.60065	−	6.23651i	−0.207194	−	0.358871i
$303$	35.4603			2.03714
$304$	0.661923	+	0.382161i	0.0379639	+	0.0219185i
$305$	3.16846	−	1.82931i	0.181426	−	0.104746i
$306$			9.06476i			0.518198i
$307$		−	7.06910i		−	0.403455i	−0.979442	−	0.201728i	$-0.935344\pi$
$307$		−	7.06910i		−	0.403455i	0.979442	−	0.201728i	$-0.0646555\pi$
$308$		0			0
$309$	15.4895	+	26.8286i	0.881166	+	1.52623i
$310$	2.59705	+	1.49941i	0.147503	+	0.0851607i
$311$	−11.1343	+	19.2852i	−0.631368	+	1.09356i	0.355904	+	0.934522i	$0.384173\pi$
$311$	−11.1343	+	19.2852i	−0.631368	+	1.09356i	−0.987272	+	0.159039i	$0.949160\pi$
$312$	−26.2340	−	0.557607i	−1.48520	−	0.0315683i
$313$	14.0420	+	24.3214i	0.793700	+	1.37473i	0.923661	+	0.383210i	$0.125181\pi$
$313$	14.0420	+	24.3214i	0.793700	+	1.37473i	−0.129961	+	0.991519i	$0.541485\pi$
$314$	4.64117	−	2.67958i	0.261916	−	0.151217i
$315$		0			0
$316$	5.23025	−	9.05906i	0.294225	−	0.509612i
$317$	−16.9009	+	9.75774i	−0.949249	+	0.548049i	−0.892848	−	0.450359i	$-0.851296\pi$
$317$	−16.9009	+	9.75774i	−0.949249	+	0.548049i	−0.0564015	+	0.998408i	$0.517963\pi$
$318$	0.757595	−	0.437398i	0.0424838	−	0.0245281i
$319$	−30.8712	+	17.8235i	−1.72845	+	0.997924i
$320$	10.9256	−	6.30792i	0.610762	−	0.352624i
$321$	−5.22702	+	9.05346i	−0.291744	+	0.505315i
$322$		0			0
$323$	−4.57550	+	2.64167i	−0.254588	+	0.146986i
$324$	3.04551	+	5.27498i	0.169195	+	0.293054i
$325$	15.4138	+	9.34142i	0.855004	+	0.518169i
$326$	−1.07584	+	1.86341i	−0.0595853	+	0.103205i
$327$	−25.9263	−	14.9686i	−1.43373	−	0.827764i
$328$	−5.10711	−	8.84577i	−0.281993	−	0.488426i
$329$		0			0
$330$			41.1700i			2.26633i
$331$		−	15.6308i		−	0.859145i	−0.903032	−	0.429573i	$-0.858664\pi$
$331$		−	15.6308i		−	0.859145i	0.903032	−	0.429573i	$-0.141336\pi$
$332$	7.09463	−	4.09609i	0.389368	−	0.224802i
$333$	22.9670	+	13.2600i	1.25858	+	0.726644i
$334$	3.20053			0.175125
$335$	9.92767	+	17.1952i	0.542407	+	0.939476i
$336$		0			0
$337$	21.7501			1.18480			0.592401	−	0.805643i	$-0.298180\pi$
$337$	21.7501			1.18480			0.592401	+	0.805643i	$0.298180\pi$
$338$	9.03603	+	5.74225i	0.491495	+	0.312337i
$339$	7.68050	−	13.3030i	0.417148	−	0.722521i
$340$		−	11.2832i		−	0.611917i
$341$	−3.42165	+	5.92647i	−0.185293	+	0.320937i
$342$	−3.28565	+	5.69092i	−0.177668	+	0.307730i
$343$		0			0
$344$	16.5633	+	9.56281i	0.893032	+	0.515592i
$345$		−	22.9601i		−	1.23613i
$346$	9.96851	+	5.75532i	0.535910	+	0.309408i
$347$	7.97952	+	13.8209i	0.428363	+	0.741946i	0.996728	−	0.0808303i	$-0.0257572\pi$
$347$	7.97952	+	13.8209i	0.428363	+	0.741946i	−0.568365	+	0.822777i	$0.692424\pi$
$348$	10.5460	−	18.2663i	0.565327	−	0.979176i
$349$	5.90375	−	3.40853i	0.316021	−	0.182455i	−0.333597	−	0.942716i	$-0.608262\pi$
$349$	5.90375	−	3.40853i	0.316021	−	0.182455i	0.649617	+	0.760261i	$0.274929\pi$
$350$		0			0
$351$	−0.219556	+	10.3295i	−0.0117190	+	0.551349i
$352$	17.2128	+	29.8135i	0.917448	+	1.58907i
$353$			14.0033i			0.745318i	0.927968	+	0.372659i	$0.121554\pi$
$353$			14.0033i			0.745318i	−0.927968	+	0.372659i	$0.878446\pi$
$354$	10.5292			0.559619
$355$	−14.2522			−0.756427
$356$			4.70725i			0.249484i
$357$		0			0
$358$	−18.0333	−	10.4115i	−0.953088	−	0.550266i
$359$	4.68947	−	2.70747i	0.247501	−	0.142895i	−0.371119	−	0.928586i	$-0.621026\pi$
$359$	4.68947	−	2.70747i	0.247501	−	0.142895i	0.618619	+	0.785691i	$0.287692\pi$
$360$	−17.6345	−	30.5438i	−0.929418	−	1.60980i
$361$	15.1700			0.798419
$362$	0.616561	+	0.355972i	0.0324057	+	0.0187094i
$363$	−64.6867			−3.39517
$364$		0			0
$365$	26.2636			1.37470
$366$	2.19531	+	1.26747i	0.114751	+	0.0662515i
$367$	30.0317			1.56764			0.783822	−	0.620985i	$-0.213267\pi$
$367$	30.0317			1.56764			0.783822	+	0.620985i	$0.213267\pi$
$368$	−0.532985	−	0.923157i	−0.0277838	−	0.0481229i
$369$	−13.1835	+	7.61152i	−0.686307	+	0.396240i
$370$	14.6695	+	8.46943i	0.762630	+	0.440305i
$371$		0			0
$372$		−	4.04914i		−	0.209938i
$373$	21.4098			1.10856			0.554278	−	0.832332i	$-0.312995\pi$
$373$	21.4098			1.10856			0.554278	+	0.832332i	$0.312995\pi$
$374$	−13.2124			−0.683199
$375$		−	0.00985519i		−	0.000508920i
$376$	0.623826	+	1.08050i	0.0321713	+	0.0557224i
$377$	−18.9557	+	10.4134i	−0.976270	+	0.536317i
$378$		0			0
$379$	−8.20693	+	4.73827i	−0.421562	+	0.243389i	−0.695745	−	0.718289i	$-0.744926\pi$
$379$	−8.20693	+	4.73827i	−0.421562	+	0.243389i	0.274184	+	0.961677i	$0.411592\pi$
$380$	4.08975	−	7.08366i	0.209800	−	0.363384i
$381$	8.15535	+	14.1255i	0.417811	+	0.723670i
$382$	−10.4613	−	6.03982i	−0.535245	−	0.309024i
$383$			5.43061i			0.277491i	0.990328	+	0.138746i	$0.0443070\pi$
$383$			5.43061i			0.277491i	−0.990328	+	0.138746i	$0.955693\pi$
$384$	−19.1225	−	11.0404i	−0.975842	−	0.563402i
$385$		0			0
$386$	6.79264	−	11.7652i	0.345736	−	0.598833i
$387$	14.2522	−	24.6855i	0.724480	−	1.25484i
$388$			4.53033i			0.229993i
$389$	−5.32109	+	9.21640i	−0.269790	+	0.467290i	−0.968807	−	0.247815i	$-0.920288\pi$
$389$	−5.32109	+	9.21640i	−0.269790	+	0.467290i	0.699018	+	0.715105i	$0.253621\pi$
$390$	−0.530805	+	24.9730i	−0.0268784	+	1.26456i
$391$	7.36845			0.372638
$392$		0			0
$393$	−13.5963	−	23.5495i	−0.685845	−	1.18792i
$394$	−9.06750			−0.456814
$395$	−21.6724	−	12.5126i	−1.09046	−	0.629575i
$396$	27.7346	−	16.0126i	1.39372	−	0.804663i
$397$		−	37.1854i		−	1.86628i	−0.359512	−	0.933140i	$-0.617057\pi$
$397$		−	37.1854i		−	1.86628i	0.359512	−	0.933140i	$-0.382943\pi$
$398$			17.4690i			0.875644i
$399$		0			0
$400$	0.976143	+	1.69073i	0.0488072	+	0.0845365i
