LMFDB - Embedded newform 637.2.k.i.569.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(459,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("637.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.4
Root			$0.655911 - 1.25291i$ of defining polynomial
Character	$\chi$	$=$	637.569
Dual form			637.2.k.i.459.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.180824i q^{2} +(-0.913006 + 1.58137i) q^{3} +1.96730 q^{4} +(2.32670 + 1.34332i) q^{5} +(-0.285950 - 0.165093i) q^{6} +0.717383i q^{8} +(-0.167162 - 0.289532i) q^{9} +O(q^{10})$	\(q+0.180824i q^{2} +(-0.913006 + 1.58137i) q^{3} +1.96730 q^{4} +(2.32670 + 1.34332i) q^{5} +(-0.285950 - 0.165093i) q^{6} +0.717383i q^{8} +(-0.167162 - 0.289532i) q^{9} +(-0.242904 + 0.420723i) q^{10} +(2.33328 + 1.34712i) q^{11} +(-1.79616 + 3.11104i) q^{12} +(-1.92153 - 3.05086i) q^{13} +(-4.24858 + 2.45292i) q^{15} +3.80489 q^{16} +4.76493 q^{17} +(0.0523543 - 0.0302268i) q^{18} +(-0.163180 + 0.0942122i) q^{19} +(4.57732 + 2.64272i) q^{20} +(-0.243592 + 0.421913i) q^{22} -4.39929 q^{23} +(-1.13445 - 0.654975i) q^{24} +(1.10902 + 1.92088i) q^{25} +(0.551667 - 0.347458i) q^{26} -4.86756 q^{27} +(-3.54280 - 6.13631i) q^{29} +(-0.443546 - 0.768245i) q^{30} +(3.20369 - 1.84965i) q^{31} +2.12278i q^{32} +(-4.26060 + 2.45986i) q^{33} +0.861613i q^{34} +(-0.328857 - 0.569598i) q^{36} -7.95413i q^{37} +(-0.0170358 - 0.0295069i) q^{38} +(6.57891 - 0.253207i) q^{39} +(-0.963675 + 1.66913i) q^{40} +(-4.70215 + 2.71479i) q^{41} +(-4.00533 + 6.93743i) q^{43} +(4.59027 + 2.65020i) q^{44} -0.898206i q^{45} -0.795496i q^{46} +(1.60118 + 0.924445i) q^{47} +(-3.47389 + 6.01695i) q^{48} +(-0.347341 + 0.200538i) q^{50} +(-4.35041 + 7.53514i) q^{51} +(-3.78023 - 6.00196i) q^{52} +(3.53622 + 6.12491i) q^{53} -0.880171i q^{54} +(3.61923 + 6.26869i) q^{55} -0.344066i q^{57} +(1.10959 - 0.640623i) q^{58} +7.58888i q^{59} +(-8.35825 + 4.82564i) q^{60} +(-0.205782 - 0.356425i) q^{61} +(0.334461 + 0.579304i) q^{62} +7.22592 q^{64} +(-0.372548 - 9.67966i) q^{65} +(-0.444801 - 0.770418i) q^{66} +(-9.87358 - 5.70051i) q^{67} +9.37407 q^{68} +(4.01658 - 6.95692i) q^{69} +(2.89675 + 1.67244i) q^{71} +(0.207705 - 0.119919i) q^{72} +(-12.3112 + 7.10790i) q^{73} +1.43830 q^{74} -4.05018 q^{75} +(-0.321025 + 0.185344i) q^{76} +(0.0457859 + 1.18962i) q^{78} +(-4.55529 + 7.89000i) q^{79} +(8.85283 + 5.11118i) q^{80} +(4.94560 - 8.56603i) q^{81} +(-0.490899 - 0.850261i) q^{82} -16.5866i q^{83} +(11.0866 + 6.40083i) q^{85} +(-1.25445 - 0.724258i) q^{86} +12.9384 q^{87} +(-0.966401 + 1.67386i) q^{88} -5.89165i q^{89} +0.162417 q^{90} -8.65473 q^{92} +6.75498i q^{93} +(-0.167162 + 0.289532i) q^{94} -0.506229 q^{95} +(-3.35691 - 1.93811i) q^{96} +(-0.390659 - 0.225547i) q^{97} -0.900747i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9	$ 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9} - 12 q^{10} + 12 q^{11} + q^{12} + 2 q^{13} - 12 q^{15} + 16 q^{16} + 34 q^{17} + 3 q^{18} - 9 q^{19} + 3 q^{20} - 15 q^{22} - 6 q^{23} - 15 q^{24} - 5 q^{25} + 6 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{31} + 6 q^{33} - 13 q^{36} - 19 q^{38} - 4 q^{39} + q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} + 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{55} - 24 q^{58} - 30 q^{60} - 5 q^{61} - 41 q^{62} + 2 q^{64} + 21 q^{65} + 34 q^{66} + 15 q^{67} - 22 q^{68} - 7 q^{69} + 30 q^{71} + 57 q^{72} - 42 q^{73} + 66 q^{74} + 2 q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} + 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 57 q^{86} + 20 q^{87} - 14 q^{88} - 66 q^{92} - q^{94} - 4 q^{95} - 21 q^{96} + 3 q^{97}+O(q^{100}) $ 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9 - 12 * q^10 + 12 * q^11 + q^12 + 2 * q^13 - 12 * q^15 + 16 * q^16 + 34 * q^17 + 3 * q^18 - 9 * q^19 + 3 * q^20 - 15 * q^22 - 6 * q^23 - 15 * q^24 - 5 * q^25 + 6 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^31 + 6 * q^33 - 13 * q^36 - 19 * q^38 - 4 * q^39 + q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 + 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 + 7 * q^52 - 8 * q^53 + 15 * q^55 - 24 * q^58 - 30 * q^60 - 5 * q^61 - 41 * q^62 + 2 * q^64 + 21 * q^65 + 34 * q^66 + 15 * q^67 - 22 * q^68 - 7 * q^69 + 30 * q^71 + 57 * q^72 - 42 * q^73 + 66 * q^74 + 2 * q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 + 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 57 * q^86 + 20 * q^87 - 14 * q^88 - 66 * q^92 - q^94 - 4 * q^95 - 21 * q^96 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$			0.180824i			0.127862i	0.997954	+	0.0639308i	$0.0203637\pi$
$2$			0.180824i			0.127862i	−0.997954	+	0.0639308i	$0.979636\pi$
$3$	−0.913006	+	1.58137i	−0.527125	+	0.913006i	0.472376	+	0.881397i	$0.343397\pi$
$3$	−0.913006	+	1.58137i	−0.527125	+	0.913006i	−0.999500	+	0.0316092i	$0.989937\pi$
$4$	1.96730			0.983651
$5$	2.32670	+	1.34332i	1.04053	+	0.600751i	0.919984	−	0.391956i	$-0.128201\pi$
$5$	2.32670	+	1.34332i	1.04053	+	0.600751i	0.120548	+	0.992708i	$0.461535\pi$
$6$	−0.285950	−	0.165093i	−0.116739	−	0.0673990i
$7$		0			0
$7$		0			0
$8$			0.717383i			0.253633i
$9$	−0.167162	−	0.289532i	−0.0557205	−	0.0965108i
$10$	−0.242904	+	0.420723i	−0.0768131	+	0.133044i
$11$	2.33328	+	1.34712i	0.703511	+	0.406172i	0.808654	−	0.588285i	$-0.200197\pi$
$11$	2.33328	+	1.34712i	0.703511	+	0.406172i	−0.105143	+	0.994457i	$0.533530\pi$
$12$	−1.79616	+	3.11104i	−0.518507	+	0.898080i
$13$	−1.92153	−	3.05086i	−0.532937	−	0.846155i
$13$	−1.92153	−	3.05086i	−0.532937	−	0.846155i
$14$		0			0
$15$	−4.24858	+	2.45292i	−1.09698	+	0.633342i
$16$	3.80489			0.951221
$17$	4.76493			1.15567			0.577833	−	0.816155i	$-0.303898\pi$
$17$	4.76493			1.15567			0.577833	+	0.816155i	$0.303898\pi$
$18$	0.0523543	−	0.0302268i	0.0123400	−	0.00712452i
$19$	−0.163180	+	0.0942122i	−0.0374361	+	0.0216138i	−0.518601	−	0.855016i	$-0.673547\pi$
$19$	−0.163180	+	0.0942122i	−0.0374361	+	0.0216138i	0.481165	+	0.876630i	$0.340214\pi$
$20$	4.57732	+	2.64272i	1.02352	+	0.590930i
$21$		0			0
$22$	−0.243592	+	0.421913i	−0.0519339	+	0.0899521i
$23$	−4.39929			−0.917315			−0.458657	−	0.888613i	$-0.651669\pi$
$23$	−4.39929			−0.917315			−0.458657	+	0.888613i	$0.651669\pi$
$24$	−1.13445	−	0.654975i	−0.231569	−	0.133696i
$25$	1.10902	+	1.92088i	0.221804	+	0.384177i
$26$	0.551667	−	0.347458i	0.108191	−	0.0681422i
$27$	−4.86756			−0.936762
$28$		0			0
$29$	−3.54280	−	6.13631i	−0.657882	−	1.13948i	−0.981163	−	0.193182i	$-0.938119\pi$
$29$	−3.54280	−	6.13631i	−0.657882	−	1.13948i	0.323281	−	0.946303i	$-0.395214\pi$
$30$	−0.443546	−	0.768245i	−0.0809801	−	0.140262i
$31$	3.20369	−	1.84965i	0.575400	−	0.332207i	−0.183903	−	0.982944i	$-0.558873\pi$
$31$	3.20369	−	1.84965i	0.575400	−	0.332207i	0.759303	+	0.650737i	$0.225540\pi$
$32$			2.12278i			0.375258i
$33$	−4.26060	+	2.45986i	−0.741676	+	0.428207i
$34$			0.861613i			0.147765i
$35$		0			0
$36$	−0.328857	−	0.569598i	−0.0548096	−	0.0949329i
$37$		−	7.95413i		−	1.30765i	−0.756645	−	0.653826i	$-0.773163\pi$
$37$		−	7.95413i		−	1.30765i	0.756645	−	0.653826i	$-0.226837\pi$
$38$	−0.0170358	−	0.0295069i	−0.00276357	−	0.00478665i
$39$	6.57891	−	0.253207i	1.05347	−	0.0405456i
$40$	−0.963675	+	1.66913i	−0.152370	+	0.263913i
$41$	−4.70215	+	2.71479i	−0.734353	+	0.423979i	−0.820013	−	0.572345i	$-0.806034\pi$
$41$	−4.70215	+	2.71479i	−0.734353	+	0.423979i	0.0856594	+	0.996324i	$0.472700\pi$
$42$		0			0
$43$	−4.00533	+	6.93743i	−0.610807	+	1.05795i	0.380298	+	0.924864i	$0.375821\pi$
$43$	−4.00533	+	6.93743i	−0.610807	+	1.05795i	−0.991105	+	0.133084i	$0.957512\pi$
$44$	4.59027	+	2.65020i	0.692010	+	0.399532i
$45$		−	0.898206i		−	0.133897i
$46$		−	0.795496i		−	0.117289i
$47$	1.60118	+	0.924445i	0.233557	+	0.134844i	0.612212	−	0.790694i	$-0.290280\pi$
$47$	1.60118	+	0.924445i	0.233557	+	0.134844i	−0.378655	+	0.925538i	$0.623613\pi$
$48$	−3.47389	+	6.01695i	−0.501412	+	0.868471i
$49$		0			0
$50$	−0.347341	+	0.200538i	−0.0491215	+	0.0283603i
$51$	−4.35041	+	7.53514i	−0.609180	+	1.05513i
$52$	−3.78023	−	6.00196i	−0.524224	−	0.832322i
$53$	3.53622	+	6.12491i	0.485737	+	0.841321i	0.999866	−	0.0163917i	$-0.00521788\pi$
$53$	3.53622	+	6.12491i	0.485737	+	0.841321i	−0.514128	+	0.857713i	$0.671885\pi$
$54$		−	0.880171i		−	0.119776i
$55$	3.61923	+	6.26869i	0.488017	+	0.845271i
$56$		0			0
$57$		−	0.344066i		−	0.0455726i
$58$	1.10959	−	0.640623i	0.145696	−	0.0841179i
$59$			7.58888i			0.987988i	0.869465	+	0.493994i	$0.164464\pi$
$59$			7.58888i			0.987988i	−0.869465	+	0.493994i	$0.835536\pi$
