LMFDB - Embedded newform 637.2.h.e.165.2

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			165.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.e.471.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205 q^{2} +(1.36603 + 2.36603i) q^{3} +1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(2.36603 + 4.09808i) q^{6} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})$	\(q+1.73205 q^{2} +(1.36603 + 2.36603i) q^{3} +1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(2.36603 + 4.09808i) q^{6} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-0.633975 - 1.09808i) q^{11} +(1.36603 + 2.36603i) q^{12} +(-3.59808 + 0.232051i) q^{13} +(-2.36603 + 4.09808i) q^{15} -5.00000 q^{16} +7.73205 q^{17} +(-3.86603 + 6.69615i) q^{18} +(1.00000 - 1.73205i) q^{19} +(0.866025 + 1.50000i) q^{20} +(-1.09808 - 1.90192i) q^{22} +4.73205 q^{23} +(-2.36603 - 4.09808i) q^{24} +(1.00000 - 1.73205i) q^{25} +(-6.23205 + 0.401924i) q^{26} -4.00000 q^{27} +(1.50000 - 2.59808i) q^{29} +(-4.09808 + 7.09808i) q^{30} +(2.09808 - 3.63397i) q^{31} -5.19615 q^{32} +(1.73205 - 3.00000i) q^{33} +13.3923 q^{34} +(-2.23205 + 3.86603i) q^{36} -7.00000 q^{37} +(1.73205 - 3.00000i) q^{38} +(-5.46410 - 8.19615i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(-2.59808 + 4.50000i) q^{41} +(0.0980762 + 0.169873i) q^{43} +(-0.633975 - 1.09808i) q^{44} -7.73205 q^{45} +8.19615 q^{46} +(6.46410 + 11.1962i) q^{47} +(-6.83013 - 11.8301i) q^{48} +(1.73205 - 3.00000i) q^{50} +(10.5622 + 18.2942i) q^{51} +(-3.59808 + 0.232051i) q^{52} +(4.96410 - 8.59808i) q^{53} -6.92820 q^{54} +(1.09808 - 1.90192i) q^{55} +5.46410 q^{57} +(2.59808 - 4.50000i) q^{58} -7.26795 q^{59} +(-2.36603 + 4.09808i) q^{60} +(-2.40192 + 4.16025i) q^{61} +(3.63397 - 6.29423i) q^{62} +1.00000 q^{64} +(-3.46410 - 5.19615i) q^{65} +(3.00000 - 5.19615i) q^{66} +(3.09808 + 5.36603i) q^{67} +7.73205 q^{68} +(6.46410 + 11.1962i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(3.86603 - 6.69615i) q^{72} +(-1.59808 + 2.76795i) q^{73} -12.1244 q^{74} +5.46410 q^{75} +(1.00000 - 1.73205i) q^{76} +(-9.46410 - 14.1962i) q^{78} +(-8.09808 - 14.0263i) q^{79} +(-4.33013 - 7.50000i) q^{80} +(1.23205 + 2.13397i) q^{81} +(-4.50000 + 7.79423i) q^{82} +2.19615 q^{83} +(6.69615 + 11.5981i) q^{85} +(0.169873 + 0.294229i) q^{86} +8.19615 q^{87} +(1.09808 + 1.90192i) q^{88} -12.9282 q^{89} -13.3923 q^{90} +4.73205 q^{92} +11.4641 q^{93} +(11.1962 + 19.3923i) q^{94} +3.46410 q^{95} +(-7.09808 - 12.2942i) q^{96} +(3.19615 + 5.53590i) q^{97} +5.66025 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.73205			1.22474			0.612372	−	0.790569i	$-0.290215\pi$
$2$	1.73205			1.22474			0.612372	+	0.790569i	$0.290215\pi$
$3$	1.36603	+	2.36603i	0.788675	+	1.36603i	0.926779	+	0.375608i	$0.122566\pi$
$3$	1.36603	+	2.36603i	0.788675	+	1.36603i	−0.138104	+	0.990418i	$0.544101\pi$
$4$	1.00000			0.500000
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	0.992085	−	0.125567i	$-0.0400750\pi$
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	−0.604787	+	0.796387i	$0.706742\pi$
$6$	2.36603	+	4.09808i	0.965926	+	1.67303i
$7$		0			0
$7$		0			0
$8$	−1.73205			−0.612372
$9$	−2.23205	+	3.86603i	−0.744017	+	1.28868i
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	0.754481	−	0.656322i	$-0.227889\pi$
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	−0.945632	+	0.325239i	$0.894555\pi$
$12$	1.36603	+	2.36603i	0.394338	+	0.683013i
$13$	−3.59808	+	0.232051i	−0.997927	+	0.0643593i
$13$	−3.59808	+	0.232051i	−0.997927	+	0.0643593i
$14$		0			0
$15$	−2.36603	+	4.09808i	−0.610905	+	1.05812i
$16$	−5.00000			−1.25000
$17$	7.73205			1.87530			0.937649	−	0.347584i	$-0.112998\pi$
$17$	7.73205			1.87530			0.937649	+	0.347584i	$0.112998\pi$
$18$	−3.86603	+	6.69615i	−0.911231	+	1.57830i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	0.866025	+	1.50000i	0.193649	+	0.335410i
$21$		0			0
$22$	−1.09808	−	1.90192i	−0.234111	−	0.405492i
$23$	4.73205			0.986701			0.493350	−	0.869831i	$-0.335772\pi$
$23$	4.73205			0.986701			0.493350	+	0.869831i	$0.335772\pi$
$24$	−2.36603	−	4.09808i	−0.482963	−	0.836516i
$25$	1.00000	−	1.73205i	0.200000	−	0.346410i
$26$	−6.23205	+	0.401924i	−1.22221	+	0.0788237i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$	−4.09808	+	7.09808i	−0.748203	+	1.29593i
$31$	2.09808	−	3.63397i	0.376826	−	0.652681i	−0.613773	−	0.789483i	$-0.710349\pi$
$31$	2.09808	−	3.63397i	0.376826	−	0.652681i	0.990598	+	0.136802i	$0.0436823\pi$
$32$	−5.19615			−0.918559
$33$	1.73205	−	3.00000i	0.301511	−	0.522233i
$34$	13.3923			2.29676
$35$		0			0
$36$	−2.23205	+	3.86603i	−0.372008	+	0.644338i
$37$	−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
$39$	−5.46410	−	8.19615i	−0.874957	−	1.31243i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	−2.59808	+	4.50000i	−0.405751	+	0.702782i	−0.994409	−	0.105601i	$-0.966323\pi$
$41$	−2.59808	+	4.50000i	−0.405751	+	0.702782i	0.588657	+	0.808383i	$0.299657\pi$
$42$		0			0
$43$	0.0980762	+	0.169873i	0.0149565	+	0.0259054i	0.873407	−	0.486991i	$-0.161906\pi$
$43$	0.0980762	+	0.169873i	0.0149565	+	0.0259054i	−0.858450	+	0.512897i	$0.828572\pi$
$44$	−0.633975	−	1.09808i	−0.0955753	−	0.165541i
$45$	−7.73205			−1.15263
$46$	8.19615			1.20846
$47$	6.46410	+	11.1962i	0.942886	+	1.63313i	0.759929	+	0.650006i	$0.225234\pi$
$47$	6.46410	+	11.1962i	0.942886	+	1.63313i	0.182957	+	0.983121i	$0.441433\pi$
$48$	−6.83013	−	11.8301i	−0.985844	−	1.70753i
$49$		0			0
$50$	1.73205	−	3.00000i	0.244949	−	0.424264i
$51$	10.5622	+	18.2942i	1.47900	+	2.56170i
$52$	−3.59808	+	0.232051i	−0.498963	+	0.0321797i
$53$	4.96410	−	8.59808i	0.681872	−	1.18104i	−0.292537	−	0.956254i	$-0.594500\pi$
$53$	4.96410	−	8.59808i	0.681872	−	1.18104i	0.974409	−	0.224782i	$-0.0721671\pi$
$54$	−6.92820			−0.942809
$55$	1.09808	−	1.90192i	0.148065	−	0.256455i
$56$		0			0
$57$	5.46410			0.723738
$58$	2.59808	−	4.50000i	0.341144	−	0.590879i
$59$	−7.26795			−0.946206			−0.473103	−	0.881007i	$-0.656866\pi$
$59$	−7.26795			−0.946206			−0.473103	+	0.881007i	$0.656866\pi$
$60$	−2.36603	+	4.09808i	−0.305453	+	0.529059i
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	−0.977822	−	0.209435i	$-0.932837\pi$
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	0.670288	+	0.742101i	$0.266171\pi$
$62$	3.63397	−	6.29423i	0.461515	−	0.799368i
$63$		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
$67$	3.09808	+	5.36603i	0.378490	+	0.655564i	0.990843	−	0.135020i	$-0.0431100\pi$
$67$	3.09808	+	5.36603i	0.378490	+	0.655564i	−0.612353	+	0.790585i	$0.709777\pi$
$68$	7.73205			0.937649
$69$	6.46410	+	11.1962i	0.778186	+	1.34786i
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	3.86603	−	6.69615i	0.455615	−	0.789149i
$73$	−1.59808	+	2.76795i	−0.187041	+	0.323964i	−0.944262	−	0.329194i	$-0.893223\pi$
$73$	−1.59808	+	2.76795i	−0.187041	+	0.323964i	0.757222	+	0.653158i	$0.226556\pi$
$74$	−12.1244			−1.40943
$75$	5.46410			0.630940
$76$	1.00000	−	1.73205i	0.114708	−	0.198680i
$77$		0			0
$78$	−9.46410	−	14.1962i	−1.07160	−	1.60740i
$79$	−8.09808	−	14.0263i	−0.911105	−	1.57808i	−0.812506	−	0.582952i	$-0.801897\pi$
$79$	−8.09808	−	14.0263i	−0.911105	−	1.57808i	−0.0985985	−	0.995127i	$-0.531436\pi$
$80$	−4.33013	−	7.50000i	−0.484123	−	0.838525i
$81$	1.23205	+	2.13397i	0.136895	+	0.237108i
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$	2.19615			0.241059			0.120530	−	0.992710i	$-0.461541\pi$
$83$	2.19615			0.241059			0.120530	+	0.992710i	$0.461541\pi$
$84$		0			0
$85$	6.69615	+	11.5981i	0.726300	+	1.25799i
$86$	0.169873	+	0.294229i	0.0183179	+	0.0317275i
$87$	8.19615			0.878720
$88$	1.09808	+	1.90192i	0.117055	+	0.202746i
