LMFDB - Embedded newform 507.2.m.b.352.16

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:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			352.16
Character	$\chi$	$=$	507.352
Dual form			507.2.m.b.157.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48760 - 2.15515i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-1.72254 - 4.54196i) q^{4} +(0.666157 + 0.590163i) q^{5} +(0.315650 - 2.59961i) q^{6} +(-4.93713 - 1.21689i) q^{7} +(-7.26583 - 1.79087i) q^{8} +(0.568065 - 0.822984i) q^{9} +O(q^{10})$	\(q+(1.48760 - 2.15515i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-1.72254 - 4.54196i) q^{4} +(0.666157 + 0.590163i) q^{5} +(0.315650 - 2.59961i) q^{6} +(-4.93713 - 1.21689i) q^{7} +(-7.26583 - 1.79087i) q^{8} +(0.568065 - 0.822984i) q^{9} +(2.26286 - 0.557746i) q^{10} +(0.944069 + 1.36772i) q^{11} +(-3.63599 - 3.22120i) q^{12} +(-2.24249 - 2.82334i) q^{13} +(-9.96705 + 8.83003i) q^{14} +(0.864115 + 0.212985i) q^{15} +(-7.39624 + 6.55250i) q^{16} +(5.60841 + 1.38235i) q^{17} +(-0.928606 - 2.44853i) q^{18} +5.85907 q^{19} +(1.53302 - 4.04224i) q^{20} +(-4.93713 + 1.21689i) q^{21} +4.35204 q^{22} +3.65649 q^{23} +(-7.26583 + 1.79087i) q^{24} +(-0.507211 - 4.17726i) q^{25} +(-9.42064 + 0.632922i) q^{26} +(0.120537 - 0.992709i) q^{27} +(2.97731 + 24.5204i) q^{28} +(3.02087 - 4.37648i) q^{29} +(1.74447 - 1.54547i) q^{30} +(0.551822 - 4.54466i) q^{31} +(1.31501 + 10.8301i) q^{32} +(1.47154 + 0.772325i) q^{33} +(11.3222 - 10.0306i) q^{34} +(-2.57074 - 3.72436i) q^{35} +(-4.71647 - 1.16251i) q^{36} +(-0.162361 + 1.33716i) q^{37} +(8.71592 - 12.6272i) q^{38} +(-3.29770 - 1.45781i) q^{39} +(-3.78328 - 5.48103i) q^{40} +(-4.57494 + 2.40111i) q^{41} +(-4.72186 + 12.4505i) q^{42} +(1.12914 + 9.29928i) q^{43} +(4.58593 - 6.64387i) q^{44} +(0.864115 - 0.212985i) q^{45} +(5.43937 - 7.88029i) q^{46} +(-3.25108 + 8.57239i) q^{47} +(-3.50395 + 9.23915i) q^{48} +(16.6962 + 8.76287i) q^{49} +(-9.75716 - 5.12096i) q^{50} +(5.60841 - 1.38235i) q^{51} +(-8.96072 + 15.0486i) q^{52} +(4.56592 + 1.12540i) q^{53} +(-1.96013 - 1.73652i) q^{54} +(-0.178280 + 1.46827i) q^{55} +(33.6931 + 17.6835i) q^{56} +(5.18795 - 2.72285i) q^{57} +(-4.93816 - 13.0209i) q^{58} +(1.17869 + 1.04422i) q^{59} +(-0.521101 - 4.29165i) q^{60} +(-3.52320 + 0.868390i) q^{61} +(-8.97356 - 7.94988i) q^{62} +(-3.80609 + 3.37191i) q^{63} +(7.79776 + 4.09258i) q^{64} +(0.172383 - 3.20422i) q^{65} +(3.85354 - 2.02249i) q^{66} +(-2.92322 + 7.70789i) q^{67} +(-3.38213 - 27.8543i) q^{68} +(3.23766 - 1.69925i) q^{69} -11.8508 q^{70} +(2.93611 - 1.54099i) q^{71} +(-5.60132 + 4.96234i) q^{72} +(-1.92463 - 2.78830i) q^{73} +(2.64026 + 2.33906i) q^{74} +(-2.39038 - 3.46307i) q^{75} +(-10.0925 - 26.6116i) q^{76} +(-2.99662 - 7.90145i) q^{77} +(-8.04743 + 4.93842i) q^{78} +(-4.38621 + 11.5655i) q^{79} -8.79410 q^{80} +(-0.354605 - 0.935016i) q^{81} +(-1.63089 + 13.4316i) q^{82} +(-9.97618 - 5.23590i) q^{83} +(14.0315 + 20.3281i) q^{84} +(2.92027 + 4.23074i) q^{85} +(21.7211 + 11.4001i) q^{86} +(0.640992 - 5.27905i) q^{87} +(-4.41004 - 11.6283i) q^{88} +2.09036 q^{89} +(0.826438 - 2.17914i) q^{90} +(7.63576 + 16.6681i) q^{91} +(-6.29843 - 16.6076i) q^{92} +(-1.62340 - 4.28055i) q^{93} +(13.6385 + 19.7588i) q^{94} +(3.90306 + 3.45781i) q^{95} +(6.19736 + 8.97842i) q^{96} +(4.98552 - 4.41679i) q^{97} +(43.7226 - 22.9474i) q^{98} +1.66190 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{9}{13}\right)$

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 $

$2$	1.48760	−	2.15515i	1.05189	−	1.52392i	0.214951	−	0.976625i	$-0.431041\pi$
$2$	1.48760	−	2.15515i	1.05189	−	1.52392i	0.836937	−	0.547299i	$-0.184344\pi$
$3$	0.885456	−	0.464723i	0.511218	−	0.268308i
$3$	0.885456	−	0.464723i	0.511218	−	0.268308i
$4$	−1.72254	−	4.54196i	−0.861269	−	2.27098i
$5$	0.666157	+	0.590163i	0.297914	+	0.263929i	0.798816	−	0.601575i	$-0.205460\pi$
$5$	0.666157	+	0.590163i	0.297914	+	0.263929i	−0.500902	+	0.865504i	$0.666998\pi$
$6$	0.315650	−	2.59961i	0.128864	−	1.06129i
$7$	−4.93713	−	1.21689i	−1.86606	−	0.459943i	−0.866809	−	0.498640i	$-0.833833\pi$
$7$	−4.93713	−	1.21689i	−1.86606	−	0.459943i	−0.999251	+	0.0386971i	$0.987679\pi$
$8$	−7.26583	−	1.79087i	−2.56886	−	0.633167i
$9$	0.568065	−	0.822984i	0.189355	−	0.274328i
$10$	2.26286	−	0.557746i	0.715581	−	0.176375i
$11$	0.944069	+	1.36772i	0.284647	+	0.412383i	0.939059	−	0.343755i	$-0.111699\pi$
$11$	0.944069	+	1.36772i	0.284647	+	0.412383i	−0.654412	+	0.756138i	$0.727084\pi$
$12$	−3.63599	−	3.22120i	−1.04962	−	0.929881i
$13$	−2.24249	−	2.82334i	−0.621954	−	0.783053i
$13$	−2.24249	−	2.82334i	−0.621954	−	0.783053i
$14$	−9.96705	+	8.83003i	−2.66380	+	2.35993i
$15$	0.864115	+	0.212985i	0.223114	+	0.0549926i
$16$	−7.39624	+	6.55250i	−1.84906	+	1.63812i
$17$	5.60841	+	1.38235i	1.36024	+	0.335269i	0.850914	−	0.525305i	$-0.176049\pi$
$17$	5.60841	+	1.38235i	1.36024	+	0.335269i	0.509326	+	0.860574i	$0.329895\pi$
$18$	−0.928606	−	2.44853i	−0.218875	−	0.577125i
$19$	5.85907			1.34416			0.672081	−	0.740477i	$-0.265401\pi$
$19$	5.85907			1.34416			0.672081	+	0.740477i	$0.265401\pi$
$20$	1.53302	−	4.04224i	0.342793	−	0.903871i
$21$	−4.93713	+	1.21689i	−1.07737	+	0.265548i
$22$	4.35204			0.927858
$23$	3.65649			0.762430			0.381215	−	0.924486i	$-0.375506\pi$
$23$	3.65649			0.762430			0.381215	+	0.924486i	$0.375506\pi$
$24$	−7.26583	+	1.79087i	−1.48313	+	0.365559i
$25$	−0.507211	−	4.17726i	−0.101442	−	0.835452i
$26$	−9.42064	+	0.632922i	−1.84754	+	0.124126i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	2.97731	+	24.5204i	0.562660	+	4.63392i
$29$	3.02087	−	4.37648i	0.560961	−	0.812692i	−0.435191	−	0.900338i	$-0.643319\pi$
$29$	3.02087	−	4.37648i	0.560961	−	0.812692i	0.996152	+	0.0876464i	$0.0279346\pi$
$30$	1.74447	−	1.54547i	0.318495	−	0.282162i
$31$	0.551822	−	4.54466i	0.0991102	−	0.816246i	−0.855379	−	0.518002i	$-0.826676\pi$
$31$	0.551822	−	4.54466i	0.0991102	−	0.816246i	0.954490	−	0.298244i	$-0.0964009\pi$
$32$	1.31501	+	10.8301i	0.232463	+	1.91450i
$33$	1.47154	+	0.772325i	0.256163	+	0.134445i
$34$	11.3222	−	10.0306i	1.94175	−	1.72024i
$35$	−2.57074	−	3.72436i	−0.434534	−	0.629531i
$36$	−4.71647	−	1.16251i	−0.786079	−	0.193751i
$37$	−0.162361	+	1.33716i	−0.0266919	+	0.219828i	−0.999951	−	0.00988176i	$-0.996854\pi$
$37$	−0.162361	+	1.33716i	−0.0266919	+	0.219828i	0.973259	+	0.229709i	$0.0737776\pi$
$38$	8.71592	−	12.6272i	1.41391	−	2.04840i
$39$	−3.29770	−	1.45781i	−0.528054	−	0.233436i
$40$	−3.78328	−	5.48103i	−0.598189	−	0.866627i
$41$	−4.57494	+	2.40111i	−0.714485	+	0.374991i	−0.782464	−	0.622696i	$-0.786037\pi$
$41$	−4.57494	+	2.40111i	−0.714485	+	0.374991i	0.0679785	+	0.997687i	$0.478345\pi$
$42$	−4.72186	+	12.4505i	−0.728599	+	1.92116i
$43$	1.12914	+	9.29928i	0.172192	+	1.41813i	0.780862	+	0.624703i	$0.214780\pi$
$43$	1.12914	+	9.29928i	0.172192	+	1.41813i	−0.608671	+	0.793423i	$0.708297\pi$
$44$	4.58593	−	6.64387i	0.691355	−	1.00160i
$45$	0.864115	−	0.212985i	0.128815	−	0.0317500i
$46$	5.43937	−	7.88029i	0.801991	−	1.16189i
$47$	−3.25108	+	8.57239i	−0.474219	+	1.25041i	0.458141	+	0.888880i	$0.348516\pi$
$47$	−3.25108	+	8.57239i	−0.474219	+	1.25041i	−0.932360	+	0.361532i	$0.882254\pi$
$48$	−3.50395	+	9.23915i	−0.505751	+	1.33356i
$49$	16.6962	+	8.76287i	2.38518	+	1.25184i
$50$	−9.75716	−	5.12096i	−1.37987	−	0.724212i
$51$	5.60841	−	1.38235i	0.785335	−	0.193568i
$52$	−8.96072	+	15.0486i	−1.24263	+	2.08687i
$53$	4.56592	+	1.12540i	0.627177	+	0.154585i	0.540079	−	0.841615i	$-0.318394\pi$
$53$	4.56592	+	1.12540i	0.627177	+	0.154585i	0.0870982	+	0.996200i	$0.472241\pi$
$54$	−1.96013	−	1.73652i	−0.266740	−	0.236311i
$55$	−0.178280	+	1.46827i	−0.0240393	+	0.197982i
$56$	33.6931	+	17.6835i	4.50243	+	2.36306i
$57$	5.18795	−	2.72285i	0.687160	−	0.360650i
$58$	−4.93816	−	13.0209i	−0.648412	−	1.70972i
$59$	1.17869	+	1.04422i	0.153452	+	0.135947i	0.736356	−	0.676595i	$-0.236545\pi$
$59$	1.17869	+	1.04422i	0.153452	+	0.135947i	−0.582904	+	0.812541i	$0.698084\pi$
$60$	−0.521101	−	4.29165i	−0.0672738	−	0.554050i
$61$	−3.52320	+	0.868390i	−0.451099	+	0.111186i	−0.458319	−	0.888788i	$-0.651548\pi$
$61$	−3.52320	+	0.868390i	−0.451099	+	0.111186i	0.00721949	+	0.999974i	$0.497702\pi$
$62$	−8.97356	−	7.94988i	−1.13964	−	1.00964i
$63$	−3.80609	+	3.37191i	−0.479523	+	0.424820i
$64$	7.79776	+	4.09258i	0.974719	+	0.511572i
$65$	0.172383	−	3.20422i	0.0213814	−	0.397435i
$66$	3.85354	−	2.02249i	0.474338	−	0.248952i
$67$	−2.92322	+	7.70789i	−0.357128	+	0.941668i	0.629255	+	0.777199i	$0.283360\pi$
$67$	−2.92322	+	7.70789i	−0.357128	+	0.941668i	−0.986382	+	0.164469i	$0.947409\pi$
$68$	−3.38213	−	27.8543i	−0.410143	−	3.37783i
$69$	3.23766	−	1.69925i	0.389768	−	0.204566i
$70$	−11.8508			−1.41644
$71$	2.93611	−	1.54099i	0.348453	−	0.182882i	−0.281412	−	0.959587i	$-0.590803\pi$
$71$	2.93611	−	1.54099i	0.348453	−	0.182882i	0.629864	+	0.776705i	$0.283110\pi$
$72$	−5.60132	+	4.96234i	−0.660122	+	0.584817i
$73$	−1.92463	−	2.78830i	−0.225260	−	0.326346i	0.694015	−	0.719960i	$-0.255840\pi$
$73$	−1.92463	−	2.78830i	−0.225260	−	0.326346i	−0.919276	+	0.393614i	$0.871225\pi$