$60$	−8.35825	+	4.82564i	−1.07905	+	0.622987i
$61$	−0.205782	−	0.356425i	−0.0263477	−	0.0456355i	0.852551	−	0.522644i	$-0.175054\pi$
$61$	−0.205782	−	0.356425i	−0.0263477	−	0.0456355i	−0.878899	+	0.477009i	$0.841721\pi$
$62$	0.334461	+	0.579304i	0.0424766	+	0.0735716i
$63$		0			0
$64$	7.22592			0.903240
$65$	−0.372548	−	9.67966i	−0.0462089	−	1.20061i
$66$	−0.444801	−	0.770418i	−0.0547512	−	0.0948319i
$67$	−9.87358	−	5.70051i	−1.20625	−	0.696429i	−0.244312	−	0.969697i	$-0.578562\pi$
$67$	−9.87358	−	5.70051i	−1.20625	−	0.696429i	−0.961938	+	0.273268i	$0.911895\pi$
$68$	9.37407			1.13677
$69$	4.01658	−	6.95692i	0.483539	−	0.837514i
$70$		0			0
$71$	2.89675	+	1.67244i	0.343781	+	0.198482i	0.661943	−	0.749554i	$-0.269732\pi$
$71$	2.89675	+	1.67244i	0.343781	+	0.198482i	−0.318162	+	0.948037i	$0.603065\pi$
$72$	0.207705	−	0.119919i	0.0244783	−	0.0141326i
$73$	−12.3112	+	7.10790i	−1.44092	+	0.831917i	−0.997911	−	0.0645994i	$-0.979423\pi$
$73$	−12.3112	+	7.10790i	−1.44092	+	0.831917i	−0.443011	+	0.896516i	$0.646090\pi$
$74$	1.43830			0.167199
$75$	−4.05018			−0.467674
$76$	−0.321025	+	0.185344i	−0.0368241	+	0.0212604i
$77$		0			0
$78$	0.0457859	+	1.18962i	0.00518423	+	0.134698i
$79$	−4.55529	+	7.89000i	−0.512511	+	0.887695i	0.487384	+	0.873188i	$0.337951\pi$
$79$	−4.55529	+	7.89000i	−0.512511	+	0.887695i	−0.999895	+	0.0145069i	$0.995382\pi$
$80$	8.85283	+	5.11118i	0.989776	+	0.571448i
$81$	4.94560	−	8.56603i	0.549511	−	0.951781i
$82$	−0.490899	−	0.850261i	−0.0542107	−	0.0938956i
$83$		−	16.5866i		−	1.82061i	−0.413934	−	0.910307i	$-0.635845\pi$
$83$		−	16.5866i		−	1.82061i	0.413934	−	0.910307i	$-0.364155\pi$
$84$		0			0
$85$	11.0866	+	6.40083i	1.20251	+	0.694268i
$86$	−1.25445	−	0.724258i	−0.135271	−	0.0780988i
$87$	12.9384			1.38714
$88$	−0.966401	+	1.67386i	−0.103019	+	0.178434i
$89$		−	5.89165i		−	0.624513i	−0.949998	−	0.312257i	$-0.898915\pi$
$89$		−	5.89165i		−	0.624513i	0.949998	−	0.312257i	$-0.101085\pi$
$90$	0.162417			0.0171203
$91$		0			0
$92$	−8.65473			−0.902318
$93$			6.75498i			0.700459i
$94$	−0.167162	+	0.289532i	−0.0172414	+	0.0298630i
$95$	−0.506229			−0.0519380
$96$	−3.35691	−	1.93811i	−0.342613	−	0.197808i
$97$	−0.390659	−	0.225547i	−0.0396654	−	0.0229008i	0.480036	−	0.877249i	$-0.340624\pi$
$97$	−0.390659	−	0.225547i	−0.0396654	−	0.0229008i	−0.519702	+	0.854348i	$0.673957\pi$
$98$		0			0
$99$		−	0.900747i		−	0.0905285i
$100$	2.18178	+	3.77896i	0.218178	+	0.377896i
$101$	3.82840	−	6.63098i	0.380940	−	0.659807i	−0.610257	−	0.792204i	$-0.708934\pi$
$101$	3.82840	−	6.63098i	0.380940	−	0.659807i	0.991197	+	0.132396i	$0.0422671\pi$
$102$	−1.36253	−	0.786658i	−0.134911	−	0.0778908i
$103$	−2.57870	+	4.46644i	−0.254087	+	0.440091i	−0.964647	−	0.263545i	$-0.915108\pi$
$103$	−2.57870	+	4.46644i	−0.254087	+	0.440091i	0.710560	+	0.703636i	$0.248442\pi$
$104$	2.18863	−	1.37847i	0.214613	−	0.135170i
$105$		0			0
$106$	−1.10753	+	0.639433i	−0.107573	+	0.0621072i
$107$	8.03289			0.776569			0.388284	−	0.921540i	$-0.373068\pi$
$107$	8.03289			0.776569			0.388284	+	0.921540i	$0.373068\pi$
$108$	−9.57597			−0.921448
$109$	1.15490	−	0.666781i	0.110619	−	0.0638660i	−0.443670	−	0.896190i	$-0.646324\pi$
$109$	1.15490	−	0.666781i	0.110619	−	0.0638660i	0.554289	+	0.832324i	$0.312990\pi$
$110$	−1.13353	+	0.654443i	−0.108078	+	0.0623987i
$111$	12.5785	+	7.26217i	1.19389	+	0.689295i
$112$		0			0
$113$	9.96917	−	17.2671i	0.937821	−	1.62435i	0.168296	−	0.985736i	$-0.446173\pi$
$113$	9.96917	−	17.2671i	0.937821	−	1.62435i	0.769525	−	0.638617i	$-0.220493\pi$
$114$	0.0622152			0.00582699
$115$	−10.2358	−	5.90965i	−0.954495	−	0.551078i
$116$	−6.96976	−	12.0720i	−0.647126	−	1.12086i
$117$	−0.562115	+	1.06633i	−0.0519676	+	0.0985823i
$118$	−1.37225			−0.126326
$119$		0			0
$120$	−1.75968	−	3.04786i	−0.160636	−	0.278230i
$121$	−1.87053	−	3.23985i	−0.170048	−	0.294532i
$122$	0.0644501	−	0.0372103i	0.00583503	−	0.00336886i
$123$		−	9.91448i		−	0.893959i
$124$	6.30263	−	3.63883i	0.565993	−	0.326776i
$125$		−	7.47412i		−	0.668505i
$126$		0			0
$127$	−3.98361	−	6.89981i	−0.353488	−	0.612259i	0.633370	−	0.773849i	$-0.281671\pi$
$127$	−3.98361	−	6.89981i	−0.353488	−	0.612259i	−0.986858	+	0.161590i	$0.948338\pi$
$128$			5.55218i			0.490748i
$129$	−7.31378	−	12.6678i	−0.643942	−	1.11534i
$130$	1.75031	−	0.0673655i	0.153513	−	0.00590835i
$131$	5.00897	−	8.67579i	0.437636	−	0.758007i	−0.559871	−	0.828580i	$-0.689149\pi$
$131$	5.00897	−	8.67579i	0.437636	−	0.758007i	0.997507	+	0.0705727i	$0.0224827\pi$
$132$	−8.38190	+	4.83929i	−0.729551	+	0.421206i
$133$		0			0
$134$	1.03079	−	1.78538i	0.0890465	−	0.154233i
$135$	−11.3254	−	6.53870i	−0.974731	−	0.562761i
$136$			3.41828i			0.293115i
$137$			5.06696i			0.432899i	0.976294	+	0.216450i	$0.0694477\pi$
$137$			5.06696i			0.432899i	−0.976294	+	0.216450i	$0.930552\pi$
$138$	1.25798	+	0.726293i	0.107086	+	0.0618261i
$139$	3.86289	−	6.69073i	0.327646	−	0.567500i	−0.654398	−	0.756150i	$-0.727078\pi$
$139$	3.86289	−	6.69073i	0.327646	−	0.567500i	0.982044	+	0.188650i	$0.0604113\pi$
$140$		0			0
$141$	−2.92378	+	1.68805i	−0.246227	+	0.142159i
$142$	−0.302417	+	0.523802i	−0.0253783	+	0.0439565i
$143$	−0.373602	−	9.70704i	−0.0312422	−	0.811744i
$144$	−0.636031	−	1.10164i	−0.0530025	−	0.0918031i
$145$		−	19.0365i		−	1.58089i
$146$	−1.28528	−	2.22617i	−0.106370	−	0.184239i
$147$		0			0
$148$		−	15.6482i		−	1.28627i
$149$	12.4002	−	7.15924i	1.01586	−	0.586507i	0.102958	−	0.994686i	$-0.467169\pi$
$149$	12.4002	−	7.15924i	1.01586	−	0.586507i	0.912902	+	0.408178i	$0.133836\pi$
$150$		−	0.732368i		−	0.0597976i
$151$	5.60534	−	3.23624i	0.456156	−	0.263362i	−0.254271	−	0.967133i	$-0.581835\pi$
$151$	5.60534	−	3.23624i	0.456156	−	0.263362i	0.710427	+	0.703771i	$0.248502\pi$
$152$	−0.0675862	−	0.117063i	−0.00548197	−	0.00949504i
$153$	−0.796513	−	1.37960i	−0.0643943	−	0.111534i
$154$		0			0
$155$	9.93871			0.798296
$156$	12.9427	−	0.498136i	1.03625	−	0.0398828i
$157$	7.95937	+	13.7860i	0.635227	+	1.10025i	0.986467	+	0.163960i	$0.0524267\pi$
$157$	7.95937	+	13.7860i	0.635227	+	1.10025i	−0.351240	+	0.936285i	$0.614240\pi$
$158$	−1.42670	−	0.823705i	−0.113502	−	0.0655305i
$159$	−12.9144			−1.02418
$160$	−2.85157	+	4.93907i	−0.225437	+	0.390468i
$161$		0			0
$162$	1.54894	+	0.894282i	0.121696	+	0.0702614i
$163$	−4.14100	+	2.39081i	−0.324348	+	0.187263i	−0.653329	−	0.757074i	$-0.726628\pi$
$163$	−4.14100	+	2.39081i	−0.324348	+	0.187263i	0.328981	+	0.944337i	$0.393295\pi$
$164$	−9.25056	+	5.34081i	−0.722348	+	0.417048i
$165$	−13.2175			−1.02898
$166$	2.99925			0.232787
$167$	2.34729	−	1.35521i	0.181639	−	0.104869i	−0.406424	−	0.913685i	$-0.633224\pi$
$167$	2.34729	−	1.35521i	0.181639	−	0.104869i	0.588062	+	0.808816i	$0.299891\pi$
$168$		0			0
$169$	−5.61544	+	11.7246i	−0.431957	+	0.901894i
$170$	−1.15742	+	2.00472i	−0.0887703	+	0.153755i
$171$	0.0545550	+	0.0314973i	0.00417192	+	0.00240866i
$172$	−7.87969	+	13.6480i	−0.600821	+	1.04065i
$173$	0.449908	+	0.779264i	0.0342059	+	0.0592463i	0.882622	−	0.470084i	$-0.155776\pi$
$173$	0.449908	+	0.779264i	0.0342059	+	0.0592463i	−0.848416	+	0.529331i	$0.822443\pi$
$174$			2.33957i			0.177362i
$175$		0			0
$176$	8.87787	+	5.12564i	0.669195	+	0.386360i
$177$	−12.0009	−	6.92870i	−0.902039	−	0.520793i
$178$	1.06535			0.0798513
$179$	−5.52791	+	9.57462i	−0.413175	+	0.715641i	−0.995235	−	0.0975054i	$-0.968914\pi$
$179$	−5.52791	+	9.57462i	−0.413175	+	0.715641i	0.582060	+	0.813146i	$0.302247\pi$
$180$		−	1.76704i		−	0.131708i
$181$	3.52898			0.262307			0.131153	−	0.991362i	$-0.458132\pi$
$181$	3.52898			0.262307			0.131153	+	0.991362i	$0.458132\pi$
$182$		0			0
$183$	0.751521			0.0555540
$184$		−	3.15597i		−	0.232661i
$185$	10.6850	−	18.5069i	0.785573	−	1.36065i
$186$	−1.22146			−0.0895619
$187$	11.1179	+	6.41894i	0.813024	+	0.469400i
$188$	3.15002	+	1.81866i	0.229738	+	0.132640i
$189$		0			0
$190$		−	0.0915382i		−	0.00664088i
$191$	10.2002	+	17.6672i	0.738059	+	1.27836i	0.953368	+	0.301810i	$0.0975909\pi$
$191$	10.2002	+	17.6672i	0.738059	+	1.27836i	−0.215309	+	0.976546i	$0.569076\pi$
$192$	−6.59731	+	11.4269i	−0.476120	+	0.824664i
$193$	−14.9515	−	8.63228i	−1.07624	−	0.621365i	−0.146357	−	0.989232i	$-0.546755\pi$
$193$	−14.9515	−	8.63228i	−1.07624	−	0.621365i	−0.929878	+	0.367867i	$0.880088\pi$
$194$	0.0407842	−	0.0706403i	0.00292814	−	0.00507168i
$195$	15.6473	+	8.24845i	1.12053	+	0.590684i
$196$		0			0
$197$	−4.29264	+	2.47836i	−0.305838	+	0.176576i	−0.645063	−	0.764130i	$-0.723169\pi$
