LMFDB - Embedded newform 507.2.q.b.16.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

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("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.13
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80906 + 0.146043i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.27728 + 0.207579i) q^{4} +(-0.0943821 - 0.0836152i) q^{5} +(-1.45095 - 1.09032i) q^{6} +(1.37395 - 1.43043i) q^{7} +(-1.24405 - 0.306631i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(1.80906 + 0.146043i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.27728 + 0.207579i) q^{4} +(-0.0943821 - 0.0836152i) q^{5} +(-1.45095 - 1.09032i) q^{6} +(1.37395 - 1.43043i) q^{7} +(-1.24405 - 0.306631i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.158532 - 0.165049i) q^{10} +(2.57877 - 5.43463i) q^{11} +(-0.968603 - 0.858107i) q^{12} +(3.50306 - 0.853550i) q^{13} +(2.69446 - 2.38708i) q^{14} +(0.0350813 + 0.121115i) q^{15} +(-4.66067 - 1.55596i) q^{16} +(2.59904 - 2.70589i) q^{17} +(0.643590 + 1.69701i) q^{18} +(-3.27209 + 5.66742i) q^{19} +(-0.103196 - 0.126392i) q^{20} +(-1.92576 + 0.474658i) q^{21} +(5.45884 - 9.45499i) q^{22} +(3.45035 + 5.97619i) q^{23} +(0.887575 + 0.924063i) q^{24} +(-0.600767 - 4.94776i) q^{25} +(6.46192 - 1.03253i) q^{26} +(0.120537 - 0.992709i) q^{27} +(2.05185 - 1.54186i) q^{28} +(3.03677 + 0.245153i) q^{29} +(0.0457764 + 0.224228i) q^{30} +(-0.191516 + 1.57728i) q^{31} +(-5.84671 - 2.49105i) q^{32} +(-5.08417 + 3.21504i) q^{33} +(5.09701 - 4.51555i) q^{34} +(-0.249282 + 0.0201241i) q^{35} +(0.360025 + 1.24295i) q^{36} +(-0.832809 + 0.354827i) q^{37} +(-6.74710 + 9.77486i) q^{38} +(-3.41695 - 1.15086i) q^{39} +(0.0917770 + 0.132962i) q^{40} +(-3.82349 - 2.41783i) q^{41} +(-3.55315 + 0.577443i) q^{42} +(-6.41217 - 2.73197i) q^{43} +(4.42193 - 6.40626i) q^{44} +(0.0350813 - 0.121115i) q^{45} +(5.36913 + 11.3152i) q^{46} +(-3.26305 + 8.60395i) q^{47} +(3.10755 + 3.80605i) q^{48} +(0.123461 + 3.06365i) q^{49} +(-0.364241 - 9.03855i) q^{50} +(-3.64289 + 0.897891i) q^{51} +(4.65158 - 0.363064i) q^{52} +(-6.23519 - 1.53684i) q^{53} +(0.363036 - 1.77827i) q^{54} +(-0.697807 + 0.297308i) q^{55} +(-2.14787 + 1.35823i) q^{56} +(5.79458 - 3.04123i) q^{57} +(5.45790 + 0.886995i) q^{58} +(12.4574 - 4.15890i) q^{59} +(0.0196679 + 0.161980i) q^{60} +(-2.14997 + 7.42254i) q^{61} +(-0.576816 + 2.82543i) q^{62} +(1.88132 + 0.628078i) q^{63} +(-1.51183 - 0.793467i) q^{64} +(-0.401996 - 0.212350i) q^{65} +(-9.66712 + 5.07370i) q^{66} +(1.22980 - 0.199862i) q^{67} +(3.88139 - 2.91668i) q^{68} +(0.277863 - 6.89511i) q^{69} -0.453905 q^{70} +(-0.566725 + 14.0631i) q^{71} +(-0.256289 - 1.25539i) q^{72} +(-1.79985 - 2.60753i) q^{73} +(-1.55842 + 0.520278i) q^{74} +(-2.13665 + 4.50289i) q^{75} +(-5.35582 + 6.55968i) q^{76} +(-4.23078 - 11.1556i) q^{77} +(-6.01340 - 2.58099i) q^{78} +(-2.68314 + 7.07486i) q^{79} +(0.309782 + 0.536558i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-6.56383 - 4.93240i) q^{82} +(6.05139 + 3.17601i) q^{83} +(-2.55827 + 0.206525i) q^{84} +(-0.471556 + 0.0380680i) q^{85} +(-11.2010 - 5.87876i) q^{86} +(-2.43562 - 1.83025i) q^{87} +(-4.87454 + 5.97022i) q^{88} +(6.02395 + 10.4338i) q^{89} +(0.0811523 - 0.213981i) q^{90} +(3.59208 - 6.18362i) q^{91} +(3.16655 + 8.34950i) q^{92} +(1.00487 - 1.23074i) q^{93} +(-7.15961 + 15.0885i) q^{94} +(0.782709 - 0.261307i) q^{95} +(3.61020 + 5.23028i) q^{96} +(-2.50937 - 12.2917i) q^{97} +(-0.224075 + 5.56037i) q^{98} +6.01542 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

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 $

$2$	1.80906	+	0.146043i	1.27920	+	0.103268i	0.701316	−	0.712850i	$-0.252596\pi$
$2$	1.80906	+	0.146043i	1.27920	+	0.103268i	0.577885	+	0.816118i	$0.303878\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	1.27728	+	0.207579i	0.638641	+	0.103789i
$5$	−0.0943821	−	0.0836152i	−0.0422089	−	0.0373939i	0.641755	−	0.766910i	$-0.278207\pi$
$5$	−0.0943821	−	0.0836152i	−0.0422089	−	0.0373939i	−0.683963	+	0.729516i	$0.739745\pi$
$6$	−1.45095	−	1.09032i	−0.592347	−	0.445120i
$7$	1.37395	−	1.43043i	0.519303	−	0.540652i	−0.408972	−	0.912547i	$-0.634112\pi$
$7$	1.37395	−	1.43043i	0.519303	−	0.540652i	0.928275	+	0.371895i	$0.121292\pi$
$8$	−1.24405	−	0.306631i	−0.439838	−	0.108410i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−0.158532	−	0.165049i	−0.0501322	−	0.0521931i
$11$	2.57877	−	5.43463i	0.777527	−	1.63860i	0.00801760	−	0.999968i	$-0.497448\pi$
$11$	2.57877	−	5.43463i	0.777527	−	1.63860i	0.769509	−	0.638636i	$-0.220501\pi$
$12$	−0.968603	−	0.858107i	−0.279612	−	0.247714i
$13$	3.50306	−	0.853550i	0.971575	−	0.236732i
$13$	3.50306	−	0.853550i	0.971575	−	0.236732i
$14$	2.69446	−	2.38708i	0.720125	−	0.637975i
$15$	0.0350813	+	0.121115i	0.00905796	+	0.0312717i
$16$	−4.66067	−	1.55596i	−1.16517	−	0.388990i
$17$	2.59904	−	2.70589i	0.630360	−	0.656274i	−0.327050	−	0.945007i	$-0.606054\pi$
$17$	2.59904	−	2.70589i	0.630360	−	0.656274i	0.957410	+	0.288733i	$0.0932339\pi$
$18$	0.643590	+	1.69701i	0.151696	+	0.399988i
$19$	−3.27209	+	5.66742i	−0.750668	+	1.30020i	0.196831	+	0.980437i	$0.436935\pi$
$19$	−3.27209	+	5.66742i	−0.750668	+	1.30020i	−0.947499	+	0.319758i	$0.896398\pi$
$20$	−0.103196	−	0.126392i	−0.0230753	−	0.0282621i
$21$	−1.92576	+	0.474658i	−0.420236	+	0.103579i
$22$	5.45884	−	9.45499i	1.16383	−	2.01581i
$23$	3.45035	+	5.97619i	0.719448	+	1.24612i	0.961219	+	0.275788i	$0.0889387\pi$
$23$	3.45035	+	5.97619i	0.719448	+	1.24612i	−0.241770	+	0.970334i	$0.577728\pi$
$24$	0.887575	+	0.924063i	0.181175	+	0.188624i
$25$	−0.600767	−	4.94776i	−0.120153	−	0.989552i
$26$	6.46192	−	1.03253i	1.26729	−	0.202496i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	2.05185	−	1.54186i	0.387762	−	0.291384i
$29$	3.03677	+	0.245153i	0.563913	+	0.0455238i	0.359137	−	0.933285i	$-0.383071\pi$
$29$	3.03677	+	0.245153i	0.563913	+	0.0455238i	0.204777	+	0.978809i	$0.434353\pi$
$30$	0.0457764	+	0.224228i	0.00835759	+	0.0409382i
$31$	−0.191516	+	1.57728i	−0.0343974	+	0.283288i	0.965353	+	0.260947i	$0.0840349\pi$
$31$	−0.191516	+	1.57728i	−0.0343974	+	0.283288i	−0.999750	+	0.0223406i	$0.992888\pi$
$32$	−5.84671	−	2.49105i	−1.03356	−	0.440360i
$33$	−5.08417	+	3.21504i	−0.885041	+	0.559666i
$34$	5.09701	−	4.51555i	0.874129	−	0.774411i
$35$	−0.249282	+	0.0201241i	−0.0421363	+	0.00340159i
$36$	0.360025	+	1.24295i	0.0600041	+	0.207158i
$37$	−0.832809	+	0.354827i	−0.136913	+	0.0583331i	−0.459336	−	0.888262i	$-0.651913\pi$
$37$	−0.832809	+	0.354827i	−0.136913	+	0.0583331i	0.322423	+	0.946596i	$0.395502\pi$
$38$	−6.74710	+	9.77486i	−1.09452	+	1.58569i
$39$	−3.41695	−	1.15086i	−0.547150	−	0.184284i
$40$	0.0917770	+	0.132962i	0.0145112	+	0.0210231i
$41$	−3.82349	−	2.41783i	−0.597129	−	0.377601i	0.201444	−	0.979500i	$-0.435437\pi$
$41$	−3.82349	−	2.41783i	−0.597129	−	0.377601i	−0.798572	+	0.601899i	$0.794411\pi$
$42$	−3.55315	+	0.577443i	−0.548263	+	0.0891013i
$43$	−6.41217	−	2.73197i	−0.977846	−	0.416621i	−0.156892	−	0.987616i	$-0.550148\pi$
$43$	−6.41217	−	2.73197i	−0.977846	−	0.416621i	−0.820954	+	0.570994i	$0.806558\pi$
$44$	4.42193	−	6.40626i	0.666630	−	0.965781i
$45$	0.0350813	−	0.121115i	0.00522961	−	0.0180547i
$46$	5.36913	+	11.3152i	0.791635	+	1.66834i
$47$	−3.26305	+	8.60395i	−0.475964	+	1.25502i	0.455191	+	0.890394i	$0.349571\pi$
$47$	−3.26305	+	8.60395i	−0.475964	+	1.25502i	−0.931156	+	0.364621i	$0.881198\pi$
$48$	3.10755	+	3.80605i	0.448536	+	0.549356i
$49$	0.123461	+	3.06365i	0.0176373	+	0.437665i
$50$	−0.364241	−	9.03855i	−0.0515115	−	1.27824i
$51$	−3.64289	+	0.897891i	−0.510106	+	0.125730i
$52$	4.65158	−	0.363064i	0.645058	−	0.0503479i
$53$	−6.23519	−	1.53684i	−0.856470	−	0.211101i	−0.213453	−	0.976953i	$-0.568471\pi$
$53$	−6.23519	−	1.53684i	−0.856470	−	0.211101i	−0.643016	+	0.765852i	$0.722317\pi$
$54$	0.363036	−	1.77827i	0.0494030	−	0.241992i
$55$	−0.697807	+	0.297308i	−0.0940923	+	0.0400890i
$56$	−2.14787	+	1.35823i	−0.287021	+	0.181501i
$57$	5.79458	−	3.04123i	0.767511	−	0.402821i
$58$	5.45790	+	0.886995i	0.716658	+	0.116468i
$59$	12.4574	−	4.15890i	1.62182	−	0.541443i	0.646628	−	0.762806i	$-0.276179\pi$
$59$	12.4574	−	4.15890i	1.62182	−	0.541443i	0.975191	+	0.221363i	$0.0710506\pi$
$60$	0.0196679	+	0.161980i	0.00253912	+	0.0209115i
$61$	−2.14997	+	7.42254i	−0.275275	+	0.950359i	0.697108	+	0.716966i	$0.254470\pi$
$61$	−2.14997	+	7.42254i	−0.275275	+	0.950359i	−0.972383	+	0.233393i	$0.925017\pi$
$62$	−0.576816	+	2.82543i	−0.0732557	+	0.358830i
$63$	1.88132	+	0.628078i	0.237025	+	0.0791304i
$64$	−1.51183	−	0.793467i	−0.188978	−	0.0991834i
$65$	−0.401996	−	0.212350i	−0.0498615	−	0.0263387i
$66$	−9.66712	+	5.07370i	−1.18994	+	0.624529i
$67$	1.22980	−	0.199862i	0.150244	−	0.0244170i	−0.0848242	−	0.996396i	$-0.527033\pi$
$67$	1.22980	−	0.199862i	0.150244	−	0.0244170i	0.235068	+	0.971979i	$0.424469\pi$
$68$	3.88139	−	2.91668i	0.470688	−	0.353699i
$69$	0.277863	−	6.89511i	0.0334508	−	0.830074i
$70$	−0.453905			−0.0542521
$71$	−0.566725	+	14.0631i	−0.0672579	+	1.66899i	0.515916	+	0.856639i	$0.327452\pi$
$71$	−0.566725	+	14.0631i	−0.0672579	+	1.66899i	−0.583174	+	0.812348i	$0.698189\pi$
$72$	−0.256289	−	1.25539i	−0.0302040	−	0.147949i
$73$	−1.79985	−	2.60753i	−0.210657	−	0.305189i	0.703385	−	0.710809i	$-0.251671\pi$
$73$	−1.79985	−	2.60753i	−0.210657	−	0.305189i	−0.914042	+	0.405620i	$0.867056\pi$
$74$	−1.55842	+	0.520278i	−0.181163	+	0.0604811i
