LMFDB - Embedded newform 637.2.h.e.471.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	637.471
Dual form			637.2.h.e.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205 q^{2} +(-0.366025 + 0.633975i) q^{3} +1.00000 q^{4} +(-0.866025 + 1.50000i) q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} +(1.23205 + 2.13397i) q^{9} +O(q^{10})$	\(q-1.73205 q^{2} +(-0.366025 + 0.633975i) q^{3} +1.00000 q^{4} +(-0.866025 + 1.50000i) q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} +(1.23205 + 2.13397i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-2.36603 + 4.09808i) q^{11} +(-0.366025 + 0.633975i) q^{12} +(1.59808 - 3.23205i) q^{13} +(-0.633975 - 1.09808i) q^{15} -5.00000 q^{16} +4.26795 q^{17} +(-2.13397 - 3.69615i) q^{18} +(1.00000 + 1.73205i) q^{19} +(-0.866025 + 1.50000i) q^{20} +(4.09808 - 7.09808i) q^{22} +1.26795 q^{23} +(-0.633975 + 1.09808i) q^{24} +(1.00000 + 1.73205i) q^{25} +(-2.76795 + 5.59808i) q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +(1.09808 + 1.90192i) q^{30} +(-3.09808 - 5.36603i) q^{31} +5.19615 q^{32} +(-1.73205 - 3.00000i) q^{33} -7.39230 q^{34} +(1.23205 + 2.13397i) q^{36} -7.00000 q^{37} +(-1.73205 - 3.00000i) q^{38} +(1.46410 + 2.19615i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(2.59808 + 4.50000i) q^{41} +(-5.09808 + 8.83013i) q^{43} +(-2.36603 + 4.09808i) q^{44} -4.26795 q^{45} -2.19615 q^{46} +(-0.464102 + 0.803848i) q^{47} +(1.83013 - 3.16987i) q^{48} +(-1.73205 - 3.00000i) q^{50} +(-1.56218 + 2.70577i) q^{51} +(1.59808 - 3.23205i) q^{52} +(-1.96410 - 3.40192i) q^{53} +6.92820 q^{54} +(-4.09808 - 7.09808i) q^{55} -1.46410 q^{57} +(-2.59808 - 4.50000i) q^{58} -10.7321 q^{59} +(-0.633975 - 1.09808i) q^{60} +(-7.59808 - 13.1603i) q^{61} +(5.36603 + 9.29423i) q^{62} +1.00000 q^{64} +(3.46410 + 5.19615i) q^{65} +(3.00000 + 5.19615i) q^{66} +(-2.09808 + 3.63397i) q^{67} +4.26795 q^{68} +(-0.464102 + 0.803848i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(2.13397 + 3.69615i) q^{72} +(3.59808 + 6.23205i) q^{73} +12.1244 q^{74} -1.46410 q^{75} +(1.00000 + 1.73205i) q^{76} +(-2.53590 - 3.80385i) q^{78} +(-2.90192 + 5.02628i) q^{79} +(4.33013 - 7.50000i) q^{80} +(-2.23205 + 3.86603i) q^{81} +(-4.50000 - 7.79423i) q^{82} -8.19615 q^{83} +(-3.69615 + 6.40192i) q^{85} +(8.83013 - 15.2942i) q^{86} -2.19615 q^{87} +(-4.09808 + 7.09808i) q^{88} +0.928203 q^{89} +7.39230 q^{90} +1.26795 q^{92} +4.53590 q^{93} +(0.803848 - 1.39230i) q^{94} -3.46410 q^{95} +(-1.90192 + 3.29423i) q^{96} +(-7.19615 + 12.4641i) q^{97} -11.6603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 4 q^{4} + 6 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 4 * q^4 + 6 * q^6 - 2 * q^9	$ 4 q + 2 q^{3} + 4 q^{4} + 6 q^{6} - 2 q^{9} + 6 q^{10} - 6 q^{11} + 2 q^{12} - 4 q^{13} - 6 q^{15} - 20 q^{16} + 24 q^{17} - 12 q^{18} + 4 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{24} + 4 q^{25} - 18 q^{26} - 16 q^{27} + 6 q^{29} - 6 q^{30} - 2 q^{31} + 12 q^{34} - 2 q^{36} - 28 q^{37} - 8 q^{39} - 6 q^{40} - 10 q^{43} - 6 q^{44} - 24 q^{45} + 12 q^{46} + 12 q^{47} - 10 q^{48} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 6 q^{55} + 8 q^{57} - 36 q^{59} - 6 q^{60} - 20 q^{61} + 18 q^{62} + 4 q^{64} + 12 q^{66} + 2 q^{67} + 24 q^{68} + 12 q^{69} - 12 q^{71} + 12 q^{72} + 4 q^{73} + 8 q^{75} + 4 q^{76} - 24 q^{78} - 22 q^{79} - 2 q^{81} - 18 q^{82} - 12 q^{83} + 6 q^{85} + 18 q^{86} + 12 q^{87} - 6 q^{88} - 24 q^{89} - 12 q^{90} + 12 q^{92} + 32 q^{93} + 24 q^{94} - 18 q^{96} - 8 q^{97} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 4 * q^4 + 6 * q^6 - 2 * q^9 + 6 * q^10 - 6 * q^11 + 2 * q^12 - 4 * q^13 - 6 * q^15 - 20 * q^16 + 24 * q^17 - 12 * q^18 + 4 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^24 + 4 * q^25 - 18 * q^26 - 16 * q^27 + 6 * q^29 - 6 * q^30 - 2 * q^31 + 12 * q^34 - 2 * q^36 - 28 * q^37 - 8 * q^39 - 6 * q^40 - 10 * q^43 - 6 * q^44 - 24 * q^45 + 12 * q^46 + 12 * q^47 - 10 * q^48 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 6 * q^55 + 8 * q^57 - 36 * q^59 - 6 * q^60 - 20 * q^61 + 18 * q^62 + 4 * q^64 + 12 * q^66 + 2 * q^67 + 24 * q^68 + 12 * q^69 - 12 * q^71 + 12 * q^72 + 4 * q^73 + 8 * q^75 + 4 * q^76 - 24 * q^78 - 22 * q^79 - 2 * q^81 - 18 * q^82 - 12 * q^83 + 6 * q^85 + 18 * q^86 + 12 * q^87 - 6 * q^88 - 24 * q^89 - 12 * q^90 + 12 * q^92 + 32 * q^93 + 24 * q^94 - 18 * q^96 - 8 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.73205			−1.22474			−0.612372	−	0.790569i	$-0.709785\pi$
$2$	−1.73205			−1.22474			−0.612372	+	0.790569i	$0.709785\pi$
$3$	−0.366025	+	0.633975i	−0.211325	+	0.366025i	−0.952129	−	0.305695i	$-0.901111\pi$
$3$	−0.366025	+	0.633975i	−0.211325	+	0.366025i	0.740805	+	0.671721i	$0.234444\pi$
$4$	1.00000			0.500000
$5$	−0.866025	+	1.50000i	−0.387298	+	0.670820i	−0.992085	−	0.125567i	$-0.959925\pi$
$5$	−0.866025	+	1.50000i	−0.387298	+	0.670820i	0.604787	+	0.796387i	$0.293258\pi$
$6$	0.633975	−	1.09808i	0.258819	−	0.448288i
$7$		0			0
$7$		0			0
$8$	1.73205			0.612372
$9$	1.23205	+	2.13397i	0.410684	+	0.711325i
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$	−2.36603	+	4.09808i	−0.713384	+	1.23562i	0.250196	+	0.968195i	$0.419505\pi$
$11$	−2.36603	+	4.09808i	−0.713384	+	1.23562i	−0.963580	+	0.267421i	$0.913828\pi$
$12$	−0.366025	+	0.633975i	−0.105662	+	0.183013i
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$14$		0			0
$15$	−0.633975	−	1.09808i	−0.163692	−	0.283522i
$16$	−5.00000			−1.25000
$17$	4.26795			1.03513			0.517565	−	0.855644i	$-0.326839\pi$
$17$	4.26795			1.03513			0.517565	+	0.855644i	$0.326839\pi$
$18$	−2.13397	−	3.69615i	−0.502983	−	0.871191i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	−0.866025	+	1.50000i	−0.193649	+	0.335410i
$21$		0			0
$22$	4.09808	−	7.09808i	0.873713	−	1.51331i
$23$	1.26795			0.264386			0.132193	−	0.991224i	$-0.457798\pi$
$23$	1.26795			0.264386			0.132193	+	0.991224i	$0.457798\pi$
$24$	−0.633975	+	1.09808i	−0.129410	+	0.224144i
$25$	1.00000	+	1.73205i	0.200000	+	0.346410i
$26$	−2.76795	+	5.59808i	−0.542839	+	1.09787i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	1.09808	+	1.90192i	0.200480	+	0.347242i
$31$	−3.09808	−	5.36603i	−0.556431	−	0.963767i	−0.997791	−	0.0664364i	$-0.978837\pi$
$31$	−3.09808	−	5.36603i	−0.556431	−	0.963767i	0.441360	−	0.897330i	$-0.354496\pi$
$32$	5.19615			0.918559
$33$	−1.73205	−	3.00000i	−0.301511	−	0.522233i
$34$	−7.39230			−1.26777
$35$		0			0
$36$	1.23205	+	2.13397i	0.205342	+	0.355662i
$37$	−7.00000			−1.15079			−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000			−1.15079			−0.575396	+	0.817875i	$0.695152\pi$
$38$	−1.73205	−	3.00000i	−0.280976	−	0.486664i
$39$	1.46410	+	2.19615i	0.234444	+	0.351666i
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	2.59808	+	4.50000i	0.405751	+	0.702782i	0.994409	−	0.105601i	$-0.0336766\pi$
$41$	2.59808	+	4.50000i	0.405751	+	0.702782i	−0.588657	+	0.808383i	$0.700343\pi$
$42$		0			0
$43$	−5.09808	+	8.83013i	−0.777449	+	1.34658i	0.155958	+	0.987764i	$0.450153\pi$
$43$	−5.09808	+	8.83013i	−0.777449	+	1.34658i	−0.933408	+	0.358818i	$0.883180\pi$
$44$	−2.36603	+	4.09808i	−0.356692	+	0.617808i
$45$	−4.26795			−0.636228
$46$	−2.19615			−0.323805
$47$	−0.464102	+	0.803848i	−0.0676962	+	0.117253i	−0.897887	−	0.440226i	$-0.854898\pi$
$47$	−0.464102	+	0.803848i	−0.0676962	+	0.117253i	0.830191	+	0.557480i	$0.188232\pi$
$48$	1.83013	−	3.16987i	0.264156	−	0.457532i
$49$		0			0
$50$	−1.73205	−	3.00000i	−0.244949	−	0.424264i
$51$	−1.56218	+	2.70577i	−0.218749	+	0.378884i
$52$	1.59808	−	3.23205i	0.221613	−	0.448205i
$53$	−1.96410	−	3.40192i	−0.269790	−	0.467290i	0.699017	−	0.715105i	$-0.253621\pi$
$53$	−1.96410	−	3.40192i	−0.269790	−	0.467290i	−0.968808	+	0.247814i	$0.920288\pi$
$54$	6.92820			0.942809
$55$	−4.09808	−	7.09808i	−0.552584	−	0.957104i
$56$		0			0
$57$	−1.46410			−0.193925
$58$	−2.59808	−	4.50000i	−0.341144	−	0.590879i
$59$	−10.7321			−1.39719			−0.698597	−	0.715515i	$-0.746192\pi$
$59$	−10.7321			−1.39719			−0.698597	+	0.715515i	$0.746192\pi$
$60$	−0.633975	−	1.09808i	−0.0818458	−	0.141761i
$61$	−7.59808	−	13.1603i	−0.972834	−	1.68500i	−0.686905	−	0.726747i	$-0.741031\pi$
$61$	−7.59808	−	13.1603i	−0.972834	−	1.68500i	−0.285929	−	0.958251i	$-0.592302\pi$