$197$	−4.29264	+	2.47836i	−0.305838	+	0.176576i	0.339224	+	0.940705i	$0.389835\pi$
$198$	0.162877			0.0115751
$199$	7.18195			0.509115			0.254557	−	0.967058i	$-0.418070\pi$
$199$	7.18195			0.509115			0.254557	+	0.967058i	$0.418070\pi$
$200$	−1.37801	+	0.795593i	−0.0974399	+	0.0562569i
$201$	18.0293	−	10.4092i	1.27169	−	0.734209i
$202$	1.19904	+	0.692265i	0.0843641	+	0.0487076i
$203$		0			0
$204$	−8.55858	+	14.8239i	−0.599221	+	1.03788i
$205$	−14.5873			−1.01882
$206$	−0.807638	−	0.466290i	−0.0562708	−	0.0324880i
$207$	0.735392	+	1.27374i	0.0511132	+	0.0885307i
$208$	−7.31121	−	11.6082i	−0.506941	−	0.804881i
$209$	−0.507661			−0.0351157
$210$		0			0
$211$	8.79636	+	15.2357i	0.605566	+	1.04887i	0.991962	+	0.126539i	$0.0403868\pi$
$211$	8.79636	+	15.2357i	0.605566	+	1.04887i	−0.386395	+	0.922333i	$0.626280\pi$
$212$	6.95682	+	12.0496i	0.477796	+	0.827567i
$213$	−5.28951	+	3.05390i	−0.362431	+	0.209250i
$214$			1.45254i			0.0992934i
$215$	−18.6384	+	10.7609i	−1.27113	+	0.733886i
$216$		−	3.49190i		−	0.237594i
$217$		0			0
$218$	0.120570	+	0.208833i	0.00816602	+	0.0141440i
$219$		−	25.9582i		−	1.75410i
$220$	7.12013	+	12.3324i	0.480039	+	0.831452i
$221$	−9.15597	−	14.5371i	−0.615897	−	0.977873i
$222$	−1.31317	+	2.27448i	−0.0881344	+	0.152653i
$223$	−12.2157	+	7.05271i	−0.818020	+	0.472284i	−0.849733	−	0.527213i	$-0.823237\pi$
$223$	−12.2157	+	7.05271i	−0.818020	+	0.472284i	0.0317129	+	0.999497i	$0.489904\pi$
$224$		0			0
$225$	0.370772	−	0.642195i	0.0247181	−	0.0428130i
$226$	3.12230	+	1.80266i	0.207693	+	0.119911i
$227$		−	2.86877i		−	0.190407i	−0.995458	−	0.0952035i	$-0.969650\pi$
$227$		−	2.86877i		−	0.190407i	0.995458	−	0.0952035i	$-0.0303502\pi$
$228$		−	0.676881i		−	0.0448275i
$229$	−7.59860	−	4.38706i	−0.502130	−	0.289905i	0.227463	−	0.973787i	$-0.426957\pi$
$229$	−7.59860	−	4.38706i	−0.502130	−	0.289905i	−0.729593	+	0.683882i	$0.760290\pi$
$230$	1.06861	−	1.85088i	0.0704618	−	0.122043i
$231$		0			0
$232$	4.40208	−	2.54154i	0.289011	−	0.166861i
$233$	2.55371	−	4.42316i	0.167299	−	0.289771i	−0.770170	−	0.637839i	$-0.779829\pi$
$233$	2.55371	−	4.42316i	0.167299	−	0.289771i	0.937469	+	0.348068i	$0.113162\pi$
$234$	−0.192818	−	0.101644i	−0.0126049	−	0.00664466i
$235$	2.48365	+	4.30181i	0.162016	+	0.280619i
$236$			14.9296i			0.971836i
$237$	−8.31803	−	14.4072i	−0.540314	−	0.935851i
$238$		0			0
$239$			2.49797i			0.161580i	0.996731	+	0.0807901i	$0.0257443\pi$
$239$			2.49797i			0.161580i	−0.996731	+	0.0807901i	$0.974256\pi$
$240$	−16.1654	+	9.33309i	−1.04347	+	0.602448i
$241$		−	7.98512i		−	0.514367i	−0.966363	−	0.257183i	$-0.917206\pi$
$241$		−	7.98512i		−	0.514367i	0.966363	−	0.257183i	$-0.0827944\pi$
$242$	0.585842	−	0.338236i	0.0376593	−	0.0217426i
$243$	1.72939	+	2.99538i	0.110940	+	0.192154i
$244$	−0.404835	−	0.701195i	−0.0259169	−	0.0448894i
$245$		0			0
$246$	1.79277			0.114303
$247$	0.600984	+	0.316808i	0.0382397	+	0.0201580i
$248$	1.32691	+	2.29827i	0.0842588	+	0.145941i
$249$	26.2296	+	15.1437i	1.66223	+	0.959690i
$250$	1.35150			0.0854762
$251$	−12.6285	+	21.8732i	−0.797105	+	1.38063i	0.124389	+	0.992234i	$0.460303\pi$
$251$	−12.6285	+	21.8732i	−0.797105	+	1.38063i	−0.921494	+	0.388393i	$0.873030\pi$
$252$		0			0
$253$	−10.2648	−	5.92637i	−0.645341	−	0.372588i
$254$	1.24765	−	0.720331i	0.0782845	−	0.0451976i
$255$	−20.2442	+	11.6880i	−1.26774	+	0.731931i
$256$	13.4479			0.840493
$257$	−3.37363			−0.210442			−0.105221	−	0.994449i	$-0.533555\pi$
$257$	−3.37363			−0.210442			−0.105221	+	0.994449i	$0.533555\pi$
$258$	2.29065	−	1.32250i	0.142609	−	0.0823355i
$259$		0			0
$260$	−0.732915	−	19.0428i	−0.0454535	−	1.18099i
$261$	−1.18444	+	2.05151i	−0.0733150	+	0.126985i
$262$	1.56879	+	0.905740i	0.0969201	+	0.0559568i
$263$	0.0794677	−	0.137642i	0.00490019	−	0.00848737i	−0.863565	−	0.504238i	$-0.831774\pi$
$263$	0.0794677	−	0.137642i	0.00490019	−	0.00848737i	0.868465	+	0.495750i	$0.165107\pi$
$264$	−1.76466	−	3.05648i	−0.108607	−	0.188114i
$265$			19.0011i			1.16723i
$266$		0			0
$267$	9.31689	+	5.37911i	0.570185	+	0.329196i
$268$	−19.4243	−	11.2146i	−1.18653	−	0.685043i
$269$	23.3266			1.42225			0.711124	−	0.703066i	$-0.248186\pi$
$269$	23.3266			1.42225			0.711124	+	0.703066i	$0.248186\pi$
$270$	1.18235	−	2.04789i	0.0719556	−	0.124631i
$271$			11.8210i			0.718074i	0.933323	+	0.359037i	$0.116895\pi$
$271$			11.8210i			0.718074i	−0.933323	+	0.359037i	$0.883105\pi$
$272$	18.1300			1.09929
$273$		0			0
$274$	−0.916226			−0.0553513
$275$			5.97595i			0.360363i
$276$	7.90182	−	13.6864i	0.475634	−	0.823822i
$277$	27.3653			1.64422			0.822111	−	0.569327i	$-0.192796\pi$
$277$	27.3653			1.64422			0.822111	+	0.569327i	$0.192796\pi$
$278$	1.20984	+	0.698503i	0.0725615	+	0.0418934i
$279$	−1.07107	−	0.618382i	−0.0641232	−	0.0370215i
$280$		0			0
$281$		−	28.5383i		−	1.70245i	−0.524801	−	0.851225i	$-0.675860\pi$
$281$		−	28.5383i		−	1.70245i	0.524801	−	0.851225i	$-0.324140\pi$
$282$	−0.305239	−	0.528690i	−0.0181767	−	0.0314830i
$283$	−8.98604	+	15.5643i	−0.534165	+	0.925201i	0.465038	+	0.885290i	$0.346040\pi$
$283$	−8.98604	+	15.5643i	−0.534165	+	0.925201i	−0.999203	+	0.0399101i	$0.987293\pi$
$284$	5.69879	+	3.29020i	0.338161	+	0.195237i
$285$	0.462190	−	0.800537i	0.0273778	−	0.0474197i
$286$	1.75526	−	0.0675561i	0.103791	−	0.00399468i
$287$		0			0
$288$	0.614613	−	0.354847i	0.0362164	−	0.0209096i
$289$	5.70459			0.335564
$290$	3.44225			0.202136
$291$	0.713347	−	0.411851i	0.0418172	−	0.0241432i
$292$	−24.2199	+	13.9834i	−1.41737	+	0.818316i
$293$	−12.8943	−	7.44453i	−0.753293	−	0.434914i	0.0735896	−	0.997289i	$-0.476554\pi$
$293$	−12.8943	−	7.44453i	−0.753293	−	0.434914i	−0.826882	+	0.562375i	$0.809888\pi$
$294$		0			0
$295$	−10.1943	+	17.6570i	−0.593535	+	1.02803i
$296$	5.70616			0.331664
$297$	−11.3574	−	6.55719i	−0.659023	−	0.380487i
$298$	1.29456	+	2.24224i	0.0749918	+	0.129890i
$299$	8.45337	+	13.4216i	0.488871	+	0.776191i
$300$	−7.96793			−0.460028
$301$		0			0
$302$	0.585190	+	1.01358i	0.0336739	+	0.0583249i
$303$	6.99071	+	12.1083i	0.401606	+	0.695601i
$304$	−0.620883	+	0.358467i	−0.0356101	+	0.0205595i
$305$		−	1.10572i		−	0.0633136i
$306$	0.249465	−	0.144029i	0.0142610	−	0.00823356i
$307$		−	23.5161i		−	1.34214i	−0.741396	−	0.671068i	$-0.765836\pi$
$307$		−	23.5161i		−	1.34214i	0.741396	−	0.671068i	$-0.234164\pi$
$308$		0			0
$309$	−4.70874	−	8.15577i	−0.267871	−	0.463966i
$310$			1.79715i			0.102072i
$311$	−0.815450	−	1.41240i	−0.0462399	−	0.0800899i	0.841979	−	0.539510i	$-0.181391\pi$
$311$	−0.815450	−	1.41240i	−0.0462399	−	0.0800899i	−0.888219	+	0.459420i	$0.848057\pi$
$312$	0.181647	+	4.71960i	0.0102837	+	0.267195i
$313$	−0.348367	+	0.603389i	−0.0196909	+	0.0341056i	−0.875703	−	0.482850i	$-0.839602\pi$
$313$	−0.348367	+	0.603389i	−0.0196909	+	0.0341056i	0.856012	+	0.516956i	$0.172935\pi$
$314$	−2.49284	+	1.43924i	−0.140679	+	0.0812212i
$315$		0			0
$316$	−8.96164	+	15.5220i	−0.504132	+	0.873182i
$317$	18.5579	+	10.7144i	1.04231	+	0.601780i	0.920488	−	0.390771i	$-0.127792\pi$
$317$	18.5579	+	10.7144i	1.04231	+	0.601780i	0.121826	+	0.992551i	$0.461125\pi$
$318$		−	2.33522i		−	0.130953i
$319$		−	19.0903i		−	1.06885i
$320$	16.8126	+	9.70673i	0.939850	+	0.542623i
$321$	−7.33408	+	12.7030i	−0.409348	+	0.709012i
$322$		0			0
$323$	−0.777544	+	0.448915i	−0.0432637	+	0.0249783i
$324$	9.72949	−	16.8520i	0.540527	−	0.936221i
$325$	3.72932	−	7.07450i	0.206865	−	0.392423i
$326$	−0.432315	−	0.748792i	−0.0239437	−	0.0414717i
$327$			2.43510i			0.134661i
$328$	−1.94754	−	3.37324i	−0.107535	−	0.186256i
$329$		0			0
$330$		−	2.39004i		−	0.131568i
$331$	−1.31676	+	0.760232i	−0.0723757	+	0.0417861i	−0.535751	−	0.844376i	$-0.679971\pi$
$331$	−1.31676	+	0.760232i	−0.0723757	+	0.0417861i	0.463375	+	0.886162i	$0.346638\pi$
$332$		−	32.6308i		−	1.79085i
$333$	−2.30298	+	1.32962i	−0.126202	+	0.0728630i
$334$	0.245054	+	0.424446i	0.0134088	+	0.0232247i
$335$	−15.3152	−	26.5268i	−0.836761	−	1.44931i
$336$		0			0
$337$	−32.2304			−1.75570			−0.877850	−	0.478936i	$-0.841023\pi$
$337$	−32.2304			−1.75570			−0.877850	+	0.478936i	$0.841023\pi$
$338$	−2.12009	−	1.01540i	−0.115318	−	0.0552307i
$339$	18.2038	+	31.5300i	0.988697	+	1.71247i
$340$	21.8106	+	12.5924i	1.18285	+	0.682918i
$341$	9.96683			0.539734
$342$	−0.00569546	+	0.00986483i	−0.000307975	+	0.000533429i
$343$		0			0
$344$	−4.97679	−	2.87335i	−0.268331	−	0.154921i
$345$	18.6907	−	10.7911i	1.00628	−	0.580974i
$346$	−0.140909	+	0.0813541i	−0.00757534	+	0.00437362i
$347$	8.18431			0.439357			0.219678	−	0.975572i	$-0.429499\pi$
