LMFDB - Embedded newform 637.2.f.c.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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([0, 4]))

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, 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:	$\Q(\sqrt{-3}, \sqrt{5})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	637.295
Dual form			637.2.f.c.393.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30902 + 2.26728i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(-2.42705 - 4.20378i) q^{4} -2.61803 q^{5} +(-3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})$	\(q+(-1.30902 + 2.26728i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(-2.42705 - 4.20378i) q^{4} -2.61803 q^{5} +(-3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +(3.42705 - 5.93583i) q^{10} +(-0.927051 + 1.60570i) q^{11} +12.7082 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} +10.0902 q^{18} +(-0.927051 - 1.60570i) q^{19} +(6.35410 + 11.0056i) q^{20} +(-2.42705 - 4.20378i) q^{22} +(2.23607 - 3.87298i) q^{23} +(-9.78115 + 16.9415i) q^{24} +1.85410 q^{25} +(2.61803 + 9.06914i) q^{26} +2.23607 q^{27} +(-3.54508 + 6.14027i) q^{29} +(8.97214 + 15.5402i) q^{30} +4.70820 q^{31} +(-5.42705 - 9.39993i) q^{32} +(-2.42705 - 4.20378i) q^{33} +3.85410 q^{34} +(-9.35410 + 16.2018i) q^{36} +(-2.00000 + 3.46410i) q^{37} +4.85410 q^{38} +(2.61803 + 9.06914i) q^{39} -19.5623 q^{40} +(0.381966 - 0.661585i) q^{41} +(-6.28115 - 10.8793i) q^{43} +9.00000 q^{44} +(5.04508 + 8.73834i) q^{45} +(5.85410 + 10.1396i) q^{46} +2.23607 q^{47} +(-12.8992 - 22.3420i) q^{48} +(-2.42705 + 4.20378i) q^{50} +3.85410 q^{51} +(-16.9894 - 4.20378i) q^{52} +3.76393 q^{53} +(-2.92705 + 5.06980i) q^{54} +(2.42705 - 4.20378i) q^{55} +4.85410 q^{57} +(-9.28115 - 16.0754i) q^{58} +(-1.11803 - 1.93649i) q^{59} -33.2705 q^{60} +(-3.00000 - 5.19615i) q^{61} +(-6.16312 + 10.6748i) q^{62} +8.70820 q^{64} +(-6.54508 + 6.80185i) q^{65} +12.7082 q^{66} +(6.35410 - 11.0056i) q^{67} +(-3.57295 + 6.18853i) q^{68} +(5.85410 + 10.1396i) q^{69} +(7.09017 + 12.2805i) q^{71} +(-14.3992 - 24.9401i) q^{72} +2.00000 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} +4.00000 q^{79} +(12.8992 - 22.3420i) q^{80} +(2.85410 - 4.94345i) q^{81} +(1.00000 + 1.73205i) q^{82} -6.70820 q^{83} +(1.92705 + 3.33775i) q^{85} +32.8885 q^{86} +(-9.28115 - 16.0754i) q^{87} +(-6.92705 + 11.9980i) q^{88} +(2.45492 - 4.25204i) q^{89} -26.4164 q^{90} -21.7082 q^{92} +(-6.16312 + 10.6748i) q^{93} +(-2.92705 + 5.06980i) q^{94} +(2.42705 + 4.20378i) q^{95} +28.4164 q^{96} +(9.42705 + 16.3281i) q^{97} +7.14590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 7 q^{6} + 12 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 7 * q^6 + 12 * q^8 - q^9	$ 4 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 7 q^{6} + 12 q^{8} - q^{9} + 7 q^{10} + 3 q^{11} + 24 q^{12} + 10 q^{13} + 7 q^{15} - 13 q^{16} + 6 q^{17} + 18 q^{18} + 3 q^{19} + 12 q^{20} - 3 q^{22} - 19 q^{24} - 6 q^{25} + 6 q^{26} - 3 q^{29} + 18 q^{30} - 8 q^{31} - 15 q^{32} - 3 q^{33} + 2 q^{34} - 24 q^{36} - 8 q^{37} + 6 q^{38} + 6 q^{39} - 38 q^{40} + 6 q^{41} - 5 q^{43} + 36 q^{44} + 9 q^{45} + 10 q^{46} - 27 q^{48} - 3 q^{50} + 2 q^{51} - 21 q^{52} + 24 q^{53} - 5 q^{54} + 3 q^{55} + 6 q^{57} - 17 q^{58} - 66 q^{60} - 12 q^{61} - 9 q^{62} + 8 q^{64} - 15 q^{65} + 24 q^{66} + 12 q^{67} - 21 q^{68} + 10 q^{69} + 6 q^{71} - 33 q^{72} + 8 q^{73} - 12 q^{74} - 3 q^{75} - 18 q^{76} - 49 q^{78} + 16 q^{79} + 27 q^{80} - 2 q^{81} + 4 q^{82} + q^{85} + 60 q^{86} - 17 q^{87} - 21 q^{88} + 21 q^{89} - 52 q^{90} - 60 q^{92} - 9 q^{93} - 5 q^{94} + 3 q^{95} + 60 q^{96} + 31 q^{97} + 42 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 7 * q^6 + 12 * q^8 - q^9 + 7 * q^10 + 3 * q^11 + 24 * q^12 + 10 * q^13 + 7 * q^15 - 13 * q^16 + 6 * q^17 + 18 * q^18 + 3 * q^19 + 12 * q^20 - 3 * q^22 - 19 * q^24 - 6 * q^25 + 6 * q^26 - 3 * q^29 + 18 * q^30 - 8 * q^31 - 15 * q^32 - 3 * q^33 + 2 * q^34 - 24 * q^36 - 8 * q^37 + 6 * q^38 + 6 * q^39 - 38 * q^40 + 6 * q^41 - 5 * q^43 + 36 * q^44 + 9 * q^45 + 10 * q^46 - 27 * q^48 - 3 * q^50 + 2 * q^51 - 21 * q^52 + 24 * q^53 - 5 * q^54 + 3 * q^55 + 6 * q^57 - 17 * q^58 - 66 * q^60 - 12 * q^61 - 9 * q^62 + 8 * q^64 - 15 * q^65 + 24 * q^66 + 12 * q^67 - 21 * q^68 + 10 * q^69 + 6 * q^71 - 33 * q^72 + 8 * q^73 - 12 * q^74 - 3 * q^75 - 18 * q^76 - 49 * q^78 + 16 * q^79 + 27 * q^80 - 2 * q^81 + 4 * q^82 + q^85 + 60 * q^86 - 17 * q^87 - 21 * q^88 + 21 * q^89 - 52 * q^90 - 60 * q^92 - 9 * q^93 - 5 * q^94 + 3 * q^95 + 60 * q^96 + 31 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	$0.790215\pi$
$3$	−1.30902	+	2.26728i	−0.755761	+	1.30902i	0.189234	+	0.981932i	$0.439400\pi$
$3$	−1.30902	+	2.26728i	−0.755761	+	1.30902i	−0.944995	+	0.327085i	$0.893934\pi$
$4$	−2.42705	−	4.20378i	−1.21353	−	2.10189i
$5$	−2.61803			−1.17082			−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803			−1.17082			−0.585410	+	0.810737i	$0.699067\pi$
$6$	−3.42705	−	5.93583i	−1.39909	−	2.42329i
$7$		0			0
$7$		0			0
$8$	7.47214			2.64180
$9$	−1.92705	−	3.33775i	−0.642350	−	1.11258i
$10$	3.42705	−	5.93583i	1.08373	−	1.87707i
$11$	−0.927051	+	1.60570i	−0.279516	+	0.484137i	−0.971265	−	0.238002i	$-0.923507\pi$
$11$	−0.927051	+	1.60570i	−0.279516	+	0.484137i	0.691748	+	0.722139i	$0.256841\pi$
$12$	12.7082			3.66854
$13$	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	0.762852	−	0.646573i	$-0.223798\pi$
$17$	−0.736068	−	1.27491i	−0.178523	−	0.309210i	−0.941375	+	0.337363i	$0.890465\pi$
$18$	10.0902			2.37828
$19$	−0.927051	−	1.60570i	−0.212680	−	0.368373i	0.739872	−	0.672747i	$-0.234886\pi$
$19$	−0.927051	−	1.60570i	−0.212680	−	0.368373i	−0.952552	+	0.304375i	$0.901553\pi$
$20$	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	$0.0122705\pi$
$24$	−9.78115	+	16.9415i	−1.99657	+	3.45816i
$25$	1.85410			0.370820
$26$	2.61803	+	9.06914i	0.513439	+	1.77860i
$27$	2.23607			0.430331
$28$		0			0
$29$	−3.54508	+	6.14027i	−0.658306	+	1.14022i	0.322748	+	0.946485i	$0.395393\pi$
$29$	−3.54508	+	6.14027i	−0.658306	+	1.14022i	−0.981054	+	0.193734i	$0.937940\pi$
$30$	8.97214	+	15.5402i	1.63808	+	2.83724i
$31$	4.70820			0.845618			0.422809	−	0.906219i	$-0.361044\pi$
$31$	4.70820			0.845618			0.422809	+	0.906219i	$0.361044\pi$
$32$	−5.42705	−	9.39993i	−0.959376	−	1.66169i
$33$	−2.42705	−	4.20378i	−0.422495	−	0.731783i
$34$	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	$0.273310\pi$
$38$	4.85410			0.787439
$39$	2.61803	+	9.06914i	0.419221	+	1.45222i
$40$	−19.5623			−3.09307
$41$	0.381966	−	0.661585i	0.0596531	−	0.103322i	−0.834657	−	0.550771i	$-0.814334\pi$
$41$	0.381966	−	0.661585i	0.0596531	−	0.103322i	0.894310	+	0.447449i	$0.147667\pi$
$42$		0			0
$43$	−6.28115	−	10.8793i	−0.957867	−	1.65907i	−0.727667	−	0.685931i	$-0.759395\pi$
$43$	−6.28115	−	10.8793i	−0.957867	−	1.65907i	−0.230200	−	0.973143i	$-0.573938\pi$
$44$	9.00000			1.35680
$45$	5.04508	+	8.73834i	0.752077	+	1.30264i
$46$	5.85410	+	10.1396i	0.863140	+	1.49500i
$47$	2.23607			0.326164			0.163082	−	0.986613i	$-0.447856\pi$
$47$	2.23607			0.326164			0.163082	+	0.986613i	$0.447856\pi$
$48$	−12.8992	−	22.3420i	−1.86184	−	3.22480i
$49$		0			0
$50$	−2.42705	+	4.20378i	−0.343237	+	0.594504i
