LMFDB - Embedded newform 520.2.ca.a.381.8

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			381.8
Character	$\chi$	$=$	520.381
Dual form			520.2.ca.a.101.8

$q$-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} +(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} + 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}+ \cdots + 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

Character values

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

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

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	0.688362	−	0.725367i	$-0.258330\pi$
$3$	0.700368	+	0.404358i	0.404358	+	0.233456i	−0.284005	+	0.958823i	$0.591663\pi$
$4$	−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	0.301513	−	0.953462i	$-0.402508\pi$
$7$	3.38125	−	1.95217i	1.27799	−	0.737849i	0.976479	+	0.215613i	$0.0691749\pi$
$8$	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	−0.897787	−	0.440429i	$-0.854826\pi$
$11$	−0.223776	+	0.387591i	−0.0674710	+	0.116863i	0.830316	+	0.557292i	$0.188160\pi$
$12$	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	−0.689264	−	0.724510i	$-0.742066\pi$
$17$	−4.00797	−	6.94201i	−0.972076	−	1.68369i	−0.282812	−	0.959175i	$-0.591267\pi$
$18$	3.25143	+	0.659890i	0.766369	+	0.155538i
$19$	−0.861493	−	1.49215i	−0.197640	−	0.342323i	0.750123	−	0.661299i	$-0.229994\pi$
$19$	−0.861493	−	1.49215i	−0.197640	−	0.342323i	−0.947763	+	0.318976i	$0.896661\pi$
$20$	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	−0.919333	−	0.393480i	$-0.871271\pi$
$23$	−0.570237	+	0.987679i	−0.118903	+	0.205945i	0.800430	+	0.599426i	$0.204604\pi$
$24$	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	0.999968	−	0.00795571i	$-0.00253241\pi$
$29$	8.04039	+	4.64212i	1.49306	+	0.862020i	0.493094	+	0.869976i	$0.335866\pi$
$30$	1.08442	−	0.363419i	0.197987	−	0.0663510i
$31$		−	5.19873i		−	0.933720i	−0.884331	−	0.466860i	$-0.845385\pi$
$31$		−	5.19873i		−	0.933720i	0.884331	−	0.466860i	$-0.154615\pi$
$32$	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	−0.569926	−	0.821696i	$-0.693028\pi$
$37$	2.59519	−	4.49501i	0.426647	−	0.738974i	0.996573	+	0.0827219i	$0.0263613\pi$
$38$	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	0.800847	−	0.598869i	$-0.204383\pi$
$41$	4.37099	+	2.52359i	0.682635	+	0.394119i	−0.118212	+	0.992988i	$0.537716\pi$
$42$	−2.95724	+	3.34578i	−0.456312	+	0.516265i
$43$	0.587643	−	0.339276i	0.0896147	−	0.0517391i	−0.454523	−	0.890735i	$-0.650190\pi$
$43$	0.587643	−	0.339276i	0.0896147	−	0.0517391i	0.544138	+	0.838996i	$0.316857\pi$
$44$	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	$0.219145\pi$
$47$			8.71152i			1.27071i	−0.772222	+	0.635353i	$0.780855\pi$
$48$	−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	$0.304501\pi$
$53$			11.8993i			1.63450i	−0.576286	+	0.817248i	$0.695499\pi$
$54$	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	−0.991568	−	0.129586i	$-0.958635\pi$
$59$	−4.67021	−	8.08904i	−0.608009	−	1.05310i	0.383559	−	0.923516i	$-0.374698\pi$
$60$	−0.630555	+	1.48946i	−0.0814043	+	0.192288i
$61$	−6.84304	+	3.95083i	−0.876162	+	0.505852i	−0.869391	−	0.494125i	$-0.835489\pi$
$61$	−6.84304	+	3.95083i	−0.876162	+	0.505852i	−0.00677098	+	0.999977i	$0.502155\pi$
$62$	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	−0.327253	−	0.944937i	$-0.606123\pi$
$67$	5.35905	−	9.28215i	0.654713	−	1.13400i	0.981966	−	0.189059i	$-0.0605437\pi$
$68$	−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	0.145352	−	0.989380i	$-0.453568\pi$
$71$	9.05690	−	5.22901i	1.07486	−	0.620569i	0.929504	+	0.368811i	$0.120235\pi$
$72$	0.511110	−	6.61572i	0.0602349	−	0.779670i
$73$			0.118228i			0.0138376i	0.999976	+	0.00691879i	$0.00220234\pi$
$73$			0.118228i			0.0138376i	−0.999976	+	0.00691879i	$0.997798\pi$
$74$	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	0.849318	−	0.527882i	$-0.177013\pi$
$89$	7.70585	+	4.44897i	0.816818	+	0.471590i	−0.0324998	+	0.999472i	$0.510347\pi$
$90$	−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	−0.0459234	−	0.998945i	$-0.514623\pi$
$97$	7.84192	−	4.52754i	0.796227	−	0.459702i	0.842150	+	0.539243i	$0.181290\pi$
$98$	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	0.501134	−	0.865370i	$-0.332917\pi$
$101$	0.0227944	+	0.0131604i	0.00226813	+	0.00130951i	−0.498866	+	0.866679i	$0.666250\pi$
$102$	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	0.248969	−	0.968511i	$-0.419908\pi$