$62$	5.36603	+	9.29423i	0.681486	+	1.18037i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.46410	+	5.19615i	0.429669	+	0.644503i
$66$	3.00000	+	5.19615i	0.369274	+	0.639602i
$67$	−2.09808	+	3.63397i	−0.256321	+	0.443961i	−0.965253	−	0.261316i	$-0.915844\pi$
$67$	−2.09808	+	3.63397i	−0.256321	+	0.443961i	0.708933	+	0.705276i	$0.249177\pi$
$68$	4.26795			0.517565
$69$	−0.464102	+	0.803848i	−0.0558713	+	0.0967719i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	2.13397	+	3.69615i	0.251491	+	0.435596i
$73$	3.59808	+	6.23205i	0.421123	+	0.729406i	0.996050	−	0.0887986i	$-0.0283027\pi$
$73$	3.59808	+	6.23205i	0.421123	+	0.729406i	−0.574927	+	0.818205i	$0.694969\pi$
$74$	12.1244			1.40943
$75$	−1.46410			−0.169060
$76$	1.00000	+	1.73205i	0.114708	+	0.198680i
$77$		0			0
$78$	−2.53590	−	3.80385i	−0.287134	−	0.430701i
$79$	−2.90192	+	5.02628i	−0.326492	+	0.565501i	−0.981813	−	0.189850i	$-0.939200\pi$
$79$	−2.90192	+	5.02628i	−0.326492	+	0.565501i	0.655321	+	0.755350i	$0.272533\pi$
$80$	4.33013	−	7.50000i	0.484123	−	0.838525i
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$	−8.19615			−0.899645			−0.449822	−	0.893118i	$-0.648513\pi$
$83$	−8.19615			−0.899645			−0.449822	+	0.893118i	$0.648513\pi$
$84$		0			0
$85$	−3.69615	+	6.40192i	−0.400904	+	0.694386i
$86$	8.83013	−	15.2942i	0.952177	−	1.64922i
$87$	−2.19615			−0.235452
$88$	−4.09808	+	7.09808i	−0.436856	+	0.756657i
$89$	0.928203			0.0983893			0.0491947	−	0.998789i	$-0.484335\pi$
$89$	0.928203			0.0983893			0.0491947	+	0.998789i	$0.484335\pi$
$90$	7.39230			0.779217
$91$		0			0
$92$	1.26795			0.132193
$93$	4.53590			0.470351
$94$	0.803848	−	1.39230i	0.0829105	−	0.143605i
$95$	−3.46410			−0.355409
$96$	−1.90192	+	3.29423i	−0.194114	+	0.336216i
$97$	−7.19615	+	12.4641i	−0.730659	+	1.26554i	0.225944	+	0.974140i	$0.427454\pi$
$97$	−7.19615	+	12.4641i	−0.730659	+	1.26554i	−0.956602	+	0.291397i	$0.905880\pi$
$98$		0			0
$99$	−11.6603			−1.17190
$100$	1.00000	+	1.73205i	0.100000	+	0.173205i
$101$	−2.13397	+	3.69615i	−0.212338	+	0.367781i	−0.952446	−	0.304708i	$-0.901441\pi$
$101$	−2.13397	+	3.69615i	−0.212338	+	0.367781i	0.740108	+	0.672489i	$0.234775\pi$
$102$	2.70577	−	4.68653i	0.267911	−	0.464036i
$103$	3.19615	−	5.53590i	0.314926	−	0.545468i	−0.664496	−	0.747292i	$-0.731354\pi$
$103$	3.19615	−	5.53590i	0.314926	−	0.545468i	0.979422	+	0.201824i	$0.0646869\pi$
$104$	2.76795	−	5.59808i	0.271420	−	0.548937i
$105$		0			0
$106$	3.40192	+	5.89230i	0.330424	+	0.572311i
$107$	19.8564			1.91959			0.959796	−	0.280700i	$-0.0905665\pi$
$107$	19.8564			1.91959			0.959796	+	0.280700i	$0.0905665\pi$
$108$	−4.00000			−0.384900
$109$	−6.19615	−	10.7321i	−0.593484	−	1.02794i	−0.993759	−	0.111549i	$-0.964419\pi$
$109$	−6.19615	−	10.7321i	−0.593484	−	1.02794i	0.400275	−	0.916395i	$-0.368915\pi$
$110$	7.09808	+	12.2942i	0.676775	+	1.17221i
$111$	2.56218	−	4.43782i	0.243191	−	0.421219i
$112$		0			0
$113$	3.69615	−	6.40192i	0.347705	−	0.602242i	−0.638137	−	0.769923i	$-0.720294\pi$
$113$	3.69615	−	6.40192i	0.347705	−	0.602242i	0.985841	+	0.167681i	$0.0536278\pi$
$114$	2.53590			0.237509
$115$	−1.09808	+	1.90192i	−0.102396	+	0.177355i
$116$	1.50000	+	2.59808i	0.139272	+	0.241225i
$117$	8.86603	−	0.571797i	0.819664	−	0.0528626i
$118$	18.5885			1.71121
$119$		0			0
$120$	−1.09808	−	1.90192i	−0.100240	−	0.173621i
$121$	−5.69615	−	9.86603i	−0.517832	−	0.896911i
$122$	13.1603	+	22.7942i	1.19147	+	2.06369i
$123$	−3.80385			−0.342981
$124$	−3.09808	−	5.36603i	−0.278215	−	0.481883i
$125$	−12.1244			−1.08444
$126$		0			0
$127$	1.19615	+	2.07180i	0.106141	+	0.183842i	0.914204	−	0.405254i	$-0.132817\pi$
$127$	1.19615	+	2.07180i	0.106141	+	0.183842i	−0.808063	+	0.589097i	$0.799484\pi$
$128$	−12.1244			−1.07165
$129$	−3.73205	−	6.46410i	−0.328589	−	0.569132i
$130$	−6.00000	−	9.00000i	−0.526235	−	0.789352i
$131$	1.73205	−	3.00000i	0.151330	−	0.262111i	−0.780387	−	0.625297i	$-0.784978\pi$
$131$	1.73205	−	3.00000i	0.151330	−	0.262111i	0.931717	+	0.363186i	$0.118311\pi$
$132$	−1.73205	−	3.00000i	−0.150756	−	0.261116i
$133$		0			0
$134$	3.63397	−	6.29423i	0.313928	−	0.543739i
$135$	3.46410	−	6.00000i	0.298142	−	0.516398i
$136$	7.39230			0.633885
$137$	21.9282			1.87345			0.936726	−	0.350062i	$-0.113840\pi$
$137$	21.9282			1.87345			0.936726	+	0.350062i	$0.113840\pi$
$138$	0.803848	−	1.39230i	0.0684280	−	0.118521i
$139$	10.2942	−	17.8301i	0.873145	−	1.51233i	0.0144194	−	0.999896i	$-0.495410\pi$
$139$	10.2942	−	17.8301i	0.873145	−	1.51233i	0.858726	−	0.512436i	$-0.171257\pi$
$140$		0			0
$141$	−0.339746	−	0.588457i	−0.0286118	−	0.0495570i
$142$	5.19615	−	9.00000i	0.436051	−	0.755263i
$143$	9.46410	+	14.1962i	0.791428	+	1.18714i
$144$	−6.16025	−	10.6699i	−0.513355	−	0.889156i
$145$	−5.19615			−0.431517
$146$	−6.23205	−	10.7942i	−0.515768	−	0.893337i
$147$		0			0
$148$	−7.00000			−0.575396
$149$	−0.232051	−	0.401924i	−0.0190103	−	0.0329269i	0.856364	−	0.516373i	$-0.172718\pi$
$149$	−0.232051	−	0.401924i	−0.0190103	−	0.0329269i	−0.875374	+	0.483446i	$0.839385\pi$
$150$	2.53590			0.207055
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	0.822464	−	0.568818i	$-0.192599\pi$
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	−0.903842	+	0.427865i	$0.859266\pi$
$152$	1.73205	+	3.00000i	0.140488	+	0.243332i
$153$	5.25833	+	9.10770i	0.425111	+	0.736314i
$154$		0			0
$155$	10.7321			0.862019
$156$	1.46410	+	2.19615i	0.117222	+	0.175833i
$157$	−4.59808	−	7.96410i	−0.366966	−	0.635605i	0.622123	−	0.782919i	$-0.286270\pi$
$157$	−4.59808	−	7.96410i	−0.366966	−	0.635605i	−0.989090	+	0.147315i	$0.952937\pi$
$158$	5.02628	−	8.70577i	0.399869	−	0.692594i
$159$	2.87564			0.228053
$160$	−4.50000	+	7.79423i	−0.355756	+	0.616188i
$161$		0			0
$162$	3.86603	−	6.69615i	0.303744	−	0.526099i
$163$	−2.90192	−	5.02628i	−0.227296	−	0.393689i	0.729710	−	0.683757i	$-0.239655\pi$
$163$	−2.90192	−	5.02628i	−0.227296	−	0.393689i	−0.957006	+	0.290069i	$0.906322\pi$
$164$	2.59808	+	4.50000i	0.202876	+	0.351391i
$165$	6.00000			0.467099
$166$	14.1962			1.10184
$167$	12.2942	+	21.2942i	0.951356	+	1.64780i	0.742495	+	0.669852i	$0.233642\pi$
$167$	12.2942	+	21.2942i	0.951356	+	1.64780i	0.208861	+	0.977945i	$0.433024\pi$
$168$		0			0
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$	6.40192	−	11.0885i	0.491005	−	0.850446i
$171$	−2.46410	+	4.26795i	−0.188435	+	0.326378i
$172$	−5.09808	+	8.83013i	−0.388725	+	0.673291i
$173$	7.73205	+	13.3923i	0.587857	+	1.01820i	0.994513	+	0.104617i	$0.0333615\pi$
$173$	7.73205	+	13.3923i	0.587857	+	1.01820i	−0.406656	+	0.913581i	$0.633305\pi$
$174$	3.80385			0.288369
$175$		0			0
$176$	11.8301	−	20.4904i	0.891729	−	1.54452i
$177$	3.92820	−	6.80385i	0.295262	−	0.511409i
$178$	−1.60770			−0.120502
$179$	−3.46410	+	6.00000i	−0.258919	+	0.448461i	−0.965953	−	0.258719i	$-0.916700\pi$
$179$	−3.46410	+	6.00000i	−0.258919	+	0.448461i	0.707034	+	0.707180i	$0.250033\pi$
$180$	−4.26795			−0.318114
$181$	25.5885			1.90198			0.950988	−	0.309229i	$-0.100071\pi$
$181$	25.5885			1.90198			0.950988	+	0.309229i	$0.100071\pi$
$182$		0			0
$183$	11.1244			0.822336
$184$	2.19615			0.161903
$185$	6.06218	−	10.5000i	0.445700	−	0.771975i
$186$	−7.85641			−0.576060
$187$	−10.0981	+	17.4904i	−0.738444	+	1.27902i
$188$	−0.464102	+	0.803848i	−0.0338481	+	0.0586266i
$189$		0			0
$190$	6.00000			0.435286
$191$	−0.633975	−	1.09808i	−0.0458728	−	0.0794540i	0.842177	−	0.539201i	$-0.181274\pi$
$191$	−0.633975	−	1.09808i	−0.0458728	−	0.0794540i	−0.888050	+	0.459747i	$0.847940\pi$
$192$	−0.366025	+	0.633975i	−0.0264156	+	0.0457532i
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$	12.4641	−	21.5885i	0.894870	−	1.54996i
$195$	−4.56218	+	0.294229i	−0.326704	+	0.0210702i
$196$		0			0
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	0.569166	−	0.822222i	$-0.307266\pi$
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	−0.996649	+	0.0818013i	$0.973933\pi$
$198$	20.1962			1.43528
$199$	−2.00000			−0.141776			−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000			−0.141776			−0.0708881	+	0.997484i	$0.522583\pi$
$200$	1.73205	+	3.00000i	0.122474	+	0.212132i
$201$	−1.53590	−	2.66025i	−0.108334	−	0.187640i
$202$	3.69615	−	6.40192i	0.260060	−	0.450438i