$75$	−2.13665	+	4.50289i	−0.246719	+	0.519949i
$76$	−5.35582	+	6.55968i	−0.614354	+	0.752447i
$77$	−4.23078	−	11.1556i	−0.482142	−	1.27130i
$78$	−6.01340	−	2.58099i	−0.680884	−	0.292240i
$79$	−2.68314	+	7.07486i	−0.301877	+	0.795984i	0.695145	+	0.718869i	$0.255340\pi$
$79$	−2.68314	+	7.07486i	−0.301877	+	0.795984i	−0.997022	+	0.0771147i	$0.975429\pi$
$80$	0.309782	+	0.536558i	0.0346347	+	0.0599890i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	−6.56383	−	4.93240i	−0.724854	−	0.544692i
$83$	6.05139	+	3.17601i	0.664226	+	0.348613i	0.762909	−	0.646506i	$-0.223771\pi$
$83$	6.05139	+	3.17601i	0.664226	+	0.348613i	−0.0986825	+	0.995119i	$0.531463\pi$
$84$	−2.55827	+	0.206525i	−0.279130	+	0.0225337i
$85$	−0.471556	+	0.0380680i	−0.0511475	+	0.00412905i
$86$	−11.2010	−	5.87876i	−1.20784	−	0.633923i
$87$	−2.43562	−	1.83025i	−0.261126	−	0.196223i
$88$	−4.87454	+	5.97022i	−0.519627	+	0.636428i
$89$	6.02395	+	10.4338i	0.638537	+	1.10598i	0.985754	+	0.168194i	$0.0537935\pi$
$89$	6.02395	+	10.4338i	0.638537	+	1.10598i	−0.347217	+	0.937785i	$0.612873\pi$
$90$	0.0811523	−	0.213981i	0.00855420	−	0.0225556i
$91$	3.59208	−	6.18362i	0.376552	−	0.648220i
$92$	3.16655	+	8.34950i	0.330135	+	0.870496i
$93$	1.00487	−	1.23074i	0.104200	−	0.127622i
$94$	−7.15961	+	15.0885i	−0.738457	+	1.55627i
$95$	0.782709	−	0.261307i	0.0803043	−	0.0268095i
$96$	3.61020	+	5.23028i	0.368465	+	0.533813i
$97$	−2.50937	−	12.2917i	−0.254788	−	1.24803i	−0.882770	−	0.469805i	$-0.844324\pi$
$97$	−2.50937	−	12.2917i	−0.254788	−	1.24803i	0.627982	−	0.778228i	$-0.283881\pi$
$98$	−0.224075	+	5.56037i	−0.0226350	+	0.561682i
$99$	6.01542			0.604572
$100$	0.259700	−	6.44440i	0.0259700	−	0.644440i
$101$	13.0013	−	9.76985i	1.29368	−	0.972137i	0.293811	−	0.955863i	$-0.405076\pi$
$101$	13.0013	−	9.76985i	1.29368	−	0.972137i	0.999868	−	0.0162731i	$-0.00518012\pi$
$102$	−6.72135	+	1.09233i	−0.665513	+	0.108156i
$103$	2.13530	−	1.12069i	0.210397	−	0.110425i	−0.356233	−	0.934397i	$-0.615939\pi$
$103$	2.13530	−	1.12069i	0.210397	−	0.110425i	0.566630	+	0.823972i	$0.308247\pi$
$104$	−4.61971	−	0.0122877i	−0.453000	−	0.00120491i
$105$	0.221446	+	0.116224i	0.0216109	+	0.0113423i
$106$	−11.0554	−	3.69084i	−1.07380	−	0.358486i
$107$	−2.54727	+	12.4774i	−0.246254	+	1.20623i	0.649039	+	0.760755i	$0.275171\pi$
$107$	−2.54727	+	12.4774i	−0.246254	+	1.20623i	−0.895293	+	0.445477i	$0.853034\pi$
$108$	0.360025	−	1.24295i	0.0346434	−	0.119603i
$109$	1.63936	+	13.5013i	0.157022	+	1.29319i	0.831760	+	0.555135i	$0.187333\pi$
$109$	1.63936	+	13.5013i	0.157022	+	1.29319i	−0.674739	+	0.738057i	$0.735744\pi$
$110$	−1.30580	+	0.435939i	−0.124503	+	0.0415652i
$111$	0.893524	+	0.145212i	0.0848096	+	0.0137829i
$112$	−8.62921	+	4.52896i	−0.815384	+	0.427946i
$113$	10.3988	−	6.57579i	0.978235	−	0.618599i	0.0532419	−	0.998582i	$-0.483045\pi$
$113$	10.3988	−	6.57579i	0.978235	−	0.618599i	0.924993	+	0.379983i	$0.124070\pi$
$114$	10.9269	−	4.65552i	1.02340	−	0.436030i
$115$	0.174049	−	0.852547i	0.0162301	−	0.0795004i
$116$	3.82792	+	0.943498i	0.355413	+	0.0876016i
$117$	2.27288	+	2.79893i	0.210128	+	0.258761i
$118$	23.1437	−	5.70440i	2.13055	−	0.525133i
$119$	−0.299640	−	7.43549i	−0.0274680	−	0.681611i
$120$	−0.00650540	−	0.161430i	−0.000593859	−	0.0147365i
$121$	−15.9283	−	19.5086i	−1.44803	−	1.77351i
$122$	−4.97343	+	13.1139i	−0.450274	+	1.18727i
$123$	1.93933	+	4.08705i	0.174863	+	0.368517i
$124$	−0.572030	+	1.97488i	−0.0513698	+	0.177349i
$125$	−0.715152	+	1.03608i	−0.0639651	+	0.0926695i
$126$	3.31171	+	1.41099i	0.295030	+	0.125701i
$127$	−19.5597	+	3.17876i	−1.73564	+	0.282069i	−0.944247	−	0.329238i	$-0.893208\pi$
$127$	−19.5597	+	3.17876i	−1.73564	+	0.282069i	−0.791394	+	0.611307i	$0.790644\pi$
$128$	8.12370	+	5.13712i	0.718041	+	0.454061i
$129$	3.95936	+	5.73612i	0.348602	+	0.505037i
$130$	−0.696225	−	0.442862i	−0.0610629	−	0.0388416i
$131$	1.99931	−	2.89649i	0.174680	−	0.253068i	−0.725858	−	0.687844i	$-0.758557\pi$
$131$	1.99931	−	2.89649i	0.174680	−	0.253068i	0.900538	+	0.434776i	$0.143173\pi$
$132$	−7.16130	+	3.05114i	−0.623311	+	0.265568i
$133$	3.61118	+	12.4672i	0.313129	+	1.08105i
$134$	2.25397	−	0.181959i	0.194713	−	0.0157189i
$135$	−0.0943821	+	0.0836152i	−0.00812312	+	0.00719645i
$136$	−4.06304	+	2.56931i	−0.348403	+	0.220317i
$137$	0.302856	+	0.129035i	0.0258747	+	0.0110242i	0.404865	−	0.914376i	$-0.367318\pi$
$137$	0.302856	+	0.129035i	0.0258747	+	0.0110242i	−0.378990	+	0.925401i	$0.623729\pi$
$138$	1.50965	−	12.4331i	0.128510	−	1.05838i
$139$	0.438465	+	2.14774i	0.0371901	+	0.182169i	0.994143	−	0.108075i	$-0.0344686\pi$
$139$	0.438465	+	2.14774i	0.0371901	+	0.182169i	−0.956953	+	0.290244i	$0.906263\pi$
$140$	−0.322581	−	0.0260414i	−0.0272630	−	0.00220090i
$141$	7.35641	−	5.52799i	0.619522	−	0.465540i
$142$	−3.07906	+	25.3583i	−0.258389	+	2.12802i
$143$	4.39485	−	21.2390i	0.367515	−	1.77609i
$144$	−0.592262	−	4.87772i	−0.0493552	−	0.406476i
$145$	−0.266118	−	0.277058i	−0.0220999	−	0.0230084i
$146$	−2.87523	−	4.98005i	−0.237956	−	0.412152i
$147$	1.53307	−	2.65535i	0.126445	−	0.219010i
$148$	−1.13739	+	0.280341i	−0.0934926	+	0.0230439i
$149$	−12.8369	−	15.7224i	−1.05164	−	1.28803i	−0.956239	−	0.292586i	$-0.905484\pi$
$149$	−12.8369	−	15.7224i	−1.05164	−	1.28803i	−0.0954011	−	0.995439i	$-0.530413\pi$
$150$	−4.52294	+	7.83397i	−0.369297	+	0.639641i
$151$	−4.13259	−	10.8968i	−0.336306	−	0.886765i	−0.991358	−	0.131182i	$-0.958123\pi$
$151$	−4.13259	−	10.8968i	−0.336306	−	0.886765i	0.655053	−	0.755583i	$-0.272646\pi$
$152$	5.80845	−	6.04723i	0.471127	−	0.490495i
$153$	3.55883	+	1.18811i	0.287714	+	0.0960530i
$154$	−6.02454	−	20.7991i	−0.485472	−	1.67604i
$155$	0.149960	−	0.132853i	0.0120451	−	0.0106710i
$156$	−4.12551	−	2.17925i	−0.330306	−	0.174480i
$157$	15.3103	+	13.5637i	1.22189	+	1.08250i	0.994064	+	0.108800i	$0.0347009\pi$
$157$	15.3103	+	13.5637i	1.22189	+	1.08250i	0.227828	+	0.973701i	$0.426838\pi$
$158$	−5.88720	+	12.4070i	−0.468361	+	0.987049i
$159$	4.44854	+	4.63142i	0.352792	+	0.367295i
$160$	0.343535	+	0.723985i	0.0271588	+	0.0572360i
$161$	13.2891	+	3.27547i	1.04733	+	0.258144i
$162$	−1.25726	+	1.30895i	−0.0987796	+	0.102840i
$163$	−3.92390	−	2.94862i	−0.307344	−	0.230954i	0.435867	−	0.900011i	$-0.356442\pi$
$163$	−3.92390	−	2.94862i	−0.307344	−	0.230954i	−0.743211	+	0.669057i	$0.766698\pi$
$164$	−4.38179	−	3.88193i	−0.342160	−	0.303127i
$165$	0.748681	+	0.121672i	0.0582847	+	0.00947219i
$166$	10.4835	+	6.62937i	0.813679	+	0.514539i
$167$	3.67349	+	0.296555i	0.284263	+	0.0229481i	0.221776	−	0.975098i	$-0.428815\pi$
$167$	3.67349	+	0.296555i	0.284263	+	0.0229481i	0.0624873	+	0.998046i	$0.480097\pi$
$168$	2.54129			0.196065
$169$	11.5429	−	5.98008i	0.887916	−	0.460006i
$170$	−0.858635			−0.0658543
$171$	−6.52295	−	0.526587i	−0.498823	−	0.0402691i
$172$	−7.62305	−	4.82053i	−0.581252	−	0.367562i
$173$	19.5781	+	3.18176i	1.48850	+	0.241904i	0.849616	−	0.527401i	$-0.176834\pi$
$173$	19.5781	+	3.18176i	1.48850	+	0.241904i	0.638881	+	0.769306i	$0.279398\pi$
$174$	−4.13890	−	3.66674i	−0.313769	−	0.277975i
$175$	−7.90285	−	5.93861i	−0.597399	−	0.448916i
$176$	−20.4749	+	21.3166i	−1.54335	+	1.60680i
$177$	−12.7517	−	3.14301i	−0.958475	−	0.236243i
$178$	9.37393	+	19.7551i	0.702606	+	1.48071i
$179$	−10.4549	−	10.8847i	−0.781434	−	0.813559i	0.204819	−	0.978800i	$-0.434339\pi$
$179$	−10.4549	−	10.8847i	−0.781434	−	0.813559i	−0.986253	+	0.165241i	$0.947160\pi$
$180$	0.0699496	−	0.147416i	0.00521373	−	0.0109877i
$181$	−16.6690	−	14.7675i	−1.23900	−	1.09766i	−0.991681	−	0.128723i	$-0.958912\pi$
$181$	−16.6690	−	14.7675i	−1.23900	−	1.09766i	−0.247319	−	0.968934i	$-0.579549\pi$
$182$	7.40137	−	10.6620i	0.548626	−	0.790318i
$183$	5.78423	−	5.12438i	0.427582	−	0.378805i
$184$	−2.45993	−	8.49266i	−0.181348	−	0.626087i
$185$	0.108271	+	0.0361462i	0.00796025	+	0.00265752i
$186$	1.99762	−	2.07974i	0.146472	−	0.152494i
$187$	−8.00319	−	21.1027i	−0.585251	−	1.54318i
$188$	−5.95383	+	10.3123i	−0.434228	+	0.752104i
$189$	−1.25439	−	1.53635i	−0.0912434	−	0.111753i
$190$	1.45413	−	0.358412i	0.105494	−	0.0260019i
$191$	10.6060	−	18.3702i	0.767425	−	1.32922i	−0.171530	−	0.985179i	$-0.554871\pi$
$191$	10.6060	−	18.3702i	0.767425	−	1.32922i	0.938955	−	0.344040i	$-0.111795\pi$
$192$	0.853699	+	1.47865i	0.0616104	+	0.106712i
$193$	8.46234	+	8.81023i	0.609132	+	0.634174i	0.952323	−	0.305092i	$-0.0986871\pi$
$193$	8.46234	+	8.81023i	0.609132	+	0.634174i	−0.343190	+	0.939266i	$0.611508\pi$
$194$	−2.74449	−	22.6029i	−0.197043	−	1.62280i
$195$	0.226270	+	0.394329i	0.0162035	+	0.0282385i
$196$	−0.478254	+	3.93878i	−0.0341610	+	0.281341i
$197$	5.39266	−	4.05232i	0.384211	−	0.288716i	−0.391034	−	0.920376i	$-0.627883\pi$
$197$	5.39266	−	4.05232i	0.384211	−	0.288716i	0.775245	+	0.631660i	$0.217626\pi$
$198$	10.8823	+	0.878508i	0.773370	+	0.0624329i
$199$	0.797433	+	3.90608i	0.0565285	+	0.276895i	0.998224	−	0.0595713i	$-0.0189734\pi$
$199$	0.797433	+	3.90608i	0.0565285	+	0.276895i	−0.941696	+	0.336466i	$0.890768\pi$
$200$	−0.769751	+	6.33947i	−0.0544296	+	0.448268i
$201$	−1.14623	−	0.488364i	−0.0808489	−	0.0344465i
$202$	24.9470	−	15.7755i	1.75527	−	1.10996i
$203$	4.52303	−	4.00706i	0.317455	−	0.281240i
$204$	−4.83938	+	0.390675i	−0.338824	+	0.0273527i
$205$	0.158702	+	0.547902i	0.0110842	+	0.0382671i
$206$	4.02656	−	1.71556i	0.280544	−	0.119528i
$207$	−3.92005	+	5.67917i	−0.272462	+	0.394730i