$107$	−4.81312	−	2.77886i	−0.465302	−	0.268642i	−0.714271	+	0.699869i	$0.753242\pi$
$108$	−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	−0.999312	−	0.0370767i	$-0.988195\pi$
$113$	−5.65275	−	9.79084i	−0.531766	−	0.921045i	0.467547	−	0.883968i	$-0.345138\pi$
$114$	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	0.479996	+	0.877271i	$0.340638\pi$
$127$	−5.85718	+	10.1449i	−0.519740	+	0.900217i	−0.999737	+	0.0229463i	$0.992695\pi$
$128$	−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	$0.170944\pi$
$131$			11.7108i			1.02318i	−0.859229	+	0.511591i	$0.829056\pi$
$132$	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	−0.751268	−	0.659997i	$-0.770558\pi$
$137$	−6.49995	+	3.75275i	−0.555329	+	0.320619i	0.195940	+	0.980616i	$0.437224\pi$
$138$	0.259435	−	1.27829i	0.0220846	−	0.108816i
$139$	−7.07331	+	4.08378i	−0.599950	+	0.346381i	−0.769022	−	0.639222i	$-0.779256\pi$
$139$	−7.07331	+	4.08378i	−0.599950	+	0.346381i	0.169072	+	0.985604i	$0.445923\pi$
$140$	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	0.953955	−	0.299951i	$-0.0969703\pi$
$149$	2.65141	+	4.59238i	0.217212	+	0.376223i	−0.736742	+	0.676173i	$0.763637\pi$
$150$	−1.08442	+	0.363419i	−0.0885425	+	0.0296731i
$151$			4.32338i			0.351831i	0.984405	+	0.175916i	$0.0562886\pi$
$151$			4.32338i			0.351831i	−0.984405	+	0.175916i	$0.943711\pi$
$152$	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	$-0.882372\pi$
$157$		−	9.05130i		−	0.722372i	0.932494	−	0.361186i	$-0.117628\pi$
$158$	−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	−0.996431	−	0.0844159i	$-0.973098\pi$
$163$	−7.29415	−	12.6338i	−0.571322	−	0.989558i	0.425109	−	0.905142i	$-0.360236\pi$
$164$	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	0.376497	−	0.926418i	$-0.377128\pi$
$167$	−3.06989	−	1.77240i	−0.237556	−	0.137153i	−0.614053	+	0.789265i	$0.710462\pi$
$168$	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	−0.0731806	−	0.997319i	$-0.523315\pi$
$173$	9.91643	−	5.72526i	0.753932	−	0.435283i	0.827113	+	0.562036i	$0.189982\pi$
$174$	−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	0.527652	−	0.849460i	$-0.323072\pi$
$179$	0.746881	+	0.431212i	0.0558245	+	0.0322303i	−0.471828	+	0.881691i	$0.656406\pi$
$180$	3.74446	−	2.82728i	0.279096	−	0.210733i
$181$			4.43168i			0.329404i	0.986343	+	0.164702i	$0.0526663\pi$
$181$			4.43168i			0.329404i	−0.986343	+	0.164702i	$0.947334\pi$
$182$	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	0.928706	+	0.370817i	$0.120922\pi$
$191$	10.8557	+	18.8026i	0.785490	+	1.36051i	−0.143216	+	0.989691i	$0.545744\pi$
$192$	−0.993730	+	6.39295i	−0.0717163	+	0.461371i
$193$	14.6746	+	8.47239i	1.05630	+	0.609856i	0.924407	−	0.381408i	$-0.124561\pi$
$193$	14.6746	+	8.47239i	1.05630	+	0.609856i	0.131894	+	0.991264i	$0.457894\pi$
$194$	−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	−0.436117	−	0.899890i	$-0.643647\pi$
$197$	7.87779	−	13.6447i	0.561269	−	0.972147i	0.997386	−	0.0722567i	$-0.0230201\pi$
$198$	−0.983359	+	1.11256i	−0.0698843	+	0.0790660i
$199$	−3.09592	−	5.36228i	−0.219464	−	0.380122i	0.735180	−	0.677871i	$-0.237097\pi$
$199$	−3.09592	−	5.36228i	−0.219464	−	0.380122i	−0.954644	+	0.297749i	$0.903764\pi$
$200$	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	0.459150	−	0.888359i	$-0.348154\pi$
$211$	−1.17103	−	0.676093i	−0.0806169	−	0.0465442i	−0.539767	+	0.841815i	$0.681487\pi$
$212$	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	0.787637	−	0.616139i	$-0.211304\pi$
$223$	9.67467	+	5.58567i	0.647864	+	0.374044i	−0.139774	+	0.990183i	$0.544637\pi$
$224$	−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	0.640548	−	0.767918i	$-0.278707\pi$
$227$	−5.19436	−	8.99690i	−0.344762	−	0.597145i	−0.985311	+	0.170772i	$0.945374\pi$
$228$	−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	$0.0105682\pi$
$239$			1.02636i			0.0663899i	−0.999449	+	0.0331950i	$0.989432\pi$
$240$	3.11125	+	0.885693i	0.200830	+	0.0571712i
$241$	14.2112	−	8.20484i	0.915424	−	0.528520i	0.0332518	−	0.999447i	$-0.489414\pi$
$241$	14.2112	−	8.20484i	0.915424	−	0.528520i	0.882172	+	0.470927i	$0.156080\pi$
$242$	−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	−0.550589	−	0.834776i	$-0.685597\pi$
$251$	−1.63097	+	0.941643i	−0.102946	+	0.0594360i	0.447643	+	0.894212i	$0.352264\pi$
$252$	−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	0.482424	+	0.875938i	$0.339756\pi$
$257$	−8.29410	+	14.3658i	−0.517372	+	0.896114i	−0.999796	+	0.0201769i	$0.993577\pi$
