LMFDB - Embedded newform 637.2.g.b.263.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (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:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.1
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.b.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30902 + 2.26728i) q^{2} -2.61803 q^{3} +(-2.42705 - 4.20378i) q^{4} +(-1.30902 - 2.26728i) q^{5} +(3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q+(-1.30902 + 2.26728i) q^{2} -2.61803 q^{3} +(-2.42705 - 4.20378i) q^{4} +(-1.30902 - 2.26728i) q^{5} +(3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +3.85410 q^{9} +6.85410 q^{10} +1.85410 q^{11} +(6.35410 + 11.0056i) q^{12} +(-2.50000 - 2.59808i) q^{13} +(3.42705 + 5.93583i) q^{15} +(-4.92705 + 8.53390i) q^{16} +(0.736068 + 1.27491i) q^{17} +(-5.04508 + 8.73834i) q^{18} -1.85410 q^{19} +(-6.35410 + 11.0056i) q^{20} +(-2.42705 + 4.20378i) q^{22} +(2.23607 - 3.87298i) q^{23} -19.5623 q^{24} +(-0.927051 + 1.60570i) q^{25} +(9.16312 - 2.26728i) q^{26} -2.23607 q^{27} +(-3.54508 - 6.14027i) q^{29} -17.9443 q^{30} +(2.35410 - 4.07742i) q^{31} +(-5.42705 - 9.39993i) q^{32} -4.85410 q^{33} -3.85410 q^{34} +(-9.35410 - 16.2018i) q^{36} +(-2.00000 + 3.46410i) q^{37} +(2.42705 - 4.20378i) q^{38} +(6.54508 + 6.80185i) q^{39} +(-9.78115 - 16.9415i) q^{40} +(-0.381966 - 0.661585i) q^{41} +(-6.28115 + 10.8793i) q^{43} +(-4.50000 - 7.79423i) q^{44} +(-5.04508 - 8.73834i) q^{45} +(5.85410 + 10.1396i) q^{46} +(1.11803 + 1.93649i) q^{47} +(12.8992 - 22.3420i) q^{48} +(-2.42705 - 4.20378i) q^{50} +(-1.92705 - 3.33775i) q^{51} +(-4.85410 + 16.8151i) q^{52} +(-1.88197 + 3.25966i) q^{53} +(2.92705 - 5.06980i) q^{54} +(-2.42705 - 4.20378i) q^{55} +4.85410 q^{57} +18.5623 q^{58} +(1.11803 + 1.93649i) q^{59} +(16.6353 - 28.8131i) q^{60} -6.00000 q^{61} +(6.16312 + 10.6748i) q^{62} +8.70820 q^{64} +(-2.61803 + 9.06914i) q^{65} +(6.35410 - 11.0056i) q^{66} -12.7082 q^{67} +(3.57295 - 6.18853i) q^{68} +(-5.85410 + 10.1396i) q^{69} +(7.09017 - 12.2805i) q^{71} +28.7984 q^{72} +(1.00000 - 1.73205i) q^{73} +(-5.23607 - 9.06914i) q^{74} +(2.42705 - 4.20378i) q^{75} +(4.50000 + 7.79423i) q^{76} +(-23.9894 + 5.93583i) q^{78} +(-2.00000 - 3.46410i) q^{79} +25.7984 q^{80} -5.70820 q^{81} +2.00000 q^{82} +6.70820 q^{83} +(1.92705 - 3.33775i) q^{85} +(-16.4443 - 28.4823i) q^{86} +(9.28115 + 16.0754i) q^{87} +13.8541 q^{88} +(-2.45492 + 4.25204i) q^{89} +26.4164 q^{90} -21.7082 q^{92} +(-6.16312 + 10.6748i) q^{93} -5.85410 q^{94} +(2.42705 + 4.20378i) q^{95} +(14.2082 + 24.6093i) q^{96} +(-9.42705 + 16.3281i) q^{97} +7.14590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 6 q^{3} - 3 q^{4} - 3 q^{5} + 7 q^{6} + 12 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - 6 * q^3 - 3 * q^4 - 3 * q^5 + 7 * q^6 + 12 * q^8 + 2 * q^9	$ 4 q - 3 q^{2} - 6 q^{3} - 3 q^{4} - 3 q^{5} + 7 q^{6} + 12 q^{8} + 2 q^{9} + 14 q^{10} - 6 q^{11} + 12 q^{12} - 10 q^{13} + 7 q^{15} - 13 q^{16} - 6 q^{17} - 9 q^{18} + 6 q^{19} - 12 q^{20} - 3 q^{22} - 38 q^{24} + 3 q^{25} + 21 q^{26} - 3 q^{29} - 36 q^{30} - 4 q^{31} - 15 q^{32} - 6 q^{33} - 2 q^{34} - 24 q^{36} - 8 q^{37} + 3 q^{38} + 15 q^{39} - 19 q^{40} - 6 q^{41} - 5 q^{43} - 18 q^{44} - 9 q^{45} + 10 q^{46} + 27 q^{48} - 3 q^{50} - q^{51} - 6 q^{52} - 12 q^{53} + 5 q^{54} - 3 q^{55} + 6 q^{57} + 34 q^{58} + 33 q^{60} - 24 q^{61} + 9 q^{62} + 8 q^{64} - 6 q^{65} + 12 q^{66} - 24 q^{67} + 21 q^{68} - 10 q^{69} + 6 q^{71} + 66 q^{72} + 4 q^{73} - 12 q^{74} + 3 q^{75} + 18 q^{76} - 49 q^{78} - 8 q^{79} + 54 q^{80} + 4 q^{81} + 8 q^{82} + q^{85} - 30 q^{86} + 17 q^{87} + 42 q^{88} - 21 q^{89} + 52 q^{90} - 60 q^{92} - 9 q^{93} - 10 q^{94} + 3 q^{95} + 30 q^{96} - 31 q^{97} + 42 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - 6 * q^3 - 3 * q^4 - 3 * q^5 + 7 * q^6 + 12 * q^8 + 2 * q^9 + 14 * q^10 - 6 * q^11 + 12 * q^12 - 10 * q^13 + 7 * q^15 - 13 * q^16 - 6 * q^17 - 9 * q^18 + 6 * q^19 - 12 * q^20 - 3 * q^22 - 38 * q^24 + 3 * q^25 + 21 * q^26 - 3 * q^29 - 36 * q^30 - 4 * q^31 - 15 * q^32 - 6 * q^33 - 2 * q^34 - 24 * q^36 - 8 * q^37 + 3 * q^38 + 15 * q^39 - 19 * q^40 - 6 * q^41 - 5 * q^43 - 18 * q^44 - 9 * q^45 + 10 * q^46 + 27 * q^48 - 3 * q^50 - q^51 - 6 * q^52 - 12 * q^53 + 5 * q^54 - 3 * q^55 + 6 * q^57 + 34 * q^58 + 33 * q^60 - 24 * q^61 + 9 * q^62 + 8 * q^64 - 6 * q^65 + 12 * q^66 - 24 * q^67 + 21 * q^68 - 10 * q^69 + 6 * q^71 + 66 * q^72 + 4 * q^73 - 12 * q^74 + 3 * q^75 + 18 * q^76 - 49 * q^78 - 8 * q^79 + 54 * q^80 + 4 * q^81 + 8 * q^82 + q^85 - 30 * q^86 + 17 * q^87 + 42 * q^88 - 21 * q^89 + 52 * q^90 - 60 * q^92 - 9 * q^93 - 10 * q^94 + 3 * q^95 + 30 * q^96 - 31 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.30902	+	2.26728i	−0.925615	+	1.60321i	−0.135045	+	0.990839i	$0.543118\pi$
$2$	−1.30902	+	2.26728i	−0.925615	+	1.60321i	−0.790569	+	0.612372i	$0.790215\pi$
$3$	−2.61803			−1.51152			−0.755761	−	0.654847i	$-0.772733\pi$
$3$	−2.61803			−1.51152			−0.755761	+	0.654847i	$0.772733\pi$
$4$	−2.42705	−	4.20378i	−1.21353	−	2.10189i
$5$	−1.30902	−	2.26728i	−0.585410	−	1.01396i	−0.994824	−	0.101611i	$-0.967600\pi$
$5$	−1.30902	−	2.26728i	−0.585410	−	1.01396i	0.409414	−	0.912349i	$-0.365733\pi$
$6$	3.42705	−	5.93583i	1.39909	−	2.42329i
$7$		0			0
$7$		0			0
$8$	7.47214			2.64180
$9$	3.85410			1.28470
$10$	6.85410			2.16746
$11$	1.85410			0.559033			0.279516	−	0.960141i	$-0.409826\pi$
$11$	1.85410			0.559033			0.279516	+	0.960141i	$0.409826\pi$
$12$	6.35410	+	11.0056i	1.83427	+	3.17705i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$13$	−2.50000	−	2.59808i	−0.693375	−	0.720577i
$14$		0			0
$15$	3.42705	+	5.93583i	0.884861	+	1.53262i
$16$	−4.92705	+	8.53390i	−1.23176	+	2.13348i
$17$	0.736068	+	1.27491i	0.178523	+	0.309210i	0.941375	−	0.337363i	$-0.109535\pi$
$17$	0.736068	+	1.27491i	0.178523	+	0.309210i	−0.762852	+	0.646573i	$0.776202\pi$
$18$	−5.04508	+	8.73834i	−1.18914	+	2.05965i
$19$	−1.85410			−0.425360			−0.212680	−	0.977122i	$-0.568219\pi$
$19$	−1.85410			−0.425360			−0.212680	+	0.977122i	$0.568219\pi$
$20$	−6.35410	+	11.0056i	−1.42082	+	2.46093i
$21$		0			0
$22$	−2.42705	+	4.20378i	−0.517449	+	0.896248i
$23$	2.23607	−	3.87298i	0.466252	−	0.807573i	−0.533005	−	0.846112i	$-0.678937\pi$
$23$	2.23607	−	3.87298i	0.466252	−	0.807573i	0.999257	+	0.0385394i	$0.0122705\pi$
$24$	−19.5623			−3.99314
$25$	−0.927051	+	1.60570i	−0.185410	+	0.321140i
$26$	9.16312	−	2.26728i	1.79704	−	0.444651i
$27$	−2.23607			−0.430331
$28$		0			0
$29$	−3.54508	−	6.14027i	−0.658306	−	1.14022i	−0.981054	−	0.193734i	$-0.937940\pi$
$29$	−3.54508	−	6.14027i	−0.658306	−	1.14022i	0.322748	−	0.946485i	$-0.395393\pi$
$30$	−17.9443			−3.27616
$31$	2.35410	−	4.07742i	0.422809	−	0.732327i	−0.573404	−	0.819273i	$-0.694377\pi$
$31$	2.35410	−	4.07742i	0.422809	−	0.732327i	0.996213	+	0.0869459i	$0.0277107\pi$
$32$	−5.42705	−	9.39993i	−0.959376	−	1.66169i
$33$	−4.85410			−0.844991
$34$	−3.85410			−0.660973
$35$		0			0
$36$	−9.35410	−	16.2018i	−1.55902	−	2.70030i
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$	2.42705	−	4.20378i	0.393720	−	0.681942i
$39$	6.54508	+	6.80185i	1.04805	+	1.08917i
$40$	−9.78115	−	16.9415i	−1.54654	−	2.67868i
$41$	−0.381966	−	0.661585i	−0.0596531	−	0.103322i	0.834657	−	0.550771i	$-0.185666\pi$
$41$	−0.381966	−	0.661585i	−0.0596531	−	0.103322i	−0.894310	+	0.447449i	$0.852333\pi$
$42$		0			0
$43$	−6.28115	+	10.8793i	−0.957867	+	1.65907i	−0.230200	+	0.973143i	$0.573938\pi$
$43$	−6.28115	+	10.8793i	−0.957867	+	1.65907i	−0.727667	+	0.685931i	$0.759395\pi$
$44$	−4.50000	−	7.79423i	−0.678401	−	1.17502i
$45$	−5.04508	−	8.73834i	−0.752077	−	1.30264i
$46$	5.85410	+	10.1396i	0.863140	+	1.49500i
$47$	1.11803	+	1.93649i	0.163082	+	0.282466i	0.935973	−	0.352073i	$-0.114523\pi$
$47$	1.11803	+	1.93649i	0.163082	+	0.282466i	−0.772890	+	0.634539i	$0.781190\pi$
$48$	12.8992	−	22.3420i	1.86184	−	3.22480i
$49$		0			0
$50$	−2.42705	−	4.20378i	−0.343237	−	0.594504i
$51$	−1.92705	−	3.33775i	−0.269841	−	0.467379i
$52$	−4.85410	+	16.8151i	−0.673143	+	2.33184i
$53$	−1.88197	+	3.25966i	−0.258508	+	0.447749i	−0.965842	−	0.259130i	$-0.916564\pi$
$53$	−1.88197	+	3.25966i	−0.258508	+	0.447749i	0.707334	+	0.706879i	$0.249897\pi$