$401$	0.776487	+	0.448305i	0.0387759	+	0.0223873i	0.519263	−	0.854615i	$-0.326207\pi$
$401$	0.776487	+	0.448305i	0.0387759	+	0.0223873i	−0.480487	+	0.877002i	$0.659540\pi$
$402$	−6.87853	+	11.9140i	−0.343070	+	0.594214i
$403$	−2.15192	+	3.55078i	−0.107195	+	0.176877i
$404$	−8.80916	−	15.2579i	−0.438272	−	0.759110i
$405$	12.6196	−	7.28590i	0.627071	−	0.362039i
$406$		0			0
$407$	−19.3273	+	33.4758i	−0.958016	+	1.65933i
$408$	17.0148	−	9.82350i	0.842359	−	0.486336i
$409$	−21.2846	+	12.2886i	−1.05245	+	0.607635i	−0.923335	−	0.383995i	$-0.874548\pi$
$409$	−21.2846	+	12.2886i	−1.05245	+	0.607635i	−0.129119	+	0.991629i	$0.541215\pi$
$410$	−8.42059	+	4.86163i	−0.415863	+	0.240099i
$411$	45.9567	−	26.5331i	2.26688	−	1.30878i
$412$	7.69589	−	13.3297i	0.379149	−	0.656706i
$413$		0			0
$414$	7.93689	−	4.58237i	0.390077	−	0.225211i
$415$	−9.79924	−	16.9728i	−0.481026	−	0.833161i
$416$	10.0566	+	18.3063i	0.493067	+	0.897540i
$417$	27.0385	−	46.8321i	1.32408	−	2.29338i
$418$	−8.29486	−	4.78904i	−0.405715	−	0.234239i
$419$	3.82279	+	6.62126i	0.186755	+	0.323470i	0.944167	−	0.329468i	$-0.106869\pi$
$419$	3.82279	+	6.62126i	0.186755	+	0.323470i	−0.757411	+	0.652938i	$0.773536\pi$
$420$		0			0
$421$			25.0780i			1.22223i	0.791544	+	0.611113i	$0.209278\pi$
$421$			25.0780i			1.22223i	−0.791544	+	0.611113i	$0.790722\pi$
$422$		−	14.7711i		−	0.719046i
$423$	1.61035	−	0.929736i	0.0782979	−	0.0452053i
$424$	−0.945966	−	0.546154i	−0.0459402	−	0.0265236i
$425$	−13.4951			−0.654606
$426$	−4.93741	−	8.55184i	−0.239218	−	0.414338i
$427$		0			0
$428$	5.19405			0.251064
$429$	−56.9884	−	1.21130i	−2.75143	−	0.0584820i
$430$	9.10317	−	15.7671i	0.438994	−	0.760359i
$431$			7.75404i			0.373499i	0.982408	+	0.186750i	$0.0597953\pi$
$431$			7.75404i			0.373499i	−0.982408	+	0.186750i	$0.940205\pi$
$432$	−0.559567	+	0.969199i	−0.0269222	+	0.0466306i
$433$	17.9880	−	31.1561i	0.864448	−	1.49727i	−0.00314644	−	0.999995i	$-0.501002\pi$
$433$	17.9880	−	31.1561i	0.864448	−	1.49727i	0.867594	−	0.497273i	$-0.165665\pi$
$434$		0			0
$435$	−43.6992	−	25.2298i	−2.09522	−	1.20967i
$436$			14.8741i			0.712342i
$437$	4.62596	+	2.67080i	0.221290	+	0.127762i
$438$	9.09853	+	15.7591i	0.434745	+	0.753000i
$439$	−14.1175	+	24.4523i	−0.673792	+	1.16704i	0.303028	+	0.952982i	$0.402002\pi$
$439$	−14.1175	+	24.4523i	−0.673792	+	1.16704i	−0.976820	+	0.214061i	$0.931331\pi$
$440$	44.5194	−	25.7033i	2.12238	−	1.22536i
$441$		0			0
$442$	−8.01444	−	0.170348i	−0.381208	−	0.00810264i
$443$	−14.3959	−	24.9344i	−0.683970	−	1.18467i	−0.973759	−	0.227580i	$-0.926919\pi$
$443$	−14.3959	−	24.9344i	−0.683970	−	1.18467i	0.289790	−	0.957090i	$-0.406415\pi$
$444$		−	22.8716i		−	1.08544i
$445$	11.2614			0.533840
$446$	13.2026			0.625159
$447$			28.5081i			1.34839i
$448$		0			0
$449$	−25.2795	−	14.5951i	−1.19301	−	0.688785i	−0.234023	−	0.972231i	$-0.575189\pi$
$449$	−25.2795	−	14.5951i	−1.19301	−	0.688785i	−0.958988	+	0.283446i	$0.908522\pi$
$450$	−14.5361	+	8.39244i	−0.685240	+	0.395624i
$451$	−11.0942	−	19.2158i	−0.522408	−	0.904836i
$452$	−7.63205			−0.358982
$453$	20.1455	+	11.6310i	0.946518	+	0.546473i
$454$	−13.4858			−0.632918
$455$		0			0
$456$	14.2427			0.666974
$457$	27.4399	+	15.8424i	1.28358	+	0.741077i	0.977501	−	0.210929i	$-0.0676489\pi$
$457$	27.4399	+	15.8424i	1.28358	+	0.741077i	0.306081	+	0.952006i	$0.400982\pi$
$458$	−22.2446			−1.03942
$459$	−3.86797	−	6.69952i	−0.180541	−	0.312707i
$460$	−9.87929	+	5.70381i	−0.460624	+	0.265942i
$461$	−19.1407	−	11.0509i	−0.891471	−	0.514691i	−0.0170480	−	0.999855i	$-0.505427\pi$
$461$	−19.1407	−	11.0509i	−0.891471	−	0.514691i	−0.874424	+	0.485163i	$0.838760\pi$
$462$		0			0
$463$		−	38.8811i		−	1.80696i	−0.428632	−	0.903479i	$-0.641004\pi$
$463$		−	38.8811i		−	1.80696i	0.428632	−	0.903479i	$-0.358996\pi$
$464$	−2.34269			−0.108757
$465$	−9.68693			−0.449220
$466$		−	9.52699i		−	0.441329i
$467$	6.64116	+	11.5028i	0.307316	+	0.532287i	0.977774	−	0.209660i	$-0.0672358\pi$
$467$	6.64116	+	11.5028i	0.307316	+	0.532287i	−0.670458	+	0.741947i	$0.733902\pi$
$468$	17.0298	−	9.35538i	0.787203	−	0.432453i
$469$		0			0
$470$	1.02856	−	0.593841i	0.0474440	−	0.0273918i
$471$	−8.65571	+	14.9921i	−0.398834	+	0.690801i
$472$	−6.57358	−	11.3858i	−0.302574	−	0.524073i
$473$	35.9807	+	20.7734i	1.65439	+	0.955164i
$474$		−	17.3390i		−	0.796406i
$475$	−8.47228	−	4.89147i	−0.388735	−	0.224436i
$476$		0			0
$477$	−0.813975	+	1.40985i	−0.0372694	+	0.0645524i
$478$	−6.04205	+	10.4651i	−0.276357	+	0.478664i
$479$			6.63512i			0.303166i	0.988445	+	0.151583i	$0.0484371\pi$
$479$			6.63512i			0.303166i	−0.988445	+	0.151583i	$0.951563\pi$
$480$	−24.3654	+	42.2021i	−1.11212	+	1.92625i
$481$	−12.1552	+	20.0566i	−0.554229	+	0.914504i
$482$	11.8153			0.538172
$483$		0			0
$484$	16.0697	+	27.8335i	0.730439	+	1.26516i
$485$	10.8381			0.492133
$486$	14.8749	+	8.58804i	0.674740	+	0.389561i
$487$	−28.9860	+	16.7351i	−1.31348	+	0.758338i	−0.982671	−	0.185359i	$-0.940655\pi$
$487$	−28.9860	+	16.7351i	−1.31348	+	0.758338i	−0.330809	+	0.943698i	$0.607322\pi$
$488$		−	3.16522i		−	0.143283i
$489$		−	6.95047i		−	0.314311i
$490$		0			0
$491$	−18.6643	−	32.3276i	−0.842310	−	1.45892i	−0.887937	−	0.459966i	$-0.847862\pi$
$491$	−18.6643	−	32.3276i	−0.842310	−	1.45892i	0.0456264	−	0.998959i	$-0.485472\pi$
$492$	11.3699	+	6.56439i	0.512593	+	0.295946i
$493$	8.09684	−	14.0241i	0.364663	−	0.631615i
$494$	−4.96977	−	3.01189i	−0.223601	−	0.135511i
$495$	−38.3076	−	66.3507i	−1.72180	−	2.98224i
$496$	−0.389483	+	0.224868i	−0.0174883	+	0.0100969i
$497$		0			0
