LMFDB - Embedded newform 546.2.bw.a.431.8

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			431.8
Character	$\chi$	$=$	546.431
Dual form			546.2.bw.a.527.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.701344 + 1.58370i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.996438 + 3.71876i) q^{5} +(0.267553 - 1.71126i) q^{6} +(0.958213 + 2.46614i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.01623 - 2.22144i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.701344 + 1.58370i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.996438 + 3.71876i) q^{5} +(0.267553 - 1.71126i) q^{6} +(0.958213 + 2.46614i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.01623 - 2.22144i) q^{9} -3.84994i q^{10} +(-2.84263 + 2.84263i) q^{11} +(0.184470 + 1.72220i) q^{12} +(3.45190 + 1.04134i) q^{13} +(-1.56385 - 2.13410i) q^{14} +(-5.19056 - 4.18619i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.38444 + 4.12997i) q^{17} +(2.52248 + 1.62391i) q^{18} +(-1.21321 + 1.21321i) q^{19} +(0.996438 + 3.71876i) q^{20} +(-4.57767 - 0.212084i) q^{21} +(2.01004 - 3.48150i) q^{22} +(3.15548 - 5.46546i) q^{23} +(-0.623923 - 1.61577i) q^{24} +(-8.50614 - 4.91102i) q^{25} +(-3.60380 - 0.112441i) q^{26} +(4.93218 - 1.63512i) q^{27} +(2.06290 + 1.65663i) q^{28} +(7.51497 - 4.33877i) q^{29} +(6.09717 + 2.70013i) q^{30} +(-0.191374 - 0.714216i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.50823 - 6.49555i) q^{33} +(-3.37210 - 3.37210i) q^{34} +(-10.1258 + 1.10601i) q^{35} +(-2.85683 - 0.915707i) q^{36} +(-3.35910 + 0.900068i) q^{37} +(0.857872 - 1.48588i) q^{38} +(-4.07014 + 4.73645i) q^{39} +(-1.92497 - 3.33415i) q^{40} +(-0.359724 + 1.34251i) q^{41} +(4.47658 - 0.979929i) q^{42} +(3.59149 + 2.07355i) q^{43} +(-1.04048 + 3.88311i) q^{44} +(10.2701 - 5.28436i) q^{45} +(-1.63340 + 6.09593i) q^{46} +(-6.98738 - 1.87226i) q^{47} +(1.02086 + 1.39923i) q^{48} +(-5.16366 + 4.72617i) q^{49} +(9.48737 + 2.54213i) q^{50} +(-8.21295 + 0.879717i) q^{51} +(3.51010 - 0.824122i) q^{52} +(-4.91024 - 2.83493i) q^{53} +(-4.34092 + 2.85595i) q^{54} +(-7.73855 - 13.4036i) q^{55} +(-2.42138 - 1.06626i) q^{56} +(-1.07049 - 2.77225i) q^{57} +(-6.13595 + 6.13595i) q^{58} +(-4.89557 - 1.31176i) q^{59} +(-6.58826 - 1.03006i) q^{60} +6.70769 q^{61} +(0.369706 + 0.640349i) q^{62} +(3.54639 - 7.10092i) q^{63} -1.00000i q^{64} +(-7.31210 + 11.7991i) q^{65} +(4.10393 + 5.62504i) q^{66} +(6.85679 - 6.85679i) q^{67} +(4.12997 + 2.38444i) q^{68} +(6.44259 + 8.83051i) q^{69} +(9.49448 - 3.68906i) q^{70} +(-9.32653 + 2.49904i) q^{71} +(2.99649 + 0.145103i) q^{72} +(9.57915 - 2.56673i) q^{73} +(3.01168 - 1.73880i) q^{74} +(13.7433 - 10.0269i) q^{75} +(-0.444067 + 1.65728i) q^{76} +(-9.73417 - 4.28647i) q^{77} +(2.70557 - 5.62849i) q^{78} +(1.97302 + 3.41737i) q^{79} +(2.72232 + 2.72232i) q^{80} +(-0.869597 + 8.95789i) q^{81} -1.38987i q^{82} +(7.55428 + 7.55428i) q^{83} +(-4.07042 + 2.10516i) q^{84} +(-17.7343 + 4.75189i) q^{85} +(-4.00578 - 1.07335i) q^{86} +(1.60075 + 14.9445i) q^{87} -4.02009i q^{88} +(-2.88401 - 10.7633i) q^{89} +(-8.55242 + 7.76238i) q^{90} +(0.739564 + 9.51068i) q^{91} -6.31097i q^{92} +(1.26533 + 0.197832i) q^{93} +7.23387 q^{94} +(-3.30276 - 5.72054i) q^{95} +(-1.34822 - 1.08734i) q^{96} +(-1.13852 - 4.24901i) q^{97} +(3.76449 - 5.90158i) q^{98} +(12.0462 + 0.583326i) 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
$3$	−0.701344	+	1.58370i	−0.404921	+	0.914352i
$3$	−0.701344	+	1.58370i	−0.404921	+	0.914352i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.996438	+	3.71876i	−0.445621	+	1.66308i	0.268672	+	0.963232i	$0.413415\pi$
$5$	−0.996438	+	3.71876i	−0.445621	+	1.66308i	−0.714293	+	0.699847i	$0.753251\pi$
$6$	0.267553	−	1.71126i	0.109228	−	0.698620i
$7$	0.958213	+	2.46614i	0.362170	+	0.932112i
$7$	0.958213	+	2.46614i	0.362170	+	0.932112i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.01623	−	2.22144i	−0.672078	−	0.740480i
$10$		−	3.84994i		−	1.21746i
$11$	−2.84263	+	2.84263i	−0.857086	+	0.857086i	−0.990994	−	0.133908i	$-0.957247\pi$
$11$	−2.84263	+	2.84263i	−0.857086	+	0.857086i	0.133908	+	0.990994i	$0.457247\pi$
$12$	0.184470	+	1.72220i	0.0532520	+	0.497156i
$13$	3.45190	+	1.04134i	0.957385	+	0.288816i
$13$	3.45190	+	1.04134i	0.957385	+	0.288816i
$14$	−1.56385	−	2.13410i	−0.417955	−	0.570363i
$15$	−5.19056	−	4.18619i	−1.34020	−	1.08087i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.38444	+	4.12997i	0.578311	+	1.00166i	0.995673	+	0.0929237i	$0.0296213\pi$
$17$	2.38444	+	4.12997i	0.578311	+	1.00166i	−0.417362	+	0.908740i	$0.637045\pi$
$18$	2.52248	+	1.62391i	0.594555	+	0.382759i
$19$	−1.21321	+	1.21321i	−0.278331	+	0.278331i	−0.832442	−	0.554112i	$-0.813058\pi$
$19$	−1.21321	+	1.21321i	−0.278331	+	0.278331i	0.554112	+	0.832442i	$0.313058\pi$
$20$	0.996438	+	3.71876i	0.222810	+	0.831539i
$21$	−4.57767	−	0.212084i	−0.998928	−	0.0462806i
$22$	2.01004	−	3.48150i	0.428543	−	0.742258i
$23$	3.15548	−	5.46546i	0.657964	−	1.13963i	−0.323178	−	0.946338i	$-0.604751\pi$
$23$	3.15548	−	5.46546i	0.657964	−	1.13963i	0.981142	−	0.193289i	$-0.0619153\pi$
$24$	−0.623923	−	1.61577i	−0.127358	−	0.329818i
$25$	−8.50614	−	4.91102i	−1.70123	−	0.982205i
$26$	−3.60380	−	0.112441i	−0.706763	−	0.0220515i
$27$	4.93218	−	1.63512i	0.949198	−	0.314680i
$28$	2.06290	+	1.65663i	0.389852	+	0.313074i
$29$	7.51497	−	4.33877i	1.39550	−	0.805689i	0.401578	−	0.915825i	$-0.368462\pi$
$29$	7.51497	−	4.33877i	1.39550	−	0.805689i	0.993917	+	0.110135i	$0.0351284\pi$
$30$	6.09717	+	2.70013i	1.11319	+	0.492974i
$31$	−0.191374	−	0.714216i	−0.0343717	−	0.128277i	0.946608	−	0.322386i	$-0.104485\pi$
$31$	−0.191374	−	0.714216i	−0.0343717	−	0.128277i	−0.980980	+	0.194109i	$0.937818\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−2.50823	−	6.49555i	−0.436626	−	1.13073i
$34$	−3.37210	−	3.37210i	−0.578311	−	0.578311i
$35$	−10.1258	+	1.10601i	−1.71157	+	0.186949i
$36$	−2.85683	−	0.915707i	−0.476138	−	0.152618i
$37$	−3.35910	+	0.900068i	−0.552232	+	0.147970i	−0.524135	−	0.851635i	$-0.675611\pi$
$37$	−3.35910	+	0.900068i	−0.552232	+	0.147970i	−0.0280970	+	0.999605i	$0.508945\pi$
$38$	0.857872	−	1.48588i	0.139165	−	0.241041i
$39$	−4.07014	+	4.73645i	−0.651744	+	0.758439i
$40$	−1.92497	−	3.33415i	−0.304365	−	0.527175i
$41$	−0.359724	+	1.34251i	−0.0561795	+	0.209665i	−0.988310	−	0.152458i	$-0.951281\pi$
$41$	−0.359724	+	1.34251i	−0.0561795	+	0.209665i	0.932130	+	0.362123i	$0.117948\pi$
$42$	4.47658	−	0.979929i	0.690751	−	0.151206i
$43$	3.59149	+	2.07355i	0.547696	+	0.316213i	0.748192	−	0.663482i	$-0.230922\pi$
$43$	3.59149	+	2.07355i	0.547696	+	0.316213i	−0.200496	+	0.979695i	$0.564255\pi$
$44$	−1.04048	+	3.88311i	−0.156858	+	0.585401i
$45$	10.2701	−	5.28436i	1.53097	−	0.787746i
$46$	−1.63340	+	6.09593i	−0.240831	+	0.898795i
$47$	−6.98738	−	1.87226i	−1.01921	−	0.273098i	−0.289740	−	0.957105i	$-0.593569\pi$
$47$	−6.98738	−	1.87226i	−1.01921	−	0.273098i	−0.729475	+	0.684008i	$0.760235\pi$
$48$	1.02086	+	1.39923i	0.147348	+	0.201962i
$49$	−5.16366	+	4.72617i	−0.737665	+	0.675167i
$50$	9.48737	+	2.54213i	1.34172	+	0.359512i
$51$	−8.21295	+	0.879717i	−1.15004	+	0.123185i
$52$	3.51010	−	0.824122i	0.486764	−	0.114285i
$53$	−4.91024	−	2.83493i	−0.674473	−	0.389407i	0.123296	−	0.992370i	$-0.460653\pi$
$53$	−4.91024	−	2.83493i	−0.674473	−	0.389407i	−0.797769	+	0.602963i	$0.793987\pi$
$54$	−4.34092	+	2.85595i	−0.590724	+	0.388646i
