LMFDB - Embedded newform 637.2.u.g.30.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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([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("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (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			30.3
Root			$0.655911 + 1.25291i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.g.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156598 + 0.0904119i) q^{2} +1.82601 q^{3} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.285950 + 0.165093i) q^{6} -0.717383i q^{8} +0.334323 q^{9} +O(q^{10})$	\(q+(-0.156598 + 0.0904119i) q^{2} +1.82601 q^{3} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.285950 + 0.165093i) q^{6} -0.717383i q^{8} +0.334323 q^{9} +0.485809 q^{10} +2.69424i q^{11} +(-1.79616 + 3.11104i) q^{12} +(-1.92153 + 3.05086i) q^{13} +(-4.24858 - 2.45292i) q^{15} +(-1.90244 - 3.29513i) q^{16} +(-2.38247 + 4.12655i) q^{17} +(-0.0523543 + 0.0302268i) q^{18} +0.188424i q^{19} +(4.57732 - 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} +(2.19964 + 3.80989i) q^{23} -1.30995i q^{24} +(1.10902 + 1.92088i) q^{25} +(0.0250743 - 0.651487i) q^{26} -4.86756 q^{27} +(-3.54280 + 6.13631i) q^{29} +0.887093 q^{30} +(-3.20369 + 1.84965i) q^{31} +(1.83838 + 1.06139i) q^{32} +4.91972i q^{33} -0.861613i q^{34} +(-0.328857 + 0.569598i) q^{36} +(6.88848 - 3.97707i) q^{37} +(-0.0170358 - 0.0295069i) q^{38} +(-3.50874 + 5.57090i) 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} +(-0.777869 - 0.449103i) q^{45} +(-0.688919 - 0.397748i) 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} +(-3.30773 - 6.27476i) q^{52} +(3.53622 + 6.12491i) q^{53} +(0.762250 - 0.440085i) q^{54} +(3.61923 - 6.26869i) q^{55} +0.344066i q^{57} -1.28125i q^{58} +(6.57216 + 3.79444i) q^{59} +(8.35825 - 4.82564i) q^{60} +0.411564 q^{61} +(0.334461 - 0.579304i) q^{62} +7.22592 q^{64} +(8.56910 - 4.51719i) q^{65} +(-0.444801 - 0.770418i) q^{66} -11.4010i q^{67} +(-4.68703 - 8.11818i) q^{68} +(4.01658 + 6.95692i) q^{69} +(2.89675 - 1.67244i) q^{71} -0.239838i q^{72} +(12.3112 - 7.10790i) q^{73} +(-0.719148 + 1.24560i) q^{74} +(2.02509 + 3.50756i) q^{75} +(-0.321025 - 0.185344i) q^{76} +(0.0457859 - 1.18962i) q^{78} +(-4.55529 + 7.89000i) q^{79} +10.2224i q^{80} -9.89120 q^{81} +0.981797 q^{82} +16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} +(1.25445 + 0.724258i) q^{86} +(-6.46920 + 11.2050i) q^{87} +1.93280 q^{88} +(5.10232 - 2.94582i) q^{89} +0.162417 q^{90} -8.65473 q^{92} +(-5.84998 + 3.37749i) q^{93} +0.334323 q^{94} +(0.253115 - 0.438407i) 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 - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9	$ 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97}+O(q^{100}) $ 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9 + 24 * q^10 + q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 - 3 * q^18 + 3 * q^20 - 15 * q^22 + 3 * q^23 - 5 * q^25 + 9 * q^26 - 12 * q^27 - q^29 - 22 * q^30 + 18 * q^31 + 18 * q^32 - 13 * q^36 + 15 * q^37 - 19 * q^38 - q^39 + q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 9 * q^45 - 30 * q^46 - 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 - 47 * q^52 - 8 * q^53 - 6 * q^54 + 15 * q^55 - 27 * q^59 + 30 * q^60 + 10 * q^61 - 41 * q^62 + 2 * q^64 - 3 * q^65 + 34 * q^66 + 11 * q^68 - 7 * q^69 + 30 * q^71 + 42 * q^73 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 - 28 * q^81 + 10 * q^82 - 21 * q^85 + 57 * q^86 - 10 * q^87 + 28 * q^88 - 48 * q^89 - 66 * q^92 - 81 * q^93 + 2 * q^94 + 2 * q^95 + 21 * q^96 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.156598	+	0.0904119i	−0.110731	+	0.0639308i	−0.554343	−	0.832288i	$-0.687030\pi$
$2$	−0.156598	+	0.0904119i	−0.110731	+	0.0639308i	0.443611	+	0.896219i	$0.353697\pi$
$3$	1.82601			1.05425			0.527125	−	0.849788i	$-0.323270\pi$
$3$	1.82601			1.05425			0.527125	+	0.849788i	$0.323270\pi$
$4$	−0.983651	+	1.70373i	−0.491826	+	0.851867i
$5$	−2.32670	−	1.34332i	−1.04053	−	0.600751i	−0.120548	−	0.992708i	$-0.538465\pi$
$5$	−2.32670	−	1.34332i	−1.04053	−	0.600751i	−0.919984	+	0.391956i	$0.871799\pi$
$6$	−0.285950	+	0.165093i	−0.116739	+	0.0673990i
$7$		0			0
$7$		0			0
$8$		−	0.717383i		−	0.253633i
$9$	0.334323			0.111441
$10$	0.485809			0.153626
$11$			2.69424i			0.812345i	0.913796	+	0.406172i	$0.133137\pi$
$11$			2.69424i			0.812345i	−0.913796	+	0.406172i	$0.866863\pi$
$12$	−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
$16$	−1.90244	−	3.29513i	−0.475611	−	0.823782i
$17$	−2.38247	+	4.12655i	−0.577833	+	1.00084i	0.417894	+	0.908496i	$0.362768\pi$
$17$	−2.38247	+	4.12655i	−0.577833	+	1.00084i	−0.995727	+	0.0923405i	$0.970565\pi$
$18$	−0.0523543	+	0.0302268i	−0.0123400	+	0.00712452i
$19$			0.188424i			0.0432275i	0.999766	+	0.0216138i	$0.00688041\pi$
$19$			0.188424i			0.0432275i	−0.999766	+	0.0216138i	$0.993120\pi$
$20$	4.57732	−	2.64272i	1.02352	−	0.590930i
$21$		0			0
$22$	−0.243592	−	0.421913i	−0.0519339	−	0.0899521i
$23$	2.19964	+	3.80989i	0.458657	+	0.794418i	0.998890	−	0.0470977i	$-0.0149972\pi$
$23$	2.19964	+	3.80989i	0.458657	+	0.794418i	−0.540233	+	0.841516i	$0.681664\pi$
$24$		−	1.30995i		−	0.267392i
$25$	1.10902	+	1.92088i	0.221804	+	0.384177i
$26$	0.0250743	−	0.651487i	0.00491747	−	0.127767i
$27$	−4.86756			−0.936762
$28$		0			0
$29$	−3.54280	+	6.13631i	−0.657882	+	1.13948i	0.323281	+	0.946303i	$0.395214\pi$
$29$	−3.54280	+	6.13631i	−0.657882	+	1.13948i	−0.981163	+	0.193182i	$0.938119\pi$
$30$	0.887093			0.161960
$31$	−3.20369	+	1.84965i	−0.575400	+	0.332207i	−0.759303	−	0.650737i	$-0.774460\pi$
$31$	−3.20369	+	1.84965i	−0.575400	+	0.332207i	0.183903	+	0.982944i	$0.441127\pi$
$32$	1.83838	+	1.06139i	0.324983	+	0.187629i
$33$			4.91972i			0.856414i
$34$		−	0.861613i		−	0.147765i
$35$		0			0
$36$	−0.328857	+	0.569598i	−0.0548096	+	0.0949329i
$37$	6.88848	−	3.97707i	1.13246	−	0.653826i	0.187907	−	0.982187i	$-0.439830\pi$
$37$	6.88848	−	3.97707i	1.13246	−	0.653826i	0.944552	+	0.328361i	$0.106496\pi$
$38$	−0.0170358	−	0.0295069i	−0.00276357	−	0.00478665i
$39$	−3.50874	+	5.57090i	−0.561848	+	0.892058i
$40$	−0.963675	+	1.66913i	−0.152370	+	0.263913i
$41$	−4.70215	−	2.71479i	−0.734353	−	0.423979i	0.0856594	−	0.996324i	$-0.472700\pi$
$41$	−4.70215	−	2.71479i	−0.734353	−	0.423979i	−0.820013	+	0.572345i	$0.806034\pi$
$42$		0			0
$43$	−4.00533	−	6.93743i	−0.610807	−	1.05795i	−0.991105	−	0.133084i	$-0.957512\pi$
$43$	−4.00533	−	6.93743i	−0.610807	−	1.05795i	0.380298	−	0.924864i	$-0.375821\pi$
$44$	−4.59027	−	2.65020i	−0.692010	−	0.399532i
$45$	−0.777869	−	0.449103i	−0.115958	−	0.0669483i
$46$	−0.688919	−	0.397748i	−0.101576	−	0.0586447i
$47$	−1.60118	−	0.924445i	−0.233557	−	0.134844i	0.378655	−	0.925538i	$-0.376387\pi$
$47$	−1.60118	−	0.924445i	−0.233557	−	0.134844i	−0.612212	+	0.790694i	$0.709720\pi$
$48$	−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
$52$	−3.30773	−	6.27476i	−0.458700	−	0.870152i
$53$	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	$0.671885\pi$
$54$	0.762250	−	0.440085i	0.103729	−	0.0598880i
$55$	3.61923	−	6.26869i	0.488017	−	0.845271i
$56$		0			0
$57$			0.344066i			0.0455726i
$58$		−	1.28125i		−	0.168236i
$59$	6.57216	+	3.79444i	0.855623	+	0.493994i	0.862544	−	0.505982i	$-0.168870\pi$
