LMFDB - Embedded newform 546.2.bw.a.431.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			431.28
Character	$\chi$	$=$	546.431
Dual form			546.2.bw.a.527.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.287995 + 1.70794i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.571804 + 2.13400i) q^{5} +(0.163866 + 1.72428i) q^{6} +(-2.64337 + 0.112194i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.83412 - 0.983756i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.287995 + 1.70794i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.571804 + 2.13400i) q^{5} +(0.163866 + 1.72428i) q^{6} +(-2.64337 + 0.112194i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.83412 - 0.983756i) q^{9} +2.20928i q^{10} +(-1.49302 + 1.49302i) q^{11} +(0.604559 + 1.62312i) q^{12} +(-3.42792 + 1.11774i) q^{13} +(-2.52426 + 0.792526i) q^{14} +(-3.48007 - 1.59119i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.09461 + 3.62798i) q^{17} +(-2.99216 - 0.216711i) q^{18} +(0.337423 - 0.337423i) q^{19} +(0.571804 + 2.13400i) q^{20} +(0.569656 - 4.54703i) q^{21} +(-1.05573 + 1.82857i) q^{22} +(2.41507 - 4.18302i) q^{23} +(1.00405 + 1.41134i) q^{24} +(0.103127 + 0.0595401i) q^{25} +(-3.02183 + 1.96687i) q^{26} +(2.49641 - 4.55719i) q^{27} +(-2.23313 + 1.41885i) q^{28} +(-0.814739 + 0.470390i) q^{29} +(-3.77332 - 0.636261i) q^{30} +(1.14902 + 4.28819i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-2.12001 - 2.97998i) q^{33} +(2.96223 + 2.96223i) q^{34} +(1.27207 - 5.70511i) q^{35} +(-2.94630 + 0.565101i) q^{36} +(-8.78173 + 2.35306i) q^{37} +(0.238594 - 0.413257i) q^{38} +(-0.921812 - 6.17659i) q^{39} +(1.10464 + 1.91329i) q^{40} +(-2.42880 + 9.06440i) q^{41} +(-0.626612 - 4.53953i) q^{42} +(2.32396 + 1.34174i) q^{43} +(-0.546485 + 2.03951i) q^{44} +(3.71990 - 5.48550i) q^{45} +(1.25013 - 4.66555i) q^{46} +(4.06004 + 1.08788i) q^{47} +(1.33512 + 1.10338i) q^{48} +(6.97482 - 0.593142i) q^{49} +(0.115023 + 0.0308202i) q^{50} +(-6.79960 + 2.53264i) q^{51} +(-2.40980 + 2.68195i) q^{52} +(4.82321 + 2.78468i) q^{53} +(1.23186 - 5.04802i) q^{54} +(-2.33240 - 4.03983i) q^{55} +(-1.78981 + 1.94848i) q^{56} +(0.479123 + 0.673475i) q^{57} +(-0.665231 + 0.665231i) q^{58} +(13.7931 + 3.69585i) q^{59} +(-3.80942 + 0.362025i) q^{60} -4.04297 q^{61} +(2.21973 + 3.84468i) q^{62} +(7.60200 + 2.28246i) q^{63} -1.00000i q^{64} +(-0.425162 - 7.95432i) q^{65} +(-2.81905 - 2.32974i) q^{66} +(-6.00262 + 6.00262i) q^{67} +(3.62798 + 2.09461i) q^{68} +(6.44882 + 5.32948i) q^{69} +(-0.247868 - 5.83995i) q^{70} +(5.98706 - 1.60423i) q^{71} +(-2.69964 + 1.30840i) q^{72} +(6.72115 - 1.80093i) q^{73} +(-7.87349 + 4.54576i) q^{74} +(-0.131391 + 0.158987i) q^{75} +(0.123506 - 0.460929i) q^{76} +(3.77911 - 4.11413i) q^{77} +(-2.48902 - 5.72755i) q^{78} +(-1.77600 - 3.07612i) q^{79} +(1.56220 + 1.56220i) q^{80} +(7.06445 + 5.57616i) q^{81} +9.38416i q^{82} +(-7.36931 - 7.36931i) q^{83} +(-1.78018 - 4.22267i) q^{84} +(-8.93981 + 2.39542i) q^{85} +(2.59204 + 0.694536i) q^{86} +(-0.568757 - 1.52699i) q^{87} +2.11145i q^{88} +(4.08834 + 15.2579i) q^{89} +(2.17339 - 6.26136i) q^{90} +(8.93587 - 3.33920i) q^{91} -4.83014i q^{92} +(-7.65488 + 0.727475i) q^{93} +4.20326 q^{94} +(0.527122 + 0.913002i) q^{95} +(1.57520 + 0.720229i) q^{96} +(-4.62372 - 17.2560i) q^{97} +(6.58365 - 2.37815i) q^{98} +(5.70018 - 2.76263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.287995	+	1.70794i	−0.166274	+	0.986080i
$3$	−0.287995	+	1.70794i	−0.166274	+	0.986080i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.571804	+	2.13400i	−0.255718	+	0.954354i	0.711971	+	0.702209i	$0.247803\pi$
$5$	−0.571804	+	2.13400i	−0.255718	+	0.954354i	−0.967689	+	0.252145i	$0.918864\pi$
$6$	0.163866	+	1.72428i	0.0668979	+	0.703935i
$7$	−2.64337	+	0.112194i	−0.999100	+	0.0424054i
$7$	−2.64337	+	0.112194i	−0.999100	+	0.0424054i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.83412	−	0.983756i	−0.944706	−	0.327919i
$10$			2.20928i			0.698636i
$11$	−1.49302	+	1.49302i	−0.450164	+	0.450164i	−0.895409	−	0.445245i	$-0.853117\pi$
$11$	−1.49302	+	1.49302i	−0.450164	+	0.450164i	0.445245	+	0.895409i	$0.353117\pi$
$12$	0.604559	+	1.62312i	0.174521	+	0.468553i
$13$	−3.42792	+	1.11774i	−0.950735	+	0.310006i
$13$	−3.42792	+	1.11774i	−0.950735	+	0.310006i
$14$	−2.52426	+	0.792526i	−0.674638	+	0.211812i
$15$	−3.48007	−	1.59119i	−0.898550	−	0.410843i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.09461	+	3.62798i	0.508018	+	0.879914i	0.999957	+	0.00928370i	$0.00295514\pi$
$17$	2.09461	+	3.62798i	0.508018	+	0.879914i	−0.491939	+	0.870630i	$0.663712\pi$
$18$	−2.99216	−	0.216711i	−0.705259	−	0.0510794i
$19$	0.337423	−	0.337423i	0.0774102	−	0.0774102i	−0.667342	−	0.744752i	$-0.732568\pi$
$19$	0.337423	−	0.337423i	0.0774102	−	0.0774102i	0.744752	+	0.667342i	$0.232568\pi$
$20$	0.571804	+	2.13400i	0.127859	+	0.477177i
$21$	0.569656	−	4.54703i	0.124309	−	0.992244i
$22$	−1.05573	+	1.82857i	−0.225082	+	0.389853i
$23$	2.41507	−	4.18302i	0.503577	−	0.872220i	−0.496415	−	0.868085i	$-0.665351\pi$
$23$	2.41507	−	4.18302i	0.503577	−	0.872220i	0.999991	−	0.00413478i	$-0.00131615\pi$
$24$	1.00405	+	1.41134i	0.204951	+	0.288088i
$25$	0.103127	+	0.0595401i	0.0206253	+	0.0119080i
$26$	−3.02183	+	1.96687i	−0.592629	+	0.385734i
$27$	2.49641	−	4.55719i	0.480434	−	0.877031i
$28$	−2.23313	+	1.41885i	−0.422022	+	0.268137i
$29$	−0.814739	+	0.470390i	−0.151293	+	0.0873492i	−0.573735	−	0.819041i	$-0.694506\pi$
$29$	−0.814739	+	0.470390i	−0.151293	+	0.0873492i	0.422442	+	0.906390i	$0.361173\pi$
$30$	−3.77332	−	0.636261i	−0.688911	−	0.116165i
$31$	1.14902	+	4.28819i	0.206369	+	0.770181i	0.989028	+	0.147730i	$0.0471966\pi$
$31$	1.14902	+	4.28819i	0.206369	+	0.770181i	−0.782658	+	0.622452i	$0.786137\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−2.12001	−	2.97998i	−0.369047	−	0.518748i
$34$	2.96223	+	2.96223i	0.508018	+	0.508018i
$35$	1.27207	−	5.70511i	0.215019	−	0.964340i
$36$	−2.94630	+	0.565101i	−0.491049	+	0.0941836i
$37$	−8.78173	+	2.35306i	−1.44371	+	0.386840i	−0.893831	−	0.448405i	$-0.851992\pi$
$37$	−8.78173	+	2.35306i	−1.44371	+	0.386840i	−0.549877	+	0.835245i	$0.685326\pi$
$38$	0.238594	−	0.413257i	0.0387051	−	0.0670392i
$39$	−0.921812	−	6.17659i	−0.147608	−	0.989046i
$40$	1.10464	+	1.91329i	0.174659	+	0.302518i
$41$	−2.42880	+	9.06440i	−0.379315	+	1.41562i	0.467623	+	0.883928i	$0.345111\pi$
$41$	−2.42880	+	9.06440i	−0.379315	+	1.41562i	−0.846937	+	0.531693i	$0.821556\pi$
$42$	−0.626612	−	4.53953i	−0.0966884	−	0.700465i
$43$	2.32396	+	1.34174i	0.354401	+	0.204613i	0.666622	−	0.745396i	$-0.267740\pi$
$43$	2.32396	+	1.34174i	0.354401	+	0.204613i	−0.312221	+	0.950010i	$0.601073\pi$
$44$	−0.546485	+	2.03951i	−0.0823857	+	0.307467i
$45$	3.71990	−	5.48550i	0.554529	−	0.817729i
$46$	1.25013	−	4.66555i	0.184322	−	0.687898i
$47$	4.06004	+	1.08788i	0.592218	+	0.158684i	0.542467	−	0.840077i	$-0.317490\pi$
$47$	4.06004	+	1.08788i	0.592218	+	0.158684i	0.0497512	+	0.998762i	$0.484157\pi$
$48$	1.33512	+	1.10338i	0.192708	+	0.159259i
$49$	6.97482	−	0.593142i	0.996404	−	0.0847345i
$50$	0.115023	+	0.0308202i	0.0162667	+	0.00435864i
$51$	−6.79960	+	2.53264i	−0.952135	+	0.354640i
$52$	−2.40980	+	2.68195i	−0.334179	+	0.371920i
$53$	4.82321	+	2.78468i	0.662518	+	0.382505i	0.793236	−	0.608915i	$-0.208395\pi$
$53$	4.82321	+	2.78468i	0.662518	+	0.382505i	−0.130718	+	0.991420i	$0.541728\pi$
$54$	1.23186	−	5.04802i	0.167635	−	0.686949i
$55$	−2.33240	−	4.03983i	−0.314500	−	0.544731i
$56$	−1.78981	+	1.94848i	−0.239174	+	0.260376i
$57$	0.479123	+	0.673475i	0.0634613	+	0.0892039i
$58$	−0.665231	+	0.665231i	−0.0873492	+	0.0873492i
$59$	13.7931	+	3.69585i	1.79571	+	0.481158i	0.993294	−	0.115612i	$-0.0368830\pi$
$59$	13.7931	+	3.69585i	1.79571	+	0.481158i	0.802412	+	0.596770i	$0.203550\pi$
$60$	−3.80942	+	0.362025i	−0.491794	+	0.0467373i
$61$	−4.04297			−0.517650			−0.258825	−	0.965924i	$-0.583335\pi$
$61$	−4.04297			−0.517650			−0.258825	+	0.965924i	$0.583335\pi$
$62$	2.21973	+	3.84468i	0.281906	+	0.488275i
$63$	7.60200	+	2.28246i	0.957762	+	0.287563i
$64$		−	1.00000i		−	0.125000i
$65$	−0.425162	−	7.95432i	−0.0527349	−	0.986612i
$66$	−2.81905	−	2.32974i	−0.347001	−	0.286771i
$67$	−6.00262	+	6.00262i	−0.733337	+	0.733337i	−0.971279	−	0.237942i	$-0.923527\pi$
$67$	−6.00262	+	6.00262i	−0.733337	+	0.733337i	0.237942	+	0.971279i	$0.423527\pi$
$68$	3.62798	+	2.09461i	0.439957	+	0.254009i
$69$	6.44882	+	5.32948i	0.776347	+	0.641594i
$70$	−0.247868	−	5.83995i	−0.0296259	−	0.698007i
$71$	5.98706	−	1.60423i	0.710533	−	0.190387i	0.114589	−	0.993413i	$-0.463445\pi$
$71$	5.98706	−	1.60423i	0.710533	−	0.190387i	0.595944	+	0.803026i	$0.296778\pi$
$72$	−2.69964	+	1.30840i	−0.318156	+	0.154197i
$73$	6.72115	−	1.80093i	0.786651	−	0.210782i	0.156936	−	0.987609i	$-0.449838\pi$
$73$	6.72115	−	1.80093i	0.786651	−	0.210782i	0.629715	+	0.776826i	$0.283172\pi$
$74$	−7.87349	+	4.54576i	−0.915274	+	0.528434i
$75$	−0.131391	+	0.158987i	−0.0151717	+	0.0183582i
$76$	0.123506	−	0.460929i	0.0141671	−	0.0528722i
$77$	3.77911	−	4.11413i	0.430669	−	0.468848i
$78$	−2.48902	−	5.72755i	−0.281826	−	0.648517i