$54$	2.92705	−	5.06980i	0.398321	−	0.689913i
$55$	−2.42705	−	4.20378i	−0.327263	−	0.566837i
$56$		0			0
$57$	4.85410			0.642942
$58$	18.5623			2.43735
$59$	1.11803	+	1.93649i	0.145556	+	0.252110i	0.929580	−	0.368620i	$-0.120170\pi$
$59$	1.11803	+	1.93649i	0.145556	+	0.252110i	−0.784024	+	0.620730i	$0.786836\pi$
$60$	16.6353	−	28.8131i	2.14760	−	3.71976i
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$	6.16312	+	10.6748i	0.782717	+	1.35571i
$63$		0			0
$64$	8.70820			1.08853
$65$	−2.61803	+	9.06914i	−0.324727	+	1.12489i
$66$	6.35410	−	11.0056i	0.782136	−	1.35470i
$67$	−12.7082			−1.55255			−0.776277	−	0.630392i	$-0.782894\pi$
$67$	−12.7082			−1.55255			−0.776277	+	0.630392i	$0.782894\pi$
$68$	3.57295	−	6.18853i	0.433284	−	0.750469i
$69$	−5.85410	+	10.1396i	−0.704751	+	1.22066i
$70$		0			0
$71$	7.09017	−	12.2805i	0.841448	−	1.45743i	−0.0472218	−	0.998884i	$-0.515037\pi$
$71$	7.09017	−	12.2805i	0.841448	−	1.45743i	0.888670	−	0.458547i	$-0.151630\pi$
$72$	28.7984			3.39392
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	−5.23607	−	9.06914i	−0.608681	−	1.05427i
$75$	2.42705	−	4.20378i	0.280252	−	0.485410i
$76$	4.50000	+	7.79423i	0.516185	+	0.894059i
$77$		0			0
$78$	−23.9894	+	5.93583i	−2.71626	+	0.672100i
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$	25.7984			2.88435
$81$	−5.70820			−0.634245
$82$	2.00000			0.220863
$83$	6.70820			0.736321			0.368161	−	0.929762i	$-0.379988\pi$
$83$	6.70820			0.736321			0.368161	+	0.929762i	$0.379988\pi$
$84$		0			0
$85$	1.92705	−	3.33775i	0.209018	−	0.362030i
$86$	−16.4443	−	28.4823i	−1.77323	−	3.07133i
$87$	9.28115	+	16.0754i	0.995044	+	1.72347i
$88$	13.8541			1.47685
$89$	−2.45492	+	4.25204i	−0.260220	+	0.450715i	−0.966300	−	0.257417i	$-0.917129\pi$
$89$	−2.45492	+	4.25204i	−0.260220	+	0.450715i	0.706080	+	0.708132i	$0.250462\pi$
$90$	26.4164			2.78453
$91$		0			0
$92$	−21.7082			−2.26324
$93$	−6.16312	+	10.6748i	−0.639086	+	1.10693i
$94$	−5.85410			−0.603805
$95$	2.42705	+	4.20378i	0.249010	+	0.431298i
$96$	14.2082	+	24.6093i	1.45012	+	2.51168i
$97$	−9.42705	+	16.3281i	−0.957172	+	1.65787i	−0.227854	+	0.973695i	$0.573171\pi$
$97$	−9.42705	+	16.3281i	−0.957172	+	1.65787i	−0.729318	+	0.684175i	$0.760162\pi$
$98$		0			0
$99$	7.14590			0.718190
$100$	9.00000			0.900000
$101$	−11.5623			−1.15049			−0.575246	−	0.817980i	$-0.695094\pi$
$101$	−11.5623			−1.15049			−0.575246	+	0.817980i	$0.695094\pi$
$102$	10.0902			0.999076
$103$	4.35410	+	7.54153i	0.429022	+	0.743089i	0.996787	−	0.0801026i	$-0.0255248\pi$
$103$	4.35410	+	7.54153i	0.429022	+	0.743089i	−0.567764	+	0.823191i	$0.692191\pi$
$104$	−18.6803	−	19.4132i	−1.83176	−	1.90362i
$105$		0			0
$106$	−4.92705	−	8.53390i	−0.478557	−	0.828886i
$107$	1.69098	−	2.92887i	0.163473	−	0.283144i	−0.772639	−	0.634846i	$-0.781064\pi$
$107$	1.69098	−	2.92887i	0.163473	−	0.283144i	0.936112	+	0.351702i	$0.114397\pi$
$108$	5.42705	+	9.39993i	0.522218	+	0.904508i
$109$	1.35410	−	2.34537i	0.129699	−	0.224646i	−0.793861	−	0.608100i	$-0.791932\pi$
$109$	1.35410	−	2.34537i	0.129699	−	0.224646i	0.923560	+	0.383454i	$0.125265\pi$
$110$	12.7082			1.21168
$111$	5.23607	−	9.06914i	0.496986	−	0.860804i
$112$		0			0
$113$	−0.736068	+	1.27491i	−0.0692435	+	0.119933i	−0.898568	−	0.438833i	$-0.855392\pi$
$113$	−0.736068	+	1.27491i	−0.0692435	+	0.119933i	0.829325	+	0.558766i	$0.188725\pi$
$114$	−6.35410	+	11.0056i	−0.595116	+	1.03077i
$115$	−11.7082			−1.09180
$116$	−17.2082	+	29.8055i	−1.59774	+	2.76737i
$117$	−9.63525	−	10.0133i	−0.890780	−	0.925725i
$118$	−5.85410			−0.538914
$119$		0			0
$120$	25.6074	+	44.3533i	2.33762	+	4.04888i
$121$	−7.56231			−0.687482
$122$	7.85410	−	13.6037i	0.711077	−	1.23162i
$123$	1.00000	+	1.73205i	0.0901670	+	0.156174i
$124$	−22.8541			−2.05236
$125$	−8.23607			−0.736656
$126$		0			0
$127$	10.4271	+	18.0602i	0.925251	+	1.60258i	0.791157	+	0.611613i	$0.209479\pi$
$127$	10.4271	+	18.0602i	0.925251	+	1.60258i	0.134094	+	0.990969i	$0.457187\pi$
$128$	−0.545085	+	0.944115i	−0.0481792	+	0.0834488i
$129$	16.4443	−	28.4823i	1.44784	−	2.50773i
$130$	−17.1353	−	17.8075i	−1.50286	−	1.56182i
$131$	7.66312	+	13.2729i	0.669530	+	1.15966i	0.978036	+	0.208437i	$0.0668377\pi$
$131$	7.66312	+	13.2729i	0.669530	+	1.15966i	−0.308506	+	0.951222i	$0.599829\pi$
$132$	11.7812	+	20.4056i	1.02542	+	1.77608i
$133$		0			0
$134$	16.6353	−	28.8131i	1.43707	−	2.48907i
$135$	2.92705	+	5.06980i	0.251920	+	0.436339i
$136$	5.50000	+	9.52628i	0.471621	+	0.816872i
$137$	1.30902	+	2.26728i	0.111837	+	0.193707i	0.916511	−	0.400010i	$-0.130993\pi$
$137$	1.30902	+	2.26728i	0.111837	+	0.193707i	−0.804674	+	0.593717i	$0.797660\pi$
$138$	−15.3262	−	26.5458i	−1.30466	−	2.25973i
$139$	−2.28115	+	3.95107i	−0.193485	+	0.335126i	−0.946403	−	0.322989i	$-0.895312\pi$
$139$	−2.28115	+	3.95107i	−0.193485	+	0.335126i	0.752918	+	0.658114i	$0.228646\pi$
$140$		0			0
$141$	−2.92705	−	5.06980i	−0.246502	−	0.426954i
$142$	18.5623	+	32.1509i	1.55771	+	2.69804i
$143$	−4.63525	−	4.81710i	−0.387619	−	0.402826i
$144$	−18.9894	+	32.8905i	−1.58245	+	2.74088i
$145$	−9.28115	+	16.0754i	−0.770758	+	1.33499i
$146$	2.61803	+	4.53457i	0.216670	+	0.375284i
$147$		0			0
$148$	19.4164			1.59602
$149$	1.85410			0.151894			0.0759470	−	0.997112i	$-0.475802\pi$
$149$	1.85410			0.151894			0.0759470	+	0.997112i	$0.475802\pi$
$150$	6.35410	+	11.0056i	0.518810	+	0.898606i
$151$	0.645898	−	1.11873i	0.0525624	−	0.0910408i	−0.838547	−	0.544829i	$-0.816594\pi$
$151$	0.645898	−	1.11873i	0.0525624	−	0.0910408i	0.891109	+	0.453788i	$0.149928\pi$
$152$	−13.8541			−1.12372
$153$	2.83688	+	4.91362i	0.229348	+	0.397243i
$154$		0			0
$155$	−12.3262			−0.990067
$156$	12.7082	−	44.0225i	1.01747	−	3.52462i
$157$	−7.42705	+	12.8640i	−0.592743	+	1.02666i	0.401118	+	0.916026i	$0.368622\pi$
$157$	−7.42705	+	12.8640i	−0.592743	+	1.02666i	−0.993861	+	0.110635i	$0.964712\pi$
$158$	10.4721			0.833118
$159$	4.92705	−	8.53390i	0.390741	−	0.676783i
$160$	−14.2082	+	24.6093i	−1.12326	+	1.94554i
$161$		0			0
$162$	7.47214	−	12.9421i	0.587066	−	1.01683i
$163$	−3.70820			−0.290449			−0.145224	−	0.989399i	$-0.546390\pi$
$163$	−3.70820			−0.290449			−0.145224	+	0.989399i	$0.546390\pi$
$164$	−1.85410	+	3.21140i	−0.144781	+	0.250768i
$165$	6.35410	+	11.0056i	0.494666	+	0.856787i
$166$	−8.78115	+	15.2094i	−0.681550	+	1.18048i
$167$	−7.11803	−	12.3288i	−0.550810	−	0.954031i	−0.998216	−	0.0597001i	$-0.980986\pi$
$167$	−7.11803	−	12.3288i	−0.550810	−	0.954031i	0.447406	−	0.894331i	$-0.352348\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	5.04508	+	8.73834i	0.386940	+	0.670200i
$171$	−7.14590			−0.546460
$172$	60.9787			4.64958
$173$	−9.00000			−0.684257			−0.342129	−	0.939653i	$-0.611148\pi$
$173$	−9.00000			−0.684257			−0.342129	+	0.939653i	$0.611148\pi$
$174$	−48.5967			−3.68411
$175$		0			0
$176$	−9.13525	+	15.8227i	−0.688596	+	1.19268i
$177$	−2.92705	−	5.06980i	−0.220011	−	0.381070i
$178$	−6.42705	−	11.1320i	−0.481728	−	0.834377i
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$	−24.4894	+	42.4168i	−1.82533	+	3.16156i
$181$	9.70820			0.721605			0.360803	−	0.932642i	$-0.382503\pi$
$181$	9.70820			0.721605			0.360803	+	0.932642i	$0.382503\pi$
$182$		0			0
$183$	15.7082			1.16118
$184$	16.7082	−	28.9395i	1.23175	−	2.13345i
$185$	10.4721			0.769927
$186$	−16.1353	−	27.9471i	−1.18309	−	2.04918i
$187$	1.36475	+	2.36381i	0.0998000	+	0.172859i
$188$	5.42705	−	9.39993i	0.395808	−	0.685560i
$189$		0			0
$190$	−12.7082			−0.921950
$191$	21.3820			1.54714			0.773572	−	0.633708i	$-0.218468\pi$
$191$	21.3820			1.54714			0.773572	+	0.633708i	$0.218468\pi$
$192$	−22.7984			−1.64533
$193$	−6.00000			−0.431889			−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000			−0.431889			−0.215945	+	0.976406i	$0.569283\pi$
$194$	−24.6803	−	42.7476i	−1.77195	−	3.06910i
$195$	6.85410	−	23.7433i	0.490832	−	1.70029i
$196$		0			0
$197$	8.39919	+	14.5478i	0.598417	+	1.03649i	0.993055	+	0.117652i	$0.0375368\pi$
$197$	8.39919	+	14.5478i	0.598417	+	1.03649i	−0.394638	+	0.918837i	$0.629130\pi$
$198$	−9.35410	+	16.2018i	−0.664767	+	1.15141i
$199$	12.2082	+	21.1452i	0.865417	+	1.49895i	0.866633	+	0.498946i	$0.166280\pi$
$199$	12.2082	+	21.1452i	0.865417	+	1.49895i	−0.00121626	+	0.999999i	$0.500387\pi$
