LMFDB - Embedded newform 91.2.u.b.30.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(30,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, 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("91.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.u (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.726638658394$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.3
Root			$0.655911 + 1.25291i$ of defining polynomial
Character	$\chi$	$=$	91.30
Dual form			91.2.u.b.88.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156598 + 0.0904119i) q^{2} -1.82601 q^{3} +(-0.983651 + 1.70373i) q^{4} +(2.32670 + 1.34332i) q^{5} +(0.285950 - 0.165093i) q^{6} +(-0.393717 + 2.61629i) q^{7} -0.717383i q^{8} +0.334323 q^{9} +O(q^{10})$	\(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} +(-0.393717 + 2.61629i) q^{7} -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} +(-0.174889 - 0.445303i) q^{14} +(-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} +(0.718933 - 4.77738i) q^{21} +(-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} +(-4.07019 - 3.24431i) q^{28} +(-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} +(-4.43058 + 5.55844i) q^{35} +(-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} +(0.319349 + 0.813129i) q^{42} +(-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} +(-6.68997 - 2.06016i) q^{49} +(-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} +(1.87688 + 0.282446i) q^{56} +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} +(-0.131629 + 0.874687i) q^{63} +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} +(0.191271 - 1.27102i) q^{70} +(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} +(-7.04893 - 1.06077i) q^{77} +(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} +(7.43221 + 5.92415i) q^{84} +(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} +(7.22539 + 6.22846i) q^{91} -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} +(1.23390 - 0.282236i) q^{98} +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} + 3 q^{7} + 2 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 4 * q^4 + 3 * q^5 - 9 * q^6 + 3 * q^7 + 2 * q^9	$ 12 q + 6 q^{3} + 4 q^{4} + 3 q^{5} - 9 q^{6} + 3 q^{7} + 2 q^{9} - 24 q^{10} - q^{12} - 2 q^{13} + 4 q^{14} - 12 q^{15} - 8 q^{16} + 17 q^{17} - 3 q^{18} - 3 q^{20} - 21 q^{21} - 15 q^{22} + 3 q^{23} - 5 q^{25} - 9 q^{26} + 12 q^{27} + 27 q^{28} - q^{29} - 22 q^{30} - 18 q^{31} + 18 q^{32} + 18 q^{35} - 13 q^{36} + 15 q^{37} + 19 q^{38} - q^{39} - q^{40} - 6 q^{41} - 8 q^{42} + 11 q^{43} + 33 q^{44} - 9 q^{45} - 30 q^{46} + 15 q^{47} + 19 q^{48} + 9 q^{49} + 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} - 54 q^{63} + 2 q^{64} - 3 q^{65} - 34 q^{66} - 11 q^{68} + 7 q^{69} - 3 q^{70} + 30 q^{71} - 42 q^{73} - 33 q^{74} + q^{75} - 45 q^{76} - 19 q^{77} + 44 q^{78} - 35 q^{79} - 28 q^{81} - 10 q^{82} + 3 q^{84} - 21 q^{85} + 57 q^{86} + 10 q^{87} + 28 q^{88} + 48 q^{89} - 16 q^{91} - 66 q^{92} - 81 q^{93} - 2 q^{94} + 2 q^{95} - 21 q^{96} - 3 q^{97} - 36 q^{98}+O(q^{100}) $ 12 * q + 6 * q^3 + 4 * q^4 + 3 * q^5 - 9 * q^6 + 3 * q^7 + 2 * q^9 - 24 * q^10 - q^12 - 2 * q^13 + 4 * q^14 - 12 * q^15 - 8 * q^16 + 17 * q^17 - 3 * q^18 - 3 * q^20 - 21 * q^21 - 15 * q^22 + 3 * q^23 - 5 * q^25 - 9 * q^26 + 12 * q^27 + 27 * q^28 - q^29 - 22 * q^30 - 18 * q^31 + 18 * q^32 + 18 * q^35 - 13 * q^36 + 15 * q^37 + 19 * q^38 - q^39 - q^40 - 6 * q^41 - 8 * q^42 + 11 * q^43 + 33 * q^44 - 9 * q^45 - 30 * q^46 + 15 * q^47 + 19 * q^48 + 9 * q^49 + 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 - 54 * q^63 + 2 * q^64 - 3 * q^65 - 34 * q^66 - 11 * q^68 + 7 * q^69 - 3 * q^70 + 30 * q^71 - 42 * q^73 - 33 * q^74 + q^75 - 45 * q^76 - 19 * q^77 + 44 * q^78 - 35 * q^79 - 28 * q^81 - 10 * q^82 + 3 * q^84 - 21 * q^85 + 57 * q^86 + 10 * q^87 + 28 * q^88 + 48 * q^89 - 16 * q^91 - 66 * q^92 - 81 * q^93 - 2 * q^94 + 2 * q^95 - 21 * q^96 - 3 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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	$-0.676730\pi$
$3$	−1.82601			−1.05425			−0.527125	+	0.849788i	$0.676730\pi$
$4$	−0.983651	+	1.70373i	−0.491826	+	0.851867i
$5$	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
$7$	−0.393717	+	2.61629i	−0.148811	+	0.988866i
$7$	−0.393717	+	2.61629i	−0.148811	+	0.988866i
$8$		−	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
$14$	−0.174889	−	0.445303i	−0.0467409	−	0.119012i
$15$	−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	$-0.637232\pi$
$17$	2.38247	−	4.12655i	0.577833	−	1.00084i	0.995727	−	0.0923405i	$-0.0294348\pi$
$18$	−0.0523543	+	0.0302268i	−0.0123400	+	0.00712452i
$19$		−	0.188424i		−	0.0432275i	−0.999766	−	0.0216138i	$-0.993120\pi$