$79$	−1.77600	−	3.07612i	−0.199816	−	0.346091i	0.748653	−	0.662962i	$-0.230701\pi$
$79$	−1.77600	−	3.07612i	−0.199816	−	0.346091i	−0.948469	+	0.316871i	$0.897368\pi$
$80$	1.56220	+	1.56220i	0.174659	+	0.174659i
$81$	7.06445	+	5.57616i	0.784939	+	0.619573i
$82$			9.38416i			1.03631i
$83$	−7.36931	−	7.36931i	−0.808887	−	0.808887i	0.175578	−	0.984465i	$-0.443820\pi$
$83$	−7.36931	−	7.36931i	−0.808887	−	0.808887i	−0.984465	+	0.175578i	$0.943820\pi$
$84$	−1.78018	−	4.22267i	−0.194233	−	0.460731i
$85$	−8.93981	+	2.39542i	−0.969659	+	0.259819i
$86$	2.59204	+	0.694536i	0.279507	+	0.0748937i
$87$	−0.568757	−	1.52699i	−0.0609771	−	0.163711i
$88$			2.11145i			0.225082i
$89$	4.08834	+	15.2579i	0.433363	+	1.61733i	0.744953	+	0.667116i	$0.232472\pi$
$89$	4.08834	+	15.2579i	0.433363	+	1.61733i	−0.311590	+	0.950217i	$0.600862\pi$
$90$	2.17339	−	6.26136i	0.229096	−	0.660005i
$91$	8.93587	−	3.33920i	0.936734	−	0.350043i
$92$		−	4.83014i		−	0.503577i
$93$	−7.65488	+	0.727475i	−0.793774	+	0.0754357i
$94$	4.20326			0.433534
$95$	0.527122	+	0.913002i	0.0540815	+	0.0936720i
$96$	1.57520	+	0.720229i	0.160769	+	0.0735081i
$97$	−4.62372	−	17.2560i	−0.469468	−	1.75208i	−0.641635	−	0.767010i	$-0.721744\pi$
$97$	−4.62372	−	17.2560i	−0.469468	−	1.75208i	0.172168	−	0.985068i	$-0.444923\pi$
$98$	6.58365	−	2.37815i	0.665049	−	0.240229i
$99$	5.70018	−	2.76263i	0.572889	−	0.277655i
$100$	0.119080			0.0119080
$101$	−8.14985			−0.810940			−0.405470	−	0.914108i	$-0.632892\pi$
$101$	−8.14985			−0.810940			−0.405470	+	0.914108i	$0.632892\pi$
$102$	−5.91242	+	4.20621i	−0.585417	+	0.416476i
$103$	10.9259	−	6.30805i	1.07656	−	0.621551i	0.146592	−	0.989197i	$-0.453170\pi$
$103$	10.9259	−	6.30805i	1.07656	−	0.621551i	0.929966	+	0.367646i	$0.119836\pi$
$104$	−1.63354	+	3.21427i	−0.160182	+	0.315185i
$105$	9.37764	+	3.81566i	0.915164	+	0.372370i
$106$	5.37959	+	1.44146i	0.522512	+	0.140007i
$107$	0.474592	+	0.274006i	0.0458806	+	0.0264892i	0.522765	−	0.852477i	$-0.324901\pi$
$107$	0.474592	+	0.274006i	0.0458806	+	0.0264892i	−0.476884	+	0.878966i	$0.658234\pi$
$108$	−0.116641	−	5.19484i	−0.0112238	−	0.499874i
$109$	−2.35063	−	8.77267i	−0.225150	−	0.840270i	−0.982345	−	0.187081i	$-0.940097\pi$
$109$	−2.35063	−	8.77267i	−0.225150	−	0.840270i	0.757195	−	0.653189i	$-0.226569\pi$
$110$	−3.29851	−	3.29851i	−0.314500	−	0.314500i
$111$	−1.48979	−	15.6763i	−0.141404	−	1.48793i
$112$	−1.22452	+	2.34532i	−0.115707	+	0.221612i
$113$	−5.76556	−	3.32875i	−0.542378	−	0.313142i	0.203664	−	0.979041i	$-0.434715\pi$
$113$	−5.76556	−	3.32875i	−0.542378	−	0.313142i	−0.746042	+	0.665899i	$0.768048\pi$
$114$	0.637105	+	0.526521i	0.0596704	+	0.0493132i
$115$	7.54563	+	7.54563i	0.703633	+	0.703633i
$116$	−0.470390	+	0.814739i	−0.0436746	+	0.0756466i
$117$	10.8147	+	0.204427i	0.999821	+	0.0188993i
$118$	14.2797			1.31455
$119$	−5.94388	−	9.35509i	−0.544874	−	0.857579i
$120$	−3.58592	+	1.33564i	−0.327348	+	0.121927i
$121$			6.54176i			0.594705i
$122$	−3.90521	+	1.04640i	−0.353561	+	0.0947365i
$123$	−14.7820	−	6.75874i	−1.33284	−	0.609415i
$124$	3.13917	+	3.13917i	0.281906	+	0.281906i
$125$	−7.99701	+	7.99701i	−0.715275	+	0.715275i
$126$	7.93371	+	0.237146i	0.706791	+	0.0211266i
$127$	4.84622	−	2.79797i	0.430033	−	0.248280i	−0.269328	−	0.963049i	$-0.586801\pi$
$127$	4.84622	−	2.79797i	0.430033	−	0.248280i	0.699361	+	0.714769i	$0.253468\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−2.96090	+	3.58277i	−0.260693	+	0.315446i
$130$	−2.46940	−	7.57324i	−0.216581	−	0.664217i
$131$	1.13235	−	0.653760i	0.0989335	−	0.0571193i	−0.449717	−	0.893171i	$-0.648475\pi$
$131$	1.13235	−	0.653760i	0.0989335	−	0.0571193i	0.548650	+	0.836052i	$0.315142\pi$
$132$	−3.32597	−	1.52073i	−0.289489	−	0.132363i
$133$	−0.854078	+	0.929792i	−0.0740580	+	0.0806232i
$134$	−4.24449	+	7.35168i	−0.366669	+	0.635089i
$135$	8.29759	+	7.93315i	0.714142	+	0.682777i
$136$	4.04648	+	1.08425i	0.346983	+	0.0929738i
$137$	16.3692	+	4.38612i	1.39852	+	0.374731i	0.877812	−	0.479005i	$-0.159003\pi$
$137$	16.3692	+	4.38612i	1.39852	+	0.374731i	0.520705	+	0.853737i	$0.325669\pi$
$138$	7.60845	+	3.47880i	0.647675	+	0.296136i
$139$	0.00803392	−	0.0139152i	0.000681428	−	0.00118027i	−0.865684	−	0.500590i	$-0.833116\pi$
$139$	0.00803392	−	0.0139152i	0.000681428	−	0.00118027i	0.866366	+	0.499410i	$0.166450\pi$
$140$	−1.75091	−	5.57680i	−0.147979	−	0.471326i
$141$	−3.02731	+	6.62100i	−0.254946	+	0.557589i
$142$	5.36785	−	3.09913i	0.450460	−	0.260073i
$143$	3.44916	−	6.78679i	0.288433	−	0.567539i
$144$	−2.26902	+	1.96254i	−0.189085	+	0.163545i
$145$	−0.537941	−	2.00762i	−0.0446736	−	0.166724i
$146$	6.02601	−	3.47912i	0.498716	−	0.287934i
$147$	−0.995663	+	12.0834i	−0.0821209	+	0.996622i
$148$	−6.42867	+	6.42867i	−0.528434	+	0.528434i
$149$	7.35460	+	7.35460i	0.602513	+	0.602513i	0.940979	−	0.338466i	$-0.109908\pi$
$149$	7.35460	+	7.35460i	0.602513	+	0.602513i	−0.338466	+	0.940979i	$0.609908\pi$
$150$	−0.0857650	+	0.187576i	−0.00700269	+	0.0153155i
$151$	14.7620	−	3.95546i	1.20131	−	0.321891i	0.397964	−	0.917401i	$-0.369717\pi$
$151$	14.7620	−	3.95546i	1.20131	−	0.321891i	0.803348	+	0.595510i	$0.203050\pi$
$152$		−	0.477189i		−	0.0387051i
$153$	−2.36734	−	12.3427i	−0.191388	−	0.997848i
$154$	2.58552	−	4.95204i	0.208347	−	0.399047i
$155$	−9.80801			−0.787798
$156$	−3.88661	−	4.88818i	−0.311178	−	0.391367i
$157$	−10.4574	+	18.1128i	−0.834592	+	1.44556i	0.0597707	+	0.998212i	$0.480963\pi$
$157$	−10.4574	+	18.1128i	−0.834592	+	1.44556i	−0.894362	+	0.447343i	$0.852370\pi$
$158$	−2.51164	−	2.51164i	−0.199816	−	0.199816i
$159$	−6.14512	+	7.43577i	−0.487340	+	0.589695i
$160$	1.91329	+	1.10464i	0.151259	+	0.0873295i
$161$	−5.91461	+	11.3282i	−0.466137	+	0.892790i
$162$	8.26695	+	3.55774i	0.649513	+	0.279523i
$163$	−17.9535	−	17.9535i	−1.40623	−	1.40623i	−0.778153	−	0.628075i	$-0.783843\pi$
$163$	−17.9535	−	17.9535i	−1.40623	−	1.40623i	−0.628075	−	0.778153i	$-0.716157\pi$
$164$	2.42880	+	9.06440i	0.189657	+	0.707811i
$165$	7.57151	−	2.82014i	0.589441	−	0.219548i
$166$	−9.02553	−	5.21089i	−0.700517	−	0.404444i
$167$	−6.53289	−	1.75048i	−0.505530	−	0.135456i	−0.00296472	−	0.999996i	$-0.500944\pi$
$167$	−6.53289	−	1.75048i	−0.505530	−	0.135456i	−0.502565	+	0.864539i	$0.667610\pi$
$168$	−2.81243	−	3.61804i	−0.216984	−	0.279138i
$169$	10.5013	−	7.66306i	0.807793	−	0.589466i
$170$	−8.01522	+	4.62759i	−0.614739	+	0.354920i
$171$	−1.28824	+	0.624355i	−0.0985141	+	0.0477456i
$172$	2.68348			0.204613
$173$	−6.71395			−0.510452			−0.255226	−	0.966881i	$-0.582150\pi$
$173$	−6.71395			−0.510452			−0.255226	+	0.966881i	$0.582150\pi$
$174$	−0.944592	−	1.32776i	−0.0716093	−	0.100657i
$175$	−0.279282	−	0.145816i	−0.0211117	−	0.0110227i
$176$	0.546485	+	2.03951i	0.0411928	+	0.153734i
$177$	−10.2846	+	22.4934i	−0.773039	+	1.69071i
$178$	7.89806	+	13.6798i	0.591985	+	1.02535i
$179$	−4.39615			−0.328584			−0.164292	−	0.986412i	$-0.552534\pi$
$179$	−4.39615			−0.328584			−0.164292	+	0.986412i	$0.552534\pi$
$180$	0.478776	−	6.61053i	0.0356859	−	0.492720i
$181$		−	26.8774i		−	1.99778i	−0.0470732	−	0.998891i	$-0.514989\pi$
$181$		−	26.8774i		−	1.99778i	0.0470732	−	0.998891i	$-0.485011\pi$
$182$	7.76714	−	5.53819i	0.575739	−	0.410518i
$183$	1.16436	−	6.90516i	0.0860716	−	0.510444i
$184$	−1.25013	−	4.66555i	−0.0921609	−	0.343949i
$185$		−	20.0857i		−	1.47673i
$186$	−7.20576	+	2.68392i	−0.528352	+	0.196794i
$187$	−8.54396	−	2.28935i	−0.624797	−	0.167414i
$188$	4.06004	−	1.08788i	0.296109	−	0.0793421i
$189$	−6.08764	+	12.3264i	−0.442811	+	0.896615i
$190$	0.745463	+	0.745463i	0.0540815	+	0.0540815i
$191$		−	4.81472i		−	0.348381i	−0.984712	−	0.174191i	$-0.944269\pi$
$191$		−	4.81472i		−	0.348381i	0.984712	−	0.174191i	$-0.0557309\pi$
$192$	1.70794	+	0.287995i	0.123260	+	0.0207842i
$193$	−0.594684	−	0.594684i	−0.0428063	−	0.0428063i	0.685380	−	0.728186i	$-0.259636\pi$
$193$	−0.594684	−	0.594684i	−0.0428063	−	0.0428063i	−0.728186	+	0.685380i	$0.759636\pi$
$194$	−8.93234	−	15.4713i	−0.641305	−	1.11077i
$195$	13.7079	+	1.56465i	0.981646	+	0.112047i
$196$	5.74380	−	4.00109i	0.410272	−	0.285792i
$197$	−3.67600	+	13.7190i	−0.261904	+	0.977440i	0.702214	+	0.711966i	$0.252195\pi$
$197$	−3.67600	+	13.7190i	−0.261904	+	0.977440i	−0.964118	+	0.265474i	$0.914472\pi$
$198$	4.79093	−	4.14381i	0.340476	−	0.294488i
$199$	6.18891	−	3.57317i	0.438720	−	0.253295i	−0.264334	−	0.964431i	$-0.585152\pi$
$199$	6.18891	−	3.57317i	0.438720	−	0.253295i	0.703055	+	0.711136i	$0.251819\pi$
$200$	0.115023	−	0.0308202i	0.00813333	−	0.00217932i
$201$	−8.52339	−	11.9808i	−0.601194	−	0.845064i
$202$	−7.87215	+	2.10934i	−0.553883	+	0.148412i
$203$	2.10088	−	1.33482i	0.147453	−	0.0936862i
$204$	−4.62231	+	5.59313i	−0.323627	+	0.391597i
$205$	−17.9546	−	10.3661i	−1.25401	−	0.724001i
$206$	8.92093	−	8.92093i	0.621551	−	0.621551i
$207$	−10.9597	+	9.47934i	−0.761749	+	0.658859i
$208$	−0.745969	+	3.52754i	−0.0517236	+	0.244591i
$209$			1.00756i			0.0696945i
$210$	10.0457	+	1.25853i	0.693217	+	0.0868469i
$211$	6.91083	+	11.9699i	0.475761	+	0.824042i	0.999614	−	0.0277663i	$-0.00883942\pi$
$211$	6.91083	+	11.9699i	0.475761	+	0.824042i	−0.523854	+	0.851808i	$0.675506\pi$
$212$	5.56936			0.382505
$213$	1.01568	+	10.6875i	0.0695934	+	0.732299i