$200$	−6.92705	+	11.9980i	−0.489816	+	0.848387i
$201$	33.2705			2.34672
$202$	15.1353	−	26.2150i	1.06491	−	1.84448i
$203$		0			0
$204$	−9.35410	+	16.2018i	−0.654918	+	1.13435i
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$	−22.7984			−1.58844
$207$	8.61803	−	14.9269i	0.598995	−	1.03749i
$208$	34.4894	−	8.53390i	2.39141	−	0.591720i
$209$	−3.43769			−0.237790
$210$		0			0
$211$	−2.35410	−	4.07742i	−0.162063	−	0.280701i	0.773545	−	0.633741i	$-0.218481\pi$
$211$	−2.35410	−	4.07742i	−0.162063	−	0.280701i	−0.935608	+	0.353039i	$0.885148\pi$
$212$	18.2705			1.25482
$213$	−18.5623	+	32.1509i	−1.27187	+	2.20294i
$214$	4.42705	+	7.66788i	0.302627	+	0.524165i
$215$	32.8885			2.24298
$216$	−16.7082			−1.13685
$217$		0			0
$218$	3.54508	+	6.14027i	0.240103	+	0.415871i
$219$	−2.61803	+	4.53457i	−0.176910	+	0.306418i
$220$	−11.7812	+	20.4056i	−0.794285	+	1.37574i
$221$	1.47214	−	5.09963i	0.0990266	−	0.343038i
$222$	13.7082	+	23.7433i	0.920034	+	1.59355i
$223$	−10.1353	−	17.5548i	−0.678707	−	1.17555i	−0.975371	−	0.220573i	$-0.929207\pi$
$223$	−10.1353	−	17.5548i	−0.678707	−	1.17555i	0.296664	−	0.954982i	$-0.404126\pi$
$224$		0			0
$225$	−3.57295	+	6.18853i	−0.238197	+	0.412569i
$226$	−1.92705	−	3.33775i	−0.128186	−	0.222024i
$227$	−0.736068	−	1.27491i	−0.0488545	−	0.0846186i	0.840564	−	0.541712i	$-0.182224\pi$
$227$	−0.736068	−	1.27491i	−0.0488545	−	0.0846186i	−0.889419	+	0.457094i	$0.848890\pi$
$228$	−11.7812	−	20.4056i	−0.780226	−	1.35139i
$229$	6.56231	+	11.3662i	0.433649	+	0.751103i	0.997184	−	0.0749895i	$-0.0238923\pi$
$229$	6.56231	+	11.3662i	0.433649	+	0.751103i	−0.563535	+	0.826092i	$0.690559\pi$
$230$	15.3262	−	26.5458i	1.01058	−	1.75038i
$231$		0			0
$232$	−26.4894	−	45.8809i	−1.73911	−	3.01223i
$233$	−1.30902	−	2.26728i	−0.0857566	−	0.148535i	0.819957	−	0.572425i	$-0.193997\pi$
$233$	−1.30902	−	2.26728i	−0.0857566	−	0.148535i	−0.905713	+	0.423891i	$0.860664\pi$
$234$	35.3156	−	8.73834i	2.30865	−	0.571243i
$235$	2.92705	−	5.06980i	0.190940	−	0.330717i
$236$	5.42705	−	9.39993i	0.353271	−	0.611883i
$237$	5.23607	+	9.06914i	0.340119	+	0.589104i
$238$		0			0
$239$	−24.7082			−1.59824			−0.799120	−	0.601171i	$-0.794701\pi$
$239$	−24.7082			−1.59824			−0.799120	+	0.601171i	$0.794701\pi$
$240$	−67.5410			−4.35975
$241$	−12.2812	−	21.2716i	−0.791099	−	1.37022i	−0.925287	−	0.379267i	$-0.876176\pi$
$241$	−12.2812	−	21.2716i	−0.791099	−	1.37022i	0.134189	−	0.990956i	$-0.457157\pi$
$242$	9.89919	−	17.1459i	0.636344	−	1.10218i
$243$	21.6525			1.38901
$244$	14.5623	+	25.2227i	0.932256	+	1.61471i
$245$		0			0
$246$	−5.23607			−0.333840
$247$	4.63525	+	4.81710i	0.294934	+	0.306505i
$248$	17.5902	−	30.4671i	1.11698	−	1.93466i
$249$	−17.5623			−1.11297
$250$	10.7812	−	18.6735i	0.681860	−	1.18102i
$251$	−0.381966	+	0.661585i	−0.0241095	+	0.0417588i	−0.877828	−	0.478975i	$-0.841008\pi$
$251$	−0.381966	+	0.661585i	−0.0241095	+	0.0417588i	0.853719	+	0.520734i	$0.174342\pi$
$252$		0			0
$253$	4.14590	−	7.18091i	0.260650	−	0.451460i
$254$	−54.5967			−3.42570
$255$	−5.04508	+	8.73834i	−0.315935	+	0.547216i
$256$	7.28115	+	12.6113i	0.455072	+	0.788208i
$257$	−8.37132	+	14.4996i	−0.522189	+	0.904457i	0.477478	+	0.878644i	$0.341551\pi$
$257$	−8.37132	+	14.4996i	−0.522189	+	0.904457i	−0.999667	+	0.0258138i	$0.991782\pi$
$258$	43.0517	+	74.5677i	2.68028	+	4.64238i
$259$		0			0
$260$	44.4787	−	11.0056i	2.75845	−	0.682540i
$261$	−13.6631	−	23.6652i	−0.845726	−	1.46484i
$262$	−40.1246			−2.47891
$263$	9.00000			0.554964			0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000			0.554964			0.277482	+	0.960731i	$0.410500\pi$
$264$	−36.2705			−2.23230
$265$	9.85410			0.605333
$266$		0			0
$267$	6.42705	−	11.1320i	0.393329	−	0.681266i
$268$	30.8435	+	53.4224i	1.88406	+	3.26329i
$269$	14.3713	+	24.8919i	0.876235	+	1.51768i	0.855441	+	0.517900i	$0.173286\pi$
$269$	14.3713	+	24.8919i	0.876235	+	1.51768i	0.0207937	+	0.999784i	$0.493381\pi$
$270$	−15.3262			−0.932725
$271$	4.20820	−	7.28882i	0.255630	−	0.442764i	−0.709436	−	0.704770i	$-0.751050\pi$
$271$	4.20820	−	7.28882i	0.255630	−	0.442764i	0.965066	+	0.262005i	$0.0843837\pi$
$272$	−14.5066			−0.879590
$273$		0			0
$274$	−6.85410			−0.414071
$275$	−1.71885	+	2.97713i	−0.103650	+	0.179528i
$276$	56.8328			3.42093
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	0.931305	−	0.364241i	$-0.118672\pi$
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	−0.781094	+	0.624413i	$0.785338\pi$
$278$	−5.97214	−	10.3440i	−0.358185	−	0.620394i
$279$	9.07295	−	15.7148i	0.543183	−	0.940821i
$280$		0			0
$281$	20.1803			1.20386			0.601929	−	0.798550i	$-0.294399\pi$
$281$	20.1803			1.20386			0.601929	+	0.798550i	$0.294399\pi$
$282$	15.3262			0.912664
$283$	13.4164			0.797523			0.398761	−	0.917055i	$-0.369440\pi$
$283$	13.4164			0.797523			0.398761	+	0.917055i	$0.369440\pi$
$284$	−68.8328			−4.08448
$285$	−6.35410	−	11.0056i	−0.376385	−	0.651917i
$286$	16.9894	−	4.20378i	1.00460	−	0.248574i
$287$		0			0
$288$	−20.9164	−	36.2283i	−1.23251	−	2.13477i
$289$	7.41641	−	12.8456i	0.436259	−	0.755623i
$290$	−24.2984	−	42.0860i	−1.42685	−	2.47138i
$291$	24.6803	−	42.7476i	1.44679	−	2.50591i
$292$	−9.70820			−0.568130
$293$	3.38197	−	5.85774i	0.197577	−	0.342213i	−0.750166	−	0.661250i	$-0.770026\pi$
$293$	3.38197	−	5.85774i	0.197577	−	0.342213i	0.947742	+	0.319037i	$0.103360\pi$
$294$		0			0
$295$	2.92705	−	5.06980i	0.170419	−	0.295175i
$296$	−14.9443	+	25.8842i	−0.868618	+	1.50449i
$297$	−4.14590			−0.240569
$298$	−2.42705	+	4.20378i	−0.140595	+	0.243518i
$299$	−15.6525	+	3.87298i	−0.905206	+	0.223980i
$300$	−23.5623			−1.36037
$301$		0			0
$302$	1.69098	+	2.92887i	0.0973051	+	0.168537i
$303$	30.2705			1.73900
$304$	9.13525	−	15.8227i	0.523943	−	0.907496i
$305$	7.85410	+	13.6037i	0.449725	+	0.778946i
$306$	−14.8541			−0.849152
$307$	−4.85410			−0.277038			−0.138519	−	0.990360i	$-0.544234\pi$
$307$	−4.85410			−0.277038			−0.138519	+	0.990360i	$0.544234\pi$
$308$		0			0
$309$	−11.3992	−	19.7440i	−0.648477	−	1.12320i
$310$	16.1353	−	27.9471i	0.916421	−	1.58729i
$311$	−1.66312	+	2.88061i	−0.0943068	+	0.163344i	−0.909319	−	0.416099i	$-0.863397\pi$
$311$	−1.66312	+	2.88061i	−0.0943068	+	0.163344i	0.815012	+	0.579444i	$0.196730\pi$
$312$	48.9058	+	50.8244i	2.76874	+	2.87736i
$313$	−12.5623	−	21.7586i	−0.710064	−	1.22987i	−0.964833	−	0.262864i	$-0.915333\pi$
$313$	−12.5623	−	21.7586i	−0.710064	−	1.22987i	0.254769	−	0.967002i	$-0.418000\pi$
$314$	−19.4443	−	33.6785i	−1.09730	−	1.90059i
$315$		0			0
$316$	−9.70820	+	16.8151i	−0.546129	+	0.945923i
$317$	−13.1180	−	22.7211i	−0.736782	−	1.27614i	−0.953937	−	0.300007i	$-0.903011\pi$
$317$	−13.1180	−	22.7211i	−0.736782	−	1.27614i	0.217155	−	0.976137i	$-0.430322\pi$
$318$	12.8992	+	22.3420i	0.723350	+	1.25288i
$319$	−6.57295	−	11.3847i	−0.368014	−	0.637420i
$320$	−11.3992	−	19.7440i	−0.637234	−	1.10372i
$321$	−4.42705	+	7.66788i	−0.247094	+	0.427979i
$322$		0			0
$323$	−1.36475	−	2.36381i	−0.0759364	−	0.131526i
$324$	13.8541	+	23.9960i	0.769672	+	1.33311i
$325$	6.48936	−	1.60570i	0.359965	−	0.0890682i
$326$	4.85410	−	8.40755i	0.268844	−	0.465651i
$327$	−3.54508	+	6.14027i	−0.196044	+	0.339558i
$328$	−2.85410	−	4.94345i	−0.157591	−	0.272956i
$329$		0			0
$330$	−33.2705			−1.83148
$331$	−10.1459			−0.557669			−0.278834	−	0.960339i	$-0.589948\pi$
$331$	−10.1459			−0.557669			−0.278834	+	0.960339i	$0.589948\pi$
$332$	−16.2812	−	28.1998i	−0.893544	−	1.54766i
$333$	−7.70820	+	13.3510i	−0.422407	+	0.731630i
$334$	37.2705			2.03935
$335$	16.6353	+	28.8131i	0.908881	+	1.57423i
$336$		0			0
$337$	−11.5623			−0.629839			−0.314919	−	0.949118i	$-0.601978\pi$
$337$	−11.5623			−0.629839			−0.314919	+	0.949118i	$0.601978\pi$
$338$	−28.7984	−	18.1383i	−1.56643	−	0.986592i
$339$	1.92705	−	3.33775i	0.104663	−	0.181282i
$340$	−18.7082			−1.01459
$341$	4.36475	−	7.55996i	0.236364	−	0.409395i
$342$	9.35410	−	16.2018i	0.505812	−	0.876092i
$343$		0			0
$344$	−46.9336	+	81.2914i	−2.53049	+	4.38294i
$345$	30.6525			1.65027
$346$	11.7812	−	20.4056i	0.633359	−	1.09701i
$347$	−15.3820	−	26.6423i	−0.825747	−	1.43024i	−0.901347	−	0.433098i	$-0.857420\pi$
$347$	−15.3820	−	26.6423i	−0.825747	−	1.43024i	0.0755997	−	0.997138i	$-0.475913\pi$
