LMFDB - Embedded newform 546.2.bw.a.431.9

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			431.9
Character	$\chi$	$=$	546.431
Dual form			546.2.bw.a.527.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.287995 - 1.70794i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.571804 - 2.13400i) q^{5} +(0.720229 + 1.57520i) q^{6} +(-2.64337 + 0.112194i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.83412 + 0.983756i) q^{9} +O(q^{10})$	\(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} +(0.720229 + 1.57520i) 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} +(-1.10338 - 1.33512i) q^{12} +(-3.42792 + 1.11774i) q^{13} +(2.52426 - 0.792526i) q^{14} +(-3.80942 - 0.362025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.09461 - 3.62798i) q^{17} +(2.48293 - 1.68376i) q^{18} +(0.337423 - 0.337423i) q^{19} +(-0.571804 - 2.13400i) q^{20} +(0.952898 + 4.48241i) q^{21} +(-1.05573 + 1.82857i) q^{22} +(-2.41507 + 4.18302i) q^{23} +(1.41134 + 1.00405i) 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} +(-2.97998 - 2.12001i) q^{33} +(2.96223 + 2.96223i) q^{34} +(-1.27207 + 5.70511i) q^{35} +(-1.96254 + 2.26902i) q^{36} +(-8.78173 + 2.35306i) q^{37} +(-0.238594 + 0.413257i) q^{38} +(2.89626 + 5.53278i) q^{39} +(1.10464 + 1.91329i) q^{40} +(2.42880 - 9.06440i) q^{41} +(-2.08056 - 4.08305i) q^{42} +(2.32396 + 1.34174i) q^{43} +(0.546485 - 2.03951i) q^{44} +(0.478776 + 6.61053i) q^{45} +(1.25013 - 4.66555i) q^{46} +(-4.06004 - 1.08788i) q^{47} +(-1.62312 - 0.604559i) q^{48} +(6.97482 - 0.593142i) q^{49} +(-0.115023 - 0.0308202i) q^{50} +(-5.59313 + 4.62231i) q^{51} +(-2.40980 + 2.68195i) q^{52} +(-4.82321 - 2.78468i) q^{53} +(-3.59083 - 3.75579i) q^{54} +(-2.33240 - 4.03983i) q^{55} +(1.78981 - 1.94848i) q^{56} +(-0.673475 - 0.479123i) q^{57} +(-0.665231 + 0.665231i) q^{58} +(-13.7931 - 3.69585i) q^{59} +(-3.48007 + 1.59119i) q^{60} -4.04297 q^{61} +(-2.21973 - 3.84468i) q^{62} +(7.38125 - 2.91840i) q^{63} -1.00000i q^{64} +(0.425162 + 7.95432i) q^{65} +(3.42714 + 1.27650i) q^{66} +(-6.00262 + 6.00262i) q^{67} +(-3.62798 - 2.09461i) q^{68} +(7.83988 + 2.92010i) q^{69} +(-0.247868 - 5.83995i) q^{70} +(-5.98706 + 1.60423i) q^{71} +(1.30840 - 2.69964i) q^{72} +(6.72115 - 1.80093i) q^{73} +(7.87349 - 4.54576i) q^{74} +(0.0719910 - 0.193281i) q^{75} +(0.123506 - 0.460929i) q^{76} +(-3.77911 + 4.11413i) q^{77} +(-4.22956 - 4.59465i) 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} +(3.06644 + 3.40543i) q^{84} +(-8.93981 + 2.39542i) q^{85} +(-2.59204 - 0.694536i) q^{86} +(-1.03804 - 1.25606i) 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} +(6.99306 - 3.19743i) q^{93} +4.20326 q^{94} +(-0.527122 - 0.913002i) q^{95} +(1.72428 + 0.163866i) q^{96} +(-4.62372 - 17.2560i) q^{97} +(-6.58365 + 2.37815i) q^{98} +(-2.76263 + 5.70018i) 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	$-0.752197\pi$
$5$	0.571804	−	2.13400i	0.255718	−	0.954354i	0.967689	−	0.252145i	$-0.0811361\pi$
$6$	0.720229	+	1.57520i	0.294032	+	0.643075i
$7$	−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	−0.445245	−	0.895409i	$-0.646883\pi$
$11$	1.49302	−	1.49302i	0.450164	−	0.450164i	0.895409	+	0.445245i	$0.146883\pi$
$12$	−1.10338	−	1.33512i	−0.318519	−	0.385417i
$13$	−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
$15$	−3.80942	−	0.362025i	−0.983589	−	0.0934745i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.09461	−	3.62798i	−0.508018	−	0.879914i	−0.999957	−	0.00928370i	$-0.997045\pi$
$17$	−2.09461	−	3.62798i	−0.508018	−	0.879914i	0.491939	−	0.870630i	$-0.336288\pi$
$18$	2.48293	−	1.68376i	0.585233	−	0.396866i
$19$	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
$21$	0.952898	+	4.48241i	0.207939	+	0.978142i
$22$	−1.05573	+	1.82857i	−0.225082	+	0.389853i
$23$	−2.41507	+	4.18302i	−0.503577	+	0.872220i	0.496415	+	0.868085i	$0.334649\pi$
$23$	−2.41507	+	4.18302i	−0.503577	+	0.872220i	−0.999991	+	0.00413478i	$0.998684\pi$
$24$	1.41134	+	1.00405i	0.288088	+	0.204951i
$25$	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	−0.422442	−	0.906390i	$-0.638827\pi$
$29$	0.814739	−	0.470390i	0.151293	−	0.0873492i	0.573735	+	0.819041i	$0.305494\pi$
$30$	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
$33$	−2.97998	−	2.12001i	−0.518748	−	0.369047i
$34$	2.96223	+	2.96223i	0.508018	+	0.508018i
$35$	−1.27207	+	5.70511i	−0.215019	+	0.964340i
$36$	−1.96254	+	2.26902i	−0.327090	+	0.378169i
$37$	−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
$39$	2.89626	+	5.53278i	0.463773	+	0.885954i
$40$	1.10464	+	1.91329i	0.174659	+	0.302518i
$41$	2.42880	−	9.06440i	0.379315	−	1.41562i	−0.467623	−	0.883928i	$-0.654889\pi$
$41$	2.42880	−	9.06440i	0.379315	−	1.41562i	0.846937	−	0.531693i	$-0.178444\pi$
$42$	−2.08056	−	4.08305i	−0.321038	−	0.630028i
$43$	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
$45$	0.478776	+	6.61053i	0.0713718	+	0.985439i
$46$	1.25013	−	4.66555i	0.184322	−	0.687898i
$47$	−4.06004	−	1.08788i	−0.592218	−	0.158684i	−0.0497512	−	0.998762i	$-0.515843\pi$
$47$	−4.06004	−	1.08788i	−0.592218	−	0.158684i	−0.542467	+	0.840077i	$0.682510\pi$
$48$	−1.62312	−	0.604559i	−0.234277	−	0.0872606i
$49$	6.97482	−	0.593142i	0.996404	−	0.0847345i
$50$	−0.115023	−	0.0308202i	−0.0162667	−	0.00435864i
$51$	−5.59313	+	4.62231i	−0.783195	+	0.647253i
$52$	−2.40980	+	2.68195i	−0.334179	+	0.371920i
$53$	−4.82321	−	2.78468i	−0.662518	−	0.382505i	0.130718	−	0.991420i	$-0.458272\pi$
$53$	−4.82321	−	2.78468i	−0.662518	−	0.382505i	−0.793236	+	0.608915i	$0.791605\pi$
$54$	−3.59083	−	3.75579i	−0.488650	−	0.511098i
$55$	−2.33240	−	4.03983i	−0.314500	−	0.544731i
$56$	1.78981	−	1.94848i	0.239174	−	0.260376i
$57$	−0.673475	−	0.479123i	−0.0892039	−	0.0634613i
$58$	−0.665231	+	0.665231i	−0.0873492	+	0.0873492i
$59$	−13.7931	−	3.69585i	−1.79571	−	0.481158i	−0.802412	−	0.596770i	$-0.796450\pi$
$59$	−13.7931	−	3.69585i	−1.79571	−	0.481158i	−0.993294	+	0.115612i	$0.963117\pi$
$60$	−3.48007	+	1.59119i	−0.449275	+	0.205421i
$61$	−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
$63$	7.38125	−	2.91840i	0.929951	−	0.367684i
$64$		−	1.00000i		−	0.125000i
$65$	0.425162	+	7.95432i	0.0527349	+	0.986612i
$66$	3.42714	+	1.27650i	0.421851	+	0.157126i
$67$	−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
$69$	7.83988	+	2.92010i	0.943810	+	0.351539i
$70$	−0.247868	−	5.83995i	−0.0296259	−	0.698007i
$71$	−5.98706	+	1.60423i	−0.710533	+	0.190387i	−0.595944	−	0.803026i	$-0.703222\pi$
$71$	−5.98706	+	1.60423i	−0.710533	+	0.190387i	−0.114589	+	0.993413i	$0.536555\pi$
$72$	1.30840	−	2.69964i	0.154197	−	0.318156i
$73$	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
$75$	0.0719910	−	0.193281i	0.00831281	−	0.0223182i
$76$	0.123506	−	0.460929i	0.0141671	−	0.0528722i
$77$	−3.77911	+	4.11413i	−0.430669	+	0.468848i
$78$	−4.22956	−	4.59465i	−0.478904	−	0.520242i
$79$	−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	0.984465	−	0.175578i	$-0.0561796\pi$