$89$	−12.9282			−1.37039			−0.685193	−	0.728361i	$-0.740282\pi$
$89$	−12.9282			−1.37039			−0.685193	+	0.728361i	$0.740282\pi$
$90$	−13.3923			−1.41167
$91$		0			0
$92$	4.73205			0.493350
$93$	11.4641			1.18877
$94$	11.1962	+	19.3923i	1.15479	+	2.00016i
$95$	3.46410			0.355409
$96$	−7.09808	−	12.2942i	−0.724444	−	1.25477i
$97$	3.19615	+	5.53590i	0.324520	+	0.562085i	0.981415	−	0.191897i	$-0.0614639\pi$
$97$	3.19615	+	5.53590i	0.324520	+	0.562085i	−0.656895	+	0.753982i	$0.728131\pi$
$98$		0			0
$99$	5.66025			0.568877
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−3.86603	−	6.69615i	−0.384684	−	0.666292i	0.607041	−	0.794670i	$-0.292356\pi$
$101$	−3.86603	−	6.69615i	−0.384684	−	0.666292i	−0.991725	+	0.128378i	$0.959023\pi$
$102$	18.2942	+	31.6865i	1.81140	+	3.13743i
$103$	−7.19615	−	12.4641i	−0.709058	−	1.22812i	−0.965207	−	0.261487i	$-0.915787\pi$
$103$	−7.19615	−	12.4641i	−0.709058	−	1.22812i	0.256149	−	0.966637i	$-0.417546\pi$
$104$	6.23205	−	0.401924i	0.611103	−	0.0394119i
$105$		0			0
$106$	8.59808	−	14.8923i	0.835119	−	1.44647i
$107$	−7.85641			−0.759507			−0.379754	−	0.925088i	$-0.623991\pi$
$107$	−7.85641			−0.759507			−0.379754	+	0.925088i	$0.623991\pi$
$108$	−4.00000			−0.384900
$109$	4.19615	−	7.26795i	0.401919	−	0.696143i	−0.592039	−	0.805909i	$-0.701677\pi$
$109$	4.19615	−	7.26795i	0.401919	−	0.696143i	0.993957	+	0.109766i	$0.0350102\pi$
$110$	1.90192	−	3.29423i	0.181341	−	0.314092i
$111$	−9.56218	−	16.5622i	−0.907602	−	1.57201i
$112$		0			0
$113$	−6.69615	−	11.5981i	−0.629921	−	1.09106i	−0.987567	−	0.157198i	$-0.949754\pi$
$113$	−6.69615	−	11.5981i	−0.629921	−	1.09106i	0.357646	−	0.933857i	$-0.383579\pi$
$114$	9.46410			0.886394
$115$	4.09808	+	7.09808i	0.382148	+	0.661899i
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$	7.13397	−	14.4282i	0.659536	−	1.33389i
$118$	−12.5885			−1.15886
$119$		0			0
$120$	4.09808	−	7.09808i	0.374101	−	0.647963i
$121$	4.69615	−	8.13397i	0.426923	−	0.739452i
$122$	−4.16025	+	7.20577i	−0.376652	+	0.652380i
$123$	−14.1962			−1.28002
$124$	2.09808	−	3.63397i	0.188413	−	0.326341i
$125$	12.1244			1.08444
$126$		0			0
$127$	−9.19615	+	15.9282i	−0.816027	+	1.41340i	0.0925619	+	0.995707i	$0.470494\pi$
$127$	−9.19615	+	15.9282i	−0.816027	+	1.41340i	−0.908588	+	0.417693i	$0.862839\pi$
$128$	12.1244			1.07165
$129$	−0.267949	+	0.464102i	−0.0235916	+	0.0408619i
$130$	−6.00000	−	9.00000i	−0.526235	−	0.789352i
$131$	−1.73205	−	3.00000i	−0.151330	−	0.262111i	0.780387	−	0.625297i	$-0.215022\pi$
$131$	−1.73205	−	3.00000i	−0.151330	−	0.262111i	−0.931717	+	0.363186i	$0.881689\pi$
$132$	1.73205	−	3.00000i	0.150756	−	0.261116i
$133$		0			0
$134$	5.36603	+	9.29423i	0.463554	+	0.802899i
$135$	−3.46410	−	6.00000i	−0.298142	−	0.516398i
$136$	−13.3923			−1.14838
$137$	8.07180			0.689620			0.344810	−	0.938672i	$-0.387943\pi$
$137$	8.07180			0.689620			0.344810	+	0.938672i	$0.387943\pi$
$138$	11.1962	+	19.3923i	0.953080	+	1.65078i
$139$	−5.29423	−	9.16987i	−0.449051	−	0.777778i	0.549274	−	0.835642i	$-0.314904\pi$
$139$	−5.29423	−	9.16987i	−0.449051	−	0.777778i	−0.998324	+	0.0578639i	$0.981571\pi$
$140$		0			0
$141$	−17.6603	+	30.5885i	−1.48726	+	2.57601i
$142$	−5.19615	−	9.00000i	−0.436051	−	0.755263i
$143$	2.53590	+	3.80385i	0.212062	+	0.318094i
$144$	11.1603	−	19.3301i	0.930021	−	1.61084i
$145$	5.19615			0.431517
$146$	−2.76795	+	4.79423i	−0.229077	+	0.396773i
$147$		0			0
$148$	−7.00000			−0.575396
$149$	3.23205	−	5.59808i	0.264780	−	0.458612i	−0.702726	−	0.711461i	$-0.748034\pi$
$149$	3.23205	−	5.59808i	0.264780	−	0.458612i	0.967506	+	0.252848i	$0.0813674\pi$
$150$	9.46410			0.772741
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$	−1.73205	+	3.00000i	−0.140488	+	0.243332i
$153$	−17.2583	+	29.8923i	−1.39525	+	2.41665i
$154$		0			0
$155$	7.26795			0.583776
$156$	−5.46410	−	8.19615i	−0.437478	−	0.656217i
$157$	0.598076	−	1.03590i	0.0477317	−	0.0826737i	−0.841172	−	0.540767i	$-0.818134\pi$
$157$	0.598076	−	1.03590i	0.0477317	−	0.0826737i	0.888904	+	0.458093i	$0.151467\pi$
$158$	−14.0263	−	24.2942i	−1.11587	−	1.93275i
$159$	27.1244			2.15110
$160$	−4.50000	−	7.79423i	−0.355756	−	0.616188i
$161$		0			0
$162$	2.13397	+	3.69615i	0.167661	+	0.290397i
$163$	−8.09808	+	14.0263i	−0.634290	+	1.09862i	0.352375	+	0.935859i	$0.385374\pi$
$163$	−8.09808	+	14.0263i	−0.634290	+	1.09862i	−0.986665	+	0.162764i	$0.947959\pi$
$164$	−2.59808	+	4.50000i	−0.202876	+	0.351391i
$165$	6.00000			0.467099
$166$	3.80385			0.295236
$167$	−3.29423	+	5.70577i	−0.254915	+	0.441526i	−0.964872	−	0.262719i	$-0.915381\pi$
$167$	−3.29423	+	5.70577i	−0.254915	+	0.441526i	0.709957	+	0.704245i	$0.248714\pi$
$168$		0			0
$169$	12.8923	−	1.66987i	0.991716	−	0.128452i
$170$	11.5981	+	20.0885i	0.889532	+	1.54071i
$171$	4.46410	+	7.73205i	0.341378	+	0.591285i
$172$	0.0980762	+	0.169873i	0.00747824	+	0.0129527i
$173$	4.26795	−	7.39230i	0.324486	−	0.562027i	−0.656922	−	0.753958i	$-0.728142\pi$
$173$	4.26795	−	7.39230i	0.324486	−	0.562027i	0.981408	+	0.191932i	$0.0614753\pi$
$174$	14.1962			1.07621
$175$		0			0
$176$	3.16987	+	5.49038i	0.238938	+	0.413853i
$177$	−9.92820	−	17.1962i	−0.746249	−	1.29254i
$178$	−22.3923			−1.67837
$179$	3.46410	+	6.00000i	0.258919	+	0.448461i	0.965953	−	0.258719i	$-0.0833004\pi$
$179$	3.46410	+	6.00000i	0.258919	+	0.448461i	−0.707034	+	0.707180i	$0.749967\pi$
$180$	−7.73205			−0.576313
$181$	−5.58846			−0.415387			−0.207693	−	0.978194i	$-0.566596\pi$
$181$	−5.58846			−0.415387			−0.207693	+	0.978194i	$0.566596\pi$
$182$		0			0
$183$	−13.1244			−0.970180
$184$	−8.19615			−0.604228
$185$	−6.06218	−	10.5000i	−0.445700	−	0.771975i
$186$	19.8564			1.45594
$187$	−4.90192	−	8.49038i	−0.358464	−	0.620878i
$188$	6.46410	+	11.1962i	0.471443	+	0.816563i
$189$		0			0
$190$	6.00000			0.435286
$191$	−2.36603	+	4.09808i	−0.171200	+	0.296526i	−0.938840	−	0.344355i	$-0.888098\pi$
$191$	−2.36603	+	4.09808i	−0.171200	+	0.296526i	0.767640	+	0.640881i	$0.221431\pi$
$192$	1.36603	+	2.36603i	0.0985844	+	0.170753i
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	5.53590	+	9.58846i	0.397454	+	0.688411i
$195$	7.56218	−	15.2942i	0.541539	−	1.09524i
$196$		0			0
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	−0.996649	−	0.0818013i	$-0.973933\pi$
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	0.569166	+	0.822222i	$0.307266\pi$
$198$	9.80385			0.696729
$199$	−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
$201$	−8.46410	+	14.6603i	−0.597012	+	1.03405i
$202$	−6.69615	−	11.5981i	−0.471140	−	0.816038i
$203$		0			0
$204$	10.5622	+	18.2942i	0.739500	+	1.28085i
$205$	−9.00000			−0.628587
$206$	−12.4641	−	21.5885i	−0.868415	−	1.50414i
$207$	−10.5622	+	18.2942i	−0.734122	+	1.27154i
$208$	17.9904	−	1.16025i	1.24741	−	0.0804491i
$209$	−2.53590			−0.175412
$210$		0			0
$211$	0.901924	−	1.56218i	0.0620910	−	0.107545i	−0.833309	−	0.552808i	$-0.813556\pi$
$211$	0.901924	−	1.56218i	0.0620910	−	0.107545i	0.895400	+	0.445263i	$0.146890\pi$
$212$	4.96410	−	8.59808i	0.340936	−	0.590518i
$213$	8.19615	−	14.1962i	0.561591	−	0.972704i
$214$	−13.6077			−0.930203
$215$	−0.169873	+	0.294229i	−0.0115852	+	0.0200662i
$216$	6.92820			0.471405
$217$		0			0
$218$	7.26795	−	12.5885i	0.492248	−	0.852598i
$219$	−8.73205			−0.590057
$220$	1.09808	−	1.90192i	0.0740323	−	0.128228i
$221$	−27.8205	+	1.79423i	−1.87141	+	0.120693i
$222$	−16.5622	−	28.6865i	−1.11158	−	1.92531i
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	−0.983451	−	0.181173i	$-0.942010\pi$
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	0.648626	+	0.761107i	$0.275344\pi$
$224$		0			0
$225$	4.46410	+	7.73205i	0.297607	+	0.515470i
$226$	−11.5981	−	20.0885i	−0.771493	−	1.33626i
$227$	−5.66025			−0.375684			−0.187842	−	0.982199i	$-0.560149\pi$
