LMFDB - Embedded newform 637.2.i.a.489.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(489,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.489");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.i (of order $4$, 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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			489.16
Character	$\chi$	$=$	637.489
Dual form			637.2.i.a.538.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.90587 + 1.90587i) q^{2} +0.759247i q^{3} +5.26469i q^{4} +(-1.78720 + 1.78720i) q^{5} +(-1.44703 + 1.44703i) q^{6} +(-6.22207 + 6.22207i) q^{8} +2.42354 q^{9} +O(q^{10})$	\(q+(1.90587 + 1.90587i) q^{2} +0.759247i q^{3} +5.26469i q^{4} +(-1.78720 + 1.78720i) q^{5} +(-1.44703 + 1.44703i) q^{6} +(-6.22207 + 6.22207i) q^{8} +2.42354 q^{9} -6.81236 q^{10} +(1.52343 - 1.52343i) q^{11} -3.99720 q^{12} +(1.44703 - 3.30244i) q^{13} +(-1.35693 - 1.35693i) q^{15} -13.1876 q^{16} +1.40173 q^{17} +(4.61896 + 4.61896i) q^{18} +(-1.48026 + 1.48026i) q^{19} +(-9.40907 - 9.40907i) q^{20} +5.80693 q^{22} -1.31506i q^{23} +(-4.72409 - 4.72409i) q^{24} -1.38820i q^{25} +(9.05187 - 3.53618i) q^{26} +4.11781i q^{27} -4.56814 q^{29} -5.17227i q^{30} +(5.14688 - 5.14688i) q^{31} +(-12.6896 - 12.6896i) q^{32} +(1.15666 + 1.15666i) q^{33} +(2.67152 + 2.67152i) q^{34} +12.7592i q^{36} +(1.61471 - 1.61471i) q^{37} -5.64238 q^{38} +(2.50737 + 1.09865i) q^{39} -22.2402i q^{40} +(-2.69291 + 2.69291i) q^{41} +0.437721i q^{43} +(8.02039 + 8.02039i) q^{44} +(-4.33137 + 4.33137i) q^{45} +(2.50632 - 2.50632i) q^{46} +(5.66738 + 5.66738i) q^{47} -10.0126i q^{48} +(2.64573 - 2.64573i) q^{50} +1.06426i q^{51} +(17.3863 + 7.61815i) q^{52} -2.53596 q^{53} +(-7.84802 + 7.84802i) q^{54} +5.44537i q^{55} +(-1.12389 - 1.12389i) q^{57} +(-8.70628 - 8.70628i) q^{58} +(5.52030 + 5.52030i) q^{59} +(7.14381 - 7.14381i) q^{60} +7.58715i q^{61} +19.6186 q^{62} -21.9945i q^{64} +(3.31600 + 8.48827i) q^{65} +4.40890i q^{66} +(0.401412 + 0.401412i) q^{67} +7.37967i q^{68} +0.998452 q^{69} +(-10.7460 - 10.7460i) q^{71} +(-15.0795 + 15.0795i) q^{72} +(-8.70795 - 8.70795i) q^{73} +6.15487 q^{74} +1.05399 q^{75} +(-7.79312 - 7.79312i) q^{76} +(2.68483 + 6.87261i) q^{78} +14.3943 q^{79} +(23.5689 - 23.5689i) q^{80} +4.14419 q^{81} -10.2647 q^{82} +(-3.82648 + 3.82648i) q^{83} +(-2.50518 + 2.50518i) q^{85} +(-0.834239 + 0.834239i) q^{86} -3.46835i q^{87} +18.9578i q^{88} +(-0.0366770 - 0.0366770i) q^{89} -16.5101 q^{90} +6.92335 q^{92} +(3.90776 + 3.90776i) q^{93} +21.6026i q^{94} -5.29107i q^{95} +(9.63457 - 9.63457i) q^{96} +(9.43761 - 9.43761i) q^{97} +(3.69210 - 3.69210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.90587	+	1.90587i	1.34765	+	1.34765i	0.888203	+	0.459451i	$0.151954\pi$
$2$	1.90587	+	1.90587i	1.34765	+	1.34765i	0.459451	+	0.888203i	$0.348046\pi$
$3$			0.759247i			0.438352i	0.975685	+	0.219176i	$0.0703368\pi$
$3$			0.759247i			0.438352i	−0.975685	+	0.219176i	$0.929663\pi$
$4$			5.26469i			2.63234i
$5$	−1.78720	+	1.78720i	−0.799262	+	0.799262i	−0.982979	−	0.183717i	$-0.941187\pi$
$5$	−1.78720	+	1.78720i	−0.799262	+	0.799262i	0.183717	+	0.982979i	$0.441187\pi$
$6$	−1.44703	+	1.44703i	−0.590746	+	0.590746i
$7$		0			0
$7$		0			0
$8$	−6.22207	+	6.22207i	−2.19983	+	2.19983i
$9$	2.42354			0.807848
$10$	−6.81236			−2.15426
$11$	1.52343	−	1.52343i	0.459332	−	0.459332i	−0.439104	−	0.898436i	$-0.644704\pi$
$11$	1.52343	−	1.52343i	0.459332	−	0.459332i	0.898436	+	0.439104i	$0.144704\pi$
$12$	−3.99720			−1.15389
$13$	1.44703	−	3.30244i	0.401333	−	0.915932i
$13$	1.44703	−	3.30244i	0.401333	−	0.915932i
$14$		0			0
$15$	−1.35693	−	1.35693i	−0.350358	−	0.350358i
$16$	−13.1876			−3.29689
$17$	1.40173			0.339970			0.169985	−	0.985447i	$-0.445628\pi$
$17$	1.40173			0.339970			0.169985	+	0.985447i	$0.445628\pi$
$18$	4.61896	+	4.61896i	1.08870	+	1.08870i
$19$	−1.48026	+	1.48026i	−0.339596	+	0.339596i	−0.856215	−	0.516619i	$-0.827190\pi$
$19$	−1.48026	+	1.48026i	−0.339596	+	0.339596i	0.516619	+	0.856215i	$0.327190\pi$
$20$	−9.40907	−	9.40907i	−2.10393	−	2.10393i
$21$		0			0
$22$	5.80693			1.23804
$23$		−	1.31506i		−	0.274208i	−0.990557	−	0.137104i	$-0.956221\pi$
$23$		−	1.31506i		−	0.274208i	0.990557	−	0.137104i	$-0.0437794\pi$
$24$	−4.72409	−	4.72409i	−0.964301	−	0.964301i
$25$		−	1.38820i		−	0.277640i
$26$	9.05187	−	3.53618i	1.77522	−	0.693501i
$27$			4.11781i			0.792473i
$28$		0			0
$29$	−4.56814			−0.848282			−0.424141	−	0.905596i	$-0.639424\pi$
$29$	−4.56814			−0.848282			−0.424141	+	0.905596i	$0.639424\pi$
$30$		−	5.17227i		−	0.944322i
$31$	5.14688	−	5.14688i	0.924407	−	0.924407i	−0.0729298	−	0.997337i	$-0.523235\pi$
$31$	5.14688	−	5.14688i	0.924407	−	0.924407i	0.997337	+	0.0729298i	$0.0232349\pi$
$32$	−12.6896	−	12.6896i	−2.24323	−	2.24323i
$33$	1.15666	+	1.15666i	0.201349	+	0.201349i
$34$	2.67152	+	2.67152i	0.458162	+	0.458162i
$35$		0			0
$36$			12.7592i			2.12653i
$37$	1.61471	−	1.61471i	0.265457	−	0.265457i	−0.561810	−	0.827267i	$-0.689895\pi$
$37$	1.61471	−	1.61471i	0.265457	−	0.265457i	0.827267	+	0.561810i	$0.189895\pi$
$38$	−5.64238			−0.915315
$39$	2.50737	+	1.09865i	0.401500	+	0.175925i
$40$		−	22.2402i		−	3.51649i
$41$	−2.69291	+	2.69291i	−0.420562	+	0.420562i	−0.885397	−	0.464835i	$-0.846114\pi$
$41$	−2.69291	+	2.69291i	−0.420562	+	0.420562i	0.464835	+	0.885397i	$0.346114\pi$
$42$		0			0
$43$			0.437721i			0.0667518i	0.999443	+	0.0333759i	$0.0106258\pi$
$43$			0.437721i			0.0667518i	−0.999443	+	0.0333759i	$0.989374\pi$
$44$	8.02039	+	8.02039i	1.20912	+	1.20912i
$45$	−4.33137	+	4.33137i	−0.645682	+	0.645682i
$46$	2.50632	−	2.50632i	0.369537	−	0.369537i
$47$	5.66738	+	5.66738i	0.826672	+	0.826672i	0.987055	−	0.160383i	$-0.0512728\pi$
$47$	5.66738	+	5.66738i	0.826672	+	0.826672i	−0.160383	+	0.987055i	$0.551273\pi$
$48$		−	10.0126i		−	1.44520i
$49$		0			0
$50$	2.64573	−	2.64573i	0.374162	−	0.374162i
$51$			1.06426i			0.149026i
$52$	17.3863	+	7.61815i	2.41105	+	1.05645i
$53$	−2.53596			−0.348341			−0.174171	−	0.984716i	$-0.555724\pi$
$53$	−2.53596			−0.348341			−0.174171	+	0.984716i	$0.555724\pi$
$54$	−7.84802	+	7.84802i	−1.06798	+	1.06798i
$55$			5.44537i			0.734253i
$56$		0			0
$57$	−1.12389	−	1.12389i	−0.148862	−	0.148862i
$58$	−8.70628	−	8.70628i	−1.14319	−	1.14319i
$59$	5.52030	+	5.52030i	0.718681	+	0.718681i	0.968335	−	0.249654i	$-0.0803169\pi$
$59$	5.52030	+	5.52030i	0.718681	+	0.718681i	−0.249654	+	0.968335i	$0.580317\pi$
$60$	7.14381	−	7.14381i	0.922262	−	0.922262i
$61$			7.58715i			0.971436i	0.874116	+	0.485718i	$0.161442\pi$
$61$			7.58715i			0.971436i	−0.874116	+	0.485718i	$0.838558\pi$
$62$	19.6186			2.49156
$63$		0			0
$64$		−	21.9945i		−	2.74931i
$65$	3.31600	+	8.48827i	0.411299	+	1.05284i
$66$			4.40890i			0.542698i
$67$	0.401412	+	0.401412i	0.0490403	+	0.0490403i	0.731202	−	0.682161i	$-0.238960\pi$
$67$	0.401412	+	0.401412i	0.0490403	+	0.0490403i	−0.682161	+	0.731202i	$0.738960\pi$
$68$			7.37967i			0.894917i
$69$	0.998452			0.120200
$70$		0			0
$71$	−10.7460	−	10.7460i	−1.27531	−	1.27531i	−0.943263	−	0.332048i	$-0.892261\pi$
$71$	−10.7460	−	10.7460i	−1.27531	−	1.27531i	−0.332048	−	0.943263i	$-0.607739\pi$
$72$	−15.0795	+	15.0795i	−1.77713	+	1.77713i
$73$	−8.70795	−	8.70795i	−1.01919	−	1.01919i	−0.999812	−	0.0193768i	$-0.993832\pi$
$73$	−8.70795	−	8.70795i	−1.01919	−	1.01919i	−0.0193768	−	0.999812i	$-0.506168\pi$
$74$	6.15487			0.715489
$75$	1.05399			0.121704
$76$	−7.79312	−	7.79312i	−0.893933	−	0.893933i