$498$	6.78954	−	11.7598i	0.304246	−	0.526970i
$499$	−29.5598	+	17.0663i	−1.32328	+	0.763994i	−0.984250	−	0.176783i	$-0.943431\pi$
$499$	−29.5598	+	17.0663i	−1.32328	+	0.763994i	−0.339027	+	0.940777i	$0.610098\pi$
$500$	−0.00424050	+	0.00244826i	−0.000189641	+	0.000109489i
$501$	−8.95342	+	5.16926i	−0.400009	+	0.230946i
$502$	−6.14405	+	3.54727i	−0.274223	+	0.158322i
$503$	−7.65447	+	13.2579i	−0.341296	+	0.591142i	−0.984674	−	0.174407i	$-0.944199\pi$
$503$	−7.65447	+	13.2579i	−0.341296	+	0.591142i	0.643378	+	0.765549i	$0.277533\pi$
$504$		0			0
$505$	−36.5022	+	21.0745i	−1.62433	+	0.937805i
$506$	6.67907	+	11.5685i	0.296921	+	0.514282i
$507$	−34.5526	−	1.46950i	−1.53453	−	0.0652630i
$508$	4.05195	−	7.01819i	0.179776	−	0.311382i
$509$	16.0189	+	9.24851i	0.710025	+	0.409933i	0.811070	−	0.584949i	$-0.198885\pi$
$509$	16.0189	+	9.24851i	0.710025	+	0.409933i	−0.101046	+	0.994882i	$0.532219\pi$
$510$	−9.35133	−	16.1970i	−0.414084	−	0.717214i
$511$		0			0
$512$			4.39924i			0.194421i
$513$		−	5.60801i		−	0.247599i
$514$	−7.39178	+	4.26765i	−0.326037	+	0.188238i
$515$	−31.8892	−	18.4112i	−1.40520	−	0.811295i
$516$	−24.5830			−1.08221
$517$	1.35515	+	2.34718i	0.0595992	+	0.103229i
$518$		0			0
$519$	−37.1823			−1.63212
$520$	27.3361	−	15.0172i	1.19877	−	0.658547i
$521$	−11.7932	+	20.4265i	−0.516671	+	0.894901i	0.483141	+	0.875542i	$0.339496\pi$
$521$	−11.7932	+	20.4265i	−0.516671	+	0.894901i	−0.999813	+	0.0193585i	$0.993838\pi$
$522$		−	20.1414i		−	0.881564i
$523$	−6.15294	+	10.6572i	−0.269049	+	0.466007i	−0.968617	−	0.248560i	$-0.920043\pi$
$523$	−6.15294	+	10.6572i	−0.269049	+	0.466007i	0.699567	+	0.714567i	$0.253376\pi$
$524$	−6.75529	+	11.7005i	−0.295106	+	0.511139i
$525$		0			0
$526$	15.7498	+	9.09312i	0.686722	+	0.396479i
$527$		−	3.10877i		−	0.135420i
$528$	−5.34711	−	3.08715i	−0.232703	−	0.134351i
$529$	7.77515	+	13.4670i	0.338050	+	0.585520i
$530$	−0.519902	+	0.900497i	−0.0225831	+	0.0391151i
$531$	−16.9691	+	9.79712i	−0.736397	+	0.425159i
$532$		0			0
$533$	−6.48183	−	11.7990i	−0.280759	−	0.511072i
$534$	3.90129	+	6.75724i	0.168825	+	0.292414i
$535$		−	12.4259i		−	0.537220i
$536$	17.1777			0.741962
$537$	67.2636			2.90264
$538$			10.6567i			0.459444i
$539$		0			0
$540$	10.3720	+	5.98829i	0.446341	+	0.257695i
$541$	16.8365	−	9.72054i	0.723857	−	0.417919i	−0.0923139	−	0.995730i	$-0.529426\pi$
$541$	16.8365	−	9.72054i	0.723857	−	0.417919i	0.816170	+	0.577811i	$0.196093\pi$
$542$	−7.27813	−	12.6061i	−0.312623	−	0.541478i
$543$	−2.29975			−0.0986919
$544$	−13.5437	−	7.81944i	−0.580680	−	0.335256i
$545$	35.5841			1.52425
$546$		0			0
$547$	40.2163			1.71953			0.859763	−	0.510693i	$-0.170611\pi$
$547$	40.2163			1.71953			0.859763	+	0.510693i	$0.170611\pi$
$548$	−22.8334	−	13.1829i	−0.975395	−	0.563145i
$549$	−4.71738			−0.201333
$550$	−12.2325	−	21.1873i	−0.521595	−	0.903429i
$551$	10.1665	−	5.86963i	0.433107	−	0.250055i
$552$	−17.2024	−	9.93184i	−0.732185	−	0.422727i
$553$		0			0
$554$			14.8364i			0.630337i
$555$	−54.7168			−2.32260
$556$	−26.8680			−1.13945
$557$			7.96399i			0.337445i	0.985664	+	0.168722i	$0.0539642\pi$
$557$			7.96399i			0.337445i	−0.985664	+	0.168722i	$0.946036\pi$
$558$	−1.93331	−	3.34860i	−0.0818437	−	0.141757i
$559$	21.5574	+	13.0647i	0.911781	+	0.552578i
$560$		0			0
$561$	36.9615	−	21.3397i	1.56052	−	0.900965i
$562$	1.00547	−	1.74153i	0.0424133	−	0.0734620i
$563$	−0.711981	−	1.23319i	−0.0300064	−	0.0519726i	0.850632	−	0.525761i	$-0.176219\pi$
$563$	−0.711981	−	1.23319i	−0.0300064	−	0.0519726i	−0.880639	+	0.473789i	$0.842886\pi$
$564$	−1.38881	−	0.801831i	−0.0584795	−	0.0337632i
$565$			18.2585i			0.768140i
$566$	−20.4865	−	11.8279i	−0.861113	−	0.497164i
$567$		0			0
$568$	−6.16506	+	10.6782i	−0.258680	+	0.448047i
$569$	−9.25946	+	16.0379i	−0.388177	+	0.672342i	−0.992204	−	0.124622i	$-0.960228\pi$
$569$	−9.25946	+	16.0379i	−0.388177	+	0.672342i	0.604028	+	0.796963i	$0.293562\pi$
$570$		−	13.5581i		−	0.567886i
$571$	2.17883	−	3.77384i	0.0911812	−	0.157930i	−0.816827	−	0.576882i	$-0.804269\pi$
$571$	2.17883	−	3.77384i	0.0911812	−	0.157930i	0.908008	+	0.418952i	$0.137602\pi$
$572$	13.6360	+	24.8220i	0.570151	+	1.03786i
$573$	39.0202			1.63009
$574$		0			0
$575$	6.82194	+	11.8159i	0.284494	+	0.492759i
$576$	−16.2667			−0.677778
$577$	−8.28280	−	4.78208i	−0.344818	−	0.199081i	0.317583	−	0.948231i	$-0.397129\pi$
$577$	−8.28280	−	4.78208i	−0.344818	−	0.199081i	−0.662400	+	0.749150i	$0.730462\pi$
$578$	−6.92674	+	3.99916i	−0.288115	+	0.166343i
$579$			43.8839i			1.82375i
$580$			25.0706i			1.04100i
$581$		0			0
$582$	3.75466	+	6.50327i	0.155636	+	0.269569i
$583$	−2.05494	−	1.18642i	−0.0851068	−	0.0491364i
$584$	11.3608	−	19.6775i	0.470114	−	0.814262i
$585$	−22.3813	−	40.7411i	−0.925352	−	1.68444i
$586$	−12.0778	−	20.9194i	−0.498929	−	0.864171i
$587$	−2.04428	+	1.18027i	−0.0843765	+	0.0487148i	−0.541595	−	0.840640i	$-0.682179\pi$
$587$	−2.04428	+	1.18027i	−0.0843765	+	0.0487148i	0.457218	+	0.889355i	$0.348846\pi$
$588$		0			0
$589$	1.12682	−	1.95171i	0.0464297	−	0.0804186i
$590$	−10.8385	+	6.25762i	−0.446214	+	0.257622i
$591$	25.3661	−	14.6452i	1.04342	−	0.602421i
$592$	−2.20000	+	1.27017i	−0.0904194	+	0.0522037i
$593$	35.0127	−	20.2146i	1.43780	−	0.830114i	0.440103	−	0.897947i	$-0.354942\pi$
$593$	35.0127	−	20.2146i	1.43780	−	0.830114i	0.997697	+	0.0678337i	$0.0216087\pi$
$594$	7.01219	−	12.1455i	0.287714	−	0.498335i
$595$		0			0
$596$	12.2665	−	7.08207i	0.502455	−	0.290093i
$597$	−28.2147	−	48.8693i	−1.15475	−	2.00009i
$598$	3.90226	+	7.10336i	0.159575	+	0.290478i