$227$	−5.66025			−0.375684			−0.187842	+	0.982199i	$0.560149\pi$
$228$	5.46410			0.361869
$229$	−7.19615	−	12.4641i	−0.475535	−	0.823651i	0.524072	−	0.851674i	$-0.324412\pi$
$229$	−7.19615	−	12.4641i	−0.475535	−	0.823651i	−0.999607	+	0.0280229i	$0.991079\pi$
$230$	7.09808	+	12.2942i	0.468033	+	0.810657i
$231$		0			0
$232$	−2.59808	+	4.50000i	−0.170572	+	0.295439i
$233$	0.928203	+	1.60770i	0.0608086	+	0.105324i	0.894827	−	0.446413i	$-0.147299\pi$
$233$	0.928203	+	1.60770i	0.0608086	+	0.105324i	−0.834018	+	0.551737i	$0.813965\pi$
$234$	12.3564	−	24.9904i	0.807764	−	1.63367i
$235$	−11.1962	+	19.3923i	−0.730356	+	1.26501i
$236$	−7.26795			−0.473103
$237$	22.1244	−	38.3205i	1.43713	−	2.48918i
$238$		0			0
$239$	−15.8038			−1.02227			−0.511133	−	0.859502i	$-0.670774\pi$
$239$	−15.8038			−1.02227			−0.511133	+	0.859502i	$0.670774\pi$
$240$	11.8301	−	20.4904i	0.763631	−	1.32265i
$241$	21.1962			1.36536			0.682682	−	0.730716i	$-0.260813\pi$
$241$	21.1962			1.36536			0.682682	+	0.730716i	$0.260813\pi$
$242$	8.13397	−	14.0885i	0.522872	−	0.905640i
$243$	−9.36603	+	16.2224i	−0.600831	+	1.04067i
$244$	−2.40192	+	4.16025i	−0.153767	+	0.266333i
$245$		0			0
$246$	−24.5885			−1.56770
$247$	−3.19615	+	6.46410i	−0.203366	+	0.411301i
$248$	−3.63397	+	6.29423i	−0.230758	+	0.399684i
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	21.0000			1.32816
$251$	−0.803848	−	1.39230i	−0.0507384	−	0.0878815i	0.839541	−	0.543297i	$-0.182824\pi$
$251$	−0.803848	−	1.39230i	−0.0507384	−	0.0878815i	−0.890279	+	0.455415i	$0.849491\pi$
$252$		0			0
$253$	−3.00000	−	5.19615i	−0.188608	−	0.326679i
$254$	−15.9282	+	27.5885i	−0.999424	+	1.73105i
$255$	−18.2942	+	31.6865i	−1.14563	+	1.98429i
$256$	19.0000			1.18750
$257$	−6.12436			−0.382027			−0.191013	−	0.981587i	$-0.561177\pi$
$257$	−6.12436			−0.382027			−0.191013	+	0.981587i	$0.561177\pi$
$258$	−0.464102	+	0.803848i	−0.0288937	+	0.0500454i
$259$		0			0
$260$	−3.46410	−	5.19615i	−0.214834	−	0.322252i
$261$	6.69615	+	11.5981i	0.414481	+	0.717903i
$262$	−3.00000	−	5.19615i	−0.185341	−	0.321019i
$263$	−0.633975	−	1.09808i	−0.0390925	−	0.0677103i	0.845817	−	0.533473i	$-0.179113\pi$
$263$	−0.633975	−	1.09808i	−0.0390925	−	0.0677103i	−0.884910	+	0.465763i	$0.845780\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$	17.1962			1.05635
$266$		0			0
$267$	−17.6603	−	30.5885i	−1.08079	−	1.87198i
$268$	3.09808	+	5.36603i	0.189245	+	0.327782i
$269$	−5.07180			−0.309233			−0.154616	−	0.987975i	$-0.549414\pi$
$269$	−5.07180			−0.309233			−0.154616	+	0.987975i	$0.549414\pi$
$270$	−6.00000	−	10.3923i	−0.365148	−	0.632456i
$271$	−5.80385			−0.352559			−0.176279	−	0.984340i	$-0.556406\pi$
$271$	−5.80385			−0.352559			−0.176279	+	0.984340i	$0.556406\pi$
$272$	−38.6603			−2.34412
$273$		0			0
$274$	13.9808			0.844609
$275$	−2.53590			−0.152920
$276$	6.46410	+	11.1962i	0.389093	+	0.673929i
$277$	17.0000			1.02143			0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000			1.02143			0.510716	+	0.859750i	$0.329381\pi$
$278$	−9.16987	−	15.8827i	−0.549972	−	0.952580i
$279$	9.36603	+	16.2224i	0.560729	+	0.971212i
$280$		0			0
$281$	13.3923			0.798918			0.399459	−	0.916751i	$-0.369198\pi$
$281$	13.3923			0.798918			0.399459	+	0.916751i	$0.369198\pi$
$282$	−30.5885	+	52.9808i	−1.82152	+	3.15496i
$283$	5.09808	+	8.83013i	0.303049	+	0.524897i	0.976825	−	0.214039i	$-0.0686620\pi$
$283$	5.09808	+	8.83013i	0.303049	+	0.524897i	−0.673776	+	0.738936i	$0.735329\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	4.73205	+	8.19615i	0.280302	+	0.485498i
$286$	4.39230	+	6.58846i	0.259722	+	0.389584i
$287$		0			0
$288$	11.5981	−	20.0885i	0.683423	−	1.18372i
$289$	42.7846			2.51674
$290$	9.00000			0.528498
$291$	−8.73205	+	15.1244i	−0.511882	+	0.886605i
$292$	−1.59808	+	2.76795i	−0.0935203	+	0.161982i
$293$	−0.401924	−	0.696152i	−0.0234806	−	0.0406697i	0.854046	−	0.520197i	$-0.174141\pi$
$293$	−0.401924	−	0.696152i	−0.0234806	−	0.0406697i	−0.877527	+	0.479527i	$0.840808\pi$
$294$		0			0
$295$	−6.29423	−	10.9019i	−0.366464	−	0.634735i
$296$	12.1244			0.704714
$297$	2.53590	+	4.39230i	0.147148	+	0.254867i
$298$	5.59808	−	9.69615i	0.324288	−	0.561683i
$299$	−17.0263	+	1.09808i	−0.984655	+	0.0635034i
$300$	5.46410			0.315470
$301$		0			0
$302$	−1.73205	+	3.00000i	−0.0996683	+	0.172631i
$303$	10.5622	−	18.2942i	0.606781	−	1.05098i
$304$	−5.00000	+	8.66025i	−0.286770	+	0.496700i
$305$	−8.32051			−0.476431
$306$	−29.8923	+	51.7750i	−1.70883	+	2.95978i
$307$	4.58846			0.261877			0.130939	−	0.991390i	$-0.458201\pi$
$307$	4.58846			0.261877			0.130939	+	0.991390i	$0.458201\pi$
$308$		0			0
$309$	19.6603	−	34.0526i	1.11843	−	1.93718i
$310$	12.5885			0.714976
$311$	0.633975	−	1.09808i	0.0359494	−	0.0622662i	−0.847491	−	0.530810i	$-0.821888\pi$
$311$	0.633975	−	1.09808i	0.0359494	−	0.0622662i	0.883440	+	0.468544i	$0.155221\pi$
$312$	9.46410	+	14.1962i	0.535799	+	0.803699i
$313$	14.3923	+	24.9282i	0.813501	+	1.40903i	0.910399	+	0.413731i	$0.135775\pi$
$313$	14.3923	+	24.9282i	0.813501	+	1.40903i	−0.0968980	+	0.995294i	$0.530892\pi$
$314$	1.03590	−	1.79423i	0.0584591	−	0.101254i
$315$		0			0
$316$	−8.09808	−	14.0263i	−0.455552	−	0.789040i
$317$	3.23205	+	5.59808i	0.181530	+	0.314419i	0.942402	−	0.334483i	$-0.108562\pi$
$317$	3.23205	+	5.59808i	0.181530	+	0.314419i	−0.760872	+	0.648902i	$0.775228\pi$
$318$	46.9808			2.63455
$319$	−3.80385			−0.212975
$320$	0.866025	+	1.50000i	0.0484123	+	0.0838525i
$321$	−10.7321	−	18.5885i	−0.599005	−	1.03751i
$322$		0			0
$323$	7.73205	−	13.3923i	0.430223	−	0.745168i
$324$	1.23205	+	2.13397i	0.0684473	+	0.118554i
$325$	−3.19615	+	6.46410i	−0.177291	+	0.358564i
$326$	−14.0263	+	24.2942i	−0.776844	+	1.34553i
$327$	22.9282			1.26793
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$		0			0
$330$	10.3923			0.572078
$331$	−12.4904	+	21.6340i	−0.686533	+	1.18911i	0.286419	+	0.958105i	$0.407535\pi$
$331$	−12.4904	+	21.6340i	−0.686533	+	1.18911i	−0.972952	+	0.231006i	$0.925798\pi$
$332$	2.19615			0.120530
$333$	15.6244	−	27.0622i	0.856209	−	1.48300i
$334$	−5.70577	+	9.88269i	−0.312206	+	0.540757i
$335$	−5.36603	+	9.29423i	−0.293177	+	0.507798i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$	22.3301	−	2.89230i	1.21460	−	0.157321i
$339$	18.2942	−	31.6865i	0.993606	−	1.72098i
$340$	6.69615	+	11.5981i	0.363150	+	0.628994i
$341$	−5.32051			−0.288122
$342$	7.73205	+	13.3923i	0.418101	+	0.724173i
$343$		0			0
$344$	−0.169873	−	0.294229i	−0.00915894	−	0.0158637i
$345$	−11.1962	+	19.3923i	−0.602781	+	1.04405i
$346$	7.39230	−	12.8038i	0.397413	−	0.688339i
$347$	7.26795			0.390164			0.195082	−	0.980787i	$-0.437503\pi$
$347$	7.26795			0.390164			0.195082	+	0.980787i	$0.437503\pi$
$348$	8.19615			0.439360
$349$	−12.3923	+	21.4641i	−0.663345	+	1.14895i	0.316386	+	0.948630i	$0.397530\pi$
$349$	−12.3923	+	21.4641i	−0.663345	+	1.14895i	−0.979731	+	0.200317i	$0.935803\pi$
$350$		0			0
$351$	14.3923	−	0.928203i	0.768204	−	0.0495438i
$352$	3.29423	+	5.70577i	0.175583	+	0.304119i
$353$	10.3301	+	17.8923i	0.549817	+	0.952311i	0.998287	+	0.0585131i	$0.0186360\pi$
$353$	10.3301	+	17.8923i	0.549817	+	0.952311i	−0.448469	+	0.893798i	$0.648031\pi$
$354$	−17.1962	−	29.7846i	−0.913965	−	1.58303i
$355$	5.19615	−	9.00000i	0.275783	−	0.477670i
$356$	−12.9282			−0.685193
$357$		0			0
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−9.46410	−	16.3923i	−0.499496	−	0.865153i	0.500504	−	0.865734i	$-0.333148\pi$
$359$	−9.46410	−	16.3923i	−0.499496	−	0.865153i	−1.00000		0.000581665i	$0.999815\pi$
$360$	13.3923			0.705836
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−9.67949			−0.508743
$363$	25.6603			1.34681
$364$		0			0
$365$	−5.53590			−0.289762
