LMFDB - Embedded newform 637.2.h.d.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.d.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	−0.740805	−	0.671721i	$-0.765556\pi$
$3$	0.366025	−	0.633975i	0.211325	−	0.366025i	0.952129	+	0.305695i	$0.0988889\pi$
$4$	1.00000			0.500000
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	−0.604787	−	0.796387i	$-0.706742\pi$
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	0.992085	+	0.125567i	$0.0400750\pi$
$6$	−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	$-0.673161\pi$
$17$	−4.26795			−1.03513			−0.517565	+	0.855644i	$0.673161\pi$
$18$	−2.13397	−	3.69615i	−0.502983	−	0.871191i
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$	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	$0.0211629\pi$
$31$	3.09808	+	5.36603i	0.556431	+	0.963767i	−0.441360	+	0.897330i	$0.645504\pi$
$32$	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	0.588657	−	0.808383i	$-0.299657\pi$
$41$	−2.59808	−	4.50000i	−0.405751	−	0.702782i	−0.994409	+	0.105601i	$0.966323\pi$
$42$		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	−0.830191	−	0.557480i	$-0.811768\pi$
$47$	0.464102	−	0.803848i	0.0676962	−	0.117253i	0.897887	+	0.440226i	$0.145102\pi$
$48$	−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	$-0.253808\pi$
$59$	10.7321			1.39719			0.698597	+	0.715515i	$0.253808\pi$
$60$	−0.633975	−	1.09808i	−0.0818458	−	0.141761i
$61$	7.59808	+	13.1603i	0.972834	+	1.68500i	0.686905	+	0.726747i	$0.258969\pi$
$61$	7.59808	+	13.1603i	0.972834	+	1.68500i	0.285929	+	0.958251i	$0.407698\pi$
$62$	−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	0.574927	−	0.818205i	$-0.305031\pi$
$73$	−3.59808	−	6.23205i	−0.421123	−	0.729406i	−0.996050	+	0.0887986i	$0.971697\pi$
$74$	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	$-0.351487\pi$
$83$	8.19615			0.899645			0.449822	+	0.893118i	$0.351487\pi$
$84$		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	$-0.515665\pi$
$89$	−0.928203			−0.0983893			−0.0491947	+	0.998789i	$0.515665\pi$
$90$	−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	$-0.572546\pi$
$97$	7.19615	−	12.4641i	0.730659	−	1.26554i	0.956602	−	0.291397i	$-0.0941202\pi$
$98$		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	−0.740108	−	0.672489i	$-0.765225\pi$
$101$	2.13397	−	3.69615i	0.212338	−	0.367781i	0.952446	+	0.304708i	$0.0985588\pi$
$102$	2.70577	−	4.68653i	0.267911	−	0.464036i
$103$	−3.19615	+	5.53590i	−0.314926	+	0.545468i	−0.979422	−	0.201824i	$-0.935313\pi$
$103$	−3.19615	+	5.53590i	−0.314926	+	0.545468i	0.664496	+	0.747292i	$0.268646\pi$
$104$	−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	−0.931717	−	0.363186i	$-0.881689\pi$
$131$	−1.73205	+	3.00000i	−0.151330	+	0.262111i	0.780387	+	0.625297i	$0.215022\pi$
$132$	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	$0.504590\pi$
$139$	−10.2942	+	17.8301i	−0.873145	+	1.51233i	−0.858726	+	0.512436i	$0.828743\pi$
$140$		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	0.989090	−	0.147315i	$-0.0470631\pi$
$157$	4.59808	+	7.96410i	0.366966	+	0.635605i	−0.622123	+	0.782919i	$0.713730\pi$
$158$	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	$-0.766358\pi$
$167$	−12.2942	−	21.2942i	−0.951356	−	1.64780i	−0.208861	−	0.977945i	$-0.566976\pi$
$168$		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	$-0.966638\pi$
$173$	−7.73205	−	13.3923i	−0.587857	−	1.01820i	0.406656	−	0.913581i	$-0.366695\pi$
$174$	−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	$-0.899929\pi$
$181$	−25.5885			−1.90198			−0.950988	+	0.309229i	$0.899929\pi$
$182$		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	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	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	0.983451	−	0.181173i	$-0.0579895\pi$
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	−0.648626	+	0.761107i	$0.724656\pi$
$224$		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	$-0.626475\pi$