$348$	45.0517	−	78.0318i	2.41502	−	4.18294i
$349$	−10.3541	−	17.9338i	−0.554242	−	0.959976i	−0.997962	−	0.0638103i	$-0.979675\pi$
$349$	−10.3541	−	17.9338i	−0.554242	−	0.959976i	0.443720	−	0.896166i	$-0.353659\pi$
$350$		0			0
$351$	5.59017	+	5.80948i	0.298381	+	0.310087i
$352$	−10.0623	−	17.4284i	−0.536323	−	0.928938i
$353$	22.1459			1.17871			0.589354	−	0.807875i	$-0.299382\pi$
$353$	22.1459			1.17871			0.589354	+	0.807875i	$0.299382\pi$
$354$	15.3262			0.814580
$355$	−37.1246			−1.97037
$356$	23.8328			1.26314
$357$		0			0
$358$	11.7812	−	20.4056i	0.622653	−	1.07847i
$359$	11.0451	+	19.1306i	0.582937	+	1.00968i	0.995129	+	0.0985799i	$0.0314300\pi$
$359$	11.0451	+	19.1306i	0.582937	+	1.00968i	−0.412192	+	0.911097i	$0.635237\pi$
$360$	−37.6976	−	65.2941i	−1.98684	−	3.44130i
$361$	−15.5623			−0.819069
$362$	−12.7082	+	22.0113i	−0.667928	+	1.15689i
$363$	19.7984			1.03915
$364$		0			0
$365$	−5.23607			−0.274068
$366$	−20.5623	+	35.6150i	−1.07481	+	1.86162i
$367$	−1.41641			−0.0739359			−0.0369679	−	0.999316i	$-0.511770\pi$
$367$	−1.41641			−0.0739359			−0.0369679	+	0.999316i	$0.511770\pi$
$368$	22.0344	+	38.1648i	1.14862	+	1.98948i
$369$	−1.47214	−	2.54981i	−0.0766363	−	0.132738i
$370$	−13.7082	+	23.7433i	−0.712656	+	1.23436i
$371$		0			0
$372$	59.8328			3.10219
$373$	−20.5623			−1.06468			−0.532338	−	0.846532i	$-0.678686\pi$
$373$	−20.5623			−1.06468			−0.532338	+	0.846532i	$0.678686\pi$
$374$	−7.14590			−0.369506
$375$	21.5623			1.11347
$376$	8.35410	+	14.4697i	0.430830	+	0.746219i
$377$	−7.09017	+	24.5611i	−0.365162	+	1.26496i
$378$		0			0
$379$	3.07295	+	5.32250i	0.157847	+	0.273399i	0.934092	−	0.357032i	$-0.116211\pi$
$379$	3.07295	+	5.32250i	0.157847	+	0.273399i	−0.776245	+	0.630431i	$0.782878\pi$
$380$	11.7812	−	20.4056i	0.604360	−	1.04678i
$381$	−27.2984	−	47.2822i	−1.39854	−	2.42234i
$382$	−27.9894	+	48.4790i	−1.43206	+	2.48040i
$383$	−21.9787			−1.12306			−0.561530	−	0.827456i	$-0.689787\pi$
$383$	−21.9787			−1.12306			−0.561530	+	0.827456i	$0.689787\pi$
$384$	1.42705	−	2.47172i	0.0728239	−	0.126135i
$385$		0			0
$386$	7.85410	−	13.6037i	0.399763	−	0.692410i
$387$	−24.2082	+	41.9298i	−1.23057	+	2.13141i
$388$	91.5197			4.64621
$389$	5.94427	−	10.2958i	0.301387	−	0.522017i	−0.675064	−	0.737759i	$-0.735884\pi$
$389$	5.94427	−	10.2958i	0.301387	−	0.522017i	0.976450	+	0.215743i	$0.0692172\pi$
$390$	44.8607	+	46.6206i	2.27161	+	2.36073i
$391$	6.58359			0.332947
$392$		0			0
$393$	−20.0623	−	34.7489i	−1.01201	−	1.75285i
$394$	−43.9787			−2.21562
$395$	−5.23607	+	9.06914i	−0.263455	+	0.456318i
$396$	−17.3435	−	30.0398i	−0.871542	−	1.50955i
$397$	1.41641			0.0710875			0.0355437	−	0.999368i	$-0.488684\pi$
$397$	1.41641			0.0710875			0.0355437	+	0.999368i	$0.488684\pi$
$398$	−63.9230			−3.20417
$399$		0			0
$400$	−9.13525	−	15.8227i	−0.456763	−	0.791136i
$401$	−17.7254	+	30.7013i	−0.885165	+	1.53315i	−0.0396416	+	0.999214i	$0.512622\pi$
$401$	−17.7254	+	30.7013i	−0.885165	+	1.53315i	−0.845524	+	0.533938i	$0.820712\pi$
$402$	−43.5517	+	75.4337i	−2.17216	+	3.76229i
$403$	−16.4787	+	4.07742i	−0.820863	+	0.203111i
$404$	28.0623	+	48.6053i	1.39615	+	2.41821i
$405$	7.47214	+	12.9421i	0.371293	+	0.643099i
$406$		0			0
$407$	−3.70820	+	6.42280i	−0.183809	+	0.318366i
$408$	−14.3992	−	24.9401i	−0.712866	−	1.23472i
$409$	−7.21885	−	12.5034i	−0.356949	−	0.618254i	0.630500	−	0.776189i	$-0.282850\pi$
$409$	−7.21885	−	12.5034i	−0.356949	−	0.618254i	−0.987450	+	0.157935i	$0.949516\pi$
$410$	−2.61803	−	4.53457i	−0.129295	−	0.223946i
$411$	−3.42705	−	5.93583i	−0.169044	−	0.292793i
$412$	21.1353	−	36.6073i	1.04126	−	1.80351i
$413$		0			0
$414$	22.5623	+	39.0791i	1.10888	+	1.92063i
$415$	−8.78115	−	15.2094i	−0.431050	−	0.746600i
$416$	−10.8541	+	37.5997i	−0.532166	+	1.84348i
$417$	5.97214	−	10.3440i	0.292457	−	0.506550i
$418$	4.50000	−	7.79423i	0.220102	−	0.381228i
$419$	5.97214	+	10.3440i	0.291758	+	0.505340i	0.974226	−	0.225576i	$-0.0724265\pi$
$419$	5.97214	+	10.3440i	0.291758	+	0.505340i	−0.682468	+	0.730916i	$0.739093\pi$
$420$		0			0
$421$	1.41641			0.0690315			0.0345157	−	0.999404i	$-0.489011\pi$
$421$	1.41641			0.0690315			0.0345157	+	0.999404i	$0.489011\pi$
$422$	12.3262			0.600032
$423$	4.30902	+	7.46344i	0.209512	+	0.362885i
$424$	−14.0623	+	24.3566i	−0.682926	+	1.18286i
$425$	−2.72949			−0.132400
$426$	−48.5967	−	84.1720i	−2.35452	−	4.07815i
$427$		0			0
$428$	−16.4164			−0.793517
$429$	12.1353	+	12.6113i	0.585896	+	0.608881i
$430$	−43.0517	+	74.5677i	−2.07614	+	3.59597i
$431$	7.79837			0.375634			0.187817	−	0.982204i	$-0.439859\pi$
$431$	7.79837			0.375634			0.187817	+	0.982204i	$0.439859\pi$
$432$	11.0172	−	19.0824i	0.530066	−	0.918102i
$433$	−0.500000	+	0.866025i	−0.0240285	+	0.0416185i	−0.877790	−	0.479046i	$-0.840983\pi$
$433$	−0.500000	+	0.866025i	−0.0240285	+	0.0416185i	0.853761	+	0.520665i	$0.174316\pi$
$434$		0			0
$435$	24.2984	−	42.0860i	1.16502	−	2.01787i
$436$	−13.1459			−0.629574
$437$	−4.14590	+	7.18091i	−0.198325	+	0.343509i
$438$	−6.85410	−	11.8717i	−0.327502	−	0.567250i
$439$	−7.42705	+	12.8640i	−0.354474	+	0.613967i	−0.987028	−	0.160550i	$-0.948673\pi$
$439$	−7.42705	+	12.8640i	−0.354474	+	0.613967i	0.632554	+	0.774516i	$0.282007\pi$
$440$	−18.1353	−	31.4112i	−0.864564	−	1.49747i
$441$		0			0
$442$	9.63525	+	10.0133i	0.458302	+	0.476282i
$443$	2.61803	+	4.53457i	0.124387	+	0.215444i	0.921493	−	0.388395i	$-0.126970\pi$
$443$	2.61803	+	4.53457i	0.124387	+	0.215444i	−0.797106	+	0.603839i	$0.793637\pi$
$444$	−50.8328			−2.41242
$445$	12.8541			0.609343
$446$	53.0689			2.51288
$447$	−4.85410			−0.229591
$448$		0			0
$449$	−9.76393	+	16.9116i	−0.460788	+	0.798109i	−0.999000	−	0.0447005i	$-0.985767\pi$
$449$	−9.76393	+	16.9116i	−0.460788	+	0.798109i	0.538212	+	0.842809i	$0.319100\pi$
$450$	−9.35410	−	16.2018i	−0.440957	−	0.763759i
$451$	−0.708204	−	1.22665i	−0.0333480	−	0.0577605i
$452$	7.14590			0.336115
$453$	−1.69098	+	2.92887i	−0.0794493	+	0.137610i
$454$	3.85410			0.180882
$455$		0			0
$456$	36.2705			1.69852
$457$	−7.70820	+	13.3510i	−0.360575	+	0.624533i	−0.988055	−	0.154098i	$-0.950753\pi$
$457$	−7.70820	+	13.3510i	−0.360575	+	0.624533i	0.627481	+	0.778632i	$0.284086\pi$
$458$	−34.3607			−1.60557
$459$	−1.64590	−	2.85078i	−0.0768239	−	0.133063i
$460$	28.4164	+	49.2187i	1.32492	+	2.29483i
$461$	6.10739	−	10.5783i	0.284450	−	0.492681i	−0.688026	−	0.725686i	$-0.741523\pi$
$461$	6.10739	−	10.5783i	0.284450	−	0.492681i	0.972476	+	0.233005i	$0.0748558\pi$
$462$		0			0
$463$	6.70820			0.311757			0.155878	−	0.987776i	$-0.450179\pi$
$463$	6.70820			0.311757			0.155878	+	0.987776i	$0.450179\pi$
$464$	69.8673			3.24351
$465$	32.2705			1.49651
$466$	6.85410			0.317510
$467$	−1.17376	−	2.03302i	−0.0543152	−	0.0940767i	0.837589	−	0.546300i	$-0.183964\pi$
$467$	−1.17376	−	2.03302i	−0.0543152	−	0.0940767i	−0.891905	+	0.452224i	$0.850631\pi$
$468$	−18.7082	+	64.8071i	−0.864787	+	2.99571i
$469$		0			0
$470$	7.66312	+	13.2729i	0.353473	+	0.612234i
$471$	19.4443	−	33.6785i	0.895945	−	1.55182i
$472$	8.35410	+	14.4697i	0.384529	+	0.666023i
$473$	−11.6459	+	20.1713i	−0.535479	+	0.927477i
$474$	−27.4164			−1.25928
$475$	1.71885	−	2.97713i	0.0788661	−	0.136600i
$476$		0			0
$477$	−7.25329	+	12.5631i	−0.332105	+	0.575223i
$478$	32.3435	−	56.0205i	1.47936	−	2.56232i
$479$	24.9787			1.14131			0.570653	−	0.821191i	$-0.306690\pi$
$479$	24.9787			1.14131			0.570653	+	0.821191i	$0.306690\pi$
$480$	37.1976	−	64.4281i	1.69783	−	2.94073i
$481$	14.0000	−	3.46410i	0.638345	−	0.157949i
$482$	64.3050			2.92901
$483$		0			0
$484$	18.3541	+	31.7902i	0.834277	+	1.44501i
$485$	49.3607			2.24135
$486$	−28.3435	+	49.0923i	−1.28569	+	2.22687i
$487$	−14.9894	−	25.9623i	−0.679233	−	1.17647i	−0.975212	−	0.221271i	$-0.928979\pi$
$487$	−14.9894	−	25.9623i	−0.679233	−	1.17647i	0.295980	−	0.955194i	$-0.404354\pi$
$488$	−44.8328			−2.02949
$489$	9.70820			0.439020
$490$		0			0
$491$	−6.19098	−	10.7231i	−0.279395	−	0.483927i	0.691839	−	0.722051i	$-0.256801\pi$
$491$	−6.19098	−	10.7231i	−0.279395	−	0.483927i	−0.971235	+	0.238125i	$0.923467\pi$
$492$	4.85410	−	8.40755i	0.218840	−	0.379042i
$493$	5.21885	−	9.03931i	0.235045	−	0.407110i
$494$	−16.9894	+	4.20378i	−0.764387	+	0.189137i
$495$	−9.35410	−	16.2018i	−0.420436	−	0.728216i