$74$	2.64026	+	2.33906i	0.306924	+	0.271911i
$75$	−2.39038	−	3.46307i	−0.276018	−	0.399881i
$76$	−10.0925	−	26.6116i	−1.15769	−	3.05257i
$77$	−2.99662	−	7.90145i	−0.341497	−	0.900453i
$78$	−8.04743	+	4.93842i	−0.911192	+	0.559166i
$79$	−4.38621	+	11.5655i	−0.493487	+	1.30122i	0.424794	+	0.905290i	$0.360347\pi$
$79$	−4.38621	+	11.5655i	−0.493487	+	1.30122i	−0.918281	+	0.395929i	$0.870423\pi$
$80$	−8.79410			−0.983210
$81$	−0.354605	−	0.935016i	−0.0394005	−	0.103891i
$82$	−1.63089	+	13.4316i	−0.180102	+	1.48327i
$83$	−9.97618	−	5.23590i	−1.09503	−	0.574715i	−0.182284	−	0.983246i	$-0.558349\pi$
$83$	−9.97618	−	5.23590i	−1.09503	−	0.574715i	−0.912745	+	0.408531i	$0.866041\pi$
$84$	14.0315	+	20.3281i	1.53096	+	2.21798i
$85$	2.92027	+	4.23074i	0.316748	+	0.458889i
$86$	21.7211	+	11.4001i	2.34224	+	1.22930i
$87$	0.640992	−	5.27905i	0.0687216	−	0.565973i
$88$	−4.41004	−	11.6283i	−0.470112	−	1.23958i
$89$	2.09036			0.221577			0.110789	−	0.993844i	$-0.464662\pi$
$89$	2.09036			0.221577			0.110789	+	0.993844i	$0.464662\pi$
$90$	0.826438	−	2.17914i	0.0871142	−	0.229701i
$91$	7.63576	+	16.6681i	0.800445	+	1.74729i
$92$	−6.29843	−	16.6076i	−0.656657	−	1.73146i
$93$	−1.62340	−	4.28055i	−0.168338	−	0.443872i
$94$	13.6385	+	19.7588i	1.40671	+	2.03797i
$95$	3.90306	+	3.45781i	0.400445	+	0.354764i
$96$	6.19736	+	8.97842i	0.632515	+	0.916356i
$97$	4.98552	−	4.41679i	0.506203	−	0.448457i	−0.370960	−	0.928649i	$-0.620971\pi$
$97$	4.98552	−	4.41679i	0.506203	−	0.448457i	0.877163	+	0.480192i	$0.159433\pi$
$98$	43.7226	−	22.9474i	4.41665	−	2.31804i
$99$	1.66190			0.167028
$100$	−18.0993	+	9.49922i	−1.80993	+	0.949922i
$101$	−1.84231	−	15.1728i	−0.183317	−	1.50975i	−0.736356	−	0.676594i	$-0.763455\pi$
$101$	−1.84231	−	15.1728i	−0.183317	−	1.50975i	0.553040	−	0.833155i	$-0.313468\pi$
$102$	5.36387	−	14.1434i	0.531103	−	1.40040i
$103$	−12.5168	+	6.56935i	−1.23332	+	0.647297i	−0.950156	−	0.311774i	$-0.899077\pi$
$103$	−12.5168	+	6.56935i	−1.23332	+	0.647297i	−0.283165	+	0.959071i	$0.591384\pi$
$104$	11.2373	+	24.5299i	1.10191	+	2.40536i
$105$	−4.00707	−	2.10307i	−0.391050	−	0.205239i
$106$	9.21764	−	8.16612i	0.895296	−	0.793163i
$107$	9.05935	+	8.02588i	0.875800	+	0.775891i	0.975701	−	0.219106i	$-0.0703141\pi$
$107$	9.05935	+	8.02588i	0.875800	+	0.775891i	−0.0999008	+	0.994997i	$0.531853\pi$
$108$	−4.71647	+	1.16251i	−0.453843	+	0.111862i
$109$	1.80703	+	14.8822i	0.173082	+	1.42546i	0.777545	+	0.628827i	$0.216465\pi$
$109$	1.80703	+	14.8822i	0.173082	+	1.42546i	−0.604463	+	0.796633i	$0.706612\pi$
$110$	2.89914	+	2.56841i	0.276422	+	0.244889i
$111$	0.477646	+	1.25945i	0.0453361	+	0.119542i
$112$	44.4899	−	23.3501i	4.20390	−	2.20638i
$113$	−1.36602	−	0.716944i	−0.128505	−	0.0674444i	0.399246	−	0.916844i	$-0.369272\pi$
$113$	−1.36602	−	0.716944i	−0.128505	−	0.0674444i	−0.527750	+	0.849400i	$0.676964\pi$
$114$	1.84942	−	15.2313i	0.173214	−	1.42654i
$115$	2.43579	+	2.15792i	0.227139	+	0.201227i
$116$	−25.0813	−	6.18200i	−2.32874	−	0.573984i
$117$	−3.59744	+	0.241692i	−0.332584	+	0.0223445i
$118$	4.00387	−	0.986866i	0.368586	−	0.0908484i
$119$	−26.0073	−	13.6497i	−2.38409	−	1.25126i
$120$	−5.89709	−	3.09503i	−0.538328	−	0.282536i
$121$	2.92126	−	7.70273i	0.265569	−	0.700249i
$122$	−3.36958	+	8.88484i	−0.305067	+	0.804396i
$123$	−2.93505	+	4.25216i	−0.264645	+	0.383404i
$124$	−21.5922	+	5.32200i	−1.93904	+	0.477930i
$125$	4.65521	−	6.74423i	0.416374	−	0.603222i
$126$	1.60505	+	13.2187i	0.142989	+	1.17762i
$127$	0.587667	−	1.54955i	0.0521470	−	0.137500i	−0.906412	−	0.422395i	$-0.861189\pi$
$127$	0.587667	−	1.54955i	0.0521470	−	0.137500i	0.958559	+	0.284895i	$0.0919587\pi$
$128$	1.10010	−	0.577376i	0.0972359	−	0.0510333i
$129$	5.32139	+	7.70936i	0.468522	+	0.678772i
$130$	−6.64915	−	5.13810i	−0.583169	−	0.450641i
$131$	−6.44929	+	9.34341i	−0.563477	+	0.816338i	−0.996372	−	0.0851067i	$-0.972877\pi$
$131$	−6.44929	+	9.34341i	−0.563477	+	0.816338i	0.432895	+	0.901445i	$0.357492\pi$
$132$	0.973081	−	8.01405i	0.0846959	−	0.697533i
$133$	−28.9270	−	7.12986i	−2.50829	−	0.618238i
$134$	12.2631	+	17.7662i	1.05937	+	1.53477i
$135$	0.666157	−	0.590163i	0.0573337	−	0.0507932i
$136$	−38.2742	−	20.0878i	−3.28199	−	1.72252i
$137$	0.783580	+	6.45336i	0.0669458	+	0.551348i	0.987137	+	0.159878i	$0.0511101\pi$
$137$	0.783580	+	6.45336i	0.0669458	+	0.551348i	−0.920191	+	0.391470i	$0.871967\pi$
$138$	1.15417	−	9.50545i	0.0982495	−	0.809158i
$139$	12.1641	−	10.7765i	1.03175	−	0.914049i	0.0353951	−	0.999373i	$-0.488731\pi$
$139$	12.1641	−	10.7765i	1.03175	−	0.914049i	0.996353	+	0.0853241i	$0.0271926\pi$
$140$	−12.4877	+	18.0915i	−1.05540	+	1.52901i
$141$	1.10510	+	9.10133i	0.0930663	+	0.766470i
$142$	1.04668	−	8.62015i	0.0878350	−	0.723387i
$143$	1.74447	−	5.73252i	0.145880	−	0.479378i
$144$	1.19106	+	9.80923i	0.0992547	+	0.817436i
$145$	4.59521	−	1.13262i	0.381611	−	0.0940587i
$146$	−8.87228			−0.734275
$147$	18.8561			1.55522
$148$	6.35299	−	1.56587i	0.522213	−	0.128714i
$149$	6.82228	−	17.9889i	0.558903	−	1.47371i	−0.296137	−	0.955145i	$-0.595699\pi$
$149$	6.82228	−	17.9889i	0.558903	−	1.47371i	0.855041	−	0.518561i	$-0.173532\pi$
$150$	−11.0194			−0.899728
$151$	−4.37855	−	11.5453i	−0.356321	−	0.939543i	−0.986598	−	0.163172i	$-0.947828\pi$
$151$	−4.37855	−	11.5453i	−0.356321	−	0.939543i	0.630276	−	0.776371i	$-0.282942\pi$
$152$	−42.5710	−	10.4928i	−3.45297	−	0.851080i
$153$	4.32359	−	3.83037i	0.349542	−	0.309667i
$154$	−21.4866	−	5.29597i	−1.73144	−	0.426761i
$155$	3.04970	−	2.70179i	0.244957	−	0.217013i
$156$	−0.940890	+	17.4891i	−0.0753315	+	1.40025i
$157$	−0.121236	−	0.107406i	−0.00967572	−	0.00857194i	0.658271	−	0.752781i	$-0.271288\pi$
$157$	−0.121236	−	0.107406i	−0.00967572	−	0.00857194i	−0.667947	+	0.744209i	$0.732827\pi$
$158$	18.4005	+	26.6577i	1.46387	+	2.12078i
$159$	4.56592	−	1.12540i	0.362101	−	0.0892498i
$160$	−5.51550	+	7.99058i	−0.436039	+	0.631711i
$161$	−18.0526	−	4.44955i	−1.42274	−	0.350674i
$162$	−2.54261	−	0.626698i	−0.199766	−	0.0492380i
$163$	1.86819	−	15.3859i	0.146328	−	1.20512i	−0.715756	−	0.698351i	$-0.753918\pi$
$163$	1.86819	−	15.3859i	0.146328	−	1.20512i	0.862083	−	0.506766i	$-0.169159\pi$
$164$	18.7863	+	16.6432i	1.46696	+	1.29961i
$165$	0.524480	+	1.38294i	0.0408307	+	0.107662i
$166$	−26.1247	+	13.7113i	−2.02767	+	1.06420i
$167$	−8.26996	+	11.9811i	−0.639949	+	0.927126i	−0.999983	−	0.00581319i	$-0.998150\pi$
$167$	−8.26996	+	11.9811i	−0.639949	+	0.927126i	0.360034	+	0.932939i	$0.382765\pi$
$168$	38.0517			2.93575
$169$	−2.94249	+	12.6626i	−0.226345	+	0.974047i
$170$	13.4621			1.03249
$171$	3.32833	−	4.82192i	0.254524	−	0.368741i
$172$	40.2919	−	21.1468i	3.07223	−	1.61243i
$173$	−3.64976	−	9.62363i	−0.277486	−	0.731671i	−0.999220	−	0.0394997i	$-0.987424\pi$
$173$	−3.64976	−	9.62363i	−0.277486	−	0.731671i	0.721733	−	0.692171i	$-0.243346\pi$
$174$	−10.4236	−	9.23452i	−0.790212	−	0.700067i
$175$	−2.57911	+	21.2409i	−0.194963	+	1.60566i
$176$	−15.9445	−	3.92998i	−1.20187	−	0.296233i
$177$	1.52895	+	0.376852i	0.114923	+	0.0283260i
$178$	3.10961	−	4.50504i	0.233075	−	0.337667i
$179$	12.3880	−	3.05336i	0.925921	−	0.228219i	0.252601	−	0.967570i	$-0.418714\pi$
$179$	12.3880	−	3.05336i	0.925921	−	0.228219i	0.673320	+	0.739351i	$0.264868\pi$
$180$	−2.45584	−	3.55790i	−0.183048	−	0.265190i
$181$	7.78628	+	6.89804i	0.578750	+	0.512728i	0.900938	−	0.433948i	$-0.142880\pi$
$181$	7.78628	+	6.89804i	0.578750	+	0.512728i	−0.322188	+	0.946676i	$0.604418\pi$
$182$	47.2812	+	8.33910i	3.50471	+	0.618136i
$183$	−2.71607	+	2.40623i	−0.200778	+	0.177874i
$184$	−26.5674	−	6.54828i	−1.95858	−	0.482746i
$185$	−0.897300	+	0.794938i	−0.0659708	+	0.0584450i
$186$	−11.6402	−	2.86905i	−0.853500	−	0.210369i
$187$	3.40406	+	8.97577i	0.248930	+	0.656374i
$188$	44.5356			3.24809
$189$	−1.80313	+	4.75445i	−0.131158	+	0.345836i
$190$	13.2583	−	3.26787i	0.961857	−	0.237076i
$191$	6.81716			0.493272			0.246636	−	0.969108i	$-0.420675\pi$
$191$	6.81716			0.493272			0.246636	+	0.969108i	$0.420675\pi$
$192$	8.80649			0.635553
$193$	5.54630	−	1.36704i	0.399232	−	0.0984018i	−0.0345877	−	0.999402i	$-0.511012\pi$
$193$	5.54630	−	1.36704i	0.399232	−	0.0984018i	0.433819	+	0.901000i	$0.357166\pi$
$194$	−2.10242	−	17.3150i	−0.150945	−	1.24314i
$195$	−1.33644	−	2.91731i	−0.0957044	−	0.208913i
$196$	11.0407	−	90.9280i	0.788619	−	6.49486i
$197$	1.69910	+	13.9934i	0.121056	+	0.996986i	0.919001	+	0.394255i	$0.128997\pi$
$197$	1.69910	+	13.9934i	0.121056	+	0.996986i	−0.797945	+	0.602730i	$0.794079\pi$
$198$	2.47224	−	3.58166i	0.175694	−	0.254537i
$199$	10.2059	−	9.04164i	0.723477	−	0.640945i	−0.218803	−	0.975769i	$-0.570215\pi$
$199$	10.2059	−	9.04164i	0.723477	−	0.640945i	0.942281	+	0.334824i	$0.108677\pi$
$200$	−3.79561	+	31.2596i	−0.268390	+	2.21039i
$201$	0.993655	+	8.18348i	0.0700870	+	0.577218i
$202$	−35.4403	−	18.6005i	−2.49357	−	1.30873i
$203$	−20.2401	+	17.9312i	−1.42058	+	1.25852i
$204$	−15.9393	−	23.0920i	−1.11597	−	1.61677i
$205$	−4.46468	−	1.10044i	−0.311827	−	0.0768583i
$206$	−4.46205	+	36.7482i	−0.310885	+	2.56037i
$207$	2.07712	−	3.00923i	0.144370	−	0.209156i
