LMFDB - Embedded newform 117.2.x.a.59.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(2,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("117.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.x (of order $12$, degree $4$, 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			59.7
Character	$\chi$	$=$	117.59
Dual form			117.2.x.a.2.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0604708 - 0.0604708i) q^{2} +(1.25573 - 1.19295i) q^{3} +1.99269i q^{4} +(0.466078 + 1.73943i) q^{5} +(0.00379642 - 0.148074i) q^{6} +(0.132635 + 0.495001i) q^{7} +(0.241441 + 0.241441i) q^{8} +(0.153731 - 2.99606i) q^{9} +(0.133369 + 0.0770004i) q^{10} +(-4.05119 - 4.05119i) q^{11} +(2.37718 + 2.50228i) q^{12} +(3.18076 - 1.69788i) q^{13} +(0.0379537 + 0.0219126i) q^{14} +(2.66032 + 1.62825i) q^{15} -3.95617 q^{16} +(-2.73683 - 4.74032i) q^{17} +(-0.171878 - 0.190470i) q^{18} +(-1.92187 + 7.17250i) q^{19} +(-3.46613 + 0.928747i) q^{20} +(0.757066 + 0.463362i) q^{21} -0.489958 q^{22} +(2.21820 + 3.84203i) q^{23} +(0.591213 + 0.0151579i) q^{24} +(1.52175 - 0.878584i) q^{25} +(0.0896707 - 0.295015i) q^{26} +(-3.38111 - 3.94564i) q^{27} +(-0.986381 + 0.264300i) q^{28} -0.515564i q^{29} +(0.259333 - 0.0624104i) q^{30} +(-3.18763 + 0.854124i) q^{31} +(-0.722115 + 0.722115i) q^{32} +(-9.92010 - 0.254338i) q^{33} +(-0.452149 - 0.121153i) q^{34} +(-0.799199 + 0.461418i) q^{35} +(5.97021 + 0.306337i) q^{36} +(-0.815602 - 3.04387i) q^{37} +(0.317510 + 0.549944i) q^{38} +(1.96869 - 5.92657i) q^{39} +(-0.307439 + 0.532499i) q^{40} +(-2.70348 - 0.724395i) q^{41} +(0.0738003 - 0.0177606i) q^{42} +(1.81412 + 1.04738i) q^{43} +(8.07276 - 8.07276i) q^{44} +(5.28307 - 1.12899i) q^{45} +(0.366467 + 0.0981945i) q^{46} +(-1.08839 + 4.06193i) q^{47} +(-4.96790 + 4.71952i) q^{48} +(5.83474 - 3.36869i) q^{49} +(0.0388929 - 0.145150i) q^{50} +(-9.09170 - 2.68768i) q^{51} +(3.38334 + 6.33825i) q^{52} +8.79692i q^{53} +(-0.443055 - 0.0341378i) q^{54} +(5.15858 - 8.93492i) q^{55} +(-0.0874900 + 0.151537i) q^{56} +(6.14310 + 11.2994i) q^{57} +(-0.0311766 - 0.0311766i) q^{58} +(5.47412 + 5.47412i) q^{59} +(-3.24458 + 5.30119i) q^{60} +(2.89997 - 5.02290i) q^{61} +(-0.141109 + 0.244409i) q^{62} +(1.50344 - 0.321286i) q^{63} -7.82501i q^{64} +(4.43582 + 4.74134i) q^{65} +(-0.615257 + 0.584497i) q^{66} +(-1.38685 + 5.17581i) q^{67} +(9.44597 - 5.45364i) q^{68} +(7.36882 + 2.17836i) q^{69} +(-0.0204259 + 0.0762306i) q^{70} +(2.49660 + 0.668962i) q^{71} +(0.760489 - 0.686255i) q^{72} +(-4.21361 + 4.21361i) q^{73} +(-0.233385 - 0.134745i) q^{74} +(0.862806 - 2.91864i) q^{75} +(-14.2925 - 3.82968i) q^{76} +(1.46801 - 2.54267i) q^{77} +(-0.239336 - 0.477433i) q^{78} +(-2.43009 - 4.20904i) q^{79} +(-1.84388 - 6.88147i) q^{80} +(-8.95273 - 0.921173i) q^{81} +(-0.207286 + 0.119677i) q^{82} +(-3.28109 - 0.879166i) q^{83} +(-0.923334 + 1.50860i) q^{84} +(6.96986 - 6.96986i) q^{85} +(0.173037 - 0.0463652i) q^{86} +(-0.615044 - 0.647411i) q^{87} -1.95625i q^{88} +(10.8505 - 2.90739i) q^{89} +(0.251201 - 0.387743i) q^{90} +(1.26233 + 1.34928i) q^{91} +(-7.65596 + 4.42017i) q^{92} +(-2.98389 + 4.87525i) q^{93} +(0.179812 + 0.311444i) q^{94} -13.3718 q^{95} +(-0.0453351 + 1.76823i) q^{96} +(2.14413 - 0.574518i) q^{97} +(0.149124 - 0.556539i) q^{98} +(-12.7604 + 11.5148i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.0604708	−	0.0604708i	0.0427593	−	0.0427593i	−0.685404	−	0.728163i	$-0.740374\pi$
$2$	0.0604708	−	0.0604708i	0.0427593	−	0.0427593i	0.728163	+	0.685404i	$0.240374\pi$
$3$	1.25573	−	1.19295i	0.724998	−	0.688751i
$3$	1.25573	−	1.19295i	0.724998	−	0.688751i
$4$			1.99269i			0.996343i
$5$	0.466078	+	1.73943i	0.208436	+	0.777895i	0.988375	+	0.152039i	$0.0485838\pi$
$5$	0.466078	+	1.73943i	0.208436	+	0.777895i	−0.779938	+	0.625857i	$0.784750\pi$
$6$	0.00379642	−	0.148074i	0.00154988	−	0.0604510i
$7$	0.132635	+	0.495001i	0.0501313	+	0.187093i	0.986451	−	0.164056i	$-0.0524578\pi$
$7$	0.132635	+	0.495001i	0.0501313	+	0.187093i	−0.936320	+	0.351149i	$0.885791\pi$
$8$	0.241441	+	0.241441i	0.0853623	+	0.0853623i
$9$	0.153731	−	2.99606i	0.0512436	−	0.998686i
$10$	0.133369	+	0.0770004i	0.0421749	+	0.0243497i
$11$	−4.05119	−	4.05119i	−1.22148	−	1.22148i	−0.967106	−	0.254375i	$-0.918130\pi$
$11$	−4.05119	−	4.05119i	−1.22148	−	1.22148i	−0.254375	−	0.967106i	$-0.581870\pi$
$12$	2.37718	+	2.50228i	0.686233	+	0.722347i
$13$	3.18076	−	1.69788i	0.882183	−	0.470907i
$13$	3.18076	−	1.69788i	0.882183	−	0.470907i
$14$	0.0379537	+	0.0219126i	0.0101435	+	0.00585638i
$15$	2.66032	+	1.62825i	0.686892	+	0.420411i
$16$	−3.95617			−0.989043
$17$	−2.73683	−	4.74032i	−0.663778	−	1.14970i	−0.979615	−	0.200883i	$-0.935619\pi$
$17$	−2.73683	−	4.74032i	−0.663778	−	1.14970i	0.315837	−	0.948813i	$-0.397715\pi$
$18$	−0.171878	−	0.190470i	−0.0405120	−	0.0448943i
$19$	−1.92187	+	7.17250i	−0.440906	+	1.64548i	0.285618	+	0.958344i	$0.407801\pi$
$19$	−1.92187	+	7.17250i	−0.440906	+	1.64548i	−0.726524	+	0.687141i	$0.758865\pi$
$20$	−3.46613	+	0.928747i	−0.775050	+	0.207674i
$21$	0.757066	+	0.463362i	0.165205	+	0.101114i
$22$	−0.489958			−0.104459
$23$	2.21820	+	3.84203i	0.462526	+	0.801118i	0.999086	−	0.0427438i	$-0.0136099\pi$
$23$	2.21820	+	3.84203i	0.462526	+	0.801118i	−0.536560	+	0.843862i	$0.680277\pi$
$24$	0.591213	+	0.0151579i	0.120681	+	0.00309409i
$25$	1.52175	−	0.878584i	0.304350	−	0.175717i
$26$	0.0896707	−	0.295015i	0.0175859	−	0.0578572i
$27$	−3.38111	−	3.94564i	−0.650695	−	0.759339i
$28$	−0.986381	+	0.264300i	−0.186409	+	0.0499480i
$29$		−	0.515564i		−	0.0957379i	−0.998854	−	0.0478690i	$-0.984757\pi$
$29$		−	0.515564i		−	0.0957379i	0.998854	−	0.0478690i	$-0.0152430\pi$
$30$	0.259333	−	0.0624104i	0.0473476	−	0.0113945i
$31$	−3.18763	+	0.854124i	−0.572516	+	0.153405i	−0.533450	−	0.845831i	$-0.679105\pi$
$31$	−3.18763	+	0.854124i	−0.572516	+	0.153405i	−0.0390658	+	0.999237i	$0.512438\pi$
$32$	−0.722115	+	0.722115i	−0.127653	+	0.127653i
$33$	−9.92010	−	0.254338i	−1.72687	−	0.0442745i
$34$	−0.452149	−	0.121153i	−0.0775430	−	0.0207776i
$35$	−0.799199	+	0.461418i	−0.135089	+	0.0779938i
$36$	5.97021	+	0.306337i	0.995034	+	0.0510562i
$37$	−0.815602	−	3.04387i	−0.134084	−	0.500409i	−1.00000		0.000219073i	$-0.999930\pi$
$37$	−0.815602	−	3.04387i	−0.134084	−	0.500409i	0.865916	−	0.500190i	$-0.166736\pi$
$38$	0.317510	+	0.549944i	0.0515070	+	0.0892127i
$39$	1.96869	−	5.92657i	0.315243	−	0.949011i
$40$	−0.307439	+	0.532499i	−0.0486103	+	0.0841955i
$41$	−2.70348	−	0.724395i	−0.422213	−	0.113132i	0.0414558	−	0.999140i	$-0.486800\pi$
$41$	−2.70348	−	0.724395i	−0.422213	−	0.113132i	−0.463668	+	0.886009i	$0.653467\pi$
$42$	0.0738003	−	0.0177606i	0.0113876	−	0.00274052i
$43$	1.81412	+	1.04738i	0.276650	+	0.159724i	0.631906	−	0.775045i	$-0.282273\pi$
$43$	1.81412	+	1.04738i	0.276650	+	0.159724i	−0.355256	+	0.934769i	$0.615606\pi$
$44$	8.07276	−	8.07276i	1.21701	−	1.21701i
$45$	5.28307	−	1.12899i	0.787554	−	0.168300i
$46$	0.366467	+	0.0981945i	0.0540326	+	0.0144780i
$47$	−1.08839	+	4.06193i	−0.158758	+	0.592493i	0.839996	+	0.542592i	$0.182557\pi$
$47$	−1.08839	+	4.06193i	−0.158758	+	0.592493i	−0.998754	+	0.0499006i	$0.984110\pi$
$48$	−4.96790	+	4.71952i	−0.717054	+	0.681205i
$49$	5.83474	−	3.36869i	0.833535	−	0.481242i
$50$	0.0388929	−	0.145150i	0.00550029	−	0.0205274i
$51$	−9.09170	−	2.68768i	−1.27309	−	0.376350i
$52$	3.38334	+	6.33825i	0.469185	+	0.878957i
$53$			8.79692i			1.20835i	0.796852	+	0.604175i	$0.206497\pi$
$53$			8.79692i			1.20835i	−0.796852	+	0.604175i	$0.793503\pi$
$54$	−0.443055	−	0.0341378i	−0.0602921	−	0.00464557i
$55$	5.15858	−	8.93492i	0.695583	−	1.20478i
$56$	−0.0874900	+	0.151537i	−0.0116913	+	0.0202500i
$57$	6.14310	+	11.2994i	0.813674	+	1.49665i
$58$	−0.0311766	−	0.0311766i	−0.00409369	−	0.00409369i
$59$	5.47412	+	5.47412i	0.712669	+	0.712669i	0.967093	−	0.254424i	$-0.0818858\pi$
$59$	5.47412	+	5.47412i	0.712669	+	0.712669i	−0.254424	+	0.967093i	$0.581886\pi$
$60$	−3.24458	+	5.30119i	−0.418874	+	0.684380i
$61$	2.89997	−	5.02290i	0.371303	−	0.643117i	−0.618463	−	0.785814i	$-0.712244\pi$
$61$	2.89997	−	5.02290i	0.371303	−	0.643117i	0.989766	+	0.142698i	$0.0455776\pi$
$62$	−0.141109	+	0.244409i	−0.0179209	+	0.0310399i
$63$	1.50344	−	0.321286i	0.189416	−	0.0404782i
$64$		−	7.82501i		−	0.978126i
$65$	4.43582	+	4.74134i	0.550195	+	0.588091i
$66$	−0.615257	+	0.584497i	−0.0757329	+	0.0719466i
$67$	−1.38685	+	5.17581i	−0.169431	+	0.632326i	0.828002	+	0.560725i	$0.189477\pi$
$67$	−1.38685	+	5.17581i	−0.169431	+	0.632326i	−0.997433	+	0.0716009i	$0.977189\pi$
$68$	9.44597	−	5.45364i	1.14549	−	0.661350i
$69$	7.36882	+	2.17836i	0.887101	+	0.262244i
$70$	−0.0204259	+	0.0762306i	−0.00244136	+	0.00911129i
$71$	2.49660	+	0.668962i	0.296292	+	0.0793912i	0.403903	−	0.914802i	$-0.367653\pi$
$71$	2.49660	+	0.668962i	0.296292	+	0.0793912i	−0.107611	+	0.994193i	$0.534320\pi$
$72$	0.760489	−	0.686255i	0.0896244	−	0.0808759i
$73$	−4.21361	+	4.21361i	−0.493166	+	0.493166i	−0.909302	−	0.416136i	$-0.863384\pi$
$73$	−4.21361	+	4.21361i	−0.493166	+	0.493166i	0.416136	+	0.909302i	$0.363384\pi$
$74$	−0.233385	−	0.134745i	−0.0271305	−	0.0156638i
$75$	0.862806	−	2.91864i	0.0996282	−	0.337016i
$76$	−14.2925	−	3.82968i	−1.63947	−	0.439294i