$599$	19.2936	−	33.4176i	0.788316	−	1.36540i	−0.138681	−	0.990337i	$-0.544286\pi$
$599$	19.2936	−	33.4176i	0.788316	−	1.36540i	0.926998	−	0.375067i	$-0.122380\pi$
$600$	31.5057	+	18.1898i	1.28621	+	0.742596i
$601$	−4.08115	−	7.06877i	−0.166474	−	0.288341i	0.770704	−	0.637193i	$-0.219905\pi$
$601$	−4.08115	−	7.06877i	−0.166474	−	0.288341i	−0.937178	+	0.348852i	$0.886571\pi$
$602$		0			0
$603$		−	25.6012i		−	1.04256i
$604$		−	11.5576i		−	0.470274i
$605$	66.5872	−	38.4442i	2.70716	−	1.56298i
$606$	−25.2910	−	14.6018i	−1.02738	−	0.593157i
$607$	7.58525			0.307876			0.153938	−	0.988081i	$-0.450804\pi$
$607$	7.58525			0.307876			0.153938	+	0.988081i	$0.450804\pi$
$608$	−5.66853	−	9.81819i	−0.229889	−	0.398180i
$609$		0			0
$610$	−3.01308			−0.121996
$611$	0.791746	+	1.44123i	0.0320306	+	0.0583060i
$612$	−7.27419	+	12.5993i	−0.294042	+	0.509295i
$613$		−	15.5778i		−	0.629183i	−0.949227	−	0.314592i	$-0.898132\pi$
$613$		−	15.5778i		−	0.629183i	0.949227	−	0.314592i	$-0.101868\pi$
$614$	−2.91090	+	5.04183i	−0.117474	+	0.203472i
$615$	15.7043	−	27.2006i	0.633258	−	1.09683i
$616$		0			0
$617$	20.6709	+	11.9343i	0.832177	+	0.480458i	0.854598	−	0.519291i	$-0.173804\pi$
$617$	20.6709	+	11.9343i	0.832177	+	0.480458i	−0.0224202	+	0.999749i	$0.507137\pi$
$618$		−	25.5129i		−	1.02628i
$619$	16.8843	+	9.74814i	0.678636	+	0.391811i	0.799341	−	0.600878i	$-0.205182\pi$
$619$	16.8843	+	9.74814i	0.678636	+	0.391811i	−0.120705	+	0.992688i	$0.538515\pi$
$620$	2.40646	+	4.16810i	0.0966456	+	0.167395i
$621$	−3.91063	+	6.77341i	−0.156928	+	0.271807i
$622$	15.8824	−	9.16972i	0.636827	−	0.367672i
$623$		0			0
$624$	−3.20366	−	1.94155i	−0.128249	−	0.0777244i
$625$	12.5029	+	21.6557i	0.500117	+	0.866228i
$626$		−	23.1287i		−	0.924410i
$627$	30.9396			1.23561
$628$	8.60111			0.343222
$629$		−	17.5599i		−	0.700161i
$630$		0			0
$631$	−22.2239	−	12.8309i	−0.884718	−	0.510792i	−0.0125066	−	0.999922i	$-0.503981\pi$
$631$	−22.2239	−	12.8309i	−0.884718	−	0.510792i	−0.872211	+	0.489130i	$0.837314\pi$
$632$	−18.7496	+	10.8251i	−0.745820	+	0.430600i
$633$	23.8572	+	41.3219i	0.948238	+	1.64240i
$634$	16.0721			0.638304
$635$	−16.7899	−	9.69366i	−0.666287	−	0.384681i
$636$	1.40399			0.0556719
$637$		0			0
$638$	29.3573			1.16227
$639$	15.9145	+	9.18826i	0.629569	+	0.363482i
$640$	26.2458			1.03746
$641$	−0.553020	−	0.957859i	−0.0218430	−	0.0378332i	0.854897	−	0.518797i	$-0.173620\pi$
$641$	−0.553020	−	0.957859i	−0.0218430	−	0.0378332i	−0.876740	+	0.480964i	$0.840287\pi$
$642$	7.45603	−	4.30474i	0.294266	−	0.169895i
$643$	10.9437	+	6.31833i	0.431576	+	0.249171i	0.700018	−	0.714125i	$-0.253175\pi$
$643$	10.9437	+	6.31833i	0.431576	+	0.249171i	−0.268442	+	0.963296i	$0.586509\pi$
$644$		0			0
$645$			58.8110i			2.31568i
$646$	4.35112			0.171192
$647$	−25.7148			−1.01095			−0.505477	−	0.862840i	$-0.668683\pi$
$647$	−25.7148			−1.01095			−0.505477	+	0.862840i	$0.668683\pi$
$648$		−	12.6066i		−	0.495236i
$649$	−14.2799	−	24.7335i	−0.560535	−	0.970875i
$650$	−7.14685	−	13.0096i	−0.280323	−	0.510277i
$651$		0			0
$652$	−2.99066	+	1.72666i	−0.117123	+	0.0676211i
$653$	−12.6303	+	21.8764i	−0.494263	+	0.856089i	−0.999978	−	0.00661158i	$-0.997895\pi$
$653$	−12.6303	+	21.8764i	−0.494263	+	0.856089i	0.505715	+	0.862701i	$0.331229\pi$
$654$	12.3275	+	21.3518i	0.482041	+	0.834920i
$655$	27.9916	+	16.1610i	1.09372	+	0.631461i
$656$		−	1.45821i		−	0.0569335i
$657$	−29.3269	−	16.9319i	−1.14415	−	0.660577i
$658$		0			0
$659$	−11.4882	+	19.8982i	−0.447517	+	0.775123i	−0.998224	−	0.0595764i	$-0.981025\pi$
$659$	−11.4882	+	19.8982i	−0.447517	+	0.775123i	0.550707	+	0.834699i	$0.314358\pi$
$660$	−33.0376	+	57.2228i	−1.28599	+	2.22739i
$661$			30.4326i			1.18369i	0.806051	+	0.591845i	$0.201600\pi$
$661$			30.4326i			1.18369i	−0.806051	+	0.591845i	$0.798400\pi$
$662$	−6.43641	+	11.1482i	−0.250158	+	0.433287i
$663$	22.6954	−	12.4678i	0.881415	−	0.484208i
$664$	−16.9554			−0.657998
$665$		0			0
$666$	−10.9204	−	18.9146i	−0.423155	−	0.732926i
$667$	−16.3723			−0.633937
$668$	4.44847	+	2.56833i	0.172117	+	0.0993715i
$669$	−36.9339	+	21.3238i	−1.42795	+	0.824425i
$670$		−	16.3520i		−	0.631733i
$671$		−	6.87586i		−	0.265440i
$672$		0			0
$673$	5.41933	+	9.38656i	0.208900	+	0.361825i	0.951368	−	0.308056i	$-0.0996784\pi$
$673$	5.41933	+	9.38656i	0.208900	+	0.361825i	−0.742468	+	0.669881i	$0.766345\pi$
$674$	−15.5126	−	8.95620i	−0.597523	−	0.344980i
$675$	7.16218	−	12.4053i	0.275672	−	0.477479i
$676$	7.95135	+	15.2324i	0.305821	+	0.585861i
$677$	9.06044	+	15.6931i	0.348221	+	0.603137i	0.985934	−	0.167138i	$-0.0534525\pi$
$677$	9.06044	+	15.6931i	0.348221	+	0.603137i	−0.637712	+	0.770275i	$0.720119\pi$
$678$	−10.9558	+	6.32532i	−0.420754	+	0.242923i
$679$		0			0
$680$	−11.6765	+	20.2242i	−0.447772	+	0.775564i
$681$	37.7261	−	21.7812i	1.44567	−	0.834656i
$682$	4.88078	−	2.81792i	0.186895	−	0.107904i
$683$	−32.7662	+	18.9176i	−1.25376	+	0.723861i	−0.971855	−	0.235580i	$-0.924301\pi$
$683$	−32.7662	+	18.9176i	−1.25376	+	0.723861i	−0.281909	+	0.959441i	$0.590968\pi$
$684$	−9.13357	+	5.27327i	−0.349231	+	0.201628i
$685$	−31.5380	+	54.6254i	−1.20500	+	2.08713i
$686$		0			0
$687$	62.2288	−	35.9278i	2.37418	−	1.37073i
$688$	1.36521	+	2.36462i	0.0520482	+	0.0901502i
$689$	−1.23119	−	0.746155i	−0.0469047	−	0.0284262i
$690$	−9.45446	+	16.3756i	−0.359925	+	0.623408i
$691$	−26.0034	−	15.0131i	−0.989216	−	0.571124i	−0.0841761	−	0.996451i	$-0.526826\pi$
$691$	−26.0034	−	15.0131i	−0.989216	−	0.571124i	−0.905040	+	0.425327i	$0.860159\pi$