$208$	35.0859	+	6.18820i	2.43277	+	0.429074i
$209$	5.53136	+	8.01357i	0.382613	+	0.554310i
$210$	−10.4933	+	5.50733i	−0.724109	+	0.380042i
$211$	3.64048	−	9.59915i	0.250621	−	0.660832i	−0.749378	−	0.662142i	$-0.769648\pi$
$211$	3.64048	−	9.59915i	0.250621	−	0.660832i	0.999999	+	0.00130951i	$0.000416830\pi$
$212$	−2.75346	−	22.6767i	−0.189108	−	1.55745i
$213$	1.88366	−	2.72896i	0.129067	−	0.186985i
$214$	30.7736	−	7.58502i	2.10364	−	0.518502i
$215$	−4.73591	+	6.86115i	−0.322986	+	0.467927i
$216$	−2.65361	+	6.99699i	−0.180555	+	0.476085i
$217$	−8.25479	+	21.7661i	−0.560372	+	1.47758i
$218$	34.7616	+	18.2443i	2.35436	+	1.23566i
$219$	−2.99996	−	1.57450i	−0.202718	−	0.106395i
$220$	6.97592	−	1.71941i	0.470317	−	0.115923i
$221$	−8.67396	−	18.9344i	−0.583474	−	1.27366i
$222$	3.42485	+	0.844149i	0.229861	+	0.0566556i
$223$	10.6553	+	9.43979i	0.713533	+	0.632135i	0.939718	−	0.341949i	$-0.111087\pi$
$223$	10.6553	+	9.43979i	0.713533	+	0.632135i	−0.226185	+	0.974084i	$0.572625\pi$
$224$	6.68666	−	55.0696i	0.446771	−	3.67949i
$225$	−3.72595	−	1.95553i	−0.248397	−	0.130369i
$226$	−3.57721	+	1.87747i	−0.237953	+	0.124887i
$227$	6.57147	+	17.3275i	0.436164	+	1.15007i	0.955368	+	0.295419i	$0.0954593\pi$
$227$	6.57147	+	17.3275i	0.436164	+	1.15007i	−0.519204	+	0.854650i	$0.673771\pi$
$228$	−21.3035	−	18.8732i	−1.41086	−	1.24991i
$229$	2.52022	+	20.7559i	0.166541	+	1.37159i	0.801015	+	0.598645i	$0.204294\pi$
$229$	2.52022	+	20.7559i	0.166541	+	1.37159i	−0.634473	+	0.772945i	$0.718783\pi$
$230$	8.27413	−	2.03939i	0.545580	−	0.134473i
$231$	−6.32536	−	5.60378i	−0.416178	−	0.368702i
$232$	−29.7868	+	26.3888i	−1.95560	+	1.73251i
$233$	−0.124755	−	0.0654764i	−0.00817297	−	0.00428950i	0.460632	−	0.887591i	$-0.347623\pi$
$233$	−0.124755	−	0.0654764i	−0.00817297	−	0.00428950i	−0.468805	+	0.883302i	$0.655315\pi$
$234$	−4.83065	+	8.11258i	−0.315790	+	0.530336i
$235$	−7.22484	+	3.79189i	−0.471297	+	0.247356i
$236$	2.71250	−	7.15226i	0.176568	−	0.465573i
$237$	1.49095	+	12.2791i	0.0968479	+	0.797614i
$238$	−68.1055	+	35.7445i	−4.41462	+	2.31697i
$239$	−13.7756			−0.891066			−0.445533	−	0.895265i	$-0.646986\pi$
$239$	−13.7756			−0.891066			−0.445533	+	0.895265i	$0.646986\pi$
$240$	−7.78679	+	4.08682i	−0.502635	+	0.263803i
$241$	−4.70124	+	4.16493i	−0.302833	+	0.268287i	−0.800830	−	0.598892i	$-0.795608\pi$
$241$	−4.70124	+	4.16493i	−0.302833	+	0.268287i	0.497996	+	0.867179i	$0.334069\pi$
$242$	−12.2549	−	17.7543i	−0.787776	−	1.14129i
$243$	−0.748511	−	0.663123i	−0.0480170	−	0.0425393i
$244$	10.0130	+	14.5064i	0.641019	+	0.928676i
$245$	5.95080	+	15.6910i	0.380182	+	1.00246i
$246$	4.79789	+	12.6510i	0.305902	+	0.806597i
$247$	−13.1389	−	16.5421i	−0.836008	−	1.05255i
$248$	−12.1483	+	32.0325i	−0.771420	+	2.03407i
$249$	−11.2667			−0.713999
$250$	−7.60979	−	20.0654i	−0.481285	−	1.26905i
$251$	−2.76697	+	22.7881i	−0.174650	+	1.43837i	0.596959	+	0.802272i	$0.296376\pi$
$251$	−2.76697	+	22.7881i	−0.174650	+	1.43837i	−0.771609	+	0.636098i	$0.780548\pi$
$252$	21.8712	+	11.4789i	1.37776	+	0.723102i
$253$	3.45197	+	5.00105i	0.217024	+	0.314413i
$254$	−2.46531	−	3.57161i	−0.154687	−	0.224103i
$255$	4.55190	+	2.38902i	0.285051	+	0.149606i
$256$	−1.73084	+	14.2548i	−0.108178	+	0.890923i
$257$	−9.70979	−	25.6026i	−0.605680	−	1.59705i	−0.789271	−	0.614044i	$-0.789542\pi$
$257$	−9.70979	−	25.6026i	−0.605680	−	1.59705i	0.183591	−	0.983003i	$-0.441228\pi$
$258$	24.5309			1.52723
$259$	2.42878	−	6.40416i	0.150917	−	0.397935i
$260$	−14.8504	+	4.73644i	−0.920981	+	0.293741i
$261$	−1.88572	−	4.97225i	−0.116723	−	0.307774i
$262$	10.5426	+	27.7984i	0.651321	+	1.71739i
$263$	−8.86733	−	12.8465i	−0.546783	−	0.792152i	0.448014	−	0.894026i	$-0.352131\pi$
$263$	−8.86733	−	12.8465i	−0.546783	−	0.792152i	−0.994797	+	0.101874i	$0.967516\pi$
$264$	−9.30885	−	8.24692i	−0.572920	−	0.507563i
$265$	2.37745	+	3.44433i	0.146045	+	0.211583i
$266$	−58.3976	+	51.7358i	−3.58059	+	3.17212i
$267$	1.85092	−	0.971438i	0.113274	−	0.0594510i
$268$	40.0443			2.44609
$269$	5.08850	−	2.67065i	0.310251	−	0.162832i	−0.302410	−	0.953178i	$-0.597791\pi$
$269$	5.08850	−	2.67065i	0.310251	−	0.162832i	0.612661	+	0.790345i	$0.290099\pi$
$270$	−0.280921	−	2.31359i	−0.0170963	−	0.140801i
$271$	2.04858	−	5.40167i	0.124443	−	0.328128i	−0.858288	−	0.513167i	$-0.828472\pi$
$271$	2.04858	−	5.40167i	0.124443	−	0.328128i	0.982731	+	0.185039i	$0.0592412\pi$
$272$	−50.5390	+	26.5249i	−3.06438	+	1.60831i
$273$	14.5072	+	11.2103i	0.878014	+	0.678480i
$274$	15.0736	+	7.91125i	0.910632	+	0.477936i
$275$	5.23448	−	4.63735i	0.315651	−	0.279642i
$276$	−13.2949	−	11.7783i	−0.800261	−	0.708969i
$277$	−12.0239	+	2.96362i	−0.722444	+	0.178066i	−0.583359	−	0.812214i	$-0.698262\pi$
$277$	−12.0239	+	2.96362i	−0.722444	+	0.178066i	−0.139084	+	0.990281i	$0.544416\pi$
$278$	−5.12967	−	42.2466i	−0.307657	−	2.53378i
$279$	−3.42671	−	3.03580i	−0.205152	−	0.181749i
$280$	12.0087	+	31.6644i	0.717659	+	1.89231i
$281$	−8.39622	+	4.40667i	−0.500876	+	0.262880i	−0.696186	−	0.717861i	$-0.745121\pi$
$281$	−8.39622	+	4.40667i	−0.500876	+	0.262880i	0.195310	+	0.980742i	$0.437429\pi$
$282$	21.2587	+	11.1574i	1.26594	+	0.664415i
$283$	−1.80904	+	14.8988i	−0.107536	+	0.885642i	0.834703	+	0.550701i	$0.185639\pi$
$283$	−1.80904	+	14.8988i	−0.107536	+	0.885642i	−0.942239	+	0.334941i	$0.891284\pi$
$284$	−12.0567	−	10.6813i	−0.715433	−	0.633818i
$285$	5.06291	+	1.24790i	0.299901	+	0.0739189i
$286$	−9.75940	−	12.2873i	−0.577085	−	0.726562i
$287$	25.5090	−	6.28740i	1.50575	−	0.371133i
$288$	9.65997	+	5.06994i	0.569219	+	0.298749i
$289$	14.4907	+	7.60529i	0.852392	+	0.447370i
$290$	4.39485	−	11.5883i	0.258074	−	0.680486i
$291$	2.36188	−	6.22776i	0.138456	−	0.365078i
$292$	−9.34911	+	13.5445i	−0.547115	+	0.792633i
$293$	−14.9248	+	3.67864i	−0.871917	+	0.214908i	−0.649794	−	0.760110i	$-0.725145\pi$
$293$	−14.9248	+	3.67864i	−0.871917	+	0.214908i	−0.222123	+	0.975019i	$0.571299\pi$
$294$	28.0502	−	40.6378i	1.63592	−	2.37004i
$295$	0.168927	+	1.39124i	0.00983528	+	0.0810008i
$296$	3.57436	−	9.42481i	0.207755	−	0.547806i
$297$	1.47154	−	0.772325i	0.0853876	−	0.0448149i
$298$	−28.6200	−	41.4632i	−1.65791	−	2.40190i
$299$	−8.19963	−	10.3235i	−0.474197	−	0.597023i
$300$	−11.6116	+	16.8223i	−0.670395	+	0.971235i
$301$	5.74153	−	47.2858i	0.330937	−	2.72551i
$302$	−31.3954	−	7.73827i	−1.80660	−	0.445287i
$303$	−8.68243	−	12.5787i	−0.498793	−	0.722626i
$304$	−43.3351	+	38.3915i	−2.48544	+	2.20191i
$305$	−2.85949	−	1.50078i	−0.163734	−	0.0859343i
$306$	−1.82328	−	15.0160i	−0.104230	−	0.858410i
$307$	−2.32104	+	19.1155i	−0.132469	+	1.09098i	0.763170	+	0.646198i	$0.223642\pi$
$307$	−2.32104	+	19.1155i	−0.132469	+	1.09098i	−0.895639	+	0.444782i	$0.853281\pi$
$308$	−30.7262	+	27.2211i	−1.75079	+	1.55106i
$309$	−8.03019	+	11.6337i	−0.456821	+	0.661820i
$310$	−1.28607	−	10.5917i	−0.0730438	−	0.601570i
$311$	−1.49502	+	12.3126i	−0.0847747	+	0.698182i	0.886917	+	0.461929i	$0.152843\pi$
$311$	−1.49502	+	12.3126i	−0.0847747	+	0.698182i	−0.971692	+	0.236253i	$0.924081\pi$
$312$	21.3498	+	16.4979i	1.20869	+	0.934010i
$313$	1.14132	+	9.39959i	0.0645111	+	0.531296i	0.988761	+	0.149507i	$0.0477688\pi$
$313$	1.14132	+	9.39959i	0.0645111	+	0.531296i	−0.924250	+	0.381789i	$0.875308\pi$
$314$	−0.411827	+	0.101506i	−0.0232407	+	0.00572833i
$315$	−4.52543			−0.254979
$316$	60.0854			3.38007
$317$	30.3421	−	7.47866i	1.70418	−	0.420043i	0.737361	−	0.675498i	$-0.236071\pi$
$317$	30.3421	−	7.47866i	1.70418	−	0.420043i	0.966821	+	0.255455i	$0.0822253\pi$
$318$	4.36683	−	11.5144i	0.244880	−	0.645695i
$319$	8.83770			0.494816
$320$	2.77924	+	7.32825i	0.155364	+	0.409662i
$321$	11.7515	+	2.89648i	0.655903	+	0.161666i
$322$	−36.4444	+	32.2869i	−2.03096	+	1.79928i
$323$	32.8601	+	8.09928i	1.82838	+	0.450656i
$324$	−3.63599	+	3.22120i	−0.201999	+	0.178956i
$325$	−10.6564	+	10.7995i	−0.591111	+	0.599048i
$326$	−30.3799	−	26.9142i	−1.68259	−	1.49064i
$327$	8.51617	+	12.3378i	0.470945	+	0.682282i
$328$	37.5408	−	9.25298i	2.07285	−	0.510910i
$329$	26.4827	−	38.3668i	1.46004	−	2.11523i
$330$	3.76066	+	0.926920i	0.207018	+	0.0510253i
$331$	−7.86177	−	1.93775i	−0.432122	−	0.106508i	0.0172542	−	0.999851i	$-0.494508\pi$
$331$	−7.86177	−	1.93775i	−0.432122	−	0.106508i	−0.449376	+	0.893343i	$0.648354\pi$
$332$	−6.59691	+	54.3305i	−0.362053	+	2.98177i
$333$	1.00823	+	0.893213i	0.0552506	+	0.0489478i
$334$	13.5188	+	35.6461i	0.739714	+	1.95047i
$335$	−6.49623	+	3.40949i	−0.354927	+	0.186280i
$336$	28.5425	−	41.3510i	1.55712	−	2.25588i
$337$	−1.99457			−0.108651			−0.0543256	−	0.998523i	$-0.517301\pi$
$337$	−1.99457			−0.108651			−0.0543256	+	0.998523i	$0.517301\pi$
$338$	22.9126	+	25.1784i	1.24628	+	1.36952i
$339$	−1.54273			−0.0837897
$340$	14.1856	−	20.5514i	0.769321	−	1.11455i
$341$	6.73679	−	3.53574i	0.364817	−	0.191471i
$342$	−5.44077	−	14.3461i	−0.294203	−	0.775750i
$343$	−45.1254	−	39.9776i	−2.43654	−	2.15859i
$344$	8.44965	−	69.5891i	0.455575	−	3.75199i
$345$	3.15962	+	0.778778i	0.170108	+	0.0419280i
$346$	−26.1698	−	6.45027i	−1.40690	−	0.346768i
$347$	−2.01968	+	2.92602i	−0.108422	+	0.157077i	−0.873439	−	0.486934i	$-0.838115\pi$