$55$	−7.73855	−	13.4036i	−1.04347	−	1.80734i
$56$	−2.42138	−	1.06626i	−0.323571	−	0.142485i
$57$	−1.07049	−	2.77225i	−0.141790	−	0.367194i
$58$	−6.13595	+	6.13595i	−0.805689	+	0.805689i
$59$	−4.89557	−	1.31176i	−0.637349	−	0.170777i	−0.0743468	−	0.997232i	$-0.523687\pi$
$59$	−4.89557	−	1.31176i	−0.637349	−	0.170777i	−0.563002	+	0.826455i	$0.690354\pi$
$60$	−6.58826	−	1.03006i	−0.850540	−	0.132981i
$61$	6.70769			0.858832			0.429416	−	0.903107i	$-0.358719\pi$
$61$	6.70769			0.858832			0.429416	+	0.903107i	$0.358719\pi$
$62$	0.369706	+	0.640349i	0.0469526	+	0.0813244i
$63$	3.54639	−	7.10092i	0.446804	−	0.894632i
$64$		−	1.00000i		−	0.125000i
$65$	−7.31210	+	11.7991i	−0.906954	+	1.46350i
$66$	4.10393	+	5.62504i	0.505159	+	0.692395i
$67$	6.85679	−	6.85679i	0.837690	−	0.837690i	−0.150864	−	0.988554i	$-0.548206\pi$
$67$	6.85679	−	6.85679i	0.837690	−	0.837690i	0.988554	+	0.150864i	$0.0482057\pi$
$68$	4.12997	+	2.38444i	0.500832	+	0.289155i
$69$	6.44259	+	8.83051i	0.775596	+	1.06307i
$70$	9.49448	−	3.68906i	1.13481	−	0.440927i
$71$	−9.32653	+	2.49904i	−1.10686	+	0.296581i	−0.765553	−	0.643373i	$-0.777535\pi$
$71$	−9.32653	+	2.49904i	−1.10686	+	0.296581i	−0.341302	+	0.939954i	$0.610868\pi$
$72$	2.99649	+	0.145103i	0.353140	+	0.0171005i
$73$	9.57915	−	2.56673i	1.12115	−	0.300413i	0.349804	−	0.936823i	$-0.386248\pi$
$73$	9.57915	−	2.56673i	1.12115	−	0.300413i	0.771351	+	0.636410i	$0.219581\pi$
$74$	3.01168	−	1.73880i	0.350101	−	0.202131i
$75$	13.7433	−	10.0269i	1.58694	−	1.15781i
$76$	−0.444067	+	1.65728i	−0.0509380	+	0.190103i
$77$	−9.73417	−	4.28647i	−1.10931	−	0.488489i
$78$	2.70557	−	5.62849i	0.306346	−	0.637301i
$79$	1.97302	+	3.41737i	0.221982	+	0.384485i	0.955410	−	0.295283i	$-0.0954140\pi$
$79$	1.97302	+	3.41737i	0.221982	+	0.384485i	−0.733428	+	0.679768i	$0.762081\pi$
$80$	2.72232	+	2.72232i	0.304365	+	0.304365i
$81$	−0.869597	+	8.95789i	−0.0966219	+	0.995321i
$82$		−	1.38987i		−	0.153485i
$83$	7.55428	+	7.55428i	0.829190	+	0.829190i	0.987405	−	0.158215i	$-0.0505738\pi$
$83$	7.55428	+	7.55428i	0.829190	+	0.829190i	−0.158215	+	0.987405i	$0.550574\pi$
$84$	−4.07042	+	2.10516i	−0.444119	+	0.229692i
$85$	−17.7343	+	4.75189i	−1.92355	+	0.515415i
$86$	−4.00578	−	1.07335i	−0.431955	−	0.115742i
$87$	1.60075	+	14.9445i	0.171618	+	1.60221i
$88$		−	4.02009i		−	0.428543i
$89$	−2.88401	−	10.7633i	−0.305705	−	1.14091i	−0.932337	−	0.361591i	$-0.882234\pi$
$89$	−2.88401	−	10.7633i	−0.305705	−	1.14091i	0.626632	−	0.779315i	$-0.284433\pi$
$90$	−8.55242	+	7.76238i	−0.901504	+	0.818227i
$91$	0.739564	+	9.51068i	0.0775273	+	0.996990i
$92$		−	6.31097i		−	0.657964i
$93$	1.26533	+	0.197832i	0.131208	+	0.0205142i
$94$	7.23387			0.746117
$95$	−3.30276	−	5.72054i	−0.338856	−	0.586915i
$96$	−1.34822	−	1.08734i	−0.137602	−	0.110976i
$97$	−1.13852	−	4.24901i	−0.115599	−	0.431422i	0.883732	−	0.467993i	$-0.155023\pi$
$97$	−1.13852	−	4.24901i	−0.115599	−	0.431422i	−0.999331	+	0.0365717i	$0.988356\pi$
$98$	3.76449	−	5.90158i	0.380271	−	0.596149i
$99$	12.0462	+	0.583326i	1.21068	+	0.0586265i
$100$	−9.82205			−0.982205
$101$	18.1691			1.80789			0.903944	−	0.427650i	$-0.140658\pi$
$101$	18.1691			1.80789			0.903944	+	0.427650i	$0.140658\pi$
$102$	7.70541	−	2.97541i	0.762950	−	0.294609i
$103$	−5.23236	+	3.02090i	−0.515559	+	0.297658i	−0.735116	−	0.677941i	$-0.762872\pi$
$103$	−5.23236	+	3.02090i	−0.515559	+	0.297658i	0.219556	+	0.975600i	$0.429539\pi$
$104$	−3.17720	+	1.70452i	−0.311550	+	0.167142i
$105$	5.35005	−	16.8119i	0.522111	−	1.64067i
$106$	5.47666	+	1.46747i	0.531940	+	0.142533i
$107$	−2.61329	−	1.50878i	−0.252636	−	0.145859i	0.368335	−	0.929693i	$-0.379928\pi$
$107$	−2.61329	−	1.50878i	−0.252636	−	0.145859i	−0.620971	+	0.783834i	$0.713261\pi$
$108$	3.45383	−	3.88215i	0.332345	−	0.373560i
$109$	3.88505	+	14.4992i	0.372120	+	1.38877i	0.857507	+	0.514473i	$0.172012\pi$
$109$	3.88505	+	14.4992i	0.372120	+	1.38877i	−0.485386	+	0.874300i	$0.661321\pi$
$110$	10.9440	+	10.9440i	1.04347	+	1.04347i
$111$	0.930441	−	5.95107i	0.0883136	−	0.564851i
$112$	2.61484	+	0.403232i	0.247079	+	0.0381018i
$113$	8.30792	+	4.79658i	0.781544	+	0.451224i	0.836977	−	0.547238i	$-0.184321\pi$
$113$	8.30792	+	4.79658i	0.781544	+	0.451224i	−0.0554335	+	0.998462i	$0.517654\pi$
$114$	1.75153	+	2.40073i	0.164046	+	0.224849i
$115$	17.1805	+	17.1805i	1.60209	+	1.60209i
$116$	4.33877	−	7.51497i	0.402845	−	0.697748i
$117$	−4.64656	−	9.76778i	−0.429575	−	0.903031i
$118$	5.06827			0.466572
$119$	−7.90026	+	9.83773i	−0.724216	+	0.901823i
$120$	6.63037	−	0.710201i	0.605267	−	0.0648321i
$121$		−	5.16112i		−	0.469193i
$122$	−6.47913	+	1.73608i	−0.586593	+	0.157177i
$123$	−1.87385	−	1.51126i	−0.168959	−	0.136265i
$124$	−0.522843	−	0.522843i	−0.0469526	−	0.0469526i
$125$	13.1271	−	13.1271i	1.17413	−	1.17413i
$126$	−1.58770	+	7.77684i	−0.141444	+	0.692816i
$127$	−14.7759	+	8.53085i	−1.31115	+	0.756991i	−0.982286	−	0.187388i	$-0.939998\pi$
$127$	−14.7759	+	8.53085i	−1.31115	+	0.756991i	−0.328860	+	0.944379i	$0.606664\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−5.80275	+	4.23358i	−0.510903	+	0.372746i
$130$	4.00910	−	13.2896i	0.351622	−	1.16558i
$131$	−4.76748	+	2.75250i	−0.416536	+	0.240487i	−0.693594	−	0.720366i	$-0.743974\pi$
$131$	−4.76748	+	2.75250i	−0.416536	+	0.240487i	0.277058	+	0.960853i	$0.410641\pi$
$132$	−5.41996	−	4.37120i	−0.471747	−	0.380464i
$133$	−4.15447	−	1.82944i	−0.360238	−	0.158632i
$134$	−4.84848	+	8.39782i	−0.418845	+	0.725461i
$135$	1.16602	+	19.9709i	0.100355	+	1.71882i
$136$	−4.60638	−	1.23428i	−0.394994	−	0.105838i
$137$	9.77639	+	2.61958i	0.835254	+	0.223806i	0.651004	−	0.759074i	$-0.274348\pi$
$137$	9.77639	+	2.61958i	0.835254	+	0.223806i	0.184249	+	0.982880i	$0.441015\pi$
$138$	−8.50857	−	6.86216i	−0.724297	−	0.584146i
$139$	−3.51840	+	6.09405i	−0.298427	+	0.516890i	−0.975776	−	0.218771i	$-0.929795\pi$
$139$	−3.51840	+	6.09405i	−0.298427	+	0.516890i	0.677349	+	0.735661i	$0.263129\pi$
$140$	−8.21616	+	6.02071i	−0.694393	+	0.508843i
$141$	7.86567	−	9.75284i	0.662409	−	0.821338i
$142$	8.36194	−	4.82777i	0.701718	−	0.405137i
$143$	−12.7726	+	6.85233i	−1.06810	+	0.573021i
$144$	−2.93194	+	0.635390i	−0.244328	+	0.0529492i
$145$	8.64663	+	32.2697i	0.718064	+	2.67985i
$146$	−8.58843	+	4.95853i	−0.710784	+	0.410371i
$147$	−3.86335	−	11.4924i	−0.318644	−	0.947875i
$148$	−2.45903	+	2.45903i	−0.202131	+	0.202131i
$149$	13.4725	+	13.4725i	1.10371	+	1.10371i	0.993959	+	0.109752i	$0.0350055\pi$
$149$	13.4725	+	13.4725i	1.10371	+	1.10371i	0.109752	+	0.993959i	$0.464994\pi$
$150$	−10.6799	+	13.2423i	−0.872009	+	1.08123i
$151$	6.30222	−	1.68868i	0.512868	−	0.137422i	0.00690207	−	0.999976i	$-0.497803\pi$
$151$	6.30222	−	1.68868i	0.512868	−	0.137422i	0.505965	+	0.862554i	$0.331136\pi$
$152$		−	1.71574i		−	0.139165i
$153$	4.36689	−	13.6239i	0.353042	−	1.10142i
$154$	10.5119	+	1.62103i	0.847073	+	0.130626i
$155$	2.84669			0.228652
$156$	−1.15662	+	6.13696i	−0.0926040	+	0.491350i
$157$	6.02174	−	10.4300i	0.480588	−	0.832402i	−0.519164	−	0.854674i	$-0.673757\pi$
$157$	6.02174	−	10.4300i	0.480588	−	0.832402i	0.999752	+	0.0222723i	$0.00709009\pi$
$158$	−2.79027	−	2.79027i	−0.221982	−	0.221982i
$159$	7.93345	−	5.78810i	0.629163	−	0.459026i
$160$	−3.33415	−	1.92497i	−0.263587	−	0.152182i
$161$	16.5022	+	2.54478i	1.30055	+	0.200557i
$162$	−1.47851	−	8.87773i	−0.116162	−	0.697500i