$19$		−	0.188424i		−	0.0432275i	0.999766	−	0.0216138i	$-0.00688041\pi$
$20$	−4.57732	+	2.64272i	−1.02352	+	0.590930i
$21$	0.718933	−	4.77738i	0.156884	−	1.04251i
$22$	−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
$28$	−4.07019	−	3.24431i	−0.769193	−	0.613117i
$29$	−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	−0.183903	−	0.982944i	$-0.558873\pi$
$31$	3.20369	−	1.84965i	0.575400	−	0.332207i	0.759303	+	0.650737i	$0.225540\pi$
$32$	1.83838	+	1.06139i	0.324983	+	0.187629i
$33$		−	4.91972i		−	0.856414i
$34$			0.861613i			0.147765i
$35$	−4.43058	+	5.55844i	−0.748905	+	0.939548i
$36$	−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	0.820013	−	0.572345i	$-0.193966\pi$
$41$	4.70215	+	2.71479i	0.734353	+	0.423979i	−0.0856594	+	0.996324i	$0.527300\pi$
$42$	0.319349	+	0.813129i	0.0492766	+	0.125468i
$43$	−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	0.612212	−	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
$49$	−6.68997	−	2.06016i	−0.955710	−	0.294308i
$50$	−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
$56$	1.87688	+	0.282446i	0.250809	+	0.0377434i
$57$			0.344066i			0.0455726i
$58$		−	1.28125i		−	0.168236i
$59$	−6.57216	−	3.79444i	−0.855623	−	0.493994i	0.00692130	−	0.999976i	$-0.497797\pi$
$59$	−6.57216	−	3.79444i	−0.855623	−	0.493994i	−0.862544	+	0.505982i	$0.831130\pi$
$60$	8.35825	−	4.82564i	1.07905	−	0.622987i
$61$	−0.411564			−0.0526954			−0.0263477	−	0.999653i	$-0.508388\pi$
$61$	−0.411564			−0.0526954			−0.0263477	+	0.999653i	$0.508388\pi$
$62$	−0.334461	+	0.579304i	−0.0424766	+	0.0735716i
$63$	−0.131629	+	0.874687i	−0.0165837	+	0.110200i
$64$	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
$70$	0.191271	−	1.27102i	0.0228613	−	0.151916i
$71$	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	−0.997911	−	0.0645994i	$-0.979423\pi$
$73$	−12.3112	+	7.10790i	−1.44092	+	0.831917i	−0.443011	+	0.896516i	$0.646090\pi$
$74$	−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
$77$	−7.04893	−	1.06077i	−0.803300	−	0.120886i
$78$	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	$-0.635845\pi$
$83$		−	16.5866i		−	1.82061i	0.413934	−	0.910307i	$-0.364155\pi$
$84$	7.43221	+	5.92415i	0.810921	+	0.646378i
$85$	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	−0.745421	−	0.666594i	$-0.767752\pi$
$89$	−5.10232	+	2.94582i	−0.540844	+	0.312257i	0.204577	+	0.978851i	$0.434418\pi$
$90$	−0.162417			−0.0171203
$91$	7.22539	+	6.22846i	0.757427	+	0.652920i
$92$	−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	−0.480036	−	0.877249i	$-0.659376\pi$
$97$	0.390659	−	0.225547i	0.0396654	−	0.0229008i	0.519702	+	0.854348i	$0.326043\pi$
$98$	1.23390	−	0.282236i	0.124643	−	0.0285102i
$99$			0.900747i			0.0905285i
$100$	−4.36356			−0.436356
$101$	7.65680			0.761880			0.380940	−	0.924600i	$-0.375600\pi$
$101$	7.65680			0.761880			0.380940	+	0.924600i	$0.375600\pi$
$102$		−	1.57332i		−	0.155782i
$103$	2.57870	−	4.46644i	0.254087	−	0.440091i	−0.710560	−	0.703636i	$-0.751558\pi$
$103$	2.57870	−	4.46644i	0.254087	−	0.440091i	0.964647	+	0.263545i	$0.0848918\pi$
$104$	−2.18863	−	1.37847i	−0.214613	−	0.135170i
$105$	8.09030	−	10.1498i	0.789532	−	0.990517i
$106$	−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
$112$	9.37004	−	3.68000i	0.885386	−	0.347727i
$113$	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
$119$	9.85825	+	7.85792i	0.903704	+	0.720335i
$120$	−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
$126$	−0.0584693	−	0.148875i	−0.00520886	−	0.0132628i
$127$	−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	−0.997507	−	0.0705727i	$-0.977517\pi$
$131$	−5.00897	+	8.67579i	−0.437636	+	0.758007i	0.559871	+	0.828580i	$0.310851\pi$
$132$	8.38190	+	4.83929i	0.729551	+	0.421206i
$133$	0.492974	+	0.0741860i	0.0427462	+	0.00643274i
$134$	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	0.654398	−	0.756150i	$-0.272922\pi$
$139$	−3.86289	−	6.69073i	−0.327646	−	0.567500i	−0.982044	+	0.188650i	$0.939589\pi$
$140$	−5.11195	−	13.0161i	−0.432039	−	1.10006i
$141$	−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
$147$	12.2160	+	3.76188i	1.00756	+	0.310274i
$148$			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
$154$	1.19975	−	0.471192i	0.0966789	−	0.0379698i
$155$	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	$-0.947573\pi$
$157$	−7.95937	−	13.7860i	−0.635227	−	1.10025i	0.351240	−	0.936285i	$-0.385760\pi$
$158$		−	1.64741i		−	0.131061i
$159$	−6.45718	−	11.1842i	−0.512088	−	0.886962i
$160$	2.85157	+	4.93907i	0.225437	+	0.390468i
$161$	−10.8338	+	4.25489i	−0.853826	+	0.335332i
$162$	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	0.406424	−	0.913685i	$-0.366776\pi$