$51$	3.85410			0.539682
$52$	−16.9894	−	4.20378i	−2.35600	−	0.582959i
$53$	3.76393			0.517016			0.258508	−	0.966009i	$-0.416769\pi$
$53$	3.76393			0.517016			0.258508	+	0.966009i	$0.416769\pi$
$54$	−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
$58$	−9.28115	−	16.0754i	−1.21868	−	2.11081i
$59$	−1.11803	−	1.93649i	−0.145556	−	0.252110i	0.784024	−	0.620730i	$-0.213164\pi$
$59$	−1.11803	−	1.93649i	−0.145556	−	0.252110i	−0.929580	+	0.368620i	$0.879830\pi$
$60$	−33.2705			−4.29520
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	0.607535	−	0.794293i	$-0.292159\pi$
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	−0.991645	+	0.128994i	$0.958825\pi$
$62$	−6.16312	+	10.6748i	−0.782717	+	1.35571i
$63$		0			0
$64$	8.70820			1.08853
$65$	−6.54508	+	6.80185i	−0.811818	+	0.843666i
$66$	12.7082			1.56427
$67$	6.35410	−	11.0056i	0.776277	−	1.34455i	−0.157797	−	0.987472i	$-0.550439\pi$
$67$	6.35410	−	11.0056i	0.776277	−	1.34455i	0.934074	−	0.357080i	$-0.116228\pi$
$68$	−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	0.888670	+	0.458547i	$0.151630\pi$
$71$	7.09017	+	12.2805i	0.841448	+	1.45743i	−0.0472218	+	0.998884i	$0.515037\pi$
$72$	−14.3992	−	24.9401i	−1.69696	−	2.93922i
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	−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
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$	12.8992	−	22.3420i	1.44217	−	2.49792i
$81$	2.85410	−	4.94345i	0.317122	−	0.549272i
$82$	1.00000	+	1.73205i	0.110432	+	0.191273i
$83$	−6.70820			−0.736321			−0.368161	−	0.929762i	$-0.620012\pi$
$83$	−6.70820			−0.736321			−0.368161	+	0.929762i	$0.620012\pi$
$84$		0			0
$85$	1.92705	+	3.33775i	0.209018	+	0.362030i
$86$	32.8885			3.54646
$87$	−9.28115	−	16.0754i	−0.995044	−	1.72347i
$88$	−6.92705	+	11.9980i	−0.738426	+	1.27899i
$89$	2.45492	−	4.25204i	0.260220	−	0.450715i	−0.706080	−	0.708132i	$-0.749538\pi$
$89$	2.45492	−	4.25204i	0.260220	−	0.450715i	0.966300	+	0.257417i	$0.0828714\pi$
$90$	−26.4164			−2.78453
$91$		0			0
$92$	−21.7082			−2.26324
$93$	−6.16312	+	10.6748i	−0.639086	+	1.10693i
$94$	−2.92705	+	5.06980i	−0.301902	+	0.522910i
$95$	2.42705	+	4.20378i	0.249010	+	0.431298i
$96$	28.4164			2.90024
$97$	9.42705	+	16.3281i	0.957172	+	1.65787i	0.729318	+	0.684175i	$0.239838\pi$
$97$	9.42705	+	16.3281i	0.957172	+	1.65787i	0.227854	+	0.973695i	$0.426829\pi$
$98$		0			0
$99$	7.14590			0.718190
$100$	−4.50000	−	7.79423i	−0.450000	−	0.779423i
$101$	−5.78115	+	10.0133i	−0.575246	+	0.996356i	0.420769	+	0.907168i	$0.361760\pi$
$101$	−5.78115	+	10.0133i	−0.575246	+	0.996356i	−0.996015	+	0.0891877i	$0.971573\pi$
$102$	−5.04508	+	8.73834i	−0.499538	+	0.865225i
$103$	8.70820			0.858045			0.429022	−	0.903294i	$-0.358858\pi$
$103$	8.70820			0.858045			0.429022	+	0.903294i	$0.358858\pi$
$104$	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
$109$	−2.70820			−0.259399			−0.129699	−	0.991553i	$-0.541401\pi$
$109$	−2.70820			−0.259399			−0.129699	+	0.991553i	$0.541401\pi$
$110$	6.35410	+	11.0056i	0.605840	+	1.04935i
$111$	−5.23607	−	9.06914i	−0.496986	−	0.860804i
$112$		0			0
$113$	−0.736068	−	1.27491i	−0.0692435	−	0.119933i	0.829325	−	0.558766i	$-0.188725\pi$
$113$	−0.736068	−	1.27491i	−0.0692435	−	0.119933i	−0.898568	+	0.438833i	$0.855392\pi$
$114$	−6.35410	+	11.0056i	−0.595116	+	1.03077i
$115$	−5.85410	+	10.1396i	−0.545898	+	0.945523i
$116$	34.4164			3.19548
$117$	−13.4894	−	3.33775i	−1.24709	−	0.308575i
$118$	5.85410			0.538914
$119$		0			0
$120$	25.6074	−	44.3533i	2.33762	−	4.04888i
$121$	3.78115	+	6.54915i	0.343741	+	0.595377i
$122$	15.7082			1.42215
$123$	1.00000	+	1.73205i	0.0901670	+	0.156174i
$124$	−11.4271	−	19.7922i	−1.02618	−	1.77739i
$125$	8.23607			0.736656
$126$		0			0
$127$	10.4271	−	18.0602i	0.925251	−	1.60258i	0.134094	−	0.990969i	$-0.457187\pi$
$127$	10.4271	−	18.0602i	0.925251	−	1.60258i	0.791157	−	0.611613i	$-0.209479\pi$
$128$	−0.545085	+	0.944115i	−0.0481792	+	0.0834488i
$129$	32.8885			2.89567
$130$	−6.85410	−	23.7433i	−0.601145	−	2.08243i
$131$	15.3262			1.33906			0.669530	−	0.742785i	$-0.266496\pi$
$131$	15.3262			1.33906			0.669530	+	0.742785i	$0.266496\pi$
$132$	−11.7812	+	20.4056i	−1.02542	+	1.77608i
$133$		0			0
$134$	16.6353	+	28.8131i	1.43707	+	2.48907i
$135$	−5.85410			−0.503841
$136$	−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	$0.797660\pi$
$138$	−30.6525			−2.60931
$139$	2.28115	+	3.95107i	0.193485	+	0.335126i	0.946403	−	0.322989i	$-0.104688\pi$
$139$	2.28115	+	3.95107i	0.193485	+	0.335126i	−0.752918	+	0.658114i	$0.771354\pi$
$140$		0			0
$141$	−2.92705	+	5.06980i	−0.246502	+	0.426954i
$142$	−37.1246			−3.11543
$143$	1.85410	+	6.42280i	0.155048	+	0.537101i
$144$	37.9787			3.16489
$145$	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
$149$	−0.927051	−	1.60570i	−0.0759470	−	0.131544i	0.825551	−	0.564328i	$-0.190865\pi$
$149$	−0.927051	−	1.60570i	−0.0759470	−	0.131544i	−0.901498	+	0.432784i	$0.857531\pi$
$150$	−6.35410	−	11.0056i	−0.518810	−	0.898606i
$151$	−1.29180			−0.105125			−0.0525624	−	0.998618i	$-0.516739\pi$
$151$	−1.29180			−0.105125			−0.0525624	+	0.998618i	$0.516739\pi$
$152$	−6.92705	−	11.9980i	−0.561858	−	0.973167i
$153$	−2.83688	+	4.91362i	−0.229348	+	0.397243i
$154$		0			0
$155$	−12.3262			−0.990067
$156$	31.7705	−	33.0169i	2.54368	−	2.64347i
$157$	−14.8541			−1.18549			−0.592743	−	0.805392i	$-0.701955\pi$
$157$	−14.8541			−1.18549			−0.592743	+	0.805392i	$0.701955\pi$
$158$	−5.23607	+	9.06914i	−0.416559	+	0.721502i
$159$	−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
$163$	1.85410	+	3.21140i	0.145224	+	0.251536i	0.929457	−	0.368931i	$-0.120276\pi$
$163$	1.85410	+	3.21140i	0.145224	+	0.251536i	−0.784232	+	0.620467i	$0.786943\pi$
$164$	−3.70820			−0.289562
$165$	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	−0.447406	−	0.894331i	$-0.647652\pi$
$167$	7.11803	−	12.3288i	0.550810	−	0.954031i	0.998216	−	0.0597001i	$-0.0190144\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	−10.0902			−0.773881
$171$	−3.57295	+	6.18853i	−0.273230	+	0.473249i
$172$	−30.4894	+	52.8091i	−2.32479	+	4.02666i
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	0.642699	−	0.766119i	$-0.277815\pi$
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	−0.984828	+	0.173534i	$0.944481\pi$
$174$	48.5967			3.68411
$175$		0			0
$176$	−9.13525	−	15.8227i	−0.688596	−	1.19268i
$177$	5.85410			0.440021
$178$	6.42705	+	11.1320i	0.481728	+	0.834377i
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	−0.647397	−	0.762153i	$-0.724142\pi$
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	0.983742	+	0.179585i	$0.0574756\pi$
$180$	24.4894	−	42.4168i	1.82533	−	3.16156i
$181$	−9.70820			−0.721605			−0.360803	−	0.932642i	$-0.617497\pi$
$181$	−9.70820			−0.721605			−0.360803	+	0.932642i	$0.617497\pi$
$182$		0			0
$183$	15.7082			1.16118
$184$	16.7082	−	28.9395i	1.23175	−	2.13345i
$185$	5.23607	−	9.06914i	0.384963	−	0.666776i
$186$	−16.1353	−	27.9471i	−1.18309	−	2.04918i
$187$	2.72949			0.199600
$188$	−5.42705	−	9.39993i	−0.395808	−	0.685560i
$189$		0			0
$190$	−12.7082			−0.921950
$191$	−10.6910	−	18.5173i	−0.773572	−	1.33987i	−0.935593	−	0.353079i	$-0.885135\pi$
$191$	−10.6910	−	18.5173i	−0.773572	−	1.33987i	0.162021	−	0.986787i	$-0.448199\pi$