$77$		0			0
$78$	2.68483	+	6.87261i	0.303998	+	0.778170i
$79$	14.3943			1.61948			0.809740	−	0.586788i	$-0.199608\pi$
$79$	14.3943			1.61948			0.809740	+	0.586788i	$0.199608\pi$
$80$	23.5689	−	23.5689i	2.63508	−	2.63508i
$81$	4.14419			0.460466
$82$	−10.2647			−1.13355
$83$	−3.82648	+	3.82648i	−0.420010	+	0.420010i	−0.885207	−	0.465197i	$-0.845984\pi$
$83$	−3.82648	+	3.82648i	−0.420010	+	0.420010i	0.465197	+	0.885207i	$0.345984\pi$
$84$		0			0
$85$	−2.50518	+	2.50518i	−0.271725	+	0.271725i
$86$	−0.834239	+	0.834239i	−0.0899583	+	0.0899583i
$87$		−	3.46835i		−	0.371846i
$88$			18.9578i			2.02091i
$89$	−0.0366770	−	0.0366770i	−0.00388776	−	0.00388776i	0.705160	−	0.709048i	$-0.250875\pi$
$89$	−0.0366770	−	0.0366770i	−0.00388776	−	0.00388776i	−0.709048	+	0.705160i	$0.750875\pi$
$90$	−16.5101			−1.74031
$91$		0			0
$92$	6.92335			0.721809
$93$	3.90776	+	3.90776i	0.405215	+	0.405215i
$94$			21.6026i			2.22814i
$95$		−	5.29107i		−	0.542852i
$96$	9.63457	−	9.63457i	0.983324	−	0.983324i
$97$	9.43761	−	9.43761i	0.958244	−	0.958244i	−0.0409188	−	0.999162i	$-0.513028\pi$
$97$	9.43761	−	9.43761i	0.958244	−	0.958244i	0.999162	+	0.0409188i	$0.0130285\pi$
$98$		0			0
$99$	3.69210	−	3.69210i	0.371070	−	0.371070i
$100$	7.30843			0.730843
$101$	14.3451			1.42739			0.713696	−	0.700456i	$-0.247020\pi$
$101$	14.3451			1.42739			0.713696	+	0.700456i	$0.247020\pi$
$102$	−2.02834	+	2.02834i	−0.200836	+	0.200836i
$103$	−9.01501			−0.888275			−0.444138	−	0.895959i	$-0.646490\pi$
$103$	−9.01501			−0.888275			−0.444138	+	0.895959i	$0.646490\pi$
$104$	11.5445	+	29.5515i	1.13203	+	2.89777i
$105$		0			0
$106$	−4.83321	−	4.83321i	−0.469443	−	0.469443i
$107$	4.30957			0.416622			0.208311	−	0.978063i	$-0.433203\pi$
$107$	4.30957			0.416622			0.208311	+	0.978063i	$0.433203\pi$
$108$	−21.6790			−2.08606
$109$	−5.21573	−	5.21573i	−0.499577	−	0.499577i	0.411729	−	0.911306i	$-0.364925\pi$
$109$	−5.21573	−	5.21573i	−0.499577	−	0.499577i	−0.911306	+	0.411729i	$0.864925\pi$
$110$	−10.3782	+	10.3782i	−0.989520	+	0.989520i
$111$	1.22597	+	1.22597i	0.116364	+	0.116364i
$112$		0			0
$113$	10.1580			0.955583			0.477792	−	0.878473i	$-0.341437\pi$
$113$	10.1580			0.955583			0.477792	+	0.878473i	$0.341437\pi$
$114$		−	4.28396i		−	0.401230i
$115$	2.35027	+	2.35027i	0.219164	+	0.219164i
$116$		−	24.0498i		−	2.23297i
$117$	3.50693	−	8.00361i	0.324216	−	0.739934i
$118$			21.0419i			1.93707i
$119$		0			0
$120$	16.8858			1.54146
$121$			6.35831i			0.578028i
$122$	−14.4601	+	14.4601i	−1.30916	+	1.30916i
$123$	−2.04459	−	2.04459i	−0.184354	−	0.184354i
$124$	27.0967	+	27.0967i	2.43336	+	2.43336i
$125$	−6.45503	−	6.45503i	−0.577355	−	0.577355i
$126$		0			0
$127$		−	8.50086i		−	0.754329i	−0.926146	−	0.377165i	$-0.876899\pi$
$127$		−	8.50086i		−	0.754329i	0.926146	−	0.377165i	$-0.123101\pi$
$128$	16.5394	−	16.5394i	1.46189	−	1.46189i
$129$	−0.332338			−0.0292607
$130$	−9.85767	+	22.4974i	−0.864575	+	1.97315i
$131$		−	9.20796i		−	0.804504i	−0.915529	−	0.402252i	$-0.868228\pi$
$131$		−	9.20796i		−	0.804504i	0.915529	−	0.402252i	$-0.131772\pi$
$132$	−6.08946	+	6.08946i	−0.530020	+	0.530020i
$133$		0			0
$134$			1.53008i			0.132179i
$135$	−7.35937	−	7.35937i	−0.633394	−	0.633394i
$136$	−8.72167	+	8.72167i	−0.747877	+	0.747877i
$137$	−6.43433	+	6.43433i	−0.549722	+	0.549722i	−0.926360	−	0.376639i	$-0.877080\pi$
$137$	−6.43433	+	6.43433i	−0.549722	+	0.549722i	0.376639	+	0.926360i	$0.377080\pi$
$138$	1.90292	+	1.90292i	0.161987	+	0.161987i
$139$		−	0.744275i		−	0.0631286i	−0.999502	−	0.0315643i	$-0.989951\pi$
$139$		−	0.744275i		−	0.0631286i	0.999502	−	0.0315643i	$-0.0100489\pi$
$140$		0			0
$141$	−4.30294	+	4.30294i	−0.362373	+	0.362373i
$142$		−	40.9608i		−	3.43735i
$143$	−2.82660	−	7.23549i	−0.236372	−	0.605062i
$144$	−31.9606			−2.66338
$145$	8.16420	−	8.16420i	0.678000	−	0.678000i
$146$		−	33.1925i		−	2.74703i
$147$		0			0
$148$	8.50095	+	8.50095i	0.698774	+	0.698774i
$149$	−10.5816	−	10.5816i	−0.866879	−	0.866879i	0.125247	−	0.992126i	$-0.460028\pi$
$149$	−10.5816	−	10.5816i	−0.866879	−	0.866879i	−0.992126	+	0.125247i	$0.960028\pi$
$150$	2.00876	+	2.00876i	0.164015	+	0.164015i
$151$	8.94496	−	8.94496i	0.727931	−	0.727931i	−0.242277	−	0.970207i	$-0.577894\pi$
$151$	8.94496	−	8.94496i	0.727931	−	0.727931i	0.970207	+	0.242277i	$0.0778941\pi$
$152$		−	18.4206i		−	1.49411i
$153$	3.39716			0.274644
$154$		0			0
$155$			18.3971i			1.47769i
$156$	−5.78406	+	13.2005i	−0.463095	+	1.05689i
$157$		−	10.5223i		−	0.839771i	−0.907577	−	0.419886i	$-0.862070\pi$
$157$		−	10.5223i		−	0.839771i	0.907577	−	0.419886i	$-0.137930\pi$
$158$	27.4336	+	27.4336i	2.18250	+	2.18250i
$159$		−	1.92542i		−	0.152696i
$160$	45.3579			3.58586
$161$		0			0
$162$	7.89830	+	7.89830i	0.620549	+	0.620549i
$163$	0.380928	−	0.380928i	0.0298366	−	0.0298366i	−0.692031	−	0.721868i	$-0.743284\pi$
$163$	0.380928	−	0.380928i	0.0298366	−	0.0298366i	0.721868	+	0.692031i	$0.243284\pi$
$164$	−14.1773	−	14.1773i	−1.10706	−	1.10706i
$165$	−4.13438			−0.321861
$166$	−14.5855			−1.13206
$167$	−4.43553	−	4.43553i	−0.343232	−	0.343232i	0.514349	−	0.857581i	$-0.328034\pi$
$167$	−4.43553	−	4.43553i	−0.343232	−	0.343232i	−0.857581	+	0.514349i	$0.828034\pi$
$168$		0			0
$169$	−8.81222	−	9.55744i	−0.677863	−	0.735188i
$170$	−9.54910			−0.732382
$171$	−3.58748	+	3.58748i	−0.274342	+	0.274342i
$172$	−2.30446			−0.175714
$173$	2.59627			0.197390			0.0986952	−	0.995118i	$-0.468533\pi$
$173$	2.59627			0.197390			0.0986952	+	0.995118i	$0.468533\pi$
$174$	6.61022	−	6.61022i	0.501120	−	0.501120i
$175$		0			0
$176$	−20.0903	+	20.0903i	−1.51437	+	1.51437i
$177$	−4.19127	+	4.19127i	−0.315035	+	0.315035i
$178$		−	0.139803i		−	0.0104787i
$179$		−	1.61484i		−	0.120699i	−0.998177	−	0.0603493i	$-0.980779\pi$
$179$		−	1.61484i		−	0.120699i	0.998177	−	0.0603493i	$-0.0192215\pi$
$180$	−22.8033	−	22.8033i	−1.69966	−	1.69966i
$181$	−2.49671			−0.185579			−0.0927895	−	0.995686i	$-0.529578\pi$
$181$	−2.49671			−0.185579			−0.0927895	+	0.995686i	$0.529578\pi$
$182$		0			0
$183$	−5.76053			−0.425830
$184$	8.18237	+	8.18237i	0.603212	+	0.603212i
$185$			5.77164i			0.424340i
$186$			14.8954i			1.09218i
$187$	2.13544	−	2.13544i	0.156159	−	0.156159i
$188$	−29.8370	+	29.8370i	−2.17609	+	2.17609i
$189$		0			0
$190$	10.0841	−	10.0841i	0.731577	−	0.731577i
$191$	−10.9325			−0.791047			−0.395523	−	0.918456i	$-0.629437\pi$
$191$	−10.9325			−0.791047			−0.395523	+	0.918456i	$0.629437\pi$
$192$	16.6993			1.20516
$193$	−4.40637	+	4.40637i	−0.317178	+	0.317178i	−0.847682	−	0.530504i	$-0.822003\pi$
$193$	−4.40637	+	4.40637i	−0.317178	+	0.317178i	0.530504	+	0.847682i	$0.322003\pi$
$194$	35.9737			2.58276
$195$	−6.44470	+	2.51767i	−0.461514	+	0.180294i
$196$		0			0
$197$	11.4927	+	11.4927i	0.818821	+	0.818821i	0.985937	−	0.167116i	$-0.0534455\pi$
$197$	11.4927	+	11.4927i	0.818821	+	0.818821i	−0.167116	+	0.985937i	$0.553446\pi$
$198$	14.0733			1.00015
$199$	18.0522			1.27969			0.639844	−	0.768505i	$-0.278999\pi$
$199$	18.0522			1.27969			0.639844	+	0.768505i	$0.278999\pi$
$200$	8.63747	+	8.63747i	0.610761	+	0.610761i
$201$	−0.304771	+	0.304771i	−0.0214969	+	0.0214969i
$202$	27.3399	+	27.3399i	1.92363	+	1.92363i
$203$		0			0
$204$	−5.60300			−0.392288
$205$		−	9.62557i		−	0.672279i
$206$	−17.1814	−	17.1814i	−1.19709	−	1.19709i
$207$		−	3.18709i		−	0.221518i
$208$	−19.0827	+	43.5511i	−1.32315	+	3.01973i
$209$			4.51016i			0.311974i
$210$		0			0
$211$	2.78534			0.191750			0.0958752	−	0.995393i	$-0.469435\pi$
