LMFDB - Embedded newform 520.2.ca.a.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.8
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.a.381.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.936579 - 1.05963i) q^{2} +(0.700368 - 0.404358i) q^{3} +(-0.245639 + 1.98486i) q^{4} -1.00000 q^{5} +(-1.08442 - 0.363419i) q^{6} +(3.38125 + 1.95217i) q^{7} +(2.33328 - 1.59869i) q^{8} +(-1.17299 + 2.03168i) q^{9} +O(q^{10})$	\(q+(-0.936579 - 1.05963i) q^{2} +(0.700368 - 0.404358i) q^{3} +(-0.245639 + 1.98486i) q^{4} -1.00000 q^{5} +(-1.08442 - 0.363419i) q^{6} +(3.38125 + 1.95217i) q^{7} +(2.33328 - 1.59869i) q^{8} +(-1.17299 + 2.03168i) q^{9} +(0.936579 + 1.05963i) q^{10} +(-0.223776 - 0.387591i) q^{11} +(0.630555 + 1.48946i) q^{12} +(-3.01089 + 1.98356i) q^{13} +(-1.09823 - 5.41124i) q^{14} +(-0.700368 + 0.404358i) q^{15} +(-3.87932 - 0.975117i) q^{16} +(-4.00797 + 6.94201i) q^{17} +(3.25143 - 0.659890i) q^{18} +(-0.861493 + 1.49215i) q^{19} +(0.245639 - 1.98486i) q^{20} +3.15749 q^{21} +(-0.201120 + 0.600130i) q^{22} +(-0.570237 - 0.987679i) q^{23} +(0.987712 - 2.06315i) q^{24} +1.00000 q^{25} +(4.92179 + 1.33268i) q^{26} +4.32338i q^{27} +(-4.70534 + 6.23177i) q^{28} +(8.04039 - 4.64212i) q^{29} +(1.08442 + 0.363419i) q^{30} +5.19873i q^{31} +(2.60003 + 5.02393i) q^{32} +(-0.313451 - 0.180971i) q^{33} +(11.1098 - 2.25477i) q^{34} +(-3.38125 - 1.95217i) q^{35} +(-3.74446 - 2.82728i) q^{36} +(2.59519 + 4.49501i) q^{37} +(2.38799 - 0.484651i) q^{38} +(-1.30666 + 2.60670i) q^{39} +(-2.33328 + 1.59869i) q^{40} +(4.37099 - 2.52359i) q^{41} +(-2.95724 - 3.34578i) q^{42} +(0.587643 + 0.339276i) q^{43} +(0.824282 - 0.348956i) q^{44} +(1.17299 - 2.03168i) q^{45} +(-0.512504 + 1.52928i) q^{46} -8.71152i q^{47} +(-3.11125 + 0.885693i) q^{48} +(4.12190 + 7.13934i) q^{49} +(-0.936579 - 1.05963i) q^{50} +6.48262i q^{51} +(-3.19750 - 6.46344i) q^{52} -11.8993i q^{53} +(4.58119 - 4.04918i) q^{54} +(0.223776 + 0.387591i) q^{55} +(11.0103 - 0.850622i) q^{56} +1.39340i q^{57} +(-12.4494 - 4.17214i) q^{58} +(-4.67021 + 8.08904i) q^{59} +(-0.630555 - 1.48946i) q^{60} +(-6.84304 - 3.95083i) q^{61} +(5.50874 - 4.86902i) q^{62} +(-7.93234 + 4.57974i) q^{63} +(2.88838 - 7.46038i) q^{64} +(3.01089 - 1.98356i) q^{65} +(0.101809 + 0.501636i) q^{66} +(5.35905 + 9.28215i) q^{67} +(-12.7944 - 9.66049i) q^{68} +(-0.798751 - 0.461159i) q^{69} +(1.09823 + 5.41124i) q^{70} +(9.05690 + 5.22901i) q^{71} +(0.511110 + 6.61572i) q^{72} -0.118228i q^{73} +(2.33245 - 6.95988i) q^{74} +(0.700368 - 0.404358i) q^{75} +(-2.75009 - 2.07647i) q^{76} -1.74739i q^{77} +(3.98594 - 1.05680i) q^{78} +17.2905 q^{79} +(3.87932 + 0.975117i) q^{80} +(-1.77078 - 3.06708i) q^{81} +(-6.76786 - 2.26810i) q^{82} -10.1833 q^{83} +(-0.775603 + 6.26717i) q^{84} +(4.00797 - 6.94201i) q^{85} +(-0.190867 - 0.940443i) q^{86} +(3.75415 - 6.50238i) q^{87} +(-1.14177 - 0.546610i) q^{88} +(7.70585 - 4.44897i) q^{89} +(-3.25143 + 0.659890i) q^{90} +(-14.0528 + 0.829158i) q^{91} +(2.10048 - 0.889227i) q^{92} +(2.10215 + 3.64103i) q^{93} +(-9.23100 + 8.15902i) q^{94} +(0.861493 - 1.49215i) q^{95} +(3.85244 + 2.46726i) q^{96} +(7.84192 + 4.52754i) q^{97} +(3.70458 - 11.0542i) q^{98} +1.04995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.936579	−	1.05963i	−0.662261	−	0.749273i
$2$	−0.936579	−	1.05963i	−0.662261	−	0.749273i
$3$	0.700368	−	0.404358i	0.404358	−	0.233456i	−0.284005	−	0.958823i	$-0.591663\pi$
$3$	0.700368	−	0.404358i	0.404358	−	0.233456i	0.688362	+	0.725367i	$0.258330\pi$
$4$	−0.245639	+	1.98486i	−0.122820	+	0.992429i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.08442	−	0.363419i	−0.442713	−	0.148365i
$7$	3.38125	+	1.95217i	1.27799	+	0.737849i	0.976479	−	0.215613i	$-0.0691749\pi$
$7$	3.38125	+	1.95217i	1.27799	+	0.737849i	0.301513	+	0.953462i	$0.402508\pi$
$8$	2.33328	−	1.59869i	0.824939	−	0.565222i
$9$	−1.17299	+	2.03168i	−0.390997	+	0.677226i
$10$	0.936579	+	1.05963i	0.296172	+	0.335085i
$11$	−0.223776	−	0.387591i	−0.0674710	−	0.116863i	0.830316	−	0.557292i	$-0.188160\pi$
$11$	−0.223776	−	0.387591i	−0.0674710	−	0.116863i	−0.897787	+	0.440429i	$0.854826\pi$
$12$	0.630555	+	1.48946i	0.182025	+	0.429969i
$13$	−3.01089	+	1.98356i	−0.835072	+	0.550141i
$13$	−3.01089	+	1.98356i	−0.835072	+	0.550141i
$14$	−1.09823	−	5.41124i	−0.293515	−	1.44621i
$15$	−0.700368	+	0.404358i	−0.180834	+	0.104405i
$16$	−3.87932	−	0.975117i	−0.969831	−	0.243779i
$17$	−4.00797	+	6.94201i	−0.972076	+	1.68369i	−0.282812	+	0.959175i	$0.591267\pi$
$17$	−4.00797	+	6.94201i	−0.972076	+	1.68369i	−0.689264	+	0.724510i	$0.742066\pi$
$18$	3.25143	−	0.659890i	0.766369	−	0.155538i
$19$	−0.861493	+	1.49215i	−0.197640	+	0.342323i	−0.947763	−	0.318976i	$-0.896661\pi$
$19$	−0.861493	+	1.49215i	−0.197640	+	0.342323i	0.750123	+	0.661299i	$0.229994\pi$
$20$	0.245639	−	1.98486i	0.0549266	−	0.443828i
$21$	3.15749			0.689021
$22$	−0.201120	+	0.600130i	−0.0428790	+	0.127948i
$23$	−0.570237	−	0.987679i	−0.118903	−	0.205945i	0.800430	−	0.599426i	$-0.204604\pi$
$23$	−0.570237	−	0.987679i	−0.118903	−	0.205945i	−0.919333	+	0.393480i	$0.871271\pi$
$24$	0.987712	−	2.06315i	0.201616	−	0.421139i
$25$	1.00000			0.200000
$26$	4.92179	+	1.33268i	0.965242	+	0.261359i
$27$			4.32338i			0.832034i
$28$	−4.70534	+	6.23177i	−0.889225	+	1.17769i
$29$	8.04039	−	4.64212i	1.49306	−	0.862020i	0.493094	−	0.869976i	$-0.335866\pi$
$29$	8.04039	−	4.64212i	1.49306	−	0.862020i	0.999968	+	0.00795571i	$0.00253241\pi$
$30$	1.08442	+	0.363419i	0.197987	+	0.0663510i
$31$			5.19873i			0.933720i	0.884331	+	0.466860i	$0.154615\pi$
$31$			5.19873i			0.933720i	−0.884331	+	0.466860i	$0.845385\pi$
$32$	2.60003	+	5.02393i	0.459624	+	0.888113i
$33$	−0.313451	−	0.180971i	−0.0545648	−	0.0315030i
$34$	11.1098	−	2.25477i	1.90531	−	0.386690i
$35$	−3.38125	−	1.95217i	−0.571535	−	0.329976i
$36$	−3.74446	−	2.82728i	−0.624077	−	0.471213i
$37$	2.59519	+	4.49501i	0.426647	+	0.738974i	0.996573	−	0.0827219i	$-0.0263613\pi$
$37$	2.59519	+	4.49501i	0.426647	+	0.738974i	−0.569926	+	0.821696i	$0.693028\pi$
$38$	2.38799	−	0.484651i	0.387382	−	0.0786207i
$39$	−1.30666	+	2.60670i	−0.209234	+	0.417406i
$40$	−2.33328	+	1.59869i	−0.368924	+	0.252775i
$41$	4.37099	−	2.52359i	0.682635	−	0.394119i	−0.118212	−	0.992988i	$-0.537716\pi$
$41$	4.37099	−	2.52359i	0.682635	−	0.394119i	0.800847	+	0.598869i	$0.204383\pi$
$42$	−2.95724	−	3.34578i	−0.456312	−	0.516265i
$43$	0.587643	+	0.339276i	0.0896147	+	0.0517391i	0.544138	−	0.838996i	$-0.316857\pi$
$43$	0.587643	+	0.339276i	0.0896147	+	0.0517391i	−0.454523	+	0.890735i	$0.650190\pi$
$44$	0.824282	−	0.348956i	0.124265	−	0.0526071i
$45$	1.17299	−	2.03168i	0.174859	−	0.302865i
$46$	−0.512504	+	1.52928i	−0.0755646	+	0.225480i
$47$		−	8.71152i		−	1.27071i	−0.772222	−	0.635353i	$-0.780855\pi$
$47$		−	8.71152i		−	1.27071i	0.772222	−	0.635353i	$-0.219145\pi$
$48$	−3.11125	+	0.885693i	−0.449070	+	0.127839i
$49$	4.12190	+	7.13934i	0.588843	+	1.01991i
$50$	−0.936579	−	1.05963i	−0.132452	−	0.149855i
$51$			6.48262i			0.907748i
$52$	−3.19750	−	6.46344i	−0.443413	−	0.896317i