$192$	−11.3992	+	19.7440i	−0.822665	+	1.42490i
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	−0.737620	−	0.675216i	$-0.764050\pi$
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	0.953564	+	0.301189i	$0.0973836\pi$
$194$	−49.3607			−3.54389
$195$	−6.85410	−	23.7433i	−0.490832	−	1.70029i
$196$		0			0
$197$	8.39919	−	14.5478i	0.598417	−	1.03649i	−0.394638	−	0.918837i	$-0.629130\pi$
$197$	8.39919	−	14.5478i	0.598417	−	1.03649i	0.993055	−	0.117652i	$-0.0375368\pi$
$198$	−9.35410	+	16.2018i	−0.664767	+	1.15141i
$199$	−12.2082	−	21.1452i	−0.865417	−	1.49895i	−0.866633	−	0.498946i	$-0.833720\pi$
$199$	−12.2082	−	21.1452i	−0.865417	−	1.49895i	0.00121626	−	0.999999i	$-0.499613\pi$
$200$	13.8541			0.979633
$201$	16.6353	+	28.8131i	1.17336	+	2.03232i
$202$	−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
$206$	−11.3992	+	19.7440i	−0.794219	+	1.37563i
$207$	−17.2361			−1.19799
$208$	9.85410	+	34.1356i	0.683259	+	2.36688i
$209$	3.43769			0.237790
$210$		0			0
$211$	−2.35410	+	4.07742i	−0.162063	+	0.280701i	−0.935608	−	0.353039i	$-0.885148\pi$
$211$	−2.35410	+	4.07742i	−0.162063	+	0.280701i	0.773545	+	0.633741i	$0.218481\pi$
$212$	−9.13525	−	15.8227i	−0.627412	−	1.08671i
$213$	−37.1246			−2.54374
$214$	4.42705	+	7.66788i	0.302627	+	0.524165i
$215$	16.4443	+	28.4823i	1.12149	+	1.94248i
$216$	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
$220$	−23.5623			−1.58857
$221$	−5.15248	−	1.27491i	−0.346593	−	0.0857595i
$222$	27.4164			1.84007
$223$	10.1353	−	17.5548i	0.678707	−	1.17555i	−0.296664	−	0.954982i	$-0.595874\pi$
$223$	10.1353	−	17.5548i	0.678707	−	1.17555i	0.975371	−	0.220573i	$-0.0707926\pi$
$224$		0			0
$225$	−3.57295	−	6.18853i	−0.238197	−	0.412569i
$226$	3.85410			0.256371
$227$	0.736068	+	1.27491i	0.0488545	+	0.0846186i	0.889419	−	0.457094i	$-0.151110\pi$
$227$	0.736068	+	1.27491i	0.0488545	+	0.0846186i	−0.840564	+	0.541712i	$0.817776\pi$
$228$	−11.7812	−	20.4056i	−0.780226	−	1.35139i
$229$	13.1246			0.867299			0.433649	−	0.901082i	$-0.357226\pi$
$229$	13.1246			0.867299			0.433649	+	0.901082i	$0.357226\pi$
$230$	−15.3262	−	26.5458i	−1.01058	−	1.75038i
$231$		0			0
$232$	−26.4894	+	45.8809i	−1.73911	+	3.01223i
$233$	2.61803			0.171513			0.0857566	−	0.996316i	$-0.472669\pi$
$233$	2.61803			0.171513			0.0857566	+	0.996316i	$0.472669\pi$
$234$	25.2254	−	26.2150i	1.64904	−	1.71373i
$235$	−5.85410			−0.381880
$236$	−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	$0.794701\pi$
$240$	33.7705	+	58.4922i	2.17988	+	3.77566i
$241$	12.2812	+	21.2716i	0.791099	+	1.37022i	0.925287	+	0.379267i	$0.123824\pi$
$241$	12.2812	+	21.2716i	0.791099	+	1.37022i	−0.134189	+	0.990956i	$0.542843\pi$
$242$	−19.7984			−1.27269
$243$	10.8262	+	18.7516i	0.694503	+	1.20292i
$244$	−14.5623	+	25.2227i	−0.932256	+	1.61471i
$245$		0			0
$246$	−5.23607			−0.333840
$247$	−6.48936	−	1.60570i	−0.412908	−	0.102168i
$248$	35.1803			2.23395
$249$	8.78115	−	15.2094i	0.556483	−	0.963857i
$250$	−10.7812	+	18.6735i	−0.681860	+	1.18102i
$251$	0.381966	+	0.661585i	0.0241095	+	0.0417588i	0.877828	−	0.478975i	$-0.158992\pi$
$251$	0.381966	+	0.661585i	0.0241095	+	0.0417588i	−0.853719	+	0.520734i	$0.825658\pi$
$252$		0			0
$253$	4.14590	+	7.18091i	0.260650	+	0.451460i
$254$	27.2984	+	47.2822i	1.71285	+	2.96675i
$255$	−10.0902			−0.631871
$256$	7.28115	+	12.6113i	0.455072	+	0.788208i
$257$	8.37132	−	14.4996i	0.522189	−	0.904457i	−0.477478	−	0.878644i	$-0.658449\pi$
$257$	8.37132	−	14.4996i	0.522189	−	0.904457i	0.999667	−	0.0258138i	$-0.00821769\pi$
$258$	−43.0517	+	74.5677i	−2.68028	+	4.64238i
$259$		0			0
$260$	44.4787	+	11.0056i	2.75845	+	0.682540i
$261$	27.3262			1.69145
$262$	−20.0623	+	34.7489i	−1.23945	+	2.14680i
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	−0.970758	−	0.240059i	$-0.922833\pi$
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	0.693276	+	0.720672i	$0.256167\pi$
$264$	−18.1353	−	31.4112i	−1.11615	−	1.93322i
$265$	−9.85410			−0.605333
$266$		0			0
$267$	6.42705	+	11.1320i	0.393329	+	0.681266i
$268$	−61.6869			−3.76813
$269$	−14.3713	−	24.8919i	−0.876235	−	1.51768i	−0.855441	−	0.517900i	$-0.826714\pi$
$269$	−14.3713	−	24.8919i	−0.876235	−	1.51768i	−0.0207937	−	0.999784i	$-0.506619\pi$
$270$	7.66312	−	13.2729i	0.466363	−	0.807764i
$271$	−4.20820	+	7.28882i	−0.255630	+	0.442764i	−0.965066	−	0.262005i	$-0.915616\pi$
$271$	−4.20820	+	7.28882i	−0.255630	+	0.442764i	0.709436	+	0.704770i	$0.248950\pi$
$272$	14.5066			0.879590
$273$		0			0
$274$	−6.85410			−0.414071
$275$	−1.71885	+	2.97713i	−0.103650	+	0.179528i
$276$	28.4164	−	49.2187i	1.71047	−	2.96262i
$277$	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	$0.785338\pi$
$278$	−11.9443			−0.716370
$279$	−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	$0.294399\pi$
$282$	−7.66312	−	13.2729i	−0.456332	−	0.790390i
$283$	6.70820	−	11.6190i	0.398761	−	0.690675i	−0.594812	−	0.803865i	$-0.702774\pi$
$283$	6.70820	−	11.6190i	0.398761	−	0.690675i	0.993573	+	0.113190i	$0.0361069\pi$
$284$	34.4164	−	59.6110i	2.04224	−	3.53726i
$285$	−12.7082			−0.752769
$286$	−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
$291$	−49.3607			−2.89357
$292$	−4.85410	−	8.40755i	−0.284065	−	0.492015i
$293$	−3.38197	−	5.85774i	−0.197577	−	0.342213i	0.750166	−	0.661250i	$-0.229974\pi$
$293$	−3.38197	−	5.85774i	−0.197577	−	0.342213i	−0.947742	+	0.319037i	$0.896640\pi$
$294$		0			0
$295$	2.92705	+	5.06980i	0.170419	+	0.295175i
$296$	−14.9443	+	25.8842i	−0.868618	+	1.50449i
$297$	−2.07295	+	3.59045i	−0.120285	+	0.208339i
$298$	4.85410			0.281191
$299$	−4.47214	−	15.4919i	−0.258630	−	0.895922i
$300$	23.5623			1.36037
$301$		0			0
$302$	1.69098	−	2.92887i	0.0973051	−	0.168537i
$303$	−15.1353	−	26.2150i	−0.869498	−	1.50601i
$304$	18.2705			1.04789
$305$	7.85410	+	13.6037i	0.449725	+	0.778946i
$306$	−7.42705	−	12.8640i	−0.424576	−	0.735388i
$307$	4.85410			0.277038			0.138519	−	0.990360i	$-0.455766\pi$
$307$	4.85410			0.277038			0.138519	+	0.990360i	$0.455766\pi$
$308$		0			0
$309$	−11.3992	+	19.7440i	−0.648477	+	1.12320i
$310$	16.1353	−	27.9471i	0.916421	−	1.58729i
$311$	−3.32624			−0.188614			−0.0943068	−	0.995543i	$-0.530063\pi$
$311$	−3.32624			−0.188614			−0.0943068	+	0.995543i	$0.530063\pi$
$312$	19.5623	+	67.7658i	1.10750	+	3.83648i
$313$	−25.1246			−1.42013			−0.710064	−	0.704138i	$-0.751334\pi$
$313$	−25.1246			−1.42013			−0.710064	+	0.704138i	$0.751334\pi$
$314$	19.4443	−	33.6785i	1.09730	−	1.90059i
$315$		0			0
$316$	−9.70820	−	16.8151i	−0.546129	−	0.945923i
$317$	26.2361			1.47356			0.736782	−	0.676130i	$-0.236344\pi$
$317$	26.2361			1.47356			0.736782	+	0.676130i	$0.236344\pi$
$318$	−12.8992	−	22.3420i	−0.723350	−	1.25288i
$319$	−6.57295	−	11.3847i	−0.368014	−	0.637420i
$320$	−22.7984			−1.27447
$321$	4.42705	+	7.66788i	0.247094	+	0.427979i
$322$		0			0
$323$	−1.36475	+	2.36381i	−0.0759364	+	0.131526i
$324$	−27.7082			−1.53934
$325$	4.63525	−	4.81710i	0.257118	−	0.267205i
$326$	−9.70820			−0.537688
$327$	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
$331$	5.07295	+	8.78661i	0.278834	+	0.482956i	0.971095	−	0.238692i	$-0.0767186\pi$
$331$	5.07295	+	8.78661i	0.278834	+	0.482956i	−0.692261	+	0.721647i	$0.743385\pi$
$332$	16.2812	+	28.1998i	0.893544	+	1.54766i
$333$	15.4164			0.844814