$203$		0			0
$204$	−1.56218	+	2.70577i	−0.109374	+	0.189442i
$205$	−9.00000			−0.628587
$206$	−5.53590	+	9.58846i	−0.385704	+	0.668059i
$207$	1.56218	+	2.70577i	0.108579	+	0.188064i
$208$	−7.99038	+	16.1603i	−0.554033	+	1.12051i
$209$	−9.46410			−0.654646
$210$		0			0
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	0.995920	−	0.0902411i	$-0.0287638\pi$
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	−0.576111	+	0.817371i	$0.695430\pi$
$212$	−1.96410	−	3.40192i	−0.134895	−	0.233645i
$213$	−2.19615	−	3.80385i	−0.150478	−	0.260635i
$214$	−34.3923			−2.35101
$215$	−8.83013	−	15.2942i	−0.602210	−	1.04306i
$216$	−6.92820			−0.471405
$217$		0			0
$218$	10.7321	+	18.5885i	0.726866	+	1.25897i
$219$	−5.26795			−0.355975
$220$	−4.09808	−	7.09808i	−0.276292	−	0.478552i
$221$	6.82051	−	13.7942i	0.458797	−	0.927900i
$222$	−4.43782	+	7.68653i	−0.297847	+	0.515886i
$223$	−5.00000	−	8.66025i	−0.334825	−	0.579934i	0.648626	−	0.761107i	$-0.275344\pi$
$223$	−5.00000	−	8.66025i	−0.334825	−	0.579934i	−0.983451	+	0.181173i	$0.942010\pi$
$224$		0			0
$225$	−2.46410	+	4.26795i	−0.164273	+	0.284530i
$226$	−6.40192	+	11.0885i	−0.425850	+	0.737593i
$227$	11.6603			0.773918			0.386959	−	0.922097i	$-0.373525\pi$
$227$	11.6603			0.773918			0.386959	+	0.922097i	$0.373525\pi$
$228$	−1.46410			−0.0969625
$229$	3.19615	−	5.53590i	0.211208	−	0.365822i	−0.740885	−	0.671632i	$-0.765594\pi$
$229$	3.19615	−	5.53590i	0.211208	−	0.365822i	0.952093	+	0.305809i	$0.0989270\pi$
$230$	1.90192	−	3.29423i	0.125409	−	0.217215i
$231$		0			0
$232$	2.59808	+	4.50000i	0.170572	+	0.295439i
$233$	−12.9282	+	22.3923i	−0.846955	+	1.46697i	0.0369580	+	0.999317i	$0.488233\pi$
$233$	−12.9282	+	22.3923i	−0.846955	+	1.46697i	−0.883913	+	0.467652i	$0.845100\pi$
$234$	−15.3564	+	0.990381i	−1.00388	+	0.0647432i
$235$	−0.803848	−	1.39230i	−0.0524372	−	0.0908240i
$236$	−10.7321			−0.698597
$237$	−2.12436	−	3.67949i	−0.137992	−	0.239009i
$238$		0			0
$239$	−26.1962			−1.69449			−0.847244	−	0.531204i	$-0.821740\pi$
$239$	−26.1962			−1.69449			−0.847244	+	0.531204i	$0.821740\pi$
$240$	3.16987	+	5.49038i	0.204614	+	0.354403i
$241$	10.8038			0.695937			0.347969	−	0.937506i	$-0.386872\pi$
$241$	10.8038			0.695937			0.347969	+	0.937506i	$0.386872\pi$
$242$	9.86603	+	17.0885i	0.634212	+	1.09849i
$243$	−7.63397	−	13.2224i	−0.489720	−	0.848219i
$244$	−7.59808	−	13.1603i	−0.486417	−	0.842499i
$245$		0			0
$246$	6.58846			0.420065
$247$	7.19615	−	0.464102i	0.457880	−	0.0295301i
$248$	−5.36603	−	9.29423i	−0.340743	−	0.590184i
$249$	3.00000	−	5.19615i	0.190117	−	0.329293i
$250$	21.0000			1.32816
$251$	−11.1962	+	19.3923i	−0.706695	+	1.22403i	0.259382	+	0.965775i	$0.416481\pi$
$251$	−11.1962	+	19.3923i	−0.706695	+	1.22403i	−0.966076	+	0.258256i	$0.916852\pi$
$252$		0			0
$253$	−3.00000	+	5.19615i	−0.188608	+	0.326679i
$254$	−2.07180	−	3.58846i	−0.129996	−	0.225160i
$255$	−2.70577	−	4.68653i	−0.169442	−	0.293482i
$256$	19.0000			1.18750
$257$	18.1244			1.13057			0.565283	−	0.824897i	$-0.308767\pi$
$257$	18.1244			1.13057			0.565283	+	0.824897i	$0.308767\pi$
$258$	6.46410	+	11.1962i	0.402437	+	0.697042i
$259$		0			0
$260$	3.46410	+	5.19615i	0.214834	+	0.322252i
$261$	−3.69615	+	6.40192i	−0.228786	+	0.396269i
$262$	−3.00000	+	5.19615i	−0.185341	+	0.321019i
$263$	−2.36603	+	4.09808i	−0.145895	+	0.252698i	−0.929707	−	0.368301i	$-0.879940\pi$
$263$	−2.36603	+	4.09808i	−0.145895	+	0.252698i	0.783811	+	0.620999i	$0.213273\pi$
$264$	−3.00000	−	5.19615i	−0.184637	−	0.319801i
$265$	6.80385			0.417957
$266$		0			0
$267$	−0.339746	+	0.588457i	−0.0207921	+	0.0360130i
$268$	−2.09808	+	3.63397i	−0.128160	+	0.221980i
$269$	−18.9282			−1.15407			−0.577036	−	0.816718i	$-0.695791\pi$
$269$	−18.9282			−1.15407			−0.577036	+	0.816718i	$0.695791\pi$
$270$	−6.00000	+	10.3923i	−0.365148	+	0.632456i
$271$	−16.1962			−0.983846			−0.491923	−	0.870639i	$-0.663706\pi$
$271$	−16.1962			−0.983846			−0.491923	+	0.870639i	$0.663706\pi$
$272$	−21.3397			−1.29391
$273$		0			0
$274$	−37.9808			−2.29450
$275$	−9.46410			−0.570707
$276$	−0.464102	+	0.803848i	−0.0279356	+	0.0483859i
$277$	17.0000			1.02143			0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000			1.02143			0.510716	+	0.859750i	$0.329381\pi$
$278$	−17.8301	+	30.8827i	−1.06938	+	1.85222i
$279$	7.63397	−	13.2224i	0.457034	−	0.791606i
$280$		0			0
$281$	−7.39230			−0.440988			−0.220494	−	0.975388i	$-0.570767\pi$
$281$	−7.39230			−0.440988			−0.220494	+	0.975388i	$0.570767\pi$
$282$	0.588457	+	1.01924i	0.0350421	+	0.0606947i
$283$	−0.0980762	+	0.169873i	−0.00583003	+	0.0100979i	−0.868926	−	0.494943i	$-0.835189\pi$
$283$	−0.0980762	+	0.169873i	−0.00583003	+	0.0100979i	0.863096	+	0.505040i	$0.168522\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$	1.26795	−	2.19615i	0.0751068	−	0.130089i
$286$	−16.3923	−	24.5885i	−0.969297	−	1.45395i
$287$		0			0
$288$	6.40192	+	11.0885i	0.377237	+	0.653394i
$289$	1.21539			0.0714935
$290$	9.00000			0.528498
$291$	−5.26795	−	9.12436i	−0.308813	−	0.534879i
$292$	3.59808	+	6.23205i	0.210561	+	0.364703i
$293$	−5.59808	+	9.69615i	−0.327043	+	0.566455i	−0.981924	−	0.189277i	$-0.939386\pi$
$293$	−5.59808	+	9.69615i	−0.327043	+	0.566455i	0.654881	+	0.755732i	$0.272719\pi$
$294$		0			0
$295$	9.29423	−	16.0981i	0.541131	−	0.937266i
$296$	−12.1244			−0.704714
$297$	9.46410	−	16.3923i	0.549163	−	0.951178i
$298$	0.401924	+	0.696152i	0.0232828	+	0.0403270i
$299$	2.02628	−	4.09808i	0.117183	−	0.236998i
$300$	−1.46410			−0.0845299
$301$		0			0
$302$	1.73205	+	3.00000i	0.0996683	+	0.172631i
$303$	−1.56218	−	2.70577i	−0.0897448	−	0.155443i
$304$	−5.00000	−	8.66025i	−0.286770	−	0.496700i
$305$	26.3205			1.50711
$306$	−9.10770	−	15.7750i	−0.520652	−	0.901796i
$307$	−26.5885			−1.51748			−0.758742	−	0.651392i	$-0.774186\pi$
$307$	−26.5885			−1.51748			−0.758742	+	0.651392i	$0.774186\pi$
$308$		0			0
$309$	2.33975	+	4.05256i	0.133103	+	0.230542i
$310$	−18.5885			−1.05575
$311$	2.36603	+	4.09808i	0.134165	+	0.232381i	0.925278	−	0.379289i	$-0.123831\pi$
$311$	2.36603	+	4.09808i	0.134165	+	0.232381i	−0.791113	+	0.611670i	$0.790498\pi$
$312$	2.53590	+	3.80385i	0.143567	+	0.215350i
$313$	−6.39230	+	11.0718i	−0.361314	+	0.625815i	−0.988177	−	0.153315i	$-0.951005\pi$
$313$	−6.39230	+	11.0718i	−0.361314	+	0.625815i	0.626863	+	0.779129i	$0.284339\pi$
$314$	7.96410	+	13.7942i	0.449440	+	0.778453i
$315$		0			0
$316$	−2.90192	+	5.02628i	−0.163246	+	0.282750i
$317$	−0.232051	+	0.401924i	−0.0130333	+	0.0225743i	−0.872468	−	0.488670i	$-0.837482\pi$
$317$	−0.232051	+	0.401924i	−0.0130333	+	0.0225743i	0.859435	+	0.511245i	$0.170815\pi$
$318$	−4.98076			−0.279307
$319$	−14.1962			−0.794832
$320$	−0.866025	+	1.50000i	−0.0484123	+	0.0838525i
$321$	−7.26795	+	12.5885i	−0.405657	+	0.702619i
$322$		0			0
$323$	4.26795	+	7.39230i	0.237475	+	0.411319i
$324$	−2.23205	+	3.86603i	−0.124003	+	0.214779i
$325$	7.19615	−	0.464102i	0.399171	−	0.0257437i
$326$	5.02628	+	8.70577i	0.278380	+	0.482168i
$327$	9.07180			0.501672
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$	−10.3923			−0.572078
$331$	13.4904	+	23.3660i	0.741498	+	1.28431i	0.951813	+	0.306679i	$0.0992179\pi$
$331$	13.4904	+	23.3660i	0.741498	+	1.28431i	−0.210315	+	0.977634i	$0.567449\pi$
$332$	−8.19615			−0.449822
$333$	−8.62436	−	14.9378i	−0.472612	−	0.818588i
$334$	−21.2942	−	36.8827i	−1.16517	−	2.01813i
$335$	−3.63397	−	6.29423i	−0.198545	−	0.343890i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$	13.6699	+	17.8923i	0.743543	+	0.973213i
$339$	2.70577	+	4.68653i	0.146957	+	0.254538i
$340$	−3.69615	+	6.40192i	−0.200452	+	0.347193i
$341$	29.3205			1.58779
$342$	4.26795	−	7.39230i	0.230784	−	0.399730i
$343$		0			0
$344$	−8.83013	+	15.2942i	−0.476089	+	0.824610i
$345$	−0.803848	−	1.39230i	−0.0432777	−	0.0749592i
$346$	−13.3923	−	23.1962i	−0.719975	−	1.24703i
$347$	10.7321			0.576127			0.288063	−	0.957611i	$-0.406989\pi$
$347$	10.7321			0.576127			0.288063	+	0.957611i	$0.406989\pi$
$348$	−2.19615			−0.117726
$349$	8.39230	+	14.5359i	0.449230	+	0.778089i	0.998336	−	0.0576637i	$-0.0183651\pi$
$349$	8.39230	+	14.5359i	0.449230	+	0.778089i	−0.549106	+	0.835753i	$0.685032\pi$
$350$		0			0
$351$	−6.39230	+	12.9282i	−0.341196	+	0.690056i