$214$	0.529339	+	0.141836i	0.0361849	+	0.00969571i
$215$	−4.19213	+	4.19213i	−0.285901	+	0.285901i
$216$	−1.45719	−	4.98764i	−0.0991493	−	0.339366i
$217$	−3.51839	−	11.2064i	−0.238844	−	0.760737i
$218$	−4.54107	−	7.86536i	−0.307560	−	0.532710i
$219$	1.14022	+	11.9980i	0.0770488	+	0.810748i
$220$	−4.03983	−	2.33240i	−0.272365	−	0.157250i
$221$	−11.2353	−	10.0952i	−0.755769	−	0.679076i
$222$	−5.49636	−	14.7566i	−0.368892	−	0.990398i
$223$	−4.03794	−	1.08196i	−0.270401	−	0.0724536i	0.121071	−	0.992644i	$-0.461367\pi$
$223$	−4.03794	−	1.08196i	−0.270401	−	0.0724536i	−0.391471	+	0.920190i	$0.628034\pi$
$224$	−0.575784	+	2.58234i	−0.0384712	+	0.172540i
$225$	−0.233700	−	0.270195i	−0.0155800	−	0.0180130i
$226$	−6.43065	−	1.72309i	−0.427760	−	0.114618i
$227$	−2.92533	+	10.9175i	−0.194161	+	0.724619i	0.798321	+	0.602232i	$0.205722\pi$
$227$	−2.92533	+	10.9175i	−0.194161	+	0.724619i	−0.992482	+	0.122387i	$0.960945\pi$
$228$	0.751670	+	0.343685i	0.0497805	+	0.0227611i
$229$	−0.512008	+	1.91084i	−0.0338344	+	0.126272i	−0.980777	−	0.195130i	$-0.937487\pi$
$229$	−0.512008	+	1.91084i	−0.0338344	+	0.126272i	0.946943	+	0.321401i	$0.104154\pi$
$230$	9.24147	+	5.33556i	0.609364	+	0.351817i
$231$	5.93832	+	7.63934i	0.390712	+	0.502631i
$232$	−0.243492	+	0.908723i	−0.0159860	+	0.0596606i
$233$	8.36770	+	14.4933i	0.548187	+	0.949487i	0.998399	+	0.0565654i	$0.0180150\pi$
$233$	8.36770	+	14.4933i	0.548187	+	0.949487i	−0.450212	+	0.892922i	$0.648652\pi$
$234$	10.4991	−	2.60159i	0.686350	−	0.170072i
$235$	−4.64309	+	8.04207i	−0.302882	+	0.524607i
$236$	13.7931	−	3.69585i	0.897853	−	0.240579i
$237$	5.76531	−	2.14739i	0.374497	−	0.139488i
$238$	−8.16262	−	7.49793i	−0.529104	−	0.486019i
$239$	10.8665	+	10.8665i	0.702893	+	0.702893i	0.965030	−	0.262138i	$-0.0844275\pi$
$239$	10.8665	+	10.8665i	0.702893	+	0.702893i	−0.262138	+	0.965030i	$0.584428\pi$
$240$	−3.11804	+	2.21823i	−0.201269	+	0.143186i
$241$	−7.04677	+	26.2989i	−0.453922	+	1.69406i	0.237315	+	0.971433i	$0.423733\pi$
$241$	−7.04677	+	26.2989i	−0.453922	+	1.69406i	−0.691237	+	0.722628i	$0.742934\pi$
$242$	1.69313	+	6.31885i	0.108839	+	0.406191i
$243$	−11.5583	+	10.4597i	−0.741463	+	0.670993i
$244$	−3.50132	+	2.02149i	−0.224149	+	0.129412i
$245$	−2.72247	+	15.2234i	−0.173932	+	0.972590i
$246$	−16.0276	−	2.70259i	−1.02188	−	0.172311i
$247$	−0.779509	+	1.53381i	−0.0495990	+	0.0975942i
$248$	3.84468	+	2.21973i	0.244138	+	0.140953i
$249$	14.7087	−	10.4640i	0.932124	−	0.663130i
$250$	−5.65474	+	9.79430i	−0.357637	+	0.619446i
$251$	9.46986	−	16.4023i	0.597732	−	1.03530i	−0.395423	−	0.918499i	$-0.629402\pi$
$251$	9.46986	−	16.4023i	0.597732	−	1.03530i	0.993155	−	0.116804i	$-0.0372648\pi$
$252$	7.72475	−	1.82433i	0.486614	−	0.114922i
$253$	2.63960	+	9.85110i	0.165950	+	0.619334i
$254$	3.95693	−	3.95693i	0.248280	−	0.248280i
$255$	−1.51661	−	15.9585i	−0.0949736	−	0.999362i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.29961	+	12.6433i	−0.455337	+	0.788667i	−0.998708	−	0.0508258i	$-0.983815\pi$
$257$	−7.29961	+	12.6433i	−0.455337	+	0.788667i	0.543370	+	0.839493i	$0.317148\pi$
$258$	−1.93272	+	4.22703i	−0.120326	+	0.263163i
$259$	22.9494	−	7.20527i	1.42601	−	0.447713i
$260$	−4.34536	−	6.67606i	−0.269488	−	0.414032i
$261$	2.77181	−	0.531636i	0.171571	−	0.0329074i
$262$	0.924557	−	0.924557i	0.0571193	−	0.0571193i
$263$		−	17.5577i		−	1.08265i	−0.840813	−	0.541326i	$-0.817922\pi$
$263$		−	17.5577i		−	1.08265i	0.840813	−	0.541326i	$-0.182078\pi$
$264$	−3.60624	−	0.608088i	−0.221949	−	0.0374252i
$265$	−8.70044	+	8.70044i	−0.534464	+	0.534464i
$266$	−0.584328	+	1.11916i	−0.0358275	+	0.0686202i
$267$	−27.2370	+	2.58844i	−1.66688	+	0.158410i
$268$	−2.19711	+	8.19973i	−0.134210	+	0.500879i
$269$	10.1402	−	5.85445i	0.618260	−	0.356952i	−0.157932	−	0.987450i	$-0.550483\pi$
$269$	10.1402	−	5.85445i	0.618260	−	0.356952i	0.776191	+	0.630498i	$0.217149\pi$
$270$	10.0681	+	5.51526i	0.612725	+	0.335648i
$271$	−13.0026	+	3.48405i	−0.789854	+	0.211641i	−0.631125	−	0.775681i	$-0.717406\pi$
$271$	−13.0026	+	3.48405i	−0.789854	+	0.211641i	−0.158729	+	0.987322i	$0.550740\pi$
$272$	4.18923			0.254009
$273$	3.12967	+	16.2236i	0.189416	+	0.981897i
$274$	16.9467			1.02379
$275$	−0.242865	+	0.0650755i	−0.0146453	+	0.00392420i
$276$	8.24958	+	1.39105i	0.496567	+	0.0837316i
$277$	2.59276	−	1.49693i	0.155784	−	0.0899418i	−0.420082	−	0.907486i	$-0.637999\pi$
$277$	2.59276	−	1.49693i	0.155784	−	0.0899418i	0.575865	+	0.817545i	$0.304665\pi$
$278$	0.00415866	−	0.0155203i	0.000249420	−	0.000930849i
$279$	0.962082	−	13.2836i	0.0575983	−	0.795267i
$280$	−3.13463	−	4.93361i	−0.187330	−	0.294840i
$281$	−7.79421	+	7.79421i	−0.464964	+	0.464964i	−0.900278	−	0.435315i	$-0.856637\pi$
$281$	−7.79421	+	7.79421i	−0.464964	+	0.464964i	0.435315	+	0.900278i	$0.356637\pi$
$282$	−1.21052	+	7.17892i	−0.0720853	+	0.427499i
$283$		−	5.58090i		−	0.331750i	−0.986147	−	0.165875i	$-0.946955\pi$
$283$		−	5.58090i		−	0.331750i	0.986147	−	0.165875i	$-0.0530449\pi$
$284$	4.38283	−	4.38283i	0.260073	−	0.260073i
$285$	−1.71116	+	0.637352i	−0.101360	+	0.0377535i
$286$	1.57508	−	7.44824i	0.0931364	−	0.440424i
$287$	5.40324	−	24.2331i	0.318943	−	1.43043i
$288$	−1.68376	+	2.48293i	−0.0992164	+	0.146308i
$289$	−0.274811	+	0.475986i	−0.0161653	+	0.0279992i
$290$	−1.03922	−	1.79999i	−0.0610253	−	0.105699i
$291$	30.8038	−	2.92741i	1.80575	−	0.171608i
$292$	4.92022	−	4.92022i	0.287934	−	0.287934i
$293$	4.48295	+	16.7306i	0.261897	+	0.977412i	0.964122	+	0.265458i	$0.0855231\pi$
$293$	4.48295	+	16.7306i	0.261897	+	0.977412i	−0.702226	+	0.711955i	$0.747810\pi$
$294$	2.16568	+	11.9294i	0.126305	+	0.695735i
$295$	−15.7739	+	27.3212i	−0.918391	+	1.59070i
$296$	−4.54576	+	7.87349i	−0.264217	+	0.457637i
$297$	3.07679	+	10.5312i	0.178534	+	0.611081i
$298$	9.00751	+	5.20049i	0.521791	+	0.301256i
$299$	−3.60313	+	17.0385i	−0.208374	+	0.985362i
$300$	−0.0342945	+	0.203382i	−0.00197999	+	0.0117423i
$301$	−6.29363	−	3.28598i	−0.362759	−	0.189401i
$302$	13.2352	−	7.64136i	0.761601	−	0.439711i
$303$	2.34712	−	13.9195i	0.134838	−	0.799652i
$304$	−0.123506	−	0.460929i	−0.00708353	−	0.0264361i
$305$	2.31179	−	8.62771i	0.132373	−	0.494021i
$306$	−5.48120	−	11.3094i	−0.313339	−	0.646517i
$307$	4.71257	+	4.71257i	0.268961	+	0.268961i	0.828681	−	0.559721i	$-0.189092\pi$
$307$	4.71257	+	4.71257i	0.268961	+	0.268961i	−0.559721	+	0.828681i	$0.689092\pi$
$308$	1.21574	−	5.45249i	0.0692733	−	0.310685i
$309$	7.62718	+	20.4774i	0.433895	+	1.16492i
$310$	−9.47381	+	2.53850i	−0.538076	+	0.144177i
$311$	−8.67825	+	15.0312i	−0.492098	+	0.852339i	−0.999959	−	0.00910006i	$-0.997103\pi$
$311$	−8.67825	+	15.0312i	−0.492098	+	0.852339i	0.507860	+	0.861440i	$0.330437\pi$
$312$	−5.01933	−	3.71569i	−0.284163	−	0.210359i
$313$	−0.700926	−	1.21404i	−0.0396187	−	0.0686215i	0.845536	−	0.533918i	$-0.179281\pi$
$313$	−0.700926	−	1.21404i	−0.0396187	−	0.0686215i	−0.885155	+	0.465297i	$0.845948\pi$
$314$	−5.41315	+	20.2022i	−0.305482	+	1.14007i
$315$	−9.21762	+	14.9176i	−0.519354	+	0.840509i
$316$	−3.07612	−	1.77600i	−0.173045	−	0.0999078i
$317$	6.62944	−	24.7414i	0.372346	−	1.38962i	−0.484837	−	0.874604i	$-0.661121\pi$
$317$	6.62944	−	24.7414i	0.372346	−	1.38962i	0.857184	−	0.515011i	$-0.172212\pi$
$318$	−4.01121	+	8.77288i	−0.224938	+	0.491959i
$319$	0.514121	−	1.91873i	0.0287853	−	0.107428i
$320$	2.13400	+	0.571804i	0.119294	+	0.0319648i
$321$	−0.604666	+	0.731663i	−0.0337492	+	0.0408374i
$322$	−2.78111	+	12.4730i	−0.154985	+	0.695096i
$323$	1.93094	+	0.517393i	0.107440	+	0.0287885i
$324$	8.90607	+	1.29687i	0.494782	+	0.0720484i
$325$	−0.420060	−	0.0888301i	−0.0233007	−	0.00492741i
$326$	−21.9885	−	12.6951i	−1.21783	−	0.703114i
$327$	15.6602	−	1.48825i	0.866009	−	0.0823005i
$328$	4.69208	+	8.12692i	0.259077	+	0.448734i
$329$	−10.8542	−	2.42017i	−0.598414	−	0.133428i
$330$	6.58361	−	4.68370i	0.362416	−	0.257829i
$331$	−3.18618	+	3.18618i	−0.175128	+	0.175128i	−0.789228	−	0.614100i	$-0.789519\pi$
$331$	−3.18618	+	3.18618i	−0.175128	+	0.175128i	0.614100	+	0.789228i	$0.289519\pi$
$332$	−10.0667	−	2.69736i	−0.552480	−	0.148037i
$333$	27.2033	+	1.97024i	1.49073	+	0.107968i
$334$	−6.76334			−0.370074
$335$	−9.37728	−	16.2419i	−0.512336	−	0.887391i
$336$	−3.65302	−	2.76685i	−0.199288	−	0.150944i
$337$		−	34.7055i		−	1.89053i	−0.326303	−	0.945265i	$-0.605803\pi$
$337$		−	34.7055i		−	1.89053i	0.326303	−	0.945265i	$-0.394197\pi$
$338$	8.16014	−	10.1199i	0.443853	−	0.550449i
$339$	7.34576	−	8.88857i	0.398967	−	0.482761i
$340$	−6.54440	+	6.54440i	−0.354920	+	0.354920i
$341$	−8.11787	−	4.68686i	−0.439608	−	0.253808i
$342$	−1.08275	+	0.936502i	−0.0585484	+	0.0506402i
$343$	−18.3705	+	2.35043i	−0.991914	+	0.126911i
$344$	2.59204	−	0.694536i	0.139754	−	0.0374469i
$345$	−15.0606	+	10.7144i	−0.810834	+	0.576843i
$346$	−6.48518	+	1.73770i	−0.348645	+	0.0934192i
$347$	−13.7162	+	7.91904i	−0.736323	+	0.425116i	−0.820731	−	0.571315i	$-0.806433\pi$
$347$	−13.7162	+	7.91904i	−0.736323	+	0.425116i	0.0844080	+	0.996431i	$0.473100\pi$
$348$	−1.25606	−	1.03804i	−0.0673316	−	0.0556447i
$349$	−7.94079	+	29.6354i	−0.425061	+	1.58635i	0.338729	+	0.940884i	$0.390003\pi$