$258$	−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	−0.354803	−	0.934941i	$-0.615452\pi$
$263$	10.2539	−	17.7602i	0.632281	−	1.09514i	0.987084	−	0.160202i	$-0.0512147\pi$
$264$	−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	−0.340096	−	0.940391i	$-0.610460\pi$
$269$	4.99021	−	2.88110i	0.304258	−	0.175664i	0.644354	+	0.764727i	$0.277126\pi$
$270$	−4.58119	−	4.04918i	−0.278802	−	0.246425i
$271$	−8.20521	−	4.73728i	−0.498431	−	0.287769i	0.229634	−	0.973277i	$-0.426247\pi$
$271$	−8.20521	−	4.73728i	−0.498431	−	0.287769i	−0.728065	+	0.685508i	$0.759580\pi$
$272$	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	−0.562935	−	0.826501i	$-0.690328\pi$
$277$	−2.14086	+	1.23602i	−0.128632	+	0.0742655i	0.434303	+	0.900767i	$0.356995\pi$
$278$	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	$-0.944579\pi$
$281$		−	5.80779i		−	0.346464i	0.984881	−	0.173232i	$-0.0554210\pi$
$282$	−3.16593	−	9.44694i	−0.188529	−	0.562557i
$283$	13.4435	+	7.76159i	0.799131	+	0.461379i	0.843167	−	0.537651i	$-0.180688\pi$
$283$	13.4435	+	7.76159i	0.799131	+	0.461379i	−0.0440362	+	0.999030i	$0.514022\pi$
$284$	−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	0.807806	+	0.589449i	$0.200655\pi$
$293$	15.6517	+	27.1095i	0.914381	+	1.58375i	0.106575	+	0.994305i	$0.466012\pi$
$294$	−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	0.995004	+	0.0998329i	$0.0318308\pi$
$331$	10.6242	+	18.4017i	0.583960	+	1.01145i	−0.411044	+	0.911615i	$0.634836\pi$
$332$	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	0.666928	−	0.745123i	$-0.267609\pi$
$347$	30.6557	−	17.6991i	1.64569	−	0.950137i	0.978759	−	0.205015i	$-0.0657243\pi$
$348$	11.9841	−	9.04870i	0.642418	−	0.485061i
$349$	4.80203	−	8.31737i	0.257047	−	0.445219i	−0.708402	−	0.705809i	$-0.750584\pi$
$349$	4.80203	−	8.31737i	0.257047	−	0.445219i	0.965450	+	0.260590i	$0.0839171\pi$
$350$	−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	0.772958	−	0.634457i	$-0.218776\pi$
$353$	11.4605	+	6.61673i	0.609981	+	0.352173i	−0.162977	+	0.986630i	$0.552110\pi$
$354$	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	$-0.642300\pi$
$359$		−	34.1706i		−	1.80345i	0.432307	−	0.901726i	$-0.357700\pi$
$360$	−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	−0.600237	−	0.799822i	$-0.704927\pi$
$367$	7.52014	−	13.0253i	0.392548	−	0.679913i	0.992785	+	0.119909i	$0.0382603\pi$
$368$	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	−0.638999	−	0.769207i	$-0.720651\pi$
$373$	−5.64614	+	3.25980i	−0.292346	+	0.168786i	0.346653	+	0.937993i	$0.387318\pi$
$374$	−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	−0.978477	−	0.206354i	$-0.933840\pi$
$379$	−6.04540	+	10.4709i	−0.310531	+	0.537856i	0.667946	+	0.744210i	$0.267174\pi$
$380$	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	−0.459236	−	0.888314i	$-0.651877\pi$
$383$	1.57440	−	0.908980i	0.0804480	−	0.0464467i	0.539684	+	0.841867i	$0.318544\pi$
$384$	−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	$0.0293768\pi$
$389$			3.63531i			0.184318i	−0.995744	+	0.0921589i	$0.970623\pi$
$390$	−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	0.826080	−	0.563552i	$-0.190566\pi$
$397$	−1.49457	−	2.58868i	−0.0750105	−	0.129922i	−0.901091	+	0.433630i	$0.857232\pi$
$398$	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	0.754783	−	0.655975i	$-0.227742\pi$
$401$	11.2958	+	6.52161i	0.564084	+	0.325674i	−0.190699	+	0.981648i	$0.561076\pi$
$402$	−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	−0.181104	−	0.983464i	$-0.557967\pi$
$409$	11.7308	−	6.77276i	0.580049	−	0.334892i	0.761153	+	0.648572i	$0.224634\pi$
$410$	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	0.940251	−	0.340481i	$-0.110590\pi$
$419$	22.8340	+	13.1832i	1.11551	+	0.644041i	0.175260	+	0.984522i	$0.443923\pi$
$420$	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	0.842535	−	0.538642i	$-0.181062\pi$
$431$	16.5529	+	9.55682i	0.797325	+	0.460336i	−0.0452099	+	0.998978i	$0.514396\pi$
$432$	4.21580	+	16.7718i	0.202833	+	0.806932i
$433$	9.52072	+	16.4904i	0.457537	+	0.792477i	0.998830	−	0.0483571i	$-0.0153986\pi$
$433$	9.52072	+	16.4904i	0.457537	+	0.792477i	−0.541294	+	0.840834i	$0.682065\pi$
$434$	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	−0.748873	−	0.662713i	$-0.769405\pi$
$439$	4.17977	−	7.23957i	0.199490	−	0.345526i	0.948363	+	0.317187i	$0.102738\pi$
$440$	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	$-0.777448\pi$
