LMFDB - Embedded newform 507.2.m.a.40.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.2
Character	$\chi$	$=$	507.40
Dual form			507.2.m.a.469.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.31903 - 0.571589i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(3.28027 + 1.72162i) q^{4} +(-2.03486 + 2.94800i) q^{5} +(0.846950 - 2.23322i) q^{6} +(-0.933245 - 0.826783i) q^{7} +(-3.04745 - 2.69981i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(-2.31903 - 0.571589i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(3.28027 + 1.72162i) q^{4} +(-2.03486 + 2.94800i) q^{5} +(0.846950 - 2.23322i) q^{6} +(-0.933245 - 0.826783i) q^{7} +(-3.04745 - 2.69981i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(6.40394 - 5.67340i) q^{10} +(-3.82991 + 0.943988i) q^{11} +(-2.10446 + 3.04884i) q^{12} +(-2.14180 + 2.90046i) q^{13} +(1.69164 + 2.45077i) q^{14} +(-2.68123 - 2.37536i) q^{15} +(1.31503 + 1.90515i) q^{16} +(-1.46759 - 1.30017i) q^{17} +(2.11485 + 1.10996i) q^{18} +1.89797 q^{19} +(-11.7502 + 6.16699i) q^{20} +(0.933245 - 0.826783i) q^{21} +9.42125 q^{22} +5.32725 q^{23} +(3.04745 - 2.69981i) q^{24} +(-2.77703 - 7.32244i) q^{25} +(6.62477 - 5.50203i) q^{26} +(0.354605 - 0.935016i) q^{27} +(-1.63789 - 4.31877i) q^{28} +(1.71353 + 0.422348i) q^{29} +(4.86012 + 7.04110i) q^{30} +(1.33285 - 3.51445i) q^{31} +(0.926812 + 2.44380i) q^{32} +(-0.475461 - 3.91577i) q^{33} +(2.66022 + 3.85400i) q^{34} +(4.33638 - 1.06882i) q^{35} +(-2.77294 - 2.45661i) q^{36} +(0.475702 - 1.25432i) q^{37} +(-4.40144 - 1.08486i) q^{38} +(-2.62115 - 2.47580i) q^{39} +(14.1602 - 3.49017i) q^{40} +(0.801528 - 6.60118i) q^{41} +(-2.63680 + 1.38390i) q^{42} +(3.37573 + 8.90106i) q^{43} +(-14.1883 - 3.49711i) q^{44} +(2.68123 - 2.37536i) q^{45} +(-12.3540 - 3.04500i) q^{46} +(-5.48873 + 2.88071i) q^{47} +(-2.04977 + 1.07580i) q^{48} +(-0.656381 - 5.40578i) q^{49} +(2.25460 + 18.5683i) q^{50} +(1.46759 - 1.30017i) q^{51} +(-12.0192 + 5.82694i) q^{52} +(-8.51836 - 7.54661i) q^{53} +(-1.35678 + 1.96564i) q^{54} +(5.01044 - 13.2115i) q^{55} +(0.611865 + 5.03916i) q^{56} +(-0.228775 + 1.88413i) q^{57} +(-3.73233 - 1.95888i) q^{58} +(0.454346 - 0.658233i) q^{59} +(-4.70569 - 12.4079i) q^{60} +(9.13806 - 8.09561i) q^{61} +(-5.09975 + 7.38826i) q^{62} +(0.708265 + 1.02610i) q^{63} +(-1.31052 - 10.7931i) q^{64} +(-4.19231 - 12.2161i) q^{65} +(-1.13561 + 9.35255i) q^{66} +(-6.96902 + 3.65762i) q^{67} +(-2.57570 - 6.79156i) q^{68} +(-0.642129 + 5.28841i) q^{69} -10.6671 q^{70} +(1.14495 - 9.42954i) q^{71} +(2.31279 + 3.35066i) q^{72} +(-15.2016 + 3.74686i) q^{73} +(-1.82012 + 2.63691i) q^{74} +(7.60379 - 1.87416i) q^{75} +(6.22585 + 3.26758i) q^{76} +(4.35472 + 2.28553i) q^{77} +(4.66339 + 7.23967i) q^{78} +(-6.96971 + 3.65799i) q^{79} -8.29229 q^{80} +(0.885456 + 0.464723i) q^{81} +(-5.63193 + 14.8502i) q^{82} +(-0.894344 - 7.36558i) q^{83} +(4.48470 - 1.10538i) q^{84} +(6.81925 - 1.68079i) q^{85} +(-2.74066 - 22.5714i) q^{86} +(-0.625813 + 1.65013i) q^{87} +(14.2201 + 7.46326i) q^{88} +15.2640 q^{89} +(-7.57559 + 3.97597i) q^{90} +(4.39688 - 0.936038i) q^{91} +(17.4748 + 9.17150i) q^{92} +(3.32817 + 1.74676i) q^{93} +(14.3751 - 3.54314i) q^{94} +(-3.86209 + 5.59521i) q^{95} +(-2.53770 + 0.625487i) q^{96} +(-4.63800 - 6.71931i) q^{97} +(-1.56772 + 12.9113i) q^{98} +3.94453 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) $ 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	−2.31903	−	0.571589i	−1.63980	−	0.404175i	−0.691711	−	0.722175i	$-0.743143\pi$
$2$	−2.31903	−	0.571589i	−1.63980	−	0.404175i	−0.948091	+	0.318000i	$0.896989\pi$
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$3$	−0.120537	+	0.992709i	−0.0695919	+	0.573141i
$4$	3.28027	+	1.72162i	1.64014	+	0.860810i
$5$	−2.03486	+	2.94800i	−0.910016	+	1.31839i	0.0377061	+	0.999289i	$0.487995\pi$
$5$	−2.03486	+	2.94800i	−0.910016	+	1.31839i	−0.947722	+	0.319097i	$0.896620\pi$
$6$	0.846950	−	2.23322i	0.345766	−	0.911710i
$7$	−0.933245	−	0.826783i	−0.352733	−	0.312495i	0.468085	−	0.883683i	$-0.344944\pi$
$7$	−0.933245	−	0.826783i	−0.352733	−	0.312495i	−0.820819	+	0.571189i	$0.806482\pi$
$8$	−3.04745	−	2.69981i	−1.07744	−	0.954526i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	6.40394	−	5.67340i	2.02510	−	1.79409i
$11$	−3.82991	+	0.943988i	−1.15476	+	0.284623i	−0.769785	−	0.638303i	$-0.779636\pi$
$11$	−3.82991	+	0.943988i	−1.15476	+	0.284623i	−0.384976	+	0.922927i	$0.625790\pi$
$12$	−2.10446	+	3.04884i	−0.607505	+	0.880123i
$13$	−2.14180	+	2.90046i	−0.594029	+	0.804444i
$13$	−2.14180	+	2.90046i	−0.594029	+	0.804444i
$14$	1.69164	+	2.45077i	0.452110	+	0.654995i
$15$	−2.68123	−	2.37536i	−0.692291	−	0.613316i
$16$	1.31503	+	1.90515i	0.328758	+	0.476288i
$17$	−1.46759	−	1.30017i	−0.355943	−	0.315338i	0.466134	−	0.884714i	$-0.345646\pi$
$17$	−1.46759	−	1.30017i	−0.355943	−	0.315338i	−0.822077	+	0.569376i	$0.807185\pi$
$18$	2.11485	+	1.10996i	0.498476	+	0.261620i
$19$	1.89797			0.435423			0.217712	−	0.976013i	$-0.430141\pi$
$19$	1.89797			0.435423			0.217712	+	0.976013i	$0.430141\pi$
$20$	−11.7502	+	6.16699i	−2.62743	+	1.37898i
$21$	0.933245	−	0.826783i	0.203651	−	0.180419i
$22$	9.42125			2.00862
$23$	5.32725			1.11081			0.555404	−	0.831581i	$-0.312564\pi$
$23$	5.32725			1.11081			0.555404	+	0.831581i	$0.312564\pi$
$24$	3.04745	−	2.69981i	0.622059	−	0.551096i
$25$	−2.77703	−	7.32244i	−0.555407	−	1.46449i
$26$	6.62477	−	5.50203i	1.29923	−	1.07904i
$27$	0.354605	−	0.935016i	0.0682437	−	0.179944i
$28$	−1.63789	−	4.31877i	−0.309532	−	0.816170i
$29$	1.71353	+	0.422348i	0.318195	+	0.0784281i	0.395179	−	0.918604i	$-0.370683\pi$
$29$	1.71353	+	0.422348i	0.318195	+	0.0784281i	−0.0769833	+	0.997032i	$0.524529\pi$
$30$	4.86012	+	7.04110i	0.887333	+	1.28552i
$31$	1.33285	−	3.51445i	0.239388	−	0.631213i	−0.760447	−	0.649400i	$-0.775020\pi$
$31$	1.33285	−	3.51445i	0.239388	−	0.631213i	0.999835	+	0.0181867i	$0.00578931\pi$
$32$	0.926812	+	2.44380i	0.163839	+	0.432007i
$33$	−0.475461	−	3.91577i	−0.0827671	−	0.681648i
$34$	2.66022	+	3.85400i	0.456225	+	0.660956i
$35$	4.33638	−	1.06882i	0.732981	−	0.180664i
$36$	−2.77294	−	2.45661i	−0.462157	−	0.409435i
$37$	0.475702	−	1.25432i	0.0782049	−	0.206209i	−0.890212	−	0.455547i	$-0.849444\pi$
$37$	0.475702	−	1.25432i	0.0782049	−	0.206209i	0.968417	+	0.249338i	$0.0802129\pi$
$38$	−4.40144	−	1.08486i	−0.714008	−	0.175987i
$39$	−2.62115	−	2.47580i	−0.419720	−	0.396445i
$40$	14.1602	−	3.49017i	2.23892	−	0.551844i
$41$	0.801528	−	6.60118i	0.125178	−	1.03093i	−0.785802	−	0.618478i	$-0.787749\pi$
$41$	0.801528	−	6.60118i	0.125178	−	1.03093i	0.910979	−	0.412452i	$-0.135328\pi$
$42$	−2.63680	+	1.38390i	−0.406868	+	0.213541i
$43$	3.37573	+	8.90106i	0.514794	+	1.35740i	0.900531	+	0.434791i	$0.143178\pi$
$43$	3.37573	+	8.90106i	0.514794	+	1.35740i	−0.385738	+	0.922608i	$0.626053\pi$
$44$	−14.1883	−	3.49711i	−2.13897	−	0.527209i
$45$	2.68123	−	2.37536i	0.399694	−	0.354098i
$46$	−12.3540	−	3.04500i	−1.82151	−	0.448961i
$47$	−5.48873	+	2.88071i	−0.800613	+	0.420194i	−0.814827	−	0.579705i	$-0.803168\pi$
$47$	−5.48873	+	2.88071i	−0.800613	+	0.420194i	0.0142135	+	0.999899i	$0.495476\pi$
$48$	−2.04977	+	1.07580i	−0.295859	+	0.155279i
$49$	−0.656381	−	5.40578i	−0.0937686	−	0.772254i
$50$	2.25460	+	18.5683i	0.318848	+	2.62595i
$51$	1.46759	−	1.30017i	0.205504	−	0.182061i
$52$	−12.0192	+	5.82694i	−1.66676	+	0.808051i
$53$	−8.51836	−	7.54661i	−1.17009	−	1.03661i	−0.998678	−	0.0514070i	$-0.983629\pi$
$53$	−8.51836	−	7.54661i	−1.17009	−	1.03661i	−0.171409	−	0.985200i	$-0.554832\pi$
$54$	−1.35678	+	1.96564i	−0.184635	+	0.267490i
$55$	5.01044	−	13.2115i	0.675608	−	1.78143i
$56$	0.611865	+	5.03916i	0.0817639	+	0.673387i
$57$	−0.228775	+	1.88413i	−0.0303019	+	0.249559i
$58$	−3.73233	−	1.95888i	−0.490079	−	0.257213i
$59$	0.454346	−	0.658233i	0.0591508	−	0.0856947i	−0.792292	−	0.610142i	$-0.791113\pi$
$59$	0.454346	−	0.658233i	0.0591508	−	0.0856947i	0.851443	+	0.524447i	$0.175728\pi$
$60$	−4.70569	−	12.4079i	−0.607503	−	1.60185i
$61$	9.13806	−	8.09561i	1.17001	−	1.03654i	0.171326	−	0.985214i	$-0.445195\pi$
$61$	9.13806	−	8.09561i	1.17001	−	1.03654i	0.998682	−	0.0513223i	$-0.0163436\pi$
$62$	−5.09975	+	7.38826i	−0.647669	+	0.938310i
$63$	0.708265	+	1.02610i	0.0892329	+	0.129276i
$64$	−1.31052	−	10.7931i	−0.163815	−	1.34914i
$65$	−4.19231	−	12.2161i	−0.519992	−	1.51522i
$66$	−1.13561	+	9.35255i	−0.139783	+	1.15122i
$67$	−6.96902	+	3.65762i	−0.851401	+	0.446850i	−0.833191	−	0.552985i	$-0.813489\pi$
$67$	−6.96902	+	3.65762i	−0.851401	+	0.446850i	−0.0182093	+	0.999834i	$0.505797\pi$
$68$	−2.57570	−	6.79156i	−0.312349	−	0.823597i
$69$	−0.642129	+	5.28841i	−0.0773032	+	0.636649i
$70$	−10.6671			−1.27496
$71$	1.14495	−	9.42954i	0.135881	−	1.11908i	−0.752051	−	0.659105i	$-0.770935\pi$
$71$	1.14495	−	9.42954i	0.135881	−	1.11908i	0.887932	−	0.459975i	$-0.152142\pi$
$72$	2.31279	+	3.35066i	0.272565	+	0.394879i
$73$	−15.2016	+	3.74686i	−1.77922	+	0.438537i	−0.985489	−	0.169737i	$-0.945708\pi$
$73$	−15.2016	+	3.74686i	−1.77922	+	0.438537i	−0.793727	+	0.608275i	$0.791862\pi$
$74$	−1.82012	+	2.63691i	−0.211585	+	0.306534i
$75$	7.60379	−	1.87416i	0.878009	−	0.216410i
$76$	6.22585	+	3.26758i	0.714154	+	0.374817i
$77$	4.35472	+	2.28553i	0.496266	+	0.260460i
$78$	4.66339	+	7.23967i	0.528024	+	0.819731i
$79$	−6.96971	+	3.65799i	−0.784154	+	0.411556i	−0.808758	−	0.588141i	$-0.799860\pi$