$347$	8.18431			0.439357			0.219678	+	0.975572i	$0.429499\pi$
$348$	25.4538			1.36446
$349$	18.9220	−	10.9246i	1.01287	−	0.584782i	0.100841	−	0.994903i	$-0.467847\pi$
$349$	18.9220	−	10.9246i	1.01287	−	0.584782i	0.912031	+	0.410120i	$0.134513\pi$
$350$		0			0
$351$	9.35317	+	14.8502i	0.499235	+	0.792646i
$352$	−2.85964	+	4.95304i	−0.152419	+	0.263998i
$353$	0.491192	+	0.283590i	0.0261435	+	0.0150940i	0.513015	−	0.858380i	$-0.328529\pi$
$353$	0.491192	+	0.283590i	0.0261435	+	0.0150940i	−0.486871	+	0.873474i	$0.661862\pi$
$354$	1.25287	−	2.17004i	0.0665894	−	0.115336i
$355$	4.49325	+	7.78254i	0.238477	+	0.413054i
$356$		−	11.5907i		−	0.614303i
$357$		0			0
$358$	−1.73132	−	0.999577i	−0.0915030	−	0.0528293i
$359$	−28.0630	−	16.2022i	−1.48111	−	0.855118i	−0.481336	−	0.876536i	$-0.659848\pi$
$359$	−28.0630	−	16.2022i	−1.48111	−	0.855118i	−0.999771	+	0.0214184i	$0.993182\pi$
$360$	0.644358			0.0339606
$361$	−9.48225	+	16.4237i	−0.499066	+	0.864407i
$362$			0.638123i			0.0335390i
$363$	6.83122			0.358546
$364$		0			0
$365$	−38.1928			−1.99910
$366$			0.135893i			0.00710323i
$367$	−3.93444	+	6.81465i	−0.205376	+	0.355722i	−0.950252	−	0.311481i	$-0.899175\pi$
$367$	−3.93444	+	6.81465i	−0.205376	+	0.355722i	0.744876	+	0.667202i	$0.232508\pi$
$368$	−16.7388			−0.872569
$369$	1.57204	+	0.907617i	0.0818371	+	0.0472487i
$370$	3.34648	+	1.93209i	0.173975	+	0.100445i
$371$		0			0
$372$			13.2891i			0.689007i
$373$	1.04581	+	1.81140i	0.0541502	+	0.0937909i	0.891830	−	0.452371i	$-0.149422\pi$
$373$	1.04581	+	1.81140i	0.0541502	+	0.0937909i	−0.837680	+	0.546162i	$0.816088\pi$
$374$	−1.16070	+	2.01039i	−0.0600182	+	0.103955i
$375$	11.8194	+	6.82392i	0.610350	+	0.352386i
$376$	−0.663180	+	1.14866i	−0.0342009	+	0.0592377i
$377$	−11.9134	+	22.5997i	−0.613571	+	1.16394i
$378$		0			0
$379$	12.3983	−	7.15817i	0.636859	−	0.367691i	−0.146545	−	0.989204i	$-0.546815\pi$
$379$	12.3983	−	7.15817i	0.636859	−	0.367691i	0.783404	+	0.621513i	$0.213482\pi$
$380$	−0.995906			−0.0510889
$381$	14.5482			0.745329
$382$	−3.19466	+	1.84444i	−0.163453	+	0.0943695i
$383$	−21.8129	+	12.5937i	−1.11459	+	0.643507i	−0.940013	−	0.341138i	$-0.889188\pi$
$383$	−21.8129	+	12.5937i	−1.11459	+	0.643507i	−0.174573	+	0.984644i	$0.555854\pi$
$384$	−8.78006	−	5.06917i	−0.448056	−	0.258685i
$385$		0			0
$386$	1.56092	−	2.70359i	0.0794488	−	0.137609i
$387$	2.67815			0.136138
$388$	−0.768544	−	0.443719i	−0.0390169	−	0.0225264i
$389$	14.0512	+	24.3373i	0.712422	+	1.23395i	0.963946	+	0.266099i	$0.0857350\pi$
$389$	14.0512	+	24.3373i	0.712422	+	1.23395i	−0.251524	+	0.967851i	$0.580932\pi$
$390$	−1.49152	+	2.82940i	−0.0755259	+	0.143272i
$391$	−20.9623			−1.06011
$392$		0			0
$393$	9.14644	+	15.8421i	0.461377	+	0.799128i
$394$	−0.448146	−	0.776212i	−0.0225773	−	0.0391050i
$395$	−21.1976	+	12.2384i	−1.06657	+	0.615783i
$396$		−	1.77204i		−	0.0890485i
$397$	18.8590	−	10.8882i	0.946504	−	0.546465i	0.0545111	−	0.998513i	$-0.482640\pi$
$397$	18.8590	−	10.8882i	0.946504	−	0.546465i	0.891993	+	0.452049i	$0.149307\pi$
$398$			1.29867i			0.0650963i
$399$		0			0
$400$	4.21970	+	7.30874i	0.210985	+	0.365437i
$401$			20.5290i			1.02517i	0.858637	+	0.512584i	$0.171312\pi$
$401$			20.5290i			1.02517i	−0.858637	+	0.512584i	$0.828688\pi$
$402$	1.88223	+	3.26012i	0.0938772	+	0.162600i
$403$	−11.7990	−	6.21984i	−0.587751	−	0.309832i
$404$	7.53162	−	13.0451i	0.374712	−	0.649020i
$405$	23.0138	−	13.2871i	1.14357	−	0.660239i
$406$		0			0
$407$	10.7152	−	18.5592i	0.531132	−	0.919947i
$408$	−5.40558	−	3.12091i	−0.267616	−	0.154508i
$409$		−	6.26862i		−	0.309963i	−0.987917	−	0.154982i	$-0.950468\pi$
$409$		−	6.26862i		−	0.309963i	0.987917	−	0.154982i	$-0.0495319\pi$
$410$		−	2.63774i		−	0.130269i
$411$	−8.01275	−	4.62616i	−0.395240	−	0.228192i
$412$	−5.07308	+	8.78683i	−0.249933	+	0.432896i
$413$		0			0
$414$	−0.230322	+	0.132976i	−0.0113197	+	0.00653543i
$415$	22.2811	−	38.5920i	1.09374	−	1.89441i
$416$	6.47629	−	4.07899i	0.317526	−	0.199989i
$417$	7.05369	+	12.2174i	0.345421	+	0.598286i
$418$		−	0.0917972i		−	0.00448995i
$419$	17.0817	+	29.5864i	0.834497	+	1.44539i	0.894439	+	0.447189i	$0.147575\pi$
$419$	17.0817	+	29.5864i	0.834497	+	1.44539i	−0.0599424	+	0.998202i	$0.519092\pi$
$420$		0			0
$421$			11.5233i			0.561613i	0.959764	+	0.280806i	$0.0906019\pi$
$421$			11.5233i			0.561613i	−0.959764	+	0.280806i	$0.909398\pi$
$422$	−2.75498	+	1.59059i	−0.134111	+	0.0774288i
$423$		−	0.618126i		−	0.0300543i
$424$	−4.39391	+	2.53682i	−0.213387	+	0.123199i
$425$	5.28442	+	9.15288i	0.256332	+	0.443980i
$426$	−0.552218	−	0.956469i	−0.0267550	−	0.0463411i
$427$		0			0
$428$	15.8031			0.763873
$429$	15.6916	+	8.27179i	0.757596	+	0.399366i
$430$	−1.94582	−	3.37026i	−0.0938359	−	0.162529i
$431$	−7.59505	−	4.38500i	−0.365841	−	0.211218i	0.305799	−	0.952096i	$-0.401076\pi$
$431$	−7.59505	−	4.38500i	−0.365841	−	0.211218i	−0.671640	+	0.740878i	$0.734410\pi$
$432$	−18.5205			−0.891069
$433$	−11.0535	+	19.1452i	−0.531196	+	0.920058i	0.468141	+	0.883654i	$0.344924\pi$
$433$	−11.0535	+	19.1452i	−0.531196	+	0.920058i	−0.999337	+	0.0364046i	$0.988409\pi$
$434$		0			0
$435$	30.1038	+	17.3804i	1.44337	+	0.833328i
$436$	2.27203	−	1.31176i	0.108811	−	0.0628219i
$437$	0.717877	−	0.414467i	0.0343407	−	0.0198266i
$438$	4.69387			0.224282
$439$	−10.3709			−0.494978			−0.247489	−	0.968891i	$-0.579605\pi$
$439$	−10.3709			−0.494978			−0.247489	+	0.968891i	$0.579605\pi$
$440$	−4.49705	+	2.59637i	−0.214389	+	0.123777i
$441$		0			0
$442$	2.62866	−	1.65562i	0.125032	−	0.0787496i
$443$	−17.9068	+	31.0156i	−0.850780	+	1.47359i	0.0297257	+	0.999558i	$0.490537\pi$
$443$	−17.9068	+	31.0156i	−0.850780	+	1.47359i	−0.880506	+	0.474036i	$0.842797\pi$
$444$	24.7456	+	14.2869i	1.17438	+	0.678026i
$445$	7.91437	−	13.7081i	0.375177	−	0.649826i
$446$	−1.27530	−	2.20888i	−0.0603871	−	0.104593i
$447$			26.1457i			1.23665i
$448$		0			0
$449$	−19.7023	−	11.3751i	−0.929809	−	0.536825i	−0.0430575	−	0.999073i	$-0.513710\pi$
$449$	−19.7023	−	11.3751i	−0.929809	−	0.536825i	−0.886751	+	0.462247i	$0.847043\pi$
$450$	0.116124	+	0.0670443i	0.00547415	+	0.00316050i
$451$	−14.6286			−0.688834
$452$	19.6124	−	33.9696i	0.922489	−	1.59780i
$453$			11.8188i			0.555298i
$454$	0.518742			0.0243458
$455$		0			0
$456$	0.246827			0.0115587
$457$			31.3172i			1.46496i	0.680791	+	0.732478i	$0.261636\pi$
$457$			31.3172i			1.46496i	−0.680791	+	0.732478i	$0.738364\pi$
$458$	0.793284	−	1.37401i	0.0370677	−	0.0642032i
$459$	−23.1936			−1.08258
$460$	−20.1370	−	11.6261i	−0.938891	−	0.542069i
$461$	7.28113	+	4.20376i	0.339116	+	0.195789i	0.659881	−	0.751370i	$-0.270607\pi$
$461$	7.28113	+	4.20376i	0.339116	+	0.195789i	−0.320765	+	0.947159i	$0.603940\pi$
$462$		0			0
$463$		−	10.0392i		−	0.466563i	−0.972409	−	0.233281i	$-0.925054\pi$
$463$		−	10.0392i		−	0.466563i	0.972409	−	0.233281i	$-0.0749463\pi$
$464$	−13.4800	−	23.3480i	−0.625791	−	1.08390i
$465$	−9.07411	+	15.7168i	−0.420802	+	0.728850i
$466$	0.799813	+	0.461772i	0.0370506	+	0.0213912i
$467$	13.1756	−	22.8209i	0.609696	−	1.05602i	−0.381594	−	0.924330i	$-0.624625\pi$
$467$	13.1756	−	22.8209i	0.609696	−	1.05602i	0.991290	−	0.131695i	$-0.0420418\pi$
$468$	−1.10585	+	2.09780i	−0.0511180	+	0.0969706i
$469$		0			0
$470$	−0.777869	+	0.449103i	−0.0358804	+	0.0207156i
$471$	−29.0678			−1.33937
$472$	−5.44413			−0.250586
$473$	−18.6911	+	10.7913i	−0.859418	+	0.496185i
$474$	2.60517	−	1.50410i	0.119660	−	0.0690855i
$475$	−0.361941	−	0.208967i	−0.0166070	−	0.00958806i
$476$		0			0
$477$	1.18224	−	2.04770i	0.0541310	−	0.0937577i
$478$	−0.451692			−0.0206599
$479$	7.43409	+	4.29207i	0.339672	+	0.196110i	0.660127	−	0.751154i	$-0.270502\pi$
$479$	7.43409	+	4.29207i	0.339672	+	0.196110i	−0.320455	+	0.947264i	$0.603836\pi$
$480$	−5.20701	−	9.01880i	−0.237666	−	0.411650i
$481$	−24.2669	+	15.2841i	−1.10648	+	0.696895i
$482$	1.44390			0.0657678
$483$		0			0
$484$	−3.67990	−	6.37377i	−0.167268	−	0.289717i
$485$	−0.605963	−	1.04956i	−0.0275154	−	0.0476580i
$486$	−0.541637	+	0.312714i	−0.0245691	+	0.0141850i
$487$			21.2562i			0.963212i	0.876388	+	0.481606i	$0.159946\pi$
$487$			21.2562i			0.963212i	−0.876388	+	0.481606i	$0.840054\pi$
$488$	0.255693	−	0.147624i	0.0115747	−	0.00668264i
$489$		−	8.73130i		−	0.394843i
$490$		0			0
$491$	−11.2268	−	19.4453i	−0.506657	−	0.877556i	−0.999970	−	0.00770409i	$-0.997548\pi$
$491$	−11.2268	−	19.4453i	−0.506657	−	0.877556i	0.493313	−	0.869852i	$-0.335786\pi$
$492$		−	19.5048i		−	0.879344i