$167$	−2.34729	−	1.35521i	−0.181639	−	0.104869i	−0.588062	+	0.808816i	$0.700109\pi$
$168$	−3.42721	−	0.515750i	−0.264415	−	0.0397910i
$169$	−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	$-0.489110\pi$
$173$	0.899816			0.0684118			0.0342059	+	0.999415i	$0.489110\pi$
$174$			2.33957i			0.177362i
$175$	−5.46223	+	2.14524i	−0.412906	+	0.162165i
$176$	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	$-0.541868\pi$
$181$	−3.52898			−0.262307			−0.131153	+	0.991362i	$0.541868\pi$
$182$	−1.69461	−	0.322103i	−0.125613	−	0.0238759i
$183$	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
$189$	−1.91644	+	12.7350i	−0.139401	+	0.926332i
$190$			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
$196$	10.0906	−	9.37146i	0.720755	−	0.669390i
$197$	−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	−0.710218	−	0.703982i	$-0.751404\pi$
$199$	3.59097	−	6.21975i	0.254557	−	0.440906i	0.964775	+	0.263076i	$0.0847369\pi$
$200$	1.37801	−	0.795593i	0.0974399	−	0.0562569i
$201$			20.8184i			1.46842i
$202$	−1.19904	+	0.692265i	−0.0843641	+	0.0487076i
$203$	−14.6595	−	11.6850i	−1.02890	−	0.820125i
$204$	−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
$210$	−0.349264	+	2.32089i	−0.0241015	+	0.160157i
$211$	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
$217$	3.57788	+	9.11004i	0.242883	+	0.618430i
$218$	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	0.849733	−	0.527213i	$-0.176763\pi$
$223$	12.2157	+	7.05271i	0.818020	+	0.472284i	−0.0317129	+	0.999497i	$0.510096\pi$
$224$	−3.50071	+	4.39185i	−0.233901	+	0.293443i
$225$	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	0.580178	−	0.814490i	$-0.302983\pi$
$227$	2.48443	+	1.43439i	0.164897	+	0.0952035i	−0.415280	+	0.909694i	$0.636316\pi$
$228$	−0.586196	−	0.338441i	−0.0388218	−	0.0224138i
$229$	−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
$231$	12.8714	+	1.93698i	0.846878	+	0.127444i
$232$	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
$238$	−2.25423	−	0.339232i	−0.146120	−	0.0219891i
$239$		−	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	0.705909	−	0.708303i	$-0.250539\pi$
$241$	6.91532	+	3.99256i	0.445455	+	0.257183i	−0.260454	+	0.965486i	$0.583872\pi$
$242$	−0.585842	+	0.338236i	−0.0376593	+	0.0217426i
$243$	3.45877			0.221880
$244$	0.404835	−	0.701195i	0.0259169	−	0.0448894i
$245$	−12.7981	−	13.7802i	−0.817641	−	0.880382i
$246$	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	$0.126970\pi$
$251$	12.6285	+	21.8732i	0.797105	+	1.38063i	−0.124389	+	0.992234i	$0.539697\pi$
$252$	−1.36076	−	1.08465i	−0.0857196	−	0.0683264i
$253$	−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	0.808608	−	0.588348i	$-0.200222\pi$
$257$	−1.68682	−	2.92165i	−0.105221	−	0.182248i	−0.913828	+	0.406101i	$0.866888\pi$
$258$	−2.29065	−	1.32250i	−0.142609	−	0.0823355i
$259$	7.69305	+	19.5881i	0.478023	+	1.21715i
$260$	−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
$266$	−0.0839059	+	0.0329533i	−0.00514460	+	0.00202050i
$267$	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	$-0.581520\pi$
$269$	11.6633	−	20.2014i	0.711124	−	1.23170i	0.964435	−	0.264318i	$-0.0851470\pi$
$270$	−2.36470			−0.143911
$271$	10.2373	−	5.91049i	0.621870	−	0.359037i	−0.155727	−	0.987800i	$-0.549772\pi$
$271$	10.2373	−	5.91049i	0.621870	−	0.359037i	0.777597	+	0.628763i	$0.216439\pi$
$272$	−18.1300			−1.09929
$273$	−13.1937	−	11.3733i	−0.798516	−	0.688340i
$274$	−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
$280$	3.98753	+	3.17842i	0.238300	+	0.189947i
$281$			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	$-0.679374\pi$
$283$	−17.9721			−1.06833			−0.534165	+	0.845380i	$0.679374\pi$
$284$			6.58040i			0.390475i
$285$	−0.462190	+	0.800537i	−0.0273778	+	0.0474197i
$286$	−1.75526	−	0.0675561i	−0.103791	−	0.00399468i
$287$	−8.95400	+	11.2334i	−0.528538	+	0.663084i
$288$	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	−0.0735896	−	0.997289i	$-0.523446\pi$
$293$	12.8943	−	7.44453i	0.753293	−	0.434914i	0.826882	+	0.562375i	$0.190112\pi$
$294$	−2.25312	+	0.515367i	−0.131404	+	0.0300568i
$295$	−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
$301$	19.7273	−	7.74772i	1.13706	−	0.446571i
$302$	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	$-0.765836\pi$
$307$		−	23.5161i		−	1.34214i	0.741396	−	0.671068i	$-0.234164\pi$
$308$	8.74096	−	10.9661i	0.498062	−	0.624850i
$309$	−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	0.888219	−	0.459420i	$-0.151943\pi$
$311$	0.815450	+	1.41240i	0.0462399	+	0.0800899i	−0.841979	+	0.539510i	$0.818609\pi$
$312$	3.99647	+	2.51711i	0.226255	+	0.142503i
$313$	0.348367	−	0.603389i	0.0196909	−	0.0341056i	−0.856012	−	0.516956i	$-0.827065\pi$
$313$	0.348367	−	0.603389i	0.0196909	−	0.0341056i	0.875703	+	0.482850i	$0.160398\pi$