$211$	2.78534			0.191750			0.0958752	+	0.995393i	$0.469435\pi$
$212$		−	13.3510i		−	0.916953i
$213$	8.15884	−	8.15884i	0.559034	−	0.559034i
$214$	8.21348	+	8.21348i	0.561462	+	0.561462i
$215$	−0.782296	−	0.782296i	−0.0533521	−	0.0533521i
$216$	−25.6213	−	25.6213i	−1.74331	−	1.74331i
$217$		0			0
$218$		−	19.8810i		−	1.34651i
$219$	6.61149	−	6.61149i	0.446763	−	0.446763i
$220$	−28.6682			−1.93281
$221$	2.02834	−	4.62913i	0.136441	−	0.311389i
$222$			4.67307i			0.313636i
$223$	12.1327	−	12.1327i	0.812463	−	0.812463i	−0.172540	−	0.985003i	$-0.555197\pi$
$223$	12.1327	−	12.1327i	0.812463	−	0.812463i	0.985003	+	0.172540i	$0.0551974\pi$
$224$		0			0
$225$		−	3.36436i		−	0.224291i
$226$	19.3598	+	19.3598i	1.28780	+	1.28780i
$227$	−12.1267	+	12.1267i	−0.804875	+	0.804875i	−0.983853	−	0.178978i	$-0.942721\pi$
$227$	−12.1267	+	12.1267i	−0.804875	+	0.804875i	0.178978	+	0.983853i	$0.442721\pi$
$228$	5.91691	−	5.91691i	0.391857	−	0.391857i
$229$	−15.4056	−	15.4056i	−1.01803	−	1.01803i	−0.999834	−	0.0181954i	$-0.994208\pi$
$229$	−15.4056	−	15.4056i	−1.01803	−	1.01803i	−0.0181954	−	0.999834i	$-0.505792\pi$
$230$			8.95863i			0.590715i
$231$		0			0
$232$	28.4233	−	28.4233i	1.86608	−	1.86608i
$233$			30.1646i			1.97615i	0.153983	+	0.988073i	$0.450790\pi$
$233$			30.1646i			1.97615i	−0.153983	+	0.988073i	$0.549210\pi$
$234$	21.9376	−	8.57008i	1.43411	−	0.560244i
$235$	−20.2575			−1.32146
$236$	−29.0626	+	29.0626i	−1.89182	+	1.89182i
$237$			10.9288i			0.709902i
$238$		0			0
$239$	10.1720	+	10.1720i	0.657969	+	0.657969i	0.954899	−	0.296930i	$-0.0959628\pi$
$239$	10.1720	+	10.1720i	0.657969	+	0.657969i	−0.296930	+	0.954899i	$0.595963\pi$
$240$	17.8946	+	17.8946i	1.15509	+	1.15509i
$241$	−15.1093	−	15.1093i	−0.973278	−	0.973278i	0.0263739	−	0.999652i	$-0.491604\pi$
$241$	−15.1093	−	15.1093i	−0.973278	−	0.973278i	−0.999652	+	0.0263739i	$0.991604\pi$
$242$	−12.1181	+	12.1181i	−0.778982	+	0.778982i
$243$			15.4999i			0.994319i
$244$	−39.9440			−2.55715
$245$		0			0
$246$		−	7.79344i		−	0.496891i
$247$	2.74650	+	7.03046i	0.174756	+	0.447338i
$248$			64.0485i			4.06709i
$249$	−2.90524	−	2.90524i	−0.184112	−	0.184112i
$250$		−	24.6049i		−	1.55615i
$251$	10.4531			0.659791			0.329896	−	0.944017i	$-0.392986\pi$
$251$	10.4531			0.659791			0.329896	+	0.944017i	$0.392986\pi$
$252$		0			0
$253$	−2.00340	−	2.00340i	−0.125952	−	0.125952i
$254$	16.2015	−	16.2015i	1.01657	−	1.01657i
$255$	−1.90205	−	1.90205i	−0.119111	−	0.119111i
$256$	19.0549			1.19093
$257$	−14.0287			−0.875085			−0.437543	−	0.899198i	$-0.644151\pi$
$257$	−14.0287			−0.875085			−0.437543	+	0.899198i	$0.644151\pi$
$258$	−0.633394	−	0.633394i	−0.0394334	−	0.0394334i
$259$		0			0
$260$	−44.6881	+	17.4577i	−2.77144	+	1.08268i
$261$	−11.0711			−0.685283
$262$	17.5492	−	17.5492i	1.08419	−	1.08419i
$263$	2.52887			0.155937			0.0779683	−	0.996956i	$-0.475157\pi$
$263$	2.52887			0.155937			0.0779683	+	0.996956i	$0.475157\pi$
$264$	−14.3937			−0.885869
$265$	4.53228	−	4.53228i	0.278416	−	0.278416i
$266$		0			0
$267$	0.0278469	−	0.0278469i	0.00170420	−	0.00170420i
$268$	−2.11331	+	2.11331i	−0.129091	+	0.129091i
$269$			8.09425i			0.493515i	0.969077	+	0.246758i	$0.0793652\pi$
$269$			8.09425i			0.493515i	−0.969077	+	0.246758i	$0.920635\pi$
$270$		−	28.0520i		−	1.70719i
$271$	19.8149	+	19.8149i	1.20367	+	1.20367i	0.973042	+	0.230629i	$0.0740782\pi$
$271$	19.8149	+	19.8149i	1.20367	+	1.20367i	0.230629	+	0.973042i	$0.425922\pi$
$272$	−18.4854			−1.12084
$273$		0			0
$274$	−24.5260			−1.48167
$275$	−2.11483	−	2.11483i	−0.127529	−	0.127529i
$276$			5.25654i			0.316406i
$277$			9.22939i			0.554540i	0.960792	+	0.277270i	$0.0894297\pi$
$277$			9.22939i			0.554540i	−0.960792	+	0.277270i	$0.910570\pi$
$278$	1.41849	−	1.41849i	0.0850755	−	0.0850755i
$279$	12.4737	−	12.4737i	0.746780	−	0.746780i
$280$		0			0
$281$	8.78641	−	8.78641i	0.524153	−	0.524153i	−0.394670	−	0.918823i	$-0.629141\pi$
$281$	8.78641	−	8.78641i	0.524153	−	0.524153i	0.918823	+	0.394670i	$0.129141\pi$
$282$	−16.4017			−0.976707
$283$	5.44134			0.323454			0.161727	−	0.986836i	$-0.448294\pi$
$283$	5.44134			0.323454			0.161727	+	0.986836i	$0.448294\pi$
$284$	56.5741	−	56.5741i	3.35705	−	3.35705i
$285$	4.01723			0.237960
$286$	8.40279	−	19.1770i	0.496867	−	1.13396i
$287$		0			0
$288$	−30.7539	−	30.7539i	−1.81219	−	1.81219i
$289$	−15.0352			−0.884421
$290$	31.1198			1.82742
$291$	7.16548	+	7.16548i	0.420048	+	0.420048i
$292$	45.8447	−	45.8447i	2.68286	−	2.68286i
$293$	−8.39280	−	8.39280i	−0.490313	−	0.490313i	0.418092	−	0.908405i	$-0.362699\pi$
$293$	−8.39280	−	8.39280i	−0.490313	−	0.490313i	−0.908405	+	0.418092i	$0.862699\pi$
$294$		0			0
$295$	−19.7318			−1.14883
$296$			20.0937i			1.16792i
$297$	6.27321	+	6.27321i	0.364008	+	0.364008i
$298$		−	40.3344i		−	2.33651i
$299$	−4.34289	−	1.90292i	−0.251156	−	0.110049i
$300$			5.54890i			0.320366i
$301$		0			0
$302$	34.0959			1.96200
$303$			10.8915i			0.625699i
$304$	19.5211	−	19.5211i	1.11961	−	1.11961i
$305$	−13.5598	−	13.5598i	−0.776432	−	0.776432i
$306$	6.47454	+	6.47454i	0.370125	+	0.370125i
$307$	−1.45103	−	1.45103i	−0.0828145	−	0.0828145i	0.664486	−	0.747301i	$-0.268650\pi$
$307$	−1.45103	−	1.45103i	−0.0828145	−	0.0828145i	−0.747301	+	0.664486i	$0.768650\pi$
$308$		0			0
$309$		−	6.84462i		−	0.389377i
$310$	−35.0624	+	35.0624i	−1.99141	+	1.99141i
$311$	3.29830			0.187029			0.0935147	−	0.995618i	$-0.470190\pi$
$311$	3.29830			0.187029			0.0935147	+	0.995618i	$0.470190\pi$
$312$	−22.4369	+	8.76514i	−1.27024	+	0.496228i
$313$		−	23.9478i		−	1.35361i	−0.736162	−	0.676805i	$-0.763364\pi$
$313$		−	23.9478i		−	1.35361i	0.736162	−	0.676805i	$-0.236636\pi$
$314$	20.0542	−	20.0542i	1.13172	−	1.13172i
$315$		0			0
$316$			75.7813i			4.26303i
$317$	−21.4273	−	21.4273i	−1.20348	−	1.20348i	−0.973102	−	0.230375i	$-0.926005\pi$
$317$	−21.4273	−	21.4273i	−1.20348	−	1.20348i	−0.230375	−	0.973102i	$-0.573995\pi$
$318$	3.66961	−	3.66961i	0.205781	−	0.205781i
$319$	−6.95925	+	6.95925i	−0.389643	+	0.389643i
$320$	39.3086	+	39.3086i	2.19742	+	2.19742i
$321$			3.27203i			0.182627i
$322$		0			0
$323$	−2.07493	+	2.07493i	−0.115452	+	0.115452i
$324$			21.8179i			1.21210i
$325$	−4.58444	−	2.00876i	−0.254299	−	0.111426i
$326$	1.45200			0.0804187
$327$	3.96003	−	3.96003i	0.218990	−	0.218990i
$328$		−	33.5110i		−	1.85034i
$329$		0			0
$330$	−7.87960	−	7.87960i	−0.433758	−	0.433758i
$331$	−6.76378	−	6.76378i	−0.371771	−	0.371771i	0.496351	−	0.868122i	$-0.334673\pi$
$331$	−6.76378	−	6.76378i	−0.371771	−	0.371771i	−0.868122	+	0.496351i	$0.834673\pi$
$332$	−20.1452	−	20.1452i	−1.10561	−	1.10561i
$333$	3.91333	−	3.91333i	0.214449	−	0.214449i
$334$		−	16.9071i		−	0.925115i
$335$	−1.43481			−0.0783921
$336$		0			0
$337$		−	24.0729i		−	1.31133i	−0.755050	−	0.655667i	$-0.772388\pi$
$337$		−	24.0729i		−	1.31133i	0.755050	−	0.655667i	$-0.227612\pi$
$338$	1.42029	−	35.0102i	0.0772537	−	1.90430i
$339$			7.71243i			0.418881i
$340$	−13.1890	−	13.1890i	−0.715273	−	0.715273i
$341$		−	15.6818i		−	0.849220i
$342$	−13.6746			−0.739435
$343$		0			0
$344$	−2.72353	−	2.72353i	−0.146843	−	0.146843i
$345$	−1.78444	+	1.78444i	−0.0960709	+	0.0960709i
$346$	4.94815	+	4.94815i	0.266014	+	0.266014i
$347$	−3.97977			−0.213645			−0.106823	−	0.994278i	$-0.534068\pi$
$347$	−3.97977			−0.213645			−0.106823	+	0.994278i	$0.534068\pi$
$348$	18.2598			0.978826
$349$	−5.05995	−	5.05995i	−0.270853	−	0.270853i	0.558591	−	0.829443i	$-0.311342\pi$