$53$		−	11.8993i		−	1.63450i	−0.576286	−	0.817248i	$-0.695499\pi$
$53$		−	11.8993i		−	1.63450i	0.576286	−	0.817248i	$-0.304501\pi$
$54$	4.58119	−	4.04918i	0.623420	−	0.551024i
$55$	0.223776	+	0.387591i	0.0301739	+	0.0522628i
$56$	11.0103	−	0.850622i	1.47131	−	0.113669i
$57$			1.39340i			0.184561i
$58$	−12.4494	−	4.17214i	−1.63469	−	0.547829i
$59$	−4.67021	+	8.08904i	−0.608009	+	1.05310i	0.383559	+	0.923516i	$0.374698\pi$
$59$	−4.67021	+	8.08904i	−0.608009	+	1.05310i	−0.991568	+	0.129586i	$0.958635\pi$
$60$	−0.630555	−	1.48946i	−0.0814043	−	0.192288i
$61$	−6.84304	−	3.95083i	−0.876162	−	0.505852i	−0.00677098	−	0.999977i	$-0.502155\pi$
$61$	−6.84304	−	3.95083i	−0.876162	−	0.505852i	−0.869391	+	0.494125i	$0.835489\pi$
$62$	5.50874	−	4.86902i	0.699611	−	0.618367i
$63$	−7.93234	+	4.57974i	−0.999381	+	0.576993i
$64$	2.88838	−	7.46038i	0.361048	−	0.932547i
$65$	3.01089	−	1.98356i	0.373455	−	0.246031i
$66$	0.101809	+	0.501636i	0.0125318	+	0.0617472i
$67$	5.35905	+	9.28215i	0.654713	+	1.13400i	0.981966	+	0.189059i	$0.0605437\pi$
$67$	5.35905	+	9.28215i	0.654713	+	1.13400i	−0.327253	+	0.944937i	$0.606123\pi$
$68$	−12.7944	−	9.66049i	−1.55155	−	1.17151i
$69$	−0.798751	−	0.461159i	−0.0961583	−	0.0555170i
$70$	1.09823	+	5.41124i	0.131264	+	0.646766i
$71$	9.05690	+	5.22901i	1.07486	+	0.620569i	0.929504	−	0.368811i	$-0.120235\pi$
$71$	9.05690	+	5.22901i	1.07486	+	0.620569i	0.145352	+	0.989380i	$0.453568\pi$
$72$	0.511110	+	6.61572i	0.0602349	+	0.779670i
$73$		−	0.118228i		−	0.0138376i	−0.999976	−	0.00691879i	$-0.997798\pi$
$73$		−	0.118228i		−	0.0138376i	0.999976	−	0.00691879i	$-0.00220234\pi$
$74$	2.33245	−	6.95988i	0.271142	−	0.809069i
$75$	0.700368	−	0.404358i	0.0808715	−	0.0466912i
$76$	−2.75009	−	2.07647i	−0.315457	−	0.238188i
$77$		−	1.74739i		−	0.199134i
$78$	3.98594	−	1.05680i	0.451319	−	0.119659i
$79$	17.2905			1.94533			0.972666	−	0.232210i	$-0.0745957\pi$
$79$	17.2905			1.94533			0.972666	+	0.232210i	$0.0745957\pi$
$80$	3.87932	+	0.975117i	0.433721	+	0.109021i
$81$	−1.77078	−	3.06708i	−0.196753	−	0.340787i
$82$	−6.76786	−	2.26810i	−0.747385	−	0.250470i
$83$	−10.1833			−1.11776			−0.558879	−	0.829250i	$-0.688768\pi$
$83$	−10.1833			−1.11776			−0.558879	+	0.829250i	$0.688768\pi$
$84$	−0.775603	+	6.26717i	−0.0846252	+	0.683805i
$85$	4.00797	−	6.94201i	0.434726	−	0.752967i
$86$	−0.190867	−	0.940443i	−0.0205817	−	0.101411i
$87$	3.75415	−	6.50238i	0.402488	−	0.697129i
$88$	−1.14177	−	0.546610i	−0.121713	−	0.0582689i
$89$	7.70585	−	4.44897i	0.816818	−	0.471590i	−0.0324998	−	0.999472i	$-0.510347\pi$
$89$	7.70585	−	4.44897i	0.816818	−	0.471590i	0.849318	+	0.527882i	$0.177013\pi$
$90$	−3.25143	+	0.659890i	−0.342731	+	0.0695585i
$91$	−14.0528	+	0.829158i	−1.47314	+	0.0869194i
$92$	2.10048	−	0.889227i	0.218990	−	0.0927083i
$93$	2.10215	+	3.64103i	0.217982	+	0.377557i
$94$	−9.23100	+	8.15902i	−0.952105	+	0.841539i
$95$	0.861493	−	1.49215i	0.0883873	−	0.153091i
$96$	3.85244	+	2.46726i	0.393188	+	0.251813i
$97$	7.84192	+	4.52754i	0.796227	+	0.459702i	0.842150	−	0.539243i	$-0.181290\pi$
$97$	7.84192	+	4.52754i	0.796227	+	0.459702i	−0.0459234	+	0.998945i	$0.514623\pi$
$98$	3.70458	−	11.0542i	0.374220	−	1.11665i
$99$	1.04995			0.105524
$100$	−0.245639	+	1.98486i	−0.0245639	+	0.198486i
$101$	0.0227944	−	0.0131604i	0.00226813	−	0.00130951i	−0.498866	−	0.866679i	$-0.666250\pi$
$101$	0.0227944	−	0.0131604i	0.00226813	−	0.00130951i	0.501134	+	0.865370i	$0.332917\pi$
$102$	6.86919	−	6.07148i	0.680151	−	0.601167i
$103$	−13.0895			−1.28974			−0.644872	−	0.764291i	$-0.723089\pi$
$103$	−13.0895			−1.28974			−0.644872	+	0.764291i	$0.723089\pi$
$104$	−3.85415	+	9.44169i	−0.377931	+	0.925834i
$105$	−3.15749			−0.308140
$106$	−12.6089	+	11.1446i	−1.22468	+	1.08246i
$107$	−4.81312	+	2.77886i	−0.465302	+	0.268642i	−0.714271	−	0.699869i	$-0.753242\pi$
$107$	−4.81312	+	2.77886i	−0.465302	+	0.268642i	0.248969	+	0.968511i	$0.419908\pi$
$108$	−8.58129	−	1.06199i	−0.825735	−	0.102190i
$109$	−0.584348			−0.0559704			−0.0279852	−	0.999608i	$-0.508909\pi$
$109$	−0.584348			−0.0559704			−0.0279852	+	0.999608i	$0.508909\pi$
$110$	0.201120	−	0.600130i	0.0191761	−	0.0572201i
$111$	3.63518	+	2.09877i	0.345036	+	0.199207i
$112$	−11.2134	−	10.8702i	−1.05956	−	1.02714i
$113$	−5.65275	+	9.79084i	−0.531766	+	0.921045i	0.467547	+	0.883968i	$0.345138\pi$
$113$	−5.65275	+	9.79084i	−0.531766	+	0.921045i	−0.999312	+	0.0370767i	$0.988195\pi$
$114$	1.47650	−	1.30503i	0.138287	−	0.122228i
$115$	0.570237	+	0.987679i	0.0531749	+	0.0921016i
$116$	7.23892	+	17.0993i	0.672117	+	1.58763i
$117$	−0.498213	−	8.44386i	−0.0460598	−	0.780636i
$118$	12.9454	−	2.62732i	1.19172	−	0.241865i
$119$	−27.1039	+	15.6485i	−2.48461	+	1.43449i
$120$	−0.987712	+	2.06315i	−0.0901653	+	0.188339i
$121$	5.39985	−	9.35281i	0.490895	−	0.850256i
$122$	2.22262	+	10.9514i	0.201227	+	0.991491i
$123$	2.04087	−	3.53489i	0.184019	−	0.318730i
$124$	−10.3187	−	1.27701i	−0.926651	−	0.114679i
$125$	−1.00000			−0.0894427
$126$	12.2821	+	4.11607i	1.09418	+	0.366689i
$127$	−5.85718	−	10.1449i	−0.519740	−	0.900217i	−0.999737	−	0.0229463i	$-0.992695\pi$
$127$	−5.85718	−	10.1449i	−0.519740	−	0.900217i	0.479996	−	0.877271i	$-0.340638\pi$
$128$	−10.6105	+	3.92661i	−0.937840	+	0.347067i
$129$	0.548755			0.0483152
$130$	−4.92179	−	1.33268i	−0.431669	−	0.116883i
$131$		−	11.7108i		−	1.02318i	−0.859229	−	0.511591i	$-0.829056\pi$
$131$		−	11.7108i		−	1.02318i	0.859229	−	0.511591i	$-0.170944\pi$
$132$	0.436198	−	0.577702i	0.0379661	−	0.0502825i
$133$	−5.82584	+	3.36355i	−0.505165	+	0.291657i
$134$	4.81649	−	14.3721i	0.416081	−	1.24156i
$135$		−	4.32338i		−	0.372097i
$136$	1.74640	+	22.6052i	0.149753	+	1.93838i
$137$	−6.49995	−	3.75275i	−0.555329	−	0.320619i	0.195940	−	0.980616i	$-0.437224\pi$
$137$	−6.49995	−	3.75275i	−0.555329	−	0.320619i	−0.751268	+	0.659997i	$0.770558\pi$
$138$	0.259435	+	1.27829i	0.0220846	+	0.108816i
$139$	−7.07331	−	4.08378i	−0.599950	−	0.346381i	0.169072	−	0.985604i	$-0.445923\pi$
$139$	−7.07331	−	4.08378i	−0.599950	−	0.346381i	−0.769022	+	0.639222i	$0.779256\pi$
$140$	4.70534	−	6.23177i	0.397674	−	0.526681i
$141$	−3.52257	−	6.10127i	−0.296654	−	0.513819i
$142$	−2.94169	−	14.4944i	−0.246861	−	1.21634i
$143$	1.44258	+	0.723122i	0.120634	+	0.0604705i
$144$	6.53153	−	6.73773i	0.544294	−	0.561478i
$145$	−8.04039	+	4.64212i	−0.667718	+	0.385507i
$146$	−0.125279	+	0.110730i	−0.0103681	+	0.00916410i
$147$	5.77369	+	3.33344i	0.476206	+	0.274938i
$148$	−9.55943	+	4.04694i	−0.785780	+	0.332656i
$149$	2.65141	−	4.59238i	0.217212	−	0.376223i	−0.736742	−	0.676173i	$-0.763637\pi$
$149$	2.65141	−	4.59238i	0.217212	−	0.376223i	0.953955	+	0.299951i	$0.0969703\pi$
$150$	−1.08442	−	0.363419i	−0.0885425	−	0.0296731i
$151$		−	4.32338i		−	0.351831i	−0.984405	−	0.175916i	$-0.943711\pi$
$151$		−	4.32338i		−	0.351831i	0.984405	−	0.175916i	$-0.0562886\pi$
$152$	0.375381	+	4.85886i	0.0304474	+	0.394106i
$153$	−9.40262	−	16.2858i	−0.760157	−	1.31663i
$154$	−1.85159	+	1.63657i	−0.149205	+	0.131879i
$155$		−	5.19873i		−	0.417572i