$366$	−22.7321			−1.18822
$367$	2.09808	+	3.63397i	0.109519	+	0.189692i	0.915575	−	0.402146i	$-0.131736\pi$
$367$	2.09808	+	3.63397i	0.109519	+	0.189692i	−0.806057	+	0.591838i	$0.798402\pi$
$368$	−23.6603			−1.23338
$369$	−11.5981	−	20.0885i	−0.603772	−	1.04576i
$370$	−10.5000	−	18.1865i	−0.545869	−	0.945473i
$371$		0			0
$372$	11.4641			0.594386
$373$	5.69615	−	9.86603i	0.294936	−	0.510843i	−0.680034	−	0.733180i	$-0.738035\pi$
$373$	5.69615	−	9.86603i	0.294936	−	0.510843i	0.974970	+	0.222337i	$0.0713685\pi$
$374$	−8.49038	−	14.7058i	−0.439027	−	0.760417i
$375$	16.5622	+	28.6865i	0.855267	+	1.48137i
$376$	−11.1962	−	19.3923i	−0.577397	−	1.00008i
$377$	−4.79423	+	9.69615i	−0.246915	+	0.499377i
$378$		0			0
$379$	−13.2942	+	23.0263i	−0.682879	+	1.18278i	0.291220	+	0.956656i	$0.405939\pi$
$379$	−13.2942	+	23.0263i	−0.682879	+	1.18278i	−0.974098	+	0.226124i	$0.927394\pi$
$380$	3.46410			0.177705
$381$	−50.2487			−2.57432
$382$	−4.09808	+	7.09808i	−0.209676	+	0.363169i
$383$	−5.83013	+	10.0981i	−0.297906	+	0.515988i	−0.975657	−	0.219304i	$-0.929621\pi$
$383$	−5.83013	+	10.0981i	−0.297906	+	0.515988i	0.677751	+	0.735291i	$0.262955\pi$
$384$	16.5622	+	28.6865i	0.845185	+	1.46390i
$385$		0			0
$386$	−4.33013	−	7.50000i	−0.220398	−	0.381740i
$387$	−0.875644			−0.0445115
$388$	3.19615	+	5.53590i	0.162260	+	0.281043i
$389$	11.7679	−	20.3827i	0.596659	−	1.03344i	−0.396652	−	0.917969i	$-0.629828\pi$
$389$	11.7679	−	20.3827i	0.596659	−	1.03344i	0.993310	−	0.115474i	$-0.0368387\pi$
$390$	13.0981	−	26.4904i	0.663247	−	1.34139i
$391$	36.5885			1.85036
$392$		0			0
$393$	4.73205	−	8.19615i	0.238700	−	0.413441i
$394$	−10.3923	+	18.0000i	−0.523557	+	0.906827i
$395$	14.0263	−	24.2942i	0.705739	−	1.22238i
$396$	5.66025			0.284438
$397$	−9.39230	+	16.2679i	−0.471386	+	0.816465i	−0.999464	−	0.0327309i	$-0.989580\pi$
$397$	−9.39230	+	16.2679i	−0.471386	+	0.816465i	0.528078	+	0.849196i	$0.322913\pi$
$398$	−3.46410			−0.173640
$399$		0			0
$400$	−5.00000	+	8.66025i	−0.250000	+	0.433013i
$401$	−10.8564			−0.542143			−0.271072	−	0.962559i	$-0.587378\pi$
$401$	−10.8564			−0.542143			−0.271072	+	0.962559i	$0.587378\pi$
$402$	−14.6603	+	25.3923i	−0.731187	+	1.26645i
$403$	−6.70577	+	13.5622i	−0.334038	+	0.675580i
$404$	−3.86603	−	6.69615i	−0.192342	−	0.333146i
$405$	−2.13397	+	3.69615i	−0.106038	+	0.183663i
$406$		0			0
$407$	4.43782	+	7.68653i	0.219975	+	0.381007i
$408$	−18.2942	−	31.6865i	−0.905699	−	1.56872i
$409$	16.8038			0.830897			0.415448	−	0.909617i	$-0.363625\pi$
$409$	16.8038			0.830897			0.415448	+	0.909617i	$0.363625\pi$
$410$	−15.5885			−0.769859
$411$	11.0263	+	19.0981i	0.543886	+	0.942039i
$412$	−7.19615	−	12.4641i	−0.354529	−	0.614062i
$413$		0			0
$414$	−18.2942	+	31.6865i	−0.899112	+	1.55731i
$415$	1.90192	+	3.29423i	0.0933618	+	0.161707i
$416$	18.6962	−	1.20577i	0.916654	−	0.0591178i
$417$	14.4641	−	25.0526i	0.708310	−	1.22683i
$418$	−4.39230			−0.214835
$419$	−16.0981	+	27.8827i	−0.786442	+	1.36216i	0.141691	+	0.989911i	$0.454746\pi$
$419$	−16.0981	+	27.8827i	−0.786442	+	1.36216i	−0.928134	+	0.372247i	$0.878587\pi$
$420$		0			0
$421$	−32.1769			−1.56821			−0.784103	−	0.620630i	$-0.786877\pi$
$421$	−32.1769			−1.56821			−0.784103	+	0.620630i	$0.786877\pi$
$422$	1.56218	−	2.70577i	0.0760456	−	0.131715i
$423$	−57.7128			−2.80609
$424$	−8.59808	+	14.8923i	−0.417559	+	0.723234i
$425$	7.73205	−	13.3923i	0.375060	−	0.649622i
$426$	14.1962	−	24.5885i	0.687806	−	1.19131i
$427$		0			0
$428$	−7.85641			−0.379754
$429$	−5.53590	+	11.1962i	−0.267276	+	0.540555i
$430$	−0.294229	+	0.509619i	−0.0141890	+	0.0245760i
$431$	−0.339746	−	0.588457i	−0.0163650	−	0.0283450i	0.857727	−	0.514106i	$-0.171876\pi$
$431$	−0.339746	−	0.588457i	−0.0163650	−	0.0283450i	−0.874092	+	0.485761i	$0.838543\pi$
$432$	20.0000			0.962250
$433$	−6.79423	−	11.7679i	−0.326510	−	0.565532i	0.655307	−	0.755363i	$-0.272539\pi$
$433$	−6.79423	−	11.7679i	−0.326510	−	0.565532i	−0.981817	+	0.189831i	$0.939206\pi$
$434$		0			0
$435$	7.09808	+	12.2942i	0.340327	+	0.589463i
$436$	4.19615	−	7.26795i	0.200959	−	0.348072i
$437$	4.73205	−	8.19615i	0.226365	−	0.392075i
$438$	−15.1244			−0.722670
$439$	−14.5885			−0.696269			−0.348135	−	0.937445i	$-0.613185\pi$
$439$	−14.5885			−0.696269			−0.348135	+	0.937445i	$0.613185\pi$
$440$	−1.90192	+	3.29423i	−0.0906707	+	0.157046i
$441$		0			0
$442$	−48.1865	+	3.10770i	−2.29200	+	0.147818i
$443$	−11.6603	−	20.1962i	−0.553995	−	0.959548i	−0.997981	−	0.0635142i	$-0.979769\pi$
$443$	−11.6603	−	20.1962i	−0.553995	−	0.959548i	0.443986	−	0.896034i	$-0.353564\pi$
$444$	−9.56218	−	16.5622i	−0.453801	−	0.786006i
$445$	−11.1962	−	19.3923i	−0.530749	−	0.919283i
$446$	−8.66025	+	15.0000i	−0.410075	+	0.710271i
$447$	17.6603			0.835301
$448$		0			0
$449$	6.00000	+	10.3923i	0.283158	+	0.490443i	0.972161	−	0.234315i	$-0.0752847\pi$
$449$	6.00000	+	10.3923i	0.283158	+	0.490443i	−0.689003	+	0.724758i	$0.741951\pi$
$450$	7.73205	+	13.3923i	0.364492	+	0.631319i
$451$	6.58846			0.310238
$452$	−6.69615	−	11.5981i	−0.314961	−	0.545528i
$453$	−5.46410			−0.256726
$454$	−9.80385			−0.460117
$455$		0			0
$456$	−9.46410			−0.443197
$457$	11.0000			0.514558			0.257279	−	0.966337i	$-0.417174\pi$
$457$	11.0000			0.514558			0.257279	+	0.966337i	$0.417174\pi$
$458$	−12.4641	−	21.5885i	−0.582409	−	1.00876i
$459$	−30.9282			−1.44360
$460$	4.09808	+	7.09808i	0.191074	+	0.330950i
$461$	−7.79423	−	13.5000i	−0.363013	−	0.628758i	0.625442	−	0.780271i	$-0.284919\pi$
$461$	−7.79423	−	13.5000i	−0.363013	−	0.628758i	−0.988455	+	0.151513i	$0.951585\pi$
$462$		0			0
$463$	−4.58846			−0.213244			−0.106622	−	0.994300i	$-0.534003\pi$
$463$	−4.58846			−0.213244			−0.106622	+	0.994300i	$0.534003\pi$
$464$	−7.50000	+	12.9904i	−0.348179	+	0.603063i
$465$	9.92820	+	17.1962i	0.460409	+	0.797452i
$466$	1.60770	+	2.78461i	0.0744750	+	0.128995i
$467$	12.7583	+	22.0981i	0.590385	+	1.02258i	0.994180	+	0.107728i	$0.0343575\pi$
$467$	12.7583	+	22.0981i	0.590385	+	1.02258i	−0.403795	+	0.914849i	$0.632309\pi$
$468$	7.13397	−	14.4282i	0.329768	−	0.666944i
$469$		0			0
$470$	−19.3923	+	33.5885i	−0.894500	+	1.54932i
$471$	3.26795			0.150579
$472$	12.5885			0.579431
$473$	0.124356	−	0.215390i	0.00571788	−	0.00990366i
$474$	38.3205	−	66.3731i	1.76012	−	3.04862i
$475$	−2.00000	−	3.46410i	−0.0917663	−	0.158944i
$476$		0			0
$477$	22.1603	+	38.3827i	1.01465	+	1.75742i
$478$	−27.3731			−1.25201
$479$	0.633975	+	1.09808i	0.0289670	+	0.0501724i	0.880146	−	0.474704i	$-0.157445\pi$
$479$	0.633975	+	1.09808i	0.0289670	+	0.0501724i	−0.851178	+	0.524876i	$0.824112\pi$
$480$	12.2942	−	21.2942i	0.561152	−	0.971944i
$481$	25.1865	−	1.62436i	1.14841	−	0.0740642i
$482$	36.7128			1.67222
$483$		0			0
$484$	4.69615	−	8.13397i	0.213461	−	0.369726i
$485$	−5.53590	+	9.58846i	−0.251372	+	0.435389i
$486$	−16.2224	+	28.0981i	−0.735864	+	1.27455i
$487$	40.7846			1.84813			0.924064	−	0.382239i	$-0.124847\pi$
$487$	40.7846			1.84813			0.924064	+	0.382239i	$0.124847\pi$
$488$	4.16025	−	7.20577i	0.188326	−	0.326190i
$489$	−44.2487			−2.00100
$490$		0			0
$491$	−3.80385	+	6.58846i	−0.171665	+	0.297333i	−0.939002	−	0.343911i	$-0.888248\pi$
$491$	−3.80385	+	6.58846i	−0.171665	+	0.297333i	0.767337	+	0.641244i	$0.221581\pi$
$492$	−14.1962			−0.640012
$493$	11.5981	−	20.0885i	0.522351	−	0.904739i
$494$	−5.53590	+	11.1962i	−0.249072	+	0.503739i
$495$	4.90192	+	8.49038i	0.220325	+	0.381614i
$496$	−10.4904	+	18.1699i	−0.471032	+	0.815851i
$497$		0			0
$498$	5.19615	+	9.00000i	0.232845	+	0.403300i
$499$	19.4904	+	33.7583i	0.872509	+	1.51123i	0.859393	+	0.511316i	$0.170842\pi$
$499$	19.4904	+	33.7583i	0.872509	+	1.51123i	0.0131168	+	0.999914i	$0.495825\pi$
$500$	12.1244			0.542218