$496$	23.1976	+	40.1794i	1.04160	+	1.80411i
$497$		0			0
$498$	22.9894	−	39.8187i	1.03018	−	1.78432i
$499$	−7.42705	−	12.8640i	−0.332480	−	0.575873i	0.650517	−	0.759492i	$-0.274552\pi$
$499$	−7.42705	−	12.8640i	−0.332480	−	0.575873i	−0.982998	+	0.183619i	$0.941219\pi$
$500$	19.9894	+	34.6226i	0.893951	+	1.54837i
$501$	18.6353	+	32.2772i	0.832562	+	1.44204i
$502$	−1.00000	−	1.73205i	−0.0446322	−	0.0773052i
$503$	−13.3090	+	23.0519i	−0.593420	+	1.02783i	0.400348	+	0.916363i	$0.368889\pi$
$503$	−13.3090	+	23.0519i	−0.593420	+	1.02783i	−0.993768	+	0.111470i	$0.964444\pi$
$504$		0			0
$505$	15.1353	+	26.2150i	0.673510	+	1.16655i
$506$	10.8541	+	18.7999i	0.482524	+	0.835756i
$507$	1.30902	−	34.0093i	0.0581355	−	1.51040i
$508$	50.6140	−	87.6660i	2.24563	−	3.88955i
$509$	9.29837	−	16.1053i	0.412143	−	0.713853i	−0.582981	−	0.812486i	$-0.698114\pi$
$509$	9.29837	−	16.1053i	0.412143	−	0.713853i	0.995124	+	0.0986331i	$0.0314470\pi$
$510$	−13.2082	−	22.8773i	−0.584869	−	1.01302i
$511$		0			0
$512$	−40.3050			−1.78124
$513$	4.14590			0.183046
$514$	−21.9164	−	37.9603i	−0.966691	−	1.67436i
$515$	11.3992	−	19.7440i	0.502308	−	0.870023i
$516$	−159.644			−7.02795
$517$	2.07295	+	3.59045i	0.0911682	+	0.157908i
$518$		0			0
$519$	23.5623			1.03427
$520$	−19.5623	+	67.7658i	−0.857864	+	2.97173i
$521$	−9.32624	+	16.1535i	−0.408590	+	0.707698i	−0.994732	−	0.102510i	$-0.967313\pi$
$521$	−9.32624	+	16.1535i	−0.408590	+	0.707698i	0.586142	+	0.810208i	$0.300646\pi$
$522$	71.5410			3.13127
$523$	−0.562306	+	0.973942i	−0.0245879	+	0.0425875i	−0.878058	−	0.478555i	$-0.841161\pi$
$523$	−0.562306	+	0.973942i	−0.0245879	+	0.0425875i	0.853470	+	0.521143i	$0.174494\pi$
$524$	37.1976	−	64.4281i	1.62498	−	2.81455i
$525$		0			0
$526$	−11.7812	+	20.4056i	−0.513683	+	0.889724i
$527$	6.93112			0.301924
$528$	23.9164	−	41.4244i	1.04083	−	1.80277i
$529$	1.50000	+	2.59808i	0.0652174	+	0.112960i
$530$	−12.8992	+	22.3420i	−0.560305	+	0.970477i
$531$	4.30902	+	7.46344i	0.186995	+	0.323886i
$532$		0			0
$533$	−0.763932	+	2.64634i	−0.0330896	+	0.114626i
$534$	16.8262	+	29.1439i	0.728143	+	1.26118i
$535$	−8.85410			−0.382796
$536$	−94.9574			−4.10154
$537$	23.5623			1.01679
$538$	−75.2492			−3.24422
$539$		0			0
$540$	14.2082	−	24.6093i	0.611424	−	1.05902i
$541$	−17.6353	−	30.5452i	−0.758199	−	1.31324i	−0.943768	−	0.330608i	$-0.892746\pi$
$541$	−17.6353	−	30.5452i	−0.758199	−	1.31324i	0.185569	−	0.982631i	$-0.440587\pi$
$542$	11.0172	+	19.0824i	0.473230	+	0.819659i
$543$	−25.4164			−1.09072
$544$	7.98936	−	13.8380i	0.342541	−	0.593298i
$545$	−7.09017			−0.303710
$546$		0			0
$547$	−3.00000			−0.128271			−0.0641354	−	0.997941i	$-0.520429\pi$
$547$	−3.00000			−0.128271			−0.0641354	+	0.997941i	$0.520429\pi$
$548$	6.35410	−	11.0056i	0.271434	−	0.470137i
$549$	−23.1246			−0.986934
$550$	−4.50000	−	7.79423i	−0.191881	−	0.332347i
$551$	6.57295	+	11.3847i	0.280017	+	0.485004i
$552$	−43.7426	+	75.7645i	−1.86181	+	3.22475i
$553$		0			0
$554$	−13.0902			−0.556148
$555$	−27.4164			−1.16376
$556$	22.1459			0.939195
$557$	−27.9787			−1.18550			−0.592748	−	0.805388i	$-0.701957\pi$
$557$	−27.9787			−1.18550			−0.592748	+	0.805388i	$0.701957\pi$
$558$	23.7533	+	41.1419i	1.00556	+	1.74168i
$559$	43.9681	−	10.8793i	1.85965	−	0.460144i
$560$		0			0
$561$	−3.57295	−	6.18853i	−0.150850	−	0.261280i
$562$	−26.4164	+	45.7546i	−1.11431	+	1.93004i
$563$	10.5279	+	18.2348i	0.443697	+	0.768505i	0.997960	−	0.0638360i	$-0.0203335\pi$
$563$	10.5279	+	18.2348i	0.443697	+	0.768505i	−0.554264	+	0.832341i	$0.687000\pi$
$564$	−14.2082	+	24.6093i	−0.598273	+	1.03624i
$565$	3.85410			0.162143
$566$	−17.5623	+	30.4188i	−0.738199	+	1.27860i
$567$		0			0
$568$	52.9787	−	91.7618i	2.22294	−	3.85024i
$569$	−7.47214	+	12.9421i	−0.313248	+	0.542562i	−0.979064	−	0.203555i	$-0.934751\pi$
$569$	−7.47214	+	12.9421i	−0.313248	+	0.542562i	0.665815	+	0.746117i	$0.268084\pi$
$570$	33.2705			1.39355
$571$	−12.3435	+	21.3795i	−0.516558	+	0.894704i	0.483257	+	0.875478i	$0.339453\pi$
$571$	−12.3435	+	21.3795i	−0.516558	+	0.894704i	−0.999815	+	0.0192259i	$0.993880\pi$
$572$	−9.00000	+	31.1769i	−0.376309	+	1.30357i
$573$	−55.9787			−2.33854
$574$		0			0
$575$	4.14590	+	7.18091i	0.172896	+	0.299464i
$576$	33.5623			1.39843
$577$	21.9164	−	37.9603i	0.912392	−	1.58031i	0.101717	−	0.994813i	$-0.467567\pi$
$577$	21.9164	−	37.9603i	0.912392	−	1.58031i	0.810675	−	0.585496i	$-0.199100\pi$
$578$	19.4164	+	33.6302i	0.807616	+	1.39883i
$579$	15.7082			0.652811
$580$	90.1033			3.74134
$581$		0			0
$582$	64.6140	+	111.915i	2.67834	+	4.63901i
$583$	−3.48936	+	6.04374i	−0.144514	+	0.250306i
$584$	7.47214	−	12.9421i	0.309199	−	0.535549i
$585$	−10.0902	+	34.9534i	−0.417177	+	1.44514i
$586$	8.85410	+	15.3358i	0.365760	+	0.633514i
$587$	9.95492	+	17.2424i	0.410883	+	0.711671i	0.994987	−	0.100009i	$-0.0318870\pi$
$587$	9.95492	+	17.2424i	0.410883	+	0.711671i	−0.584103	+	0.811679i	$0.698554\pi$
$588$		0			0
$589$	−4.36475	+	7.55996i	−0.179846	+	0.311503i
$590$	7.66312	+	13.2729i	0.315486	+	0.546437i
$591$	−21.9894	−	38.0867i	−0.904521	−	1.56668i
$592$	−19.7082	−	34.1356i	−0.810002	−	1.40296i
$593$	−21.8992	−	37.9305i	−0.899292	−	1.55762i	−0.828401	−	0.560135i	$-0.810749\pi$
$593$	−21.8992	−	37.9305i	−0.899292	−	1.55762i	−0.0708905	−	0.997484i	$-0.522584\pi$
$594$	5.42705	−	9.39993i	0.222675	−	0.385684i
$595$		0			0
$596$	−4.50000	−	7.79423i	−0.184327	−	0.319264i
$597$	−31.9615	−	55.3589i	−1.30810	−	2.26569i
$598$	11.7082	−	40.5584i	0.478784	−	1.65856i
$599$	−14.7533	+	25.5534i	−0.602803	+	1.04409i	0.389592	+	0.920988i	$0.372616\pi$
$599$	−14.7533	+	25.5534i	−0.602803	+	1.04409i	−0.992395	+	0.123098i	$0.960717\pi$
$600$	18.1353	−	31.4112i	0.740369	−	1.28236i
$601$	−20.1976	−	34.9832i	−0.823876	−	1.42699i	−0.902776	−	0.430112i	$-0.858474\pi$
$601$	−20.1976	−	34.9832i	−0.823876	−	1.42699i	0.0788998	−	0.996883i	$-0.474859\pi$
$602$		0			0
$603$	−48.9787			−1.99457
$604$	−6.27051			−0.255143
$605$	9.89919	+	17.1459i	0.402459	+	0.697080i
$606$	−39.6246	+	68.6318i	−1.60964	+	2.78798i
$607$	−23.0000			−0.933541			−0.466771	−	0.884378i	$-0.654583\pi$
$607$	−23.0000			−0.933541			−0.466771	+	0.884378i	$0.654583\pi$
$608$	10.0623	+	17.4284i	0.408080	+	0.706816i
$609$		0			0
$610$	−41.1246			−1.66509
$611$	2.23607	−	7.74597i	0.0904616	−	0.313368i
$612$	13.7705	−	23.8512i	0.556640	−	0.964129i
$613$	34.5623			1.39596			0.697979	−	0.716118i	$-0.254083\pi$
$613$	34.5623			1.39596			0.697979	+	0.716118i	$0.254083\pi$
$614$	6.35410	−	11.0056i	0.256431	−	0.444151i
$615$	2.61803	−	4.53457i	0.105569	−	0.182851i
$616$		0			0
$617$	−0.0278640	+	0.0482619i	−0.00112176	+	0.00194295i	−0.866586	−	0.499028i	$-0.833690\pi$
$617$	−0.0278640	+	0.0482619i	−0.00112176	+	0.00194295i	0.865464	+	0.500971i	$0.167024\pi$
$618$	59.6869			2.40096
$619$	−4.70820	+	8.15485i	−0.189239	+	0.327771i	−0.944997	−	0.327080i	$-0.893935\pi$
$619$	−4.70820	+	8.15485i	−0.189239	+	0.327771i	0.755758	+	0.654851i	$0.227269\pi$
$620$	29.9164	+	51.8167i	1.20147	+	2.08101i
$621$	−5.00000	+	8.66025i	−0.200643	+	0.347524i
$622$	−4.35410	−	7.54153i	−0.174584	−	0.302388i
$623$		0			0
$624$	−90.2943	+	22.3420i	−3.61467	+	0.894398i
$625$	15.4164	+	26.7020i	0.616656	+	1.06808i
$626$	65.7771			2.62898
$627$	9.00000			0.359425
$628$	72.1033			2.87724
$629$	−5.88854			−0.234792
$630$		0			0
$631$	−17.1976	+	29.7870i	−0.684624	+	1.18580i	0.288931	+	0.957350i	$0.406700\pi$
$631$	−17.1976	+	29.7870i	−0.684624	+	1.18580i	−0.973555	+	0.228454i	$0.926633\pi$
$632$	−14.9443	−	25.8842i	−0.594451	−	1.02962i
$633$	6.16312	+	10.6748i	0.244962	+	0.424287i
$634$	68.6869			2.72791
$635$	27.2984	−	47.2822i	1.08330	−	1.87634i
$636$	−47.8328			−1.89669
$637$		0			0
$638$	34.4164			1.36256
$639$	27.3262	−	47.3304i	1.08101	−	1.87236i
$640$	2.85410			0.112818
$641$	23.7533	+	41.1419i	0.938199	+	1.62501i	0.768829	+	0.639455i	$0.220840\pi$
$641$	23.7533	+	41.1419i	0.938199	+	1.62501i	0.169370	+	0.985553i	$0.445827\pi$
$642$	−11.5902	−	20.0748i	−0.457428	−	0.792288i
$643$	3.50000	−	6.06218i	0.138027	−	0.239069i	−0.788723	−	0.614749i	$-0.789257\pi$
$643$	3.50000	−	6.06218i	0.138027	−	0.239069i	0.926750	+	0.375680i	$0.122591\pi$
$644$		0			0
$645$	−86.1033			−3.39032