$163$	6.60665	+	6.60665i	0.517473	+	0.517473i	0.916806	−	0.399333i	$-0.130758\pi$
$163$	6.60665	+	6.60665i	0.517473	+	0.517473i	−0.399333	+	0.916806i	$0.630758\pi$
$164$	0.359724	+	1.34251i	0.0280898	+	0.104832i
$165$	26.6547	−	2.85507i	2.07506	−	0.222267i
$166$	−9.25207	−	5.34168i	−0.718100	−	0.414595i
$167$	−1.42509	−	0.381851i	−0.110277	−	0.0295485i	0.203259	−	0.979125i	$-0.434847\pi$
$167$	−1.42509	−	0.381851i	−0.110277	−	0.0295485i	−0.313535	+	0.949577i	$0.601513\pi$
$168$	3.38686	−	3.08693i	0.261302	−	0.238162i
$169$	10.8312	+	7.18921i	0.833171	+	0.553016i
$170$	15.9001	−	9.17994i	1.21948	−	0.704069i
$171$	5.14121	+	0.248959i	0.393158	+	0.0190384i
$172$	4.14709			0.316213
$173$	−3.05789			−0.232487			−0.116243	−	0.993221i	$-0.537085\pi$
$173$	−3.05789			−0.232487			−0.116243	+	0.993221i	$0.537085\pi$
$174$	−5.41412	−	14.0209i	−0.410443	−	1.06292i
$175$	3.96056	−	25.6831i	0.299390	−	1.94146i
$176$	1.04048	+	3.88311i	0.0784288	+	0.292700i
$177$	5.51092	−	6.83314i	0.414226	−	0.513610i
$178$	5.57149	+	9.65010i	0.417601	+	0.723305i
$179$	−22.1067			−1.65233			−0.826164	−	0.563429i	$-0.809482\pi$
$179$	−22.1067			−1.65233			−0.826164	+	0.563429i	$0.809482\pi$
$180$	6.25195	−	9.71141i	0.465993	−	0.723846i
$181$		−	8.17207i		−	0.607426i	−0.952764	−	0.303713i	$-0.901774\pi$
$181$		−	8.17207i		−	0.607426i	0.952764	−	0.303713i	$-0.0982263\pi$
$182$	−3.17591	−	8.99520i	−0.235414	−	0.666768i
$183$	−4.70440	+	10.6230i	−0.347759	+	0.785274i
$184$	1.63340	+	6.09593i	0.120416	+	0.449398i
$185$		−	13.3885i		−	0.984344i
$186$	−1.27341	+	0.136400i	−0.0933712	+	0.0100013i
$187$	−18.5181	−	4.96190i	−1.35417	−	0.362850i
$188$	−6.98738	+	1.87226i	−0.509607	+	0.136549i
$189$	8.75851	+	10.5966i	0.637088	+	0.770791i
$190$	4.67080	+	4.67080i	0.338856	+	0.338856i
$191$			1.35317i			0.0979122i	0.998801	+	0.0489561i	$0.0155894\pi$
$191$			1.35317i			0.0979122i	−0.998801	+	0.0489561i	$0.984411\pi$
$192$	1.58370	+	0.701344i	0.114294	+	0.0506151i
$193$	−16.9546	−	16.9546i	−1.22042	−	1.22042i	−0.967483	−	0.252934i	$-0.918604\pi$
$193$	−16.9546	−	16.9546i	−1.22042	−	1.22042i	−0.252934	−	0.967483i	$-0.581396\pi$
$194$	2.19945	+	3.80956i	0.157911	+	0.273510i
$195$	−13.5581	−	19.8555i	−0.970912	−	1.42188i
$196$	−2.10878	+	6.67481i	−0.150627	+	0.476772i
$197$	2.18679	−	8.16122i	0.155803	−	0.581463i	−0.843233	−	0.537549i	$-0.819350\pi$
$197$	2.18679	−	8.16122i	0.155803	−	0.581463i	0.999035	−	0.0439145i	$-0.0139829\pi$
$198$	−11.7867	+	2.55432i	−0.837642	+	0.181528i
$199$	−2.84037	+	1.63989i	−0.201348	+	0.116249i	−0.597284	−	0.802030i	$-0.703754\pi$
$199$	−2.84037	+	1.63989i	−0.201348	+	0.116249i	0.395936	+	0.918278i	$0.370420\pi$
$200$	9.48737	−	2.54213i	0.670858	−	0.179756i
$201$	6.05016	+	15.6681i	0.426745	+	1.10514i
$202$	−17.5500	+	4.70250i	−1.23481	+	0.330867i
$203$	17.9009	+	14.3755i	1.25640	+	1.00896i
$204$	−6.67277	+	4.86833i	−0.467187	+	0.340851i
$205$	−4.63402	−	2.67546i	−0.323654	−	0.186862i
$206$	4.27220	−	4.27220i	0.297658	−	0.297658i
$207$	−18.5034	+	4.00992i	−1.28607	+	0.278709i
$208$	2.62778	−	2.46876i	0.182204	−	0.171178i
$209$		−	6.89745i		−	0.477106i
$210$	−0.816512	+	17.6237i	−0.0563447	+	1.21615i
$211$	2.78527	+	4.82423i	0.191746	+	0.332113i	0.945829	−	0.324666i	$-0.105252\pi$
$211$	2.78527	+	4.82423i	0.191746	+	0.332113i	−0.754083	+	0.656779i	$0.771918\pi$
$212$	−5.66985			−0.389407
$213$	2.58337	−	16.5231i	0.177009	−	1.13215i
$214$	2.91474	+	0.781003i	0.199248	+	0.0533882i
$215$	−11.2897	+	11.2897i	−0.769951	+	0.769951i
$216$	−2.33137	+	4.64378i	−0.158629	+	0.315969i
$217$	1.57798	−	1.15632i	0.107120	−	0.0784964i
$218$	−7.50534	−	12.9996i	−0.508326	−	0.880447i
$219$	−2.65334	+	16.9707i	−0.179296	+	1.14677i
$220$	−13.4036	−	7.73855i	−0.903668	−	0.521733i
$221$	3.93013	+	16.7392i	0.264369	+	1.12600i
$222$	0.641513	+	5.98911i	0.0430556	+	0.401963i
$223$	−16.0081	−	4.28935i	−1.07198	−	0.287236i	−0.320674	−	0.947190i	$-0.603909\pi$
$223$	−16.0081	−	4.28935i	−1.07198	−	0.287236i	−0.751307	+	0.659953i	$0.770576\pi$
$224$	−2.63011	+	0.287279i	−0.175732	+	0.0191946i
$225$	6.24083	+	28.7977i	0.416055	+	1.91984i
$226$	−9.26628	−	2.48289i	−0.616384	−	0.165160i
$227$	5.98213	−	22.3256i	0.397048	−	1.48180i	−0.421217	−	0.906960i	$-0.638397\pi$
$227$	5.98213	−	22.3256i	0.397048	−	1.48180i	0.818264	−	0.574842i	$-0.194937\pi$
$228$	−2.31320	−	1.86560i	−0.153195	−	0.123552i
$229$	−2.65046	+	9.89167i	−0.175148	+	0.653660i	0.821379	+	0.570383i	$0.193205\pi$
$229$	−2.65046	+	9.89167i	−0.175148	+	0.653660i	−0.996526	+	0.0832768i	$0.973461\pi$
$230$	−21.0417	−	12.1484i	−1.38745	−	0.801043i
$231$	13.6155	−	12.4097i	0.895834	−	0.816501i
$232$	−2.24591	+	8.38186i	−0.147451	+	0.550296i
$233$	−3.27880	−	5.67905i	−0.214801	−	0.372047i	0.738410	−	0.674352i	$-0.235577\pi$
$233$	−3.27880	−	5.67905i	−0.214801	−	0.372047i	−0.953211	+	0.302305i	$0.902244\pi$
$234$	7.01632	+	8.23233i	0.458671	+	0.538164i
$235$	13.9250	−	24.1188i	0.908366	−	1.57334i
$236$	−4.89557	+	1.31176i	−0.318675	+	0.0853886i
$237$	−6.79587	+	0.727928i	−0.441439	+	0.0472840i
$238$	5.08487	−	11.5473i	0.329603	−	0.748498i
$239$	−13.1617	−	13.1617i	−0.851359	−	0.851359i	0.138942	−	0.990301i	$-0.455630\pi$
$239$	−13.1617	−	13.1617i	−0.851359	−	0.851359i	−0.990301	+	0.138942i	$0.955630\pi$
$240$	−6.22063	+	2.40207i	−0.401540	+	0.155053i
$241$	−3.42723	+	12.7906i	−0.220767	+	0.823914i	0.763289	+	0.646057i	$0.223583\pi$
$241$	−3.42723	+	12.7906i	−0.220767	+	0.823914i	−0.984056	+	0.177857i	$0.943084\pi$
$242$	1.33580	+	4.98526i	0.0858683	+	0.320465i
$243$	−13.5768	−	7.65974i	−0.870949	−	0.491373i
$244$	5.80903	−	3.35385i	0.371885	−	0.214708i
$245$	−12.4302	−	23.9117i	−0.794136	−	1.52766i
$246$	2.20114	+	0.974775i	0.140340	+	0.0621494i
$247$	−5.45126	+	2.92452i	−0.346856	+	0.186083i
$248$	0.640349	+	0.369706i	0.0406622	+	0.0234763i
$249$	−17.2619	+	6.66560i	−1.09393	+	0.422415i
$250$	−9.28230	+	16.0774i	−0.587064	+	1.01682i
$251$	−9.38960	+	16.2633i	−0.592666	+	1.02653i	0.401206	+	0.915988i	$0.368591\pi$
$251$	−9.38960	+	16.2633i	−0.592666	+	1.02653i	−0.993872	+	0.110540i	$0.964742\pi$
$252$	−0.479193	−	7.92278i	−0.0301863	−	0.499088i
$253$	6.56641	+	24.5062i	0.412827	+	1.54069i
$254$	12.0644	−	12.0644i	0.756991	−	0.756991i
$255$	4.91225	−	31.4186i	0.307617	−	1.96751i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.74038	+	15.1388i	−0.545210	+	0.944331i	0.453384	+	0.891315i	$0.350217\pi$
$257$	−8.74038	+	15.1388i	−0.545210	+	0.944331i	−0.998594	+	0.0530159i	$0.983117\pi$
$258$	4.50929	−	5.59119i	0.280736	−	0.348092i
$259$	−5.43842	−	7.42154i	−0.337927	−	0.461152i
$260$	−0.432891	+	13.8744i	−0.0268468	+	0.860454i
$261$	−24.7903	−	7.94608i	−1.53448	−	0.491850i
$262$	3.89263	−	3.89263i	0.240487	−	0.240487i
$263$		−	10.5963i		−	0.653395i	−0.945129	−	0.326698i	$-0.894064\pi$
$263$		−	10.5963i		−	0.653395i	0.945129	−	0.326698i	$-0.105936\pi$
$264$	6.36663	+	2.81946i	0.391839	+	0.173526i
$265$	15.4352	−	15.4352i	0.948174	−	0.948174i
$266$	4.48640	+	0.691843i	0.275079	+	0.0424196i
$267$	19.0685	+	2.98134i	1.16698	+	0.182455i
$268$	2.50976	−	9.36655i	0.153308	−	0.572153i
$269$	1.00283	−	0.578986i	0.0611438	−	0.0353014i	−0.469116	−	0.883136i	$-0.655428\pi$
$269$	1.00283	−	0.578986i	0.0611438	−	0.0353014i	0.530260	+	0.847835i	$0.322094\pi$
$270$	−6.29513	−	18.9886i	−0.383110	−	1.15561i
$271$	−0.518337	+	0.138888i	−0.0314867	+	0.00843684i	−0.274528	−	0.961579i	$-0.588522\pi$