$83$	7.36931	+	7.36931i	0.808887	+	0.808887i	−0.175578	+	0.984465i	$0.556180\pi$
$84$	3.06644	+	3.40543i	0.334576	+	0.371563i
$85$	−8.93981	+	2.39542i	−0.969659	+	0.259819i
$86$	−2.59204	−	0.694536i	−0.279507	−	0.0748937i
$87$	−1.03804	−	1.25606i	−0.111289	−	0.134663i
$88$			2.11145i			0.225082i
$89$	−4.08834	−	15.2579i	−0.433363	−	1.61733i	−0.744953	−	0.667116i	$-0.767528\pi$
$89$	−4.08834	−	15.2579i	−0.433363	−	1.61733i	0.311590	−	0.950217i	$-0.399138\pi$
$90$	−2.17339	−	6.26136i	−0.229096	−	0.660005i
$91$	8.93587	−	3.33920i	0.936734	−	0.350043i
$92$			4.83014i			0.503577i
$93$	6.99306	−	3.19743i	0.725146	−	0.331558i
$94$	4.20326			0.433534
$95$	−0.527122	−	0.913002i	−0.0540815	−	0.0936720i
$96$	1.72428	+	0.163866i	0.175984	+	0.0167245i
$97$	−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
$99$	−2.76263	+	5.70018i	−0.277655	+	0.572889i
$100$	0.119080			0.0119080
$101$	8.14985			0.810940			0.405470	−	0.914108i	$-0.367108\pi$
$101$	8.14985			0.810940			0.405470	+	0.914108i	$0.367108\pi$
$102$	4.20621	−	5.91242i	0.416476	−	0.585417i
$103$	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
$105$	10.1103	+	0.529573i	0.986668	+	0.0516810i
$106$	5.37959	+	1.44146i	0.522512	+	0.140007i
$107$	−0.474592	−	0.274006i	−0.0458806	−	0.0264892i	0.476884	−	0.878966i	$-0.341766\pi$
$107$	−0.474592	−	0.274006i	−0.0458806	−	0.0264892i	−0.522765	+	0.852477i	$0.675099\pi$
$108$	4.44055	+	2.69844i	0.427292	+	0.259657i
$109$	−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
$111$	6.54798	+	14.3210i	0.621506	+	1.35929i
$112$	−1.22452	+	2.34532i	−0.115707	+	0.221612i
$113$	5.76556	+	3.32875i	0.542378	+	0.313142i	0.746042	−	0.665899i	$-0.231952\pi$
$113$	5.76556	+	3.32875i	0.542378	+	0.313142i	−0.203664	+	0.979041i	$0.565285\pi$
$114$	0.774533	+	0.288489i	0.0725416	+	0.0270194i
$115$	7.54563	+	7.54563i	0.703633	+	0.703633i
$116$	0.470390	−	0.814739i	0.0436746	−	0.0756466i
$117$	8.61555	−	6.54005i	0.796508	−	0.604628i
$118$	14.2797			1.31455
$119$	5.94388	+	9.35509i	0.544874	+	0.857579i
$120$	2.94966	−	2.43768i	0.269266	−	0.222529i
$121$			6.54176i			0.594705i
$122$	3.90521	−	1.04640i	0.353561	−	0.0947365i
$123$	−16.1809	−	1.53774i	−1.45899	−	0.138653i
$124$	3.13917	+	3.13917i	0.281906	+	0.281906i
$125$	7.99701	−	7.99701i	0.715275	−	0.715275i
$126$	−6.37441	+	4.72937i	−0.567877	+	0.421326i
$127$	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
$129$	1.62232	−	4.35560i	0.142838	−	0.383489i
$130$	−2.46940	−	7.57324i	−0.216581	−	0.664217i
$131$	−1.13235	+	0.653760i	−0.0989335	+	0.0571193i	−0.548650	−	0.836052i	$-0.684858\pi$
$131$	−1.13235	+	0.653760i	−0.0989335	+	0.0571193i	0.449717	+	0.893171i	$0.351525\pi$
$132$	−3.64074	−	0.345995i	−0.316886	−	0.0301150i
$133$	−0.854078	+	0.929792i	−0.0740580	+	0.0806232i
$134$	4.24449	−	7.35168i	0.366669	−	0.635089i
$135$	11.1525	−	2.72152i	0.959854	−	0.234231i
$136$	4.04648	+	1.08425i	0.346983	+	0.0929738i
$137$	−16.3692	−	4.38612i	−1.39852	−	0.374731i	−0.520705	−	0.853737i	$-0.674331\pi$
$137$	−16.3692	−	4.38612i	−1.39852	−	0.374731i	−0.877812	+	0.479005i	$0.840997\pi$
$138$	−8.32852	−	0.791494i	−0.708970	−	0.0673764i
$139$	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
$141$	−0.688771	+	7.24761i	−0.0580050	+	0.610359i
$142$	5.36785	−	3.09913i	0.450460	−	0.260073i
$143$	−3.44916	+	6.78679i	−0.288433	+	0.567539i
$144$	−0.565101	+	2.94630i	−0.0470918	+	0.245525i
$145$	−0.537941	−	2.00762i	−0.0446736	−	0.166724i
$146$	−6.02601	+	3.47912i	−0.498716	+	0.287934i
$147$	−3.02176	−	11.7418i	−0.249231	−	0.968444i
$148$	−6.42867	+	6.42867i	−0.528434	+	0.528434i
$149$	−7.35460	−	7.35460i	−0.602513	−	0.602513i	0.338466	−	0.940979i	$-0.390092\pi$
$149$	−7.35460	−	7.35460i	−0.602513	−	0.602513i	−0.940979	+	0.338466i	$0.890092\pi$
$150$	−0.0195132	+	0.205328i	−0.00159324	+	0.0167650i
$151$	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
$153$	9.50542	+	8.22153i	0.768468	+	0.664671i
$154$	2.58552	−	4.95204i	0.208347	−	0.399047i
$155$	9.80801			0.787798
$156$	5.27463	+	3.34340i	0.422308	+	0.267686i
$157$	−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
$159$	−3.36701	+	9.03972i	−0.267021	+	0.716896i
$160$	1.91329	+	1.10464i	0.151259	+	0.0873295i
$161$	5.91461	−	11.3282i	0.466137	−	0.892790i
$162$	−5.38052	+	7.21457i	−0.422733	+	0.566830i
$163$	−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
$165$	−6.22807	+	5.14705i	−0.484855	+	0.400697i
$166$	−9.02553	−	5.21089i	−0.700517	−	0.404444i
$167$	6.53289	+	1.75048i	0.505530	+	0.135456i	0.502565	−	0.864539i	$-0.332390\pi$
$167$	6.53289	+	1.75048i	0.505530	+	0.135456i	0.00296472	+	0.999996i	$0.499056\pi$
$168$	−3.84334	−	2.49574i	−0.296520	−	0.192551i
$169$	10.5013	−	7.66306i	0.807793	−	0.589466i
$170$	8.01522	−	4.62759i	0.614739	−	0.354920i
$171$	−0.624355	+	1.28824i	−0.0477456	+	0.0985141i
$172$	2.68348			0.204613
$173$	6.71395			0.510452			0.255226	−	0.966881i	$-0.417850\pi$
$173$	6.71395			0.510452			0.255226	+	0.966881i	$0.417850\pi$
$174$	1.32776	+	0.944592i	0.100657	+	0.0716093i
$175$	−0.279282	−	0.145816i	−0.0211117	−	0.0110227i
$176$	−0.546485	−	2.03951i	−0.0411928	−	0.153734i
$177$	−2.33995	+	24.6221i	−0.175881	+	1.85071i
$178$	7.89806	+	13.6798i	0.591985	+	1.02535i
$179$	4.39615			0.328584			0.164292	−	0.986412i	$-0.447466\pi$
$179$	4.39615			0.328584			0.164292	+	0.986412i	$0.447466\pi$
$180$	3.71990	+	5.48550i	0.277265	+	0.408865i
$181$		−	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
$186$	−5.92722	+	4.89841i	−0.434605	+	0.359169i
$187$	−8.54396	−	2.28935i	−0.624797	−	0.167414i
$188$	−4.06004	+	1.08788i	−0.296109	+	0.0793421i
$189$	−7.11022	−	11.7663i	−0.517193	−	0.855869i
$190$	0.745463	+	0.745463i	0.0540815	+	0.0540815i
$191$			4.81472i			0.348381i	0.984712	+	0.174191i	$0.0557309\pi$
$191$			4.81472i			0.348381i	−0.984712	+	0.174191i	$0.944269\pi$
$192$	−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
$195$	13.4631	−	3.01695i	0.964109	−	0.216049i
$196$	5.74380	−	4.00109i	0.410272	−	0.285792i
$197$	3.67600	−	13.7190i	0.261904	−	0.977440i	−0.702214	−	0.711966i	$-0.747805\pi$
$197$	3.67600	−	13.7190i	0.261904	−	0.977440i	0.964118	−	0.265474i	$-0.0855285\pi$
$198$	1.19319	−	6.22097i	0.0847960	−	0.442105i
$199$	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
$201$	11.9808	+	8.52339i	0.845064	+	0.601194i
$202$	−7.87215	+	2.10934i	−0.553883	+	0.148412i
$203$	−2.10088	+	1.33482i	−0.147453	+	0.0936862i
$204$	−2.53264	+	6.79960i	−0.177320	+	0.476068i
$205$	−17.9546	−	10.3661i	−1.25401	−	0.724001i
$206$	−8.92093	+	8.92093i	−0.621551	+	0.621551i
$207$	2.72952	−	14.2310i	0.189715	−	0.989124i
$208$	−0.745969	+	3.52754i	−0.0517236	+	0.244591i
$209$		−	1.00756i		−	0.0696945i
$210$	−9.90290	+	2.10522i	−0.683365	+	0.145274i
$211$	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
$213$	4.46417	+	9.76353i	0.305880	+	0.668986i