$334$	18.6353	+	32.2772i	1.01968	+	1.76613i
$335$	−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	$0.601978\pi$
$338$	30.1074	+	15.8710i	1.63763	+	0.863268i
$339$	3.85410			0.209326
$340$	9.35410	−	16.2018i	0.507297	−	0.878665i
$341$	−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
$345$	−15.3262	−	26.5458i	−0.825137	−	1.42918i
$346$	23.5623			1.26672
$347$	−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	−0.443720	−	0.896166i	$-0.646341\pi$
$349$	10.3541	−	17.9338i	0.554242	−	0.959976i	0.997962	−	0.0638103i	$-0.0203253\pi$
$350$		0			0
$351$	5.59017	−	5.80948i	0.298381	−	0.310087i
$352$	20.1246			1.07265
$353$	11.0729	−	19.1789i	0.589354	−	1.02079i	−0.404964	−	0.914333i	$-0.632716\pi$
$353$	11.0729	−	19.1789i	0.589354	−	1.02079i	0.994317	−	0.106458i	$-0.0339508\pi$
$354$	−7.66312	+	13.2729i	−0.407290	+	0.705447i
$355$	−18.5623	−	32.1509i	−0.985185	−	1.70639i
$356$	−23.8328			−1.26314
$357$		0			0
$358$	11.7812	+	20.4056i	0.622653	+	1.07847i
$359$	−22.0902			−1.16587			−0.582937	−	0.812517i	$-0.698097\pi$
$359$	−22.0902			−1.16587			−0.582937	+	0.812517i	$0.698097\pi$
$360$	37.6976	+	65.2941i	1.98684	+	3.44130i
$361$	7.78115	−	13.4774i	0.409534	−	0.709334i
$362$	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
$367$	−0.708204	+	1.22665i	−0.0369679	+	0.0640304i	−0.883917	−	0.467643i	$-0.845103\pi$
$367$	−0.708204	+	1.22665i	−0.0369679	+	0.0640304i	0.846949	+	0.531673i	$0.178437\pi$
$368$	22.0344	+	38.1648i	1.14862	+	1.98948i
$369$	−2.94427			−0.153273
$370$	13.7082	+	23.7433i	0.712656	+	1.23436i
$371$		0			0
$372$	59.8328			3.10219
$373$	10.2812	+	17.8075i	0.532338	+	0.922036i	0.999287	+	0.0377522i	$0.0120198\pi$
$373$	10.2812	+	17.8075i	0.532338	+	0.922036i	−0.466949	+	0.884284i	$0.654647\pi$
$374$	−3.57295	+	6.18853i	−0.184753	+	0.320001i
$375$	−10.7812	+	18.6735i	−0.556736	+	0.964296i
$376$	16.7082			0.861660
$377$	7.09017	+	24.5611i	0.365162	+	1.26496i
$378$		0			0
$379$	3.07295	−	5.32250i	0.157847	−	0.273399i	−0.776245	−	0.630431i	$-0.782878\pi$
$379$	3.07295	−	5.32250i	0.157847	−	0.273399i	0.934092	+	0.357032i	$0.116211\pi$
$380$	11.7812	−	20.4056i	0.604360	−	1.04678i
$381$	27.2984	+	47.2822i	1.39854	+	2.42234i
$382$	55.9787			2.86412
$383$	−10.9894	−	19.0341i	−0.561530	−	0.972598i	−0.997363	−	0.0725709i	$-0.976880\pi$
$383$	−10.9894	−	19.0341i	−0.561530	−	0.972598i	0.435833	−	0.900027i	$-0.356454\pi$
$384$	−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
$388$	45.7599	−	79.2584i	2.32311	−	4.02374i
$389$	−11.8885			−0.602773			−0.301387	−	0.953502i	$-0.597449\pi$
$389$	−11.8885			−0.602773			−0.301387	+	0.953502i	$0.597449\pi$
$390$	62.8050	+	15.5402i	3.18025	+	0.786908i
$391$	−6.58359			−0.332947
$392$		0			0
$393$	−20.0623	+	34.7489i	−1.01201	+	1.75285i
$394$	21.9894	+	38.0867i	1.10781	+	1.91878i
$395$	−10.4721			−0.526910
$396$	−17.3435	−	30.0398i	−0.871542	−	1.50955i
$397$	0.708204	+	1.22665i	0.0355437	+	0.0615636i	0.883250	−	0.468902i	$-0.155350\pi$
$397$	0.708204	+	1.22665i	0.0355437	+	0.0615636i	−0.847706	+	0.530466i	$0.822017\pi$
$398$	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	$0.820712\pi$
$402$	−87.1033			−4.34432
$403$	11.7705	−	12.2323i	0.586331	−	0.609333i
$404$	56.1246			2.79230
$405$	−7.47214	+	12.9421i	−0.371293	+	0.643099i
$406$		0			0
$407$	−3.70820	−	6.42280i	−0.183809	−	0.318366i
$408$	28.7984			1.42573
$409$	7.21885	+	12.5034i	0.356949	+	0.618254i	0.987450	−	0.157935i	$-0.0504837\pi$
$409$	7.21885	+	12.5034i	0.356949	+	0.618254i	−0.630500	+	0.776189i	$0.717150\pi$
$410$	−2.61803	−	4.53457i	−0.129295	−	0.223946i
$411$	−6.85410			−0.338088
$412$	−21.1353	−	36.6073i	−1.04126	−	1.80351i
$413$		0			0
$414$	22.5623	−	39.0791i	1.10888	−	1.92063i
$415$	17.5623			0.862100
$416$	−37.9894	−	9.39993i	−1.86258	−	0.460869i
$417$	−11.9443			−0.584914
$418$	−4.50000	+	7.79423i	−0.220102	+	0.381228i
$419$	−5.97214	+	10.3440i	−0.291758	+	0.505340i	−0.974226	−	0.225576i	$-0.927574\pi$
$419$	−5.97214	+	10.3440i	−0.291758	+	0.505340i	0.682468	+	0.730916i	$0.260907\pi$
$420$		0			0
$421$	1.41641			0.0690315			0.0345157	−	0.999404i	$-0.489011\pi$
$421$	1.41641			0.0690315			0.0345157	+	0.999404i	$0.489011\pi$
$422$	−6.16312	−	10.6748i	−0.300016	−	0.519643i
$423$	−4.30902	−	7.46344i	−0.209512	−	0.362885i
$424$	28.1246			1.36585
$425$	−1.36475	−	2.36381i	−0.0661999	−	0.114662i
$426$	48.5967	−	84.1720i	2.35452	−	4.07815i
$427$		0			0
$428$	−16.4164			−0.793517
$429$	−16.9894	−	4.20378i	−0.820254	−	0.202960i
$430$	−86.1033			−4.15227
$431$	−3.89919	+	6.75359i	−0.187817	+	0.325309i	−0.944522	−	0.328448i	$-0.893475\pi$
$431$	−3.89919	+	6.75359i	−0.187817	+	0.325309i	0.756705	+	0.653756i	$0.226808\pi$
$432$	−11.0172	+	19.0824i	−0.530066	+	0.918102i
$433$	0.500000	+	0.866025i	0.0240285	+	0.0416185i	0.877790	−	0.479046i	$-0.159017\pi$
$433$	0.500000	+	0.866025i	0.0240285	+	0.0416185i	−0.853761	+	0.520665i	$0.825684\pi$
$434$		0			0
$435$	24.2984	+	42.0860i	1.16502	+	2.01787i
$436$	6.57295	+	11.3847i	0.314787	+	0.545227i
$437$	−8.29180			−0.396650
$438$	−6.85410	−	11.8717i	−0.327502	−	0.567250i
$439$	7.42705	−	12.8640i	0.354474	−	0.613967i	−0.632554	−	0.774516i	$-0.717993\pi$
$439$	7.42705	−	12.8640i	0.354474	−	0.613967i	0.987028	+	0.160550i	$0.0513267\pi$
$440$	18.1353	−	31.4112i	0.864564	−	1.49747i
$441$		0			0
$442$	9.63525	−	10.0133i	0.458302	−	0.476282i
$443$	−5.23607			−0.248773			−0.124387	−	0.992234i	$-0.539696\pi$
$443$	−5.23607			−0.248773			−0.124387	+	0.992234i	$0.539696\pi$
$444$	−25.4164	+	44.0225i	−1.20621	+	2.08922i
$445$	−6.42705	+	11.1320i	−0.304671	+	0.527706i
$446$	26.5344	+	45.9590i	1.25644	+	2.17622i
$447$	4.85410			0.229591
$448$		0			0
$449$	−9.76393	−	16.9116i	−0.460788	−	0.798109i	0.538212	−	0.842809i	$-0.319100\pi$
$449$	−9.76393	−	16.9116i	−0.460788	−	0.798109i	−0.999000	+	0.0447005i	$0.985767\pi$
$450$	18.7082			0.881913
$451$	0.708204	+	1.22665i	0.0333480	+	0.0577605i
$452$	−3.57295	+	6.18853i	−0.168057	+	0.291084i
$453$	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	$0.284086\pi$
$458$	−17.1803	+	29.7572i	−0.802785	+	1.39046i
$459$	−1.64590	−	2.85078i	−0.0768239	−	0.133063i
$460$	56.8328			2.64984
$461$	−6.10739	−	10.5783i	−0.284450	−	0.492681i	0.688026	−	0.725686i	$-0.258477\pi$
$461$	−6.10739	−	10.5783i	−0.284450	−	0.492681i	−0.972476	+	0.233005i	$0.925144\pi$
$462$		0			0
$463$	6.70820			0.311757			0.155878	−	0.987776i	$-0.450179\pi$
$463$	6.70820			0.311757			0.155878	+	0.987776i	$0.450179\pi$
$464$	−34.9336	−	60.5068i	−1.62175	−	2.80896i
$465$	16.1353	−	27.9471i	0.748255	−	1.29601i
$466$	−3.42705	+	5.93583i	−0.158755	+	0.274972i
$467$	−2.34752			−0.108630			−0.0543152	−	0.998524i	$-0.517298\pi$
$467$	−2.34752			−0.108630			−0.0543152	+	0.998524i	$0.517298\pi$
$468$	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
$473$	23.2918			1.07096
$474$	−13.7082	−	23.7433i	−0.629639	−	1.09057i
$475$	−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
$479$	12.4894	−	21.6322i	0.570653	−	0.988400i	−0.425846	−	0.904796i	$-0.640023\pi$
$479$	12.4894	−	21.6322i	0.570653	−	0.988400i	0.996499	−	0.0836047i	$-0.0266433\pi$
$480$	−74.3951			−3.39566
$481$	4.00000	+	13.8564i	0.182384	+	0.631798i
$482$	−64.3050			−2.92901
$483$		0			0