$646$	7.14590			0.281152
$647$	24.7639			0.973571			0.486785	−	0.873522i	$-0.338169\pi$
$647$	24.7639			0.973571			0.486785	+	0.873522i	$0.338169\pi$
$648$	−42.6525			−1.67555
$649$	2.07295	+	3.59045i	0.0813704	+	0.140938i
$650$	−4.85410	+	16.8151i	−0.190394	+	0.659543i
$651$		0			0
$652$	9.00000	+	15.5885i	0.352467	+	0.610491i
$653$	0.190983	−	0.330792i	0.00747374	−	0.0129449i	−0.862264	−	0.506458i	$-0.830954\pi$
$653$	0.190983	−	0.330792i	0.00747374	−	0.0129449i	0.869738	+	0.493514i	$0.164288\pi$
$654$	−9.28115	−	16.0754i	−0.362922	−	0.628599i
$655$	20.0623	−	34.7489i	0.783899	−	1.35775i
$656$	7.52786			0.293914
$657$	3.85410	−	6.67550i	0.150363	−	0.260436i
$658$		0			0
$659$	11.9443	−	20.6881i	0.465283	−	0.805893i	−0.533931	−	0.845528i	$-0.679286\pi$
$659$	11.9443	−	20.6881i	0.465283	−	0.805893i	0.999214	+	0.0396343i	$0.0126193\pi$
$660$	30.8435	−	53.4224i	1.20058	−	2.07947i
$661$	−48.5410			−1.88803			−0.944013	−	0.329907i	$-0.892983\pi$
$661$	−48.5410			−1.88803			−0.944013	+	0.329907i	$0.892983\pi$
$662$	13.2812	−	23.0036i	0.516187	−	0.894062i
$663$	−3.85410	+	13.3510i	−0.149681	+	0.518510i
$664$	50.1246			1.94521
$665$		0			0
$666$	−20.1803	−	34.9534i	−0.781972	−	1.35442i
$667$	−31.7082			−1.22775
$668$	−34.5517	+	59.8452i	−1.33684	+	2.31548i
$669$	26.5344	+	45.9590i	1.02588	+	1.77688i
$670$	−87.1033			−3.36510
$671$	−11.1246			−0.429461
$672$		0			0
$673$	19.6246	+	33.9908i	0.756473	+	1.31025i	0.944639	+	0.328113i	$0.106413\pi$
$673$	19.6246	+	33.9908i	0.756473	+	1.31025i	−0.188165	+	0.982137i	$0.560254\pi$
$674$	15.1353	−	26.2150i	0.582988	−	1.00977i
$675$	2.07295	−	3.59045i	0.0797878	−	0.138197i
$676$	55.8222	−	29.4264i	2.14701	−	1.13179i
$677$	−21.8713	−	37.8822i	−0.840583	−	1.45593i	−0.889402	−	0.457125i	$-0.848879\pi$
$677$	−21.8713	−	37.8822i	−0.840583	−	1.45593i	0.0488191	−	0.998808i	$-0.484454\pi$
$678$	5.04508	+	8.73834i	0.193755	+	0.335594i
$679$		0			0
$680$	14.3992	−	24.9401i	0.552184	−	0.956410i
$681$	1.92705	+	3.33775i	0.0738448	+	0.127903i
$682$	11.4271	+	19.7922i	0.437564	+	0.757884i
$683$	−0.736068	−	1.27491i	−0.0281649	−	0.0487830i	0.851599	−	0.524193i	$-0.175633\pi$
$683$	−0.736068	−	1.27491i	−0.0281649	−	0.0487830i	−0.879764	+	0.475410i	$0.842300\pi$
$684$	17.3435	+	30.0398i	0.663144	+	1.14860i
$685$	3.42705	−	5.93583i	0.130941	−	0.226796i
$686$		0			0
$687$	−17.1803	−	29.7572i	−0.655471	−	1.13531i
$688$	−61.8951	−	107.205i	−2.35973	−	4.08717i
$689$	13.1738	−	3.25966i	0.501880	−	0.124183i
$690$	−40.1246	+	69.4979i	−1.52752	+	2.64574i
$691$	2.92705	−	5.06980i	0.111350	−	0.192864i	−0.804965	−	0.593323i	$-0.797816\pi$
$691$	2.92705	−	5.06980i	0.111350	−	0.192864i	0.916315	+	0.400458i	$0.131149\pi$
$692$	21.8435	+	37.8340i	0.830364	+	1.43823i
$693$		0			0
$694$	80.5410			3.05730
$695$	11.9443			0.453072
$696$	69.3500	+	120.118i	2.62871	+	4.55305i
$697$	0.562306	−	0.973942i	0.0212989	−	0.0368907i
$698$	54.2148			2.05206
$699$	3.42705	+	5.93583i	0.129623	+	0.224514i
$700$		0			0
$701$	11.2361			0.424380			0.212190	−	0.977228i	$-0.431940\pi$
$701$	11.2361			0.424380			0.212190	+	0.977228i	$0.431940\pi$
$702$	−20.4894	+	5.06980i	−0.773321	+	0.191347i
$703$	3.70820	−	6.42280i	0.139858	−	0.242240i
$704$	16.1459			0.608521
$705$	−7.66312	+	13.2729i	−0.288610	+	0.499887i
$706$	−28.9894	+	50.2110i	−1.09103	+	1.88972i
$707$		0			0
$708$	−14.2082	+	24.6093i	−0.533977	+	0.924875i
$709$	23.5623			0.884901			0.442450	−	0.896793i	$-0.354109\pi$
$709$	23.5623			0.884901			0.442450	+	0.896793i	$0.354109\pi$
$710$	48.5967	−	84.1720i	1.82380	−	3.15892i
$711$	−7.70820	−	13.3510i	−0.289080	−	0.500702i
$712$	−18.3435	+	31.7718i	−0.687450	+	1.19070i
$713$	−10.5279	−	18.2348i	−0.394272	−	0.682898i
$714$		0			0
$715$	−4.85410	+	16.8151i	−0.181533	+	0.628849i
$716$	21.8435	+	37.8340i	0.816328	+	1.41392i
$717$	64.6869			2.41578
$718$	−57.8328			−2.15830
$719$	8.12461			0.302997			0.151498	−	0.988457i	$-0.451590\pi$
$719$	8.12461			0.302997			0.151498	+	0.988457i	$0.451590\pi$
$720$	99.4296			3.70552
$721$		0			0
$722$	20.3713	−	35.2842i	0.758142	−	1.31314i
$723$	32.1525	+	55.6897i	1.19576	+	2.07112i
$724$	−23.5623	−	40.8111i	−0.875686	−	1.51673i
$725$	13.1459			0.488226
$726$	−25.9164	+	44.8885i	−0.961848	+	1.66597i
$727$	−30.7082			−1.13890			−0.569452	−	0.822025i	$-0.692845\pi$
$727$	−30.7082			−1.13890			−0.569452	+	0.822025i	$0.692845\pi$
$728$		0			0
$729$	−39.5623			−1.46527
$730$	6.85410	−	11.8717i	0.253682	−	0.439390i
$731$	−18.4934			−0.684004
$732$	−38.1246	−	66.0338i	−1.40913	−	2.44068i
$733$	16.1353	+	27.9471i	0.595969	+	1.03225i	0.993409	+	0.114621i	$0.0365653\pi$
$733$	16.1353	+	27.9471i	0.595969	+	1.03225i	−0.397440	+	0.917628i	$0.630101\pi$
$734$	1.85410	−	3.21140i	0.0684362	−	0.118535i
$735$		0			0
$736$	−48.5410			−1.78925
$737$	−23.5623			−0.867929
$738$	7.70820			0.283743
$739$	−6.87539			−0.252915			−0.126458	−	0.991972i	$-0.540361\pi$
$739$	−6.87539			−0.252915			−0.126458	+	0.991972i	$0.540361\pi$
$740$	−25.4164	−	44.0225i	−0.934326	−	1.61830i
$741$	−12.1353	−	12.6113i	−0.445800	−	0.463289i
$742$		0			0
$743$	−19.6631	−	34.0575i	−0.721370	−	1.24945i	−0.960451	−	0.278450i	$-0.910179\pi$
$743$	−19.6631	−	34.0575i	−0.721370	−	1.24945i	0.239081	−	0.971000i	$-0.423154\pi$
$744$	−46.0517	+	79.7638i	−1.68834	+	2.92428i
$745$	−2.42705	−	4.20378i	−0.0889203	−	0.154014i
$746$	26.9164	−	46.6206i	0.985480	−	1.70690i
$747$	25.8541			0.945952
$748$	6.62461	−	11.4742i	0.242220	−	0.419537i
$749$		0			0
$750$	−28.2254	+	48.8879i	−1.03065	+	1.78513i
$751$	−11.3541	+	19.6659i	−0.414317	+	0.717618i	−0.995356	−	0.0962572i	$-0.969313\pi$
$751$	−11.3541	+	19.6659i	−0.414317	+	0.717618i	0.581039	+	0.813875i	$0.302646\pi$
$752$	−22.0344			−0.803513
$753$	1.00000	−	1.73205i	0.0364420	−	0.0631194i
$754$	−46.4058	−	48.2263i	−1.69000	−	1.75630i
$755$	−3.38197			−0.123082
$756$		0			0
$757$	−14.0000	−	24.2487i	−0.508839	−	0.881334i	−0.999948	−	0.0102362i	$-0.996742\pi$
$757$	−14.0000	−	24.2487i	−0.508839	−	0.881334i	0.491109	−	0.871098i	$-0.336592\pi$
$758$	−16.0902			−0.584421
$759$	−10.8541	+	18.7999i	−0.393979	+	0.682392i
$760$	18.1353	+	31.4112i	0.657835	+	1.13940i
$761$	−28.8541			−1.04596			−0.522980	−	0.852345i	$-0.675180\pi$
$761$	−28.8541			−1.04596			−0.522980	+	0.852345i	$0.675180\pi$
$762$	142.936			5.17803
$763$		0			0
$764$	−51.8951	−	89.8850i	−1.87750	−	3.25192i
$765$	7.42705	−	12.8640i	0.268526	−	0.465100i
$766$	28.7705	−	49.8320i	1.03952	−	1.80050i
$767$	2.23607	−	7.74597i	0.0807397	−	0.279691i
$768$	−19.0623	−	33.0169i	−0.687852	−	1.19139i
$769$	9.20820	+	15.9491i	0.332056	+	0.575138i	0.982915	−	0.184061i	$-0.0589243\pi$
$769$	9.20820	+	15.9491i	0.332056	+	0.575138i	−0.650859	+	0.759199i	$0.725591\pi$
$770$		0			0
$771$	21.9164	−	37.9603i	0.789300	−	1.36711i
$772$	14.5623	+	25.2227i	0.524109	+	0.907783i
$773$	−12.6803	−	21.9630i	−0.456080	−	0.789954i	0.542669	−	0.839946i	$-0.317414\pi$
$773$	−12.6803	−	21.9630i	−0.456080	−	0.789954i	−0.998750	+	0.0499924i	$0.984080\pi$
$774$	−63.3779	−	109.774i	−2.27807	−	3.94574i
$775$	4.36475	+	7.55996i	0.156786	+	0.271562i
$776$	−70.4402	+	122.006i	−2.52866	+	4.37976i
$777$		0			0
$778$	15.5623	+	26.9547i	0.557936	+	0.966373i
$779$	0.708204	+	1.22665i	0.0253740	+	0.0439491i
$780$	−116.447	+	28.8131i	−4.16946	+	1.03167i
$781$	13.1459	−	22.7694i	0.470397	−	0.814752i
$782$	−8.61803	+	14.9269i	−0.308180	+	0.533784i
$783$	7.92705	+	13.7301i	0.283290	+	0.490672i
$784$		0			0
$785$	38.8885			1.38799
$786$	105.048			3.74692
$787$	−1.29180	−	2.23746i	−0.0460476	−	0.0797567i	0.842083	−	0.539348i	$-0.181329\pi$
$787$	−1.29180	−	2.23746i	−0.0460476	−	0.0797567i	−0.888131	+	0.459591i	$0.847996\pi$
$788$	40.7705	−	70.6166i	1.45239	−	2.51561i
$789$	−23.5623			−0.838840
$790$	−13.7082	−	23.7433i	−0.487716	−	0.844749i
$791$		0			0
$792$	53.3951			1.89731
$793$	15.0000	+	15.5885i	0.532666	+	0.553562i
$794$	−1.85410	+	3.21140i	−0.0657996	+	0.113968i
$795$	−25.7984			−0.914974
$796$	59.2599	−	102.641i	2.10041	−	3.63802i
$797$	4.09017	−	7.08438i	0.144881	−	0.250942i	−0.784447	−	0.620195i	$-0.787053\pi$
$797$	4.09017	−	7.08438i	0.144881	−	0.250942i	0.929329	+	0.369254i	$0.120387\pi$
$798$		0			0
$799$	−1.64590	+	2.85078i	−0.0582277	+	0.100853i