$208$	−17.6547	−	1.47251i	−1.22413	−	0.102100i
$209$	22.3624	+	32.3975i	1.54684	+	2.24099i
$210$	0.383636	+	0.242597i	0.0264734	+	0.0167408i
$211$	−21.8758	+	3.55516i	−1.50599	+	0.244747i	−0.856709	−	0.515800i	$-0.827495\pi$
$211$	−21.8758	+	3.55516i	−1.50599	+	0.244747i	−0.649282	+	0.760548i	$0.724931\pi$
$212$	−7.64509	−	3.25727i	−0.525067	−	0.223710i
$213$	7.99525	−	11.5831i	0.547826	−	0.793663i
$214$	−6.43040	+	22.2003i	−0.439573	+	1.51758i
$215$	0.376759	+	0.794004i	0.0256948	+	0.0541506i
$216$	−0.454349	+	1.19802i	−0.0309145	+	0.0815149i
$217$	1.99306	+	2.44105i	0.135297	+	0.165709i
$218$	0.993932	+	24.6642i	0.0673175	+	1.67047i
$219$	0.127578	+	3.16582i	0.00862094	+	0.213926i
$220$	−0.953012	+	0.234896i	−0.0642520	+	0.0158367i
$221$	6.79499	−	11.6973i	0.457081	−	0.786846i
$222$	1.59524	+	0.393190i	0.107065	+	0.0263892i
$223$	−4.65625	+	22.8078i	−0.311805	+	1.52732i	0.457946	+	0.888980i	$0.348585\pi$
$223$	−4.65625	+	22.8078i	−0.311805	+	1.52732i	−0.769752	+	0.638344i	$0.779620\pi$
$224$	−11.5963	+	4.94074i	−0.774813	+	0.330117i
$225$	4.21251	−	2.66383i	0.280834	−	0.177589i
$226$	19.7724	−	10.3774i	1.31524	−	0.690292i
$227$	7.03265	+	1.14292i	0.466773	+	0.0758580i	0.389249	−	0.921132i	$-0.372734\pi$
$227$	7.03265	+	1.14292i	0.466773	+	0.0758580i	0.0775239	+	0.996990i	$0.475299\pi$
$228$	8.03261	−	2.68168i	0.531973	−	0.177599i
$229$	1.02668	+	8.45548i	0.0678450	+	0.558754i	0.986508	+	0.163712i	$0.0523468\pi$
$229$	1.02668	+	8.45548i	0.0678450	+	0.558754i	−0.918663	+	0.395042i	$0.870730\pi$
$230$	0.439374	−	1.51689i	0.0289714	−	0.100021i
$231$	−2.38650	+	11.6898i	−0.157020	+	0.769135i
$232$	−3.70272	−	1.23615i	−0.243095	−	0.0811571i
$233$	−6.10996	−	3.20675i	−0.400277	−	0.210081i	0.252558	−	0.967582i	$-0.418728\pi$
$233$	−6.10996	−	3.20675i	−0.400277	−	0.210081i	−0.652835	+	0.757500i	$0.726420\pi$
$234$	3.70302	+	5.39539i	0.242074	+	0.352707i
$235$	1.02739	−	0.539218i	0.0670198	−	0.0351747i
$236$	16.7750	−	2.72620i	1.09196	−	0.177460i
$237$	6.04903	−	4.54555i	0.392927	−	0.295266i
$238$	0.543832	−	13.4950i	0.0352514	−	0.874754i
$239$	−7.94600			−0.513984			−0.256992	−	0.966414i	$-0.582731\pi$
$239$	−7.94600			−0.513984			−0.256992	+	0.966414i	$0.582731\pi$
$240$	0.0249473	−	0.619061i	0.00161034	−	0.0399602i
$241$	1.95012	+	9.55234i	0.125619	+	0.615320i	0.993043	+	0.117751i	$0.0375686\pi$
$241$	1.95012	+	9.55234i	0.125619	+	0.615320i	−0.867425	+	0.497569i	$0.834226\pi$
$242$	−25.9662	−	37.6186i	−1.66917	−	2.41821i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−4.28688	+	9.03440i	−0.274439	+	0.578368i
$245$	0.244515	−	0.299477i	0.0156215	−	0.0191329i
$246$	2.91149	+	7.67696i	0.185630	+	0.489465i
$247$	−6.62490	+	22.6462i	−0.421532	+	1.44095i
$248$	0.721898	−	1.90349i	0.0458406	−	0.120872i
$249$	−3.41710	−	5.91860i	−0.216550	−	0.375076i
$250$	−1.44507	+	1.76989i	−0.0913940	+	0.111937i
$251$	0.465799	+	0.350025i	0.0294010	+	0.0220934i	0.615341	−	0.788261i	$-0.289018\pi$
$251$	0.465799	+	0.350025i	0.0294010	+	0.0220934i	−0.585940	+	0.810354i	$0.699275\pi$
$252$	2.27261	+	1.19276i	0.143161	+	0.0751366i
$253$	41.3760	−	3.34022i	2.60129	−	0.209998i
$254$	−35.8489	+	2.89403i	−2.24936	+	0.181587i
$255$	0.418901	+	0.219856i	0.0262326	+	0.0137679i
$256$	16.6760	+	12.5312i	1.04225	+	0.783200i
$257$	−10.1452	+	12.4256i	−0.632838	+	0.775086i	−0.987108	−	0.160058i	$-0.948832\pi$
$257$	−10.1452	+	12.4256i	−0.632838	+	0.775086i	0.354270	+	0.935143i	$0.384729\pi$
$258$	6.32501	+	10.9552i	0.393778	+	0.682043i
$259$	−0.636680	+	1.67879i	−0.0395614	+	0.104315i
$260$	−0.469383	−	0.354676i	−0.0291099	−	0.0219961i
$261$	1.08036	+	2.84866i	0.0668723	+	0.176328i
$262$	4.03988	−	4.94796i	0.249585	−	0.305686i
$263$	1.95524	−	4.12058i	0.120565	−	0.254086i	−0.834191	−	0.551476i	$-0.814065\pi$
$263$	1.95524	−	4.12058i	0.120565	−	0.254086i	0.954756	+	0.297390i	$0.0961162\pi$
$264$	7.31079	−	2.44070i	0.449948	−	0.150215i
$265$	0.459988	+	0.666407i	0.0282568	+	0.0409371i
$266$	4.71210	+	23.0814i	0.288918	+	1.41521i
$267$	0.485120	−	12.0381i	0.0296889	−	0.736721i
$268$	1.61229			0.0984860
$269$	0.136741	−	3.39320i	0.00833727	−	0.206887i	−0.989651	−	0.143493i	$-0.954166\pi$
$269$	0.136741	−	3.39320i	0.00833727	−	0.206887i	0.997989	−	0.0633940i	$-0.0201925\pi$
$270$	−0.182955	+	0.137481i	−0.0111343	+	0.00836685i
$271$	−15.9246	+	2.58800i	−0.967351	+	0.157210i	−0.623508	−	0.781817i	$-0.714293\pi$
$271$	−15.9246	+	2.58800i	−0.967351	+	0.157210i	−0.343843	+	0.939027i	$0.611729\pi$
$272$	−16.3235	+	8.56725i	−0.989760	+	0.519466i
$273$	−6.34092	+	3.30649i	−0.383770	+	0.200118i
$274$	0.529041	+	0.277662i	0.0319605	+	0.0167742i
$275$	−28.4385	−	9.49417i	−1.71491	−	0.572520i
$276$	1.78619	−	8.74933i	0.107516	−	0.526648i
$277$	5.01984	−	17.3305i	0.301613	−	1.04129i	−0.656364	−	0.754445i	$-0.727906\pi$
$277$	5.01984	−	17.3305i	0.301613	−	1.04129i	0.957977	−	0.286845i	$-0.0926065\pi$
$278$	0.479549	+	3.94944i	0.0287614	+	0.236872i
$279$	−1.50710	+	0.503143i	−0.0902275	+	0.0301224i
$280$	0.316289	+	0.0514020i	0.0189019	+	0.00307186i
$281$	−11.5810	+	6.07816i	−0.690863	+	0.362593i	−0.773332	−	0.634001i	$-0.781412\pi$
$281$	−11.5810	+	6.07816i	−0.690863	+	0.362593i	0.0824695	+	0.996594i	$0.473719\pi$
$282$	14.1155	−	8.92613i	0.840568	−	0.531543i
$283$	−10.6900	+	4.55457i	−0.635453	+	0.270741i	−0.685575	−	0.728002i	$-0.740449\pi$
$283$	−10.6900	+	4.55457i	−0.635453	+	0.270741i	0.0501224	+	0.998743i	$0.484039\pi$
$284$	−3.64307	+	17.8450i	−0.216177	+	1.05890i
$285$	−0.801198	−	0.197477i	−0.0474588	−	0.0116976i
$286$	11.0524	−	37.7808i	0.653539	−	2.23403i
$287$	−8.71181	+	2.14727i	−0.514242	+	0.126749i
$288$	−0.255901	−	6.35011i	−0.0150791	−	0.374184i
$289$	0.117704	+	2.92078i	0.00692374	+	0.171811i
$290$	−0.440962	−	0.540080i	−0.0258942	−	0.0317146i
$291$	−4.44860	+	11.7300i	−0.260782	+	0.687624i
$292$	−1.75765	−	3.70417i	−0.102859	−	0.216770i
$293$	4.58944	−	15.8446i	0.268118	−	0.925651i	−0.707599	−	0.706615i	$-0.750221\pi$
$293$	4.58944	−	15.8446i	0.268118	−	0.925651i	0.975717	−	0.219036i	$-0.0702913\pi$
$294$	3.16122	−	4.57981i	0.184366	−	0.267100i
$295$	−1.52351	−	0.649105i	−0.0887019	−	0.0377923i
$296$	1.14486	−	0.186057i	0.0665434	−	0.0108144i
$297$	−5.08417	−	3.21504i	−0.295014	−	0.186555i
$298$	−20.9266	−	30.3175i	−1.21225	−	1.75624i
$299$	17.1878	+	17.9899i	0.993995	+	1.04038i
$300$	−3.66380	+	5.30794i	−0.211530	+	0.306454i
$301$	−12.7179	+	5.41858i	−0.733046	+	0.312322i
$302$	−5.88473	−	20.3165i	−0.338628	−	1.16908i
$303$	−16.2102	+	1.30863i	−0.931253	+	0.0751786i
$304$	24.0684	−	21.3228i	1.38042	−	1.22294i
$305$	0.823556	−	0.520785i	0.0471567	−	0.0298201i
$306$	6.26463	+	2.66911i	0.358125	+	0.152583i
$307$	−1.13170	+	9.32036i	−0.0645894	+	0.531941i	0.924121	+	0.382101i	$0.124799\pi$
$307$	−1.13170	+	9.32036i	−0.0645894	+	0.531941i	−0.988710	+	0.149841i	$0.952124\pi$
$308$	−3.08822	−	15.1271i	−0.175968	−	0.861948i
$309$	−2.40370	−	0.194047i	−0.136742	−	0.0110389i
$310$	0.290690	−	0.218439i	0.0165101	−	0.0124065i
$311$	−2.07201	+	17.0645i	−0.117493	+	0.967640i	0.808081	+	0.589072i	$0.200507\pi$
$311$	−2.07201	+	17.0645i	−0.117493	+	0.967640i	−0.925573	+	0.378568i	$0.876416\pi$
$312$	3.89797	+	2.47946i	0.220679	+	0.140372i
$313$	−2.37909	−	19.5936i	−0.134474	−	1.10750i	−0.891151	−	0.453706i	$-0.850102\pi$
$313$	−2.37909	−	19.5936i	−0.134474	−	1.10750i	0.756677	−	0.653789i	$-0.226822\pi$
$314$	25.7164	+	26.7736i	1.45126	+	1.51092i
$315$	−0.125046	−	0.216587i	−0.00704556	−	0.0122033i
$316$	−4.89572	+	8.47963i	−0.275406	+	0.477017i
$317$	9.54266	−	2.35205i	0.535969	−	0.132105i	0.0379648	−	0.999279i	$-0.487913\pi$
$317$	9.54266	−	2.35205i	0.535969	−	0.132105i	0.498004	+	0.867175i	$0.334066\pi$
$318$	7.37130	+	9.02821i	0.413362	+	0.506277i
$319$	9.16342	−	15.8715i	0.513053	−	0.888634i
$320$	0.0763433	+	0.201301i	0.00426772	+	0.0112531i
$321$	8.82165	−	9.18431i	0.492377	−	0.512618i
$322$	23.5625	+	7.86632i	1.31309	+	0.438373i
$323$	6.83112	+	23.5838i	0.380094	+	1.31224i
$324$	−0.968603	+	0.858107i	−0.0538113	+	0.0476726i
$325$	−6.32769	−	16.8195i	−0.350997	−	0.932980i
$326$	−6.66796	−	5.90730i	−0.369304	−	0.327175i
$327$	5.83042	−	12.2874i	0.322423	−	0.679493i
$328$	4.01523	+	4.18030i	0.221704	+	0.230818i
$329$	7.82410	+	16.4889i	0.431356	+	0.909064i
$330$	1.33664	+	0.329453i	0.0735797	+	0.0181358i
$331$	16.2665	−	16.9352i	0.894086	−	0.930842i	−0.103880	−	0.994590i	$-0.533126\pi$
$331$	16.2665	−	16.9352i	0.894086	−	0.930842i	0.997966	+	0.0637479i	$0.0203054\pi$
$332$	7.07006	+	5.31281i	0.388020	+	0.291578i
$333$	−0.677587	−	0.600290i	−0.0371316	−	0.0328957i
$334$	6.60227	+	1.07297i	0.361260	+	0.0587105i
$335$	−0.132782	−	0.0839664i	−0.00725467	−	0.00458758i
$336$	9.71390	+	0.784187i	0.529937	+	0.0427809i
$337$	6.97619			0.380017			0.190009	−	0.981782i	$-0.439148\pi$
$337$	6.97619			0.380017			0.190009	+	0.981782i	$0.439148\pi$
$338$	21.7552	−	9.13259i	1.18333	−	0.496747i
$339$	−12.3035			−0.668234
$340$	−0.610213	−	0.0492615i	−0.0330934	−	0.00267158i
$341$	8.07806	+	5.10826i	0.437452	+	0.276628i
$342$	−11.7235	−	1.90526i	−0.633936	−	0.103025i
$343$	14.9441	+	13.2393i	0.806907	+	0.714857i
$344$	7.13935	+	5.36487i	0.384928	+	0.289255i
$345$	−0.602762	+	0.627541i	−0.0324516	+	0.0337857i
$346$	34.9534	+	8.61524i	1.87911	+	0.463158i
$347$	−9.99615	−	21.0664i	−0.536621	−	1.13091i	−0.972928	−	0.231108i	$-0.925765\pi$
$347$	−9.99615	−	21.0664i	−0.536621	−	1.13091i	0.436307	−	0.899798i	$-0.356286\pi$