$77$	1.46801	−	2.54267i	0.167296	−	0.289765i
$78$	−0.239336	−	0.477433i	−0.0270995	−	0.0540587i
$79$	−2.43009	−	4.20904i	−0.273407	−	0.473554i	0.696325	−	0.717726i	$-0.254817\pi$
$79$	−2.43009	−	4.20904i	−0.273407	−	0.473554i	−0.969732	+	0.244172i	$0.921484\pi$
$80$	−1.84388	−	6.88147i	−0.206153	−	0.769372i
$81$	−8.95273	−	0.921173i	−0.994748	−	0.102353i
$82$	−0.207286	+	0.119677i	−0.0228910	+	0.0132161i
$83$	−3.28109	−	0.879166i	−0.360147	−	0.0965010i	0.0742084	−	0.997243i	$-0.476357\pi$
$83$	−3.28109	−	0.879166i	−0.360147	−	0.0965010i	−0.434355	+	0.900742i	$0.643024\pi$
$84$	−0.923334	+	1.50860i	−0.100744	+	0.164601i
$85$	6.96986	−	6.96986i	0.755988	−	0.755988i
$86$	0.173037	−	0.0463652i	0.0186591	−	0.00499969i
$87$	−0.615044	−	0.647411i	−0.0659396	−	0.0694098i
$88$		−	1.95625i		−	0.208537i
$89$	10.8505	−	2.90739i	1.15015	−	0.308183i	0.367128	−	0.930171i	$-0.380341\pi$
$89$	10.8505	−	2.90739i	1.15015	−	0.308183i	0.783027	+	0.621988i	$0.213675\pi$
$90$	0.251201	−	0.387743i	0.0264789	−	0.0408717i
$91$	1.26233	+	1.34928i	0.132328	+	0.141443i
$92$	−7.65596	+	4.42017i	−0.798189	+	0.460835i
$93$	−2.98389	+	4.87525i	−0.309415	+	0.505540i
$94$	0.179812	+	0.311444i	0.0185462	+	0.0321230i
$95$	−13.3718			−1.37192
$96$	−0.0453351	+	1.76823i	−0.00462699	+	0.180470i
$97$	2.14413	−	0.574518i	0.217703	−	0.0583334i	−0.148319	−	0.988940i	$-0.547386\pi$
$97$	2.14413	−	0.574518i	0.217703	−	0.0583334i	0.366022	+	0.930606i	$0.380719\pi$
$98$	0.149124	−	0.556539i	0.0150638	−	0.0562190i
$99$	−12.7604	+	11.5148i	−1.28247	+	1.15728i
$100$	1.75074	+	3.03238i	0.175074	+	0.303238i
$101$	11.8701			1.18112			0.590558	−	0.806995i	$-0.298908\pi$
$101$	11.8701			1.18112			0.590558	+	0.806995i	$0.298908\pi$
$102$	−0.712309	+	0.387257i	−0.0705291	+	0.0383441i
$103$	−8.74348	−	5.04805i	−0.861521	−	0.497399i	0.00300033	−	0.999995i	$-0.499045\pi$
$103$	−8.74348	−	5.04805i	−0.861521	−	0.497399i	−0.864521	+	0.502596i	$0.832378\pi$
$104$	1.17790	+	0.358027i	0.115503	+	0.0351074i
$105$	−0.453131	+	1.53282i	−0.0442211	+	0.149588i
$106$	0.531957	+	0.531957i	0.0516682	+	0.0516682i
$107$	−2.46578	−	1.42362i	−0.238376	−	0.137626i	0.376054	−	0.926598i	$-0.377281\pi$
$107$	−2.46578	−	1.42362i	−0.238376	−	0.137626i	−0.614430	+	0.788971i	$0.710614\pi$
$108$	7.86243	−	6.73749i	0.756563	−	0.648315i
$109$	−6.88447	−	6.88447i	−0.659412	−	0.659412i	0.295829	−	0.955241i	$-0.404404\pi$
$109$	−6.88447	−	6.88447i	−0.659412	−	0.659412i	−0.955241	+	0.295829i	$0.904404\pi$
$110$	−0.228359	−	0.852246i	−0.0217731	−	0.0812585i
$111$	−4.65537	−	2.84931i	−0.441868	−	0.270445i
$112$	−0.524727	−	1.95831i	−0.0495821	−	0.185043i
$113$			15.1786i			1.42788i	0.700208	+	0.713939i	$0.253091\pi$
$113$			15.1786i			1.42788i	−0.700208	+	0.713939i	$0.746909\pi$
$114$	1.05477	+	0.311808i	0.0987878	+	0.0292035i
$115$	−5.64907	+	5.64907i	−0.526779	+	0.526779i
$116$	1.02736			0.0953878
$117$	−4.59797	−	9.79074i	−0.425082	−	0.905155i
$118$	0.662049			0.0609465
$119$	1.98346	−	1.98346i	0.181824	−	0.181824i
$120$	0.249185	+	1.03544i	0.0227474	+	0.0945220i
$121$			21.8243i			1.98403i
$122$	−0.128375	−	0.479103i	−0.0116225	−	0.0433759i
$123$	−4.25902	+	2.31547i	−0.384023	+	0.208779i
$124$	−1.70200	−	6.35196i	−0.152844	−	0.570423i
$125$	8.60423	+	8.60423i	0.769586	+	0.769586i
$126$	0.0714860	−	0.110343i	0.00636848	−	0.00983012i
$127$	7.16053	+	4.13413i	0.635394	+	0.366845i	0.782838	−	0.622225i	$-0.213771\pi$
$127$	7.16053	+	4.13413i	0.635394	+	0.366845i	−0.147444	+	0.989070i	$0.547105\pi$
$128$	−1.91742	−	1.91742i	−0.169477	−	0.169477i
$129$	3.52752	−	0.848925i	0.310581	−	0.0747436i
$130$	0.554951	+	0.0184755i	0.0486724	+	0.00162041i
$131$	−8.77573	−	5.06667i	−0.766739	−	0.442677i	0.0649708	−	0.997887i	$-0.479305\pi$
$131$	−8.77573	−	5.06667i	−0.766739	−	0.442677i	−0.831710	+	0.555210i	$0.812638\pi$
$132$	0.506816	−	19.7676i	0.0441126	−	1.72055i
$133$	−3.80530			−0.329961
$134$	0.229121	+	0.396850i	0.0197931	+	0.0342826i
$135$	5.28729	−	7.72017i	0.455058	−	0.664446i
$136$	0.483726	−	1.80529i	0.0414792	−	0.154802i
$137$	−8.98344	+	2.40710i	−0.767507	+	0.205653i	−0.621270	−	0.783597i	$-0.713383\pi$
$137$	−8.98344	+	2.40710i	−0.767507	+	0.205653i	−0.146237	+	0.989250i	$0.546716\pi$
$138$	0.577326	−	0.313871i	0.0491452	−	0.0267185i
$139$	13.5884			1.15255			0.576277	−	0.817255i	$-0.304505\pi$
$139$	13.5884			1.15255			0.576277	+	0.817255i	$0.304505\pi$
$140$	−0.919461	−	1.59255i	−0.0777086	−	0.134595i
$141$	3.47896	+	6.39909i	0.292981	+	0.538901i
$142$	0.191424	−	0.110519i	0.0160640	−	0.00927454i
$143$	−19.7643	−	6.00741i	−1.65277	−	0.502365i
$144$	−0.608186	+	11.8529i	−0.0506821	+	0.987744i
$145$	0.896786	−	0.240293i	0.0744740	−	0.0199553i
$146$			0.509602i			0.0421749i
$147$	3.30819	−	11.1907i	0.272855	−	0.922997i
$148$	6.06547	−	1.62524i	0.498579	−	0.133594i
$149$	−1.45878	+	1.45878i	−0.119508	+	0.119508i	−0.764331	−	0.644824i	$-0.776931\pi$
$149$	−1.45878	+	1.45878i	−0.119508	+	0.119508i	0.644824	+	0.764331i	$0.276931\pi$
$150$	−0.124318	−	0.228667i	−0.0101505	−	0.0186706i
$151$	1.98170	+	0.530995i	0.161269	+	0.0432118i	0.338550	−	0.940948i	$-0.390064\pi$
$151$	1.98170	+	0.530995i	0.161269	+	0.0432118i	−0.177281	+	0.984160i	$0.556730\pi$
$152$	−2.19575	+	1.26772i	−0.178099	+	0.102826i
$153$	−14.6230	+	7.47096i	−1.18220	+	0.603991i
$154$	−0.0649856	−	0.242530i	−0.00523669	−	0.0195436i
$155$	−2.97137	−	5.14657i	−0.238666	−	0.413382i
$156$	11.8098	+	3.92298i	0.945541	+	0.314090i
$157$	0.367627	−	0.636748i	0.0293398	−	0.0508180i	−0.850983	−	0.525194i	$-0.823993\pi$
$157$	0.367627	−	0.636748i	0.0293398	−	0.0508180i	0.880322	+	0.474376i	$0.157326\pi$
$158$	−0.401474	−	0.107575i	−0.0319395	−	0.00855817i
$159$	10.4943	+	11.0466i	0.832252	+	0.876051i
$160$	−1.59263	−	0.919504i	−0.125908	−	0.0726932i
$161$	−1.60760	+	1.60760i	−0.126696	+	0.126696i
$162$	−0.597083	+	0.485675i	−0.0469113	+	0.0381582i
$163$	7.01940	+	1.88084i	0.549801	+	0.147319i	0.523017	−	0.852322i	$-0.324806\pi$
$163$	7.01940	+	1.88084i	0.549801	+	0.147319i	0.0267847	+	0.999641i	$0.491473\pi$
$164$	1.44349	−	5.38719i	0.112718	−	0.420669i
$165$	−4.18114	−	17.3738i	−0.325501	−	1.35255i
$166$	−0.251574	+	0.145246i	−0.0195259	+	0.0112733i
$167$	6.17150	−	23.0324i	0.477565	−	1.78230i	−0.133866	−	0.990999i	$-0.542739\pi$
$167$	6.17150	−	23.0324i	0.477565	−	1.78230i	0.611431	−	0.791298i	$-0.290594\pi$
$168$	0.0709124	+	0.294662i	0.00547101	+	0.0227336i
$169$	7.23441	−	10.8011i	0.556493	−	0.830852i
$170$		−	0.842947i		−	0.0646511i
$171$	21.1938	+	6.86066i	1.62073	+	0.524648i
$172$	−2.08710	+	3.61497i	−0.159140	+	0.275639i
$173$	4.11922	−	7.13471i	0.313179	−	0.542442i	−0.665870	−	0.746068i	$-0.731939\pi$
$173$	4.11922	−	7.13471i	0.313179	−	0.542442i	0.979049	+	0.203626i	$0.0652727\pi$
$174$	−0.0763417	−	0.00195730i	−0.00578745	−	0.000148382i
$175$	0.636738	+	0.636738i	0.0481328	+	0.0481328i
$176$	16.0272	+	16.0272i	1.20810	+	1.20810i
$177$	13.4044	+	0.343670i	1.00754	+	0.0258318i
$178$	0.480329	−	0.831953i	0.0360021	−	0.0623576i
$179$	−7.94103	+	13.7543i	−0.593541	+	1.02804i	0.400210	+	0.916423i	$0.368937\pi$
$179$	−7.94103	+	13.7543i	−0.593541	+	1.02804i	−0.993751	+	0.111619i	$0.964396\pi$
$180$	2.24973	+	10.5275i	0.167685	+	0.784674i
$181$			21.7854i			1.61929i	0.586918	+	0.809646i	$0.300341\pi$
$181$			21.7854i			1.61929i	−0.586918	+	0.809646i	$0.699659\pi$
$182$	0.157926	+	0.00525771i	0.0117063	+	0.000389727i
$183$	−2.35049	−	9.76695i	−0.173753	−	0.721994i
$184$	−0.392060	+	1.46319i	−0.0289030	+	0.107868i
$185$	4.91445	−	2.83736i	0.361317	−	0.208607i
$186$	0.114372	+	0.475249i	0.00838616	+	0.0348469i
$187$	−8.11655	+	30.2914i	−0.593541	+	2.21512i
$188$	−8.09415	−	2.16882i	−0.590326	−	0.158177i
$189$	1.50464	−	2.19698i	0.109447	−	0.159807i
$190$	−0.808603	+	0.808603i	−0.0586622	+	0.0586622i
$191$	−7.31301	−	4.22217i	−0.529151	−	0.305505i	0.211520	−	0.977374i	$-0.432159\pi$
$191$	−7.31301	−	4.22217i	−0.529151	−	0.305505i	−0.740671	+	0.671868i	$0.765492\pi$
$192$	−9.33486	−	9.82613i	−0.673686	−	0.709140i
$193$	−4.11483	−	1.10257i	−0.296192	−	0.0793644i	0.107663	−	0.994187i	$-0.465663\pi$
$193$	−4.11483	−	1.10257i	−0.296192	−	0.0793644i	−0.403855	+	0.914823i	$0.632330\pi$
$194$	0.0949157	−	0.164399i	0.00681455	−	0.0118032i
$195$	11.2264	+	0.662146i	0.803939	+	0.0474173i
$196$	6.71275	+	11.6268i	0.479482	+	0.830487i
$197$	2.32810	+	8.68859i	0.165870	+	0.619036i	0.997928	+	0.0643467i	$0.0204964\pi$
$197$	2.32810	+	8.68859i	0.165870	+	0.619036i	−0.832057	+	0.554690i	$0.812837\pi$
$198$	−0.0753217	+	1.46794i	−0.00535288	+	0.104322i
$199$	−6.29646	+	3.63526i	−0.446344	+	0.257697i	−0.706285	−	0.707928i	$-0.749630\pi$
$199$	−6.29646	+	3.63526i	−0.446344	+	0.257697i	0.259941	+	0.965625i	$0.416297\pi$
$200$	0.579540	+	0.155287i	0.0409797	+	0.0109805i
$201$	4.43297	+	8.15388i	0.312678	+	0.575131i
$202$	0.717793	−	0.717793i	0.0505037	−	0.0505037i
$203$	0.255205	−	0.0683819i	0.0179119	−	0.00479947i
$204$	5.35570	−	18.1169i	0.374974	−	1.26844i
$205$		−	5.04013i		−	0.352018i
$206$	−0.833986	+	0.223466i	−0.0581065	+	0.0155696i
$207$	11.8519	−	6.05521i	0.823767	−	0.420866i
$208$	−12.5836	+	6.71711i	−0.872517	+	0.465748i
$209$	36.8430	−	21.2713i	2.54849	−	1.47137i