$214$	0.529339	+	0.141836i	0.0361849	+	0.00969571i
$215$	4.19213	−	4.19213i	0.285901	−	0.285901i
$216$	−4.98764	−	1.45719i	−0.339366	−	0.0991493i
$217$	−3.51839	−	11.2064i	−0.238844	−	0.760737i
$218$	4.54107	+	7.86536i	0.307560	+	0.532710i
$219$	−5.01153	−	10.9607i	−0.338648	−	0.740652i
$220$	−4.03983	−	2.33240i	−0.272365	−	0.157250i
$221$	11.2353	+	10.0952i	0.755769	+	0.679076i
$222$	−10.0314	−	12.1383i	−0.673264	−	0.814668i
$223$	−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
$225$	−0.350846	−	0.0672924i	−0.0233897	−	0.00448616i
$226$	−6.43065	−	1.72309i	−0.427760	−	0.114618i
$227$	2.92533	−	10.9175i	0.194161	−	0.724619i	−0.798321	−	0.602232i	$-0.794278\pi$
$227$	2.92533	−	10.9175i	0.194161	−	0.724619i	0.992482	−	0.122387i	$-0.0390549\pi$
$228$	−0.822808	−	0.0781949i	−0.0544918	−	0.00517858i
$229$	−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
$231$	8.11504	+	5.26964i	0.533931	+	0.346717i
$232$	−0.243492	+	0.908723i	−0.0159860	+	0.0596606i
$233$	−8.36770	−	14.4933i	−0.548187	−	0.949487i	−0.998399	−	0.0565654i	$-0.981985\pi$
$233$	−8.36770	−	14.4933i	−0.548187	−	0.949487i	0.450212	−	0.892922i	$-0.351348\pi$
$234$	−6.62929	+	8.54707i	−0.433371	+	0.558740i
$235$	−4.64309	+	8.04207i	−0.302882	+	0.524607i
$236$	−13.7931	+	3.69585i	−0.897853	+	0.240579i
$237$	−4.74235	+	3.91921i	−0.308049	+	0.254580i
$238$	−8.16262	−	7.49793i	−0.529104	−	0.486019i
$239$	−10.8665	−	10.8665i	−0.702893	−	0.702893i	0.262138	−	0.965030i	$-0.415572\pi$
$239$	−10.8665	−	10.8665i	−0.702893	−	0.702893i	−0.965030	+	0.262138i	$0.915572\pi$
$240$	−2.21823	+	3.11804i	−0.143186	+	0.201269i
$241$	−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
$249$	10.4640	−	14.7087i	0.663130	−	0.932124i
$250$	−5.65474	+	9.79430i	−0.357637	+	0.619446i
$251$	−9.46986	+	16.4023i	−0.597732	+	1.03530i	0.395423	+	0.918499i	$0.370598\pi$
$251$	−9.46986	+	16.4023i	−0.597732	+	1.03530i	−0.993155	+	0.116804i	$0.962735\pi$
$252$	4.93315	−	6.21804i	0.310759	−	0.391700i
$253$	2.63960	+	9.85110i	0.165950	+	0.619334i
$254$	−3.95693	+	3.95693i	−0.248280	+	0.248280i
$255$	6.66585	+	14.5788i	0.417432	+	0.912960i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.29961	−	12.6433i	0.455337	−	0.788667i	−0.543370	−	0.839493i	$-0.682852\pi$
$257$	7.29961	−	12.6433i	0.455337	−	0.788667i	0.998708	+	0.0508258i	$0.0161853\pi$
$258$	−0.439730	+	4.62708i	−0.0273764	+	0.288069i
$259$	22.9494	−	7.20527i	1.42601	−	0.447713i
$260$	4.34536	+	6.67606i	0.269488	+	0.414032i
$261$	−1.84632	+	2.13464i	−0.114284	+	0.132131i
$262$	0.924557	−	0.924557i	0.0571193	−	0.0571193i
$263$			17.5577i			1.08265i	0.840813	+	0.541326i	$0.182078\pi$
$263$			17.5577i			1.08265i	−0.840813	+	0.541326i	$0.817922\pi$
$264$	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
$267$	−24.8821	+	11.3768i	−1.52276	+	0.696251i
$268$	−2.19711	+	8.19973i	−0.134210	+	0.500879i
$269$	−10.1402	+	5.85445i	−0.618260	+	0.356952i	−0.776191	−	0.630498i	$-0.782851\pi$
$269$	−10.1402	+	5.85445i	−0.618260	+	0.356952i	0.157932	+	0.987450i	$0.449517\pi$
$270$	−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
$273$	−8.27664	−	14.3003i	−0.500925	−	0.865491i
$274$	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
$279$	−7.47498	−	11.0229i	−0.447515	−	0.659922i
$280$	−3.13463	−	4.93361i	−0.187330	−	0.294840i
$281$	7.79421	−	7.79421i	0.464964	−	0.464964i	−0.435315	−	0.900278i	$-0.643363\pi$
$281$	7.79421	−	7.79421i	0.464964	−	0.464964i	0.900278	+	0.435315i	$0.143363\pi$
$282$	−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
$285$	−1.40754	+	1.16323i	−0.0833757	+	0.0689039i
$286$	1.57508	−	7.44824i	0.0931364	−	0.440424i
$287$	−5.40324	+	24.2331i	−0.318943	+	1.43043i
$288$	−0.216711	−	2.99216i	−0.0127698	−	0.176315i
$289$	−0.274811	+	0.475986i	−0.0161653	+	0.0279992i
$290$	1.03922	+	1.79999i	0.0610253	+	0.105699i
$291$	−28.1405	+	12.8667i	−1.64963	+	0.754257i
$292$	4.92022	−	4.92022i	0.287934	−	0.287934i
$293$	−4.48295	−	16.7306i	−0.261897	−	0.977412i	−0.964122	−	0.265458i	$-0.914477\pi$
$293$	−4.48295	−	16.7306i	−0.261897	−	0.977412i	0.702226	−	0.711955i	$-0.252190\pi$
$294$	5.95779	+	10.5596i	0.347465	+	0.615847i
$295$	−15.7739	+	27.3212i	−0.918391	+	1.59070i
$296$	4.54576	−	7.87349i	0.264217	−	0.457637i
$297$	10.5312	+	3.07679i	0.611081	+	0.178534i
$298$	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
$306$	−11.3094	−	5.48120i	−0.646517	−	0.313339i
$307$	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
$309$	−13.9204	−	16.8440i	−0.791902	−	0.958224i
$310$	−9.47381	+	2.53850i	−0.538076	+	0.144177i
$311$	8.67825	−	15.0312i	0.492098	−	0.852339i	−0.507860	−	0.861440i	$-0.669563\pi$
$311$	8.67825	−	15.0312i	0.492098	−	0.852339i	0.999959	+	0.00910006i	$0.00289668\pi$
$312$	−5.96023	−	1.86430i	−0.337432	−	0.105545i
$313$	−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
$315$	−2.00725	−	17.4204i	−0.113096	−	0.981526i
$316$	−3.07612	−	1.77600i	−0.173045	−	0.0999078i
$317$	−6.62944	+	24.7414i	−0.372346	+	1.38962i	0.484837	+	0.874604i	$0.338879\pi$
$317$	−6.62944	+	24.7414i	−0.372346	+	1.38962i	−0.857184	+	0.515011i	$0.827788\pi$
$318$	0.912627	−	9.60314i	0.0511776	−	0.538518i
$319$	0.514121	−	1.91873i	0.0287853	−	0.107428i
$320$	−2.13400	−	0.571804i	−0.119294	−	0.0319648i
$321$	−0.331306	+	0.889488i	−0.0184917	+	0.0496464i
$322$	−2.78111	+	12.4730i	−0.154985	+	0.695096i
$323$	−1.93094	−	0.517393i	−0.107440	−	0.0287885i
$324$	3.32991	−	8.36132i	0.184995	−	0.464518i
$325$	−0.420060	−	0.0888301i	−0.0233007	−	0.00492741i
$326$	21.9885	+	12.6951i	1.21783	+	0.703114i
$327$	−14.3062	+	6.54122i	−0.791136	+	0.361730i
$328$	4.69208	+	8.12692i	0.259077	+	0.448734i
$329$	10.8542	+	2.42017i	0.598414	+	0.133428i
$330$	4.68370	−	6.58361i	0.257829	−	0.362416i
$331$	−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
$333$	22.5736	−	15.3079i	1.23703	−	0.838869i
$334$	−6.76334			−0.370074
$335$	9.37728	+	16.2419i	0.512336	+	0.887391i
$336$	4.35833	+	1.41597i	0.237766	+	0.0772475i
$337$		−	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
$339$	4.02485	−	10.8059i	0.218600	−	0.586896i
$340$	−6.54440	+	6.54440i	−0.354920	+	0.354920i
$341$	8.11787	+	4.68686i	0.439608	+	0.253808i
$342$	0.269660	−	1.40594i	0.0145815	−	0.0760245i
$343$	−18.3705	+	2.35043i	−0.991914	+	0.126911i
$344$	−2.59204	+	0.694536i	−0.139754	+	0.0374469i
$345$	10.7144	−	15.0606i	0.576843	−	0.810834i
$346$	−6.48518	+	1.73770i	−0.348645	+	0.0934192i
$347$	13.7162	−	7.91904i	0.736323	−	0.425116i	−0.0844080	−	0.996431i	$-0.526900\pi$
$347$	13.7162	−	7.91904i	0.736323	−	0.425116i	0.820731	+	0.571315i	$0.193567\pi$
$348$	−1.52699	−	0.568757i	−0.0818555	−	0.0304886i
$349$	−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
$351$	−13.6512	−	12.8313i	−0.728650	−	0.684887i
$352$	1.05573	+	1.82857i	0.0562705	+	0.0974633i
$353$	7.76783	+	7.76783i	0.413440	+	0.413440i	0.882935	−	0.469495i	$-0.155564\pi$