$347$	−2.01968	+	2.92602i	−0.108422	+	0.157077i	0.765017	+	0.644011i	$0.222731\pi$
$348$	−25.0813	+	6.18200i	−1.34450	+	0.331390i
$349$	9.81831	+	14.2243i	0.525562	+	0.761408i	0.992416	−	0.122926i	$-0.0392278\pi$
$349$	9.81831	+	14.2243i	0.525562	+	0.761408i	−0.466853	+	0.884335i	$0.654612\pi$
$350$	41.9407	+	37.1563i	2.24183	+	1.98609i
$351$	−3.07306	+	1.88582i	−0.164028	+	0.100658i
$352$	−13.5710	+	12.0229i	−0.723338	+	0.640822i
$353$	−22.6143	−	5.57392i	−1.20364	−	0.296670i	−0.414019	−	0.910268i	$-0.635875\pi$
$353$	−22.6143	−	5.57392i	−1.20364	−	0.296670i	−0.789618	+	0.613599i	$0.789721\pi$
$354$	3.08663	−	2.73452i	0.164053	−	0.145338i
$355$	2.86535	+	0.706245i	0.152077	+	0.0374836i
$356$	−3.60072	−	9.49432i	−0.190838	−	0.503198i
$357$	−29.3717			−1.55451
$358$	11.8478	−	31.2402i	0.626177	−	1.65109i
$359$	−22.1424	+	5.45762i	−1.16863	+	0.288042i	−0.775444	−	0.631416i	$-0.782474\pi$
$359$	−22.1424	+	5.45762i	−1.16863	+	0.288042i	−0.393188	+	0.919458i	$0.628628\pi$
$360$	−6.65995			−0.351010
$361$	15.3287			0.806773
$362$	26.4492	−	6.51914i	1.39014	−	0.342638i
$363$	−0.992990	−	8.17801i	−0.0521185	−	0.429234i
$364$	62.5528	−	63.3927i	3.27866	−	3.32268i
$365$	0.363451	−	2.99329i	0.0190239	−	0.156676i
$366$	1.14538	+	9.43306i	0.0598700	+	0.493074i
$367$	−7.66711	+	11.1077i	−0.400220	+	0.579818i	−0.970340	−	0.241743i	$-0.922281\pi$
$367$	−7.66711	+	11.1077i	−0.400220	+	0.579818i	0.570121	+	0.821561i	$0.306896\pi$
$368$	−27.0442	+	23.9591i	−1.40978	+	1.24896i
$369$	−0.622784	+	5.12909i	−0.0324208	+	0.267010i
$370$	0.378395	+	3.11637i	0.0196718	+	0.162012i
$371$	−21.1730	−	11.1125i	−1.09925	−	0.576931i
$372$	−16.6457	+	14.7468i	−0.863039	+	0.764586i
$373$	9.11477	+	13.2050i	0.471945	+	0.683730i	0.984592	−	0.174869i	$-0.0559503\pi$
$373$	9.11477	+	13.2050i	0.471945	+	0.683730i	−0.512647	+	0.858600i	$0.671335\pi$
$374$	24.4080	+	6.01604i	1.26211	+	0.311082i
$375$	0.987780	−	8.13510i	0.0510087	−	0.420095i
$376$	38.9738	−	56.4633i	2.00992	−	2.91187i
$377$	−19.1305	+	1.28528i	−0.985273	+	0.0661951i
$378$	7.56426	+	10.9587i	0.389063	+	0.563656i
$379$	29.3420	−	15.3999i	1.50720	−	0.791039i	0.509609	−	0.860406i	$-0.329790\pi$
$379$	29.3420	−	15.3999i	1.50720	−	0.791039i	0.997591	+	0.0693669i	$0.0220979\pi$
$380$	8.98206	−	23.6837i	0.460770	−	1.21495i
$381$	−0.199759	−	1.64516i	−0.0102339	−	0.0842841i
$382$	10.1412	−	14.6920i	0.518867	−	0.751709i
$383$	−22.5195	+	5.55056i	−1.15069	+	0.283620i	−0.768120	−	0.640305i	$-0.778808\pi$
$383$	−22.5195	+	5.55056i	−1.15069	+	0.283620i	−0.382572	+	0.923926i	$0.624962\pi$
$384$	0.705769	−	1.02248i	0.0360161	−	0.0521783i
$385$	2.66692	−	7.03210i	0.135919	−	0.358389i
$386$	5.30447	−	13.9867i	0.269990	−	0.711906i
$387$	8.29458	+	4.35333i	0.421637	+	0.221292i
$388$	−28.6486	−	15.0360i	−1.45441	−	0.763335i
$389$	24.9934	−	6.16031i	1.26721	−	0.312340i	0.452271	−	0.891881i	$-0.350614\pi$
$389$	24.9934	−	6.16031i	1.26721	−	0.312340i	0.814943	+	0.579541i	$0.196768\pi$
$390$	−8.27533	−	1.45954i	−0.419037	−	0.0739067i
$391$	20.5071	+	5.05454i	1.03709	+	0.255619i
$392$	−105.619	−	93.5703i	−5.33457	−	4.72601i
$393$	−1.36846	+	11.2703i	−0.0690299	+	0.568512i
$394$	32.6854	+	17.1546i	1.64667	+	0.864238i
$395$	−9.74744	+	5.11585i	−0.490447	+	0.257406i
$396$	−2.86269	−	7.54830i	−0.143856	−	0.379316i
$397$	−18.8697	−	16.7171i	−0.947044	−	0.839008i	0.0400418	−	0.999198i	$-0.487251\pi$
$397$	−18.8697	−	16.7171i	−0.947044	−	0.839008i	−0.987086	+	0.160190i	$0.948789\pi$
$398$	−4.30387	−	35.4456i	−0.215734	−	1.77673i
$399$	−28.9270	+	7.12986i	−1.44816	+	0.356940i
$400$	31.1230	+	27.5725i	1.55615	+	1.37863i
$401$	−0.486535	+	0.431033i	−0.0242964	+	0.0215247i	−0.675184	−	0.737650i	$-0.735936\pi$
$401$	−0.486535	+	0.431033i	−0.0242964	+	0.0215247i	0.650887	+	0.759175i	$0.274397\pi$
$402$	19.1148	+	10.0322i	0.953360	+	0.500362i
$403$	−14.0686	+	8.63338i	−0.700806	+	0.430059i
$404$	−65.7407	+	34.5034i	−3.27072	+	1.71661i
$405$	0.315590	−	0.832142i	0.0156818	−	0.0413495i
$406$	8.53535	+	70.2949i	0.423602	+	3.48868i
$407$	−1.98214	+	1.04031i	−0.0982510	+	0.0515661i
$408$	−43.2254			−2.13998
$409$	−16.7123	+	8.77127i	−0.826368	+	0.433711i	−0.824209	−	0.566286i	$-0.808380\pi$
$409$	−16.7123	+	8.77127i	−0.826368	+	0.433711i	−0.00215946	+	0.999998i	$0.500687\pi$
$410$	−9.01326	+	7.98505i	−0.445133	+	0.394353i
$411$	3.69285	+	5.35002i	0.182155	+	0.263897i
$412$	51.3984	+	45.5350i	2.53222	+	2.24335i
$413$	−4.54862	−	6.58981i	−0.223823	−	0.324263i
$414$	−3.39544	−	8.95303i	−0.166877	−	0.440017i
$415$	−3.55566	−	9.37551i	−0.174541	−	0.460226i
$416$	27.6280	−	27.9990i	1.35458	−	1.37276i
$417$	5.76272	−	15.1951i	0.282202	−	0.744105i
$418$	25.4989			1.24719
$419$	−8.01900	−	21.1444i	−0.391754	−	1.03297i	−0.975299	−	0.220889i	$-0.929104\pi$
$419$	−8.01900	−	21.1444i	−0.391754	−	1.03297i	0.583545	−	0.812081i	$-0.301665\pi$
$420$	−2.64974	+	21.8226i	−0.129294	+	1.06483i
$421$	1.51014	+	0.792580i	0.0735995	+	0.0386280i	0.501121	−	0.865377i	$-0.332921\pi$
$421$	1.51014	+	0.792580i	0.0735995	+	0.0386280i	−0.427522	+	0.904005i	$0.640613\pi$
$422$	−15.2721	−	22.1254i	−0.743433	−	1.07705i
$423$	5.20812	+	7.54526i	0.253227	+	0.366863i
$424$	−31.1598	−	16.3539i	−1.51325	−	0.794216i
$425$	2.92979	−	24.1290i	0.142115	−	1.17043i
$426$	−3.07920	−	8.11917i	−0.149188	−	0.393375i
$427$	18.4512			0.892917
$428$	20.8482	−	54.9721i	1.00773	−	2.65718i
$429$	−1.11938	−	5.88659i	−0.0540443	−	0.284207i
$430$	7.74172	+	20.4132i	0.373339	+	0.984413i
$431$	−6.96442	−	18.3637i	−0.335464	−	0.884547i	−0.991534	−	0.129846i	$-0.958552\pi$
$431$	−6.96442	−	18.3637i	−0.335464	−	0.884547i	0.656070	−	0.754700i	$-0.272218\pi$
$432$	5.61320	+	8.13213i	0.270065	+	0.391257i
$433$	2.94702	+	2.61083i	0.141625	+	0.125469i	0.730961	−	0.682419i	$-0.239072\pi$
$433$	2.94702	+	2.61083i	0.141625	+	0.125469i	−0.589336	+	0.807888i	$0.700611\pi$
$434$	34.6295	+	50.1695i	1.66227	+	2.40821i
$435$	3.54250	−	3.13838i	0.169850	−	0.150474i
$436$	64.4818	−	33.8427i	3.08812	−	1.62077i
$437$	21.4236			1.02483
$438$	−7.85601	+	4.12315i	−0.375375	+	0.197012i
$439$	−1.02327	−	8.42741i	−0.0488381	−	0.402218i	−0.996544	−	0.0830718i	$-0.973527\pi$
$439$	−1.02327	−	8.42741i	−0.0488381	−	0.402218i	0.947705	−	0.319146i	$-0.103396\pi$
$440$	3.92483	−	10.3489i	0.187109	−	0.493366i
$441$	16.6962	−	8.76287i	0.795059	−	0.417279i
$442$	−53.7098	−	9.47294i	−2.55471	−	0.450582i
$443$	−15.2430	−	8.00013i	−0.724216	−	0.380098i	0.0619782	−	0.998078i	$-0.480259\pi$
$443$	−15.2430	−	8.00013i	−0.724216	−	0.380098i	−0.786194	+	0.617980i	$0.787951\pi$
$444$	4.89760	−	4.33889i	0.232430	−	0.205915i
$445$	1.39251	+	1.23365i	0.0660111	+	0.0584808i
$446$	36.1950	−	8.92127i	1.71388	−	0.422434i
$447$	−2.31902	−	19.0988i	−0.109686	−	0.903344i
$448$	−33.5183	−	29.6946i	−1.58359	−	1.40294i
$449$	1.64016	+	4.32475i	0.0774039	+	0.204097i	0.968133	−	0.250438i	$-0.0805746\pi$
$449$	1.64016	+	4.32475i	0.0774039	+	0.204097i	−0.890729	+	0.454535i	$0.849805\pi$
$450$	−9.75716	+	5.12096i	−0.459957	+	0.241404i
$451$	−7.60311	−	3.99042i	−0.358016	−	0.187902i
$452$	−0.903304	+	7.43938i	−0.0424878	+	0.349919i
$453$	−9.24238	−	8.18803i	−0.434245	−	0.384707i
$454$	47.1192	+	11.6138i	2.21141	+	0.545065i
$455$	−4.75027	+	15.6099i	−0.222696	+	0.731803i
$456$	−42.5710	+	10.4928i	−1.99357	+	0.491371i
$457$	8.57399	+	4.49998i	0.401074	+	0.210500i	0.653185	−	0.757198i	$-0.273432\pi$
$457$	8.57399	+	4.49998i	0.401074	+	0.210500i	−0.252111	+	0.967698i	$0.581125\pi$
$458$	48.4813	+	25.4449i	2.26538	+	1.18896i
$459$	2.04829	−	5.40090i	0.0956060	−	0.252092i
$460$	5.60546	−	14.7804i	0.261356	−	0.689139i
$461$	14.4894	−	20.9915i	0.674839	−	0.977673i	−0.324654	−	0.945833i	$-0.605248\pi$
$461$	14.4894	−	20.9915i	0.674839	−	0.977673i	0.999493	−	0.0318402i	$-0.0101368\pi$
$462$	−21.4866	+	5.29597i	−0.999647	+	0.246391i
$463$	−16.4364	+	23.8122i	−0.763865	+	1.10665i	0.227276	+	0.973830i	$0.427018\pi$
$463$	−16.4364	+	23.8122i	−0.763865	+	1.10665i	−0.991140	+	0.132819i	$0.957597\pi$
$464$	6.33382	+	52.1637i	0.294040	+	2.42164i
$465$	1.44478	−	3.80958i	0.0670003	−	0.176665i
$466$	−0.326697	+	0.171464i	−0.0151339	+	0.00794290i
$467$	6.45693	+	9.35448i	0.298791	+	0.432874i	0.943409	−	0.331631i	$-0.107599\pi$
$467$	6.45693	+	9.35448i	0.298791	+	0.432874i	−0.644618	+	0.764505i	$0.722984\pi$
$468$	7.29449	+	15.9231i	0.337188	+	0.736046i
$469$	23.8120	−	34.4976i	1.09954	−	1.59295i
$470$	−2.57554	+	21.2114i	−0.118801	+	0.978411i
$471$	−0.157264	−	0.0387620i	−0.00724632	−	0.00178606i
$472$	−6.69407	−	9.69803i	−0.308120	−	0.446388i
$473$	−11.6528	+	10.3235i	−0.535797	+	0.474675i
$474$	28.6813	+	15.0531i	1.31738	+	0.691412i
$475$	−2.97179	−	24.4749i	−0.136355	−	1.12298i
$476$	−17.1978	+	141.636i	−0.788258	+	6.49189i
$477$	3.51992	−	3.11838i	0.161166	−	0.142781i
$478$	−20.4924	+	29.6884i	−0.937302	+	1.35792i
$479$	−1.04729	−	8.62517i	−0.0478517	−	0.394094i	−0.996882	−	0.0789089i	$-0.974856\pi$
$479$	−1.04729	−	8.62517i	−0.0478517	−	0.394094i	0.949030	−	0.315185i	$-0.102067\pi$
$480$	−1.17032	+	9.63849i	−0.0534178	+	0.439935i