$210$	0.0652899	+	0.120092i	0.00450543	+	0.00828716i
$211$	−9.51719	−	16.4843i	−0.655191	−	1.13482i	−0.981846	−	0.189680i	$-0.939255\pi$
$211$	−9.51719	−	16.4843i	−0.655191	−	1.13482i	0.326655	−	0.945143i	$-0.394078\pi$
$212$	−17.5295			−1.20393
$213$	3.93311	−	2.13829i	0.269492	−	0.146513i
$214$	−0.235195	+	0.0630203i	−0.0160776	+	0.00430798i
$215$	−0.976323	+	3.64369i	−0.0665847	+	0.248497i
$216$	0.136302	−	1.76898i	0.00927415	−	0.120364i
$217$	−0.845584	−	1.46460i	−0.0574020	−	0.0994232i
$218$	−0.832619			−0.0563921
$219$	−0.264535	+	10.3178i	−0.0178756	+	0.697213i
$220$	17.8045	+	10.2794i	1.20038	+	0.693039i
$221$	−16.7537	−	10.4310i	−1.12697	−	0.701665i
$222$	−0.453814	+	0.109214i	−0.0304580	+	0.00732994i
$223$	−1.43067	−	1.43067i	−0.0958051	−	0.0958051i	0.657580	−	0.753385i	$-0.271580\pi$
$223$	−1.43067	−	1.43067i	−0.0958051	−	0.0958051i	−0.753385	+	0.657580i	$0.771580\pi$
$224$	−0.453225	−	0.261670i	−0.0302824	−	0.0174836i
$225$	−2.39835	−	4.69432i	−0.159890	−	0.312955i
$226$	0.917860	+	0.917860i	0.0610551	+	0.0610551i
$227$	1.61467	+	6.02603i	0.107169	+	0.399962i	0.998582	−	0.0532304i	$-0.0169518\pi$
$227$	1.61467	+	6.02603i	0.107169	+	0.399962i	−0.891413	+	0.453192i	$0.850285\pi$
$228$	−22.5162	+	12.2413i	−1.49117	+	0.810698i
$229$	−5.67722	−	21.1877i	−0.375161	−	1.40012i	−0.853109	−	0.521733i	$-0.825286\pi$
$229$	−5.67722	−	21.1877i	−0.375161	−	1.40012i	0.477947	−	0.878389i	$-0.341381\pi$
$230$			0.683208i			0.0450494i
$231$	−1.18986	−	4.94419i	−0.0782867	−	0.325304i
$232$	0.124478	−	0.124478i	0.00817241	−	0.00817241i
$233$	−15.5136			−1.01633			−0.508164	−	0.861260i	$-0.669676\pi$
$233$	−15.5136			−1.01633			−0.508164	+	0.861260i	$0.669676\pi$
$234$	−0.870098	−	0.314012i	−0.0568801	−	0.0205276i
$235$	−7.57270			−0.493988
$236$	−10.9082	+	10.9082i	−0.710063	+	0.710063i
$237$	−8.07273	−	2.38645i	−0.524380	−	0.155017i
$238$		−	0.239883i		−	0.0155493i
$239$	−5.56653	−	20.7746i	−0.360069	−	1.34380i	−0.873984	−	0.485954i	$-0.838472\pi$
$239$	−5.56653	−	20.7746i	−0.360069	−	1.34380i	0.513915	−	0.857841i	$-0.328195\pi$
$240$	−10.5247	−	6.44162i	−0.679366	−	0.415805i
$241$	−5.30489	−	19.7981i	−0.341718	−	1.27531i	−0.896400	−	0.443246i	$-0.853827\pi$
$241$	−5.30489	−	19.7981i	−0.341718	−	1.27531i	0.554682	−	0.832062i	$-0.312840\pi$
$242$	1.31974	+	1.31974i	0.0848358	+	0.0848358i
$243$	−12.3412	+	9.52343i	−0.791686	+	0.610929i
$244$	10.0091	+	5.77874i	0.640765	+	0.369946i
$245$	8.57903	+	8.57903i	0.548094	+	0.548094i
$246$	−0.117528	+	0.397565i	−0.00749329	+	0.0253478i
$247$	6.06506	+	26.0771i	0.385911	+	1.65924i
$248$	−0.975847	−	0.563405i	−0.0619663	−	0.0357763i
$249$	−5.16898	+	2.81019i	−0.327571	+	0.178088i
$250$	1.04061			0.0658139
$251$	2.74538	+	4.75513i	0.173287	+	0.300141i	0.939567	−	0.342365i	$-0.111228\pi$
$251$	2.74538	+	4.75513i	0.173287	+	0.300141i	−0.766280	+	0.642506i	$0.777895\pi$
$252$	0.640221	+	2.99589i	0.0403302	+	0.188723i
$253$	6.57846	−	24.5511i	0.413584	−	1.54352i
$254$	0.682998	−	0.183009i	0.0428551	−	0.0114830i
$255$	0.437575	−	17.0670i	0.0274020	−	1.06878i
$256$	15.4181			0.963633
$257$	−5.50207	−	9.52986i	−0.343209	−	0.594456i	0.641817	−	0.766858i	$-0.278181\pi$
$257$	−5.50207	−	9.52986i	−0.343209	−	0.594456i	−0.985027	+	0.172401i	$0.944847\pi$
$258$	0.161977	−	0.264648i	0.0100843	−	0.0164762i
$259$	1.39854	−	0.807447i	0.0869010	−	0.0501723i
$260$	−9.44801	+	8.83919i	−0.585941	+	0.548183i
$261$	−1.54466	−	0.0792582i	−0.0956121	−	0.00490596i
$262$	−0.837062	+	0.224290i	−0.0517139	+	0.0138567i
$263$			23.5579i			1.45264i	0.687355	+	0.726322i	$0.258772\pi$
$263$			23.5579i			1.45264i	−0.687355	+	0.726322i	$0.741228\pi$
$264$	−2.33371	−	2.45653i	−0.143630	−	0.151189i
$265$	−15.3016	+	4.10005i	−0.939969	+	0.251864i
$266$	−0.230110	+	0.230110i	−0.0141089	+	0.0141089i
$267$	10.1570	−	16.5951i	0.621598	−	1.01560i
$268$	−10.3138	−	2.76357i	−0.630013	−	0.168812i
$269$	−8.45703	+	4.88267i	−0.515634	+	0.297701i	−0.735147	−	0.677908i	$-0.762887\pi$
$269$	−8.45703	+	4.88267i	−0.515634	+	0.297701i	0.219512	+	0.975610i	$0.429553\pi$
$270$	−0.147118	−	0.786572i	−0.00895330	−	0.0478693i
$271$	−3.75576	−	14.0167i	−0.228146	−	0.851453i	−0.981120	−	0.193402i	$-0.938048\pi$
$271$	−3.75576	−	14.0167i	−0.228146	−	0.851453i	0.752973	−	0.658051i	$-0.228619\pi$
$272$	10.8274	+	18.7535i	0.656505	+	1.13710i
$273$	3.19478	+	0.188432i	0.193357	+	0.0114044i
$274$	−0.397676	+	0.688796i	−0.0240245	+	0.0416117i
$275$	−9.72423	−	2.60560i	−0.586393	−	0.157124i
$276$	−4.34079	+	14.6837i	−0.261285	+	0.883857i
$277$	14.0333	+	8.10215i	0.843181	+	0.486811i	0.858344	−	0.513074i	$-0.171493\pi$
$277$	14.0333	+	8.10215i	0.843181	+	0.486811i	−0.0151630	+	0.999885i	$0.504827\pi$
$278$	0.821702	−	0.821702i	0.0492824	−	0.0492824i
$279$	2.06897	+	9.68165i	0.123866	+	0.579625i
$280$	−0.304365	−	0.0815543i	−0.0181893	−	0.00487380i
$281$	6.62158	−	24.7121i	0.395010	−	1.47420i	−0.426753	−	0.904368i	$-0.640343\pi$
$281$	6.62158	−	24.7121i	0.395010	−	1.47420i	0.821763	−	0.569829i	$-0.192991\pi$
$282$	0.597334	+	0.176583i	0.0355707	+	0.0105154i
$283$	−4.62683	+	2.67130i	−0.275036	+	0.158792i	−0.631174	−	0.775641i	$-0.717427\pi$
$283$	−4.62683	+	2.67130i	−0.275036	+	0.158792i	0.356138	+	0.934433i	$0.384093\pi$
$284$	−1.33303	+	4.97494i	−0.0791009	+	0.295209i
$285$	−16.7914	+	15.9519i	−0.994636	+	0.944908i
$286$	−1.55844	+	0.831890i	−0.0921523	+	0.0491907i
$287$		−	1.43430i		−	0.0846643i
$288$	2.05249	+	2.27451i	0.120944	+	0.134027i
$289$	−6.48043	+	11.2244i	−0.381202	+	0.660261i
$290$	0.0396987	−	0.0687601i	0.00233119	−	0.00403773i
$291$	2.00708	−	3.27928i	0.117657	−	0.192235i
$292$	−8.39641	−	8.39641i	−0.491363	−	0.491363i
$293$	11.1976	+	11.1976i	0.654171	+	0.654171i	0.953995	−	0.299824i	$-0.0969278\pi$
$293$	11.1976	+	11.1976i	0.654171	+	0.654171i	−0.299824	+	0.953995i	$0.596928\pi$
$294$	−0.476665	−	0.876763i	−0.0277996	−	0.0511339i
$295$	−6.97046	+	12.0732i	−0.405836	+	0.702928i
$296$	0.537995	−	0.931835i	0.0312703	−	0.0541618i
$297$	−2.28704	+	29.6821i	−0.132707	+	1.72233i
$298$			0.176427i			0.0102202i
$299$	13.5788	+	8.45432i	0.785285	+	0.488926i
$300$	5.81594	+	1.71930i	0.335784	+	0.0992639i
$301$	−0.277839	+	1.03691i	−0.0160144	+	0.0597665i
$302$	0.151945	−	0.0877254i	0.00874345	−	0.00504803i
$303$	14.9056	−	14.1604i	0.856306	−	0.813495i
$304$	7.60323	−	28.3757i	0.436075	−	1.62746i
$305$	10.0886	+	2.70323i	0.577670	+	0.154786i
$306$	−0.432491	+	1.33604i	−0.0247239	+	0.0763764i
$307$	21.2032	−	21.2032i	1.21013	−	1.21013i	0.239150	−	0.970983i	$-0.423131\pi$
$307$	21.2032	−	21.2032i	1.21013	−	1.21013i	0.970983	−	0.239150i	$-0.0768687\pi$
$308$	5.06675	+	2.92529i	0.288705	+	0.166684i
$309$	−17.0016	+	4.09155i	−0.967185	+	0.232760i
$310$	−0.490899	−	0.131536i	−0.0278812	−	0.00747074i
$311$	9.06279	−	15.6972i	0.513903	−	0.890107i	−0.485966	−	0.873977i	$-0.661532\pi$
$311$	9.06279	−	15.6972i	0.513903	−	0.890107i	0.999870	−	0.0161295i	$-0.00513439\pi$
$312$	1.90624	−	0.955596i	0.107920	−	0.0540999i
$313$	−8.03021	−	13.9087i	−0.453894	−	0.786168i	0.544730	−	0.838612i	$-0.316632\pi$
$313$	−8.03021	−	13.9087i	−0.453894	−	0.786168i	−0.998624	+	0.0524437i	$0.983299\pi$
$314$	−0.0162740	−	0.0607354i	−0.000918394	−	0.00342749i
$315$	1.25957	+	2.46538i	0.0709689	+	0.138909i
$316$	8.38730	−	4.84241i	0.471822	−	0.272407i
$317$	−17.2705	−	4.62761i	−0.970006	−	0.259912i	−0.261175	−	0.965291i	$-0.584110\pi$
$317$	−17.2705	−	4.62761i	−0.970006	−	0.259912i	−0.708830	+	0.705379i	$0.750777\pi$
$318$	1.30260	+	0.0333968i	0.0730459	+	0.00187280i
$319$	−2.08865	+	2.08865i	−0.116942	+	0.116942i
$320$	13.6110	−	3.64706i	0.760880	−	0.203877i
$321$	−4.79467	+	1.15387i	−0.267612	+	0.0644028i
$322$			0.194425i			0.0108349i
$323$	39.2598	−	10.5196i	2.18447	−	0.585328i
$324$	1.83561	−	17.8400i	0.101978	−	0.991111i
$325$	3.34859	−	5.37831i	0.185746	−	0.298335i
$326$	0.538205	−	0.310733i	0.0298084	−	0.0172099i
$327$	−16.8579	−	0.432213i	−0.932243	−	0.0239015i
$328$	−0.477832	−	0.827630i	−0.0263839	−	0.0456982i
$329$	−2.15502			−0.118810
$330$	−1.30345	−	0.797773i	−0.0717523	−	0.0439159i
$331$	1.60047	−	0.428846i	0.0879700	−	0.0235715i	−0.214566	−	0.976710i	$-0.568834\pi$
$331$	1.60047	−	0.428846i	0.0879700	−	0.0235715i	0.302536	+	0.953138i	$0.402167\pi$
$332$	1.75190	−	6.53819i	0.0961481	−	0.358830i
$333$	−9.24499	+	1.97565i	−0.506622	+	0.108265i
$334$	−1.01959	−	1.76598i	−0.0557895	−	0.0966302i
$335$	−9.64932			−0.527199
$336$	−2.99509	−	1.83314i	−0.163395	−	0.100006i
$337$	−17.1704	−	9.91335i	−0.935333	−	0.540015i	−0.0468388	−	0.998902i	$-0.514915\pi$
$337$	−17.1704	−	9.91335i	−0.935333	−	0.540015i	−0.888494	+	0.458888i	$0.848248\pi$
$338$	−0.215680	−	1.09062i	−0.0117314	−	0.0593220i
$339$	18.1073	+	19.0602i	0.983453	+	1.03521i
$340$	13.8888	+	13.8888i	0.753223	+	0.753223i
$341$	16.3739	+	9.45350i	0.886699	+	0.511936i
$342$	1.69648	−	0.866736i	0.0917349	−	0.0468677i
$343$	4.97796	+	4.97796i	0.268784	+	0.268784i
$344$	0.185122	+	0.690884i	0.00998110	+	0.0372500i
$345$	−0.354654	+	13.8328i	−0.0190939	+	0.744733i
$346$	−0.182349	−	0.680535i	−0.00980313	−	0.0365858i
$347$			16.1885i			0.869044i	0.900661	+	0.434522i	$0.143083\pi$
$347$			16.1885i			0.869044i	−0.900661	+	0.434522i	$0.856917\pi$