$314$	2.49284	+	1.43924i	0.140679	+	0.0812212i
$315$	−1.48125	+	1.85831i	−0.0834587	+	0.104704i
$316$	−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
$322$	1.31186	−	1.64581i	0.0731073	−	0.0917177i
$323$	−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
$329$	−3.04903	+	3.82520i	−0.168099	+	0.210890i
$330$			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
$336$	−17.1098	+	6.71972i	−0.933417	+	0.366591i
$337$	−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
$343$	8.02394	−	16.6918i	0.433252	−	0.901273i
$344$	−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	−0.100841	−	0.994903i	$-0.532153\pi$
$349$	−18.9220	−	10.9246i	−1.01287	−	0.584782i	−0.912031	+	0.410120i	$0.865487\pi$
$350$	0.661419	−	0.829791i	0.0353543	−	0.0443542i
$351$	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	$-0.995195\pi$
$353$		−	0.567179i		−	0.0301879i	0.999886	−	0.0150940i	$-0.00480474\pi$
$354$	−2.50575			−0.133179
$355$	8.98650			0.476954
$356$		−	11.5907i		−	0.614303i
$357$	−18.0013	−	14.3487i	−0.952730	−	0.759412i
$358$	−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
$364$	−17.7189	+	6.18351i	−0.928723	+	0.324104i
$365$	−38.1928			−1.99910
$366$	−0.117687	+	0.0679464i	−0.00615158	+	0.00355162i
$367$	−7.86888			−0.410752			−0.205376	−	0.978683i	$-0.565842\pi$
$367$	−7.86888			−0.410752			−0.205376	+	0.978683i	$0.565842\pi$
$368$	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
$371$	−17.4168	+	6.84030i	−0.904237	+	0.355131i
$372$		−	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
$378$	−0.851281	−	2.16754i	−0.0437852	−	0.111486i
$379$	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	$-0.777479\pi$
$383$		−	25.1873i		−	1.28701i	0.765441	−	0.643507i	$-0.222521\pi$
$384$	8.78006	−	5.06917i	0.448056	−	0.258685i
$385$	−14.9758	−	11.9371i	−0.763237	−	0.608369i
$386$	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
$392$	−1.47792	+	4.79927i	−0.0746463	+	0.242400i
$393$	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	$0.184027\pi$
$397$			21.7765i			1.09293i	−0.837482	+	0.546465i	$0.815973\pi$
$398$			1.29867i			0.0650963i
$399$	−0.900176	−	0.135465i	−0.0450652	−	0.00678171i
$400$	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
$406$	3.35211	+	0.504448i	0.166363	+	0.0250354i
$407$	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	0.628177	−	0.778071i	$-0.283801\pi$
$409$	5.42879	+	3.13431i	0.268436	+	0.154982i	−0.359741	+	0.933052i	$0.617135\pi$
$410$	−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
$413$	12.5149	−	15.7008i	0.615820	−	0.772584i
$414$	−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	$0.480908\pi$
$419$	−17.0817	+	29.5864i	−0.834497	+	1.44539i	−0.894439	+	0.447189i	$0.852425\pi$
$420$	9.33450	+	23.7676i	0.455477	+	1.15974i
$421$		−	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
$427$	0.162040	−	1.07677i	0.00784165	−	0.0521086i
$428$	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	$0.0115905\pi$
$433$	11.0535	+	19.1452i	0.531196	+	0.920058i	−0.468141	+	0.883654i	$0.655076\pi$
$434$	−1.38394	−	1.10313i	−0.0664315	−	0.0529519i
$435$	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	0.715339	−	0.698777i	$-0.246272\pi$
$439$	−5.18547	−	8.98150i	−0.247489	−	0.428664i	−0.962828	+	0.270114i	$0.912939\pi$
$440$	4.49705	+	2.59637i	0.214389	+	0.123777i
$441$	−2.23661	−	0.688759i	−0.106505	−	0.0327980i
$442$	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
$448$	−2.84497	+	18.9051i	−0.134412	+	0.893183i
$449$	−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
$455$	8.44449	+	24.1978i	0.395884	+	1.13441i
$456$	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	−0.659881	−	0.751370i	$-0.729393\pi$
$461$	−7.28113	+	4.20376i	−0.339116	+	0.195789i	0.320765	+	0.947159i	$0.396060\pi$
$462$	−2.19077	+	0.860403i	−0.101924	+	0.0400296i
$463$			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	$0.375375\pi$
$467$	−13.1756	+	22.8209i	−0.609696	+	1.05602i	−0.991290	+	0.131695i	$0.957958\pi$
$468$	1.10585	+	2.09780i	0.0511180	+	0.0969706i
$469$	29.8284	+	4.48878i	1.37735	+	0.207273i
$470$	−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
$476$	−23.0849	+	9.06638i	−1.05809	+	0.415557i
$477$	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	$-0.937169\pi$
$479$		−	8.58414i		−	0.392220i	0.980582	−	0.196110i	$-0.0628309\pi$
$480$	−5.20701	−	9.01880i	−0.237666	−	0.411650i
$481$	1.10297	−	28.6578i	0.0502913	−	1.30668i
$482$	−1.44390			−0.0657678
$483$	19.7827	−	7.76948i	0.900145	−	0.353524i
$484$	−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
$490$	3.25005	+	1.00084i	0.146822	+	0.0452135i
$491$	−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