$79$	−6.96971	+	3.65799i	−0.784154	+	0.411556i	0.0246040	+	0.999697i	$0.492168\pi$
$80$	−8.29229			−0.927106
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	−5.63193	+	14.8502i	−0.621943	+	1.63993i
$83$	−0.894344	−	7.36558i	−0.0981670	−	0.808478i	−0.955760	−	0.294149i	$-0.904964\pi$
$83$	−0.894344	−	7.36558i	−0.0981670	−	0.808478i	0.857593	−	0.514329i	$-0.171959\pi$
$84$	4.48470	−	1.10538i	0.489321	−	0.120607i
$85$	6.81925	−	1.68079i	0.739652	−	0.182308i
$86$	−2.74066	−	22.5714i	−0.295533	−	2.43393i
$87$	−0.625813	+	1.65013i	−0.0670942	+	0.176913i
$88$	14.2201	+	7.46326i	1.51586	+	0.795586i
$89$	15.2640			1.61798			0.808989	−	0.587824i	$-0.200015\pi$
$89$	15.2640			1.61798			0.808989	+	0.587824i	$0.200015\pi$
$90$	−7.57559	+	3.97597i	−0.798537	+	0.419105i
$91$	4.39688	−	0.936038i	0.460918	−	0.0981235i
$92$	17.4748	+	9.17150i	1.82188	+	0.956195i
$93$	3.32817	+	1.74676i	0.345115	+	0.181130i
$94$	14.3751	−	3.54314i	1.48268	−	0.365447i
$95$	−3.86209	+	5.59521i	−0.396242	+	0.574056i
$96$	−2.53770	+	0.625487i	−0.259003	+	0.0638385i
$97$	−4.63800	−	6.71931i	−0.470918	−	0.682242i	0.513500	−	0.858090i	$-0.328349\pi$
$97$	−4.63800	−	6.71931i	−0.470918	−	0.682242i	−0.984417	+	0.175848i	$0.943733\pi$
$98$	−1.56772	+	12.9113i	−0.158364	+	1.30424i
$99$	3.94453			0.396440
$100$	3.49702	−	28.8006i	0.349702	−	2.88006i
$101$	0.380183	+	1.00246i	0.0378296	+	0.0997484i	0.952600	−	0.304226i	$-0.0983978\pi$
$101$	0.380183	+	1.00246i	0.0378296	+	0.0997484i	−0.914770	+	0.403974i	$0.867629\pi$
$102$	−4.14655	+	2.17628i	−0.410570	+	0.215484i
$103$	−1.21068	+	9.97082i	−0.119292	+	0.982454i	0.803005	+	0.595972i	$0.203233\pi$
$103$	−1.21068	+	9.97082i	−0.119292	+	0.982454i	−0.922297	+	0.386482i	$0.873690\pi$
$104$	14.3577	−	3.05657i	1.40789	−	0.299722i
$105$	0.538336	+	4.43359i	0.0525362	+	0.432674i
$106$	15.4408	+	22.3698i	1.49974	+	2.17275i
$107$	4.05418	−	5.87349i	0.391932	−	0.567812i	−0.576498	−	0.817099i	$-0.695581\pi$
$107$	4.05418	−	5.87349i	0.391932	−	0.567812i	0.968430	+	0.249287i	$0.0801963\pi$
$108$	2.77294	−	2.45661i	0.266827	−	0.236388i
$109$	7.09607	+	18.7108i	0.679680	+	1.79217i	0.606838	+	0.794826i	$0.292438\pi$
$109$	7.09607	+	18.7108i	0.679680	+	1.79217i	0.0728423	+	0.997343i	$0.476793\pi$
$110$	−19.1709	+	27.7738i	−1.82787	+	2.64813i
$111$	1.18784	+	0.623425i	0.112745	+	0.0591729i
$112$	0.347901	−	2.86522i	0.0328735	−	0.270738i
$113$	−0.790733	−	6.51227i	−0.0743859	−	0.612623i	−0.981462	−	0.191656i	$-0.938614\pi$
$113$	−0.790733	−	6.51227i	−0.0743859	−	0.612623i	0.907076	−	0.420967i	$-0.138309\pi$
$114$	1.60748	−	4.23858i	0.150555	−	0.396980i
$115$	−10.8402	+	15.7047i	−1.01085	+	1.46447i
$116$	4.89374	+	4.33547i	0.454372	+	0.402539i
$117$	2.77369	−	2.30361i	0.256428	−	0.212969i
$118$	−1.42988	+	1.26676i	−0.131631	+	0.116615i
$119$	0.294662	+	2.42676i	0.0270116	+	0.222461i
$120$	1.75790	+	14.4776i	0.160474	+	1.32162i
$121$	4.03707	−	2.11882i	0.367007	−	0.192620i
$122$	−25.8188	+	13.5507i	−2.33752	+	1.22683i
$123$	6.45643	+	1.59137i	0.582157	+	0.143489i
$124$	10.4227	−	9.23368i	0.935983	−	0.829209i
$125$	9.84743	+	2.42717i	0.880781	+	0.217093i
$126$	−1.05598	−	2.78439i	−0.0940741	−	0.248053i
$127$	−2.05824	+	1.08025i	−0.182639	+	0.0958565i	−0.553565	−	0.832806i	$-0.686733\pi$
$127$	−2.05824	+	1.08025i	−0.182639	+	0.0958565i	0.370925	+	0.928663i	$0.379041\pi$
$128$	−2.50001	+	20.5895i	−0.220972	+	1.81987i
$129$	−9.24306	+	2.27821i	−0.813806	+	0.200585i
$130$	2.73951	+	30.7257i	0.240271	+	2.69482i
$131$	−11.0056	−	2.71263i	−0.961562	−	0.237004i	−0.272865	−	0.962052i	$-0.587971\pi$
$131$	−11.0056	−	2.71263i	−0.961562	−	0.237004i	−0.688698	+	0.725049i	$0.741817\pi$
$132$	5.18183	−	13.6634i	0.451020	−	1.18924i
$133$	−1.77127	−	1.56921i	−0.153588	−	0.136067i
$134$	18.2520	−	4.49872i	1.57673	−	0.388630i
$135$	2.03486	+	2.94800i	0.175133	+	0.253723i
$136$	0.962200	+	7.92443i	0.0825080	+	0.679514i
$137$	4.00130	+	10.5506i	0.341854	+	0.901395i	0.990151	+	0.140007i	$0.0447125\pi$
$137$	4.00130	+	10.5506i	0.341854	+	0.901395i	−0.648297	+	0.761388i	$0.724518\pi$
$138$	4.51191	−	11.8969i	0.384080	−	1.01273i
$139$	−1.25877	−	1.82364i	−0.106767	−	0.154679i	0.765958	−	0.642890i	$-0.222265\pi$
$139$	−1.25877	−	1.82364i	−0.106767	−	0.154679i	−0.872725	+	0.488211i	$0.837650\pi$
$140$	16.0646	+	3.95957i	1.35771	+	0.334645i
$141$	−2.19811	−	5.79594i	−0.185114	−	0.488106i
$142$	−8.04501	+	21.2129i	−0.675122	+	1.78015i
$143$	5.46490	−	13.1303i	0.456998	−	1.09801i
$144$	−0.820886	−	2.16450i	−0.0684072	−	0.180375i
$145$	−4.73188	+	4.19208i	−0.392961	+	0.348133i
$146$	37.3947			3.09481
$147$	5.44548			0.449136
$148$	3.71990	−	3.29554i	0.305774	−	0.270892i
$149$	2.91301	−	1.52887i	0.238643	−	0.125250i	−0.341163	−	0.940004i	$-0.610821\pi$
$149$	2.91301	−	1.52887i	0.238643	−	0.125250i	0.579806	+	0.814755i	$0.303128\pi$
$150$	−18.7047			−1.52723
$151$	−16.9436	−	8.89268i	−1.37885	−	0.723676i	−0.397808	−	0.917469i	$-0.630229\pi$
$151$	−16.9436	−	8.89268i	−1.37885	−	0.723676i	−0.981043	+	0.193793i	$0.937921\pi$
$152$	−5.78396	−	5.12415i	−0.469141	−	0.415623i
$153$	1.11379	+	1.61361i	0.0900450	+	0.130453i
$154$	−8.79233	−	7.78933i	−0.708506	−	0.627682i
$155$	7.64842	+	11.0807i	0.614336	+	0.890020i
$156$	−4.33570	−	12.6339i	−0.347134	−	1.01152i
$157$	−0.516402	+	0.748137i	−0.0412134	+	0.0597079i	−0.843049	−	0.537837i	$-0.819242\pi$
$157$	−0.516402	+	0.748137i	−0.0412134	+	0.0597079i	0.801836	+	0.597545i	$0.203857\pi$
$158$	18.2538	−	4.49917i	1.45220	−	0.357935i
$159$	8.51836	−	7.54661i	0.675550	−	0.598485i
$160$	−9.09026	−	2.24055i	−0.718648	−	0.177131i
$161$	−4.97163	−	4.40448i	−0.391819	−	0.347122i
$162$	−1.78777	−	1.58382i	−0.140460	−	0.124437i
$163$	6.00548	−	15.8351i	0.470385	−	1.24030i	−0.464570	−	0.885537i	$-0.653791\pi$
$163$	6.00548	−	15.8351i	0.470385	−	1.24030i	0.934955	−	0.354767i	$-0.115440\pi$
$164$	13.9939	−	20.2737i	1.09274	−	1.58311i
$165$	12.5112	+	6.56638i	0.973994	+	0.511192i
$166$	−2.13608	+	17.5922i	−0.165792	+	1.36542i
$167$	4.25119	+	1.04782i	0.328967	+	0.0810831i	0.400340	−	0.916367i	$-0.368892\pi$
$167$	4.25119	+	1.04782i	0.328967	+	0.0810831i	−0.0713731	+	0.997450i	$0.522738\pi$
$168$	−5.07618			−0.391635
$169$	−3.82538	−	12.4244i	−0.294260	−	0.955726i
$170$	−16.7748			−1.28657
$171$	−1.84282	−	0.454213i	−0.140924	−	0.0347346i
$172$	−4.25094	+	35.0096i	−0.324131	+	2.66946i
$173$	−15.4779	−	8.12343i	−1.17676	−	0.617613i	−0.241098	−	0.970501i	$-0.577507\pi$
$173$	−15.4779	−	8.12343i	−1.17676	−	0.617613i	−0.935666	+	0.352888i	$0.885200\pi$
$174$	2.39448	−	3.46900i	0.181525	−	0.262984i
$175$	−3.46241	+	9.12964i	−0.261734	+	0.690136i
$176$	−6.83489	−	6.05519i	−0.515199	−	0.456427i
$177$	0.598669	+	0.530374i	0.0449987	+	0.0398654i
$178$	−35.3976	−	8.72473i	−2.65316	−	0.653946i
$179$	−8.66885	+	7.67993i	−0.647940	+	0.574025i	−0.921762	−	0.387755i	$-0.873251\pi$
$179$	−8.66885	+	7.67993i	−0.647940	+	0.574025i	0.273822	+	0.961780i	$0.411712\pi$
$180$	12.8846	−	3.17578i	0.960364	−	0.236709i
$181$	6.59582	−	9.55569i	0.490263	−	0.710269i	−0.497285	−	0.867587i	$-0.665670\pi$
$181$	6.59582	−	9.55569i	0.490263	−	0.710269i	0.987548	+	0.157319i	$0.0502850\pi$
$182$	−10.7315	−	0.342509i	−0.795473	−	0.0253885i
$183$	6.93511	+	10.0472i	0.512658	+	0.742714i
$184$	−16.2345	−	14.3825i	−1.19683	−	1.06030i
$185$	2.72976	+	3.95474i	0.200696	+	0.290758i
$186$	−6.71969	−	5.95312i	−0.492711	−	0.436504i
$187$	6.84809	+	3.59416i	0.500782	+	0.262831i
$188$	−22.9640			−1.67482
$189$	−1.10399	+	0.579418i	−0.0803034	+	0.0421465i
$190$	12.1545	−	10.7679i	0.881778	−	0.781187i
$191$	−7.29091			−0.527551			−0.263776	−	0.964584i	$-0.584968\pi$
$191$	−7.29091			−0.527551			−0.263776	+	0.964584i	$0.584968\pi$
$192$	10.8724			0.784647
$193$	−6.98465	+	6.18786i	−0.502766	+	0.445412i	−0.875990	−	0.482329i	$-0.839791\pi$
$193$	−6.98465	+	6.18786i	−0.502766	+	0.445412i	0.373224	+	0.927741i	$0.378252\pi$
$194$	6.91498	+	18.2333i	0.496467	+	1.30907i
$195$	12.6323	−	2.68926i	0.904619	−	0.192582i
$196$	7.15359	−	18.8625i	0.510971	−	1.34732i
$197$	7.99439	+	21.0795i	0.569577	+	1.50185i	0.841894	+	0.539643i	$0.181441\pi$
$197$	7.99439	+	21.0795i	0.569577	+	1.50185i	−0.272318	+	0.962207i	$0.587790\pi$
$198$	−9.14748	−	2.25465i	−0.650083	−	0.160231i
$199$	14.6079	+	21.1632i	1.03553	+	1.50022i	0.856347	+	0.516400i	$0.172728\pi$
$199$	14.6079	+	21.1632i	1.03553	+	1.50022i	0.179178	+	0.983817i	$0.442656\pi$
$200$	−11.3063	+	29.8122i	−0.799476	+	2.10804i
$201$	−2.79093	−	7.35908i	−0.196857	−	0.519070i
$202$	−0.308660	−	2.54204i	−0.0217172	−	0.178857i
$203$	−1.24996	−	1.81088i	−0.0877298	−	0.127099i
$204$	7.05250	−	1.73829i	0.493774	−	0.121704i
$205$	17.8293	+	15.7954i	1.24525	+	1.10320i
$206$	8.50681	−	22.4306i	0.592698	−	1.56282i
$207$	−5.17245	−	1.27489i	−0.359510	−	0.0886113i
$208$	−8.34236	−	0.266256i	−0.578439	−	0.0184615i
$209$	−7.26904	+	1.79166i	−0.502810	+	0.123932i
$210$	1.28578	−	10.5893i	0.0887271	−	0.730734i
$211$	−21.0021	+	11.0227i	−1.44584	+	0.758836i	−0.991267	−	0.131872i	$-0.957901\pi$
$211$	−21.0021	+	11.0227i	−1.44584	+	0.758836i	−0.454575	+	0.890708i	$0.650209\pi$
$212$	−14.9502	−	39.4203i	−1.02678	−	2.70740i
$213$	9.22278	+	2.27321i	0.631934	+	0.155758i
$214$	−12.7590	+	11.3035i	−0.872186	+	0.772689i
$215$	−33.1095	−	8.16075i	−2.25805	−	0.556558i
$216$	−3.60501	+	1.89205i	−0.245290	+	0.128738i
$217$	−4.14956	+	2.17786i	−0.281691	+	0.147843i
$218$	−5.76110	−	47.4469i	−0.390191	−	3.21351i