$353$	7.76783	+	7.76783i	0.413440	+	0.413440i	−0.469495	+	0.882935i	$0.655564\pi$
$354$	−4.11247	−	24.3888i	−0.218575	−	1.29625i
$355$			13.6937i			0.726786i
$356$	−11.1696	−	11.1696i	−0.591985	−	0.591985i
$357$	14.2661	−	12.8460i	0.755043	−	0.679883i
$358$	−4.24635	+	1.13781i	−0.224427	+	0.0601350i
$359$	−3.14697	−	0.843227i	−0.166091	−	0.0445038i	0.174815	−	0.984601i	$-0.444067\pi$
$359$	−3.14697	−	0.843227i	−0.166091	−	0.0445038i	−0.340906	+	0.940097i	$0.610734\pi$
$360$	−5.01289	−	4.33580i	−0.264203	−	0.228517i
$361$			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
$366$	−2.91187	−	6.36851i	−0.152206	−	0.332887i
$367$	−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
$369$	2.03365	+	28.0789i	0.105868	+	1.46173i
$370$	−5.19857	−	19.4013i	−0.270261	−	1.00863i
$371$	13.0619	+	6.81981i	0.678143	+	0.354067i
$372$	4.45745	−	6.26558i	0.231108	−	0.324855i
$373$	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
$375$	−15.9615	−	11.3553i	−0.824249	−	0.586386i
$376$	3.64013	−	2.10163i	0.187726	−	0.108383i
$377$	−2.26709	+	2.52313i	−0.116761	+	0.129948i
$378$	9.91328	+	9.52507i	0.509884	+	0.489917i
$379$	−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
$381$	−6.17445	−	7.47126i	−0.316327	−	0.382764i
$382$	−1.24614	−	4.65067i	−0.0637582	−	0.237949i
$383$	17.5749	+	17.5749i	0.898038	+	0.898038i	0.995262	−	0.0972248i	$-0.0309966\pi$
$383$	17.5749	+	17.5749i	0.898038	+	0.898038i	−0.0972248	+	0.995262i	$0.530997\pi$
$384$	1.57520	−	0.720229i	0.0803843	−	0.0367540i
$385$	6.61864	+	10.4171i	0.337317	+	0.530904i
$386$	0.728336	+	0.420505i	0.0370713	+	0.0214032i
$387$	−7.90633	−	1.51644i	−0.401901	−	0.0770849i
$388$	−12.6322	−	12.6322i	−0.641305	−	0.641305i
$389$	−5.33488	+	9.24029i	−0.270489	+	0.468501i	−0.968987	−	0.247111i	$-0.920519\pi$
$389$	−5.33488	+	9.24029i	−0.270489	+	0.468501i	0.698498	+	0.715612i	$0.253852\pi$
$390$	−12.2235	+	6.39865i	−0.618959	+	0.324008i
$391$	20.2345			1.02330
$392$	−4.51253	+	5.35136i	−0.227917	+	0.270285i
$393$	1.44269	+	1.74570i	0.0727743	+	0.0880589i
$394$			14.2030i			0.715536i
$395$	−7.57997	+	2.03105i	−0.381390	+	0.102193i
$396$	0.457576	+	6.31782i	0.0229941	+	0.317482i
$397$	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
$399$	1.83400	+	1.19094i	0.0918148	+	0.0596215i
$400$	0.103127	−	0.0595401i	0.00515633	−	0.00297701i
$401$	1.90657	+	7.11542i	0.0952096	+	0.355327i	0.997051	−	0.0767398i	$-0.0244511\pi$
$401$	1.90657	+	7.11542i	0.0952096	+	0.355327i	−0.901842	+	0.432067i	$0.857784\pi$
$402$	−13.7786	−	5.13210i	−0.687215	−	0.255966i
$403$	−8.73182	−	13.4153i	−0.434963	−	0.668262i
$404$	7.05798	−	4.07493i	0.351148	−	0.202735i
$405$	−7.86005	−	18.2640i	−0.390569	−	0.907546i
$406$	1.68382	−	1.83309i	0.0835665	−	0.0909747i
$407$	−9.59816	+	16.6245i	−0.475763	+	0.824046i
$408$	0.686471	−	7.22341i	0.0339854	−	0.357612i
$409$	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
$411$	−2.77698	+	29.2208i	−0.136978	+	1.44136i
$412$	6.30805	−	10.9259i	0.310775	−	0.538279i
$413$	36.8749	+	8.22199i	1.81450	+	0.404578i
$414$	1.04675	+	14.4526i	0.0514448	+	0.710304i
$415$	19.9399	−	11.5123i	0.978812	−	0.565117i
$416$	−0.192444	−	3.60041i	−0.00943534	−	0.176525i
$417$	−0.0260800	−	0.00971396i	−0.00127714	−	0.000475695i
$418$	0.260776	+	0.973230i	0.0127550	+	0.0476022i
$419$	−13.8736	+	8.00994i	−0.677771	+	0.391311i	−0.799015	−	0.601312i	$-0.794645\pi$
$419$	−13.8736	+	8.00994i	−0.677771	+	0.391311i	0.121244	+	0.992623i	$0.461312\pi$
$420$	9.02059	−	4.59654i	0.440160	−	0.224288i
$421$	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
$423$	12.5768	−	0.910895i	0.611507	−	0.0442893i
$424$	5.37959	−	1.44146i	0.261256	−	0.0700033i
$425$		−	0.498854i		−	0.0241980i
$426$	−6.83904	−	8.27543i	−0.331353	−	0.400946i
$427$	10.6871	−	0.453598i	0.517184	−	0.0219511i
$428$	−0.548012			−0.0264892
$429$	12.5848	+	3.93639i	0.607598	+	0.190051i
$430$	−2.96428	+	5.13428i	−0.142950	+	0.247597i
$431$	22.4057	+	22.4057i	1.07924	+	1.07924i	0.996577	+	0.0826660i	$0.0263435\pi$
$431$	22.4057	+	22.4057i	1.07924	+	1.07924i	0.0826660	+	0.996577i	$0.473657\pi$
$432$	5.19484	+	0.116641i	0.249937	+	0.00561190i
$433$	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
$435$	−3.27398	+	1.49696i	−0.156975	+	0.0717736i
$436$	−6.42204	−	6.42204i	−0.307560	−	0.307560i
$437$	0.596548	+	2.22635i	0.0285368	+	0.106501i
$438$	7.67759	+	9.29010i	0.366849	+	0.443898i
$439$	−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
$441$	−19.1840	+	8.54256i	−0.913522	+	0.406788i
$442$	−13.4653	−	6.84329i	−0.640479	−	0.325502i
$443$	−27.1823	+	15.6937i	−1.29147	+	0.745631i	−0.978915	−	0.204269i	$-0.934518\pi$
$443$	−27.1823	+	15.6937i	−1.29147	+	0.745631i	−0.312555	+	0.949900i	$0.601185\pi$
$444$	12.8312	+	9.12837i	0.608943	+	0.433213i
$445$	−34.8981			−1.65433
$446$	4.18039			0.197947
$447$	−10.4431	+	14.6793i	−0.493943	+	0.694307i
$448$	0.112194	+	2.64337i	0.00530068	+	0.124888i
$449$	1.27900	+	4.77331i	0.0603600	+	0.225266i	0.989516	−	0.144420i	$-0.0461317\pi$
$449$	1.27900	+	4.77331i	0.0603600	+	0.225266i	−0.929156	+	0.369687i	$0.879465\pi$
$450$	0.356307	−	0.0258061i	0.0167965	−	0.00121651i
$451$	−9.90711	−	17.1596i	−0.466508	−	0.808015i
$452$	6.65750			0.313142
$453$	−11.0071	−	24.0734i	−0.517157	−	1.13107i
$454$			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
$459$	11.3044	−	18.6025i	0.527642	−	0.868288i
$460$	10.3075	+	2.76189i	0.480590	+	0.128774i
$461$	36.8262	−	9.86755i	1.71517	−	0.459578i	0.738485	−	0.674270i	$-0.235541\pi$
$461$	36.8262	−	9.86755i	1.71517	−	0.459578i	0.976682	+	0.214692i	$0.0688748\pi$
$462$	−9.20241	−	2.98976i	−0.428135	−	0.139096i
$463$	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	0.957289	−	0.289134i	$-0.0933673\pi$
$467$	4.93246	+	8.54326i	0.228247	+	0.395335i	−0.729042	+	0.684469i	$0.760034\pi$
$468$	4.19126	−	9.97163i	0.193741	−	0.460939i
$469$	15.1937	−	16.5406i	0.701580	−	0.763775i
$470$	2.40344	−	8.96977i	0.110863	−	0.413745i
$471$	33.9472	+	12.6442i	1.56420	+	0.582616i
$472$	12.3665	−	7.13983i	0.569216	−	0.328637i
$473$	5.47298	−	1.46648i	0.251648	−	0.0674289i
$474$	3.56639	−	5.01308i	0.163810	−	0.230258i
$475$	0.0548875	−	0.0147071i	0.00251841	−	0.000674806i
$476$	9.82509	+	5.12980i	0.450332	+	0.235124i
$477$	16.4090	+	3.14725i	0.751316	+	0.144103i
$478$	13.3086	+	7.68374i	0.608723	+	0.351446i
$479$	−11.0918	+	11.0918i	−0.506799	+	0.506799i	−0.913542	−	0.406744i	$-0.866664\pi$
$479$	−11.0918	+	11.0918i	−0.506799	+	0.506799i	0.406744	+	0.913542i	$0.366664\pi$
$480$	1.33564	−	3.58592i	0.0609634	−	0.163674i
$481$	27.4730	−	17.8818i	1.25266	−	0.815340i
$482$		−	27.2266i		−	1.24014i
$483$	−21.0513	−	6.83933i	−0.957868	−	0.311200i
$484$	3.27088	+	5.66533i	0.148676	+	0.257515i
$485$	−39.4681			−1.79215
$486$	13.8716	+	7.11184i	0.629229	+	0.322600i
$487$	−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
$489$	−25.4930	+	35.8340i	−1.15283	+	1.62047i
$490$	1.31042	+	15.4093i	0.0591986	+	0.696123i