$349$	−7.94079	+	29.6354i	−0.425061	+	1.58635i	−0.763790	+	0.645465i	$0.776664\pi$
$350$	−0.307505	−	0.0685644i	−0.0164369	−	0.00366492i
$351$	−3.46373	+	18.4120i	−0.184880	+	0.982761i
$352$	1.05573	+	1.82857i	0.0562705	+	0.0974633i
$353$	−7.76783	−	7.76783i	−0.413440	−	0.413440i	0.469495	−	0.882935i	$-0.344436\pi$
$353$	−7.76783	−	7.76783i	−0.413440	−	0.413440i	−0.882935	+	0.469495i	$0.844436\pi$
$354$	−4.11247	+	24.3888i	−0.218575	+	1.29625i
$355$			13.6937i			0.726786i
$356$	11.1696	+	11.1696i	0.591985	+	0.591985i
$357$	17.6897	−	7.45757i	0.936240	−	0.394697i
$358$	−4.24635	+	1.13781i	−0.224427	+	0.0601350i
$359$	3.14697	+	0.843227i	0.166091	+	0.0445038i	0.340906	−	0.940097i	$-0.389266\pi$
$359$	3.14697	+	0.843227i	0.166091	+	0.0445038i	−0.174815	+	0.984601i	$0.555933\pi$
$360$	−1.24847	−	6.50919i	−0.0658000	−	0.343065i
$361$			18.7723i			0.988015i
$362$	−6.95639	−	25.9616i	−0.365620	−	1.36451i
$363$	−11.1729	−	1.88399i	−0.586427	−	0.0988840i
$364$	6.06909	−	7.35977i	0.318107	−	0.385757i
$365$			15.3727i			0.804644i
$366$	−0.662505	−	6.97123i	−0.0346297	−	0.364392i
$367$	−20.6079			−1.07573			−0.537863	−	0.843032i	$-0.680768\pi$
$367$	−20.6079			−1.07573			−0.537863	+	0.843032i	$0.680768\pi$
$368$	−2.41507	−	4.18302i	−0.125894	−	0.218055i
$369$	15.8007	−	23.3002i	0.822549	−	1.21296i
$370$	−5.19857	−	19.4013i	−0.270261	−	1.00863i
$371$	−13.0619	−	6.81981i	−0.678143	−	0.354067i
$372$	−6.26558	+	4.45745i	−0.324855	+	0.231108i
$373$	1.41011			0.0730125			0.0365063	−	0.999333i	$-0.488377\pi$
$373$	1.41011			0.0730125			0.0365063	+	0.999333i	$0.488377\pi$
$374$	−8.84536			−0.457383
$375$	−11.3553	−	15.9615i	−0.586386	−	0.824249i
$376$	3.64013	−	2.10163i	0.187726	−	0.108383i
$377$	2.26709	−	2.52313i	0.116761	−	0.129948i
$378$	−2.68990	+	13.4820i	−0.138353	+	0.693439i
$379$	−15.7641	−	4.22399i	−0.809749	−	0.216972i	−0.169889	−	0.985463i	$-0.554341\pi$
$379$	−15.7641	−	4.22399i	−0.809749	−	0.216972i	−0.639860	+	0.768492i	$0.721008\pi$
$380$	0.913002	+	0.527122i	0.0468360	+	0.0270408i
$381$	3.38308	+	9.08286i	0.173320	+	0.465329i
$382$	−1.24614	−	4.65067i	−0.0637582	−	0.237949i
$383$	−17.5749	−	17.5749i	−0.898038	−	0.898038i	0.0972248	−	0.995262i	$-0.469003\pi$
$383$	−17.5749	−	17.5749i	−0.898038	−	0.898038i	−0.995262	+	0.0972248i	$0.969003\pi$
$384$	1.72428	−	0.163866i	0.0879919	−	0.00836224i
$385$	6.61864	+	10.4171i	0.337317	+	0.530904i
$386$	−0.728336	−	0.420505i	−0.0370713	−	0.0214032i
$387$	−5.26644	−	6.08886i	−0.267708	−	0.309514i
$388$	−12.6322	−	12.6322i	−0.641305	−	0.641305i
$389$	5.33488	−	9.24029i	0.270489	−	0.468501i	−0.698498	−	0.715612i	$-0.746148\pi$
$389$	5.33488	−	9.24029i	0.270489	−	0.468501i	0.968987	+	0.247111i	$0.0794812\pi$
$390$	13.6458	−	2.03654i	0.690983	−	0.103124i
$391$	20.2345			1.02330
$392$	4.51253	−	5.35136i	0.227917	−	0.270285i
$393$	0.790474	+	2.12226i	0.0398741	+	0.107054i
$394$			14.2030i			0.715536i
$395$	7.57997	−	2.03105i	0.381390	−	0.102193i
$396$	3.55518	−	5.24260i	0.178655	−	0.263451i
$397$	14.0420	+	14.0420i	0.704746	+	0.704746i	0.965425	−	0.260679i	$-0.0839465\pi$
$397$	14.0420	+	14.0420i	0.704746	+	0.704746i	−0.260679	+	0.965425i	$0.583947\pi$
$398$	5.05322	−	5.05322i	0.253295	−	0.253295i
$399$	−1.34206	−	1.72649i	−0.0671870	−	0.0864326i
$400$	0.103127	−	0.0595401i	0.00515633	−	0.00297701i
$401$	−1.90657	−	7.11542i	−0.0952096	−	0.355327i	0.901842	−	0.432067i	$-0.142216\pi$
$401$	−1.90657	−	7.11542i	−0.0952096	−	0.355327i	−0.997051	+	0.0767398i	$0.975549\pi$
$402$	−11.3338	−	9.36659i	−0.565280	−	0.467163i
$403$	−8.73182	−	13.4153i	−0.434963	−	0.668262i
$404$	−7.05798	+	4.07493i	−0.351148	+	0.202735i
$405$	−15.9390	+	11.8871i	−0.792016	+	0.590673i
$406$	1.68382	−	1.83309i	0.0835665	−	0.0909747i
$407$	9.59816	−	16.6245i	0.475763	−	0.824046i
$408$	−3.01720	+	6.59889i	−0.149374	+	0.326694i
$409$	38.9605	+	10.4394i	1.92647	+	0.516196i	0.982538	+	0.186060i	$0.0595717\pi$
$409$	38.9605	+	10.4394i	1.92647	+	0.516196i	0.943933	+	0.330137i	$0.107095\pi$
$410$	−20.0258	−	5.36590i	−0.989004	−	0.265003i
$411$	−12.2055	+	26.6945i	−0.602052	+	1.31674i
$412$	6.30805	−	10.9259i	0.310775	−	0.538279i
$413$	−36.8749	−	8.22199i	−1.81450	−	0.404578i
$414$	−8.13279	+	11.9929i	−0.399705	+	0.589419i
$415$	19.9399	−	11.5123i	0.978812	−	0.565117i
$416$	0.192444	+	3.60041i	0.00943534	+	0.176525i
$417$	0.0214525	+	0.0177290i	0.00105054	+	0.000868191i
$418$	0.260776	+	0.973230i	0.0127550	+	0.0476022i
$419$	13.8736	−	8.00994i	0.677771	−	0.391311i	−0.121244	−	0.992623i	$-0.538688\pi$
$419$	13.8736	−	8.00994i	0.677771	−	0.391311i	0.799015	+	0.601312i	$0.205355\pi$
$420$	10.0291	−	1.38436i	0.489370	−	0.0675500i
$421$	14.1022	−	14.1022i	0.687301	−	0.687301i	−0.274334	−	0.961635i	$-0.588457\pi$
$421$	14.1022	−	14.1022i	0.687301	−	0.687301i	0.961635	+	0.274334i	$0.0884573\pi$
$422$	9.77338	+	9.77338i	0.475761	+	0.475761i
$423$	−10.4364	−	7.07728i	−0.507436	−	0.344109i
$424$	5.37959	−	1.44146i	0.261256	−	0.0700033i
$425$			0.498854i			0.0241980i
$426$	3.74721	+	10.0605i	0.181553	+	0.487433i
$427$	10.6871	−	0.453598i	0.517184	−	0.0219511i
$428$	0.548012			0.0264892
$429$	10.5981	+	7.84551i	0.511680	+	0.378785i
$430$	−2.96428	+	5.13428i	−0.142950	+	0.247597i
$431$	−22.4057	−	22.4057i	−1.07924	−	1.07924i	−0.996577	−	0.0826660i	$-0.973657\pi$
$431$	−22.4057	−	22.4057i	−1.07924	−	1.07924i	−0.0826660	−	0.996577i	$-0.526343\pi$
$432$	−2.69844	−	4.44055i	−0.129829	−	0.213646i
$433$	23.8503	+	13.7700i	1.14617	+	0.661744i	0.947952	−	0.318414i	$-0.103150\pi$
$433$	23.8503	+	13.7700i	1.14617	+	0.661744i	0.198222	+	0.980157i	$0.436483\pi$
$434$	−6.29892	−	9.91389i	−0.302358	−	0.475882i
$435$	3.58383	−	0.340586i	0.171831	−	0.0163298i
$436$	−6.42204	−	6.42204i	−0.307560	−	0.307560i
$437$	−0.596548	−	2.22635i	−0.0285368	−	0.106501i
$438$	4.20667	+	11.2940i	0.201002	+	0.539650i
$439$	−1.60920	−	0.929070i	−0.0768028	−	0.0443421i	0.461107	−	0.887345i	$-0.347452\pi$
$439$	−1.60920	−	0.929070i	−0.0768028	−	0.0443421i	−0.537910	+	0.843003i	$0.680786\pi$
$440$	−4.50585	−	1.20734i	−0.214808	−	0.0575576i
$441$	−20.3510	−	5.18049i	−0.969094	−	0.246690i
$442$	−13.4653	−	6.84329i	−0.640479	−	0.325502i
$443$	27.1823	−	15.6937i	1.29147	−	0.745631i	0.312555	−	0.949900i	$-0.398815\pi$
$443$	27.1823	−	15.6937i	1.29147	−	0.745631i	0.978915	+	0.204269i	$0.0654817\pi$
$444$	−9.12837	−	12.8312i	−0.433213	−	0.608943i
$445$	−34.8981			−1.65433
$446$	−4.18039			−0.197947
$447$	−14.6793	+	10.4431i	−0.694307	+	0.493943i
$448$	0.112194	+	2.64337i	0.00530068	+	0.124888i
$449$	−1.27900	−	4.77331i	−0.0603600	−	0.225266i	0.929156	−	0.369687i	$-0.120535\pi$
$449$	−1.27900	−	4.77331i	−0.0603600	−	0.225266i	−0.989516	+	0.144420i	$0.953868\pi$
$450$	−0.295668	−	0.200502i	−0.0139379	−	0.00945177i
$451$	−9.90711	−	17.1596i	−0.466508	−	0.808015i
$452$	−6.65750			−0.313142
$453$	2.50431	+	26.3517i	0.117663	+	1.23811i
$454$			11.3026i			0.530458i
$455$	2.01629	+	20.9785i	0.0945251	+	0.983488i
$456$	0.815010	+	0.137428i	0.0381663	+	0.00643565i
$457$	0.529511	+	1.97616i	0.0247695	+	0.0924410i	0.977204	−	0.212302i	$-0.0680961\pi$
$457$	0.529511	+	1.97616i	0.0247695	+	0.0924410i	−0.952435	+	0.304743i	$0.901429\pi$
$458$			1.97825i			0.0924374i
$459$	21.7624	−	0.488636i	1.01578	−	0.0228076i
$460$	10.3075	+	2.76189i	0.480590	+	0.128774i
$461$	−36.8262	+	9.86755i	−1.71517	+	0.459578i	−0.976682	−	0.214692i	$-0.931125\pi$
$461$	−36.8262	+	9.86755i	−1.71517	+	0.459578i	−0.738485	+	0.674270i	$0.764459\pi$
$462$	7.71318	+	5.84208i	0.358850	+	0.271798i
$463$	13.6453	+	13.6453i	0.634149	+	0.634149i	0.949106	−	0.314957i	$-0.101990\pi$
$463$	13.6453	+	13.6453i	0.634149	+	0.634149i	−0.314957	+	0.949106i	$0.601990\pi$
$464$			0.940779i			0.0436746i
$465$	2.82466	−	16.7515i	0.130990	−	0.776832i
$466$	11.8337	+	11.8337i	0.548187	+	0.548187i
$467$	−4.93246	−	8.54326i	−0.228247	−	0.395335i	0.729042	−	0.684469i	$-0.239966\pi$
$467$	−4.93246	−	8.54326i	−0.228247	−	0.395335i	−0.957289	+	0.289134i	$0.906633\pi$
$468$	9.46804	−	5.23032i	0.437660	−	0.241772i
$469$	15.1937	−	16.5406i	0.701580	−	0.763775i
$470$	−2.40344	+	8.96977i	−0.110863	+	0.413745i
$471$	−27.9238	−	23.0770i	−1.28666	−	1.06333i
$472$	12.3665	−	7.13983i	0.569216	−	0.328637i
$473$	−5.47298	+	1.46648i	−0.251648	+	0.0674289i
$474$	5.01308	−	3.56639i	0.230258	−	0.163810i
$475$	0.0548875	−	0.0147071i	0.00251841	−	0.000674806i
$476$	−9.82509	−	5.12980i	−0.450332	−	0.235124i
$477$	−10.9301	−	12.6370i	−0.500454	−	0.578607i
$478$	13.3086	+	7.68374i	0.608723	+	0.351446i
$479$	11.0918	−	11.0918i	0.506799	−	0.506799i	−0.406744	−	0.913542i	$-0.633336\pi$
$479$	11.0918	−	11.0918i	0.506799	−	0.506799i	0.913542	+	0.406744i	$0.133336\pi$
$480$	−2.43768	+	2.94966i	−0.111264	+	0.134633i
$481$	27.4730	−	17.8818i	1.25266	−	0.815340i
$482$			27.2266i			1.24014i
$483$	−17.6446	−	13.3643i	−0.802856	−	0.608096i
$484$	3.27088	+	5.66533i	0.148676	+	0.257515i
$485$	39.4681			1.79215
$486$	−8.45725	+	13.0948i	−0.383629	+	0.593994i
$487$	−35.2651	−	9.44927i	−1.59802	−	0.428187i	−0.653573	−	0.756863i	$-0.726731\pi$
$487$	−35.2651	−	9.44927i	−1.59802	−	0.428187i	−0.944443	+	0.328676i	$0.893398\pi$
$488$	−2.85881	+	2.85881i	−0.129412	+	0.129412i