$348$	1.29009	−	1.22559i	0.0691560	−	0.0656985i
$349$	−16.0469	+	16.0469i	−0.858970	+	0.858970i	−0.991217	−	0.132247i	$-0.957781\pi$
$349$	−16.0469	+	16.0469i	−0.858970	+	0.858970i	0.132247	+	0.991217i	$0.457781\pi$
$350$	0.0770081			0.00411626
$351$	−17.4537	−	6.80941i	−0.931610	−	0.363459i
$352$	5.85086			0.311852
$353$	8.18677	−	8.18677i	0.435738	−	0.435738i	−0.454837	−	0.890575i	$-0.650302\pi$
$353$	8.18677	−	8.18677i	0.435738	−	0.435738i	0.890575	+	0.454837i	$0.150302\pi$
$354$	0.831356	−	0.789792i	0.0441861	−	0.0419770i
$355$			4.65444i			0.247032i
$356$	5.79352	+	21.6217i	0.307056	+	1.14595i
$357$	0.124524	−	4.85688i	0.00659050	−	0.257053i
$358$	0.351531	+	1.31193i	0.0185790	+	0.0693378i
$359$	7.58368	+	7.58368i	0.400251	+	0.400251i	0.878322	−	0.478070i	$-0.158664\pi$
$359$	7.58368	+	7.58368i	0.400251	+	0.400251i	−0.478070	+	0.878322i	$0.658664\pi$
$360$	1.54814	+	1.00297i	0.0815939	+	0.0528609i
$361$	−31.2967	−	18.0692i	−1.64720	−	0.951009i
$362$	1.31738	+	1.31738i	0.0692399	+	0.0692399i
$363$	26.0354	+	27.4055i	1.36650	+	1.43842i
$364$	−2.68869	+	2.51543i	−0.140926	+	0.131844i
$365$	−9.29314	−	5.36540i	−0.486425	−	0.280838i
$366$	−0.732752	−	0.448480i	−0.0383015	−	0.0234424i
$367$	23.3494			1.21883			0.609415	−	0.792851i	$-0.291404\pi$
$367$	23.3494			1.21883			0.609415	+	0.792851i	$0.291404\pi$
$368$	−8.77557	−	15.1997i	−0.457458	−	0.792341i
$369$	−2.58594	+	7.98842i	−0.134619	+	0.415861i
$370$	0.125603	−	0.468758i	0.00652981	−	0.0243696i
$371$	−4.35448	+	1.16678i	−0.226073	+	0.0605762i
$372$	−9.71484	−	5.94596i	−0.503691	−	0.308283i
$373$	−2.45355			−0.127040			−0.0635199	−	0.997981i	$-0.520233\pi$
$373$	−2.45355			−0.127040			−0.0635199	+	0.997981i	$0.520233\pi$
$374$	1.34093	+	2.32256i	0.0693378	+	0.120097i
$375$	21.0690	+	0.540182i	1.08800	+	0.0278949i
$376$	−1.24350	+	0.717934i	−0.0641285	+	0.0370246i
$377$	−0.875367	−	1.63988i	−0.0450837	−	0.0844583i
$378$	−0.0418664	−	0.223840i	−0.00215337	−	0.0115131i
$379$	−12.8719	+	3.44903i	−0.661187	+	0.177165i	−0.573782	−	0.819008i	$-0.694524\pi$
$379$	−12.8719	+	3.44903i	−0.661187	+	0.177165i	−0.0874055	+	0.996173i	$0.527858\pi$
$380$		−	26.6458i		−	1.36690i
$381$	13.9235	−	3.35080i	0.713324	−	0.171667i
$382$	−0.697542	+	0.186906i	−0.0356893	+	0.00956293i
$383$	26.4716	−	26.4716i	1.35264	−	1.35264i	0.469938	−	0.882700i	$-0.344276\pi$
$383$	26.4716	−	26.4716i	1.35264	−	1.35264i	0.882700	−	0.469938i	$-0.155724\pi$
$384$	−4.69515	−	0.120377i	−0.239598	−	0.00614297i
$385$	5.10700	+	1.36842i	0.260277	+	0.0697410i
$386$	−0.315500	+	0.182154i	−0.0160585	+	0.00927141i
$387$	3.41690	−	5.27419i	0.173691	−	0.268102i
$388$	1.14483	+	4.27258i	0.0581201	+	0.216907i
$389$	11.9117	+	20.6316i	0.603945	+	1.04606i	0.992217	+	0.124519i	$0.0397387\pi$
$389$	11.9117	+	20.6316i	0.603945	+	1.04606i	−0.388272	+	0.921545i	$0.626928\pi$
$390$	0.718910	−	0.638829i	0.0364034	−	0.0323484i
$391$	12.1416	−	21.0299i	0.614029	−	1.06353i
$392$	2.22209	+	0.595407i	0.112232	+	0.0300726i
$393$	−17.0643	+	4.10664i	−0.860779	+	0.207153i
$394$	0.666189	+	0.384624i	0.0335621	+	0.0193771i
$395$	6.18870	−	6.18870i	0.311387	−	0.311387i
$396$	−22.9454	−	25.4275i	−1.15305	−	1.27778i
$397$	21.9602	+	5.88421i	1.10215	+	0.295320i	0.763639	−	0.645643i	$-0.223411\pi$
$397$	21.9602	+	5.88421i	1.10215	+	0.295320i	0.338510	+	0.940963i	$0.390077\pi$
$398$	−0.160925	+	0.600579i	−0.00806643	+	0.0301043i
$399$	−4.77844	+	4.53954i	−0.239221	+	0.227261i
$400$	−6.02032	+	3.47583i	−0.301016	+	0.173792i
$401$	−7.36155	+	27.4737i	−0.367618	+	1.37197i	0.496218	+	0.868198i	$0.334722\pi$
$401$	−7.36155	+	27.4737i	−0.367618	+	1.37197i	−0.863836	+	0.503772i	$0.831945\pi$
$402$	0.761138	+	0.225007i	0.0379621	+	0.0112223i
$403$	−8.68889	+	8.12898i	−0.432824	+	0.404933i
$404$			23.6533i			1.17680i
$405$	−2.57036	−	16.0020i	−0.127722	−	0.795144i
$406$	0.0112973	−	0.0195676i	0.000560677	−	0.000971122i
$407$	−9.02714	+	15.6355i	−0.447459	+	0.775021i
$408$	−1.54619	−	2.84402i	−0.0765480	−	0.140800i
$409$	2.31831	+	2.31831i	0.114633	+	0.114633i	0.762096	−	0.647463i	$-0.224170\pi$
$409$	2.31831	+	2.31831i	0.114633	+	0.114633i	−0.647463	+	0.762096i	$0.724170\pi$
$410$	−0.304781	−	0.304781i	−0.0150520	−	0.0150520i
$411$	−8.40924	+	13.7395i	−0.414797	+	0.677719i
$412$	10.0592	−	17.4230i	0.495581	−	0.858371i
$413$	−1.98363	+	3.43575i	−0.0976082	+	0.169062i
$414$	0.350534	−	1.08286i	0.0172278	−	0.0532197i
$415$		−	6.11698i		−	0.300271i
$416$	−1.07081	+	3.52294i	−0.0525006	+	0.172726i
$417$	17.0634	−	16.2103i	0.835599	−	0.793823i
$418$	0.941634	−	3.51423i	0.0460568	−	0.171886i
$419$	−7.99132	+	4.61379i	−0.390402	+	0.225399i	−0.682334	−	0.731040i	$-0.739035\pi$
$419$	−7.99132	+	4.61379i	−0.390402	+	0.225399i	0.291932	+	0.956439i	$0.405702\pi$
$420$	−3.05444	−	0.902949i	−0.149041	−	0.0440594i
$421$	−0.574114	+	2.14262i	−0.0279806	+	0.104425i	−0.978504	−	0.206228i	$-0.933881\pi$
$421$	−0.574114	+	2.14262i	−0.0279806	+	0.104425i	0.950523	+	0.310653i	$0.100548\pi$
$422$	−1.57233	−	0.421304i	−0.0765398	−	0.0205088i
$423$	12.0024	+	3.88532i	0.583579	+	0.188911i
$424$	−2.12394	+	2.12394i	−0.103148	+	0.103148i
$425$	−8.32954	−	4.80906i	−0.404042	−	0.233274i
$426$	0.108534	−	0.367142i	0.00525850	−	0.0177881i
$427$	2.87098	+	0.769276i	0.138936	+	0.0372279i
$428$	2.83682	−	4.91352i	0.137123	−	0.237504i
$429$	−31.9852	+	16.0341i	−1.54426	+	0.774136i
$430$	0.161298	+	0.279376i	0.00777847	+	0.0134727i
$431$	−7.72277	−	28.8218i	−0.371993	−	1.38830i	−0.857690	−	0.514168i	$-0.828101\pi$
$431$	−7.72277	−	28.8218i	−0.371993	−	1.38830i	0.485697	−	0.874127i	$-0.338566\pi$
$432$	13.3763	+	15.6096i	0.643565	+	0.751019i
$433$	−11.3084	+	6.52890i	−0.543446	+	0.313759i	−0.746474	−	0.665414i	$-0.768255\pi$
$433$	−11.3084	+	6.52890i	−0.543446	+	0.313759i	0.203028	+	0.979173i	$0.434922\pi$
$434$	−0.139698	−	0.0374321i	−0.00670574	−	0.00179680i
$435$	0.839466	−	1.37157i	0.0402493	−	0.0657616i
$436$	13.7186	−	13.7186i	0.657001	−	0.657001i
$437$	−31.8200	+	8.52615i	−1.52216	+	0.407861i
$438$	0.607930	+	0.639923i	0.0290480	+	0.0305767i
$439$		−	14.3104i		−	0.683000i	−0.939882	−	0.341500i	$-0.889065\pi$
$439$		−	14.3104i		−	0.683000i	0.939882	−	0.341500i	$-0.110935\pi$
$440$	3.40275	−	0.911764i	0.162220	−	0.0434667i
$441$	−9.19582	−	17.9991i	−0.437896	−	0.857100i
$442$	−1.64388	+	0.382337i	−0.0781914	+	0.0181859i
$443$	−14.2467	+	8.22531i	−0.676879	+	0.390796i	−0.798678	−	0.601758i	$-0.794467\pi$
$443$	−14.2467	+	8.22531i	−0.676879	+	0.390796i	0.121799	+	0.992555i	$0.461134\pi$
$444$	5.67778	−	9.27669i	0.269456	−	0.440252i
$445$	10.1144	+	17.5186i	0.479468	+	0.830463i
$446$	−0.173028			−0.00819312
$447$	−0.0915837	+	3.57209i	−0.00433176	+	0.168954i
$448$	3.87339	−	1.03787i	0.183000	−	0.0490348i
$449$	6.52875	−	24.3656i	0.308111	−	1.14989i	−0.622123	−	0.782919i	$-0.713730\pi$
$449$	6.52875	−	24.3656i	0.308111	−	1.14989i	0.930234	−	0.366966i	$-0.119604\pi$
$450$	−0.428900	−	0.138840i	−0.0202185	−	0.00654496i
$451$	8.01765	+	13.8870i	0.377537	+	0.653913i
$452$	−30.2461			−1.42266
$453$	3.12194	−	1.69729i	0.146682	−	0.0797455i
$454$	0.462040	+	0.266759i	0.0216846	+	0.0125196i
$455$	−1.75862	+	2.82460i	−0.0824456	+	0.132419i
$456$	−1.24495	+	4.21135i	−0.0583003	+	0.197214i
$457$	−3.18313	−	3.18313i	−0.148901	−	0.148901i	0.628726	−	0.777627i	$-0.283577\pi$
$457$	−3.18313	−	3.18313i	−0.148901	−	0.148901i	−0.777627	+	0.628726i	$0.783577\pi$
$458$	−1.62454	−	0.937931i	−0.0759099	−	0.0438266i
$459$	−9.45011	+	26.8261i	−0.441093	+	1.25213i
$460$	−11.2568	−	11.2568i	−0.524852	−	0.524852i
$461$	−1.15832	−	4.32292i	−0.0539485	−	0.201339i	0.933691	−	0.358079i	$-0.116568\pi$
$461$	−1.15832	−	4.32292i	−0.0539485	−	0.201339i	−0.987640	+	0.156740i	$0.949901\pi$
$462$	−0.370931	−	0.227028i	−0.0172573	−	0.0105623i
$463$	4.33486	+	16.1779i	0.201458	+	0.751851i	0.990500	+	0.137512i	$0.0439107\pi$
$463$	4.33486	+	16.1779i	0.201458	+	0.751851i	−0.789042	+	0.614339i	$0.789423\pi$
$464$			2.03966i			0.0946889i
$465$	−9.87086	−	2.91801i	−0.457750	−	0.135319i
$466$	−0.938118	+	0.938118i	−0.0434575	+	0.0434575i
$467$	−34.2212			−1.58357			−0.791785	−	0.610800i	$-0.790848\pi$
$467$	−34.2212			−1.58357			−0.791785	+	0.610800i	$0.790848\pi$
$468$	19.5099	−	9.16231i	0.901845	−	0.423528i
$469$	−2.74598			−0.126797
$470$	−0.457927	+	0.457927i	−0.0211226	+	0.0211226i
$471$	−0.297969	−	1.23815i	−0.0137297	−	0.0570508i
$472$			2.64335i			0.121670i
$473$	−3.10620	−	11.5925i	−0.142823	−	0.533023i
$474$	−0.632475	+	0.343854i	−0.0290505	+	0.0157937i
$475$	3.37704	+	12.6033i	0.154949	+	0.578279i
$476$	3.95242	+	3.95242i	0.181159	+	0.181159i
$477$	26.3561	+	1.35236i	1.20676	+	0.0619202i
$478$	−1.59287	−	0.919643i	−0.0728561	−	0.0420635i
$479$	−23.3970	−	23.3970i	−1.06904	−	1.06904i	−0.997433	−	0.0716026i	$-0.977189\pi$
$479$	−23.3970	−	23.3970i	−1.06904	−	1.06904i	−0.0716026	−	0.997433i	$-0.522811\pi$
$480$	−3.09684	+	0.745277i	−0.141351	+	0.0340171i
$481$	−7.76235	−	8.29700i	−0.353933	−	0.378311i
$482$	−1.51800	−	0.876417i	−0.0691430	−	0.0399197i
$483$	−0.100926	+	3.93650i	−0.00459231	+	0.179117i
$484$	−43.4891			−1.97678
$485$	1.99866	+	3.46179i	0.0907546	+	0.157192i