$497$	3.23509	+	8.23722i	0.145114	+	0.369490i
$498$	−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	0.798764	−	0.601645i	$-0.205488\pi$
$503$	−2.72850	−	4.72591i	−0.121658	−	0.210718i	−0.920422	+	0.390927i	$0.872154\pi$
$504$	0.627485	+	0.0944282i	0.0279504	+	0.00420616i
$505$	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	−0.276154	−	0.961113i	$-0.589060\pi$
$509$	9.43315	−	5.44623i	0.418117	−	0.241400i	0.694271	+	0.719713i	$0.255727\pi$
$510$	2.11347	−	3.66064i	0.0935860	−	0.162096i
$511$	−13.7492	−	35.0083i	−0.608229	−	1.54868i
$512$		−	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
$518$	−2.97572	−	2.37192i	−0.130745	−	0.104216i
$519$	−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	$-0.957404\pi$
$521$	−13.9480	−	24.1587i	−0.611074	−	1.05841i	0.379985	−	0.924993i	$-0.375929\pi$
$522$		−	0.428350i		−	0.0187484i
$523$	−8.36180	−	14.4831i	−0.365636	−	0.633300i	0.623242	−	0.782029i	$-0.285815\pi$
$523$	−8.36180	−	14.4831i	−0.365636	−	0.633300i	−0.988878	+	0.148729i	$0.952482\pi$
$524$	−9.85416	−	17.0679i	−0.430481	−	0.745615i
$525$	9.97411	−	3.91724i	0.435306	−	0.170962i
$526$	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
$532$	−0.611307	+	0.766923i	−0.0265035	+	0.0332503i
$533$	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
$539$	5.55057	−	18.0244i	0.239080	−	0.776366i
$540$	−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
$546$	3.09438	+	0.588165i	0.132427	+	0.0251711i
$547$	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
$553$	−18.8491	−	15.0244i	−0.801543	−	0.638903i
$554$		−	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
$560$	26.7447	+	4.02472i	1.13017	+	0.170076i
$561$	−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	−0.615309	−	0.788286i	$-0.710969\pi$
$563$	8.89836	−	15.4124i	0.375021	−	0.649556i	0.990330	+	0.138730i	$0.0443021\pi$
$564$	5.75197	−	3.32090i	0.242202	−	0.139835i
$565$			53.5672i			2.25359i
$566$	2.81439	−	1.62489i	0.118298	−	0.0682992i
$567$	3.89433	−	25.8783i	0.163547	−	1.08679i
$568$	−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
$574$	0.386550	−	2.56867i	0.0161343	−	0.107214i
$575$	−4.87891	+	8.45051i	−0.203464	+	0.352411i
$576$	2.41579			0.100658
$577$	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	$0.328235\pi$
$578$	0.893326	+	0.515762i	0.0371575	+	0.0214529i
$579$			31.5253i			1.31015i
$580$		−	37.4505i		−	1.55505i
$581$	43.3954	+	6.53042i	1.80034	+	0.270928i
$582$	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	0.268051	−	0.963405i	$-0.413620\pi$
$587$	−10.4727	−	6.04644i	−0.432256	−	0.249563i	−0.700307	+	0.713841i	$0.746954\pi$
$588$	−18.4255	+	17.1124i	−0.759855	+	0.705704i
$589$	−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	0.756018	−	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
$595$	12.3815	+	31.5258i	0.507591	+	1.29243i
$596$	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	−0.996329	−	0.0856011i	$-0.972719\pi$
$601$	−10.3953	+	18.0051i	−0.424032	+	0.734445i	0.572297	+	0.820046i	$0.306052\pi$
$602$	−2.38877	+	2.99686i	−0.0973590	+	0.122143i
$603$		−	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	$-0.550038\pi$
$607$	−7.71405			−0.313104			−0.156552	+	0.987670i	$0.550038\pi$
$608$	0.199992	−	0.346396i	0.00811074	−	0.0140482i
$609$	26.7685	+	21.3369i	1.08471	+	0.864616i
$610$	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
$616$	−0.760978	+	5.05678i	−0.0306607	+	0.203743i
$617$	−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	−0.314728	−	0.949182i	$-0.601913\pi$
$619$	8.70599	−	5.02641i	0.349923	−	0.202028i	0.664651	+	0.747154i	$0.268580\pi$
$620$	−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
$623$	−5.69827	−	14.5090i	−0.228296	−	0.581290i
$624$	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
$630$	0.0639464	−	0.424930i	0.00254768	−	0.0169296i
$631$	−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
$637$	−19.1402	+	16.4515i	−0.758364	+	0.651831i
$638$	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	−0.450065	−	0.892996i	$-0.648599\pi$
$643$	2.49163	−	1.43855i	0.0982605	−	0.0567307i	0.548325	+	0.836265i	$0.315266\pi$
$644$	3.40752	−	22.6433i	0.134275	−	0.892271i
$645$			39.2990i			1.54740i
$646$	0.162349			0.00638754
$647$	−37.1001			−1.45856			−0.729278	−	0.684218i	$-0.760144\pi$
$647$	−37.1001			−1.45856			−0.729278	+	0.684218i	$0.760144\pi$
$648$			7.09577i			0.278748i
$649$	10.2231	−	17.7070i	0.401293	−	0.695061i
$650$	−1.27924	+	0.674349i	−0.0501758	+	0.0264501i
$651$	−6.53326	−	16.6350i	−0.256059	−	0.651979i
$652$	−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
$658$	0.131629	−	0.874687i	0.00513142	−	0.0340988i
$659$	−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	$0.370558\pi$