$692$	9.23693	+	15.9988i	0.351135	+	0.608184i
$693$		0			0
$694$		−	13.1432i		−	0.498907i
$695$			64.2774i			2.43818i
$696$	−37.8059	+	21.8273i	−1.43303	+	0.827360i
$697$	8.72934	+	5.03988i	0.330647	+	0.190899i
$698$	−5.61423			−0.212502
$699$	15.3873	+	26.6516i	0.582001	+	1.00805i
$700$		0			0
$701$	0.116177			0.00438796			0.00219398	−	0.999998i	$-0.499302\pi$
$701$	0.116177			0.00438796			0.00219398	+	0.999998i	$0.499302\pi$
$702$	4.41006	−	7.27682i	0.166447	−	0.274646i
$703$	6.36485	−	11.0242i	0.240055	−	0.415787i
$704$		−	23.7097i		−	0.893591i
$705$	−1.91825	+	3.32251i	−0.0722456	+	0.125133i
$706$	5.76624	−	9.98741i	0.217015	−	0.375881i
$707$		0			0
$708$	14.6347	+	8.44932i	0.550004	+	0.317545i
$709$		−	6.72993i		−	0.252748i	−0.991983	−	0.126374i	$-0.959666\pi$
$709$		−	6.72993i		−	0.252748i	0.991983	−	0.126374i	$-0.0403339\pi$
$710$	10.1649	+	5.86873i	0.381483	+	0.220249i
$711$	16.1335	+	27.9440i	0.605053	+	1.04798i
$712$	4.87132	−	8.43738i	0.182561	−	0.316204i
$713$	−2.72196	+	1.57153i	−0.101938	+	0.0588541i
$714$		0			0
$715$	59.3826	−	32.6221i	2.22078	−	1.22000i
$716$	−16.7098	−	28.9423i	−0.624476	−	1.08162i
$717$		−	39.0347i		−	1.45778i
$718$	−4.45950			−0.166427
$719$	−46.8078			−1.74564			−0.872818	−	0.488046i	$-0.837710\pi$
$719$	−46.8078			−1.74564			−0.872818	+	0.488046i	$0.837710\pi$
$720$		−	5.03509i		−	0.187647i
$721$		0			0
$722$	−10.8195	−	6.24666i	−0.402661	−	0.232476i
$723$	−33.0530	+	19.0832i	−1.22926	+	0.709711i
$724$	0.571312	+	0.989541i	0.0212326	+	0.0367760i
$725$	29.9852			1.11362
$726$	46.1359	+	26.6366i	1.71226	+	0.988576i
$727$	13.3362			0.494611			0.247305	−	0.968938i	$-0.420455\pi$
$727$	13.3362			0.494611			0.247305	+	0.968938i	$0.420455\pi$
$728$		0			0
$729$	−41.6582			−1.54290
$730$	−18.7317	−	10.8148i	−0.693291	−	0.400272i
$731$	−18.8739			−0.698076
$732$	2.03420	+	3.52334i	0.0751863	+	0.130226i
$733$	25.5142	−	14.7306i	0.942387	−	0.544087i	0.0516792	−	0.998664i	$-0.483543\pi$
$733$	25.5142	−	14.7306i	0.942387	−	0.544087i	0.890708	+	0.454576i	$0.150209\pi$
$734$	−21.4193	−	12.3664i	−0.790599	−	0.456453i
$735$		0			0
$736$			15.8113i			0.582814i
$737$	37.3153			1.37453
$738$	12.5370			0.461494
$739$		−	12.0302i		−	0.442537i	−0.975213	−	0.221269i	$-0.928980\pi$
$739$		−	12.0302i		−	0.442537i	0.975213	−	0.221269i	$-0.0710198\pi$
$740$	13.5929	+	23.5436i	0.499685	+	0.865480i
$741$	18.7674	+	0.398904i	0.689438	+	0.0146541i
$742$		0			0
$743$	−18.9509	+	10.9413i	−0.695242	+	0.401398i	−0.805573	−	0.592497i	$-0.798142\pi$
$743$	−18.9509	+	10.9413i	−0.695242	+	0.401398i	0.110331	+	0.993895i	$0.464809\pi$
$744$	−4.19027	+	7.25777i	−0.153623	+	0.266083i
$745$	−16.9427	−	29.3457i	−0.620734	−	1.07514i
$746$	−15.2699	−	8.81607i	−0.559070	−	0.322779i
$747$			25.2700i			0.924580i
$748$	−18.3642	−	10.6026i	−0.671461	−	0.387668i
$749$		0			0
$750$	−0.00405815	+	0.00702892i	−0.000148183	+	0.000256660i
$751$	17.3746	−	30.0937i	0.634008	−	1.09813i	−0.352717	−	0.935730i	$-0.614742\pi$
$751$	17.3746	−	30.0937i	0.634008	−	1.09813i	0.986724	−	0.162403i	$-0.0519245\pi$
$752$			0.178118i			0.00649529i
$753$	11.4586	−	19.8468i	0.417574	−	0.723259i
$754$	17.8076	+	0.378504i	0.648515	+	0.0137843i
$755$	−27.6498			−1.00628
$756$		0			0
$757$	−21.9632	−	38.0413i	−0.798265	−	1.38264i	−0.920745	−	0.390164i	$-0.872418\pi$
$757$	−21.9632	−	38.0413i	−0.798265	−	1.38264i	0.122481	−	0.992471i	$-0.460915\pi$
$758$	7.80447			0.283471
$759$	−37.3691	−	21.5751i	−1.35641	−	0.783126i
$760$	−14.6611	+	8.46461i	−0.531815	+	0.307044i
$761$		−	0.141391i		−	0.00512543i	−0.999997	−	0.00256272i	$-0.999184\pi$
$761$		−	0.141391i		−	0.00512543i	0.999997	−	0.00256272i	$-0.000815739\pi$
$762$		−	13.4328i		−	0.486618i
$763$		0			0
$764$	−9.69352	−	16.7897i	−0.350699	−	0.607429i
$765$	30.1418	+	17.4024i	1.08978	+	0.629183i
$766$	2.23620	−	3.87322i	0.0807973	−	0.139945i
$767$	−8.34305	−	15.1870i	−0.301250	−	0.548372i
$768$	19.7062	+	34.1321i	0.711086	+	1.23164i
$769$	11.8200	−	6.82429i	0.426241	−	0.246090i	−0.271503	−	0.962438i	$-0.587521\pi$
$769$	11.8200	−	6.82429i	0.426241	−	0.246090i	0.697744	+	0.716347i	$0.254187\pi$
$770$		0			0
$771$	13.7856	−	23.8773i	0.496475	−	0.859920i
$772$	18.8824	−	10.9018i	0.679593	−	0.392363i
$773$	−15.2328	+	8.79469i	−0.547887	+	0.316323i	−0.748269	−	0.663395i	$-0.769115\pi$
$773$	−15.2328	+	8.79469i	−0.547887	+	0.316323i	0.200382	+	0.979718i	$0.435782\pi$
$774$	−20.3299	+	11.7375i	−0.730744	+	0.421895i
$775$	4.98518	−	2.87820i	0.179073	−	0.103388i
$776$	4.68824	−	8.12026i	0.168298	−	0.291500i
$777$		0			0
$778$	7.59022	−	4.38221i	0.272123	−	0.157110i
$779$	3.65356	+	6.32814i	0.130902	+	0.226729i
$780$	−20.7778	+	34.2844i	−0.743965	+	1.22758i
$781$	−13.3924	+	23.1964i	−0.479219	+	0.830032i
$782$	−5.25533	−	3.03416i	−0.187930	−	0.108501i
$783$	8.59441	+	14.8860i	0.307139	+	0.531981i
$784$		0			0
$785$		−	20.5768i		−	0.734418i
$786$			22.3947i			0.798792i
$787$	−2.57075	+	1.48422i	−0.0916374	+	0.0529069i	−0.545118	−	0.838359i	$-0.683515\pi$
$787$	−2.57075	+	1.48422i	−0.0916374	+	0.0529069i	0.453481	+	0.891266i	$0.350182\pi$
$788$	−12.6031	−	7.27639i	−0.448966	−	0.259210i
$789$	−58.7461			−2.09142
$790$	10.3048	+	17.8484i	0.366628	+	0.635018i
$791$		0			0
$792$	−66.2829			−2.35526
$793$	0.0886506	−	4.17078i	0.00314807	−	0.148109i
$794$	−15.3121	+	26.5214i	−0.543407	+	0.941208i
$795$		−	3.35883i		−	0.119125i
$796$	−14.0184	+	24.2805i	−0.496867	+	0.860600i
$797$	4.72611	−	8.18586i	0.167407	−	0.289958i	−0.770100	−	0.637923i	$-0.779794\pi$