$219$	−1.88719	−	15.5424i	−0.127525	−	1.05026i
$220$	39.1807	−	34.7111i	2.64156	−	2.34022i
$221$	6.91439	−	1.47198i	0.465113	−	0.0990164i
$222$	−2.39829	−	2.12470i	−0.160963	−	0.142600i
$223$	8.61286	−	12.4779i	0.576760	−	0.835581i	−0.420671	−	0.907213i	$-0.638205\pi$
$223$	8.61286	−	12.4779i	0.576760	−	0.835581i	0.997431	+	0.0716324i	$0.0228209\pi$
$224$	1.15555	−	3.04694i	0.0772086	−	0.203582i
$225$	0.943965	+	7.77425i	0.0629310	+	0.518283i
$226$	−1.88861	+	15.5541i	−0.125629	+	1.03465i
$227$	−19.2361	−	10.0959i	−1.27675	−	0.670089i	−0.316329	−	0.948650i	$-0.602450\pi$
$227$	−19.2361	−	10.0959i	−1.27675	−	0.670089i	−0.960419	+	0.278561i	$0.910143\pi$
$228$	−3.99420	+	5.78659i	−0.264522	+	0.383226i
$229$	−7.56916	−	19.9582i	−0.500184	−	1.31888i	−0.912962	−	0.408045i	$-0.866211\pi$
$229$	−7.56916	−	19.9582i	−0.500184	−	1.31888i	0.412778	−	0.910832i	$-0.364559\pi$
$230$	34.1154	−	30.2236i	2.24950	−	1.99289i
$231$	−2.79377	+	4.04748i	−0.183817	+	0.266304i
$232$	−4.08166	−	5.91330i	−0.267974	−	0.388227i
$233$	2.44901	+	20.1695i	0.160440	+	1.32134i	0.821154	+	0.570707i	$0.193331\pi$
$233$	2.44901	+	20.1695i	0.160440	+	1.32134i	−0.660714	+	0.750638i	$0.729746\pi$
$234$	−7.74899	+	3.75674i	−0.506568	+	0.245586i
$235$	2.67646	−	22.0426i	0.174593	−	1.43790i
$236$	2.62361	−	1.37697i	0.170782	−	0.0896334i
$237$	−2.79121	−	7.35982i	−0.181309	−	0.478072i
$238$	0.703781	−	5.79615i	0.0456193	−	0.375709i
$239$	−8.55710			−0.553513			−0.276756	−	0.960940i	$-0.589260\pi$
$239$	−8.55710			−0.553513			−0.276756	+	0.960940i	$0.589260\pi$
$240$	0.999525	−	8.23183i	0.0645191	−	0.531362i
$241$	−13.3787	−	19.3824i	−0.861797	−	1.24853i	−0.967179	−	0.254097i	$-0.918222\pi$
$241$	−13.3787	−	19.3824i	−0.861797	−	1.24853i	0.105381	−	0.994432i	$-0.466394\pi$
$242$	−10.5732	+	2.60606i	−0.679670	+	0.167524i
$243$	−0.568065	+	0.822984i	−0.0364414	+	0.0527944i
$244$	43.9129	−	10.8235i	2.81123	−	0.692907i
$245$	17.2719	+	9.06498i	1.10346	+	0.579140i
$246$	−14.0630	−	7.38086i	−0.896627	−	0.470586i
$247$	−4.06507	+	5.50498i	−0.258654	+	0.350274i
$248$	−13.5501	+	7.11166i	−0.860435	+	0.451591i
$249$	7.41968			0.470203
$250$	−21.4491	−	11.2574i	−1.35656	−	0.711979i
$251$	−9.84267	+	25.9530i	−0.621264	+	1.63814i	0.140347	+	0.990102i	$0.455178\pi$
$251$	−9.84267	+	25.9530i	−0.621264	+	1.63814i	−0.761610	+	0.648035i	$0.775591\pi$
$252$	0.556749	+	4.58524i	0.0350719	+	0.288843i
$253$	−20.4029	+	5.02886i	−1.28272	+	0.316162i
$254$	5.39058	−	1.32866i	0.338235	−	0.0833674i
$255$	0.846570	+	6.97213i	0.0530142	+	0.436612i
$256$	9.85551	−	25.9869i	0.615970	−	1.62418i
$257$	−11.5969	−	6.08652i	−0.723394	−	0.379667i	0.0624854	−	0.998046i	$-0.480097\pi$
$257$	−11.5969	−	6.08652i	−0.723394	−	0.379667i	−0.785880	+	0.618379i	$0.787790\pi$
$258$	22.7371			1.41555
$259$	−1.48100	+	0.777288i	−0.0920248	+	0.0482983i
$260$	7.27950	−	47.2896i	0.451456	−	2.93277i
$261$	−1.56267	−	0.820151i	−0.0967267	−	0.0507661i
$262$	23.9718	+	12.5813i	1.48098	+	0.777278i
$263$	−1.38651	+	0.341743i	−0.0854956	+	0.0210728i	−0.281831	−	0.959464i	$-0.590942\pi$
$263$	−1.38651	+	0.341743i	−0.0854956	+	0.0210728i	0.196336	+	0.980537i	$0.437096\pi$
$264$	−9.12288	+	13.2168i	−0.561475	+	0.813436i
$265$	39.5811	−	9.75586i	2.43145	−	0.599298i
$266$	3.21068	+	4.65147i	0.196859	+	0.285200i
$267$	−1.83987	+	15.1527i	−0.112598	+	0.927329i
$268$	−29.1573			−1.78107
$269$	0.580208	−	4.77844i	0.0353759	−	0.291347i	−0.964274	−	0.264905i	$-0.914659\pi$
$269$	0.580208	−	4.77844i	0.0353759	−	0.291347i	0.999650	−	0.0264416i	$-0.00841760\pi$
$270$	−3.03385	−	7.99960i	−0.184634	−	0.486840i
$271$	−1.83278	+	0.961919i	−0.111334	+	0.0584324i	−0.519471	−	0.854488i	$-0.673871\pi$
$271$	−1.83278	+	0.961919i	−0.111334	+	0.0584324i	0.408137	+	0.912921i	$0.366179\pi$
$272$	0.547098	−	4.50575i	0.0331727	−	0.273201i
$273$	0.399228	+	4.47765i	0.0241624	+	0.271000i
$274$	−3.24854	−	26.7541i	−0.196252	−	1.61628i
$275$	17.5481	+	25.4228i	1.05819	+	1.53305i
$276$	−11.2110	+	16.2419i	−0.674822	+	0.977648i
$277$	−8.73098	+	7.73498i	−0.524594	+	0.464750i	−0.883372	−	0.468673i	$-0.844732\pi$
$277$	−8.73098	+	7.73498i	−0.524594	+	0.464750i	0.358778	+	0.933423i	$0.383194\pi$
$278$	1.87675	+	4.94857i	0.112560	+	0.296796i
$279$	−2.13519	+	3.09335i	−0.127830	+	0.185194i
$280$	−16.1005	−	8.45020i	−0.962190	−	0.504996i
$281$	−0.492824	+	4.05877i	−0.0293994	+	0.242126i	0.970600	+	0.240700i	$0.0773770\pi$
$281$	−0.492824	+	4.05877i	−0.0293994	+	0.242126i	−0.999999	+	0.00142600i	$0.999546\pi$
$282$	1.78458	+	14.6974i	0.106270	+	0.875216i
$283$	−5.16496	+	13.6189i	−0.307025	+	0.809559i	0.689345	+	0.724433i	$0.257898\pi$
$283$	−5.16496	+	13.6189i	−0.307025	+	0.809559i	−0.996370	+	0.0851258i	$0.972871\pi$
$284$	19.9898	−	28.9603i	1.18618	−	1.71848i
$285$	−5.08889	−	4.50836i	−0.301440	−	0.267052i
$286$	−20.1784	+	27.3260i	−1.19318	+	1.61582i
$287$	−6.20576	+	5.49782i	−0.366314	+	0.324526i
$288$	−0.315040	−	2.59459i	−0.0185639	−	0.152888i
$289$	−1.58575	−	13.0598i	−0.0932793	−	0.768224i
$290$	13.3695	−	7.01687i	0.785086	−	0.412045i
$291$	7.22936	−	3.79426i	0.423793	−	0.222424i
$292$	−56.3162	−	13.8807i	−3.29565	−	0.812306i
$293$	21.1864	−	18.7695i	1.23772	−	1.09653i	0.245850	−	0.969308i	$-0.420933\pi$
$293$	21.1864	−	18.7695i	1.23772	−	1.09653i	0.991874	−	0.127221i	$-0.0406056\pi$
$294$	−12.6282	−	3.11258i	−0.736494	−	0.181529i
$295$	1.01594	+	2.67882i	0.0591505	+	0.155967i
$296$	−4.83611	+	2.53819i	−0.281093	+	0.147529i
$297$	−0.475461	+	3.91577i	−0.0275890	+	0.227216i
$298$	−7.62924	+	1.88044i	−0.441950	+	0.108931i
$299$	−11.4099	+	15.4515i	−0.659852	+	0.893583i
$300$	28.1691	+	6.94306i	1.62634	+	0.400857i
$301$	4.20887	−	11.0979i	0.242595	−	0.639670i
$302$	34.2097	+	30.3072i	1.96855	+	1.74398i
$303$	−1.04098	+	0.256578i	−0.0598025	+	0.0147400i
$304$	2.49589	+	3.61592i	0.143149	+	0.207387i
$305$	5.27122	+	43.4124i	0.301829	+	2.48579i
$306$	−1.66060	−	4.37864i	−0.0949302	−	0.250310i
$307$	−11.2660	+	29.7059i	−0.642983	+	1.69541i	0.0730383	+	0.997329i	$0.476730\pi$
$307$	−11.2660	+	29.7059i	−0.642983	+	1.69541i	−0.716022	+	0.698078i	$0.754039\pi$
$308$	10.3498	+	14.9943i	0.589737	+	0.854381i
$309$	−9.75219	−	2.40370i	−0.554783	−	0.136742i
$310$	−11.4033	−	30.0681i	−0.647666	−	1.70775i
$311$	6.78907	−	17.9013i	0.384973	−	1.01509i	−0.592786	−	0.805360i	$-0.701972\pi$
$311$	6.78907	−	17.9013i	0.384973	−	1.01509i	0.977759	−	0.209731i	$-0.0672587\pi$
$312$	1.30366	+	14.6215i	0.0738049	+	0.827778i
$313$	−1.09460	−	2.88623i	−0.0618705	−	0.163139i	0.900516	−	0.434822i	$-0.143189\pi$
$313$	−1.09460	−	2.88623i	−0.0618705	−	0.163139i	−0.962387	+	0.271683i	$0.912420\pi$
$314$	1.62518	−	1.43978i	0.0917141	−	0.0812516i
$315$	−4.46616			−0.251639
$316$	−29.1602			−1.64039
$317$	8.73273	−	7.73652i	0.490479	−	0.434526i	−0.381281	−	0.924459i	$-0.624517\pi$
$317$	8.73273	−	7.73652i	0.490479	−	0.434526i	0.871760	+	0.489933i	$0.162979\pi$
$318$	−24.0679	+	12.6318i	−1.34966	+	0.708357i
$319$	−6.96137			−0.389762
$320$	34.4848	+	18.0990i	1.92776	+	1.01177i
$321$	5.34199	+	4.73259i	0.298161	+	0.264147i
$322$	9.01180	+	13.0558i	0.502208	+	0.727574i
$323$	−2.78544	−	2.46769i	−0.154986	−	0.137306i
$324$	2.10446	+	3.04884i	0.116914	+	0.169380i
$325$	27.1863	+	7.62852i	1.50803	+	0.423154i
$326$	−22.9781	+	33.2895i	−1.27264	+	1.84373i
$327$	−19.4297	+	4.78899i	−1.07447	+	0.264832i
$328$	−20.2645	+	17.9528i	−1.11892	+	0.991277i
$329$	7.50405	+	1.84958i	0.413711	+	0.101971i
$330$	−25.2605	−	22.3789i	−1.39055	−	1.23192i
$331$	−1.09555	−	0.970574i	−0.0602169	−	0.0533476i	0.632478	−	0.774579i	$-0.282038\pi$
$331$	−1.09555	−	0.970574i	−0.0602169	−	0.0533476i	−0.692694	+	0.721231i	$0.743577\pi$
$332$	9.74704	−	25.7008i	0.534939	−	1.41052i
$333$	−0.762058	+	1.10403i	−0.0417605	+	0.0605006i
$334$	−9.25972	−	4.85987i	−0.506669	−	0.265920i
$335$	3.39829	−	27.9874i	0.185668	−	1.52911i
$336$	2.80239	+	0.690728i	0.152883	+	0.0376823i
$337$	−13.6109			−0.741433			−0.370716	−	0.928746i	$-0.620888\pi$
$337$	−13.6109			−0.741433			−0.370716	+	0.928746i	$0.620888\pi$
$338$	1.76949	+	30.9992i	0.0962473	+	1.68613i
$339$	6.56010			0.356296
$340$	25.2627	+	6.22669i	1.37006	+	0.337690i
$341$	−1.78711	+	14.7182i	−0.0967777	+	0.797036i
$342$	4.01392	+	2.10667i	0.217048	+	0.113916i
$343$	−8.81469	+	12.7703i	−0.475949	+	0.689531i
$344$	13.7438	−	36.2394i	0.741015	−	1.95390i
$345$	−14.2836	−	12.6542i	−0.769002	−	0.681277i
$346$	31.2505	+	27.6855i	1.68003	+	1.48838i
$347$	5.00950	+	1.23473i	0.268924	+	0.0662838i	0.371472	−	0.928444i	$-0.378853\pi$
$347$	5.00950	+	1.23473i	0.268924	+	0.0662838i	−0.102548	+	0.994728i	$0.532699\pi$
$348$	−4.89374	+	4.33547i	−0.262332	+	0.232406i
$349$	24.8253	−	6.11888i	1.32887	−	0.327536i	0.489928	−	0.871763i	$-0.337023\pi$
$349$	24.8253	−	6.11888i	1.32887	−	0.327536i	0.838938	+	0.544227i	$0.183177\pi$
$350$	13.2478	−	19.1928i	0.708127	−	1.02590i
$351$	1.95249	+	3.03114i	0.104216	+	0.161790i
$352$	−5.85653	−	8.48464i	−0.312154	−	0.452233i
$353$	−17.6220	−	15.6117i	−0.937923	−	0.830927i	0.0478765	−	0.998853i	$-0.484755\pi$
$353$	−17.6220	−	15.6117i	−0.937923	−	0.830927i	−0.985800	+	0.167926i	$0.946293\pi$
$354$	−1.08517	−	1.57215i	−0.0576764	−	0.0835587i
$355$	25.4685	+	22.5631i	1.35173	+	1.19752i
$356$	50.0700	+	26.2788i	2.65370	+	1.39277i
$357$	−2.44458			−0.129381
$358$	24.4931	−	12.8550i	1.29450	−	0.679406i
$359$	−5.73950	+	5.08475i	−0.302919	+	0.268363i	−0.800865	−	0.598845i	$-0.795626\pi$