$349$	−5.05995	−	5.05995i	−0.270853	−	0.270853i	−0.829443	+	0.558591i	$0.811342\pi$
$350$		0			0
$351$	13.5988	+	5.95859i	0.725852	+	0.318046i
$352$	−38.6636			−2.06078
$353$	−6.92323	+	6.92323i	−0.368486	+	0.368486i	−0.866925	−	0.498439i	$-0.833907\pi$
$353$	−6.92323	+	6.92323i	−0.368486	+	0.368486i	0.498439	+	0.866925i	$0.333907\pi$
$354$	−15.9760			−0.849117
$355$	38.4104			2.03861
$356$	0.193093	−	0.193093i	0.0102339	−	0.0102339i
$357$		0			0
$358$	3.07767	−	3.07767i	0.162660	−	0.162660i
$359$	26.3129	−	26.3129i	1.38874	−	1.38874i	0.560772	−	0.827970i	$-0.310504\pi$
$359$	26.3129	−	26.3129i	1.38874	−	1.38874i	0.827970	−	0.560772i	$-0.189496\pi$
$360$		−	53.9001i		−	2.84079i
$361$			14.6176i			0.769349i
$362$	−4.75841	−	4.75841i	−0.250096	−	0.250096i
$363$	−4.82753			−0.253380
$364$		0			0
$365$	31.1258			1.62920
$366$	−10.9788	−	10.9788i	−0.573872	−	0.573872i
$367$		−	28.5020i		−	1.48779i	−0.668297	−	0.743895i	$-0.732976\pi$
$367$		−	28.5020i		−	1.48779i	0.668297	−	0.743895i	$-0.267024\pi$
$368$			17.3424i			0.904033i
$369$	−6.52639	+	6.52639i	−0.339750	+	0.339750i
$370$	−11.0000	+	11.0000i	−0.571863	+	0.571863i
$371$		0			0
$372$	−20.5731	+	20.5731i	−1.06667	+	1.06667i
$373$	−4.72029			−0.244407			−0.122204	−	0.992505i	$-0.538996\pi$
$373$	−4.72029			−0.244407			−0.122204	+	0.992505i	$0.538996\pi$
$374$	8.13975			0.420897
$375$	4.90096	−	4.90096i	0.253085	−	0.253085i
$376$	−70.5257			−3.63708
$377$	−6.61022	+	15.0860i	−0.340444	+	0.776969i
$378$		0			0
$379$	4.79288	+	4.79288i	0.246193	+	0.246193i	0.819406	−	0.573213i	$-0.194303\pi$
$379$	4.79288	+	4.79288i	0.246193	+	0.246193i	−0.573213	+	0.819406i	$0.694303\pi$
$380$	27.8558			1.42897
$381$	6.45425			0.330661
$382$	−20.8359	−	20.8359i	−1.06606	−	1.06606i
$383$	−3.75826	+	3.75826i	−0.192038	+	0.192038i	−0.796576	−	0.604538i	$-0.793358\pi$
$383$	−3.75826	+	3.75826i	−0.192038	+	0.192038i	0.604538	+	0.796576i	$0.293358\pi$
$384$	12.5575	+	12.5575i	0.640821	+	0.640821i
$385$		0			0
$386$	−16.7960			−0.854892
$387$			1.06083i			0.0539253i
$388$	49.6860	+	49.6860i	2.52243	+	2.52243i
$389$			34.8724i			1.76810i	0.467393	+	0.884050i	$0.345193\pi$
$389$			34.8724i			1.76810i	−0.467393	+	0.884050i	$0.654807\pi$
$390$	−17.0811	−	7.48441i	−0.864935	−	0.378988i
$391$		−	1.84335i		−	0.0932224i
$392$		0			0
$393$	6.99112			0.352655
$394$			43.8072i			2.20697i
$395$	−25.7255	+	25.7255i	−1.29439	+	1.29439i
$396$	19.4378	+	19.4378i	0.976785	+	0.976785i
$397$	−25.7626	−	25.7626i	−1.29299	−	1.29299i	−0.932929	−	0.360060i	$-0.882756\pi$
$397$	−25.7626	−	25.7626i	−1.29299	−	1.29299i	−0.360060	−	0.932929i	$-0.617244\pi$
$398$	34.4052	+	34.4052i	1.72458	+	1.72458i
$399$		0			0
$400$			18.3069i			0.915347i
$401$	−10.3998	+	10.3998i	−0.519339	+	0.519339i	−0.917371	−	0.398032i	$-0.869693\pi$
$401$	−10.3998	+	10.3998i	−0.519339	+	0.519339i	0.398032	+	0.917371i	$0.369693\pi$
$402$	−1.16171			−0.0579408
$403$	−9.54959	−	24.4449i	−0.475699	−	1.21769i
$404$			75.5225i			3.75738i
$405$	−7.40652	+	7.40652i	−0.368033	+	0.368033i
$406$		0			0
$407$		−	4.91981i		−	0.243866i
$408$	−6.62191	−	6.62191i	−0.327833	−	0.327833i
$409$	1.55419	−	1.55419i	0.0768496	−	0.0768496i	−0.667637	−	0.744487i	$-0.732694\pi$
$409$	1.55419	−	1.55419i	0.0768496	−	0.0768496i	0.744487	+	0.667637i	$0.232694\pi$
$410$	18.3451	−	18.3451i	0.906000	−	0.906000i
$411$	−4.88525	−	4.88525i	−0.240971	−	0.240971i
$412$		−	47.4612i		−	2.33825i
$413$		0			0
$414$	6.07419	−	6.07419i	0.298530	−	0.298530i
$415$		−	13.6774i		−	0.671396i
$416$	−60.2690	+	23.5445i	−2.95493	+	1.15436i
$417$	0.565089			0.0276725
$418$	−8.59579	+	8.59579i	−0.420434	+	0.420434i
$419$			31.5129i			1.53951i	0.638342	+	0.769753i	$0.279620\pi$
$419$			31.5129i			1.53951i	−0.638342	+	0.769753i	$0.720380\pi$
$420$		0			0
$421$	−10.0626	−	10.0626i	−0.490422	−	0.490422i	0.418017	−	0.908439i	$-0.362725\pi$
$421$	−10.0626	−	10.0626i	−0.490422	−	0.490422i	−0.908439	+	0.418017i	$0.862725\pi$
$422$	5.30849	+	5.30849i	0.258413	+	0.258413i
$423$	13.7351	+	13.7351i	0.667825	+	0.667825i
$424$	15.7789	−	15.7789i	0.766293	−	0.766293i
$425$		−	1.94588i		−	0.0943891i
$426$	31.0994			1.50677
$427$		0			0
$428$			22.6885i			1.09669i
$429$	5.49353	−	2.14609i	0.265230	−	0.103614i
$430$		−	2.98191i		−	0.143800i
$431$	9.41278	+	9.41278i	0.453398	+	0.453398i	0.896481	−	0.443083i	$-0.146115\pi$
$431$	9.41278	+	9.41278i	0.453398	+	0.453398i	−0.443083	+	0.896481i	$0.646115\pi$
$432$		−	54.3039i		−	2.61270i
$433$	−29.1175			−1.39930			−0.699648	−	0.714488i	$-0.746660\pi$
$433$	−29.1175			−1.39930			−0.699648	+	0.714488i	$0.746660\pi$
$434$		0			0
$435$	6.19865	+	6.19865i	0.297202	+	0.297202i
$436$	27.4592	−	27.4592i	1.31506	−	1.31506i
$437$	1.94663	+	1.94663i	0.0931198	+	0.0931198i
$438$	25.2013			1.20416
$439$	10.3134			0.492230			0.246115	−	0.969241i	$-0.420846\pi$
$439$	10.3134			0.492230			0.246115	+	0.969241i	$0.420846\pi$
$440$	−33.8815	−	33.8815i	−1.61524	−	1.61524i
$441$		0			0
$442$	12.6883	−	4.95677i	0.603520	−	0.235769i
$443$	0.614967			0.0292179			0.0146090	−	0.999893i	$-0.495350\pi$
$443$	0.614967			0.0292179			0.0146090	+	0.999893i	$0.495350\pi$
$444$	−6.45433	+	6.45433i	−0.306309	+	0.306309i
$445$	0.131099			0.00621467
$446$	46.2465			2.18984
$447$	8.03406	−	8.03406i	0.379998	−	0.379998i
$448$		0			0
$449$	8.66406	−	8.66406i	0.408882	−	0.408882i	−0.472466	−	0.881349i	$-0.656636\pi$
$449$	8.66406	−	8.66406i	0.408882	−	0.408882i	0.881349	+	0.472466i	$0.156636\pi$
$450$	6.41203	−	6.41203i	0.302266	−	0.302266i
$451$			8.20494i			0.386356i
$452$			53.4786i			2.51542i
$453$	6.79144	+	6.79144i	0.319090	+	0.319090i
$454$	−46.2237			−2.16939
$455$		0			0
$456$	13.9858			0.654945
$457$	−13.0748	−	13.0748i	−0.611615	−	0.611615i	0.331752	−	0.943367i	$-0.392360\pi$
$457$	−13.0748	−	13.0748i	−0.611615	−	0.611615i	−0.943367	+	0.331752i	$0.892360\pi$
$458$		−	58.7221i		−	2.74390i
$459$			5.77206i			0.269417i
$460$	−12.3734	+	12.3734i	−0.576915	+	0.576915i
$461$	−5.20251	+	5.20251i	−0.242305	+	0.242305i	−0.817803	−	0.575498i	$-0.804808\pi$
$461$	−5.20251	+	5.20251i	−0.242305	+	0.242305i	0.575498	+	0.817803i	$0.304808\pi$
$462$		0			0
$463$	−13.9818	+	13.9818i	−0.649788	+	0.649788i	−0.952942	−	0.303154i	$-0.901960\pi$
$463$	−13.9818	+	13.9818i	−0.649788	+	0.649788i	0.303154	+	0.952942i	$0.401960\pi$
$464$	60.2426			2.79669
$465$	−13.9679			−0.647747
$466$	−57.4898	+	57.4898i	−2.66316	+	2.66316i
$467$	−9.88926			−0.457620			−0.228810	−	0.973471i	$-0.573483\pi$
$467$	−9.88926			−0.457620			−0.228810	+	0.973471i	$0.573483\pi$
$468$	42.1365	+	18.4629i	1.94776	+	0.853448i
$469$		0			0
$470$	−38.6082	−	38.6082i	−1.78086	−	1.78086i
$471$	7.98903			0.368115
$472$	−68.6953			−3.16196
$473$	0.666837	+	0.666837i	0.0306612	+	0.0306612i
$474$	−20.8289	+	20.8289i	−0.956703	+	0.956703i
$475$	2.05490	+	2.05490i	0.0942852	+	0.0942852i
$476$		0			0
$477$	−6.14601			−0.281407
$478$			38.7729i			1.77343i
$479$	−9.60128	−	9.60128i	−0.438694	−	0.438694i	0.452879	−	0.891572i	$-0.350397\pi$
$479$	−9.60128	−	9.60128i	−0.438694	−	0.438694i	−0.891572	+	0.452879i	$0.850397\pi$
$480$			34.4379i			1.57187i
$481$	−2.99596	−	7.66902i	−0.136604	−	0.349677i
$482$		−	57.5929i		−	2.62328i
$483$		0			0
$484$	−33.4745			−1.52157
$485$			33.7339i			1.53178i
$486$	−29.5408	+	29.5408i	−1.34000	+	1.34000i
$487$	4.34347	+	4.34347i	0.196821	+	0.196821i	0.798636	−	0.601815i	$-0.205555\pi$
$487$	4.34347	+	4.34347i	0.196821	+	0.196821i	−0.601815	+	0.798636i	$0.705555\pi$