$443$		−	27.0916i		−	1.28716i	0.765378	−	0.643580i	$-0.222552\pi$
$444$	−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	−0.504547	−	0.863384i	$-0.668341\pi$
$449$	−0.192996	+	0.111426i	−0.00910804	+	0.00525853i	0.495439	+	0.868643i	$0.335007\pi$
$450$	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	0.335427	−	0.942066i	$-0.391119\pi$
$457$	−6.68503	−	3.85960i	−0.312712	−	0.180545i	−0.648140	+	0.761522i	$0.724453\pi$
$458$	−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	0.708059	−	0.706153i	$-0.249571\pi$
$461$	−5.52913	−	9.57673i	−0.257517	−	0.446033i	−0.965576	+	0.260120i	$0.916238\pi$
$462$	−0.635035	−	1.89491i	−0.0295445	−	0.0881590i
$463$			28.7883i			1.33791i	0.743304	+	0.668954i	$0.233258\pi$
$463$			28.7883i			1.33791i	−0.743304	+	0.668954i	$0.766742\pi$
$464$	−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	$-0.713160\pi$
$467$		−	33.8862i		−	1.56806i	0.620720	−	0.784032i	$-0.286840\pi$
$468$	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	0.126695	−	0.991942i	$-0.459563\pi$
$479$	−14.6419	−	8.45349i	−0.669004	−	0.386250i	−0.795699	+	0.605692i	$0.792896\pi$
$480$	−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	0.318305	−	0.947988i	$-0.396886\pi$
$487$	28.6541	−	16.5434i	1.29844	−	0.749654i	0.980135	+	0.198334i	$0.0635530\pi$
$488$	−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	−0.240446	−	0.970663i	$-0.577294\pi$
$491$	−26.6188	−	15.3683i	−1.20129	−	0.693564i	−0.960841	+	0.277099i	$0.910627\pi$
$492$	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	−0.789636	−	0.613576i	$-0.789730\pi$
$503$	−20.7723	−	35.9786i	−0.926190	−	1.60421i	−0.136555	−	0.990633i	$-0.543603\pi$
$504$	−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	−0.990984	−	0.133984i	$-0.957223\pi$
$509$	−8.56097	+	14.8280i	−0.379458	+	0.657241i	0.611525	+	0.791225i	$0.290556\pi$
$510$	−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	0.457178	−	0.889375i	$-0.348860\pi$
$523$	−1.93140	−	1.11509i	−0.0844542	−	0.0487597i	−0.541632	+	0.840615i	$0.682194\pi$
$524$	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	$0.333779\pi$
$547$			40.5419i			1.73345i	−0.498788	+	0.866724i	$0.666221\pi$
$548$	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	0.376746	+	0.926317i	$0.377043\pi$
$557$	−14.4872	+	25.0925i	−0.613841	+	1.06320i	−0.990587	+	0.136887i	$0.956290\pi$
$558$	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	0.0779201	−	0.996960i	$-0.475172\pi$
$563$	23.2595	−	13.4289i	0.980272	−	0.565961i	0.902352	+	0.430999i	$0.141839\pi$
$564$	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	−0.930544	−	0.366181i	$-0.880665\pi$
$569$	−3.53392	+	6.12094i	−0.148150	+	0.256603i	0.782394	+	0.622784i	$0.213998\pi$
$570$	−1.47650	−	1.30503i	−0.0618436	−	0.0546618i
$571$		−	14.6144i		−	0.611594i	−0.952097	−	0.305797i	$-0.901077\pi$
$571$		−	14.6144i		−	0.611594i	0.952097	−	0.305797i	$-0.0989230\pi$
$572$	−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	$-0.963567\pi$
$577$		−	5.48671i		−	0.228415i	0.993457	−	0.114207i	$-0.0364328\pi$
$578$	−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	−0.599378	−	0.800466i	$-0.704585\pi$
$587$	9.53461	−	16.5144i	0.393536	−	0.681623i	0.992913	+	0.118843i	$0.0379185\pi$
$588$	−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	$0.201630\pi$
$593$			28.8284i			1.18384i	−0.805997	+	0.591920i	$0.798370\pi$
$594$	−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	−0.988592	−	0.150619i	$-0.951873\pi$
$601$	−8.92004	+	15.4500i	−0.363856	+	0.630217i	0.624736	+	0.780836i	$0.285207\pi$
$602$	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	0.997871	+	0.0652243i	$0.0207763\pi$
$607$	13.6841	+	23.7016i	0.555421	+	0.962018i	−0.442449	+	0.896793i	$0.645890\pi$
$608$	−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	−0.821530	−	0.570165i	$-0.806879\pi$
$613$	2.05530	−	3.55988i	0.0830127	−	0.143782i	0.904543	+	0.426383i	$0.140212\pi$
$614$	−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	−0.930921	−	0.365220i	$-0.880994\pi$
$617$	−26.8289	+	15.4897i	−1.08009	+	0.623591i	−0.149170	+	0.988812i	$0.547660\pi$
$618$	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	−0.451662	−	0.892189i	$-0.649169\pi$
$631$	2.39053	−	1.38018i	0.0951657	−	0.0549439i	0.546828	+	0.837245i	$0.315835\pi$
$632$	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	0.947810	−	0.318836i	$-0.103292\pi$
$641$	5.00752	+	8.67328i	0.197785	+	0.342574i	−0.750025	+	0.661410i	$0.769958\pi$
$642$	6.22933	+	1.26427i	0.245852	+	0.0498966i