$359$	−5.73950	+	5.08475i	−0.302919	+	0.268363i	0.497945	+	0.867208i	$0.334088\pi$
$360$	−14.5839			−0.768642
$361$	−15.3977			−0.810406
$362$	−20.7578	+	18.3898i	−1.09101	+	0.966548i
$363$	1.61676	+	4.26303i	0.0848577	+	0.223751i
$364$	16.0345	+	4.49929i	0.840434	+	0.235827i
$365$	19.8874	−	52.4387i	1.04095	−	2.74477i
$366$	−10.3398	−	27.2639i	−0.540472	−	1.42511i
$367$	−15.3451	−	3.78224i	−0.801009	−	0.197431i	−0.182497	−	0.983206i	$-0.558418\pi$
$367$	−15.3451	−	3.78224i	−0.801009	−	0.197431i	−0.618512	+	0.785775i	$0.712264\pi$
$368$	7.00550	+	10.1492i	0.365187	+	0.529065i
$369$	−2.35800	+	6.21754i	−0.122753	+	0.323672i
$370$	−4.06990	−	10.7315i	−0.211584	−	0.557902i
$371$	1.71031	+	14.0857i	0.0887949	+	0.731292i
$372$	7.91004	+	11.4597i	0.410116	+	0.594156i
$373$	32.0788	−	7.90670i	1.66097	−	0.409394i	0.706507	−	0.707706i	$-0.250270\pi$
$373$	32.0788	−	7.90670i	1.66097	−	0.409394i	0.954468	+	0.298313i	$0.0964239\pi$
$374$	−13.8265	−	12.2493i	−0.714954	−	0.633394i
$375$	−3.59645	+	9.48307i	−0.185720	+	0.489704i
$376$	24.5040	+	6.03969i	1.26370	+	0.311473i
$377$	−4.89506	+	4.06546i	−0.252108	+	0.209382i
$378$	2.89137	−	0.712659i	0.148716	−	0.0366552i
$379$	−0.607523	+	5.00340i	−0.0312064	+	0.257007i	0.968753	+	0.248026i	$0.0797819\pi$
$379$	−0.607523	+	5.00340i	−0.0312064	+	0.257007i	−0.999960	+	0.00898121i	$0.997141\pi$
$380$	−22.3015	+	11.7047i	−1.14404	+	0.600441i
$381$	−0.824278	−	2.17344i	−0.0422290	−	0.111349i
$382$	16.9078	+	4.16740i	0.865080	+	0.213223i
$383$	11.3908	−	10.0913i	0.582041	−	0.515643i	−0.319929	−	0.947441i	$-0.603659\pi$
$383$	11.3908	−	10.0913i	0.582041	−	0.515643i	0.901970	+	0.431798i	$0.142121\pi$
$384$	−20.1380	−	4.96357i	−1.02766	−	0.253296i
$385$	−15.5990	+	8.18697i	−0.794997	+	0.417247i
$386$	19.7345	−	10.3575i	1.00446	−	0.527182i
$387$	−1.14747	−	9.45028i	−0.0583293	−	0.480385i
$388$	−3.64582	−	30.0260i	−0.185088	−	1.52434i
$389$	−13.6354	+	12.0799i	−0.691344	+	0.612477i	−0.933847	−	0.357673i	$-0.883570\pi$
$389$	−13.6354	+	12.0799i	−0.691344	+	0.612477i	0.242503	+	0.970151i	$0.422032\pi$
$390$	−30.8319	−	0.984035i	−1.56123	−	0.0498285i
$391$	−7.81823	−	6.92635i	−0.395385	−	0.350280i
$392$	−12.5943	+	18.2460i	−0.636107	+	0.921560i
$393$	4.01943	−	10.5984i	0.202753	−	0.534617i
$394$	−6.49042	−	53.4534i	−0.326983	−	2.69294i
$395$	3.39863	−	27.9902i	0.171003	−	1.40834i
$396$	12.9391	+	6.79098i	0.650216	+	0.341260i
$397$	12.1234	−	17.5638i	0.608457	−	0.881502i	−0.390783	−	0.920483i	$-0.627796\pi$
$397$	12.1234	−	17.5638i	0.608457	−	0.881502i	0.999240	+	0.0389808i	$0.0124111\pi$
$398$	−21.7795	−	57.4277i	−1.09171	−	2.87859i
$399$	1.77127	−	1.56921i	0.0886743	−	0.0785586i
$400$	10.2985	−	14.9199i	0.514924	−	0.745996i
$401$	15.3691	+	22.2660i	0.767498	+	1.11191i	0.990556	+	0.137108i	$0.0437806\pi$
$401$	15.3691	+	22.2660i	0.767498	+	1.11191i	−0.223058	+	0.974805i	$0.571604\pi$
$402$	2.26588	+	18.6612i	0.113012	+	0.930736i
$403$	7.33882	+	11.3931i	0.365573	+	0.567533i
$404$	−0.478751	+	3.94287i	−0.0238187	+	0.196165i
$405$	−3.17178	+	1.66468i	−0.157607	+	0.0827186i
$406$	1.86361	+	4.91394i	0.0924894	+	0.243875i
$407$	−0.637830	+	5.25300i	−0.0316160	+	0.260381i
$408$	−7.98263			−0.395199
$409$	3.58594	−	29.5328i	0.177313	−	1.46031i	−0.583912	−	0.811817i	$-0.698479\pi$
$409$	3.58594	−	29.5328i	0.177313	−	1.46031i	0.761225	−	0.648488i	$-0.224598\pi$
$410$	−32.3181	−	46.8209i	−1.59608	−	2.31232i
$411$	−10.9559	+	2.70039i	−0.540416	+	0.133201i
$412$	−21.1373	+	30.6227i	−1.04136	+	1.50867i
$413$	−0.968232	+	0.238648i	−0.0476436	+	0.0117431i
$414$	11.2663	+	5.91304i	0.553711	+	0.290610i
$415$	23.5336	+	12.3514i	1.15522	+	0.606306i
$416$	−9.07321	−	2.54596i	−0.444851	−	0.124826i
$417$	1.96207	−	1.02977i	0.0960830	−	0.0504283i
$418$	17.8812			0.874599
$419$	−12.0627	−	6.33098i	−0.589300	−	0.309288i	0.143588	−	0.989637i	$-0.454136\pi$
$419$	−12.0627	−	6.33098i	−0.589300	−	0.309288i	−0.732888	+	0.680349i	$0.761828\pi$
$420$	−5.86707	+	15.4702i	−0.286284	+	0.754868i
$421$	−0.210114	−	1.73044i	−0.0102403	−	0.0843367i	0.986693	−	0.162596i	$-0.0519868\pi$
$421$	−0.210114	−	1.73044i	−0.0102403	−	0.0843367i	−0.996933	+	0.0782595i	$0.975064\pi$
$422$	55.0049	−	13.5575i	2.67760	−	0.659968i
$423$	6.01863	−	1.48346i	0.292636	−	0.0721283i
$424$	5.58491	+	45.9959i	0.271227	+	2.23376i
$425$	−5.44488	+	14.3570i	−0.264116	+	0.696416i
$426$	−20.0886	−	10.5433i	−0.973294	−	0.510824i
$427$	−15.2214			−0.736613
$428$	23.4107	−	12.2869i	1.13160	−	0.593909i
$429$	12.3759	+	7.00774i	0.597514	+	0.338337i
$430$	72.1172	+	37.8500i	3.47780	+	1.82529i
$431$	14.6115	+	7.66871i	0.703812	+	0.369389i	0.778351	−	0.627829i	$-0.216056\pi$
$431$	14.6115	+	7.66871i	0.703812	+	0.369389i	−0.0745395	+	0.997218i	$0.523749\pi$
$432$	2.24766	−	0.554000i	0.108141	−	0.0266543i
$433$	23.1982	−	33.6085i	1.11484	−	1.61512i	0.398832	−	0.917024i	$-0.369416\pi$
$433$	23.1982	−	33.6085i	1.11484	−	1.61512i	0.716004	−	0.698096i	$-0.245969\pi$
$434$	10.8678	−	2.67867i	0.521671	−	0.128580i
$435$	−3.59115	−	5.20268i	−0.172183	−	0.249449i
$436$	−8.93584	+	73.5932i	−0.427949	+	3.52448i
$437$	10.1109			0.483672
$438$	−4.50743	+	37.1220i	−0.215373	+	1.77376i
$439$	−1.08179	−	2.85246i	−0.0516312	−	0.136140i	0.906720	−	0.421734i	$-0.138578\pi$
$439$	−1.08179	−	2.85246i	−0.0516312	−	0.136140i	−0.958351	+	0.285594i	$0.907809\pi$
$440$	−50.9375	+	26.7340i	−2.42835	+	1.27450i
$441$	−0.656381	+	5.40578i	−0.0312562	+	0.257418i
$442$	−16.8761	−	0.538619i	−0.802712	−	0.0256195i
$443$	0.399718	+	3.29198i	0.0189912	+	0.156407i	0.999119	−	0.0419588i	$-0.0133598\pi$
$443$	0.399718	+	3.29198i	0.0189912	+	0.156407i	−0.980128	+	0.198365i	$0.936437\pi$
$444$	2.82313	+	4.09001i	0.133980	+	0.194103i
$445$	−31.0600	+	44.9982i	−1.47239	+	2.13312i
$446$	−27.1057	+	24.0136i	−1.28349	+	1.13707i
$447$	1.16659	+	3.07606i	0.0551780	+	0.145492i
$448$	−7.70053	+	11.1561i	−0.363816	+	0.527078i
$449$	28.1958	+	14.7983i	1.33064	+	0.698375i	0.971974	−	0.235089i	$-0.0755382\pi$
$449$	28.1958	+	14.7983i	1.33064	+	0.698375i	0.358669	+	0.933465i	$0.383231\pi$
$450$	2.25460	−	18.5683i	0.106283	−	0.875317i
$451$	3.16165	+	26.0385i	0.148876	+	1.22611i
$452$	8.61784	−	22.7234i	0.405349	−	1.06882i
$453$	10.8702	−	15.7482i	0.510725	−	0.739913i
$454$	38.8385	+	34.4079i	1.82278	+	1.61484i
$455$	−6.18758	+	14.8667i	−0.290078	+	0.696962i
$456$	5.78396	−	5.12415i	0.270859	−	0.239960i
$457$	−2.62645	−	21.6308i	−0.122860	−	1.01185i	−0.915546	−	0.402214i	$-0.868241\pi$
$457$	−2.62645	−	21.6308i	−0.122860	−	1.01185i	0.792685	−	0.609631i	$-0.208682\pi$
$458$	6.14519	+	50.6102i	0.287146	+	2.36486i
$459$	−1.73610	+	0.911175i	−0.0810341	+	0.0425300i
$460$	−62.5964	+	32.8531i	−2.91857	+	1.53178i
$461$	−8.91481	−	2.19730i	−0.415204	−	0.102339i	0.0261791	−	0.999657i	$-0.491666\pi$
$461$	−8.91481	−	2.19730i	−0.415204	−	0.102339i	−0.441383	+	0.897319i	$0.645512\pi$
$462$	8.79233	−	7.78933i	0.409056	−	0.362392i
$463$	31.9165	+	7.86671i	1.48328	+	0.365597i	0.896099	−	0.443855i	$-0.146390\pi$
$463$	31.9165	+	7.86671i	1.48328	+	0.365597i	0.587186	+	0.809452i	$0.300236\pi$
$464$	1.44871	+	3.81995i	0.0672549	+	0.177337i
$465$	−11.9218	+	6.25703i	−0.552859	+	0.290163i
$466$	5.84931	−	48.1734i	0.270964	−	2.23159i
$467$	−19.5721	+	4.82409i	−0.905688	+	0.223232i	−0.664537	−	0.747256i	$-0.731371\pi$
$467$	−19.5721	+	4.82409i	−0.905688	+	0.223232i	−0.241151	+	0.970488i	$0.577525\pi$
$468$	13.0644	−	2.78124i	0.603902	−	0.128563i
$469$	9.52786	+	2.34841i	0.439956	+	0.108439i
$470$	−18.8061	+	49.5876i	−0.867460	+	2.28731i
$471$	−0.680437	−	0.602815i	−0.0313529	−	0.0277762i
$472$	−3.16170	+	0.779289i	−0.145529	+	0.0358697i
$473$	−21.3312	−	30.9036i	−0.980811	−	1.42095i
$474$	2.26611	+	18.6631i	0.104086	+	0.857223i
$475$	−5.27072	−	13.8977i	−0.241837	−	0.637672i
$476$	−3.21139	+	8.46773i	−0.147194	+	0.388118i
$477$	6.46481	+	9.36590i	0.296003	+	0.428835i
$478$	19.8442	+	4.89115i	0.907651	+	0.223716i
$479$	−9.09610	−	23.9845i	−0.415612	−	1.09588i	−0.965446	−	0.260604i	$-0.916078\pi$
$479$	−9.09610	−	23.9845i	−0.415612	−	1.09588i	0.549834	−	0.835274i	$-0.314691\pi$
$480$	3.31992	−	8.75392i	0.151533	−	0.399560i
$481$	2.61926	+	4.06627i	0.119428	+	0.185406i
$482$	19.9468	+	52.5954i	0.908553	+	2.39566i
$483$	4.97163	−	4.40448i	0.226217	−	0.200411i
$484$	16.8905			0.767750
$485$	29.2462			1.32800
$486$	1.78777	−	1.58382i	0.0810948	−	0.0718437i
$487$	−9.87981	+	5.18532i	−0.447697	+	0.234969i	−0.673476	−	0.739209i	$-0.735200\pi$
$487$	−9.87981	+	5.18532i	−0.447697	+	0.234969i	0.225779	+	0.974178i	$0.427507\pi$
$488$	−49.7044			−2.25001
$489$	14.9958	+	7.87040i	0.678134	+	0.355912i
$490$	−34.8726	−	30.8944i	−1.57538	−	1.39567i
$491$	−4.68204	−	6.78310i	−0.211297	−	0.306117i	0.702977	−	0.711213i	$-0.251854\pi$
$491$	−4.68204	−	6.78310i	−0.211297	−	0.306117i	−0.914274	+	0.405095i	$0.867238\pi$
$492$	18.4391	+	16.3356i	0.831300	+	0.736467i
$493$	−1.96564	−	2.84773i	−0.0885281	−	0.128255i
$494$	12.5736	−	10.4427i	0.565713	−	0.469838i
$495$	−8.02656	+	11.6285i	−0.360767	+	0.522661i
$496$	8.44830	−	2.08232i	0.379340	−	0.0934989i
$497$	−8.86471	+	7.85344i	−0.397636	+	0.352275i
$498$	−17.2065	−	4.24101i	−0.771040	−	0.190044i
$499$	−22.1829	−	19.6524i	−0.993045	−	0.879761i	−0.000299704	−	1.00000i	$-0.500095\pi$
$499$	−22.1829	−	19.6524i	−0.993045	−	0.879761i	−0.992745	+	0.120239i	$0.961634\pi$