$488$	−47.2078	−	47.2078i	−2.13700	−	2.13700i
$489$	0.289218	+	0.289218i	0.0130789	+	0.0130789i
$490$		0			0
$491$			22.4430i			1.01284i	0.862287	+	0.506420i	$0.169032\pi$
$491$			22.4430i			1.01284i	−0.862287	+	0.506420i	$0.830968\pi$
$492$	10.7641	−	10.7641i	0.485284	−	0.485284i
$493$	−6.40330			−0.288390
$494$	−8.16468	+	18.6336i	−0.367346	+	0.838367i
$495$			13.1971i			0.593165i
$496$	−67.8748	+	67.8748i	−3.04767	+	3.04767i
$497$		0			0
$498$		−	11.0740i		−	0.496239i
$499$	26.3570	+	26.3570i	1.17990	+	1.17990i	0.979769	+	0.200134i	$0.0641377\pi$
$499$	26.3570	+	26.3570i	1.17990	+	1.17990i	0.200134	+	0.979769i	$0.435862\pi$
$500$	33.9837	−	33.9837i	1.51980	−	1.51980i
$501$	3.36766	−	3.36766i	0.150456	−	0.150456i
$502$	19.9222	+	19.9222i	0.889171	+	0.889171i
$503$		−	22.9063i		−	1.02134i	−0.859776	−	0.510671i	$-0.829397\pi$
$503$		−	22.9063i		−	1.02134i	0.859776	−	0.510671i	$-0.170603\pi$
$504$		0			0
$505$	−25.6376	+	25.6376i	−1.14086	+	1.14086i
$506$		−	7.63643i		−	0.339481i
$507$	7.25646	−	6.69066i	0.322271	−	0.297143i
$508$	44.7543			1.98565
$509$	−29.5653	+	29.5653i	−1.31046	+	1.31046i	−0.389383	+	0.921076i	$0.627312\pi$
$509$	−29.5653	+	29.5653i	−1.31046	+	1.31046i	−0.921076	+	0.389383i	$0.872688\pi$
$510$		−	7.25013i		−	0.321041i
$511$		0			0
$512$	3.23738	+	3.23738i	0.143073	+	0.143073i
$513$	−6.09545	−	6.09545i	−0.269120	−	0.269120i
$514$	−26.7369	−	26.7369i	−1.17931	−	1.17931i
$515$	16.1117	−	16.1117i	0.709965	−	0.709965i
$516$		−	1.74966i		−	0.0770243i
$517$	17.2677			0.759434
$518$		0			0
$519$			1.97121i			0.0865264i
$520$	−73.4470	−	32.1822i	−3.22086	−	1.41128i
$521$		−	11.2798i		−	0.494176i	−0.968993	−	0.247088i	$-0.920526\pi$
$521$		−	11.2798i		−	0.494176i	0.968993	−	0.247088i	$-0.0794737\pi$
$522$	−21.1001	−	21.1001i	−0.923524	−	0.923524i
$523$			31.6471i			1.38383i	0.721979	+	0.691915i	$0.243233\pi$
$523$			31.6471i			1.38383i	−0.721979	+	0.691915i	$0.756767\pi$
$524$	48.4770			2.11773
$525$		0			0
$526$	4.81969	+	4.81969i	0.210149	+	0.210149i
$527$	7.21454	−	7.21454i	0.314270	−	0.314270i
$528$	−15.2535	−	15.2535i	−0.663825	−	0.663825i
$529$	21.2706			0.924810
$530$	17.2759			0.750416
$531$	13.3787	+	13.3787i	0.580585	+	0.580585i
$532$		0			0
$533$	4.99647	+	12.7899i	0.216421	+	0.553992i
$534$	0.106145			0.00459336
$535$	−7.70208	+	7.70208i	−0.332990	+	0.332990i
$536$	−4.99523			−0.215761
$537$	1.22606			0.0529084
$538$	−15.4266	+	15.4266i	−0.665088	+	0.665088i
$539$		0			0
$540$	38.7448	−	38.7448i	1.66731	−	1.66731i
$541$	22.5768	−	22.5768i	0.970651	−	0.970651i	−0.0289301	−	0.999581i	$-0.509210\pi$
$541$	22.5768	−	22.5768i	0.970651	−	0.970651i	0.999581	+	0.0289301i	$0.00921003\pi$
$542$			75.5293i			3.24426i
$543$		−	1.89562i		−	0.0813489i
$544$	−17.7874	−	17.7874i	−0.762631	−	0.762631i
$545$	18.6432			0.798585
$546$		0			0
$547$	−10.5664			−0.451787			−0.225893	−	0.974152i	$-0.572530\pi$
$547$	−10.5664			−0.451787			−0.225893	+	0.974152i	$0.572530\pi$
$548$	−33.8747	−	33.8747i	−1.44706	−	1.44706i
$549$			18.3878i			0.784772i
$550$		−	8.06117i		−	0.343729i
$551$	6.76205	−	6.76205i	0.288073	−	0.288073i
$552$	−6.21244	+	6.21244i	−0.264419	+	0.264419i
$553$		0			0
$554$	−17.5900	+	17.5900i	−0.747328	+	0.747328i
$555$	−4.38210			−0.186010
$556$	3.91838			0.166176
$557$	3.42470	−	3.42470i	0.145109	−	0.145109i	−0.630820	−	0.775929i	$-0.717281\pi$
$557$	3.42470	−	3.42470i	0.145109	−	0.145109i	0.775929	+	0.630820i	$0.217281\pi$
$558$	47.5465			2.01280
$559$	1.44555	+	0.633394i	0.0611401	+	0.0267897i
$560$		0			0
$561$	1.62133	+	1.62133i	0.0684526	+	0.0684526i
$562$	33.4915			1.41276
$563$	10.5450			0.444417			0.222209	−	0.974999i	$-0.428673\pi$
$563$	10.5450			0.444417			0.222209	+	0.974999i	$0.428673\pi$
$564$	−22.6536	−	22.6536i	−0.953890	−	0.953890i
$565$	−18.1544	+	18.1544i	−0.763761	+	0.763761i
$566$	10.3705	+	10.3705i	0.435904	+	0.435904i
$567$		0			0
$568$	133.724			5.61094
$569$			10.9892i			0.460692i	0.973109	+	0.230346i	$0.0739859\pi$
$569$			10.9892i			0.460692i	−0.973109	+	0.230346i	$0.926014\pi$
$570$	7.65632	+	7.65632i	0.320688	+	0.320688i
$571$			15.1107i			0.632363i	0.948699	+	0.316182i	$0.102401\pi$
$571$			15.1107i			0.632363i	−0.948699	+	0.316182i	$0.897599\pi$
$572$	38.0926	−	14.8811i	1.59273	−	0.622212i
$573$		−	8.30046i		−	0.346757i
$574$		0			0
$575$	−1.82556			−0.0761310
$576$		−	53.3046i		−	2.22102i
$577$	3.34785	−	3.34785i	0.139373	−	0.139373i	−0.633978	−	0.773351i	$-0.718579\pi$
$577$	3.34785	−	3.34785i	0.139373	−	0.139373i	0.773351	+	0.633978i	$0.218579\pi$
$578$	−28.6551	−	28.6551i	−1.19189	−	1.19189i
$579$	−3.34553	−	3.34553i	−0.139035	−	0.139035i
$580$	42.9819	+	42.9819i	1.78473	+	1.78473i
$581$		0			0
$582$			27.3129i			1.13216i
$583$	−3.86336	+	3.86336i	−0.160004	+	0.160004i
$584$	108.363			4.48409
$585$	8.03647	+	20.5717i	0.332267	+	0.850535i
$586$		−	31.9912i		−	1.32154i
$587$	−7.44792	+	7.44792i	−0.307409	+	0.307409i	−0.843904	−	0.536495i	$-0.819748\pi$
$587$	−7.44792	+	7.44792i	−0.307409	+	0.307409i	0.536495	+	0.843904i	$0.319748\pi$
$588$		0			0
$589$			15.2375i			0.627850i
$590$	−37.6062	−	37.6062i	−1.54822	−	1.54822i
$591$	−8.72580	+	8.72580i	−0.358932	+	0.358932i
$592$	−21.2941	+	21.2941i	−0.875182	+	0.875182i
$593$	−15.9382	−	15.9382i	−0.654502	−	0.654502i	0.299572	−	0.954074i	$-0.403156\pi$
$593$	−15.9382	−	15.9382i	−0.654502	−	0.654502i	−0.954074	+	0.299572i	$0.903156\pi$
$594$			23.9118i			0.981115i
$595$		0			0
$596$	55.7089	−	55.7089i	2.28192	−	2.28192i
$597$			13.7061i			0.560953i
$598$	−4.65027	−	11.9037i	−0.190164	−	0.486779i
$599$	46.0681			1.88229			0.941146	−	0.338001i	$-0.109751\pi$
$599$	46.0681			1.88229			0.941146	+	0.338001i	$0.109751\pi$
$600$	−6.55797	+	6.55797i	−0.267728	+	0.267728i
$601$		−	1.03260i		−	0.0421204i	−0.999778	−	0.0210602i	$-0.993296\pi$
$601$		−	1.03260i		−	0.0421204i	0.999778	−	0.0210602i	$-0.00670417\pi$
$602$		0			0
$603$	0.972840	+	0.972840i	0.0396171	+	0.0396171i
$604$	47.0924	+	47.0924i	1.91616	+	1.91616i
$605$	−11.3636	−	11.3636i	−0.461996	−	0.461996i
$606$	−20.7578	+	20.7578i	−0.843226	+	0.843226i
$607$			27.3160i			1.10872i	0.832277	+	0.554360i	$0.187037\pi$
$607$			27.3160i			1.10872i	−0.832277	+	0.554360i	$0.812963\pi$
$608$	37.5680			1.52358
$609$		0			0
$610$		−	51.6864i		−	2.09272i
$611$	26.9170	−	10.5153i	1.08895	−	0.425405i
$612$			17.8850i			0.722957i
$613$	−19.6763	−	19.6763i	−0.794717	−	0.794717i	0.187540	−	0.982257i	$-0.439949\pi$
$613$	−19.6763	−	19.6763i	−0.794717	−	0.794717i	−0.982257	+	0.187540i	$0.939949\pi$
$614$		−	5.53094i		−	0.223211i
$615$	7.30819			0.294695
$616$		0			0
$617$	11.4818	+	11.4818i	0.462241	+	0.462241i	0.899390	−	0.437148i	$-0.144011\pi$
$617$	11.4818	+	11.4818i	0.462241	+	0.462241i	−0.437148	+	0.899390i	$0.644011\pi$
$618$	13.0450	−	13.0450i	0.524745	−	0.524745i
$619$	−26.6016	−	26.6016i	−1.06921	−	1.06921i	−0.997420	−	0.0717875i	$-0.977130\pi$
$619$	−26.6016	−	26.6016i	−1.06921	−	1.06921i	−0.0717875	−	0.997420i	$-0.522870\pi$
$620$	−96.8548			−3.88978
$621$	5.41515			0.217302
$622$	6.28613	+	6.28613i	0.252051	+	0.252051i
$623$		0			0
$624$	−33.0661	−	14.4885i	−1.32370	−	0.580005i
$625$	30.0139			1.20056
$626$	45.6414	−	45.6414i	1.82420	−	1.82420i
$627$	−3.42433			−0.136754
$628$	55.3966			2.21057
$629$	2.26339	−	2.26339i	0.0902474	−	0.0902474i
$630$		0			0
$631$	1.20311	−	1.20311i	0.0478949	−	0.0478949i	−0.682754	−	0.730649i	$-0.739218\pi$