$643$	−14.2515	−	24.6843i	−0.562024	−	0.973454i	−0.997320	−	0.0731662i	$-0.976690\pi$
$643$	−14.2515	−	24.6843i	−0.562024	−	0.973454i	0.435296	−	0.900287i	$-0.356644\pi$
$644$	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	−0.975242	−	0.221138i	$-0.929023\pi$
$647$	−7.53191	+	13.0456i	−0.296110	+	0.512877i	0.679133	+	0.734016i	$0.262356\pi$
$648$	−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	0.760650	−	0.649163i	$-0.224881\pi$
$653$	14.7901	+	8.53909i	0.578783	+	0.334161i	−0.181867	+	0.983323i	$0.558214\pi$
$654$	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	−0.973522	−	0.228593i	$-0.926588\pi$
$659$	−32.4049	+	18.7090i	−1.26232	+	0.728799i	−0.288794	+	0.957391i	$0.593254\pi$
$660$	−0.436198	−	0.577702i	−0.0169790	−	0.0224870i
$661$	8.83203	−	15.2975i	0.343526	−	0.595005i	−0.641559	−	0.767074i	$-0.721712\pi$
$661$	8.83203	−	15.2975i	0.343526	−	0.595005i	0.985085	+	0.172069i	$0.0550453\pi$
$662$	−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	−0.568420	−	0.822738i	$-0.692445\pi$
$673$	11.1111	−	19.2450i	0.428302	−	0.741841i	0.996722	+	0.0808970i	$0.0257785\pi$
$674$	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	$-0.963255\pi$
$677$		−	5.99382i		−	0.230361i	0.993345	−	0.115181i	$-0.0367447\pi$
$678$	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	0.765333	−	0.643634i	$-0.222574\pi$
$683$	−4.56662	−	7.90963i	−0.174737	−	0.302653i	−0.940070	+	0.340981i	$0.889241\pi$
$684$	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	−0.989131	−	0.147037i	$-0.953026\pi$
$691$	−9.65327	+	16.7200i	−0.367228	+	0.636057i	0.621903	+	0.783094i	$0.286360\pi$
$692$	−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	$0.0688825\pi$
$701$			11.3698i			0.429432i	−0.976677	+	0.214716i	$0.931117\pi$
$702$	−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	0.912304	−	0.409513i	$-0.134301\pi$
$709$	2.70275	+	4.68129i	0.101504	+	0.175810i	−0.810801	+	0.585322i	$0.800968\pi$
$710$	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	0.925146	−	0.379612i	$-0.123942\pi$
$719$	3.58826	+	6.21504i	0.133819	+	0.231782i	−0.791326	+	0.611394i	$0.790609\pi$
$720$	−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	−0.789879	−	0.613263i	$-0.789857\pi$
$739$	3.70149	−	6.41116i	0.136161	−	0.235838i	0.926041	+	0.377424i	$0.123190\pi$
$740$	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	−0.407856	−	0.913046i	$-0.633724\pi$
$743$	−38.2295	−	22.0718i	−1.40251	−	0.809737i	−0.994649	+	0.103309i	$0.967057\pi$
$744$	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	−0.875456	−	0.483297i	$-0.839439\pi$
$751$	−0.525634	+	0.910425i	−0.0191807	+	0.0332219i	0.856276	+	0.516519i	$0.172772\pi$
$752$	−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	0.881417	−	0.472339i	$-0.156590\pi$
$757$	25.1218	+	14.5041i	0.913068	+	0.527160i	0.0316510	+	0.999499i	$0.489924\pi$
$758$	−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	−0.315514	−	0.948921i	$-0.602177\pi$
$761$	9.61433	−	5.55084i	0.348519	−	0.201218i	0.664033	+	0.747703i	$0.268843\pi$
$762$	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	−	7.92220i	−0.494815	−	0.285682i	0.231755	−	0.972774i	$-0.425553\pi$
$769$	−13.7216	−	7.92220i	−0.494815	−	0.285682i	−0.726570	+	0.687093i	$0.758887\pi$
$770$	1.85159	+	1.63657i	0.0667267	+	0.0589779i
$771$	−11.6178	+	6.70757i	−0.418407	+	0.241567i
$772$	13.2118	−	31.2082i	0.475504	−	1.12321i
$773$	23.4377	+	40.5953i	0.842995	+	1.46011i	0.887351	+	0.461095i	$0.152543\pi$
$773$	23.4377	+	40.5953i	0.842995	+	1.46011i	−0.0443558	+	0.999016i	$0.514124\pi$
$774$	2.13456	−	0.715351i	0.0767253	−	0.0257128i
$775$		−	5.19873i		−	0.186744i
$776$	25.5355	+	1.97280i	0.916672	+	0.0708192i
$777$	8.19430	−	14.1929i	0.293969	−	0.509169i
$778$	−3.85209	−	3.40476i	−0.138104	−	0.122067i
$779$		−	8.69623i		−	0.311575i
$780$	4.85296	−	3.23385i	0.173764	−	0.115790i
$781$			4.68050i			0.167482i
$782$	−8.56218	+	9.68713i	−0.306183	+	0.346411i
$783$	20.0696	−	34.7616i	0.717230	−	1.24228i
$784$	−9.02848	+	31.7151i	−0.322446	+	1.13268i
$785$			9.05130i			0.323055i
$786$	−4.25595	−	12.6995i	−0.151805	−	0.452975i
$787$	−3.04879	−	5.28066i	−0.108678	−	0.188235i	0.806557	−	0.591156i	$-0.201328\pi$
$787$	−3.04879	−	5.28066i	−0.108678	−	0.188235i	−0.915235	+	0.402921i	$0.867995\pi$
$788$	−29.0179	−	12.2846i	−1.03372	−	0.437621i
$789$	14.3630	−	8.29247i	0.511336	−	0.295220i
$790$	16.1939	−	18.3215i	0.576153	−	0.651851i
$791$	−38.2267	−	22.0702i	−1.35918	−	0.784725i