$352$	−12.2942	+	21.2942i	−0.655285	+	1.13499i
$353$	1.66987	−	2.89230i	0.0888784	−	0.153942i	−0.818159	−	0.574992i	$-0.805005\pi$
$353$	1.66987	−	2.89230i	0.0888784	−	0.153942i	0.907037	+	0.421050i	$0.138338\pi$
$354$	−6.80385	+	11.7846i	−0.361620	+	0.626345i
$355$	−5.19615	−	9.00000i	−0.275783	−	0.477670i
$356$	0.928203			0.0491947
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	−2.53590	+	4.39230i	−0.133840	+	0.231817i	−0.925154	−	0.379593i	$-0.876064\pi$
$359$	−2.53590	+	4.39230i	−0.133840	+	0.231817i	0.791314	+	0.611410i	$0.209397\pi$
$360$	−7.39230			−0.389609
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−44.3205			−2.32943
$363$	8.33975			0.437723
$364$		0			0
$365$	−12.4641			−0.652401
$366$	−19.2679			−1.00715
$367$	−3.09808	+	5.36603i	−0.161718	+	0.280104i	−0.935485	−	0.353366i	$-0.885037\pi$
$367$	−3.09808	+	5.36603i	−0.161718	+	0.280104i	0.773767	+	0.633471i	$0.218370\pi$
$368$	−6.33975			−0.330482
$369$	−6.40192	+	11.0885i	−0.333271	+	0.577242i
$370$	−10.5000	+	18.1865i	−0.545869	+	0.945473i
$371$		0			0
$372$	4.53590			0.235175
$373$	−4.69615	−	8.13397i	−0.243158	−	0.421161i	0.718454	−	0.695574i	$-0.244850\pi$
$373$	−4.69615	−	8.13397i	−0.243158	−	0.421161i	−0.961612	+	0.274413i	$0.911517\pi$
$374$	17.4904	−	30.2942i	0.904406	−	1.56648i
$375$	4.43782	−	7.68653i	0.229168	−	0.396931i
$376$	−0.803848	+	1.39230i	−0.0414553	+	0.0718026i
$377$	10.7942	−	0.696152i	0.555931	−	0.0358537i
$378$		0			0
$379$	2.29423	+	3.97372i	0.117847	+	0.204116i	0.918914	−	0.394458i	$-0.129068\pi$
$379$	2.29423	+	3.97372i	0.117847	+	0.204116i	−0.801067	+	0.598574i	$0.795734\pi$
$380$	−3.46410			−0.177705
$381$	−1.75129			−0.0897212
$382$	1.09808	+	1.90192i	0.0561825	+	0.0973109i
$383$	2.83013	+	4.90192i	0.144613	+	0.250477i	0.929228	−	0.369506i	$-0.120473\pi$
$383$	2.83013	+	4.90192i	0.144613	+	0.250477i	−0.784616	+	0.619982i	$0.787140\pi$
$384$	4.43782	−	7.68653i	0.226467	−	0.392252i
$385$		0			0
$386$	4.33013	−	7.50000i	0.220398	−	0.381740i
$387$	−25.1244			−1.27714
$388$	−7.19615	+	12.4641i	−0.365329	+	0.632769i
$389$	15.2321	+	26.3827i	0.772296	+	1.33766i	0.936302	+	0.351196i	$0.114225\pi$
$389$	15.2321	+	26.3827i	0.772296	+	1.33766i	−0.164006	+	0.986459i	$0.552442\pi$
$390$	7.90192	−	0.509619i	0.400129	−	0.0258056i
$391$	5.41154			0.273673
$392$		0			0
$393$	1.26795	+	2.19615i	0.0639596	+	0.110781i
$394$	10.3923	+	18.0000i	0.523557	+	0.906827i
$395$	−5.02628	−	8.70577i	−0.252900	−	0.438035i
$396$	−11.6603			−0.585950
$397$	11.3923	+	19.7321i	0.571763	+	0.990323i	0.996385	+	0.0849523i	$0.0270738\pi$
$397$	11.3923	+	19.7321i	0.571763	+	0.990323i	−0.424622	+	0.905371i	$0.639593\pi$
$398$	3.46410			0.173640
$399$		0			0
$400$	−5.00000	−	8.66025i	−0.250000	−	0.433013i
$401$	16.8564			0.841769			0.420884	−	0.907114i	$-0.361720\pi$
$401$	16.8564			0.841769			0.420884	+	0.907114i	$0.361720\pi$
$402$	2.66025	+	4.60770i	0.132681	+	0.229811i
$403$	−22.2942	+	1.43782i	−1.11055	+	0.0716230i
$404$	−2.13397	+	3.69615i	−0.106169	+	0.183890i
$405$	−3.86603	−	6.69615i	−0.192104	−	0.332734i
$406$		0			0
$407$	16.5622	−	28.6865i	0.820957	−	1.42194i
$408$	−2.70577	+	4.68653i	−0.133956	+	0.232018i
$409$	27.1962			1.34476			0.672382	−	0.740205i	$-0.265271\pi$
$409$	27.1962			1.34476			0.672382	+	0.740205i	$0.265271\pi$
$410$	15.5885			0.769859
$411$	−8.02628	+	13.9019i	−0.395907	+	0.685731i
$412$	3.19615	−	5.53590i	0.157463	−	0.272734i
$413$		0			0
$414$	−2.70577	−	4.68653i	−0.132981	−	0.230331i
$415$	7.09808	−	12.2942i	0.348431	−	0.603500i
$416$	8.30385	−	16.7942i	0.407130	−	0.823405i
$417$	7.53590	+	13.0526i	0.369035	+	0.639187i
$418$	16.3923			0.801774
$419$	−10.9019	−	18.8827i	−0.532594	−	0.922480i	−0.999276	−	0.0380543i	$-0.987884\pi$
$419$	−10.9019	−	18.8827i	−0.532594	−	0.922480i	0.466682	−	0.884425i	$-0.345449\pi$
$420$		0			0
$421$	30.1769			1.47073			0.735366	−	0.677670i	$-0.237010\pi$
$421$	30.1769			1.47073			0.735366	+	0.677670i	$0.237010\pi$
$422$	−10.5622	−	18.2942i	−0.514159	−	0.890549i
$423$	−2.28719			−0.111207
$424$	−3.40192	−	5.89230i	−0.165212	−	0.286156i
$425$	4.26795	+	7.39230i	0.207026	+	0.358579i
$426$	3.80385	+	6.58846i	0.184297	+	0.319212i
$427$		0			0
$428$	19.8564			0.959796
$429$	−12.4641	+	0.803848i	−0.601772	+	0.0388101i
$430$	15.2942	+	26.4904i	0.737553	+	1.27748i
$431$	−17.6603	+	30.5885i	−0.850665	+	1.47339i	0.0299451	+	0.999552i	$0.490467\pi$
$431$	−17.6603	+	30.5885i	−0.850665	+	1.47339i	−0.880610	+	0.473843i	$0.842867\pi$
$432$	20.0000			0.962250
$433$	8.79423	−	15.2321i	0.422624	−	0.732006i	−0.573572	−	0.819155i	$-0.694443\pi$
$433$	8.79423	−	15.2321i	0.422624	−	0.732006i	0.996195	+	0.0871498i	$0.0277759\pi$
$434$		0			0
$435$	1.90192	−	3.29423i	0.0911903	−	0.157946i
$436$	−6.19615	−	10.7321i	−0.296742	−	0.513972i
$437$	1.26795	+	2.19615i	0.0606542	+	0.105056i
$438$	9.12436			0.435979
$439$	16.5885			0.791724			0.395862	−	0.918310i	$-0.370446\pi$
$439$	16.5885			0.791724			0.395862	+	0.918310i	$0.370446\pi$
$440$	−7.09808	−	12.2942i	−0.338388	−	0.586104i
$441$		0			0
$442$	−11.8135	+	23.8923i	−0.561909	+	1.13644i
$443$	5.66025	−	9.80385i	0.268927	−	0.465795i	−0.699658	−	0.714478i	$-0.746664\pi$
$443$	5.66025	−	9.80385i	0.268927	−	0.465795i	0.968585	+	0.248683i	$0.0799977\pi$
$444$	2.56218	−	4.43782i	0.121596	−	0.210610i
$445$	−0.803848	+	1.39230i	−0.0381060	+	0.0660016i
$446$	8.66025	+	15.0000i	0.410075	+	0.710271i
$447$	0.339746			0.0160694
$448$		0			0
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	−0.689003	−	0.724758i	$-0.741951\pi$
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	0.972161	+	0.234315i	$0.0752847\pi$
$450$	4.26795	−	7.39230i	0.201193	−	0.348477i
$451$	−24.5885			−1.15783
$452$	3.69615	−	6.40192i	0.173852	−	0.301121i
$453$	1.46410			0.0687895
$454$	−20.1962			−0.947852
$455$		0			0
$456$	−2.53590			−0.118754
$457$	11.0000			0.514558			0.257279	−	0.966337i	$-0.417174\pi$
$457$	11.0000			0.514558			0.257279	+	0.966337i	$0.417174\pi$
$458$	−5.53590	+	9.58846i	−0.258676	+	0.448039i
$459$	−17.0718			−0.796843
$460$	−1.09808	+	1.90192i	−0.0511981	+	0.0886777i
$461$	7.79423	−	13.5000i	0.363013	−	0.628758i	−0.625442	−	0.780271i	$-0.715081\pi$
$461$	7.79423	−	13.5000i	0.363013	−	0.628758i	0.988455	+	0.151513i	$0.0484146\pi$
$462$		0			0
$463$	26.5885			1.23567			0.617835	−	0.786308i	$-0.288010\pi$
$463$	26.5885			1.23567			0.617835	+	0.786308i	$0.288010\pi$
$464$	−7.50000	−	12.9904i	−0.348179	−	0.603063i
$465$	−3.92820	+	6.80385i	−0.182166	+	0.315521i
$466$	22.3923	−	38.7846i	1.03730	−	1.79666i
$467$	−9.75833	+	16.9019i	−0.451562	+	0.782128i	−0.998483	−	0.0550561i	$-0.982466\pi$
$467$	−9.75833	+	16.9019i	−0.451562	+	0.782128i	0.546922	+	0.837184i	$0.315800\pi$
$468$	8.86603	−	0.571797i	0.409832	−	0.0264313i
$469$		0			0
$470$	1.39230	+	2.41154i	0.0642222	+	0.111236i
$471$	6.73205			0.310197
$472$	−18.5885			−0.855603
$473$	−24.1244	−	41.7846i	−1.10924	−	1.92126i
$474$	3.67949	+	6.37307i	0.169005	+	0.292725i
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$		0			0
$477$	4.83975	−	8.38269i	0.221597	−	0.383817i
$478$	45.3731			2.07532
$479$	2.36603	−	4.09808i	0.108106	−	0.187246i	−0.806897	−	0.590693i	$-0.798855\pi$
$479$	2.36603	−	4.09808i	0.108106	−	0.187246i	0.915003	+	0.403447i	$0.132188\pi$
$480$	−3.29423	−	5.70577i	−0.150360	−	0.260432i
$481$	−11.1865	+	22.6244i	−0.510062	+	1.03158i
$482$	−18.7128			−0.852345
$483$		0			0
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$	−12.4641	−	21.5885i	−0.565966	−	0.980281i
$486$	13.2224	+	22.9019i	0.599782	+	1.03885i
$487$	−0.784610			−0.0355541			−0.0177770	−	0.999842i	$-0.505659\pi$
$487$	−0.784610			−0.0355541			−0.0177770	+	0.999842i	$0.505659\pi$
$488$	−13.1603	−	22.7942i	−0.595737	−	1.03185i
$489$	4.24871			0.192133
$490$		0			0
$491$	−14.1962	−	24.5885i	−0.640663	−	1.10966i	−0.985285	−	0.170920i	$-0.945326\pi$
$491$	−14.1962	−	24.5885i	−0.640663	−	1.10966i	0.344622	−	0.938742i	$-0.388007\pi$
$492$	−3.80385			−0.171491
$493$	6.40192	+	11.0885i	0.288328	+	0.499399i
$494$	−12.4641	+	0.803848i	−0.560786	+	0.0361668i
$495$	10.0981	−	17.4904i	0.453875	−	0.786134i
$496$	15.4904	+	26.8301i	0.695539	+	1.20471i
$497$		0			0
$498$	−5.19615	+	9.00000i	−0.232845	+	0.403300i