$501$	−18.0000			−0.804181
$502$	−1.39230	−	2.41154i	−0.0621416	−	0.107632i
$503$	−9.29423	−	16.0981i	−0.414409	−	0.717778i	0.580957	−	0.813934i	$-0.302678\pi$
$503$	−9.29423	−	16.0981i	−0.414409	−	0.717778i	−0.995366	+	0.0961565i	$0.969345\pi$
$504$		0			0
$505$	6.69615	−	11.5981i	0.297975	−	0.516108i
$506$	−5.19615	−	9.00000i	−0.230997	−	0.400099i
$507$	21.5622	+	28.2224i	0.957610	+	1.25340i
$508$	−9.19615	+	15.9282i	−0.408013	+	0.706700i
$509$	−13.7321			−0.608662			−0.304331	−	0.952566i	$-0.598433\pi$
$509$	−13.7321			−0.608662			−0.304331	+	0.952566i	$0.598433\pi$
$510$	−31.6865	+	54.8827i	−1.40310	+	2.43025i
$511$		0			0
$512$	8.66025			0.382733
$513$	−4.00000	+	6.92820i	−0.176604	+	0.305888i
$514$	−10.6077			−0.467885
$515$	12.4641	−	21.5885i	0.549234	−	0.951301i
$516$	−0.267949	+	0.464102i	−0.0117958	+	0.0204309i
$517$	8.19615	−	14.1962i	0.360466	−	0.624346i
$518$		0			0
$519$	23.3205			1.02366
$520$	6.00000	+	9.00000i	0.263117	+	0.394676i
$521$	−12.0622	+	20.8923i	−0.528454	+	0.915308i	0.470996	+	0.882135i	$0.343895\pi$
$521$	−12.0622	+	20.8923i	−0.528454	+	0.915308i	−0.999450	+	0.0331732i	$0.989439\pi$
$522$	11.5981	+	20.0885i	0.507634	+	0.879248i
$523$	29.1769			1.27582			0.637909	−	0.770112i	$-0.279800\pi$
$523$	29.1769			1.27582			0.637909	+	0.770112i	$0.279800\pi$
$524$	−1.73205	−	3.00000i	−0.0756650	−	0.131056i
$525$		0			0
$526$	−1.09808	−	1.90192i	−0.0478784	−	0.0829278i
$527$	16.2224	−	28.0981i	0.706660	−	1.22397i
$528$	−8.66025	+	15.0000i	−0.376889	+	0.652791i
$529$	−0.607695			−0.0264215
$530$	29.7846			1.29376
$531$	16.2224	−	28.0981i	0.703994	−	1.21935i
$532$		0			0
$533$	8.30385	−	16.7942i	0.359680	−	0.727439i
$534$	−30.5885	−	52.9808i	−1.32369	−	2.29270i
$535$	−6.80385	−	11.7846i	−0.294156	−	0.509493i
$536$	−5.36603	−	9.29423i	−0.231777	−	0.401450i
$537$	−9.46410	+	16.3923i	−0.408406	+	0.707380i
$538$	−8.78461			−0.378731
$539$		0			0
$540$	−3.46410	−	6.00000i	−0.149071	−	0.258199i
$541$	7.30385	+	12.6506i	0.314017	+	0.543893i	0.979228	−	0.202762i	$-0.0649918\pi$
$541$	7.30385	+	12.6506i	0.314017	+	0.543893i	−0.665211	+	0.746655i	$0.731658\pi$
$542$	−10.0526			−0.431794
$543$	−7.63397	−	13.2224i	−0.327605	−	0.567429i
$544$	−40.1769			−1.72257
$545$	14.5359			0.622649
$546$		0			0
$547$	17.8038			0.761238			0.380619	−	0.924732i	$-0.375711\pi$
$547$	17.8038			0.761238			0.380619	+	0.924732i	$0.375711\pi$
$548$	8.07180			0.344810
$549$	−10.7224	−	18.5718i	−0.457622	−	0.792625i
$550$	−4.39230			−0.187289
$551$	−3.00000	−	5.19615i	−0.127804	−	0.221364i
$552$	−11.1962	−	19.3923i	−0.476540	−	0.825391i
$553$		0			0
$554$	29.4449			1.25099
$555$	16.5622	−	28.6865i	0.703025	−	1.21768i
$556$	−5.29423	−	9.16987i	−0.224525	−	0.388889i
$557$	−21.8205	−	37.7942i	−0.924565	−	1.60139i	−0.792260	−	0.610184i	$-0.791096\pi$
$557$	−21.8205	−	37.7942i	−0.924565	−	1.60139i	−0.132305	−	0.991209i	$-0.542238\pi$
$558$	16.2224	+	28.0981i	0.686750	+	1.18949i
$559$	−0.392305	−	0.588457i	−0.0165927	−	0.0248891i
$560$		0			0
$561$	13.3923	−	23.1962i	0.565424	−	0.979342i
$562$	23.1962			0.978471
$563$	−28.0526			−1.18227			−0.591137	−	0.806571i	$-0.701321\pi$
$563$	−28.0526			−1.18227			−0.591137	+	0.806571i	$0.701321\pi$
$564$	−17.6603	+	30.5885i	−0.743631	+	1.28801i
$565$	11.5981	−	20.0885i	0.487935	−	0.845128i
$566$	8.83013	+	15.2942i	0.371158	+	0.642864i
$567$		0			0
$568$	5.19615	+	9.00000i	0.218026	+	0.377632i
$569$	42.9282			1.79964			0.899822	−	0.436257i	$-0.143696\pi$
$569$	42.9282			1.79964			0.899822	+	0.436257i	$0.143696\pi$
$570$	8.19615	+	14.1962i	0.343299	+	0.594611i
$571$	−8.39230	+	14.5359i	−0.351207	+	0.608308i	−0.986461	−	0.163995i	$-0.947562\pi$
$571$	−8.39230	+	14.5359i	−0.351207	+	0.608308i	0.635254	+	0.772303i	$0.280895\pi$
$572$	2.53590	+	3.80385i	0.106031	+	0.159047i
$573$	−12.9282			−0.540083
$574$		0			0
$575$	4.73205	−	8.19615i	0.197340	−	0.341803i
$576$	−2.23205	+	3.86603i	−0.0930021	+	0.161084i
$577$	21.5981	−	37.4090i	0.899140	−	1.55736i	0.0705436	−	0.997509i	$-0.477527\pi$
$577$	21.5981	−	37.4090i	0.899140	−	1.55736i	0.828596	−	0.559847i	$-0.189140\pi$
$578$	74.1051			3.08237
$579$	6.83013	−	11.8301i	0.283850	−	0.491643i
$580$	5.19615			0.215758
$581$		0			0
$582$	−15.1244	+	26.1962i	−0.626925	+	1.08587i
$583$	−12.5885			−0.521361
$584$	2.76795	−	4.79423i	0.114539	−	0.198387i
$585$	27.8205	−	1.79423i	1.15024	−	0.0741822i
$586$	−0.696152	−	1.20577i	−0.0287578	−	0.0498100i
$587$	8.19615	−	14.1962i	0.338291	−	0.585938i	−0.645820	−	0.763490i	$-0.723484\pi$
$587$	8.19615	−	14.1962i	0.338291	−	0.585938i	0.984111	+	0.177552i	$0.0568177\pi$
$588$		0			0
$589$	−4.19615	−	7.26795i	−0.172899	−	0.299471i
$590$	−10.9019	−	18.8827i	−0.448825	−	0.777388i
$591$	−32.7846			−1.34858
$592$	35.0000			1.43849
$593$	−8.72243	−	15.1077i	−0.358187	−	0.620399i	0.629471	−	0.777024i	$-0.283272\pi$
$593$	−8.72243	−	15.1077i	−0.358187	−	0.620399i	−0.987658	+	0.156626i	$0.949938\pi$
$594$	4.39230	+	7.60770i	0.180218	+	0.312148i
$595$		0			0
$596$	3.23205	−	5.59808i	0.132390	−	0.229306i
$597$	−2.73205	−	4.73205i	−0.111815	−	0.193670i
$598$	−29.4904	+	1.90192i	−1.20595	+	0.0777754i
$599$	−21.9282	+	37.9808i	−0.895962	+	1.55185i	−0.0633527	+	0.997991i	$0.520179\pi$
$599$	−21.9282	+	37.9808i	−0.895962	+	1.55185i	−0.832609	+	0.553861i	$0.813154\pi$
$600$	−9.46410			−0.386370
$601$	−14.9904	+	25.9641i	−0.611470	+	1.05910i	0.379522	+	0.925183i	$0.376088\pi$
$601$	−14.9904	+	25.9641i	−0.611470	+	1.05910i	−0.990993	+	0.133915i	$0.957245\pi$
$602$		0			0
$603$	−27.6603			−1.12641
$604$	−1.00000	+	1.73205i	−0.0406894	+	0.0704761i
$605$	16.2679			0.661386
$606$	18.2942	−	31.6865i	0.743152	−	1.28718i
$607$	−7.19615	+	12.4641i	−0.292083	+	0.505902i	−0.974302	−	0.225245i	$-0.927682\pi$
$607$	−7.19615	+	12.4641i	−0.292083	+	0.505902i	0.682219	+	0.731148i	$0.261015\pi$
$608$	−5.19615	+	9.00000i	−0.210732	+	0.364998i
$609$		0			0
$610$	−14.4115			−0.583506
$611$	−25.8564	−	38.7846i	−1.04604	−	1.56906i
$612$	−17.2583	+	29.8923i	−0.697627	+	1.20832i
$613$	−1.69615	−	2.93782i	−0.0685070	−	0.118658i	0.829737	−	0.558154i	$-0.188490\pi$
$613$	−1.69615	−	2.93782i	−0.0685070	−	0.118658i	−0.898244	+	0.439497i	$0.855157\pi$
$614$	7.94744			0.320733
$615$	−12.2942	−	21.2942i	−0.495751	−	0.858666i
$616$		0			0
$617$	−24.6962	−	42.7750i	−0.994230	−	1.72206i	−0.590016	−	0.807392i	$-0.700878\pi$
$617$	−24.6962	−	42.7750i	−0.994230	−	1.72206i	−0.404214	−	0.914664i	$-0.632455\pi$
$618$	34.0526	−	58.9808i	1.36979	−	2.37255i
$619$	17.6865	−	30.6340i	0.710882	−	1.23128i	−0.253645	−	0.967297i	$-0.581629\pi$
$619$	17.6865	−	30.6340i	0.710882	−	1.23128i	0.964527	−	0.263986i	$-0.0850373\pi$
$620$	7.26795			0.291888
$621$	−18.9282			−0.759563
$622$	1.09808	−	1.90192i	0.0440288	−	0.0762602i
$623$		0			0
$624$	27.3205	+	40.9808i	1.09370	+	1.64054i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	24.9282	+	43.1769i	0.996331	+	1.72570i
$627$	−3.46410	−	6.00000i	−0.138343	−	0.239617i
$628$	0.598076	−	1.03590i	0.0238658	−	0.0413368i
$629$	−54.1244			−2.15808
$630$		0			0
$631$	6.39230	+	11.0718i	0.254474	+	0.440761i	0.964752	−	0.263159i	$-0.0847645\pi$
$631$	6.39230	+	11.0718i	0.254474	+	0.440761i	−0.710279	+	0.703920i	$0.751431\pi$
$632$	14.0263	+	24.2942i	0.557935	+	0.966373i
$633$	4.92820			0.195878
$634$	5.59808	+	9.69615i	0.222328	+	0.385083i
$635$	−31.8564			−1.26418
$636$	27.1244			1.07555
$637$		0			0
$638$	−6.58846			−0.260840
$639$	26.7846			1.05958
$640$	10.5000	+	18.1865i	0.415049	+	0.718886i
$641$	28.8564			1.13976			0.569880	−	0.821728i	$-0.306990\pi$
$641$	28.8564			1.13976			0.569880	+	0.821728i	$0.306990\pi$
$642$	−18.5885	−	32.1962i	−0.733628	−	1.27068i