$227$	−11.6603			−0.773918			−0.386959	+	0.922097i	$0.626475\pi$
$228$	−1.46410			−0.0969625
$229$	−3.19615	+	5.53590i	−0.211208	+	0.365822i	−0.952093	−	0.305809i	$-0.901073\pi$
$229$	−3.19615	+	5.53590i	−0.211208	+	0.365822i	0.740885	+	0.671632i	$0.234406\pi$
$230$	−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	$-0.613128\pi$
$241$	−10.8038			−0.695937			−0.347969	+	0.937506i	$0.613128\pi$
$242$	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	$-0.583519\pi$
$251$	11.1962	−	19.3923i	0.706695	−	1.22403i	0.966076	−	0.258256i	$-0.0831480\pi$
$252$		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	$-0.691233\pi$
$257$	−18.1244			−1.13057			−0.565283	+	0.824897i	$0.691233\pi$
$258$	−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	$-0.304209\pi$
$269$	18.9282			1.15407			0.577036	+	0.816718i	$0.304209\pi$
$270$	−6.00000	+	10.3923i	−0.365148	+	0.632456i
$271$	16.1962			0.983846			0.491923	−	0.870639i	$-0.336294\pi$
$271$	16.1962			0.983846			0.491923	+	0.870639i	$0.336294\pi$
$272$	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	−0.863096	−	0.505040i	$-0.831478\pi$
$283$	0.0980762	−	0.169873i	0.00583003	−	0.0100979i	0.868926	+	0.494943i	$0.164811\pi$
$284$	−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	−0.654881	−	0.755732i	$-0.727281\pi$
$293$	5.59808	−	9.69615i	0.327043	−	0.566455i	0.981924	+	0.189277i	$0.0606144\pi$
$294$		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	$-0.225814\pi$
$307$	26.5885			1.51748			0.758742	+	0.651392i	$0.225814\pi$
$308$		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	0.791113	−	0.611670i	$-0.209502\pi$
$311$	−2.36603	−	4.09808i	−0.134165	−	0.232381i	−0.925278	+	0.379289i	$0.876169\pi$
$312$	2.53590	+	3.80385i	0.143567	+	0.215350i
$313$	6.39230	−	11.0718i	0.361314	−	0.625815i	−0.626863	−	0.779129i	$-0.715661\pi$
$313$	6.39230	−	11.0718i	0.361314	−	0.625815i	0.988177	+	0.153315i	$0.0489948\pi$
$314$	−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	0.549106	−	0.835753i	$-0.314968\pi$
$349$	−8.39230	−	14.5359i	−0.449230	−	0.778089i	−0.998336	+	0.0576637i	$0.981635\pi$
$350$		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	−0.907037	−	0.421050i	$-0.861662\pi$
$353$	−1.66987	+	2.89230i	−0.0888784	+	0.153942i	0.818159	+	0.574992i	$0.194995\pi$
$354$	−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	−0.773767	−	0.633471i	$-0.781630\pi$
$367$	3.09808	−	5.36603i	0.161718	−	0.280104i	0.935485	+	0.353366i	$0.114963\pi$
$368$	−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	0.784616	−	0.619982i	$-0.212860\pi$
$383$	−2.83013	−	4.90192i	−0.144613	−	0.250477i	−0.929228	+	0.369506i	$0.879527\pi$
$384$	−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	$-0.972926\pi$
$397$	−11.3923	−	19.7321i	−0.571763	−	0.990323i	0.424622	−	0.905371i	$-0.360407\pi$
$398$	−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	$-0.734729\pi$
$409$	−27.1962			−1.34476			−0.672382	+	0.740205i	$0.734729\pi$
$410$	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	$0.0121160\pi$
$419$	10.9019	+	18.8827i	0.532594	+	0.922480i	−0.466682	+	0.884425i	$0.654551\pi$
$420$		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	−0.996195	−	0.0871498i	$-0.972224\pi$
$433$	−8.79423	+	15.2321i	−0.422624	+	0.732006i	0.573572	+	0.819155i	$0.305557\pi$
$434$		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	$-0.629554\pi$
$439$	−16.5885			−0.791724			−0.395862	+	0.918310i	$0.629554\pi$
$440$	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	−0.988455	−	0.151513i	$-0.951585\pi$
$461$	−7.79423	+	13.5000i	−0.363013	+	0.628758i	0.625442	+	0.780271i	$0.284919\pi$
$462$		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	−0.546922	−	0.837184i	$-0.684200\pi$
$467$	9.75833	−	16.9019i	0.451562	−	0.782128i	0.998483	+	0.0550561i	$0.0175338\pi$
$468$	−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	−0.915003	−	0.403447i	$-0.867812\pi$