$491$	−16.2655	−	28.1727i	−0.734053	−	1.27142i	−0.955138	−	0.296163i	$-0.904293\pi$
$491$	−16.2655	−	28.1727i	−0.734053	−	1.27142i	0.221084	−	0.975255i	$-0.429040\pi$
$492$	−14.7820	+	6.75874i	−0.666422	+	0.304708i
$493$	−3.41313	−	1.97057i	−0.153719	−	0.0887500i
$494$	0.355968	−	1.68330i	0.0160157	−	0.0757353i
$495$	10.5845	+	9.15485i	0.475738	+	0.411480i
$496$	4.28819	+	1.14902i	0.192545	+	0.0515924i
$497$	15.6460	−	4.91228i	0.701821	−	0.220346i
$498$	−6.30058	+	16.9158i	−0.282336	+	0.758014i
$499$	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
$501$	1.10828	−	11.6619i	0.0495143	−	0.521016i
$502$	4.90196	−	18.2944i	0.218785	−	0.816518i
$503$	−9.85823	−	5.69165i	−0.439557	−	0.253778i	0.263853	−	0.964563i	$-0.415007\pi$
$503$	−9.85823	−	5.69165i	−0.439557	−	0.253778i	−0.703410	+	0.710785i	$0.748340\pi$
$504$	−3.15571	+	7.28296i	−0.140567	+	0.324409i
$505$	4.66012	−	17.3918i	0.207372	−	0.773925i
$506$	−5.09931	−	8.83226i	−0.226692	−	0.392642i
$507$	−16.1124	−	15.7287i	−0.715576	−	0.698535i
$508$	2.79797	−	4.84622i	0.124140	−	0.215016i
$509$	−26.3143	+	7.05090i	−1.16636	+	0.312525i	−0.789504	−	0.613746i	$-0.789662\pi$
$509$	−26.3143	+	7.05090i	−1.16636	+	0.312525i	−0.376857	+	0.926271i	$0.622995\pi$
$510$	−10.2120	−	12.3568i	−0.452194	−	0.547168i
$511$	−17.5644	+	5.51459i	−0.777005	+	0.243951i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.38005	+	0.695355i	0.105082	+	0.0307007i
$514$	−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	−0.109655	−	0.993970i	$-0.534975\pi$
$521$	−23.4026	−	13.5115i	−1.02529	−	0.591949i	−0.915631	+	0.402021i	$0.868308\pi$
$522$	1.23092	−	2.53977i	0.0538759	−	0.111163i
$523$	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
$525$	−0.168614	+	0.518991i	−0.00735892	+	0.0226506i
$526$	−4.54426	−	16.9594i	−0.198139	−	0.739465i
$527$	13.1507	−	13.1507i	0.572853	−	0.572853i
$528$	−3.32597	+	1.52073i	−0.144744	+	0.0661813i
$529$	−0.165110	−	0.285979i	−0.00717869	−	0.0124338i
$530$	6.15214	−	10.6558i	0.267232	−	0.462859i
$531$	42.7270	−	3.09456i	1.85420	−	0.134293i
$532$	−0.274757	+	1.23226i	−0.0119122	+	0.0534254i
$533$	1.80592	+	33.7868i	0.0782232	+	1.46347i
$534$	21.0898	−	17.4291i	0.912643	−	0.754233i
$535$	−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
$540$	8.29759	−	7.93315i	0.357071	−	0.341389i
$541$	−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
$546$	11.6958	+	11.6708i	0.500534	+	0.499466i
$547$	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
$552$	−7.60845	+	3.47880i	−0.323837	+	0.148068i
$553$	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	$0.512120\pi$
$557$	−24.4821	+	24.4821i	−1.03734	+	1.03734i	−0.999275	+	0.0380657i	$0.987880\pi$
$558$	10.0732	+	8.71262i	0.426433	+	0.368834i
$559$	−9.46608	−	2.00179i	−0.400373	−	0.0846668i
$560$	4.30474	+	3.95420i	0.181908	+	0.167095i
$561$	−1.44945	+	15.2519i	−0.0611959	+	0.643936i
$562$	−5.51134	+	9.54592i	−0.232482	+	0.402670i
$563$	−15.6649	−	27.1323i	−0.660195	−	1.14349i	−0.980564	−	0.196199i	$-0.937140\pi$
$563$	−15.6649	−	27.1323i	−0.660195	−	1.14349i	0.320369	−	0.947293i	$-0.396193\pi$
$564$	3.02731	+	6.62100i	0.127473	+	0.278794i
$565$	10.4003	−	10.4003i	0.437545	−	0.437545i
$566$	1.44444	+	5.39074i	0.0607145	+	0.226590i
$567$	−18.0483	+	15.5325i	−0.757959	+	0.652302i
$568$	3.09913	−	5.36785i	0.130037	−	0.225230i
$569$	−18.1789	+	31.4868i	−0.762098	+	1.31999i	0.179669	+	0.983727i	$0.442497\pi$
$569$	−18.1789	+	31.4868i	−0.762098	+	1.31999i	−0.941767	+	0.336266i	$0.890836\pi$
$570$	1.05852	−	1.48789i	0.0443364	−	0.0623211i
$571$	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
$579$	−0.844419	+	1.18695i	−0.0350929	+	0.0493280i
$580$	−1.46968	−	1.46968i	−0.0610253	−	0.0610253i
$581$	−20.3066	−	18.6530i	−0.842461	−	0.773858i
$582$	23.8515	−	19.7116i	0.988678	−	0.817070i
$583$	−11.3588	+	3.04357i	−0.470432	+	0.126052i
$584$	−3.47912	+	6.02601i	−0.143967	+	0.249358i
$585$	−9.03007	−	22.1252i	−0.373347	−	0.914765i
$586$	8.66040	+	15.0003i	0.357758	+	0.619655i
$587$	11.4129	−	42.5935i	0.471061	−	1.75802i	−0.164909	−	0.986309i	$-0.552733\pi$
$587$	11.4129	−	42.5935i	0.471061	−	1.75802i	0.635970	−	0.771714i	$-0.280600\pi$
$588$	−8.48780	−	8.65778i	−0.350031	−	0.357041i
$589$	1.83464	+	1.05923i	0.0755950	+	0.0436448i
$590$	8.16516	−	30.4728i	0.336154	−	1.25454i
$591$	−24.4900	−	2.32738i	−1.00738	−	0.0957357i
$592$	−2.35306	+	8.78173i	−0.0967101	+	0.360927i
$593$	24.8024	+	6.64578i	1.01851	+	0.272909i	0.729182	−	0.684320i	$-0.239901\pi$
$593$	24.8024	+	6.64578i	1.01851	+	0.272909i	0.289330	+	0.957229i	$0.406568\pi$
$594$	−10.9687	−	0.246283i	−0.450050	−	0.0101051i
$595$	23.3625	−	7.33497i	0.957769	−	0.300704i
$596$	−10.0466	−	2.69197i	−0.411524	−	0.110267i
$597$	−7.88513	−	9.54123i	−0.322717	−	0.390497i
$598$	0.929530	+	17.3905i	0.0380113	+	0.711150i
$599$	0.0523660	+	0.0302335i	0.00213962	+	0.00123531i	0.501069	−	0.865407i	$-0.332940\pi$
$599$	0.0523660	+	0.0302335i	0.00213962	+	0.00123531i	−0.498930	+	0.866642i	$0.666273\pi$
$600$	0.0857650	+	0.187576i	0.00350134	+	0.00765775i
$601$	−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
$603$	11.1070	−	22.9173i	0.452313	−	0.933263i
$604$	10.8065	−	10.8065i	0.439711	−	0.439711i
$605$	13.9601	+	3.74060i	0.567560	+	0.152077i
$606$	5.86976	+	12.8377i	0.238443	+	0.521495i
$607$	−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
$609$	2.88484	+	3.20376i	0.116900	+	0.129823i
$610$		−	8.93206i		−	0.361649i
$611$	15.1335	−	0.808892i	0.612235	−	0.0327243i
$612$	12.3427	+	2.36734i	0.498924	+	0.0956940i
$613$	−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
$615$	−12.5339	+	33.6508i	−0.505414	+	1.35693i
$616$	−0.236893	−	5.58136i	−0.00954469	−	0.224879i
$617$	−35.0869	+	9.40151i	−1.41255	+	0.378491i	−0.882833	−	0.469686i	$-0.844367\pi$
$617$	−35.0869	+	9.40151i	−1.41255	+	0.378491i	−0.529713	+	0.848177i	$0.677700\pi$
$618$	17.8056	+	12.6672i	0.716246	+	0.509551i
$619$	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
$621$	−25.0918	−	0.563393i	−1.00690	−	0.0226082i
$622$	−4.49219	+	16.7651i	−0.180121	+	0.672219i
$623$	12.5188	+	39.8736i	0.501557	+	1.59750i
$624$	6.23966	+	0.258157i	0.249786	+	0.0103345i
$625$	−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
$630$	6.44757	+	16.3073i	0.256877	+	0.649697i
$631$	−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
$633$	18.4536	−	15.2505i	0.733464	−	0.606155i
$634$		−	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
$639$	15.3899	−	10.4364i	0.608814	−	0.412857i
$640$	2.20928			0.0873295
$641$	0.930813	+	1.61221i	0.0367649	+	0.0636787i	0.883822	−	0.467823i	$-0.154961\pi$
$641$	0.930813	+	1.61221i	0.0367649	+	0.0636787i	−0.847057	+	0.531501i	$0.821628\pi$
$642$	0.0898004	−	0.944927i	0.00354414	−	0.0372933i
$643$	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
$645$	−8.36721	−	5.95259i	−0.329459	−	0.234383i
$646$	1.99905			0.0786516