$59$	6.57216	+	3.79444i	0.855623	+	0.493994i	−0.00692130	+	0.999976i	$0.502203\pi$
$60$	8.35825	−	4.82564i	1.07905	−	0.622987i
$61$	0.411564			0.0526954			0.0263477	−	0.999653i	$-0.491612\pi$
$61$	0.411564			0.0526954			0.0263477	+	0.999653i	$0.491612\pi$
$62$	0.334461	−	0.579304i	0.0424766	−	0.0735716i
$63$		0			0
$64$	7.22592			0.903240
$65$	8.56910	−	4.51719i	1.06287	−	0.560289i
$66$	−0.444801	−	0.770418i	−0.0547512	−	0.0948319i
$67$		−	11.4010i		−	1.39286i	−0.717626	−	0.696429i	$-0.754771\pi$
$67$		−	11.4010i		−	1.39286i	0.717626	−	0.696429i	$-0.245229\pi$
$68$	−4.68703	−	8.11818i	−0.568386	−	0.984474i
$69$	4.01658	+	6.95692i	0.483539	+	0.837514i
$70$		0			0
$71$	2.89675	−	1.67244i	0.343781	−	0.198482i	−0.318162	−	0.948037i	$-0.603065\pi$
$71$	2.89675	−	1.67244i	0.343781	−	0.198482i	0.661943	+	0.749554i	$0.269732\pi$
$72$		−	0.239838i		−	0.0282651i
$73$	12.3112	−	7.10790i	1.44092	−	0.831917i	0.443011	−	0.896516i	$-0.353910\pi$
$73$	12.3112	−	7.10790i	1.44092	−	0.831917i	0.997911	+	0.0645994i	$0.0205769\pi$
$74$	−0.719148	+	1.24560i	−0.0835993	+	0.144798i
$75$	2.02509	+	3.50756i	0.233837	+	0.405018i
$76$	−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	$0.995382\pi$
$80$			10.2224i			1.14290i
$81$	−9.89120			−1.09902
$82$	0.981797			0.108421
$83$			16.5866i			1.82061i	0.413934	+	0.910307i	$0.364155\pi$
$83$			16.5866i			1.82061i	−0.413934	+	0.910307i	$0.635845\pi$
$84$		0			0
$85$	11.0866	−	6.40083i	1.20251	−	0.694268i
$86$	1.25445	+	0.724258i	0.135271	+	0.0780988i
$87$	−6.46920	+	11.2050i	−0.693571	+	1.20130i
$88$	1.93280			0.206037
$89$	5.10232	−	2.94582i	0.540844	−	0.312257i	−0.204577	−	0.978851i	$-0.565582\pi$
$89$	5.10232	−	2.94582i	0.540844	−	0.312257i	0.745421	+	0.666594i	$0.232248\pi$
$90$	0.162417			0.0171203
$91$		0			0
$92$	−8.65473			−0.902318
$93$	−5.84998	+	3.37749i	−0.606615	+	0.350229i
$94$	0.334323			0.0344828
$95$	0.253115	−	0.438407i	0.0259690	−	0.0449796i
$96$	3.35691	+	1.93811i	0.342613	+	0.197808i
$97$	−0.390659	+	0.225547i	−0.0396654	+	0.0229008i	−0.519702	−	0.854348i	$-0.673957\pi$
$97$	−0.390659	+	0.225547i	−0.0396654	+	0.0229008i	0.480036	+	0.877249i	$0.340624\pi$
$98$		0			0
$99$			0.900747i			0.0905285i
$100$	−4.36356			−0.436356
$101$	−7.65680			−0.761880			−0.380940	−	0.924600i	$-0.624400\pi$
$101$	−7.65680			−0.761880			−0.380940	+	0.924600i	$0.624400\pi$
$102$		−	1.57332i		−	0.155782i
$103$	−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
$107$	−4.01644	−	6.95669i	−0.388284	−	0.672528i	0.603935	−	0.797034i	$-0.293599\pi$
$107$	−4.01644	−	6.95669i	−0.388284	−	0.672528i	−0.992219	+	0.124506i	$0.960265\pi$
$108$	4.78798	−	8.29303i	0.460724	−	0.797997i
$109$	−1.15490	+	0.666781i	−0.110619	+	0.0638660i	−0.554289	−	0.832324i	$-0.687010\pi$
$109$	−1.15490	+	0.666781i	−0.110619	+	0.0638660i	0.443670	+	0.896190i	$0.353676\pi$
$110$			1.30889i			0.124797i
$111$	12.5785	−	7.26217i	1.19389	−	0.689295i
$112$		0			0
$113$	9.96917	+	17.2671i	0.937821	+	1.62435i	0.769525	+	0.638617i	$0.220493\pi$
$113$	9.96917	+	17.2671i	0.937821	+	1.62435i	0.168296	+	0.985736i	$0.446173\pi$
$114$	−0.0311076	−	0.0538800i	−0.00291349	−	0.00504632i
$115$		−	11.8193i		−	1.10216i
$116$	−6.96976	−	12.0720i	−0.647126	−	1.12086i
$117$	−0.642412	+	1.01997i	−0.0593910	+	0.0942964i
$118$	−1.37225			−0.126326
$119$		0			0
$120$	−1.75968	+	3.04786i	−0.160636	+	0.278230i
$121$	3.74106			0.340096
$122$	−0.0644501	+	0.0372103i	−0.00583503	+	0.00336886i
$123$	−8.58619	−	4.95724i	−0.774191	−	0.446979i
$124$		−	7.27765i		−	0.653553i
$125$			7.47412i			0.668505i
$126$		0			0
$127$	−3.98361	+	6.89981i	−0.353488	+	0.612259i	−0.986858	−	0.161590i	$-0.948338\pi$
$127$	−3.98361	+	6.89981i	−0.353488	+	0.612259i	0.633370	+	0.773849i	$0.281671\pi$
$128$	−4.80833	+	2.77609i	−0.425000	+	0.245374i
$129$	−7.31378	−	12.6678i	−0.643942	−	1.11534i
$130$	−0.933496	+	1.48213i	−0.0818730	+	0.129992i
$131$	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
$136$	2.96032	+	1.70914i	0.253845	+	0.146558i
$137$	4.38811	+	2.53348i	0.374902	+	0.216450i	0.675598	−	0.737270i	$-0.263886\pi$
$137$	4.38811	+	2.53348i	0.374902	+	0.216450i	−0.300696	+	0.953720i	$0.597219\pi$
$138$	−1.25798	−	0.726293i	−0.107086	−	0.0618261i
$139$	3.86289	+	6.69073i	0.327646	+	0.567500i	0.982044	−	0.188650i	$-0.0604113\pi$
$139$	3.86289	+	6.69073i	0.327646	+	0.567500i	−0.654398	+	0.756150i	$0.727078\pi$
$140$		0			0
$141$	−2.92378	−	1.68805i	−0.246227	−	0.142159i
$142$	−0.302417	+	0.523802i	−0.0253783	+	0.0439565i
$143$	−8.21974	−	5.17707i	−0.687370	−	0.432928i
$144$	−0.636031	−	1.10164i	−0.0530025	−	0.0918031i
$145$	16.4861	−	9.51824i	1.36909	−	0.790447i
$146$	−1.28528	+	2.22617i	−0.106370	+	0.184239i
$147$		0			0
$148$			15.6482i			1.28627i
$149$		−	14.3185i		−	1.17301i	−0.809944	−	0.586507i	$-0.800502\pi$
$149$		−	14.3185i		−	1.17301i	0.809944	−	0.586507i	$-0.199498\pi$
$150$	−0.634250	−	0.366184i	−0.0517863	−	0.0298988i
$151$	−5.60534	+	3.23624i	−0.456156	+	0.263362i	−0.710427	−	0.703771i	$-0.751498\pi$
$151$	−5.60534	+	3.23624i	−0.456156	+	0.263362i	0.254271	+	0.967133i	$0.418165\pi$
$152$	0.135172			0.0109639
$153$	−0.796513	+	1.37960i	−0.0643943	+	0.111534i
$154$		0			0
$155$	9.93871			0.798296
$156$	−6.03996	−	11.4578i	−0.483584	−	0.917357i
$157$	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	$0.614240\pi$
$158$		−	1.64741i		−	0.131061i
$159$	6.45718	+	11.1842i	0.512088	+	0.886962i
$160$	−2.85157	−	4.93907i	−0.225437	−	0.390468i
$161$		0			0
$162$	1.54894	−	0.894282i	0.121696	−	0.0702614i
$163$			4.78162i			0.374525i	0.982310	+	0.187263i	$0.0599616\pi$
$163$			4.78162i			0.374525i	−0.982310	+	0.187263i	$0.940038\pi$
$164$	9.25056	−	5.34081i	0.722348	−	0.417048i
$165$	6.60876	−	11.4467i	0.514492	−	0.891126i
$166$	−1.49962	−	2.59743i	−0.116393	−	0.201599i
$167$	2.34729	+	1.35521i	0.181639	+	0.104869i	0.588062	−	0.808816i	$-0.299891\pi$
$167$	2.34729	+	1.35521i	0.181639	+	0.104869i	−0.406424	+	0.913685i	$0.633224\pi$
$168$		0			0
$169$	−5.61544	−	11.7246i	−0.431957	−	0.901894i
$170$	−1.15742	+	2.00472i	−0.0887703	+	0.153755i
$171$			0.0629946i			0.00481732i
$172$	15.7594			1.20164
$173$	−0.899816			−0.0684118			−0.0342059	−	0.999415i	$-0.510890\pi$
$173$	−0.899816			−0.0684118			−0.0342059	+	0.999415i	$0.510890\pi$
$174$		−	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
$178$	−0.532675	+	0.922620i	−0.0399257	+	0.0691533i
$179$	11.0558			0.826351			0.413175	−	0.910651i	$-0.364420\pi$
$179$	11.0558			0.826351			0.413175	+	0.910651i	$0.364420\pi$
$180$	1.53030	−	0.883522i	0.114062	−	0.0658538i
$181$	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
$184$	2.73315	−	1.57799i	0.201491	−	0.116331i
$185$	−21.3699			−1.57115
$186$	0.610730	−	1.05782i	0.0447809	−	0.0775628i
$187$	−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
$191$	−20.4004			−1.47612			−0.738059	−	0.674736i	$-0.764258\pi$
$191$	−20.4004			−1.47612			−0.738059	+	0.674736i	$0.764258\pi$
$192$	13.1946			0.952240
$193$		−	17.2646i		−	1.24273i	−0.783521	−	0.621365i	$-0.786578\pi$
$193$		−	17.2646i		−	1.24273i	0.783521	−	0.621365i	$-0.213422\pi$
$194$	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	0.339224	−	0.940705i	$-0.389835\pi$
$197$	−4.29264	−	2.47836i	−0.305838	−	0.176576i	−0.645063	+	0.764130i	$0.723169\pi$