$499$	−6.49038	+	11.2417i	−0.290549	+	0.503246i	−0.973940	−	0.226807i	$-0.927171\pi$
$499$	−6.49038	+	11.2417i	−0.290549	+	0.503246i	0.683390	+	0.730053i	$0.260505\pi$
$500$	−12.1244			−0.542218
$501$	−18.0000			−0.804181
$502$	19.3923	−	33.5885i	0.865521	−	1.49913i
$503$	6.29423	−	10.9019i	0.280646	−	0.486093i	−0.690898	−	0.722952i	$-0.742785\pi$
$503$	6.29423	−	10.9019i	0.280646	−	0.486093i	0.971544	+	0.236859i	$0.0761181\pi$
$504$		0			0
$505$	−3.69615	−	6.40192i	−0.164477	−	0.284882i
$506$	5.19615	−	9.00000i	0.230997	−	0.400099i
$507$	9.43782	−	1.22243i	0.419148	−	0.0542901i
$508$	1.19615	+	2.07180i	0.0530707	+	0.0919211i
$509$	−10.2679			−0.455119			−0.227559	−	0.973764i	$-0.573075\pi$
$509$	−10.2679			−0.455119			−0.227559	+	0.973764i	$0.573075\pi$
$510$	4.68653	+	8.11731i	0.207523	+	0.359441i
$511$		0			0
$512$	−8.66025			−0.382733
$513$	−4.00000	−	6.92820i	−0.176604	−	0.305888i
$514$	−31.3923			−1.38466
$515$	5.53590	+	9.58846i	0.243941	+	0.422518i
$516$	−3.73205	−	6.46410i	−0.164294	−	0.284566i
$517$	−2.19615	−	3.80385i	−0.0965867	−	0.167293i
$518$		0			0
$519$	−11.3205			−0.496915
$520$	6.00000	+	9.00000i	0.263117	+	0.394676i
$521$	0.0621778	+	0.107695i	0.00272406	+	0.00471821i	0.867384	−	0.497639i	$-0.165800\pi$
$521$	0.0621778	+	0.107695i	0.00272406	+	0.00471821i	−0.864660	+	0.502357i	$0.832466\pi$
$522$	6.40192	−	11.0885i	0.280205	−	0.485329i
$523$	−33.1769			−1.45073			−0.725363	−	0.688367i	$-0.758328\pi$
$523$	−33.1769			−1.45073			−0.725363	+	0.688367i	$0.758328\pi$
$524$	1.73205	−	3.00000i	0.0756650	−	0.131056i
$525$		0			0
$526$	4.09808	−	7.09808i	0.178685	−	0.309491i
$527$	−13.2224	−	22.9019i	−0.575978	−	0.997623i
$528$	8.66025	+	15.0000i	0.376889	+	0.652791i
$529$	−21.3923			−0.930100
$530$	−11.7846			−0.511891
$531$	−13.2224	−	22.9019i	−0.573805	−	0.993859i
$532$		0			0
$533$	18.6962	−	1.20577i	0.809820	−	0.0522278i
$534$	0.588457	−	1.01924i	0.0254650	−	0.0441067i
$535$	−17.1962	+	29.7846i	−0.743455	+	1.28770i
$536$	−3.63397	+	6.29423i	−0.156964	+	0.271869i
$537$	−2.53590	−	4.39230i	−0.109432	−	0.189542i
$538$	32.7846			1.41344
$539$		0			0
$540$	3.46410	−	6.00000i	0.149071	−	0.258199i
$541$	17.6962	−	30.6506i	0.760817	−	1.31777i	−0.181613	−	0.983370i	$-0.558132\pi$
$541$	17.6962	−	30.6506i	0.760817	−	1.31777i	0.942430	−	0.334404i	$-0.108535\pi$
$542$	28.0526			1.20496
$543$	−9.36603	+	16.2224i	−0.401935	+	0.696171i
$544$	22.1769			0.950827
$545$	21.4641			0.919421
$546$		0			0
$547$	28.1962			1.20558			0.602790	−	0.797900i	$-0.294056\pi$
$547$	28.1962			1.20558			0.602790	+	0.797900i	$0.294056\pi$
$548$	21.9282			0.936726
$549$	18.7224	−	32.4282i	0.799054	−	1.38400i
$550$	16.3923			0.698970
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$	−0.803848	+	1.39230i	−0.0342140	+	0.0592604i
$553$		0			0
$554$	−29.4449			−1.25099
$555$	4.43782	+	7.68653i	0.188375	+	0.326275i
$556$	10.2942	−	17.8301i	0.436573	−	0.756166i
$557$	12.8205	−	22.2058i	0.543222	−	0.940889i	−0.455494	−	0.890239i	$-0.650537\pi$
$557$	12.8205	−	22.2058i	0.543222	−	0.940889i	0.998716	−	0.0506499i	$-0.0161293\pi$
$558$	−13.2224	+	22.9019i	−0.559750	+	0.969516i
$559$	20.3923	+	30.5885i	0.862503	+	1.29375i
$560$		0			0
$561$	−7.39230	−	12.8038i	−0.312103	−	0.540579i
$562$	12.8038			0.540098
$563$	10.0526			0.423665			0.211832	−	0.977306i	$-0.432057\pi$
$563$	10.0526			0.423665			0.211832	+	0.977306i	$0.432057\pi$
$564$	−0.339746	−	0.588457i	−0.0143059	−	0.0247785i
$565$	6.40192	+	11.0885i	0.269331	+	0.466495i
$566$	0.169873	−	0.294229i	0.00714029	−	0.0123674i
$567$		0			0
$568$	−5.19615	+	9.00000i	−0.218026	+	0.377632i
$569$	29.0718			1.21875			0.609377	−	0.792881i	$-0.291420\pi$
$569$	29.0718			1.21875			0.609377	+	0.792881i	$0.291420\pi$
$570$	−2.19615	+	3.80385i	−0.0919867	+	0.159326i
$571$	12.3923	+	21.4641i	0.518602	+	0.898245i	0.999766	+	0.0216144i	$0.00688062\pi$
$571$	12.3923	+	21.4641i	0.518602	+	0.898245i	−0.481165	+	0.876630i	$0.659786\pi$
$572$	9.46410	+	14.1962i	0.395714	+	0.593571i
$573$	0.928203			0.0387762
$574$		0			0
$575$	1.26795	+	2.19615i	0.0528771	+	0.0915859i
$576$	1.23205	+	2.13397i	0.0513355	+	0.0889156i
$577$	16.4019	+	28.4090i	0.682821	+	1.18268i	0.974116	+	0.226048i	$0.0725805\pi$
$577$	16.4019	+	28.4090i	0.682821	+	1.18268i	−0.291295	+	0.956633i	$0.594086\pi$
$578$	−2.10512			−0.0875614
$579$	−1.83013	−	3.16987i	−0.0760575	−	0.131735i
$580$	−5.19615			−0.215758
$581$		0			0
$582$	9.12436	+	15.8038i	0.378217	+	0.655091i
$583$	18.5885			0.769855
$584$	6.23205	+	10.7942i	0.257884	+	0.446668i
$585$	−6.82051	+	13.7942i	−0.281993	+	0.570321i
$586$	9.69615	−	16.7942i	0.400544	−	0.693763i
$587$	−2.19615	−	3.80385i	−0.0906449	−	0.157002i	0.817138	−	0.576442i	$-0.195559\pi$
$587$	−2.19615	−	3.80385i	−0.0906449	−	0.157002i	−0.907783	+	0.419441i	$0.862226\pi$
$588$		0			0
$589$	6.19615	−	10.7321i	0.255308	−	0.442206i
$590$	−16.0981	+	27.8827i	−0.662747	+	1.14791i
$591$	8.78461			0.361351
$592$	35.0000			1.43849
$593$	20.7224	−	35.8923i	0.850968	−	1.47392i	−0.0293672	−	0.999569i	$-0.509349\pi$
$593$	20.7224	−	35.8923i	0.850968	−	1.47392i	0.880335	−	0.474352i	$-0.157317\pi$
$594$	−16.3923	+	28.3923i	−0.672584	+	1.16495i
$595$		0			0
$596$	−0.232051	−	0.401924i	−0.00950517	−	0.0164634i
$597$	0.732051	−	1.26795i	0.0299608	−	0.0518937i
$598$	−3.50962	+	7.09808i	−0.143519	+	0.290262i
$599$	−8.07180	−	13.9808i	−0.329805	−	0.571238i	0.652668	−	0.757644i	$-0.273650\pi$
$599$	−8.07180	−	13.9808i	−0.329805	−	0.571238i	−0.982473	+	0.186405i	$0.940316\pi$
$600$	−2.53590			−0.103528
$601$	10.9904	+	19.0359i	0.448307	+	0.776490i	0.998276	−	0.0586946i	$-0.0186938\pi$
$601$	10.9904	+	19.0359i	0.448307	+	0.776490i	−0.549969	+	0.835185i	$0.685360\pi$
$602$		0			0
$603$	−10.3397			−0.421067
$604$	−1.00000	−	1.73205i	−0.0406894	−	0.0704761i
$605$	19.7321			0.802222
$606$	2.70577	+	4.68653i	0.109914	+	0.190377i
$607$	3.19615	+	5.53590i	0.129728	+	0.224695i	0.923571	−	0.383427i	$-0.125256\pi$
$607$	3.19615	+	5.53590i	0.129728	+	0.224695i	−0.793843	+	0.608122i	$0.791923\pi$
$608$	5.19615	+	9.00000i	0.210732	+	0.364998i
$609$		0			0
$610$	−45.5885			−1.84582
$611$	1.85641	+	2.78461i	0.0751022	+	0.112653i
$612$	5.25833	+	9.10770i	0.212555	+	0.368157i
$613$	8.69615	−	15.0622i	0.351234	−	0.608356i	−0.635232	−	0.772322i	$-0.719095\pi$
$613$	8.69615	−	15.0622i	0.351234	−	0.608356i	0.986466	+	0.163966i	$0.0524287\pi$
$614$	46.0526			1.85853
$615$	3.29423	−	5.70577i	0.132836	−	0.230079i
$616$		0			0
$617$	−14.3038	+	24.7750i	−0.575851	+	0.997404i	0.420097	+	0.907479i	$0.361996\pi$
$617$	−14.3038	+	24.7750i	−0.575851	+	0.997404i	−0.995949	+	0.0899245i	$0.971337\pi$
$618$	−4.05256	−	7.01924i	−0.163018	−	0.282355i
$619$	−18.6865	−	32.3660i	−0.751075	−	1.30090i	−0.947302	−	0.320342i	$-0.896202\pi$
$619$	−18.6865	−	32.3660i	−0.751075	−	1.30090i	0.196227	−	0.980559i	$-0.437131\pi$
$620$	10.7321			0.431010
$621$	−5.07180			−0.203524
$622$	−4.09808	−	7.09808i	−0.164318	−	0.284607i
$623$		0			0
$624$	−7.32051	−	10.9808i	−0.293055	−	0.439582i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	11.0718	−	19.1769i	0.442518	−	0.766464i
$627$	3.46410	−	6.00000i	0.138343	−	0.239617i
$628$	−4.59808	−	7.96410i	−0.183483	−	0.317802i
$629$	−29.8756			−1.19122
$630$		0			0
$631$	−14.3923	+	24.9282i	−0.572949	+	0.992376i	0.423313	+	0.905984i	$0.360867\pi$
$631$	−14.3923	+	24.9282i	−0.572949	+	0.992376i	−0.996261	+	0.0863924i	$0.972466\pi$
$632$	−5.02628	+	8.70577i	−0.199935	+	0.346297i
$633$	−8.92820			−0.354864
$634$	0.401924	−	0.696152i	0.0159624	−	0.0276477i
$635$	−4.14359			−0.164433
$636$	2.87564			0.114027
$637$		0			0
$638$	24.5885			0.973466
$639$	−14.7846			−0.584870
$640$	10.5000	−	18.1865i	0.415049	−	0.718886i
$641$	1.14359			0.0451692			0.0225846	−	0.999745i	$-0.492810\pi$
$641$	1.14359			0.0451692			0.0225846	+	0.999745i	$0.492810\pi$
$642$	12.5885	−	21.8038i	0.496827	−	0.860529i
$643$	20.3923	−	35.3205i	0.804194	−	1.39290i	−0.112640	−	0.993636i	$-0.535931\pi$
$643$	20.3923	−	35.3205i	0.804194	−	1.39290i	0.916834	−	0.399269i	$-0.130736\pi$
$644$		0			0
$645$	12.9282			0.509048
$646$	−7.39230	−	12.8038i	−0.290846	−	0.503761i
$647$	−22.5167	+	39.0000i	−0.885221	+	1.53325i	−0.0397614	+	0.999209i	$0.512660\pi$