$643$	−0.392305	−	0.679492i	−0.0154710	−	0.0267965i	0.858186	−	0.513338i	$-0.171591\pi$
$643$	−0.392305	−	0.679492i	−0.0154710	−	0.0267965i	−0.873657	+	0.486542i	$0.838258\pi$
$644$		0			0
$645$	−0.928203			−0.0365480
$646$	13.3923	−	23.1962i	0.526913	−	0.912640i
$647$	22.5167	+	39.0000i	0.885221	+	1.53325i	0.845460	+	0.534039i	$0.179326\pi$
$647$	22.5167	+	39.0000i	0.885221	+	1.53325i	0.0397614	+	0.999209i	$0.487340\pi$
$648$	−2.13397	−	3.69615i	−0.0838304	−	0.145199i
$649$	4.60770	+	7.98076i	0.180868	+	0.313272i
$650$	−5.53590	+	11.1962i	−0.217136	+	0.439149i
$651$		0			0
$652$	−8.09808	+	14.0263i	−0.317145	+	0.549311i
$653$	−37.8564			−1.48144			−0.740718	−	0.671816i	$-0.765514\pi$
$653$	−37.8564			−1.48144			−0.740718	+	0.671816i	$0.765514\pi$
$654$	39.7128			1.55289
$655$	3.00000	−	5.19615i	0.117220	−	0.203030i
$656$	12.9904	−	22.5000i	0.507189	−	0.878477i
$657$	−7.13397	−	12.3564i	−0.278323	−	0.482069i
$658$		0			0
$659$	−14.1962	−	24.5885i	−0.553004	−	0.957830i	−0.998056	−	0.0623257i	$-0.980148\pi$
$659$	−14.1962	−	24.5885i	−0.553004	−	0.957830i	0.445052	−	0.895505i	$-0.353185\pi$
$660$	6.00000			0.233550
$661$	−16.5981	−	28.7487i	−0.645590	−	1.11820i	−0.984165	−	0.177256i	$-0.943278\pi$
$661$	−16.5981	−	28.7487i	−0.645590	−	1.11820i	0.338574	−	0.940940i	$-0.390055\pi$
$662$	−21.6340	+	37.4711i	−0.840828	+	1.45636i
$663$	−42.2487	−	63.3731i	−1.64080	−	2.46121i
$664$	−3.80385			−0.147618
$665$		0			0
$666$	27.0622	−	46.8731i	1.04864	−	1.81629i
$667$	7.09808	−	12.2942i	0.274839	−	0.476034i
$668$	−3.29423	+	5.70577i	−0.127458	+	0.220763i
$669$	−27.3205			−1.05627
$670$	−9.29423	+	16.0981i	−0.359067	+	0.621923i
$671$	6.09103			0.235142
$672$		0			0
$673$	22.0885	−	38.2583i	0.851447	−	1.47475i	−0.0284546	−	0.999595i	$-0.509059\pi$
$673$	22.0885	−	38.2583i	0.851447	−	1.47475i	0.879902	−	0.475155i	$-0.157608\pi$
$674$	19.0526			0.733877
$675$	−4.00000	+	6.92820i	−0.153960	+	0.266667i
$676$	12.8923	−	1.66987i	0.495858	−	0.0642259i
$677$	−11.5359	−	19.9808i	−0.443361	−	0.767923i	0.554576	−	0.832133i	$-0.312881\pi$
$677$	−11.5359	−	19.9808i	−0.443361	−	0.767923i	−0.997936	+	0.0642101i	$0.979547\pi$
$678$	31.6865	−	54.8827i	1.21691	−	2.10776i
$679$		0			0
$680$	−11.5981	−	20.0885i	−0.444766	−	0.770357i
$681$	−7.73205	−	13.3923i	−0.296293	−	0.513194i
$682$	−9.21539			−0.352876
$683$	15.4641			0.591717			0.295859	−	0.955232i	$-0.404394\pi$
$683$	15.4641			0.591717			0.295859	+	0.955232i	$0.404394\pi$
$684$	4.46410	+	7.73205i	0.170689	+	0.295642i
$685$	6.99038	+	12.1077i	0.267089	+	0.462611i
$686$		0			0
$687$	19.6603	−	34.0526i	0.750085	−	1.29919i
$688$	−0.490381	−	0.849365i	−0.0186956	−	0.0323817i
$689$	−15.8660	+	32.0885i	−0.604447	+	1.22247i
$690$	−19.3923	+	33.5885i	−0.738252	+	1.27869i
$691$	−0.392305			−0.0149240			−0.00746199	−	0.999972i	$-0.502375\pi$
$691$	−0.392305			−0.0149240			−0.00746199	+	0.999972i	$0.502375\pi$
$692$	4.26795	−	7.39230i	0.162243	−	0.281013i
$693$		0			0
$694$	12.5885			0.477851
$695$	9.16987	−	15.8827i	0.347833	−	0.602465i
$696$	−14.1962			−0.538104
$697$	−20.0885	+	34.7942i	−0.760905	+	1.31793i
$698$	−21.4641	+	37.1769i	−0.812428	+	1.40717i
$699$	−2.53590	+	4.39230i	−0.0959165	+	0.166132i
$700$		0			0
$701$	20.7846			0.785024			0.392512	−	0.919747i	$-0.371606\pi$
$701$	20.7846			0.785024			0.392512	+	0.919747i	$0.371606\pi$
$702$	24.9282	−	1.60770i	0.940854	−	0.0606785i
$703$	−7.00000	+	12.1244i	−0.264010	+	0.457279i
$704$	−0.633975	−	1.09808i	−0.0238938	−	0.0413853i
$705$	−61.1769			−2.30406
$706$	17.8923	+	30.9904i	0.673386	+	1.16634i
$707$		0			0
$708$	−9.92820	−	17.1962i	−0.373125	−	0.646271i
$709$	−15.0885	+	26.1340i	−0.566659	+	0.981482i	0.430234	+	0.902717i	$0.358431\pi$
$709$	−15.0885	+	26.1340i	−0.566659	+	0.981482i	−0.996893	+	0.0787648i	$0.974902\pi$
$710$	9.00000	−	15.5885i	0.337764	−	0.585024i
$711$	72.3013			2.71151
$712$	22.3923			0.839187
$713$	9.92820	−	17.1962i	0.371814	−	0.644001i
$714$		0			0
$715$	−3.50962	+	7.09808i	−0.131252	+	0.265453i
$716$	3.46410	+	6.00000i	0.129460	+	0.224231i
$717$	−21.5885	−	37.3923i	−0.806236	−	1.39644i
$718$	−16.3923	−	28.3923i	−0.611755	−	1.05959i
$719$	−3.63397	+	6.29423i	−0.135524	+	0.234735i	−0.925798	−	0.378019i	$-0.876605\pi$
$719$	−3.63397	+	6.29423i	−0.135524	+	0.234735i	0.790273	+	0.612755i	$0.209939\pi$
$720$	38.6603			1.44078
$721$		0			0
$722$	12.9904	+	22.5000i	0.483452	+	0.837363i
$723$	28.9545	+	50.1506i	1.07683	+	1.86512i
$724$	−5.58846			−0.207693
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	44.4449			1.64950
$727$	41.1769			1.52717			0.763584	−	0.645709i	$-0.223438\pi$
$727$	41.1769			1.52717			0.763584	+	0.645709i	$0.223438\pi$
$728$		0			0
$729$	−43.7846			−1.62165
$730$	−9.58846			−0.354885
$731$	0.758330	+	1.31347i	0.0280479	+	0.0485803i
$732$	−13.1244			−0.485090
$733$	11.7942	+	20.4282i	0.435630	+	0.754533i	0.997347	−	0.0727965i	$-0.0231924\pi$
$733$	11.7942	+	20.4282i	0.435630	+	0.754533i	−0.561717	+	0.827329i	$0.689859\pi$
$734$	3.63397	+	6.29423i	0.134132	+	0.232324i
$735$		0			0
$736$	−24.5885			−0.906343
$737$	3.92820	−	6.80385i	0.144697	−	0.250623i
$738$	−20.0885	−	34.7942i	−0.739466	−	1.28079i
$739$	−20.3923	−	35.3205i	−0.750143	−	1.29929i	−0.947753	−	0.319005i	$-0.896651\pi$
$739$	−20.3923	−	35.3205i	−0.750143	−	1.29929i	0.197610	−	0.980281i	$-0.436682\pi$
$740$	−6.06218	−	10.5000i	−0.222850	−	0.385988i
$741$	−19.6603	+	1.26795i	−0.722237	+	0.0465793i
$742$		0			0
$743$	3.80385	−	6.58846i	0.139550	−	0.241707i	−0.787777	−	0.615961i	$-0.788768\pi$
$743$	3.80385	−	6.58846i	0.139550	−	0.241707i	0.927326	+	0.374254i	$0.122101\pi$
$744$	−19.8564			−0.727971
$745$	11.1962			0.410195
$746$	9.86603	−	17.0885i	0.361221	−	0.625653i
$747$	−4.90192	+	8.49038i	−0.179352	+	0.310647i
$748$	−4.90192	−	8.49038i	−0.179232	−	0.310439i
$749$		0			0
$750$	28.6865	+	49.6865i	1.04748	+	1.81430i
$751$	35.8038			1.30650			0.653250	−	0.757142i	$-0.273405\pi$
$751$	35.8038			1.30650			0.653250	+	0.757142i	$0.273405\pi$
$752$	−32.3205	−	55.9808i	−1.17861	−	2.04141i
$753$	2.19615	−	3.80385i	0.0800322	−	0.138620i
$754$	−8.30385	+	16.7942i	−0.302408	+	0.611610i
$755$	−3.46410			−0.126072
$756$		0			0
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	−0.683226	−	0.730207i	$-0.739424\pi$
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	0.973991	+	0.226587i	$0.0727569\pi$
$758$	−23.0263	+	39.8827i	−0.836352	+	1.44860i
$759$	8.19615	−	14.1962i	0.297501	−	0.515288i
$760$	−6.00000			−0.217643
$761$	20.6603	−	35.7846i	0.748934	−	1.29719i	−0.199401	−	0.979918i	$-0.563900\pi$
$761$	20.6603	−	35.7846i	0.748934	−	1.29719i	0.948334	−	0.317273i	$-0.102767\pi$
$762$	−87.0333			−3.15288
$763$		0			0
$764$	−2.36603	+	4.09808i	−0.0855998	+	0.148263i
$765$	−59.7846			−2.16152
$766$	−10.0981	+	17.4904i	−0.364858	+	0.631953i
$767$	26.1506	−	1.68653i	0.944245	−	0.0608972i
$768$	25.9545	+	44.9545i	0.936552	+	1.62216i
$769$	7.58846	−	13.1436i	0.273647	−	0.473970i	−0.696146	−	0.717900i	$-0.745103\pi$
$769$	7.58846	−	13.1436i	0.273647	−	0.473970i	0.969793	+	0.243930i	$0.0784367\pi$
$770$		0			0
$771$	−8.36603	−	14.4904i	−0.301295	−	0.521858i
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	12.9282			0.464995			0.232498	−	0.972597i	$-0.425310\pi$
$773$	12.9282			0.464995			0.232498	+	0.972597i	$0.425310\pi$
$774$	−1.51666			−0.0545152
$775$	−4.19615	−	7.26795i	−0.150730	−	0.261072i
$776$	−5.53590	−	9.58846i	−0.198727	−	0.344206i
$777$		0			0
$778$	20.3827	−	35.3038i	0.730755	−	1.26570i
$779$	5.19615	+	9.00000i	0.186171	+	0.322458i
$780$	7.56218	−	15.2942i	0.270769	−	0.547621i
$781$	−3.80385	+	6.58846i	−0.136112	+	0.235754i
$782$	63.3731			2.26622
$783$	−6.00000	+	10.3923i	−0.214423	+	0.371391i