$792$	2.44982	+	1.67854i	0.0870506	+	0.0596443i
$793$	28.4404	+	1.67807i	1.00995	+	0.0595899i
$794$	4.14283	+	0.840804i	0.147024	+	0.0298390i
$795$	4.81158	−	8.33390i	0.170649	−	0.295573i
$796$	−9.88289	+	7.46214i	−0.350290	+	0.264489i
$797$	−22.9312	+	13.2393i	−0.812265	+	0.468962i	−0.847742	−	0.530409i	$-0.822038\pi$
$797$	−22.9312	+	13.2393i	−0.812265	+	0.468962i	0.0354766	+	0.999371i	$0.488705\pi$
$798$	7.54004	+	1.53028i	0.266915	+	0.0541713i
$799$	60.4755	−	34.9155i	2.13947	−	1.23522i
$800$	2.60003	−	5.02393i	0.0919249	−	0.177623i
$801$		−	20.8744i		−	0.737561i
$802$	−17.4899	+	5.86134i	−0.617589	+	0.206971i
$803$	−0.0458243	−	0.0264567i	−0.00161710	−	0.000933635i
$804$	−10.4462	−	13.8350i	−0.368409	−	0.487922i
$805$		−	4.45279i		−	0.156940i
$806$	−6.92822	−	25.5870i	−0.244036	−	0.901265i
$807$	4.65998			0.164039
$808$	0.0321464	+	0.0671480i	0.00113091	+	0.00236226i
$809$	8.25341	−	14.2953i	0.290174	−	0.502597i	−0.683676	−	0.729785i	$-0.739620\pi$
$809$	8.25341	−	14.2953i	0.290174	−	0.502597i	0.973851	+	0.227189i	$0.0729534\pi$
$810$	1.59150	+	4.74894i	0.0559196	+	0.166861i
$811$	3.10399			0.108996			0.0544980	−	0.998514i	$-0.482644\pi$
$811$	3.10399			0.108996			0.0544980	+	0.998514i	$0.482644\pi$
$812$	−8.90411	−	71.9486i	−0.312473	−	2.52490i
$813$	−3.83111	−	6.63568i	−0.134363	−	0.232723i
$814$	−3.21953	−	0.653417i	−0.112845	−	0.0229022i
$815$	7.29415	+	12.6338i	0.255503	+	0.442544i
$816$	6.32131	+	25.1482i	0.221290	+	0.880362i
$817$	−1.01250	−	0.584567i	−0.0354229	−	0.0204514i
$818$	−3.81016	+	18.7735i	−0.133219	+	0.656401i
$819$	14.7992	+	29.5234i	0.517127	+	1.03163i
$820$	−3.93529	+	9.29570i	−0.137426	+	0.324620i
$821$	14.9440	−	25.8838i	0.521550	−	0.903350i	−0.478136	−	0.878286i	$-0.658687\pi$
$821$	14.9440	−	25.8838i	0.521550	−	0.903350i	0.999686	−	0.0250648i	$-0.00797920\pi$
$822$	5.68486	−	6.43177i	0.198282	−	0.224334i
$823$	−1.82874	−	3.16748i	−0.0637460	−	0.110411i	0.832391	−	0.554189i	$-0.186971\pi$
$823$	−1.82874	−	3.16748i	−0.0637460	−	0.110411i	−0.896137	+	0.443777i	$0.853638\pi$
$824$	−30.5414	−	20.9260i	−1.06396	−	0.728992i
$825$	−0.313451	+	0.180971i	−0.0109130	+	0.00630060i
$826$	48.9007	−	16.3880i	1.70147	−	0.570210i
$827$	21.7337			0.755755			0.377878	−	0.925856i	$-0.376654\pi$
$827$	21.7337			0.755755			0.377878	+	0.925856i	$0.376654\pi$
$828$	−0.657214	−	5.31054i	−0.0228398	−	0.184554i
$829$	8.09758	+	4.67514i	0.281240	+	0.162374i	0.633985	−	0.773345i	$-0.281418\pi$
$829$	8.09758	+	4.67514i	0.281240	+	0.162374i	−0.352744	+	0.935720i	$0.614751\pi$
$830$	−9.53742	+	10.7905i	−0.331049	+	0.374544i
$831$	−1.99918			−0.0693509
$832$	6.10151	−	28.1917i	0.211532	−	0.977371i
$833$	−66.0818			−2.28960
$834$	6.18631	−	6.99910i	0.214215	−	0.242359i
$835$	3.06989	+	1.77240i	0.106238	+	0.0613366i
$836$	−0.189419	−	1.53057i	−0.00655118	−	0.0529360i
$837$	−22.4761			−0.776887
$838$	−35.3551	+	11.8485i	−1.22132	+	0.409299i
$839$	−44.9503	+	25.9521i	−1.55186	+	0.895965i	−0.553865	+	0.832606i	$0.686848\pi$
$839$	−44.9503	+	25.9521i	−1.55186	+	0.895965i	−0.997991	+	0.0633583i	$0.979819\pi$
$840$	−7.36731	−	5.04785i	−0.254196	−	0.174167i
$841$	28.5986	+	49.5342i	0.986157	+	1.70807i
$842$	17.1702	−	19.4261i	0.591723	−	0.669467i
$843$	2.34842	−	4.06759i	0.0808840	−	0.140095i
$844$	−1.05430	+	2.49040i	−0.0362905	+	0.0857231i
$845$	−5.13096	−	11.9446i	−0.176510	−	0.410906i
$846$	−5.74864	+	28.3249i	−0.197642	+	0.973829i
$847$	36.5165	+	21.0828i	1.25472	+	0.724413i
$848$	−11.6032	−	46.1613i	−0.398456	−	1.58518i
$849$	6.27691	+	10.8719i	0.215423	+	0.373124i
$850$	11.1098	+	2.25477i	0.381062	+	0.0773379i
$851$	2.95975	+	5.12644i	0.101459	+	0.175732i
$852$	−2.07751	−	16.7870i	−0.0711742	−	0.575115i
$853$	−20.0902			−0.687876			−0.343938	−	0.938992i	$-0.611761\pi$
$853$	−20.0902			−0.687876			−0.343938	+	0.938992i	$0.611761\pi$
$854$	−13.8636	−	41.3683i	−0.474404	−	1.41559i
$855$	2.02104	−	3.50055i	0.0691183	−	0.119716i
$856$	−6.78782	−	14.1785i	−0.232003	−	0.484612i
$857$	−33.2720			−1.13655			−0.568275	−	0.822839i	$-0.692389\pi$
$857$	−33.2720			−1.13655			−0.568275	+	0.822839i	$0.692389\pi$
$858$	−1.30156	+	1.30843i	−0.0444346	+	0.0446690i
$859$			24.8144i			0.846655i	0.905977	+	0.423328i	$0.139138\pi$
$859$			24.8144i			0.846655i	−0.905977	+	0.423328i	$0.860862\pi$
$860$	0.817762	+	1.08305i	0.0278855	+	0.0369316i
$861$	13.8014	+	7.96823i	0.470350	+	0.271556i
$862$	−25.6298	+	8.58926i	−0.872955	+	0.292551i