$348$	−2.73105	−	2.84333i	−0.146400	−	0.152418i
$349$	−2.44659	+	5.15607i	−0.130963	+	0.275998i	−0.958330	−	0.285663i	$-0.907786\pi$
$349$	−2.44659	+	5.15607i	−0.130963	+	0.275998i	0.827367	+	0.561661i	$0.189838\pi$
$350$	−13.4295	−	11.8975i	−0.717835	−	0.635947i
$351$	−0.425079	−	3.58041i	−0.0226891	−	0.191108i
$352$	−28.6152	+	25.3509i	−1.52520	+	1.35121i
$353$	0.499517	+	1.72453i	0.0265866	+	0.0917877i	0.972714	−	0.232006i	$-0.0745289\pi$
$353$	0.499517	+	1.72453i	0.0265866	+	0.0917877i	−0.946128	+	0.323794i	$0.895042\pi$
$354$	−22.6096	−	7.54819i	−1.20169	−	0.401182i
$355$	1.22938	−	1.27992i	0.0652488	−	0.0679311i
$356$	5.52845	+	14.5773i	0.293007	+	0.772597i
$357$	−3.72076	+	6.44455i	−0.196924	+	0.341082i
$358$	−17.3239	−	21.2179i	−0.915597	−	1.12140i
$359$	−7.27702	+	1.79363i	−0.384067	+	0.0946639i	−0.426622	−	0.904430i	$-0.640296\pi$
$359$	−7.27702	+	1.79363i	−0.384067	+	0.0946639i	0.0425550	+	0.999094i	$0.486450\pi$
$360$	−0.0807804	+	0.139916i	−0.00425750	+	0.00737421i
$361$	−11.9131	−	20.6341i	−0.627006	−	1.08601i
$362$	−27.9987	−	29.1497i	−1.47158	−	1.53207i
$363$	3.03575	+	25.0016i	0.159335	+	1.31225i
$364$	5.87169	−	7.15259i	0.307760	−	0.374898i
$365$	−0.0481559	+	0.396599i	−0.00252059	+	0.0207590i
$366$	11.2124	−	8.42558i	0.586082	−	0.440412i
$367$	9.41647	+	0.760176i	0.491536	+	0.0396809i	0.323750	−	0.946143i	$-0.395056\pi$
$367$	9.41647	+	0.760176i	0.491536	+	0.0396809i	0.167786	+	0.985823i	$0.446338\pi$
$368$	−6.78225	−	33.2217i	−0.353549	−	1.73180i
$369$	0.545287	−	4.49084i	0.0283865	−	0.233784i
$370$	0.190590	+	0.0812030i	0.00990833	+	0.00422154i
$371$	−10.7652	+	6.80748i	−0.558899	+	0.353427i
$372$	1.53898	−	1.36342i	0.0797923	−	0.0706898i
$373$	16.9230	−	1.36617i	0.876239	−	0.0707374i	0.365843	−	0.930677i	$-0.380781\pi$
$373$	16.9230	−	1.36617i	0.876239	−	0.0707374i	0.510396	+	0.859939i	$0.329499\pi$
$374$	−11.3964	−	39.3449i	−0.589293	−	2.03448i
$375$	1.15819	−	0.493457i	0.0598085	−	0.0254820i
$376$	6.69763	−	9.70319i	0.345404	−	0.500404i
$377$	10.8472	−	1.73325i	0.558661	−	0.0892667i
$378$	−2.04490	−	2.96255i	−0.105178	−	0.152377i
$379$	13.7444	+	8.69143i	0.706003	+	0.446449i	0.838619	−	0.544718i	$-0.183363\pi$
$379$	13.7444	+	8.69143i	0.706003	+	0.446449i	−0.132616	+	0.991167i	$0.542338\pi$
$380$	1.05398	−	0.171289i	0.0540682	−	0.00878693i
$381$	18.2306	+	7.76732i	0.933981	+	0.397932i
$382$	21.8698	−	31.6839i	1.11896	−	1.62109i
$383$	−2.60214	+	8.98362i	−0.132963	+	0.459042i	−0.999174	−	0.0406369i	$-0.987061\pi$
$383$	−2.60214	+	8.98362i	−0.132963	+	0.459042i	0.866211	+	0.499678i	$0.166548\pi$
$384$	−4.12046	−	8.68368i	−0.210271	−	0.443137i
$385$	−0.533472	+	1.40665i	−0.0271882	+	0.0716895i
$386$	14.0222	+	17.1741i	0.713713	+	0.874140i
$387$	−0.280650	−	6.96425i	−0.0142662	−	0.354013i
$388$	−0.653678	−	16.2209i	−0.0331855	−	0.823490i
$389$	−14.4547	+	3.56275i	−0.732880	+	0.180639i	−0.588058	−	0.808819i	$-0.700107\pi$
$389$	−14.4547	+	3.56275i	−0.732880	+	0.180639i	−0.144822	+	0.989458i	$0.546261\pi$
$390$	0.351747	+	0.746411i	0.0178114	+	0.0377960i
$391$	25.1385	+	6.19609i	1.27131	+	0.313349i
$392$	0.785818	−	3.84919i	0.0396898	−	0.194414i
$393$	−3.23787	+	1.37953i	−0.163329	+	0.0695880i
$394$	10.3475	−	6.54335i	0.521298	−	0.329649i
$395$	0.844806	−	0.443389i	0.0425068	−	0.0223093i
$396$	7.68339	+	1.24867i	0.386105	+	0.0627481i
$397$	−17.1603	+	5.72895i	−0.861251	+	0.287528i	−0.712779	−	0.701389i	$-0.752564\pi$
$397$	−17.1603	+	5.72895i	−0.861251	+	0.287528i	−0.148472	+	0.988917i	$0.547435\pi$
$398$	0.872151	+	7.18281i	0.0437170	+	0.360042i
$399$	3.61118	−	12.4672i	0.180785	−	0.624142i
$400$	−4.89855	+	23.9947i	−0.244927	+	1.19973i
$401$	−26.4553	−	8.83208i	−1.32111	−	0.441053i	−0.433298	−	0.901251i	$-0.642650\pi$
$401$	−26.4553	−	8.83208i	−1.32111	−	0.441053i	−0.887816	+	0.460198i	$0.847778\pi$
$402$	−2.00228	−	1.05088i	−0.0998649	−	0.0524131i
$403$	0.675394	+	5.68878i	0.0336438	+	0.283378i
$404$	18.6344	−	9.78007i	0.927094	−	0.486577i
$405$	0.124460	−	0.0202268i	0.00618448	−	0.00100508i
$406$	8.76765	−	6.58846i	0.435131	−	0.326980i
$407$	−0.219266	+	5.44102i	−0.0108686	+	0.269702i
$408$	4.80726			0.237995
$409$	1.14046	−	28.3001i	0.0563919	−	1.39935i	−0.685129	−	0.728422i	$-0.740254\pi$
$409$	1.14046	−	28.3001i	0.0563919	−	1.39935i	0.741521	−	0.670930i	$-0.234105\pi$
$410$	0.207084	+	1.01437i	0.0102272	+	0.0500960i
$411$	−0.187006	−	0.270925i	−0.00922433	−	0.0133637i
$412$	2.96001	−	0.988197i	0.145829	−	0.0486849i
$413$	11.1668	−	23.5336i	0.549484	−	1.15801i
$414$	−7.92102	+	9.70149i	−0.389297	+	0.476802i
$415$	−0.305580	−	0.805747i	−0.0150003	−	0.0395526i
$416$	−22.6076	−	3.73585i	−1.10843	−	0.183165i
$417$	0.777309	−	2.04960i	0.0380650	−	0.100369i
$418$	35.7236	+	61.8751i	1.74730	+	3.02641i
$419$	4.60660	−	5.64206i	0.225047	−	0.275633i	−0.649723	−	0.760171i	$-0.725115\pi$
$419$	4.60660	−	5.64206i	0.225047	−	0.275633i	0.874770	+	0.484538i	$0.161012\pi$
$420$	0.258724	+	0.194418i	0.0126244	+	0.00948664i
$421$	−26.0576	−	13.6761i	−1.26997	−	0.666533i	−0.311102	−	0.950377i	$-0.600698\pi$
$421$	−26.0576	−	13.6761i	−1.26997	−	0.666533i	−0.958870	+	0.283844i	$0.908390\pi$
$422$	−40.0939	+	3.23671i	−1.95174	+	0.157561i
$423$	−9.17209	+	0.740447i	−0.445962	+	0.0360018i
$424$	7.28565	+	3.82380i	0.353822	+	0.185700i
$425$	−14.9495	−	11.2338i	−0.725158	−	0.544921i
$426$	16.1556	−	19.7870i	0.782739	−	0.958682i
$427$	7.66349	+	13.2736i	0.370862	+	0.642352i
$428$	−5.84362	+	15.4084i	−0.282462	+	0.744791i
$429$	−15.0660	+	15.6021i	−0.727392	+	0.753275i
$430$	0.565623	+	1.49143i	0.0272768	+	0.0719230i
$431$	−21.5963	+	26.4506i	−1.04026	+	1.27408i	−0.0794568	+	0.996838i	$0.525319\pi$
$431$	−21.5963	+	26.4506i	−1.04026	+	1.27408i	−0.960799	+	0.277244i	$0.910579\pi$
$432$	−2.10640	+	4.43914i	−0.101344	+	0.213578i
$433$	16.1135	−	5.37949i	0.774368	−	0.258522i	0.0980986	−	0.995177i	$-0.468724\pi$
$433$	16.1135	−	5.37949i	0.774368	−	0.258522i	0.676269	+	0.736655i	$0.263596\pi$
$434$	3.24907	+	4.70709i	0.155960	+	0.225947i
$435$	0.0768421	+	0.376397i	0.00368430	+	0.0180469i
$436$	−0.708663	+	17.5853i	−0.0339388	+	0.842183i
$437$	−45.1594			−2.16027
$438$	−0.231548	+	5.74580i	−0.0110638	+	0.274545i
$439$	−5.66320	+	4.25562i	−0.270290	+	0.203110i	−0.727241	−	0.686382i	$-0.759198\pi$
$439$	−5.66320	+	4.25562i	−0.270290	+	0.203110i	0.456951	+	0.889492i	$0.348941\pi$
$440$	0.959271	−	0.155897i	0.0457314	−	0.00743208i
$441$	−2.71493	+	1.42491i	−0.129282	+	0.0678526i
$442$	14.0009	−	20.1688i	0.665954	−	0.959333i
$443$	20.0142	+	10.5043i	0.950904	+	0.499073i	0.867497	−	0.497443i	$-0.165728\pi$
$443$	20.0142	+	10.5043i	0.950904	+	0.499073i	0.0834069	+	0.996516i	$0.473420\pi$
$444$	1.11114	+	0.370953i	0.0527324	+	0.0176047i
$445$	0.303871	−	1.48846i	0.0144048	−	0.0705596i
$446$	−11.7544	+	40.5808i	−0.556585	+	1.92155i
$447$	2.44656	+	20.1493i	0.115718	+	0.953027i
$448$	−3.21217	+	1.07238i	−0.151761	+	0.0506651i
$449$	−32.2168	−	5.23573i	−1.52040	−	0.247089i	−0.657886	−	0.753118i	$-0.728549\pi$
$449$	−32.2168	−	5.23573i	−1.52040	−	0.247089i	−0.862517	+	0.506028i	$0.831113\pi$
$450$	8.00974	−	4.20383i	0.377583	−	0.198171i
$451$	−22.9999	+	14.5443i	−1.08302	+	0.684862i
$452$	14.6472	−	6.24058i	0.688945	−	0.293532i
$453$	−2.33112	+	11.4186i	−0.109525	+	0.536491i
$454$	12.5556	+	3.09468i	0.589263	+	0.145240i
$455$	−0.856073	+	0.283270i	−0.0401333	+	0.0132799i
$456$	−8.14128	+	2.00665i	−0.381250	+	0.0939698i
$457$	1.33681	+	33.1725i	0.0625332	+	1.55175i	0.660870	+	0.750501i	$0.270188\pi$
$457$	1.33681	+	33.1725i	0.0625332	+	1.55175i	−0.598336	+	0.801245i	$0.704171\pi$
$458$	0.622471	+	15.4464i	0.0290861	+	0.721765i
$459$	−2.37288	−	2.90625i	−0.110757	−	0.135652i
$460$	0.399280	−	1.05281i	0.0186165	−	0.0490877i
$461$	5.98720	+	12.6177i	0.278852	+	0.587667i	0.993759	−	0.111552i	$-0.0355823\pi$
$461$	5.98720	+	12.6177i	0.278852	+	0.587667i	−0.714907	+	0.699220i	$0.753531\pi$
$462$	−6.02454	+	20.7991i	−0.280287	+	0.967664i
$463$	−1.30392	+	1.88905i	−0.0605983	+	0.0877918i	−0.852112	−	0.523360i	$-0.824678\pi$
$463$	−1.30392	+	1.88905i	−0.0605983	+	0.0877918i	0.791513	+	0.611152i	$0.209294\pi$
$464$	−13.7719	−	5.86767i	−0.639346	−	0.272400i
$465$	−0.197751	+	0.0321376i	−0.00917046	+	0.00149035i
$466$	−10.5850	−	6.69354i	−0.490340	−	0.310072i
$467$	−7.60773	−	11.0217i	−0.352044	−	0.510023i	0.606456	−	0.795117i	$-0.292591\pi$
$467$	−7.60773	−	11.0217i	−0.352044	−	0.510023i	−0.958500	+	0.285094i	$0.907975\pi$
$468$	2.32211	+	4.04683i	0.107339	+	0.187065i
$469$	1.40379	−	2.03374i	0.0648209	−	0.0939093i
$470$	1.93737	−	0.825437i	0.0893643	−	0.0380746i
$471$	−5.69074	−	19.6467i	−0.262216	−	0.905273i
$472$	−16.7729	+	1.35405i	−0.772036	+	0.0623252i
$473$	−31.3827	+	27.8027i	−1.44298	+	1.27837i
$474$	11.6069	−	7.33978i	0.533124	−	0.337127i
$475$	30.0068	+	12.7847i	1.37681	+	0.586603i
$476$	1.16072	−	9.55943i	0.0532017	−	0.438156i
$477$	−1.28452	−	6.29202i	−0.0588144	−	0.288092i
$478$	−14.3748	−	1.16046i	−0.657489	−	0.0530780i
$479$	−7.66328	+	5.75858i	−0.350144	+	0.263116i	−0.761232	−	0.648479i	$-0.775405\pi$
$479$	−7.66328	+	5.75858i	−0.350144	+	0.263116i	0.411088	+	0.911596i	$0.365149\pi$
$480$	0.0965927	−	0.795512i	0.00440883	−	0.0363100i
$481$	−2.61452	+	1.95382i	−0.119212	+	0.0890867i
$482$	2.13285	+	17.5656i	0.0971486	+	0.800091i
$483$	−9.48121	−	9.87098i	−0.431410	−	0.449145i
$484$	−16.2954	−	28.2244i	−0.740699	−	1.28293i