$647$	−1.45851			−0.0573401			−0.0286701	−	0.999589i	$-0.509127\pi$
$647$	−1.45851			−0.0573401			−0.0286701	+	0.999589i	$0.509127\pi$
$648$	−1.05238	+	8.93826i	−0.0413414	+	0.351128i
$649$	−26.1114	+	15.0754i	−1.02496	+	0.591762i
$650$	0.428738	−	0.0229163i	0.0168165	−	0.000898849i
$651$	−18.1265	+	9.23657i	−0.710434	+	0.362010i
$652$	−24.5250	−	6.57144i	−0.960471	−	0.257358i
$653$	39.0756	+	22.5603i	1.52915	+	0.882852i	0.999398	+	0.0346969i	$0.0110466\pi$
$653$	39.0756	+	22.5603i	1.52915	+	0.882852i	0.529747	+	0.848155i	$0.322287\pi$
$654$	12.1258	−	10.0211i	0.474155	−	0.391854i
$655$	0.747645	+	2.79025i	0.0292129	+	0.109024i
$656$	−6.63560	−	6.63560i	−0.259077	−	0.259077i
$657$	−17.2768	+	11.7160i	−0.674034	+	0.457085i
$658$	−11.1108	+	0.471582i	−0.433144	+	0.0183842i
$659$	6.23306	+	3.59866i	0.242805	+	0.140184i	0.616465	−	0.787382i	$-0.288564\pi$
$659$	6.23306	+	3.59866i	0.242805	+	0.140184i	−0.373660	+	0.927566i	$0.621897\pi$
$660$	−2.82014	+	7.57151i	−0.109774	+	0.294721i
$661$	−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
$663$	14.0063	−	22.0966i	0.543958	−	0.858161i
$664$	−10.4218			−0.404444
$665$	1.49581	+	2.35426i	0.0580051	+	0.0912944i
$666$	−17.8425	+	20.6288i	−0.691382	+	0.799350i
$667$			4.54409i			0.175948i
$668$	6.53289	−	1.75048i	0.252765	−	0.0677282i
$669$	−0.685022	+	7.20816i	−0.0264845	+	0.278684i
$670$	−13.2615	−	13.2615i	−0.512336	−	0.512336i
$671$	−6.03626	+	6.03626i	−0.233027	+	0.233027i
$672$	−4.57630	−	0.239704i	−0.176535	−	0.00924677i
$673$	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
$675$	−0.0138897	+	0.618603i	−0.000534613	+	0.0238100i
$676$	5.26287	−	11.8871i	0.202418	−	0.457195i
$677$	−26.6494	+	15.3860i	−1.02422	+	0.591333i	−0.915323	−	0.402721i	$-0.868065\pi$
$677$	−26.6494	+	15.3860i	−1.02422	+	0.591333i	−0.108895	+	0.994053i	$0.534731\pi$
$678$	−1.09094	+	11.4794i	−0.0418971	+	0.440864i
$679$	14.1582	+	45.0952i	0.543343	+	1.73059i
$680$	4.62759	−	8.01522i	0.177460	−	0.307370i
$681$	−19.4889	−	1.85211i	−0.746816	−	0.0709730i
$682$	−9.05431	−	2.42610i	−0.346708	−	0.0929000i
$683$	−33.6861	−	9.02617i	−1.28896	−	0.345377i	−0.451697	−	0.892171i	$-0.649181\pi$
$683$	−33.6861	−	9.02617i	−1.28896	−	0.345377i	−0.837267	+	0.546795i	$0.815848\pi$
$684$	0.103412	+	1.42783i	0.00395407	+	0.0545943i
$685$	−18.7200	+	32.4239i	−0.715253	+	1.23885i
$686$	17.1362	−	7.02498i	0.654264	−	0.268215i
$687$	3.41105	+	0.324167i	0.130140	+	0.0123677i
$688$	2.32396	−	1.34174i	0.0886002	−	0.0511534i
$689$	19.6461	+	4.15457i	0.748458	+	0.158276i
$690$	−6.45133	+	17.3205i	−0.245598	+	0.659380i
$691$	−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
$693$	6.66314	−	15.3776i	0.253112	−	0.584148i
$694$	−11.1992	+	11.1992i	−0.425116	+	0.425116i
$695$	−0.0251011	−	0.0251011i	−0.000952141	−	0.000952141i
$696$	1.62217	+	0.154161i	0.0614881	+	0.00584348i
$697$	−37.9728	+	10.1748i	−1.43832	+	0.385398i
$698$		−	30.6809i		−	1.16129i
$699$	−22.3438	+	18.4655i	−0.845121	+	0.698430i
$700$	−0.314773	+	0.0133601i	−0.0118973	+	0.000504965i
$701$	−33.7188			−1.27354			−0.636771	−	0.771053i	$-0.719730\pi$
$701$	−33.7188			−1.27354			−0.636771	+	0.771053i	$0.719730\pi$
$702$	16.5071	+	8.86092i	0.623020	+	0.334434i
$703$	−2.16918	+	3.75714i	−0.0818123	+	0.141703i
$704$	−1.49302	−	1.49302i	−0.0562705	−	0.0562705i
$705$	15.0726	+	5.61405i	0.567666	+	0.211437i
$706$	−9.51361	−	5.49269i	−0.358049	−	0.206720i
$707$	−21.5431	+	0.914366i	−0.810211	+	0.0343883i
$708$	10.2846	+	22.4934i	0.386520	+	0.845353i
$709$	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
$711$	8.05954	+	6.97094i	0.302257	+	0.261431i
$712$	13.6798	+	7.89806i	0.512674	+	0.295992i
$713$	−20.7125	−	5.54991i	−0.775690	−	0.207846i
$714$	−10.4552	+	16.1006i	−0.391277	+	0.602551i
$715$	12.5108	+	11.2412i	0.467876	+	0.420397i
$716$	3.80718	−	2.19808i	0.142281	−	0.0821459i
$717$	−15.4298	+	21.6887i	−0.576235	+	0.809981i
$718$	3.25798			0.121587
$719$	0.827456			0.0308589			0.0154294	−	0.999881i	$-0.495088\pi$
$719$	0.827456			0.0308589			0.0154294	+	0.999881i	$0.495088\pi$
$720$	5.96427	+	2.89063i	0.222275	+	0.107727i
$721$	−28.1734	+	17.9003i	−1.04923	+	0.666644i
$722$	−4.85863	−	18.1326i	−0.180819	−	0.674827i
$723$	46.9464	+	4.46151i	1.74595	+	0.165925i
$724$	−13.4387	−	23.2765i	−0.499446	−	0.865065i
$725$	0.112028			0.00416062
$726$	−10.3046	+	4.71157i	−0.382440	+	0.174863i
$727$			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
$732$	4.46094	+	5.39786i	0.164881	+	0.199511i
$733$	−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
$735$	−26.7848	−	0.265536i	−0.987972	−	0.00979446i
$736$	−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
$741$	2.84416	+	0.889624i	0.104483	+	0.0326812i
$742$	−14.3820	−	3.20675i	−0.527979	−	0.117723i
$743$	1.98573	−	7.41084i	0.0728493	−	0.271877i	−0.919888	−	0.392182i	$-0.871720\pi$
$743$	1.98573	−	7.41084i	0.0728493	−	0.271877i	0.992737	+	0.120305i	$0.0383871\pi$
$744$	−2.68392	+	7.20576i	−0.0983971	+	0.264176i
$745$	−19.9001	+	11.4893i	−0.729084	+	0.420937i
$746$	−1.36206	+	0.364962i	−0.0498685	+	0.0133622i
$747$	−28.1351	−	13.6359i	−1.02941	−	0.498911i
$748$	−8.54396	+	2.28935i	−0.312398	+	0.0837069i
$749$	1.28527	+	0.671053i	0.0469626	+	0.0245198i
$750$	18.3566	+	6.83725i	0.670289	+	0.249661i
$751$	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
$753$	30.7414	+	11.4502i	1.12028	+	0.417268i
$754$	1.53681	−	3.02392i	0.0559671	−	0.110125i
$755$		−	33.7638i		−	1.22879i
$756$	−12.0408	−	6.63476i	−0.437918	−	0.241304i
$757$	−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
$759$	16.0649	−	7.34534i	0.583119	−	0.266619i
$760$	1.01832	+	0.272858i	0.0369384	+	0.00989761i
$761$	−5.56319	+	5.56319i	−0.201665	+	0.201665i	−0.800713	−	0.599048i	$-0.795546\pi$
$761$	−5.56319	+	5.56319i	−0.201665	+	0.201665i	0.599048	+	0.800713i	$0.295546\pi$
$762$	7.89777	+	5.61862i	0.286106	+	0.203541i
$763$	7.19783	+	22.9257i	0.260579	+	0.829966i
$764$	2.40736	+	4.16967i	0.0870953	+	0.150853i
$765$	22.9800	−	15.5835i	0.830843	−	0.563422i
$766$	−21.5248	−	12.4274i	−0.777723	−	0.449019i
$767$	51.4126	−	2.74803i	1.85640	−	0.0992256i
$768$	−1.33512	+	1.10338i	−0.0481771	+	0.0398148i
$769$	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
$771$	−23.6963	−	8.82610i	−0.853400	−	0.317864i
$772$	−0.812354	−	0.217670i	−0.0292372	−	0.00783410i
$773$	7.25258	−	27.0670i	0.260857	−	0.973533i	−0.703880	−	0.710319i	$-0.748551\pi$
$773$	7.25258	−	27.0670i	0.260857	−	0.973533i	0.964737	−	0.263214i	$-0.0847825\pi$
$774$	8.02941	−	0.581541i	0.288611	−	0.0209031i
$775$	−0.136825	+	0.510638i	−0.00491490	+	0.0183427i
$776$	15.4713	+	8.93234i	0.555386	+	0.320652i
$777$	−18.9155	−	37.1211i	−0.678589	−	1.33171i
$778$	2.76154	−	10.3062i	0.0990059	−	0.369495i
$779$	−2.23901	−	3.87807i	−0.0802207	−	0.138946i
$780$	10.1509	−	9.34429i	0.363459	−	0.334579i
$781$	−6.54367	+	11.3340i	−0.234151	+	0.405561i