$156$	−4.85296	−	3.23385i	−0.388548	−	0.258915i
$157$			9.05130i			0.722372i	0.932494	+	0.361186i	$0.117628\pi$
$157$			9.05130i			0.722372i	−0.932494	+	0.361186i	$0.882372\pi$
$158$	−16.1939	−	18.3215i	−1.28832	−	1.45758i
$159$	−4.81158	−	8.33390i	−0.381583	−	0.660921i
$160$	−2.60003	−	5.02393i	−0.205550	−	0.397176i
$161$		−	4.45279i		−	0.350929i
$162$	−1.59150	+	4.74894i	−0.125040	+	0.373112i
$163$	−7.29415	+	12.6338i	−0.571322	+	0.989558i	0.425109	+	0.905142i	$0.360236\pi$
$163$	−7.29415	+	12.6338i	−0.571322	+	0.989558i	−0.996431	+	0.0844159i	$0.973098\pi$
$164$	3.93529	+	9.29570i	0.307295	+	0.725872i
$165$	0.313451	+	0.180971i	0.0244021	+	0.0140886i
$166$	9.53742	+	10.7905i	0.740247	+	0.837505i
$167$	−3.06989	+	1.77240i	−0.237556	+	0.137153i	−0.614053	−	0.789265i	$-0.710462\pi$
$167$	−3.06989	+	1.77240i	−0.237556	+	0.137153i	0.376497	+	0.926418i	$0.377128\pi$
$168$	7.36731	−	5.04785i	0.568400	−	0.389450i
$169$	5.13096	−	11.9446i	0.394689	−	0.918815i
$170$	−11.1098	+	2.25477i	−0.852080	+	0.172933i
$171$	−2.02104	−	3.50055i	−0.154553	−	0.267694i
$172$	−0.817762	+	1.08305i	−0.0623538	+	0.0825816i
$173$	9.91643	+	5.72526i	0.753932	+	0.435283i	0.827113	−	0.562036i	$-0.189982\pi$
$173$	9.91643	+	5.72526i	0.753932	+	0.435283i	−0.0731806	+	0.997319i	$0.523315\pi$
$174$	−10.4062	+	2.11198i	−0.788892	+	0.160109i
$175$	3.38125	+	1.95217i	0.255598	+	0.147570i
$176$	0.490152	+	1.72180i	0.0369466	+	0.129786i
$177$			7.55374i			0.567774i
$178$	−11.9314	−	3.99855i	−0.894297	−	0.299704i
$179$	0.746881	−	0.431212i	0.0558245	−	0.0322303i	−0.471828	−	0.881691i	$-0.656406\pi$
$179$	0.746881	−	0.431212i	0.0558245	−	0.0322303i	0.527652	+	0.849460i	$0.323072\pi$
$180$	3.74446	+	2.82728i	0.279096	+	0.210733i
$181$		−	4.43168i		−	0.329404i	−0.986343	−	0.164702i	$-0.947334\pi$
$181$		−	4.43168i		−	0.329404i	0.986343	−	0.164702i	$-0.0526663\pi$
$182$	14.0402	+	14.1142i	1.04073	+	1.04622i
$183$	−6.39020			−0.472377
$184$	−2.90951	−	1.39290i	−0.214492	−	0.102686i
$185$	−2.59519	−	4.49501i	−0.190802	−	0.330479i
$186$	1.88932	−	5.63761i	0.138532	−	0.413370i
$187$	3.58755			0.262348
$188$	17.2911	+	2.13989i	1.26108	+	0.156067i
$189$	−8.43994	+	14.6184i	−0.613915	+	1.06333i
$190$	−2.38799	+	0.484651i	−0.173243	+	0.0351603i
$191$	10.8557	−	18.8026i	0.785490	−	1.36051i	−0.143216	−	0.989691i	$-0.545744\pi$
$191$	10.8557	−	18.8026i	0.785490	−	1.36051i	0.928706	−	0.370817i	$-0.120922\pi$
$192$	−0.993730	−	6.39295i	−0.0717163	−	0.461371i
$193$	14.6746	−	8.47239i	1.05630	−	0.609856i	0.131894	−	0.991264i	$-0.457894\pi$
$193$	14.6746	−	8.47239i	1.05630	−	0.609856i	0.924407	+	0.381408i	$0.124561\pi$
$194$	−2.54706	−	12.5499i	−0.182868	−	0.901034i
$195$	1.30666	−	2.60670i	0.0935722	−	0.186670i
$196$	−15.1831	+	6.42768i	−1.08450	+	0.459120i
$197$	7.87779	+	13.6447i	0.561269	+	0.972147i	0.997386	+	0.0722567i	$0.0230201\pi$
$197$	7.87779	+	13.6447i	0.561269	+	0.972147i	−0.436117	+	0.899890i	$0.643647\pi$
$198$	−0.983359	−	1.11256i	−0.0698843	−	0.0790660i
$199$	−3.09592	+	5.36228i	−0.219464	+	0.380122i	−0.954644	−	0.297749i	$-0.903764\pi$
$199$	−3.09592	+	5.36228i	−0.219464	+	0.380122i	0.735180	+	0.677871i	$0.237097\pi$
$200$	2.33328	−	1.59869i	0.164988	−	0.113044i
$201$	7.50662	+	4.33395i	0.529476	+	0.305693i
$202$	−0.0352939	−	0.0118280i	−0.00248327	−	0.000832213i
$203$	36.2487			2.54416
$204$	−12.8671	−	1.59238i	−0.900876	−	0.111489i
$205$	−4.37099	+	2.52359i	−0.305283	+	0.176255i
$206$	12.2593	+	13.8700i	0.854147	+	0.966370i
$207$	2.67553			0.185962
$208$	13.6144	−	4.75891i	0.943991	−	0.329971i
$209$	0.771125			0.0533399
$210$	2.95724	+	3.34578i	0.204069	+	0.230881i
$211$	−1.17103	+	0.676093i	−0.0806169	+	0.0465442i	−0.539767	−	0.841815i	$-0.681487\pi$
$211$	−1.17103	+	0.676093i	−0.0806169	+	0.0465442i	0.459150	+	0.888359i	$0.348154\pi$
$212$	23.6184	+	2.92294i	1.62212	+	0.200748i
$213$	8.45755			0.579502
$214$	7.45243	+	2.49752i	0.509438	+	0.170727i
$215$	−0.587643	−	0.339276i	−0.0400769	−	0.0231384i
$216$	6.91174	+	10.0876i	0.470284	+	0.686377i
$217$	−10.1488	+	17.5782i	−0.688944	+	1.19329i
$218$	0.547288	+	0.619194i	0.0370670	+	0.0419371i
$219$	−0.0478065	−	0.0828034i	−0.00323047	−	0.00559533i
$220$	−0.824282	+	0.348956i	−0.0555731	+	0.0235266i
$221$	−1.70234	−	28.8517i	−0.114512	−	1.94078i
$222$	−1.18071	−	5.81762i	−0.0792439	−	0.390453i
$223$	9.67467	−	5.58567i	0.647864	−	0.374044i	−0.139774	−	0.990183i	$-0.544637\pi$
$223$	9.67467	−	5.58567i	0.647864	−	0.374044i	0.787637	+	0.616139i	$0.211304\pi$
$224$	−1.01620	+	22.0628i	−0.0678975	+	1.47414i
$225$	−1.17299	+	2.03168i	−0.0781993	+	0.135445i
$226$	15.6689	−	3.18007i	1.04228	−	0.211535i
$227$	−5.19436	+	8.99690i	−0.344762	+	0.597145i	−0.985311	−	0.170772i	$-0.945374\pi$
$227$	−5.19436	+	8.99690i	−0.344762	+	0.597145i	0.640548	+	0.767918i	$0.278707\pi$
$228$	−2.76571	−	0.342275i	−0.183164	−	0.0226677i
$229$	23.1100			1.52715			0.763574	−	0.645720i	$-0.223443\pi$
$229$	23.1100			1.52715			0.763574	+	0.645720i	$0.223443\pi$
$230$	0.512504	−	1.52928i	0.0337935	−	0.100838i
$231$	−0.706571	−	1.22382i	−0.0464889	−	0.0805212i
$232$	11.3392	−	23.6854i	0.744452	−	1.55503i
$233$	−8.57015			−0.561449			−0.280725	−	0.959788i	$-0.590575\pi$
$233$	−8.57015			−0.561449			−0.280725	+	0.959788i	$0.590575\pi$
$234$	−8.48077	+	8.43627i	−0.554405	+	0.551496i
$235$			8.71152i			0.568277i
$236$	−14.9084	−	11.2567i	−0.970454	−	0.732748i
$237$	12.1097	−	6.99154i	0.786609	−	0.454149i
$238$	41.9666	+	14.0642i	2.72029	+	0.911644i
$239$		−	1.02636i		−	0.0663899i	−0.999449	−	0.0331950i	$-0.989432\pi$
$239$		−	1.02636i		−	0.0663899i	0.999449	−	0.0331950i	$-0.0105682\pi$
$240$	3.11125	−	0.885693i	0.200830	−	0.0571712i
$241$	14.2112	+	8.20484i	0.915424	+	0.528520i	0.882172	−	0.470927i	$-0.156080\pi$
$241$	14.2112	+	8.20484i	0.915424	+	0.528520i	0.0332518	+	0.999447i	$0.489414\pi$
$242$	−14.9679	+	3.03780i	−0.962175	+	0.195277i
$243$	−13.7129	−	7.91712i	−0.879680	−	0.507883i
$244$	9.52276	−	12.6120i	0.609632	−	0.807400i
$245$	−4.12190	−	7.13934i	−0.263338	−	0.456115i
$246$	−5.65712	+	1.14813i	−0.360685	+	0.0732023i
$247$	−0.365908	−	6.20153i	−0.0232822	−	0.394594i
$248$	8.31116	+	12.1301i	0.527759	+	0.770262i
$249$	−7.13202	+	4.11768i	−0.451974	+	0.260947i
$250$	0.936579	+	1.05963i	0.0592345	+	0.0670170i
$251$	−1.63097	−	0.941643i	−0.102946	−	0.0594360i	0.447643	−	0.894212i	$-0.352264\pi$
$251$	−1.63097	−	0.941643i	−0.102946	−	0.0594360i	−0.550589	+	0.834776i	$0.685597\pi$
$252$	−7.14164	−	16.8695i	−0.449881	−	1.06268i
$253$	−0.255211	+	0.442038i	−0.0160449	+	0.0277907i
$254$	−5.26418	+	15.7080i	−0.330304	+	0.985606i
$255$		−	6.48262i		−	0.405957i
$256$	14.0983	+	7.56559i	0.881143	+	0.472849i
$257$	−8.29410	−	14.3658i	−0.517372	−	0.896114i	−0.999796	−	0.0201769i	$-0.993577\pi$
$257$	−8.29410	−	14.3658i	−0.517372	−	0.896114i	0.482424	−	0.875938i	$-0.339756\pi$
$258$	−0.513952	−	0.581478i	−0.0319973	−	0.0362012i
$259$			20.2650i			1.25920i
$260$	3.19750	+	6.46344i	0.198300	+	0.400845i
$261$			21.7806i			1.34819i
$262$	−12.4092	+	10.9681i	−0.766642	+	0.677613i