$800$	20.1246			0.711512
$801$	−9.46149	+	16.3878i	−0.334305	+	0.579034i
$802$	−46.4058	−	80.3771i	−1.63864	−	2.83822i
$803$	1.85410	−	3.21140i	0.0654298	−	0.113328i
$804$	−80.7492	−	139.862i	−2.84781	−	4.93254i
$805$		0			0
$806$	12.3262	−	42.6993i	0.434173	−	1.50402i
$807$	−37.6246	−	65.1677i	−1.32445	−	2.29401i
$808$	−86.3951			−3.03937
$809$	−4.41641			−0.155273			−0.0776363	−	0.996982i	$-0.524737\pi$
$809$	−4.41641			−0.155273			−0.0776363	+	0.996982i	$0.524737\pi$
$810$	−39.1246			−1.37470
$811$	39.2705			1.37897			0.689487	−	0.724298i	$-0.257836\pi$
$811$	39.2705			1.37897			0.689487	+	0.724298i	$0.257836\pi$
$812$		0			0
$813$	−11.0172	+	19.0824i	−0.386391	+	0.669249i
$814$	−9.70820	−	16.8151i	−0.340272	−	0.589369i
$815$	4.85410	+	8.40755i	0.170032	+	0.294504i
$816$	37.9787			1.32952
$817$	11.6459	−	20.1713i	0.407438	−	0.705704i
$818$	37.7984			1.32159
$819$		0			0
$820$	9.70820			0.339025
$821$	3.68034	−	6.37454i	0.128445	−	0.222473i	−0.794629	−	0.607095i	$-0.792335\pi$
$821$	3.68034	−	6.37454i	0.128445	−	0.222473i	0.923074	+	0.384622i	$0.125668\pi$
$822$	17.9443			0.625878
$823$	19.2082	+	33.2696i	0.669556	+	1.15970i	0.978028	+	0.208472i	$0.0668489\pi$
$823$	19.2082	+	33.2696i	0.669556	+	1.15970i	−0.308473	+	0.951233i	$0.599818\pi$
$824$	32.5344	+	56.3513i	1.13339	+	1.96309i
$825$	4.50000	−	7.79423i	0.156670	−	0.271360i
$826$		0			0
$827$	15.9787			0.555634			0.277817	−	0.960634i	$-0.410389\pi$
$827$	15.9787			0.555634			0.277817	+	0.960634i	$0.410389\pi$
$828$	−83.6656			−2.90758
$829$	7.56231			0.262650			0.131325	−	0.991339i	$-0.458077\pi$
$829$	7.56231			0.262650			0.131325	+	0.991339i	$0.458077\pi$
$830$	45.9787			1.59594
$831$	−6.54508	−	11.3364i	−0.227046	−	0.393256i
$832$	−21.7705	−	22.6246i	−0.754757	−	0.784366i
$833$		0			0
$834$	15.6353	+	27.0811i	0.541405	+	0.937740i
$835$	−18.6353	+	32.2772i	−0.644900	+	1.11700i
$836$	8.34346	+	14.4513i	0.288565	+	0.499808i
$837$	−5.26393	+	9.11740i	−0.181948	+	0.315143i
$838$	−31.2705			−1.08022
$839$	−6.87132	+	11.9015i	−0.237224	+	0.410885i	−0.959917	−	0.280285i	$-0.909571\pi$
$839$	−6.87132	+	11.9015i	−0.237224	+	0.410885i	0.722692	+	0.691170i	$0.242904\pi$
$840$		0			0
$841$	−10.6353	+	18.4208i	−0.366733	+	0.635200i
$842$	−1.85410	+	3.21140i	−0.0638966	+	0.110672i
$843$	−52.8328			−1.81966
$844$	−11.4271	+	19.7922i	−0.393335	+	0.681277i
$845$	30.1074	−	15.8710i	1.03573	−	0.545979i
$846$	−22.5623			−0.775708
$847$		0			0
$848$	−18.5451	−	32.1210i	−0.636841	−	1.10304i
$849$	−35.1246			−1.20547
$850$	3.57295	−	6.18853i	0.122551	−	0.212265i
$851$	8.94427	+	15.4919i	0.306606	+	0.531057i
$852$	180.207			6.17378
$853$	14.1246			0.483617			0.241809	−	0.970324i	$-0.422259\pi$
$853$	14.1246			0.483617			0.241809	+	0.970324i	$0.422259\pi$
$854$		0			0
$855$	9.35410	+	16.2018i	0.319904	+	0.554089i
$856$	12.6353	−	21.8849i	0.431864	−	0.748011i
$857$	13.2254	−	22.9071i	0.451772	−	0.782492i	−0.546724	−	0.837313i	$-0.684125\pi$
$857$	13.2254	−	22.9071i	0.451772	−	0.782492i	0.998496	+	0.0548208i	$0.0174588\pi$
$858$	−44.4787	+	11.0056i	−1.51848	+	0.375726i
$859$	22.1246	+	38.3210i	0.754882	+	1.30749i	0.945433	+	0.325817i	$0.105639\pi$
$859$	22.1246	+	38.3210i	0.754882	+	1.30749i	−0.190551	+	0.981677i	$0.561027\pi$
$860$	−79.8222	−	138.256i	−2.72191	−	4.71449i
$861$		0			0
$862$	−10.2082	+	17.6811i	−0.347693	+	0.602222i
$863$	−5.94427	−	10.2958i	−0.202345	−	0.350472i	0.746938	−	0.664893i	$-0.231523\pi$
$863$	−5.94427	−	10.2958i	−0.202345	−	0.350472i	−0.949284	+	0.314421i	$0.898190\pi$
$864$	12.1353	+	21.0189i	0.412850	+	0.715077i
$865$	11.7812	+	20.4056i	0.400571	+	0.693810i
$866$	−1.30902	−	2.26728i	−0.0444822	−	0.0770454i
$867$	−19.4164	+	33.6302i	−0.659416	+	1.14214i
$868$		0			0
$869$	−3.70820	−	6.42280i	−0.125792	−	0.217878i
$870$	63.6140	+	110.183i	2.15672	+	3.73554i
$871$	31.7705	+	33.0169i	1.07650	+	1.11873i
$872$	10.1180	−	17.5249i	0.342640	−	0.593470i
$873$	−36.3328	+	62.9303i	−1.22968	+	2.12987i
$874$	−10.8541	−	18.7999i	−0.367145	−	0.635915i
$875$		0			0
$876$	25.4164			0.858741
$877$	0.708204			0.0239143			0.0119572	−	0.999929i	$-0.496194\pi$
$877$	0.708204			0.0239143			0.0119572	+	0.999929i	$0.496194\pi$
$878$	−19.4443	−	33.6785i	−0.656212	−	1.13659i
$879$	−8.85410	+	15.3358i	−0.298641	+	0.517262i
$880$	47.8328			1.61244
$881$	18.2984	+	31.6937i	0.616488	+	1.06779i	0.990122	+	0.140212i	$0.0447784\pi$
$881$	18.2984	+	31.6937i	0.616488	+	1.06779i	−0.373634	+	0.927576i	$0.621888\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	−25.0106	+	6.18853i	−0.841199	+	0.208143i
$885$	−7.66312	+	13.2729i	−0.257593	+	0.446164i
$886$	−13.7082			−0.460536
$887$	−27.3262	+	47.3304i	−0.917525	+	1.58920i	−0.114364	+	0.993439i	$0.536483\pi$
$887$	−27.3262	+	47.3304i	−0.917525	+	1.58920i	−0.803161	+	0.595761i	$0.796850\pi$
$888$	39.1246	−	67.7658i	1.31294	−	2.27407i
$889$		0			0
$890$	−16.8262	+	29.1439i	−0.564017	+	0.976906i
$891$	−10.5836			−0.354564
$892$	−49.1976	+	85.2127i	−1.64726	+	2.85313i
$893$	−2.07295	−	3.59045i	−0.0693686	−	0.120150i
$894$	6.35410	−	11.0056i	0.212513	−	0.368083i
$895$	11.7812	+	20.4056i	0.393801	+	0.682082i
$896$		0			0
$897$	40.9787	−	10.1396i	1.36824	−	0.338551i
$898$	−25.5623	−	44.2752i	−0.853025	−	1.47748i
$899$	−33.3820			−1.11335
$900$	34.6869			1.15623
$901$	−5.54102			−0.184598
$902$	3.70820			0.123470
$903$		0			0
$904$	−5.50000	+	9.52628i	−0.182927	+	0.316839i
$905$	−12.7082	−	22.0113i	−0.422435	−	0.731679i
$906$	−4.42705	−	7.66788i	−0.147079	−	0.254748i
$907$	−24.0000			−0.796907			−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000			−0.796907			−0.398453	+	0.917189i	$0.630453\pi$
$908$	−3.57295	+	6.18853i	−0.118572	+	0.205374i
$909$	−44.5623			−1.47804
$910$		0			0
$911$	−22.6869			−0.751651			−0.375826	−	0.926690i	$-0.622641\pi$
$911$	−22.6869			−0.751651			−0.375826	+	0.926690i	$0.622641\pi$
$912$	−23.9164	+	41.4244i	−0.791951	+	1.37170i
$913$	12.4377			0.411628
$914$	−20.1803	−	34.9534i	−0.667506	−	1.15615i
$915$	−20.5623	−	35.6150i	−0.679769	−	1.17739i
$916$	31.8541	−	55.1729i	1.05249	−	1.82296i
$917$		0			0
$918$	8.61803			0.284438
$919$	−30.0000			−0.989609			−0.494804	−	0.869004i	$-0.664760\pi$
$919$	−30.0000			−0.989609			−0.494804	+	0.869004i	$0.664760\pi$
$920$	−87.4853			−2.88430
$921$	12.7082			0.418750
$922$	15.9894	+	27.6944i	0.526581	+	0.912066i
$923$	−49.6312	+	12.2805i	−1.63363	+	0.404219i
$924$		0			0
$925$	−3.70820	−	6.42280i	−0.121925	−	0.211180i
$926$	−8.78115	+	15.2094i	−0.288567	+	0.499812i
$927$	16.7812	+	29.0658i	0.551165	+	0.954646i
$928$	−38.4787	+	66.6471i	−1.26313	+	2.18780i
$929$	11.0689			0.363158			0.181579	−	0.983376i	$-0.441879\pi$
$929$	11.0689			0.363158			0.181579	+	0.983376i	$0.441879\pi$
$930$	−42.2426	+	73.1664i	−1.38519	+	2.39922i
$931$		0			0
$932$	−6.35410	+	11.0056i	−0.208136	+	0.360501i
$933$	4.35410	−	7.54153i	0.142547	−	0.246898i
$934$	6.14590			0.201100
$935$	3.57295	−	6.18853i	0.116848	−	0.202387i
$936$	−71.9959	−	74.8204i	−2.35326	−	2.44558i
$937$	−15.8754			−0.518626			−0.259313	−	0.965793i	$-0.583496\pi$
$937$	−15.8754			−0.518626			−0.259313	+	0.965793i	$0.583496\pi$
$938$		0			0
$939$	32.8885	+	56.9646i	1.07328	+	1.85897i
$940$	−28.4164			−0.926841
$941$	−10.1738	+	17.6215i	−0.331655	+	0.574444i	−0.982837	−	0.184479i	$-0.940940\pi$
$941$	−10.1738	+	17.6215i	−0.331655	+	0.574444i	0.651181	+	0.758922i	$0.274274\pi$
$942$	50.9058	+	88.1714i	1.65860	+	2.87278i
$943$	−3.41641			−0.111254
$944$	−22.0344			−0.717160
$945$		0			0
$946$	−30.4894	−	52.8091i	−0.991294	−	1.71697i
$947$	18.4336	−	31.9280i	0.599012	−	1.03752i	−0.393955	−	0.919130i	$-0.628893\pi$
$947$	18.4336	−	31.9280i	0.599012	−	1.03752i	0.992967	−	0.118390i	$-0.0377733\pi$
$948$	25.4164	−	44.0225i	0.825487	−	1.42978i
$949$	−7.00000	+	1.73205i	−0.227230	+	0.0562247i
$950$	4.50000	+	7.79423i	0.145999	+	0.252878i
$951$	34.3435	+	59.4846i	1.11366	+	1.92892i
$952$		0			0
$953$	−13.3885	+	23.1896i	−0.433697	+	0.751186i	−0.997188	−	0.0749362i	$-0.976125\pi$
$953$	−13.3885	+	23.1896i	−0.433697	+	0.751186i	0.563491	+	0.826122i	$0.309458\pi$
$954$	−18.9894	−	32.8905i	−0.614803	−	1.06487i
$955$	−27.9894	−	48.4790i	−0.905714	−	1.56874i
$956$	59.9681	+	103.868i	1.93951	+	3.35932i