$782$	−19.5451	+	5.23708i	−0.698930	+	0.187278i
$783$	4.17757	+	2.53863i	0.149294	+	0.0907233i
$784$	2.97374	−	6.33695i	0.106205	−	0.226320i
$785$	32.6731	+	32.6731i	1.16615	+	1.16615i
$786$	−1.84536	−	1.31282i	−0.0658216	−	0.0468267i
$787$	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
$795$	17.3655	+	12.3541i	0.615891	+	0.438156i
$796$	3.57317	−	6.18891i	0.126648	−	0.219360i
$797$	10.0633	−	17.4302i	0.356462	−	0.617410i	−0.630905	−	0.775860i	$-0.717316\pi$
$797$	10.0633	−	17.4302i	0.356462	−	0.617410i	0.987367	+	0.158450i	$0.0506496\pi$
$798$	−2.07974	−	0.675685i	−0.0736222	−	0.0239190i
$799$	4.55740	+	17.0084i	0.161229	+	0.601715i
$800$	−0.0842024	+	0.0842024i	−0.00297701	+	0.00297701i
$801$	26.5969	+	39.2207i	0.939754	+	1.38580i
$802$	−3.68321	−	6.37951i	−0.130059	−	0.225268i
$803$	7.34601	−	12.7237i	0.259235	−	0.449008i
$804$	14.6374	+	1.39105i	0.516222	+	0.0490587i
$805$	−20.7925	−	19.0993i	−0.732838	−	0.673162i
$806$	11.9064	+	10.6982i	0.419386	+	0.376828i
$807$	12.9194	+	15.6328i	0.454784	+	0.550301i
$808$	−5.76282	+	5.76282i	−0.202735	+	0.202735i
$809$		−	14.6682i		−	0.515708i	−0.966184	−	0.257854i	$-0.916985\pi$
$809$		−	14.6682i		−	0.515708i	0.966184	−	0.257854i	$-0.0830153\pi$
$810$	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
$813$	9.69524	+	21.2043i	0.340027	+	0.743669i
$814$	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
$819$	−22.0403	+	18.2544i	−0.770152	+	0.637860i
$820$	−20.7322			−0.724001
$821$	−12.7264	+	3.41003i	−0.444155	+	0.119011i	−0.473963	−	0.880545i	$-0.657177\pi$
$821$	−12.7264	+	3.41003i	−0.444155	+	0.119011i	0.0298081	+	0.999556i	$0.490510\pi$
$822$	−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
$825$	−0.181089	−	0.396058i	−0.00630471	−	0.0137890i
$826$	−37.7464	+	1.60209i	−1.31337	+	0.0557440i
$827$	38.4155	−	38.4155i	1.33584	−	1.33584i	0.435790	−	0.900048i	$-0.356469\pi$
$827$	38.4155	−	38.4155i	1.33584	−	1.33584i	0.900048	−	0.435790i	$-0.143531\pi$
$828$	−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
$831$	−3.30337	−	3.99717i	−0.114593	−	0.138660i
$832$	1.11774	+	3.42792i	0.0387507	+	0.118842i
$833$	−16.7615	−	24.0621i	−0.580750	−	0.833702i
$834$	0.0277055	+	0.00263297i	0.000959363	+	9.11723e-5i
$835$	7.47106	−	12.9403i	0.258547	−	0.447816i
$836$	−0.503781	−	0.872574i	−0.0174236	−	0.0301786i
$837$	−16.6737	+	15.9413i	−0.576326	+	0.551013i
$838$	11.3278	−	11.3278i	0.391311	−	0.391311i
$839$	7.06393	+	26.3630i	0.243874	+	0.910151i	0.973946	+	0.226780i	$0.0728199\pi$
$839$	7.06393	+	26.3630i	0.243874	+	0.910151i	−0.730072	+	0.683370i	$0.760513\pi$
$840$	−7.52355	+	6.77462i	−0.259587	+	0.233747i
$841$	−14.0575	+	24.3482i	−0.484740	+	0.839595i
$842$	−9.97179	+	17.2716i	−0.343650	+	0.595220i
$843$	−15.5567	−	11.0674i	−0.535803	−	0.381180i
$844$	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
$852$	8.74785	+	6.22338i	0.299696	+	0.213209i
$853$	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
$855$	2.39210	+	2.06900i	0.0818079	+	0.0707581i
$856$	0.529339	−	0.141836i	0.0180924	−	0.00484785i
$857$	17.4389	−	30.2051i	0.595702	−	1.03179i	−0.397745	−	0.917496i	$-0.630207\pi$
$857$	17.4389	−	30.2051i	0.595702	−	1.03179i	0.993447	−	0.114290i	$-0.0364594\pi$
$858$	−13.1748	−	0.545086i	−0.449779	−	0.0186089i
$859$	−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
$861$	42.9447	+	2.24942i	1.46355	+	0.0766599i
$862$	−27.4412	−	15.8432i	−0.934652	−	0.539622i
$863$	9.89593	−	36.9321i	0.336861	−	1.25718i	−0.564976	−	0.825107i	$-0.691115\pi$
$863$	9.89593	−	36.9321i	0.336861	−	1.25718i	0.901837	−	0.432076i	$-0.142219\pi$
$864$	−5.04802	+	1.23186i	−0.171737	+	0.0419086i
$865$	3.83906	−	14.3276i	0.130532	−	0.487152i
$866$	−26.6016	−	7.12787i	−0.903959	−	0.242215i
$867$	0.892100	+	0.332279i	0.0302973	+	0.0112848i
$868$	−8.65019	−	7.94580i	−0.293607	−	0.269698i
$869$	−7.24433	−	1.94111i	−0.245747	−	0.0658478i
$870$	2.77498	−	2.29332i	0.0940806	−	0.0777507i
$871$	13.8671	−	27.2859i	0.469870	−	0.924548i
$872$	7.86536	+	4.54107i	0.266355	+	0.153780i
$873$	30.0798	+	44.3568i	1.01805	+	1.50125i
$874$	−1.15244	−	1.99609i	−0.0389820	−	0.0675188i
$875$	−20.2419	+	22.0363i	−0.684300	+	0.744963i
$876$	−9.82044	−	6.98644i	−0.331802	−	0.236050i
$877$	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
$879$	−27.2838	+	12.4749i	−0.920260	+	0.420769i
$880$	−4.66480			−0.157250
$881$	−14.7724	−	25.5866i	−0.497695	−	0.862034i	0.502301	−	0.864693i	$-0.332487\pi$
$881$	−14.7724	−	25.5866i	−0.497695	−	0.862034i	−0.999996	+	0.00265902i	$0.999154\pi$
$882$	16.3193	−	13.2167i	0.549500	−	0.445028i
$883$			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
$885$	51.2057	+	19.0725i	1.72126	+	0.641114i
$886$	22.1943	−	22.1943i	0.745631	−	0.745631i
$887$	−23.9110	−	13.8050i	−0.802851	−	0.463527i	0.0416158	−	0.999134i	$-0.486749\pi$
$887$	−23.9110	−	13.8050i	−0.802851	−	0.463527i	−0.844467	+	0.535607i	$0.820083\pi$
$888$	−14.7566	−	5.49636i	−0.495199	−	0.184446i
$889$	−12.4965	+	7.93979i	−0.419118	+	0.266292i
$890$	33.7090	−	9.03229i	1.12993	−	0.302763i
$891$	2.22205	−	18.8727i	0.0744415	−	0.632260i
$892$	−4.03794	+	1.08196i	−0.135200	+	0.0362268i
$893$	−1.73703	+	1.00287i	−0.0581275	+	0.0335599i
$894$	6.28801	−	16.8820i	0.210302	−	0.564619i
$895$	2.51374	−	9.38139i	0.0840249	−	0.313585i
$896$	−0.792526	−	2.52426i	−0.0264764	−	0.0843297i
$897$	−30.1384	−	1.24693i	−1.00629	−	0.0416339i
$898$	−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
$903$	−3.79973	+	11.6955i	−0.126447	+	0.389202i
$904$	−6.43065	+	1.72309i	−0.213880	+	0.0573090i
$905$	−57.3564	−	15.3686i	−1.90659	−	0.510870i
$906$	16.8627	+	20.4043i	0.560224	+	0.677887i
$907$			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	$-0.919285\pi$
$911$		−	15.1436i		−	0.501729i	0.968022	−	0.250864i	$-0.0807148\pi$
$912$	−0.751670	+	0.343685i	−0.0248903	+	0.0113806i
$913$	22.0051			0.728263
$914$	−1.02294	−	1.77178i	−0.0338358	−	0.0586053i
$915$	15.4014	+	1.46366i	0.509154	+	0.0483871i
$916$	0.512008	+	1.91084i	0.0169172	+	0.0631359i
$917$	2.91986	−	1.85517i	0.0964224	−	0.0612632i
$918$	−6.10450	+	20.8944i	−0.201479	+	0.689617i
$919$	−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
$921$	6.69159	−	9.40598i	0.220495	−	0.309938i
$922$	−33.0175	+	19.0626i	−1.08737	+	0.627795i
$923$	18.7301	−	12.1912i	0.616507	−	0.401277i
$924$	9.66265	+	0.506123i	0.317878	+	0.0166502i
$925$	−1.04573	−	0.280203i	−0.0343834	−	0.00921301i
$926$	−16.7120	−	9.64866i	−0.549189	−	0.317075i
$927$	−24.7596	+	28.6262i	−0.813212	+	0.940206i
$928$	0.243492	+	0.908723i	0.00799300	+	0.0298303i
$929$	15.7180	+	15.7180i	0.515691	+	0.515691i	0.916265	−	0.400574i	$-0.131189\pi$
$929$	15.7180	+	15.7180i	0.515691	+	0.515691i	−0.400574	+	0.916265i	$0.631189\pi$
$930$	7.06401	+	15.4496i	0.231638	+	0.506613i
$931$	2.15333	−	2.55361i	0.0705725	−	0.0836911i
$932$	−14.4933	−	8.36770i	−0.474743	−	0.274093i