$263$	10.2539	+	17.7602i	0.632281	+	1.09514i	0.987084	+	0.160202i	$0.0512147\pi$
$263$	10.2539	+	17.7602i	0.632281	+	1.09514i	−0.354803	+	0.934941i	$0.615452\pi$
$264$	−1.02068	+	0.0788550i	−0.0628188	+	0.00485319i
$265$			11.8993i			0.730969i
$266$	9.02049	+	3.02302i	0.553082	+	0.185353i
$267$	3.59795	−	6.23184i	0.220191	−	0.381382i
$268$	−19.7401	+	8.35690i	−1.20582	+	0.510479i
$269$	4.99021	+	2.88110i	0.304258	+	0.175664i	0.644354	−	0.764727i	$-0.277126\pi$
$269$	4.99021	+	2.88110i	0.304258	+	0.175664i	−0.340096	+	0.940391i	$0.610460\pi$
$270$	−4.58119	+	4.04918i	−0.278802	+	0.246425i
$271$	−8.20521	+	4.73728i	−0.498431	+	0.287769i	−0.728065	−	0.685508i	$-0.759580\pi$
$271$	−8.20521	+	4.73728i	−0.498431	+	0.287769i	0.229634	+	0.973277i	$0.426247\pi$
$272$	22.3175	−	23.0221i	1.35320	−	1.39592i
$273$	−9.50687	+	6.26308i	−0.575382	+	0.379059i
$274$	2.11119	+	10.4023i	0.127542	+	0.628426i
$275$	−0.223776	−	0.387591i	−0.0134942	−	0.0233726i
$276$	1.11154	−	1.47213i	0.0669068	−	0.0886118i
$277$	−2.14086	−	1.23602i	−0.128632	−	0.0742655i	0.434303	−	0.900767i	$-0.356995\pi$
$277$	−2.14086	−	1.23602i	−0.128632	−	0.0742655i	−0.562935	+	0.826501i	$0.690328\pi$
$278$	2.29741	+	11.3199i	0.137790	+	0.678921i
$279$	−10.5621	−	6.09806i	−0.632339	−	0.365081i
$280$	−11.0103	+	0.850622i	−0.657992	+	0.0508344i
$281$			5.80779i			0.346464i	0.984881	+	0.173232i	$0.0554210\pi$
$281$			5.80779i			0.346464i	−0.984881	+	0.173232i	$0.944579\pi$
$282$	−3.16593	+	9.44694i	−0.188529	+	0.562557i
$283$	13.4435	−	7.76159i	0.799131	−	0.461379i	−0.0440362	−	0.999030i	$-0.514022\pi$
$283$	13.4435	−	7.76159i	0.799131	−	0.461379i	0.843167	+	0.537651i	$0.180688\pi$
$284$	−12.6036	+	16.6922i	−0.747884	+	0.990501i
$285$		−	1.39340i		−	0.0825382i
$286$	−0.584844	−	2.20586i	−0.0345825	−	0.130435i
$287$	19.7059			1.16320
$288$	−13.2568	−	0.610598i	−0.781165	−	0.0359798i
$289$	−23.6277	−	40.9244i	−1.38986	−	2.40732i
$290$	12.4494	+	4.17214i	0.731054	+	0.244996i
$291$	7.32297			0.429280
$292$	0.234667	+	0.0290415i	0.0137328	+	0.00169953i
$293$	15.6517	−	27.1095i	0.914381	−	1.58375i	0.106575	−	0.994305i	$-0.466012\pi$
$293$	15.6517	−	27.1095i	0.914381	−	1.58375i	0.807806	−	0.589449i	$-0.200655\pi$
$294$	−1.87530	−	9.24002i	−0.109370	−	0.538889i
$295$	4.67021	−	8.08904i	0.271910	−	0.470962i
$296$	13.2414	+	6.33919i	0.769642	+	0.368458i
$297$	1.67570	−	0.967467i	0.0972341	−	0.0561381i
$298$	−7.34949	+	1.49161i	−0.425745	+	0.0864065i
$299$	3.67605	+	1.84270i	0.212591	+	0.106566i
$300$	0.630555	+	1.48946i	0.0364051	+	0.0859938i
$301$	1.32464	+	2.29435i	0.0763512	+	0.132244i
$302$	−4.58119	+	4.04918i	−0.263618	+	0.233004i
$303$	0.0106430	−	0.0184342i	0.000611424	−	0.00105902i
$304$	4.79703	−	4.94847i	0.275129	−	0.283814i
$305$	6.84304	+	3.95083i	0.391832	+	0.226224i
$306$	−8.45067	+	25.2163i	−0.483093	+	1.44152i
$307$	3.84349			0.219359			0.109680	−	0.993967i	$-0.465018\pi$
$307$	3.84349			0.219359			0.109680	+	0.993967i	$0.465018\pi$
$308$	3.46832	+	0.429227i	0.197626	+	0.0244575i
$309$	−9.16744	+	5.29283i	−0.521518	+	0.301098i
$310$	−5.50874	+	4.86902i	−0.312876	+	0.276542i
$311$	−21.8342			−1.23810			−0.619052	−	0.785350i	$-0.712483\pi$
$311$	−21.8342			−1.23810			−0.619052	+	0.785350i	$0.712483\pi$
$312$	1.11849	+	8.17111i	0.0633222	+	0.462598i
$313$	10.5613			0.596961			0.298481	−	0.954416i	$-0.403520\pi$
$313$	10.5613			0.596961			0.298481	+	0.954416i	$0.403520\pi$
$314$	9.59104	−	8.47726i	0.541254	−	0.478399i
$315$	7.93234	−	4.57974i	0.446937	−	0.258039i
$316$	−4.24722	+	34.3192i	−0.238925	+	1.93060i
$317$	−19.3125			−1.08470			−0.542350	−	0.840153i	$-0.682465\pi$
$317$	−19.3125			−1.08470			−0.542350	+	0.840153i	$0.682465\pi$
$318$	−4.32444	+	12.9039i	−0.242502	+	0.723612i
$319$	−3.59849	−	2.07759i	−0.201477	−	0.116323i
$320$	−2.88838	+	7.46038i	−0.161466	+	0.417048i
$321$	−2.24730	+	3.89244i	−0.125432	+	0.217255i
$322$	−4.71831	+	4.17039i	−0.262941	+	0.232407i
$323$	−6.90568	−	11.9610i	−0.384242	−	0.665527i
$324$	6.52269	−	2.76135i	0.362372	−	0.153408i
$325$	−3.01089	+	1.98356i	−0.167014	+	0.110028i
$326$	20.2188	−	4.10347i	1.11981	−	0.227270i
$327$	−0.409259	+	0.236286i	−0.0226321	+	0.0130666i
$328$	6.16430	−	12.8761i	0.340367	−	0.710964i
$329$	17.0063	−	29.4558i	0.937589	−	1.62395i
$330$	−0.101809	−	0.501636i	−0.00560440	−	0.0276142i
$331$	10.6242	−	18.4017i	0.583960	−	1.01145i	−0.411044	−	0.911615i	$-0.634836\pi$
$331$	10.6242	−	18.4017i	0.583960	−	1.01145i	0.995004	−	0.0998329i	$-0.0318308\pi$
$332$	2.50140	−	20.2123i	0.137282	−	1.10929i
$333$	−12.1765			−0.667270
$334$	4.75329	+	1.59296i	0.260089	+	0.0871629i
$335$	−5.35905	−	9.28215i	−0.292796	−	0.507138i
$336$	−12.2489	−	3.07892i	−0.668234	−	0.167969i
$337$	−22.4148			−1.22101			−0.610506	−	0.792012i	$-0.709034\pi$
$337$	−22.4148			−1.22101			−0.610506	+	0.792012i	$0.709034\pi$
$338$	−17.4624	+	5.75013i	−0.949830	+	0.312766i
$339$			9.14292i			0.496575i
$340$	12.7944	+	9.66049i	0.693874	+	0.523914i
$341$	2.01498	−	1.16335i	0.109117	−	0.0629990i
$342$	−1.81643	+	5.42011i	−0.0982212	+	0.293086i
$343$			4.85619i			0.262210i
$344$	1.91353	−	0.147833i	0.103171	−	0.00797065i
$345$	0.798751	+	0.461159i	0.0430033	+	0.0248280i
$346$	−3.22086	−	15.8699i	−0.173155	−	0.853172i
$347$	30.6557	+	17.6991i	1.64569	+	0.950137i	0.978759	+	0.205015i	$0.0657243\pi$
$347$	30.6557	+	17.6991i	1.64569	+	0.950137i	0.666928	+	0.745123i	$0.267609\pi$
$348$	11.9841	+	9.04870i	0.642418	+	0.485061i
$349$	4.80203	+	8.31737i	0.257047	+	0.445219i	0.965450	−	0.260590i	$-0.0839171\pi$
$349$	4.80203	+	8.31737i	0.257047	+	0.445219i	−0.708402	+	0.705809i	$0.750584\pi$
$350$	−1.09823	−	5.41124i	−0.0587029	−	0.289243i
$351$	−8.57568	−	13.0172i	−0.457736	−	0.694808i
$352$	1.36541	−	2.13198i	0.0727764	−	0.113635i
$353$	11.4605	−	6.61673i	0.609981	−	0.352173i	−0.162977	−	0.986630i	$-0.552110\pi$
$353$	11.4605	−	6.61673i	0.609981	−	0.352173i	0.772958	+	0.634457i	$0.218776\pi$
$354$	8.00418	−	7.07467i	0.425417	−	0.376015i
$355$	−9.05690	−	5.22901i	−0.480691	−	0.277527i
$356$	6.93772	+	16.3879i	0.367699	+	0.868555i
$357$	−12.6551	+	21.9193i	−0.669781	+	1.16009i
$358$	−1.15644	−	0.387555i	−0.0611197	−	0.0204829i
$359$			34.1706i			1.80345i	0.432307	+	0.901726i	$0.357700\pi$
$359$			34.1706i			1.80345i	−0.432307	+	0.901726i	$0.642300\pi$
$360$	−0.511110	−	6.61572i	−0.0269379	−	0.348679i
$361$	8.01566	+	13.8835i	0.421877	+	0.730712i
$362$	−4.69595	+	4.15062i	−0.246814	+	0.218152i
$363$		−	8.73388i		−	0.458410i
$364$	1.80616	−	28.0965i	0.0946686	−	1.47266i
$365$			0.118228i			0.00618836i
$366$	5.98493	+	6.77126i	0.312837	+	0.353939i
$367$	7.52014	+	13.0253i	0.392548	+	0.679913i	0.992785	−	0.119909i	$-0.0382603\pi$
$367$	7.52014	+	13.0253i	0.392548	+	0.679913i	−0.600237	+	0.799822i	$0.704927\pi$
$368$	1.24903	+	4.38757i	0.0651102	+	0.228718i
$369$			11.8406i			0.616397i
$370$	−2.33245	+	6.95988i	−0.121258	+	0.361827i
$371$	23.2294	−	40.2345i	1.20601	−	2.08887i
$372$	−7.74329	+	3.27809i	−0.401471	+	0.169961i
$373$	−5.64614	−	3.25980i	−0.292346	−	0.168786i	0.346653	−	0.937993i	$-0.387318\pi$