$481$	4.13935	−	2.54017i	0.188738	−	0.115822i
$482$	1.98253	+	16.3276i	0.0903018	+	0.743702i
$483$	−18.0526	+	4.44955i	−0.821419	+	0.202462i
$484$	−40.0175			−1.81898
$485$	5.92777			0.269166
$486$	−2.54261	+	0.626698i	−0.115335	+	0.0284276i
$487$	4.69557	−	12.3812i	0.212777	−	0.561046i	−0.785555	−	0.618792i	$-0.787622\pi$
$487$	4.69557	−	12.3812i	0.212777	−	0.561046i	0.998331	+	0.0577464i	$0.0183915\pi$
$488$	27.1541			1.22921
$489$	−5.49599	−	14.4917i	−0.248537	−	0.655339i
$490$	42.6688	+	10.5169i	1.92758	+	0.475106i
$491$	5.58183	−	4.94507i	0.251904	−	0.223168i	−0.527715	−	0.849421i	$-0.676951\pi$
$491$	5.58183	−	4.94507i	0.251904	−	0.223168i	0.779619	+	0.626254i	$0.215413\pi$
$492$	24.3689	+	6.00639i	1.09863	+	0.270789i
$493$	22.9921	−	20.3692i	1.03551	−	0.917383i
$494$	−55.1962	+	3.70833i	−2.48339	+	0.166846i
$495$	1.10709	+	0.980795i	0.0497599	+	0.0440835i
$496$	25.6975	+	37.2292i	1.15385	+	1.67164i
$497$	−16.3712	+	4.03514i	−0.734349	+	0.181001i
$498$	−16.7603	+	24.2815i	−0.751048	+	1.08808i
$499$	−16.0767	−	3.96255i	−0.719691	−	0.177388i	−0.137572	−	0.990492i	$-0.543930\pi$
$499$	−16.0767	−	3.96255i	−0.719691	−	0.177388i	−0.582119	+	0.813104i	$0.697776\pi$
$500$	−38.6508	−	9.52656i	−1.72852	−	0.426041i
$501$	−1.75479	+	14.4520i	−0.0783982	+	0.645667i
$502$	44.9956	+	39.8627i	2.00825	+	1.77916i
$503$	9.99824	+	26.3632i	0.445800	+	1.17548i	0.950099	+	0.311948i	$0.100982\pi$
$503$	9.99824	+	26.3632i	0.445800	+	1.17548i	−0.504299	+	0.863529i	$0.668249\pi$
$504$	33.6931	−	17.6835i	1.50081	−	0.787685i
$505$	7.72716	−	11.1947i	0.343854	−	0.498159i
$506$	15.9132			0.707427
$507$	3.27916	+	12.5796i	0.145633	+	0.558681i
$508$	−8.05027			−0.357173
$509$	−9.80520	+	14.2053i	−0.434608	+	0.629638i	−0.977693	−	0.210040i	$-0.932641\pi$
$509$	−9.80520	+	14.2053i	−0.434608	+	0.629638i	0.543085	+	0.839678i	$0.317256\pi$
$510$	11.9201	−	6.25614i	0.527830	−	0.277027i
$511$	6.10906	+	16.1083i	0.270249	+	0.712588i
$512$	30.0063	+	26.5833i	1.32611	+	1.17483i
$513$	0.706233	−	5.81635i	0.0311809	−	0.256798i
$514$	−69.6218	−	17.1602i	−3.07089	−	0.756905i
$515$	−12.2152	−	3.01077i	−0.538265	−	0.132670i
$516$	25.8493	−	37.4492i	1.13795	−	1.64861i
$517$	−14.7939	+	3.64636i	−0.650634	+	0.160367i
$518$	−10.1889	−	14.7612i	−0.447675	−	0.648569i
$519$	−7.70403	−	6.82517i	−0.338169	−	0.299592i
$520$	−6.99084	+	22.9726i	−0.306569	+	1.00742i
$521$	15.9710	−	14.1491i	0.699703	−	0.619882i	−0.236381	−	0.971660i	$-0.575961\pi$
$521$	15.9710	−	14.1491i	0.699703	−	0.619882i	0.936083	+	0.351778i	$0.114423\pi$
$522$	−13.5212	−	3.33266i	−0.591805	−	0.145867i
$523$	−22.2665	+	19.7264i	−0.973647	+	0.862576i	−0.990532	−	0.137281i	$-0.956164\pi$
$523$	−22.2665	+	19.7264i	−0.973647	+	0.862576i	0.0168848	+	0.999857i	$0.494625\pi$
$524$	53.5466	+	13.1980i	2.33919	+	0.576559i
$525$	7.58745	+	20.0065i	0.331144	+	0.873154i
$526$	−40.8773			−1.78233
$527$	9.37716	−	24.7255i	0.408476	−	1.07706i
$528$	−15.9445	+	3.92998i	−0.693897	+	0.171030i
$529$	−9.63011			−0.418701
$530$	10.9597			0.476061
$531$	1.52895	−	0.376852i	0.0663508	−	0.0163540i
$532$	17.4443	+	143.667i	0.756306	+	6.22874i
$533$	17.0384	+	7.53214i	0.738015	+	0.326253i
$534$	0.659822	−	5.43412i	0.0285533	−	0.235157i
$535$	1.29836	+	10.6930i	0.0561332	+	0.462298i
$536$	35.0434	−	50.7691i	1.51364	−	2.19289i
$537$	9.55004	−	8.46060i	0.412115	−	0.365102i
$538$	1.81396	−	14.9393i	0.0782056	−	0.644081i
$539$	3.77726	+	31.1085i	0.162698	+	1.33994i
$540$	−3.82798	−	2.00908i	−0.164730	−	0.0864570i
$541$	9.77026	−	8.65570i	0.420056	−	0.372137i	−0.426454	−	0.904509i	$-0.640238\pi$
$541$	9.77026	−	8.65570i	0.420056	−	0.372137i	0.846511	+	0.532372i	$0.178699\pi$
$542$	−8.59397	−	12.4505i	−0.369143	−	0.534796i
$543$	10.1001	+	2.48945i	0.433436	+	0.106832i
$544$	−7.59582	+	62.5572i	−0.325668	+	2.68212i
$545$	−7.57919	+	10.9804i	−0.324657	+	0.470347i
$546$	45.7408	−	14.5887i	1.95752	−	0.624340i
$547$	5.95644	+	8.62939i	0.254679	+	0.368966i	0.929380	−	0.369125i	$-0.120343\pi$
$547$	5.95644	+	8.62939i	0.254679	+	0.368966i	−0.674701	+	0.738091i	$0.735727\pi$
$548$	27.9612	−	14.6751i	1.19444	−	0.626891i
$549$	−1.28673	+	3.39284i	−0.0549164	+	0.144803i
$550$	−2.20740	−	18.1796i	−0.0941240	−	0.775181i
$551$	17.6995	−	25.6421i	0.754022	−	1.09239i
$552$	−26.5674	+	6.54828i	−1.13078	+	0.278713i
$553$	35.7293	−	51.7628i	1.51936	−	2.20118i
$554$	−11.4996	+	30.3219i	−0.488571	+	1.28826i
$555$	−0.425093	+	1.12088i	−0.0180442	+	0.0475787i
$556$	−69.8995	−	36.6861i	−2.96440	−	1.55584i
$557$	−19.3574	−	10.1596i	−0.820200	−	0.430474i	0.00177446	−	0.999998i	$-0.499435\pi$
$557$	−19.3574	−	10.1596i	−0.820200	−	0.430474i	−0.821975	+	0.569524i	$0.807127\pi$
$558$	−11.6402	+	2.86905i	−0.492768	+	0.121457i
$559$	23.7229	−	24.0415i	1.00337	−	1.01685i
$560$	43.4176	+	10.7015i	1.83473	+	0.452220i
$561$	7.18540	+	6.36571i	0.303368	+	0.268760i
$562$	−2.99311	+	24.6505i	−0.126257	+	1.03982i
$563$	−17.9497	−	9.42073i	−0.756489	−	0.397036i	0.0419436	−	0.999120i	$-0.486645\pi$
$563$	−17.9497	−	9.42073i	−0.756489	−	0.397036i	−0.798433	+	0.602084i	$0.794337\pi$
$564$	39.4343	−	20.6967i	1.66048	−	0.871489i
$565$	−0.486871	−	1.28377i	−0.0204828	−	0.0540087i
$566$	29.4181	+	26.0621i	1.23653	+	1.09547i
$567$	0.612916	+	5.04781i	0.0257400	+	0.211988i
$568$	−24.0930	+	5.93840i	−1.01092	+	0.249170i
$569$	−4.72376	−	4.18489i	−0.198030	−	0.175440i	0.558280	−	0.829653i	$-0.311462\pi$
$569$	−4.72376	−	4.18489i	−0.198030	−	0.175440i	−0.756310	+	0.654213i	$0.773000\pi$
$570$	10.2210	−	9.05499i	0.428109	−	0.379272i
$571$	−22.8266	−	11.9803i	−0.955265	−	0.501362i	−0.0863185	−	0.996268i	$-0.527510\pi$
$571$	−22.8266	−	11.9803i	−0.955265	−	0.501362i	−0.868947	+	0.494906i	$0.835203\pi$
$572$	−29.0418	+	1.95116i	−1.21430	+	0.0815821i
$573$	6.03629	−	3.16809i	0.252170	−	0.132349i
$574$	24.3967	−	64.3289i	1.01830	−	2.68503i
$575$	−1.85461	−	15.2741i	−0.0773426	−	0.636974i
$576$	7.79776	−	4.09258i	0.324906	−	0.170524i
$577$	−13.6529			−0.568376			−0.284188	−	0.958769i	$-0.591724\pi$
$577$	−13.6529			−0.568376			−0.284188	+	0.958769i	$0.591724\pi$
$578$	37.9468	−	19.9160i	1.57838	−	0.828397i
$579$	4.27571	−	3.78795i	0.177693	−	0.157422i
$580$	−13.0597	−	18.9203i	−0.542275	−	0.785622i
$581$	42.8822	+	37.9903i	1.77905	+	1.57610i
$582$	−9.90826	−	14.3546i	−0.410711	−	0.595017i
$583$	2.77131	+	7.30735i	0.114776	+	0.302639i
$584$	8.99053	+	23.7061i	0.372031	+	0.980964i
$585$	−2.53910	−	1.96207i	−0.104979	−	0.0811218i
$586$	−14.2741	+	37.6376i	−0.589656	+	1.55479i
$587$	20.8588			0.860934			0.430467	−	0.902606i	$-0.358349\pi$
$587$	20.8588			0.860934			0.430467	+	0.902606i	$0.358349\pi$
$588$	−32.4803	−	85.6436i	−1.33947	−	3.53188i
$589$	3.23316	−	26.6275i	0.133220	−	1.09717i
$590$	3.24962	+	1.70553i	0.133785	+	0.0702156i
$591$	8.00752	+	11.6009i	0.329385	+	0.477197i
$592$	−7.56087	−	10.9538i	−0.310750	−	0.450199i
$593$	30.0622	+	15.7779i	1.23451	+	0.647920i	0.950447	−	0.310886i	$-0.100626\pi$
$593$	30.0622	+	15.7779i	1.23451	+	0.647920i	0.284061	+	0.958806i	$0.408318\pi$
$594$	0.524580	−	4.32031i	0.0215238	−	0.177264i
$595$	−9.26940	−	24.4414i	−0.380008	−	1.00200i
$596$	−93.4564			−3.82812
$597$	4.83502	−	12.7489i	0.197884	−	0.521778i
$598$	−34.4465	+	2.31427i	−1.40862	+	0.0946375i
$599$	12.4677	+	32.8745i	0.509414	+	1.34322i	0.905244	+	0.424892i	$0.139688\pi$
$599$	12.4677	+	32.8745i	0.509414	+	1.34322i	−0.395830	+	0.918324i	$0.629543\pi$
$600$	11.1662	+	29.4429i	0.455860	+	1.20200i
$601$	3.17105	+	4.59406i	0.129350	+	0.187396i	0.882308	−	0.470673i	$-0.155989\pi$
$601$	3.17105	+	4.59406i	0.129350	+	0.187396i	−0.752958	+	0.658069i	$0.771374\pi$
$602$	−93.3671	−	82.7160i	−3.80536	−	3.37125i
$603$	4.68289	+	6.78434i	0.190702	+	0.276280i
$604$	−44.8960	+	39.7744i	−1.82679	+	1.61840i
$605$	6.49189	−	3.40721i	0.263933	−	0.138523i
$606$	−40.0249			−1.62590
$607$	33.7283	−	17.7020i	1.36899	−	0.718501i	0.389696	−	0.920944i	$-0.372580\pi$
$607$	33.7283	−	17.7020i	1.36899	−	0.718501i	0.979294	+	0.202442i	$0.0648878\pi$
$608$	7.70471	+	63.4540i	0.312467	+	2.57340i
$609$	−9.58870	+	25.2833i	−0.388554	+	1.02453i
$610$	−7.48817	+	3.93010i	−0.303187	+	0.159125i
$611$	31.4933	−	10.0446i	1.27408	−	0.406361i
$612$	−24.8449	−	13.0396i	−1.00430	−	0.527096i
$613$	13.7018	−	12.1388i	0.553412	−	0.490280i	−0.339442	−	0.940627i	$-0.610238\pi$
$613$	13.7018	−	12.1388i	0.553412	−	0.490280i	0.892854	+	0.450347i	$0.148700\pi$
$614$	37.7441	+	33.4383i	1.52323	+	1.34946i
$615$	−4.46468	+	1.10044i	−0.180033	+	0.0443742i
$616$	7.62252	+	62.7771i	0.307120	+	2.52936i
$617$	−11.5560	−	10.2377i	−0.465226	−	0.412154i	0.397676	−	0.917526i	$-0.369817\pi$
$617$	−11.5560	−	10.2377i	−0.465226	−	0.412154i	−0.862902	+	0.505372i	$0.831355\pi$
$618$	13.1268	+	34.6126i	0.528038	+	1.39232i
$619$	−23.3996	+	12.2811i	−0.940511	+	0.493618i	−0.864023	−	0.503452i	$-0.832063\pi$
$619$	−23.3996	+	12.2811i	−0.940511	+	0.493618i	−0.0764880	+	0.997070i	$0.524371\pi$
$620$	−17.5247	−	9.19765i	−0.703807	−	0.369386i
$621$	0.440741	−	3.62983i	0.0176863	−	0.145660i
$622$	24.3115	+	21.5381i	0.974803	+	0.863600i