$489$	35.8340	−	25.4930i	1.62047	−	1.15283i
$490$	1.31042	+	15.4093i	0.0591986	+	0.696123i
$491$	16.2655	+	28.1727i	0.734053	+	1.27142i	0.955138	+	0.296163i	$0.0957071\pi$
$491$	16.2655	+	28.1727i	0.734053	+	1.27142i	−0.221084	+	0.975255i	$0.570960\pi$
$492$	−16.1809	+	1.53774i	−0.729493	+	0.0693267i
$493$	−3.41313	−	1.97057i	−0.153719	−	0.0887500i
$494$	−0.355968	+	1.68330i	−0.0160157	+	0.0757353i
$495$	2.63608	+	13.7439i	0.118483	+	0.617741i
$496$	4.28819	+	1.14902i	0.192545	+	0.0515924i
$497$	−15.6460	+	4.91228i	−0.701821	+	0.220346i
$498$	11.4992	−	13.9143i	0.515291	−	0.623517i
$499$	33.1116	+	8.87224i	1.48228	+	0.397176i	0.907123	−	0.420866i	$-0.138274\pi$
$499$	33.1116	+	8.87224i	1.48228	+	0.397176i	0.575158	+	0.818042i	$0.304941\pi$
$500$	−2.92711	+	10.9241i	−0.130904	+	0.488542i
$501$	4.87116	−	10.6537i	0.217627	−	0.475970i
$502$	4.90196	−	18.2944i	0.218785	−	0.816518i
$503$	9.85823	+	5.69165i	0.439557	+	0.253778i	0.703410	−	0.710785i	$-0.251660\pi$
$503$	9.85823	+	5.69165i	0.439557	+	0.253778i	−0.263853	+	0.964563i	$0.584993\pi$
$504$	6.98937	−	3.76148i	0.311331	−	0.167550i
$505$	4.66012	−	17.3918i	0.207372	−	0.773925i
$506$	5.09931	+	8.83226i	0.226692	+	0.392642i
$507$	10.0637	+	20.1425i	0.446946	+	0.894561i
$508$	2.79797	−	4.84622i	0.124140	−	0.215016i
$509$	26.3143	−	7.05090i	1.16636	−	0.312525i	0.376857	−	0.926271i	$-0.377005\pi$
$509$	26.3143	−	7.05090i	1.16636	−	0.312525i	0.789504	+	0.613746i	$0.210338\pi$
$510$	−5.59530	−	15.0222i	−0.247764	−	0.665196i
$511$	−17.5644	+	5.51459i	−0.777005	+	0.243951i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.695355	−	2.38005i	−0.0307007	−	0.105082i
$514$	−3.77856	+	14.1018i	−0.166665	+	0.622002i
$515$	7.21394	+	26.9228i	0.317884	+	1.18636i
$516$	−0.772829	+	4.58322i	−0.0340219	+	0.201765i
$517$	−7.68598	+	4.43750i	−0.338029	+	0.195161i
$518$	20.3025	−	12.8995i	0.892042	−	0.566771i
$519$	1.93358	−	11.4670i	0.0848749	−	0.503346i
$520$	−5.92519	−	5.32392i	−0.259837	−	0.233469i
$521$	23.4026	+	13.5115i	1.02529	+	0.591949i	0.915631	−	0.402021i	$-0.131692\pi$
$521$	23.4026	+	13.5115i	1.02529	+	0.591949i	0.109655	+	0.993970i	$0.465025\pi$
$522$	2.53977	−	1.23092i	0.111163	−	0.0538759i
$523$	12.7790	−	22.1340i	0.558789	−	0.967850i	−0.438809	−	0.898580i	$-0.644600\pi$
$523$	12.7790	−	22.1340i	0.558789	−	0.967850i	0.997598	−	0.0692700i	$-0.0220670\pi$
$524$	0.653760	−	1.13235i	0.0285597	−	0.0494668i
$525$	0.329477	−	0.435002i	0.0143796	−	0.0189850i
$526$	−4.54426	−	16.9594i	−0.198139	−	0.739465i
$527$	−13.1507	+	13.1507i	−0.572853	+	0.572853i
$528$	−3.64074	+	0.345995i	−0.158443	+	0.0150575i
$529$	−0.165110	−	0.285979i	−0.00717869	−	0.0124338i
$530$	−6.15214	+	10.6558i	−0.267232	+	0.462859i
$531$	−35.4554	−	24.0435i	−1.53863	−	1.04340i
$532$	−0.274757	+	1.23226i	−0.0119122	+	0.0534254i
$533$	−1.80592	−	33.7868i	−0.0782232	−	1.46347i
$534$	−25.6390	+	9.54969i	−1.10951	+	0.413256i
$535$	−0.856103	+	0.856103i	−0.0370126	+	0.0370126i
$536$			8.48899i			0.366669i
$537$	1.26607	−	7.50836i	0.0546349	−	0.324010i
$538$	8.27945	−	8.27945i	0.356952	−	0.356952i
$539$	−9.52801	+	11.2992i	−0.410400	+	0.486689i
$540$	11.1525	+	2.72152i	0.479927	+	0.117116i
$541$	−3.03870	+	11.3406i	−0.130644	+	0.487569i	−0.999978	−	0.00665574i	$-0.997881\pi$
$541$	−3.03870	+	11.3406i	−0.130644	+	0.487569i	0.869334	+	0.494225i	$0.164548\pi$
$542$	−11.6578	+	6.73066i	−0.500747	+	0.289107i
$543$	45.9050	+	7.74056i	1.96997	+	0.332179i
$544$	4.04648	−	1.08425i	0.173492	−	0.0464869i
$545$	20.0650			0.859490
$546$	7.22200	+	14.8608i	0.309073	+	0.635983i
$547$	40.5275			1.73283			0.866415	−	0.499324i	$-0.166418\pi$
$547$	40.5275			1.73283			0.866415	+	0.499324i	$0.166418\pi$
$548$	16.3692	−	4.38612i	0.699258	−	0.187366i
$549$	11.4583	+	3.97730i	0.489027	+	0.169747i
$550$	−0.217747	+	0.125716i	−0.00928476	+	0.00536056i
$551$	−0.116191	+	0.433632i	−0.00494992	+	0.0184734i
$552$	8.32852	−	0.791494i	0.354485	−	0.0336882i
$553$	5.03975	+	7.93208i	0.214312	+	0.337306i
$554$	2.11698	−	2.11698i	0.0899418	−	0.0899418i
$555$	34.3052	+	5.78458i	1.45617	+	0.245542i
$556$		−	0.0160678i		−	0.000681428i
$557$	24.4821	−	24.4821i	1.03734	−	1.03734i	0.0380657	−	0.999275i	$-0.487880\pi$
$557$	24.4821	−	24.4821i	1.03734	−	1.03734i	0.999275	−	0.0380657i	$-0.0121196\pi$
$558$	−2.50874	−	13.0800i	−0.106204	−	0.553719i
$559$	−9.46608	−	2.00179i	−0.400373	−	0.0846668i
$560$	−4.30474	−	3.95420i	−0.181908	−	0.167095i
$561$	6.37069	−	13.9333i	0.268971	−	0.588263i
$562$	−5.51134	+	9.54592i	−0.232482	+	0.402670i
$563$	15.6649	+	27.1323i	0.660195	+	1.14349i	0.980564	+	0.196199i	$0.0628597\pi$
$563$	15.6649	+	27.1323i	0.660195	+	1.14349i	−0.320369	+	0.947293i	$0.603807\pi$
$564$	0.688771	+	7.24761i	0.0290025	+	0.305179i
$565$	10.4003	−	10.4003i	0.437545	−	0.437545i
$566$	−1.44444	−	5.39074i	−0.0607145	−	0.226590i
$567$	−19.2996	−	13.9473i	−0.810506	−	0.585730i
$568$	3.09913	−	5.36785i	0.130037	−	0.225230i
$569$	18.1789	−	31.4868i	0.762098	−	1.31999i	−0.179669	−	0.983727i	$-0.557503\pi$
$569$	18.1789	−	31.4868i	0.762098	−	1.31999i	0.941767	−	0.336266i	$-0.109164\pi$
$570$	−1.48789	+	1.05852i	−0.0623211	+	0.0443364i
$571$	19.2095	+	11.0906i	0.803891	+	0.464126i	0.844830	−	0.535035i	$-0.179702\pi$
$571$	19.2095	+	11.0906i	0.803891	+	0.464126i	−0.0409392	+	0.999162i	$0.513035\pi$
$572$	−0.406336	−	7.60211i	−0.0169898	−	0.317860i
$573$	8.22326	+	1.38662i	0.343532	+	0.0579267i
$574$	−1.05285	−	24.8058i	−0.0439450	−	1.03537i
$575$	0.498115	−	0.287587i	0.0207728	−	0.0119932i
$576$	−0.983756	+	2.83412i	−0.0409898	+	0.118088i
$577$	−8.72943	−	32.5787i	−0.363411	−	1.35627i	−0.869562	−	0.493823i	$-0.835599\pi$
$577$	−8.72943	−	32.5787i	−0.363411	−	1.35627i	0.506151	−	0.862445i	$-0.331068\pi$
$578$	−0.142252	+	0.530893i	−0.00591692	+	0.0220823i
$579$	1.18695	−	0.844419i	0.0493280	−	0.0350929i
$580$	−1.46968	−	1.46968i	−0.0610253	−	0.0610253i
$581$	20.3066	+	18.6530i	0.842461	+	0.773858i
$582$	28.9965	−	10.8003i	1.20194	−	0.447685i
$583$	−11.3588	+	3.04357i	−0.470432	+	0.126052i
$584$	3.47912	−	6.02601i	0.143967	−	0.249358i
$585$	−6.62015	+	22.9617i	−0.273709	+	0.949351i
$586$	8.66040	+	15.0003i	0.357758	+	0.619655i
$587$	−11.4129	+	42.5935i	−0.471061	+	1.75802i	0.164909	+	0.986309i	$0.447267\pi$
$587$	−11.4129	+	42.5935i	−0.471061	+	1.75802i	−0.635970	+	0.771714i	$0.719400\pi$
$588$	5.17943	+	10.9624i	0.213596	+	0.452080i
$589$	1.83464	+	1.05923i	0.0755950	+	0.0436448i
$590$	−8.16516	+	30.4728i	−0.336154	+	1.25454i
$591$	−22.3726	−	10.2294i	−0.920286	−	0.420781i
$592$	−2.35306	+	8.78173i	−0.0967101	+	0.360927i
$593$	−24.8024	−	6.64578i	−1.01851	−	0.272909i	−0.289330	−	0.957229i	$-0.593432\pi$
$593$	−24.8024	−	6.64578i	−1.01851	−	0.272909i	−0.729182	+	0.684320i	$0.760099\pi$
$594$	5.69762	+	9.37601i	0.233776	+	0.384702i
$595$	23.3625	−	7.33497i	0.957769	−	0.300704i
$596$	10.0466	+	2.69197i	0.411524	+	0.110267i
$597$	4.32038	+	11.5993i	0.176822	+	0.474729i
$598$	0.929530	+	17.3905i	0.0380113	+	0.711150i
$599$	−0.0523660	−	0.0302335i	−0.00213962	−	0.00123531i	0.498930	−	0.866642i	$-0.333727\pi$
$599$	−0.0523660	−	0.0302335i	−0.00213962	−	0.00123531i	−0.501069	+	0.865407i	$0.667060\pi$
$600$	0.0195132	+	0.205328i	0.000796622	+	0.00838248i
$601$	−5.10069	−	8.83465i	−0.208061	−	0.360373i	0.743042	−	0.669244i	$-0.233382\pi$
$601$	−5.10069	−	8.83465i	−0.208061	−	0.360373i	−0.951104	+	0.308872i	$0.900049\pi$
$602$	−6.92966	−	1.54510i	−0.282432	−	0.0629737i
$603$	22.9173	−	11.1070i	0.933263	−	0.452313i
$604$	10.8065	−	10.8065i	0.439711	−	0.439711i
$605$	−13.9601	−	3.74060i	−0.567560	−	0.152077i
$606$	−1.33548	−	14.0526i	−0.0542502	−	0.570850i
$607$	−0.527175			−0.0213974			−0.0106987	−	0.999943i	$-0.503406\pi$
$607$	−0.527175			−0.0213974			−0.0106987	+	0.999943i	$0.503406\pi$
$608$	−0.238594	−	0.413257i	−0.00967628	−	0.0167598i
$609$	1.67476	+	3.97260i	0.0678645	+	0.160978i
$610$		−	8.93206i		−	0.361649i
$611$	−15.1335	+	0.808892i	−0.612235	+	0.0327243i
$612$	−8.22153	−	9.50542i	−0.332335	−	0.384234i
$613$	−5.56818	+	5.56818i	−0.224897	+	0.224897i	−0.810557	−	0.585660i	$-0.800835\pi$
$613$	−5.56818	+	5.56818i	−0.224897	+	0.224897i	0.585660	+	0.810557i	$0.300835\pi$
$614$	5.77169	+	3.33229i	0.232927	+	0.134480i
$615$	22.8755	−	27.6801i	0.922431	−	1.11617i
$616$	−0.236893	−	5.58136i	−0.00954469	−	0.224879i
$617$	35.0869	−	9.40151i	1.41255	−	0.378491i	0.529713	−	0.848177i	$-0.322300\pi$
$617$	35.0869	−	9.40151i	1.41255	−	0.378491i	0.882833	+	0.469686i	$0.155633\pi$
$618$	12.6672	+	17.8056i	0.509551	+	0.716246i
$619$	21.3680	−	5.72554i	0.858853	−	0.230129i	0.197591	−	0.980284i	$-0.436688\pi$
$619$	21.3680	−	5.72554i	0.858853	−	0.230129i	0.661261	+	0.750156i	$0.270021\pi$
$620$	−8.49398	+	4.90400i	−0.341127	+	0.196950i
$621$	−13.0338	−	21.4484i	−0.523029	−	0.860696i
$622$	−4.49219	+	16.7651i	−0.180121	+	0.672219i
$623$	−12.5188	−	39.8736i	−0.501557	−	1.59750i
$624$	−5.80999	−	2.28998i	−0.232586	−	0.0916727i
$625$	−12.1952	−	21.1227i	−0.487808	−	0.844909i
$626$	−0.991259	−	0.991259i	−0.0396187	−	0.0396187i
$627$	−1.72086	−	0.290173i	−0.0687244	−	0.0115884i
$628$			20.9148i			0.834592i
$629$	−26.9312	−	26.9312i	−1.07382	−	1.07382i