$373$	−5.64614	−	3.25980i	−0.292346	−	0.168786i	−0.638999	+	0.769207i	$0.720651\pi$
$374$	−3.36003	−	3.80148i	−0.173743	−	0.196570i
$375$	−0.700368	+	0.404358i	−0.0361668	+	0.0208809i
$376$	−13.9270	−	20.3264i	−0.718231	−	1.04825i
$377$	−15.0008	+	29.9255i	−0.772581	+	1.54124i
$378$	23.3948	−	4.74807i	1.20330	−	0.244214i
$379$	−6.04540	−	10.4709i	−0.310531	−	0.537856i	0.667946	−	0.744210i	$-0.267174\pi$
$379$	−6.04540	−	10.4709i	−0.310531	−	0.537856i	−0.978477	+	0.206354i	$0.933840\pi$
$380$	2.75009	+	2.07647i	0.141077	+	0.106521i
$381$	−8.20436	−	4.73679i	−0.420322	−	0.242673i
$382$	−30.0910	+	6.10709i	−1.53959	+	0.312466i
$383$	1.57440	+	0.908980i	0.0804480	+	0.0464467i	0.539684	−	0.841867i	$-0.318544\pi$
$383$	1.57440	+	0.908980i	0.0804480	+	0.0464467i	−0.459236	+	0.888314i	$0.651877\pi$
$384$	−5.84347	+	7.04049i	−0.298198	+	0.359284i
$385$			1.74739i			0.0890552i
$386$	−22.7215	−	7.61462i	−1.15650	−	0.387574i
$387$	−1.37860	+	0.795934i	−0.0700781	+	0.0404596i
$388$	−10.9128	+	14.4530i	−0.554013	+	0.733738i
$389$		−	3.63531i		−	0.184318i	−0.995744	−	0.0921589i	$-0.970623\pi$
$389$		−	3.63531i		−	0.184318i	0.995744	−	0.0921589i	$-0.0293768\pi$
$390$	−3.98594	+	1.05680i	−0.201836	+	0.0535131i
$391$	9.14198			0.462330
$392$	21.0311	+	10.0684i	1.06223	+	0.508532i
$393$	−4.73537	−	8.20190i	−0.238868	−	0.413731i
$394$	7.08022	−	21.1269i	0.356696	−	1.06436i
$395$	−17.2905			−0.869979
$396$	−0.257908	+	2.08400i	−0.0129604	+	0.104725i
$397$	−1.49457	+	2.58868i	−0.0750105	+	0.129922i	−0.901091	−	0.433630i	$-0.857232\pi$
$397$	−1.49457	+	2.58868i	−0.0750105	+	0.129922i	0.826080	+	0.563552i	$0.190566\pi$
$398$	8.58162	−	1.74167i	0.430158	−	0.0873021i
$399$	−2.72016	+	4.71145i	−0.136178	+	0.235867i
$400$	−3.87932	−	0.975117i	−0.193966	−	0.0487559i
$401$	11.2958	−	6.52161i	0.564084	−	0.325674i	−0.190699	−	0.981648i	$-0.561076\pi$
$401$	11.2958	−	6.52161i	0.564084	−	0.325674i	0.754783	+	0.655975i	$0.227742\pi$
$402$	−2.43815	−	12.0133i	−0.121604	−	0.599171i
$403$	−10.3120	−	15.6528i	−0.513678	−	0.779723i
$404$	0.0205223	+	0.0484764i	0.00102102	+	0.00241179i
$405$	1.77078	+	3.06708i	0.0879908	+	0.152404i
$406$	−33.9498	−	38.4103i	−1.68490	−	1.90627i
$407$	1.16148	−	2.01175i	0.0575726	−	0.0997186i
$408$	10.3637	+	15.1258i	0.513079	+	0.748837i
$409$	11.7308	+	6.77276i	0.580049	+	0.334892i	0.761153	−	0.648572i	$-0.224634\pi$
$409$	11.7308	+	6.77276i	0.580049	+	0.334892i	−0.181104	+	0.983464i	$0.557967\pi$
$410$	6.76786	+	2.26810i	0.334241	+	0.112013i
$411$	−6.06981			−0.299402
$412$	3.21528	−	25.9807i	0.158406	−	1.27998i
$413$	−31.5823	+	18.2340i	−1.55406	+	0.897238i
$414$	−2.50584	−	2.83507i	−0.123156	−	0.139336i
$415$	10.1833			0.499876
$416$	−17.7937	−	9.96920i	−0.872407	−	0.488780i
$417$	−6.60522			−0.323459
$418$	−0.722220	−	0.817109i	−0.0353249	−	0.0399661i
$419$	22.8340	−	13.1832i	1.11551	−	0.644041i	0.175260	−	0.984522i	$-0.443923\pi$
$419$	22.8340	−	13.1832i	1.11551	−	0.644041i	0.940251	+	0.340481i	$0.110590\pi$
$420$	0.775603	−	6.26717i	0.0378456	−	0.305807i
$421$	−18.3329			−0.893489			−0.446744	−	0.894662i	$-0.647417\pi$
$421$	−18.3329			−0.893489			−0.446744	+	0.894662i	$0.647417\pi$
$422$	1.81317	+	0.607643i	0.0882637	+	0.0295796i
$423$	17.6990	+	10.2185i	0.860555	+	0.496841i
$424$	−19.0233	−	27.7644i	−0.923853	−	1.34836i
$425$	−4.00797	+	6.94201i	−0.194415	+	0.336737i
$426$	−7.92117	−	8.96189i	−0.383782	−	0.434205i
$427$	−15.4254	−	26.7175i	−0.746485	−	1.29295i
$428$	−4.33334	−	10.2360i	−0.209460	−	0.494774i
$429$	1.30273	−	0.0768652i	0.0628966	−	0.00371109i
$430$	0.190867	+	0.940443i	0.00920440	+	0.0453522i
$431$	16.5529	−	9.55682i	0.797325	−	0.460336i	−0.0452099	−	0.998978i	$-0.514396\pi$
$431$	16.5529	−	9.55682i	0.797325	−	0.460336i	0.842535	+	0.538642i	$0.181062\pi$
$432$	4.21580	−	16.7718i	0.202833	−	0.806932i
$433$	9.52072	−	16.4904i	0.457537	−	0.792477i	−0.541294	−	0.840834i	$-0.682065\pi$
$433$	9.52072	−	16.4904i	0.457537	−	0.792477i	0.998830	+	0.0483571i	$0.0153986\pi$
$434$	28.1316	−	5.70941i	1.35036	−	0.274060i
$435$	−3.75415	+	6.50238i	−0.179998	+	0.311765i
$436$	0.143539	−	1.15985i	0.00687426	−	0.0555466i
$437$	1.96502			0.0939996
$438$	−0.0429665	+	0.128209i	−0.00205302	+	0.00612607i
$439$	4.17977	+	7.23957i	0.199490	+	0.345526i	0.948363	−	0.317187i	$-0.102738\pi$
$439$	4.17977	+	7.23957i	0.199490	+	0.345526i	−0.748873	+	0.662713i	$0.769405\pi$
$440$	1.14177	+	0.546610i	0.0544317	+	0.0260586i
$441$	−19.3398			−0.920942
$442$	−28.9778	+	28.8258i	−1.37834	+	1.37110i
$443$			27.0916i			1.28716i	0.765378	+	0.643580i	$0.222552\pi$
$443$			27.0916i			1.28716i	−0.765378	+	0.643580i	$0.777448\pi$
$444$	−5.05871	+	6.69977i	−0.240076	+	0.317957i
$445$	−7.70585	+	4.44897i	−0.365292	+	0.210902i
$446$	−14.9798	−	5.02016i	−0.709316	−	0.237712i
$447$		−	4.28848i		−	0.202838i
$448$	24.3302	−	19.5868i	1.14950	−	0.925389i
$449$	−0.192996	−	0.111426i	−0.00910804	−	0.00525853i	0.495439	−	0.868643i	$-0.335007\pi$
$449$	−0.192996	−	0.111426i	−0.00910804	−	0.00525853i	−0.504547	+	0.863384i	$0.668341\pi$
$450$	3.25143	−	0.659890i	0.153274	−	0.0311075i
$451$	−1.95625	−	1.12944i	−0.0921160	−	0.0531832i
$452$	−18.0449	−	13.6249i	−0.848761	−	0.640862i
$453$	−1.74819	−	3.02795i	−0.0821371	−	0.142266i
$454$	14.3983	−	2.92220i	0.675747	−	0.137146i
$455$	14.0528	−	0.829158i	0.658807	−	0.0388715i
$456$	2.22762	+	3.25120i	0.104318	+	0.152251i
$457$	−6.68503	+	3.85960i	−0.312712	+	0.180545i	−0.648140	−	0.761522i	$-0.724453\pi$
$457$	−6.68503	+	3.85960i	−0.312712	+	0.180545i	0.335427	+	0.942066i	$0.391119\pi$
$458$	−21.6443	−	24.4880i	−1.01137	−	1.14425i
$459$	−30.0129	−	17.3280i	−1.40088	−	0.808800i
$460$	−2.10048	+	0.889227i	−0.0979352	+	0.0414604i
$461$	−5.52913	+	9.57673i	−0.257517	+	0.446033i	−0.965576	−	0.260120i	$-0.916238\pi$
$461$	−5.52913	+	9.57673i	−0.257517	+	0.446033i	0.708059	+	0.706153i	$0.249571\pi$
$462$	−0.635035	+	1.89491i	−0.0295445	+	0.0881590i
$463$		−	28.7883i		−	1.33791i	−0.743304	−	0.668954i	$-0.766742\pi$
$463$		−	28.7883i		−	1.33791i	0.743304	−	0.668954i	$-0.233258\pi$
$464$	−35.7179	+	10.1680i	−1.65816	+	0.472036i
$465$	−2.10215	−	3.64103i	−0.0974847	−	0.168848i
$466$	8.02663	+	9.08121i	0.371826	+	0.420679i
$467$			33.8862i			1.56806i	0.620720	+	0.784032i	$0.286840\pi$
$467$			33.8862i			1.56806i	−0.620720	+	0.784032i	$0.713160\pi$
$468$	16.8823	+	1.08526i	0.780382	+	0.0501662i
$469$			41.8470i			1.93232i
$470$	9.23100	−	8.15902i	0.425794	−	0.376348i
$471$	3.65996	+	6.33924i	0.168642	+	0.292097i
$472$	2.03496	+	26.3402i	0.0936667	+	1.21241i
$473$		−	0.303687i		−	0.0139635i
$474$	−18.7501	−	6.28369i	−0.861223	−	0.288620i
$475$	−0.861493	+	1.49215i	−0.0395280	+	0.0684645i
$476$	−24.4022	−	57.6413i	−1.11847	−	2.64198i
$477$	24.1756	+	13.9578i	1.10692	+	0.639082i
$478$	−1.08757	+	0.961270i	−0.0497442	+	0.0439675i
$479$	−14.6419	+	8.45349i	−0.669004	+	0.386250i	−0.795699	−	0.605692i	$-0.792896\pi$
$479$	−14.6419	+	8.45349i	−0.669004	+	0.386250i	0.126695	+	0.991942i	$0.459563\pi$
$480$	−3.85244	−	2.46726i	−0.175839	−	0.112614i