$198$	−0.0814383	−	0.141055i	−0.00578757	−	0.0100244i
$199$	−3.59097	+	6.21975i	−0.254557	+	0.440906i	−0.964775	−	0.263076i	$-0.915263\pi$
$199$	−3.59097	+	6.21975i	−0.254557	+	0.440906i	0.710218	+	0.703982i	$0.248596\pi$
$200$	1.37801	−	0.795593i	0.0974399	−	0.0562569i
$201$		−	20.8184i		−	1.46842i
$202$	1.19904	−	0.692265i	0.0843641	−	0.0487076i
$203$		0			0
$204$	−8.55858	−	14.8239i	−0.599221	−	1.03788i
$205$	7.29367	+	12.6330i	0.509412	+	0.882327i
$206$		−	0.932580i		−	0.0649759i
$207$	0.735392	+	1.27374i	0.0511132	+	0.0885307i
$208$	13.7086	+	0.527611i	0.950518	+	0.0365833i
$209$	−0.507661			−0.0351157
$210$		0			0
$211$	8.79636	−	15.2357i	0.605566	−	1.04887i	−0.386395	−	0.922333i	$-0.626280\pi$
$211$	8.79636	−	15.2357i	0.605566	−	1.04887i	0.991962	−	0.126539i	$-0.0403868\pi$
$212$	−13.9136			−0.955592
$213$	5.28951	−	3.05390i	0.362431	−	0.209250i
$214$	1.25793	+	0.726269i	0.0859906	+	0.0496467i
$215$			21.5218i			1.46777i
$216$			3.49190i			0.237594i
$217$		0			0
$218$	0.120570	−	0.208833i	0.00816602	−	0.0141440i
$219$	22.4805	−	12.9791i	1.51909	−	0.877048i
$220$	7.12013	+	12.3324i	0.480039	+	0.831452i
$221$	−8.01153	−	15.1979i	−0.538914	−	1.02232i
$222$	−1.31317	+	2.27448i	−0.0881344	+	0.152653i
$223$	−12.2157	−	7.05271i	−0.818020	−	0.472284i	0.0317129	−	0.999497i	$-0.489904\pi$
$223$	−12.2157	−	7.05271i	−0.818020	−	0.472284i	−0.849733	+	0.527213i	$0.823237\pi$
$224$		0			0
$225$	0.370772	+	0.642195i	0.0247181	+	0.0428130i
$226$	−3.12230	−	1.80266i	−0.207693	−	0.119911i
$227$	−2.48443	−	1.43439i	−0.164897	−	0.0952035i	0.415280	−	0.909694i	$-0.363684\pi$
$227$	−2.48443	−	1.43439i	−0.164897	−	0.0952035i	−0.580178	+	0.814490i	$0.697017\pi$
$228$	−0.586196	−	0.338441i	−0.0388218	−	0.0224138i
$229$	7.59860	+	4.38706i	0.502130	+	0.289905i	0.729593	−	0.683882i	$-0.239710\pi$
$229$	7.59860	+	4.38706i	0.502130	+	0.289905i	−0.227463	+	0.973787i	$0.573043\pi$
$230$	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	$0.113162\pi$
$234$	0.00838290	−	0.217807i	0.000548007	−	0.0142385i
$235$	2.48365	+	4.30181i	0.162016	+	0.280619i
$236$	−12.9294	+	7.46481i	−0.841634	+	0.485918i
$237$	−8.31803	+	14.4072i	−0.540314	+	0.935851i
$238$		0			0
$239$		−	2.49797i		−	0.161580i	−0.996731	−	0.0807901i	$-0.974256\pi$
$239$		−	2.49797i		−	0.161580i	0.996731	−	0.0807901i	$-0.0257443\pi$
$240$			18.6662i			1.20490i
$241$	−6.91532	−	3.99256i	−0.445455	−	0.257183i	0.260454	−	0.965486i	$-0.416128\pi$
$241$	−6.91532	−	3.99256i	−0.445455	−	0.257183i	−0.705909	+	0.708303i	$0.749461\pi$
$242$	−0.585842	+	0.338236i	−0.0376593	+	0.0217426i
$243$	−3.45877			−0.221880
$244$	−0.404835	+	0.701195i	−0.0259169	+	0.0448894i
$245$		0			0
$246$	1.79277			0.114303
$247$	−0.574856	−	0.362063i	−0.0365772	−	0.0230375i
$248$	1.32691	+	2.29827i	0.0842588	+	0.145941i
$249$			30.2873i			1.91938i
$250$	−0.675749	−	1.17043i	−0.0427381	−	0.0740246i
$251$	−12.6285	−	21.8732i	−0.797105	−	1.38063i	−0.921494	−	0.388393i	$-0.873030\pi$
$251$	−12.6285	−	21.8732i	−0.797105	−	1.38063i	0.124389	−	0.992234i	$-0.460303\pi$
$252$		0			0
$253$	−10.2648	+	5.92637i	−0.645341	+	0.372588i
$254$		−	1.44066i		−	0.0903952i
$255$	20.2442	−	11.6880i	1.26774	−	0.731931i
$256$	−6.72394	+	11.6462i	−0.420246	+	0.727888i
$257$	1.68682	+	2.92165i	0.105221	+	0.182248i	0.913828	−	0.406101i	$-0.133112\pi$
$257$	1.68682	+	2.92165i	0.105221	+	0.182248i	−0.808608	+	0.588348i	$0.799778\pi$
$258$	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
$262$			1.81148i			0.111914i
$263$	−0.158935			−0.00980037			−0.00490019	−	0.999988i	$-0.501560\pi$
$263$	−0.158935			−0.00980037			−0.00490019	+	0.999988i	$0.501560\pi$
$264$	3.52932			0.217215
$265$		−	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
$269$	−11.6633	+	20.2014i	−0.711124	+	1.23170i	0.253311	+	0.967385i	$0.418480\pi$
$269$	−11.6633	+	20.2014i	−0.711124	+	1.23170i	−0.964435	+	0.264318i	$0.914853\pi$
$270$	−2.36470			−0.143911
$271$	−10.2373	+	5.91049i	−0.621870	+	0.359037i	−0.777597	−	0.628763i	$-0.783561\pi$
$271$	−10.2373	+	5.91049i	−0.621870	+	0.359037i	0.155727	+	0.987800i	$0.450228\pi$
$272$	18.1300			1.09929
$273$		0			0
$274$	−0.916226			−0.0553513
$275$	−5.17532	+	2.98797i	−0.312084	+	0.180182i
$276$	−15.8036			−0.951268
$277$	−13.6827	+	23.6991i	−0.822111	+	1.42394i	0.0819961	+	0.996633i	$0.473870\pi$
$277$	−13.6827	+	23.6991i	−0.822111	+	1.42394i	−0.904107	+	0.427306i	$0.859463\pi$
$278$	−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	$0.324140\pi$
$281$			28.5383i			1.70245i	−0.524801	+	0.851225i	$0.675860\pi$
$282$	0.610478			0.0363534
$283$	17.9721			1.06833			0.534165	−	0.845380i	$-0.320626\pi$
$283$	17.9721			1.06833			0.534165	+	0.845380i	$0.320626\pi$
$284$			6.58040i			0.390475i
$285$	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
$289$	−2.85229	−	4.94032i	−0.167782	−	0.290607i
$290$	−1.72112	+	2.98107i	−0.101068	+	0.175055i
$291$	−0.713347	+	0.411851i	−0.0418172	+	0.0241432i
$292$			27.9668i			1.63663i
$293$	−12.8943	+	7.44453i	−0.753293	+	0.434914i	−0.826882	−	0.562375i	$-0.809888\pi$
$293$	−12.8943	+	7.44453i	−0.753293	+	0.434914i	0.0735896	+	0.997289i	$0.476554\pi$
$294$		0			0
$295$	−10.1943	−	17.6570i	−0.593535	−	1.02803i
$296$	−2.85308	−	4.94168i	−0.165832	−	0.287229i
$297$		−	13.1144i		−	0.760974i
$298$	1.29456	+	2.24224i	0.0749918	+	0.129890i
$299$	−15.8501	−	0.610035i	−0.916636	−	0.0352792i
$300$	−7.96793			−0.460028
$301$		0			0
$302$	0.585190	−	1.01358i	0.0336739	−	0.0583249i
$303$	−13.9814			−0.803211
$304$	0.620883	−	0.358467i	0.0356101	−	0.0205595i
$305$	−0.957586	−	0.552862i	−0.0548312	−	0.0316568i
$306$		−	0.288057i		−	0.0164671i
$307$			23.5161i			1.34214i	0.741396	+	0.671068i	$0.234164\pi$
$307$			23.5161i			1.34214i	−0.741396	+	0.671068i	$0.765836\pi$
$308$		0			0
$309$	−4.70874	+	8.15577i	−0.267871	+	0.463966i
$310$	−1.55638	+	0.898577i	−0.0883965	+	0.0510358i
$311$	−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	$0.848057\pi$
$312$	3.99647	+	2.51711i	0.226255	+	0.142503i
$313$	−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	−0.121826	−	0.992551i	$-0.538875\pi$
$317$	−18.5579	−	10.7144i	−1.04231	−	0.601780i	−0.920488	+	0.390771i	$0.872208\pi$
$318$	−2.02236	−	1.16761i	−0.113409	−	0.0654764i
$319$	−16.5327	−	9.54517i	−0.925654	−	0.534427i
$320$	−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
$325$	−7.99136	−	0.307569i	−0.443281	−	0.0170609i
$326$	−0.432315	−	0.748792i	−0.0239437	−	0.0414717i
$327$	−2.10886	+	1.21755i	−0.116620	+	0.0673307i
$328$	−1.94754	+	3.37324i	−0.107535	+	0.186256i
$329$		0			0
$330$			2.39004i			0.131568i
$331$			1.52046i			0.0835722i	0.999127	+	0.0417861i	$0.0133048\pi$
$331$			1.52046i			0.0835722i	−0.999127	+	0.0417861i	$0.986695\pi$
$332$	−28.2591	−	16.3154i	−1.55092	−	0.895425i
$333$	2.30298	−	1.32962i	0.126202	−	0.0728630i
$334$	−0.490108			−0.0268175
$335$	−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	$0.841023\pi$
$338$	1.93941	+	1.32835i	0.105490	+	0.0722527i
$339$	18.2038	+	31.5300i	0.988697	+	1.71247i
$340$			25.1848i			1.36584i
$341$	−4.98341	−	8.63153i	−0.269867	−	0.467423i
$342$	−0.00569546	−	0.00986483i	−0.000307975	−	0.000533429i
$343$		0			0
$344$	−4.97679	+	2.87335i	−0.268331	+	0.154921i
$345$		−	21.5822i		−	1.16195i
$346$	0.140909	−	0.0813541i	0.00757534	−	0.00437362i