$630$	−5.04260	+	16.7949i	−0.200902	+	0.669127i
$631$	−2.70265	+	0.724172i	−0.107591	+	0.0288288i	−0.312213	−	0.950012i	$-0.601070\pi$
$631$	−2.70265	+	0.724172i	−0.107591	+	0.0288288i	0.204622	+	0.978841i	$0.434403\pi$
$632$	−3.43097	−	0.919325i	−0.136477	−	0.0365688i
$633$	−22.4342	+	8.35601i	−0.891678	+	0.332121i
$634$		−	25.6142i		−	1.01727i
$635$	3.19978	+	11.9417i	0.126979	+	0.473893i
$636$	−1.60395	+	9.51213i	−0.0636006	+	0.377180i
$637$	−23.2462	+	9.82930i	−0.921047	+	0.389451i
$638$		−	1.98641i		−	0.0786428i
$639$	−18.5462	−	1.34323i	−0.733676	−	0.0531375i
$640$	2.20928			0.0873295
$641$	−0.930813	−	1.61221i	−0.0367649	−	0.0636787i	0.847057	−	0.531501i	$-0.178372\pi$
$641$	−0.930813	−	1.61221i	−0.0367649	−	0.0636787i	−0.883822	+	0.467823i	$0.845039\pi$
$642$	−0.394694	+	0.863231i	−0.0155773	+	0.0340690i
$643$	4.16762	+	15.5538i	0.164355	+	0.613381i	0.998122	+	0.0612638i	$0.0195131\pi$
$643$	4.16762	+	15.5538i	0.164355	+	0.613381i	−0.833767	+	0.552117i	$0.813820\pi$
$644$	0.541913	+	12.7678i	0.0213544	+	0.503124i
$645$	−5.95259	−	8.36721i	−0.234383	−	0.329459i
$646$	1.99905			0.0786516
$647$	1.45851			0.0573401			0.0286701	−	0.999589i	$-0.490873\pi$
$647$	1.45851			0.0573401			0.0286701	+	0.999589i	$0.490873\pi$
$648$	8.93826	−	1.05238i	0.351128	−	0.0413414i
$649$	−26.1114	+	15.0754i	−1.02496	+	0.591762i
$650$	−0.428738	+	0.0229163i	−0.0168165	+	0.000898849i
$651$	20.1531	−	2.78182i	0.789861	−	0.109028i
$652$	−24.5250	−	6.57144i	−0.960471	−	0.257358i
$653$	−39.0756	−	22.5603i	−1.52915	−	0.882852i	−0.999398	−	0.0346969i	$-0.988953\pi$
$653$	−39.0756	−	22.5603i	−1.52915	−	0.882852i	−0.529747	−	0.848155i	$-0.677713\pi$
$654$	14.7414	−	5.49069i	0.576433	−	0.214703i
$655$	0.747645	+	2.79025i	0.0292129	+	0.109024i
$656$	6.63560	+	6.63560i	0.259077	+	0.259077i
$657$	−20.8202	−	1.50793i	−0.812273	−	0.0588300i
$658$	−11.1108	+	0.471582i	−0.433144	+	0.0183842i
$659$	−6.23306	−	3.59866i	−0.242805	−	0.140184i	0.373660	−	0.927566i	$-0.378103\pi$
$659$	−6.23306	−	3.59866i	−0.242805	−	0.140184i	−0.616465	+	0.787382i	$0.711436\pi$
$660$	5.14705	−	6.22807i	0.200348	−	0.242427i
$661$	−8.25522	−	8.25522i	−0.321091	−	0.321091i	0.528095	−	0.849185i	$-0.322907\pi$
$661$	−8.25522	−	8.25522i	−0.321091	−	0.321091i	−0.849185	+	0.528095i	$0.822907\pi$
$662$	−2.25297	+	3.90225i	−0.0875641	+	0.151665i
$663$	20.4777	−	16.2819i	0.795287	−	0.632336i
$664$	−10.4218			−0.404444
$665$	−1.49581	−	2.35426i	−0.0580051	−	0.0912944i
$666$	26.7863	−	5.13763i	1.03795	−	0.199079i
$667$			4.54409i			0.175948i
$668$	−6.53289	+	1.75048i	−0.252765	+	0.0677282i
$669$	3.01084	−	6.58496i	0.116406	−	0.254589i
$670$	−13.2615	−	13.2615i	−0.512336	−	0.512336i
$671$	6.03626	−	6.03626i	0.233027	−	0.233027i
$672$	−4.24466	−	1.72710i	−0.163741	−	0.0666245i
$673$	10.8414	−	6.25926i	0.417903	−	0.241277i	−0.276276	−	0.961078i	$-0.589101\pi$
$673$	10.8414	−	6.25926i	0.417903	−	0.241277i	0.694180	+	0.719802i	$0.255767\pi$
$674$	−8.98245	−	33.5230i	−0.345991	−	1.29126i
$675$	0.528781	−	0.321330i	0.0203528	−	0.0123680i
$676$	5.26287	−	11.8871i	0.202418	−	0.457195i
$677$	26.6494	−	15.3860i	1.02422	−	0.591333i	0.108895	−	0.994053i	$-0.465269\pi$
$677$	26.6494	−	15.3860i	1.02422	−	0.591333i	0.915323	+	0.402721i	$0.131935\pi$
$678$	4.79492	−	10.4869i	0.184148	−	0.402748i
$679$	14.1582	+	45.0952i	0.543343	+	1.73059i
$680$	−4.62759	+	8.01522i	−0.177460	+	0.307370i
$681$	−17.8039	−	8.14047i	−0.682248	−	0.311943i
$682$	−9.05431	−	2.42610i	−0.346708	−	0.0929000i
$683$	33.6861	+	9.02617i	1.28896	+	0.345377i	0.837267	−	0.546795i	$-0.184152\pi$
$683$	33.6861	+	9.02617i	1.28896	+	0.345377i	0.451697	+	0.892171i	$0.350819\pi$
$684$	−0.803471	+	1.18483i	−0.0307215	+	0.0453030i
$685$	−18.7200	+	32.4239i	−0.715253	+	1.23885i
$686$	−17.1362	+	7.02498i	−0.654264	+	0.268215i
$687$	−3.11614	−	1.42479i	−0.118888	−	0.0543591i
$688$	2.32396	−	1.34174i	0.0886002	−	0.0511534i
$689$	−19.6461	−	4.15457i	−0.748458	−	0.158276i
$690$	−11.7743	+	14.2473i	−0.448241	+	0.542384i
$691$	−10.6296	−	39.6701i	−0.404368	−	1.50912i	−0.805219	−	0.592977i	$-0.797952\pi$
$691$	−10.6296	−	39.6701i	−0.404368	−	1.50912i	0.400852	−	0.916143i	$-0.368714\pi$
$692$	−5.81445	+	3.35697i	−0.221032	+	0.127613i
$693$	−14.7577	+	7.94220i	−0.560600	+	0.301699i
$694$	−11.1992	+	11.1992i	−0.425116	+	0.425116i
$695$	0.0251011	+	0.0251011i	0.000952141	+	0.000952141i
$696$	−1.48192	−	0.677577i	−0.0561720	−	0.0256835i
$697$	−37.9728	+	10.1748i	−1.43832	+	0.385398i
$698$			30.6809i			1.16129i
$699$	−27.1635	+	10.1175i	−1.02742	+	0.382681i
$700$	−0.314773	+	0.0133601i	−0.0118973	+	0.000504965i
$701$	33.7188			1.27354			0.636771	−	0.771053i	$-0.280270\pi$
$701$	33.7188			1.27354			0.636771	+	0.771053i	$0.280270\pi$
$702$	1.41967	+	18.6811i	0.0535821	+	0.705074i
$703$	−2.16918	+	3.75714i	−0.0818123	+	0.141703i
$704$	1.49302	+	1.49302i	0.0562705	+	0.0562705i
$705$	−12.3982	−	10.2462i	−0.466943	−	0.385894i
$706$	−9.51361	−	5.49269i	−0.358049	−	0.206720i
$707$	21.5431	−	0.914366i	0.810211	−	0.0343883i
$708$	2.33995	+	24.6221i	0.0879405	+	0.925357i
$709$	5.99300	+	5.99300i	0.225072	+	0.225072i	0.810630	−	0.585558i	$-0.199125\pi$
$709$	5.99300	+	5.99300i	0.225072	+	0.225072i	−0.585558	+	0.810630i	$0.699125\pi$
$710$	3.54419	+	13.2271i	0.133011	+	0.496404i
$711$	2.00724	+	10.4652i	0.0752774	+	0.392477i
$712$	13.6798	+	7.89806i	0.512674	+	0.295992i
$713$	20.7125	+	5.54991i	0.775690	+	0.207846i
$714$	15.1568	−	11.7819i	0.567229	−	0.440927i
$715$	12.5108	+	11.2412i	0.467876	+	0.420397i
$716$	−3.80718	+	2.19808i	−0.142281	+	0.0821459i
$717$	−21.6887	+	15.4298i	−0.809981	+	0.576235i
$718$	3.25798			0.121587
$719$	−0.827456			−0.0308589			−0.0154294	−	0.999881i	$-0.504912\pi$
$719$	−0.827456			−0.0308589			−0.0154294	+	0.999881i	$0.504912\pi$
$720$	−2.89063	−	5.96427i	−0.107727	−	0.222275i
$721$	−28.1734	+	17.9003i	−1.04923	+	0.666644i
$722$	4.85863	+	18.1326i	0.180819	+	0.674827i
$723$	−42.8875	−	19.6094i	−1.59500	−	0.729281i
$724$	−13.4387	−	23.2765i	−0.499446	−	0.865065i
$725$	−0.112028			−0.00416062
$726$	−11.2798	+	1.07197i	−0.418634	+	0.0397845i
$727$			4.04016i			0.149841i	0.997190	+	0.0749206i	$0.0238703\pi$
$727$			4.04016i			0.149841i	−0.997190	+	0.0749206i	$0.976130\pi$
$728$	3.95744	−	8.67978i	0.146673	−	0.321694i
$729$	−14.5359	−	22.7532i	−0.538367	−	0.842711i
$730$	3.97875	+	14.8489i	0.147260	+	0.549582i
$731$			11.2417i			0.415790i
$732$	−2.44422	−	6.56222i	−0.0903409	−	0.242547i
$733$	−36.5502	−	9.79359i	−1.35001	−	0.361735i	−0.489873	−	0.871794i	$-0.662957\pi$
$733$	−36.5502	−	9.79359i	−1.35001	−	0.361735i	−0.860139	+	0.510059i	$0.829623\pi$
$734$	−19.9057	+	5.33373i	−0.734735	+	0.196872i
$735$	−25.2167	−	9.03408i	−0.930131	−	0.333227i
$736$	−3.41542	−	3.41542i	−0.125894	−	0.125894i
$737$		−	17.9241i		−	0.660243i
$738$	9.23172	−	26.5958i	0.339824	−	0.979005i
$739$	27.5299	+	27.5299i	1.01270	+	1.01270i	0.999918	+	0.0127856i	$0.00406990\pi$
$739$	27.5299	+	27.5299i	1.01270	+	1.01270i	0.0127856	+	0.999918i	$0.495930\pi$
$740$	−10.0429	−	17.3947i	−0.369183	−	0.639443i
$741$	−2.39517	−	1.77308i	−0.0879886	−	0.0651359i
$742$	−14.3820	−	3.20675i	−0.527979	−	0.117723i
$743$	−1.98573	+	7.41084i	−0.0728493	+	0.271877i	−0.992737	−	0.120305i	$-0.961613\pi$
$743$	−1.98573	+	7.41084i	−0.0728493	+	0.271877i	0.919888	+	0.392182i	$0.128280\pi$
$744$	−4.89841	+	5.92722i	−0.179585	+	0.217302i
$745$	−19.9001	+	11.4893i	−0.729084	+	0.420937i
$746$	1.36206	−	0.364962i	0.0498685	−	0.0133622i
$747$	13.6359	+	28.1351i	0.498911	+	1.02941i
$748$	−8.54396	+	2.28935i	−0.312398	+	0.0837069i
$749$	−1.28527	−	0.671053i	−0.0469626	−	0.0245198i
$750$	−15.0995	−	12.4787i	−0.551357	−	0.455657i
$751$	32.2926	+	18.6442i	1.17837	+	0.680335i	0.955638	−	0.294544i	$-0.0951676\pi$
$751$	32.2926	+	18.6442i	1.17837	+	0.680335i	0.222737	+	0.974879i	$0.428501\pi$
$752$	2.97216	−	2.97216i	0.108383	−	0.108383i
$753$	25.2868	+	20.8977i	0.921504	+	0.761556i
$754$	1.53681	−	3.02392i	0.0559671	−	0.110125i
$755$			33.7638i			1.22879i
$756$	0.891157	+	13.7188i	0.0324111	+	0.498948i
$757$	−6.78893	−	11.7588i	−0.246748	−	0.427380i	0.715874	−	0.698230i	$-0.246029\pi$
$757$	−6.78893	−	11.7588i	−0.246748	−	0.427380i	−0.962622	+	0.270850i	$0.912695\pi$
$758$	−16.3202			−0.592777
$759$	−17.5853	+	1.67120i	−0.638305	+	0.0606608i
$760$	1.01832	+	0.272858i	0.0369384	+	0.00989761i
$761$	5.56319	−	5.56319i	0.201665	−	0.201665i	−0.599048	−	0.800713i	$-0.704454\pi$
$761$	5.56319	−	5.56319i	0.201665	−	0.201665i	0.800713	+	0.599048i	$0.204454\pi$
$762$	5.61862	+	7.89777i	0.203541	+	0.286106i
$763$	7.19783	+	22.9257i	0.260579	+	0.829966i
$764$	−2.40736	−	4.16967i	−0.0870953	−	0.150853i
$765$	27.6930	+	2.00570i	1.00124	+	0.0725163i
$766$	−21.5248	−	12.4274i	−0.777723	−	0.449019i
$767$	−51.4126	+	2.74803i	−1.85640	+	0.0992256i
$768$	1.62312	−	0.604559i	0.0585692	−	0.0218151i
$769$	17.5074	+	4.69109i	0.631333	+	0.169165i	0.560274	−	0.828307i	$-0.310696\pi$
$769$	17.5074	+	4.69109i	0.631333	+	0.169165i	0.0710583	+	0.997472i	$0.477362\pi$
$770$	9.08926	+	8.34911i	0.327554	+	0.300881i
$771$	−19.4917	−	16.1085i	−0.701978	−	0.580134i
$772$	−0.812354	−	0.217670i	−0.0292372	−	0.00783410i