$485$	−0.790934	+	1.36994i	−0.0359144	+	0.0622056i
$486$	1.76221	−	0.434346i	0.0799355	−	0.0197023i
$487$	−5.02954	−	6.16007i	−0.227910	−	0.279139i	0.647972	−	0.761664i	$-0.275617\pi$
$487$	−5.02954	−	6.16007i	−0.227910	−	0.279139i	−0.875882	+	0.482525i	$0.839720\pi$
$488$	4.95064	−	8.57477i	0.224105	−	0.388161i
$489$	1.74051	+	4.58933i	0.0787084	+	0.207537i
$490$	0.486080	−	0.506063i	0.0219589	−	0.0228616i
$491$	10.0441	+	3.35320i	0.453283	+	0.151328i	0.534137	−	0.845398i	$-0.320637\pi$
$491$	10.0441	+	3.35320i	0.453283	+	0.151328i	−0.0808544	+	0.996726i	$0.525765\pi$
$492$	1.62869	+	5.62288i	0.0734269	+	0.253499i
$493$	8.55604	−	7.57999i	0.385345	−	0.341385i
$494$	−15.2922	+	40.0010i	−0.688028	+	1.79973i
$495$	−0.567748	−	0.502981i	−0.0255184	−	0.0226073i
$496$	3.34678	−	7.05319i	0.150275	−	0.316698i
$497$	19.3377	+	20.1327i	0.867414	+	0.903073i
$498$	−5.31739	−	11.2062i	−0.238278	−	0.502160i
$499$	−21.9311	−	5.40554i	−0.981773	−	0.241985i	−0.284409	−	0.958703i	$-0.591798\pi$
$499$	−21.9311	−	5.40554i	−0.981773	−	0.241985i	−0.697364	+	0.716718i	$0.745644\pi$
$500$	−1.12852	+	1.17491i	−0.0504689	+	0.0525437i
$501$	−2.94630	−	2.21400i	−0.131631	−	0.0989142i
$502$	0.791541	+	0.701244i	0.0353282	+	0.0312981i
$503$	−30.5117	−	4.95864i	−1.36045	−	0.221095i	−0.563989	−	0.825782i	$-0.690734\pi$
$503$	−30.5117	−	4.95864i	−1.36045	−	0.221095i	−0.796463	+	0.604688i	$0.793298\pi$
$504$	−2.14787	−	1.35823i	−0.0956738	−	0.0605005i
$505$	−2.04400	−	0.165009i	−0.0909568	−	0.00734279i
$506$	75.3397			3.34926
$507$	−12.9521	−	1.11498i	−0.575223	−	0.0495181i
$508$	−25.6431			−1.13773
$509$	12.1099	+	0.977616i	0.536764	+	0.0433320i	0.345877	−	0.938280i	$-0.387582\pi$
$509$	12.1099	+	0.977616i	0.536764	+	0.0433320i	0.190887	+	0.981612i	$0.438864\pi$
$510$	0.725710	+	0.458911i	0.0321350	+	0.0203209i
$511$	−6.20280	−	1.00805i	−0.274396	−	0.0445936i
$512$	13.9489	+	12.3577i	0.616462	+	0.546137i
$513$	5.23169	+	3.93136i	0.230985	+	0.173574i
$514$	−20.1679	+	20.9970i	−0.889568	+	0.926139i
$515$	−0.295241	−	0.0727703i	−0.0130099	−	0.00320664i
$516$	3.86652	+	8.14852i	0.170214	+	0.358719i
$517$	38.3447	+	39.9210i	1.68640	+	1.75573i
$518$	−1.39697	+	2.94405i	−0.0613793	+	0.129354i
$519$	−14.8467	−	13.1530i	−0.651698	−	0.577354i
$520$	0.434990	+	0.387438i	0.0190756	+	0.0169903i
$521$	25.2137	−	22.3374i	1.10463	−	0.978619i	0.104758	−	0.994498i	$-0.466593\pi$
$521$	25.2137	−	22.3374i	1.10463	−	0.978619i	0.999874	+	0.0158790i	$0.00505466\pi$
$522$	1.53841	+	5.31119i	0.0673342	+	0.232465i
$523$	−9.80755	−	3.27424i	−0.428854	−	0.143173i	0.0940433	−	0.995568i	$-0.470021\pi$
$523$	−9.80755	−	3.27424i	−0.428854	−	0.143173i	−0.522898	+	0.852396i	$0.675149\pi$
$524$	3.15493	−	3.28463i	0.137824	−	0.143490i
$525$	3.50543	+	9.24305i	0.152989	+	0.403400i
$526$	4.13893	−	7.16884i	0.180466	−	0.312576i
$527$	3.77018	+	4.61764i	0.164232	+	0.201147i
$528$	28.6981	−	7.07345i	1.24893	−	0.307833i
$529$	−12.3099	+	21.3213i	−0.535212	+	0.927015i
$530$	0.734823	+	1.27275i	0.0319187	+	0.0552847i
$531$	9.09777	+	9.47178i	0.394809	+	0.411040i
$532$	2.02456	+	16.6738i	0.0877760	+	0.722900i
$533$	−15.4577	−	5.20627i	−0.669546	−	0.225508i
$534$	2.63569	−	21.7069i	0.114058	−	0.939349i
$535$	1.28371	−	0.964649i	0.0554998	−	0.0417054i
$536$	−1.59121	−	0.128456i	−0.0687299	−	0.00554845i
$537$	3.01887	+	14.7874i	0.130274	+	0.638123i
$538$	0.742926	−	6.11855i	0.0320298	−	0.263789i
$539$	16.9682	+	7.22947i	0.730872	+	0.311395i
$540$	−0.137909	+	0.0872086i	−0.00593467	+	0.00375286i
$541$	11.5960	−	10.2732i	0.498552	−	0.441679i	−0.375993	−	0.926622i	$-0.622698\pi$
$541$	11.5960	−	10.2732i	0.498552	−	0.441679i	0.874545	+	0.484944i	$0.161160\pi$
$542$	−29.1866	+	2.35619i	−1.25367	+	0.101207i
$543$	6.19579	+	21.3903i	0.265887	+	0.917948i
$544$	−21.9363	+	9.34620i	−0.940513	+	0.400715i
$545$	0.974190	−	1.41136i	0.0417297	−	0.0604559i
$546$	−11.9540	+	5.05561i	−0.511585	+	0.216360i
$547$	10.5119	+	15.2292i	0.449458	+	0.651153i	0.980575	−	0.196146i	$-0.0628427\pi$
$547$	10.5119	+	15.2292i	0.449458	+	0.651153i	−0.531116	+	0.847299i	$0.678227\pi$
$548$	0.360048	+	0.227680i	0.0153805	+	0.00972602i
$549$	−7.62757	+	1.23960i	−0.325537	+	0.0529049i
$550$	−50.0605	−	21.3288i	−2.13459	−	0.909463i
$551$	−11.3260	+	16.4085i	−0.482502	+	0.699025i
$552$	−2.45993	+	8.49266i	−0.104702	+	0.361472i
$553$	6.43360	+	13.5585i	0.273585	+	0.576567i
$554$	11.6122	−	30.6189i	0.493356	−	1.30087i
$555$	−0.0721908	−	0.0884176i	−0.00306433	−	0.00375312i
$556$	0.114218	+	2.83429i	0.00484392	+	0.120201i
$557$	0.542646	+	13.4656i	0.0229927	+	0.570557i	0.969095	+	0.246689i	$0.0793425\pi$
$557$	0.542646	+	13.4656i	0.0229927	+	0.570557i	−0.946102	+	0.323868i	$0.895017\pi$
$558$	−2.79991	+	0.690117i	−0.118530	+	0.0292150i
$559$	−24.7941	−	4.09715i	−1.04868	−	0.173291i
$560$	1.19313	+	0.294081i	0.0504191	+	0.0124272i
$561$	−4.51444	+	22.1132i	−0.190600	+	0.933621i
$562$	−21.8384	+	9.30447i	−0.921197	+	0.392485i
$563$	26.3687	−	16.6745i	1.11131	−	0.702748i	0.152925	−	0.988238i	$-0.451131\pi$
$563$	26.3687	−	16.6745i	1.11131	−	0.702748i	0.958382	+	0.285490i	$0.0921564\pi$
$564$	10.5437	−	5.53377i	0.443970	−	0.233014i
$565$	−1.53130	−	0.248860i	−0.0644221	−	0.0104696i
$566$	−20.0040	+	6.67831i	−0.840831	+	0.280711i
$567$	0.239072	+	1.96894i	0.0100401	+	0.0826875i
$568$	5.01722	−	17.3215i	0.210518	−	0.726792i
$569$	−3.47483	+	17.0209i	−0.145673	+	0.713552i	0.839688	+	0.543069i	$0.182738\pi$
$569$	−3.47483	+	17.0209i	−0.145673	+	0.713552i	−0.985361	+	0.170483i	$0.945467\pi$
$570$	−1.42058	−	0.474258i	−0.0595014	−	0.0198645i
$571$	−31.3058	−	16.4305i	−1.31011	−	0.687596i	−0.342370	−	0.939565i	$-0.611230\pi$
$571$	−31.3058	−	16.4305i	−1.31011	−	0.687596i	−0.967735	+	0.251969i	$0.918922\pi$
$572$	10.0222	−	26.2159i	0.419050	−	1.09614i
$573$	−18.7823	+	9.85773i	−0.784643	+	0.411812i
$574$	−16.0738	+	2.61225i	−0.670908	+	0.109033i
$575$	27.4959	−	20.6618i	1.14666	−	0.861657i
$576$	0.0687500	−	1.70601i	0.00286458	−	0.0710839i
$577$	−11.3847			−0.473953			−0.236977	−	0.971515i	$-0.576156\pi$
$577$	−11.3847			−0.473953			−0.236977	+	0.971515i	$0.576156\pi$
$578$	−0.213626	+	5.30107i	−0.00888567	+	0.220496i
$579$	−2.44352	−	11.9691i	−0.101549	−	0.497421i
$580$	−0.282396	−	0.409122i	−0.0117259	−	0.0169879i
$581$	12.8574	−	4.29242i	0.533413	−	0.178079i
$582$	−9.76088	+	20.5706i	−0.404601	+	0.852680i
$583$	−24.4312	+	29.9228i	−1.01184	+	1.23928i
$584$	1.43955	+	3.79579i	0.0595692	+	0.157071i
$585$	0.0195145	−	0.454216i	0.000806826	−	0.0187795i
$586$	10.6166	−	27.9936i	0.438567	−	1.15641i
$587$	1.20478	+	2.08674i	0.0497266	+	0.0861290i	0.889817	−	0.456317i	$-0.150832\pi$
$587$	1.20478	+	2.08674i	0.0497266	+	0.0861290i	−0.840091	+	0.542446i	$0.817498\pi$
$588$	2.50936	−	3.07340i	0.103484	−	0.126745i
$589$	−8.31245	−	6.24640i	−0.342509	−	0.257379i
$590$	−2.66132	−	1.39677i	−0.109565	−	0.0575041i
$591$	−6.72365	+	0.542789i	−0.276574	+	0.0223274i
$592$	4.43355	−	0.357913i	0.182218	−	0.0147101i
$593$	6.08257	+	3.19238i	0.249781	+	0.131095i	0.584968	−	0.811056i	$-0.301107\pi$
$593$	6.08257	+	3.19238i	0.249781	+	0.131095i	−0.335187	+	0.942152i	$0.608799\pi$
$594$	−8.72806	−	6.55871i	−0.358117	−	0.269107i
$595$	−0.593440	+	0.726832i	−0.0243287	+	0.0297972i
$596$	−13.1327	−	22.7466i	−0.537938	−	0.931735i
$597$	1.41369	−	3.72758i	0.0578583	−	0.152560i
$598$	28.4665	+	35.0550i	1.16408	+	1.43351i
$599$	−10.5982	−	27.9451i	−0.433030	−	1.14181i	−0.957005	−	0.290073i	$-0.906321\pi$
$599$	−10.5982	−	27.9451i	−0.433030	−	1.14181i	0.523974	−	0.851734i	$-0.324449\pi$
$600$	4.03882	−	4.94665i	0.164884	−	0.201946i
$601$	−6.12345	+	12.9049i	−0.249781	+	0.526402i	−0.989152	−	0.146896i	$-0.953072\pi$
$601$	−6.12345	+	12.9049i	−0.249781	+	0.526402i	0.739371	+	0.673298i	$0.235123\pi$
$602$	−23.7988	+	7.94520i	−0.969966	+	0.323822i
$603$	0.707770	+	1.02538i	0.0288226	+	0.0417568i
$604$	−3.01656	−	14.7761i	−0.122742	−	0.601230i
$605$	−0.127872	+	3.17311i	−0.00519874	+	0.129005i
$606$	−29.5165			−1.19902
$607$	0.239870	−	5.95230i	0.00973601	−	0.241597i	−0.986992	−	0.160769i	$-0.948603\pi$
$607$	0.239870	−	5.95230i	0.00973601	−	0.241597i	0.996728	−	0.0808277i	$-0.0257563\pi$
$608$	33.2488	−	24.9848i	1.34842	−	1.01327i
$609$	−5.96445	+	0.969318i	−0.241692	+	0.0392788i
$610$	1.56592	−	0.821859i	0.0634023	−	0.0332761i
$611$	−4.08676	+	32.9254i	−0.165333	+	1.33202i
$612$	4.29900	+	2.25629i	0.173777	+	0.0912051i
$613$	−4.17779	−	1.39475i	−0.168739	−	0.0563335i	0.231043	−	0.972943i	$-0.425786\pi$
$613$	−4.17779	−	1.39475i	−0.168739	−	0.0563335i	−0.399782	+	0.916610i	$0.630914\pi$
$614$	−3.40848	+	16.6959i	−0.137555	+	0.673790i
$615$	0.158702	−	0.547902i	0.00639947	−	0.0220935i
$616$	1.84263	+	15.1755i	0.0742418	+	0.611437i
$617$	−16.4511	+	5.49219i	−0.662297	+	0.221107i	−0.627891	−	0.778301i	$-0.716082\pi$
$617$	−16.4511	+	5.49219i	−0.662297	+	0.221107i	−0.0344050	+	0.999408i	$0.510954\pi$
$618$	−4.32011	−	0.702087i	−0.173780	−	0.0282421i
$619$	1.84534	−	0.968509i	0.0741704	−	0.0389276i	−0.427230	−	0.904143i	$-0.640511\pi$
$619$	1.84534	−	0.968509i	0.0741704	−	0.0389276i	0.501401	+	0.865215i	$0.332818\pi$
$620$	0.219119	−	0.138563i	0.00880004	−	0.00556481i
$621$	6.34851	−	2.70485i	0.254757	−	0.108542i
$622$	−6.24054	+	30.5682i	−0.250223	+	1.22567i
$623$	23.2014	+	5.71863i	0.929544	+	0.229112i
$624$	14.1346	+	10.6804i	0.565836	+	0.427558i
$625$	−24.0422	+	5.92588i	−0.961689	+	0.237035i