$500$	28.1236	+	24.9153i	1.25772	+	1.11425i
$501$	−1.55261	+	4.09390i	−0.0693655	+	0.182902i
$502$	37.6599	−	54.5598i	1.68084	−	2.43512i
$503$	−29.7902	−	15.6351i	−1.32828	−	0.697134i	−0.356781	−	0.934188i	$-0.616126\pi$
$503$	−29.7902	−	15.6351i	−1.32828	−	0.697134i	−0.971496	+	0.237054i	$0.923818\pi$
$504$	0.611865	−	5.03916i	0.0272546	−	0.224462i
$505$	−3.72887	−	0.919083i	−0.165932	−	0.0408987i
$506$	50.1893			2.23119
$507$	12.7949	−	2.29988i	0.568243	−	0.102141i
$508$	−8.61136			−0.382067
$509$	−11.4887	−	2.83172i	−0.509229	−	0.125514i	−0.0236737	−	0.999720i	$-0.507536\pi$
$509$	−11.4887	−	2.83172i	−0.509229	−	0.125514i	−0.485555	+	0.874206i	$0.661382\pi$
$510$	2.02198	−	16.6525i	0.0895346	−	0.737383i
$511$	17.2847	+	9.07170i	0.764630	+	0.401309i
$512$	−14.1449	+	20.4925i	−0.625124	+	0.905649i
$513$	0.673028	−	1.77463i	0.0297149	−	0.0783518i
$514$	23.4146	+	20.7435i	1.03277	+	0.914956i
$515$	−26.9304	−	23.8583i	−1.18670	−	1.05132i
$516$	−34.2420	−	8.43989i	−1.50742	−	0.371545i
$517$	18.3020	−	16.2141i	0.804920	−	0.713097i
$518$	3.87877	−	0.956031i	0.170423	−	0.0420056i
$519$	9.92986	−	14.3859i	0.435872	−	0.631470i
$520$	−20.2052	+	48.5463i	−0.886055	+	2.12890i
$521$	−3.67595	−	5.32554i	−0.161046	−	0.233316i	0.734151	−	0.678987i	$-0.237581\pi$
$521$	−3.67595	−	5.32554i	−0.161046	−	0.233316i	−0.895197	+	0.445671i	$0.852965\pi$
$522$	3.15508	+	2.79516i	0.138094	+	0.122341i
$523$	3.20624	+	4.64504i	0.140199	+	0.203114i	0.886793	−	0.462166i	$-0.152928\pi$
$523$	3.20624	+	4.64504i	0.140199	+	0.203114i	−0.746594	+	0.665280i	$0.768312\pi$
$524$	−31.4312	−	27.8456i	−1.37308	−	1.21644i
$525$	−8.64572	−	4.53763i	−0.377330	−	0.198038i
$526$	3.41068			0.148713
$527$	−6.52548	+	3.42483i	−0.284254	+	0.149188i
$528$	6.83489	−	6.05519i	0.297450	−	0.263518i
$529$	5.37959			0.233895
$530$	−97.3660			−4.22931
$531$	−0.598669	+	0.530374i	−0.0259800	+	0.0230163i
$532$	−3.10866	−	8.19687i	−0.134778	−	0.355380i
$533$	17.4298	+	16.4632i	0.754966	+	0.713101i
$534$	12.9278	−	34.0879i	0.559442	−	1.47513i
$535$	9.06537	+	23.9034i	0.391930	+	1.03344i
$536$	31.1126	+	7.66857i	1.34386	+	0.331232i
$537$	−6.57902	−	9.53136i	−0.283906	−	0.411308i
$538$	−4.07683	+	10.7497i	−0.175765	+	0.463453i
$539$	7.61687	+	20.0840i	0.328082	+	0.865080i
$540$	1.59955	+	13.1735i	0.0688337	+	0.566897i
$541$	−1.61206	−	2.33548i	−0.0693080	−	0.100410i	0.786797	−	0.617212i	$-0.211738\pi$
$541$	−1.61206	−	2.33548i	−0.0693080	−	0.100410i	−0.856105	+	0.516802i	$0.827122\pi$
$542$	4.80010	−	1.18312i	0.206182	−	0.0508193i
$543$	8.69098	+	7.69954i	0.372966	+	0.330419i
$544$	1.81718	−	4.79152i	0.0779112	−	0.205435i
$545$	−69.5989	−	17.1546i	−2.98129	−	0.734822i
$546$	1.63355	−	10.6120i	0.0699097	−	0.454151i
$547$	−2.75506	+	0.679060i	−0.117798	+	0.0290345i	−0.297774	−	0.954636i	$-0.596244\pi$
$547$	−2.75506	+	0.679060i	−0.117798	+	0.0290345i	0.179976	+	0.983671i	$0.442398\pi$
$548$	−5.03870	+	41.4974i	−0.215242	+	1.77268i
$549$	−10.8099	+	5.67349i	−0.461356	+	0.242139i
$550$	−26.1631	−	68.9865i	−1.11560	−	2.94159i
$551$	3.25223	+	0.801603i	0.138550	+	0.0341494i
$552$	16.2345	−	14.3825i	0.690988	−	0.612162i
$553$	9.52881	+	2.34864i	0.405206	+	0.0998744i
$554$	24.6686	−	12.9471i	1.04807	−	0.550070i
$555$	−4.25494	+	2.23316i	−0.180612	+	0.0947925i
$556$	−0.989486	−	8.14915i	−0.0419636	−	0.345601i
$557$	−1.29943	−	10.7018i	−0.0550586	−	0.453449i	−0.994001	−	0.109373i	$-0.965116\pi$
$557$	−1.29943	−	10.7018i	−0.0550586	−	0.453449i	0.938942	−	0.344075i	$-0.111808\pi$
$558$	6.71969	−	5.95312i	0.284467	−	0.252016i
$559$	−33.0473	−	9.27313i	−1.39775	−	0.392212i
$560$	7.73874	+	6.85592i	0.327021	+	0.289716i
$561$	−4.39340	+	6.36493i	−0.185489	+	0.268728i
$562$	3.46282	−	9.13072i	0.146070	−	0.385156i
$563$	0.523280	+	4.30960i	0.0220536	+	0.181628i	0.999573	−	0.0292173i	$-0.00930148\pi$
$563$	0.523280	+	4.30960i	0.0220536	+	0.181628i	−0.977519	+	0.210845i	$0.932378\pi$
$564$	2.76800	−	22.7966i	0.116554	−	0.959908i
$565$	20.8072	+	10.9205i	0.875366	+	0.459427i
$566$	19.7621	−	28.6304i	0.830664	−	1.20342i
$567$	−0.442122	−	1.16578i	−0.0185674	−	0.0489582i
$568$	−28.9471	+	25.6449i	−1.21459	+	1.07604i
$569$	−7.73930	+	11.2123i	−0.324448	+	0.470044i	−0.950936	−	0.309387i	$-0.899876\pi$
$569$	−7.73930	+	11.2123i	−0.324448	+	0.470044i	0.626488	+	0.779431i	$0.284492\pi$
$570$	9.22435	+	13.3638i	0.386365	+	0.559747i
$571$	−0.0771566	−	0.635442i	−0.00322890	−	0.0265924i	0.991005	−	0.133822i	$-0.0427251\pi$
$571$	−0.0771566	−	0.635442i	−0.00322890	−	0.0265924i	−0.994234	+	0.107230i	$0.965802\pi$
$572$	40.5318	−	33.6626i	1.69472	−	1.40750i
$573$	0.878822	−	7.23775i	0.0367133	−	0.302361i
$574$	17.5338	−	9.20247i	0.731848	−	0.384104i
$575$	−14.7940	−	39.0085i	−0.616951	−	1.62677i
$576$	−1.31052	+	10.7931i	−0.0546051	+	0.449713i
$577$	−22.9345			−0.954774			−0.477387	−	0.878693i	$-0.658416\pi$
$577$	−22.9345			−0.954774			−0.477387	+	0.878693i	$0.658416\pi$
$578$	−3.78745	+	31.1925i	−0.157537	+	1.29744i
$579$	−5.30084	−	7.67959i	−0.220295	−	0.319153i
$580$	−22.7390	+	5.60467i	−0.944187	+	0.232721i
$581$	−5.25510	+	7.61332i	−0.218018	+	0.315854i
$582$	−18.9339	+	4.66678i	−0.784834	+	0.193444i
$583$	39.7485	+	20.8616i	1.64621	+	0.863999i
$584$	56.4421	+	29.6231i	2.33559	+	1.22581i
$585$	1.14699	+	12.8644i	0.0474222	+	0.531876i
$586$	−59.8604	+	31.4172i	−2.47281	+	1.29783i
$587$	−31.7920			−1.31220			−0.656098	−	0.754676i	$-0.727794\pi$
$587$	−31.7920			−1.31220			−0.656098	+	0.754676i	$0.727794\pi$
$588$	17.8627	+	9.37505i	0.736644	+	0.386621i
$589$	2.52971	−	6.67030i	0.104235	−	0.274845i
$590$	−0.824816	−	6.79297i	−0.0339571	−	0.279662i
$591$	−21.8894	+	5.39525i	−0.900409	+	0.221931i
$592$	3.01524	−	0.743190i	0.123926	−	0.0305449i
$593$	4.16154	+	34.2734i	0.170894	+	1.40744i	0.785626	+	0.618702i	$0.212341\pi$
$593$	4.16154	+	34.2734i	0.170894	+	1.40744i	−0.614732	+	0.788736i	$0.710736\pi$
$594$	3.34082	−	8.80902i	0.137075	−	0.361438i
$595$	−7.75368	−	4.06945i	−0.317870	−	0.166831i
$596$	12.1876			0.499223
$597$	−22.7696	+	11.9504i	−0.931900	+	0.489099i
$598$	35.2918	−	29.3107i	1.44319	−	1.19860i
$599$	−0.399647	−	0.209751i	−0.0163291	−	0.00857018i	0.456539	−	0.889703i	$-0.349089\pi$
$599$	−0.399647	−	0.209751i	−0.0163291	−	0.00857018i	−0.472868	+	0.881133i	$0.656781\pi$
$600$	−28.2321	−	14.8173i	−1.15257	−	0.604915i
$601$	−5.10854	+	1.25914i	−0.208382	+	0.0513614i	−0.342125	−	0.939655i	$-0.611146\pi$
$601$	−5.10854	+	1.25914i	−0.208382	+	0.0513614i	0.133743	+	0.991016i	$0.457300\pi$
$602$	−16.1039	+	23.3305i	−0.656346	+	0.950882i
$603$	7.64184	−	1.88354i	0.311200	−	0.0767038i
$604$	−40.2698	−	58.3408i	−1.63855	−	2.37386i
$605$	−1.96859	+	16.2128i	−0.0800345	+	0.659144i
$606$	2.56071			0.104022
$607$	−0.0991681	+	0.816723i	−0.00402511	+	0.0331498i	−0.994583	−	0.103945i	$-0.966853\pi$
$607$	−0.0991681	+	0.816723i	−0.00402511	+	0.0331498i	0.990558	+	0.137095i	$0.0437765\pi$
$608$	1.75906	+	4.63826i	0.0713393	+	0.188106i
$609$	1.94834	−	1.02257i	0.0789506	−	0.0414365i
$610$	12.5900	−	103.688i	0.509752	−	4.19819i
$611$	3.40038	−	22.0897i	0.137565	−	0.893656i
$612$	0.875527	+	7.21061i	0.0353911	+	0.291472i
$613$	−18.2127	−	26.3856i	−0.735604	−	1.06571i	−0.994994	−	0.0999333i	$-0.968137\pi$
$613$	−18.2127	−	26.3856i	−0.735604	−	1.06571i	0.259391	−	0.965773i	$-0.416478\pi$
$614$	43.1057	−	62.4494i	1.73961	−	2.52025i
$615$	−17.8293	+	15.7954i	−0.718946	+	0.636930i
$616$	−7.10030	−	18.7219i	−0.286079	−	0.754329i
$617$	19.1562	−	27.7526i	0.771201	−	1.11728i	−0.218738	−	0.975784i	$-0.570194\pi$
$617$	19.1562	−	27.7526i	0.771201	−	1.11728i	0.989939	−	0.141494i	$-0.0451905\pi$
$618$	21.2417	+	11.1485i	0.854466	+	0.448458i
$619$	1.13201	−	9.32298i	0.0454995	−	0.374722i	−0.952118	−	0.305731i	$-0.901099\pi$
$619$	1.13201	−	9.32298i	0.0454995	−	0.374722i	0.997617	−	0.0689907i	$-0.0219779\pi$
$620$	6.01224	+	49.5152i	0.241457	+	1.98858i
$621$	1.88907	−	4.98106i	0.0758057	−	0.199883i
$622$	−25.9763	+	37.6331i	−1.04155	+	1.50895i
$623$	−14.2450	−	12.6200i	−0.570715	−	0.505609i
$624$	1.26988	−	8.24944i	0.0508357	−	0.330242i
$625$	2.11582	−	1.87445i	0.0846328	−	0.0749781i
$626$	0.888676	+	7.31890i	0.0355186	+	0.292522i
$627$	−0.902408	−	7.43200i	−0.0360387	−	0.296806i
$628$	−2.98195	+	1.56505i	−0.118993	+	0.0624521i
$629$	−2.32897	+	1.22234i	−0.0928622	+	0.0487379i
$630$	10.3571	+	2.55281i	0.412639	+	0.101706i
$631$	24.3861	−	21.6042i	0.970797	−	0.860051i	−0.0193882	−	0.999812i	$-0.506172\pi$
$631$	24.3861	−	21.6042i	0.970797	−	0.860051i	0.990185	+	0.139761i	$0.0446334\pi$
$632$	31.1157	+	7.66934i	1.23772	+	0.305070i
$633$	−8.41085	−	22.1776i	−0.334301	−	0.881480i
$634$	−24.6736	+	12.9497i	−0.979913	+	0.514298i
$635$	1.00365	−	8.26584i	0.0398288	−	0.328020i
$636$	40.9349	−	10.0896i	1.62318	−	0.400077i
$637$	17.0851	+	9.67430i	0.676936	+	0.383310i
$638$	16.1436	+	3.97905i	0.639133	+	0.157532i
$639$	−3.36832	+	8.88153i	−0.133249	+	0.351348i
$640$	−55.6105	−	49.2666i	−2.19820	−	1.94744i
$641$	−28.4184	+	7.00450i	−1.12246	+	0.276661i	−0.756515	−	0.653976i	$-0.773100\pi$
$641$	−28.4184	+	7.00450i	−1.12246	+	0.276661i	−0.365943	+	0.930637i	$0.619254\pi$
$642$	−9.68313	−	14.0284i	−0.382163	−	0.553658i
$643$	4.15801	+	34.2443i	0.163976	+	1.35046i	0.809678	+	0.586874i	$0.199642\pi$
$643$	4.15801	+	34.2443i	0.163976	+	1.35046i	−0.645702	+	0.763590i	$0.723435\pi$
$644$	−8.72546	−	23.0071i	−0.343831	−	0.906608i
$645$	12.0922	−	31.8844i	0.476128	−	1.25545i