$481$	−16.7300	−	8.38626i	−0.762821	−	0.382380i
$482$	−4.61581	−	22.7431i	−0.210244	−	1.03592i
$483$	−1.80052	−	3.11859i	−0.0819264	−	0.141901i
$484$	17.2376	+	13.0153i	0.783527	+	0.591607i
$485$	−7.84192	−	4.52754i	−0.356083	−	0.205585i
$486$	4.45394	+	21.9456i	0.202035	+	0.995472i
$487$	28.6541	+	16.5434i	1.29844	+	0.749654i	0.980135	−	0.198334i	$-0.0635530\pi$
$487$	28.6541	+	16.5434i	1.29844	+	0.749654i	0.318305	+	0.947988i	$0.396886\pi$
$488$	−22.2829	+	1.72151i	−1.00870	+	0.0779290i
$489$			11.7978i			0.533514i
$490$	−3.70458	+	11.0542i	−0.167356	+	0.499380i
$491$	−26.6188	+	15.3683i	−1.20129	+	0.693564i	−0.960841	−	0.277099i	$-0.910627\pi$
$491$	−26.6188	+	15.3683i	−1.20129	+	0.693564i	−0.240446	+	0.970663i	$0.577294\pi$
$492$	6.51494	+	4.91914i	0.293716	+	0.221772i
$493$			74.4220i			3.35180i
$494$	−6.22863	+	6.19595i	−0.280239	+	0.278769i
$495$	−1.04995			−0.0471916
$496$	5.06937	−	20.1676i	0.227622	−	0.905550i
$497$	20.4158	+	35.3611i	0.915772	+	1.58616i
$498$	11.0429	+	3.70079i	0.494845	+	0.165836i
$499$	6.58714			0.294881			0.147440	−	0.989071i	$-0.452897\pi$
$499$	6.58714			0.294881			0.147440	+	0.989071i	$0.452897\pi$
$500$	0.245639	−	1.98486i	0.0109853	−	0.0887656i
$501$	−1.43337	+	2.48267i	−0.0640383	+	0.110918i
$502$	0.529741	+	2.61015i	0.0236435	+	0.116497i
$503$	−20.7723	+	35.9786i	−0.926190	+	1.60421i	−0.136555	+	0.990633i	$0.543603\pi$
$503$	−20.7723	+	35.9786i	−0.926190	+	1.60421i	−0.789636	+	0.613576i	$0.789730\pi$
$504$	−11.1868	+	23.3672i	−0.498299	+	1.04086i
$505$	−0.0227944	+	0.0131604i	−0.00101434	+	0.000585629i
$506$	0.707422	−	0.143574i	0.0314487	−	0.00638264i
$507$	−1.23633	−	10.4404i	−0.0549072	−	0.463672i
$508$	21.5750	−	9.13367i	0.957236	−	0.405241i
$509$	−8.56097	−	14.8280i	−0.379458	−	0.657241i	0.611525	−	0.791225i	$-0.290556\pi$
$509$	−8.56097	−	14.8280i	−0.379458	−	0.657241i	−0.990984	+	0.133984i	$0.957223\pi$
$510$	−6.86919	+	6.07148i	−0.304173	+	0.268850i
$511$	0.230801	−	0.399760i	0.0102100	−	0.0176843i
$512$	−5.18743	−	22.0248i	−0.229254	−	0.973367i
$513$	−6.45112	−	3.72456i	−0.284824	−	0.164443i
$514$	−7.45438	+	22.2434i	−0.328799	+	0.981115i
$515$	13.0895			0.576791
$516$	−0.134796	+	1.08920i	−0.00593405	+	0.0479494i
$517$	−3.37651	+	1.94943i	−0.148499	+	0.0857357i
$518$	21.4734	−	18.9798i	0.943488	−	0.833923i
$519$	9.26020			0.406478
$520$	3.85415	−	9.44169i	0.169016	−	0.414045i
$521$	−23.5385			−1.03124			−0.515621	−	0.856817i	$-0.672439\pi$
$521$	−23.5385			−1.03124			−0.515621	+	0.856817i	$0.672439\pi$
$522$	23.0795	−	20.3993i	1.01016	−	0.892853i
$523$	−1.93140	+	1.11509i	−0.0844542	+	0.0487597i	−0.541632	−	0.840615i	$-0.682194\pi$
$523$	−1.93140	+	1.11509i	−0.0844542	+	0.0487597i	0.457178	+	0.889375i	$0.348860\pi$
$524$	23.2444	+	2.87664i	1.01543	+	0.125667i
$525$	3.15749			0.137804
$526$	9.21575	−	27.4992i	0.401826	−	1.19902i
$527$	−36.0897	−	20.8364i	−1.57209	−	0.907647i
$528$	1.03951	+	1.00770i	0.0452388	+	0.0438544i
$529$	10.8497	−	18.7922i	0.471724	−	0.817051i
$530$	12.6089	−	11.1446i	0.547695	−	0.484093i
$531$	−10.9562	−	18.9767i	−0.475459	−	0.823519i
$532$	−5.24512	−	12.3897i	−0.227405	−	0.537161i
$533$	−8.15489	+	16.2684i	−0.353227	+	0.704663i
$534$	−9.97322	+	2.02410i	−0.431583	+	0.0875915i
$535$	4.81312	−	2.77886i	0.208089	−	0.120140i
$536$	27.3434	+	13.0904i	1.18106	+	0.565419i
$537$	0.348728	−	0.604014i	0.0150487	−	0.0260651i
$538$	−1.62082	−	7.98616i	−0.0698786	−	0.344308i
$539$	1.84476	−	3.19522i	0.0794596	−	0.137628i
$540$	8.58129	+	1.06199i	0.369280	+	0.0457008i
$541$	27.5466			1.18432			0.592161	−	0.805820i	$-0.298275\pi$
$541$	27.5466			1.18432			0.592161	+	0.805820i	$0.298275\pi$
$542$	12.7046	+	4.25766i	0.545709	+	0.182882i
$543$	−1.79198	−	3.10381i	−0.0769014	−	0.133197i
$544$	−45.2970	−	2.08634i	−1.94209	−	0.0894513i
$545$	0.584348			0.0250307
$546$	15.5405	+	4.20791i	0.665072	+	0.180082i
$547$		−	40.5419i		−	1.73345i	−0.498788	−	0.866724i	$-0.666221\pi$
$547$		−	40.5419i		−	1.73345i	0.498788	−	0.866724i	$-0.333779\pi$
$548$	9.04532	−	11.9797i	0.386397	−	0.511746i
$549$	16.0536	−	9.26857i	0.685153	−	0.395573i
$550$	−0.201120	+	0.600130i	−0.00857579	+	0.0255896i
$551$			15.9966i			0.681479i
$552$	−2.60096	+	0.200942i	−0.110704	+	0.00855266i
$553$	58.4634	+	33.7539i	2.48612	+	1.43536i
$554$	0.695351	+	3.42615i	0.0295426	+	0.145563i
$555$	−3.63518	−	2.09877i	−0.154305	−	0.0890879i
$556$	9.84320	−	13.0364i	0.417444	−	0.552865i
$557$	−14.4872	−	25.0925i	−0.613841	−	1.06320i	−0.990587	−	0.136887i	$-0.956290\pi$
$557$	−14.4872	−	25.0925i	−0.613841	−	1.06320i	0.376746	−	0.926317i	$-0.377043\pi$
$558$	3.43059	+	16.9033i	0.145228	+	0.715574i
$559$	−2.44230	+	0.144103i	−0.103298	+	0.00609491i
$560$	11.2134	+	10.8702i	0.473851	+	0.459350i
$561$	2.51261	−	1.45065i	0.106082	−	0.0612466i
$562$	6.15412	−	5.43945i	0.259596	−	0.229450i
$563$	23.2595	+	13.4289i	0.980272	+	0.565961i	0.902352	−	0.430999i	$-0.141839\pi$
$563$	23.2595	+	13.4289i	0.980272	+	0.565961i	0.0779201	+	0.996960i	$0.475172\pi$
$564$	12.9754	−	5.49309i	0.546364	−	0.231301i
$565$	5.65275	−	9.79084i	0.237813	−	0.411904i
$566$	−20.8153	−	6.97578i	−0.874932	−	0.293214i
$567$		−	13.8274i		−	0.580697i
$568$	29.4918	−	2.27845i	1.23745	−	0.0956016i
$569$	−3.53392	−	6.12094i	−0.148150	−	0.256603i	0.782394	−	0.622784i	$-0.213998\pi$
$569$	−3.53392	−	6.12094i	−0.148150	−	0.256603i	−0.930544	+	0.366181i	$0.880665\pi$
$570$	−1.47650	+	1.30503i	−0.0618436	+	0.0546618i
$571$			14.6144i			0.611594i	0.952097	+	0.305797i	$0.0989230\pi$
$571$			14.6144i			0.611594i	−0.952097	+	0.305797i	$0.901077\pi$
$572$	−1.78965	+	2.68568i	−0.0748290	+	0.112294i
$573$		−	17.5583i		−	0.733509i
$574$	−18.4561	−	20.8810i	−0.770344	−	0.871556i
$575$	−0.570237	−	0.987679i	−0.0237805	−	0.0411891i
$576$	11.7690	+	14.6192i	0.490377	+	0.609134i
$577$			5.48671i			0.228415i	0.993457	+	0.114207i	$0.0364328\pi$
$577$			5.48671i			0.228415i	−0.993457	+	0.114207i	$0.963567\pi$
$578$	−21.2356	+	63.3656i	−0.883283	+	2.63566i
$579$	6.85175	−	11.8676i	0.284749	−	0.493200i
$580$	−7.23892	−	17.0993i	−0.300580	−	0.710010i
$581$	−34.4321	−	19.8794i	−1.42848	−	0.824736i
$582$	−6.85855	−	7.75966i	−0.284296	−	0.321648i
$583$	−4.61207	+	2.66278i	−0.191012	+	0.110281i
$584$	−0.189010	−	0.275860i	−0.00782131	−	0.0114152i
$585$	0.498213	+	8.44386i	0.0205986	+	0.349111i
$586$	−43.3851	+	8.80518i	−1.79222	+	0.363738i
$587$	9.53461	+	16.5144i	0.393536	+	0.681623i	0.992913	−	0.118843i	$-0.0379185\pi$
$587$	9.53461	+	16.5144i	0.393536	+	0.681623i	−0.599378	+	0.800466i	$0.704585\pi$
$588$	−8.03465	+	10.6411i	−0.331343	+	0.438833i
$589$	−7.75728	−	4.47867i	−0.319633	−	0.184540i
$590$	−12.9454	+	2.62732i	−0.532954	+	0.108165i
$591$	11.0347	+	6.37089i	0.453907	+	0.262063i
$592$	−5.68443	−	19.9682i	−0.233629	−	0.820688i
$593$		−	28.8284i		−	1.18384i	−0.805997	−	0.591920i	$-0.798370\pi$
$593$		−	28.8284i		−	1.18384i	0.805997	−	0.591920i	$-0.201630\pi$
$594$	−2.59459	−	0.869518i	−0.106457	−	0.0356768i
$595$	27.1039	−	15.6485i	1.11115	−	0.641524i
$596$	8.46394	+	6.39075i	0.346696	+	0.261775i