$797$	4.72611	−	8.18586i	0.167407	−	0.289958i	0.937508	+	0.347965i	$0.113127\pi$
$798$		0			0
$799$	−1.06628	−	0.615614i	−0.0377221	−	0.0217789i
$800$		−	28.9579i		−	1.02382i
$801$	−12.5749	−	7.26011i	−0.444312	−	0.256523i
$802$	−0.369204	−	0.639481i	−0.0130371	−	0.0225809i
$803$	24.6793	−	42.7458i	0.870913	−	1.50847i
$804$	−19.1212	+	11.0396i	−0.674351	+	0.389337i
$805$		0			0
$806$	2.99693	−	1.64637i	0.105562	−	0.0579911i
$807$	−17.2120	−	29.8120i	−0.605890	−	1.04943i
$808$			36.4648i			1.28283i
$809$	−1.16255			−0.0408729			−0.0204365	−	0.999791i	$-0.506506\pi$
$809$	−1.16255			−0.0408729			−0.0204365	+	0.999791i	$0.506506\pi$
$810$	−12.0007			−0.421662
$811$			19.5561i			0.686706i	0.939206	+	0.343353i	$0.111563\pi$
$811$			19.5561i			0.686706i	−0.939206	+	0.343353i	$0.888437\pi$
$812$		0			0
$813$	40.7209	+	23.5102i	1.42814	+	0.824538i
$814$	27.5692	−	15.9171i	0.966299	−	0.557893i
$815$	4.13075	+	7.15467i	0.144694	+	0.250617i
$816$	2.80486			0.0981897
$817$	−11.8491	−	6.84111i	−0.414549	−	0.239340i
$818$	20.2408			0.707702
$819$		0			0
$820$	−15.6052			−0.544958
$821$	−10.9283	−	6.30945i	−0.381400	−	0.220201i	0.297027	−	0.954869i	$-0.404005\pi$
$821$	−10.9283	−	6.30945i	−0.381400	−	0.220201i	−0.678427	+	0.734668i	$0.737338\pi$
$822$	−43.7030			−1.52432
$823$	−3.28404	−	5.68812i	−0.114474	−	0.198275i	0.803095	−	0.595851i	$-0.203185\pi$
$823$	−3.28404	−	5.68812i	−0.114474	−	0.198275i	−0.917570	+	0.397575i	$0.869852\pi$
$824$	−27.5886	+	15.9283i	−0.961094	+	0.554888i
$825$	68.4403	+	39.5140i	2.38278	+	1.37570i
$826$		0			0
$827$		−	17.3050i		−	0.601754i	−0.953663	−	0.300877i	$-0.902721\pi$
$827$		−	17.3050i		−	0.601754i	0.953663	−	0.300877i	$-0.0972794\pi$
$828$	14.7088			0.511167
$829$	3.75674			0.130477			0.0652385	−	0.997870i	$-0.479219\pi$
$829$	3.75674			0.130477			0.0652385	+	0.997870i	$0.479219\pi$
$830$			16.1404i			0.560243i
$831$	−23.9626	−	41.5044i	−0.831253	−	1.43977i
$832$	0.305689	−	14.3819i	0.0105979	−	0.498602i
$833$		0			0
$834$	−38.5688	+	22.2677i	−1.33553	+	0.771068i
$835$	6.14432	−	10.6423i	0.212633	−	0.368291i
$836$	−7.68610	−	13.3127i	−0.265829	−	0.460430i
$837$	2.85772	+	1.64991i	0.0987773	+	0.0570291i
$838$		−	6.29656i		−	0.217511i
$839$	−40.1340	−	23.1714i	−1.38558	−	0.799965i	−0.392766	−	0.919638i	$-0.628482\pi$
$839$	−40.1340	−	23.1714i	−1.38558	−	0.799965i	−0.992813	+	0.119674i	$0.961815\pi$
$840$		0			0
$841$	−3.49071	+	6.04609i	−0.120369	+	0.208486i
$842$	10.3266	−	17.8861i	0.355877	−	0.616396i
$843$			6.49586i			0.223729i
$844$	11.8534	−	20.5306i	0.408009	−	0.706693i
$845$	36.4411	−	19.0224i	1.25361	−	0.654389i
$846$	−1.53138			−0.0526499
$847$		0			0
$848$	−0.0779704	−	0.135049i	−0.00267751	−	0.00463759i
$849$	76.4142			2.62253
$850$	9.62495	+	5.55697i	0.330133	+	0.190602i
$851$	−15.3751	+	8.87679i	−0.527050	+	0.304293i
$852$		−	15.8485i		−	0.542959i
$853$		−	15.3103i		−	0.524215i	−0.965039	−	0.262107i	$-0.915583\pi$
$853$		−	15.3103i		−	0.524215i	0.965039	−	0.262107i	$-0.0844174\pi$
$854$		0			0
$855$	12.6155	+	21.8506i	0.431440	+	0.747275i
$856$	−9.30993	−	5.37509i	−0.318207	−	0.183717i
$857$	1.29624	−	2.24515i	0.0442787	−	0.0766929i	−0.843037	−	0.537856i	$-0.819234\pi$
$857$	1.29624	−	2.24515i	0.0442787	−	0.0766929i	0.887315	+	0.461163i	$0.152568\pi$
$858$	40.1465	+	24.3305i	1.37058	+	0.830629i
$859$	6.88689	+	11.9284i	0.234978	+	0.406993i	0.959266	−	0.282504i	$-0.0911650\pi$
$859$	6.88689	+	11.9284i	0.234978	+	0.406993i	−0.724289	+	0.689497i	$0.757832\pi$
$860$	25.3053	−	14.6100i	0.862903	−	0.498197i
$861$		0			0
$862$	3.19294	−	5.53034i	0.108752	−	0.188364i
$863$	25.7723	−	14.8796i	0.877298	−	0.506508i	0.00753143	−	0.999972i	$-0.497603\pi$
$863$	25.7723	−	14.8796i	0.877298	−	0.506508i	0.869767	+	0.493463i	$0.164269\pi$
$864$	14.3760	−	8.29996i	0.489080	−	0.282370i
$865$	38.2747	−	22.0979i	1.30138	−	0.751351i
$866$	−25.6588	+	14.8141i	−0.871922	+	0.503404i
$867$	12.9183	−	22.3751i	0.438728	−	0.759899i
$868$		0			0
$869$	−40.7301	+	23.5155i	−1.38167	+	0.797710i
$870$	20.7781	+	35.9888i	0.704444	+	1.22013i
$871$	22.6348	+	0.481106i	0.766951	+	0.0163017i
$872$	15.3926	−	26.6607i	0.521259	−	0.902847i
$873$	−12.1023	−	6.98724i	−0.409599	−	0.236482i
$874$	−2.19955	−	3.80974i	−0.0744009	−	0.128866i
$875$		0			0
$876$			29.2051i			0.986750i
$877$			1.44332i			0.0487374i	0.999703	+	0.0243687i	$0.00775757\pi$
$877$			1.44332i			0.0487374i	−0.999703	+	0.0243687i	$0.992242\pi$
$878$	20.1378	−	11.6266i	0.679618	−	0.392378i
$879$	67.5748	+	39.0143i	2.27924	+	1.31592i
$880$	7.33894			0.247396
$881$	−17.9402	−	31.0733i	−0.604420	−	1.04689i	−0.992143	−	0.125110i	$-0.960072\pi$
$881$	−17.9402	−	31.0733i	−0.604420	−	1.04689i	0.387723	−	0.921776i	$-0.373262\pi$
$882$		0			0
$883$	10.5626			0.355458			0.177729	−	0.984079i	$-0.443125\pi$
$883$	10.5626			0.355458			0.177729	+	0.984079i	$0.443125\pi$
$884$	−11.0027	−	6.66810i	−0.370061	−	0.224273i
$885$	20.2137	−	35.0111i	0.679475	−	1.17689i
$886$			23.7116i			0.796608i
$887$	−6.11401	+	10.5898i	−0.205288	+	0.355570i	−0.950225	−	0.311566i	$-0.899147\pi$
$887$	−6.11401	+	10.5898i	−0.205288	+	0.355570i	0.744936	+	0.667136i	$0.232480\pi$
$888$	−23.6688	+	40.9956i	−0.794274	+	1.37572i
$889$		0			0
$890$	−8.03183	−	4.63718i	−0.269228	−	0.155439i
$891$		−	27.3856i		−	0.917452i
$892$	18.3504	+	10.5946i	0.614418	+	0.354735i
$893$	−0.446276	−	0.772973i	−0.0149341	−	0.0258666i
$894$	11.7390	−	20.3326i	0.392611	−	0.680022i
$895$	−69.2399	+	39.9757i	−2.31443	+	1.33624i
$896$		0			0
$897$	−22.3893	−	13.5689i	−0.747557	−	0.453051i