$347$	−4.09215	+	7.08782i	−0.219678	+	0.380494i	−0.954710	−	0.297539i	$-0.903834\pi$
$347$	−4.09215	+	7.08782i	−0.219678	+	0.380494i	0.735031	+	0.678033i	$0.237167\pi$
$348$	−12.7269	−	22.0436i	−0.682232	−	1.18166i
$349$	18.9220	+	10.9246i	1.01287	+	0.584782i	0.912031	−	0.410120i	$-0.134513\pi$
$349$	18.9220	+	10.9246i	1.01287	+	0.584782i	0.100841	+	0.994903i	$0.467847\pi$
$350$		0			0
$351$	9.35317	−	14.8502i	0.499235	−	0.792646i
$352$	−2.85964	+	4.95304i	−0.152419	+	0.263998i
$353$			0.567179i			0.0301879i	0.999886	+	0.0150940i	$0.00480474\pi$
$353$			0.567179i			0.0301879i	−0.999886	+	0.0150940i	$0.995195\pi$
$354$	−2.50575			−0.133179
$355$	−8.98650			−0.476954
$356$			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	0.999771	−	0.0214184i	$-0.00681822\pi$
$359$	28.0630	+	16.2022i	1.48111	+	0.855118i	0.481336	+	0.876536i	$0.340152\pi$
$360$	−0.322179	+	0.558030i	−0.0169803	+	0.0294108i
$361$	18.9645			0.998131
$362$	−0.552631	+	0.319061i	−0.0290456	+	0.0167695i
$363$	6.83122			0.358546
$364$		0			0
$365$	−38.1928			−1.99910
$366$	−0.117687	+	0.0679464i	−0.00615158	+	0.00355162i
$367$	7.86888			0.410752			0.205376	−	0.978683i	$-0.434158\pi$
$367$	7.86888			0.410752			0.205376	+	0.978683i	$0.434158\pi$
$368$	8.36939	−	14.4962i	0.436285	−	0.755667i
$369$	−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
$373$	−2.09163			−0.108300			−0.0541502	−	0.998533i	$-0.517245\pi$
$373$	−2.09163			−0.108300			−0.0541502	+	0.998533i	$0.517245\pi$
$374$	2.32139			0.120036
$375$			13.6478i			0.704771i
$376$	−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	0.783404	−	0.621513i	$-0.213482\pi$
$379$	12.3983	+	7.15817i	0.636859	+	0.367691i	−0.146545	+	0.989204i	$0.546815\pi$
$380$	0.497953	+	0.862480i	0.0255444	+	0.0442443i
$381$	−7.27412	+	12.5991i	−0.372665	+	0.645474i
$382$	3.19466	−	1.84444i	0.163453	−	0.0943695i
$383$			25.1873i			1.28701i	0.765441	+	0.643507i	$0.222521\pi$
$383$			25.1873i			1.28701i	−0.765441	+	0.643507i	$0.777479\pi$
$384$	−8.78006	+	5.06917i	−0.448056	+	0.258685i
$385$		0			0
$386$	1.56092	+	2.70359i	0.0794488	+	0.137609i
$387$	−1.33907	−	2.31934i	−0.0680689	−	0.117899i
$388$		−	0.887438i		−	0.0450528i
$389$	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	$0.580932\pi$
$390$	−1.70458	+	2.70639i	−0.0863146	+	0.137043i
$391$	−20.9623			−1.06011
$392$		0			0
$393$	9.14644	−	15.8421i	0.461377	−	0.799128i
$394$	0.896292			0.0451546
$395$	21.1976	−	12.2384i	1.06657	−	0.615783i
$396$	−1.53463	−	0.886021i	−0.0771183	−	0.0445243i
$397$		−	21.7765i		−	1.09293i	−0.837482	−	0.546465i	$-0.815973\pi$
$397$		−	21.7765i		−	1.09293i	0.837482	−	0.546465i	$-0.184027\pi$
$398$		−	1.29867i		−	0.0650963i
$399$		0			0
$400$	4.21970	−	7.30874i	0.210985	−	0.365437i
$401$	−17.7786	+	10.2645i	−0.887821	+	0.512584i	−0.873229	−	0.487310i	$-0.837978\pi$
$401$	−17.7786	+	10.2645i	−0.887821	+	0.512584i	−0.0145918	+	0.999894i	$0.504645\pi$
$402$	1.88223	+	3.26012i	0.0938772	+	0.162600i
$403$	0.512971	−	13.3282i	0.0255529	−	0.663923i
$404$	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
$409$	−5.42879	−	3.13431i	−0.268436	−	0.154982i	0.359741	−	0.933052i	$-0.382865\pi$
$409$	−5.42879	−	3.13431i	−0.268436	−	0.154982i	−0.628177	+	0.778071i	$0.716199\pi$
$410$	−2.28435	−	1.31887i	−0.112816	−	0.0651343i
$411$	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
$416$	−6.77065	+	3.56914i	−0.331958	+	0.174991i
$417$	7.05369	+	12.2174i	0.345421	+	0.598286i
$418$	0.0794987	−	0.0458986i	0.00388841	−	0.00224497i
$419$	17.0817	−	29.5864i	0.834497	−	1.44539i	−0.0599424	−	0.998202i	$-0.519092\pi$
$419$	17.0817	−	29.5864i	0.834497	−	1.44539i	0.894439	−	0.447189i	$-0.147575\pi$
$420$		0			0
$421$		−	11.5233i		−	0.561613i	−0.959764	−	0.280806i	$-0.909398\pi$
$421$		−	11.5233i		−	0.561613i	0.959764	−	0.280806i	$-0.0906019\pi$
$422$			3.18118i			0.154858i
$423$	−0.535313	−	0.309063i	−0.0260278	−	0.0150272i
$424$	4.39391	−	2.53682i	0.213387	−	0.123199i
$425$	−10.5688			−0.512664
$426$	−0.552218	+	0.956469i	−0.0267550	+	0.0463411i
$427$		0			0
$428$	15.8031			0.763873
$429$	−15.0094	−	9.45340i	−0.724659	−	0.456414i
$430$	−1.94582	−	3.37026i	−0.0938359	−	0.162529i
$431$		−	8.77001i		−	0.422436i	−0.977439	−	0.211218i	$-0.932257\pi$
$431$		−	8.77001i		−	0.422436i	0.977439	−	0.211218i	$-0.0677431\pi$
$432$	9.26026	+	16.0392i	0.445534	+	0.771688i
$433$	−11.0535	−	19.1452i	−0.531196	−	0.920058i	−0.999337	−	0.0364046i	$-0.988409\pi$
$433$	−11.0535	−	19.1452i	−0.531196	−	0.920058i	0.468141	−	0.883654i	$-0.344924\pi$
$434$		0			0
$435$	30.1038	−	17.3804i	1.44337	−	0.833328i
$436$		−	2.62352i		−	0.125644i
$437$	−0.717877	+	0.414467i	−0.0343407	+	0.0198266i
$438$	−2.34693	+	4.06501i	−0.112141	+	0.194234i
$439$	5.18547	+	8.98150i	0.247489	+	0.428664i	0.962828	−	0.270114i	$-0.0870612\pi$
$439$	5.18547	+	8.98150i	0.247489	+	0.428664i	−0.715339	+	0.698777i	$0.753728\pi$
$440$	−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	$0.842797\pi$
$444$			28.5738i			1.35605i
$445$	−15.8287			−0.750354
$446$	2.55059			0.120774
$447$		−	26.1457i		−	1.23665i
$448$		0			0
$449$	−19.7023	+	11.3751i	−0.929809	+	0.536825i	−0.886751	−	0.462247i	$-0.847043\pi$
$449$	−19.7023	+	11.3751i	−0.929809	+	0.536825i	−0.0430575	+	0.999073i	$0.513710\pi$
$450$	−0.116124	−	0.0670443i	−0.00547415	−	0.00316050i
$451$	7.31430	−	12.6687i	0.344417	−	0.596548i
$452$	−39.2248			−1.84498
$453$	−10.2354	+	5.90942i	−0.480902	+	0.277649i
$454$	0.518742			0.0243458
$455$		0			0
$456$	0.246827			0.0115587
$457$	−27.1215	+	15.6586i	−1.26869	+	0.732478i	−0.974740	−	0.223344i	$-0.928303\pi$
$457$	−27.1215	+	15.6586i	−1.26869	+	0.732478i	−0.293949	+	0.955821i	$0.594969\pi$
$458$	−1.58657			−0.0741354
$459$	11.5968	−	20.0862i	0.541292	−	0.937546i
$460$	20.1370	+	11.6261i	0.938891	+	0.542069i
$461$	7.28113	−	4.20376i	0.339116	−	0.195789i	−0.320765	−	0.947159i	$-0.603940\pi$
$461$	7.28113	−	4.20376i	0.339116	−	0.195789i	0.659881	+	0.751370i	$0.270607\pi$
$462$		0			0
$463$			10.0392i			0.466563i	0.972409	+	0.233281i	$0.0749463\pi$
$463$			10.0392i			0.466563i	−0.972409	+	0.233281i	$0.925054\pi$
$464$	26.9599			1.25158
$465$	18.1482			0.841603
$466$			0.923545i			0.0427824i
$467$	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
$471$	14.5339	+	25.1735i	0.669687	+	1.15993i
$472$	2.72206	−	4.71475i	0.125293	−	0.217014i
$473$	18.6911	−	10.7913i	0.859418	−	0.496185i
$474$		−	3.00819i		−	0.138171i
$475$	−0.361941	+	0.208967i	−0.0166070	+	0.00958806i
$476$		0			0
$477$	1.18224	+	2.04770i	0.0541310	+	0.0937577i
$478$	0.225846	+	0.391177i	0.0103300	+	0.0178920i
$479$			8.58414i			0.392220i	0.980582	+	0.196110i	$0.0628309\pi$
$479$			8.58414i			0.392220i	−0.980582	+	0.196110i	$0.937169\pi$
$480$	−5.20701	−	9.01880i	−0.237666	−	0.411650i
$481$	−1.10297	+	28.6578i	−0.0502913	+	1.30668i
$482$	1.44390			0.0657678
$483$		0			0
$484$	−3.67990	+	6.37377i	−0.167268	+	0.289717i
$485$	1.21193			0.0550308
$486$	0.541637	−	0.312714i	0.0245691	−	0.0141850i
$487$	18.4084	+	10.6281i	0.834166	+	0.481606i	0.855277	−	0.518171i	$-0.173387\pi$
$487$	18.4084	+	10.6281i	0.834166	+	0.481606i	−0.0211110	+	0.999777i	$0.506720\pi$
$488$		−	0.295249i		−	0.0133653i
$489$			8.73130i			0.394843i
$490$		0			0
$491$	−11.2268	+	19.4453i	−0.506657	+	0.877556i	0.493313	+	0.869852i	$0.335786\pi$