$484$	18.3541	−	31.7902i	0.834277	−	1.44501i
$485$	−24.6803	−	42.7476i	−1.12068	−	1.94107i
$486$	−56.6869			−2.57137
$487$	−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	$-0.404354\pi$
$488$	−22.4164	−	38.8264i	−1.01474	−	1.75759i
$489$	−9.70820			−0.439020
$490$		0			0
$491$	−6.19098	+	10.7231i	−0.279395	+	0.483927i	−0.971235	−	0.238125i	$-0.923467\pi$
$491$	−6.19098	+	10.7231i	−0.279395	+	0.483927i	0.691839	+	0.722051i	$0.256801\pi$
$492$	4.85410	−	8.40755i	0.218840	−	0.379042i
$493$	10.4377			0.470090
$494$	12.1353	−	12.6113i	0.545991	−	0.567410i
$495$	−18.7082			−0.840871
$496$	−23.1976	+	40.1794i	−1.04160	+	1.80411i
$497$		0			0
$498$	22.9894	+	39.8187i	1.03018	+	1.78432i
$499$	14.8541			0.664961			0.332480	−	0.943110i	$-0.392114\pi$
$499$	14.8541			0.664961			0.332480	+	0.943110i	$0.392114\pi$
$500$	−19.9894	−	34.6226i	−0.893951	−	1.54837i
$501$	18.6353	+	32.2772i	0.832562	+	1.44204i
$502$	−2.00000			−0.0892644
$503$	13.3090	+	23.0519i	0.593420	+	1.02783i	0.993768	+	0.111470i	$0.0355559\pi$
$503$	13.3090	+	23.0519i	0.593420	+	1.02783i	−0.400348	+	0.916363i	$0.631111\pi$
$504$		0			0
$505$	15.1353	−	26.2150i	0.673510	−	1.16655i
$506$	−21.7082			−0.965047
$507$	30.1074	+	15.8710i	1.33712	+	0.704855i
$508$	−101.228			−4.49126
$509$	−9.29837	+	16.1053i	−0.412143	+	0.713853i	−0.995124	−	0.0986331i	$-0.968553\pi$
$509$	−9.29837	+	16.1053i	−0.412143	+	0.713853i	0.582981	+	0.812486i	$0.301886\pi$
$510$	13.2082	−	22.8773i	0.584869	−	1.01302i
$511$		0			0
$512$	−40.3050			−1.78124
$513$	−2.07295	−	3.59045i	−0.0915229	−	0.158522i
$514$	21.9164	+	37.9603i	0.966691	+	1.67436i
$515$	−22.7984			−1.00462
$516$	−79.8222	−	138.256i	−3.51398	−	6.08638i
$517$	−2.07295	+	3.59045i	−0.0911682	+	0.157908i
$518$		0			0
$519$	23.5623			1.03427
$520$	−48.9058	+	50.8244i	−2.14466	+	2.22880i
$521$	−18.6525			−0.817180			−0.408590	−	0.912718i	$-0.633979\pi$
$521$	−18.6525			−0.817180			−0.408590	+	0.912718i	$0.633979\pi$
$522$	−35.7705	+	61.9563i	−1.56563	+	2.71176i
$523$	0.562306	−	0.973942i	0.0245879	−	0.0425875i	−0.853470	−	0.521143i	$-0.825506\pi$
$523$	0.562306	−	0.973942i	0.0245879	−	0.0425875i	0.878058	+	0.478555i	$0.158839\pi$
$524$	−37.1976	−	64.4281i	−1.62498	−	2.81455i
$525$		0			0
$526$	−11.7812	−	20.4056i	−0.513683	−	0.889724i
$527$	−3.46556	−	6.00252i	−0.150962	−	0.261474i
$528$	47.8328			2.08166
$529$	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
$534$	−33.6525			−1.45629
$535$	−4.42705	+	7.66788i	−0.191398	+	0.331511i
$536$	47.4787	−	82.2355i	2.05077	−	3.55203i
$537$	11.7812	+	20.4056i	0.508394	+	0.880565i
$538$	75.2492			3.24422
$539$		0			0
$540$	14.2082	+	24.6093i	0.611424	+	1.05902i
$541$	35.2705			1.51640			0.758199	−	0.652023i	$-0.226080\pi$
$541$	35.2705			1.51640			0.758199	+	0.652023i	$0.226080\pi$
$542$	−11.0172	−	19.0824i	−0.473230	−	0.819659i
$543$	12.7082	−	22.0113i	0.545361	−	0.944593i
$544$	−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
$549$	−11.5623	+	20.0265i	−0.493467	+	0.854710i
$550$	−4.50000	−	7.79423i	−0.191881	−	0.332347i
$551$	13.1459			0.560034
$552$	43.7426	+	75.7645i	1.86181	+	3.22475i
$553$		0			0
$554$	−13.0902			−0.556148
$555$	13.7082	+	23.7433i	0.581881	+	1.00785i
$556$	11.0729	−	19.1789i	0.469598	−	0.813367i
$557$	13.9894	−	24.2303i	0.592748	−	1.02667i	−0.401112	−	0.916029i	$-0.631376\pi$
$557$	13.9894	−	24.2303i	0.592748	−	1.02667i	0.993860	−	0.110641i	$-0.0352904\pi$
$558$	47.5066			2.01111
$559$	−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	0.554264	−	0.832341i	$-0.313000\pi$
$563$	−10.5279	−	18.2348i	−0.443697	−	0.768505i	−0.997960	+	0.0638360i	$0.979667\pi$
$564$	28.4164			1.19655
$565$	1.92705	+	3.33775i	0.0810716	+	0.140420i
$566$	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	$0.268084\pi$
$570$	16.6353	−	28.8131i	0.696774	−	1.20685i
$571$	24.6869			1.03312			0.516558	−	0.856252i	$-0.327213\pi$
$571$	24.6869			1.03312			0.516558	+	0.856252i	$0.327213\pi$
$572$	22.5000	−	23.3827i	0.940772	−	0.977679i
$573$	55.9787			2.33854
$574$		0			0
$575$	4.14590	−	7.18091i	0.172896	−	0.299464i
$576$	−16.7812	−	29.0658i	−0.699215	−	1.21108i
$577$	43.8328			1.82478			0.912392	−	0.409318i	$-0.134233\pi$
$577$	43.8328			1.82478			0.912392	+	0.409318i	$0.134233\pi$
$578$	19.4164	+	33.6302i	0.807616	+	1.39883i
$579$	7.85410	+	13.6037i	0.326405	+	0.565351i
$580$	−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
$584$	14.9443			0.618398
$585$	35.3156	+	8.73834i	1.46012	+	0.361286i
$586$	17.7082			0.731519
$587$	−9.95492	+	17.2424i	−0.410883	+	0.711671i	−0.994987	−	0.100009i	$-0.968113\pi$
$587$	−9.95492	+	17.2424i	−0.410883	+	0.711671i	0.584103	+	0.811679i	$0.301446\pi$
$588$		0			0
$589$	−4.36475	−	7.55996i	−0.179846	−	0.311503i
$590$	−15.3262			−0.630971
$591$	21.9894	+	38.0867i	0.904521	+	1.56668i
$592$	−19.7082	−	34.1356i	−0.810002	−	1.40296i
$593$	−43.7984			−1.79858			−0.899292	−	0.437349i	$-0.855917\pi$
$593$	−43.7984			−1.79858			−0.899292	+	0.437349i	$0.855917\pi$
$594$	−5.42705	−	9.39993i	−0.222675	−	0.385684i
$595$		0			0
$596$	−4.50000	+	7.79423i	−0.184327	+	0.319264i
$597$	63.9230			2.61619
$598$	40.9787	+	10.1396i	1.67574	+	0.414639i
$599$	29.5066			1.20561			0.602803	−	0.797890i	$-0.294050\pi$
$599$	29.5066			1.20561			0.602803	+	0.797890i	$0.294050\pi$
$600$	−18.1353	+	31.4112i	−0.740369	+	1.28236i
$601$	20.1976	−	34.9832i	0.823876	−	1.42699i	−0.0788998	−	0.996883i	$-0.525141\pi$
$601$	20.1976	−	34.9832i	0.823876	−	1.42699i	0.902776	−	0.430112i	$-0.141526\pi$
$602$		0			0
$603$	−48.9787			−1.99457
$604$	3.13525	+	5.43042i	0.127572	+	0.220961i
$605$	−9.89919	−	17.1459i	−0.402459	−	0.697080i
$606$	79.2492			3.21928
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$	−10.0623	+	17.4284i	−0.408080	+	0.706816i
$609$		0			0
$610$	−41.1246			−1.66509
$611$	5.59017	−	5.80948i	0.226154	−	0.235026i
$612$	27.5410			1.11328
$613$	−17.2812	+	29.9318i	−0.697979	+	1.20894i	0.271187	+	0.962527i	$0.412584\pi$
$613$	−17.2812	+	29.9318i	−0.697979	+	1.20894i	−0.969166	+	0.246409i	$0.920749\pi$
$614$	−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	0.865464	−	0.500971i	$-0.167024\pi$
$617$	−0.0278640	−	0.0482619i	−0.00112176	−	0.00194295i	−0.866586	+	0.499028i	$0.833690\pi$
$618$	−29.8435	−	51.6904i	−1.20048	−	2.07929i
$619$	−9.41641			−0.378477			−0.189239	−	0.981931i	$-0.560602\pi$
$619$	−9.41641			−0.378477			−0.189239	+	0.981931i	$0.560602\pi$
$620$	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
$625$	−30.8328			−1.23331
$626$	32.8885	−	56.9646i	1.31449	−	2.27676i
$627$	−4.50000	+	7.79423i	−0.179713	+	0.311272i
$628$	36.0517	+	62.4433i	1.43862	+	2.49176i
$629$	5.88854			0.234792
$630$		0			0
$631$	−17.1976	−	29.7870i	−0.684624	−	1.18580i	−0.973555	−	0.228454i	$-0.926633\pi$
$631$	−17.1976	−	29.7870i	−0.684624	−	1.18580i	0.288931	−	0.957350i	$-0.406700\pi$
$632$	29.8885			1.18890
$633$	−6.16312	−	10.6748i	−0.244962	−	0.424287i
$634$	−34.3435	+	59.4846i	−1.36395	+	2.36244i
$635$	−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
$640$	1.42705	−	2.47172i	0.0564091	−	0.0977035i
$641$	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	$0.445827\pi$
$642$	−23.1803			−0.914855
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	0.788723	−	0.614749i	$-0.210743\pi$