$647$	−22.5167	+	39.0000i	−0.885221	+	1.53325i	−0.845460	+	0.534039i	$0.820674\pi$
$648$	−3.86603	+	6.69615i	−0.151872	+	0.263050i
$649$	25.3923	−	43.9808i	0.996735	−	1.72640i
$650$	−12.4641	+	0.803848i	−0.488882	+	0.0315295i
$651$		0			0
$652$	−2.90192	−	5.02628i	−0.113648	−	0.196844i
$653$	−10.1436			−0.396949			−0.198475	−	0.980106i	$-0.563599\pi$
$653$	−10.1436			−0.396949			−0.198475	+	0.980106i	$0.563599\pi$
$654$	−15.7128			−0.614420
$655$	3.00000	+	5.19615i	0.117220	+	0.203030i
$656$	−12.9904	−	22.5000i	−0.507189	−	0.878477i
$657$	−8.86603	+	15.3564i	−0.345897	+	0.599110i
$658$		0			0
$659$	−3.80385	+	6.58846i	−0.148177	+	0.256650i	−0.930554	−	0.366156i	$-0.880674\pi$
$659$	−3.80385	+	6.58846i	−0.148177	+	0.256650i	0.782377	+	0.622805i	$0.214007\pi$
$660$	6.00000			0.233550
$661$	−11.4019	+	19.7487i	−0.443483	+	0.768136i	−0.997945	−	0.0640734i	$-0.979591\pi$
$661$	−11.4019	+	19.7487i	−0.443483	+	0.768136i	0.554462	+	0.832209i	$0.312924\pi$
$662$	−23.3660	−	40.4711i	−0.908146	−	1.57296i
$663$	6.24871	+	9.37307i	0.242680	+	0.364020i
$664$	−14.1962			−0.550918
$665$		0			0
$666$	14.9378	+	25.8731i	0.578829	+	1.00256i
$667$	1.90192	+	3.29423i	0.0736428	+	0.127553i
$668$	12.2942	+	21.2942i	0.475678	+	0.823898i
$669$	7.32051			0.283027
$670$	6.29423	+	10.9019i	0.243167	+	0.421178i
$671$	71.9090			2.77601
$672$		0			0
$673$	−9.08846	−	15.7417i	−0.350334	−	0.606797i	0.635974	−	0.771711i	$-0.280599\pi$
$673$	−9.08846	−	15.7417i	−0.350334	−	0.606797i	−0.986308	+	0.164914i	$0.947265\pi$
$674$	−19.0526			−0.733877
$675$	−4.00000	−	6.92820i	−0.153960	−	0.266667i
$676$	−7.89230	−	10.3301i	−0.303550	−	0.397313i
$677$	−18.4641	+	31.9808i	−0.709633	+	1.22912i	0.255360	+	0.966846i	$0.417806\pi$
$677$	−18.4641	+	31.9808i	−0.709633	+	1.22912i	−0.964993	+	0.262275i	$0.915527\pi$
$678$	−4.68653	−	8.11731i	−0.179985	−	0.311744i
$679$		0			0
$680$	−6.40192	+	11.0885i	−0.245503	+	0.425223i
$681$	−4.26795	+	7.39230i	−0.163548	+	0.283274i
$682$	−50.7846			−1.94464
$683$	8.53590			0.326617			0.163309	−	0.986575i	$-0.447783\pi$
$683$	8.53590			0.326617			0.163309	+	0.986575i	$0.447783\pi$
$684$	−2.46410	+	4.26795i	−0.0942173	+	0.163189i
$685$	−18.9904	+	32.8923i	−0.725585	+	1.25675i
$686$		0			0
$687$	2.33975	+	4.05256i	0.0892669	+	0.154615i
$688$	25.4904	−	44.1506i	0.971812	−	1.68323i
$689$	−14.1340	+	0.911543i	−0.538462	+	0.0347270i
$690$	1.39230	+	2.41154i	0.0530041	+	0.0918059i
$691$	20.3923			0.775760			0.387880	−	0.921710i	$-0.373208\pi$
$691$	20.3923			0.775760			0.387880	+	0.921710i	$0.373208\pi$
$692$	7.73205	+	13.3923i	0.293928	+	0.509099i
$693$		0			0
$694$	−18.5885			−0.705608
$695$	17.8301	+	30.8827i	0.676335	+	1.17145i
$696$	−3.80385			−0.144184
$697$	11.0885	+	19.2058i	0.420005	+	0.727470i
$698$	−14.5359	−	25.1769i	−0.550192	−	0.952960i
$699$	−9.46410	−	16.3923i	−0.357965	−	0.620014i
$700$		0			0
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$	11.0718	−	22.3923i	0.417878	−	0.845143i
$703$	−7.00000	−	12.1244i	−0.264010	−	0.457279i
$704$	−2.36603	+	4.09808i	−0.0891729	+	0.154452i
$705$	1.17691			0.0443252
$706$	−2.89230	+	5.00962i	−0.108853	+	0.188539i
$707$		0			0
$708$	3.92820	−	6.80385i	0.147631	−	0.255704i
$709$	16.0885	+	27.8660i	0.604215	+	1.04653i	0.992175	+	0.124854i	$0.0398464\pi$
$709$	16.0885	+	27.8660i	0.604215	+	1.04653i	−0.387960	+	0.921676i	$0.626820\pi$
$710$	9.00000	+	15.5885i	0.337764	+	0.585024i
$711$	−14.3013			−0.536340
$712$	1.60770			0.0602509
$713$	−3.92820	−	6.80385i	−0.147112	−	0.254806i
$714$		0			0
$715$	−29.4904	+	1.90192i	−1.10288	+	0.0711279i
$716$	−3.46410	+	6.00000i	−0.129460	+	0.224231i
$717$	9.58846	−	16.6077i	0.358087	−	0.620226i
$718$	4.39230	−	7.60770i	0.163919	−	0.283917i
$719$	−5.36603	−	9.29423i	−0.200119	−	0.346616i	0.748448	−	0.663194i	$-0.230800\pi$
$719$	−5.36603	−	9.29423i	−0.200119	−	0.346616i	−0.948567	+	0.316578i	$0.897466\pi$
$720$	21.3397			0.795285
$721$		0			0
$722$	−12.9904	+	22.5000i	−0.483452	+	0.837363i
$723$	−3.95448	+	6.84936i	−0.147069	+	0.254731i
$724$	25.5885			0.950988
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$	−14.4449			−0.536099
$727$	−21.1769			−0.785408			−0.392704	−	0.919665i	$-0.628460\pi$
$727$	−21.1769			−0.785408			−0.392704	+	0.919665i	$0.628460\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$	21.5885			0.799025
$731$	−21.7583	+	37.6865i	−0.804761	+	1.39389i
$732$	11.1244			0.411168
$733$	−3.79423	+	6.57180i	−0.140143	+	0.242735i	−0.927550	−	0.373698i	$-0.878090\pi$
$733$	−3.79423	+	6.57180i	−0.140143	+	0.242735i	0.787407	+	0.616433i	$0.211423\pi$
$734$	5.36603	−	9.29423i	0.198064	−	0.343056i
$735$		0			0
$736$	6.58846			0.242854
$737$	−9.92820	−	17.1962i	−0.365710	−	0.633428i
$738$	11.0885	−	19.2058i	0.408172	−	0.706974i
$739$	0.392305	−	0.679492i	0.0144312	−	0.0249955i	−0.858720	−	0.512446i	$-0.828740\pi$
$739$	0.392305	−	0.679492i	0.0144312	−	0.0249955i	0.873151	+	0.487450i	$0.162073\pi$
$740$	6.06218	−	10.5000i	0.222850	−	0.385988i
$741$	−2.33975	+	4.73205i	−0.0859527	+	0.173836i
$742$		0			0
$743$	14.1962	+	24.5885i	0.520806	+	0.902063i	0.999707	+	0.0241941i	$0.00770196\pi$
$743$	14.1962	+	24.5885i	0.520806	+	0.902063i	−0.478901	+	0.877869i	$0.658965\pi$
$744$	7.85641			0.288030
$745$	0.803848			0.0294507
$746$	8.13397	+	14.0885i	0.297806	+	0.515815i
$747$	−10.0981	−	17.4904i	−0.369469	−	0.639940i
$748$	−10.0981	+	17.4904i	−0.369222	+	0.639512i
$749$		0			0
$750$	−7.68653	+	13.3135i	−0.280673	+	0.486139i
$751$	46.1962			1.68572			0.842861	−	0.538132i	$-0.180870\pi$
$751$	46.1962			1.68572			0.842861	+	0.538132i	$0.180870\pi$
$752$	2.32051	−	4.01924i	0.0846202	−	0.146567i
$753$	−8.19615	−	14.1962i	−0.298684	−	0.517337i
$754$	−18.6962	+	1.20577i	−0.680874	+	0.0439116i
$755$	3.46410			0.126072
$756$		0			0
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	0.973991	−	0.226587i	$-0.0727569\pi$
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	−0.683226	+	0.730207i	$0.739424\pi$
$758$	−3.97372	−	6.88269i	−0.144332	−	0.249990i
$759$	−2.19615	−	3.80385i	−0.0797153	−	0.138071i
$760$	−6.00000			−0.217643
$761$	3.33975	+	5.78461i	0.121066	+	0.209692i	0.920188	−	0.391476i	$-0.128035\pi$
$761$	3.33975	+	5.78461i	0.121066	+	0.209692i	−0.799123	+	0.601168i	$0.794702\pi$
$762$	3.03332			0.109886
$763$		0			0
$764$	−0.633975	−	1.09808i	−0.0229364	−	0.0397270i
$765$	−18.2154			−0.658579
$766$	−4.90192	−	8.49038i	−0.177114	−	0.306770i
$767$	−17.1506	+	34.6865i	−0.619274	+	1.25246i
$768$	−6.95448	+	12.0455i	−0.250948	+	0.434655i
$769$	−23.5885	−	40.8564i	−0.850622	−	1.47332i	−0.880648	−	0.473771i	$-0.842893\pi$
$769$	−23.5885	−	40.8564i	−0.850622	−	1.47332i	0.0300268	−	0.999549i	$-0.490441\pi$
$770$		0			0
$771$	−6.63397	+	11.4904i	−0.238917	+	0.413816i
$772$	−2.50000	+	4.33013i	−0.0899770	+	0.155845i
$773$	−0.928203			−0.0333851			−0.0166926	−	0.999861i	$-0.505314\pi$
$773$	−0.928203			−0.0333851			−0.0166926	+	0.999861i	$0.505314\pi$
$774$	43.5167			1.56417
$775$	6.19615	−	10.7321i	0.222572	−	0.385507i
$776$	−12.4641	+	21.5885i	−0.447435	+	0.774980i
$777$		0			0
$778$	−26.3827	−	45.6962i	−0.945865	−	1.63829i
$779$	−5.19615	+	9.00000i	−0.186171	+	0.322458i
$780$	−4.56218	+	0.294229i	−0.163352	+	0.0105351i
$781$	−14.1962	−	24.5885i	−0.507978	−	0.879844i
$782$	−9.37307			−0.335180
$783$	−6.00000	−	10.3923i	−0.214423	−	0.371391i
$784$		0			0
$785$	15.9282			0.568502
$786$	−2.19615	−	3.80385i	−0.0783342	−	0.135679i
$787$	38.9808			1.38951			0.694757	−	0.719244i	$-0.255512\pi$
$787$	38.9808			1.38951			0.694757	+	0.719244i	$0.255512\pi$
$788$	−6.00000	−	10.3923i	−0.213741	−	0.370211i
$789$	−1.73205	−	3.00000i	−0.0616626	−	0.106803i
$790$	8.70577	+	15.0788i	0.309737	+	0.536481i
$791$		0			0
$792$	−20.1962			−0.717639
$793$	−54.6769	+	3.52628i	−1.94163	+	0.125222i
$794$	−19.7321	−	34.1769i	−0.700264	−	1.21289i
$795$	−2.49038	+	4.31347i	−0.0883247	+	0.152983i
$796$	−2.00000			−0.0708881
$797$	−6.80385	+	11.7846i	−0.241005	+	0.417432i	−0.961001	−	0.276546i	$-0.910810\pi$
$797$	−6.80385	+	11.7846i	−0.241005	+	0.417432i	0.719996	+	0.693978i	$0.244144\pi$
$798$		0			0
$799$	−1.98076	+	3.43078i	−0.0700743	+	0.121372i
$800$	5.19615	+	9.00000i	0.183712	+	0.318198i
$801$	1.14359	+	1.98076i	0.0404069	+	0.0699868i