$631$	1.20311	−	1.20311i	0.0478949	−	0.0478949i	0.730649	+	0.682754i	$0.239218\pi$
$632$	−89.5621	+	89.5621i	−3.56259	+	3.56259i
$633$			2.11476i			0.0840541i
$634$		−	81.6753i		−	3.24374i
$635$	15.1928	+	15.1928i	0.602907	+	0.602907i
$636$	10.1367			0.401948
$637$		0			0
$638$	−26.5269			−1.05021
$639$	−26.0433	−	26.0433i	−1.03026	−	1.03026i
$640$			59.1185i			2.33686i
$641$			1.50565i			0.0594694i	0.999558	+	0.0297347i	$0.00946625\pi$
$641$			1.50565i			0.0594694i	−0.999558	+	0.0297347i	$0.990534\pi$
$642$	−6.23606	+	6.23606i	−0.246118	+	0.246118i
$643$	−27.5811	+	27.5811i	−1.08769	+	1.08769i	−0.0919256	+	0.995766i	$0.529302\pi$
$643$	−27.5811	+	27.5811i	−1.08769	+	1.08769i	−0.995766	+	0.0919256i	$0.970698\pi$
$644$		0			0
$645$	0.593956	−	0.593956i	0.0233870	−	0.0233870i
$646$	−7.90910			−0.311179
$647$	−7.88147			−0.309853			−0.154926	−	0.987926i	$-0.549514\pi$
$647$	−7.88147			−0.309853			−0.154926	+	0.987926i	$0.549514\pi$
$648$	−25.7855	+	25.7855i	−1.01295	+	1.01295i
$649$	16.8196			0.660227
$650$	−4.90891	−	12.5658i	−0.192543	−	0.492871i
$651$		0			0
$652$	2.00546	+	2.00546i	0.0785401	+	0.0785401i
$653$	6.36629			0.249132			0.124566	−	0.992211i	$-0.460246\pi$
$653$	6.36629			0.249132			0.124566	+	0.992211i	$0.460246\pi$
$654$	15.0946			0.590246
$655$	16.4565	+	16.4565i	0.643009	+	0.643009i
$656$	35.5129	−	35.5129i	1.38655	−	1.38655i
$657$	−21.1041	−	21.1041i	−0.823350	−	0.823350i
$658$		0			0
$659$	−25.8902			−1.00854			−0.504270	−	0.863546i	$-0.668238\pi$
$659$	−25.8902			−1.00854			−0.504270	+	0.863546i	$0.668238\pi$
$660$		−	21.7662i		−	0.847249i
$661$	27.1771	+	27.1771i	1.05707	+	1.05707i	0.998270	+	0.0587963i	$0.0187262\pi$
$661$	27.1771	+	27.1771i	1.05707	+	1.05707i	0.0587963	+	0.998270i	$0.481274\pi$
$662$		−	25.7818i		−	1.00204i
$663$	3.51466	+	1.54001i	0.136498	+	0.0598092i
$664$		−	47.6172i		−	1.84791i
$665$		0			0
$666$	14.9166			0.578006
$667$			6.00736i			0.232606i
$668$	23.3517	−	23.3517i	0.903503	−	0.903503i
$669$	9.21169	+	9.21169i	0.356144	+	0.356144i
$670$	−2.73456	−	2.73456i	−0.105645	−	0.105645i
$671$	11.5585	+	11.5585i	0.446212	+	0.446212i
$672$		0			0
$673$		−	5.66768i		−	0.218473i	−0.994016	−	0.109236i	$-0.965159\pi$
$673$		−	5.66768i		−	0.218473i	0.994016	−	0.109236i	$-0.0348406\pi$
$674$	45.8798	−	45.8798i	1.76722	−	1.76722i
$675$	5.71634			0.220022
$676$	50.3169	−	46.3936i	1.93527	−	1.78437i
$677$			2.68646i			0.103249i	0.998667	+	0.0516244i	$0.0164399\pi$
$677$			2.68646i			0.103249i	−0.998667	+	0.0516244i	$0.983560\pi$
$678$	−14.6989	+	14.6989i	−0.564507	+	0.564507i
$679$		0			0
$680$		−	31.1748i		−	1.19550i
$681$	−9.20714	−	9.20714i	−0.352818	−	0.352818i
$682$	29.8876	−	29.8876i	1.14445	−	1.14445i
$683$	9.22366	−	9.22366i	0.352934	−	0.352934i	−0.508266	−	0.861200i	$-0.669713\pi$
$683$	9.22366	−	9.22366i	0.352934	−	0.352934i	0.861200	+	0.508266i	$0.169713\pi$
$684$	−18.8870	−	18.8870i	−0.722161	−	0.722161i
$685$		−	22.9989i		−	0.878743i
$686$		0			0
$687$	11.6967	−	11.6967i	0.446255	−	0.446255i
$688$		−	5.77246i		−	0.220073i
$689$	−3.66961	+	8.37486i	−0.139801	+	0.319057i
$690$	−6.80182			−0.258941
$691$	−1.83672	+	1.83672i	−0.0698722	+	0.0698722i	−0.741179	−	0.671307i	$-0.765733\pi$
$691$	−1.83672	+	1.83672i	−0.0698722	+	0.0698722i	0.671307	+	0.741179i	$0.265733\pi$
$692$			13.6685i			0.519599i
$693$		0			0
$694$	−7.58493	−	7.58493i	−0.287920	−	0.287920i
$695$	1.33017	+	1.33017i	0.0504563	+	0.0504563i
$696$	21.5803	+	21.5803i	0.817999	+	0.817999i
$697$	−3.77474	+	3.77474i	−0.142978	+	0.142978i
$698$		−	19.2872i		−	0.730032i
$699$	−22.9024			−0.866247
$700$		0			0
$701$		−	42.5214i		−	1.60601i	−0.595972	−	0.803005i	$-0.703233\pi$
$701$		−	42.5214i		−	1.60601i	0.595972	−	0.803005i	$-0.296767\pi$
$702$	14.5613	+	37.2739i	0.549581	+	1.40681i
$703$			4.78040i			0.180296i
$704$	−33.5071	−	33.5071i	−1.26285	−	1.26285i
$705$		−	15.3805i		−	0.579262i
$706$	−26.3896			−0.993184
$707$		0			0
$708$	−22.0657	−	22.0657i	−0.829281	−	0.829281i
$709$	−33.7610	+	33.7610i	−1.26792	+	1.26792i	−0.320761	+	0.947160i	$0.603939\pi$
$709$	−33.7610	+	33.7610i	−1.26792	+	1.26792i	−0.947160	+	0.320761i	$0.896061\pi$
$710$	73.2053	+	73.2053i	2.74735	+	2.74735i
$711$	34.8851			1.30829
$712$	0.456414			0.0171048
$713$	−6.76843	−	6.76843i	−0.253480	−	0.253480i
$714$		0			0
$715$	17.9830	+	7.87960i	0.672526	+	0.294680i
$716$	8.50161			0.317720
$717$	−7.72303	+	7.72303i	−0.288422	+	0.288422i
$718$	100.298			3.74309
$719$	18.5588			0.692126			0.346063	−	0.938211i	$-0.387518\pi$
$719$	18.5588			0.692126			0.346063	+	0.938211i	$0.387518\pi$
$720$	57.1201	−	57.1201i	2.12874	−	2.12874i
$721$		0			0
$722$	−27.8593	+	27.8593i	−1.03682	+	1.03682i
$723$	11.4717	−	11.4717i	0.426638	−	0.426638i
$724$		−	13.1444i		−	0.488508i
$725$			6.34148i			0.235517i
$726$	−9.20065	−	9.20065i	−0.341468	−	0.341468i
$727$	32.8685			1.21903			0.609513	−	0.792776i	$-0.291365\pi$
$727$	32.8685			1.21903			0.609513	+	0.792776i	$0.291365\pi$
$728$		0			0
$729$	0.664320			0.0246045
$730$	59.3217	+	59.3217i	2.19560	+	2.19560i
$731$			0.613566i			0.0226936i
$732$		−	30.3274i		−	1.12093i
$733$	−26.5138	+	26.5138i	−0.979308	+	0.979308i	−0.999790	−	0.0204819i	$-0.993480\pi$
$733$	−26.5138	+	26.5138i	−0.979308	+	0.979308i	0.0204819	+	0.999790i	$0.493480\pi$
$734$	54.3210	−	54.3210i	2.00503	−	2.00503i
$735$		0			0
$736$	−16.6876	+	16.6876i	−0.615112	+	0.615112i
$737$	1.22305			0.0450516
$738$	−24.8769			−0.915732
$739$	−3.76689	+	3.76689i	−0.138567	+	0.138567i	−0.772988	−	0.634421i	$-0.781239\pi$
$739$	−3.76689	+	3.76689i	−0.138567	+	0.138567i	0.634421	+	0.772988i	$0.281239\pi$
$740$	−30.3859			−1.11701
$741$	−5.33786	+	2.08527i	−0.196091	+	0.0766044i
$742$		0			0
$743$	−12.3984	−	12.3984i	−0.454854	−	0.454854i	0.442108	−	0.896962i	$-0.354231\pi$
$743$	−12.3984	−	12.3984i	−0.454854	−	0.454854i	−0.896962	+	0.442108i	$0.854231\pi$
$744$	−48.6287			−1.78281
$745$	37.8230			1.38573
$746$	−8.99626	−	8.99626i	−0.329376	−	0.329376i
$747$	−9.27363	+	9.27363i	−0.339304	+	0.339304i
$748$	11.2424	+	11.2424i	0.411064	+	0.411064i
$749$		0			0
$750$	18.6812			0.682141
$751$		−	31.6584i		−	1.15523i	−0.816309	−	0.577615i	$-0.803983\pi$
$751$		−	31.6584i		−	1.15523i	0.816309	−	0.577615i	$-0.196017\pi$
$752$	−74.7389	−	74.7389i	−2.72545	−	2.72545i
$753$			7.93646i			0.289221i
$754$	−41.3502	+	16.1538i	−1.50589	+	0.588285i
$755$			31.9730i			1.16361i
$756$		0			0
$757$	−20.0484			−0.728670			−0.364335	−	0.931268i	$-0.618704\pi$
$757$	−20.0484			−0.728670			−0.364335	+	0.931268i	$0.618704\pi$
$758$			18.2692i			0.663567i
$759$	1.52107	−	1.52107i	0.0552115	−	0.0552115i
$760$	32.9214	+	32.9214i	1.19418	+	1.19418i
$761$	32.4612	+	32.4612i	1.17672	+	1.17672i	0.980576	+	0.196142i	$0.0628412\pi$
$761$	32.4612	+	32.4612i	1.17672	+	1.17672i	0.196142	+	0.980576i	$0.437159\pi$
$762$	12.3010	+	12.3010i	0.445617	+	0.445617i
$763$		0			0
$764$		−	57.5561i		−	2.08231i
$765$	−6.07141	+	6.07141i	−0.219512	+	0.219512i
$766$	−14.3255			−0.517602
$767$	26.2185	−	10.2424i	0.946694	−	0.369833i
$768$			14.4674i			0.522046i
$769$	−4.10750	+	4.10750i	−0.148120	+	0.148120i	−0.777278	−	0.629158i	$-0.783400\pi$
$769$	−4.10750	+	4.10750i	−0.148120	+	0.148120i	0.629158	+	0.777278i	$0.283400\pi$
$770$		0			0
$771$		−	10.6512i		−	0.383595i
$772$	−23.1982	−	23.1982i	−0.834920	−	0.834920i
$773$	−29.7099	+	29.7099i	−1.06859	+	1.06859i	−0.0711244	+	0.997467i	$0.522659\pi$
$773$	−29.7099	+	29.7099i	−1.06859	+	1.06859i	−0.997467	+	0.0711244i	$0.977341\pi$