$661$			47.2266i			1.83690i	−0.395537	+	0.918450i	$0.629442\pi$
$662$	−0.137468	−	0.238102i	−0.00534284	−	0.00925408i
$663$	14.6292	+	27.7515i	0.568150	+	1.07778i
$664$	−11.8989			−0.461768
$665$	1.04735	+	0.834830i	0.0406143	+	0.0323733i
$666$	−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
$672$	6.39234	−	8.01958i	0.246590	−	0.309362i
$673$	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	−0.722908	−	0.690945i	$-0.757195\pi$
$677$	6.16453	−	10.6773i	0.236922	−	0.410361i	0.959830	+	0.280584i	$0.0905281\pi$
$678$	5.70137	+	3.29169i	0.218960	+	0.126416i
$679$	0.436287	+	1.11088i	0.0167432	+	0.0426316i
$680$	−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
$686$	0.252606	+	3.33936i	0.00964453	+	0.127497i
$687$	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	−0.642459	−	0.766320i	$-0.722086\pi$
$691$	−7.88703	+	4.55358i	−0.300037	+	0.173226i	0.342423	+	0.939546i	$0.388753\pi$
$692$	−0.885106	+	1.53305i	−0.0336467	+	0.0582777i
$693$	−2.35662	−	0.354640i	−0.0895205	−	0.0134717i
$694$		−	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
$700$	1.71801	−	11.4164i	0.0649347	−	0.431498i
$701$	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
$707$	−3.01461	+	20.0324i	−0.113376	+	0.753397i
$708$	−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
$714$	4.11626	+	0.619442i	0.154047	+	0.0231820i
$715$	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	$-0.783502\pi$
$719$	−41.6949			−1.55496			−0.777479	+	0.628909i	$0.783502\pi$
$720$		−	3.41757i		−	0.127365i
$721$	10.6702	+	8.50514i	0.397380	+	0.316748i
$722$	−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	$-0.292589\pi$
$727$	32.7039			1.21292			0.606461	+	0.795113i	$0.292589\pi$
$728$	4.46819	−	5.18337i	0.165602	−	0.192108i
$729$	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	0.332609	−	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
$735$	23.3695	+	25.1627i	0.861997	+	0.928142i
$736$			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
$742$	2.10900	−	2.64587i	0.0774237	−	0.0971328i
$743$	−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
$749$	19.7821	−	7.76923i	0.722821	−	0.283881i
$750$	−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
$756$	−19.8119	−	15.7919i	−0.720551	−	0.574345i
$757$	−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	$-0.623692\pi$
$761$		−	51.0590i		−	1.85089i	0.378885	−	0.925444i	$-0.376308\pi$
$762$			2.63067i			0.0952990i
$763$	−1.28979	−	3.28407i	−0.0466935	−	0.118891i
$764$	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	0.488960	−	0.872306i	$-0.337376\pi$
$769$	−0.610062	−	0.352220i	−0.0219994	−	0.0127014i	−0.510959	+	0.859605i	$0.670710\pi$
$770$	3.42443	+	0.515331i	0.123408	+	0.0185712i
$771$	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	0.480166	−	0.877178i	$-0.340577\pi$
$773$	−1.09571	−	0.632607i	−0.0394099	−	0.0227533i	−0.519575	+	0.854425i	$0.673910\pi$
$774$	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
$777$	−14.0476	−	35.7682i	−0.503955	−	1.28318i
$778$	−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
$784$	5.93881	+	25.9637i	0.212100	+	0.927273i
$785$		−	42.7679i		−	1.52645i
$786$			3.30779i			0.117985i
$787$	37.9292	+	21.8984i	1.35203	+	0.780595i	0.988534	−	0.151000i	$-0.0482494\pi$
$787$	37.9292	+	21.8984i	1.35203	+	0.780595i	0.363497	+	0.931595i	$0.381583\pi$
$788$	8.44493	−	4.87568i	0.300838	−	0.173689i
$789$	0.290218			0.0103320
$790$	2.21300	−	3.83303i	0.0787351	−	0.136373i
$791$	−49.1009	+	19.2839i	−1.74583	+	0.685657i
$792$	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	0.961383	−	0.275213i	$-0.0887484\pi$
$797$	6.84183	+	11.8504i	0.242350	+	0.419763i	−0.719033	+	0.694976i	$0.755415\pi$
$798$	0.153213	−	0.0601731i	0.00542369	−	0.00213011i
$799$	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
$805$	−30.9228	−	4.65347i	−1.08988	−	0.164013i
$806$	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	$0.0129637\pi$
$811$			2.31899i			0.0814309i	−0.999171	+	0.0407154i	$0.987036\pi$
$812$	34.3280	−	13.4820i	1.20468	−	0.473125i
$813$	−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
$819$	2.41561	+	2.08232i	0.0844084	+	0.0727621i
$820$	−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
$826$	−0.540278	+	3.59021i	−0.0187987	+	0.124919i
$827$		−	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	$-0.566068\pi$
$829$	−11.8666			−0.412142			−0.206071	+	0.978537i	$0.566068\pi$
$830$			8.05791i			0.279694i
$831$	24.9847	−	43.2748i	0.866710	−	1.50119i
$832$	13.8848	−	22.0452i	0.481370	−	0.764281i
$833$	−24.4400	+	22.6983i	−0.846796	+	0.786448i
$834$	−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	−0.918418	−	0.395611i	$-0.870533\pi$