$646$	5.04902	+	7.31476i	0.198651	+	0.287796i
$647$	−5.29538	−	1.30519i	−0.208183	−	0.0513125i	0.133845	−	0.991002i	$-0.457268\pi$
$647$	−5.29538	−	1.30519i	−0.208183	−	0.0513125i	−0.342028	+	0.939690i	$0.611114\pi$
$648$	−1.44372	−	3.80678i	−0.0567148	−	0.149545i
$649$	−1.11874	+	2.94987i	−0.0439143	+	0.115793i
$650$	−58.6855	−	33.2302i	−2.30184	−	1.30340i
$651$	−1.66181	−	4.38182i	−0.0651313	−	0.171737i
$652$	46.9617	−	41.6044i	1.83916	−	1.62935i
$653$	20.9165			0.818527			0.409263	−	0.912416i	$-0.365786\pi$
$653$	20.9165			0.818527			0.409263	+	0.912416i	$0.365786\pi$
$654$	47.7954			1.86895
$655$	30.3916	−	26.9246i	1.18750	−	1.05203i
$656$	13.6303	−	7.15372i	0.532173	−	0.279306i
$657$	15.6566			0.610821
$658$	−16.3449	−	8.57847i	−0.637191	−	0.334423i
$659$	0.230830	+	0.204498i	0.00899188	+	0.00796611i	0.667607	−	0.744514i	$-0.267319\pi$
$659$	0.230830	+	0.204498i	0.00899188	+	0.00796611i	−0.658615	+	0.752480i	$0.728857\pi$
$660$	29.7353	+	43.0790i	1.15744	+	1.67685i
$661$	−18.0327	−	15.9755i	−0.701389	−	0.621377i	0.235142	−	0.971961i	$-0.424445\pi$
$661$	−18.0327	−	15.9755i	−0.701389	−	0.621377i	−0.936531	+	0.350584i	$0.885983\pi$
$662$	1.98585	+	2.87699i	0.0771821	+	0.111818i
$663$	0.627814	+	7.04141i	0.0243823	+	0.273466i
$664$	−17.1602	+	24.8608i	−0.665945	+	0.964787i
$665$	8.23030	−	2.02859i	0.319157	−	0.0786652i
$666$	2.39829	−	2.12470i	0.0929318	−	0.0823304i
$667$	9.12843	+	2.24996i	0.353454	+	0.0871186i
$668$	12.1411	+	10.7561i	0.469754	+	0.416166i
$669$	11.3487	+	10.0541i	0.438767	+	0.388714i
$670$	−23.8780	+	62.9612i	−0.922489	+	2.43240i
$671$	−27.3558	+	39.6317i	−1.05606	+	1.52996i
$672$	2.88544	+	1.51439i	0.111308	+	0.0584190i
$673$	−4.31981	+	35.5768i	−0.166516	+	1.37139i	0.634583	+	0.772854i	$0.281172\pi$
$673$	−4.31981	+	35.5768i	−0.166516	+	1.37139i	−0.801100	+	0.598531i	$0.795751\pi$
$674$	31.5641	+	7.77985i	1.21580	+	0.299668i
$675$	−7.83135			−0.301429
$676$	8.84187	−	47.3414i	0.340072	−	1.82082i
$677$	−22.0072			−0.845804			−0.422902	−	0.906175i	$-0.638989\pi$
$677$	−22.0072			−0.845804			−0.422902	+	0.906175i	$0.638989\pi$
$678$	−15.2131	−	3.74969i	−0.584255	−	0.144006i
$679$	−1.22702	+	10.1054i	−0.0470885	+	0.387809i
$680$	−25.3192	−	13.2885i	−0.970946	−	0.509592i
$681$	12.3410	−	17.8790i	0.472906	−	0.685123i
$682$	12.5571	−	33.1105i	0.480838	−	1.26787i
$683$	25.9167	+	22.9602i	0.991675	+	0.878547i	0.992597	−	0.121452i	$-0.0387552\pi$
$683$	25.9167	+	22.9602i	0.991675	+	0.878547i	−0.000922524		1.00000i	$0.500294\pi$
$684$	−5.26295	−	4.66257i	−0.201234	−	0.178278i
$685$	−39.2451	−	9.67305i	−1.49948	−	0.369588i
$686$	27.7409	−	24.5763i	1.05915	−	0.938327i
$687$	20.7251	−	5.10827i	0.790711	−	0.194893i
$688$	−12.5187	+	18.1365i	−0.477271	+	0.691446i
$689$	40.1333	−	8.54386i	1.52896	−	0.325495i
$690$	25.8911	+	37.5097i	0.985657	+	1.42797i
$691$	35.2108	+	31.1940i	1.33948	+	1.18668i	0.965851	+	0.259099i	$0.0834255\pi$
$691$	35.2108	+	31.1940i	1.33948	+	1.18668i	0.373630	+	0.927578i	$0.378113\pi$
$692$	−36.7863	−	53.2941i	−1.39840	−	2.02594i
$693$	−3.68121	−	3.26127i	−0.139838	−	0.123885i
$694$	−10.9114	−	5.72675i	−0.414192	−	0.217385i
$695$	7.93750			0.301087
$696$	6.36218	−	3.33913i	0.241158	−	0.126569i
$697$	−9.75899	+	8.64571i	−0.369648	+	0.327480i
$698$	−61.0680			−2.31146
$699$	−20.3176			−0.768482
$700$	−27.0754	+	23.9867i	−1.02335	+	0.906613i
$701$	−2.33069	−	6.14553i	−0.0880290	−	0.232113i	0.883771	−	0.467919i	$-0.154996\pi$
$701$	−2.33069	−	6.14553i	−0.0880290	−	0.232113i	−0.971800	+	0.235806i	$0.924227\pi$
$702$	−2.79531	−	8.14532i	−0.105502	−	0.307425i
$703$	0.902866	−	2.38066i	0.0340522	−	0.0897884i
$704$	15.2077	+	40.0995i	0.573164	+	1.51131i
$705$	21.5593	+	5.31388i	0.811969	+	0.200132i
$706$	31.9424	+	46.2765i	1.20217	+	1.74164i
$707$	0.474013	−	1.24987i	0.0178271	−	0.0470061i
$708$	1.05069	+	2.77045i	0.0394875	+	0.104120i
$709$	4.87726	+	40.1679i	0.183169	+	1.50854i	0.736992	+	0.675901i	$0.236245\pi$
$709$	4.87726	+	40.1679i	0.183169	+	1.50854i	−0.553823	+	0.832635i	$0.686831\pi$
$710$	−46.1653	−	66.8820i	−1.73255	−	2.51004i
$711$	7.64260	−	1.88373i	0.286620	−	0.0706455i
$712$	−46.5162	−	41.2098i	−1.74327	−	1.54440i
$713$	7.10045	−	18.7223i	0.265914	−	0.701157i
$714$	5.66906	+	1.39730i	0.212159	+	0.0522926i
$715$	27.5880	+	42.8289i	1.03173	+	1.60171i
$716$	−41.6581	+	10.2678i	−1.55684	+	0.383726i
$717$	1.03144	−	8.49471i	0.0385200	−	0.317241i
$718$	16.2165	−	8.51106i	0.605193	−	0.317630i
$719$	17.7704	+	46.8567i	0.662724	+	1.74746i	0.664305	+	0.747461i	$0.268727\pi$
$719$	17.7704	+	46.8567i	0.662724	+	1.74746i	−0.00158121	+	0.999999i	$0.500503\pi$
$720$	8.05133	+	1.98447i	0.300055	+	0.0739570i
$721$	9.37356	−	8.30425i	0.349090	−	0.309267i
$722$	35.7078	+	8.80118i	1.32891	+	0.327546i
$723$	20.8537	−	10.9449i	0.775557	−	0.407044i
$724$	38.0873	−	19.9898i	1.41550	−	0.742914i
$725$	−1.66593	−	13.7201i	−0.0618709	−	0.509553i
$726$	−1.31260	−	10.8102i	−0.0487151	−	0.401205i
$727$	37.5961	−	33.3073i	1.39436	−	1.23530i	0.455849	−	0.890057i	$-0.349336\pi$
$727$	37.5961	−	33.3073i	1.39436	−	1.23530i	0.938514	−	0.345241i	$-0.112203\pi$
$728$	−15.9264	−	9.01819i	−0.590272	−	0.334237i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	−76.0929	+	110.240i	−2.81632	+	4.08015i
$731$	6.61873	−	17.4522i	0.244803	−	0.645491i
$732$	5.45152	+	44.8973i	0.201494	+	1.65945i
$733$	−0.111012	+	0.914268i	−0.00410033	+	0.0337693i	−0.994615	−	0.103635i	$-0.966953\pi$
$733$	−0.111012	+	0.914268i	−0.00410033	+	0.0337693i	0.990515	+	0.137404i	$0.0438758\pi$
$734$	33.4239	+	17.5422i	1.23370	+	0.647496i
$735$	−11.0808	+	16.0533i	−0.408721	+	0.592134i
$736$	4.93736	+	13.0188i	0.181994	+	0.479877i
$737$	23.2379	−	20.5870i	0.855981	−	0.758333i
$738$	9.02216	−	13.0708i	0.332110	−	0.481145i
$739$	−2.63023	−	3.81055i	−0.0967547	−	0.140173i	0.771617	−	0.636088i	$-0.219448\pi$
$739$	−2.63023	−	3.81055i	−0.0967547	−	0.140173i	−0.868371	+	0.495914i	$0.834833\pi$
$740$	2.14580	+	17.6722i	0.0788810	+	0.649644i
$741$	−4.97486	−	4.69898i	−0.182756	−	0.172621i
$742$	4.08496	−	33.6427i	0.149964	−	1.23506i
$743$	−23.5872	+	12.3795i	−0.865332	+	0.454161i	−0.838131	−	0.545469i	$-0.816352\pi$
$743$	−23.5872	+	12.3795i	−0.865332	+	0.454161i	−0.0272009	+	0.999630i	$0.508659\pi$
$744$	−5.42652	−	14.3086i	−0.198946	−	0.524577i
$745$	−1.42046	+	11.6986i	−0.0520418	+	0.428603i
$746$	−78.9110			−2.88914
$747$	−0.894344	+	7.36558i	−0.0327223	+	0.269493i
$748$	16.2758	+	23.5796i	0.595103	+	0.862156i
$749$	−8.63964	+	2.12948i	−0.315686	+	0.0778095i
$750$	13.7607	−	19.9358i	0.502470	−	0.727953i
$751$	10.5332	−	2.59619i	0.384360	−	0.0947363i	−0.0424008	−	0.999101i	$-0.513501\pi$
$751$	10.5332	−	2.59619i	0.384360	−	0.0947363i	0.426761	+	0.904364i	$0.359654\pi$
$752$	−12.7060	−	6.66864i	−0.463341	−	0.243180i
$753$	−24.5774	−	12.8992i	−0.895649	−	0.470073i
$754$	13.6756	−	6.62996i	0.498034	−	0.241449i
$755$	60.6934	−	31.8544i	2.20886	−	1.15930i
$756$	−4.61892			−0.167989
$757$	−31.6980	−	16.6364i	−1.15208	−	0.604661i	−0.223106	−	0.974794i	$-0.571620\pi$
$757$	−31.6980	−	16.6364i	−1.15208	−	0.604661i	−0.928979	+	0.370133i	$0.879312\pi$
$758$	4.26876	−	11.2558i	0.155048	−	0.408828i
$759$	−2.53290	−	20.8603i	−0.0919383	−	0.757180i
$760$	26.8755	−	6.62422i	0.974878	−	0.240286i
$761$	−32.7282	+	8.06678i	−1.18640	+	0.292420i	−0.782657	−	0.622453i	$-0.786136\pi$
$761$	−32.7282	+	8.06678i	−1.18640	+	0.292420i	−0.403740	+	0.914874i	$0.632290\pi$
$762$	0.669208	+	5.51142i	0.0242429	+	0.199658i
$763$	8.84740	−	23.3287i	0.320297	−	0.844554i
$764$	−23.9162	−	12.5522i	−0.865256	−	0.454121i
$765$	−7.02334			−0.253929
$766$	−32.1836	+	16.8913i	−1.16284	+	0.610306i
$767$	0.936064	+	2.72762i	0.0337993	+	0.0984886i
$768$	24.6094	+	12.9160i	0.888016	+	0.466067i
$769$	−37.5815	−	19.7243i	−1.35522	−	0.711276i	−0.378464	−	0.925616i	$-0.623548\pi$
$769$	−37.5815	−	19.7243i	−1.35522	−	0.711276i	−0.976759	+	0.214340i	$0.931240\pi$
$770$	40.8541	−	10.0696i	1.47228	−	0.362884i
$771$	7.43999	−	10.7787i	0.267945	−	0.388185i
$772$	−33.5647	+	8.27295i	−1.20802	+	0.297750i
$773$	−24.0587	−	34.8551i	−0.865333	−	1.25365i	−0.965951	−	0.258725i	$-0.916697\pi$
$773$	−24.0587	−	34.8551i	−0.865333	−	1.25365i	0.100618	−	0.994925i	$-0.467918\pi$
$774$	−2.74066	+	22.5714i	−0.0985110	+	0.811311i
$775$	−29.4357			−1.05736
$776$	−4.00674	+	32.9985i	−0.143834	+	1.18458i
$777$	−0.593106	−	1.56389i	−0.0212776	−	0.0561043i
$778$	38.5257	−	20.2199i	1.38121	−	0.724917i
$779$	1.52127	−	12.5288i	0.0545053	−	0.448891i
$780$	46.0673	+	12.9266i	1.64947	+	0.462845i
$781$	4.51630	+	37.1951i	0.161606	+	1.33095i
$782$	14.1717	+	20.5312i	0.506778	+	0.734195i
$783$	1.00253	−	1.45242i	0.0358275	−	0.0519051i
$784$	9.43567	−	8.35928i	0.336988	−	0.298546i
$785$	−1.15470	−	3.04471i	−0.0412132	−	0.108670i
$786$	−15.3791	+	22.2805i	−0.548554	+	0.794718i
$787$	−10.2170	−	5.36228i	−0.364195	−	0.191144i	0.272692	−	0.962101i	$-0.412086\pi$
$787$	−10.2170	−	5.36228i	−0.364195	−	0.191144i	−0.636887	+	0.770957i	$0.719778\pi$
$788$	−10.0671	+	82.9097i	−0.358624	+	2.95354i
$789$	−0.172126	−	1.41759i	−0.00612787	−	0.0504675i
$790$	−23.8804	+	62.9675i	−0.849627	+	2.24028i
$791$	−4.64629	+	6.73131i	−0.165203	+	0.239338i
$792$	−12.0208	−	10.6495i	−0.427139	−	0.378412i
$793$	3.90912	+	43.8438i	0.138817	+	1.55694i
$794$	−38.1538	+	33.8014i	−1.35403	+	1.19957i
$795$	4.91376	+	40.4684i	0.174273	+	1.43527i