$773$	−7.25258	+	27.0670i	−0.260857	+	0.973533i	0.703880	+	0.710319i	$0.251449\pi$
$773$	−7.25258	+	27.0670i	−0.260857	+	0.973533i	−0.964737	+	0.263214i	$0.915217\pi$
$774$	−6.66290	−	4.51833i	−0.239493	−	0.162408i
$775$	−0.136825	+	0.510638i	−0.00491490	+	0.0183427i
$776$	−15.4713	−	8.93234i	−0.555386	−	0.320652i
$777$	5.69686	+	41.2712i	0.204374	+	1.48060i
$778$	2.76154	−	10.3062i	0.0990059	−	0.369495i
$779$	2.23901	+	3.87807i	0.0802207	+	0.138946i
$780$	12.6538	−	5.49894i	0.453077	−	0.196894i
$781$	−6.54367	+	11.3340i	−0.234151	+	0.405561i
$782$	19.5451	−	5.23708i	0.698930	−	0.187278i
$783$	0.109734	+	4.88720i	0.00392156	+	0.174654i
$784$	2.97374	−	6.33695i	0.106205	−	0.226320i
$785$	−32.6731	−	32.6731i	−1.16615	−	1.16615i
$786$	1.31282	+	1.84536i	0.0468267	+	0.0658216i
$787$	7.24146	−	27.0255i	0.258130	−	0.963355i	−0.708192	−	0.706020i	$-0.750489\pi$
$787$	7.24146	−	27.0255i	0.258130	−	0.963355i	0.966322	−	0.257335i	$-0.0828444\pi$
$788$	3.67600	+	13.7190i	0.130952	+	0.488720i
$789$	29.9875	+	5.05652i	1.06758	+	0.180017i
$790$	6.79601	−	3.92368i	0.241791	−	0.139598i
$791$	15.6140	+	8.15226i	0.555169	+	0.289861i
$792$	2.07716	−	5.98411i	0.0738085	−	0.212636i
$793$	13.8590	−	4.51900i	0.492148	−	0.160474i
$794$	17.1978	+	9.92917i	0.610328	+	0.352373i
$795$	−12.3541	−	17.3655i	−0.438156	−	0.615891i
$796$	3.57317	−	6.18891i	0.126648	−	0.219360i
$797$	−10.0633	+	17.4302i	−0.356462	+	0.617410i	−0.987367	−	0.158450i	$-0.949350\pi$
$797$	−10.0633	+	17.4302i	−0.356462	+	0.617410i	0.630905	+	0.775860i	$0.282684\pi$
$798$	−1.74318	−	1.32031i	−0.0617078	−	0.0467385i
$799$	4.55740	+	17.0084i	0.161229	+	0.601715i
$800$	0.0842024	−	0.0842024i	0.00297701	−	0.00297701i
$801$	3.42320	−	47.2646i	0.120953	−	1.67001i
$802$	−3.68321	−	6.37951i	−0.130059	−	0.225268i
$803$	−7.34601	+	12.7237i	−0.259235	+	0.449008i
$804$	−13.3719	−	6.11402i	−0.471590	−	0.215625i
$805$	−20.7925	−	19.0993i	−0.732838	−	0.673162i
$806$	−11.9064	−	10.6982i	−0.419386	−	0.376828i
$807$	7.07873	+	19.0049i	0.249183	+	0.669005i
$808$	−5.76282	+	5.76282i	−0.202735	+	0.202735i
$809$			14.6682i			0.515708i	0.966184	+	0.257854i	$0.0830153\pi$
$809$			14.6682i			0.515708i	−0.966184	+	0.257854i	$0.916985\pi$
$810$	−12.3193	+	15.6073i	−0.432856	+	0.548386i
$811$	−28.5937	+	28.5937i	−1.00406	+	1.00406i	−0.00406780	+	0.999992i	$0.501295\pi$
$811$	−28.5937	+	28.5937i	−1.00406	+	1.00406i	−0.999992	+	0.00406780i	$0.998705\pi$
$812$	1.15201	−	2.20643i	0.0404275	−	0.0774306i
$813$	−2.20585	−	23.2111i	−0.0773625	−	0.814049i
$814$	4.96838	−	18.5422i	0.174141	−	0.649905i
$815$	48.5787	−	28.0469i	1.70164	−	0.982441i
$816$	−1.20648	+	7.15495i	−0.0422351	+	0.250473i
$817$	1.23689	−	0.331425i	0.0432734	−	0.0115951i
$818$	40.3349			1.41028
$819$	−28.6103	+	0.672971i	−0.999723	+	0.0235155i
$820$	−20.7322			−0.724001
$821$	12.7264	−	3.41003i	0.444155	−	0.119011i	−0.0298081	−	0.999556i	$-0.509490\pi$
$821$	12.7264	−	3.41003i	0.444155	−	0.119011i	0.473963	+	0.880545i	$0.342823\pi$
$822$	−4.88055	+	28.9439i	−0.170229	+	1.00953i
$823$	47.7479	−	27.5673i	1.66439	−	0.960935i	0.693806	−	0.720162i	$-0.255932\pi$
$823$	47.7479	−	27.5673i	1.66439	−	0.960935i	0.970581	−	0.240773i	$-0.0774010\pi$
$824$	3.26529	−	12.1862i	0.113752	−	0.424527i
$825$	−0.0412012	−	0.433540i	−0.00143444	−	0.0150939i
$826$	−37.7464	+	1.60209i	−1.31337	+	0.0557440i
$827$	−38.4155	+	38.4155i	−1.33584	+	1.33584i	−0.435790	+	0.900048i	$0.643531\pi$
$827$	−38.4155	+	38.4155i	−1.33584	+	1.33584i	−0.900048	+	0.435790i	$0.856469\pi$
$828$	−4.75168	+	13.6892i	−0.165132	+	0.475732i
$829$		−	21.1061i		−	0.733046i	−0.930409	−	0.366523i	$-0.880548\pi$
$829$		−	21.1061i		−	0.733046i	0.930409	−	0.366523i	$-0.119452\pi$
$830$	16.2809	−	16.2809i	0.565117	−	0.565117i
$831$	1.80996	+	4.85938i	0.0627870	+	0.168570i
$832$	1.11774	+	3.42792i	0.0387507	+	0.118842i
$833$	16.7615	+	24.0621i	0.580750	+	0.833702i
$834$	0.0253101	+	0.0115725i	0.000876419	+	0.000400724i
$835$	7.47106	−	12.9403i	0.258547	−	0.447816i
$836$	0.503781	+	0.872574i	0.0174236	+	0.0301786i
$837$	22.4105	+	5.46878i	0.774620	+	0.189029i
$838$	11.3278	−	11.3278i	0.391311	−	0.391311i
$839$	−7.06393	−	26.3630i	−0.243874	−	0.910151i	−0.973946	−	0.226780i	$-0.927180\pi$
$839$	−7.06393	−	26.3630i	−0.243874	−	0.910151i	0.730072	−	0.683370i	$-0.239487\pi$
$840$	9.32907	−	3.93291i	0.321883	−	0.135698i
$841$	−14.0575	+	24.3482i	−0.484740	+	0.839595i
$842$	9.97179	−	17.2716i	0.343650	−	0.595220i
$843$	−11.0674	−	15.5567i	−0.381180	−	0.535803i
$844$	11.9699	+	6.91083i	0.412021	+	0.237880i
$845$	10.3483	+	26.7916i	0.355992	+	0.921658i
$846$	−11.9125	−	4.13498i	−0.409562	−	0.142164i
$847$	−0.733947	−	17.2923i	−0.0252187	−	0.594170i
$848$	4.82321	−	2.78468i	0.165630	−	0.0956263i
$849$	9.53185	+	1.60727i	0.327132	+	0.0551614i
$850$	0.129113	+	0.481856i	0.00442854	+	0.0165275i
$851$	−11.3656	+	42.4170i	−0.389608	+	1.45403i
$852$	6.22338	+	8.74785i	0.213209	+	0.299696i
$853$	8.20742	+	8.20742i	0.281017	+	0.281017i	0.833514	−	0.552498i	$-0.186325\pi$
$853$	8.20742	+	8.20742i	0.281017	+	0.281017i	−0.552498	+	0.833514i	$0.686325\pi$
$854$	10.2055	−	3.20416i	0.349226	−	0.109644i
$855$	−0.595754	−	3.10611i	−0.0203744	−	0.106227i
$856$	0.529339	−	0.141836i	0.0180924	−	0.00484785i
$857$	−17.4389	+	30.2051i	−0.595702	+	1.03179i	0.397745	+	0.917496i	$0.369793\pi$
$857$	−17.4389	+	30.2051i	−0.595702	+	1.03179i	−0.993447	+	0.114290i	$0.963541\pi$
$858$	12.2675	+	4.83519i	0.418807	+	0.165071i
$859$	−11.1504	−	19.3130i	−0.380445	−	0.658950i	0.610681	−	0.791877i	$-0.290896\pi$
$859$	−11.1504	−	19.3130i	−0.380445	−	0.658950i	−0.991126	+	0.132927i	$0.957563\pi$
$860$	−1.53442	+	5.72655i	−0.0523234	+	0.195274i
$861$	39.8325	+	16.2074i	1.35749	+	0.552347i
$862$	−27.4412	−	15.8432i	−0.934652	−	0.539622i
$863$	−9.89593	+	36.9321i	−0.336861	+	1.25718i	0.564976	+	0.825107i	$0.308885\pi$
$863$	−9.89593	+	36.9321i	−0.336861	+	1.25718i	−0.901837	+	0.432076i	$0.857781\pi$
$864$	−3.75579	−	3.59083i	−0.127774	−	0.122163i
$865$	3.83906	−	14.3276i	0.130532	−	0.487152i
$866$	26.6016	+	7.12787i	0.903959	+	0.242215i
$867$	−0.733811	−	0.606442i	−0.0249215	−	0.0205958i
$868$	−8.65019	−	7.94580i	−0.293607	−	0.269698i
$869$	7.24433	+	1.94111i	0.245747	+	0.0658478i
$870$	3.37356	−	1.25654i	0.114374	−	0.0426008i
$871$	13.8671	−	27.2859i	0.469870	−	0.924548i
$872$	−7.86536	−	4.54107i	−0.266355	−	0.153780i
$873$	−3.87148	+	53.4540i	−0.131030	+	1.80915i
$874$	−1.15244	−	1.99609i	−0.0389820	−	0.0675188i
$875$	20.2419	−	22.0363i	0.684300	−	0.744963i
$876$	6.98644	+	9.82044i	0.236050	+	0.331802i
$877$	23.4505	−	23.4505i	0.791868	−	0.791868i	−0.189930	−	0.981798i	$-0.560826\pi$
$877$	23.4505	−	23.4505i	0.791868	−	0.791868i	0.981798	+	0.189930i	$0.0608260\pi$
$878$	−1.79483	−	0.480922i	−0.0605724	−	0.0162303i
$879$	−29.8659	+	2.83829i	−1.00735	+	0.0957330i
$880$	−4.66480			−0.157250
$881$	14.7724	+	25.5866i	0.497695	+	0.862034i	0.999996	−	0.00265902i	$-0.000846393\pi$
$881$	14.7724	+	25.5866i	0.497695	+	0.862034i	−0.502301	+	0.864693i	$0.667513\pi$
$882$	−20.9983	+	0.263252i	−0.707051	+	0.00886414i
$883$			35.1158i			1.18174i	0.806767	+	0.590870i	$0.201215\pi$
$883$			35.1158i			1.18174i	−0.806767	+	0.590870i	$0.798785\pi$
$884$	−14.7777	−	3.12503i	−0.497027	−	0.105106i
$885$	−42.1201	−	34.8092i	−1.41585	−	1.17010i
$886$	22.1943	−	22.1943i	0.745631	−	0.745631i
$887$	23.9110	+	13.8050i	0.802851	+	0.463527i	0.844467	−	0.535607i	$-0.179917\pi$
$887$	23.9110	+	13.8050i	0.802851	+	0.463527i	−0.0416158	+	0.999134i	$0.513251\pi$
$888$	−12.1383	−	10.0314i	−0.407334	−	0.336632i
$889$	−12.4965	+	7.93979i	−0.419118	+	0.266292i
$890$	−33.7090	+	9.03229i	−1.12993	+	0.302763i
$891$	−18.8727	+	2.22205i	−0.632260	+	0.0744415i
$892$	−4.03794	+	1.08196i	−0.135200	+	0.0362268i
$893$	1.73703	−	1.00287i	0.0581275	−	0.0335599i
$894$	−11.4762	+	13.8866i	−0.383823	+	0.464437i
$895$	2.51374	−	9.38139i	0.0840249	−	0.313585i
$896$	0.792526	+	2.52426i	0.0264764	+	0.0843297i
$897$	−28.0630	−	11.0609i	−0.936998	−	0.369314i
$898$	−2.47085	−	4.27963i	−0.0824532	−	0.142813i
$899$	−2.95327	−	2.95327i	−0.0984970	−	0.0984970i
$900$	−0.337487	−	0.117146i	−0.0112496	−	0.00390486i
$901$			23.3313i			0.777278i
$902$	−14.0108	−	14.0108i	−0.466508	−	0.466508i
$903$	7.42479	−	9.80280i	0.247082	−	0.326217i
$904$	−6.43065	+	1.72309i	−0.213880	+	0.0573090i
$905$	57.3564	+	15.3686i	1.90659	+	0.510870i
$906$	9.23931	+	24.8056i	0.306955	+	0.824112i
$907$			55.8542i			1.85461i	0.374309	+	0.927304i	$0.377880\pi$
$907$			55.8542i			1.85461i	−0.374309	+	0.927304i	$0.622120\pi$
$908$	2.92533	+	10.9175i	0.0970805	+	0.362309i
$909$	23.0976	+	8.01746i	0.766100	+	0.265922i
$910$	7.37723	+	19.7418i	0.244553	+	0.654436i
$911$			15.1436i			0.501729i	0.968022	+	0.250864i	$0.0807148\pi$
$911$			15.1436i			0.501729i	−0.968022	+	0.250864i	$0.919285\pi$
$912$	0.822808	−	0.0781949i	0.0272459	−	0.00258929i
$913$	22.0051			0.728263
$914$	1.02294	+	1.77178i	0.0338358	+	0.0586053i
$915$	14.0698	+	6.43313i	0.465134	+	0.212673i
$916$	0.512008	+	1.91084i	0.0169172	+	0.0631359i
$917$	−2.91986	+	1.85517i	−0.0964224	+	0.0612632i
$918$	20.8944	−	6.10450i	0.689617	−	0.201479i