$271$	−0.518337	+	0.138888i	−0.0314867	+	0.00843684i	0.243041	+	0.970016i	$0.421855\pi$
$272$	4.76887			0.289155
$273$	−15.5808	−	5.49900i	−0.942992	−	0.332815i
$274$	−10.1213			−0.611448
$275$	38.1401	−	10.2196i	2.29993	−	0.616265i
$276$	9.99470	+	4.42616i	0.601610	+	0.266423i
$277$	−15.3811	+	8.88027i	−0.924159	+	0.533564i	−0.884960	−	0.465668i	$-0.845814\pi$
$277$	−15.3811	+	8.88027i	−0.924159	+	0.533564i	−0.0391996	+	0.999231i	$0.512481\pi$
$278$	1.82126	−	6.79703i	0.109232	−	0.407658i
$279$	−1.20073	+	1.86515i	−0.0718861	+	0.111664i
$280$	6.37793	−	7.94206i	0.381154	−	0.474629i
$281$	8.89317	−	8.89317i	0.530522	−	0.530522i	−0.390206	−	0.920728i	$-0.627596\pi$
$281$	8.89317	−	8.89317i	0.530522	−	0.530522i	0.920728	+	0.390206i	$0.127596\pi$
$282$	−5.07343	+	11.4563i	−0.302118	+	0.682213i
$283$			17.8969i			1.06386i	0.846788	+	0.531930i	$0.178533\pi$
$283$			17.8969i			1.06386i	−0.846788	+	0.531930i	$0.821467\pi$
$284$	−6.82749	+	6.82749i	−0.405137	+	0.405137i
$285$	11.3760	−	1.21852i	0.673857	−	0.0721791i
$286$	10.5639	−	9.92464i	0.624657	−	0.586857i
$287$	−3.65550	+	0.399280i	−0.215778	+	0.0235688i
$288$	2.66759	−	1.37258i	0.157189	−	0.0808802i
$289$	−2.87108	+	4.97286i	−0.168887	+	0.292521i
$290$	−16.7040	−	28.9322i	−0.980893	−	1.69896i
$291$	7.52767	+	1.17694i	0.441280	+	0.0689934i
$292$	7.01242	−	7.01242i	0.410371	−	0.410371i
$293$	6.18403	+	23.0791i	0.361275	+	1.34830i	0.872401	+	0.488791i	$0.162562\pi$
$293$	6.18403	+	23.0791i	0.361275	+	1.34830i	−0.511126	+	0.859506i	$0.670772\pi$
$294$	6.70615	+	10.1009i	0.391111	+	0.589095i
$295$	9.75627	−	16.8984i	0.568032	−	0.983860i
$296$	1.73880	−	3.01168i	0.101066	−	0.175051i
$297$	−9.37231	+	18.6684i	−0.543836	+	1.08325i
$298$	−16.5004	−	9.52650i	−0.955841	−	0.551855i
$299$	16.5838	−	15.5803i	0.959067	−	0.901031i
$300$	6.88863	−	15.5552i	0.397715	−	0.898080i
$301$	−1.67224	+	10.8440i	−0.0963862	+	0.625037i
$302$	−5.65042	+	3.26227i	−0.325145	+	0.187723i
$303$	−12.7428	+	28.7744i	−0.732052	+	1.65305i
$304$	0.444067	+	1.65728i	0.0254690	+	0.0950516i
$305$	−6.68380	+	24.9443i	−0.382713	+	1.42831i
$306$	−0.691976	+	14.2899i	−0.0395577	+	0.816898i
$307$	−1.18591	−	1.18591i	−0.0676832	−	0.0676832i	0.672455	−	0.740138i	$-0.265240\pi$
$307$	−1.18591	−	1.18591i	−0.0676832	−	0.0676832i	−0.740138	+	0.672455i	$0.765240\pi$
$308$	−10.5733	+	1.15489i	−0.602468	+	0.0658059i
$309$	−1.11453	−	10.4052i	−0.0634037	−	0.591931i
$310$	−2.74969	+	0.736777i	−0.156172	+	0.0418461i
$311$	−2.52872	+	4.37988i	−0.143391	+	0.248360i	−0.928771	−	0.370653i	$-0.879134\pi$
$311$	−2.52872	+	4.37988i	−0.143391	+	0.248360i	0.785381	+	0.619013i	$0.212467\pi$
$312$	−0.471148	−	6.22720i	−0.0266735	−	0.352546i
$313$	−8.23916	−	14.2706i	−0.465705	−	0.806624i	0.533528	−	0.845782i	$-0.320866\pi$
$313$	−8.23916	−	14.2706i	−0.465705	−	0.806624i	−0.999233	+	0.0391578i	$0.987532\pi$
$314$	−3.11708	+	11.6331i	−0.175907	+	0.656495i
$315$	22.8728	+	20.2638i	1.28874	+	1.14174i
$316$	3.41737	+	1.97302i	0.192242	+	0.110991i
$317$	5.40345	−	20.1659i	0.303488	−	1.13263i	−0.630751	−	0.775985i	$-0.717253\pi$
$317$	5.40345	−	20.1659i	0.303488	−	1.13263i	0.934239	−	0.356647i	$-0.116080\pi$
$318$	−6.16505	+	7.64421i	−0.345719	+	0.428666i
$319$	−9.02877	+	33.6958i	−0.505514	+	1.88660i
$320$	3.71876	+	0.996438i	0.207885	+	0.0557026i
$321$	4.22227	−	3.08050i	0.235664	−	0.171937i
$322$	−16.5985	+	1.81301i	−0.925000	+	0.101035i
$323$	−7.90337	−	2.11770i	−0.439755	−	0.117832i
$324$	3.72585	+	8.19256i	0.206992	+	0.455142i
$325$	−24.2483	−	25.8102i	−1.34505	−	1.43169i
$326$	−8.09146	−	4.67161i	−0.448145	−	0.258736i
$327$	−25.6872	−	4.01616i	−1.42051	−	0.222094i
$328$	−0.694934	−	1.20366i	−0.0383713	−	0.0664611i
$329$	−2.07814	−	19.0259i	−0.114572	−	1.04893i
$330$	−25.0075	+	9.65652i	−1.37662	+	0.531574i
$331$	3.22092	−	3.22092i	0.177038	−	0.177038i	−0.613025	−	0.790063i	$-0.710048\pi$
$331$	3.22092	−	3.22092i	0.177038	−	0.177038i	0.790063	+	0.613025i	$0.210048\pi$
$332$	10.3193	+	2.76506i	0.566347	+	0.151752i
$333$	8.77218	+	5.64729i	0.480712	+	0.309470i
$334$	1.47536			0.0807280
$335$	18.6664	+	32.3311i	1.01985	+	1.76644i
$336$	−2.47250	+	3.85833i	−0.134886	+	0.210489i
$337$		−	20.9388i		−	1.14061i	−0.821434	−	0.570304i	$-0.806825\pi$
$337$		−	20.9388i		−	1.14061i	0.821434	−	0.570304i	$-0.193175\pi$
$338$	−12.3229	−	4.14092i	−0.670275	−	0.225236i
$339$	−13.4231	+	9.79323i	−0.729041	+	0.531895i
$340$	−12.9824	+	12.9824i	−0.704069	+	0.704069i
$341$	2.57426	+	1.48625i	0.139404	+	0.0804849i
$342$	−5.03046	+	1.09017i	−0.272016	+	0.0589495i
$343$	−16.6033	−	8.20561i	−0.896491	−	0.443061i
$344$	−4.00578	+	1.07335i	−0.215977	+	0.0578709i
$345$	−39.2582	+	15.1594i	−2.11359	+	0.816152i
$346$	2.95369	−	0.791439i	0.158791	−	0.0425480i
$347$	3.71329	−	2.14387i	0.199340	−	0.115089i	−0.397008	−	0.917815i	$-0.629951\pi$
$347$	3.71329	−	2.14387i	0.199340	−	0.115089i	0.596348	+	0.802726i	$0.296618\pi$
$348$	8.85852	+	12.1419i	0.474866	+	0.650874i
$349$	0.480623	−	1.79371i	0.0257272	−	0.0960151i	−0.951868	−	0.306507i	$-0.900840\pi$
$349$	0.480623	−	1.79371i	0.0257272	−	0.0960151i	0.977596	+	0.210492i	$0.0675065\pi$
$350$	2.82167	+	25.8330i	0.150825	+	1.38083i
$351$	18.7281	−	0.508207i	0.999632	−	0.0271261i
$352$	−2.01004	−	3.48150i	−0.107136	−	0.185565i
$353$	23.5636	+	23.5636i	1.25416	+	1.25416i	0.953837	+	0.300325i	$0.0970952\pi$
$353$	23.5636	+	23.5636i	1.25416	+	1.25416i	0.300325	+	0.953837i	$0.402905\pi$
$354$	−3.55460	+	8.02664i	−0.188925	+	0.426611i
$355$		−	37.1732i		−	1.97295i
$356$	−7.87927	−	7.87927i	−0.417601	−	0.417601i
$357$	−10.0393	−	19.4113i	−0.531334	−	1.02736i
$358$	21.3534	−	5.72162i	1.12856	−	0.302397i
$359$	0.0912401	+	0.0244477i	0.00481547	+	0.00129030i	0.261226	−	0.965278i	$-0.415873\pi$
$359$	0.0912401	+	0.0244477i	0.00481547	+	0.00129030i	−0.256411	+	0.966568i	$0.582540\pi$
$360$	−3.52542	+	10.9986i	−0.185806	+	0.579679i
$361$			16.0562i			0.845064i
$362$	2.11509	+	7.89362i	0.111167	+	0.414879i
$363$	8.17369	+	3.61972i	0.429007	+	0.189986i
$364$	5.39582	+	7.86671i	0.282818	+	0.412328i
$365$			38.1801i			1.99844i
$366$	1.79466	−	11.4786i	0.0938086	−	0.599997i
$367$	0.868852			0.0453537			0.0226769	−	0.999743i	$-0.492781\pi$
$367$	0.868852			0.0453537			0.0226769	+	0.999743i	$0.492781\pi$
$368$	−3.15548	−	5.46546i	−0.164491	−	0.284907i
$369$	3.70759	−	1.90771i	0.193010	−	0.0993113i
$370$	3.46521	+	12.9323i	0.180148	+	0.672320i
$371$	2.28627	−	14.8258i	0.118697	−	0.769716i
$372$	1.19472	−	0.461335i	0.0619433	−	0.0239191i
$373$	25.0612			1.29762			0.648809	−	0.760952i	$-0.275268\pi$
$373$	25.0612			1.29762			0.648809	+	0.760952i	$0.275268\pi$
$374$	19.1713			0.991324
$375$	11.5829	+	29.9962i	0.598137	+	1.54899i
$376$	6.26472	−	3.61694i	0.323078	−	0.186529i
$377$	30.4591	−	7.15135i	1.56872	−	0.368313i
$378$	−11.2027	−	7.96868i	−0.576204	−	0.409865i
$379$	−19.8801	−	5.32687i	−1.02117	−	0.273623i	−0.290883	−	0.956759i	$-0.593949\pi$
$379$	−19.8801	−	5.32687i	−1.02117	−	0.273623i	−0.730291	+	0.683136i	$0.760616\pi$
$380$	−5.72054	−	3.30276i	−0.293458	−	0.169428i
$381$	−3.14738	−	29.3837i	−0.161245	−	1.50537i
$382$	−0.350227	−	1.30707i	−0.0179192	−	0.0668753i
$383$	16.8769	+	16.8769i	0.862371	+	0.862371i	0.991613	−	0.129242i	$-0.0412546\pi$
$383$	16.8769	+	16.8769i	0.862371	+	0.862371i	−0.129242	+	0.991613i	$0.541255\pi$
$384$	−1.71126	−	0.267553i	−0.0873274	−	0.0136535i