$493$	−16.8812	−	29.2391i	−0.760292	−	1.31686i
$494$	−0.0572864	+	0.108672i	−0.00257744	+	0.00488939i
$495$	1.20999	−	2.09577i	0.0543851	−	0.0941978i
$496$	12.1897	−	7.03772i	0.547333	−	0.316003i
$497$		0			0
$498$	−2.73833	+	4.74293i	−0.122708	+	0.212536i
$499$	−33.6694	−	19.4390i	−1.50725	−	0.870210i	−0.999964	−	0.00843082i	$-0.997316\pi$
$499$	−33.6694	−	19.4390i	−1.50725	−	0.870210i	−0.507284	−	0.861779i	$-0.669350\pi$
$500$		−	14.7039i		−	0.657576i
$501$			4.94926i			0.221117i
$502$	−3.95520	−	2.28354i	−0.176529	−	0.101919i
$503$	2.72850	−	4.72591i	0.121658	−	0.210718i	−0.798764	−	0.601645i	$-0.794512\pi$
$503$	2.72850	−	4.72591i	0.121658	−	0.210718i	0.920422	+	0.390927i	$0.127846\pi$
$504$		0			0
$505$	17.8151	−	10.2855i	0.792760	−	0.457700i
$506$	1.07163	−	1.85612i	0.0476397	−	0.0825144i
$507$	−13.4141	−	19.5848i	−0.595740	−	0.869790i
$508$	−7.83697	−	13.5740i	−0.347709	−	0.602250i
$509$			10.8925i			0.482800i	0.970426	+	0.241400i	$0.0776066\pi$
$509$			10.8925i			0.482800i	−0.970426	+	0.241400i	$0.922393\pi$
$510$	−2.11347	−	3.66064i	−0.0935860	−	0.162096i
$511$		0			0
$512$			13.5360i			0.598214i
$513$	0.794290	−	0.458584i	0.0350688	−	0.0202470i
$514$		−	0.610033i		−	0.0269074i
$515$	−11.9997	+	6.92804i	−0.528771	+	0.305286i
$516$	−14.3884	−	24.9215i	−0.633415	−	1.09711i
$517$	2.49068	+	4.31398i	0.109540	+	0.189729i
$518$		0			0
$519$	−1.64308			−0.0721230
$520$	6.94402	−	0.267260i	0.304515	−	0.0117201i
$521$	13.9480	+	24.1587i	0.611074	+	1.05841i	0.991060	+	0.133419i	$0.0425957\pi$
$521$	13.9480	+	24.1587i	0.611074	+	1.05841i	−0.379985	+	0.924993i	$0.624071\pi$
$522$	−0.370962	−	0.214175i	−0.0162366	−	0.00937418i
$523$	−16.7236			−0.731272			−0.365636	−	0.930758i	$-0.619148\pi$
$523$	−16.7236			−0.731272			−0.365636	+	0.930758i	$0.619148\pi$
$524$	9.85416	−	17.0679i	0.430481	−	0.745615i
$525$		0			0
$526$	0.0248890	+	0.0143696i	0.00108521	+	0.000626546i
$527$	15.2654	−	8.81347i	0.664970	−	0.383921i
$528$	−16.2111	+	9.35949i	−0.705498	+	0.407319i
$529$	−3.64627			−0.158534
$530$	−3.43585			−0.149244
$531$	2.19723	−	1.26857i	0.0953515	−	0.0550512i
$532$		0			0
$533$	17.3178	+	9.12904i	0.750116	+	0.395423i
$534$	−0.972671	+	1.68472i	−0.0420916	+	0.0729048i
$535$	18.6901	+	10.7907i	0.808045	+	0.466525i
$536$	4.08945	−	7.08313i	0.176637	−	0.305945i
$537$	−10.0940	−	17.4834i	−0.435590	−	0.754464i
$538$			4.21800i			0.181851i
$539$		0			0
$540$	−22.2804	−	12.8636i	−0.958796	−	0.553561i
$541$	9.66528	+	5.58025i	0.415543	+	0.239914i	0.693169	−	0.720776i	$-0.256214\pi$
$541$	9.66528	+	5.58025i	0.415543	+	0.239914i	−0.277626	+	0.960689i	$0.589547\pi$
$542$	−2.13751			−0.0918141
$543$	−3.22198	+	5.58063i	−0.138268	+	0.239488i
$544$			10.1149i			0.433673i
$545$	3.58280			0.153470
$546$		0			0
$547$	36.6556			1.56728			0.783640	−	0.621215i	$-0.213361\pi$
$547$	36.6556			1.56728			0.783640	+	0.621215i	$0.213361\pi$
$548$			9.96824i			0.425822i
$549$	−0.0687976	+	0.119161i	−0.00293621	+	0.00508567i
$550$	−1.08059			−0.0460767
$551$	1.15623	+	0.667551i	0.0492571	+	0.0284386i
$552$	4.99077	+	2.88142i	0.212421	+	0.122641i
$553$		0			0
$554$			4.94830i			0.210233i
$555$	19.5109	+	33.7938i	0.828190	+	1.43447i
$556$	7.59948	−	13.1627i	0.322290	−	0.558222i
$557$	−28.6461	−	16.5388i	−1.21377	−	0.700772i	−0.250193	−	0.968196i	$-0.580494\pi$
$557$	−28.6461	−	16.5388i	−1.21377	−	0.700772i	−0.963579	+	0.267424i	$0.913827\pi$
$558$	0.111818	−	0.193675i	0.00473364	−	0.00819890i
$559$	28.8615	−	1.11081i	1.22071	−	0.0469823i
$560$		0			0
$561$	−20.3015	+	11.7211i	−0.857130	+	0.494864i
$562$	5.16039			0.217678
$563$	17.7967			0.750043			0.375021	−	0.927016i	$-0.377635\pi$
$563$	17.7967			0.750043			0.375021	+	0.927016i	$0.377635\pi$
$564$	−5.75197	+	3.32090i	−0.242202	+	0.139835i
$565$	46.3906	−	26.7836i	1.95167	−	1.12679i
$566$	−2.81439	−	1.62489i	−0.118298	−	0.0682992i
$567$		0			0
$568$	−1.19978	+	2.07808i	−0.0503417	+	0.0871943i
$569$	8.22094			0.344640			0.172320	−	0.985041i	$-0.444874\pi$
$569$	8.22094			0.344640			0.172320	+	0.985041i	$0.444874\pi$
$570$	0.144756	+	0.0835750i	0.00606317	+	0.00350057i
$571$	−12.8776	−	22.3047i	−0.538912	−	0.933424i	−0.998963	−	0.0455309i	$-0.985502\pi$
$571$	−12.8776	−	22.3047i	−0.538912	−	0.933424i	0.460051	−	0.887893i	$-0.347831\pi$
$572$	−0.734988	−	19.0967i	−0.0307314	−	0.798473i
$573$	−37.2513			−1.55620
$574$		0			0
$575$	−4.87891	−	8.45051i	−0.203464	−	0.352411i
$576$	−1.20790	−	2.09214i	−0.0503290	−	0.0871724i
$577$	0.666314	−	0.384697i	0.0277390	−	0.0160151i	−0.486066	−	0.873922i	$-0.661569\pi$
$577$	0.666314	−	0.384697i	0.0277390	−	0.0160151i	0.513805	+	0.857907i	$0.328235\pi$
$578$			1.03152i			0.0429058i
$579$	27.3017	−	15.7626i	1.13462	−	0.655073i
$580$		−	37.4505i		−	1.55505i
$581$		0			0
$582$	0.0744725	+	0.128990i	0.00308698	+	0.00534681i
$583$			19.0549i			0.789172i
$584$	−5.09908	−	8.83187i	−0.211002	−	0.365465i
$585$	−2.74030	+	1.72593i	−0.113297	+	0.0713585i
$586$	1.34615	−	2.33159i	0.0556088	−	0.0963173i
$587$	10.4727	−	6.04644i	0.432256	−	0.249563i	−0.268051	−	0.963405i	$-0.586380\pi$
$587$	10.4727	−	6.04644i	0.432256	−	0.249563i	0.700307	+	0.713841i	$0.253046\pi$
$588$		0			0
$589$	−0.348520	+	0.603654i	−0.0143605	+	0.0248731i
$590$	−3.19281	−	1.84337i	−0.131446	−	0.0758904i
$591$		−	9.05103i		−	0.372310i
$592$		−	30.2646i		−	1.24387i
$593$	13.8115	+	7.97406i	0.567170	+	0.327456i	0.756018	−	0.654551i	$-0.227142\pi$
$593$	13.8115	+	7.97406i	0.567170	+	0.327456i	−0.188848	+	0.982006i	$0.560475\pi$
$594$	1.18570	−	2.05369i	0.0486497	−	0.0842638i
$595$		0			0
$596$	24.3949	−	14.0844i	0.999253	−	0.576919i
$597$	−6.55717	+	11.3573i	−0.268367	+	0.464825i
$598$	−2.42694	+	1.52857i	−0.0992450	+	0.0625078i
$599$	3.55511	+	6.15763i	0.145258	+	0.251594i	0.929469	−	0.368900i	$-0.120266\pi$
$599$	3.55511	+	6.15763i	0.145258	+	0.251594i	−0.784211	+	0.620494i	$0.786932\pi$
$600$		−	2.90553i		−	0.118618i
$601$	10.3953	+	18.0051i	0.424032	+	0.734445i	0.996329	−	0.0856011i	$-0.0272811\pi$
$601$	10.3953	+	18.0051i	0.424032	+	0.734445i	−0.572297	+	0.820046i	$0.693948\pi$
$602$		0			0
$603$			3.81163i			0.155221i
$604$	11.0274	−	6.36667i	0.448698	−	0.259056i
$605$		−	10.0509i		−	0.408626i
$606$	−2.18946	+	1.26409i	−0.0889408	+	0.0513500i
$607$	−3.85702	−	6.68056i	−0.156552	−	0.271156i	0.777071	−	0.629413i	$-0.216704\pi$
$607$	−3.85702	−	6.68056i	−0.156552	−	0.271156i	−0.933623	+	0.358257i	$0.883371\pi$
$608$	−0.199992	−	0.346396i	−0.00811074	−	0.0140482i
$609$		0			0
$610$	0.199941			0.00809539
$611$	−0.256380	−	6.66133i	−0.0103720	−	0.269489i
$612$	−1.56698	−	2.71409i	−0.0633415	−	0.109711i
$613$	−17.6997	−	10.2189i	−0.714883	−	0.412738i	0.0979832	−	0.995188i	$-0.468761\pi$
$613$	−17.6997	−	10.2189i	−0.714883	−	0.412738i	−0.812867	+	0.582450i	$0.802094\pi$
$614$	4.25227			0.171608
$615$	13.3183	−	23.0680i	0.537047	−	0.930193i
$616$		0			0
$617$	−3.98209	−	2.29906i	−0.160313	−	0.0925567i	0.417697	−	0.908586i	$-0.362837\pi$
$617$	−3.98209	−	2.29906i	−0.160313	−	0.0925567i	−0.578010	+	0.816030i	$0.696171\pi$
$618$	1.47476	−	0.851451i	0.0593234	−	0.0342504i
$619$	8.70599	−	5.02641i	0.349923	−	0.202028i	−0.314728	−	0.949182i	$-0.601913\pi$
$619$	8.70599	−	5.02641i	0.349923	−	0.202028i	0.664651	+	0.747154i	$0.268580\pi$
$620$	19.5525			0.785245
$621$	21.4138			0.859306
$622$	0.255396	−	0.147453i	0.0102404	−	0.00591232i
$623$		0			0
$624$	25.0320	−	0.963425i	1.00208	−	0.0385679i
$625$	15.5853	−	26.9944i	0.623410	−	1.07978i
$626$	−0.109107	−	0.0629930i	−0.00436080	−	0.00251771i
$627$	0.463498	−	0.802802i	0.0185103	−	0.0320608i
$628$	15.6585	+	27.1213i	0.624842	+	1.08226i
$629$		−	37.9009i		−	1.51121i
$630$		0			0
$631$	−6.29923	−	3.63686i	−0.250768	−	0.144781i	0.369348	−	0.929291i	$-0.379581\pi$
$631$	−6.29923	−	3.63686i	−0.250768	−	0.144781i	−0.620116	+	0.784510i	$0.712914\pi$
$632$	−5.66015	−	3.26789i	−0.225149	−	0.129990i
$633$	−32.1245			−1.27684
$634$	−1.93742	+	3.35570i	−0.0769447	+	0.133272i
$635$		−	21.4051i		−	0.849434i
$636$	−25.4065			−1.00743
$637$		0			0
$638$	3.45199			0.136665
$639$		−	1.11827i		−	0.0442381i
$640$	−7.45835	+	12.9182i	−0.294817	+	0.510639i
$641$	−3.85033			−0.152079			−0.0760394	−	0.997105i	$-0.524227\pi$
$641$	−3.85033			−0.152079			−0.0760394	+	0.997105i	$0.524227\pi$
$642$	−2.29700	−	1.32618i	−0.0906555	−	0.0523400i
$643$	−2.49163	−	1.43855i	−0.0982605	−	0.0567307i	0.450065	−	0.892996i	$-0.351401\pi$
$643$	−2.49163	−	1.43855i	−0.0982605	−	0.0567307i	−0.548325	+	0.836265i	$0.684734\pi$
$644$		0			0