$479$	−2.36603	+	4.09808i	−0.108106	+	0.187246i	0.806897	+	0.590693i	$0.201145\pi$
$480$	−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	−0.971544	−	0.236859i	$-0.923882\pi$
$503$	−6.29423	+	10.9019i	−0.280646	+	0.486093i	0.690898	+	0.722952i	$0.257215\pi$
$504$		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	$-0.426925\pi$
$509$	10.2679			0.455119			0.227559	+	0.973764i	$0.426925\pi$
$510$	−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	0.864660	−	0.502357i	$-0.167534\pi$
$521$	−0.0621778	−	0.107695i	−0.00272406	−	0.00471821i	−0.867384	+	0.497639i	$0.834200\pi$
$522$	6.40192	−	11.0885i	0.280205	−	0.485329i
$523$	33.1769			1.45073			0.725363	−	0.688367i	$-0.241672\pi$
$523$	33.1769			1.45073			0.725363	+	0.688367i	$0.241672\pi$
$524$	−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	$-0.567943\pi$
$563$	−10.0526			−0.423665			−0.211832	+	0.977306i	$0.567943\pi$
$564$	−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	$-0.927420\pi$
$577$	−16.4019	−	28.4090i	−0.682821	−	1.18268i	0.291295	−	0.956633i	$-0.405914\pi$
$578$	−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	0.907783	−	0.419441i	$-0.137774\pi$
$587$	2.19615	+	3.80385i	0.0906449	+	0.157002i	−0.817138	+	0.576442i	$0.804441\pi$
$588$		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	$0.490651\pi$
$593$	−20.7224	+	35.8923i	−0.850968	+	1.47392i	−0.880335	+	0.474352i	$0.842683\pi$
$594$	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	0.549969	−	0.835185i	$-0.314640\pi$
$601$	−10.9904	−	19.0359i	−0.448307	−	0.776490i	−0.998276	+	0.0586946i	$0.981306\pi$
$602$		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	0.793843	−	0.608122i	$-0.208077\pi$
$607$	−3.19615	−	5.53590i	−0.129728	−	0.224695i	−0.923571	+	0.383427i	$0.874744\pi$
$608$	−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	$0.103798\pi$
$619$	18.6865	+	32.3660i	0.751075	+	1.30090i	−0.196227	+	0.980559i	$0.562869\pi$
$620$	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	$0.464069\pi$
$643$	−20.3923	+	35.3205i	−0.804194	+	1.39290i	−0.916834	+	0.399269i	$0.869264\pi$
$644$		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	$-0.487340\pi$
$647$	22.5167	−	39.0000i	0.885221	−	1.53325i	0.845460	−	0.534039i	$-0.179326\pi$
$648$	−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	−0.554462	−	0.832209i	$-0.687076\pi$
$661$	11.4019	−	19.7487i	0.443483	−	0.768136i	0.997945	+	0.0640734i	$0.0204092\pi$
$662$	−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	$-0.582194\pi$
$677$	18.4641	−	31.9808i	0.709633	−	1.22912i	0.964993	−	0.262275i	$-0.0844726\pi$
$678$	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	$-0.626792\pi$
$691$	−20.3923			−0.775760			−0.387880	+	0.921710i	$0.626792\pi$
$692$	−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	0.948567	−	0.316578i	$-0.102534\pi$
$719$	5.36603	+	9.29423i	0.200119	+	0.346616i	−0.748448	+	0.663194i	$0.769200\pi$
$720$	−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	$-0.371540\pi$
$727$	21.1769			0.785408			0.392704	+	0.919665i	$0.371540\pi$
$728$		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	−0.787407	−	0.616433i	$-0.788577\pi$
$733$	3.79423	−	6.57180i	0.140143	−	0.242735i	0.927550	+	0.373698i	$0.121910\pi$
$734$	−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	0.799123	−	0.601168i	$-0.205298\pi$
$761$	−3.33975	−	5.78461i	−0.121066	−	0.209692i	−0.920188	+	0.391476i	$0.871965\pi$
$762$	−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	$0.157107\pi$
$769$	23.5885	+	40.8564i	0.850622	+	1.47332i	−0.0300268	+	0.999549i	$0.509559\pi$
$770$		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	$-0.494686\pi$
$773$	0.928203			0.0333851			0.0166926	+	0.999861i	$0.494686\pi$
$774$	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	$-0.744488\pi$
$787$	−38.9808			−1.38951			−0.694757	+	0.719244i	$0.744488\pi$
$788$	−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	−0.719996	−	0.693978i	$-0.755856\pi$