$623$	−10.3204	−	2.54374i	−0.413477	−	0.101913i
$624$	33.9428	−	10.8259i	1.35880	−	0.433381i
$625$	−13.3470	+	3.28975i	−0.533882	+	0.131590i
$626$	21.9554	+	11.5231i	0.877514	+	0.460555i
$627$	8.62187	+	4.52511i	0.344324	+	0.180715i
$628$	−0.279000	+	0.735662i	−0.0111333	+	0.0293561i
$629$	−2.75901	+	7.27490i	−0.110009	+	0.290069i
$630$	−6.73201	+	9.75300i	−0.268210	+	0.388569i
$631$	34.1619	−	8.42015i	1.35996	−	0.335201i	0.509155	−	0.860675i	$-0.329958\pi$
$631$	34.1619	−	8.42015i	1.35996	−	0.335201i	0.850810	+	0.525474i	$0.176112\pi$
$632$	52.5817	−	76.1778i	2.09159	−	3.03019i
$633$	−1.23746	−	10.1914i	−0.0491848	−	0.405073i
$634$	29.0191	−	76.5171i	1.15250	−	3.03888i
$635$	1.30597	−	0.685424i	0.0518257	−	0.0272002i
$636$	−12.9765	−	18.7997i	−0.514551	−	0.745455i
$637$	−12.7006	−	66.7898i	−0.503216	−	2.64631i
$638$	13.1469	−	19.0466i	0.520492	−	0.754062i
$639$	0.399692	−	3.29176i	0.0158116	−	0.130220i
$640$	1.07358	+	0.264615i	0.0424372	+	0.0104598i
$641$	10.4041	+	15.0730i	0.410939	+	0.595348i	0.972733	−	0.231930i	$-0.0745039\pi$
$641$	10.4041	+	15.0730i	0.410939	+	0.595348i	−0.561794	+	0.827277i	$0.689889\pi$
$642$	23.7238	−	21.0174i	0.936303	−	0.829492i
$643$	1.10983	+	0.582486i	0.0437676	+	0.0229710i	0.486465	−	0.873700i	$-0.338286\pi$
$643$	1.10983	+	0.582486i	0.0437676	+	0.0229710i	−0.442697	+	0.896671i	$0.645978\pi$
$644$	10.8865	+	89.6585i	0.428989	+	3.53304i
$645$	−1.00490	+	8.27614i	−0.0395681	+	0.325873i
$646$	66.3377	−	58.7701i	2.61002	−	2.31228i
$647$	−9.88095	+	14.3150i	−0.388460	+	0.562782i	−0.967613	−	0.252437i	$-0.918768\pi$
$647$	−9.88095	+	14.3150i	−0.388460	+	0.562782i	0.579153	+	0.815219i	$0.303383\pi$
$648$	0.902010	+	7.42872i	0.0354343	+	0.291828i
$649$	−0.315446	+	2.59793i	−0.0123823	+	0.101978i
$650$	7.42214	+	39.0315i	0.291120	+	1.53094i
$651$	2.80595	+	23.1091i	0.109974	+	0.905718i
$652$	−73.1002	+	18.0176i	−2.86282	+	0.705623i
$653$	37.2898			1.45926			0.729632	−	0.683840i	$-0.239691\pi$
$653$	37.2898			1.45926			0.729632	+	0.683840i	$0.239691\pi$
$654$	39.2585			1.53513
$655$	−9.81038	+	2.41804i	−0.383323	+	0.0944807i
$656$	18.1041	−	47.7365i	0.706845	−	1.86380i
$657$	−3.38804			−0.132180
$658$	−43.2908	−	114.149i	−1.68765	−	4.44997i
$659$	−40.1166	−	9.88786i	−1.56272	−	0.385176i	−0.639298	−	0.768959i	$-0.720775\pi$
$659$	−40.1166	−	9.88786i	−1.56272	−	0.385176i	−0.923423	+	0.383783i	$0.874621\pi$
$660$	5.37782	−	4.76433i	0.209331	−	0.185451i
$661$	−39.3263	−	9.69306i	−1.52962	−	0.377016i	−0.617374	−	0.786670i	$-0.711804\pi$
$661$	−39.3263	−	9.69306i	−1.52962	−	0.377016i	−0.912241	+	0.409653i	$0.865650\pi$
$662$	−15.8713	+	14.0607i	−0.616855	+	0.546486i
$663$	−16.4796	−	12.7346i	−0.640017	−	0.494569i
$664$	63.1085	+	55.9092i	2.44908	+	2.16970i
$665$	−15.0621	−	21.8213i	−0.584084	−	0.846192i
$666$	3.42485	−	0.844149i	0.132710	−	0.0327101i
$667$	11.0458	−	16.0025i	0.427693	−	0.619621i
$668$	68.6630	+	16.9239i	2.65665	+	0.654806i
$669$	13.8217	+	3.40675i	0.534378	+	0.131712i
$670$	−2.31580	+	19.0723i	−0.0894671	+	0.736828i
$671$	−4.51385	−	3.99893i	−0.174255	−	0.154377i
$672$	−19.6714	−	51.8692i	−0.758840	−	2.00090i
$673$	10.3488	−	5.43146i	0.398916	−	0.209367i	−0.253321	−	0.967382i	$-0.581523\pi$
$673$	10.3488	−	5.43146i	0.398916	−	0.209367i	0.652237	+	0.758015i	$0.273831\pi$
$674$	−2.96711	+	4.29861i	−0.114289	+	0.165576i
$675$	−4.20794			−0.161964
$676$	62.5816	−	8.44716i	2.40699	−	0.324891i
$677$	−5.96430			−0.229227			−0.114613	−	0.993410i	$-0.536563\pi$
$677$	−5.96430			−0.229227			−0.114613	+	0.993410i	$0.536563\pi$
$678$	−2.29496	+	3.32483i	−0.0881375	+	0.127689i
$679$	−29.9889	+	15.7394i	−1.15087	+	0.604023i
$680$	−13.6415	−	35.9697i	−0.523128	−	1.37937i
$681$	13.8713	+	12.2889i	0.531548	+	0.470910i
$682$	2.40155	−	19.7786i	0.0919602	−	0.757360i
$683$	−16.2862	−	4.01420i	−0.623175	−	0.153599i	−0.0849297	−	0.996387i	$-0.527067\pi$
$683$	−16.2862	−	4.01420i	−0.623175	−	0.153599i	−0.538246	+	0.842788i	$0.680913\pi$
$684$	−27.6341	−	6.81120i	−1.05662	−	0.260433i
$685$	−3.28655	+	4.76139i	−0.125573	+	0.181923i
$686$	−153.286	+	37.7817i	−5.85250	+	1.44251i
$687$	11.8773	+	17.2072i	0.453147	+	0.656497i
$688$	−69.2849	−	61.3810i	−2.64146	−	2.34013i
$689$	−7.06164	−	15.4148i	−0.269027	−	0.587258i
$690$	6.37863	−	5.65097i	0.242830	−	0.215129i
$691$	1.35544	+	0.334087i	0.0515635	+	0.0127093i	0.265013	−	0.964245i	$-0.414624\pi$
$691$	1.35544	+	0.334087i	0.0515635	+	0.0127093i	−0.213450	+	0.976954i	$0.568470\pi$
$692$	−37.4233	+	33.1541i	−1.42262	+	1.26033i
$693$	−8.20504	−	2.02236i	−0.311684	−	0.0768231i
$694$	3.30154	+	8.70545i	0.125325	+	0.330455i
$695$	14.4631			0.548617
$696$	−14.1114	+	37.2087i	−0.534892	+	1.41039i
$697$	−28.9773	+	7.14227i	−1.09759	+	0.270533i
$698$	45.2612			1.71316
$699$	−0.140893			−0.00532908
$700$	100.918	−	24.8740i	3.81434	−	0.940151i
$701$	−4.91833	−	40.5061i	−0.185763	−	1.52989i	−0.725595	−	0.688122i	$-0.758436\pi$
$701$	−4.91833	−	40.5061i	−0.185763	−	1.52989i	0.539833	−	0.841772i	$-0.318487\pi$
$702$	−0.507226	+	9.42825i	−0.0191440	+	0.355846i
$703$	−0.951281	+	7.83451i	−0.0358783	+	0.295484i
$704$	1.76412	+	14.5288i	0.0664877	+	0.547576i
$705$	−4.63510	+	6.71510i	−0.174568	+	0.252905i
$706$	−45.6535	+	40.4455i	−1.71819	+	1.52219i
$707$	−9.36794	+	77.1519i	−0.352318	+	2.90160i
$708$	−0.922027	−	7.59357i	−0.0346519	−	0.285384i
$709$	26.6526	+	13.9884i	1.00096	+	0.525344i	0.883848	−	0.467775i	$-0.154944\pi$
$709$	26.6526	+	13.9884i	1.00096	+	0.525344i	0.117112	+	0.993119i	$0.462636\pi$
$710$	5.78454	−	5.12466i	0.217090	−	0.192325i
$711$	7.02656	+	10.1797i	0.263517	+	0.381770i
$712$	−15.1882	−	3.74355i	−0.569202	−	0.140296i
$713$	2.01773	−	16.6175i	0.0755646	−	0.622330i
$714$	−43.6931	+	63.3004i	−1.63517	+	2.36896i
$715$	4.54522	−	2.78924i	0.169982	−	0.104311i
$716$	−35.2070	−	51.0062i	−1.31575	−	1.90619i
$717$	−12.1976	+	6.40182i	−0.455529	+	0.239080i
$718$	−21.1770	+	55.8390i	−0.790317	+	2.08389i
$719$	5.70842	+	47.0131i	0.212888	+	1.75329i	0.572236	+	0.820089i	$0.306076\pi$
$719$	5.70842	+	47.0131i	0.212888	+	1.75329i	−0.359348	+	0.933204i	$0.617001\pi$
$720$	−4.99562	+	7.23740i	−0.186176	+	0.269722i
$721$	69.7915	−	17.2021i	2.59917	−	0.640638i
$722$	22.8029	−	33.0357i	0.848635	−	1.22946i
$723$	−2.22720	+	5.87264i	−0.0828304	+	0.218406i
$724$	17.9185	−	47.2471i	0.665935	−	1.75593i
$725$	−19.8139	−	10.3991i	−0.735870	−	0.386215i
$726$	−19.1020	−	10.0255i	−0.708943	−	0.372082i
$727$	−22.6089	+	5.57260i	−0.838519	+	0.206676i	−0.635114	−	0.772418i	$-0.719047\pi$
$727$	−22.6089	+	5.57260i	−0.838519	+	0.206676i	−0.203405	+	0.979095i	$0.565201\pi$
$728$	−25.6299	−	134.782i	−0.949906	−	4.99535i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−5.91033	−	5.23610i	−0.218751	−	0.193797i
$731$	−6.52219	+	53.7151i	−0.241232	+	1.98672i
$732$	15.6075	+	8.19147i	0.576872	+	0.302766i
$733$	−28.0601	+	14.7271i	−1.03642	+	0.543957i	−0.895035	−	0.445997i	$-0.852849\pi$
$733$	−28.0601	+	14.7271i	−1.03642	+	0.543957i	−0.141389	+	0.989954i	$0.545157\pi$
$734$	12.5333	+	33.0476i	0.462612	+	1.21981i
$735$	12.5611	+	11.1282i	0.463324	+	0.410469i
$736$	4.80830	+	39.5999i	0.177236	+	1.45967i
$737$	−13.3020	+	3.27864i	−0.489984	+	0.120770i
$738$	10.1275	+	8.97220i	0.372799	+	0.330271i
$739$	−34.0720	+	30.1852i	−1.25336	+	1.11038i	−0.264056	+	0.964507i	$0.585060\pi$
$739$	−34.0720	+	30.1852i	−1.25336	+	1.11038i	−0.989303	+	0.145873i	$0.953401\pi$
$740$	5.15621	+	2.70619i	0.189546	+	0.0994815i
$741$	−19.3214	−	8.54139i	−0.709790	−	0.313776i
$742$	−55.4460	+	29.1003i	−2.03549	+	1.06831i
$743$	−2.58245	+	6.80935i	−0.0947408	+	0.249811i	−0.974006	−	0.226521i	$-0.927265\pi$
$743$	−2.58245	+	6.80935i	−0.0947408	+	0.249811i	0.879265	+	0.476332i	$0.158034\pi$
$744$	4.12944	+	34.0090i	0.151393	+	1.24683i
$745$	15.1611	−	7.95715i	0.555459	−	0.291528i
$746$	42.0180			1.53839
$747$	−9.97618	+	5.23590i	−0.365009	+	0.191572i
$748$	34.9040	−	30.9222i	1.27622	−	1.13063i
$749$	−34.9605	−	50.6491i	−1.27743	−	1.85068i
$750$	−16.0630	−	14.2306i	−0.586537	−	0.519626i
$751$	7.25314	+	10.5080i	0.264671	+	0.383442i	0.932676	−	0.360714i	$-0.117467\pi$
$751$	7.25314	+	10.5080i	0.264671	+	0.383442i	−0.668005	+	0.744156i	$0.732852\pi$
$752$	−32.1248	−	84.7062i	−1.17147	−	3.08892i
$753$	8.14011	+	21.4637i	0.296642	+	0.782181i
$754$	−25.6885	+	43.1412i	−0.935521	+	1.57111i
$755$	3.89681	−	10.2750i	0.141819	−	0.373947i
$756$	24.7005			0.898348
$757$	−5.04434	−	13.3008i	−0.183340	−	0.483427i	0.811563	−	0.584264i	$-0.198617\pi$
$757$	−5.04434	−	13.3008i	−0.183340	−	0.483427i	−0.994903	+	0.100838i	$0.967848\pi$
$758$	10.4599	−	86.1454i	0.379922	−	3.12894i
$759$	5.38067	+	2.82400i	0.195306	+	0.102505i
$760$	−22.1665	−	32.1137i	−0.804063	−	1.16489i
$761$	17.2628	+	25.0095i	0.625777	+	0.906594i	0.999783	−	0.0208321i	$-0.00663155\pi$
$761$	17.2628	+	25.0095i	0.625777	+	0.906594i	−0.374006	+	0.927426i	$0.622016\pi$
$762$	−3.84273	−	2.01682i	−0.139207	−	0.0730617i
$763$	9.18855	−	75.6745i	0.332648	−	2.73960i
$764$	−11.7428	−	30.9633i	−0.424840	−	1.12021i
$765$	5.14074			0.185864
$766$	−21.5376	+	56.7900i	−0.778185	+	2.05190i