$385$	25.6399	−	31.9278i	1.30673	−	1.62719i
$386$	20.7650	+	11.9887i	1.05691	+	0.610209i
$387$	−2.63502	−	12.1590i	−0.133946	−	0.618078i
$388$	−3.11049	−	3.11049i	−0.157911	−	0.157911i
$389$	−7.04572	+	12.2036i	−0.357232	+	0.618745i	−0.987497	−	0.157635i	$-0.949613\pi$
$389$	−7.04572	+	12.2036i	−0.357232	+	0.618745i	0.630265	+	0.776380i	$0.282946\pi$
$390$	18.2350	+	15.6698i	0.923367	+	0.793472i
$391$	30.0962			1.52203
$392$	0.309353	−	6.99316i	0.0156247	−	0.353208i
$393$	−1.01551	−	9.48072i	−0.0512258	−	0.478239i
$394$			8.44912i			0.425661i
$395$	−14.6744	+	3.93199i	−0.738348	+	0.197840i
$396$	10.7239	−	5.51790i	0.538898	−	0.277285i
$397$	−1.50493	−	1.50493i	−0.0755302	−	0.0755302i	0.668332	−	0.743863i	$-0.267008\pi$
$397$	−1.50493	−	1.50493i	−0.0755302	−	0.0755302i	−0.743863	+	0.668332i	$0.767008\pi$
$398$	2.31915	−	2.31915i	0.116249	−	0.116249i
$399$	5.81099	−	5.29639i	0.290914	−	0.265151i
$400$	−8.50614	+	4.91102i	−0.425307	+	0.245551i
$401$	−8.37184	−	31.2441i	−0.418070	−	1.56026i	−0.778607	−	0.627512i	$-0.784073\pi$
$401$	−8.37184	−	31.2441i	−0.418070	−	1.56026i	0.360537	−	0.932745i	$-0.382593\pi$
$402$	−9.89920	−	13.5683i	−0.493727	−	0.676726i
$403$	0.0831402	−	2.66469i	0.00414151	−	0.132738i
$404$	15.7349	−	9.08453i	0.782839	−	0.451972i
$405$	−32.4457	−	12.1598i	−1.61224	−	0.604226i
$406$	−21.0116	−	9.25254i	−1.04279	−	0.459196i
$407$	6.99012	−	12.1072i	0.346487	−	0.600134i
$408$	5.18538	−	6.42949i	0.256715	−	0.318307i
$409$	−27.2627	−	7.30503i	−1.34806	−	0.361210i	−0.488639	−	0.872486i	$-0.662506\pi$
$409$	−27.2627	−	7.30503i	−1.34806	−	0.361210i	−0.859417	+	0.511276i	$0.829173\pi$
$410$	5.16858	+	1.38492i	0.255258	+	0.0683962i
$411$	−11.0052	+	13.6457i	−0.542849	+	0.673092i
$412$	−3.02090	+	5.23236i	−0.148829	+	0.257780i
$413$	−1.45601	−	13.3301i	−0.0716455	−	0.655931i
$414$	16.8351	−	8.66232i	0.827398	−	0.425730i
$415$	−35.6199	+	20.5652i	−1.74851	+	1.00950i
$416$	−1.89928	+	3.06476i	−0.0931196	+	0.150262i
$417$	−7.18356	−	9.84612i	−0.351780	−	0.482167i
$418$	1.78519	+	6.66242i	0.0873165	+	0.325870i
$419$	16.2655	−	9.39087i	0.794620	−	0.458774i	−0.0469666	−	0.998896i	$-0.514955\pi$
$419$	16.2655	−	9.39087i	0.794620	−	0.458774i	0.841586	+	0.540122i	$0.181622\pi$
$420$	−3.77267	−	17.2346i	−0.184087	−	0.840960i
$421$	6.36724	−	6.36724i	0.310320	−	0.310320i	−0.534713	−	0.845034i	$-0.679580\pi$
$421$	6.36724	−	6.36724i	0.310320	−	0.310320i	0.845034	+	0.534713i	$0.179580\pi$
$422$	−3.93896	−	3.93896i	−0.191746	−	0.191746i
$423$	9.92908	+	19.2970i	0.482768	+	0.938251i
$424$	5.47666	−	1.46747i	0.265970	−	0.0712665i
$425$		−	46.8401i		−	2.27208i
$426$	1.78116	+	16.6288i	0.0862975	+	0.805666i
$427$	6.42739	+	16.5421i	0.311043	+	0.800527i
$428$	−3.01756			−0.145859
$429$	−1.89406	−	25.0339i	−0.0914460	−	1.20865i
$430$	7.98303	−	13.8270i	0.384976	−	0.666798i
$431$	−16.6867	−	16.6867i	−0.803771	−	0.803771i	0.179912	−	0.983683i	$-0.442419\pi$
$431$	−16.6867	−	16.6867i	−0.803771	−	0.803771i	−0.983683	+	0.179912i	$0.942419\pi$
$432$	1.05003	−	5.08895i	0.0505195	−	0.244842i
$433$	0.164373	+	0.0949005i	0.00789924	+	0.00456063i	0.503944	−	0.863736i	$-0.331882\pi$
$433$	0.164373	+	0.0949005i	0.00789924	+	0.00456063i	−0.496045	+	0.868297i	$0.665215\pi$
$434$	−1.22493	+	1.52533i	−0.0587986	+	0.0732184i
$435$	−57.1699	−	8.93842i	−2.74108	−	0.428565i
$436$	10.6142	+	10.6142i	0.508326	+	0.508326i
$437$	2.80249	+	10.4591i	0.134061	+	0.500324i
$438$	−1.82941	−	17.0792i	−0.0874124	−	0.816074i
$439$	15.4140	+	8.89925i	0.735668	+	0.424738i	0.820492	−	0.571658i	$-0.193700\pi$
$439$	15.4140	+	8.89925i	0.735668	+	0.424738i	−0.0848241	+	0.996396i	$0.527033\pi$
$440$	14.9497	+	4.00577i	0.712701	+	0.190968i
$441$	20.9100	+	1.94170i	0.995716	+	0.0924619i
$442$	−8.12865	−	15.1517i	−0.386640	−	0.720691i
$443$	24.8326	−	14.3371i	1.17983	−	0.681176i	0.223855	−	0.974622i	$-0.428136\pi$
$443$	24.8326	−	14.3371i	1.17983	−	0.681176i	0.955975	+	0.293447i	$0.0948023\pi$
$444$	−2.16975	−	5.61900i	−0.102972	−	0.266666i
$445$	42.8998			2.03364
$446$	16.5728			0.784744
$447$	−30.7853	+	11.8876i	−1.45610	+	0.562264i
$448$	2.46614	−	0.958213i	0.116514	−	0.0452713i
$449$	−4.61100	−	17.2085i	−0.217606	−	0.812118i	−0.985233	−	0.171221i	$-0.945229\pi$
$449$	−4.61100	−	17.2085i	−0.217606	−	0.812118i	0.767626	−	0.640898i	$-0.221438\pi$
$450$	−13.4816	−	26.2012i	−0.635527	−	1.23513i
$451$	−2.79370	−	4.83883i	−0.131550	−	0.227851i
$452$	9.59316			0.451224
$453$	−1.74566	+	11.1652i	−0.0820183	+	0.524587i
$454$			23.1132i			1.08475i
$455$	−36.1048	−	6.72655i	−1.69262	−	0.315345i
$456$	2.71723	+	1.20333i	0.127246	+	0.0563509i
$457$	−6.84618	−	25.5503i	−0.320251	−	1.19519i	−0.919001	−	0.394256i	$-0.871002\pi$
$457$	−6.84618	−	25.5503i	−0.320251	−	1.19519i	0.598750	−	0.800936i	$-0.295664\pi$
$458$		−	10.2406i		−	0.478512i
$459$	18.5135	+	16.4709i	0.864135	+	0.768794i
$460$	23.4690	+	6.28849i	1.09425	+	0.293202i
$461$	1.17017	−	0.313547i	0.0545004	−	0.0146033i	−0.231466	−	0.972843i	$-0.574352\pi$
$461$	1.17017	−	0.313547i	0.0545004	−	0.0146033i	0.285966	+	0.958240i	$0.407685\pi$
$462$	−9.93968	+	15.5108i	−0.462436	+	0.721630i
$463$	13.0245	+	13.0245i	0.605302	+	0.605302i	0.941715	−	0.336413i	$-0.109214\pi$
$463$	13.0245	+	13.0245i	0.605302	+	0.605302i	−0.336413	+	0.941715i	$0.609214\pi$
$464$		−	8.67754i		−	0.402845i
$465$	−1.99651	+	4.50831i	−0.0925858	+	0.209068i
$466$	4.63693	+	4.63693i	0.214801	+	0.214801i
$467$	9.52020	+	16.4895i	0.440542	+	0.763042i	0.997730	−	0.0673449i	$-0.0214528\pi$
$467$	9.52020	+	16.4895i	0.440542	+	0.763042i	−0.557187	+	0.830387i	$0.688119\pi$
$468$	−8.90793	−	6.13586i	−0.411769	−	0.283630i
$469$	23.4800	+	10.3395i	1.08421	+	0.477435i
$470$	−7.20811	+	26.9010i	−0.332485	+	1.24085i
$471$	12.2947	+	16.8517i	0.566508	+	0.776483i
$472$	4.38925	−	2.53413i	0.202032	−	0.116643i
$473$	−16.1036	+	4.31495i	−0.740444	+	0.198401i
$474$	6.37591	−	2.46203i	0.292855	−	0.113085i
$475$	16.2779	−	4.36165i	0.746881	−	0.200126i
$476$	−1.92296	+	12.4699i	−0.0881388	+	0.571555i
$477$	3.60257	+	16.6237i	0.164950	+	0.761146i
$478$	16.1197	+	9.30672i	0.737298	+	0.425679i
$479$	21.7583	−	21.7583i	0.994164	−	0.994164i	−0.00581938	−	0.999983i	$-0.501852\pi$
$479$	21.7583	−	21.7583i	0.994164	−	0.994164i	0.999983	+	0.00581938i	$0.00185238\pi$
$480$	5.38697	−	3.93023i	0.245880	−	0.179390i
$481$	−12.5325	−	0.391024i	−0.571435	−	0.0178292i
$482$		−	13.2418i		−	0.603147i
$483$	−15.6039	+	24.3498i	−0.710001	+	1.10795i
$484$	−2.58056	−	4.46966i	−0.117298	−	0.203166i
$485$	16.9355			0.769002
$486$	15.0966	+	3.88482i	0.684797	+	0.176219i
$487$	12.3270	+	3.30302i	0.558591	+	0.149674i	0.527059	−	0.849829i	$-0.323295\pi$
$487$	12.3270	+	3.30302i	0.558591	+	0.149674i	0.0315322	+	0.999503i	$0.489961\pi$
$488$	−4.74305	+	4.74305i	−0.214708	+	0.214708i
$489$	−15.0965	+	5.82945i	−0.682688	+	0.263617i
$490$	18.1955	+	19.8798i	0.821987	+	0.898077i
$491$	−1.59689	−	2.76589i	−0.0720664	−	0.124823i	0.827740	−	0.561111i	$-0.189626\pi$
$491$	−1.59689	−	2.76589i	−0.0720664	−	0.124823i	−0.899807	+	0.436289i	$0.856293\pi$
$492$	−2.37843	−	0.371864i	−0.107228	−	0.0167649i
$493$	35.8380	+	20.6911i	1.61406	+	0.931878i
$494$	4.50859	−	4.23576i	0.202851	−	0.190576i
$495$	−14.1725	+	44.2155i	−0.637006	+	1.98734i
$496$	−0.714216	−	0.191374i	−0.0320693	−	0.00859293i
$497$	−15.0998	−	20.6059i	−0.677317	−	0.924300i
$498$	14.9485	−	10.9062i	0.669859	−	0.488717i