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	−0.926750	+	0.375680i	$0.877409\pi$
$644$		0			0
$645$	−86.1033			−3.39032
$646$	−3.57295	−	6.18853i	−0.140576	−	0.243484i
$647$	12.3820	−	21.4462i	0.486785	−	0.843137i	−0.513099	−	0.858329i	$-0.671503\pi$
$647$	12.3820	−	21.4462i	0.486785	−	0.843137i	0.999885	+	0.0151924i	$0.00483607\pi$
$648$	21.3262	−	36.9381i	0.837774	−	1.45107i
$649$	4.14590			0.162741
$650$	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
$655$	−40.1246			−1.56780
$656$	3.76393	+	6.51932i	0.146957	+	0.254537i
$657$	−3.85410	−	6.67550i	−0.150363	−	0.260436i
$658$		0			0
$659$	11.9443	+	20.6881i	0.465283	+	0.805893i	0.999214	−	0.0396343i	$-0.0126193\pi$
$659$	11.9443	+	20.6881i	0.465283	+	0.805893i	−0.533931	+	0.845528i	$0.679286\pi$
$660$	30.8435	−	53.4224i	1.20058	−	2.07947i
$661$	−24.2705	+	42.0378i	−0.944013	+	1.63508i	−0.186299	+	0.982493i	$0.559649\pi$
$661$	−24.2705	+	42.0378i	−0.944013	+	1.63508i	−0.757715	+	0.652586i	$0.773684\pi$
$662$	−26.5623			−1.03237
$663$	9.63525	−	10.0133i	0.374202	−	0.388882i
$664$	−50.1246			−1.94521
$665$		0			0
$666$	−20.1803	+	34.9534i	−0.781972	+	1.35442i
$667$	15.8541	+	27.4601i	0.613873	+	1.06326i
$668$	−69.1033			−2.67369
$669$	26.5344	+	45.9590i	1.02588	+	1.77688i
$670$	−43.5517	−	75.4337i	−1.68255	−	2.91426i
$671$	11.1246			0.429461
$672$		0			0
$673$	19.6246	−	33.9908i	0.756473	−	1.31025i	−0.188165	−	0.982137i	$-0.560254\pi$
$673$	19.6246	−	33.9908i	0.756473	−	1.31025i	0.944639	−	0.328113i	$-0.106413\pi$
$674$	15.1353	−	26.2150i	0.582988	−	1.00977i
$675$	4.14590			0.159576
$676$	−53.3951	+	33.6302i	−2.05366	+	1.29347i
$677$	−43.7426			−1.68117			−0.840583	−	0.541682i	$-0.817788\pi$
$677$	−43.7426			−1.68117			−0.840583	+	0.541682i	$0.817788\pi$
$678$	−5.04508	+	8.73834i	−0.193755	+	0.335594i
$679$		0			0
$680$	14.3992	+	24.9401i	0.552184	+	0.956410i
$681$	−3.85410			−0.147690
$682$	−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	$0.842300\pi$
$684$	34.6869			1.32629
$685$	−3.42705	−	5.93583i	−0.130941	−	0.226796i
$686$		0			0
$687$	−17.1803	+	29.7572i	−0.655471	+	1.13531i
$688$	123.790			4.71946
$689$	9.40983	−	9.77898i	0.358486	−	0.372550i
$690$	80.2492			3.05504
$691$	−2.92705	+	5.06980i	−0.111350	+	0.192864i	−0.916315	−	0.400458i	$-0.868851\pi$
$691$	−2.92705	+	5.06980i	−0.111350	+	0.192864i	0.804965	+	0.593323i	$0.202184\pi$
$692$	−21.8435	+	37.8340i	−0.830364	+	1.43823i
$693$		0			0
$694$	80.5410			3.05730
$695$	−5.97214	−	10.3440i	−0.226536	−	0.392372i
$696$	−69.3500	−	120.118i	−2.62871	−	4.55305i
$697$	−1.12461			−0.0425977
$698$	27.1074	+	46.9514i	1.02603	+	1.77714i
$699$	−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	$0.431940\pi$
$702$	5.85410	+	20.2792i	0.220949	+	0.765389i
$703$	7.41641			0.279715
$704$	−8.07295	+	13.9828i	−0.304261	+	0.526995i
$705$	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
$709$	−11.7812	−	20.4056i	−0.442450	−	0.766347i	0.555420	−	0.831570i	$-0.312557\pi$
$709$	−11.7812	−	20.4056i	−0.442450	−	0.766347i	−0.997871	+	0.0652231i	$0.979224\pi$
$710$	97.1935			3.64761
$711$	−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
$716$	−43.6869			−1.63266
$717$	32.3435	−	56.0205i	1.20789	−	2.09212i
$718$	28.9164	−	50.0847i	1.07915	−	1.86914i
$719$	4.06231	+	7.03612i	0.151498	+	0.262403i	0.931779	−	0.363027i	$-0.118257\pi$
$719$	4.06231	+	7.03612i	0.151498	+	0.262403i	−0.780280	+	0.625430i	$0.784923\pi$
$720$	−99.4296			−3.70552
$721$		0			0
$722$	20.3713	+	35.2842i	0.758142	+	1.31314i
$723$	−64.3050			−2.39153
$724$	23.5623	+	40.8111i	0.875686	+	1.51673i
$725$	−6.57295	+	11.3847i	−0.244113	+	0.422816i
$726$	25.9164	−	44.8885i	0.961848	−	1.66597i
$727$	30.7082			1.13890			0.569452	−	0.822025i	$-0.307155\pi$
$727$	30.7082			1.13890			0.569452	+	0.822025i	$0.307155\pi$
$728$		0			0
$729$	−39.5623			−1.46527
$730$	6.85410	−	11.8717i	0.253682	−	0.439390i
$731$	−9.24671	+	16.0158i	−0.342002	+	0.592365i
$732$	−38.1246	−	66.0338i	−1.40913	−	2.44068i
$733$	32.2705			1.19194			0.595969	−	0.803007i	$-0.296768\pi$
$733$	32.2705			1.19194			0.595969	+	0.803007i	$0.296768\pi$
$734$	−1.85410	−	3.21140i	−0.0684362	−	0.118535i
$735$		0			0
$736$	−48.5410			−1.78925
$737$	11.7812	+	20.4056i	0.433964	+	0.751648i
$738$	3.85410	−	6.67550i	0.141871	−	0.245729i
$739$	3.43769	−	5.95426i	0.126458	−	0.219031i	−0.795844	−	0.605502i	$-0.792973\pi$
$739$	3.43769	−	5.95426i	0.126458	−	0.219031i	0.922302	+	0.386470i	$0.126306\pi$
$740$	−50.8328			−1.86865
$741$	12.1353	−	12.6113i	0.445800	−	0.463289i
$742$		0			0
$743$	−19.6631	+	34.0575i	−0.721370	+	1.24945i	0.239081	+	0.971000i	$0.423154\pi$
$743$	−19.6631	+	34.0575i	−0.721370	+	1.24945i	−0.960451	+	0.278450i	$0.910179\pi$
$744$	−46.0517	+	79.7638i	−1.68834	+	2.92428i
$745$	2.42705	+	4.20378i	0.0889203	+	0.154014i
$746$	−53.8328			−1.97096
$747$	12.9271	+	22.3903i	0.472976	+	0.819219i
$748$	−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	$0.302646\pi$
$752$	−11.0172	+	19.0824i	−0.401757	+	0.695863i
$753$	−2.00000			−0.0728841
$754$	−64.9681	−	16.0754i	−2.36600	−	0.585433i
$755$	3.38197			0.123082
$756$		0			0
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	0.491109	+	0.871098i	$0.336592\pi$
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	−0.999948	+	0.0102362i	$0.996742\pi$
$758$	8.04508	+	13.9345i	0.292211	+	0.506124i
$759$	−21.7082			−0.787958
$760$	18.1353	+	31.4112i	0.657835	+	1.13940i
$761$	−14.4271	−	24.9884i	−0.522980	−	0.905828i	−0.999642	−	0.0267417i	$-0.991487\pi$
$761$	−14.4271	−	24.9884i	−0.522980	−	0.905828i	0.476662	−	0.879087i	$-0.341846\pi$
$762$	−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
$766$	57.5410			2.07904
$767$	−7.82624	−	1.93649i	−0.282589	−	0.0699227i
$768$	−38.1246			−1.37570
$769$	−9.20820	+	15.9491i	−0.332056	+	0.575138i	−0.982915	−	0.184061i	$-0.941076\pi$
$769$	−9.20820	+	15.9491i	−0.332056	+	0.575138i	0.650859	+	0.759199i	$0.274409\pi$
$770$		0			0
$771$	21.9164	+	37.9603i	0.789300	+	1.36711i
$772$	−29.1246			−1.04822
$773$	12.6803	+	21.9630i	0.456080	+	0.789954i	0.998750	−	0.0499924i	$-0.0159197\pi$
$773$	12.6803	+	21.9630i	0.456080	+	0.789954i	−0.542669	+	0.839946i	$0.682586\pi$
$774$	−63.3779	−	109.774i	−2.27807	−	3.94574i
$775$	8.72949			0.313573
$776$	70.4402	+	122.006i	2.52866	+	4.37976i
$777$		0			0
$778$	15.5623	−	26.9547i	0.557936	−	0.966373i
$779$	−1.41641			−0.0507481
$780$	−83.1763	+	86.4393i	−2.97819	+	3.09502i
$781$	−26.2918			−0.940794
$782$	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
$786$	−52.5238	−	90.9739i	−1.87346	−	3.24493i
$787$	1.29180	+	2.23746i	0.0460476	+	0.0797567i	0.888131	−	0.459591i	$-0.152004\pi$
$787$	1.29180	+	2.23746i	0.0460476	+	0.0797567i	−0.842083	+	0.539348i	$0.818671\pi$
$788$	−81.5410			−2.90478
$789$	−11.7812	−	20.4056i	−0.419420	−	0.726457i
$790$	13.7082	−	23.7433i	0.487716	−	0.844749i
$791$		0			0
$792$	53.3951			1.89731
$793$	−21.0000	−	5.19615i	−0.745732	−	0.184521i
$794$	−3.70820			−0.131599
$795$	12.8992	−	22.3420i	0.457487	−	0.792391i
$796$	−59.2599	+	102.641i	−2.10041	+	3.63802i
$797$	−4.09017	−	7.08438i	−0.144881	−	0.250942i	0.784447	−	0.620195i	$-0.212947\pi$
$797$	−4.09017	−	7.08438i	−0.144881	−	0.250942i	−0.929329	+	0.369254i	$0.879613\pi$
$798$		0			0