$784$		0			0
$785$	2.07180			0.0739456
$786$	8.19615	−	14.1962i	0.292347	−	0.506360i
$787$	−12.9808			−0.462714			−0.231357	−	0.972869i	$-0.574317\pi$
$787$	−12.9808			−0.462714			−0.231357	+	0.972869i	$0.574317\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$	1.73205	−	3.00000i	0.0616626	−	0.106803i
$790$	24.2942	−	42.0788i	0.864350	−	1.49710i
$791$		0			0
$792$	−9.80385			−0.348365
$793$	7.67691	−	15.5263i	0.272615	−	0.551354i
$794$	−16.2679	+	28.1769i	−0.577328	+	0.999961i
$795$	23.4904	+	40.6865i	0.833118	+	1.44300i
$796$	−2.00000			−0.0708881
$797$	−17.1962	−	29.7846i	−0.609119	−	1.05503i	−0.991386	−	0.130973i	$-0.958190\pi$
$797$	−17.1962	−	29.7846i	−0.609119	−	1.05503i	0.382267	−	0.924052i	$-0.375143\pi$
$798$		0			0
$799$	49.9808	+	86.5692i	1.76819	+	3.06260i
$800$	−5.19615	+	9.00000i	−0.183712	+	0.318198i
$801$	28.8564	−	49.9808i	1.01959	−	1.76598i
$802$	−18.8038			−0.663987
$803$	4.05256			0.143012
$804$	−8.46410	+	14.6603i	−0.298506	+	0.517027i
$805$		0			0
$806$	−11.6147	+	23.4904i	−0.409112	+	0.827413i
$807$	−6.92820	−	12.0000i	−0.243884	−	0.422420i
$808$	6.69615	+	11.5981i	0.235570	+	0.408019i
$809$	−1.03590	−	1.79423i	−0.0364202	−	0.0630817i	0.847241	−	0.531209i	$-0.178262\pi$
$809$	−1.03590	−	1.79423i	−0.0364202	−	0.0630817i	−0.883661	+	0.468127i	$0.844929\pi$
$810$	−3.69615	+	6.40192i	−0.129870	+	0.224941i
$811$	16.5885			0.582500			0.291250	−	0.956647i	$-0.405929\pi$
$811$	16.5885			0.582500			0.291250	+	0.956647i	$0.405929\pi$
$812$		0			0
$813$	−7.92820	−	13.7321i	−0.278054	−	0.481604i
$814$	7.68653	+	13.3135i	0.269413	+	0.466637i
$815$	−28.0526			−0.982638
$816$	−52.8109	−	91.4711i	−1.84875	−	3.20213i
$817$	0.392305			0.0137250
$818$	29.1051			1.01764
$819$		0			0
$820$	−9.00000			−0.314294
$821$	4.14359			0.144612			0.0723062	−	0.997382i	$-0.476964\pi$
$821$	4.14359			0.144612			0.0723062	+	0.997382i	$0.476964\pi$
$822$	19.0981	+	33.0788i	0.666122	+	1.15376i
$823$	−41.1769			−1.43534			−0.717669	−	0.696385i	$-0.754791\pi$
$823$	−41.1769			−1.43534			−0.717669	+	0.696385i	$0.754791\pi$
$824$	12.4641	+	21.5885i	0.434208	+	0.752070i
$825$	−3.46410	−	6.00000i	−0.120605	−	0.208893i
$826$		0			0
$827$	−16.9808			−0.590479			−0.295239	−	0.955423i	$-0.595399\pi$
$827$	−16.9808			−0.590479			−0.295239	+	0.955423i	$0.595399\pi$
$828$	−10.5622	+	18.2942i	−0.367061	+	0.635768i
$829$	−0.205771	−	0.356406i	−0.00714673	−	0.0123785i	0.862430	−	0.506176i	$-0.168942\pi$
$829$	−0.205771	−	0.356406i	−0.00714673	−	0.0123785i	−0.869577	+	0.493798i	$0.835608\pi$
$830$	3.29423	+	5.70577i	0.114344	+	0.198050i
$831$	23.2224	+	40.2224i	0.805577	+	1.39530i
$832$	−3.59808	+	0.232051i	−0.124741	+	0.00804491i
$833$		0			0
$834$	25.0526	−	43.3923i	0.867499	−	1.50255i
$835$	−11.4115			−0.394913
$836$	−2.53590			−0.0877059
$837$	−8.39230	+	14.5359i	−0.290080	+	0.502434i
$838$	−27.8827	+	48.2942i	−0.963191	+	1.66830i
$839$	−9.00000	−	15.5885i	−0.310715	−	0.538173i	0.667803	−	0.744338i	$-0.267235\pi$
$839$	−9.00000	−	15.5885i	−0.310715	−	0.538173i	−0.978517	+	0.206165i	$0.933902\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	−55.7321			−1.92065
$843$	18.2942	+	31.6865i	0.630087	+	1.09134i
$844$	0.901924	−	1.56218i	0.0310455	−	0.0537724i
$845$	13.6699	+	17.8923i	0.470258	+	0.615514i
$846$	−99.9615			−3.43675
$847$		0			0
$848$	−24.8205	+	42.9904i	−0.852340	+	1.47630i
$849$	−13.9282	+	24.1244i	−0.478015	+	0.827946i
$850$	13.3923	−	23.1962i	0.459352	−	0.795621i
$851$	−33.1244			−1.13549
$852$	8.19615	−	14.1962i	0.280796	−	0.486352i
$853$	−5.58846			−0.191345			−0.0956726	−	0.995413i	$-0.530500\pi$
$853$	−5.58846			−0.191345			−0.0956726	+	0.995413i	$0.530500\pi$
$854$		0			0
$855$	−7.73205	+	13.3923i	−0.264431	+	0.458007i
$856$	13.6077			0.465101
$857$	−15.0622	+	26.0885i	−0.514514	+	0.891165i	0.485344	+	0.874323i	$0.338694\pi$
$857$	−15.0622	+	26.0885i	−0.514514	+	0.891165i	−0.999858	+	0.0168414i	$0.994639\pi$
$858$	−9.58846	+	19.3923i	−0.327345	+	0.662042i
$859$	−3.90192	−	6.75833i	−0.133132	−	0.230591i	0.791750	−	0.610845i	$-0.209170\pi$
$859$	−3.90192	−	6.75833i	−0.133132	−	0.230591i	−0.924882	+	0.380254i	$0.875837\pi$
$860$	−0.169873	+	0.294229i	−0.00579262	+	0.0100331i
$861$		0			0
$862$	−0.588457	−	1.01924i	−0.0200429	−	0.0347154i
$863$	−3.75833	−	6.50962i	−0.127935	−	0.221590i	0.794941	−	0.606686i	$-0.207502\pi$
$863$	−3.75833	−	6.50962i	−0.127935	−	0.221590i	−0.922876	+	0.385096i	$0.874168\pi$
$864$	20.7846			0.707107
$865$	14.7846			0.502692
$866$	−11.7679	−	20.3827i	−0.399891	−	0.692632i
$867$	58.4449	+	101.229i	1.98489	+	3.43793i
$868$		0			0
$869$	−10.2679	+	17.7846i	−0.348316	+	0.603302i
$870$	12.2942	+	21.2942i	0.416813	+	0.721942i
$871$	−12.3923	−	18.5885i	−0.419897	−	0.629846i
$872$	−7.26795	+	12.5885i	−0.246124	+	0.426299i
$873$	−28.5359			−0.965794
$874$	8.19615	−	14.1962i	0.277239	−	0.480192i
$875$		0			0
$876$	−8.73205			−0.295029
$877$	−9.89230	+	17.1340i	−0.334039	+	0.578573i	−0.983300	−	0.181993i	$-0.941745\pi$
$877$	−9.89230	+	17.1340i	−0.334039	+	0.578573i	0.649260	+	0.760566i	$0.275079\pi$
$878$	−25.2679			−0.852752
$879$	1.09808	−	1.90192i	0.0370372	−	0.0641503i
$880$	−5.49038	+	9.50962i	−0.185081	+	0.320569i
$881$	−4.20577	+	7.28461i	−0.141696	+	0.245425i	−0.928135	−	0.372243i	$-0.878589\pi$
$881$	−4.20577	+	7.28461i	−0.141696	+	0.245425i	0.786439	+	0.617667i	$0.211922\pi$
$882$		0			0
$883$	−47.7654			−1.60743			−0.803716	−	0.595013i	$-0.797147\pi$
$883$	−47.7654			−1.60743			−0.803716	+	0.595013i	$0.797147\pi$
$884$	−27.8205	+	1.79423i	−0.935705	+	0.0603464i
$885$	17.1962	−	29.7846i	0.578042	−	1.00120i
$886$	−20.1962	−	34.9808i	−0.678503	−	1.17520i
$887$	−11.3205			−0.380105			−0.190053	−	0.981774i	$-0.560866\pi$
$887$	−11.3205			−0.380105			−0.190053	+	0.981774i	$0.560866\pi$
$888$	16.5622	+	28.6865i	0.555790	+	0.962657i
$889$		0			0
$890$	−19.3923	−	33.5885i	−0.650032	−	1.12589i
$891$	1.56218	−	2.70577i	0.0523349	−	0.0906468i
$892$	−5.00000	+	8.66025i	−0.167412	+	0.289967i
$893$	25.8564			0.865252
$894$	30.5885			1.02303
$895$	−6.00000	+	10.3923i	−0.200558	+	0.347376i
$896$		0			0
$897$	−25.8564	−	38.7846i	−0.863320	−	1.29498i
$898$	10.3923	+	18.0000i	0.346796	+	0.600668i
$899$	−6.29423	−	10.9019i	−0.209924	−	0.363600i
$900$	4.46410	+	7.73205i	0.148803	+	0.257735i
$901$	38.3827	−	66.4808i	1.27871	−	2.21480i
$902$	11.4115			0.379963
$903$		0			0
$904$	11.5981	+	20.0885i	0.385746	+	0.668132i
$905$	−4.83975	−	8.38269i	−0.160879	−	0.278650i
$906$	−9.46410			−0.314424
$907$	8.29423	+	14.3660i	0.275405	+	0.477016i	0.970237	−	0.242156i	$-0.0778546\pi$
$907$	8.29423	+	14.3660i	0.275405	+	0.477016i	−0.694832	+	0.719172i	$0.744521\pi$
$908$	−5.66025			−0.187842
$909$	34.5167			1.14485
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−27.3205			−0.904672
$913$	−1.39230	−	2.41154i	−0.0460786	−	0.0798104i
$914$	19.0526			0.630203
$915$	−11.3660	−	19.6865i	−0.375749	−	0.650817i
$916$	−7.19615	−	12.4641i	−0.237768	−	0.411826i
$917$		0			0
$918$	−53.5692			−1.76805
$919$	19.7846	−	34.2679i	0.652634	−	1.13040i	−0.329847	−	0.944034i	$-0.606997\pi$
$919$	19.7846	−	34.2679i	0.652634	−	1.13040i	0.982481	−	0.186361i	$-0.0596694\pi$
$920$	−7.09808	−	12.2942i	−0.234017	−	0.405329i
$921$	6.26795	+	10.8564i	0.206536	+	0.357731i
$922$	−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
$926$	−7.94744			−0.261169
$927$	64.2487			2.11020
$928$	−7.79423	+	13.5000i	−0.255858	+	0.443159i
$929$	26.2583	−	45.4808i	0.861508	−	1.49218i	−0.00896546	−	0.999960i	$-0.502854\pi$
$929$	26.2583	−	45.4808i	0.861508	−	1.49218i	0.870473	−	0.492216i	$-0.163813\pi$
$930$	17.1962	+	29.7846i	0.563884	+	0.976676i
$931$		0			0
$932$	0.928203	+	1.60770i	0.0304043	+	0.0526618i