$863$			47.6763i			1.62292i	0.584407	+	0.811461i	$0.301327\pi$
$863$			47.6763i			1.62292i	−0.584407	+	0.811461i	$0.698673\pi$
$864$	−21.7203	−	11.2409i	−0.738941	−	0.382423i
$865$	−9.91643	+	5.72526i	−0.337169	+	0.194665i
$866$	−26.3906	−	5.35608i	−0.896790	−	0.182007i
$867$	−33.0962	+	19.1081i	−1.12400	+	0.648944i
$868$	−32.3973	+	24.4618i	−1.09964	+	0.830287i
$869$	−3.86919	+	6.70164i	−0.131253	+	0.227338i
$870$	10.4062	+	2.11198i	0.352803	+	0.0716027i
$871$	−34.5473	+	17.3176i	−1.17059	+	0.586783i
$872$	−1.36345	−	0.934191i	−0.0461721	−	0.0316357i
$873$	−18.3970	−	10.6215i	−0.622644	−	0.359484i
$874$	−1.84040	+	2.08220i	−0.0622523	+	0.0704314i
$875$	−3.38125	+	1.95217i	−0.114307	+	0.0659952i
$876$	0.176096	+	0.0745495i	0.00594973	+	0.00251879i
$877$	3.83100	+	6.63549i	0.129364	+	0.224065i	0.923430	−	0.383766i	$-0.125373\pi$
$877$	3.83100	+	6.63549i	0.129364	+	0.224065i	−0.794066	+	0.607831i	$0.792040\pi$
$878$	3.75660	+	11.2095i	0.126779	+	0.378301i
$879$			25.3155i			0.853870i
$880$	−0.490152	+	1.72180i	−0.0165230	+	0.0580418i
$881$	10.3478	−	17.9229i	0.348627	−	0.603839i	−0.637379	−	0.770550i	$-0.719981\pi$
$881$	10.3478	−	17.9229i	0.348627	−	0.603839i	0.986006	+	0.166711i	$0.0533147\pi$
$882$	18.1132	−	20.4930i	0.609904	−	0.690037i
$883$		−	36.7201i		−	1.23573i	−0.786284	−	0.617865i	$-0.787998\pi$
$883$		−	36.7201i		−	1.23573i	0.786284	−	0.617865i	$-0.212002\pi$
$884$	57.6847	−	3.70821i	1.94015	−	0.124721i
$885$			7.55374i			0.253916i
$886$	28.7071	+	25.3734i	0.964435	+	0.852437i
$887$	−2.06997	+	3.58529i	−0.0695028	+	0.120382i	−0.898683	−	0.438600i	$-0.855475\pi$
$887$	−2.06997	+	3.58529i	−0.0695028	+	0.120382i	0.829180	+	0.558982i	$0.188808\pi$
$888$	11.8372	+	0.914503i	0.397230	+	0.0306887i
$889$			45.7367i			1.53396i
$890$	11.9314	−	3.99855i	0.399942	−	0.134032i
$891$	−0.792516	−	1.37268i	−0.0265503	−	0.0459864i
$892$	8.71029	−	20.5749i	0.291642	−	0.688899i
$893$	12.9989	−	7.50491i	0.434991	−	0.251142i
$894$	−4.54421	−	4.01650i	−0.151981	−	0.134332i
$895$	−0.746881	−	0.431212i	−0.0249655	−	0.0144138i
$896$	−43.5420	+	7.43650i	−1.45464	+	0.248436i
$897$	3.31969	+	0.195872i	0.110841	+	0.00653996i
$898$	0.0626851	−	0.308864i	0.00209183	−	0.0103069i
$899$	24.1331	−	41.7998i	0.804885	−	1.39410i
$900$	−3.74446	+	2.82728i	−0.124815	+	0.0942426i
$901$	82.6052	−	47.6921i	2.75198	−	1.58886i
$902$	0.635390	−	3.13071i	0.0211562	−	0.104241i
$903$	1.85548	−	1.07126i	0.0617464	−	0.0356493i
$904$	2.46309	−	31.8818i	0.0819210	−	1.06037i
$905$		−	4.43168i		−	0.147314i
$906$	−1.57120	−	4.68836i	−0.0521995	−	0.155760i
$907$	−1.73495	−	1.00167i	−0.0576081	−	0.0332600i	0.470919	−	0.882176i	$-0.343922\pi$
$907$	−1.73495	−	1.00167i	−0.0576081	−	0.0332600i	−0.528527	+	0.848916i	$0.677256\pi$
$908$	−16.5816	+	12.5201i	−0.550281	+	0.415493i
$909$		−	0.0617479i		−	0.00204805i
$910$	−14.0402	+	14.1142i	−0.465428	+	0.467883i
$911$	11.2850			0.373888			0.186944	−	0.982371i	$-0.440142\pi$
$911$	11.2850			0.373888			0.186944	+	0.982371i	$0.440142\pi$
$912$	1.35873	+	5.40547i	0.0449921	+	0.178993i
$913$	2.27877	−	3.94694i	0.0754162	−	0.130625i
$914$	10.3508	−	3.46884i	0.342374	−	0.114739i
$915$	6.39020			0.211253
$916$	−5.67671	−	45.8700i	−0.187564	−	1.51559i
$917$	22.8615	+	39.5973i	0.754953	+	1.30762i
$918$	9.74821	−	48.0317i	0.321739	−	1.58528i
$919$	−2.32099	−	4.02006i	−0.0765622	−	0.132610i	0.825202	−	0.564837i	$-0.191061\pi$
$919$	−2.32099	−	4.02006i	−0.0765622	−	0.132610i	−0.901765	+	0.432228i	$0.857728\pi$
$920$	2.90951	−	1.39290i	0.0959238	−	0.0459225i
$921$	2.69185	+	1.55414i	0.0886996	+	0.0512107i
$922$	15.3263	+	3.11053i	0.504744	+	0.102440i
$923$	−37.6414	−	2.22096i	−1.23898	−	0.0731036i
$924$	2.60266	+	1.10183i	0.0856213	+	0.0362474i
$925$	2.59519	−	4.49501i	0.0853294	−	0.147795i
$926$	−30.5050	−	26.9626i	−1.00246	−	0.886044i
$927$	15.3538	+	26.5936i	0.504285	+	0.873448i
$928$	44.2269	−	28.3247i	1.45182	−	0.929804i
$929$	−32.6268	+	18.8371i	−1.07045	+	0.618026i	−0.928305	−	0.371820i	$-0.878734\pi$
$929$	−32.6268	+	18.8371i	−1.07045	+	0.618026i	−0.142147	+	0.989846i	$0.545401\pi$
$930$	−1.88932	−	5.63761i	−0.0619532	−	0.184865i
$931$	−14.2039			−0.465515
$932$	2.10516	+	17.0105i	0.0689569	+	0.557199i
$933$	−15.2920	−	8.82882i	−0.500637	−	0.289043i
$934$	35.9068	+	31.7371i	1.17491	+	1.03847i
$935$	−3.58755			−0.117325
$936$	−14.6616	+	18.9054i	−0.479229	+	0.617943i
$937$	6.94069			0.226743			0.113371	−	0.993553i	$-0.463835\pi$