$799$	−1.64590	−	2.85078i	−0.0582277	−	0.100853i
$800$	−10.0623	−	17.4284i	−0.355756	−	0.616188i
$801$	−18.9230			−0.668611
$802$	−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
$807$	75.2492			2.64890
$808$	−43.1976	+	74.8204i	−1.51968	+	2.63217i
$809$	2.20820	−	3.82472i	0.0776363	−	0.134470i	−0.824593	−	0.565726i	$-0.808596\pi$
$809$	2.20820	−	3.82472i	0.0776363	−	0.134470i	0.902230	+	0.431256i	$0.141929\pi$
$810$	−19.5623	−	33.8829i	−0.687349	−	1.19052i
$811$	−39.2705			−1.37897			−0.689487	−	0.724298i	$-0.742164\pi$
$811$	−39.2705			−1.37897			−0.689487	+	0.724298i	$0.742164\pi$
$812$		0			0
$813$	−11.0172	−	19.0824i	−0.386391	−	0.669249i
$814$	19.4164			0.680545
$815$	−4.85410	−	8.40755i	−0.170032	−	0.294504i
$816$	−18.9894	+	32.8905i	−0.664760	+	1.15140i
$817$	−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	$0.125668\pi$
$822$	8.97214	−	15.5402i	0.312939	−	0.542027i
$823$	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	$0.599818\pi$
$824$	65.0689			2.26678
$825$	−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	$0.410389\pi$
$828$	41.8328	+	72.4566i	1.45379	+	2.51804i
$829$	3.78115	−	6.54915i	0.131325	−	0.227461i	−0.792863	−	0.609400i	$-0.791410\pi$
$829$	3.78115	−	6.54915i	0.131325	−	0.227461i	0.924188	+	0.381939i	$0.124744\pi$
$830$	−22.9894	+	39.8187i	−0.797972	+	1.38213i
$831$	−13.0902			−0.454093
$832$	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
$837$	10.5279			0.363896
$838$	−15.6353	−	27.0811i	−0.540111	−	0.935500i
$839$	6.87132	+	11.9015i	0.237224	+	0.410885i	0.959917	−	0.280285i	$-0.0904290\pi$
$839$	6.87132	+	11.9015i	0.237224	+	0.410885i	−0.722692	+	0.691170i	$0.757096\pi$
$840$		0			0
$841$	−10.6353	−	18.4208i	−0.366733	−	0.635200i
$842$	−1.85410	+	3.21140i	−0.0638966	+	0.110672i
$843$	−26.4164	+	45.7546i	−0.909829	+	1.57587i
$844$	22.8541			0.786671
$845$	1.30902	+	34.0093i	0.0450316	+	1.16995i
$846$	22.5623			0.775708
$847$		0			0
$848$	−18.5451	+	32.1210i	−0.636841	+	1.10304i
$849$	17.5623	+	30.4188i	0.602737	+	1.04397i
$850$	7.14590			0.245102
$851$	8.94427	+	15.4919i	0.306606	+	0.531057i
$852$	90.1033	+	156.064i	3.08689	+	5.34665i
$853$	−14.1246			−0.483617			−0.241809	−	0.970324i	$-0.577741\pi$
$853$	−14.1246			−0.483617			−0.241809	+	0.970324i	$0.577741\pi$
$854$		0			0
$855$	9.35410	−	16.2018i	0.319904	−	0.554089i
$856$	12.6353	−	21.8849i	0.431864	−	0.748011i
$857$	26.4508			0.903544			0.451772	−	0.892133i	$-0.350792\pi$
$857$	26.4508			0.903544			0.451772	+	0.892133i	$0.350792\pi$
$858$	31.7705	−	33.0169i	1.08463	−	1.12718i
$859$	44.2492			1.50976			0.754882	−	0.655861i	$-0.227694\pi$
$859$	44.2492			1.50976			0.754882	+	0.655861i	$0.227694\pi$
$860$	79.8222	−	138.256i	2.72191	−	4.71449i
$861$		0			0
$862$	−10.2082	−	17.6811i	−0.347693	−	0.602222i
$863$	11.8885			0.404691			0.202345	−	0.979314i	$-0.435144\pi$
$863$	11.8885			0.404691			0.202345	+	0.979314i	$0.435144\pi$
$864$	−12.1353	−	21.0189i	−0.412850	−	0.715077i
$865$	11.7812	+	20.4056i	0.400571	+	0.693810i
$866$	−2.61803			−0.0889644
$867$	19.4164	+	33.6302i	0.659416	+	1.14214i
$868$		0			0
$869$	−3.70820	+	6.42280i	−0.125792	+	0.217878i
$870$	−127.228			−4.31343
$871$	−12.7082	−	44.0225i	−0.430601	−	1.49165i
$872$	−20.2361			−0.685280
$873$	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
$877$	−0.354102	−	0.613323i	−0.0119572	−	0.0207104i	0.859985	−	0.510319i	$-0.170473\pi$
$877$	−0.354102	−	0.613323i	−0.0119572	−	0.0207104i	−0.871942	+	0.489609i	$0.837140\pi$
$878$	19.4443	+	33.6785i	0.656212	+	1.13659i
$879$	17.7082			0.597283
$880$	23.9164	+	41.4244i	0.806222	+	1.39642i
$881$	−18.2984	+	31.6937i	−0.616488	+	1.06779i	0.373634	+	0.927576i	$0.378112\pi$
$881$	−18.2984	+	31.6937i	−0.616488	+	1.06779i	−0.990122	+	0.140212i	$0.955222\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	7.14590	+	24.7541i	0.240343	+	0.832571i
$885$	−15.3262			−0.515186
$886$	6.85410	−	11.8717i	0.230268	−	0.398836i
$887$	27.3262	−	47.3304i	0.917525	−	1.58920i	0.114364	−	0.993439i	$-0.463517\pi$
$887$	27.3262	−	47.3304i	0.917525	−	1.58920i	0.803161	−	0.595761i	$-0.203150\pi$
$888$	−39.1246	−	67.7658i	−1.31294	−	2.27407i
$889$		0			0
$890$	−16.8262	−	29.1439i	−0.564017	−	0.976906i
$891$	5.29180	+	9.16566i	0.177282	+	0.307061i
$892$	−98.3951			−3.29451
$893$	−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
$898$	51.1246			1.70605
$899$	−16.6910	+	28.9096i	−0.556675	+	0.964190i
$900$	−17.3435	+	30.0398i	−0.578115	+	1.00133i
$901$	−2.77051	−	4.79866i	−0.0922991	−	0.159867i
$902$	−3.70820			−0.123470
$903$		0			0
$904$	−5.50000	−	9.52628i	−0.182927	−	0.316839i
$905$	25.4164			0.844870
$906$	4.42705	+	7.66788i	0.147079	+	0.254748i
$907$	12.0000	−	20.7846i	0.398453	−	0.690142i	−0.595082	−	0.803665i	$-0.702880\pi$
$907$	12.0000	−	20.7846i	0.398453	−	0.690142i	0.993535	+	0.113523i	$0.0362137\pi$
$908$	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
$913$	6.21885	−	10.7714i	0.205814	−	0.356480i
$914$	−20.1803	−	34.9534i	−0.667506	−	1.15615i
$915$	−41.1246			−1.35954
$916$	−31.8541	−	55.1729i	−1.05249	−	1.82296i
$917$		0			0
$918$	8.61803			0.284438
$919$	15.0000	+	25.9808i	0.494804	+	0.857026i	0.999982	−	0.00598907i	$-0.00190639\pi$
$919$	15.0000	+	25.9808i	0.494804	+	0.857026i	−0.505178	+	0.863015i	$0.668573\pi$
$920$	−43.7426	+	75.7645i	−1.44215	+	2.49788i
$921$	−6.35410	+	11.0056i	−0.209375	+	0.362648i
$922$	31.9787			1.05316
$923$	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
$928$	76.9574			2.52625
$929$	5.53444	+	9.58593i	0.181579	+	0.314504i	0.942418	−	0.334436i	$-0.108546\pi$
$929$	5.53444	+	9.58593i	0.181579	+	0.314504i	−0.760839	+	0.648940i	$0.775212\pi$
$930$	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
$934$	3.07295	−	5.32250i	0.100550	−	0.174158i
$935$	−7.14590			−0.233696
$936$	−100.794	−	24.9401i	−3.29457	−	0.815193i
$937$	15.8754			0.518626			0.259313	−	0.965793i	$-0.416504\pi$
$937$	15.8754			0.518626			0.259313	+	0.965793i	$0.416504\pi$
$938$		0			0
$939$	32.8885	−	56.9646i	1.07328	−	1.85897i
$940$	14.2082	+	24.6093i	0.463421	+	0.802668i
$941$	−20.3475			−0.663310			−0.331655	−	0.943401i	$-0.607607\pi$
$941$	−20.3475			−0.663310			−0.331655	+	0.943401i	$0.607607\pi$
$942$	50.9058	+	88.1714i	1.65860	+	2.87278i
$943$	−1.70820	−	2.95870i	−0.0556268	−	0.0963484i
$944$	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	$-0.0377733\pi$
$948$	50.8328			1.65097
$949$	5.00000	−	5.19615i	0.162307	−	0.168674i
$950$	9.00000			0.291999
$951$	−34.3435	+	59.4846i	−1.11366	+	1.92892i
$952$		0			0
$953$	−13.3885	−	23.1896i	−0.433697	−	0.751186i	0.563491	−	0.826122i	$-0.309458\pi$
$953$	−13.3885	−	23.1896i	−0.433697	−	0.751186i	−0.997188	+	0.0749362i	$0.976125\pi$
$954$	37.9787			1.22961
$955$	27.9894	+	48.4790i	0.905714	+	1.56874i
$956$	59.9681	+	103.868i	1.93951	+	3.35932i
$957$	34.4164			1.11252
$958$	32.6976	+	56.6338i	1.05641	+	1.82976i
$959$		0			0
$960$	29.8435	−	51.6904i	0.963193	−	1.66830i
$961$	−8.83282			−0.284930
$962$	−36.6525	−	9.06914i	−1.18172	−	0.292401i
$963$	−13.0344			−0.420029
$964$	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	$0.715749\pi$
$968$	28.2533	+	48.9361i	0.908095	+	1.57287i
$969$	−3.57295	−	6.18853i	−0.114780	−	0.198804i
$970$	129.228			4.14926