$933$	3.46410			0.113410
$934$	22.0981	+	38.2750i	0.723071	+	1.25240i
$935$	8.49038	−	14.7058i	0.277665	−	0.480930i
$936$	−12.3564	+	24.9904i	−0.403882	+	0.816836i
$937$	51.1962			1.67251			0.836253	−	0.548344i	$-0.184742\pi$
$937$	51.1962			1.67251			0.836253	+	0.548344i	$0.184742\pi$
$938$		0			0
$939$	−39.3205	+	68.1051i	−1.28318	+	2.22253i
$940$	−11.1962	+	19.3923i	−0.365178	+	0.632507i
$941$	−14.0718	+	24.3731i	−0.458727	+	0.794539i	−0.998894	−	0.0470189i	$-0.985028\pi$
$941$	−14.0718	+	24.3731i	−0.458727	+	0.794539i	0.540167	+	0.841558i	$0.318361\pi$
$942$	5.66025			0.184421
$943$	−12.2942	+	21.2942i	−0.400355	+	0.693435i
$944$	36.3397			1.18276
$945$		0			0
$946$	0.215390	−	0.373067i	0.00700294	−	0.0121295i
$947$	−7.26795			−0.236177			−0.118088	−	0.993003i	$-0.537677\pi$
$947$	−7.26795			−0.236177			−0.118088	+	0.993003i	$0.537677\pi$
$948$	22.1244	−	38.3205i	0.718566	−	1.24459i
$949$	5.10770	−	10.3301i	0.165803	−	0.335330i
$950$	−3.46410	−	6.00000i	−0.112390	−	0.194666i
$951$	−8.83013	+	15.2942i	−0.286336	+	0.495949i
$952$		0			0
$953$	12.5885	+	21.8038i	0.407780	+	0.706296i	0.994641	−	0.103392i	$-0.0329697\pi$
$953$	12.5885	+	21.8038i	0.407780	+	0.706296i	−0.586861	+	0.809688i	$0.699636\pi$
$954$	38.3827	+	66.4808i	1.24269	+	2.15239i
$955$	−8.19615			−0.265221
$956$	−15.8038			−0.511133
$957$	−5.19615	−	9.00000i	−0.167968	−	0.290929i
$958$	1.09808	+	1.90192i	0.0354772	+	0.0614484i
$959$		0			0
$960$	−2.36603	+	4.09808i	−0.0763631	+	0.132265i
$961$	6.69615	+	11.5981i	0.216005	+	0.374131i
$962$	43.6244	−	2.81347i	1.40651	−	0.0907098i
$963$	17.5359	−	30.3731i	0.565086	−	0.978758i
$964$	21.1962			0.682682
$965$	4.33013	−	7.50000i	0.139392	−	0.241434i
$966$		0			0
$967$	54.9808			1.76806			0.884031	−	0.467428i	$-0.154819\pi$
$967$	54.9808			1.76806			0.884031	+	0.467428i	$0.154819\pi$
$968$	−8.13397	+	14.0885i	−0.261436	+	0.452820i
$969$	42.2487			1.35722
$970$	−9.58846	+	16.6077i	−0.307867	+	0.533241i
$971$	−26.3205	+	45.5885i	−0.844665	+	1.46300i	0.0412463	+	0.999149i	$0.486867\pi$
$971$	−26.3205	+	45.5885i	−0.844665	+	1.46300i	−0.885912	+	0.463854i	$0.846466\pi$
$972$	−9.36603	+	16.2224i	−0.300415	+	0.520335i
$973$		0			0
$974$	70.6410			2.26348
$975$	−19.6603	+	1.26795i	−0.629632	+	0.0406069i
$976$	12.0096	−	20.8013i	0.384419	−	0.665832i
$977$	−15.8205	−	27.4019i	−0.506143	−	0.876665i	−0.999975	−	0.00710779i	$-0.997738\pi$
$977$	−15.8205	−	27.4019i	−0.506143	−	0.876665i	0.493832	−	0.869557i	$-0.335596\pi$
$978$	−76.6410			−2.45071
$979$	8.19615	+	14.1962i	0.261950	+	0.453711i
$980$		0			0
$981$	18.7321	+	32.4449i	0.598068	+	1.03588i
$982$	−6.58846	+	11.4115i	−0.210246	+	0.364157i
$983$	−8.66025	+	15.0000i	−0.276219	+	0.478426i	−0.970442	−	0.241334i	$-0.922415\pi$
$983$	−8.66025	+	15.0000i	−0.276219	+	0.478426i	0.694223	+	0.719760i	$0.255748\pi$
$984$	24.5885			0.783851
$985$	−20.7846			−0.662253
$986$	20.0885	−	34.7942i	0.639747	−	1.10807i
$987$		0			0
$988$	−3.19615	+	6.46410i	−0.101683	+	0.205650i
$989$	0.464102	+	0.803848i	0.0147576	+	0.0255609i
$990$	8.49038	+	14.7058i	0.269842	+	0.467380i
$991$	−9.49038	−	16.4378i	−0.301472	−	0.522165i	0.674998	−	0.737820i	$-0.264145\pi$
$991$	−9.49038	−	16.4378i	−0.301472	−	0.522165i	−0.976470	+	0.215655i	$0.930811\pi$
$992$	−10.9019	+	18.8827i	−0.346136	+	0.599526i
$993$	−68.2487			−2.16581
$994$		0			0
$995$	−1.73205	−	3.00000i	−0.0549097	−	0.0951064i
$996$	3.00000	+	5.19615i	0.0950586	+	0.164646i
$997$	4.80385			0.152139			0.0760697	−	0.997103i	$-0.475763\pi$
$997$	4.80385			0.152139			0.0760697	+	0.997103i	$0.475763\pi$
$998$	33.7583	+	58.4711i	1.06860	+	1.85087i
$999$	28.0000			0.885881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.e.165.2		4
7.2	even	3		637.2.g.d.373.1		4
7.3	odd	6		91.2.f.b.22.1	✓	4
7.4	even	3		637.2.f.d.295.1		4
7.5	odd	6		637.2.g.e.373.1		4
7.6	odd	2		637.2.h.d.165.2		4
13.3	even	3		637.2.g.d.263.1		4
21.17	even	6		819.2.o.b.568.2		4
28.3	even	6		1456.2.s.o.113.2		4
91.3	odd	6		91.2.f.b.29.1	yes	4
91.4	even	6		8281.2.a.t.1.1		2
91.16	even	3	inner	637.2.h.e.471.2		4
91.17	odd	6		1183.2.a.e.1.1		2
91.45	even	12		1183.2.c.e.337.2		4
91.55	odd	6		637.2.g.e.263.1		4
91.59	even	12		1183.2.c.e.337.4		4
91.68	odd	6		637.2.h.d.471.2		4
91.74	even	3		8281.2.a.r.1.2		2
91.81	even	3		637.2.f.d.393.1		4
91.87	odd	6		1183.2.a.f.1.2		2
273.185	even	6		819.2.o.b.757.2		4
364.3	even	6		1456.2.s.o.1121.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.b.22.1	✓	4	7.3	odd	6
91.2.f.b.29.1	yes	4	91.3	odd	6
637.2.f.d.295.1		4	7.4	even	3
637.2.f.d.393.1		4	91.81	even	3
637.2.g.d.263.1		4	13.3	even	3
637.2.g.d.373.1		4	7.2	even	3
637.2.g.e.263.1		4	91.55	odd	6
637.2.g.e.373.1		4	7.5	odd	6
637.2.h.d.165.2		4	7.6	odd	2
637.2.h.d.471.2		4	91.68	odd	6
637.2.h.e.165.2		4	1.1	even	1	trivial
637.2.h.e.471.2		4	91.16	even	3	inner
819.2.o.b.568.2		4	21.17	even	6
819.2.o.b.757.2		4	273.185	even	6
1183.2.a.e.1.1		2	91.17	odd	6
1183.2.a.f.1.2		2	91.87	odd	6
1183.2.c.e.337.2		4	91.45	even	12
1183.2.c.e.337.4		4	91.59	even	12
1456.2.s.o.113.2		4	28.3	even	6
1456.2.s.o.1121.2		4	364.3	even	6
8281.2.a.r.1.2		2	91.74	even	3
8281.2.a.t.1.1		2	91.4	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)

\(f(q)\)	\(=\)	\(q+1.73205 q^{2} +(1.36603 + 2.36603i) q^{3} +1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(2.36603 + 4.09808i) q^{6} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})\)	\(q+1.73205 q^{2} +(1.36603 + 2.36603i) q^{3} +1.00000 q^{4} +(0.866025 + 1.50000i) q^{5} +(2.36603 + 4.09808i) q^{6} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-0.633975 - 1.09808i) q^{11} +(1.36603 + 2.36603i) q^{12} +(-3.59808 + 0.232051i) q^{13} +(-2.36603 + 4.09808i) q^{15} -5.00000 q^{16} +7.73205 q^{17} +(-3.86603 + 6.69615i) q^{18} +(1.00000 - 1.73205i) q^{19} +(0.866025 + 1.50000i) q^{20} +(-1.09808 - 1.90192i) q^{22} +4.73205 q^{23} +(-2.36603 - 4.09808i) q^{24} +(1.00000 - 1.73205i) q^{25} +(-6.23205 + 0.401924i) q^{26} -4.00000 q^{27} +(1.50000 - 2.59808i) q^{29} +(-4.09808 + 7.09808i) q^{30} +(2.09808 - 3.63397i) q^{31} -5.19615 q^{32} +(1.73205 - 3.00000i) q^{33} +13.3923 q^{34} +(-2.23205 + 3.86603i) q^{36} -7.00000 q^{37} +(1.73205 - 3.00000i) q^{38} +(-5.46410 - 8.19615i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(-2.59808 + 4.50000i) q^{41} +(0.0980762 + 0.169873i) q^{43} +(-0.633975 - 1.09808i) q^{44} -7.73205 q^{45} +8.19615 q^{46} +(6.46410 + 11.1962i) q^{47} +(-6.83013 - 11.8301i) q^{48} +(1.73205 - 3.00000i) q^{50} +(10.5622 + 18.2942i) q^{51} +(-3.59808 + 0.232051i) q^{52} +(4.96410 - 8.59808i) q^{53} -6.92820 q^{54} +(1.09808 - 1.90192i) q^{55} +5.46410 q^{57} +(2.59808 - 4.50000i) q^{58} -7.26795 q^{59} +(-2.36603 + 4.09808i) q^{60} +(-2.40192 + 4.16025i) q^{61} +(3.63397 - 6.29423i) q^{62} +1.00000 q^{64} +(-3.46410 - 5.19615i) q^{65} +(3.00000 - 5.19615i) q^{66} +(3.09808 + 5.36603i) q^{67} +7.73205 q^{68} +(6.46410 + 11.1962i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(3.86603 - 6.69615i) q^{72} +(-1.59808 + 2.76795i) q^{73} -12.1244 q^{74} +5.46410 q^{75} +(1.00000 - 1.73205i) q^{76} +(-9.46410 - 14.1962i) q^{78} +(-8.09808 - 14.0263i) q^{79} +(-4.33013 - 7.50000i) q^{80} +(1.23205 + 2.13397i) q^{81} +(-4.50000 + 7.79423i) q^{82} +2.19615 q^{83} +(6.69615 + 11.5981i) q^{85} +(0.169873 + 0.294229i) q^{86} +8.19615 q^{87} +(1.09808 + 1.90192i) q^{88} -12.9282 q^{89} -13.3923 q^{90} +4.73205 q^{92} +11.4641 q^{93} +(11.1962 + 19.3923i) q^{94} +3.46410 q^{95} +(-7.09808 - 12.2942i) q^{96} +(3.19615 + 5.53590i) q^{97} +5.66025 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

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