$774$	−2.02181	+	2.02181i	−0.0726726	+	0.0726726i
$775$	−7.14489	−	7.14489i	−0.256652	−	0.256652i
$776$			117.443i			4.21595i
$777$		0			0
$778$	−66.4622	+	66.4622i	−2.38279	+	2.38279i
$779$		−	7.97244i		−	0.285642i
$780$	−13.2547	−	33.9293i	−0.474595	−	1.21486i
$781$	−32.7415			−1.17158
$782$	3.51319	−	3.51319i	0.125632	−	0.125632i
$783$		−	18.8107i		−	0.672241i
$784$		0			0
$785$	18.8055	+	18.8055i	0.671197	+	0.671197i
$786$	13.3242	+	13.3242i	0.475258	+	0.475258i
$787$	10.0539	+	10.0539i	0.358381	+	0.358381i	0.863216	−	0.504835i	$-0.168447\pi$
$787$	10.0539	+	10.0539i	0.358381	+	0.358381i	−0.504835	+	0.863216i	$0.668447\pi$
$788$	−60.5055	+	60.5055i	−2.15542	+	2.15542i
$789$			1.92004i			0.0683551i
$790$	−98.0589			−3.48878
$791$		0			0
$792$			45.9451i			1.63259i
$793$	25.0561	+	10.9788i	0.889769	+	0.389869i
$794$		−	98.2005i		−	3.48500i
$795$	3.44112	+	3.44112i	0.122044	+	0.122044i
$796$			95.0392i			3.36858i
$797$	−31.4048			−1.11241			−0.556207	−	0.831044i	$-0.687744\pi$
$797$	−31.4048			−1.11241			−0.556207	+	0.831044i	$0.687744\pi$
$798$		0			0
$799$	7.94414	+	7.94414i	0.281044	+	0.281044i
$800$	−17.6157	+	17.6157i	−0.622810	+	0.622810i
$801$	−0.0888884	−	0.0888884i	−0.00314072	−	0.00314072i
$802$	−39.6412			−1.39978
$803$	−26.5320			−0.936292
$804$	−1.60452	−	1.60452i	−0.0565872	−	0.0565872i
$805$		0			0
$806$	28.3886	−	64.7892i	0.999947	−	2.28210i
$807$	−6.14554			−0.216333
$808$	−89.2562	+	89.2562i	−3.14002	+	3.14002i
$809$	−29.8071			−1.04796			−0.523981	−	0.851730i	$-0.675554\pi$
$809$	−29.8071			−1.04796			−0.523981	+	0.851730i	$0.675554\pi$
$810$	−28.2317			−0.991962
$811$	7.04429	−	7.04429i	0.247359	−	0.247359i	−0.572527	−	0.819886i	$-0.694037\pi$
$811$	7.04429	−	7.04429i	0.247359	−	0.247359i	0.819886	+	0.572527i	$0.194037\pi$
$812$		0			0
$813$	−15.0444	+	15.0444i	−0.527631	+	0.527631i
$814$	9.37652	−	9.37652i	0.328647	−	0.328647i
$815$			1.36159i			0.0476945i
$816$		−	14.0350i		−	0.491323i
$817$	−0.647942	−	0.647942i	−0.0226686	−	0.0226686i
$818$	5.92416			0.207133
$819$		0			0
$820$	50.6756			1.76967
$821$	17.0765	+	17.0765i	0.595974	+	0.595974i	0.939239	−	0.343265i	$-0.111533\pi$
$821$	17.0765	+	17.0765i	0.595974	+	0.595974i	−0.343265	+	0.939239i	$0.611533\pi$
$822$		−	18.6213i		−	0.649492i
$823$			13.5135i			0.471052i	0.971868	+	0.235526i	$0.0756813\pi$
$823$			13.5135i			0.471052i	−0.971868	+	0.235526i	$0.924319\pi$
$824$	56.0920	−	56.0920i	1.95406	−	1.95406i
$825$	1.60568	−	1.60568i	0.0559024	−	0.0559024i
$826$		0			0
$827$	29.8965	−	29.8965i	1.03960	−	1.03960i	0.0404191	−	0.999183i	$-0.487131\pi$
$827$	29.8965	−	29.8965i	1.03960	−	1.03960i	0.999183	−	0.0404191i	$-0.0128693\pi$
$828$	16.7790			0.583112
$829$	−54.8150			−1.90381			−0.951903	−	0.306401i	$-0.900875\pi$
$829$	−54.8150			−1.90381			−0.951903	+	0.306401i	$0.900875\pi$
$830$	26.0673	−	26.0673i	0.904810	−	0.904810i
$831$	−7.00739			−0.243084
$832$	−72.6355	−	31.8266i	−2.51818	−	1.10339i
$833$		0			0
$834$	1.07699	+	1.07699i	0.0372930	+	0.0372930i
$835$	15.8544			0.548664
$836$	−23.7446			−0.821224
$837$	21.1939	+	21.1939i	0.732568	+	0.732568i
$838$	−60.0595	+	60.0595i	−2.07472	+	2.07472i
$839$	1.27402	+	1.27402i	0.0439842	+	0.0439842i	0.728757	−	0.684773i	$-0.240098\pi$
$839$	1.27402	+	1.27402i	0.0439842	+	0.0439842i	−0.684773	+	0.728757i	$0.740098\pi$
$840$		0			0
$841$	−8.13210			−0.280417
$842$		−	38.3561i		−	1.32184i
$843$	6.67106	+	6.67106i	0.229764	+	0.229764i
$844$			14.6639i			0.504753i
$845$	32.8303	+	1.33186i	1.12940	+	0.0458173i
$846$			52.3548i			1.80000i
$847$		0			0
$848$	33.4431			1.14844
$849$			4.13132i			0.141787i
$850$	3.70860	−	3.70860i	0.127204	−	0.127204i
$851$	−2.12344	−	2.12344i	−0.0727904	−	0.0727904i
$852$	42.9537	+	42.9537i	1.47157	+	1.47157i
$853$	−2.51606	−	2.51606i	−0.0861481	−	0.0861481i	0.662720	−	0.748868i	$-0.269402\pi$
$853$	−2.51606	−	2.51606i	−0.0861481	−	0.0861481i	−0.748868	+	0.662720i	$0.769402\pi$
$854$		0			0
$855$		−	12.8231i		−	0.438542i
$856$	−26.8144	+	26.8144i	−0.916499	+	0.916499i
$857$	21.1818			0.723556			0.361778	−	0.932264i	$-0.382170\pi$
$857$	21.1818			0.723556			0.361778	+	0.932264i	$0.382170\pi$
$858$	14.5601	+	6.37979i	0.497074	+	0.217803i
$859$		−	8.62218i		−	0.294185i	−0.989123	−	0.147093i	$-0.953008\pi$
$859$		−	8.62218i		−	0.294185i	0.989123	−	0.147093i	$-0.0469915\pi$
$860$	4.11854	−	4.11854i	0.140441	−	0.140441i
$861$		0			0
$862$			35.8791i			1.22205i
$863$	25.6877	+	25.6877i	0.874418	+	0.874418i	0.992950	−	0.118532i	$-0.0378189\pi$
$863$	25.6877	+	25.6877i	0.874418	+	0.874418i	−0.118532	+	0.992950i	$0.537819\pi$
$864$	52.2535	−	52.2535i	1.77770	−	1.77770i
$865$	−4.64006	+	4.64006i	−0.157767	+	0.157767i
$866$	−55.4941	−	55.4941i	−1.88577	−	1.88577i
$867$		−	11.4154i		−	0.387687i
$868$		0			0
$869$	21.9287	−	21.9287i	0.743879	−	0.743879i
$870$			23.6276i			0.801052i
$871$	1.90649	−	0.744785i	0.0645991	−	0.0252361i
$872$	64.9053			2.19797
$873$	22.8724	−	22.8724i	0.774115	−	0.774115i
$874$			7.42004i			0.250987i
$875$		0			0
$876$	34.8074	+	34.8074i	1.17603	+	1.17603i
$877$	−24.9794	−	24.9794i	−0.843496	−	0.843496i	0.145816	−	0.989312i	$-0.453419\pi$
$877$	−24.9794	−	24.9794i	−0.843496	−	0.843496i	−0.989312	+	0.145816i	$0.953419\pi$
$878$	19.6559	+	19.6559i	0.663356	+	0.663356i
$879$	6.37221	−	6.37221i	0.214929	−	0.214929i
$880$		−	71.8111i		−	2.42075i
$881$	48.8409			1.64549			0.822747	−	0.568408i	$-0.192441\pi$
$881$	48.8409			1.64549			0.822747	+	0.568408i	$0.192441\pi$
$882$		0			0
$883$			56.2857i			1.89417i	0.320989	+	0.947083i	$0.395985\pi$
$883$			56.2857i			1.89417i	−0.320989	+	0.947083i	$0.604015\pi$
$884$	24.3709	+	10.6786i	0.819683	+	0.359160i
$885$		−	14.9813i		−	0.503591i
$886$	1.17205	+	1.17205i	0.0393757	+	0.0393757i
$887$		−	28.0744i		−	0.942647i	−0.881960	−	0.471324i	$-0.843776\pi$
$887$		−	28.0744i		−	0.942647i	0.881960	−	0.471324i	$-0.156224\pi$
$888$	−15.2561			−0.511961
$889$		0			0
$890$	0.249857	+	0.249857i	0.00837523	+	0.00837523i
$891$	6.31340	−	6.31340i	0.211507	−	0.211507i
$892$	63.8746	+	63.8746i	2.13868	+	2.13868i
$893$	−16.7784			−0.561469
$894$	30.6238			1.02421
$895$	2.88604	+	2.88604i	0.0964698	+	0.0964698i
$896$		0			0
$897$	1.44479	−	3.29733i	0.0482400	−	0.110095i
$898$	33.0251			1.10206
$899$	−23.5117	+	23.5117i	−0.784158	+	0.784158i
$900$	17.7123			0.590410
$901$	−3.55474			−0.118425
$902$	−15.6376	+	15.6376i	−0.520674	+	0.520674i
$903$		0			0
$904$	−63.2037	+	63.2037i	−2.10212	+	2.10212i
$905$	4.46213	−	4.46213i	0.148326	−	0.148326i
$906$			25.8872i			0.860045i
$907$		−	46.3633i		−	1.53947i	−0.638365	−	0.769733i	$-0.720389\pi$
$907$		−	46.3633i		−	1.53947i	0.638365	−	0.769733i	$-0.279611\pi$
$908$	−63.8431	−	63.8431i	−2.11871	−	2.11871i
$909$	34.7660			1.15311
$910$		0			0
$911$	−23.8152			−0.789032			−0.394516	−	0.918889i	$-0.629088\pi$
$911$	−23.8152			−0.789032			−0.394516	+	0.918889i	$0.629088\pi$
$912$	14.8213	+	14.8213i	0.490783	+	0.490783i
$913$			11.6588i			0.385848i
$914$		−	49.8379i		−	1.64849i
$915$	10.2952	−	10.2952i	0.340350	−	0.340350i
$916$	81.1056	−	81.1056i	2.67980	−	2.67980i
$917$		0			0
$918$	−11.0008	+	11.0008i	−0.363081	+	0.363081i
$919$	−57.7538			−1.90512			−0.952561	−	0.304348i	$-0.901561\pi$
$919$	−57.7538			−1.90512			−0.952561	+	0.304348i	$0.901561\pi$
$920$	−29.2471			−0.964249
$921$	1.10169	−	1.10169i	0.0363019	−	0.0363019i
$922$	−19.8306			−0.653087
$923$	−51.0376	+	19.9382i	−1.67992	+	0.656273i