$802$	−29.1962			−1.03095
$803$	−34.0526			−1.20169
$804$	−1.53590	−	2.66025i	−0.0541670	−	0.0938199i
$805$		0			0
$806$	38.6147	−	2.49038i	1.36015	−	0.0877199i
$807$	6.92820	−	12.0000i	0.243884	−	0.422420i
$808$	−3.69615	+	6.40192i	−0.130030	+	0.225219i
$809$	−7.96410	+	13.7942i	−0.280003	+	0.484979i	−0.971385	−	0.237510i	$-0.923669\pi$
$809$	−7.96410	+	13.7942i	−0.280003	+	0.484979i	0.691382	+	0.722489i	$0.257002\pi$
$810$	6.69615	+	11.5981i	0.235279	+	0.407515i
$811$	−14.5885			−0.512270			−0.256135	−	0.966641i	$-0.582449\pi$
$811$	−14.5885			−0.512270			−0.256135	+	0.966641i	$0.582449\pi$
$812$		0			0
$813$	5.92820	−	10.2679i	0.207911	−	0.360113i
$814$	−28.6865	+	49.6865i	−1.00546	+	1.74151i
$815$	10.0526			0.352126
$816$	7.81089	−	13.5289i	0.273436	−	0.473605i
$817$	−20.3923			−0.713436
$818$	−47.1051			−1.64699
$819$		0			0
$820$	−9.00000			−0.314294
$821$	31.8564			1.11180			0.555898	−	0.831250i	$-0.312374\pi$
$821$	31.8564			1.11180			0.555898	+	0.831250i	$0.312374\pi$
$822$	13.9019	−	24.0788i	0.484885	−	0.839846i
$823$	21.1769			0.738181			0.369090	−	0.929393i	$-0.379669\pi$
$823$	21.1769			0.738181			0.369090	+	0.929393i	$0.379669\pi$
$824$	5.53590	−	9.58846i	0.192852	−	0.334030i
$825$	3.46410	−	6.00000i	0.120605	−	0.208893i
$826$		0			0
$827$	34.9808			1.21640			0.608200	−	0.793784i	$-0.291892\pi$
$827$	34.9808			1.21640			0.608200	+	0.793784i	$0.291892\pi$
$828$	1.56218	+	2.70577i	0.0542894	+	0.0940321i
$829$	−15.7942	+	27.3564i	−0.548556	+	0.950127i	0.449818	+	0.893120i	$0.351489\pi$
$829$	−15.7942	+	27.3564i	−0.548556	+	0.950127i	−0.998374	+	0.0570068i	$0.981844\pi$
$830$	−12.2942	+	21.2942i	−0.426739	+	0.739133i
$831$	−6.22243	+	10.7776i	−0.215854	+	0.373870i
$832$	1.59808	−	3.23205i	0.0554033	−	0.112051i
$833$		0			0
$834$	−13.0526	−	22.6077i	−0.451973	−	0.782840i
$835$	−42.5885			−1.47383
$836$	−9.46410			−0.327323
$837$	12.3923	+	21.4641i	0.428341	+	0.741908i
$838$	18.8827	+	32.7058i	0.652292	+	1.12980i
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	−0.978517	−	0.206165i	$-0.933902\pi$
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	0.667803	+	0.744338i	$0.267235\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−52.2679			−1.80127
$843$	2.70577	−	4.68653i	0.0931917	−	0.161413i
$844$	6.09808	+	10.5622i	0.209904	+	0.363565i
$845$	22.3301	−	2.89230i	0.768180	−	0.0994983i
$846$	3.96152			0.136200
$847$		0			0
$848$	9.82051	+	17.0096i	0.337238	+	0.584113i
$849$	−0.0717968	−	0.124356i	−0.00246406	−	0.00426787i
$850$	−7.39230	−	12.8038i	−0.253554	−	0.439168i
$851$	−8.87564			−0.304253
$852$	−2.19615	−	3.80385i	−0.0752389	−	0.130318i
$853$	25.5885			0.876132			0.438066	−	0.898943i	$-0.355664\pi$
$853$	25.5885			0.876132			0.438066	+	0.898943i	$0.355664\pi$
$854$		0			0
$855$	−4.26795	−	7.39230i	−0.145961	−	0.252811i
$856$	34.3923			1.17550
$857$	−2.93782	−	5.08846i	−0.100354	−	0.173818i	0.811476	−	0.584385i	$-0.198664\pi$
$857$	−2.93782	−	5.08846i	−0.100354	−	0.173818i	−0.911831	+	0.410567i	$0.865331\pi$
$858$	21.5885	−	1.39230i	0.737018	−	0.0475325i
$859$	−9.09808	+	15.7583i	−0.310422	+	0.537667i	−0.978454	−	0.206466i	$-0.933804\pi$
$859$	−9.09808	+	15.7583i	−0.310422	+	0.537667i	0.668031	+	0.744133i	$0.267137\pi$
$860$	−8.83013	−	15.2942i	−0.301105	−	0.521529i
$861$		0			0
$862$	30.5885	−	52.9808i	1.04185	−	1.80453i
$863$	18.7583	−	32.4904i	0.638541	−	1.10599i	−0.347212	−	0.937787i	$-0.612872\pi$
$863$	18.7583	−	32.4904i	0.638541	−	1.10599i	0.985753	−	0.168199i	$-0.0537951\pi$
$864$	−20.7846			−0.707107
$865$	−26.7846			−0.910704
$866$	−15.2321	+	26.3827i	−0.517606	+	0.896520i
$867$	−0.444864	+	0.770527i	−0.0151084	+	0.0261685i
$868$		0			0
$869$	−13.7321	−	23.7846i	−0.465828	−	0.806838i
$870$	−3.29423	+	5.70577i	−0.111685	+	0.193444i
$871$	8.39230	+	12.5885i	0.284362	+	0.426544i
$872$	−10.7321	−	18.5885i	−0.363433	−	0.629485i
$873$	−35.4641			−1.20028
$874$	−2.19615	−	3.80385i	−0.0742860	−	0.128667i
$875$		0			0
$876$	−5.26795			−0.177988
$877$	10.8923	+	18.8660i	0.367807	+	0.637060i	0.989222	−	0.146421i	$-0.0467754\pi$
$877$	10.8923	+	18.8660i	0.367807	+	0.637060i	−0.621415	+	0.783481i	$0.713442\pi$
$878$	−28.7321			−0.969660
$879$	−4.09808	−	7.09808i	−0.138225	−	0.239412i
$880$	20.4904	+	35.4904i	0.690731	+	1.19638i
$881$	−19.7942	−	34.2846i	−0.666885	−	1.15508i	−0.978771	−	0.204958i	$-0.934294\pi$
$881$	−19.7942	−	34.2846i	−0.666885	−	1.15508i	0.311886	−	0.950119i	$-0.399039\pi$
$882$		0			0
$883$	45.7654			1.54013			0.770064	−	0.637967i	$-0.220224\pi$
$883$	45.7654			1.54013			0.770064	+	0.637967i	$0.220224\pi$
$884$	6.82051	−	13.7942i	0.229399	−	0.463950i
$885$	6.80385	+	11.7846i	0.228709	+	0.396135i
$886$	−9.80385	+	16.9808i	−0.329367	+	0.570480i
$887$	23.3205			0.783026			0.391513	−	0.920173i	$-0.371952\pi$
$887$	23.3205			0.783026			0.391513	+	0.920173i	$0.371952\pi$
$888$	4.43782	−	7.68653i	0.148924	−	0.257943i
$889$		0			0
$890$	1.39230	−	2.41154i	0.0466702	−	0.0808351i
$891$	−10.5622	−	18.2942i	−0.353846	−	0.612880i
$892$	−5.00000	−	8.66025i	−0.167412	−	0.289967i
$893$	−1.85641			−0.0621223
$894$	−0.588457			−0.0196810
$895$	−6.00000	−	10.3923i	−0.200558	−	0.347376i
$896$		0			0
$897$	1.85641	+	2.78461i	0.0619836	+	0.0929754i
$898$	−10.3923	+	18.0000i	−0.346796	+	0.600668i
$899$	9.29423	−	16.0981i	0.309980	−	0.536901i
$900$	−2.46410	+	4.26795i	−0.0821367	+	0.142265i
$901$	−8.38269	−	14.5192i	−0.279268	−	0.483706i
$902$	42.5885			1.41804
$903$		0			0
$904$	6.40192	−	11.0885i	0.212925	−	0.368797i
$905$	−22.1603	+	38.3827i	−0.736632	+	1.27588i
$906$	−2.53590			−0.0842496
$907$	−7.29423	+	12.6340i	−0.242201	+	0.419504i	−0.961341	−	0.275361i	$-0.911203\pi$
$907$	−7.29423	+	12.6340i	−0.242201	+	0.419504i	0.719140	+	0.694865i	$0.244536\pi$
$908$	11.6603			0.386959
$909$	−10.5167			−0.348816
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	7.32051			0.242406
$913$	19.3923	−	33.5885i	0.641792	−	1.11162i
$914$	−19.0526			−0.630203
$915$	−9.63397	+	16.6865i	−0.318489	+	0.551640i
$916$	3.19615	−	5.53590i	0.105604	−	0.182911i
$917$		0			0
$918$	29.5692			0.975930
$919$	−21.7846	−	37.7321i	−0.718608	−	1.24467i	−0.961551	−	0.274625i	$-0.911446\pi$
$919$	−21.7846	−	37.7321i	−0.718608	−	1.24467i	0.242943	−	0.970040i	$-0.421887\pi$
$920$	−1.90192	+	3.29423i	−0.0627046	+	0.108608i
$921$	9.73205	−	16.8564i	0.320682	−	0.555437i
$922$	−13.5000	+	23.3827i	−0.444599	+	0.770068i
$923$	12.0000	+	18.0000i	0.394985	+	0.592477i
$924$		0			0
$925$	−7.00000	−	12.1244i	−0.230159	−	0.398646i
$926$	−46.0526			−1.51338
$927$	15.7513			0.517340
$928$	7.79423	+	13.5000i	0.255858	+	0.443159i
$929$	3.74167	+	6.48076i	0.122760	+	0.212627i	0.920855	−	0.389905i	$-0.127492\pi$
$929$	3.74167	+	6.48076i	0.122760	+	0.212627i	−0.798095	+	0.602532i	$0.794159\pi$
$930$	6.80385	−	11.7846i	0.223107	−	0.386433i
$931$		0			0
$932$	−12.9282	+	22.3923i	−0.423477	+	0.733484i
$933$	−3.46410			−0.113410
$934$	16.9019	−	29.2750i	0.553048	−	0.957907i
$935$	−17.4904	−	30.2942i	−0.571997	−	0.990727i
$936$	15.3564	−	0.990381i	0.501940	−	0.0323716i
$937$	40.8038			1.33300			0.666502	−	0.745503i	$-0.267791\pi$
$937$	40.8038			1.33300			0.666502	+	0.745503i	$0.267791\pi$
$938$		0			0
$939$	−4.67949	−	8.10512i	−0.152709	−	0.264501i
$940$	−0.803848	−	1.39230i	−0.0262186	−	0.0454120i
$941$	−27.9282	−	48.3731i	−0.910433	−	1.57692i	−0.813453	−	0.581631i	$-0.802415\pi$
$941$	−27.9282	−	48.3731i	−0.910433	−	1.57692i	−0.0969804	−	0.995286i	$-0.530918\pi$
$942$	−11.6603			−0.379912
$943$	3.29423	+	5.70577i	0.107275	+	0.185805i
$944$	53.6603			1.74649
$945$		0			0
$946$	41.7846	+	72.3731i	1.35853	+	2.35305i
$947$	−10.7321			−0.348745			−0.174372	−	0.984680i	$-0.555790\pi$
$947$	−10.7321			−0.348745			−0.174372	+	0.984680i	$0.555790\pi$
$948$	−2.12436	−	3.67949i	−0.0689959	−	0.119504i
$949$	25.8923	−	1.66987i	0.840500	−	0.0542064i
$950$	3.46410	−	6.00000i	0.112390	−	0.194666i
$951$	−0.169873	−	0.294229i	−0.00550851	−	0.00954102i
$952$		0			0
$953$	−18.5885	+	32.1962i	−0.602139	+	1.04294i	0.390357	+	0.920663i	$0.372351\pi$
$953$	−18.5885	+	32.1962i	−0.602139	+	1.04294i	−0.992497	+	0.122272i	$0.960982\pi$
$954$	−8.38269	+	14.5192i	−0.271399	+	0.470078i
$955$	2.19615			0.0710658