$767$	0.305011	−	5.66949i	0.0110133	−	0.204714i
$768$	5.09194	+	13.4263i	0.183739	+	0.484481i
$769$	−15.4768	−	40.8089i	−0.558106	−	1.47161i	−0.855984	−	0.517002i	$-0.827048\pi$
$769$	−15.4768	−	40.8089i	−0.558106	−	1.47161i	0.297878	−	0.954604i	$-0.403721\pi$
$770$	−11.1880	−	16.2085i	−0.403186	−	0.584115i
$771$	−20.4957	−	18.1576i	−0.738135	−	0.653931i
$772$	−15.7628	−	22.8363i	−0.567314	−	0.821896i
$773$	−3.82756	+	3.39092i	−0.137668	+	0.121963i	−0.729147	−	0.684358i	$-0.760083\pi$
$773$	−3.82756	+	3.39092i	−0.137668	+	0.121963i	0.591479	+	0.806320i	$0.298544\pi$
$774$	21.7211	−	11.4001i	0.780748	−	0.409768i
$775$	−19.2641			−0.691988
$776$	−44.1339	+	23.1632i	−1.58431	+	0.831512i
$777$	−0.825585	−	6.79931i	−0.0296177	−	0.243924i
$778$	23.9036	−	63.0286i	0.856985	−	2.25968i
$779$	−26.8049	+	14.0683i	−0.960385	+	0.504049i
$780$	−10.9482	+	11.0952i	−0.392009	+	0.397273i
$781$	4.87954	+	2.56098i	0.174604	+	0.0916390i
$782$	41.3996	−	36.6768i	1.48045	−	1.31156i
$783$	−3.98044	−	3.52637i	−0.142249	−	0.126022i
$784$	−180.908	+	44.5899i	−6.46100	+	1.59249i
$785$	−0.0173753	−	0.143099i	−0.000620151	−	0.00510741i
$786$	22.2535	+	19.7149i	0.793758	+	0.703208i
$787$	11.4839	+	30.2807i	0.409358	+	1.07939i	0.968214	+	0.250124i	$0.0804714\pi$
$787$	11.4839	+	30.2807i	0.409358	+	1.07939i	−0.558855	+	0.829265i	$0.688759\pi$
$788$	60.6305	−	31.8213i	2.15987	−	1.13359i
$789$	−13.8217	−	7.25420i	−0.492066	−	0.258256i
$790$	−3.47480	+	28.6175i	−0.123628	+	1.01817i
$791$	5.87179	+	5.20195i	0.208777	+	0.184960i
$792$	−12.0751	−	2.97625i	−0.429071	−	0.105756i
$793$	10.3525	+	7.99982i	0.367628	+	0.284082i
$794$	−64.0985	+	15.7989i	−2.27477	+	0.560680i
$795$	3.70579	+	1.94495i	0.131431	+	0.0689801i
$796$	−58.6468	−	30.7802i	−2.07868	−	1.09098i
$797$	−6.03100	+	15.9024i	−0.213629	+	0.563293i	−0.998403	−	0.0564884i	$-0.982010\pi$
$797$	−6.03100	+	15.9024i	−0.213629	+	0.563293i	0.784774	+	0.619782i	$0.212779\pi$
$798$	−27.6657	+	72.9485i	−0.979355	+	2.58235i
$799$	−30.0835	+	43.5834i	−1.06428	+	1.54187i
$800$	44.5730	−	10.9863i	1.57589	−	0.388423i
$801$	1.18746	−	1.72033i	0.0419568	−	0.0607849i
$802$	0.205174	+	1.68976i	0.00724495	+	0.0596675i
$803$	1.99664	−	5.26470i	0.0704598	−	0.185787i
$804$	35.4574	−	18.6095i	1.25049	−	0.656306i
$805$	−9.39987	−	13.6181i	−0.331302	−	0.479973i
$806$	−2.32210	+	43.1629i	−0.0817926	+	1.52035i
$807$	3.26453	−	4.72949i	0.114917	−	0.166486i
$808$	−13.7865	+	113.542i	−0.485008	+	3.99440i
$809$	0.799052	+	0.196949i	0.0280932	+	0.00692434i	0.253337	−	0.967378i	$-0.418472\pi$
$809$	0.799052	+	0.196949i	0.0280932	+	0.00692434i	−0.225244	+	0.974302i	$0.572318\pi$
$810$	−1.32392	−	1.91804i	−0.0465180	−	0.0673929i
$811$	−17.3161	+	15.3407i	−0.608049	+	0.538684i	−0.909984	−	0.414644i	$-0.863906\pi$
$811$	−17.3161	+	15.3407i	−0.608049	+	0.538684i	0.301935	+	0.953329i	$0.402368\pi$
$812$	116.307	+	61.0427i	4.08158	+	2.14218i
$813$	−0.696351	−	5.73497i	−0.0244221	−	0.201134i
$814$	−0.706599	+	5.81937i	−0.0247663	+	0.203969i
$815$	10.3247	−	9.14689i	0.361659	−	0.320402i
$816$	−32.4233	+	46.9733i	−1.13504	+	1.64440i
$817$	6.61569	+	54.4851i	0.231454	+	1.90619i
$818$	−5.95764	+	49.0656i	−0.208304	+	1.71554i
$819$	18.0552	+	3.18444i	0.630898	+	0.111273i
$820$	2.69240	+	22.1739i	0.0940228	+	0.774347i
$821$	−1.66189	+	0.409619i	−0.0580004	+	0.0142958i	−0.268209	−	0.963361i	$-0.586432\pi$
$821$	−1.66189	+	0.409619i	−0.0580004	+	0.0142958i	0.210209	+	0.977657i	$0.432586\pi$
$822$	17.0236			0.593766
$823$	35.1489			1.22521			0.612606	−	0.790388i	$-0.290121\pi$
$823$	35.1489			1.22521			0.612606	+	0.790388i	$0.290121\pi$
$824$	102.710	−	25.3158i	3.57808	−	0.881917i
$825$	2.47982	−	6.53875i	0.0863363	−	0.227650i
$826$	−20.9686			−0.729589
$827$	−18.0667	−	47.6380i	−0.628241	−	1.65654i	−0.747973	−	0.663730i	$-0.768973\pi$
$827$	−18.0667	−	47.6380i	−0.628241	−	1.65654i	0.119731	−	0.992806i	$-0.461797\pi$
$828$	−17.2457	−	4.25069i	−0.599330	−	0.147722i
$829$	−18.9973	+	16.8302i	−0.659804	+	0.584535i	−0.925142	−	0.379620i	$-0.876055\pi$
$829$	−18.9973	+	16.8302i	−0.659804	+	0.584535i	0.265339	+	0.964155i	$0.414516\pi$
$830$	−25.4951	−	6.28397i	−0.884946	−	0.218120i
$831$	−9.26934	+	8.21192i	−0.321550	+	0.284868i
$832$	−5.93164	−	31.1933i	−0.205643	−	1.08143i
$833$	81.5261	+	72.2258i	2.82471	+	2.50248i
$834$	−24.1751	−	35.0236i	−0.837114	−	1.21277i
$835$	−12.5799	+	3.10067i	−0.435345	+	0.107303i
$836$	26.8693	−	38.9269i	0.929294	−	1.34632i
$837$	−4.44501	−	1.09560i	−0.153642	−	0.0378694i
$838$	−57.4984	−	14.1721i	−1.98625	−	0.489566i
$839$	2.25364	−	18.5604i	0.0778042	−	0.640775i	−0.900684	−	0.434474i	$-0.856934\pi$
$839$	2.25364	−	18.5604i	0.0778042	−	0.640775i	0.978489	−	0.206301i	$-0.0661426\pi$
$840$	25.3484	+	22.4567i	0.874602	+	0.774830i
$841$	0.255600	+	0.673963i	0.00881380	+	0.0232401i
$842$	3.95460	−	2.07554i	0.136285	−	0.0715277i
$843$	−5.38660	+	7.80383i	−0.185524	+	0.268778i
$844$	−49.8698			−1.71659
$845$	−9.43317	+	6.69874i	−0.324511	+	0.230444i
$846$	24.0088			0.825438
$847$	−23.7961	+	34.4746i	−0.817642	+	1.18456i
$848$	−41.1448	+	21.5944i	−1.41292	+	0.741556i
$849$	5.32199	+	14.0329i	0.182650	+	0.481609i
$850$	−47.6433	−	42.2083i	−1.63415	−	1.44773i
$851$	−0.593669	+	4.88930i	−0.0203507	+	0.167603i
$852$	−15.6395	−	3.85479i	−0.535801	−	0.132063i
$853$	−5.97867	−	1.47361i	−0.204706	−	0.0504554i	0.135629	−	0.990760i	$-0.456694\pi$
$853$	−5.97867	−	1.47361i	−0.204706	−	0.0504554i	−0.340335	+	0.940304i	$0.610540\pi$
$854$	27.4479	−	39.7652i	0.939249	−	1.36074i
$855$	5.06291	−	1.24790i	0.173148	−	0.0426771i
$856$	−51.4504	−	74.5388i	−1.75854	−	2.54768i
$857$	9.27972	+	8.22111i	0.316989	+	0.280828i	0.806581	−	0.591124i	$-0.201316\pi$
$857$	9.27972	+	8.22111i	0.316989	+	0.280828i	−0.489591	+	0.871952i	$0.662854\pi$
$858$	−14.3517	−	6.34443i	−0.489959	−	0.216595i
$859$	17.7429	−	15.7188i	0.605379	−	0.536319i	−0.303794	−	0.952738i	$-0.598253\pi$
$859$	17.7429	−	15.7188i	0.605379	−	0.536319i	0.909173	+	0.416419i	$0.136715\pi$
$860$	39.3209	+	9.69172i	1.34083	+	0.330485i
$861$	19.6652	−	17.4218i	0.670187	−	0.593734i
$862$	−49.9368	−	12.3083i	−1.70085	−	0.419222i
$863$	−14.1319	−	37.2629i	−0.481057	−	1.26844i	−0.927564	−	0.373663i	$-0.878102\pi$
$863$	−14.1319	−	37.2629i	−0.481057	−	1.26844i	0.446507	−	0.894780i	$-0.352668\pi$
$864$	10.9096			0.371152
$865$	3.24820	−	8.56480i	0.110442	−	0.291212i
$866$	10.0107	−	2.46742i	0.340178	−	0.0838464i
$867$	16.3652			0.555791
$868$	113.080			3.83818
$869$	−19.9592	+	4.91951i	−0.677071	+	0.166883i
$870$	−1.49389	−	12.3033i	−0.0506476	−	0.417120i
$871$	28.3173	−	9.03162i	0.959494	−	0.306025i
$872$	13.5225	−	111.368i	0.457931	−	3.77140i
$873$	−0.802845	−	6.61203i	−0.0271722	−	0.223783i
$874$	31.8696	−	46.1711i	1.07801	−	1.56176i
$875$	−31.1904	+	27.6323i	−1.05443	+	0.934141i
$876$	−1.98377	+	16.3378i	−0.0670254	+	0.552004i
$877$	−0.948197	−	7.80910i	−0.0320183	−	0.263695i	−0.999923	−	0.0123785i	$-0.996060\pi$
$877$	−0.948197	−	7.80910i	−0.0320183	−	0.263695i	0.967905	−	0.251316i	$-0.0808634\pi$
$878$	−19.6846	−	10.3313i	−0.664322	−	0.348663i
$879$	−11.5057	+	10.1932i	−0.388078	+	0.343807i
$880$	−8.30224	−	12.0279i	−0.279868	−	0.405459i
$881$	35.9816	+	8.86867i	1.21225	+	0.298793i	0.793082	−	0.609115i	$-0.208475\pi$
$881$	35.9816	+	8.86867i	1.21225	+	0.298793i	0.419169	+	0.907908i	$0.362321\pi$
$882$	5.95193	−	49.0186i	0.200412	−	1.65054i
$883$	7.50182	−	10.8683i	0.252456	−	0.365746i	−0.676181	−	0.736736i	$-0.736366\pi$
$883$	7.50182	−	10.8683i	0.252456	−	0.365746i	0.928637	+	0.370990i	$0.120981\pi$
$884$	−71.0579	+	72.0119i	−2.38993	+	2.42202i
$885$	0.796116	+	1.15337i	0.0267612	+	0.0387702i
$886$	−39.9169	+	20.9500i	−1.34103	+	0.703829i
$887$	18.4101	−	48.5435i	0.618151	−	1.62993i	−0.149276	−	0.988796i	$-0.547694\pi$
$887$	18.4101	−	48.5435i	0.618151	−	1.62993i	0.767428	−	0.641136i	$-0.221536\pi$
$888$	−1.21499	−	10.0063i	−0.0407724	−	0.335791i
$889$	−4.78702	+	6.93520i	−0.160552	+	0.232599i
$890$	4.73020	−	1.16589i	0.158557	−	0.0390807i
$891$	0.944069	−	1.36772i	0.0316275	−	0.0458203i
$892$	24.5210	−	64.6564i	0.821022	−	2.16486i
$893$	−19.0483	+	50.2262i	−0.637427	+	1.68076i
$894$	−44.6107	−	23.4135i	−1.49200	−	0.783064i
$895$	10.0543	+	5.27691i	0.336079	+	0.176388i
$896$	−6.13394	+	1.51188i	−0.204920	+	0.0505083i
$897$	−12.0580	−	5.33045i	−0.402604	−	0.177978i
$898$	11.7604	+	2.89868i	0.392449	+	0.0967300i
$899$	−18.2226	−	16.1439i	−0.607759	−	0.538428i
$900$	−2.46384	+	20.2916i	−0.0821281	+	0.676386i
$901$	24.0519	+	12.6234i	0.801284	+	0.420546i
$902$	−19.9103	+	10.4497i	−0.662941	+	0.347938i
$903$	−16.8909	−	44.5377i	−0.562095	−	1.48212i
$904$	8.64134	+	7.65556i	0.287407	+	0.254620i
$905$	1.11591	+	9.19036i	0.0370942	+	0.305498i
$906$	−31.3954	+	7.73827i	−1.04304	+	0.257087i
$907$	−8.29934	−	7.35257i	−0.275575	−	0.244138i	0.514003	−	0.857788i	$-0.328162\pi$
$907$	−8.29934	−	7.35257i	−0.275575	−	0.244138i	−0.789578	+	0.613650i	$0.789701\pi$
$908$	67.3814	−	59.6947i	2.23613	−	1.98104i
$909$	−13.5335	−	7.10293i	−0.448878	−	0.235589i
$910$	26.5752	+	33.4588i	0.880960	+	1.10915i