$796$	11.4829	+	94.5702i	0.407000	+	3.35195i
$797$	−16.5419	+	8.68187i	−0.585945	+	0.307528i	−0.731520	−	0.681820i	$-0.761189\pi$
$797$	−16.5419	+	8.68187i	−0.585945	+	0.307528i	0.145575	+	0.989347i	$0.453497\pi$
$798$	−5.00457	+	2.62660i	−0.177160	+	0.0929806i
$799$	11.8006	+	2.90859i	0.417476	+	0.102899i
$800$	15.3208	−	13.5731i	0.541672	−	0.479880i
$801$	−14.8204	−	3.65291i	−0.523654	−	0.129069i
$802$	−22.9144	−	60.4204i	−0.809137	−	2.13352i
$803$	54.6839	−	28.7003i	1.92975	−	1.01281i
$804$	3.51452	−	28.9447i	0.123948	−	1.02080i
$805$	23.1010	−	5.69388i	0.814202	−	0.200683i
$806$	−10.5067	−	30.6158i	−0.370084	−	1.07840i
$807$	4.67367	+	1.15196i	0.164521	+	0.0405508i
$808$	1.54786	−	4.08137i	0.0544535	−	0.143582i
$809$	5.21643	+	4.62136i	0.183400	+	0.162478i	0.749828	−	0.661633i	$-0.230136\pi$
$809$	5.21643	+	4.62136i	0.183400	+	0.162478i	−0.566428	+	0.824112i	$0.691675\pi$
$810$	8.30697	−	2.04748i	0.291877	−	0.0719412i
$811$	30.4422	+	44.1031i	1.06897	+	1.54867i	0.813246	+	0.581921i	$0.197699\pi$
$811$	30.4422	+	44.1031i	1.06897	+	1.54867i	0.255724	+	0.966750i	$0.417686\pi$
$812$	−0.982561	−	8.09212i	−0.0344811	−	0.283978i
$813$	−0.733988	−	1.93537i	−0.0257421	−	0.0678763i
$814$	4.48170	−	11.8173i	0.157084	−	0.414196i
$815$	34.4617	+	49.9264i	1.20714	+	1.74885i
$816$	4.40696	+	1.08622i	0.154274	+	0.0380252i
$817$	6.40702	+	16.8939i	0.224153	+	0.591043i
$818$	−25.1966	+	66.4379i	−0.880977	+	2.32295i
$819$	−4.49312	−	0.143403i	−0.157002	−	0.00501091i
$820$	31.2913	+	82.5083i	1.09274	+	2.88131i
$821$	22.4238	−	19.8657i	0.782595	−	0.693318i	−0.173998	−	0.984746i	$-0.555669\pi$
$821$	22.4238	−	19.8657i	0.782595	−	0.693318i	0.956593	+	0.291428i	$0.0941303\pi$
$822$	26.9506			0.940012
$823$	−5.39974			−0.188223			−0.0941115	−	0.995562i	$-0.530001\pi$
$823$	−5.39974			−0.188223			−0.0941115	+	0.995562i	$0.530001\pi$
$824$	30.6088	−	27.1170i	1.06631	−	0.944666i
$825$	−27.3526	+	14.3558i	−0.952296	+	0.499803i
$826$	2.38177			0.0828723
$827$	50.4011	+	26.4525i	1.75262	+	0.919845i	0.942935	+	0.332978i	$0.108053\pi$
$827$	50.4011	+	26.4525i	1.75262	+	0.919845i	0.809683	+	0.586867i	$0.199639\pi$
$828$	−14.7722	−	13.0870i	−0.513368	−	0.454804i
$829$	−6.55928	−	9.50276i	−0.227813	−	0.330045i	0.692363	−	0.721550i	$-0.256570\pi$
$829$	−6.55928	−	9.50276i	−0.227813	−	0.330045i	−0.920176	+	0.391505i	$0.871954\pi$
$830$	−47.5152	−	42.0948i	−1.64928	−	1.46113i
$831$	−6.62618	−	9.59967i	−0.229860	−	0.333009i
$832$	34.1119	+	19.3156i	1.18262	+	0.669648i
$833$	−6.06515	+	8.78689i	−0.210145	+	0.304448i
$834$	−5.13871	+	1.26658i	−0.177939	+	0.0438580i
$835$	−11.7396	+	10.4003i	−0.406264	+	0.359919i
$836$	−26.9290	−	6.63740i	−0.931358	−	0.229559i
$837$	−2.81343	−	2.49248i	−0.0972463	−	0.0861527i
$838$	24.3550	+	21.5766i	0.841328	+	0.745352i
$839$	2.08628	−	5.50106i	0.0720263	−	0.189918i	−0.894169	−	0.447730i	$-0.852232\pi$
$839$	2.08628	−	5.50106i	0.0720263	−	0.189918i	0.966195	+	0.257813i	$0.0830017\pi$
$840$	10.3293	−	14.9646i	0.356394	−	0.516327i
$841$	−22.9204	−	12.0296i	−0.790359	−	0.414812i
$842$	−0.501843	+	4.13305i	−0.0172947	+	0.142434i
$843$	−3.96977	−	0.978462i	−0.136726	−	0.0337000i
$844$	−87.8694			−3.02459
$845$	44.4113	+	14.0047i	1.52780	+	0.481778i
$846$	−14.8053			−0.509017
$847$	−5.51938	−	1.36041i	−0.189648	−	0.0467441i
$848$	3.17553	−	26.1528i	0.109048	−	0.898091i
$849$	−12.8970	−	6.76888i	−0.442625	−	0.232307i
$850$	20.8331	−	30.1820i	0.714571	−	1.03523i
$851$	2.53418	−	6.68209i	0.0868707	−	0.229059i
$852$	26.3396	+	23.3349i	0.902381	+	0.799439i
$853$	4.10719	+	3.63865i	0.140627	+	0.124585i	0.730504	−	0.682908i	$-0.239285\pi$
$853$	4.10719	+	3.63865i	0.140627	+	0.124585i	−0.589877	+	0.807493i	$0.700824\pi$
$854$	35.2988	+	8.70037i	1.20790	+	0.297720i
$855$	5.08889	−	4.50836i	0.174036	−	0.154183i
$856$	−28.2122	+	6.95368i	−0.964273	+	0.237672i
$857$	10.0021	−	14.4905i	0.341664	−	0.494986i	−0.614056	−	0.789262i	$-0.710463\pi$
$857$	10.0021	−	14.4905i	0.341664	−	0.494986i	0.955720	+	0.294276i	$0.0950785\pi$
$858$	−24.6945	−	23.3251i	−0.843056	−	0.796306i
$859$	−17.5494	−	25.4248i	−0.598779	−	0.867481i	0.400018	−	0.916507i	$-0.369004\pi$
$859$	−17.5494	−	25.4248i	−0.598779	−	0.867481i	−0.998798	+	0.0490257i	$0.984388\pi$
$860$	−94.5583	−	83.7714i	−3.22441	−	2.85658i
$861$	−4.70972	−	6.82320i	−0.160507	−	0.232534i
$862$	−29.5012	−	26.1358i	−1.00481	−	0.890187i
$863$	−16.6460	−	8.73647i	−0.566635	−	0.297393i	0.156974	−	0.987603i	$-0.449826\pi$
$863$	−16.6460	−	8.73647i	−0.566635	−	0.297393i	−0.723609	+	0.690210i	$0.757518\pi$
$864$	2.61365			0.0889181
$865$	55.4432	−	29.0988i	1.88513	−	0.989390i
$866$	−73.0077	+	64.6791i	−2.48090	+	2.19789i
$867$	13.1557			0.446792
$868$	−17.3611			−0.589276
$869$	23.2403	−	20.5891i	0.788372	−	0.698437i
$870$	5.35419	+	14.1178i	0.181524	+	0.478639i
$871$	4.31745	−	28.0473i	0.146291	−	0.950346i
$872$	28.8906	−	76.1783i	0.978360	−	2.57972i
$873$	2.89520	+	7.63400i	0.0979875	+	0.258372i
$874$	−23.4476	−	5.77931i	−0.793126	−	0.195488i
$875$	−7.18332	−	10.4068i	−0.242841	−	0.351815i
$876$	20.5676	−	54.2324i	0.694916	−	1.83234i
$877$	−1.52942	−	4.03274i	−0.0516447	−	0.136176i	0.906712	−	0.421751i	$-0.138585\pi$
$877$	−1.52942	−	4.03274i	−0.0516447	−	0.136176i	−0.958356	+	0.285575i	$0.907815\pi$
$878$	0.878278	+	7.23327i	0.0296405	+	0.244111i
$879$	16.0789	+	23.2944i	0.542329	+	0.785700i
$880$	31.7587	−	7.82782i	1.07059	−	0.263876i
$881$	17.0924	+	15.1426i	0.575858	+	0.510166i	0.900027	−	0.435833i	$-0.143546\pi$
$881$	17.0924	+	15.1426i	0.575858	+	0.510166i	−0.324169	+	0.945999i	$0.605085\pi$
$882$	4.61205	−	12.1610i	0.155296	−	0.409482i
$883$	−48.0983	−	11.8552i	−1.61864	−	0.398958i	−0.677106	−	0.735885i	$-0.736766\pi$
$883$	−48.0983	−	11.8552i	−1.61864	−	0.398958i	−0.941531	+	0.336927i	$0.890612\pi$
$884$	25.2153	+	7.07545i	0.848082	+	0.237973i
$885$	−2.78175	+	0.685640i	−0.0935075	+	0.0230475i
$886$	0.954701	−	7.86267i	0.0320738	−	0.264152i
$887$	9.72561	−	5.10439i	0.326554	−	0.171389i	−0.293477	−	0.955966i	$-0.594812\pi$
$887$	9.72561	−	5.10439i	0.326554	−	0.171389i	0.620031	+	0.784577i	$0.287120\pi$
$888$	−1.93675	−	5.10679i	−0.0649931	−	0.171373i
$889$	2.81397	+	0.693582i	0.0943776	+	0.0232620i
$890$	97.7496	−	86.5986i	3.27657	−	2.90279i
$891$	−3.82991	−	0.943988i	−0.128307	−	0.0316248i
$892$	49.7347	−	26.1028i	1.66524	−	0.873986i
$893$	−10.4174	+	5.46748i	−0.348606	+	0.182962i
$894$	−0.947125	−	7.80028i	−0.0316766	−	0.260880i
$895$	−5.00056	−	41.1833i	−0.167150	−	1.37661i
$896$	19.3561	−	17.1480i	0.646643	−	0.572876i
$897$	−13.9635	−	13.1892i	−0.466228	−	0.440374i
$898$	−56.9284	−	50.4342i	−1.89973	−	1.68301i
$899$	3.76821	−	5.45920i	0.125677	−	0.182074i
$900$	−10.2878	+	27.1268i	−0.342928	+	0.904227i
$901$	2.68958	+	22.1507i	0.0896029	+	0.737947i
$902$	7.55139	−	62.1913i	0.251434	−	2.07074i
$903$	10.5096	+	5.51588i	0.349738	+	0.183557i
$904$	−15.1722	+	21.9807i	−0.504619	+	0.731066i
$905$	14.7486	+	38.8889i	0.490261	+	1.29271i
$906$	−34.2097	+	30.3072i	−1.13654	+	1.00689i
$907$	15.9322	−	23.0818i	0.529020	−	0.766417i	−0.463813	−	0.885933i	$-0.653519\pi$
$907$	15.9322	−	23.0818i	0.529020	−	0.766417i	0.992832	+	0.119516i	$0.0381343\pi$
$908$	−45.7185	−	66.2346i	−1.51722	−	2.19807i
$909$	−0.129231	−	1.06431i	−0.00428632	−	0.0353010i
$910$	22.8468	−	30.9396i	0.757365	−	1.02564i
$911$	−1.08389	+	8.92660i	−0.0359107	+	0.295751i	0.963678	+	0.267068i	$0.0860547\pi$
$911$	−1.08389	+	8.92660i	−0.0359107	+	0.295751i	−0.999589	+	0.0286838i	$0.990868\pi$
$912$	−3.89040	+	2.04184i	−0.128824	+	0.0676120i
$913$	10.3783	+	27.3653i	0.343471	+	0.905658i
$914$	−6.27311	+	51.6637i	−0.207496	+	1.70888i
$915$	−43.7313			−1.44571
$916$	9.53158	−	78.4996i	0.314932	−	2.59370i
$917$	8.02815	+	11.6308i	0.265113	+	0.384082i
$918$	4.54688	−	1.12071i	0.150069	−	0.0369888i
$919$	−8.60023	+	12.4596i	−0.283696	+	0.411004i	−0.938761	−	0.344568i	$-0.888025\pi$
$919$	−8.60023	+	12.4596i	−0.283696	+	0.411004i	0.655066	+	0.755572i	$0.272641\pi$
$920$	75.4347	−	18.5930i	2.48701	−	0.612993i
$921$	−28.1314	−	14.7645i	−0.926961	−	0.486506i
$922$	19.4178	+	10.1912i	0.639490	+	0.335630i
$923$	24.8978	+	23.5171i	0.819520	+	0.774075i
$924$	−16.1325	+	8.46701i	−0.530722	+	0.278544i
$925$	−10.5057			−0.345427
$926$	−69.5187	−	36.4862i	−2.28453	−	1.19901i
$927$	3.56167	−	9.39135i	0.116981	−	0.308453i
$928$	0.555989	+	4.57898i	0.0182512	+	0.150312i
$929$	−40.9792	+	10.1005i	−1.34448	+	0.331385i	−0.844920	−	0.534892i	$-0.820352\pi$
$929$	−40.9792	+	10.1005i	−1.34448	+	0.331385i	−0.499563	+	0.866278i	$0.666506\pi$
$930$	31.2234	−	7.69588i	1.02386	−	0.252358i
$931$	−1.24579	−	10.2600i	−0.0408291	−	0.336258i
$932$	−26.6907	+	70.3776i	−0.874283	+	2.30529i
$933$	16.9525	+	8.89734i	0.554999	+	0.291286i
$934$	48.1456			1.57537
$935$	−24.5305	+	12.8746i	−0.802232	+	0.421044i
$936$	−14.6720	−	0.468274i	−0.479570	−	0.0153060i
$937$	2.84110	+	1.49112i	0.0928147	+	0.0487129i	0.510492	−	0.859883i	$-0.329463\pi$
$937$	2.84110	+	1.49112i	0.0928147	+	0.0487129i	−0.417677	+	0.908596i	$0.637156\pi$
$938$	−20.7531	−	10.8920i	−0.677612	−	0.355638i
$939$	2.99712	−	0.738724i	0.0978073	−	0.0241073i
$940$	46.7285	−	67.6979i	1.52411	−	2.20806i
$941$	11.2603	−	2.77543i	0.367077	−	0.0904763i	−0.0514627	−	0.998675i	$-0.516388\pi$
$941$	11.2603	−	2.77543i	0.367077	−	0.0904763i	0.418539	+	0.908199i	$0.362542\pi$
$942$	1.23339	+	1.78688i	0.0401861	+	0.0582196i