$839$	−29.9798	+	17.3088i	−1.03502	+	0.597568i	−0.116600	+	0.993179i	$0.537199\pi$
$840$	−7.28128	−	5.80384i	−0.251228	−	0.200252i
$841$	−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
$847$	−1.47292	+	9.78770i	−0.0506101	+	0.336309i
$848$	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	$0.166563\pi$
$853$			29.1897i			0.999436i	−0.866188	+	0.499718i	$0.833437\pi$
$854$	0.0719778	+	0.183271i	0.00246303	+	0.00627139i
$855$	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	0.564629	−	0.825345i	$-0.309019\pi$
$857$	−12.6599	−	21.9276i	−0.432455	−	0.749033i	−0.997084	+	0.0763112i	$0.975686\pi$
$858$	3.20513	+	0.123358i	0.109421	+	0.00421139i
$859$	−13.0424	+	22.5902i	−0.445002	+	0.770766i	−0.998052	−	0.0623818i	$-0.980130\pi$
$859$	−13.0424	+	22.5902i	−0.445002	+	0.770766i	0.553050	+	0.833148i	$0.313464\pi$
$860$	36.6674	+	21.1699i	1.25035	+	0.721888i
$861$	16.3501	−	20.5122i	0.557211	−	0.699055i
$862$	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
$868$	−19.0405	−	2.86534i	−0.646276	−	0.0972559i
$869$	−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
$875$	19.5545	+	2.94269i	0.661062	+	0.0994811i
$876$			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	−0.735122	−	0.677935i	$-0.762875\pi$
$881$	6.51653	−	11.2870i	0.219548	−	0.380268i	0.954670	+	0.297667i	$0.0962085\pi$
$882$	0.412521	−	0.0943581i	0.0138903	−	0.00317720i
$883$	−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	$0.124258\pi$
$887$	23.5857	+	40.8517i	0.791932	+	1.37167i	−0.132838	+	0.991138i	$0.542409\pi$
$888$	5.20976	+	9.02356i	0.174828	+	0.302811i
$889$	−16.4835	−	13.1389i	−0.552839	−	0.440663i
$890$	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
$896$	−5.36994	−	13.6730i	−0.179397	−	0.456782i
$897$	−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
$903$	−36.0223	+	14.1474i	−1.19875	+	0.470797i
$904$	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
$910$	−3.51016	−	3.02584i	−0.116361	−	0.100306i
$911$	−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
$917$	−20.7263	−	16.5207i	−0.684442	−	0.545563i
$918$			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
$924$	−15.9611	+	20.0242i	−0.525082	+	0.658747i
$925$	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	$0.282914\pi$
$929$			47.3235i			1.55263i	−0.630342	+	0.776317i	$0.717086\pi$
$930$	2.84197	−	1.64081i	0.0931920	−	0.0538044i
$931$	−0.388184	+	1.26055i	−0.0127222	+	0.0413130i
$932$	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	$-0.661253\pi$
$937$	−29.7044			−0.970401			−0.485200	+	0.874403i	$0.661253\pi$
$938$	−5.07691	+	1.99391i	−0.165767	+	0.0651035i
$939$	−0.636122	+	1.10180i	−0.0207591	+	0.0359558i
$940$	−9.77219			−0.318734
$941$	−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	$0.562297\pi$
$942$	−4.55196	−	2.62808i	−0.148311	−	0.0856273i
$943$			23.8863i			0.777844i
$944$			28.8748i			0.939795i
$945$	−21.5661	+	27.0560i	−0.701546	+	0.880133i
$946$	−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
$952$	5.63714	−	7.07214i	0.182701	−	0.229209i
$953$	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
$959$	−8.35600	+	10.4831i	−0.269829	+	0.338517i
$960$	−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
$966$	−2.39548	+	3.00528i	−0.0770733	+	0.0966932i
$967$		−	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	$-0.609271\pi$
$971$	−20.9763			−0.673163			−0.336581	+	0.941654i	$0.609271\pi$
$972$	−3.40223	+	5.89283i	−0.109126	+	0.189013i
$973$	19.0258	−	7.47220i	0.609939	−	0.239548i
$974$	−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
$980$	36.0666	−	8.24971i	1.15211	−	0.263527i
$981$	−0.386109	+	0.222920i	−0.0123275	+	0.00711729i
$982$		−	4.06013i		−	0.129564i
$983$	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	$0.211829\pi$
$984$	−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
$987$	5.56757	−	6.98486i	0.177218	−	0.222331i
$988$	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
$994$	−1.25135	−	0.997441i	−0.0396905	−	0.0316369i
$995$	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	$-0.529971\pi$
$997$	25.7396	−	44.5822i	0.815180	−	1.41193i	0.909199	−	0.416363i	$-0.136695\pi$
$998$	−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	91.2.u.b.30.3	yes	12
3.2	odd	2		819.2.do.e.667.4		12
7.2	even	3		637.2.q.g.589.4		12
7.3	odd	6		637.2.k.i.459.3		12
7.4	even	3		91.2.k.b.4.3	✓	12
7.5	odd	6		637.2.q.i.589.4		12
7.6	odd	2		637.2.u.g.30.3		12
13.6	odd	12		1183.2.e.j.170.7		24
13.7	odd	12		1183.2.e.j.170.6		24
13.10	even	6		91.2.k.b.23.4	yes	12
21.11	odd	6		819.2.bm.f.550.4		12
39.23	odd	6		819.2.bm.f.478.3		12
91.10	odd	6		637.2.u.g.361.3		12
91.19	even	12		8281.2.a.co.1.6		12
91.23	even	6		637.2.q.g.491.4		12
91.32	odd	12		1183.2.e.j.508.7		24