$937$	6.94069			0.226743			0.113371	+	0.993553i	$0.463835\pi$
$938$	44.3424	+	39.1931i	1.44783	+	1.27970i
$939$	7.39681	+	4.27055i	0.241386	+	0.139364i
$940$	−17.2911	+	2.13989i	−0.563974	+	0.0697955i
$941$	−5.89583			−0.192199			−0.0960993	−	0.995372i	$-0.530637\pi$
$941$	−5.89583			−0.192199			−0.0960993	+	0.995372i	$0.530637\pi$
$942$	3.28942	+	9.81541i	0.107175	+	0.319803i
$943$	−4.98500	+	2.87809i	−0.162334	+	0.0937236i
$944$	26.0050	+	26.8260i	0.846391	+	0.873111i
$945$	8.43994	+	14.6184i	0.274551	+	0.475537i
$946$	−0.321796	−	0.284427i	−0.0104625	−	0.00924751i
$947$	19.3243	−	33.4706i	0.627954	−	1.08765i	−0.360007	−	0.932950i	$-0.617226\pi$
$947$	19.3243	−	33.4706i	0.627954	−	1.08765i	0.987962	−	0.154699i	$-0.0494409\pi$
$948$	10.9026	−	25.7534i	0.354100	−	0.836432i
$949$	0.234513	−	0.355973i	0.00761263	−	0.0115554i
$950$	2.38799	+	0.484651i	0.0774765	+	0.0157241i
$951$	−13.5259	−	7.80917i	−0.438607	−	0.253230i
$952$	−38.2240	−	79.8430i	−1.23885	−	2.58773i
$953$	6.44411	+	11.1615i	0.208745	+	0.361557i	0.951320	−	0.308206i	$-0.0997287\pi$
$953$	6.44411	+	11.1615i	0.208745	+	0.361557i	−0.742574	+	0.669764i	$0.766395\pi$
$954$	−7.85224	+	38.6898i	−0.254226	+	1.25263i
$955$	−10.8557	−	18.8026i	−0.351282	−	0.608438i
$956$	2.03719	−	0.252115i	0.0658873	−	0.00815398i
$957$	−3.36036			−0.108625
$958$	22.6709	−	7.59763i	0.732462	−	0.245468i
$959$	−14.6520	+	25.3780i	−0.473137	+	0.819497i
$960$	0.993730	−	6.39295i	0.0320725	−	0.206332i
$961$	3.97319			0.128167
$962$	6.78260	−	25.5820i	0.218680	−	0.824797i
$963$			13.0383i			0.420153i
$964$	−19.7763	−	26.1918i	−0.636951	−	0.843581i
$965$	−14.6746	−	8.47239i	−0.472392	−	0.272736i
$966$	−1.61823	−	4.82869i	−0.0520656	−	0.155361i
$967$			5.89312i			0.189510i	0.995501	+	0.0947550i	$0.0302068\pi$
$967$			5.89312i			0.189510i	−0.995501	+	0.0947550i	$0.969793\pi$
$968$	−2.35289	+	30.4554i	−0.0756248	+	0.978874i
$969$	−9.67303	+	5.58473i	−0.310743	+	0.179407i
$970$	2.54706	−	12.5499i	0.0817812	−	0.402954i
$971$	41.4348	−	23.9224i	1.32971	−	0.767707i	0.344453	−	0.938804i	$-0.388064\pi$
$971$	41.4348	−	23.9224i	1.32971	−	0.767707i	0.985254	+	0.171097i	$0.0547310\pi$
$972$	19.0828	+	25.2733i	0.612080	+	0.810642i
$973$	−15.9444	+	27.6165i	−0.511154	+	0.885345i
$974$	−9.30685	+	45.8570i	−0.298211	+	1.46935i
$975$	−1.30666	−	2.60670i	−0.0418468	−	0.0834813i
$976$	22.6939	−	21.9993i	0.726412	−	0.704181i
$977$	31.9115	+	18.4241i	1.02094	+	0.589440i	0.914376	−	0.404866i	$-0.132682\pi$
$977$	31.9115	+	18.4241i	1.02094	+	0.589440i	0.106564	+	0.994306i	$0.466015\pi$
$978$	12.5013	+	11.0495i	0.399747	+	0.353326i
$979$	−3.44877	+	1.99115i	−0.110223	+	0.0636373i
$980$	15.1831	+	6.42768i	0.485005	+	0.205325i
$981$	0.685434	+	1.18721i	0.0218842	+	0.0379046i
$982$	41.2154	−	13.8124i	1.31523	−	0.440772i
$983$		−	15.1109i		−	0.481963i	−0.970530	−	0.240981i	$-0.922531\pi$
$983$		−	15.1109i		−	0.481963i	0.970530	−	0.240981i	$-0.0774692\pi$
$984$	−0.889273	+	11.5106i	−0.0283490	+	0.366945i
$985$	−7.87779	+	13.6447i	−0.251007	+	0.434757i
$986$	78.8599	+	69.7021i	2.51141	+	2.21977i
$987$			27.5065i			0.875543i
$988$	12.3990	−	0.797061i	0.394466	−	0.0253579i
$989$			0.773870i			0.0246076i
$990$	0.983359	−	1.11256i	0.0312532	−	0.0353594i
$991$	13.4677	−	23.3267i	0.427815	−	0.740998i	−0.568864	−	0.822432i	$-0.692617\pi$
$991$	13.4677	−	23.3267i	0.427815	−	0.740998i	0.996679	+	0.0814344i	$0.0259501\pi$
$992$	−26.1181	−	13.5168i	−0.829249	−	0.429160i
$993$			17.1839i			0.545316i
$994$	18.3488	+	54.7517i	0.581989	+	1.73662i
$995$	3.09592	+	5.36228i	0.0981471	+	0.169996i
$996$	−6.42110	+	15.1675i	−0.203460	+	0.480601i
$997$	−30.1185	+	17.3889i	−0.953861	+	0.550712i	−0.894278	−	0.447511i	$-0.852310\pi$
$997$	−30.1185	+	17.3889i	−0.953861	+	0.550712i	−0.0595828	+	0.998223i	$0.518977\pi$
$998$	−6.16938	+	6.97994i	−0.195288	+	0.220946i
$999$	−19.4336	−	11.2200i	−0.614852	−	0.354985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.ca.a.381.8	yes	56
8.5	even	2		520.2.ca.b.381.18	yes	56
13.10	even	6		520.2.ca.b.101.18	yes	56
104.101	even	6	inner	520.2.ca.a.101.8	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.ca.a.101.8	✓	56	104.101	even	6	inner
520.2.ca.a.381.8	yes	56	1.1	even	1	trivial
520.2.ca.b.101.18	yes	56	13.10	even	6
520.2.ca.b.381.18	yes	56	8.5	even	2

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30}+ \cdots + 48 q^{99}+O(q^{100}) \) 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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