$943$	4.26994	−	35.1661i	0.139048	−	1.14517i
$944$	1.85151			0.0602616
$945$	0.538336	−	4.43359i	0.0175121	−	0.144225i
$946$	31.8036	+	83.8591i	1.03402	+	2.72649i
$947$	−37.1979	+	19.5230i	−1.20877	+	0.634411i	−0.944014	−	0.329905i	$-0.892983\pi$
$947$	−37.1979	+	19.5230i	−1.20877	+	0.634411i	−0.264755	+	0.964316i	$0.585291\pi$
$948$	3.51488	−	28.9476i	0.114158	−	0.940175i
$949$	21.6912	−	52.1168i	0.704127	−	1.69178i
$950$	4.27915	+	35.2420i	0.138834	+	1.14340i
$951$	6.62750	+	9.60159i	0.214911	+	0.311353i
$952$	5.65382	−	8.19097i	0.183241	−	0.265471i
$953$	3.52275	−	3.12088i	0.114113	−	0.101095i	−0.604137	−	0.796881i	$-0.706482\pi$
$953$	3.52275	−	3.12088i	0.114113	−	0.101095i	0.718250	+	0.695785i	$0.244944\pi$
$954$	−9.63864	−	25.4150i	−0.312063	−	0.822842i
$955$	14.8360	−	21.4936i	0.480080	−	0.695516i
$956$	−28.0696	−	14.7321i	−0.907836	−	0.476469i
$957$	0.839101	−	6.91062i	0.0271243	−	0.223389i
$958$	7.38487	+	60.8199i	0.238594	+	1.96500i
$959$	4.98883	−	13.1545i	0.161098	−	0.424780i
$960$	−22.1238	+	32.0518i	−0.714041	+	1.03447i
$961$	12.6290	+	11.1883i	0.407387	+	0.360913i
$962$	−3.74990	−	10.9269i	−0.120902	−	0.352298i
$963$	−5.34199	+	4.73259i	−0.172143	+	0.152506i
$964$	−10.5167	−	86.6125i	−0.338719	−	2.78960i
$965$	−4.02904	−	33.1822i	−0.129699	−	1.06817i
$966$	−14.0469	+	7.37239i	−0.451952	+	0.237203i
$967$	17.1131	−	8.98166i	0.550321	−	0.288831i	−0.166554	−	0.986032i	$-0.553264\pi$
$967$	17.1131	−	8.98166i	0.550321	−	0.288831i	0.716875	+	0.697202i	$0.245572\pi$
$968$	−18.0232	−	4.44232i	−0.579287	−	0.142782i
$969$	2.78544	−	2.46769i	0.0894813	−	0.0792735i
$970$	−67.8228	−	16.7168i	−2.17766	−	0.536745i
$971$	8.12442	+	21.4223i	0.260725	+	0.687475i	0.999902	+	0.0139647i	$0.00444525\pi$
$971$	8.12442	+	21.4223i	0.260725	+	0.687475i	−0.739177	+	0.673511i	$0.764786\pi$
$972$	−3.28027	+	1.72162i	−0.105215	+	0.0552210i
$973$	−0.333016	+	2.74263i	−0.0106760	+	0.0879247i
$974$	25.8754	−	6.37772i	0.829103	−	0.204355i
$975$	−10.8498	+	26.0686i	−0.347473	+	0.834863i
$976$	27.4402	+	6.76340i	0.878339	+	0.216491i
$977$	3.64971	−	9.62350i	0.116765	−	0.307883i	−0.863874	−	0.503707i	$-0.831969\pi$
$977$	3.64971	−	9.62350i	0.116765	−	0.307883i	0.980639	+	0.195824i	$0.0627382\pi$
$978$	−30.2771	−	26.8231i	−0.968154	−	0.857710i
$979$	−58.4596	+	14.4090i	−1.86838	+	0.460514i
$980$	41.0500	+	59.4712i	1.31129	+	1.89974i
$981$	−2.41208	−	19.8653i	−0.0770119	−	0.634250i
$982$	6.98063	+	18.4064i	0.222761	+	0.587373i
$983$	−16.6051	+	43.7842i	−0.529622	+	1.39650i	0.357044	+	0.934087i	$0.383785\pi$
$983$	−16.6051	+	43.7842i	−0.529622	+	1.39650i	−0.886666	+	0.462410i	$0.846985\pi$
$984$	−15.3793	−	22.2807i	−0.490274	−	0.710284i
$985$	−78.4097	−	19.3263i	−2.49834	−	0.615786i
$986$	2.93066	+	7.72750i	0.0933311	+	0.246094i
$987$	−2.74061	+	7.22639i	−0.0872345	+	0.230019i
$988$	−22.8120	+	11.0593i	−0.725747	+	0.351845i
$989$	17.9833	+	47.4182i	0.571837	+	1.50781i
$990$	25.2605	−	22.3789i	0.802833	−	0.711248i
$991$	2.51282			0.0798223			0.0399112	−	0.999203i	$-0.487293\pi$
$991$	2.51282			0.0798223			0.0399112	+	0.999203i	$0.487293\pi$
$992$	9.82392			0.311910
$993$	1.09555	−	0.970574i	0.0347663	−	0.0308002i
$994$	25.0465	−	13.1454i	0.794426	−	0.416947i
$995$	−92.1140			−2.92021
$996$	24.3386	+	12.7739i	0.771197	+	0.404756i
$997$	−2.95802	−	2.62058i	−0.0936814	−	0.0829945i	0.614982	−	0.788541i	$-0.289163\pi$
$997$	−2.95802	−	2.62058i	−0.0936814	−	0.0829945i	−0.708664	+	0.705546i	$0.750702\pi$
$998$	40.2098	+	58.2540i	1.27282	+	1.84400i
$999$	−1.00413	−	0.889578i	−0.0317691	−	0.0281450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.a.40.2	✓	180
169.131	even	13	inner	507.2.m.a.469.2	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.a.40.2	✓	180	1.1	even	1	trivial
507.2.m.a.469.2	yes	180	169.131	even	13	inner

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.31903 - 0.571589i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(3.28027 + 1.72162i) q^{4} +(-2.03486 + 2.94800i) q^{5} +(0.846950 - 2.23322i) q^{6} +(-0.933245 - 0.826783i) q^{7} +(-3.04745 - 2.69981i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(-2.31903 - 0.571589i) q^{2} +(-0.120537 + 0.992709i) q^{3} +(3.28027 + 1.72162i) q^{4} +(-2.03486 + 2.94800i) q^{5} +(0.846950 - 2.23322i) q^{6} +(-0.933245 - 0.826783i) q^{7} +(-3.04745 - 2.69981i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(6.40394 - 5.67340i) q^{10} +(-3.82991 + 0.943988i) q^{11} +(-2.10446 + 3.04884i) q^{12} +(-2.14180 + 2.90046i) q^{13} +(1.69164 + 2.45077i) q^{14} +(-2.68123 - 2.37536i) q^{15} +(1.31503 + 1.90515i) q^{16} +(-1.46759 - 1.30017i) q^{17} +(2.11485 + 1.10996i) q^{18} +1.89797 q^{19} +(-11.7502 + 6.16699i) q^{20} +(0.933245 - 0.826783i) q^{21} +9.42125 q^{22} +5.32725 q^{23} +(3.04745 - 2.69981i) q^{24} +(-2.77703 - 7.32244i) q^{25} +(6.62477 - 5.50203i) q^{26} +(0.354605 - 0.935016i) q^{27} +(-1.63789 - 4.31877i) q^{28} +(1.71353 + 0.422348i) q^{29} +(4.86012 + 7.04110i) q^{30} +(1.33285 - 3.51445i) q^{31} +(0.926812 + 2.44380i) q^{32} +(-0.475461 - 3.91577i) q^{33} +(2.66022 + 3.85400i) q^{34} +(4.33638 - 1.06882i) q^{35} +(-2.77294 - 2.45661i) q^{36} +(0.475702 - 1.25432i) q^{37} +(-4.40144 - 1.08486i) q^{38} +(-2.62115 - 2.47580i) q^{39} +(14.1602 - 3.49017i) q^{40} +(0.801528 - 6.60118i) q^{41} +(-2.63680 + 1.38390i) q^{42} +(3.37573 + 8.90106i) q^{43} +(-14.1883 - 3.49711i) q^{44} +(2.68123 - 2.37536i) q^{45} +(-12.3540 - 3.04500i) q^{46} +(-5.48873 + 2.88071i) q^{47} +(-2.04977 + 1.07580i) q^{48} +(-0.656381 - 5.40578i) q^{49} +(2.25460 + 18.5683i) q^{50} +(1.46759 - 1.30017i) q^{51} +(-12.0192 + 5.82694i) q^{52} +(-8.51836 - 7.54661i) q^{53} +(-1.35678 + 1.96564i) q^{54} +(5.01044 - 13.2115i) q^{55} +(0.611865 + 5.03916i) q^{56} +(-0.228775 + 1.88413i) q^{57} +(-3.73233 - 1.95888i) q^{58} +(0.454346 - 0.658233i) q^{59} +(-4.70569 - 12.4079i) q^{60} +(9.13806 - 8.09561i) q^{61} +(-5.09975 + 7.38826i) q^{62} +(0.708265 + 1.02610i) q^{63} +(-1.31052 - 10.7931i) q^{64} +(-4.19231 - 12.2161i) q^{65} +(-1.13561 + 9.35255i) q^{66} +(-6.96902 + 3.65762i) q^{67} +(-2.57570 - 6.79156i) q^{68} +(-0.642129 + 5.28841i) q^{69} -10.6671 q^{70} +(1.14495 - 9.42954i) q^{71} +(2.31279 + 3.35066i) q^{72} +(-15.2016 + 3.74686i) q^{73} +(-1.82012 + 2.63691i) q^{74} +(7.60379 - 1.87416i) q^{75} +(6.22585 + 3.26758i) q^{76} +(4.35472 + 2.28553i) q^{77} +(4.66339 + 7.23967i) q^{78} +(-6.96971 + 3.65799i) q^{79} -8.29229 q^{80} +(0.885456 + 0.464723i) q^{81} +(-5.63193 + 14.8502i) q^{82} +(-0.894344 - 7.36558i) q^{83} +(4.48470 - 1.10538i) q^{84} +(6.81925 - 1.68079i) q^{85} +(-2.74066 - 22.5714i) q^{86} +(-0.625813 + 1.65013i) q^{87} +(14.2201 + 7.46326i) q^{88} +15.2640 q^{89} +(-7.57559 + 3.97597i) q^{90} +(4.39688 - 0.936038i) q^{91} +(17.4748 + 9.17150i) q^{92} +(3.32817 + 1.74676i) q^{93} +(14.3751 - 3.54314i) q^{94} +(-3.86209 + 5.59521i) q^{95} +(-2.53770 + 0.625487i) q^{96} +(-4.63800 - 6.71931i) q^{97} +(-1.56772 + 12.9113i) q^{98} +3.94453 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9}+O(q^{10}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9	\( 180 q - q^{2} + 15 q^{3} - 15 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} - 15 q^{9} - 2 q^{10} - 4 q^{11} + 15 q^{12} - 14 q^{13} + 6 q^{14} + 2 q^{15} - 15 q^{16} - 2 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} - 28 q^{22} - 52 q^{23} - 3 q^{24} - 67 q^{25} - 40 q^{26} + 15 q^{27} - 4 q^{28} - 27 q^{29} + 2 q^{30} + 22 q^{31} - 5 q^{32} - 9 q^{33} + 63 q^{34} - 31 q^{35} - 15 q^{36} + 2 q^{37} + 65 q^{38} + q^{39} + 45 q^{40} - 6 q^{41} + 59 q^{42} - 60 q^{43} - 35 q^{44} - 2 q^{45} - 156 q^{46} + 15 q^{48} + 59 q^{49} - 51 q^{50} + 2 q^{51} + 66 q^{52} + 50 q^{53} + q^{54} + 55 q^{55} - 14 q^{56} - 13 q^{57} + 36 q^{58} + 92 q^{59} - 15 q^{60} + 6 q^{61} + 61 q^{62} + 4 q^{63} - 203 q^{64} - 54 q^{65} + 54 q^{66} + 86 q^{67} + 32 q^{68} + 112 q^{70} + 39 q^{71} + 3 q^{72} - 158 q^{73} - 80 q^{74} + 15 q^{75} + 130 q^{76} - 64 q^{77} + 66 q^{78} - 10 q^{79} - 310 q^{80} - 15 q^{81} + 59 q^{82} - 82 q^{83} + 4 q^{84} + 22 q^{85} - q^{86} + 40 q^{87} + 10 q^{88} + 2 q^{89} - 2 q^{90} - 100 q^{91} - 54 q^{92} + 43 q^{93} + 65 q^{94} + 58 q^{95} - 60 q^{96} + 16 q^{97} - 113 q^{98} - 30 q^{99}+O(q^{100}) \) 180 * q - q^2 + 15 * q^3 - 15 * q^4 - 2 * q^5 + q^6 + 4 * q^7 + 3 * q^8 - 15 * q^9 - 2 * q^10 - 4 * q^11 + 15 * q^12 - 14 * q^13 + 6 * q^14 + 2 * q^15 - 15 * q^16 - 2 * q^17 - q^18 + 2 * q^20 - 4 * q^21 - 28 * q^22 - 52 * q^23 - 3 * q^24 - 67 * q^25 - 40 * q^26 + 15 * q^27 - 4 * q^28 - 27 * q^29 + 2 * q^30 + 22 * q^31 - 5 * q^32 - 9 * q^33 + 63 * q^34 - 31 * q^35 - 15 * q^36 + 2 * q^37 + 65 * q^38 + q^39 + 45 * q^40 - 6 * q^41 + 59 * q^42 - 60 * q^43 - 35 * q^44 - 2 * q^45 - 156 * q^46 + 15 * q^48 + 59 * q^49 - 51 * q^50 + 2 * q^51 + 66 * q^52 + 50 * q^53 + q^54 + 55 * q^55 - 14 * q^56 - 13 * q^57 + 36 * q^58 + 92 * q^59 - 15 * q^60 + 6 * q^61 + 61 * q^62 + 4 * q^63 - 203 * q^64 - 54 * q^65 + 54 * q^66 + 86 * q^67 + 32 * q^68 + 112 * q^70 + 39 * q^71 + 3 * q^72 - 158 * q^73 - 80 * q^74 + 15 * q^75 + 130 * q^76 - 64 * q^77 + 66 * q^78 - 10 * q^79 - 310 * q^80 - 15 * q^81 + 59 * q^82 - 82 * q^83 + 4 * q^84 + 22 * q^85 - q^86 + 40 * q^87 + 10 * q^88 + 2 * q^89 - 2 * q^90 - 100 * q^91 - 54 * q^92 + 43 * q^93 + 65 * q^94 + 58 * q^95 - 60 * q^96 + 16 * q^97 - 113 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more