$933$	−28.1716	−	10.4930i	−0.922298	−	0.343526i
$934$	−6.97555	−	6.97555i	−0.228247	−	0.228247i
$935$	−9.77094	+	16.9238i	−0.319544	+	0.553466i
$936$	−1.46760	+	10.7166i	−0.0479701	+	0.350284i
$937$	−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
$939$	−1.87164	+	1.54678i	−0.0610787	+	0.0504771i
$940$			9.28619i			0.302882i
$941$	17.9196	−	4.80156i	0.584164	−	0.156526i	0.0453793	−	0.998970i	$-0.485550\pi$
$941$	17.9196	−	4.80156i	0.584164	−	0.156526i	0.538785	+	0.842444i	$0.318884\pi$
$942$	−36.0630	−	3.42722i	−1.17500	−	0.111665i
$943$	32.0509	+	32.0509i	1.04372	+	1.04372i
$944$	−10.0972	+	10.0972i	−0.328637	+	0.328637i
$945$	−29.1749	+	8.44523i	−0.949058	+	0.274723i
$946$	−4.90694	+	2.83302i	−0.159538	+	0.0921095i
$947$	2.37156	+	8.85078i	0.0770654	+	0.287612i	0.993694	−	0.112129i	$-0.0357669\pi$
$947$	2.37156	+	8.85078i	0.0770654	+	0.287612i	−0.916628	+	0.399741i	$0.869100\pi$
$948$	−2.14739	+	5.76531i	−0.0697441	+	0.187249i
$949$	−21.0266	+	13.6859i	−0.682552	+	0.444264i
$950$	−0.0492108	+	0.0284119i	−0.00159661	+	0.000921803i
$951$	44.1661	+	4.19729i	1.43218	+	0.136106i
$952$	−10.8180	−	2.41209i	−0.350613	−	0.0781762i
$953$	17.2880	−	29.9437i	0.560013	−	0.969972i	−0.437481	−	0.899228i	$-0.644129\pi$
$953$	17.2880	−	29.9437i	0.560013	−	0.969972i	0.997495	−	0.0707440i	$-0.0225373\pi$
$954$	−16.6644	+	1.20694i	−0.539531	+	0.0390763i
$955$	10.2746	+	2.75308i	0.332479	+	0.0890875i
$956$	−14.8439	−	3.97740i	−0.480085	−	0.128638i
$957$	−3.42514	−	0.325505i	−0.110719	−	0.0105221i
$958$	7.84311	−	13.5847i	0.253399	−	0.438901i
$959$	43.7620	+	9.75761i	1.41315	+	0.315090i
$960$	−0.362025	+	3.80942i	−0.0116843	+	0.122949i
$961$	9.77847	−	5.64560i	0.315435	−	0.182116i
$962$	−21.9087	+	24.3830i	−0.706365	+	0.786141i
$963$	1.61461	+	0.309682i	0.0520299	+	0.00997938i
$964$	7.04677	+	26.2989i	0.226961	+	0.847030i
$965$	−1.60910	+	0.929014i	−0.0517987	+	0.0299060i
$966$	22.1042	+	1.15780i	0.711190	+	0.0372516i
$967$	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
$969$	−0.327576	+	3.44693i	−0.0105233	+	0.110731i
$970$	38.1233	−	10.2151i	1.22406	−	0.327987i
$971$			9.20017i			0.295248i	0.989044	+	0.147624i	$0.0471625\pi$
$971$			9.20017i			0.295248i	−0.989044	+	0.147624i	$0.952838\pi$
$972$	−15.2396	−	3.27927i	−0.488811	−	0.105183i
$973$	−0.0196754	+	0.0376843i	−0.000630766	+	0.00120810i
$974$	36.5092			1.16983
$975$	−0.0307414	+	0.743020i	−0.000984511	+	0.0237957i
$976$	−2.02149	+	3.50132i	−0.0647062	+	0.112074i
$977$	32.1789	+	32.1789i	1.02949	+	1.02949i	0.999552	+	0.0299419i	$0.00953222\pi$
$977$	32.1789	+	32.1789i	1.02949	+	1.02949i	0.0299419	+	0.999552i	$0.490468\pi$
$978$	15.3498	−	41.2111i	0.490833	−	1.31779i
$979$	−28.8844	−	16.6764i	−0.923149	−	0.532980i
$980$	−5.25400	−	14.5451i	−0.167833	−	0.464627i
$981$	15.2921	+	22.5503i	0.488240	+	0.719977i
$982$	23.0029	+	23.0029i	0.734053	+	0.734053i
$983$	−0.406277	−	1.51625i	−0.0129582	−	0.0483607i	0.959144	−	0.282918i	$-0.0913025\pi$
$983$	−0.406277	−	1.51625i	−0.0129582	−	0.0483607i	−0.972102	+	0.234558i	$0.924636\pi$
$984$	12.5290	−	10.3543i	0.399410	−	0.330083i
$985$	−27.1745	−	15.6892i	−0.865851	−	0.499899i
$986$	3.80685	+	1.02004i	0.121235	+	0.0324847i
$987$	1.00754	−	19.2354i	0.0320703	−	0.612270i
$988$	0.0918320	+	1.71808i	0.00292157	+	0.0546593i
$989$	−11.2251	+	6.48079i	−0.356936	+	0.206077i
$990$	−12.5933	−	6.10343i	−0.400241	−	0.193980i
$991$	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
$993$	6.35940	+	4.52420i	0.201810	+	0.143571i
$994$	−13.8415	+	8.79439i	−0.439026	+	0.278941i
$995$	−4.08630	−	15.2503i	−0.129545	−	0.483467i
$996$	1.70777	−	17.9701i	0.0541128	−	0.569404i
$997$	−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
$999$	−32.6461	−	34.1458i	−1.03288	−	1.08033i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.9	✓	152	1.1	even	1	trivial
546.2.bw.a.431.28	yes	152	3.2	odd	2	inner
546.2.bw.a.527.9	yes	152	273.254	even	12	inner
546.2.bw.a.527.28	yes	152	91.72	odd	12	inner
546.2.ch.a.137.5	yes	152	13.7	odd	12
546.2.ch.a.137.36	yes	152	39.20	even	12
546.2.ch.a.275.5	yes	152	21.2	odd	6
546.2.ch.a.275.36	yes	152	7.2	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.287995 - 1.70794i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.571804 - 2.13400i) q^{5} +(0.720229 + 1.57520i) q^{6} +(-2.64337 + 0.112194i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.83412 + 0.983756i) q^{9} +O(q^{10})\)	\(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} +(0.720229 + 1.57520i) 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} +(-1.10338 - 1.33512i) q^{12} +(-3.42792 + 1.11774i) q^{13} +(2.52426 - 0.792526i) q^{14} +(-3.80942 - 0.362025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.09461 - 3.62798i) q^{17} +(2.48293 - 1.68376i) q^{18} +(0.337423 - 0.337423i) q^{19} +(-0.571804 - 2.13400i) q^{20} +(0.952898 + 4.48241i) q^{21} +(-1.05573 + 1.82857i) q^{22} +(-2.41507 + 4.18302i) q^{23} +(1.41134 + 1.00405i) 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} +(-2.97998 - 2.12001i) q^{33} +(2.96223 + 2.96223i) q^{34} +(-1.27207 + 5.70511i) q^{35} +(-1.96254 + 2.26902i) q^{36} +(-8.78173 + 2.35306i) q^{37} +(-0.238594 + 0.413257i) q^{38} +(2.89626 + 5.53278i) q^{39} +(1.10464 + 1.91329i) q^{40} +(2.42880 - 9.06440i) q^{41} +(-2.08056 - 4.08305i) q^{42} +(2.32396 + 1.34174i) q^{43} +(0.546485 - 2.03951i) q^{44} +(0.478776 + 6.61053i) q^{45} +(1.25013 - 4.66555i) q^{46} +(-4.06004 - 1.08788i) q^{47} +(-1.62312 - 0.604559i) q^{48} +(6.97482 - 0.593142i) q^{49} +(-0.115023 - 0.0308202i) q^{50} +(-5.59313 + 4.62231i) q^{51} +(-2.40980 + 2.68195i) q^{52} +(-4.82321 - 2.78468i) q^{53} +(-3.59083 - 3.75579i) q^{54} +(-2.33240 - 4.03983i) q^{55} +(1.78981 - 1.94848i) q^{56} +(-0.673475 - 0.479123i) q^{57} +(-0.665231 + 0.665231i) q^{58} +(-13.7931 - 3.69585i) q^{59} +(-3.48007 + 1.59119i) q^{60} -4.04297 q^{61} +(-2.21973 - 3.84468i) q^{62} +(7.38125 - 2.91840i) q^{63} -1.00000i q^{64} +(0.425162 + 7.95432i) q^{65} +(3.42714 + 1.27650i) q^{66} +(-6.00262 + 6.00262i) q^{67} +(-3.62798 - 2.09461i) q^{68} +(7.83988 + 2.92010i) q^{69} +(-0.247868 - 5.83995i) q^{70} +(-5.98706 + 1.60423i) q^{71} +(1.30840 - 2.69964i) q^{72} +(6.72115 - 1.80093i) q^{73} +(7.87349 - 4.54576i) q^{74} +(0.0719910 - 0.193281i) q^{75} +(0.123506 - 0.460929i) q^{76} +(-3.77911 + 4.11413i) q^{77} +(-4.22956 - 4.59465i) 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} +(3.06644 + 3.40543i) q^{84} +(-8.93981 + 2.39542i) q^{85} +(-2.59204 - 0.694536i) q^{86} +(-1.03804 - 1.25606i) 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} +(6.99306 - 3.19743i) q^{93} +4.20326 q^{94} +(-0.527122 - 0.913002i) q^{95} +(1.72428 + 0.163866i) q^{96} +(-4.62372 - 17.2560i) q^{97} +(-6.58365 + 2.37815i) q^{98} +(-2.76263 + 5.70018i) 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

L-functions

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