$626$	−1.44243	−	35.7935i	−0.0576510	−	1.43060i
$627$	−1.58511	−	39.3340i	−0.0633031	−	1.57085i
$628$	16.7400	+	20.5028i	0.667998	+	0.818150i
$629$	−1.20438	+	3.17570i	−0.0480219	+	0.126623i
$630$	−0.194586	−	0.410081i	−0.00775249	−	0.0163380i
$631$	6.74281	−	23.2789i	0.268427	−	0.926718i	−0.707151	−	0.707063i	$-0.750020\pi$
$631$	6.74281	−	23.2789i	0.268427	−	0.926718i	0.975578	−	0.219655i	$-0.0704931\pi$
$632$	5.50733	−	7.97874i	0.219070	−	0.317377i
$633$	20.3893	+	8.68707i	0.810402	+	0.345280i
$634$	17.6068	−	2.86138i	0.699255	−	0.113640i
$635$	2.11188	+	1.33547i	0.0838072	+	0.0529965i
$636$	4.72066	+	6.83905i	0.187186	+	0.271186i
$637$	3.04747	+	10.6268i	0.120745	+	0.421049i
$638$	18.8951	−	27.3743i	0.748066	−	1.08376i
$639$	−12.9483	+	5.51675i	−0.512227	+	0.218239i
$640$	−0.337191	−	1.16412i	−0.0133286	−	0.0460158i
$641$	33.5965	−	2.71219i	1.32698	−	0.107125i	0.603442	−	0.797407i	$-0.293795\pi$
$641$	33.5965	−	2.71219i	1.32698	−	0.107125i	0.723541	+	0.690282i	$0.242513\pi$
$642$	17.3002	−	15.3267i	0.682786	−	0.604895i
$643$	6.01067	−	3.80092i	0.237038	−	0.149894i	−0.410666	−	0.911786i	$-0.634704\pi$
$643$	6.01067	−	3.80092i	0.237038	−	0.149894i	0.647704	+	0.761892i	$0.275729\pi$
$644$	16.2940	+	6.94224i	0.642075	+	0.273563i
$645$	0.105935	−	0.872449i	0.00417117	−	0.0343527i
$646$	8.91370	+	43.6622i	0.350705	+	1.71787i
$647$	7.07050	+	0.570790i	0.277970	+	0.0224401i	0.218666	−	0.975800i	$-0.429830\pi$
$647$	7.07050	+	0.570790i	0.277970	+	0.0224401i	0.0593046	+	0.998240i	$0.481112\pi$
$648$	1.02431	−	0.769720i	0.0402387	−	0.0302375i
$649$	9.52269	−	78.4264i	0.373798	−	3.07850i
$650$	−8.99082	−	31.3517i	−0.352649	−	1.22972i
$651$	−0.379853	−	3.12837i	−0.0148876	−	0.122611i
$652$	−4.39986	−	4.58074i	−0.172312	−	0.179396i
$653$	−4.80443	−	8.32152i	−0.188012	−	0.325646i	0.756575	−	0.653906i	$-0.226871\pi$
$653$	−4.80443	−	8.32152i	−0.188012	−	0.325646i	−0.944587	+	0.328260i	$0.893538\pi$
$654$	12.3421	−	21.3771i	0.482614	−	0.835912i
$655$	−0.430890	+	0.106205i	−0.0168363	+	0.00414976i
$656$	14.0580	+	17.2179i	0.548872	+	0.672246i
$657$	1.58420	−	2.74391i	0.0618053	−	0.107050i
$658$	11.7462	+	30.9722i	0.457915	+	1.20742i
$659$	9.96123	−	10.3707i	0.388035	−	0.403987i	−0.498320	−	0.866993i	$-0.666050\pi$
$659$	9.96123	−	10.3707i	0.388035	−	0.403987i	0.886355	+	0.463006i	$0.153229\pi$
$660$	0.931020	+	0.310820i	0.0362399	+	0.0120987i
$661$	0.667364	+	2.30401i	0.0259575	+	0.0896155i	0.972451	−	0.233107i	$-0.0748892\pi$
$661$	0.667364	+	2.30401i	0.0259575	+	0.0896155i	−0.946494	+	0.322722i	$0.895402\pi$
$662$	31.9003	−	28.2612i	1.23984	−	1.09840i
$663$	−11.9949	+	6.25476i	−0.465842	+	0.242915i
$664$	−6.55437	−	5.80666i	−0.254359	−	0.225342i
$665$	0.701620	−	1.47863i	0.0272077	−	0.0573389i
$666$	−1.13813	−	1.18492i	−0.0441017	−	0.0459147i
$667$	9.01284	+	18.9941i	0.348978	+	0.735456i
$668$	4.63053	+	1.14132i	0.179160	+	0.0441591i
$669$	16.1254	−	16.7883i	0.623444	−	0.649074i
$670$	−0.227949	−	0.171293i	−0.00880644	−	0.00661761i
$671$	34.7945	+	30.8253i	1.34323	+	1.19000i
$672$	12.4418	+	2.02199i	0.479952	+	0.0779998i
$673$	−24.9582	−	15.7826i	−0.962069	−	0.608375i	−0.0415761	−	0.999135i	$-0.513238\pi$
$673$	−24.9582	−	15.7826i	−0.962069	−	0.608375i	−0.920493	+	0.390760i	$0.872212\pi$
$674$	12.6204	+	1.01882i	0.486119	+	0.0392436i
$675$	−4.98410			−0.191838
$676$	15.9849	−	5.24219i	0.614803	−	0.201623i
$677$	1.23440			0.0474420			0.0237210	−	0.999719i	$-0.492449\pi$
$677$	1.23440			0.0474420			0.0237210	+	0.999719i	$0.492449\pi$
$678$	−22.2578	−	1.79683i	−0.854805	−	0.0690070i
$679$	−21.0302	−	13.2987i	−0.807063	−	0.510356i
$680$	0.598312	+	0.0972352i	0.0229442	+	0.00372880i
$681$	−5.33307	−	4.72469i	−0.204364	−	0.181051i
$682$	13.8677	+	10.4209i	0.531022	+	0.399037i
$683$	−8.35051	+	8.69380i	−0.319523	+	0.332659i	−0.861522	−	0.507720i	$-0.830488\pi$
$683$	−8.35051	+	8.69380i	−0.319523	+	0.332659i	0.541999	+	0.840379i	$0.317668\pi$
$684$	−8.22235	−	2.02663i	−0.314389	−	0.0774900i
$685$	−0.0177949	−	0.0375019i	−0.000679908	−	0.00143288i
$686$	25.1014	+	26.1333i	0.958375	+	0.997774i
$687$	3.65143	−	7.69522i	0.139311	−	0.293591i
$688$	25.6342	+	22.7099i	0.977294	+	0.865807i
$689$	−23.1540	−	0.0615862i	−0.882099	−	0.00234625i
$690$	−1.18208	+	1.04723i	−0.0450011	+	0.0398675i
$691$	−7.48864	−	25.8538i	−0.284881	−	0.983524i	−0.967525	−	0.252773i	$-0.918657\pi$
$691$	−7.48864	−	25.8538i	−0.284881	−	0.983524i	0.682644	−	0.730751i	$-0.260830\pi$
$692$	24.3463	+	8.12800i	0.925509	+	0.308980i
$693$	8.26487	−	8.60464i	0.313956	−	0.326863i
$694$	−15.0071	−	39.5704i	−0.569661	−	1.50207i
$695$	0.138201	−	0.239371i	0.00524226	−	0.00907985i
$696$	2.46882	+	3.02376i	0.0935804	+	0.114615i
$697$	−16.4798	+	4.06190i	−0.624216	+	0.153856i
$698$	−5.17904	+	8.97036i	−0.196030	+	0.339533i
$699$	3.45018	+	5.97588i	0.130498	+	0.226029i
$700$	−8.86144	−	9.22574i	−0.334931	−	0.348700i
$701$	−2.03318	−	16.7447i	−0.0767920	−	0.632439i	−0.979393	−	0.201962i	$-0.935268\pi$
$701$	−2.03318	−	16.7447i	−0.0767920	−	0.632439i	0.902601	−	0.430477i	$-0.141655\pi$
$702$	−0.246103	−	6.53926i	−0.00928858	−	0.246809i
$703$	0.714071	−	5.88090i	0.0269317	−	0.221802i
$704$	−8.21085	+	6.17005i	−0.309458	+	0.232543i
$705$	−1.15654	−	0.0933653i	−0.0435577	−	0.00351634i
$706$	0.651803	+	3.19274i	0.0245309	+	0.120160i
$707$	3.88802	−	32.0207i	0.146224	−	1.20426i
$708$	−15.6351	−	6.66149i	−0.587602	−	0.250354i
$709$	−7.46769	+	4.72228i	−0.280455	+	0.177349i	−0.667286	−	0.744802i	$-0.732544\pi$
$709$	−7.46769	+	4.72228i	−0.280455	+	0.177349i	0.386831	+	0.922151i	$0.373570\pi$
$710$	2.41095	−	2.13592i	0.0904814	−	0.0801595i
$711$	−7.54203	+	0.608855i	−0.282848	+	0.0228339i
$712$	−4.29477	−	14.8273i	−0.160953	−	0.555676i
$713$	−10.0869	+	4.29764i	−0.377758	+	0.160948i
$714$	−7.67228	+	11.1152i	−0.287128	+	0.415977i
$715$	−2.19070	+	1.63710i	−0.0819274	+	0.0612241i
$716$	−11.0944	−	16.0730i	−0.414617	−	0.600677i
$717$	6.71588	+	4.24687i	0.250809	+	0.158602i
$718$	−13.4265	+	2.18203i	−0.501074	+	0.0814325i
$719$	−16.4247	−	6.99791i	−0.612537	−	0.260978i	0.0633398	−	0.997992i	$-0.479825\pi$
$719$	−16.4247	−	6.99791i	−0.612537	−	0.260978i	−0.675877	+	0.737014i	$0.736235\pi$
$720$	−0.351952	+	0.509891i	−0.0131165	+	0.0190025i
$721$	1.33072	−	4.59416i	0.0495584	−	0.171096i
$722$	−18.5381	−	39.0683i	−0.689918	−	1.45397i
$723$	3.45717	−	9.11582i	0.128574	−	0.339021i
$724$	−18.2257	−	22.3224i	−0.677351	−	0.829604i
$725$	−0.611430	−	15.1725i	−0.0227079	−	0.563492i
$726$	1.84055	+	45.6729i	0.0683094	+	1.69508i
$727$	−20.9451	+	5.16251i	−0.776811	+	0.191467i	−0.607739	−	0.794137i	$-0.707923\pi$
$727$	−20.9451	+	5.16251i	−0.776811	+	0.191467i	−0.169072	+	0.985604i	$0.554077\pi$
$728$	−6.36481	+	6.59129i	−0.235896	+	0.244289i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−0.145038	+	0.710441i	−0.00536808	+	0.0262946i
$731$	−24.0579	+	10.2501i	−0.889813	+	0.379114i
$732$	8.45180	−	5.34460i	0.312388	−	0.197542i
$733$	29.0646	−	15.2543i	1.07353	−	0.563429i	0.167162	−	0.985929i	$-0.446540\pi$
$733$	29.0646	−	15.2543i	1.07353	−	0.563429i	0.906363	+	0.422500i	$0.138847\pi$
$734$	16.9240	+	2.75041i	0.624676	+	0.101520i
$735$	−0.366722	+	0.122430i	−0.0135268	+	0.00451589i
$736$	−5.28623	−	43.5360i	−0.194853	−	1.60476i
$737$	2.08518	−	7.19889i	0.0768088	−	0.265175i
$738$	1.64231	−	8.04458i	0.0604544	−	0.296125i
$739$	−11.5905	−	3.86946i	−0.426362	−	0.142340i	0.0953859	−	0.995440i	$-0.469591\pi$
$739$	−11.5905	−	3.86946i	−0.426362	−	0.142340i	−0.521748	+	0.853100i	$0.674720\pi$
$740$	0.130790	+	0.0686437i	0.00480792	+	0.00252339i
$741$	17.7029	−	15.5996i	0.650334	−	0.573065i
$742$	−20.4691	+	10.7430i	−0.751442	+	0.394387i
$743$	31.4476	−	5.11073i	1.15370	−	0.187494i	0.446683	−	0.894692i	$-0.352605\pi$
$743$	31.4476	−	5.11073i	1.15370	−	0.187494i	0.707016	+	0.707198i	$0.250041\pi$
$744$	−1.62749	+	1.22298i	−0.0596667	+	0.0448366i
$745$	−0.103054	+	2.55727i	−0.00377562	+	0.0936911i
$746$	30.8143			1.12819
$747$	−0.275186	+	6.82867i	−0.0100685	+	0.249848i
$748$	−5.84187	−	28.6154i	−0.213600	−	1.04628i
$749$	14.3482	+	20.7869i	0.524271	+	0.759538i
$750$	2.16730	−	0.723551i	0.0791386	−	0.0264203i
$751$	15.9507	−	33.6153i	0.582048	−	1.22664i	−0.372348	−	0.928093i	$-0.621447\pi$
$751$	15.9507	−	33.6153i	0.582048	−	1.22664i	0.954395	−	0.298546i	$-0.0965016\pi$
$752$	28.5954	−	35.0230i	1.04277	−	1.27716i
$753$	−0.206612	−	0.544791i	−0.00752936	−	0.0198533i
$754$	19.8765	−	1.55139i	0.723858	−	0.0564984i
$755$	−0.521092	+	1.37401i	−0.0189645	+	0.0500052i
$756$	−1.28330	−	2.22274i	−0.0466731	−	0.0808401i
$757$	15.1497	−	18.5550i	0.550625	−	0.674393i	−0.422048	−	0.906574i	$-0.638689\pi$
$757$	15.1497	−	18.5550i	0.550625	−	0.674393i	0.972673	+	0.232180i	$0.0745860\pi$
$758$	23.5952	+	17.7306i	0.857016	+	0.644005i
$759$	−36.7558	−	19.2910i	−1.33415	−	0.700217i
$760$	−1.05385	+	0.0850759i	−0.0382273	+	0.00308603i
$761$	−40.0508	+	3.23324i	−1.45184	+	0.117205i	−0.781063	−	0.624452i	$-0.785322\pi$
$761$	−40.0508	+	3.23324i	−1.45184	+	0.117205i	−0.670779	+	0.741657i	$0.734040\pi$
$762$	31.8459	+	16.7140i	1.15366	+	0.605485i
$763$	21.5651	+	16.2051i	0.780708	+	0.586664i
$764$	17.3601	−	21.2623i	0.628068	−	0.769243i
$765$	−0.236545	−	0.409708i	−0.00855231	−	0.0148130i
$766$	−6.01943	+	15.8719i	−0.217491	+	0.573476i
$767$	40.0893	−	25.2019i	1.44754	−	0.909989i
$768$	−7.39689	−	19.5040i	−0.266912	−	0.703789i