$645$		−	39.2990i		−	1.54740i
$646$	−0.0811745	−	0.140598i	−0.00319377	−	0.00553177i
$647$	−18.5501	+	32.1296i	−0.729278	+	1.26315i	0.227911	+	0.973682i	$0.426810\pi$
$647$	−18.5501	+	32.1296i	−0.729278	+	1.26315i	−0.957189	+	0.289464i	$0.906523\pi$
$648$	6.14512	+	3.54789i	0.241403	+	0.139374i
$649$	−10.2231	+	17.7070i	−0.401293	+	0.695061i
$650$	1.27924	+	0.674349i	0.0501758	+	0.0264501i
$651$		0			0
$652$	−8.14661	+	4.70345i	−0.319046	+	0.184201i
$653$	20.0950			0.786377			0.393189	−	0.919458i	$-0.371372\pi$
$653$	20.0950			0.786377			0.393189	+	0.919458i	$0.371372\pi$
$654$	−0.440324			−0.0172180
$655$	23.3087	−	13.4573i	0.910748	−	0.525820i
$656$	−17.8912	+	10.3295i	−0.698532	+	0.403298i
$657$	4.11593	+	2.37634i	0.160578	+	0.0927097i
$658$		0			0
$659$	−4.95529	+	8.58281i	−0.193031	+	0.334339i	−0.946253	−	0.323427i	$-0.895165\pi$
$659$	−4.95529	+	8.58281i	−0.193031	+	0.334339i	0.753223	+	0.657766i	$0.228498\pi$
$660$	−26.0029			−1.01216
$661$	−40.8994	−	23.6133i	−1.59080	−	0.918450i	−0.993170	−	0.116680i	$-0.962775\pi$
$661$	−40.8994	−	23.6133i	−1.59080	−	0.918450i	−0.597633	−	0.801770i	$-0.703892\pi$
$662$	−0.137468	−	0.238102i	−0.00534284	−	0.00925408i
$663$	31.3481	−	1.20652i	1.21746	−	0.0468572i
$664$	11.8989			0.461768
$665$		0			0
$666$	−0.240428	−	0.416433i	−0.00931639	−	0.0161365i
$667$	15.5858	+	26.9954i	0.603485	+	1.04527i
$668$	4.61783	−	2.66611i	0.178669	−	0.103155i
$669$		−	25.7567i		−	0.995811i
$670$	4.79667	−	2.76936i	0.185312	−	0.106990i
$671$		−	1.10885i		−	0.0428068i
$672$		0			0
$673$	3.45845	+	5.99020i	0.133313	+	0.230905i	0.924952	−	0.380084i	$-0.124105\pi$
$673$	3.45845	+	5.99020i	0.133313	+	0.230905i	−0.791639	+	0.610990i	$0.790772\pi$
$674$		−	5.82801i		−	0.224487i
$675$	−5.39823	−	9.35001i	−0.207778	−	0.359882i
$676$	−11.0473	+	23.0659i	−0.424895	+	0.887150i
$677$	−6.16453	+	10.6773i	−0.236922	+	0.410361i	−0.959830	−	0.280584i	$-0.909472\pi$
$677$	−6.16453	+	10.6773i	−0.236922	+	0.410361i	0.722908	+	0.690945i	$0.242805\pi$
$678$	−5.70137	+	3.29169i	−0.218960	+	0.126416i
$679$		0			0
$680$	−4.59185	+	7.95331i	−0.176089	+	0.304996i
$681$	4.53660	+	2.61921i	0.173843	+	0.100368i
$682$			1.80224i			0.0690113i
$683$			24.5364i			0.938859i	0.882970	+	0.469430i	$0.155540\pi$
$683$			24.5364i			0.938859i	−0.882970	+	0.469430i	$0.844460\pi$
$684$	0.107326	+	0.0619648i	0.00410372	+	0.00236928i
$685$	−6.80655	+	11.7893i	−0.260065	+	0.450446i
$686$		0			0
$687$	13.8751	−	8.01082i	0.529370	−	0.305632i
$688$	−15.2398	+	26.3961i	−0.581012	+	1.00634i
$689$	11.8913	−	22.5577i	0.453021	−	0.859380i
$690$	1.95129	+	3.37973i	0.0742843	+	0.128664i
$691$		−	9.10716i		−	0.346453i	−0.984882	−	0.173226i	$-0.944581\pi$
$691$		−	9.10716i		−	0.346453i	0.984882	−	0.173226i	$-0.0554192\pi$
$692$	0.885106	+	1.53305i	0.0336467	+	0.0582777i
$693$		0			0
$694$			1.47992i			0.0561769i
$695$	17.9756	−	10.3782i	0.681853	−	0.393668i
$696$			9.28179i			0.351825i
$697$	−22.4055	+	12.9358i	−0.848667	+	0.489978i
$698$	1.97543	+	3.42155i	0.0747712	+	0.129508i
$699$	4.66312	+	8.07675i	0.176375	+	0.305491i
$700$		0			0
$701$	0.286950			0.0108380			0.00541898	−	0.999985i	$-0.498275\pi$
$701$	0.286950			0.0108380			0.00541898	+	0.999985i	$0.498275\pi$
$702$	−2.68527	+	1.69127i	−0.101349	+	0.0638331i
$703$	0.749377	+	1.29796i	0.0282633	+	0.0489534i
$704$	16.8601	+	9.73419i	0.635440	+	0.366871i
$705$	−9.07036			−0.341609
$706$	−0.0512797	+	0.0888191i	−0.00192994	+	0.00334275i
$707$		0			0
$708$	−23.6093	−	13.6308i	−0.887292	−	0.512278i
$709$	16.0949	−	9.29241i	0.604457	−	0.348984i	−0.166336	−	0.986069i	$-0.553194\pi$
$709$	16.0949	−	9.29241i	0.604457	−	0.348984i	0.770793	+	0.637086i	$0.219860\pi$
$710$	−1.40727	+	0.812486i	−0.0528138	+	0.0304921i
$711$	3.04588			0.114229
$712$	4.22656			0.158397
$713$	−14.0940	+	8.13715i	−0.527823	+	0.304739i
$714$		0			0
$715$	12.1704	−	23.0872i	0.455148	−	0.863414i
$716$	−10.8751	+	18.8362i	−0.406421	+	0.703941i
$717$	−3.95022	−	2.28066i	−0.147524	−	0.0851729i
$718$	2.92974	−	5.07445i	0.109337	−	0.189377i
$719$	−20.8475	−	36.1088i	−0.777479	−	1.34663i	−0.933391	−	0.358862i	$-0.883165\pi$
$719$	−20.8475	−	36.1088i	−0.777479	−	1.34663i	0.155912	−	0.987771i	$-0.450168\pi$
$720$		−	3.41757i		−	0.127365i
$721$		0			0
$722$	−2.96980	−	1.71462i	−0.110525	−	0.0638114i
$723$	12.6275	+	7.29046i	0.469620	+	0.271135i
$724$	6.94257			0.258019
$725$	7.85809	−	13.6106i	0.291842	−	0.505486i
$726$			1.23525i			0.0458443i
$727$	−32.7039			−1.21292			−0.606461	−	0.795113i	$-0.707411\pi$
$727$	−32.7039			−1.21292			−0.606461	+	0.795113i	$0.707411\pi$
$728$		0			0
$729$	23.3578			0.865105
$730$		−	6.90616i		−	0.255608i
$731$	−19.0851	+	33.0564i	−0.705888	+	1.22263i
$732$	1.47847			0.0546458
$733$	−8.60423	−	4.96765i	−0.317804	−	0.183484i	0.332609	−	0.943065i	$-0.392071\pi$
$733$	−8.60423	−	4.96765i	−0.317804	−	0.183484i	−0.650413	+	0.759580i	$0.725404\pi$
$734$	−1.23225	−	0.711440i	−0.0454832	−	0.0262597i
$735$		0			0
$736$		−	9.33871i		−	0.344230i
$737$	−15.3586	−	26.6018i	−0.565740	−	0.979891i
$738$	−0.164119	+	0.284262i	−0.00604129	+	0.0104638i
$739$	−9.00853	−	5.20108i	−0.331384	−	0.191325i	0.325071	−	0.945690i	$-0.394612\pi$
$739$	−9.00853	−	5.20108i	−0.331384	−	0.191325i	−0.656455	+	0.754365i	$0.727945\pi$
$740$	21.0205	−	36.4086i	0.772730	−	1.33841i
$741$	−1.04969	+	0.661133i	−0.0385615	+	0.0242873i
$742$		0			0
$743$	−1.47972	+	0.854317i	−0.0542857	+	0.0313419i	−0.526897	−	0.849929i	$-0.676645\pi$
$743$	−1.47972	+	0.854317i	−0.0542857	+	0.0313419i	0.472612	+	0.881271i	$0.343311\pi$
$744$	−4.84590			−0.177659
$745$	38.4686			1.40938
$746$	−0.327545	+	0.189108i	−0.0119923	+	0.00692374i
$747$	−4.80235	+	2.77264i	−0.175709	+	0.101446i
$748$	21.8723	+	12.6280i	0.799732	+	0.461726i
$749$		0			0
$750$	−1.23393	+	2.13722i	−0.0450566	+	0.0780404i
$751$	−29.9812			−1.09403			−0.547015	−	0.837123i	$-0.684236\pi$
$751$	−29.9812			−1.09403			−0.547015	+	0.837123i	$0.684236\pi$
$752$	6.09233	+	3.51741i	0.222164	+	0.128267i
$753$	−23.0598	−	39.9408i	−0.840347	−	1.45552i
$754$	−4.08656	−	2.15423i	−0.148824	−	0.0784523i
$755$	17.3893			0.632860
$756$		0			0
$757$	−4.20229	−	7.27858i	−0.152735	−	0.264545i	0.779497	−	0.626406i	$-0.215475\pi$
$757$	−4.20229	−	7.27858i	−0.152735	−	0.264545i	−0.932232	+	0.361861i	$0.882141\pi$
$758$	1.29437	+	2.24191i	0.0470136	+	0.0814299i
$759$	18.7436	−	10.8216i	0.680350	−	0.392800i
$760$		−	0.363160i		−	0.0131732i
$761$	−44.2184	+	25.5295i	−1.60292	+	0.925444i	−0.612015	+	0.790846i	$0.709641\pi$
$761$	−44.2184	+	25.5295i	−1.60292	+	0.925444i	−0.990900	+	0.134598i	$0.957026\pi$
$762$			2.63067i			0.0952990i
$763$		0			0
$764$	20.0668	+	34.7568i	0.725993	+	1.25746i
$765$		−	4.27989i		−	0.154740i
$766$	−2.27723	−	3.94429i	−0.0822798	−	0.142513i
$767$	23.1526	−	14.5823i	0.835991	−	0.526535i
$768$	−12.2780	+	21.2661i	−0.443044	+	0.767375i
$769$	0.610062	−	0.352220i	0.0219994	−	0.0127014i	−0.488960	−	0.872306i	$-0.662624\pi$
$769$	0.610062	−	0.352220i	0.0219994	−	0.0127014i	0.510959	+	0.859605i	$0.329290\pi$
$770$		0			0
$771$	3.08015	−	5.33498i	0.110929	−	0.192134i
$772$	−29.4142	−	16.9823i	−1.05864	−	0.611206i
$773$			1.26521i			0.0455066i	0.999741	+	0.0227533i	$0.00724323\pi$
$773$			1.26521i			0.0455066i	−0.999741	+	0.0227533i	$0.992757\pi$
$774$			0.484272i			0.0174068i
$775$	7.10593	+	4.10261i	0.255253	+	0.147370i
$776$	0.161803	−	0.280252i	0.00580840	−	0.0100604i
$777$		0			0
$778$	−4.40076	+	2.54078i	−0.157775	+	0.0910914i
$779$	0.511533	−	0.886001i	0.0183276	−	0.0317443i
$780$	30.7830	+	16.2272i	1.10221	+	0.581027i
$781$	4.50596	+	7.80456i	0.161236	+	0.279269i
$782$		−	3.79048i		−	0.135547i
$783$	17.2448	+	29.8689i	0.616279	+	1.06743i
$784$		0			0
$785$			42.7679i			1.52645i
$786$	−2.86463	+	1.65389i	−0.102178	+	0.0589924i
$787$		−	43.7969i		−	1.56119i	−0.625037	−	0.780595i	$-0.714916\pi$
$787$		−	43.7969i		−	1.56119i	0.625037	−	0.780595i	$-0.285084\pi$
$788$	−8.44493	+	4.87568i	−0.300838	+	0.173689i
$789$	0.145109	+	0.251336i	0.00516602	+	0.00894780i
$790$	−2.21300	−	3.83303i	−0.0787351	−	0.136373i
$791$		0			0
$792$	0.646180			0.0229610
$793$	−0.691984	+	1.31269i	−0.0245731	+	0.0466151i
$794$	1.96885	+	3.41015i	0.0698719	+	0.121022i
$795$	−30.0479	−	17.3481i	−1.06569	−	0.615275i
$796$	14.1291			0.500792
$797$	−6.84183	+	11.8504i	−0.242350	+	0.419763i	−0.961383	−	0.275213i	$-0.911252\pi$
$797$	−6.84183	+	11.8504i	−0.242350	+	0.419763i	0.719033	+	0.694976i	$0.244585\pi$
$798$		0			0
$799$	7.62954	+	4.40492i	0.269914	+	0.155835i