$956$	−26.1962			−0.847244
$957$	5.19615	−	9.00000i	0.167968	−	0.290929i
$958$	−4.09808	+	7.09808i	−0.132403	+	0.229328i
$959$		0			0
$960$	−0.633975	−	1.09808i	−0.0204614	−	0.0354403i
$961$	−3.69615	+	6.40192i	−0.119231	+	0.206514i
$962$	19.3756	−	39.1865i	0.624696	−	1.26342i
$963$	24.4641	+	42.3731i	0.788345	+	1.36545i
$964$	10.8038			0.347969
$965$	−4.33013	−	7.50000i	−0.139392	−	0.241434i
$966$		0			0
$967$	3.01924			0.0970921			0.0485461	−	0.998821i	$-0.484541\pi$
$967$	3.01924			0.0970921			0.0485461	+	0.998821i	$0.484541\pi$
$968$	−9.86603	−	17.0885i	−0.317106	−	0.549244i
$969$	−6.24871			−0.200738
$970$	21.5885	+	37.3923i	0.693164	+	1.20059i
$971$	8.32051	+	14.4115i	0.267018	+	0.462488i	0.968090	−	0.250602i	$-0.0806284\pi$
$971$	8.32051	+	14.4115i	0.267018	+	0.462488i	−0.701072	+	0.713090i	$0.747295\pi$
$972$	−7.63397	−	13.2224i	−0.244860	−	0.424110i
$973$		0			0
$974$	1.35898			0.0435447
$975$	−2.33975	+	4.73205i	−0.0749318	+	0.151547i
$976$	37.9904	+	65.8013i	1.21604	+	2.10625i
$977$	18.8205	−	32.5981i	0.602121	−	1.04290i	−0.390378	−	0.920655i	$-0.627656\pi$
$977$	18.8205	−	32.5981i	0.602121	−	1.04290i	0.992499	−	0.122250i	$-0.0390110\pi$
$978$	−7.35898			−0.235314
$979$	−2.19615	+	3.80385i	−0.0701893	+	0.121571i
$980$		0			0
$981$	15.2679	−	26.4449i	0.487468	−	0.844320i
$982$	24.5885	+	42.5885i	0.784649	+	1.35905i
$983$	8.66025	+	15.0000i	0.276219	+	0.478426i	0.970442	−	0.241334i	$-0.0775851\pi$
$983$	8.66025	+	15.0000i	0.276219	+	0.478426i	−0.694223	+	0.719760i	$0.744252\pi$
$984$	−6.58846			−0.210032
$985$	20.7846			0.662253
$986$	−11.0885	−	19.2058i	−0.353128	−	0.611636i
$987$		0			0
$988$	7.19615	−	0.464102i	0.228940	−	0.0147650i
$989$	−6.46410	+	11.1962i	−0.205546	+	0.356017i
$990$	−17.4904	+	30.2942i	−0.555881	+	0.962814i
$991$	16.4904	−	28.5622i	0.523834	−	0.907307i	−0.475781	−	0.879564i	$-0.657834\pi$
$991$	16.4904	−	28.5622i	0.523834	−	0.907307i	0.999615	−	0.0277436i	$-0.00883220\pi$
$992$	−16.0981	−	27.8827i	−0.511114	−	0.885276i
$993$	−19.7513			−0.626788
$994$		0			0
$995$	1.73205	−	3.00000i	0.0549097	−	0.0951064i
$996$	3.00000	−	5.19615i	0.0950586	−	0.164646i
$997$	15.1962			0.481267			0.240633	−	0.970616i	$-0.422645\pi$
$997$	15.1962			0.481267			0.240633	+	0.970616i	$0.422645\pi$
$998$	11.2417	−	19.4711i	0.355849	−	0.616348i
$999$	28.0000			0.885881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.e.471.1		4
7.2	even	3		637.2.f.d.393.2		4
7.3	odd	6		637.2.g.e.263.2		4
7.4	even	3		637.2.g.d.263.2		4
7.5	odd	6		91.2.f.b.29.2	yes	4
7.6	odd	2		637.2.h.d.471.1		4
13.9	even	3		637.2.g.d.373.2		4
21.5	even	6		819.2.o.b.757.1		4
28.19	even	6		1456.2.s.o.1121.1		4
91.9	even	3		637.2.f.d.295.2		4
91.16	even	3		8281.2.a.r.1.1		2
91.23	even	6		8281.2.a.t.1.2		2
91.48	odd	6		637.2.g.e.373.2		4
91.54	even	12		1183.2.c.e.337.3		4
91.61	odd	6		91.2.f.b.22.2	✓	4
91.68	odd	6		1183.2.a.f.1.1		2
91.74	even	3	inner	637.2.h.e.165.1		4
91.75	odd	6		1183.2.a.e.1.2		2
91.87	odd	6		637.2.h.d.165.1		4
91.89	even	12		1183.2.c.e.337.1		4
273.152	even	6		819.2.o.b.568.1		4
364.243	even	6		1456.2.s.o.113.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.b.22.2	✓	4	91.61	odd	6
91.2.f.b.29.2	yes	4	7.5	odd	6
637.2.f.d.295.2		4	91.9	even	3
637.2.f.d.393.2		4	7.2	even	3
637.2.g.d.263.2		4	7.4	even	3
637.2.g.d.373.2		4	13.9	even	3
637.2.g.e.263.2		4	7.3	odd	6
637.2.g.e.373.2		4	91.48	odd	6
637.2.h.d.165.1		4	91.87	odd	6
637.2.h.d.471.1		4	7.6	odd	2
637.2.h.e.165.1		4	91.74	even	3	inner
637.2.h.e.471.1		4	1.1	even	1	trivial
819.2.o.b.568.1		4	273.152	even	6
819.2.o.b.757.1		4	21.5	even	6
1183.2.a.e.1.2		2	91.75	odd	6
1183.2.a.f.1.1		2	91.68	odd	6
1183.2.c.e.337.1		4	91.89	even	12
1183.2.c.e.337.3		4	91.54	even	12
1456.2.s.o.113.1		4	364.243	even	6
1456.2.s.o.1121.1		4	28.19	even	6
8281.2.a.r.1.1		2	91.16	even	3
8281.2.a.t.1.2		2	91.23	even	6

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.73205 q^{2} +(-0.366025 + 0.633975i) q^{3} +1.00000 q^{4} +(-0.866025 + 1.50000i) q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} +(1.23205 + 2.13397i) q^{9} +O(q^{10})\)	\(q-1.73205 q^{2} +(-0.366025 + 0.633975i) q^{3} +1.00000 q^{4} +(-0.866025 + 1.50000i) q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} +(1.23205 + 2.13397i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-2.36603 + 4.09808i) q^{11} +(-0.366025 + 0.633975i) q^{12} +(1.59808 - 3.23205i) q^{13} +(-0.633975 - 1.09808i) q^{15} -5.00000 q^{16} +4.26795 q^{17} +(-2.13397 - 3.69615i) q^{18} +(1.00000 + 1.73205i) q^{19} +(-0.866025 + 1.50000i) q^{20} +(4.09808 - 7.09808i) q^{22} +1.26795 q^{23} +(-0.633975 + 1.09808i) q^{24} +(1.00000 + 1.73205i) q^{25} +(-2.76795 + 5.59808i) q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +(1.09808 + 1.90192i) q^{30} +(-3.09808 - 5.36603i) q^{31} +5.19615 q^{32} +(-1.73205 - 3.00000i) q^{33} -7.39230 q^{34} +(1.23205 + 2.13397i) q^{36} -7.00000 q^{37} +(-1.73205 - 3.00000i) q^{38} +(1.46410 + 2.19615i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(2.59808 + 4.50000i) q^{41} +(-5.09808 + 8.83013i) q^{43} +(-2.36603 + 4.09808i) q^{44} -4.26795 q^{45} -2.19615 q^{46} +(-0.464102 + 0.803848i) q^{47} +(1.83013 - 3.16987i) q^{48} +(-1.73205 - 3.00000i) q^{50} +(-1.56218 + 2.70577i) q^{51} +(1.59808 - 3.23205i) q^{52} +(-1.96410 - 3.40192i) q^{53} +6.92820 q^{54} +(-4.09808 - 7.09808i) q^{55} -1.46410 q^{57} +(-2.59808 - 4.50000i) q^{58} -10.7321 q^{59} +(-0.633975 - 1.09808i) q^{60} +(-7.59808 - 13.1603i) q^{61} +(5.36603 + 9.29423i) q^{62} +1.00000 q^{64} +(3.46410 + 5.19615i) q^{65} +(3.00000 + 5.19615i) q^{66} +(-2.09808 + 3.63397i) q^{67} +4.26795 q^{68} +(-0.464102 + 0.803848i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(2.13397 + 3.69615i) q^{72} +(3.59808 + 6.23205i) q^{73} +12.1244 q^{74} -1.46410 q^{75} +(1.00000 + 1.73205i) q^{76} +(-2.53590 - 3.80385i) q^{78} +(-2.90192 + 5.02628i) q^{79} +(4.33013 - 7.50000i) q^{80} +(-2.23205 + 3.86603i) q^{81} +(-4.50000 - 7.79423i) q^{82} -8.19615 q^{83} +(-3.69615 + 6.40192i) q^{85} +(8.83013 - 15.2942i) q^{86} -2.19615 q^{87} +(-4.09808 + 7.09808i) q^{88} +0.928203 q^{89} +7.39230 q^{90} +1.26795 q^{92} +4.53590 q^{93} +(0.803848 - 1.39230i) q^{94} -3.46410 q^{95} +(-1.90192 + 3.29423i) q^{96} +(-7.19615 + 12.4641i) q^{97} -11.6603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 4 q^{4} + 6 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 4 * q^4 + 6 * q^6 - 2 * q^9	\( 4 q + 2 q^{3} + 4 q^{4} + 6 q^{6} - 2 q^{9} + 6 q^{10} - 6 q^{11} + 2 q^{12} - 4 q^{13} - 6 q^{15} - 20 q^{16} + 24 q^{17} - 12 q^{18} + 4 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{24} + 4 q^{25} - 18 q^{26} - 16 q^{27} + 6 q^{29} - 6 q^{30} - 2 q^{31} + 12 q^{34} - 2 q^{36} - 28 q^{37} - 8 q^{39} - 6 q^{40} - 10 q^{43} - 6 q^{44} - 24 q^{45} + 12 q^{46} + 12 q^{47} - 10 q^{48} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 6 q^{55} + 8 q^{57} - 36 q^{59} - 6 q^{60} - 20 q^{61} + 18 q^{62} + 4 q^{64} + 12 q^{66} + 2 q^{67} + 24 q^{68} + 12 q^{69} - 12 q^{71} + 12 q^{72} + 4 q^{73} + 8 q^{75} + 4 q^{76} - 24 q^{78} - 22 q^{79} - 2 q^{81} - 18 q^{82} - 12 q^{83} + 6 q^{85} + 18 q^{86} + 12 q^{87} - 6 q^{88} - 24 q^{89} - 12 q^{90} + 12 q^{92} + 32 q^{93} + 24 q^{94} - 18 q^{96} - 8 q^{97} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 4 * q^4 + 6 * q^6 - 2 * q^9 + 6 * q^10 - 6 * q^11 + 2 * q^12 - 4 * q^13 - 6 * q^15 - 20 * q^16 + 24 * q^17 - 12 * q^18 + 4 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^24 + 4 * q^25 - 18 * q^26 - 16 * q^27 + 6 * q^29 - 6 * q^30 - 2 * q^31 + 12 * q^34 - 2 * q^36 - 28 * q^37 - 8 * q^39 - 6 * q^40 - 10 * q^43 - 6 * q^44 - 24 * q^45 + 12 * q^46 + 12 * q^47 - 10 * q^48 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 6 * q^55 + 8 * q^57 - 36 * q^59 - 6 * q^60 - 20 * q^61 + 18 * q^62 + 4 * q^64 + 12 * q^66 + 2 * q^67 + 24 * q^68 + 12 * q^69 - 12 * q^71 + 12 * q^72 + 4 * q^73 + 8 * q^75 + 4 * q^76 - 24 * q^78 - 22 * q^79 - 2 * q^81 - 18 * q^82 - 12 * q^83 + 6 * q^85 + 18 * q^86 + 12 * q^87 - 6 * q^88 - 24 * q^89 - 12 * q^90 + 12 * q^92 + 32 * q^93 + 24 * q^94 - 18 * q^96 - 8 * q^97 - 12 * q^99

Introduction

L-functions

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