$486$	−0.170390	+	1.32217i	−0.00772905	+	0.0599749i
$487$	−9.41355	+	35.1319i	−0.426569	+	1.59198i	0.333904	+	0.942607i	$0.391634\pi$
$487$	−9.41355	+	35.1319i	−0.426569	+	1.59198i	−0.760473	+	0.649369i	$0.775033\pi$
$488$	1.91291	−	0.512562i	0.0865932	−	0.0232026i
$489$	11.0582	−	6.01197i	0.500071	−	0.271871i
$490$	1.03756			0.0468723
$491$	14.3100	+	24.7857i	0.645802	+	1.11856i	0.984116	+	0.177529i	$0.0568103\pi$
$491$	14.3100	+	24.7857i	0.645802	+	1.11856i	−0.338313	+	0.941034i	$0.609856\pi$
$492$	−4.61402	−	8.48689i	−0.208016	−	0.382618i
$493$	−2.44394	+	1.41101i	−0.110070	+	0.0635487i
$494$	1.94366	+	1.21014i	0.0874495	+	0.0544469i
$495$	−25.9765	−	16.8290i	−1.16756	−	0.756406i
$496$	12.6108	−	3.37906i	0.566243	−	0.151724i
$497$			1.32455i			0.0594141i
$498$	−0.142638	+	0.482507i	−0.00639176	+	0.0216216i
$499$	−16.2614	+	4.35722i	−0.727959	+	0.195056i	−0.603720	−	0.797196i	$-0.706316\pi$
$499$	−16.2614	+	4.35722i	−0.727959	+	0.195056i	−0.124239	+	0.992252i	$0.539649\pi$
$500$	−17.1455	+	17.1455i	−0.766771	+	0.766771i
$501$	−19.7267	−	36.2848i	−0.881326	−	1.62109i
$502$	0.453562	+	0.121532i	0.0202435	+	0.00542422i
$503$	23.3028	−	13.4539i	1.03902	−	0.599878i	0.119464	−	0.992839i	$-0.461882\pi$
$503$	23.3028	−	13.4539i	1.03902	−	0.599878i	0.919555	+	0.392960i	$0.128549\pi$
$504$	0.440564	+	0.285421i	0.0196243	+	0.0127137i
$505$	5.53238	+	20.6471i	0.246187	+	0.918784i
$506$	−1.08682	−	1.88243i	−0.0483152	−	0.0836843i
$507$	−3.80069	−	22.1936i	−0.168795	−	0.985651i
$508$	−8.23803	+	14.2687i	−0.365504	+	0.633071i
$509$	36.1565	+	9.68811i	1.60261	+	0.429418i	0.945829	−	0.324664i	$-0.105251\pi$
$509$	36.1565	+	9.68811i	1.60261	+	0.429418i	0.656780	+	0.754082i	$0.271918\pi$
$510$	−1.00560	−	1.05852i	−0.0445285	−	0.0468719i
$511$	−2.64462	−	1.52687i	−0.116991	−	0.0675447i
$512$	4.76718	−	4.76718i	0.210682	−	0.210682i
$513$	34.7982	−	16.6680i	1.53638	−	0.735911i
$514$	−0.908993	−	0.243564i	−0.0400940	−	0.0107431i
$515$	4.70557	−	17.5614i	0.207352	−	0.773849i
$516$	1.69164	+	7.02925i	0.0744703	+	0.309446i
$517$	20.8649	−	12.0464i	0.917638	−	0.529799i
$518$	0.0357439	−	0.133398i	0.00157049	−	0.00586117i
$519$	−3.33872	−	13.8733i	−0.146553	−	0.608971i
$520$	−0.0737669	+	2.21574i	−0.00323489	+	0.0971668i
$521$			3.14358i			0.137723i	0.997626	+	0.0688615i	$0.0219366\pi$
$521$			3.14358i			0.137723i	−0.997626	+	0.0688615i	$0.978063\pi$
$522$	−0.0981998	+	0.0886142i	−0.00429809	+	0.00387854i
$523$	0.246164	−	0.426368i	0.0107640	−	0.0186438i	−0.860593	−	0.509293i	$-0.829907\pi$
$523$	0.246164	−	0.426368i	0.0107640	−	0.0186438i	0.871357	+	0.490649i	$0.163240\pi$
$524$	10.0963	−	17.4873i	0.441058	−	0.763936i
$525$	1.55917	+	0.0399750i	0.0680477	+	0.00174465i
$526$	1.42457	+	1.42457i	0.0621141	+	0.0621141i
$527$	12.7728	+	12.7728i	0.556393	+	0.556393i
$528$	39.2456	+	1.00620i	1.70795	+	0.0437894i
$529$	1.65921	−	2.87384i	0.0721397	−	0.124950i
$530$	−0.677367	+	1.17323i	−0.0294229	+	0.0509620i
$531$	17.2423	−	15.5592i	0.748253	−	0.675213i
$532$		−	7.58277i		−	0.328755i
$533$	−9.82904	+	2.28606i	−0.425743	+	0.0990203i
$534$	−0.389316	−	1.61772i	−0.0168474	−	0.0700056i
$535$	1.32703	−	4.95256i	0.0573727	−	0.214118i
$536$	−1.58450	+	0.914810i	−0.0684398	+	0.0395138i
$537$	6.43637	+	26.7450i	0.277750	+	1.15413i
$538$	−0.216145	+	0.806662i	−0.00931865	+	0.0347777i
$539$	−37.2849	−	9.99046i	−1.60597	−	0.430319i
$540$	15.3839	+	10.5359i	0.662016	+	0.453394i
$541$	−9.46307	+	9.46307i	−0.406849	+	0.406849i	−0.880638	−	0.473789i	$-0.842886\pi$
$541$	−9.46307	+	9.46307i	−0.406849	+	0.406849i	0.473789	+	0.880638i	$0.342886\pi$
$542$	−1.07471	−	0.620487i	−0.0461629	−	0.0266522i
$543$	25.9889	+	27.3566i	1.11529	+	1.17398i
$544$	5.39936	+	1.44675i	0.231496	+	0.0620291i
$545$	8.76632	−	15.1837i	0.375508	−	0.650399i
$546$	0.204585	−	0.181796i	0.00875545	−	0.00778016i
$547$	9.38285	+	16.2516i	0.401182	+	0.694867i	0.993869	−	0.110566i	$-0.0352663\pi$
$547$	9.38285	+	16.2516i	0.401182	+	0.694867i	−0.592687	+	0.805433i	$0.701933\pi$
$548$	−4.79660	−	17.9012i	−0.204901	−	0.764700i
$549$	−14.6031	−	9.46066i	−0.623245	−	0.403771i
$550$	−0.745595	+	0.430469i	−0.0317923	+	0.0183553i
$551$	3.69789	+	0.990846i	0.157535	+	0.0422115i
$552$	1.25319	+	2.30508i	0.0533393	+	0.0981108i
$553$	1.76116	−	1.76116i	0.0748923	−	0.0748923i
$554$	1.33855	−	0.358664i	0.0568696	−	0.0152382i
$555$	2.78640	−	9.42567i	0.118276	−	0.400097i
$556$			27.0774i			1.14834i
$557$	−36.4402	+	9.76411i	−1.54402	+	0.413719i	−0.927562	−	0.373669i	$-0.878099\pi$
$557$	−36.4402	+	9.76411i	−1.54402	+	0.413719i	−0.616457	+	0.787388i	$0.711433\pi$
$558$	0.710569	+	0.460345i	0.0300808	+	0.0194880i
$559$	7.54860	+	0.251309i	0.319272	+	0.0106292i
$560$	3.16177	−	1.82545i	0.133609	−	0.0771393i
$561$	25.9439	+	47.7205i	1.09535	+	2.01476i
$562$	−1.09395	−	1.89477i	−0.0461453	−	0.0799261i
$563$	−2.74973			−0.115887			−0.0579437	−	0.998320i	$-0.518454\pi$
$563$	−2.74973			−0.115887			−0.0579437	+	0.998320i	$0.518454\pi$
$564$	−12.7514	+	6.93247i	−0.536930	+	0.291910i
$565$	−26.4020	+	7.07439i	−1.11074	+	0.297622i
$566$	−0.118252	+	0.441324i	−0.00497052	+	0.0185502i
$567$	−0.731465	−	4.55379i	−0.0307186	−	0.191241i
$568$	0.441267	+	0.764297i	0.0185152	+	0.0320692i
$569$	15.7889			0.661906			0.330953	−	0.943647i	$-0.392630\pi$
$569$	15.7889			0.661906			0.330953	+	0.943647i	$0.392630\pi$
$570$	−0.0507649	+	1.98001i	−0.00212631	+	0.0829336i
$571$	24.3390	+	14.0521i	1.01855	+	0.588062i	0.913685	−	0.406424i	$-0.133224\pi$
$571$	24.3390	+	14.0521i	1.01855	+	0.588062i	0.104869	+	0.994486i	$0.466558\pi$
$572$	11.9709	−	39.3840i	0.500528	−	1.64673i
$573$	−14.2200	+	3.42215i	−0.594050	+	0.142963i
$574$	−0.0867336	−	0.0867336i	−0.00362019	−	0.00362019i
$575$	6.75109	+	3.89774i	0.281540	+	0.162547i
$576$	−23.4442	−	1.20295i	−0.976841	−	0.0501227i
$577$	18.1311	+	18.1311i	0.754805	+	0.754805i	0.975372	−	0.220566i	$-0.0707906\pi$
$577$	18.1311	+	18.1311i	0.754805	+	0.754805i	−0.220566	+	0.975372i	$0.570791\pi$
$578$	0.286874	+	1.07063i	0.0119324	+	0.0445322i
$579$	−6.48244	+	3.52427i	−0.269401	+	0.146464i
$580$	0.478829	+	1.78701i	0.0198823	+	0.0742017i
$581$		−	1.74075i		−	0.0722185i
$582$	−0.0769312	−	0.319671i	−0.00318890	−	0.0132508i
$583$	35.6380	−	35.6380i	1.47598	−	1.47598i
$584$	−2.03468			−0.0841956
$585$	14.8873	−	12.5611i	0.615513	−	0.519337i
$586$	1.35426			0.0559439
$587$	−19.1347	+	19.1347i	−0.789775	+	0.789775i	−0.981457	−	0.191682i	$-0.938606\pi$
$587$	−19.1347	+	19.1347i	−0.789775	+	0.789775i	0.191682	+	0.981457i	$0.438606\pi$
$588$	22.2997	+	6.59219i	0.919622	+	0.271857i
$589$		−	24.5048i		−	1.00970i
$590$	0.308566	+	1.15158i	0.0127035	+	0.0474100i
$591$	13.2885	+	8.13324i	0.546618	+	0.334557i
$592$	3.22666	+	12.0421i	0.132615	+	0.494926i
$593$	14.1213	+	14.1213i	0.579890	+	0.579890i	0.934873	−	0.354982i	$-0.115513\pi$
$593$	14.1213	+	14.1213i	0.579890	+	0.579890i	−0.354982	+	0.934873i	$0.615513\pi$
$594$	1.65660	+	1.93320i	0.0679712	+	0.0793202i
$595$	4.37454	+	2.52564i	0.179339	+	0.103541i
$596$	−2.90689	−	2.90689i	−0.119071	−	0.119071i
$597$	−3.56998	+	12.0763i	−0.146109	+	0.494250i
$598$	1.33236	−	0.309884i	0.0544844	−	0.0126721i
$599$	26.7528	+	15.4457i	1.09309	+	0.631096i	0.934397	−	0.356232i	$-0.115939\pi$
$599$	26.7528	+	15.4457i	1.09309	+	0.631096i	0.158693	+	0.987328i	$0.449272\pi$
$600$	0.912998	−	0.496364i	0.0372730	−	0.0202640i
$601$	13.5608			0.553158			0.276579	−	0.960991i	$-0.410799\pi$
$601$	13.5608			0.553158			0.276579	+	0.960991i	$0.410799\pi$
$602$	0.0459016	+	0.0795040i	0.00187081	+	0.00324034i
$603$	15.2938	+	4.95078i	0.622813	+	0.201611i
$604$	−1.05811	+	3.94891i	−0.0430538	+	0.160679i
$605$	−37.9618	+	10.1718i	−1.54337	+	0.413544i
$606$	0.0450637	−	1.75765i	0.00183059	−	0.0713996i
$607$	−34.4682			−1.39902			−0.699510	−	0.714623i	$-0.746598\pi$
$607$	−34.4682			−1.39902			−0.699510	+	0.714623i	$0.746598\pi$
$608$	−3.79156	−	6.56718i	−0.153768	−	0.266334i
$609$	0.238893	−	0.390317i	0.00968042	−	0.0158164i
$610$	0.773531	−	0.446598i	0.0313194	−	0.0180822i
$611$	3.43476	+	14.7679i	0.138956	+	0.597447i
$612$	−14.8873	−	29.1391i	−0.601782	−	1.17788i
$613$	4.38796	−	1.17575i	0.177228	−	0.0474881i	−0.169114	−	0.985597i	$-0.554090\pi$
$613$	4.38796	−	1.17575i	0.177228	−	0.0474881i	0.346342	+	0.938108i	$0.387424\pi$
$614$		−	2.56435i		−	0.103489i
$615$	−6.01263	−	6.32906i	−0.242453	−	0.255212i
$616$	0.968345	−	0.259467i	0.0390157	−	0.0104542i
$617$	4.53555	−	4.53555i	0.182594	−	0.182594i	−0.609891	−	0.792485i	$-0.708787\pi$
$617$	4.53555	−	4.53555i	0.182594	−	0.182594i	0.792485	+	0.609891i	$0.208787\pi$
$618$	−0.780679	+	1.27552i	−0.0314035	+	0.0513089i
$619$	−14.7951	−	3.96432i	−0.594663	−	0.159340i	−0.0510797	−	0.998695i	$-0.516266\pi$
$619$	−14.7951	−	3.96432i	−0.594663	−	0.159340i	−0.543584	+	0.839355i	$0.682933\pi$
$620$	10.2555	−	5.92101i	0.411871	−	0.237794i
$621$	7.65931	−	21.7425i	0.307357	−	0.872498i
$622$	−0.401189	−	1.49726i	−0.0160862	−	0.0600346i
$623$	2.87832	+	4.98540i	0.115318	+	0.199736i
$624$	−7.78848	+	23.4465i	−0.311789	+	0.938613i
$625$	−6.56326	+	11.3679i	−0.262530	+	0.454716i
$626$	−1.32667	−	0.355479i	−0.0530242	−	0.0142078i
$627$	20.8893	−	70.6631i	0.834240	−	2.82201i