$499$	30.6608	+	8.21553i	1.37256	+	0.367777i	0.868415	−	0.495839i	$-0.165139\pi$
$499$	30.6608	+	8.21553i	1.37256	+	0.367777i	0.504150	+	0.863616i	$0.331806\pi$
$500$	4.80487	−	17.9320i	0.214880	−	0.801944i
$501$	1.60421	−	1.98911i	0.0716710	−	0.0888667i
$502$	4.86041	−	18.1393i	0.216931	−	0.809597i
$503$	31.4519	+	18.1588i	1.40237	+	0.809659i	0.994636	−	0.103441i	$-0.0329853\pi$
$503$	31.4519	+	18.1588i	1.40237	+	0.809659i	0.407735	+	0.913100i	$0.366319\pi$
$504$	2.51343	+	7.52879i	0.111957	+	0.335359i
$505$	−18.1043	+	67.5663i	−0.805633	+	3.00666i
$506$	−12.6853	−	21.9716i	−0.563932	−	0.976758i
$507$	−18.9820	+	12.1113i	−0.843019	+	0.537883i
$508$	−8.53085	+	14.7759i	−0.378495	+	0.655573i
$509$	−35.6549	+	9.55370i	−1.58037	+	0.423460i	−0.939042	−	0.343802i	$-0.888285\pi$
$509$	−35.6549	+	9.55370i	−1.58037	+	0.423460i	−0.641333	+	0.767263i	$0.721618\pi$
$510$	3.38686	+	31.6194i	0.149973	+	1.40013i
$511$	15.5088	+	21.1640i	0.686067	+	0.936241i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.00003	+	7.96755i	−0.176606	+	0.351776i
$514$	4.52435	−	16.8851i	0.199561	−	0.744771i
$515$	−6.02029	−	22.4680i	−0.265285	−	0.990059i
$516$	−2.90854	+	6.56776i	−0.128041	+	0.289130i
$517$	25.1847	−	14.5404i	1.10762	−	0.639486i
$518$	7.17394	+	5.76109i	0.315205	+	0.253128i
$519$	2.14463	−	4.84279i	0.0941387	−	0.212575i
$520$	−3.17282	−	13.5137i	−0.139137	−	0.592614i
$521$	1.64039	+	0.947080i	0.0718668	+	0.0414923i	0.535503	−	0.844533i	$-0.320122\pi$
$521$	1.64039	+	0.947080i	0.0718668	+	0.0414923i	−0.463636	+	0.886026i	$0.653455\pi$
$522$	26.0022	+	1.25913i	1.13808	+	0.0551108i
$523$	15.2438	−	26.4030i	0.666565	−	1.15452i	−0.312294	−	0.949986i	$-0.601097\pi$
$523$	15.2438	−	26.4030i	0.666565	−	1.15452i	0.978858	−	0.204539i	$-0.0655694\pi$
$524$	−2.75250	+	4.76748i	−0.120244	+	0.208268i
$525$	37.8967	+	24.2850i	1.65395	+	1.05989i
$526$	2.74252	+	10.2352i	0.119580	+	0.446277i
$527$	2.49337	−	2.49337i	0.108613	−	0.108613i
$528$	−6.87942	−	1.07559i	−0.299389	−	0.0468090i
$529$	−8.41415	−	14.5737i	−0.365833	−	0.633641i
$530$	−10.9143	+	18.9041i	−0.474087	+	0.821143i
$531$	6.95661	+	13.5200i	0.301891	+	0.586720i
$532$	−4.51259	+	0.492898i	−0.195646	+	0.0213698i
$533$	−2.63974	+	4.25961i	−0.114340	+	0.184504i
$534$	−19.1904	+	2.05555i	−0.830451	+	0.0889523i
$535$	8.21477	−	8.21477i	0.355155	−	0.355155i
$536$			9.69696i			0.418845i
$537$	15.5044	−	35.0104i	0.669062	−	1.51081i
$538$	−0.818810	+	0.818810i	−0.0353014	+	0.0353014i
$539$	1.24363	−	28.1131i	0.0535669	−	1.21092i
$540$	10.9952	+	16.7123i	0.473160	+	0.719182i
$541$	−7.79299	+	29.0838i	−0.335047	+	1.25041i	0.568772	+	0.822495i	$0.307419\pi$
$541$	−7.79299	+	29.0838i	−0.335047	+	1.25041i	−0.903819	+	0.427916i	$0.859248\pi$
$542$	0.464728	−	0.268311i	0.0199618	−	0.0115249i
$543$	12.9421	+	5.73143i	0.555401	+	0.245959i
$544$	−4.60638	+	1.23428i	−0.197497	+	0.0529191i
$545$	−57.7903			−2.47546
$546$	16.4731	+	1.27903i	0.704985	+	0.0547373i
$547$	−25.1916			−1.07711			−0.538557	−	0.842589i	$-0.681030\pi$
$547$	−25.1916			−1.07711			−0.538557	+	0.842589i	$0.681030\pi$
$548$	9.77639	−	2.61958i	0.417627	−	0.111903i
$549$	−13.5243	−	14.9007i	−0.577202	−	0.635948i
$550$	−34.1955	+	19.7428i	−1.45810	+	0.841834i
$551$	−3.85341	+	14.3811i	−0.164161	+	0.612657i
$552$	−10.7997	−	1.68852i	−0.459666	−	0.0718682i
$553$	−6.53713	+	8.14031i	−0.277987	+	0.346161i
$554$	12.5586	−	12.5586i	0.533564	−	0.533564i
$555$	21.2035	+	9.38996i	0.900037	+	0.398582i
$556$			7.03680i			0.298427i
$557$	−23.6352	+	23.6352i	−1.00146	+	1.00146i	−0.00145828	+	0.999999i	$0.500464\pi$
$557$	−23.6352	+	23.6352i	−1.00146	+	1.00146i	−0.999999	+	0.00145828i	$0.999536\pi$
$558$	0.677084	−	2.11237i	0.0286632	−	0.0894238i
$559$	10.2382	+	10.8976i	0.433029	+	0.460921i
$560$	−4.10505	+	9.32217i	−0.173470	+	0.393934i
$561$	20.8457	−	25.8471i	0.880106	−	1.09127i
$562$	−6.28842	+	10.8919i	−0.265261	+	0.459445i
$563$	14.1183	+	24.4536i	0.595016	+	1.03060i	0.993545	+	0.113442i	$0.0361877\pi$
$563$	14.1183	+	24.4536i	0.595016	+	1.03060i	−0.398528	+	0.917156i	$0.630479\pi$
$564$	1.93545	−	12.3790i	0.0814970	−	0.521252i
$565$	−26.1156	+	26.1156i	−1.09869	+	1.09869i
$566$	−4.63206	−	17.2871i	−0.194700	−	0.726630i
$567$	−22.9246	+	6.43902i	−0.962744	+	0.270413i
$568$	4.82777	−	8.36194i	0.202569	−	0.350859i
$569$	−13.0253	+	22.5604i	−0.546047	+	0.945781i	0.452493	+	0.891768i	$0.350535\pi$
$569$	−13.0253	+	22.5604i	−0.546047	+	0.945781i	−0.998540	+	0.0540133i	$0.982799\pi$
$570$	−10.6730	+	4.12133i	−0.447043	+	0.172624i
$571$	−26.2753	−	15.1701i	−1.09959	−	0.634848i	−0.163475	−	0.986547i	$-0.552270\pi$
$571$	−26.2753	−	15.1701i	−1.09959	−	0.634848i	−0.936113	+	0.351700i	$0.885604\pi$
$572$	−7.63526	+	12.3206i	−0.319246	+	0.515151i
$573$	−2.14303	−	0.949039i	−0.0895262	−	0.0396467i
$574$	3.42760	−	1.33179i	0.143065	−	0.0555878i
$575$	−53.6820	+	30.9933i	−2.23869	+	1.29251i
$576$	−2.22144	+	2.01623i	−0.0925600	+	0.0840098i
$577$	−4.12503	−	15.3948i	−0.171727	−	0.640895i	−0.997086	−	0.0762863i	$-0.975694\pi$
$577$	−4.12503	−	15.3948i	−0.171727	−	0.640895i	0.825359	−	0.564609i	$-0.190973\pi$
$578$	1.48618	−	5.54650i	0.0618170	−	0.230704i
$579$	38.7420	−	14.9600i	1.61006	−	0.621718i
$580$	23.6230	+	23.6230i	0.980893	+	0.980893i
$581$	−11.3913	+	25.8685i	−0.472590	+	1.07321i
$582$	−7.57578	+	0.811467i	−0.314026	+	0.0336364i
$583$	22.0167	−	5.89935i	0.911837	−	0.244326i
$584$	−4.95853	+	8.58843i	−0.205186	+	0.355392i
$585$	40.9540	−	7.54645i	1.69324	−	0.312007i
$586$	−11.9466	−	20.6922i	−0.493511	−	0.854786i
$587$	6.60185	−	24.6384i	0.272487	−	1.01694i	−0.685019	−	0.728525i	$-0.740206\pi$
$587$	6.60185	−	24.6384i	0.272487	−	1.01694i	0.957506	−	0.288412i	$-0.0931272\pi$
$588$	−9.09194	−	8.02101i	−0.374945	−	0.330781i
$589$	1.09867	+	0.634320i	0.0452701	+	0.0261367i
$590$	−5.05022	+	18.8477i	−0.207914	+	0.775946i
$591$	11.3913	+	9.18705i	0.468574	+	0.377905i
$592$	−0.900068	+	3.35910i	−0.0369925	+	0.138058i
$593$	23.0441	+	6.17464i	0.946307	+	0.253562i	0.698795	−	0.715322i	$-0.253720\pi$
$593$	23.0441	+	6.17464i	0.946307	+	0.253562i	0.247513	+	0.968885i	$0.420387\pi$
$594$	4.22121	−	20.4580i	0.173198	−	0.839404i
$595$	−28.7120	−	39.1818i	−1.17708	−	1.60630i
$596$	18.4038	+	4.93128i	0.753848	+	0.201993i
$597$	−0.605022	−	5.64843i	−0.0247619	−	0.231175i
$598$	−11.9863	+	19.3416i	−0.490155	+	0.790937i
$599$	19.8526	+	11.4619i	0.811153	+	0.468320i	0.847356	−	0.531025i	$-0.178193\pi$
$599$	19.8526	+	11.4619i	0.811153	+	0.468320i	−0.0362029	+	0.999344i	$0.511526\pi$
$600$	−2.62792	+	16.8081i	−0.107284	+	0.686187i
$601$	12.1680	+	21.0756i	0.496343	+	0.859690i	0.999991	−	0.00421817i	$-0.00134269\pi$
$601$	12.1680	+	21.0756i	0.496343	+	0.859690i	−0.503649	+	0.863909i	$0.668009\pi$
$602$	−1.19137	−	10.9073i	−0.0485567	−	0.444548i
$603$	−29.0568	−	1.40706i	−1.18329	−	0.0572997i
$604$	4.61355	−	4.61355i	0.187723	−	0.187723i
$605$	19.1930	+	5.14274i	0.780305	+	0.209082i
$606$	4.86119	−	31.0920i	0.197472	−	1.26303i
$607$	13.1454			0.533557			0.266779	−	0.963758i	$-0.414041\pi$
$607$	13.1454			0.533557			0.266779	+	0.963758i	$0.414041\pi$
$608$	−0.857872	−	1.48588i	−0.0347913	−	0.0602603i
$609$	−35.3212	+	18.2676i	−1.43129	+	0.740242i
$610$		−	25.8242i		−	1.04559i
$611$	−22.1701	−	13.7391i	−0.896905	−	0.555825i
$612$	−3.03009	−	13.9821i	−0.122484	−	0.565191i