$797$	6.80385	−	11.7846i	0.241005	−	0.417432i	0.961001	+	0.276546i	$0.0891898\pi$
$798$		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	$-0.417551\pi$
$811$	14.5885			0.512270			0.256135	+	0.966641i	$0.417551\pi$
$812$		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	$-0.648511\pi$
$829$	15.7942	−	27.3564i	0.548556	−	0.950127i	0.998374	−	0.0570068i	$-0.0181557\pi$
$830$	−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	−0.667803	−	0.744338i	$-0.732765\pi$
$839$	9.00000	−	15.5885i	0.310715	−	0.538173i	0.978517	+	0.206165i	$0.0660984\pi$
$840$		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	$-0.644336\pi$
$853$	−25.5885			−0.876132			−0.438066	+	0.898943i	$0.644336\pi$
$854$		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	0.911831	−	0.410567i	$-0.134669\pi$
$857$	2.93782	+	5.08846i	0.100354	+	0.173818i	−0.811476	+	0.584385i	$0.801336\pi$
$858$	21.5885	−	1.39230i	0.737018	−	0.0475325i
$859$	9.09808	−	15.7583i	0.310422	−	0.537667i	−0.668031	−	0.744133i	$-0.732863\pi$
$859$	9.09808	−	15.7583i	0.310422	−	0.537667i	0.978454	+	0.206466i	$0.0661962\pi$
$860$	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	$0.0657059\pi$
$881$	19.7942	+	34.2846i	0.666885	+	1.15508i	−0.311886	+	0.950119i	$0.600961\pi$
$882$		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	$-0.628048\pi$
$887$	−23.3205			−0.783026			−0.391513	+	0.920173i	$0.628048\pi$
$888$	−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	0.798095	−	0.602532i	$-0.205841\pi$
$929$	−3.74167	−	6.48076i	−0.122760	−	0.212627i	−0.920855	+	0.389905i	$0.872508\pi$
$930$	−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	$-0.732209\pi$
$937$	−40.8038			−1.33300			−0.666502	+	0.745503i	$0.732209\pi$
$938$		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	$0.197585\pi$
$941$	27.9282	+	48.3731i	0.910433	+	1.57692i	0.0969804	+	0.995286i	$0.469082\pi$
$942$	−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	0.701072	−	0.713090i	$-0.252705\pi$
$971$	−8.32051	−	14.4115i	−0.267018	−	0.462488i	−0.968090	+	0.250602i	$0.919372\pi$
$972$	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	0.694223	−	0.719760i	$-0.255748\pi$
$983$	−8.66025	−	15.0000i	−0.276219	−	0.478426i	−0.970442	+	0.241334i	$0.922415\pi$
$984$	−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	$-0.577355\pi$
$997$	−15.1962			−0.481267			−0.240633	+	0.970616i	$0.577355\pi$
$998$	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.d.471.1		4
7.2	even	3		91.2.f.b.29.2	yes	4
7.3	odd	6		637.2.g.d.263.2		4
7.4	even	3		637.2.g.e.263.2		4
7.5	odd	6		637.2.f.d.393.2		4
7.6	odd	2		637.2.h.e.471.1		4
13.9	even	3		637.2.g.e.373.2		4
21.2	odd	6		819.2.o.b.757.1		4
28.23	odd	6		1456.2.s.o.1121.1		4
91.2	odd	12		1183.2.c.e.337.3		4
91.9	even	3		91.2.f.b.22.2	✓	4
91.16	even	3		1183.2.a.f.1.1		2
91.23	even	6		1183.2.a.e.1.2		2
91.37	odd	12		1183.2.c.e.337.1		4
91.48	odd	6		637.2.g.d.373.2		4
91.61	odd	6		637.2.f.d.295.2		4
91.68	odd	6		8281.2.a.r.1.1		2
91.74	even	3	inner	637.2.h.d.165.1		4
91.75	odd	6		8281.2.a.t.1.2		2
91.87	odd	6		637.2.h.e.165.1		4
273.191	odd	6		819.2.o.b.568.1		4
364.191	odd	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	91.9	even	3
91.2.f.b.29.2	yes	4	7.2	even	3
637.2.f.d.295.2		4	91.61	odd	6
637.2.f.d.393.2		4	7.5	odd	6
637.2.g.d.263.2		4	7.3	odd	6
637.2.g.d.373.2		4	91.48	odd	6
637.2.g.e.263.2		4	7.4	even	3
637.2.g.e.373.2		4	13.9	even	3
637.2.h.d.165.1		4	91.74	even	3	inner
637.2.h.d.471.1		4	1.1	even	1	trivial
637.2.h.e.165.1		4	91.87	odd	6
637.2.h.e.471.1		4	7.6	odd	2
819.2.o.b.568.1		4	273.191	odd	6
819.2.o.b.757.1		4	21.2	odd	6
1183.2.a.e.1.2		2	91.23	even	6
1183.2.a.f.1.1		2	91.16	even	3
1183.2.c.e.337.1		4	91.37	odd	12
1183.2.c.e.337.3		4	91.2	odd	12
1456.2.s.o.113.1		4	364.191	odd	6
1456.2.s.o.1121.1		4	28.23	odd	6
8281.2.a.r.1.1		2	91.68	odd	6
8281.2.a.t.1.2		2	91.75	odd	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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more