$628$	1.26884	+	0.732564i	0.0506322	+	0.0292325i
$629$	−12.1967	+	12.1967i	−0.486316	+	0.486316i
$630$	0.225251	+	0.0729162i	0.00897422	+	0.00290505i
$631$	−22.3199	−	5.98060i	−0.888542	−	0.238084i	−0.214453	−	0.976734i	$-0.568797\pi$
$631$	−22.3199	−	5.98060i	−0.888542	−	0.238084i	−0.674089	+	0.738650i	$0.735464\pi$
$632$	0.429512	−	1.60296i	0.0170851	−	0.0637623i
$633$	−31.6160	−	9.34628i	−1.25662	−	0.371481i
$634$	−1.32419	+	0.764524i	−0.0525905	+	0.0303631i
$635$	−3.85366	+	14.3820i	−0.152928	+	0.570734i
$636$	−22.0124	+	20.9119i	−0.872847	+	0.829209i
$637$	12.8393	−	20.6217i	0.508710	−	0.817061i
$638$			0.252605i			0.0100007i
$639$	2.38806	−	7.37713i	0.0944700	−	0.291835i
$640$	2.44154	−	4.22887i	0.0965103	−	0.167161i
$641$	12.0181	−	20.8159i	0.474685	−	0.822178i	−0.524895	−	0.851167i	$-0.675895\pi$
$641$	12.0181	−	20.8159i	0.474685	−	0.822178i	0.999580	+	0.0289891i	$0.00922880\pi$
$642$	−0.220162	+	0.359713i	−0.00868910	+	0.0141967i
$643$	10.9466	+	10.9466i	0.431690	+	0.431690i	0.889203	−	0.457513i	$-0.151260\pi$
$643$	10.9466	+	10.9466i	0.431690	+	0.431690i	−0.457513	+	0.889203i	$0.651260\pi$
$644$	−3.20344	−	3.20344i	−0.126233	−	0.126233i
$645$	3.12074	+	5.74020i	0.122879	+	0.226020i
$646$	1.73794	−	3.01020i	0.0683784	−	0.118435i
$647$	16.2559	−	28.1560i	0.639084	−	1.10693i	−0.346550	−	0.938032i	$-0.612647\pi$
$647$	16.2559	−	28.1560i	0.639084	−	1.10693i	0.985634	−	0.168895i	$-0.0540199\pi$
$648$	−1.93915	−	2.38397i	−0.0761770	−	0.0936511i
$649$		−	44.3534i		−	1.74102i
$650$	−0.122739	−	0.527723i	−0.00481422	−	0.0206990i
$651$	−2.80902	−	0.830399i	−0.110094	−	0.0325459i
$652$	−3.74793	+	13.9875i	−0.146780	+	0.547791i
$653$	−28.4531	+	16.4274i	−1.11346	+	0.642854i	−0.939722	−	0.341939i	$-0.888917\pi$
$653$	−28.4531	+	16.4274i	−1.11346	+	0.642854i	−0.173734	+	0.984793i	$0.555583\pi$
$654$	−1.04555	+	0.993274i	−0.0408841	+	0.0388401i
$655$	4.72293	−	17.6262i	0.184540	−	0.688713i
$656$	10.6954	+	2.86583i	0.417587	+	0.111892i
$657$	11.9765	+	13.2720i	0.467247	+	0.517790i
$658$	−0.130316	+	0.130316i	−0.00508023	+	0.00508023i
$659$	−12.1233	−	6.99940i	−0.472257	−	0.272658i	0.244927	−	0.969542i	$-0.421236\pi$
$659$	−12.1233	−	6.99940i	−0.472257	−	0.272658i	−0.717184	+	0.696884i	$0.754569\pi$
$660$	34.6206	−	8.33169i	1.34760	−	0.324311i
$661$	13.5253	+	3.62408i	0.526072	+	0.140961i	0.512074	−	0.858941i	$-0.328877\pi$
$661$	13.5253	+	3.62408i	0.526072	+	0.140961i	0.0139982	+	0.999902i	$0.495544\pi$
$662$	0.0708494	−	0.122715i	0.00275364	−	0.00476944i
$663$	−33.4818	+	6.88777i	−1.30033	+	0.267499i
$664$	−0.579924	−	1.00446i	−0.0225054	−	0.0389805i
$665$	−1.77357	−	6.61904i	−0.0687760	−	0.256675i
$666$	−0.439583	+	0.678522i	−0.0170335	+	0.0262922i
$667$	1.98081	−	1.14362i	0.0766974	−	0.0442813i
$668$	45.8963	+	12.2979i	1.77578	+	0.475819i
$669$	−3.50327	−	0.0898192i	−0.135444	−	0.00347261i
$670$	−0.583502	+	0.583502i	−0.0225427	+	0.0225427i
$671$	−32.0971	+	8.60039i	−1.23909	+	0.332014i
$672$	−0.881290	+	0.212089i	−0.0339965	+	0.00818150i
$673$			5.82726i			0.224624i	0.993673	+	0.112312i	$0.0358257\pi$
$673$			5.82726i			0.224624i	−0.993673	+	0.112312i	$0.964174\pi$
$674$	−1.63778	+	0.438842i	−0.0630849	+	0.0169035i
$675$	−8.61179	−	3.03370i	−0.331468	−	0.116767i
$676$	21.5232	+	14.4159i	0.827814	+	0.554458i
$677$	−7.74373	+	4.47084i	−0.297616	+	0.171828i	−0.641371	−	0.767231i	$-0.721634\pi$
$677$	−7.74373	+	4.47084i	−0.297616	+	0.171828i	0.343756	+	0.939059i	$0.388301\pi$
$678$	2.24755	+	0.0576241i	0.0863166	+	0.00221304i
$679$	0.568774	+	0.985145i	0.0218275	+	0.0378064i
$680$	3.36562			0.129066
$681$	9.21636	+	5.64086i	0.353172	+	0.216158i
$682$	1.56181	−	0.418485i	0.0598047	−	0.0160246i
$683$	6.18232	−	23.0727i	0.236560	−	0.882854i	−0.740879	−	0.671638i	$-0.765591\pi$
$683$	6.18232	−	23.0727i	0.236560	−	0.882854i	0.977439	−	0.211216i	$-0.0677423\pi$
$684$	−13.6711	+	42.2326i	−0.522729	+	1.61480i
$685$	−8.37396	−	14.5041i	−0.319953	−	0.554174i
$686$	0.602042			0.0229861
$687$	−32.4050	−	19.8334i	−1.23633	−	0.756692i
$688$	−7.17697	−	4.14362i	−0.273619	−	0.157974i
$689$	14.9361	+	27.9808i	0.569021	+	1.06599i
$690$	0.815035	+	0.857927i	0.0310278	+	0.0326607i
$691$	−25.8128	−	25.8128i	−0.981966	−	0.981966i	0.0178746	−	0.999840i	$-0.494310\pi$
$691$	−25.8128	−	25.8128i	−0.981966	−	0.981966i	−0.999840	+	0.0178746i	$0.994310\pi$
$692$	14.2172	+	8.20832i	0.540458	+	0.312034i
$693$	−7.39232	−	4.78914i	−0.280811	−	0.181924i
$694$	0.978931	+	0.978931i	0.0371597	+	0.0371597i
$695$	6.33325	+	23.6360i	0.240234	+	0.896566i
$696$	0.00781488	−	0.304809i	0.000296222	−	0.0115537i
$697$	3.96509	+	14.7979i	0.150188	+	0.560511i
$698$			1.94074i			0.0734579i
$699$	−19.4809	+	18.5069i	−0.736835	+	0.699997i
$700$	−1.26882	+	1.26882i	−0.0479568	+	0.0479568i
$701$	19.6744			0.743092			0.371546	−	0.928415i	$-0.378828\pi$
$701$	19.6744			0.743092			0.371546	+	0.928415i	$0.378828\pi$
$702$	−1.46721	+	0.643670i	−0.0553763	+	0.0242938i
$703$	23.3996			0.882534
$704$	−31.7006	+	31.7006i	−1.19476	+	1.19476i
$705$	−9.50928	+	9.03386i	−0.358140	+	0.340235i
$706$		−	0.990121i		−	0.0372637i
$707$	1.57439	+	5.87569i	0.0592109	+	0.220978i
$708$	−0.684827	+	26.7107i	−0.0257374	+	1.00385i
$709$	9.38929	+	35.0413i	0.352622	+	1.31600i	0.883450	+	0.468525i	$0.155214\pi$
$709$	9.38929	+	35.0413i	0.352622	+	1.31600i	−0.530828	+	0.847480i	$0.678119\pi$
$710$	0.281458	+	0.281458i	0.0105629	+	0.0105629i
$711$	−12.9841	+	6.63363i	−0.486942	+	0.248781i
$712$	3.32173	+	1.91780i	0.124487	+	0.0718726i
$713$	−10.3524	−	10.3524i	−0.387699	−	0.387699i
$714$	−0.286169	−	0.301230i	−0.0107096	−	0.0112732i
$715$	1.23775	−	37.1785i	0.0462893	−	1.39040i
$716$	−27.4080	−	15.8240i	−1.02428	−	0.591370i
$717$	−31.7731	−	19.4467i	−1.18659	−	0.726251i
$718$	0.917183			0.0342290
$719$	1.23089	+	2.13196i	0.0459043	+	0.0795086i	0.888065	−	0.459719i	$-0.152050\pi$
$719$	1.23089	+	2.13196i	0.0459043	+	0.0795086i	−0.842160	+	0.539227i	$0.818716\pi$
$720$	−20.9008	+	4.46649i	−0.778925	+	0.166456i
$721$	1.33910	−	4.99758i	0.0498706	−	0.186120i
$722$	−2.98520	+	0.799881i	−0.111098	+	0.0297685i
$723$	−30.2797	−	18.5327i	−1.12611	−	0.689237i
$724$	−43.4114			−1.61337
$725$	−0.452967	−	0.784561i	−0.0168228	−	0.0291379i
$726$	3.23162	+	0.0828543i	0.119937	+	0.00307501i
$727$	−34.1223	+	19.7005i	−1.26552	+	0.730651i	−0.974138	−	0.225955i	$-0.927450\pi$
$727$	−34.1223	+	19.7005i	−1.26552	+	0.730651i	−0.291387	+	0.956605i	$0.594117\pi$
$728$	−0.0209924	+	0.630550i	−0.000778029	+	0.0233697i
$729$	−4.13620	+	26.6813i	−0.153193	+	0.988196i
$730$	−0.886414	+	0.237514i	−0.0328077	+	0.00879079i
$731$		−	11.4660i		−	0.424086i
$732$	19.4625	−	4.68379i	0.719354	−	0.173118i
$733$	26.0719	−	6.98594i	0.962988	−	0.258032i	0.257123	−	0.966379i	$-0.417225\pi$
$733$	26.0719	−	6.98594i	0.962988	−	0.258032i	0.705864	+	0.708347i	$0.250559\pi$
$734$	1.41196	−	1.41196i	0.0521164	−	0.0521164i
$735$	21.0074	+	0.538600i	0.774868	+	0.0198666i
$736$	−4.37618	−	1.17259i	−0.161308	−	0.0432224i
$737$	26.5866	−	15.3498i	0.979331	−	0.565417i
$738$	0.326693	+	0.639440i	0.0120257	+	0.0235381i
$739$	−1.77661	−	6.63041i	−0.0653537	−	0.243903i	0.925520	−	0.378700i	$-0.123629\pi$
$739$	−1.77661	−	6.63041i	−0.0653537	−	0.243903i	−0.990873	+	0.134796i	$0.956962\pi$
$740$	5.65397	+	9.79296i	0.207844	+	0.359996i
$741$	38.7248	+	25.5105i	1.42259	+	0.937152i
$742$	−0.192763	+	0.333875i	−0.00707655	+	0.0122569i
$743$	46.8324	+	12.5487i	1.71811	+	0.460367i	0.977390	−	0.211444i	$-0.0678166\pi$
$743$	46.8324	+	12.5487i	1.71811	+	0.460367i	0.740723	+	0.671811i	$0.234483\pi$
$744$	−1.89752	+	0.456652i	−0.0695664	+	0.0167417i
$745$	−3.21735	−	1.85754i	−0.117874	−	0.0680549i
$746$	−0.148368	+	0.148368i	−0.00543214	+	0.00543214i
$747$	−3.13844	+	9.69519i	−0.114829	+	0.354728i
$748$	−60.3612	−	16.1737i	−2.20702	−	0.591370i
$749$	0.377643	−	1.40938i	0.0137988	−	0.0514978i
$750$	1.30673	−	1.24140i	0.0477150	−	0.0453294i
$751$	−3.31754	+	1.91539i	−0.121059	+	0.0698934i	−0.559307	−	0.828961i	$-0.688933\pi$
$751$	−3.31754	+	1.91539i	−0.121059	+	0.0698934i	0.438248	+	0.898854i	$0.355599\pi$
$752$	4.30586	−	16.0697i	0.157019	−	0.586001i
$753$	9.12010	+	2.69607i	0.332355	+	0.0982503i
$754$	−0.152099	−	0.0462310i	−0.00553913	−	0.00168363i
$755$			3.69451i			0.134457i
$756$	4.37790	+	2.99828i	0.159223	+	0.109046i
$757$	11.7765	−	20.3975i	0.428024	−	0.741360i	−0.568673	−	0.822563i	$-0.692543\pi$
$757$	11.7765	−	20.3975i	0.428024	−	0.741360i	0.996698	+	0.0812038i	$0.0258765\pi$
$758$	−0.569812	+	0.986943i	−0.0206965	+	0.0358474i
$759$	−21.0275	−	38.6775i	−0.763252	−	1.40390i
$760$	−3.22850	−	3.22850i	−0.117110	−	0.117110i
$761$	−20.4670	−	20.4670i	−0.741929	−	0.741929i	0.231020	−	0.972949i	$-0.425794\pi$
$761$	−20.4670	−	20.4670i	−0.741929	−	0.741929i	−0.972949	+	0.231020i	$0.925794\pi$
$762$	0.639342	−	1.04459i	0.0231609	−	0.0378416i
$763$	2.49469	−	4.32094i	0.0903140	−	0.156428i
$764$	8.41346	−	14.5725i	0.304388	−	0.527216i
$765$	−19.8106	−	21.9536i	−0.716255	−	0.793734i
$766$		−	3.20152i		−	0.115676i
$767$	26.7062	+	8.11743i	0.964306	+	0.293103i
$768$	19.3611	−	18.3931i	0.698632	−	0.663703i
$769$	−1.58276	+	5.90694i	−0.0570757	+	0.213010i	−0.988574	−	0.150736i	$-0.951836\pi$