$971$	15.7918	+	27.3522i	0.506783	+	0.877774i	0.999969	+	0.00784995i	$0.00249874\pi$
$971$	15.7918	+	27.3522i	0.506783	+	0.877774i	−0.493186	+	0.869924i	$0.664168\pi$
$972$	52.5517	−	91.0221i	1.68560	−	2.91954i
$973$		0			0
$974$	78.4853			2.51483
$975$	4.85410	+	16.8151i	0.155456	+	0.538514i
$976$	59.1246			1.89253
$977$	11.2639	−	19.5097i	0.360365	−	0.624171i	−0.627656	−	0.778491i	$-0.715985\pi$
$977$	11.2639	−	19.5097i	0.360365	−	0.624171i	0.988021	+	0.154320i	$0.0493188\pi$
$978$	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
$982$	−16.2082	−	28.0734i	−0.517225	−	0.895859i
$983$	−18.3820			−0.586294			−0.293147	−	0.956067i	$-0.594702\pi$
$983$	−18.3820			−0.586294			−0.293147	+	0.956067i	$0.594702\pi$
$984$	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
$989$	−56.1803			−1.78643
$990$	24.4894	−	42.4168i	0.778323	−	1.34809i
$991$	8.07295	−	13.9828i	0.256446	−	0.444177i	−0.708842	−	0.705368i	$-0.750782\pi$
$991$	8.07295	−	13.9828i	0.256446	−	0.444177i	0.965287	+	0.261191i	$0.0841152\pi$
$992$	−25.5517	−	44.2568i	−0.811266	−	1.40515i
$993$	−26.5623			−0.842929
$994$		0			0
$995$	31.9615	+	55.3589i	1.01325	+	1.75500i
$996$	−85.2492			−2.70123
$997$	24.5000	+	42.4352i	0.775923	+	1.34394i	0.934274	+	0.356555i	$0.116049\pi$
$997$	24.5000	+	42.4352i	0.775923	+	1.34394i	−0.158352	+	0.987383i	$0.550618\pi$
$998$	−19.4443	+	33.6785i	−0.615498	+	1.06607i
$999$	−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.f.c.295.1		4
7.2	even	3		637.2.h.f.165.2		4
7.3	odd	6		637.2.g.b.373.1		4
7.4	even	3		637.2.g.c.373.1		4
7.5	odd	6		637.2.h.g.165.2		4
7.6	odd	2		91.2.f.a.22.1	✓	4
13.3	even	3	inner	637.2.f.c.393.1		4
13.4	even	6		8281.2.a.n.1.1		2
13.9	even	3		8281.2.a.bb.1.2		2
21.20	even	2		819.2.o.c.568.2		4
28.27	even	2		1456.2.s.h.113.1		4
91.3	odd	6		637.2.h.g.471.2		4
91.6	even	12		1183.2.c.c.337.1		4
91.16	even	3		637.2.g.c.263.1		4
91.20	even	12		1183.2.c.c.337.4		4
91.48	odd	6		1183.2.a.g.1.2		2
91.55	odd	6		91.2.f.a.29.1	yes	4
91.68	odd	6		637.2.g.b.263.1		4
91.69	odd	6		1183.2.a.c.1.1		2
91.81	even	3		637.2.h.f.471.2		4
273.146	even	6		819.2.o.c.757.2		4
364.55	even	6		1456.2.s.h.1121.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.a.22.1	✓	4	7.6	odd	2
91.2.f.a.29.1	yes	4	91.55	odd	6
637.2.f.c.295.1		4	1.1	even	1	trivial
637.2.f.c.393.1		4	13.3	even	3	inner
637.2.g.b.263.1		4	91.68	odd	6
637.2.g.b.373.1		4	7.3	odd	6
637.2.g.c.263.1		4	91.16	even	3
637.2.g.c.373.1		4	7.4	even	3
637.2.h.f.165.2		4	7.2	even	3
637.2.h.f.471.2		4	91.81	even	3
637.2.h.g.165.2		4	7.5	odd	6
637.2.h.g.471.2		4	91.3	odd	6
819.2.o.c.568.2		4	21.20	even	2
819.2.o.c.757.2		4	273.146	even	6
1183.2.a.c.1.1		2	91.69	odd	6
1183.2.a.g.1.2		2	91.48	odd	6
1183.2.c.c.337.1		4	91.6	even	12
1183.2.c.c.337.4		4	91.20	even	12
1456.2.s.h.113.1		4	28.27	even	2
1456.2.s.h.1121.1		4	364.55	even	6
8281.2.a.n.1.1		2	13.4	even	6
8281.2.a.bb.1.2		2	13.9	even	3

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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 + 2.26728i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(-2.42705 - 4.20378i) q^{4} -2.61803 q^{5} +(-3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +O(q^{10})\)	\(q+(-1.30902 + 2.26728i) q^{2} +(-1.30902 + 2.26728i) q^{3} +(-2.42705 - 4.20378i) q^{4} -2.61803 q^{5} +(-3.42705 - 5.93583i) q^{6} +7.47214 q^{8} +(-1.92705 - 3.33775i) q^{9} +(3.42705 - 5.93583i) q^{10} +(-0.927051 + 1.60570i) q^{11} +12.7082 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} +10.0902 q^{18} +(-0.927051 - 1.60570i) q^{19} +(6.35410 + 11.0056i) q^{20} +(-2.42705 - 4.20378i) q^{22} +(2.23607 - 3.87298i) q^{23} +(-9.78115 + 16.9415i) q^{24} +1.85410 q^{25} +(2.61803 + 9.06914i) q^{26} +2.23607 q^{27} +(-3.54508 + 6.14027i) q^{29} +(8.97214 + 15.5402i) q^{30} +4.70820 q^{31} +(-5.42705 - 9.39993i) q^{32} +(-2.42705 - 4.20378i) q^{33} +3.85410 q^{34} +(-9.35410 + 16.2018i) q^{36} +(-2.00000 + 3.46410i) q^{37} +4.85410 q^{38} +(2.61803 + 9.06914i) q^{39} -19.5623 q^{40} +(0.381966 - 0.661585i) q^{41} +(-6.28115 - 10.8793i) q^{43} +9.00000 q^{44} +(5.04508 + 8.73834i) q^{45} +(5.85410 + 10.1396i) q^{46} +2.23607 q^{47} +(-12.8992 - 22.3420i) q^{48} +(-2.42705 + 4.20378i) q^{50} +3.85410 q^{51} +(-16.9894 - 4.20378i) q^{52} +3.76393 q^{53} +(-2.92705 + 5.06980i) q^{54} +(2.42705 - 4.20378i) q^{55} +4.85410 q^{57} +(-9.28115 - 16.0754i) q^{58} +(-1.11803 - 1.93649i) q^{59} -33.2705 q^{60} +(-3.00000 - 5.19615i) q^{61} +(-6.16312 + 10.6748i) q^{62} +8.70820 q^{64} +(-6.54508 + 6.80185i) q^{65} +12.7082 q^{66} +(6.35410 - 11.0056i) q^{67} +(-3.57295 + 6.18853i) q^{68} +(5.85410 + 10.1396i) q^{69} +(7.09017 + 12.2805i) q^{71} +(-14.3992 - 24.9401i) q^{72} +2.00000 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} +4.00000 q^{79} +(12.8992 - 22.3420i) q^{80} +(2.85410 - 4.94345i) q^{81} +(1.00000 + 1.73205i) q^{82} -6.70820 q^{83} +(1.92705 + 3.33775i) q^{85} +32.8885 q^{86} +(-9.28115 - 16.0754i) q^{87} +(-6.92705 + 11.9980i) q^{88} +(2.45492 - 4.25204i) q^{89} -26.4164 q^{90} -21.7082 q^{92} +(-6.16312 + 10.6748i) q^{93} +(-2.92705 + 5.06980i) q^{94} +(2.42705 + 4.20378i) q^{95} +28.4164 q^{96} +(9.42705 + 16.3281i) q^{97} +7.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 7 q^{6} + 12 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 7 * q^6 + 12 * q^8 - q^9	\( 4 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 7 q^{6} + 12 q^{8} - q^{9} + 7 q^{10} + 3 q^{11} + 24 q^{12} + 10 q^{13} + 7 q^{15} - 13 q^{16} + 6 q^{17} + 18 q^{18} + 3 q^{19} + 12 q^{20} - 3 q^{22} - 19 q^{24} - 6 q^{25} + 6 q^{26} - 3 q^{29} + 18 q^{30} - 8 q^{31} - 15 q^{32} - 3 q^{33} + 2 q^{34} - 24 q^{36} - 8 q^{37} + 6 q^{38} + 6 q^{39} - 38 q^{40} + 6 q^{41} - 5 q^{43} + 36 q^{44} + 9 q^{45} + 10 q^{46} - 27 q^{48} - 3 q^{50} + 2 q^{51} - 21 q^{52} + 24 q^{53} - 5 q^{54} + 3 q^{55} + 6 q^{57} - 17 q^{58} - 66 q^{60} - 12 q^{61} - 9 q^{62} + 8 q^{64} - 15 q^{65} + 24 q^{66} + 12 q^{67} - 21 q^{68} + 10 q^{69} + 6 q^{71} - 33 q^{72} + 8 q^{73} - 12 q^{74} - 3 q^{75} - 18 q^{76} - 49 q^{78} + 16 q^{79} + 27 q^{80} - 2 q^{81} + 4 q^{82} + q^{85} + 60 q^{86} - 17 q^{87} - 21 q^{88} + 21 q^{89} - 52 q^{90} - 60 q^{92} - 9 q^{93} - 5 q^{94} + 3 q^{95} + 60 q^{96} + 31 q^{97} + 42 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 7 * q^6 + 12 * q^8 - q^9 + 7 * q^10 + 3 * q^11 + 24 * q^12 + 10 * q^13 + 7 * q^15 - 13 * q^16 + 6 * q^17 + 18 * q^18 + 3 * q^19 + 12 * q^20 - 3 * q^22 - 19 * q^24 - 6 * q^25 + 6 * q^26 - 3 * q^29 + 18 * q^30 - 8 * q^31 - 15 * q^32 - 3 * q^33 + 2 * q^34 - 24 * q^36 - 8 * q^37 + 6 * q^38 + 6 * q^39 - 38 * q^40 + 6 * q^41 - 5 * q^43 + 36 * q^44 + 9 * q^45 + 10 * q^46 - 27 * q^48 - 3 * q^50 + 2 * q^51 - 21 * q^52 + 24 * q^53 - 5 * q^54 + 3 * q^55 + 6 * q^57 - 17 * q^58 - 66 * q^60 - 12 * q^61 - 9 * q^62 + 8 * q^64 - 15 * q^65 + 24 * q^66 + 12 * q^67 - 21 * q^68 + 10 * q^69 + 6 * q^71 - 33 * q^72 + 8 * q^73 - 12 * q^74 - 3 * q^75 - 18 * q^76 - 49 * q^78 + 16 * q^79 + 27 * q^80 - 2 * q^81 + 4 * q^82 + q^85 + 60 * q^86 - 17 * q^87 - 21 * q^88 + 21 * q^89 - 52 * q^90 - 60 * q^92 - 9 * q^93 - 5 * q^94 + 3 * q^95 + 60 * q^96 + 31 * q^97 + 42 * q^99

Introduction

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