$800$	−4.07761	+	2.35421i	−0.144165	+	0.0832338i
$801$	−1.70582	+	0.984857i	−0.0602722	+	0.0347982i
$802$	−3.71212			−0.131080
$803$	−38.3008			−1.35161
$804$	35.4691	−	20.4781i	1.25090	−	0.722206i
$805$		0			0
$806$	1.12469	−	2.13354i	0.0396157	−	0.0751508i
$807$	−21.2973	+	36.8881i	−0.749702	+	1.29852i
$808$	4.75695	+	2.74643i	0.167349	+	0.0966189i
$809$	−4.55688	+	7.89274i	−0.160211	+	0.277494i	−0.934944	−	0.354794i	$-0.884551\pi$
$809$	−4.55688	+	7.89274i	−0.160211	+	0.277494i	0.774733	+	0.632288i	$0.217884\pi$
$810$	2.40261	+	4.16145i	0.0844193	+	0.146218i
$811$			2.31899i			0.0814309i	0.999171	+	0.0407154i	$0.0129637\pi$
$811$			2.31899i			0.0814309i	−0.999171	+	0.0407154i	$0.987036\pi$
$812$		0			0
$813$	−18.6934	−	10.7926i	−0.655606	−	0.378514i
$814$	3.35595	+	1.93756i	0.117626	+	0.0679114i
$815$	−12.8465			−0.449993
$816$	−16.5528	+	28.6703i	−0.579465	+	1.00366i
$817$		−	1.50940i		−	0.0528073i
$818$	1.13352			0.0396325
$819$		0			0
$820$	−28.6977			−1.00217
$821$		−	10.1447i		−	0.354053i	−0.984206	−	0.177026i	$-0.943352\pi$
$821$		−	10.1447i		−	0.354053i	0.984206	−	0.177026i	$-0.0566478\pi$
$822$	0.836520	−	1.44890i	0.0291770	−	0.0505360i
$823$	26.8178			0.934811			0.467405	−	0.884043i	$-0.345189\pi$
$823$	26.8178			0.934811			0.467405	+	0.884043i	$0.345189\pi$
$824$	−3.20414	−	1.84991i	−0.111622	−	0.0644448i
$825$	−9.45021	−	5.45608i	−0.329014	−	0.189956i
$826$		0			0
$827$			33.6015i			1.16844i	0.811596	+	0.584219i	$0.198599\pi$
$827$			33.6015i			1.16844i	−0.811596	+	0.584219i	$0.801401\pi$
$828$	1.44674	+	2.50582i	0.0502776	+	0.0870834i
$829$	−5.93328	+	10.2767i	−0.206071	+	0.356926i	−0.950473	−	0.310806i	$-0.899401\pi$
$829$	−5.93328	+	10.2767i	−0.206071	+	0.356926i	0.744402	+	0.667731i	$0.232735\pi$
$830$	6.97835	+	4.02895i	0.242222	+	0.139847i
$831$	−24.9847	+	43.2748i	−0.866710	+	1.50119i
$832$	−13.8848	−	22.0452i	−0.481370	−	0.764281i
$833$		0			0
$834$	−2.20919	+	1.27547i	−0.0764979	+	0.0441661i
$835$	7.28193			0.252001
$836$	−0.998723			−0.0345416
$837$	−15.5942	+	9.00330i	−0.539013	+	0.311199i
$838$	−5.34993	+	3.08878i	−0.184810	+	0.106700i
$839$	29.9798	+	17.3088i	1.03502	+	0.597568i	0.918418	−	0.395611i	$-0.129467\pi$
$839$	29.9798	+	17.3088i	1.03502	+	0.597568i	0.116600	+	0.993179i	$0.462801\pi$
$840$		0			0
$841$	−10.6029	+	18.3648i	−0.365617	+	0.633267i
$842$	−2.08369			−0.0718088
$843$	45.1296	+	26.0556i	1.55435	+	0.897403i
$844$	17.3051	+	29.9733i	0.595666	+	1.03172i
$845$	−28.8154	+	19.7364i	−0.991279	+	0.678951i
$846$	0.111772			0.00384280
$847$		0			0
$848$	13.4549	+	23.3046i	0.462044	+	0.800283i
$849$	−16.4086	−	28.4206i	−0.563143	−	0.975392i
$850$	−1.65506	+	0.955548i	−0.0567680	+	0.0327750i
$851$			34.9925i			1.19953i
$852$	−10.4061	+	6.00795i	−0.356506	+	0.205829i
$853$			29.1897i			0.999436i	0.866188	+	0.499718i	$0.166563\pi$
$853$			29.1897i			0.999436i	−0.866188	+	0.499718i	$0.833437\pi$
$854$		0			0
$855$	0.0846220	+	0.146570i	0.00289401	+	0.00501258i
$856$			5.76265i			0.196963i
$857$	12.6599	+	21.9276i	0.432455	+	0.749033i	0.997084	−	0.0763112i	$-0.0243142\pi$
$857$	12.6599	+	21.9276i	0.432455	+	0.749033i	−0.564629	+	0.825345i	$0.690981\pi$
$858$	−1.49574	+	2.83741i	−0.0510636	+	0.0968675i
$859$	13.0424	−	22.5902i	0.445002	−	0.770766i	−0.553050	−	0.833148i	$-0.686536\pi$
$859$	13.0424	−	22.5902i	0.445002	−	0.770766i	0.998052	+	0.0623818i	$0.0198696\pi$
$860$	−36.6674	+	21.1699i	−1.25035	+	0.721888i
$861$		0			0
$862$	0.792913	−	1.37337i	0.0270067	−	0.0467770i
$863$	31.2061	+	18.0169i	1.06227	+	0.613302i	0.926059	−	0.377378i	$-0.123174\pi$
$863$	31.2061	+	18.0169i	1.06227	+	0.613302i	0.136210	+	0.990680i	$0.456508\pi$
$864$		−	10.3328i		−	0.351527i
$865$			2.41748i			0.0821969i
$866$	−3.46190	−	1.99873i	−0.117640	−	0.0679196i
$867$	−5.20832	+	9.02108i	−0.176884	+	0.306372i
$868$		0			0
$869$	−21.2576	+	12.2731i	−0.721114	+	0.416335i
$870$	−3.14279	+	5.44348i	−0.106551	+	0.184551i
$871$	1.58094	+	41.0766i	0.0535683	+	1.39183i
$872$	0.478337	+	0.828504i	0.0161985	+	0.0280567i
$873$			0.150811i			0.00510418i
$874$	0.0749454	+	0.129809i	0.00253507	+	0.00439086i
$875$		0			0
$876$		−	51.0677i		−	1.72542i
$877$	7.89961	−	4.56084i	0.266751	−	0.154009i	−0.360659	−	0.932698i	$-0.617448\pi$
$877$	7.89961	−	4.56084i	0.266751	−	0.154009i	0.627410	+	0.778689i	$0.284115\pi$
$878$		−	1.87531i		−	0.0632887i
$879$	23.5452	−	13.5938i	0.794158	−	0.458507i
$880$	13.7708	+	23.8517i	0.464212	+	0.804039i
$881$	−6.51653	−	11.2870i	−0.219548	−	0.380268i	0.735122	−	0.677935i	$-0.237125\pi$
$881$	−6.51653	−	11.2870i	−0.219548	−	0.380268i	−0.954670	+	0.297667i	$0.903791\pi$
$882$		0			0
$883$	−2.13222			−0.0717548			−0.0358774	−	0.999356i	$-0.511423\pi$
$883$	−2.13222			−0.0717548			−0.0358774	+	0.999356i	$0.511423\pi$
$884$	−18.0126	−	28.5989i	−0.605828	−	0.961886i
$885$	−18.6149	−	32.2420i	−0.625734	−	1.08380i
$886$	−5.60835	−	3.23798i	−0.188416	−	0.108782i
$887$	47.1715			1.58386			0.791932	−	0.610610i	$-0.209076\pi$
$887$	47.1715			1.58386			0.791932	+	0.610610i	$0.209076\pi$
$888$	−5.20976	+	9.02356i	−0.174828	+	0.302811i
$889$		0			0
$890$	2.47875	+	1.43111i	0.0830878	+	0.0479708i
$891$	23.0790	−	13.3246i	0.773174	−	0.446392i
$892$	−24.0319	+	13.8748i	−0.804647	+	0.464563i
$893$	−0.348376			−0.0116580
$894$	−4.72777			−0.158120
$895$	−25.7236	+	14.8515i	−0.859844	+	0.496431i
$896$		0			0
$897$	−28.9425	+	1.11393i	−0.966363	+	0.0371931i
$898$	2.05689	−	3.56264i	0.0686394	−	0.118887i
$899$	−22.7001	−	13.1059i	−0.757091	−	0.437107i
$900$	0.729420	−	1.26339i	0.0243140	−	0.0421131i
$901$	16.8499	+	29.1848i	0.561350	+	0.972287i
$902$		−	2.64520i		−	0.0880755i
$903$		0			0
$904$	12.3871	+	7.15171i	0.411990	+	0.237862i
$905$	8.21087	+	4.74055i	0.272939	+	0.157581i
$906$	−2.13713			−0.0710013
$907$	8.02154	−	13.8937i	0.266351	−	0.461333i	−0.701566	−	0.712605i	$-0.747515\pi$
$907$	8.02154	−	13.8937i	0.266351	−	0.461333i	0.967917	+	0.251271i	$0.0808487\pi$
$908$		−	5.64374i		−	0.187294i
$909$	−2.55984			−0.0849047
$910$		0			0
$911$	−24.4319			−0.809466			−0.404733	−	0.914435i	$-0.632636\pi$
$911$	−24.4319			−0.809466			−0.404733	+	0.914435i	$0.632636\pi$
$912$		−	1.30913i		−	0.0433496i
$913$	22.3441	−	38.7012i	0.739483	−	1.28082i
$914$	−5.66289			−0.187312
$915$	1.74856	+	1.00953i	0.0578057	+	0.0333742i
$916$	−14.9488	−	8.63067i	−0.493921	−	0.285165i
$917$		0			0
$918$		−	4.19395i		−	0.138421i
$919$	−7.95800	−	13.7837i	−0.262510	−	0.454681i	0.704398	−	0.709805i	$-0.251217\pi$
$919$	−7.95800	−	13.7837i	−0.262510	−	0.454681i	−0.966908	+	0.255124i	$0.917884\pi$
$920$	4.23948	−	7.34300i	0.139772	−	0.242092i
$921$	37.1878	+	21.4704i	1.22538	+	0.707472i
$922$	−0.760140	+	1.31660i	−0.0250339	+	0.0433600i
$923$	−0.463824	−	12.0512i	−0.0152670	−	0.396671i
$924$		0			0
$925$	15.2790	−	8.82131i	0.502369	−	0.290043i
$926$	1.81533			0.0596555
$927$	1.72424			0.0566314
$928$	13.0260	−	7.52059i	0.427601	−	0.246875i
$929$	40.9834	−	23.6618i	1.34462	−	0.776317i	0.357139	−	0.934051i	$-0.383752\pi$
$929$	40.9834	−	23.6618i	1.34462	−	0.776317i	0.987482	+	0.157734i	$0.0504189\pi$
$930$	−2.84197	−	1.64081i	−0.0931920	−	0.0538044i
$931$		0			0
$932$	5.02393	−	8.70170i	0.164564	−	0.285034i
$933$	2.97805			0.0974968
$934$	4.12656	+	2.38247i	0.135025	+	0.0779568i
$935$	17.2454	+	29.8699i	0.563985	+	0.976850i
$936$	−0.764967	−	0.403252i	−0.0250037	−	0.0131807i
$937$	29.7044			0.970401			0.485200	−	0.874403i	$-0.338747\pi$
$937$	29.7044			0.970401			0.485200	+	0.874403i	$0.338747\pi$
$938$		0			0
$939$	−0.636122	−	1.10180i	−0.0207591	−	0.0359558i
$940$	4.88609	+	8.46296i	0.159367	+	0.276031i
$941$	−35.0068	+	20.2112i	−1.14119	+	0.658866i	−0.946725	−	0.322043i	$-0.895630\pi$
$941$	−35.0068	+	20.2112i	−1.14119	+	0.658866i	−0.194465	+	0.980909i	$0.562297\pi$
$942$		−	5.25615i		−	0.171255i
$943$	20.6861	−	11.9431i	0.673633	−	0.388922i
$944$			28.8748i			0.939795i
$945$		0			0
$946$	−1.95133	−	3.37980i	−0.0634431	−	0.109887i
$947$		−	45.9228i		−	1.49229i	−0.665783	−	0.746146i	$-0.731902\pi$
$947$		−	45.9228i		−	1.49229i	0.665783	−	0.746146i	$-0.268098\pi$
$948$	−16.3641	−	28.3434i	−0.531481	−	0.920551i
$949$	45.3416	+	23.9018i	1.47185	+	0.775885i
$950$	0.0377862	−	0.0654476i	0.00122595	−	0.00212340i
$951$	−33.8869	+	19.5646i	−1.09886	+	0.634426i
$952$		0			0
$953$	6.19465	−	10.7294i	0.200664	−	0.347561i	−0.748078	−	0.663610i	$-0.769023\pi$
$953$	6.19465	−	10.7294i	0.200664	−	0.347561i	0.948743	+	0.316050i	$0.102357\pi$