$769$	−1.58276	+	5.90694i	−0.0570757	+	0.213010i	0.931498	+	0.363746i	$0.118502\pi$
$770$	0.391574	−	0.226075i	0.0141114	−	0.00814719i
$771$	−18.2778	−	5.40326i	−0.658259	−	0.194594i
$772$	2.19707	−	8.19957i	0.0790742	−	0.295109i
$773$	−0.445447	−	0.119357i	−0.0160216	−	0.00429298i	0.250799	−	0.968039i	$-0.419307\pi$
$773$	−0.445447	−	0.119357i	−0.0160216	−	0.00429298i	−0.266821	+	0.963746i	$0.585973\pi$
$774$	−0.112312	−	0.525558i	−0.00403696	−	0.0188908i
$775$	−4.10037	+	4.10037i	−0.147290	+	0.147290i
$776$	0.656393	+	0.378969i	0.0235631	+	0.0136042i
$777$	0.792947	−	2.68233i	0.0284468	−	0.0962280i
$778$	1.96792	+	0.527302i	0.0705533	+	0.0189047i
$779$	10.3915	−	17.9985i	0.372312	−	0.644864i
$780$	−1.31945	+	22.3707i	−0.0472439	+	0.800999i
$781$	−7.40412	−	12.8243i	−0.264940	−	0.458890i
$782$	−0.537482	−	2.00591i	−0.0192203	−	0.0717312i
$783$	−2.03423	+	1.74318i	−0.0726976	+	0.0622962i
$784$	−23.0833	+	13.3271i	−0.824402	+	0.475969i
$785$	1.27892	+	0.342685i	0.0456466	+	0.0122310i
$786$	−0.783559	+	1.28022i	−0.0279486	+	0.0456640i
$787$	−22.4505	+	22.4505i	−0.800274	+	0.800274i	−0.983138	−	0.182864i	$-0.941463\pi$
$787$	−22.4505	+	22.4505i	−0.800274	+	0.800274i	0.182864	+	0.983138i	$0.441463\pi$
$788$	−17.3136	+	4.63917i	−0.616773	+	0.165264i
$789$	28.1035	+	29.5825i	1.00051	+	1.05316i
$790$		−	0.748472i		−	0.0266294i
$791$	−7.51340	+	2.01321i	−0.267146	+	0.0715815i
$792$	−5.86104	−	0.300736i	−0.208263	−	0.0106862i
$793$	0.695820	−	20.9004i	0.0247093	−	0.742196i
$794$	1.68377	−	0.972126i	0.0597548	−	0.0344995i
$795$	−14.3236	+	23.4026i	−0.508004	+	0.830006i
$796$	−7.24394	−	12.5469i	−0.256754	−	0.444712i
$797$	37.3254			1.32213			0.661067	−	0.750327i	$-0.270104\pi$
$797$	37.3254			1.32213			0.661067	+	0.750327i	$0.270104\pi$
$798$	−0.0144465	+	0.563466i	−0.000511401	+	0.0199465i
$799$	22.2336	−	5.95747i	0.786567	−	0.210760i
$800$	−0.464442	+	1.73332i	−0.0164205	+	0.0612821i
$801$	−7.04266	−	32.9558i	−0.248840	−	1.16444i
$802$	1.21620	+	2.10652i	0.0429454	+	0.0743837i
$803$	34.1403			1.20479
$804$	−16.2481	+	8.83353i	−0.573028	+	0.311534i
$805$	−3.54556	−	2.04703i	−0.124965	−	0.0721483i
$806$	−0.0338578	+	1.01699i	−0.00119259	+	0.0358220i
$807$	−4.79498	+	16.2202i	−0.168791	+	0.570976i
$808$	2.86592	+	2.86592i	0.100823	+	0.100823i
$809$	−36.4293	−	21.0325i	−1.28079	−	0.739462i	−0.303793	−	0.952738i	$-0.598253\pi$
$809$	−36.4293	−	21.0325i	−1.28079	−	0.739462i	−0.976992	+	0.213276i	$0.931587\pi$
$810$	−1.12308	−	0.812220i	−0.0394611	−	0.0285385i
$811$	−11.9459	−	11.9459i	−0.419478	−	0.419478i	0.465546	−	0.885024i	$-0.345858\pi$
$811$	−11.9459	−	11.9459i	−0.419478	−	0.419478i	−0.885024	+	0.465546i	$0.845858\pi$
$812$	0.136264	+	0.508543i	0.00478192	+	0.0178464i
$813$	−21.4375	−	13.1208i	−0.751845	−	0.460166i
$814$	0.399611	+	1.49137i	0.0140064	+	0.0522724i
$815$			13.0863i			0.458394i
$816$	35.9683	+	10.6329i	1.25914	+	0.372226i
$817$	−10.9988	+	10.9988i	−0.384801	+	0.384801i
$818$	0.280380			0.00980326
$819$	4.23658	−	3.57459i	0.148038	−	0.124906i
$820$	10.0434			0.350731
$821$	12.0935	−	12.0935i	0.422066	−	0.422066i	−0.463848	−	0.885915i	$-0.653532\pi$
$821$	12.0935	−	12.0935i	0.422066	−	0.422066i	0.885915	+	0.463848i	$0.153532\pi$
$822$	0.322325	+	1.33935i	0.0112424	+	0.0467153i
$823$		−	47.9181i		−	1.67032i	−0.550008	−	0.835160i	$-0.685375\pi$
$823$		−	47.9181i		−	1.67032i	0.550008	−	0.835160i	$-0.314625\pi$
$824$	−0.892229	−	3.32984i	−0.0310823	−	0.116001i
$825$	−15.3194	+	8.32860i	−0.533353	+	0.289965i
$826$	0.0878109	+	0.327715i	0.00305533	+	0.0114027i
$827$	17.3519	+	17.3519i	0.603386	+	0.603386i	0.941209	−	0.337824i	$-0.109691\pi$
$827$	17.3519	+	17.3519i	0.603386	+	0.603386i	−0.337824	+	0.941209i	$0.609691\pi$
$828$	12.0661	+	23.6172i	0.419327	+	0.820755i
$829$	18.5597	+	10.7155i	0.644606	+	0.372164i	0.786387	−	0.617735i	$-0.211949\pi$
$829$	18.5597	+	10.7155i	0.644606	+	0.372164i	−0.141780	+	0.989898i	$0.545283\pi$
$830$	−0.369899	−	0.369899i	−0.0128394	−	0.0128394i
$831$	27.2876	−	6.56696i	0.946596	−	0.227805i
$832$	−13.2859	−	24.8894i	−0.460607	−	0.862886i
$833$	−31.9374	−	18.4390i	−1.10656	−	0.638875i
$834$	0.0515873	−	2.01209i	0.00178632	−	0.0696730i
$835$	42.9395			1.48598
$836$	42.3871	+	73.4166i	1.46599	+	2.53917i
$837$	14.1478	+	9.68938i	0.489020	+	0.334914i
$838$	−0.204242	+	0.762242i	−0.00705543	+	0.0263312i
$839$	−38.1327	+	10.2176i	−1.31649	+	0.352752i	−0.847661	−	0.530539i	$-0.821990\pi$
$839$	−38.1327	+	10.2176i	−1.31649	+	0.352752i	−0.468826	+	0.883291i	$0.655323\pi$
$840$	−0.479491	+	0.260682i	−0.0165440	+	0.00899439i
$841$	28.7342			0.990834
$842$	0.0948491	+	0.164283i	0.00326872	+	0.00566158i
$843$	−21.1654	−	38.9310i	−0.728974	−	1.34085i
$844$	32.8480	−	18.9648i	1.13067	−	0.652795i
$845$	22.1595	+	7.54957i	0.762309	+	0.259713i
$846$	0.960747	−	0.490849i	0.0330312	−	0.0168758i
$847$	−10.8031	+	2.89467i	−0.371198	+	0.0994621i
$848$		−	34.8021i		−	1.19511i
$849$	−2.62333	+	8.87402i	−0.0900324	+	0.304556i
$850$	−0.794502	+	0.212886i	−0.0272512	+	0.00730194i
$851$	9.88546	−	9.88546i	0.338869	−	0.338869i
$852$	4.26094	+	7.83745i	0.145977	+	0.268506i
$853$	27.1772	+	7.28211i	0.930530	+	0.249335i	0.692081	−	0.721820i	$-0.256694\pi$
$853$	27.1772	+	7.28211i	0.930530	+	0.249335i	0.238449	+	0.971155i	$0.423361\pi$
$854$	0.220129	−	0.127092i	0.00753267	−	0.00434899i
$855$	−2.05565	+	40.0626i	−0.0703019	+	1.37011i
$856$	−0.251620	−	0.939060i	−0.00860021	−	0.0320964i
$857$	19.3381	+	33.4945i	0.660576	+	1.14415i	0.980465	+	0.196696i	$0.0630211\pi$
$857$	19.3381	+	33.4945i	0.660576	+	1.14415i	−0.319889	+	0.947455i	$0.603646\pi$
$858$	−0.964575	+	2.90377i	−0.0329301	+	0.0991332i
$859$	8.08690	−	14.0069i	0.275921	−	0.477910i	−0.694446	−	0.719545i	$-0.744350\pi$
$859$	8.08690	−	14.0069i	0.275921	−	0.477910i	0.970367	+	0.241635i	$0.0776837\pi$
$860$	−7.26073	−	1.94551i	−0.247589	−	0.0663412i
$861$	−1.71106	−	1.80110i	−0.0583127	−	0.0613815i
$862$	−2.20988	−	1.27587i	−0.0752687	−	0.0434564i
$863$	−24.7751	+	24.7751i	−0.843353	+	0.843353i	−0.989293	−	0.145941i	$-0.953379\pi$
$863$	−24.7751	+	24.7751i	−0.843353	+	0.843353i	0.145941	+	0.989293i	$0.453379\pi$
$864$	5.29076	+	0.407659i	0.179995	+	0.0138688i
$865$	14.3302	+	3.83976i	0.487241	+	0.130556i
$866$	−0.289019	+	1.07864i	−0.00982128	+	0.0366535i
$867$	5.25252	+	21.8257i	0.178385	+	0.741241i
$868$	2.91848	−	1.68498i	0.0990596	−	0.0571921i
$869$	−7.20687	+	26.8964i	−0.244476	+	0.912398i
$870$	−0.0321766	−	0.133703i	−0.00109089	−	0.00453296i
$871$	4.37666	+	18.8177i	0.148298	+	0.637613i
$872$		−	3.32439i		−	0.112578i
$873$	−1.39167	−	6.51226i	−0.0471009	−	0.220407i
$874$	−1.40860	+	2.43977i	−0.0476466	+	0.0825264i
$875$	−3.11788	+	5.40032i	−0.105404	+	0.182564i
$876$	−20.5602	−	0.527135i	−0.694664	−	0.0178102i
$877$	14.1609	+	14.1609i	0.478178	+	0.478178i	0.904549	−	0.426370i	$-0.140208\pi$
$877$	14.1609	+	14.1609i	0.478178	+	0.478178i	−0.426370	+	0.904549i	$0.640208\pi$
$878$	−0.865364	−	0.865364i	−0.0292046	−	0.0292046i
$879$	27.4194	+	0.702997i	0.924834	+	0.0237115i
$880$	−20.4082	+	35.3481i	−0.687961	+	1.19158i
$881$	7.53795	−	13.0561i	0.253960	−	0.439872i	−0.710653	−	0.703543i	$-0.751600\pi$
$881$	7.53795	−	13.0561i	0.253960	−	0.439872i	0.964613	+	0.263672i	$0.0849335\pi$
$882$	−1.64450	−	0.532342i	−0.0553732	−	0.0179249i
$883$			39.2575i			1.32112i	0.750773	+	0.660560i	$0.229681\pi$
$883$			39.2575i			1.32112i	−0.750773	+	0.660560i	$0.770319\pi$
$884$	20.7857	−	33.3848i	0.699099	−	1.12285i
$885$	5.64970	+	23.4761i	0.189913	+	0.789141i
$886$	−0.364116	+	1.35890i	−0.0122327	+	0.0456531i
$887$	13.5741	−	7.83699i	0.455773	−	0.263140i	−0.254492	−	0.967075i	$-0.581908\pi$
$887$	13.5741	−	7.83699i	0.455773	−	0.263140i	0.710265	+	0.703934i	$0.248575\pi$
$888$	−0.436056	−	1.81194i	−0.0146331	−	0.0608046i
$889$	−1.09666	+	4.09280i	−0.0367809	+	0.137268i
$890$	1.67099	+	0.447741i	0.0560118	+	0.0150083i
$891$	32.5374	+	40.0011i	1.09004	+	1.34009i
$892$	2.85089	−	2.85089i	0.0954547	−	0.0954547i
$893$	−27.0424	−	15.6130i	−0.904941	−	0.522468i
$894$	0.210469	+	0.221546i	0.00703915	+	0.00740960i
$895$	−27.6257	−	7.40228i	−0.923425	−	0.247431i
$896$	0.694806	−	1.20344i	0.0232118	−	0.0402041i
$897$	27.1370	−	5.58254i	0.906078	−	0.186396i
$898$	−1.07861	−	1.86821i	−0.0359937	−	0.0623430i
$899$	0.440356	+	1.64343i	0.0146867	+	0.0548115i
$900$	9.35432	−	4.77916i	0.311811	−	0.159305i
$901$	41.7002	−	24.0756i	1.38924	−	0.802076i
$902$	1.32459	+	0.354923i	0.0441041	+	0.0118177i
$903$	0.888092	+	1.63353i	0.0295538	+	0.0543605i
$904$	−3.66473	+	3.66473i	−0.121887	+	0.121887i
$905$	−37.8940	+	10.1537i	−1.25964	+	0.337519i
$906$	0.0861500	−	0.291423i	0.00286214	−	0.00968187i
$907$		−	6.13756i		−	0.203794i	−0.994795	−	0.101897i	$-0.967509\pi$
$907$		−	6.13756i		−	0.203794i	0.994795	−	0.101897i	$-0.0324912\pi$
$908$	−12.0080	+	3.21753i	−0.398499	+	0.106778i
$909$	1.82480	−	35.5634i	0.0605246	−	1.17956i
$910$	0.0644605	+	0.277152i	0.00213685	+	0.00918748i
$911$	7.64862	−	4.41593i	0.253410	−	0.146306i	−0.367915	−	0.929860i	$-0.619928\pi$
$911$	7.64862	−	4.41593i	0.253410	−	0.146306i	0.621325	+	0.783553i	$0.286595\pi$
$912$	−24.3032	−	44.7025i	−0.804758	−	1.48025i
$913$	9.73067	+	16.8540i	0.322038	+	0.557786i