$957$	17.2082	+	29.8055i	0.556262	+	0.963474i
$958$	−32.6976	+	56.6338i	−1.05641	+	1.82976i
$959$		0			0
$960$	29.8435	+	51.6904i	0.963193	+	1.66830i
$961$	4.41641	+	7.64944i	0.142465	+	0.246756i
$962$	−10.4721	+	36.2765i	−0.337635	+	1.16960i
$963$	6.51722	−	11.2882i	0.210015	−	0.363756i
$964$	−59.6140	+	103.254i	−1.92004	+	3.32560i
$965$	7.85410	+	13.6037i	0.252832	+	0.437919i
$966$		0			0
$967$	−39.0000			−1.25416			−0.627078	−	0.778957i	$-0.715749\pi$
$967$	−39.0000			−1.25416			−0.627078	+	0.778957i	$0.715749\pi$
$968$	−56.5066			−1.81619
$969$	3.57295	+	6.18853i	0.114780	+	0.198804i
$970$	−64.6140	+	111.915i	−2.07463	+	3.59336i
$971$	31.5836			1.01357			0.506783	−	0.862074i	$-0.330835\pi$
$971$	31.5836			1.01357			0.506783	+	0.862074i	$0.330835\pi$
$972$	−52.5517	−	91.0221i	−1.68560	−	2.91954i
$973$		0			0
$974$	78.4853			2.51483
$975$	−16.9894	+	4.20378i	−0.544095	+	0.134629i
$976$	29.5623	−	51.2034i	0.946266	−	1.63898i
$977$	−22.5279			−0.720730			−0.360365	−	0.932811i	$-0.617348\pi$
$977$	−22.5279			−0.720730			−0.360365	+	0.932811i	$0.617348\pi$
$978$	−12.7082	+	22.0113i	−0.406364	+	0.703842i
$979$	−4.55166	+	7.88371i	−0.145472	+	0.251965i
$980$		0			0
$981$	5.21885	−	9.03931i	0.166625	−	0.288603i
$982$	32.4164			1.03445
$983$	−9.19098	+	15.9192i	−0.293147	+	0.507745i	−0.974552	−	0.224161i	$-0.928036\pi$
$983$	−9.19098	+	15.9192i	−0.293147	+	0.507745i	0.681405	+	0.731906i	$0.261369\pi$
$984$	7.47214	+	12.9421i	0.238203	+	0.412580i
$985$	21.9894	−	38.0867i	0.700639	−	1.21354i
$986$	13.6631	+	23.6652i	0.435122	+	0.753654i
$987$		0			0
$988$	9.00000	−	31.1769i	0.286328	−	0.991870i
$989$	28.0902	+	48.6536i	0.893215	+	1.54709i
$990$	48.9787			1.55665
$991$	−16.1459			−0.512891			−0.256446	−	0.966559i	$-0.582551\pi$
$991$	−16.1459			−0.512891			−0.256446	+	0.966559i	$0.582551\pi$
$992$	−51.1033			−1.62253
$993$	26.5623			0.842929
$994$		0			0
$995$	31.9615	−	55.3589i	1.01325	−	1.75500i
$996$	42.6246	+	73.8280i	1.35061	+	2.33933i
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	−0.934274	−	0.356555i	$-0.883951\pi$
$997$	−24.5000	−	42.4352i	−0.775923	−	1.34394i	0.158352	−	0.987383i	$-0.449382\pi$
$998$	38.8885			1.23100
$999$	4.47214	−	7.74597i	0.141492	−	0.245072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.b.263.1		4
7.2	even	3		637.2.h.g.471.2		4
7.3	odd	6		637.2.f.c.393.1		4
7.4	even	3		91.2.f.a.29.1	yes	4
7.5	odd	6		637.2.h.f.471.2		4
7.6	odd	2		637.2.g.c.263.1		4
13.9	even	3		637.2.h.g.165.2		4
21.11	odd	6		819.2.o.c.757.2		4
28.11	odd	6		1456.2.s.h.1121.1		4
91.3	odd	6		8281.2.a.bb.1.2		2
91.9	even	3	inner	637.2.g.b.373.1		4
91.10	odd	6		8281.2.a.n.1.1		2
91.11	odd	12		1183.2.c.c.337.4		4
91.48	odd	6		637.2.h.f.165.2		4
91.61	odd	6		637.2.g.c.373.1		4
91.67	odd	12		1183.2.c.c.337.1		4
91.74	even	3		91.2.f.a.22.1	✓	4
91.81	even	3		1183.2.a.g.1.2		2
91.87	odd	6		637.2.f.c.295.1		4
91.88	even	6		1183.2.a.c.1.1		2
273.74	odd	6		819.2.o.c.568.2		4
364.347	odd	6		1456.2.s.h.113.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.a.22.1	✓	4	91.74	even	3
91.2.f.a.29.1	yes	4	7.4	even	3
637.2.f.c.295.1		4	91.87	odd	6
637.2.f.c.393.1		4	7.3	odd	6
637.2.g.b.263.1		4	1.1	even	1	trivial
637.2.g.b.373.1		4	91.9	even	3	inner
637.2.g.c.263.1		4	7.6	odd	2
637.2.g.c.373.1		4	91.61	odd	6
637.2.h.f.165.2		4	91.48	odd	6
637.2.h.f.471.2		4	7.5	odd	6
637.2.h.g.165.2		4	13.9	even	3
637.2.h.g.471.2		4	7.2	even	3
819.2.o.c.568.2		4	273.74	odd	6
819.2.o.c.757.2		4	21.11	odd	6
1183.2.a.c.1.1		2	91.88	even	6
1183.2.a.g.1.2		2	91.81	even	3
1183.2.c.c.337.1		4	91.67	odd	12
1183.2.c.c.337.4		4	91.11	odd	12
1456.2.s.h.113.1		4	364.347	odd	6
1456.2.s.h.1121.1		4	28.11	odd	6
8281.2.a.n.1.1		2	91.10	odd	6
8281.2.a.bb.1.2		2	91.3	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 + 2.26728i) q^{2} -2.61803 q^{3} +(-2.42705 - 4.20378i) q^{4} +(-1.30902 - 2.26728i) q^{5} +(3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q+(-1.30902 + 2.26728i) q^{2} -2.61803 q^{3} +(-2.42705 - 4.20378i) q^{4} +(-1.30902 - 2.26728i) q^{5} +(3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +3.85410 q^{9} +6.85410 q^{10} +1.85410 q^{11} +(6.35410 + 11.0056i) q^{12} +(-2.50000 - 2.59808i) q^{13} +(3.42705 + 5.93583i) q^{15} +(-4.92705 + 8.53390i) q^{16} +(0.736068 + 1.27491i) q^{17} +(-5.04508 + 8.73834i) q^{18} -1.85410 q^{19} +(-6.35410 + 11.0056i) q^{20} +(-2.42705 + 4.20378i) q^{22} +(2.23607 - 3.87298i) q^{23} -19.5623 q^{24} +(-0.927051 + 1.60570i) q^{25} +(9.16312 - 2.26728i) q^{26} -2.23607 q^{27} +(-3.54508 - 6.14027i) q^{29} -17.9443 q^{30} +(2.35410 - 4.07742i) q^{31} +(-5.42705 - 9.39993i) q^{32} -4.85410 q^{33} -3.85410 q^{34} +(-9.35410 - 16.2018i) q^{36} +(-2.00000 + 3.46410i) q^{37} +(2.42705 - 4.20378i) q^{38} +(6.54508 + 6.80185i) q^{39} +(-9.78115 - 16.9415i) q^{40} +(-0.381966 - 0.661585i) q^{41} +(-6.28115 + 10.8793i) q^{43} +(-4.50000 - 7.79423i) q^{44} +(-5.04508 - 8.73834i) q^{45} +(5.85410 + 10.1396i) q^{46} +(1.11803 + 1.93649i) q^{47} +(12.8992 - 22.3420i) q^{48} +(-2.42705 - 4.20378i) q^{50} +(-1.92705 - 3.33775i) q^{51} +(-4.85410 + 16.8151i) q^{52} +(-1.88197 + 3.25966i) q^{53} +(2.92705 - 5.06980i) q^{54} +(-2.42705 - 4.20378i) q^{55} +4.85410 q^{57} +18.5623 q^{58} +(1.11803 + 1.93649i) q^{59} +(16.6353 - 28.8131i) q^{60} -6.00000 q^{61} +(6.16312 + 10.6748i) q^{62} +8.70820 q^{64} +(-2.61803 + 9.06914i) q^{65} +(6.35410 - 11.0056i) q^{66} -12.7082 q^{67} +(3.57295 - 6.18853i) q^{68} +(-5.85410 + 10.1396i) q^{69} +(7.09017 - 12.2805i) q^{71} +28.7984 q^{72} +(1.00000 - 1.73205i) q^{73} +(-5.23607 - 9.06914i) q^{74} +(2.42705 - 4.20378i) q^{75} +(4.50000 + 7.79423i) q^{76} +(-23.9894 + 5.93583i) q^{78} +(-2.00000 - 3.46410i) q^{79} +25.7984 q^{80} -5.70820 q^{81} +2.00000 q^{82} +6.70820 q^{83} +(1.92705 - 3.33775i) q^{85} +(-16.4443 - 28.4823i) q^{86} +(9.28115 + 16.0754i) q^{87} +13.8541 q^{88} +(-2.45492 + 4.25204i) q^{89} +26.4164 q^{90} -21.7082 q^{92} +(-6.16312 + 10.6748i) q^{93} -5.85410 q^{94} +(2.42705 + 4.20378i) q^{95} +(14.2082 + 24.6093i) q^{96} +(-9.42705 + 16.3281i) q^{97} +7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 6 q^{3} - 3 q^{4} - 3 q^{5} + 7 q^{6} + 12 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - 6 * q^3 - 3 * q^4 - 3 * q^5 + 7 * q^6 + 12 * q^8 + 2 * q^9	\( 4 q - 3 q^{2} - 6 q^{3} - 3 q^{4} - 3 q^{5} + 7 q^{6} + 12 q^{8} + 2 q^{9} + 14 q^{10} - 6 q^{11} + 12 q^{12} - 10 q^{13} + 7 q^{15} - 13 q^{16} - 6 q^{17} - 9 q^{18} + 6 q^{19} - 12 q^{20} - 3 q^{22} - 38 q^{24} + 3 q^{25} + 21 q^{26} - 3 q^{29} - 36 q^{30} - 4 q^{31} - 15 q^{32} - 6 q^{33} - 2 q^{34} - 24 q^{36} - 8 q^{37} + 3 q^{38} + 15 q^{39} - 19 q^{40} - 6 q^{41} - 5 q^{43} - 18 q^{44} - 9 q^{45} + 10 q^{46} + 27 q^{48} - 3 q^{50} - q^{51} - 6 q^{52} - 12 q^{53} + 5 q^{54} - 3 q^{55} + 6 q^{57} + 34 q^{58} + 33 q^{60} - 24 q^{61} + 9 q^{62} + 8 q^{64} - 6 q^{65} + 12 q^{66} - 24 q^{67} + 21 q^{68} - 10 q^{69} + 6 q^{71} + 66 q^{72} + 4 q^{73} - 12 q^{74} + 3 q^{75} + 18 q^{76} - 49 q^{78} - 8 q^{79} + 54 q^{80} + 4 q^{81} + 8 q^{82} + q^{85} - 30 q^{86} + 17 q^{87} + 42 q^{88} - 21 q^{89} + 52 q^{90} - 60 q^{92} - 9 q^{93} - 10 q^{94} + 3 q^{95} + 30 q^{96} - 31 q^{97} + 42 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 6 * q^3 - 3 * q^4 - 3 * q^5 + 7 * q^6 + 12 * q^8 + 2 * q^9 + 14 * q^10 - 6 * q^11 + 12 * q^12 - 10 * q^13 + 7 * q^15 - 13 * q^16 - 6 * q^17 - 9 * q^18 + 6 * q^19 - 12 * q^20 - 3 * q^22 - 38 * q^24 + 3 * q^25 + 21 * q^26 - 3 * q^29 - 36 * q^30 - 4 * q^31 - 15 * q^32 - 6 * q^33 - 2 * q^34 - 24 * q^36 - 8 * q^37 + 3 * q^38 + 15 * q^39 - 19 * q^40 - 6 * q^41 - 5 * q^43 - 18 * q^44 - 9 * q^45 + 10 * q^46 + 27 * q^48 - 3 * q^50 - q^51 - 6 * q^52 - 12 * q^53 + 5 * q^54 - 3 * q^55 + 6 * q^57 + 34 * q^58 + 33 * q^60 - 24 * q^61 + 9 * q^62 + 8 * q^64 - 6 * q^65 + 12 * q^66 - 24 * q^67 + 21 * q^68 - 10 * q^69 + 6 * q^71 + 66 * q^72 + 4 * q^73 - 12 * q^74 + 3 * q^75 + 18 * q^76 - 49 * q^78 - 8 * q^79 + 54 * q^80 + 4 * q^81 + 8 * q^82 + q^85 - 30 * q^86 + 17 * q^87 + 42 * q^88 - 21 * q^89 + 52 * q^90 - 60 * q^92 - 9 * q^93 - 10 * q^94 + 3 * q^95 + 30 * q^96 - 31 * q^97 + 42 * q^99

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