$919$	−2.67980			−0.0883983			−0.0441991	−	0.999023i	$-0.514074\pi$
$919$	−2.67980			−0.0883983			−0.0441991	+	0.999023i	$0.514074\pi$
$920$	10.6711			0.351817
$921$	−9.40598	+	6.69159i	−0.309938	+	0.220495i
$922$	−33.0175	+	19.0626i	−1.08737	+	0.627795i
$923$	−18.7301	+	12.1912i	−0.616507	+	0.401277i
$924$	8.96240	+	3.64670i	0.294841	+	0.119968i
$925$	−1.04573	−	0.280203i	−0.0343834	−	0.00921301i
$926$	16.7120	+	9.64866i	0.549189	+	0.317075i
$927$	−37.1708	+	7.12938i	−1.22085	+	0.234160i
$928$	0.243492	+	0.908723i	0.00799300	+	0.0298303i
$929$	−15.7180	−	15.7180i	−0.515691	−	0.515691i	0.400574	−	0.916265i	$-0.368811\pi$
$929$	−15.7180	−	15.7180i	−0.515691	−	0.515691i	−0.916265	+	0.400574i	$0.868811\pi$
$930$	−1.60720	−	16.9118i	−0.0527020	−	0.554559i
$931$	2.15333	−	2.55361i	0.0705725	−	0.0836911i
$932$	14.4933	+	8.36770i	0.474743	+	0.274093i
$933$	−23.1730	−	19.1508i	−0.758651	−	0.626970i
$934$	−6.97555	−	6.97555i	−0.228247	−	0.228247i
$935$	9.77094	−	16.9238i	0.319544	−	0.553466i
$936$	7.79172	−	7.50261i	0.254680	−	0.245231i
$937$	−51.8315			−1.69326			−0.846631	−	0.532180i	$-0.821373\pi$
$937$	−51.8315			−1.69326			−0.846631	+	0.532180i	$0.821373\pi$
$938$	10.3950	−	19.9094i	0.339408	−	0.650066i
$939$	2.27537	−	0.847502i	0.0742538	−	0.0276572i
$940$			9.28619i			0.302882i
$941$	−17.9196	+	4.80156i	−0.584164	+	0.156526i	−0.538785	−	0.842444i	$-0.681116\pi$
$941$	−17.9196	+	4.80156i	−0.584164	+	0.156526i	−0.0453793	+	0.998970i	$0.514450\pi$
$942$	−32.9451	−	15.0635i	−1.07341	−	0.490794i
$943$	32.0509	+	32.0509i	1.04372	+	1.04372i
$944$	10.0972	−	10.0972i	0.328637	−	0.328637i
$945$	−22.8237	−	20.0393i	−0.742454	−	0.651879i
$946$	−4.90694	+	2.83302i	−0.159538	+	0.0921095i
$947$	−2.37156	−	8.85078i	−0.0770654	−	0.287612i	0.916628	−	0.399741i	$-0.130900\pi$
$947$	−2.37156	−	8.85078i	−0.0770654	−	0.287612i	−0.993694	+	0.112129i	$0.964233\pi$
$948$	3.91921	−	4.74235i	0.127290	−	0.154024i
$949$	−21.0266	+	13.6859i	−0.682552	+	0.444264i
$950$	0.0492108	−	0.0284119i	0.00159661	−	0.000921803i
$951$	40.3476	+	18.4481i	1.30836	+	0.598220i
$952$	−10.8180	−	2.41209i	−0.350613	−	0.0781762i
$953$	−17.2880	+	29.9437i	−0.560013	+	0.969972i	0.437481	+	0.899228i	$0.355871\pi$
$953$	−17.2880	+	29.9437i	−0.560013	+	0.969972i	−0.997495	+	0.0707440i	$0.977463\pi$
$954$	−13.8283	−	9.37746i	−0.447709	−	0.303606i
$955$	10.2746	+	2.75308i	0.332479	+	0.0890875i
$956$	14.8439	+	3.97740i	0.480085	+	0.128638i
$957$	3.12901	+	1.43067i	0.101146	+	0.0462471i
$958$	7.84311	−	13.5847i	0.253399	−	0.438901i
$959$	−43.7620	−	9.75761i	−1.41315	−	0.315090i
$960$	−1.59119	+	3.48007i	−0.0513554	+	0.112319i
$961$	9.77847	−	5.64560i	0.315435	−	0.182116i
$962$	21.9087	−	24.3830i	0.706365	−	0.786141i
$963$	−1.07550	−	1.24345i	−0.0346574	−	0.0400696i
$964$	7.04677	+	26.2989i	0.226961	+	0.847030i
$965$	1.60910	−	0.929014i	0.0517987	−	0.0299060i
$966$	−20.5023	−	8.34215i	−0.659650	−	0.268404i
$967$	9.72642	−	9.72642i	0.312781	−	0.312781i	−0.533205	−	0.845986i	$-0.679013\pi$
$967$	9.72642	−	9.72642i	0.312781	−	0.312781i	0.845986	+	0.533205i	$0.179013\pi$
$968$	4.62572	+	4.62572i	0.148676	+	0.148676i
$969$	−1.43977	+	3.14892i	−0.0462522	+	0.101158i
$970$	38.1233	−	10.2151i	1.22406	−	0.327987i
$971$		−	9.20017i		−	0.295248i	−0.989044	−	0.147624i	$-0.952838\pi$
$971$		−	9.20017i		−	0.295248i	0.989044	−	0.147624i	$-0.0471625\pi$
$972$	−4.77988	+	14.8375i	−0.153315	+	0.475914i
$973$	−0.0196754	+	0.0376843i	−0.000630766	+	0.00120810i
$974$	−36.5092			−1.16983
$975$	0.272692	−	0.691855i	0.00873312	−	0.0221571i
$976$	−2.02149	+	3.50132i	−0.0647062	+	0.112074i
$977$	−32.1789	−	32.1789i	−1.02949	−	1.02949i	−0.999552	−	0.0299419i	$-0.990468\pi$
$977$	−32.1789	−	32.1789i	−1.02949	−	1.02949i	−0.0299419	−	0.999552i	$-0.509532\pi$
$978$	28.0150	−	33.8989i	0.895819	−	1.08397i
$979$	−28.8844	−	16.6764i	−0.923149	−	0.532980i
$980$	5.25400	+	14.5451i	0.167833	+	0.464627i
$981$	−1.96820	+	27.1752i	−0.0628399	+	0.867638i
$982$	23.0029	+	23.0029i	0.734053	+	0.734053i
$983$	0.406277	+	1.51625i	0.0129582	+	0.0483607i	0.972102	−	0.234558i	$-0.0753641\pi$
$983$	0.406277	+	1.51625i	0.0129582	+	0.0483607i	−0.959144	+	0.282918i	$0.908697\pi$
$984$	−15.2316	+	5.67328i	−0.485565	+	0.180857i
$985$	−27.1745	−	15.6892i	−0.865851	−	0.499899i
$986$	−3.80685	−	1.02004i	−0.121235	−	0.0324847i
$987$	7.25947	−	17.8414i	0.231072	−	0.567898i
$988$	0.0918320	+	1.71808i	0.00292157	+	0.0546593i
$989$	11.2251	−	6.48079i	0.356936	−	0.206077i
$990$	6.10343	+	12.5933i	0.193980	+	0.400241i
$991$	7.94584			0.252408			0.126204	−	0.992004i	$-0.459721\pi$
$991$	7.94584			0.252408			0.126204	+	0.992004i	$0.459721\pi$
$992$	4.43946			0.140953
$993$	−4.52420	−	6.35940i	−0.143571	−	0.201810i
$994$	−13.8415	+	8.79439i	−0.439026	+	0.278941i
$995$	4.08630	+	15.2503i	0.129545	+	0.483467i
$996$	7.50607	−	16.4164i	0.237839	−	0.520175i
$997$	−28.6071	−	49.5489i	−0.905996	−	1.56923i	−0.819575	−	0.572972i	$-0.805790\pi$
$997$	−28.6071	−	49.5489i	−0.905996	−	1.56923i	−0.0864205	−	0.996259i	$-0.527543\pi$
$998$	34.2797			1.08510
$999$	−11.1995	+	45.8942i	−0.354335	+	1.45203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.431.28	yes	152
3.2	odd	2	inner	546.2.bw.a.431.9	✓	152
7.2	even	3		546.2.ch.a.275.5	yes	152
13.7	odd	12		546.2.ch.a.137.36	yes	152
21.2	odd	6		546.2.ch.a.275.36	yes	152
39.20	even	12		546.2.ch.a.137.5	yes	152
91.72	odd	12	inner	546.2.bw.a.527.9	yes	152
273.254	even	12	inner	546.2.bw.a.527.28	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.9	✓	152	3.2	odd	2	inner
546.2.bw.a.431.28	yes	152	1.1	even	1	trivial
546.2.bw.a.527.9	yes	152	91.72	odd	12	inner
546.2.bw.a.527.28	yes	152	273.254	even	12	inner
546.2.ch.a.137.5	yes	152	39.20	even	12
546.2.ch.a.137.36	yes	152	13.7	odd	12
546.2.ch.a.275.5	yes	152	7.2	even	3
546.2.ch.a.275.36	yes	152	21.2	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.287995 + 1.70794i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.571804 + 2.13400i) q^{5} +(0.163866 + 1.72428i) q^{6} +(-2.64337 + 0.112194i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.83412 - 0.983756i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.287995 + 1.70794i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.571804 + 2.13400i) q^{5} +(0.163866 + 1.72428i) q^{6} +(-2.64337 + 0.112194i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.83412 - 0.983756i) q^{9} +2.20928i q^{10} +(-1.49302 + 1.49302i) q^{11} +(0.604559 + 1.62312i) q^{12} +(-3.42792 + 1.11774i) q^{13} +(-2.52426 + 0.792526i) q^{14} +(-3.48007 - 1.59119i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.09461 + 3.62798i) q^{17} +(-2.99216 - 0.216711i) q^{18} +(0.337423 - 0.337423i) q^{19} +(0.571804 + 2.13400i) q^{20} +(0.569656 - 4.54703i) q^{21} +(-1.05573 + 1.82857i) q^{22} +(2.41507 - 4.18302i) q^{23} +(1.00405 + 1.41134i) q^{24} +(0.103127 + 0.0595401i) q^{25} +(-3.02183 + 1.96687i) q^{26} +(2.49641 - 4.55719i) q^{27} +(-2.23313 + 1.41885i) q^{28} +(-0.814739 + 0.470390i) q^{29} +(-3.77332 - 0.636261i) q^{30} +(1.14902 + 4.28819i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-2.12001 - 2.97998i) q^{33} +(2.96223 + 2.96223i) q^{34} +(1.27207 - 5.70511i) q^{35} +(-2.94630 + 0.565101i) q^{36} +(-8.78173 + 2.35306i) q^{37} +(0.238594 - 0.413257i) q^{38} +(-0.921812 - 6.17659i) q^{39} +(1.10464 + 1.91329i) q^{40} +(-2.42880 + 9.06440i) q^{41} +(-0.626612 - 4.53953i) q^{42} +(2.32396 + 1.34174i) q^{43} +(-0.546485 + 2.03951i) q^{44} +(3.71990 - 5.48550i) q^{45} +(1.25013 - 4.66555i) q^{46} +(4.06004 + 1.08788i) q^{47} +(1.33512 + 1.10338i) q^{48} +(6.97482 - 0.593142i) q^{49} +(0.115023 + 0.0308202i) q^{50} +(-6.79960 + 2.53264i) q^{51} +(-2.40980 + 2.68195i) q^{52} +(4.82321 + 2.78468i) q^{53} +(1.23186 - 5.04802i) q^{54} +(-2.33240 - 4.03983i) q^{55} +(-1.78981 + 1.94848i) q^{56} +(0.479123 + 0.673475i) q^{57} +(-0.665231 + 0.665231i) q^{58} +(13.7931 + 3.69585i) q^{59} +(-3.80942 + 0.362025i) q^{60} -4.04297 q^{61} +(2.21973 + 3.84468i) q^{62} +(7.60200 + 2.28246i) q^{63} -1.00000i q^{64} +(-0.425162 - 7.95432i) q^{65} +(-2.81905 - 2.32974i) q^{66} +(-6.00262 + 6.00262i) q^{67} +(3.62798 + 2.09461i) q^{68} +(6.44882 + 5.32948i) q^{69} +(-0.247868 - 5.83995i) q^{70} +(5.98706 - 1.60423i) q^{71} +(-2.69964 + 1.30840i) q^{72} +(6.72115 - 1.80093i) q^{73} +(-7.87349 + 4.54576i) q^{74} +(-0.131391 + 0.158987i) q^{75} +(0.123506 - 0.460929i) q^{76} +(3.77911 - 4.11413i) q^{77} +(-2.48902 - 5.72755i) q^{78} +(-1.77600 - 3.07612i) q^{79} +(1.56220 + 1.56220i) q^{80} +(7.06445 + 5.57616i) q^{81} +9.38416i q^{82} +(-7.36931 - 7.36931i) q^{83} +(-1.78018 - 4.22267i) q^{84} +(-8.93981 + 2.39542i) q^{85} +(2.59204 + 0.694536i) q^{86} +(-0.568757 - 1.52699i) q^{87} +2.11145i q^{88} +(4.08834 + 15.2579i) q^{89} +(2.17339 - 6.26136i) q^{90} +(8.93587 - 3.33920i) q^{91} -4.83014i q^{92} +(-7.65488 + 0.727475i) q^{93} +4.20326 q^{94} +(0.527122 + 0.913002i) q^{95} +(1.57520 + 0.720229i) q^{96} +(-4.62372 - 17.2560i) q^{97} +(6.58365 - 2.37815i) q^{98} +(5.70018 - 2.76263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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