$491$	−11.2268	+	19.4453i	−0.506657	+	0.877556i	−0.999970	+	0.00770409i	$0.997548\pi$
$492$	16.8916	−	9.75240i	0.761534	−	0.439672i
$493$	−16.8812	−	29.2391i	−0.760292	−	1.31686i
$494$	0.122756	+	0.00472460i	0.00552306	+	0.000212570i
$495$	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	$0.00268365\pi$
$499$	33.6694	+	19.4390i	1.50725	+	0.870210i	0.507284	+	0.861779i	$0.330650\pi$
$500$	−12.7339	−	7.35193i	−0.569478	−	0.328788i
$501$	4.28619	+	2.47463i	0.191493	+	0.110558i
$502$	3.95520	+	2.28354i	0.176529	+	0.101919i
$503$	2.72850	+	4.72591i	0.121658	+	0.210718i	0.920422	−	0.390927i	$-0.127846\pi$
$503$	2.72850	+	4.72591i	0.121658	+	0.210718i	−0.798764	+	0.601645i	$0.794512\pi$
$504$		0			0
$505$	17.8151	+	10.2855i	0.792760	+	0.457700i
$506$	1.07163	−	1.85612i	0.0476397	−	0.0825144i
$507$	−10.2539	−	21.4093i	−0.455390	−	0.950821i
$508$	−7.83697	−	13.5740i	−0.347709	−	0.602250i
$509$	−9.43315	+	5.44623i	−0.418117	+	0.241400i	−0.694271	−	0.719713i	$-0.744273\pi$
$509$	−9.43315	+	5.44623i	−0.418117	+	0.241400i	0.276154	+	0.961113i	$0.410940\pi$
$510$	−2.11347	+	3.66064i	−0.0935860	+	0.162096i
$511$		0			0
$512$		−	13.5360i		−	0.598214i
$513$		−	0.917168i		−	0.0404939i
$514$	−0.528304	−	0.305017i	−0.0233025	−	0.0134537i
$515$	11.9997	−	6.92804i	0.528771	−	0.305286i
$516$	28.7768			1.26683
$517$	2.49068	−	4.31398i	0.109540	−	0.189729i
$518$		0			0
$519$	−1.64308			−0.0721230
$520$	−3.24056	−	6.14733i	−0.142108	−	0.269578i
$521$	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	$0.624071\pi$
$522$		−	0.428350i		−	0.0187484i
$523$	8.36180	+	14.4831i	0.365636	+	0.633300i	0.988878	−	0.148729i	$-0.0475182\pi$
$523$	8.36180	+	14.4831i	0.365636	+	0.633300i	−0.623242	+	0.782029i	$0.714185\pi$
$524$	9.85416	+	17.0679i	0.430481	+	0.745615i
$525$		0			0
$526$	0.0248890	−	0.0143696i	0.00108521	−	0.000626546i
$527$		−	17.6269i		−	0.767842i
$528$	16.2111	−	9.35949i	0.705498	−	0.407319i
$529$	1.82314	−	3.15777i	0.0792668	−	0.137294i
$530$	1.71793	+	2.97554i	0.0746219	+	0.129249i
$531$	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
$535$			21.5815i			0.933049i
$536$	−8.17890			−0.353275
$537$	20.1881			0.871179
$538$		−	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	0.277626	−	0.960689i	$-0.410453\pi$
$541$	−9.66528	−	5.58025i	−0.415543	−	0.239914i	−0.693169	+	0.720776i	$0.743786\pi$
$542$	1.06876	−	1.85114i	0.0459070	−	0.0795133i
$543$	6.44396			0.276537
$544$	−8.75976	+	5.05745i	−0.375572	+	0.216836i
$545$	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	$0.213361\pi$
$548$	−8.63275	+	4.98412i	−0.368773	+	0.212911i
$549$	0.137595			0.00587242
$550$	0.540297	−	0.935821i	0.0230383	−	0.0399036i
$551$	−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
$555$	−39.0217			−1.65638
$556$	−15.1990			−0.644579
$557$		−	33.0776i		−	1.40154i	−0.713386	−	0.700772i	$-0.752839\pi$
$557$		−	33.0776i		−	1.40154i	0.713386	−	0.700772i	$-0.247161\pi$
$558$	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
$562$	−2.58020	−	4.46903i	−0.108839	−	0.188515i
$563$	−8.89836	+	15.4124i	−0.375021	+	0.649556i	−0.990330	−	0.138730i	$-0.955698\pi$
$563$	−8.89836	+	15.4124i	−0.375021	+	0.649556i	0.615309	+	0.788286i	$0.289031\pi$
$564$	5.75197	−	3.32090i	0.242202	−	0.139835i
$565$		−	53.5672i		−	2.25359i
$566$	−2.81439	+	1.62489i	−0.118298	+	0.0682992i
$567$		0			0
$568$	−1.19978	−	2.07808i	−0.0503417	−	0.0871943i
$569$	−4.11047	−	7.11954i	−0.172320	−	0.298467i	0.766911	−	0.641754i	$-0.221793\pi$
$569$	−4.11047	−	7.11954i	−0.172320	−	0.298467i	−0.939231	+	0.343287i	$0.888460\pi$
$570$			0.167150i			0.00700114i
$571$	−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	$-0.347831\pi$
$572$	16.9057	−	8.91183i	0.706863	−	0.372622i
$573$	−37.2513			−1.55620
$574$		0			0
$575$	−4.87891	+	8.45051i	−0.203464	+	0.352411i
$576$	2.41579			0.100658
$577$	−0.666314	+	0.384697i	−0.0277390	+	0.0160151i	−0.513805	−	0.857907i	$-0.671765\pi$
$577$	−0.666314	+	0.384697i	−0.0277390	+	0.0160151i	0.486066	+	0.873922i	$0.338431\pi$
$578$	0.893326	+	0.515762i	0.0371575	+	0.0214529i
$579$		−	31.5253i		−	1.31015i
$580$			37.4505i			1.55505i
$581$		0			0
$582$	0.0744725	−	0.128990i	0.00308698	−	0.00534681i
$583$	−16.5020	+	9.52743i	−0.683443	+	0.394586i
$584$	−5.09908	−	8.83187i	−0.211002	−	0.365465i
$585$	2.86485	−	1.51020i	0.118447	−	0.0624392i
$586$	1.34615	−	2.33159i	0.0556088	−	0.0963173i
$587$	10.4727	+	6.04644i	0.432256	+	0.249563i	0.700307	−	0.713841i	$-0.253046\pi$
$587$	10.4727	+	6.04644i	0.432256	+	0.249563i	−0.268051	+	0.963405i	$0.586380\pi$
$588$		0			0
$589$	−0.348520	−	0.603654i	−0.0143605	−	0.0248731i
$590$	3.19281	+	1.84337i	0.131446	+	0.0758904i
$591$	−7.83842	−	4.52552i	−0.322430	−	0.186155i
$592$	−26.2099	−	15.1323i	−1.07722	−	0.621933i
$593$	−13.8115	−	7.97406i	−0.567170	−	0.327456i	0.188848	−	0.982006i	$-0.439525\pi$
$593$	−13.8115	−	7.97406i	−0.567170	−	0.327456i	−0.756018	+	0.654551i	$0.772858\pi$
$594$	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
$598$	2.53725	−	1.33751i	0.103756	−	0.0546948i
$599$	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	$0.786932\pi$
$600$	2.51626	−	1.45276i	0.102726	−	0.0593088i
$601$	10.3953	−	18.0051i	0.424032	−	0.734445i	−0.572297	−	0.820046i	$-0.693948\pi$
$601$	10.3953	−	18.0051i	0.424032	−	0.734445i	0.996329	+	0.0856011i	$0.0272811\pi$
$602$		0			0
$603$		−	3.81163i		−	0.155221i
$604$		−	12.7333i		−	0.518112i
$605$	−8.70432	−	5.02544i	−0.353881	−	0.204313i
$606$	2.18946	−	1.26409i	0.0889408	−	0.0513500i
$607$	7.71405			0.313104			0.156552	−	0.987670i	$-0.449962\pi$
$607$	7.71405			0.313104			0.156552	+	0.987670i	$0.449962\pi$
$608$	−0.199992	+	0.346396i	−0.00811074	+	0.0140482i
$609$		0			0
$610$	0.199941			0.00809539
$611$	5.89707	−	3.10864i	0.238570	−	0.125762i
$612$	−1.56698	−	2.71409i	−0.0633415	−	0.109711i
$613$		−	20.4378i		−	0.825476i	−0.910850	−	0.412738i	$-0.864572\pi$
$613$		−	20.4378i		−	0.825476i	0.910850	−	0.412738i	$-0.135428\pi$
$614$	−2.12614	−	3.68257i	−0.0858038	−	0.148617i
$615$	13.3183	+	23.0680i	0.537047	+	0.930193i
$616$		0			0
$617$	−3.98209	+	2.29906i	−0.160313	+	0.0925567i	−0.578010	−	0.816030i	$-0.696171\pi$
$617$	−3.98209	+	2.29906i	−0.160313	+	0.0925567i	0.417697	+	0.908586i	$0.362837\pi$
$618$		−	1.70290i		−	0.0685008i
$619$	−8.70599	+	5.02641i	−0.349923	+	0.202028i	−0.664651	−	0.747154i	$-0.731420\pi$
$619$	−8.70599	+	5.02641i	−0.349923	+	0.202028i	0.314728	+	0.949182i	$0.398087\pi$
$620$	−9.77623	+	16.9329i	−0.392623	+	0.680042i
$621$	−10.7069	−	18.5449i	−0.429653	−	0.744181i
$622$	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
$626$		−	0.125986i		−	0.00503541i
$627$	−0.926996			−0.0370207
$628$	−31.3170			−1.24968
$629$			37.9009i			1.51121i
$630$		0			0
$631$	−6.29923	+	3.63686i	−0.250768	+	0.144781i	−0.620116	−	0.784510i	$-0.712914\pi$
$631$	−6.29923	+	3.63686i	−0.250768	+	0.144781i	0.369348	+	0.929291i	$0.379581\pi$
$632$	5.66015	+	3.26789i	0.225149	+	0.129990i
$633$	16.0623	−	27.8207i	0.638418	−	1.10577i
$634$	3.87483			0.153889
$635$	18.5373	−	10.7025i	0.735631	−	0.424717i
$636$	−25.4065			−1.00743
$637$		0			0
$638$	3.45199			0.136665
$639$	0.968451	−	0.559136i	0.0383113	−	0.0221191i
$640$	14.9167			0.589635
$641$	1.92516	−	3.33448i	0.0760394	−	0.131704i	−0.825498	−	0.564404i	$-0.809106\pi$