$954$	0.370273	+	0.213777i	0.0119880	+	0.00692129i
$955$			54.8085i			1.77356i
$956$			4.91426i			0.158939i
$957$	30.1890	+	17.4296i	0.975870	+	0.563419i
$958$	−0.776108	+	1.34426i	−0.0250749	+	0.0434310i
$959$		0			0
$960$	−30.6999	+	17.7246i	−0.990836	+	0.572060i
$961$	−8.65757	+	14.9953i	−0.279276	+	0.483721i
$962$	−2.76373	−	4.38803i	−0.0891062	−	0.141476i
$963$	−1.34279	−	2.32578i	−0.0432708	−	0.0749472i
$964$		−	15.7091i		−	0.505958i
$965$	−23.1918	−	40.1694i	−0.746572	−	1.29310i
$966$		0			0
$967$			9.44932i			0.303870i	0.988391	+	0.151935i	$0.0485504\pi$
$967$			9.44932i			0.303870i	−0.988391	+	0.151935i	$0.951450\pi$
$968$	2.32421	−	1.34188i	0.0747030	−	0.0431298i
$969$		−	1.63945i		−	0.0526667i
$970$	0.189785	−	0.109573i	0.00609364	−	0.00351816i
$971$	−10.4882	−	18.1660i	−0.336581	−	0.582976i	0.647206	−	0.762315i	$-0.275937\pi$
$971$	−10.4882	−	18.1660i	−0.336581	−	0.582976i	−0.983787	+	0.179339i	$0.942604\pi$
$972$	3.40223	+	5.89283i	0.109126	+	0.189013i
$973$		0			0
$974$	−3.84363			−0.123158
$975$	7.78254	+	12.3565i	0.249241	+	0.395725i
$976$	−0.782977	−	1.35616i	−0.0250625	−	0.0434095i
$977$	−11.4179	−	6.59214i	−0.365292	−	0.210901i	0.306108	−	0.951997i	$-0.400973\pi$
$977$	−11.4179	−	6.59214i	−0.365292	−	0.210901i	−0.671400	+	0.741096i	$0.734307\pi$
$978$	1.57883			0.0504853
$979$	7.93676	−	13.7469i	0.253660	−	0.439352i
$980$		0			0
$981$	−0.386109	−	0.222920i	−0.0123275	−	0.00711729i
$982$	3.51618	−	2.03007i	0.112206	−	0.0647820i
$983$	20.2294	−	11.6794i	0.645216	−	0.372516i	−0.141405	−	0.989952i	$-0.545162\pi$
$983$	20.2294	−	11.6794i	0.645216	−	0.372516i	0.786621	+	0.617436i	$0.211829\pi$
$984$	7.11248			0.226738
$985$	−13.3169			−0.424313
$986$	5.28713	−	3.05252i	0.168376	−	0.0972122i
$987$		0			0
$988$	1.18232	+	0.623257i	0.0376145	+	0.0198285i
$989$	17.6206	−	30.5197i	0.560302	−	0.970471i
$990$	0.378965	+	0.218795i	0.0120443	+	0.00695378i
$991$	−19.7465	+	34.2019i	−0.627267	+	1.08646i	0.360831	+	0.932631i	$0.382493\pi$
$991$	−19.7465	+	34.2019i	−0.627267	+	1.08646i	−0.988098	+	0.153827i	$0.950840\pi$
$992$	3.92640	+	6.80073i	0.124663	+	0.215923i
$993$		−	2.77639i		−	0.0881060i
$994$		0			0
$995$	16.7102	+	9.64766i	0.529750	+	0.305851i
$996$	51.6015	+	29.7922i	1.63506	+	0.944001i
$997$	51.4791			1.63036			0.815180	−	0.579208i	$-0.196638\pi$
$997$	51.4791			1.63036			0.815180	+	0.579208i	$0.196638\pi$
$998$	3.51504	−	6.08822i	0.111267	−	0.192719i
$999$			38.7172i			1.22496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.i.569.4		12
7.2	even	3		637.2.q.i.491.4		12
7.3	odd	6		91.2.u.b.88.3	yes	12
7.4	even	3		637.2.u.g.361.3		12
7.5	odd	6		637.2.q.g.491.4		12
7.6	odd	2		91.2.k.b.23.4	yes	12
13.4	even	6		637.2.u.g.30.3		12
21.17	even	6		819.2.do.e.361.4		12
21.20	even	2		819.2.bm.f.478.3		12
91.2	odd	12		8281.2.a.co.1.7		12
91.4	even	6	inner	637.2.k.i.459.3		12
91.17	odd	6		91.2.k.b.4.3	✓	12
91.24	even	12		1183.2.e.j.508.7		24
91.30	even	6		637.2.q.i.589.4		12
91.37	odd	12		8281.2.a.co.1.6		12
91.41	even	12		1183.2.e.j.170.6		24
91.54	even	12		8281.2.a.cp.1.7		12
91.69	odd	6		91.2.u.b.30.3	yes	12
91.76	even	12		1183.2.e.j.170.7		24
91.80	even	12		1183.2.e.j.508.6		24
91.82	odd	6		637.2.q.g.589.4		12
91.89	even	12		8281.2.a.cp.1.6		12
273.17	even	6		819.2.bm.f.550.4		12
273.251	even	6		819.2.do.e.667.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.3	✓	12	91.17	odd	6
91.2.k.b.23.4	yes	12	7.6	odd	2
91.2.u.b.30.3	yes	12	91.69	odd	6
91.2.u.b.88.3	yes	12	7.3	odd	6
637.2.k.i.459.3		12	91.4	even	6	inner
637.2.k.i.569.4		12	1.1	even	1	trivial
637.2.q.g.491.4		12	7.5	odd	6
637.2.q.g.589.4		12	91.82	odd	6
637.2.q.i.491.4		12	7.2	even	3
637.2.q.i.589.4		12	91.30	even	6
637.2.u.g.30.3		12	13.4	even	6
637.2.u.g.361.3		12	7.4	even	3
819.2.bm.f.478.3		12	21.20	even	2
819.2.bm.f.550.4		12	273.17	even	6
819.2.do.e.361.4		12	21.17	even	6
819.2.do.e.667.4		12	273.251	even	6
1183.2.e.j.170.6		24	91.41	even	12
1183.2.e.j.170.7		24	91.76	even	12
1183.2.e.j.508.6		24	91.80	even	12
1183.2.e.j.508.7		24	91.24	even	12
8281.2.a.co.1.6		12	91.37	odd	12
8281.2.a.co.1.7		12	91.2	odd	12
8281.2.a.cp.1.6		12	91.89	even	12
8281.2.a.cp.1.7		12	91.54	even	12

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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.180824i q^{2} +(-0.913006 + 1.58137i) q^{3} +1.96730 q^{4} +(2.32670 + 1.34332i) q^{5} +(-0.285950 - 0.165093i) q^{6} +0.717383i q^{8} +(-0.167162 - 0.289532i) q^{9} +O(q^{10})\)	\(q+0.180824i q^{2} +(-0.913006 + 1.58137i) q^{3} +1.96730 q^{4} +(2.32670 + 1.34332i) q^{5} +(-0.285950 - 0.165093i) q^{6} +0.717383i q^{8} +(-0.167162 - 0.289532i) q^{9} +(-0.242904 + 0.420723i) q^{10} +(2.33328 + 1.34712i) q^{11} +(-1.79616 + 3.11104i) q^{12} +(-1.92153 - 3.05086i) q^{13} +(-4.24858 + 2.45292i) q^{15} +3.80489 q^{16} +4.76493 q^{17} +(0.0523543 - 0.0302268i) q^{18} +(-0.163180 + 0.0942122i) q^{19} +(4.57732 + 2.64272i) q^{20} +(-0.243592 + 0.421913i) q^{22} -4.39929 q^{23} +(-1.13445 - 0.654975i) q^{24} +(1.10902 + 1.92088i) q^{25} +(0.551667 - 0.347458i) q^{26} -4.86756 q^{27} +(-3.54280 - 6.13631i) q^{29} +(-0.443546 - 0.768245i) q^{30} +(3.20369 - 1.84965i) q^{31} +2.12278i q^{32} +(-4.26060 + 2.45986i) q^{33} +0.861613i q^{34} +(-0.328857 - 0.569598i) q^{36} -7.95413i q^{37} +(-0.0170358 - 0.0295069i) q^{38} +(6.57891 - 0.253207i) q^{39} +(-0.963675 + 1.66913i) q^{40} +(-4.70215 + 2.71479i) q^{41} +(-4.00533 + 6.93743i) q^{43} +(4.59027 + 2.65020i) q^{44} -0.898206i q^{45} -0.795496i q^{46} +(1.60118 + 0.924445i) q^{47} +(-3.47389 + 6.01695i) q^{48} +(-0.347341 + 0.200538i) q^{50} +(-4.35041 + 7.53514i) q^{51} +(-3.78023 - 6.00196i) q^{52} +(3.53622 + 6.12491i) q^{53} -0.880171i q^{54} +(3.61923 + 6.26869i) q^{55} -0.344066i q^{57} +(1.10959 - 0.640623i) q^{58} +7.58888i q^{59} +(-8.35825 + 4.82564i) q^{60} +(-0.205782 - 0.356425i) q^{61} +(0.334461 + 0.579304i) q^{62} +7.22592 q^{64} +(-0.372548 - 9.67966i) q^{65} +(-0.444801 - 0.770418i) q^{66} +(-9.87358 - 5.70051i) q^{67} +9.37407 q^{68} +(4.01658 - 6.95692i) q^{69} +(2.89675 + 1.67244i) q^{71} +(0.207705 - 0.119919i) q^{72} +(-12.3112 + 7.10790i) q^{73} +1.43830 q^{74} -4.05018 q^{75} +(-0.321025 + 0.185344i) q^{76} +(0.0457859 + 1.18962i) q^{78} +(-4.55529 + 7.89000i) q^{79} +(8.85283 + 5.11118i) q^{80} +(4.94560 - 8.56603i) q^{81} +(-0.490899 - 0.850261i) q^{82} -16.5866i q^{83} +(11.0866 + 6.40083i) q^{85} +(-1.25445 - 0.724258i) q^{86} +12.9384 q^{87} +(-0.966401 + 1.67386i) q^{88} -5.89165i q^{89} +0.162417 q^{90} -8.65473 q^{92} +6.75498i q^{93} +(-0.167162 + 0.289532i) q^{94} -0.506229 q^{95} +(-3.35691 - 1.93811i) q^{96} +(-0.390659 - 0.225547i) q^{97} -0.900747i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9	\( 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9} - 12 q^{10} + 12 q^{11} + q^{12} + 2 q^{13} - 12 q^{15} + 16 q^{16} + 34 q^{17} + 3 q^{18} - 9 q^{19} + 3 q^{20} - 15 q^{22} - 6 q^{23} - 15 q^{24} - 5 q^{25} + 6 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{31} + 6 q^{33} - 13 q^{36} - 19 q^{38} - 4 q^{39} + q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} + 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{55} - 24 q^{58} - 30 q^{60} - 5 q^{61} - 41 q^{62} + 2 q^{64} + 21 q^{65} + 34 q^{66} + 15 q^{67} - 22 q^{68} - 7 q^{69} + 30 q^{71} + 57 q^{72} - 42 q^{73} + 66 q^{74} + 2 q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} + 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 57 q^{86} + 20 q^{87} - 14 q^{88} - 66 q^{92} - q^{94} - 4 q^{95} - 21 q^{96} + 3 q^{97}+O(q^{100}) \) 12 * q + 3 * q^3 - 8 * q^4 + 3 * q^5 + 9 * q^6 - q^9 - 12 * q^10 + 12 * q^11 + q^12 + 2 * q^13 - 12 * q^15 + 16 * q^16 + 34 * q^17 + 3 * q^18 - 9 * q^19 + 3 * q^20 - 15 * q^22 - 6 * q^23 - 15 * q^24 - 5 * q^25 + 6 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^31 + 6 * q^33 - 13 * q^36 - 19 * q^38 - 4 * q^39 + q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 + 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 + 7 * q^52 - 8 * q^53 + 15 * q^55 - 24 * q^58 - 30 * q^60 - 5 * q^61 - 41 * q^62 + 2 * q^64 + 21 * q^65 + 34 * q^66 + 15 * q^67 - 22 * q^68 - 7 * q^69 + 30 * q^71 + 57 * q^72 - 42 * q^73 + 66 * q^74 + 2 * q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 + 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 57 * q^86 + 20 * q^87 - 14 * q^88 - 66 * q^92 - q^94 - 4 * q^95 - 21 * q^96 + 3 * q^97

Introduction

L-functions

Modular forms

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