$769$	−9.59065	+	11.7464i	−0.345848	+	0.423586i	−0.918012	−	0.396552i	$-0.870206\pi$
$769$	−9.59065	+	11.7464i	−0.345848	+	0.423586i	0.572164	+	0.820139i	$0.306104\pi$
$770$	−1.17052	+	2.46681i	−0.0421825	+	0.0888976i
$771$	15.2156	−	5.07972i	0.547978	−	0.182942i
$772$	8.97998	+	13.0098i	0.323197	+	0.468231i
$773$	−1.64262	−	8.04610i	−0.0590811	−	0.289398i	0.939506	−	0.342531i	$-0.111284\pi$
$773$	−1.64262	−	8.04610i	−0.0590811	−	0.289398i	−0.998587	+	0.0531332i	$0.983079\pi$
$774$	0.509365	−	12.6398i	0.0183087	−	0.454327i
$775$	7.91906			0.284461
$776$	−0.647233	+	16.0609i	−0.0232343	+	0.576554i
$777$	1.43537	−	1.07861i	0.0514936	−	0.0386950i
$778$	−26.6697	+	4.33425i	−0.956155	+	0.155390i
$779$	26.2137	−	13.7580i	0.939202	−	0.492931i
$780$	0.207156	+	0.550638i	0.00741737	+	0.0197160i
$781$	74.9665	+	39.3455i	2.68251	+	1.40789i
$782$	44.5723	+	14.8804i	1.59390	+	0.532122i
$783$	0.609407	−	2.98507i	0.0217784	−	0.106678i
$784$	4.19151	−	14.4708i	0.149697	−	0.516813i
$785$	−0.310882	−	2.56034i	−0.0110958	−	0.0913825i
$786$	−6.05898	+	2.02279i	−0.216117	+	0.0721504i
$787$	15.6762	+	2.54764i	0.558797	+	0.0908134i	0.433249	−	0.901274i	$-0.357367\pi$
$787$	15.6762	+	2.54764i	0.558797	+	0.0908134i	0.125548	+	0.992088i	$0.459931\pi$
$788$	7.72913	−	4.05656i	0.275339	−	0.144509i
$789$	−3.85486	+	2.43766i	−0.137237	+	0.0867831i
$790$	1.59306	−	0.678740i	0.0566786	−	0.0241485i
$791$	4.88116	−	23.9095i	0.173554	−	0.850125i
$792$	−7.48348	−	1.84451i	−0.265914	−	0.0655419i
$793$	−1.19595	+	27.8367i	−0.0424695	+	0.988512i
$794$	−31.8807	+	7.85790i	−1.13141	+	0.278866i
$795$	−0.0326051	−	0.809088i	−0.00115639	−	0.0286954i
$796$	0.207727	+	5.15470i	0.00736270	+	0.182704i
$797$	−8.19682	−	10.0393i	−0.290346	−	0.355610i	0.608749	−	0.793363i	$-0.291672\pi$
$797$	−8.19682	−	10.0393i	−0.290346	−	0.355610i	−0.899095	+	0.437753i	$0.855774\pi$
$798$	8.35360	−	22.0266i	0.295714	−	0.779734i
$799$	14.8005	+	31.1915i	0.523605	+	1.10347i
$800$	−8.81261	+	30.4247i	−0.311573	+	1.07567i
$801$	−6.84399	+	9.91523i	−0.241820	+	0.350337i
$802$	−46.5695	−	19.8414i	−1.64442	−	0.700624i
$803$	−18.8124	+	3.05731i	−0.663875	+	0.107890i
$804$	−1.36269	−	0.861712i	−0.0480583	−	0.0303902i
$805$	−0.980375	−	1.42032i	−0.0345537	−	0.0500597i
$806$	0.391025	+	10.3900i	0.0137733	+	0.365972i
$807$	−1.92912	+	2.79482i	−0.0679083	+	0.0983822i
$808$	−19.1700	+	8.16758i	−0.674399	+	0.287334i
$809$	−11.0180	−	38.0384i	−0.387371	−	1.33736i	−0.883224	−	0.468952i	$-0.844632\pi$
$809$	−11.0180	−	38.0384i	−0.387371	−	1.33736i	0.495853	−	0.868406i	$-0.334855\pi$
$810$	0.228111	−	0.0184150i	0.00801499	−	0.000647037i
$811$	−29.0424	+	25.7294i	−1.01982	+	0.903480i	−0.995360	−	0.0962211i	$-0.969324\pi$
$811$	−29.0424	+	25.7294i	−1.01982	+	0.903480i	−0.0244579	+	0.999701i	$0.507786\pi$
$812$	6.60897	−	4.17926i	0.231929	−	0.146663i
$813$	14.8425	+	6.32381i	0.520550	+	0.221786i
$814$	−1.19129	+	9.81114i	−0.0417546	+	0.343880i
$815$	0.123796	+	0.606395i	0.00433640	+	0.0212411i
$816$	18.3754	+	1.48342i	0.643267	+	0.0519299i
$817$	36.4644	−	27.4012i	1.27573	−	0.958647i
$818$	6.19619	−	51.0302i	0.216645	−	1.78423i
$819$	7.12649	+	0.594393i	0.249020	+	0.0207698i
$820$	0.0889742	+	0.732768i	0.00310711	+	0.0255894i
$821$	13.0278	+	13.5634i	0.454675	+	0.473367i	0.908597	−	0.417675i	$-0.137155\pi$
$821$	13.0278	+	13.5634i	0.454675	+	0.473367i	−0.453922	+	0.891042i	$0.649975\pi$
$822$	−0.298739	−	0.517432i	−0.0104197	−	0.0180475i
$823$	−13.5250	+	23.4260i	−0.471453	+	0.816580i	−0.999467	−	0.0326554i	$-0.989604\pi$
$823$	−13.5250	+	23.4260i	−0.471453	+	0.816580i	0.528014	+	0.849236i	$0.322937\pi$
$824$	−3.00005	+	0.739447i	−0.104512	+	0.0257599i
$825$	18.9616	+	23.2238i	0.660159	+	0.808548i
$826$	23.6384	−	40.9429i	0.822486	−	1.42459i
$827$	−6.58577	−	17.3652i	−0.229010	−	0.603849i	0.770423	−	0.637533i	$-0.220045\pi$
$827$	−6.58577	−	17.3652i	−0.229010	−	0.603849i	−0.999433	+	0.0336846i	$0.989276\pi$
$828$	−6.18588	+	6.44019i	−0.214974	+	0.223812i
$829$	35.7695	+	11.9416i	1.24233	+	0.414749i	0.860484	−	0.509478i	$-0.170162\pi$
$829$	35.7695	+	11.9416i	1.24233	+	0.414749i	0.381842	+	0.924228i	$0.375290\pi$
$830$	−0.435139	−	1.50228i	−0.0151039	−	0.0521447i
$831$	−13.5053	+	11.9646i	−0.468493	+	0.415049i
$832$	−5.97328	−	1.48915i	−0.207086	−	0.0516269i
$833$	8.61078	+	7.62849i	0.298346	+	0.264311i
$834$	1.70553	−	3.59433i	0.0590577	−	0.124461i
$835$	−0.321915	−	0.335149i	−0.0111403	−	0.0115983i
$836$	21.8381	+	46.0228i	0.755286	+	1.59173i
$837$	1.54270	+	0.380240i	0.0533233	+	0.0131430i
$838$	9.15762	−	9.53409i	0.316345	−	0.329350i
$839$	−28.0627	−	21.0878i	−0.968834	−	0.728031i	−0.00652149	−	0.999979i	$-0.502076\pi$
$839$	−28.0627	−	21.0878i	−0.968834	−	0.728031i	−0.962312	+	0.271948i	$0.912332\pi$
$840$	−0.239852	−	0.212490i	−0.00827568	−	0.00733162i
$841$	−19.4626	−	3.16298i	−0.671124	−	0.109068i
$842$	−45.1426	−	28.5465i	−1.55572	−	0.983777i
$843$	13.0367	+	1.05243i	0.449008	+	0.0362476i
$844$	−28.6795			−0.987190
$845$	−1.58947	−	0.400750i	−0.0546794	−	0.0137862i
$846$	−16.7010			−0.574193
$847$	−49.7904	−	4.01949i	−1.71082	−	0.138111i
$848$	26.6689	+	16.8644i	0.915815	+	0.579126i
$849$	11.4693	+	1.86395i	0.393626	+	0.0639704i
$850$	−25.4040	−	22.5060i	−0.871350	−	0.771948i
$851$	−4.99400	−	3.75274i	−0.171192	−	0.128642i
$852$	12.6166	−	13.1353i	0.432238	−	0.450007i
$853$	54.4711	+	13.4259i	1.86506	+	0.459695i	0.999177	−	0.0405590i	$-0.0129139\pi$
$853$	54.4711	+	13.4259i	1.86506	+	0.459695i	0.865879	+	0.500254i	$0.166760\pi$
$854$	11.9252	+	25.1319i	0.408073	+	0.859996i
$855$	0.571619	+	0.595119i	0.0195490	+	0.0203526i
$856$	6.99487	−	14.7414i	0.239080	−	0.503850i
$857$	9.37687	+	8.30718i	0.320308	+	0.283768i	0.807920	−	0.589293i	$-0.200593\pi$
$857$	9.37687	+	8.30718i	0.320308	+	0.283768i	−0.487612	+	0.873060i	$0.662132\pi$
$858$	−29.5339	+	26.0249i	−1.00827	+	0.888474i
$859$	37.4472	−	33.1753i	1.27768	−	1.13193i	0.293274	−	0.956029i	$-0.405255\pi$
$859$	37.4472	−	33.1753i	1.27768	−	1.13193i	0.984408	−	0.175899i	$-0.0562831\pi$
$860$	0.316410	+	1.09237i	0.0107895	+	0.0372497i
$861$	8.51078	+	2.84131i	0.290046	+	0.0968317i
$862$	−42.9320	+	44.6969i	−1.46227	+	1.52238i
$863$	6.85663	+	18.0794i	0.233402	+	0.615431i	0.999632	−	0.0271359i	$-0.00863867\pi$
$863$	6.85663	+	18.0794i	0.233402	+	0.615431i	−0.766230	+	0.642567i	$0.777869\pi$
$864$	−3.17763	+	5.50382i	−0.108105	+	0.187244i
$865$	−1.58178	−	1.93733i	−0.0537822	−	0.0658712i
$866$	29.9361	−	7.37858i	1.01727	−	0.250734i
$867$	1.46158	−	2.53153i	0.0496378	−	0.0859751i
$868$	2.03899	+	3.53163i	0.0692077	+	0.119871i
$869$	31.5301	+	32.8263i	1.06958	+	1.11356i
$870$	0.0840421	+	0.692149i	0.00284930	+	0.0234661i
$871$	4.13747	−	1.74982i	0.140193	−	0.0592904i
$872$	2.10048	−	17.2990i	0.0711311	−	0.585818i
$873$	10.0292	−	7.53645i	0.339437	−	0.255070i
$874$	−81.6963	−	6.59521i	−2.76342	−	0.223086i
$875$	0.499454	+	2.44649i	0.0168846	+	0.0827064i
$876$	−0.494203	+	4.07013i	−0.0166976	+	0.137517i
$877$	23.2908	+	9.92328i	0.786474	+	0.335085i	0.747592	−	0.664158i	$-0.231210\pi$
$877$	23.2908	+	9.92328i	0.786474	+	0.335085i	0.0388825	+	0.999244i	$0.487620\pi$
$878$	−10.8666	+	6.87162i	−0.366730	+	0.231906i
$879$	−12.3473	+	10.9388i	−0.416466	+	0.368956i
$880$	3.71485	−	0.299894i	0.125228	−	0.0101094i
$881$	−15.5326	−	53.6247i	−0.523306	−	1.80666i	−0.588131	−	0.808765i	$-0.700136\pi$
$881$	−15.5326	−	53.6247i	−0.523306	−	1.80666i	0.0648253	−	0.997897i	$-0.479351\pi$
$882$	−5.11958	+	2.18125i	−0.172385	+	0.0734465i
$883$	−1.78469	+	2.58557i	−0.0600595	+	0.0870112i	−0.851863	−	0.523765i	$-0.824527\pi$
$883$	−1.78469	+	2.58557i	−0.0600595	+	0.0870112i	0.791803	+	0.610776i	$0.209142\pi$
$884$	11.1072	−	13.5303i	0.373577	−	0.455072i
$885$	0.940727	+	1.36288i	0.0316222	+	0.0458127i
$886$	34.6729	+	21.9258i	1.16486	+	0.736612i
$887$	11.9089	−	1.93538i	0.399862	−	0.0649838i	0.0428447	−	0.999082i	$-0.486358\pi$
$887$	11.9089	−	1.93538i	0.399862	−	0.0649838i	0.357017	+	0.934098i	$0.383794\pi$
$888$	−1.06706	−	0.454633i	−0.0358083	−	0.0152565i
$889$	−22.3270	+	32.3462i	−0.748823	+	1.08486i
$890$	0.767099	−	2.64833i	0.0257132	−	0.0887724i
$891$	2.57877	+	5.43463i	0.0863919	+	0.182067i
$892$	−10.6818	+	28.1655i	−0.357652	+	0.943050i
$893$	−38.0852	−	46.6460i	−1.27447	−	1.56095i
$894$	1.48334	+	36.8086i	0.0496102	+	1.23106i
$895$	0.0766280	+	1.90150i	0.00256139	+	0.0635603i
$896$	18.5098	−	4.56226i	0.618370	−	0.152414i
$897$	−4.91195	−	24.3912i	−0.164005	−	0.814398i
$898$	−57.5175	−	14.1768i	−1.91938	−	0.473086i
$899$	−0.968266	+	4.74288i	−0.0322935	+	0.158184i
$900$	5.93352	−	2.52804i	0.197784	−	0.0842679i
$901$	−20.3640	+	12.8774i	−0.678424	+	0.429010i
$902$	−43.7324	+	22.9525i	−1.45613	+	0.764235i
$903$	13.6451	+	2.21754i	0.454079	+	0.0737951i
$904$	−14.9529	+	4.99203i	−0.497327	+	0.166032i
$905$	0.338472	+	2.78757i	0.0112512	+	0.0926619i
$906$	−5.88473	+	20.3165i	−0.195507	+	0.674969i
$907$	6.77419	−	33.1822i	0.224933	−	1.10180i	−0.697781	−	0.716311i	$-0.745829\pi$
$907$	6.77419	−	33.1822i	0.224933	−	1.10180i	0.922714	−	0.385485i	$-0.125966\pi$
$908$	8.74543	+	2.91965i	0.290227	+	0.0968921i
$909$	14.4001	+	7.55778i	0.477623	+	0.250676i
$910$	−1.59006	+	0.387431i	−0.0527100	+	0.0128432i
$911$	5.36772	−	2.81720i	0.177840	−	0.0933379i	−0.373454	−	0.927649i	$-0.621827\pi$
$911$	5.36772	−	2.81720i	0.177840	−	0.0933379i	0.551294	+	0.834311i	$0.314134\pi$
$912$	−31.7387	+	5.15804i	−1.05097	+	0.170800i