$641$	1.92516	−	3.33448i	0.0760394	−	0.131704i	0.901538	+	0.432700i	$0.142439\pi$
$642$	2.29700	+	1.32618i	0.0906555	+	0.0523400i
$643$	−2.49163	+	1.43855i	−0.0982605	+	0.0567307i	−0.548325	−	0.836265i	$-0.684734\pi$
$643$	−2.49163	+	1.43855i	−0.0982605	+	0.0567307i	0.450065	+	0.892996i	$0.351401\pi$
$644$		0			0
$645$			39.2990i			1.54740i
$646$	0.162349			0.00638754
$647$	37.1001			1.45856			0.729278	−	0.684218i	$-0.239856\pi$
$647$	37.1001			1.45856			0.729278	+	0.684218i	$0.239856\pi$
$648$			7.09577i			0.278748i
$649$	−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
$653$	−10.0475	−	17.4028i	−0.393189	−	0.681023i	0.599679	−	0.800240i	$-0.295295\pi$
$653$	−10.0475	−	17.4028i	−0.393189	−	0.681023i	−0.992868	+	0.119218i	$0.961961\pi$
$654$	0.220162	−	0.381332i	0.00860902	−	0.0149113i
$655$	−23.3087	+	13.4573i	−0.910748	+	0.525820i
$656$			20.6589i			0.806596i
$657$	4.11593	−	2.37634i	0.160578	−	0.0927097i
$658$		0			0
$659$	−4.95529	−	8.58281i	−0.193031	−	0.334339i	0.753223	−	0.657766i	$-0.228498\pi$
$659$	−4.95529	−	8.58281i	−0.193031	−	0.334339i	−0.946253	+	0.323427i	$0.895165\pi$
$660$	13.0014	+	22.5192i	0.506080	+	0.876557i
$661$		−	47.2266i		−	1.83690i	−0.395537	−	0.918450i	$-0.629442\pi$
$661$		−	47.2266i		−	1.83690i	0.395537	−	0.918450i	$-0.370558\pi$
$662$	−0.137468	−	0.238102i	−0.00534284	−	0.00925408i
$663$	−14.6292	−	27.7515i	−0.568150	−	1.07778i
$664$	11.8989			0.461768
$665$		0			0
$666$	−0.240428	+	0.416433i	−0.00931639	+	0.0161365i
$667$	−31.1716			−1.20697
$668$	−4.61783	+	2.66611i	−0.178669	+	0.103155i
$669$	−22.3059	−	12.8783i	−0.862397	−	0.497905i
$670$		−	5.53872i		−	0.213979i
$671$			1.10885i			0.0428068i
$672$		0			0
$673$	3.45845	−	5.99020i	0.133313	−	0.230905i	−0.791639	−	0.610990i	$-0.790772\pi$
$673$	3.45845	−	5.99020i	0.133313	−	0.230905i	0.924952	+	0.380084i	$0.124105\pi$
$674$	5.04721	−	2.91401i	0.194411	−	0.112243i
$675$	−5.39823	−	9.35001i	−0.207778	−	0.359882i
$676$	25.4993	+	1.96573i	0.980742	+	0.0756050i
$677$	−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
$682$	1.56078	+	0.901120i	0.0597655	+	0.0345057i
$683$	21.2491	+	12.2682i	0.813076	+	0.469430i	0.848023	−	0.529960i	$-0.177793\pi$
$683$	21.2491	+	12.2682i	0.813076	+	0.469430i	−0.0349470	+	0.999389i	$0.511126\pi$
$684$	−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
$689$	−25.4812	−	0.980713i	−0.970756	−	0.0373622i
$690$	1.95129	+	3.37973i	0.0742843	+	0.128664i
$691$	7.88703	−	4.55358i	0.300037	−	0.173226i	−0.342423	−	0.939546i	$-0.611247\pi$
$691$	7.88703	−	4.55358i	0.300037	−	0.173226i	0.642459	+	0.766320i	$0.277914\pi$
$692$	0.885106	−	1.53305i	0.0336467	−	0.0582777i
$693$		0			0
$694$		−	1.47992i		−	0.0561769i
$695$		−	20.7564i		−	0.787336i
$696$	8.03826	+	4.64089i	0.304690	+	0.175913i
$697$	22.4055	−	12.9358i	0.848667	−	0.489978i
$698$	−3.95087			−0.149542
$699$	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	$0.498275\pi$
$702$	−0.122050	+	3.17115i	−0.00460650	+	0.119687i
$703$	0.749377	+	1.29796i	0.0282633	+	0.0489534i
$704$			19.4684i			0.733742i
$705$	4.53518	+	7.85516i	0.170805	+	0.295842i
$706$	−0.0512797	−	0.0888191i	−0.00192994	−	0.00334275i
$707$		0			0
$708$	−23.6093	+	13.6308i	−0.887292	+	0.512278i
$709$		−	18.5848i		−	0.697967i	−0.937129	−	0.348984i	$-0.886527\pi$
$709$		−	18.5848i		−	0.697967i	0.937129	−	0.348984i	$-0.113473\pi$
$710$	1.40727	−	0.812486i	0.0528138	−	0.0304921i
$711$	−1.52294	+	2.63781i	−0.0571147	+	0.0989256i
$712$	−2.11328	−	3.66031i	−0.0791986	−	0.137176i
$713$	−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
$717$		−	4.56132i		−	0.170346i
$718$	−5.85947			−0.218674
$719$	41.6949			1.55496			0.777479	−	0.628909i	$-0.216498\pi$
$719$	41.6949			1.55496			0.777479	+	0.628909i	$0.216498\pi$
$720$			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
$724$	−3.47128	+	6.01244i	−0.129009	+	0.223451i
$725$	−15.7162			−0.583684
$726$	−1.06975	+	0.617623i	−0.0397023	+	0.0229221i
$727$	−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
$730$	5.98091	−	3.45308i	0.221363	−	0.127804i
$731$	38.1702			1.41178
$732$	−0.739235	+	1.28039i	−0.0273229	+	0.0473246i
$733$	8.60423	+	4.96765i	0.317804	+	0.183484i	0.650413	−	0.759580i	$-0.274596\pi$
$733$	8.60423	+	4.96765i	0.317804	+	0.183484i	−0.332609	+	0.943065i	$0.607929\pi$
$734$	−1.23225	+	0.711440i	−0.0454832	+	0.0262597i
$735$		0			0
$736$			9.33871i			0.344230i
$737$	30.7171			1.13148
$738$	0.328237			0.0120826
$739$		−	10.4022i		−	0.382649i	−0.981527	−	0.191325i	$-0.938722\pi$
$739$		−	10.4022i		−	0.382649i	0.981527	−	0.191325i	$-0.0612784\pi$
$740$	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	0.472612	−	0.881271i	$-0.343311\pi$
$743$	−1.47972	−	0.854317i	−0.0542857	−	0.0313419i	−0.526897	+	0.849929i	$0.676645\pi$
$744$	2.42295	+	4.19668i	0.0888297	+	0.153858i
$745$	−19.2343	+	33.3148i	−0.704690	+	1.22056i
$746$	0.327545	−	0.189108i	0.0119923	−	0.00692374i
$747$			5.54528i			0.202891i
$748$	21.8723	−	12.6280i	0.799732	−	0.461726i
$749$		0			0
$750$	−1.23393	−	2.13722i	−0.0450566	−	0.0780404i
$751$	14.9906	+	25.9645i	0.547015	+	0.947458i	0.998477	+	0.0551673i	$0.0175692\pi$
$751$	14.9906	+	25.9645i	0.547015	+	0.947458i	−0.451462	+	0.892290i	$0.649097\pi$
$752$			7.03481i			0.256533i
$753$	−23.0598	−	39.9408i	−0.840347	−	1.45552i
$754$	3.90890	+	2.46195i	0.142354	+	0.0896590i
$755$	17.3893			0.632860
$756$		0			0
$757$	−4.20229	+	7.27858i	−0.152735	+	0.264545i	−0.932232	−	0.361861i	$-0.882141\pi$
$757$	−4.20229	+	7.27858i	−0.152735	+	0.264545i	0.779497	+	0.626406i	$0.215475\pi$
$758$	−2.58874			−0.0940271
$759$	−18.7436	+	10.8216i	−0.680350	+	0.392800i
$760$	−0.314506	−	0.181580i	−0.0114083	−	0.00658660i
$761$			51.0590i			1.85089i	0.378885	+	0.925444i	$0.376308\pi$
$761$			51.0590i			1.85089i	−0.378885	+	0.925444i	$0.623692\pi$
$762$		−	2.63067i		−	0.0952990i
$763$		0			0
$764$	20.0668	−	34.7568i	0.725993	−	1.25746i
$765$	3.70650	−	2.13995i	0.134009	−	0.0773699i
$766$	−2.27723	−	3.94429i	−0.0822798	−	0.142513i
$767$	−24.2049	+	12.7596i	−0.873988	+	0.460722i
$768$	−12.2780	+	21.2661i	−0.443044	+	0.767375i
$769$	0.610062	+	0.352220i	0.0219994	+	0.0127014i	0.510959	−	0.859605i	$-0.329290\pi$
$769$	0.610062	+	0.352220i	0.0219994	+	0.0127014i	−0.488960	+	0.872306i	$0.662624\pi$
$770$		0			0
$771$	3.08015	+	5.33498i	0.110929	+	0.192134i
$772$	29.4142	+	16.9823i	1.05864	+	0.611206i
$773$	1.09571	+	0.632607i	0.0394099	+	0.0227533i	0.519575	−	0.854425i	$-0.326090\pi$
$773$	1.09571	+	0.632607i	0.0394099	+	0.0227533i	−0.480166	+	0.877178i	$0.659423\pi$
$774$	0.419392	+	0.242136i	0.0150747	+	0.00870341i
$775$	−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
$780$	−1.33831	+	34.7724i	−0.0479193	+	1.24505i
$781$	4.50596	+	7.80456i	0.161236	+	0.279269i
$782$	3.28265	−	1.89524i	0.117387	−	0.0677737i
$783$	17.2448	−	29.8689i	0.616279	−	1.06743i
$784$		0			0
$785$		−	42.7679i		−	1.52645i
$786$			3.30779i			0.117985i
$787$	−37.9292	−	21.8984i	−1.35203	−	0.780595i	−0.363497	−	0.931595i	$-0.618417\pi$
$787$	−37.9292	−	21.8984i	−1.35203	−	0.780595i	−0.988534	+	0.151000i	$0.951751\pi$
$788$	8.44493	−	4.87568i	0.300838	−	0.173689i
$789$	−0.290218			−0.0103320
$790$	−2.21300	+	3.83303i	−0.0787351	+	0.136373i
$791$		0			0
$792$	0.646180			0.0229610