$911$	−0.509618	+	0.267468i	−0.0168844	+	0.00886161i	−0.473144	−	0.880985i	$-0.656881\pi$
$911$	−0.509618	+	0.267468i	−0.0168844	+	0.00886161i	0.456260	+	0.889847i	$0.349189\pi$
$912$	−20.5299	+	54.1328i	−0.679812	+	1.79252i
$913$	−2.25695	−	18.5877i	−0.0746942	−	0.615162i
$914$	22.4528	−	11.7841i	0.742671	−	0.389784i
$915$	−3.22940			−0.106761
$916$	89.9313	−	47.1996i	2.97141	−	1.55952i
$917$	43.2109	−	38.2816i	1.42695	−	1.26417i
$918$	−8.59274	−	12.4487i	−0.283603	−	0.410869i
$919$	−40.0706	−	35.4995i	−1.32181	−	1.17102i	−0.972207	−	0.234121i	$-0.924779\pi$
$919$	−40.0706	−	35.4995i	−1.32181	−	1.17102i	−0.349601	−	0.936899i	$-0.613683\pi$
$920$	−13.8335	−	20.0413i	−0.456077	−	0.660742i
$921$	6.82824	+	18.0046i	0.224998	+	0.593271i
$922$	−23.6856	−	62.4538i	−0.780044	−	2.05681i
$923$	−10.9349	−	4.83399i	−0.359928	−	0.159113i
$924$	−14.5565	+	38.3823i	−0.478873	+	1.26268i
$925$	5.66801			0.186363
$926$	26.8683	+	70.8460i	0.882948	+	2.32814i
$927$	−1.70391	+	14.0330i	−0.0559638	+	0.460903i
$928$	51.3700	+	26.9610i	1.68630	+	0.885039i
$929$	−7.64314	−	11.0730i	−0.250763	−	0.363293i	0.677306	−	0.735702i	$-0.263147\pi$
$929$	−7.64314	−	11.0730i	−0.250763	−	0.363293i	−0.928069	+	0.372408i	$0.878532\pi$
$930$	−6.06098	−	8.78085i	−0.198747	−	0.287935i
$931$	97.8245	+	51.3422i	3.20607	+	1.68267i
$932$	−0.0824962	+	0.679418i	−0.00270225	+	0.0222551i
$933$	4.39817	+	11.5970i	0.143990	+	0.379669i
$934$	29.7657			0.973962
$935$	−3.02953	+	7.98823i	−0.0990764	+	0.261243i
$936$	26.5712	+	4.68644i	0.868508	+	0.153181i
$937$	10.2667	+	27.0711i	0.335399	+	0.884375i	0.991548	+	0.129743i	$0.0414153\pi$
$937$	10.2667	+	27.0711i	0.335399	+	0.884375i	−0.656148	+	0.754632i	$0.727816\pi$
$938$	−38.9251	−	102.637i	−1.27095	−	3.35122i
$939$	5.37879	+	7.79253i	0.175530	+	0.254300i
$940$	29.6677	+	26.2833i	0.967653	+	0.857266i
$941$	−17.3670	−	25.1605i	−0.566150	−	0.820209i	0.430449	−	0.902615i	$-0.358355\pi$
$941$	−17.3670	−	25.1605i	−0.566150	−	0.820209i	−0.996599	+	0.0824055i	$0.973740\pi$
$942$	−0.317483	+	0.281265i	−0.0103441	+	0.00916411i
$943$	−16.7282	+	8.77964i	−0.544745	+	0.285904i
$944$	−15.5601			−0.506439
$945$	−4.00707	+	2.10307i	−0.130350	+	0.0684130i
$946$	4.91405	+	40.4708i	0.159769	+	1.31582i
$947$	−17.0691	+	45.0076i	−0.554673	+	1.46255i	0.305322	+	0.952249i	$0.401236\pi$
$947$	−17.0691	+	45.0076i	−0.554673	+	1.46255i	−0.859995	+	0.510303i	$0.829533\pi$
$948$	53.2030	−	27.9231i	1.72795	−	0.906899i
$949$	−3.55637	+	11.6866i	−0.115445	+	0.379363i
$950$	−57.1679	−	30.0040i	−1.85477	−	0.973459i
$951$	23.3911	−	20.7227i	0.758508	−	0.671980i
$952$	164.520	+	145.752i	5.33212	+	4.72385i
$953$	−35.0610	+	8.64175i	−1.13574	+	0.279934i	−0.761985	−	0.647595i	$-0.775775\pi$
$953$	−35.0610	+	8.64175i	−1.13574	+	0.279934i	−0.373751	+	0.927529i	$0.621929\pi$
$954$	−1.48437	−	12.2249i	−0.0480581	−	0.395794i
$955$	4.54130	+	4.02324i	0.146953	+	0.130189i
$956$	23.7289	+	62.5680i	0.767448	+	2.02359i
$957$	7.82540	−	4.10709i	0.252959	−	0.132763i
$958$	−20.1465	−	10.5737i	−0.650904	−	0.341621i
$959$	3.98442	−	32.8146i	0.128664	−	1.05964i
$960$	5.86650	+	5.19727i	0.189340	+	0.167741i
$961$	9.74973	+	2.40309i	0.314507	+	0.0775191i
$962$	0.683224	−	12.6997i	0.0220280	−	0.409454i
$963$	11.7515	−	2.89648i	0.378686	−	0.0933377i
$964$	27.0150	+	14.1786i	0.870095	+	0.456661i
$965$	4.50149	+	2.36256i	0.144908	+	0.0760536i
$966$	−17.2654	+	45.5252i	−0.555506	+	1.46475i
$967$	4.84698	−	12.7804i	0.155868	−	0.410991i	−0.834221	−	0.551430i	$-0.814082\pi$
$967$	4.84698	−	12.7804i	0.155868	−	0.410991i	0.990089	+	0.140439i	$0.0448515\pi$
$968$	−35.0200	+	50.7352i	−1.12558	+	1.63069i
$969$	32.8601	−	8.09928i	1.05562	−	0.260186i
$970$	8.81812	−	12.7752i	0.283133	−	0.410188i
$971$	−4.43934	−	36.5613i	−0.142465	−	1.17331i	−0.872050	−	0.489417i	$-0.837210\pi$
$971$	−4.43934	−	36.5613i	−0.142465	−	1.17331i	0.729585	−	0.683890i	$-0.239713\pi$
$972$	−1.72254	+	4.54196i	−0.0552504	+	0.145683i
$973$	−73.1698	+	38.4025i	−2.34571	+	1.23113i
$974$	−19.6983	−	28.5379i	−0.631174	−	0.914413i
$975$	−4.41701	+	14.5148i	−0.141458	+	0.464844i
$976$	20.3683	−	29.5086i	0.651973	−	0.944546i
$977$	−1.10037	+	9.06235i	−0.0352039	+	0.289930i	0.964465	+	0.264210i	$0.0851111\pi$
$977$	−1.10037	+	9.06235i	−0.0352039	+	0.289930i	−0.999669	+	0.0257205i	$0.991812\pi$
$978$	−39.4077	−	9.71313i	−1.26012	−	0.310592i
$979$	1.97344	+	2.85902i	0.0630715	+	0.0913748i
$980$	61.0172	−	54.0565i	1.94912	−	1.72677i
$981$	13.2744	+	6.96692i	0.423818	+	0.222437i
$982$	−2.35388	−	19.3859i	−0.0751153	−	0.618630i
$983$	5.59152	−	46.0503i	0.178342	−	1.46878i	−0.578770	−	0.815491i	$-0.696467\pi$
$983$	5.59152	−	46.0503i	0.178342	−	1.46878i	0.757112	−	0.653285i	$-0.226610\pi$
$984$	28.9407	−	25.6392i	0.922595	−	0.817348i
$985$	−7.12650	+	10.3245i	−0.227069	+	0.328967i
$986$	−9.69586	−	79.8526i	−0.308779	−	2.54303i
$987$	5.61932	−	46.2793i	0.178865	−	1.47308i
$988$	−52.5015	+	88.1708i	−1.67029	+	2.80509i
$989$	4.12867	+	34.0027i	0.131284	+	1.08122i
$990$	3.76066	−	0.926920i	0.119522	−	0.0294595i
$991$	6.13123			0.194765			0.0973825	−	0.995247i	$-0.468953\pi$
$991$	6.13123			0.194765			0.0973825	+	0.995247i	$0.468953\pi$
$992$	49.9446			1.58574
$993$	−7.86177	+	1.93775i	−0.249486	+	0.0614927i
$994$	−15.6574	+	41.2851i	−0.496622	+	1.30948i
$995$	12.1348			0.384698
$996$	19.4073	+	51.1730i	0.614945	+	1.62148i
$997$	4.89184	+	1.20573i	0.154926	+	0.0381859i	0.316016	−	0.948754i	$-0.397655\pi$
$997$	4.89184	+	1.20573i	0.154926	+	0.0381859i	−0.161090	+	0.986940i	$0.551501\pi$
$998$	−32.4555	+	28.7531i	−1.02736	+	0.910162i
$999$	1.30784	+	0.322353i	0.0413782	+	0.0101988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.352.16	yes	204
169.157	even	13	inner	507.2.m.b.157.16	✓	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.157.16	✓	204	169.157	even	13	inner
507.2.m.b.352.16	yes	204	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.48760 - 2.15515i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-1.72254 - 4.54196i) q^{4} +(0.666157 + 0.590163i) q^{5} +(0.315650 - 2.59961i) q^{6} +(-4.93713 - 1.21689i) q^{7} +(-7.26583 - 1.79087i) q^{8} +(0.568065 - 0.822984i) q^{9} +O(q^{10})\)	\(q+(1.48760 - 2.15515i) q^{2} +(0.885456 - 0.464723i) q^{3} +(-1.72254 - 4.54196i) q^{4} +(0.666157 + 0.590163i) q^{5} +(0.315650 - 2.59961i) q^{6} +(-4.93713 - 1.21689i) q^{7} +(-7.26583 - 1.79087i) q^{8} +(0.568065 - 0.822984i) q^{9} +(2.26286 - 0.557746i) q^{10} +(0.944069 + 1.36772i) q^{11} +(-3.63599 - 3.22120i) q^{12} +(-2.24249 - 2.82334i) q^{13} +(-9.96705 + 8.83003i) q^{14} +(0.864115 + 0.212985i) q^{15} +(-7.39624 + 6.55250i) q^{16} +(5.60841 + 1.38235i) q^{17} +(-0.928606 - 2.44853i) q^{18} +5.85907 q^{19} +(1.53302 - 4.04224i) q^{20} +(-4.93713 + 1.21689i) q^{21} +4.35204 q^{22} +3.65649 q^{23} +(-7.26583 + 1.79087i) q^{24} +(-0.507211 - 4.17726i) q^{25} +(-9.42064 + 0.632922i) q^{26} +(0.120537 - 0.992709i) q^{27} +(2.97731 + 24.5204i) q^{28} +(3.02087 - 4.37648i) q^{29} +(1.74447 - 1.54547i) q^{30} +(0.551822 - 4.54466i) q^{31} +(1.31501 + 10.8301i) q^{32} +(1.47154 + 0.772325i) q^{33} +(11.3222 - 10.0306i) q^{34} +(-2.57074 - 3.72436i) q^{35} +(-4.71647 - 1.16251i) q^{36} +(-0.162361 + 1.33716i) q^{37} +(8.71592 - 12.6272i) q^{38} +(-3.29770 - 1.45781i) q^{39} +(-3.78328 - 5.48103i) q^{40} +(-4.57494 + 2.40111i) q^{41} +(-4.72186 + 12.4505i) q^{42} +(1.12914 + 9.29928i) q^{43} +(4.58593 - 6.64387i) q^{44} +(0.864115 - 0.212985i) q^{45} +(5.43937 - 7.88029i) q^{46} +(-3.25108 + 8.57239i) q^{47} +(-3.50395 + 9.23915i) q^{48} +(16.6962 + 8.76287i) q^{49} +(-9.75716 - 5.12096i) q^{50} +(5.60841 - 1.38235i) q^{51} +(-8.96072 + 15.0486i) q^{52} +(4.56592 + 1.12540i) q^{53} +(-1.96013 - 1.73652i) q^{54} +(-0.178280 + 1.46827i) q^{55} +(33.6931 + 17.6835i) q^{56} +(5.18795 - 2.72285i) q^{57} +(-4.93816 - 13.0209i) q^{58} +(1.17869 + 1.04422i) q^{59} +(-0.521101 - 4.29165i) q^{60} +(-3.52320 + 0.868390i) q^{61} +(-8.97356 - 7.94988i) q^{62} +(-3.80609 + 3.37191i) q^{63} +(7.79776 + 4.09258i) q^{64} +(0.172383 - 3.20422i) q^{65} +(3.85354 - 2.02249i) q^{66} +(-2.92322 + 7.70789i) q^{67} +(-3.38213 - 27.8543i) q^{68} +(3.23766 - 1.69925i) q^{69} -11.8508 q^{70} +(2.93611 - 1.54099i) q^{71} +(-5.60132 + 4.96234i) q^{72} +(-1.92463 - 2.78830i) q^{73} +(2.64026 + 2.33906i) q^{74} +(-2.39038 - 3.46307i) q^{75} +(-10.0925 - 26.6116i) q^{76} +(-2.99662 - 7.90145i) q^{77} +(-8.04743 + 4.93842i) q^{78} +(-4.38621 + 11.5655i) q^{79} -8.79410 q^{80} +(-0.354605 - 0.935016i) q^{81} +(-1.63089 + 13.4316i) q^{82} +(-9.97618 - 5.23590i) q^{83} +(14.0315 + 20.3281i) q^{84} +(2.92027 + 4.23074i) q^{85} +(21.7211 + 11.4001i) q^{86} +(0.640992 - 5.27905i) q^{87} +(-4.41004 - 11.6283i) q^{88} +2.09036 q^{89} +(0.826438 - 2.17914i) q^{90} +(7.63576 + 16.6681i) q^{91} +(-6.29843 - 16.6076i) q^{92} +(-1.62340 - 4.28055i) q^{93} +(13.6385 + 19.7588i) q^{94} +(3.90306 + 3.45781i) q^{95} +(6.19736 + 8.97842i) q^{96} +(4.98552 - 4.41679i) q^{97} +(43.7226 - 22.9474i) q^{98} +1.66190 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more