$613$	−5.27274	+	5.27274i	−0.212964	+	0.212964i	−0.805525	−	0.592561i	$-0.798117\pi$
$613$	−5.27274	+	5.27274i	−0.212964	+	0.212964i	0.592561	+	0.805525i	$0.298117\pi$
$614$	1.45243	+	0.838562i	0.0586154	+	0.0338416i
$615$	7.48717	−	5.46251i	0.301912	−	0.220270i
$616$	9.91409	−	3.85210i	0.399450	−	0.155206i
$617$	19.6403	−	5.26260i	0.790688	−	0.211864i	0.159196	−	0.987247i	$-0.449110\pi$
$617$	19.6403	−	5.26260i	0.790688	−	0.211864i	0.631492	+	0.775383i	$0.282443\pi$
$618$	3.76962	+	9.76218i	0.151636	+	0.392693i
$619$	−13.3339	+	3.57282i	−0.535936	+	0.143604i	−0.516628	−	0.856210i	$-0.672813\pi$
$619$	−13.3339	+	3.57282i	−0.535936	+	0.143604i	−0.0193082	+	0.999814i	$0.506146\pi$
$620$	2.46530	−	1.42334i	0.0990090	−	0.0571629i
$621$	6.62670	−	32.1162i	0.265920	−	1.28878i
$622$	1.30896	−	4.88512i	0.0524847	−	0.195875i
$623$	23.7802	−	17.4259i	0.952735	−	0.698153i
$624$	2.06681	+	5.89307i	0.0827387	+	0.235912i
$625$	11.1812	+	19.3664i	0.447247	+	0.774655i
$626$	11.6519	+	11.6519i	0.465705	+	0.465705i
$627$	10.9235	+	4.83748i	0.436243	+	0.193190i
$628$		−	12.0435i		−	0.480588i
$629$	−11.7268	−	11.7268i	−0.467578	−	0.467578i
$630$	−27.3381	−	13.6534i	−1.08918	−	0.543965i
$631$	−41.0333	+	10.9948i	−1.63351	+	0.437697i	−0.954930	−	0.296830i	$-0.904070\pi$
$631$	−41.0333	+	10.9948i	−1.63351	+	0.437697i	−0.678579	+	0.734528i	$0.737404\pi$
$632$	−3.81158	−	1.02131i	−0.151617	−	0.0406256i
$633$	−9.59357	+	1.02760i	−0.381310	+	0.0408434i
$634$			20.8773i			0.829144i
$635$	−17.0009	−	63.4483i	−0.674661	−	2.51787i
$636$	3.97652	−	8.97937i	0.157679	−	0.356055i
$637$	−22.7460	+	10.9371i	−0.901228	+	0.433344i
$638$		−	34.8845i		−	1.38109i
$639$	24.3559	+	15.6797i	0.963506	+	0.620279i
$640$	−3.84994			−0.152182
$641$	−0.867888	−	1.50323i	−0.0342795	−	0.0593738i	0.848377	−	0.529393i	$-0.177580\pi$
$641$	−0.867888	−	1.50323i	−0.0342795	−	0.0593738i	−0.882656	+	0.470019i	$0.844247\pi$
$642$	−3.28111	+	4.06834i	−0.129495	+	0.160564i
$643$	−3.79013	−	14.1449i	−0.149468	−	0.557822i	−0.999516	−	0.0311165i	$-0.990094\pi$
$643$	−3.79013	−	14.1449i	−0.149468	−	0.557822i	0.850048	−	0.526706i	$-0.176573\pi$
$644$	15.5637	−	6.04725i	0.613296	−	0.238295i
$645$	−9.96158	−	25.7975i	−0.392237	−	1.01578i
$646$	8.18217			0.321923
$647$	−12.3557			−0.485751			−0.242876	−	0.970057i	$-0.578091\pi$
$647$	−12.3557			−0.485751			−0.242876	+	0.970057i	$0.578091\pi$
$648$	−5.71929	−	6.94908i	−0.224675	−	0.272986i
$649$	17.6452	−	10.1874i	0.692634	−	0.399892i
$650$	30.1022	+	18.6548i	1.18071	+	0.731700i
$651$	0.724571	+	3.31003i	0.0283982	+	0.129730i
$652$	9.02485	+	2.41820i	0.353441	+	0.0947041i
$653$	−26.0607	−	15.0461i	−1.01983	−	0.588801i	−0.105778	−	0.994390i	$-0.533733\pi$
$653$	−26.0607	−	15.0461i	−1.01983	−	0.588801i	−0.914056	+	0.405589i	$0.867067\pi$
$654$	25.8514	−	2.76903i	1.01087	−	0.108278i
$655$	−5.48540	−	20.4718i	−0.214332	−	0.799899i
$656$	0.982785	+	0.982785i	0.0383713	+	0.0383713i
$657$	−25.0156	−	16.1044i	−0.975953	−	0.628292i
$658$	6.93159	+	17.8397i	0.270221	+	0.695464i
$659$	29.0006	+	16.7435i	1.12970	+	0.652235i	0.943861	−	0.330344i	$-0.107165\pi$
$659$	29.0006	+	16.7435i	1.12970	+	0.652235i	0.185844	+	0.982579i	$0.440498\pi$
$660$	21.6561	−	15.7999i	0.842962	−	0.615010i
$661$	8.95487	+	8.95487i	0.348304	+	0.348304i	0.859478	−	0.511173i	$-0.170789\pi$
$661$	8.95487	+	8.95487i	0.348304	+	0.348304i	−0.511173	+	0.859478i	$0.670789\pi$
$662$	−2.27754	+	3.94481i	−0.0885190	+	0.153319i
$663$	−29.2664	−	5.51579i	−1.13661	−	0.214216i
$664$	−10.6834			−0.414595
$665$	10.9429	−	13.6265i	0.424347	−	0.528415i
$666$	−9.93490	−	3.18446i	−0.384969	−	0.123395i
$667$		−	54.7637i		−	2.12046i
$668$	−1.42509	+	0.381851i	−0.0551383	+	0.0147743i
$669$	18.0202	−	22.3438i	0.696703	−	0.863859i
$670$	−26.3982	−	26.3982i	−1.01985	−	1.01985i
$671$	−19.0675	+	19.0675i	−0.736093	+	0.736093i
$672$	1.38964	−	4.36679i	0.0536067	−	0.168453i
$673$	14.9509	−	8.63190i	0.576315	−	0.332735i	−0.183353	−	0.983047i	$-0.558695\pi$
$673$	14.9509	−	8.63190i	0.576315	−	0.332735i	0.759667	+	0.650312i	$0.225362\pi$
$674$	5.41935	+	20.2253i	0.208746	+	0.779050i
$675$	−49.9839	−	10.3134i	−1.92388	−	0.396964i
$676$	12.9747	+	0.810430i	0.499027	+	0.0311704i
$677$	−2.21973	+	1.28156i	−0.0853113	+	0.0492545i	−0.542049	−	0.840347i	$-0.682351\pi$
$677$	−2.21973	+	1.28156i	−0.0853113	+	0.0492545i	0.456738	+	0.889602i	$0.349018\pi$
$678$	10.4310	−	12.9337i	0.400601	−	0.496715i
$679$	9.38770	−	6.87920i	0.360267	−	0.263999i
$680$	9.17994	−	15.9001i	0.352035	−	0.609742i
$681$	31.1616	+	25.1318i	1.19412	+	0.963054i
$682$	−2.87121	−	0.769339i	−0.109944	−	0.0294595i
$683$	36.9434	+	9.89894i	1.41360	+	0.378773i	0.883208	−	0.468981i	$-0.155379\pi$
$683$	36.9434	+	9.89894i	1.41360	+	0.378773i	0.530390	+	0.847754i	$0.322045\pi$
$684$	4.57690	−	2.35500i	0.175002	−	0.0900457i
$685$	−19.4831	+	33.7458i	−0.744413	+	1.28936i
$686$	18.1613	+	3.62878i	0.693401	+	0.138547i
$687$	−13.8066	−	11.1350i	−0.526754	−	0.424827i
$688$	3.59149	−	2.07355i	0.136924	−	0.0790532i
$689$	−13.9975	−	14.8991i	−0.533263	−	0.567611i
$690$	33.9970	−	24.8036i	1.29424	−	0.944256i
$691$	−5.93254	−	22.1405i	−0.225684	−	0.842266i	−0.982129	−	0.188208i	$-0.939732\pi$
$691$	−5.93254	−	22.1405i	−0.225684	−	0.842266i	0.756445	−	0.654058i	$-0.226935\pi$
$692$	−2.64821	+	1.52894i	−0.100670	+	0.0581217i
$693$	10.1042	+	30.2664i	0.383827	+	1.14973i
$694$	−3.03189	+	3.03189i	−0.115089	+	0.115089i
$695$	−19.1564	−	19.1564i	−0.726644	−	0.726644i
$696$	−11.6992	−	9.43542i	−0.443458	−	0.357649i
$697$	−6.40226	+	1.71548i	−0.242503	+	0.0649784i
$698$			1.85699i			0.0702879i
$699$	11.2935	−	1.20968i	0.427159	−	0.0457545i
$700$	−9.41161	−	24.2225i	−0.355725	−	0.915525i
$701$	−24.3586			−0.920011			−0.460006	−	0.887916i	$-0.652153\pi$
$701$	−24.3586			−0.920011			−0.460006	+	0.887916i	$0.652153\pi$
$702$	−17.9584	+	5.33808i	−0.677797	+	0.201473i
$703$	2.98333	−	5.16728i	0.112518	−	0.194888i
$704$	2.84263	+	2.84263i	0.107136	+	0.107136i
$705$	28.4308	+	38.9686i	1.07077	+	1.46764i
$706$	−28.8594	−	16.6620i	−1.08614	−	0.627081i
$707$	17.4098	+	44.8074i	0.654764	+	1.68515i
$708$	1.35603	−	8.67313i	0.0509628	−	0.325956i
$709$	22.6676	+	22.6676i	0.851299	+	0.851299i	0.990293	−	0.138994i	$-0.0443870\pi$
$709$	22.6676	+	22.6676i	0.851299	+	0.851299i	−0.138994	+	0.990293i	$0.544387\pi$
$710$	9.62114	+	35.9066i	0.361075	+	1.34755i
$711$	3.61342	−	11.2732i	0.135514	−	0.422777i
$712$	9.65010	+	5.57149i	0.361653	+	0.208800i
$713$	−4.50739	−	1.20775i	−0.168803	−	0.0452307i
$714$	14.7212	+	16.1515i	0.550927	+	0.604456i
$715$	−12.7550	−	54.3262i	−0.477011	−	2.03169i
$716$	−19.1449	+	11.0533i	−0.715479	+	0.413082i
$717$	30.0751	−	11.6133i	1.12317	−	0.433708i
$718$	−0.0944587			−0.00352517
$719$	17.8248			0.664751			0.332376	−	0.943147i	$-0.392150\pi$
$719$	17.8248			0.664751			0.332376	+	0.943147i	$0.392150\pi$
$720$	0.558637	−	11.5363i	0.0208192	−	0.429933i
$721$	−12.4637	−	10.0090i	−0.464171	−	0.372756i
$722$	−4.15566	−	15.5091i	−0.154657	−	0.577190i
$723$	−17.8528	−	14.3983i	−0.663954	−	0.535479i
$724$	−4.08604	−	7.07722i	−0.151856	−	0.263023i
$725$	−85.2312			−3.16541
$726$	−8.83203	−	1.38087i	−0.327787	−	0.0512491i
$727$			35.4327i			1.31413i	0.753835	+	0.657064i	$0.228202\pi$
$727$			35.4327i			1.31413i	−0.753835	+	0.657064i	$0.771798\pi$
$728$	−7.24802	−	6.20212i	−0.268629	−	0.229866i
$729$	21.6527	−	16.1294i	0.801953	−	0.597387i