$793$	−0.790833	+	1.25562i	−0.0280833	+	0.0445884i
$794$	1.96885	+	3.41015i	0.0698719	+	0.121022i
$795$		−	34.6963i		−	1.23055i
$796$	−7.06453	−	12.2361i	−0.250396	−	0.433698i
$797$	−6.84183	−	11.8504i	−0.242350	−	0.419763i	0.719033	−	0.694976i	$-0.244585\pi$
$797$	−6.84183	−	11.8504i	−0.242350	−	0.419763i	−0.961383	+	0.275213i	$0.911252\pi$
$798$		0			0
$799$	7.62954	−	4.40492i	0.269914	−	0.155835i
$800$			4.70842i			0.166468i
$801$	1.70582	−	0.984857i	0.0602722	−	0.0347982i
$802$	1.85606	−	3.21479i	0.0655398	−	0.113518i
$803$	19.1504	+	33.1695i	0.675803	+	1.17053i
$804$	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
$808$			5.49285i			0.193238i
$809$	9.11375			0.320422			0.160211	−	0.987083i	$-0.448782\pi$
$809$	9.11375			0.320422			0.160211	+	0.987083i	$0.448782\pi$
$810$	−4.80523			−0.168839
$811$		−	2.31899i		−	0.0814309i	−0.999171	−	0.0407154i	$-0.987036\pi$
$811$		−	2.31899i		−	0.0814309i	0.999171	−	0.0407154i	$-0.0129637\pi$
$812$		0			0
$813$	−18.6934	+	10.7926i	−0.655606	+	0.378514i
$814$	−3.35595	−	1.93756i	−0.117626	−	0.0679114i
$815$	6.42325	−	11.1254i	0.224997	−	0.389706i
$816$	33.1057			1.15893
$817$	1.30718	−	0.754702i	0.0457325	−	0.0264037i
$818$	1.13352			0.0396325
$819$		0			0
$820$	−28.6977			−1.00217
$821$	8.78557	−	5.07235i	0.306619	−	0.177026i	−0.338794	−	0.940861i	$-0.610019\pi$
$821$	8.78557	−	5.07235i	0.306619	−	0.177026i	0.645412	+	0.763834i	$0.276686\pi$
$822$	−1.67304			−0.0583540
$823$	−13.4089	+	23.2249i	−0.467405	+	0.809570i	−0.999306	−	0.0372366i	$-0.988144\pi$
$823$	−13.4089	+	23.2249i	−0.467405	+	0.809570i	0.531901	+	0.846806i	$0.321478\pi$
$824$	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	$-0.801401\pi$
$827$		−	33.6015i		−	1.16844i	0.811596	−	0.584219i	$-0.198599\pi$
$828$	−2.89348			−0.100555
$829$	11.8666			0.412142			0.206071	−	0.978537i	$-0.433932\pi$
$829$	11.8666			0.412142			0.206071	+	0.978537i	$0.433932\pi$
$830$			8.05791i			0.279694i
$831$	−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
$835$	−3.64096	−	6.30633i	−0.126001	−	0.218240i
$836$	0.499362	−	0.864920i	0.0172708	−	0.0299139i
$837$	15.5942	−	9.00330i	0.539013	−	0.311199i
$838$			6.17756i			0.213400i
$839$	29.9798	−	17.3088i	1.03502	−	0.597568i	0.116600	−	0.993179i	$-0.462801\pi$
$839$	29.9798	−	17.3088i	1.03502	−	0.597568i	0.918418	+	0.395611i	$0.129467\pi$
$840$		0			0
$841$	−10.6029	−	18.3648i	−0.365617	−	0.633267i
$842$	1.04185	+	1.80453i	0.0359044	+	0.0621882i
$843$			52.1112i			1.79481i
$844$	17.3051	+	29.9733i	0.595666	+	1.03172i
$845$	−2.68450	+	34.8230i	−0.0923494	+	1.19795i
$846$	0.111772			0.00384280
$847$		0			0
$848$	13.4549	−	23.3046i	0.462044	−	0.800283i
$849$	32.8173			1.12629
$850$	1.65506	−	0.955548i	0.0567680	−	0.0327750i
$851$	30.3044	+	17.4963i	1.03882	+	0.599764i
$852$			12.0159i			0.411658i
$853$		−	29.1897i		−	0.999436i	−0.866188	−	0.499718i	$-0.833437\pi$
$853$		−	29.1897i		−	0.999436i	0.866188	−	0.499718i	$-0.166563\pi$
$854$		0			0
$855$	0.0846220	−	0.146570i	0.00289401	−	0.00501258i
$856$	−4.99061	+	2.88133i	−0.170575	+	0.0984817i
$857$	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	$0.690981\pi$
$858$	3.20513	+	0.123358i	0.109421	+	0.00421139i
$859$	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	−0.136210	−	0.990680i	$-0.543492\pi$
$863$	−31.2061	−	18.0169i	−1.06227	−	0.613302i	−0.926059	+	0.377378i	$0.876826\pi$
$864$	−8.94843	−	5.16638i	−0.304432	−	0.175764i
$865$	2.09360	+	1.20874i	0.0711846	+	0.0410985i
$866$	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
$871$	34.7829	+	21.9074i	1.17857	+	0.742305i
$872$	0.478337	+	0.828504i	0.0161985	+	0.0280567i
$873$	−0.130606	+	0.0754055i	−0.00442035	+	0.00255209i
$874$	0.0749454	−	0.129809i	0.00253507	−	0.00439086i
$875$		0			0
$876$			51.0677i			1.72542i
$877$		−	9.12168i		−	0.308017i	−0.988070	−	0.154009i	$-0.950782\pi$
$877$		−	9.12168i		−	0.308017i	0.988070	−	0.154009i	$-0.0492184\pi$
$878$	−1.62407	−	0.937657i	−0.0548097	−	0.0316444i
$879$	−23.5452	+	13.5938i	−0.794158	+	0.458507i
$880$	−27.5415			−0.928425
$881$	−6.51653	+	11.2870i	−0.219548	+	0.380268i	−0.954670	−	0.297667i	$-0.903791\pi$
$881$	−6.51653	+	11.2870i	−0.219548	+	0.380268i	0.735122	+	0.677935i	$0.237125\pi$
$882$		0			0
$883$	−2.13222			−0.0717548			−0.0358774	−	0.999356i	$-0.511423\pi$
$883$	−2.13222			−0.0717548			−0.0358774	+	0.999356i	$0.511423\pi$
$884$	33.7737	+	1.29987i	1.13593	+	0.0437194i
$885$	−18.6149	−	32.2420i	−0.625734	−	1.08380i
$886$		−	6.47597i		−	0.217564i
$887$	−23.5857	−	40.8517i	−0.791932	−	1.37167i	−0.924769	−	0.380528i	$-0.875742\pi$
$887$	−23.5857	−	40.8517i	−0.791932	−	1.37167i	0.132838	−	0.991138i	$-0.457591\pi$
$888$	−5.20976	−	9.02356i	−0.174828	−	0.302811i
$889$		0			0
$890$	2.47875	−	1.43111i	0.0830878	−	0.0479708i
$891$		−	26.6493i		−	0.892785i
$892$	24.0319	−	13.8748i	0.804647	−	0.464563i
$893$	0.174188	−	0.301702i	0.00582898	−	0.0100961i
$894$	2.36388	+	4.09437i	0.0790601	+	0.136936i
$895$	−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
$899$		−	26.2118i		−	0.874213i
$900$	−1.45884			−0.0486280
$901$	−33.6997			−1.12270
$902$			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
$906$	1.06856	−	1.85081i	0.0355007	−	0.0614889i
$907$	−16.0431			−0.532702			−0.266351	−	0.963876i	$-0.585818\pi$
$907$	−16.0431			−0.532702			−0.266351	+	0.963876i	$0.585818\pi$
$908$	4.88763	−	2.82187i	0.162202	−	0.0936471i
$909$	−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	$0.632636\pi$
$912$	1.13374	−	0.654565i	0.0375419	−	0.0216748i
$913$	−44.6883			−1.47897
$914$	2.83144	−	4.90420i	0.0936558	−	0.162217i
$915$	−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
$919$	15.9160			0.525020			0.262510	−	0.964929i	$-0.415450\pi$
$919$	15.9160			0.525020			0.262510	+	0.964929i	$0.415450\pi$
$920$	−8.47897			−0.279543
$921$			42.9407i			1.41494i
$922$	−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
$926$	−0.907665	−	1.57212i	−0.0298277	−	0.0516632i
$927$	−0.862118	+	1.49323i	−0.0283157	+	0.0490442i
$928$	−13.0260	+	7.52059i	−0.427601	+	0.246875i
$929$		−	47.3235i		−	1.55263i	−0.630342	−	0.776317i	$-0.717086\pi$
$929$		−	47.3235i		−	1.55263i	0.630342	−	0.776317i	$-0.282914\pi$
$930$	−2.84197	+	1.64081i	−0.0931920	+	0.0538044i
$931$		0			0
$932$	5.02393	+	8.70170i	0.164564	+	0.285034i
$933$	−1.48902	−	2.57906i	−0.0487484	−	0.0844347i
$934$			4.76494i			0.155914i
$935$	17.2454	+	29.8699i	0.563985	+	0.976850i
$936$	0.731710	+	0.460855i	0.0239167	+	0.0150635i
$937$	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
$940$	−9.77219			−0.318734
$941$	35.0068	−	20.2112i	1.14119	−	0.658866i	0.194465	−	0.980909i	$-0.437703\pi$
$941$	35.0068	−	20.2112i	1.14119	−	0.658866i	0.946725	+	0.322043i	$0.104370\pi$
$942$	−4.55196	−	2.62808i	−0.148311	−	0.0856273i
$943$		−	23.8863i		−	0.777844i
$944$		−	28.8748i		−	0.939795i
$945$		0			0
$946$	−1.95133	+	3.37980i	−0.0634431	+	0.109887i
$947$	39.7703	−	22.9614i	1.29236	−	0.746146i	0.313290	−	0.949658i	$-0.398569\pi$
$947$	39.7703	−	22.9614i	1.29236	−	0.746146i	0.979072	+	0.203512i	$0.0652356\pi$
$948$	−16.3641	−	28.3434i	−0.531481	−	0.920551i
$949$	−1.97126	+	51.2179i	−0.0639898	+	1.66260i
$950$	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	0.948743	−	0.316050i	$-0.102357\pi$