$914$	−0.384973			−0.0127338
$915$	15.8934	−	8.64066i	0.525419	−	0.285651i
$916$	42.2204	−	11.3129i	1.39500	−	0.373790i
$917$	1.34404	−	5.01601i	0.0443840	−	0.165643i
$918$	1.05074	+	2.19365i	0.0346796	+	0.0724013i
$919$	−5.30900	−	9.19546i	−0.175128	−	0.303330i	0.765078	−	0.643938i	$-0.222701\pi$
$919$	−5.30900	−	9.19546i	−0.175128	−	0.303330i	−0.940205	+	0.340608i	$0.889367\pi$
$920$	−2.72784			−0.0899341
$921$	1.33116	−	51.9200i	0.0438632	−	1.71082i
$922$	−0.331456	−	0.191366i	−0.0109159	−	0.00630230i
$923$	9.07690	−	2.11113i	0.298770	−	0.0694885i
$924$	9.85222	−	2.37101i	0.324114	−	0.0780005i
$925$	−3.91544	−	3.91544i	−0.128739	−	0.128739i
$926$	1.24042	+	0.716159i	0.0407629	+	0.0235345i
$927$	−16.4684	+	25.4199i	−0.540893	+	0.834901i
$928$	0.372297	+	0.372297i	0.0122212	+	0.0122212i
$929$	8.01779	+	29.9228i	0.263055	+	0.981735i	0.963430	+	0.267960i	$0.0863494\pi$
$929$	8.01779	+	29.9228i	0.263055	+	0.981735i	−0.700375	+	0.713775i	$0.746984\pi$
$930$	−0.773354	+	0.420444i	−0.0253593	+	0.0137869i
$931$	12.9483	+	48.3239i	0.424365	+	1.58375i
$932$		−	30.9137i		−	1.01261i
$933$	−7.34557	−	30.5230i	−0.240483	−	0.999277i
$934$	−2.06939	+	2.06939i	−0.0677124	+	0.0677124i
$935$	−56.4725			−1.84685
$936$	1.25375	−	3.47403i	0.0409801	−	0.113552i
$937$	−47.1338			−1.53979			−0.769897	−	0.638168i	$-0.779692\pi$
$937$	−47.1338			−1.53979			−0.769897	+	0.638168i	$0.779692\pi$
$938$	−0.166051	+	0.166051i	−0.00542177	+	0.00542177i
$939$	−26.6763	−	7.88600i	−0.870547	−	0.257350i
$940$		−	15.0900i		−	0.492182i
$941$	−0.0981573	−	0.366328i	−0.00319984	−	0.0119420i	0.964307	−	0.264785i	$-0.0853010\pi$
$941$	−0.0981573	−	0.366328i	−0.00319984	−	0.0119420i	−0.967507	+	0.252843i	$0.918634\pi$
$942$	−0.0928902	−	0.0568533i	−0.00302652	−	0.00185238i
$943$	−3.21370	−	11.9937i	−0.104653	−	0.390568i
$944$	−21.6565	−	21.6565i	−0.704861	−	0.704861i
$945$	4.52277	+	1.59325i	0.147126	+	0.0518284i
$946$	−0.888842	−	0.513173i	−0.0288988	−	0.0166847i
$947$	22.1926	+	22.1926i	0.721163	+	0.721163i	0.968842	−	0.247679i	$-0.0796680\pi$
$947$	22.1926	+	22.1926i	0.721163	+	0.721163i	−0.247679	+	0.968842i	$0.579668\pi$
$948$	4.75545	−	16.0864i	0.154450	−	0.522463i
$949$	−6.24826	+	20.5567i	−0.202827	+	0.667298i
$950$	0.966344	+	0.557919i	0.0313523	+	0.0181013i
$951$	−27.2076	+	14.7918i	−0.882267	+	0.479657i
$952$	0.957779			0.0310418
$953$	13.5922	+	23.5423i	0.440294	+	0.762611i	0.997711	−	0.0676211i	$-0.0215409\pi$
$953$	13.5922	+	23.5423i	0.440294	+	0.762611i	−0.557417	+	0.830233i	$0.688208\pi$
$954$	1.67555	−	1.51200i	0.0542480	−	0.0489527i
$955$	3.93572	−	14.6883i	0.127357	−	0.475302i
$956$	41.3972	−	11.0923i	1.33888	−	0.358752i
$957$	−0.131128	+	5.11445i	−0.00423875	+	0.165327i
$958$	−2.82967			−0.0914225
$959$	−2.38304	−	4.12754i	−0.0769523	−	0.133285i
$960$	12.7410	−	20.8170i	0.411216	−	0.671867i
$961$	−17.4153	+	10.0547i	−0.561784	+	0.324346i
$962$	−0.971123	−	0.0323308i	−0.0313103	−	0.00104239i
$963$	−4.64431	+	7.16876i	−0.149661	+	0.231010i
$964$	39.4514	−	10.5710i	1.27064	−	0.340468i
$965$		−	7.67133i		−	0.246949i
$966$	0.231940	+	0.244146i	0.00746255	+	0.00785528i
$967$	33.7881	−	9.05350i	1.08655	−	0.291141i	0.329275	−	0.944234i	$-0.393196\pi$
$967$	33.7881	−	9.05350i	1.08655	−	0.291141i	0.757278	+	0.653093i	$0.226529\pi$
$968$	−5.26929	+	5.26929i	−0.169361	+	0.169361i
$969$	36.7504	−	60.0449i	1.18059	−	1.92892i
$970$	0.330198	+	0.0884762i	0.0106020	+	0.00284080i
$971$	2.18627	−	1.26224i	0.0701606	−	0.0405072i	−0.464509	−	0.885568i	$-0.653769\pi$
$971$	2.18627	−	1.26224i	0.0701606	−	0.0405072i	0.534670	+	0.845061i	$0.320436\pi$
$972$	−18.9772	−	24.5921i	−0.608695	−	0.788791i
$973$	1.80230	+	6.72627i	0.0577791	+	0.215634i
$974$	1.55521	+	2.69370i	0.0498321	+	0.0863117i
$975$	−2.21113	−	10.7484i	−0.0708130	−	0.344225i
$976$	−11.4728	+	19.8715i	−0.367235	+	0.636070i
$977$	0.347770	+	0.0931847i	0.0111262	+	0.00298124i	0.264378	−	0.964419i	$-0.414833\pi$
$977$	0.347770	+	0.0931847i	0.0111262	+	0.00298124i	−0.253252	+	0.967400i	$0.581500\pi$
$978$	0.305152	−	1.03225i	0.00975770	−	0.0330077i
$979$	−55.7360	−	32.1792i	−1.78133	−	1.02845i
$980$	−17.0953	+	17.0953i	−0.546090	+	0.546090i
$981$	−21.6846	+	19.5679i	−0.692336	+	0.624755i
$982$	2.36415	+	0.633472i	0.0754431	+	0.0202149i
$983$	−5.27343	+	19.6807i	−0.168196	+	0.627717i	0.829415	+	0.558634i	$0.188674\pi$
$983$	−5.27343	+	19.6807i	−0.168196	+	0.627717i	−0.997611	+	0.0690837i	$0.977992\pi$
$984$	−1.58735	−	0.469251i	−0.0506030	−	0.0149592i
$985$	−14.0281	+	8.09912i	−0.446972	+	0.258059i
$986$	−0.0624622	+	0.233112i	−0.00198920	+	0.00742380i
$987$	−2.70612	+	2.57083i	−0.0861369	+	0.0818304i
$988$	−51.9634	+	12.0858i	−1.65318	+	0.384500i
$989$			9.29319i			0.295506i
$990$	−2.58848	+	0.553159i	−0.0822674	+	0.0175806i
$991$	−10.5948	+	18.3508i	−0.336556	+	0.582931i	−0.983782	−	0.179366i	$-0.942595\pi$
$991$	−10.5948	+	18.3508i	−0.336556	+	0.582931i	0.647227	+	0.762298i	$0.275929\pi$
$992$	1.68506	−	2.91862i	0.0535008	−	0.0926661i
$993$	1.49818	−	2.44781i	0.0475432	−	0.0776788i
$994$	0.0800965	+	0.0800965i	0.00254051	+	0.00254051i
$995$	−9.25791	−	9.25791i	−0.293495	−	0.293495i
$996$	−5.59982	−	10.3002i	−0.177437	−	0.326373i
$997$	−1.82391	+	3.15911i	−0.0577638	+	0.100050i	−0.893461	−	0.449140i	$-0.851730\pi$
$997$	−1.82391	+	3.15911i	−0.0577638	+	0.100050i	0.835697	+	0.549190i	$0.185064\pi$
$998$	−0.719854	+	1.24682i	−0.0227866	+	0.0394675i
$999$	−9.25238	+	13.5097i	−0.292732	+	0.427429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.59.7	yes	48
3.2	odd	2		351.2.ba.a.98.6		48
9.2	odd	6		117.2.bc.a.20.7	yes	48
9.7	even	3		351.2.bf.a.332.6		48
13.2	odd	12		117.2.bc.a.41.7	yes	48
39.2	even	12		351.2.bf.a.314.6		48
117.2	even	12	inner	117.2.x.a.2.7	✓	48
117.106	odd	12		351.2.ba.a.197.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.2.7	✓	48	117.2	even	12	inner
117.2.x.a.59.7	yes	48	1.1	even	1	trivial
117.2.bc.a.20.7	yes	48	9.2	odd	6
117.2.bc.a.41.7	yes	48	13.2	odd	12
351.2.ba.a.98.6		48	3.2	odd	2
351.2.ba.a.197.6		48	117.106	odd	12
351.2.bf.a.314.6		48	39.2	even	12
351.2.bf.a.332.6		48	9.7	even	3

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0604708 - 0.0604708i) q^{2} +(1.25573 - 1.19295i) q^{3} +1.99269i q^{4} +(0.466078 + 1.73943i) q^{5} +(0.00379642 - 0.148074i) q^{6} +(0.132635 + 0.495001i) q^{7} +(0.241441 + 0.241441i) q^{8} +(0.153731 - 2.99606i) q^{9} +(0.133369 + 0.0770004i) q^{10} +(-4.05119 - 4.05119i) q^{11} +(2.37718 + 2.50228i) q^{12} +(3.18076 - 1.69788i) q^{13} +(0.0379537 + 0.0219126i) q^{14} +(2.66032 + 1.62825i) q^{15} -3.95617 q^{16} +(-2.73683 - 4.74032i) q^{17} +(-0.171878 - 0.190470i) q^{18} +(-1.92187 + 7.17250i) q^{19} +(-3.46613 + 0.928747i) q^{20} +(0.757066 + 0.463362i) q^{21} -0.489958 q^{22} +(2.21820 + 3.84203i) q^{23} +(0.591213 + 0.0151579i) q^{24} +(1.52175 - 0.878584i) q^{25} +(0.0896707 - 0.295015i) q^{26} +(-3.38111 - 3.94564i) q^{27} +(-0.986381 + 0.264300i) q^{28} -0.515564i q^{29} +(0.259333 - 0.0624104i) q^{30} +(-3.18763 + 0.854124i) q^{31} +(-0.722115 + 0.722115i) q^{32} +(-9.92010 - 0.254338i) q^{33} +(-0.452149 - 0.121153i) q^{34} +(-0.799199 + 0.461418i) q^{35} +(5.97021 + 0.306337i) q^{36} +(-0.815602 - 3.04387i) q^{37} +(0.317510 + 0.549944i) q^{38} +(1.96869 - 5.92657i) q^{39} +(-0.307439 + 0.532499i) q^{40} +(-2.70348 - 0.724395i) q^{41} +(0.0738003 - 0.0177606i) q^{42} +(1.81412 + 1.04738i) q^{43} +(8.07276 - 8.07276i) q^{44} +(5.28307 - 1.12899i) q^{45} +(0.366467 + 0.0981945i) q^{46} +(-1.08839 + 4.06193i) q^{47} +(-4.96790 + 4.71952i) q^{48} +(5.83474 - 3.36869i) q^{49} +(0.0388929 - 0.145150i) q^{50} +(-9.09170 - 2.68768i) q^{51} +(3.38334 + 6.33825i) q^{52} +8.79692i q^{53} +(-0.443055 - 0.0341378i) q^{54} +(5.15858 - 8.93492i) q^{55} +(-0.0874900 + 0.151537i) q^{56} +(6.14310 + 11.2994i) q^{57} +(-0.0311766 - 0.0311766i) q^{58} +(5.47412 + 5.47412i) q^{59} +(-3.24458 + 5.30119i) q^{60} +(2.89997 - 5.02290i) q^{61} +(-0.141109 + 0.244409i) q^{62} +(1.50344 - 0.321286i) q^{63} -7.82501i q^{64} +(4.43582 + 4.74134i) q^{65} +(-0.615257 + 0.584497i) q^{66} +(-1.38685 + 5.17581i) q^{67} +(9.44597 - 5.45364i) q^{68} +(7.36882 + 2.17836i) q^{69} +(-0.0204259 + 0.0762306i) q^{70} +(2.49660 + 0.668962i) q^{71} +(0.760489 - 0.686255i) q^{72} +(-4.21361 + 4.21361i) q^{73} +(-0.233385 - 0.134745i) q^{74} +(0.862806 - 2.91864i) q^{75} +(-14.2925 - 3.82968i) q^{76} +(1.46801 - 2.54267i) q^{77} +(-0.239336 - 0.477433i) q^{78} +(-2.43009 - 4.20904i) q^{79} +(-1.84388 - 6.88147i) q^{80} +(-8.95273 - 0.921173i) q^{81} +(-0.207286 + 0.119677i) q^{82} +(-3.28109 - 0.879166i) q^{83} +(-0.923334 + 1.50860i) q^{84} +(6.96986 - 6.96986i) q^{85} +(0.173037 - 0.0463652i) q^{86} +(-0.615044 - 0.647411i) q^{87} -1.95625i q^{88} +(10.8505 - 2.90739i) q^{89} +(0.251201 - 0.387743i) q^{90} +(1.26233 + 1.34928i) q^{91} +(-7.65596 + 4.42017i) q^{92} +(-2.98389 + 4.87525i) q^{93} +(0.179812 + 0.311444i) q^{94} -13.3718 q^{95} +(-0.0453351 + 1.76823i) q^{96} +(2.14413 - 0.574518i) q^{97} +(0.149124 - 0.556539i) q^{98} +(-12.7604 + 11.5148i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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