$597$			5.00743i			0.204940i
$598$	−1.49033	−	5.62109i	−0.0609440	−	0.229863i
$599$	−4.08040			−0.166721			−0.0833603	−	0.996519i	$-0.526565\pi$
$599$	−4.08040			−0.166721			−0.0833603	+	0.996519i	$0.526565\pi$
$600$	0.987712	−	2.06315i	0.0403232	−	0.0842278i
$601$	−8.92004	−	15.4500i	−0.363856	−	0.630217i	0.624736	−	0.780836i	$-0.285207\pi$
$601$	−8.92004	−	15.4500i	−0.363856	−	0.630217i	−0.988592	+	0.150619i	$0.951873\pi$
$602$	1.19053	−	3.55248i	0.0485225	−	0.144788i
$603$	−25.1445			−1.02396
$604$	8.58129	+	1.06199i	0.349168	+	0.0432118i
$605$	−5.39985	+	9.35281i	−0.219535	+	0.380246i
$606$	−0.0295015	+	0.00598744i	−0.00119842	+	0.000243223i
$607$	13.6841	−	23.7016i	0.555421	−	0.962018i	−0.442449	−	0.896793i	$-0.645890\pi$
$607$	13.6841	−	23.7016i	0.555421	−	0.962018i	0.997871	−	0.0652243i	$-0.0207763\pi$
$608$	−9.73636	−	0.448449i	−0.394861	−	0.0181870i
$609$	25.3875	−	14.6575i	1.02875	−	0.593950i
$610$	−2.22262	−	10.9514i	−0.0899914	−	0.443408i
$611$	17.2798	+	26.2294i	0.699067	+	1.06113i
$612$	34.6347	−	14.6624i	1.40002	−	0.592694i
$613$	2.05530	+	3.55988i	0.0830127	+	0.143782i	0.904543	−	0.426383i	$-0.140212\pi$
$613$	2.05530	+	3.55988i	0.0830127	+	0.143782i	−0.821530	+	0.570165i	$0.806879\pi$
$614$	−3.59973	−	4.07268i	−0.145273	−	0.164360i
$615$	−2.04087	+	3.53489i	−0.0822958	+	0.142540i
$616$	−2.79353	−	4.07715i	−0.112555	−	0.164273i
$617$	−26.8289	−	15.4897i	−1.08009	−	0.623591i	−0.149170	−	0.988812i	$-0.547660\pi$
$617$	−26.8289	−	15.4897i	−1.08009	−	0.623591i	−0.930921	+	0.365220i	$0.880994\pi$
$618$	14.1945	+	4.75696i	0.570986	+	0.191353i
$619$	43.4702			1.74722			0.873608	−	0.486631i	$-0.161774\pi$
$619$	43.4702			1.74722			0.873608	+	0.486631i	$0.161774\pi$
$620$	10.3187	+	1.27701i	0.414411	+	0.0512860i
$621$	4.27011	−	2.46535i	0.171354	−	0.0989310i
$622$	20.4495	+	23.1362i	0.819948	+	0.927678i
$623$	34.7405			1.39185
$624$	7.61081	−	8.83808i	0.304676	−	0.353807i
$625$	1.00000			0.0400000
$626$	−9.89151	−	11.1911i	−0.395344	−	0.447287i
$627$	0.540071	−	0.311810i	0.0215684	−	0.0124525i
$628$	−17.9655	−	2.22335i	−0.716903	−	0.0887214i
$629$	−41.6059			−1.65893
$630$	−12.2821	−	4.11607i	−0.489331	−	0.163988i
$631$	2.39053	+	1.38018i	0.0951657	+	0.0549439i	0.546828	−	0.837245i	$-0.315835\pi$
$631$	2.39053	+	1.38018i	0.0951657	+	0.0549439i	−0.451662	+	0.892189i	$0.649169\pi$
$632$	40.3435	−	27.6421i	1.60478	−	1.09954i
$633$	−0.546767	+	0.947028i	−0.0217320	+	0.0376410i
$634$	18.0877	+	20.4642i	0.718355	+	0.812736i
$635$	5.85718	+	10.1449i	0.232435	+	0.402589i
$636$	17.7235	−	7.50317i	0.702783	−	0.297520i
$637$	−26.5719	−	13.3197i	−1.05282	−	0.527747i
$638$	1.16879	+	5.75890i	0.0462729	+	0.227997i
$639$	−21.2473	+	12.2671i	−0.840531	+	0.485281i
$640$	10.6105	−	3.92661i	0.419415	−	0.155213i
$641$	5.00752	−	8.67328i	0.197785	−	0.342574i	−0.750025	−	0.661410i	$-0.769958\pi$
$641$	5.00752	−	8.67328i	0.197785	−	0.342574i	0.947810	+	0.318836i	$0.103292\pi$
$642$	6.22933	−	1.26427i	0.245852	−	0.0498966i
$643$	−14.2515	+	24.6843i	−0.562024	+	0.973454i	0.435296	+	0.900287i	$0.356644\pi$
$643$	−14.2515	+	24.6843i	−0.562024	+	0.973454i	−0.997320	+	0.0731662i	$0.976690\pi$
$644$	8.83815	+	1.09378i	0.348272	+	0.0431009i
$645$	−0.548755			−0.0216072
$646$	−6.20653	+	18.5199i	−0.244193	+	0.728655i
$647$	−7.53191	−	13.0456i	−0.296110	−	0.512877i	0.679133	−	0.734016i	$-0.262356\pi$
$647$	−7.53191	−	13.0456i	−0.296110	−	0.512877i	−0.975242	+	0.221138i	$0.929023\pi$
$648$	−9.03503	−	4.32543i	−0.354930	−	0.169919i
$649$	4.18032			0.164092
$650$	4.92179	+	1.33268i	0.193048	+	0.0522718i
$651$			16.4150i			0.643353i
$652$	−23.2846	−	17.5812i	−0.911897	−	0.688533i
$653$	14.7901	−	8.53909i	0.578783	−	0.334161i	−0.181867	−	0.983323i	$-0.558214\pi$
$653$	14.7901	−	8.53909i	0.578783	−	0.334161i	0.760650	+	0.649163i	$0.224881\pi$
$654$	0.633679	+	0.212363i	0.0247788	+	0.00830406i
$655$			11.7108i			0.457581i
$656$	−19.4173	+	5.52761i	−0.758118	+	0.215817i
$657$	0.240202	+	0.138681i	0.00937117	+	0.00541045i
$658$	−47.1401	+	9.56726i	−1.83771	+	0.372971i
$659$	−32.4049	−	18.7090i	−1.26232	−	0.728799i	−0.288794	−	0.957391i	$-0.593254\pi$
$659$	−32.4049	−	18.7090i	−1.26232	−	0.728799i	−0.973522	+	0.228593i	$0.926588\pi$
$660$	−0.436198	+	0.577702i	−0.0169790	+	0.0224870i
$661$	8.83203	+	15.2975i	0.343526	+	0.595005i	0.985085	−	0.172069i	$-0.0550453\pi$
$661$	8.83203	+	15.2975i	0.343526	+	0.595005i	−0.641559	+	0.767074i	$0.721712\pi$
$662$	−29.4494	+	5.97688i	−1.14458	+	0.232298i
$663$	−12.8587	−	19.5185i	−0.499390	−	0.758035i
$664$	−23.7604	+	16.2799i	−0.922081	+	0.631781i
$665$	5.82584	−	3.36355i	0.225917	−	0.130433i
$666$	11.4043	+	12.9026i	0.441907	+	0.499967i
$667$	−9.16985	−	5.29422i	−0.355058	−	0.204993i
$668$	−2.76388	−	6.52868i	−0.106938	−	0.252602i
$669$	4.51722	−	7.82405i	0.174646	−	0.302495i
$670$	−4.81649	+	14.3721i	−0.186077	+	0.555242i
$671$			3.53641i			0.136521i
$672$	8.20956	+	15.8630i	0.316691	+	0.611929i
$673$	11.1111	+	19.2450i	0.428302	+	0.741841i	0.996722	−	0.0808970i	$-0.0257785\pi$
$673$	11.1111	+	19.2450i	0.428302	+	0.741841i	−0.568420	+	0.822738i	$0.692445\pi$
$674$	20.9932	+	23.7514i	0.808629	+	0.914870i
$675$			4.32338i			0.166407i
$676$	22.4480	+	13.1183i	0.863383	+	0.504549i
$677$			5.99382i			0.230361i	0.993345	+	0.115181i	$0.0367447\pi$
$677$			5.99382i			0.230361i	−0.993345	+	0.115181i	$0.963255\pi$
$678$	9.68813	−	8.56307i	0.372070	−	0.328863i
$679$	17.6770	+	30.6175i	0.678381	+	1.17499i
$680$	−1.74640	−	22.6052i	−0.0669716	−	0.866868i
$681$			8.40152i			0.321947i
$682$	−3.11991	−	1.04557i	−0.119468	−	0.0400369i
$683$	−4.56662	+	7.90963i	−0.174737	+	0.302653i	−0.940070	−	0.340981i	$-0.889241\pi$
$683$	−4.56662	+	7.90963i	−0.174737	+	0.302653i	0.765333	+	0.643634i	$0.222574\pi$
$684$	7.44455	−	3.15161i	0.284649	−	0.120505i
$685$	6.49995	+	3.75275i	0.248350	+	0.143385i
$686$	5.14577	−	4.54821i	0.196467	−	0.173651i
$687$	16.1855	−	9.34469i	0.617514	−	0.356522i
$688$	−1.94882	−	1.88918i	−0.0742981	−	0.0720243i
$689$	23.6030	+	35.8276i	0.899204	+	1.36492i
$690$	−0.259435	−	1.27829i	−0.00987651	−	0.0486638i
$691$	−9.65327	−	16.7200i	−0.367228	−	0.636057i	0.621903	−	0.783094i	$-0.286360\pi$
$691$	−9.65327	−	16.7200i	−0.367228	−	0.636057i	−0.989131	+	0.147037i	$0.953026\pi$
$692$	−13.7997	+	18.2764i	−0.524585	+	0.694763i
$693$	3.55013	+	2.04967i	0.134858	+	0.0778606i
$694$	−9.95700	−	49.0604i	−0.377962	−	1.86231i
$695$	7.07331	+	4.08378i	0.268306	+	0.154906i
$696$	−1.63581	−	21.1736i	−0.0620051	−	0.802583i
$697$			40.4580i			1.53246i
$698$	4.31586	−	12.8783i	0.163358	−	0.487449i
$699$	−6.00226	+	3.46541i	−0.227026	+	0.131074i
$700$	−4.70534	+	6.23177i	−0.177845	+	0.235539i
$701$		−	11.3698i		−	0.429432i	−0.976677	−	0.214716i	$-0.931117\pi$
$701$		−	11.3698i		−	0.429432i	0.976677	−	0.214716i	$-0.0688825\pi$
$702$	−5.76165	+	21.2787i	−0.217460	+	0.803114i
$703$	−8.94296			−0.337290
$704$	−3.53793	+	0.549941i	−0.133341	+	0.0207267i
$705$	3.52257	+	6.10127i	0.132668	+	0.229787i
$706$	−17.7450	−	5.94683i	−0.667841	−	0.223812i