$953$	6.19465	+	10.7294i	0.200664	+	0.347561i	−0.748078	+	0.663610i	$0.769023\pi$
$954$	−0.370273	−	0.213777i	−0.0119880	−	0.00692129i
$955$	47.4655	+	27.4042i	1.53595	+	0.886780i
$956$	4.25587	+	2.45713i	0.137645	+	0.0794693i
$957$	−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
$962$	−2.41828	−	4.58748i	−0.0779686	−	0.147906i
$963$	−1.34279	−	2.32578i	−0.0432708	−	0.0749472i
$964$	13.6045	−	7.85457i	0.438172	−	0.252979i
$965$	−23.1918	+	40.1694i	−0.746572	+	1.29310i
$966$		0			0
$967$		−	9.44932i		−	0.303870i	−0.988391	−	0.151935i	$-0.951450\pi$
$967$		−	9.44932i		−	0.303870i	0.988391	−	0.151935i	$-0.0485504\pi$
$968$		−	2.68377i		−	0.0862596i
$969$	−1.41980	−	0.819725i	−0.0456107	−	0.0263333i
$970$	−0.189785	+	0.109573i	−0.00609364	+	0.00351816i
$971$	20.9763			0.673163			0.336581	−	0.941654i	$-0.390729\pi$
$971$	20.9763			0.673163			0.336581	+	0.941654i	$0.390729\pi$
$972$	3.40223	−	5.89283i	0.109126	−	0.189013i
$973$		0			0
$974$	−3.84363			−0.123158
$975$	−14.5923	−	0.561625i	−0.467328	−	0.0179864i
$976$	−0.782977	−	1.35616i	−0.0250625	−	0.0434095i
$977$		−	13.1843i		−	0.421802i	−0.977507	−	0.210901i	$-0.932360\pi$
$977$		−	13.1843i		−	0.421802i	0.977507	−	0.210901i	$-0.0676398\pi$
$978$	−0.789413	−	1.36730i	−0.0252426	−	0.0437215i
$979$	7.93676	+	13.7469i	0.253660	+	0.439352i
$980$		0			0
$981$	−0.386109	+	0.222920i	−0.0123275	+	0.00711729i
$982$		−	4.06013i		−	0.129564i
$983$	−20.2294	+	11.6794i	−0.645216	+	0.372516i	−0.786621	−	0.617436i	$-0.788171\pi$
$983$	−20.2294	+	11.6794i	−0.645216	+	0.372516i	0.141405	+	0.989952i	$0.454838\pi$
$984$	−3.55624	+	6.15959i	−0.113369	+	0.196360i
$985$	6.65846	+	11.5328i	0.212156	+	0.367465i
$986$	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
$990$			0.437591i			0.0139076i
$991$	39.4929			1.25453			0.627267	−	0.778804i	$-0.284173\pi$
$991$	39.4929			1.25453			0.627267	+	0.778804i	$0.284173\pi$
$992$	−7.85281			−0.249327
$993$			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
$997$	−25.7396	+	44.5822i	−0.815180	+	1.41193i	0.0940184	+	0.995570i	$0.470029\pi$
$997$	−25.7396	+	44.5822i	−0.815180	+	1.41193i	−0.909199	+	0.416363i	$0.863305\pi$
$998$	−7.03007			−0.222533
$999$	−33.5301	+	19.3586i	−1.06085	+	0.612479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.g.30.3		12
7.2	even	3		637.2.q.i.589.4		12
7.3	odd	6		91.2.k.b.4.3	✓	12
7.4	even	3		637.2.k.i.459.3		12
7.5	odd	6		637.2.q.g.589.4		12
7.6	odd	2		91.2.u.b.30.3	yes	12
13.10	even	6		637.2.k.i.569.4		12
21.17	even	6		819.2.bm.f.550.4		12
21.20	even	2		819.2.do.e.667.4		12
91.6	even	12		1183.2.e.j.170.7		24
91.10	odd	6		91.2.u.b.88.3	yes	12
91.19	even	12		8281.2.a.cp.1.6		12
91.20	even	12		1183.2.e.j.170.6		24
91.23	even	6		637.2.q.i.491.4		12
91.33	even	12		8281.2.a.cp.1.7		12
91.45	even	12		1183.2.e.j.508.7		24
91.58	odd	12		8281.2.a.co.1.6		12
91.59	even	12		1183.2.e.j.508.6		24
91.62	odd	6		91.2.k.b.23.4	yes	12
91.72	odd	12		8281.2.a.co.1.7		12
91.75	odd	6		637.2.q.g.491.4		12
91.88	even	6	inner	637.2.u.g.361.3		12
273.62	even	6		819.2.bm.f.478.3		12
273.101	even	6		819.2.do.e.361.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.3	✓	12	7.3	odd	6
91.2.k.b.23.4	yes	12	91.62	odd	6
91.2.u.b.30.3	yes	12	7.6	odd	2
91.2.u.b.88.3	yes	12	91.10	odd	6
637.2.k.i.459.3		12	7.4	even	3
637.2.k.i.569.4		12	13.10	even	6
637.2.q.g.491.4		12	91.75	odd	6
637.2.q.g.589.4		12	7.5	odd	6
637.2.q.i.491.4		12	91.23	even	6
637.2.q.i.589.4		12	7.2	even	3
637.2.u.g.30.3		12	1.1	even	1	trivial
637.2.u.g.361.3		12	91.88	even	6	inner
819.2.bm.f.478.3		12	273.62	even	6
819.2.bm.f.550.4		12	21.17	even	6
819.2.do.e.361.4		12	273.101	even	6
819.2.do.e.667.4		12	21.20	even	2
1183.2.e.j.170.6		24	91.20	even	12
1183.2.e.j.170.7		24	91.6	even	12
1183.2.e.j.508.6		24	91.59	even	12
1183.2.e.j.508.7		24	91.45	even	12
8281.2.a.co.1.6		12	91.58	odd	12
8281.2.a.co.1.7		12	91.72	odd	12
8281.2.a.cp.1.6		12	91.19	even	12
8281.2.a.cp.1.7		12	91.33	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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.156598 + 0.0904119i) q^{2} +1.82601 q^{3} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.285950 + 0.165093i) q^{6} -0.717383i q^{8} +0.334323 q^{9} +O(q^{10})\)	\(q+(-0.156598 + 0.0904119i) q^{2} +1.82601 q^{3} +(-0.983651 + 1.70373i) q^{4} +(-2.32670 - 1.34332i) q^{5} +(-0.285950 + 0.165093i) q^{6} -0.717383i q^{8} +0.334323 q^{9} +0.485809 q^{10} +2.69424i q^{11} +(-1.79616 + 3.11104i) q^{12} +(-1.92153 + 3.05086i) q^{13} +(-4.24858 - 2.45292i) q^{15} +(-1.90244 - 3.29513i) q^{16} +(-2.38247 + 4.12655i) q^{17} +(-0.0523543 + 0.0302268i) q^{18} +0.188424i q^{19} +(4.57732 - 2.64272i) q^{20} +(-0.243592 - 0.421913i) q^{22} +(2.19964 + 3.80989i) q^{23} -1.30995i q^{24} +(1.10902 + 1.92088i) q^{25} +(0.0250743 - 0.651487i) q^{26} -4.86756 q^{27} +(-3.54280 + 6.13631i) q^{29} +0.887093 q^{30} +(-3.20369 + 1.84965i) q^{31} +(1.83838 + 1.06139i) q^{32} +4.91972i q^{33} -0.861613i q^{34} +(-0.328857 + 0.569598i) q^{36} +(6.88848 - 3.97707i) q^{37} +(-0.0170358 - 0.0295069i) q^{38} +(-3.50874 + 5.57090i) 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} +(-0.777869 - 0.449103i) q^{45} +(-0.688919 - 0.397748i) 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} +(-3.30773 - 6.27476i) q^{52} +(3.53622 + 6.12491i) q^{53} +(0.762250 - 0.440085i) q^{54} +(3.61923 - 6.26869i) q^{55} +0.344066i q^{57} -1.28125i q^{58} +(6.57216 + 3.79444i) q^{59} +(8.35825 - 4.82564i) q^{60} +0.411564 q^{61} +(0.334461 - 0.579304i) q^{62} +7.22592 q^{64} +(8.56910 - 4.51719i) q^{65} +(-0.444801 - 0.770418i) q^{66} -11.4010i q^{67} +(-4.68703 - 8.11818i) q^{68} +(4.01658 + 6.95692i) q^{69} +(2.89675 - 1.67244i) q^{71} -0.239838i q^{72} +(12.3112 - 7.10790i) q^{73} +(-0.719148 + 1.24560i) q^{74} +(2.02509 + 3.50756i) q^{75} +(-0.321025 - 0.185344i) q^{76} +(0.0457859 - 1.18962i) q^{78} +(-4.55529 + 7.89000i) q^{79} +10.2224i q^{80} -9.89120 q^{81} +0.981797 q^{82} +16.5866i q^{83} +(11.0866 - 6.40083i) q^{85} +(1.25445 + 0.724258i) q^{86} +(-6.46920 + 11.2050i) q^{87} +1.93280 q^{88} +(5.10232 - 2.94582i) q^{89} +0.162417 q^{90} -8.65473 q^{92} +(-5.84998 + 3.37749i) q^{93} +0.334323 q^{94} +(0.253115 - 0.438407i) q^{95} +(3.35691 + 1.93811i) q^{96} +(-0.390659 + 0.225547i) q^{97} +0.900747i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9	\( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97}+O(q^{100}) \) 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9 + 24 * q^10 + q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 - 3 * q^18 + 3 * q^20 - 15 * q^22 + 3 * q^23 - 5 * q^25 + 9 * q^26 - 12 * q^27 - q^29 - 22 * q^30 + 18 * q^31 + 18 * q^32 - 13 * q^36 + 15 * q^37 - 19 * q^38 - q^39 + q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 9 * q^45 - 30 * q^46 - 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 - 47 * q^52 - 8 * q^53 - 6 * q^54 + 15 * q^55 - 27 * q^59 + 30 * q^60 + 10 * q^61 - 41 * q^62 + 2 * q^64 - 3 * q^65 + 34 * q^66 + 11 * q^68 - 7 * q^69 + 30 * q^71 + 42 * q^73 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 - 28 * q^81 + 10 * q^82 - 21 * q^85 + 57 * q^86 - 10 * q^87 + 28 * q^88 - 48 * q^89 - 66 * q^92 - 81 * q^93 + 2 * q^94 + 2 * q^95 + 21 * q^96 + 3 * q^97

Introduction

L-functions

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