91.33	even	12		8281.2.a.co.1.7		12
91.46	odd	12		1183.2.e.j.508.6		24
91.58	odd	12		8281.2.a.cp.1.6		12
91.62	odd	6		637.2.k.i.569.4		12
91.72	odd	12		8281.2.a.cp.1.7		12
91.75	odd	6		637.2.q.i.491.4		12
91.88	even	6	inner	91.2.u.b.88.3	yes	12
273.179	odd	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	7.4	even	3
91.2.k.b.23.4	yes	12	13.10	even	6
91.2.u.b.30.3	yes	12	1.1	even	1	trivial
91.2.u.b.88.3	yes	12	91.88	even	6	inner
637.2.k.i.459.3		12	7.3	odd	6
637.2.k.i.569.4		12	91.62	odd	6
637.2.q.g.491.4		12	91.23	even	6
637.2.q.g.589.4		12	7.2	even	3
637.2.q.i.491.4		12	91.75	odd	6
637.2.q.i.589.4		12	7.5	odd	6
637.2.u.g.30.3		12	7.6	odd	2
637.2.u.g.361.3		12	91.10	odd	6
819.2.bm.f.478.3		12	39.23	odd	6
819.2.bm.f.550.4		12	21.11	odd	6
819.2.do.e.361.4		12	273.179	odd	6
819.2.do.e.667.4		12	3.2	odd	2
1183.2.e.j.170.6		24	13.7	odd	12
1183.2.e.j.170.7		24	13.6	odd	12
1183.2.e.j.508.6		24	91.46	odd	12
1183.2.e.j.508.7		24	91.32	odd	12
8281.2.a.co.1.6		12	91.19	even	12
8281.2.a.co.1.7		12	91.33	even	12
8281.2.a.cp.1.6		12	91.58	odd	12
8281.2.a.cp.1.7		12	91.72	odd	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156598 + 0.0904119i) q^{2} -1.82601 q^{3} +(-0.983651 + 1.70373i) q^{4} +(2.32670 + 1.34332i) q^{5} +(0.285950 - 0.165093i) q^{6} +(-0.393717 + 2.61629i) q^{7} -0.717383i q^{8} +0.334323 q^{9} +O(q^{10})\)	\(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} +(-0.393717 + 2.61629i) q^{7} -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} +(-0.174889 - 0.445303i) q^{14} +(-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} +(0.718933 - 4.77738i) q^{21} +(-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} +(-4.07019 - 3.24431i) q^{28} +(-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} +(-4.43058 + 5.55844i) q^{35} +(-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} +(0.319349 + 0.813129i) q^{42} +(-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} +(-6.68997 - 2.06016i) q^{49} +(-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} +(1.87688 + 0.282446i) q^{56} +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} +(-0.131629 + 0.874687i) q^{63} +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} +(0.191271 - 1.27102i) q^{70} +(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} +(-7.04893 - 1.06077i) q^{77} +(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} +(7.43221 + 5.92415i) q^{84} +(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} +(7.22539 + 6.22846i) q^{91} -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} +(1.23390 - 0.282236i) q^{98} +0.900747i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 4 q^{4} + 3 q^{5} - 9 q^{6} + 3 q^{7} + 2 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 4 * q^4 + 3 * q^5 - 9 * q^6 + 3 * q^7 + 2 * q^9	\( 12 q + 6 q^{3} + 4 q^{4} + 3 q^{5} - 9 q^{6} + 3 q^{7} + 2 q^{9} - 24 q^{10} - q^{12} - 2 q^{13} + 4 q^{14} - 12 q^{15} - 8 q^{16} + 17 q^{17} - 3 q^{18} - 3 q^{20} - 21 q^{21} - 15 q^{22} + 3 q^{23} - 5 q^{25} - 9 q^{26} + 12 q^{27} + 27 q^{28} - q^{29} - 22 q^{30} - 18 q^{31} + 18 q^{32} + 18 q^{35} - 13 q^{36} + 15 q^{37} + 19 q^{38} - q^{39} - q^{40} - 6 q^{41} - 8 q^{42} + 11 q^{43} + 33 q^{44} - 9 q^{45} - 30 q^{46} + 15 q^{47} + 19 q^{48} + 9 q^{49} + 18 q^{50} + 4 q^{51} + 47 q^{52} - 8 q^{53} + 6 q^{54} - 15 q^{55} + 27 q^{59} + 30 q^{60} - 10 q^{61} + 41 q^{62} - 54 q^{63} + 2 q^{64} - 3 q^{65} - 34 q^{66} - 11 q^{68} + 7 q^{69} - 3 q^{70} + 30 q^{71} - 42 q^{73} - 33 q^{74} + q^{75} - 45 q^{76} - 19 q^{77} + 44 q^{78} - 35 q^{79} - 28 q^{81} - 10 q^{82} + 3 q^{84} - 21 q^{85} + 57 q^{86} + 10 q^{87} + 28 q^{88} + 48 q^{89} - 16 q^{91} - 66 q^{92} - 81 q^{93} - 2 q^{94} + 2 q^{95} - 21 q^{96} - 3 q^{97} - 36 q^{98}+O(q^{100}) \) 12 * q + 6 * q^3 + 4 * q^4 + 3 * q^5 - 9 * q^6 + 3 * q^7 + 2 * q^9 - 24 * q^10 - q^12 - 2 * q^13 + 4 * q^14 - 12 * q^15 - 8 * q^16 + 17 * q^17 - 3 * q^18 - 3 * q^20 - 21 * q^21 - 15 * q^22 + 3 * q^23 - 5 * q^25 - 9 * q^26 + 12 * q^27 + 27 * q^28 - q^29 - 22 * q^30 - 18 * q^31 + 18 * q^32 + 18 * q^35 - 13 * q^36 + 15 * q^37 + 19 * q^38 - q^39 - q^40 - 6 * q^41 - 8 * q^42 + 11 * q^43 + 33 * q^44 - 9 * q^45 - 30 * q^46 + 15 * q^47 + 19 * q^48 + 9 * q^49 + 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 - 54 * q^63 + 2 * q^64 - 3 * q^65 - 34 * q^66 - 11 * q^68 + 7 * q^69 - 3 * q^70 + 30 * q^71 - 42 * q^73 - 33 * q^74 + q^75 - 45 * q^76 - 19 * q^77 + 44 * q^78 - 35 * q^79 - 28 * q^81 - 10 * q^82 + 3 * q^84 - 21 * q^85 + 57 * q^86 + 10 * q^87 + 28 * q^88 + 48 * q^89 - 16 * q^91 - 66 * q^92 - 81 * q^93 - 2 * q^94 + 2 * q^95 - 21 * q^96 - 3 * q^97 - 36 * q^98

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