$898$	12.0199	+	20.8190i	0.401109	+	0.694741i
$899$			6.90751i			0.230378i
$900$	−26.9387			−0.897956
$901$	1.07793			0.0359110
$902$			18.2735i			0.608440i
$903$		0			0
$904$	13.6799	+	7.89807i	0.454985	+	0.262686i
$905$	2.36732	−	1.36677i	0.0786924	−	0.0454331i
$906$	−9.57879	−	16.5909i	−0.318234	−	0.551197i
$907$	−4.52555			−0.150269			−0.0751343	−	0.997173i	$-0.523939\pi$
$907$	−4.52555			−0.150269			−0.0751343	+	0.997173i	$0.523939\pi$
$908$	−18.7441	−	10.8219i	−0.622044	−	0.359137i
$909$	54.3464			1.80256
$910$		0			0
$911$	−57.2723			−1.89751			−0.948757	−	0.316006i	$-0.897658\pi$
$911$	−57.2723			−1.89751			−0.948757	+	0.316006i	$0.897658\pi$
$912$	1.76091	+	1.01666i	0.0583095	+	0.0336650i
$913$	−36.8325			−1.21898
$914$	−13.0471	−	22.5983i	−0.431560	−	0.747484i
$915$	8.42904	−	4.86651i	0.278655	−	0.160882i
$916$	−30.9181	−	17.8506i	−1.02156	−	0.589800i
$917$		0			0
$918$			6.37098i			0.210274i
$919$	−40.7551			−1.34439			−0.672193	−	0.740376i	$-0.734648\pi$
$919$	−40.7551			−1.34439			−0.672193	+	0.740376i	$0.734648\pi$
$920$	23.6105			0.778415
$921$		−	18.8059i		−	0.619675i
$922$	9.10103	+	15.7634i	0.299726	+	0.519141i
$923$	−8.42270	+	13.8979i	−0.277236	+	0.457454i
$924$		0			0
$925$	28.1589	−	16.2575i	0.925858	−	0.534545i
$926$	−16.0104	+	27.7308i	−0.526134	+	0.911291i
$927$	23.7391	+	41.1174i	0.779696	+	1.35047i
$928$	30.0932	+	17.3743i	0.987859	+	0.570341i
$929$		−	52.2791i		−	1.71522i	−0.514298	−	0.857611i	$-0.671948\pi$
$929$		−	52.2791i		−	1.71522i	0.514298	−	0.857611i	$-0.328052\pi$
$930$	6.90891	+	3.98886i	0.226552	+	0.130800i
$931$		0			0
$932$	7.64511	−	13.2417i	0.250424	−	0.433747i
$933$	−29.6205	+	51.3042i	−0.969731	+	1.67962i
$934$		−	10.9387i		−	0.357926i
$935$	−25.3650	+	43.9334i	−0.829523	+	1.43678i
$936$	−40.2061	−	0.854586i	−1.31418	−	0.0279330i
$937$	−6.38634			−0.208633			−0.104316	−	0.994544i	$-0.533265\pi$
$937$	−6.38634			−0.208633			−0.104316	+	0.994544i	$0.533265\pi$
$938$		0			0
$939$	37.3558	+	64.7021i	1.21906	+	2.11147i
$940$	1.90615			0.0621719
$941$	21.9720	+	12.6855i	0.716266	+	0.413536i	0.813377	−	0.581737i	$-0.197627\pi$
$941$	21.9720	+	12.6855i	0.716266	+	0.413536i	−0.0971107	+	0.995274i	$0.530960\pi$
$942$	12.3469	−	7.12846i	0.402282	−	0.232258i
$943$		−	10.1909i		−	0.331862i
$944$		−	1.87692i		−	0.0610887i
$945$		0			0
$946$	−17.1081	−	29.6321i	−0.556232	−	0.963422i
$947$	−23.5612	−	13.6031i	−0.765635	−	0.442040i	0.0656800	−	0.997841i	$-0.479078\pi$
$947$	−23.5612	−	13.6031i	−0.765635	−	0.442040i	−0.831315	+	0.555801i	$0.812412\pi$
$948$	13.9140	−	24.0997i	0.451905	−	0.782723i
$949$	15.5211	−	25.6107i	0.503838	−	0.831357i
$950$	4.02840	+	6.97740i	0.130699	+	0.226377i
$951$	−44.9613	+	25.9584i	−1.45797	+	0.841760i
$952$		0			0
$953$	13.2939	−	23.0258i	0.430633	−	0.745878i	−0.566295	−	0.824203i	$-0.691624\pi$
$953$	13.2939	−	23.0258i	0.430633	−	0.745878i	0.996928	+	0.0783248i	$0.0249571\pi$
$954$	1.16109	−	0.670354i	0.0375916	−	0.0217035i
$955$	−40.1667	+	23.1902i	−1.29976	+	0.750418i
$956$	−16.7959	+	9.69711i	−0.543218	+	0.313627i
$957$	−82.1264	+	47.4157i	−2.65477	+	1.53273i
$958$	2.73220	−	4.73230i	0.0882732	−	0.152894i
$959$		0			0
$960$	29.0654	−	16.7809i	0.938082	−	0.541602i
$961$	−14.8370	−	25.6984i	−0.478612	−	0.828980i
$962$	16.9282	−	9.29957i	0.545787	−	0.299830i
$963$	−8.01091	+	13.8753i	−0.258148	+	0.447125i
$964$	16.4223	+	9.48141i	0.528926	+	0.305376i
$965$	−26.0808	−	45.1732i	−0.839569	−	1.45418i
$966$		0			0
$967$			35.2467i			1.13346i	0.823904	+	0.566729i	$0.191791\pi$
$967$			35.2467i			1.13346i	−0.823904	+	0.566729i	$0.808209\pi$
$968$		−	66.5191i		−	2.13801i
$969$	−12.1722	+	7.02760i	−0.391026	+	0.225759i
$970$	−7.72995	−	4.46289i	−0.248194	−	0.143295i
$971$	36.9783			1.18669			0.593344	−	0.804949i	$-0.297807\pi$
$971$	36.9783			1.18669			0.593344	+	0.804949i	$0.297807\pi$
$972$	13.7833	+	23.8733i	0.442098	+	0.765737i
$973$		0			0
$974$	27.5645			0.883224
$975$	41.0052	+	24.8509i	1.31322	+	0.795866i
$976$	0.225938	−	0.391336i	0.00723209	−	0.0125264i
$977$		−	24.7525i		−	0.791902i	−0.918272	−	0.395951i	$-0.870415\pi$
$977$		−	24.7525i		−	0.791902i	0.918272	−	0.395951i	$-0.129585\pi$
$978$	−2.86205	+	4.95721i	−0.0915182	+	0.158514i
$979$	10.5820	−	18.3286i	0.338204	−	0.585786i
$980$		0			0
$981$	−39.7346	−	22.9408i	−1.26863	−	0.732442i
$982$			30.7423i			0.981025i
$983$	−3.94679	−	2.27868i	−0.125883	−	0.0726786i	0.435736	−	0.900074i	$-0.356488\pi$
$983$	−3.94679	−	2.27868i	−0.125883	−	0.0726786i	−0.561619	+	0.827396i	$0.689821\pi$
$984$	−13.5864	−	23.5323i	−0.433119	−	0.750183i
$985$	−17.4076	+	30.1509i	−0.554652	+	0.960686i
$986$	−11.5497	+	6.66820i	−0.367816	+	0.212359i
$987$		0			0
$988$	−4.49062	−	8.17436i	−0.142866	−	0.260061i
$989$	9.54101	+	16.5255i	0.303386	+	0.525481i
$990$			63.0969i			2.00535i
$991$	−27.1963			−0.863919			−0.431960	−	0.901893i	$-0.642178\pi$
$991$	−27.1963			−0.863919			−0.431960	+	0.901893i	$0.642178\pi$
$992$	6.67085			0.211800
$993$		−	41.5824i		−	1.31958i
$994$		0			0
$995$	58.0873	+	33.5367i	1.84149	+	1.06319i
$996$	18.8738	−	10.8968i	0.598039	−	0.345278i
$997$	15.1137	+	26.1777i	0.478656	+	0.829057i	0.999700	−	0.0244727i	$-0.00779070\pi$
$997$	15.1137	+	26.1777i	0.478656	+	0.829057i	−0.521044	+	0.853530i	$0.674457\pi$
$998$	28.1102			0.889812
$999$	16.1419	+	9.31952i	0.510707	+	0.294857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.h.361.3		12
7.2	even	3		637.2.k.h.569.4		12
7.3	odd	6		637.2.q.h.491.4		12
7.4	even	3		91.2.q.a.36.4	✓	12
7.5	odd	6		637.2.k.g.569.4		12