$707$	0.102765			0.00386487
$708$	−14.9931	−	1.85549i	−0.563475	−	0.0697337i
$709$	2.70275	−	4.68129i	0.101504	−	0.175810i	−0.810801	−	0.585322i	$-0.800968\pi$
$709$	2.70275	−	4.68129i	0.101504	−	0.175810i	0.912304	+	0.409513i	$0.134301\pi$
$710$	2.94169	+	14.4944i	0.110400	+	0.543964i
$711$	−20.2816	+	35.1287i	−0.760618	+	1.31743i
$712$	10.8674	−	22.7000i	0.407272	−	0.850717i
$713$	5.13468	−	2.96451i	0.192295	−	0.111022i
$714$	35.0790	−	7.11941i	1.31280	−	0.266437i
$715$	−1.44258	−	0.723122i	−0.0539493	−	0.0270432i
$716$	0.672432	+	1.58838i	0.0251299	+	0.0593604i
$717$	−0.415018	−	0.718832i	−0.0154991	−	0.0268453i
$718$	36.2082	−	32.0034i	1.35128	−	1.19436i
$719$	3.58826	−	6.21504i	0.133819	−	0.231782i	−0.791326	−	0.611394i	$-0.790609\pi$
$719$	3.58826	−	6.21504i	0.133819	−	0.231782i	0.925146	+	0.379612i	$0.123942\pi$
$720$	−6.53153	+	6.73773i	−0.243416	+	0.251100i
$721$	−44.2587	−	25.5528i	−1.64828	−	0.951636i
$722$	7.20413	−	21.4967i	0.268110	−	0.800023i
$723$	13.2708			0.493545
$724$	8.79626	+	1.08859i	0.326911	+	0.0404573i
$725$	8.04039	−	4.64212i	0.298613	−	0.172404i
$726$	−9.25470	+	8.17997i	−0.343474	+	0.303587i
$727$	−13.9387			−0.516958			−0.258479	−	0.966017i	$-0.583221\pi$
$727$	−13.9387			−0.516958			−0.258479	+	0.966017i	$0.583221\pi$
$728$	−31.4636	+	24.4008i	−1.16612	+	0.904352i
$729$	−2.18071			−0.0807670
$730$	0.125279	−	0.110730i	0.00463677	−	0.00409831i
$731$	−4.71051	+	2.71962i	−0.174225	+	0.100589i
$732$	1.56968	−	12.6836i	0.0580171	−	0.468801i
$733$	51.7217			1.91039			0.955193	−	0.295983i	$-0.0956472\pi$
$733$	51.7217			1.91039			0.955193	+	0.295983i	$0.0956472\pi$
$734$	6.75878	−	20.1678i	0.249471	−	0.744406i
$735$	−5.77369	−	3.33344i	−0.212966	−	0.122956i
$736$	3.47940	−	5.43282i	0.128252	−	0.200256i
$737$	2.39845	−	4.15424i	0.0883482	−	0.153024i
$738$	12.5467	−	11.0897i	0.461850	−	0.408216i
$739$	3.70149	+	6.41116i	0.136161	+	0.235838i	0.926041	−	0.377424i	$-0.123190\pi$
$739$	3.70149	+	6.41116i	0.136161	+	0.235838i	−0.789879	+	0.613263i	$0.789857\pi$
$740$	9.55943	−	4.04694i	0.351412	−	0.148768i
$741$	−2.76391	−	4.19539i	−0.101535	−	0.154122i
$742$	−64.3900	+	13.0682i	−2.36383	+	0.479749i
$743$	−38.2295	+	22.0718i	−1.40251	+	0.809737i	−0.994649	−	0.103309i	$-0.967057\pi$
$743$	−38.2295	+	22.0718i	−1.40251	+	0.809737i	−0.407856	+	0.913046i	$0.633724\pi$
$744$	10.7258	+	5.13485i	0.393226	+	0.188253i
$745$	−2.65141	+	4.59238i	−0.0971403	+	0.168252i
$746$	1.83387	+	9.03589i	0.0671427	+	0.330827i
$747$	11.9449	−	20.6891i	0.437039	−	0.756974i
$748$	−0.881243	+	7.12078i	−0.0322214	+	0.260362i
$749$	−21.6991			−0.792869
$750$	1.08442	+	0.363419i	0.0395974	+	0.0132702i
$751$	−0.525634	−	0.910425i	−0.0191807	−	0.0332219i	0.856276	−	0.516519i	$-0.172772\pi$
$751$	−0.525634	−	0.910425i	−0.0191807	−	0.0332219i	−0.875456	+	0.483297i	$0.839439\pi$
$752$	−8.49475	+	33.7948i	−0.309772	+	1.23237i
$753$	−1.52304			−0.0555027
$754$	45.7595	−	12.1323i	1.66646	−	0.441832i
$755$			4.32338i			0.157344i
$756$	−26.9423	−	20.3429i	−0.979882	−	0.739866i
$757$	25.1218	−	14.5041i	0.913068	−	0.527160i	0.0316510	−	0.999499i	$-0.489924\pi$
$757$	25.1218	−	14.5041i	0.913068	−	0.527160i	0.881417	+	0.472339i	$0.156590\pi$
$758$	−5.43334	+	16.2128i	−0.197348	+	0.588874i
$759$			0.412785i			0.0149832i
$760$	−0.375381	−	4.85886i	−0.0136165	−	0.176249i
$761$	9.61433	+	5.55084i	0.348519	+	0.201218i	0.664033	−	0.747703i	$-0.268843\pi$
$761$	9.61433	+	5.55084i	0.348519	+	0.201218i	−0.315514	+	0.948921i	$0.602177\pi$
$762$	2.66478	+	13.1300i	0.0965348	+	0.475649i
$763$	−1.97583	−	1.14074i	−0.0715297	−	0.0412977i
$764$	34.6539	+	26.1656i	1.25373	+	0.946640i
$765$	9.40262	+	16.2858i	0.339953	+	0.588815i
$766$	−0.511366	−	2.51962i	−0.0184764	−	0.0910374i
$767$	−1.98361	−	33.6189i	−0.0716241	−	1.21391i
$768$	12.9332	−	0.402055i	0.466686	−	0.0145079i
$769$	−13.7216

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.936579 - 1.05963i) q^{2} +(0.700368 - 0.404358i) q^{3} +(-0.245639 + 1.98486i) q^{4} -1.00000 q^{5} +(-1.08442 - 0.363419i) q^{6} +(3.38125 + 1.95217i) q^{7} +(2.33328 - 1.59869i) q^{8} +(-1.17299 + 2.03168i) q^{9} +O(q^{10})\)	\(q+(-0.936579 - 1.05963i) q^{2} +(0.700368 - 0.404358i) q^{3} +(-0.245639 + 1.98486i) q^{4} -1.00000 q^{5} +(-1.08442 - 0.363419i) q^{6} +(3.38125 + 1.95217i) q^{7} +(2.33328 - 1.59869i) q^{8} +(-1.17299 + 2.03168i) q^{9} +(0.936579 + 1.05963i) q^{10} +(-0.223776 - 0.387591i) q^{11} +(0.630555 + 1.48946i) q^{12} +(-3.01089 + 1.98356i) q^{13} +(-1.09823 - 5.41124i) q^{14} +(-0.700368 + 0.404358i) q^{15} +(-3.87932 - 0.975117i) q^{16} +(-4.00797 + 6.94201i) q^{17} +(3.25143 - 0.659890i) q^{18} +(-0.861493 + 1.49215i) q^{19} +(0.245639 - 1.98486i) q^{20} +3.15749 q^{21} +(-0.201120 + 0.600130i) q^{22} +(-0.570237 - 0.987679i) q^{23} +(0.987712 - 2.06315i) q^{24} +1.00000 q^{25} +(4.92179 + 1.33268i) q^{26} +4.32338i q^{27} +(-4.70534 + 6.23177i) q^{28} +(8.04039 - 4.64212i) q^{29} +(1.08442 + 0.363419i) q^{30} +5.19873i q^{31} +(2.60003 + 5.02393i) q^{32} +(-0.313451 - 0.180971i) q^{33} +(11.1098 - 2.25477i) q^{34} +(-3.38125 - 1.95217i) q^{35} +(-3.74446 - 2.82728i) q^{36} +(2.59519 + 4.49501i) q^{37} +(2.38799 - 0.484651i) q^{38} +(-1.30666 + 2.60670i) q^{39} +(-2.33328 + 1.59869i) q^{40} +(4.37099 - 2.52359i) q^{41} +(-2.95724 - 3.34578i) q^{42} +(0.587643 + 0.339276i) q^{43} +(0.824282 - 0.348956i) q^{44} +(1.17299 - 2.03168i) q^{45} +(-0.512504 + 1.52928i) q^{46} -8.71152i q^{47} +(-3.11125 + 0.885693i) q^{48} +(4.12190 + 7.13934i) q^{49} +(-0.936579 - 1.05963i) q^{50} +6.48262i q^{51} +(-3.19750 - 6.46344i) q^{52} -11.8993i q^{53} +(4.58119 - 4.04918i) q^{54} +(0.223776 + 0.387591i) q^{55} +(11.0103 - 0.850622i) q^{56} +1.39340i q^{57} +(-12.4494 - 4.17214i) q^{58} +(-4.67021 + 8.08904i) q^{59} +(-0.630555 - 1.48946i) q^{60} +(-6.84304 - 3.95083i) q^{61} +(5.50874 - 4.86902i) q^{62} +(-7.93234 + 4.57974i) q^{63} +(2.88838 - 7.46038i) q^{64} +(3.01089 - 1.98356i) q^{65} +(0.101809 + 0.501636i) q^{66} +(5.35905 + 9.28215i) q^{67} +(-12.7944 - 9.66049i) q^{68} +(-0.798751 - 0.461159i) q^{69} +(1.09823 + 5.41124i) q^{70} +(9.05690 + 5.22901i) q^{71} +(0.511110 + 6.61572i) q^{72} -0.118228i q^{73} +(2.33245 - 6.95988i) q^{74} +(0.700368 - 0.404358i) q^{75} +(-2.75009 - 2.07647i) q^{76} -1.74739i q^{77} +(3.98594 - 1.05680i) q^{78} +17.2905 q^{79} +(3.87932 + 0.975117i) q^{80} +(-1.77078 - 3.06708i) q^{81} +(-6.76786 - 2.26810i) q^{82} -10.1833 q^{83} +(-0.775603 + 6.26717i) q^{84} +(4.00797 - 6.94201i) q^{85} +(-0.190867 - 0.940443i) q^{86} +(3.75415 - 6.50238i) q^{87} +(-1.14177 - 0.546610i) q^{88} +(7.70585 - 4.44897i) q^{89} +(-3.25143 + 0.659890i) q^{90} +(-14.0528 + 0.829158i) q^{91} +(2.10048 - 0.889227i) q^{92} +(2.10215 + 3.64103i) q^{93} +(-9.23100 + 8.15902i) q^{94} +(0.861493 - 1.49215i) q^{95} +(3.85244 + 2.46726i) q^{96} +(7.84192 + 4.52754i) q^{97} +(3.70458 - 11.0542i) q^{98} +1.04995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

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