$924$		0			0
$925$	−2.24154	−	2.24154i	−0.0737014	−	0.0737014i
$926$	−53.2949			−1.75138
$927$	−21.8483			−0.717591
$928$	57.9680	+	57.9680i	1.90289	+	1.90289i
$929$	−13.5299	+	13.5299i	−0.443903	+	0.443903i	−0.893321	−	0.449418i	$-0.851631\pi$
$929$	−13.5299	+	13.5299i	−0.443903	+	0.443903i	0.449418	+	0.893321i	$0.351631\pi$
$930$	−26.6210	−	26.6210i	−0.872939	−	0.872939i
$931$		0			0
$932$	−158.807			−5.20190
$933$			2.50423i			0.0819846i
$934$	−18.8476	−	18.8476i	−0.616714	−	0.616714i
$935$			7.63294i			0.249624i
$936$	27.9786	+	71.6194i	0.914510	+	2.34095i
$937$		−	8.53986i		−	0.278985i	−0.990223	−	0.139492i	$-0.955453\pi$
$937$		−	8.53986i		−	0.278985i	0.990223	−	0.139492i	$-0.0445471\pi$
$938$		0			0
$939$	18.1823			0.593357
$940$		−	106.650i		−	3.47852i
$941$	18.9788	−	18.9788i	0.618692	−	0.618692i	−0.326504	−	0.945196i	$-0.605871\pi$
$941$	18.9788	−	18.9788i	0.618692	−	0.618692i	0.945196	+	0.326504i	$0.105871\pi$
$942$	15.2261	+	15.2261i	0.496092	+	0.496092i
$943$	3.54133	+	3.54133i	0.115322	+	0.115322i
$944$	−72.7992	−	72.7992i	−2.36941	−	2.36941i
$945$		0			0
$946$			2.54181i			0.0826414i
$947$	−25.8219	+	25.8219i	−0.839099	+	0.839099i	−0.988740	−	0.149641i	$-0.952188\pi$
$947$	−25.8219	+	25.8219i	−0.839099	+	0.839099i	0.149641	+	0.988740i	$0.452188\pi$
$948$	−57.5367			−1.86871
$949$	−41.3582	+	16.1569i	−1.34254	+	0.524474i
$950$			7.83274i			0.254128i
$951$	16.2686	−	16.2686i	0.527546	−	0.527546i
$952$		0			0
$953$			41.8966i			1.35716i	0.734525	+	0.678581i	$0.237405\pi$
$953$			41.8966i			1.35716i	−0.734525	+	0.678581i	$0.762595\pi$
$954$	−11.7135	−	11.7135i	−0.379239	−	0.379239i
$955$	19.5386	−	19.5386i	0.632253	−	0.632253i
$956$	−53.5522	+	53.5522i	−1.73200	+	1.73200i
$957$	−5.28379	−	5.28379i	−0.170801	−	0.170801i
$958$		−	36.5976i		−	1.18241i
$959$		0			0
$960$	−29.8450	+	29.8450i	−0.963242	+	0.963242i
$961$		−	21.9808i		−	0.709058i
$962$	8.90626	−	20.3261i	0.287149	−	0.655339i
$963$	10.4444			0.336567
$964$	79.5460	−	79.5460i	2.56200	−	2.56200i
$965$		−	15.7502i		−	0.507016i
$966$		0			0
$967$	−26.8795	−	26.8795i	−0.864388	−	0.864388i	0.127456	−	0.991844i	$-0.459319\pi$
$967$	−26.8795	−	26.8795i	−0.864388	−	0.864388i	−0.991844	+	0.127456i	$0.959319\pi$
$968$	−39.5619	−	39.5619i	−1.27157	−	1.27157i
$969$	−1.57539	−	1.57539i	−0.0506087	−	0.0506087i
$970$	−64.2924	+	64.2924i	−2.06430	+	2.06430i
$971$			40.9681i			1.31473i	0.753573	+	0.657364i	$0.228329\pi$
$971$			40.9681i			1.31473i	−0.753573	+	0.657364i	$0.771671\pi$
$972$	−81.6021			−2.61739
$973$		0			0
$974$			16.5562i			0.530494i
$975$	1.52515	−	3.48072i	0.0488438	−	0.111472i
$976$		−	100.056i		−	3.20271i
$977$	−18.7148	−	18.7148i	−0.598739	−	0.598739i	0.341238	−	0.939977i	$-0.389154\pi$
$977$	−18.7148	−	18.7148i	−0.598739	−	0.598739i	−0.939977	+	0.341238i	$0.889154\pi$
$978$			1.10243i			0.0352517i
$979$	−0.111750			−0.00357154
$980$		0			0
$981$	−12.6406	−	12.6406i	−0.403582	−	0.403582i
$982$	−42.7735	+	42.7735i	−1.36496	+	1.36496i
$983$	−33.2563	−	33.2563i	−1.06071	−	1.06071i	−0.998034	−	0.0626774i	$-0.980036\pi$
$983$	−33.2563	−	33.2563i	−1.06071	−	1.06071i	−0.0626774	−	0.998034i	$-0.519964\pi$
$984$	25.4431			0.811097
$985$	−41.0796			−1.30890
$986$	−12.2039	−	12.2039i	−0.388650	−	0.388650i
$987$		0			0
$988$	−37.0132	+	14.4595i	−1.17755	+	0.460017i
$989$	0.575627			0.0183039
$990$	−25.1519	+	25.1519i	−0.799381	+	0.799381i
$991$	−24.0583			−0.764238			−0.382119	−	0.924113i	$-0.624806\pi$
$991$	−24.0583			−0.764238			−0.382119	+	0.924113i	$0.624806\pi$
$992$	−130.624			−4.14732
$993$	5.13538	−	5.13538i	0.162966	−	0.162966i
$994$		0			0
$995$	−32.2630	+	32.2630i	−1.02281	+	1.02281i
$996$	15.2952	−	15.2952i	0.484647	−	0.484647i
$997$		−	6.65377i		−	0.210727i	−0.994434	−	0.105364i	$-0.966399\pi$
$997$		−	6.65377i		−	0.210727i	0.994434	−	0.105364i	$-0.0336006\pi$
$998$			100.466i			3.18020i
$999$	6.64908	+	6.64908i	0.210368	+	0.210368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.i.a.489.16		32
7.2	even	3		91.2.bb.a.73.8	yes	32
7.3	odd	6		91.2.bb.a.47.1	yes	32
7.4	even	3		637.2.bc.b.411.1		32
7.5	odd	6		637.2.bc.b.619.8		32
7.6	odd	2	inner	637.2.i.a.489.15		32
13.5	odd	4	inner	637.2.i.a.538.16		32
21.2	odd	6		819.2.fn.e.73.1		32
21.17	even	6		819.2.fn.e.775.8		32
91.5	even	12		637.2.bc.b.31.1		32
91.18	odd	12		637.2.bc.b.460.8		32
91.31	even	12		91.2.bb.a.5.8	✓	32
91.44	odd	12		91.2.bb.a.31.1	yes	32
91.83	even	4	inner	637.2.i.a.538.15		32
273.44	even	12		819.2.fn.e.577.8		32
273.122	odd	12		819.2.fn.e.460.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.8	✓	32	91.31	even	12
91.2.bb.a.31.1	yes	32	91.44	odd	12
91.2.bb.a.47.1	yes	32	7.3	odd	6
91.2.bb.a.73.8	yes	32	7.2	even	3
637.2.i.a.489.15		32	7.6	odd	2	inner
637.2.i.a.489.16		32	1.1	even	1	trivial
637.2.i.a.538.15		32	91.83	even	4	inner
637.2.i.a.538.16		32	13.5	odd	4	inner
637.2.bc.b.31.1		32	91.5	even	12
637.2.bc.b.411.1		32	7.4	even	3
637.2.bc.b.460.8		32	91.18	odd	12
637.2.bc.b.619.8		32	7.5	odd	6
819.2.fn.e.73.1		32	21.2	odd	6
819.2.fn.e.460.1		32	273.122	odd	12
819.2.fn.e.577.8		32	273.44	even	12
819.2.fn.e.775.8		32	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.90587 + 1.90587i) q^{2} +0.759247i q^{3} +5.26469i q^{4} +(-1.78720 + 1.78720i) q^{5} +(-1.44703 + 1.44703i) q^{6} +(-6.22207 + 6.22207i) q^{8} +2.42354 q^{9} +O(q^{10})\)	\(q+(1.90587 + 1.90587i) q^{2} +0.759247i q^{3} +5.26469i q^{4} +(-1.78720 + 1.78720i) q^{5} +(-1.44703 + 1.44703i) q^{6} +(-6.22207 + 6.22207i) q^{8} +2.42354 q^{9} -6.81236 q^{10} +(1.52343 - 1.52343i) q^{11} -3.99720 q^{12} +(1.44703 - 3.30244i) q^{13} +(-1.35693 - 1.35693i) q^{15} -13.1876 q^{16} +1.40173 q^{17} +(4.61896 + 4.61896i) q^{18} +(-1.48026 + 1.48026i) q^{19} +(-9.40907 - 9.40907i) q^{20} +5.80693 q^{22} -1.31506i q^{23} +(-4.72409 - 4.72409i) q^{24} -1.38820i q^{25} +(9.05187 - 3.53618i) q^{26} +4.11781i q^{27} -4.56814 q^{29} -5.17227i q^{30} +(5.14688 - 5.14688i) q^{31} +(-12.6896 - 12.6896i) q^{32} +(1.15666 + 1.15666i) q^{33} +(2.67152 + 2.67152i) q^{34} +12.7592i q^{36} +(1.61471 - 1.61471i) q^{37} -5.64238 q^{38} +(2.50737 + 1.09865i) q^{39} -22.2402i q^{40} +(-2.69291 + 2.69291i) q^{41} +0.437721i q^{43} +(8.02039 + 8.02039i) q^{44} +(-4.33137 + 4.33137i) q^{45} +(2.50632 - 2.50632i) q^{46} +(5.66738 + 5.66738i) q^{47} -10.0126i q^{48} +(2.64573 - 2.64573i) q^{50} +1.06426i q^{51} +(17.3863 + 7.61815i) q^{52} -2.53596 q^{53} +(-7.84802 + 7.84802i) q^{54} +5.44537i q^{55} +(-1.12389 - 1.12389i) q^{57} +(-8.70628 - 8.70628i) q^{58} +(5.52030 + 5.52030i) q^{59} +(7.14381 - 7.14381i) q^{60} +7.58715i q^{61} +19.6186 q^{62} -21.9945i q^{64} +(3.31600 + 8.48827i) q^{65} +4.40890i q^{66} +(0.401412 + 0.401412i) q^{67} +7.37967i q^{68} +0.998452 q^{69} +(-10.7460 - 10.7460i) q^{71} +(-15.0795 + 15.0795i) q^{72} +(-8.70795 - 8.70795i) q^{73} +6.15487 q^{74} +1.05399 q^{75} +(-7.79312 - 7.79312i) q^{76} +(2.68483 + 6.87261i) q^{78} +14.3943 q^{79} +(23.5689 - 23.5689i) q^{80} +4.14419 q^{81} -10.2647 q^{82} +(-3.82648 + 3.82648i) q^{83} +(-2.50518 + 2.50518i) q^{85} +(-0.834239 + 0.834239i) q^{86} -3.46835i q^{87} +18.9578i q^{88} +(-0.0366770 - 0.0366770i) q^{89} -16.5101 q^{90} +6.92335 q^{92} +(3.90776 + 3.90776i) q^{93} +21.6026i q^{94} -5.29107i q^{95} +(9.63457 - 9.63457i) q^{96} +(9.43761 - 9.43761i) q^{97} +(3.69210 - 3.69210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

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