7.6	odd	2		637.2.u.i.361.3		12
13.4	even	6		637.2.k.h.459.3		12
21.11	odd	6		819.2.ct.a.127.3		12
28.11	odd	6		1456.2.cc.c.673.6		12
91.4	even	6		91.2.q.a.43.4	yes	12
91.11	odd	12		1183.2.a.p.1.2		6
91.17	odd	6		637.2.q.h.589.4		12
91.24	even	12		8281.2.a.ch.1.2		6
91.30	even	6	inner	637.2.u.h.30.3		12
91.67	odd	12		1183.2.a.m.1.5		6
91.69	odd	6		637.2.k.g.459.3		12
91.80	even	12		8281.2.a.by.1.5		6
91.81	even	3		1183.2.c.i.337.8		12
91.82	odd	6		637.2.u.i.30.3		12
91.88	even	6		1183.2.c.i.337.5		12
273.95	odd	6		819.2.ct.a.316.3		12
364.95	odd	6		1456.2.cc.c.225.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.4	✓	12	7.4	even	3
91.2.q.a.43.4	yes	12	91.4	even	6
637.2.k.g.459.3		12	91.69	odd	6
637.2.k.g.569.4		12	7.5	odd	6
637.2.k.h.459.3		12	13.4	even	6
637.2.k.h.569.4		12	7.2	even	3
637.2.q.h.491.4		12	7.3	odd	6
637.2.q.h.589.4		12	91.17	odd	6
637.2.u.h.30.3		12	91.30	even	6	inner
637.2.u.h.361.3		12	1.1	even	1	trivial
637.2.u.i.30.3		12	91.82	odd	6
637.2.u.i.361.3		12	7.6	odd	2
819.2.ct.a.127.3		12	21.11	odd	6
819.2.ct.a.316.3		12	273.95	odd	6
1183.2.a.m.1.5		6	91.67	odd	12
1183.2.a.p.1.2		6	91.11	odd	12
1183.2.c.i.337.5		12	91.88	even	6
1183.2.c.i.337.8		12	91.81	even	3
1456.2.cc.c.225.6		12	364.95	odd	6
1456.2.cc.c.673.6		12	28.11	odd	6
8281.2.a.by.1.5		6	91.80	even	12
8281.2.a.ch.1.2		6	91.24	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.713220 - 0.411778i) q^{2} +2.66029 q^{3} +(-0.660878 - 1.14467i) q^{4} +(-2.73845 + 1.58105i) q^{5} +(-1.89737 - 1.09545i) q^{6} +2.73565i q^{8} +4.07715 q^{9} +O(q^{10})\)	\(q+(-0.713220 - 0.411778i) q^{2} +2.66029 q^{3} +(-0.660878 - 1.14467i) q^{4} +(-2.73845 + 1.58105i) q^{5} +(-1.89737 - 1.09545i) q^{6} +2.73565i q^{8} +4.07715 q^{9} +2.60416 q^{10} +5.94270i q^{11} +(-1.75813 - 3.04517i) q^{12} +(-0.0766193 + 3.60474i) q^{13} +(-7.28508 + 4.20604i) q^{15} +(-0.195274 + 0.338225i) q^{16} +(-1.34982 - 2.33796i) q^{17} +(-2.90791 - 1.67888i) q^{18} -1.95705i q^{19} +(3.61956 + 2.08976i) q^{20} +(2.44707 - 4.23845i) q^{22} +(-1.36471 + 2.36374i) q^{23} +7.27763i q^{24} +(2.49941 - 4.32911i) q^{25} +(1.53900 - 2.53942i) q^{26} +2.86554 q^{27} +(2.99923 + 5.19481i) q^{29} +6.92783 q^{30} +(0.997270 + 0.575774i) q^{31} +(5.01684 - 2.89647i) q^{32} +15.8093i q^{33} +2.22331i q^{34} +(-2.69450 - 4.66701i) q^{36} +(5.63310 + 3.25227i) q^{37} +(-0.805869 + 1.39581i) q^{38} +(-0.203830 + 9.58965i) q^{39} +(-4.32519 - 7.49145i) q^{40} +(-3.23351 + 1.86687i) q^{41} +(3.49562 - 6.05460i) q^{43} +(6.80245 - 3.92740i) q^{44} +(-11.1651 + 6.44617i) q^{45} +(1.94667 - 1.12391i) q^{46} +(0.394969 - 0.228035i) q^{47} +(-0.519487 + 0.899778i) q^{48} +(-3.56527 + 2.05841i) q^{50} +(-3.59092 - 6.21965i) q^{51} +(4.17688 - 2.29459i) q^{52} +(-0.199643 + 0.345792i) q^{53} +(-2.04376 - 1.17997i) q^{54} +(-9.39568 - 16.2738i) q^{55} -5.20632i q^{57} -4.94006i q^{58} +(-4.16200 + 2.40293i) q^{59} +(9.62910 + 5.55936i) q^{60} -1.15703 q^{61} +(-0.474182 - 0.821308i) q^{62} -3.98971 q^{64} +(-5.48944 - 9.99254i) q^{65} +(6.50993 - 11.2755i) q^{66} -6.27918i q^{67} +(-1.78413 + 3.09021i) q^{68} +(-3.63052 + 6.28825i) q^{69} +(3.90335 + 2.25360i) q^{71} +11.1537i q^{72} +(-7.19299 - 4.15288i) q^{73} +(-2.67843 - 4.63917i) q^{74} +(6.64917 - 11.5167i) q^{75} +(-2.24018 + 1.29337i) q^{76} +(4.09418 - 6.75560i) q^{78} +(3.95705 + 6.85381i) q^{79} -1.23495i q^{80} -4.60828 q^{81} +3.07494 q^{82} +6.19795i q^{83} +(7.39284 + 4.26826i) q^{85} +(-4.98630 + 2.87884i) q^{86} +(7.97882 + 13.8197i) q^{87} -16.2571 q^{88} +(-3.08423 - 1.78068i) q^{89} +10.6176 q^{90} +3.60762 q^{92} +(2.65303 + 1.53173i) q^{93} -0.375600 q^{94} +(3.09418 + 5.35928i) q^{95} +(13.3462 - 7.70546i) q^{96} +(-2.96831 - 1.71375i) q^{97} +24.2293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 - 6 * q^5 - 18 * q^6 + 8 * q^9	\( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29} - 16 q^{30} + 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} - 2 q^{38} - 10 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} + 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} + 26 q^{52} + 22 q^{53} - 12 q^{54} - 6 q^{55} - 18 q^{59} + 66 q^{60} - 28 q^{61} - 4 q^{62} - 52 q^{64} - 42 q^{65} + 26 q^{66} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 30 q^{73} + 6 q^{74} + 46 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} - 28 q^{82} - 48 q^{85} - 60 q^{86} - 2 q^{87} + 28 q^{88} + 12 q^{89} + 24 q^{90} + 24 q^{92} + 18 q^{93} - 8 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 - 6 * q^5 - 18 * q^6 + 8 * q^9 - 24 * q^10 + 2 * q^12 + 4 * q^13 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^18 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 + 24 * q^26 + 12 * q^27 + 8 * q^29 - 16 * q^30 + 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 - 2 * q^38 - 10 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 + 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 + 26 * q^52 + 22 * q^53 - 12 * q^54 - 6 * q^55 - 18 * q^59 + 66 * q^60 - 28 * q^61 - 4 * q^62 - 52 * q^64 - 42 * q^65 + 26 * q^66 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 30 * q^73 + 6 * q^74 + 46 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 - 28 * q^82 - 48 * q^85 - 60 * q^86 - 2 * q^87 + 28 * q^88 + 12 * q^89 + 24 * q^90 + 24 * q^92 + 18 * q^93 - 8 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^97

Introduction

L-functions

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Database

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