$913$	32.8656	−	24.6969i	1.08769	−	0.817348i
$914$	−2.42624	+	60.2065i	−0.0802528	+	1.99145i
$915$	−0.974403			−0.0322128
$916$	−0.443815	+	11.0132i	−0.0146641	+	0.363885i
$917$	−1.39629	−	6.83950i	−0.0461097	−	0.225860i
$918$	−3.86825	−	5.60413i	−0.127671	−	0.184964i
$919$	34.7656	−	11.6064i	1.14681	−	0.382861i	0.321149	−	0.947029i	$-0.395931\pi$
$919$	34.7656	−	11.6064i	1.14681	−	0.382861i	0.825661	+	0.564167i	$0.190803\pi$
$920$	−0.477942	+	1.00724i	−0.0157573	+	0.0332078i
$921$	5.93792	−	7.27263i	0.195661	−	0.239641i
$922$	8.98849	+	23.7007i	0.296020	+	0.780541i
$923$	10.0183	+	49.7478i	0.329757	+	1.63747i
$924$	−5.47479	+	14.4358i	−0.180108	+	0.474904i
$925$	2.25592	+	3.90737i	0.0741742	+	0.128474i
$926$	−2.63476	+	3.22699i	−0.0865835	+	0.106046i
$927$	1.92787	+	1.44870i	0.0633197	+	0.0475817i
$928$	−17.1444	−	8.99808i	−0.562793	−	0.295376i
$929$	−50.2013	+	4.05267i	−1.64705	+	0.132964i	−0.868858	−	0.495062i	$-0.835145\pi$
$929$	−50.2013	+	4.05267i	−1.64705	+	0.132964i	−0.778193	+	0.628026i	$0.783863\pi$
$930$	−0.362437	+	0.0292589i	−0.0118848	+	0.000959438i
$931$	−17.7670	−	9.32483i	−0.582289	−	0.305609i
$932$	−7.13849	−	5.36423i	−0.233829	−	0.175711i
$933$	10.8716	−	13.3153i	0.355922	−	0.435925i
$934$	−12.1532	−	21.0500i	−0.397666	−	0.688777i
$935$	−1.00915	+	2.66090i	−0.0330027	+	0.0870209i
$936$	−1.96933	−	4.17895i	−0.0643697	−	0.136593i
$937$	−12.4577	−	32.8482i	−0.406975	−	1.07310i	−0.969234	−	0.246143i	$-0.920837\pi$
$937$	−12.4577	−	32.8482i	−0.406975	−	1.07310i	0.562259	−	0.826961i	$-0.309933\pi$
$938$	2.83656	−	3.47415i	0.0926168	−	0.113435i
$939$	−8.46132	+	17.8318i	−0.276125	+	0.581920i
$940$	1.42420	−	0.475469i	0.0464524	−	0.0155081i
$941$	6.13506	+	8.88817i	0.199997	+	0.289746i	0.910131	−	0.414321i	$-0.135981\pi$
$941$	6.13506	+	8.88817i	0.199997	+	0.289746i	−0.710134	+	0.704067i	$0.751366\pi$
$942$	−7.42566	−	36.3733i	−0.241941	−	1.18511i
$943$	1.25701	−	31.1923i	0.0409337	−	1.01576i
$944$	−64.5311			−2.10031
$945$	−0.0100702	+	0.249890i	−0.000327584	+	0.00812892i
$946$	−60.8337	+	45.7136i	−1.97788	+	1.48628i
$947$	46.6762	−	7.58562i	1.51677	−	0.246500i	0.655716	−	0.755008i	$-0.272367\pi$
$947$	46.6762	−	7.58562i	1.51677	−	0.246500i	0.861057	+	0.508508i	$0.169803\pi$
$948$	8.66989	−	4.55031i	0.281585	−	0.147787i
$949$	−8.53065	−	7.59809i	−0.276917	−	0.246645i
$950$	52.4171	+	27.5106i	1.70064	+	0.892563i
$951$	−9.32245	−	3.11229i	−0.302301	−	0.100923i
$952$	−1.90718	+	9.34200i	−0.0618122	+	0.302776i
$953$	−6.99553	+	24.1514i	−0.226608	+	0.782340i	0.763954	+	0.645271i	$0.223255\pi$
$953$	−6.99553	+	24.1514i	−0.226608	+	0.782340i	−0.990561	+	0.137069i	$0.956232\pi$
$954$	−1.40488	−	11.5703i	−0.0454848	−	0.374601i
$955$	−2.53704	+	0.846990i	−0.0820968	+	0.0274079i
$956$	−10.1493	−	1.64942i	−0.328251	−	0.0533461i
$957$	−16.2276	+	8.51691i	−0.524564	+	0.275313i
$958$	−14.7044	+	9.29848i	−0.475076	+	0.300420i
$959$	0.600683	−	0.255927i	0.0193971	−	0.00826432i
$960$	0.0430638	−	0.210940i	0.00138988	−	0.00680807i
$961$	27.6481	+	6.81464i	0.891873	+	0.219827i
$962$	−5.01517	+	3.15276i	−0.161696	+	0.101649i
$963$	−12.3647	+	3.04762i	−0.398446	+	0.0982081i
$964$	0.507998	+	12.6058i	0.0163615	+	0.406007i
$965$	−0.0620239	−	1.53911i	−0.00199662	−	0.0495456i
$966$	−15.7105	−	19.2419i	−0.505478	−	0.619098i
$967$	1.80383	−	4.75631i	0.0580072	−	0.152953i	−0.902880	−	0.429893i	$-0.858551\pi$
$967$	1.80383	−	4.75631i	0.0580072	−	0.152953i	0.960887	+	0.276941i	$0.0893205\pi$
$968$	13.8337	+	29.1538i	0.444630	+	0.937039i
$969$	6.83112	−	23.5838i	0.219447	−	0.757620i
$970$	−1.63092	+	2.36279i	−0.0523656	+	0.0758647i
$971$	50.1395	+	21.3624i	1.60905	+	0.685553i	0.994637	−	0.103429i	$-0.0329814\pi$
$971$	50.1395	+	21.3624i	1.60905	+	0.685553i	0.614416	+	0.788982i	$0.289392\pi$
$972$	1.27728	−	0.207579i	0.0409689	−	0.00665809i
$973$	3.67463	+	2.32369i	0.117803	+	0.0744941i
$974$	−8.19913	−	11.8785i	−0.262717	−	0.380611i
$975$	−3.64137	+	17.5976i	−0.116617	+	0.563575i
$976$	21.5695	−	31.2488i	0.690422	−	1.00025i
$977$	−14.1869	+	6.04449i	−0.453880	+	0.193380i	−0.606794	−	0.794859i	$-0.707545\pi$
$977$	−14.1869	+	6.04449i	−0.453880	+	0.193380i	0.152914	+	0.988240i	$0.451134\pi$
$978$	2.47845	+	8.55659i	0.0792520	+	0.273609i
$979$	72.2381	−	5.83167i	2.30874	−	0.186381i
$980$	0.374480	−	0.331761i	0.0119623	−	0.0105977i
$981$	−11.4950	+	7.26899i	−0.367007	+	0.232081i
$982$	17.6807	+	7.53302i	0.564212	+	0.240388i
$983$	−6.87201	+	56.5961i	−0.219183	+	1.80513i	0.303740	+	0.952755i	$0.401764\pi$
$983$	−6.87201	+	56.5961i	−0.219183	+	1.80513i	−0.522923	+	0.852380i	$0.675159\pi$
$984$	−1.15941	−	5.67915i	−0.0369605	−	0.181045i
$985$	−0.847806	−	0.0684420i	−0.0270134	−	0.00218074i
$986$	16.5854	−	12.4631i	0.528187	−	0.396907i
$987$	2.19992	−	18.1180i	0.0700243	−	0.576702i
$988$	−13.1627	+	27.5504i	−0.418763	+	0.876497i
$989$	−5.79748	−	47.7466i	−0.184349	−	1.51825i
$990$	−0.953635	−	0.992839i	−0.0303085	−	0.0315545i
$991$	0.963812	+	1.66937i	0.0306165	+	0.0530293i	0.880928	−	0.473251i	$-0.156920\pi$
$991$	0.963812	+	1.66937i	0.0306165	+	0.0530293i	−0.850311	+	0.526280i	$0.823586\pi$
$992$	5.04883	−	8.74482i	0.160300	−	0.277648i
$993$	−22.7995	+	5.61958i	−0.723521	+	0.178332i
$994$	32.0429	+	39.2454i	1.01634	+	1.24479i
$995$	0.251345	−	0.435342i	0.00796816	−	0.0138013i
$996$	−3.13603	−	8.26904i	−0.0993690	−	0.262015i
$997$	11.8994	−	12.3886i	0.376859	−	0.392352i	−0.505579	−	0.862780i	$-0.668721\pi$
$997$	11.8994	−	12.3886i	0.376859	−	0.392352i	0.882438	+	0.470428i	$0.155901\pi$
$998$	−38.8854	−	12.9819i	−1.23090	−	0.410933i
$999$	0.251856	+	0.869506i	0.00796836	+	0.0275100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.b.16.13	✓	384
169.74	even	39	inner	507.2.q.b.412.13	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.16.13	✓	384	1.1	even	1	trivial
507.2.q.b.412.13	yes	384	169.74	even	39	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.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80906 + 0.146043i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.27728 + 0.207579i) q^{4} +(-0.0943821 - 0.0836152i) q^{5} +(-1.45095 - 1.09032i) q^{6} +(1.37395 - 1.43043i) q^{7} +(-1.24405 - 0.306631i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(1.80906 + 0.146043i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.27728 + 0.207579i) q^{4} +(-0.0943821 - 0.0836152i) q^{5} +(-1.45095 - 1.09032i) q^{6} +(1.37395 - 1.43043i) q^{7} +(-1.24405 - 0.306631i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.158532 - 0.165049i) q^{10} +(2.57877 - 5.43463i) q^{11} +(-0.968603 - 0.858107i) q^{12} +(3.50306 - 0.853550i) q^{13} +(2.69446 - 2.38708i) q^{14} +(0.0350813 + 0.121115i) q^{15} +(-4.66067 - 1.55596i) q^{16} +(2.59904 - 2.70589i) q^{17} +(0.643590 + 1.69701i) q^{18} +(-3.27209 + 5.66742i) q^{19} +(-0.103196 - 0.126392i) q^{20} +(-1.92576 + 0.474658i) q^{21} +(5.45884 - 9.45499i) q^{22} +(3.45035 + 5.97619i) q^{23} +(0.887575 + 0.924063i) q^{24} +(-0.600767 - 4.94776i) q^{25} +(6.46192 - 1.03253i) q^{26} +(0.120537 - 0.992709i) q^{27} +(2.05185 - 1.54186i) q^{28} +(3.03677 + 0.245153i) q^{29} +(0.0457764 + 0.224228i) q^{30} +(-0.191516 + 1.57728i) q^{31} +(-5.84671 - 2.49105i) q^{32} +(-5.08417 + 3.21504i) q^{33} +(5.09701 - 4.51555i) q^{34} +(-0.249282 + 0.0201241i) q^{35} +(0.360025 + 1.24295i) q^{36} +(-0.832809 + 0.354827i) q^{37} +(-6.74710 + 9.77486i) q^{38} +(-3.41695 - 1.15086i) q^{39} +(0.0917770 + 0.132962i) q^{40} +(-3.82349 - 2.41783i) q^{41} +(-3.55315 + 0.577443i) q^{42} +(-6.41217 - 2.73197i) q^{43} +(4.42193 - 6.40626i) q^{44} +(0.0350813 - 0.121115i) q^{45} +(5.36913 + 11.3152i) q^{46} +(-3.26305 + 8.60395i) q^{47} +(3.10755 + 3.80605i) q^{48} +(0.123461 + 3.06365i) q^{49} +(-0.364241 - 9.03855i) q^{50} +(-3.64289 + 0.897891i) q^{51} +(4.65158 - 0.363064i) q^{52} +(-6.23519 - 1.53684i) q^{53} +(0.363036 - 1.77827i) q^{54} +(-0.697807 + 0.297308i) q^{55} +(-2.14787 + 1.35823i) q^{56} +(5.79458 - 3.04123i) q^{57} +(5.45790 + 0.886995i) q^{58} +(12.4574 - 4.15890i) q^{59} +(0.0196679 + 0.161980i) q^{60} +(-2.14997 + 7.42254i) q^{61} +(-0.576816 + 2.82543i) q^{62} +(1.88132 + 0.628078i) q^{63} +(-1.51183 - 0.793467i) q^{64} +(-0.401996 - 0.212350i) q^{65} +(-9.66712 + 5.07370i) q^{66} +(1.22980 - 0.199862i) q^{67} +(3.88139 - 2.91668i) q^{68} +(0.277863 - 6.89511i) q^{69} -0.453905 q^{70} +(-0.566725 + 14.0631i) q^{71} +(-0.256289 - 1.25539i) q^{72} +(-1.79985 - 2.60753i) q^{73} +(-1.55842 + 0.520278i) q^{74} +(-2.13665 + 4.50289i) q^{75} +(-5.35582 + 6.55968i) q^{76} +(-4.23078 - 11.1556i) q^{77} +(-6.01340 - 2.58099i) q^{78} +(-2.68314 + 7.07486i) q^{79} +(0.309782 + 0.536558i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-6.56383 - 4.93240i) q^{82} +(6.05139 + 3.17601i) q^{83} +(-2.55827 + 0.206525i) q^{84} +(-0.471556 + 0.0380680i) q^{85} +(-11.2010 - 5.87876i) q^{86} +(-2.43562 - 1.83025i) q^{87} +(-4.87454 + 5.97022i) q^{88} +(6.02395 + 10.4338i) q^{89} +(0.0811523 - 0.213981i) q^{90} +(3.59208 - 6.18362i) q^{91} +(3.16655 + 8.34950i) q^{92} +(1.00487 - 1.23074i) q^{93} +(-7.15961 + 15.0885i) q^{94} +(0.782709 - 0.261307i) q^{95} +(3.61020 + 5.23028i) q^{96} +(-2.50937 - 12.2917i) q^{97} +(-0.224075 + 5.56037i) q^{98} +6.01542 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

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Database

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