$730$	−9.88174	−	36.8792i	−0.365740	−	1.36496i
$731$			19.7770i			0.731477i
$732$	1.23737	+	11.5520i	0.0457346	+	0.426974i
$733$	33.4761	+	8.96990i	1.23647	+	0.331311i	0.817095	−	0.576503i	$-0.195583\pi$
$733$	33.4761	+	8.96990i	1.23647	+	0.331311i	0.419374	+	0.907814i	$0.362250\pi$
$734$	−0.839247	+	0.224876i	−0.0309772	+	0.00830031i
$735$	46.5869	−	2.91542i	1.71838	−	0.107537i
$736$	4.46253	+	4.46253i	0.164491	+	0.164491i
$737$			38.9827i			1.43595i
$738$	−3.08751	+	2.80230i	−0.113653	+	0.103154i
$739$	−2.52499	−	2.52499i	−0.0928834	−	0.0928834i	0.659138	−	0.752022i	$-0.270921\pi$
$739$	−2.52499	−	2.52499i	−0.0928834	−	0.0928834i	−0.752022	+	0.659138i	$0.770921\pi$
$740$	−6.69427	−	11.5948i	−0.246086	−	0.426234i
$741$	−0.808370	−	10.6843i	−0.0296962	−	0.392497i
$742$	1.62883	+	14.9123i	0.0597963	+	0.547449i
$743$	10.7093	−	39.9675i	0.392884	−	1.46626i	−0.432469	−	0.901649i	$-0.642358\pi$
$743$	10.7093	−	39.9675i	0.392884	−	1.46626i	0.825354	−	0.564616i	$-0.190976\pi$
$744$	−1.03461	+	0.754832i	−0.0379306	+	0.0276735i
$745$	−63.5255	+	36.6765i	−2.32739	+	1.34372i
$746$	−24.2072	+	6.48630i	−0.886289	+	0.237480i
$747$	1.55019	−	32.0126i	0.0567183	−	1.17128i
$748$	−18.5181	+	4.96190i	−0.677087	+	0.181425i
$749$	1.21678	−	7.89045i	0.0444601	−	0.288311i
$750$	−18.9518	−	25.9762i	−0.692021	−	0.948516i
$751$	−13.0442	−	7.53105i	−0.475988	−	0.274812i	0.242755	−	0.970088i	$-0.421949\pi$
$751$	−13.0442	−	7.53105i	−0.475988	−	0.274812i	−0.718743	+	0.695276i	$0.755282\pi$
$752$	−5.11512	+	5.11512i	−0.186529	+	0.186529i
$753$	−19.1709	−	26.2765i	−0.698625	−	0.957568i
$754$	−27.5703	+	14.7911i	−1.00405	+	0.538659i
$755$			25.1191i			0.914177i
$756$	12.8834	+	4.79769i	0.468565	+	0.174490i
$757$	−23.3536	−	40.4496i	−0.848802	−	1.47017i	−0.882278	−	0.470728i	$-0.843991\pi$
$757$	−23.3536	−	40.4496i	−0.848802	−	1.47017i	0.0334769	−	0.999439i	$-0.489342\pi$
$758$	20.5814			0.747552
$759$	−43.4158	−	6.78800i	−1.57589	−	0.246389i
$760$	6.38044	+	1.70963i	0.231443	+	0.0620149i
$761$	17.5333	−	17.5333i	0.635583	−	0.635583i	−0.313880	−	0.949463i	$-0.601629\pi$
$761$	17.5333	−	17.5333i	0.635583	−	0.635583i	0.949463	+	0.313880i	$0.101629\pi$
$762$	10.6452	+	27.5678i	0.385634	+	0.998677i
$763$	−32.0343	+	23.4744i	−1.15972	+	0.849830i
$764$	0.676587	+	1.17188i	0.0244780	+	0.0423972i
$765$	46.3125	+	29.8147i	1.67443	+	1.07795i
$766$	−20.6699	−	11.9338i	−0.746835	−	0.431185i
$767$	−15.5330	−	9.62604i	−0.560865	−	0.347576i
$768$	1.72220	−	0.184470i	0.0621445	−	0.00665651i
$769$	−22.1205	−	5.92717i	−0.797686	−	0.213739i	−0.163118	−	0.986607i	$-0.552155\pi$
$769$	−22.1205	−	5.92717i	−0.797686	−	0.213739i	−0.634568	+	0.772867i	$0.718822\pi$
$770$	−16.5027	+	37.4760i	−0.594715	+	1.35054i
$771$	−17.8453	−	24.4597i	−0.642684	−	0.880893i
$772$	−23.1604	−	6.20581i	−0.833561	−	0.223352i
$773$	−3.67678	+	13.7219i	−0.132245	+	0.493544i	−0.999994	−	0.00345832i	$-0.998899\pi$
$773$	−3.67678	+	13.7219i	−0.132245	+	0.493544i	0.867749	+	0.497002i	$0.165566\pi$
$774$	5.69222	+	11.0627i	0.204603	+	0.397641i
$775$	−1.87968	+	7.01506i	−0.0675201	+	0.251989i
$776$	3.80956	+	2.19945i	0.136755	+	0.0789557i
$777$	15.5677	−	3.40780i	0.558489	−	0.122254i
$778$	3.64714	−	13.6113i	0.130756	−	0.487989i
$779$	−1.19233	−	2.06518i	−0.0427196	−	0.0739926i
$780$	−21.6693	−	10.4163i	−0.775887	−	0.372963i
$781$	19.4081	−	33.6157i	0.694475	−	1.20287i
$782$	−29.0707	+	7.78947i	−1.03957	+	0.278551i
$783$	29.9707	−	33.6875i	1.07107	−	1.20389i
$784$	1.51115	+	6.83494i	0.0539697	+	0.244105i
$785$	32.7862	+	32.7862i	1.17019	+	1.17019i
$786$	3.43470	+	8.89484i	0.122512	+	0.317268i
$787$	9.91468	−	37.0021i	0.353420	−	1.31898i	−0.529041	−	0.848596i	$-0.677448\pi$
$787$	9.91468	−	37.0021i	0.353420	−	1.31898i	0.882461	−	0.470386i	$-0.155885\pi$
$788$	−2.18679	−	8.16122i	−0.0779013	−	0.290732i
$789$	16.7814	+	7.43164i	0.597433	+	0.264573i
$790$	13.1567	−	7.59602i	0.468094	−	0.270254i
$791$	−3.86827	+	25.0846i	−0.137540	+	0.891906i
$792$	−8.93039	+	8.10544i	−0.317328	+	0.288014i
$793$	23.1543	+	6.98500i	0.822232	+	0.248044i
$794$	1.84315	+	1.06414i	0.0654110	+	0.0377651i
$795$	13.6194	+	35.2701i	0.483029	+	1.25090i
$796$	−1.63989	+	2.84037i	−0.0581243	+	0.100674i
$797$	−5.71829	+	9.90437i	−0.202552	+	0.350831i	−0.949350	−	0.314220i	$-0.898257\pi$
$797$	−5.71829	+	9.90437i	−0.202552	+	0.350831i	0.746798	+	0.665051i	$0.231590\pi$
$798$	−4.24218	+	6.61991i	−0.150172	+	0.234342i
$799$	−8.92859	−	33.3220i	−0.315871	−	1.17885i
$800$	6.94524	−	6.94524i	0.245551	−	0.245551i
$801$	−18.0952	+	28.1080i	−0.639361	+	0.993146i
$802$	16.1732	+	28.0127i	0.571094	+	0.989163i
$803$	−19.9337	+	34.5263i	−0.703447	+	1.21841i
$804$	13.0736	+	10.5439i	0.461072	+	0.371854i
$805$	−25.9068	+	58.8319i	−0.913096	+	2.07355i
$806$	0.609365	+	2.59541i	0.0214640	+	0.0914194i
$807$	0.213612	+	1.99426i	0.00751949	+	0.0702012i
$808$	−12.8475	+	12.8475i	−0.451972	+	0.451972i
$809$		−	22.5036i		−	0.791183i	−0.918427	−	0.395591i	$-0.870540\pi$
$809$		−	22.5036i		−	0.791183i	0.918427	−	0.395591i	$-0.129460\pi$
$810$	34.4873	+	3.34790i	1.21176	+	0.117633i
$811$	−13.3542	+	13.3542i	−0.468928	+	0.468928i	−0.901567	−	0.432639i	$-0.857582\pi$
$811$	−13.3542	+	13.3542i	−0.468928	+	0.468928i	0.432639	+	0.901567i	$0.357582\pi$
$812$	22.6904	+	3.49906i	0.796277	+	0.122793i
$813$	0.143575	−	0.918300i	0.00503539	−	0.0322062i
$814$	−3.61835	+	13.5039i	−0.126823	+	0.473311i
$815$	−31.1517	+	17.9854i	−1.09119	+	0.630002i
$816$	−3.34462	+	7.55248i	−0.117085	+	0.264390i
$817$	−6.87290	+	1.84159i	−0.240452	+	0.0644290i
$818$	28.2245			0.986845
$819$	19.6363	−	20.8187i	0.686147	−	0.727463i
$820$	−5.35091			−0.186862
$821$	2.02986	−	0.543901i	0.0708428	−	0.0189823i	−0.223224	−	0.974767i	$-0.571658\pi$
$821$	2.02986	−	0.543901i	0.0708428	−	0.0189823i	0.294066	+	0.955785i	$0.404991\pi$
$822$	7.09849	−	16.0291i	0.247588	−	0.559079i
$823$	38.4146	−	22.1787i	1.33905	−	0.773099i	0.352381	−	0.935857i	$-0.385372\pi$
$823$	38.4146	−	22.1787i	1.33905	−	0.773099i	0.986666	+	0.162757i	$0.0520387\pi$
$824$	1.56373	−	5.83594i	0.0544753	−	0.203304i
$825$	−10.5645	+	67.5700i	−0.367808	+	2.35249i
$826$	4.85648	+	12.4990i	0.168979	+	0.434897i
$827$	8.95024	−	8.95024i	0.311231	−	0.311231i	−0.534156	−	0.845386i	$-0.679370\pi$
$827$	8.95024	−	8.95024i	0.311231	−	0.311231i	0.845386	+	0.534156i	$0.179370\pi$
$828$	−14.0194	+	12.7244i	−0.487209	+	0.442203i
$829$		−	32.7643i		−	1.13795i	−0.822354	−	0.568976i	$-0.807340\pi$
$829$		−	32.7643i		−	1.13795i	0.822354	−	0.568976i	$-0.192660\pi$
$830$	29.0835	−	29.0835i	1.00950	−	1.00950i
$831$	−3.27629	−	30.5872i	−0.113653	−	1.06106i
$832$	1.04134	−	3.45190i	0.0361020	−	0.119673i
$833$	−31.8313	−	10.0565i	−1.10289	−	0.348437i
$834$	9.48715	+	7.65138i	0.328513	+	0.264946i
$835$	2.84002	−	4.91906i	0.0982830	−	0.170231i
$836$	−3.44872	−	5.97336i	−0.119277	−	0.206593i
$837$	−2.11172	−	3.20972i	−0.0729918	−	0.110944i
$838$	−13.2807	+	13.2807i	−0.458774	+	0.458774i
$839$	−0.880405	−	3.28572i	−0.0303950	−	0.113436i	0.949062	−	0.315090i	$-0.102035\pi$
$839$	−0.880405	−	3.28572i	−0.0303950	−	0.113436i	−0.979457	+	0.201655i	$0.935368\pi$
$840$	8.10475	+	15.6709i	0.279640	+	0.540696i
$841$	23.1499	−	40.0967i	0.798271	−	1.38265i
$842$	−4.50232	+	7.79824i	−0.155160	+	0.268745i
$843$	7.84698	+	20.3213i	0.270264	+	0.699903i
$844$	4.82423	+	2.78527i	0.166057	+	0.0958729i
$845$	−37.5276	+	33.1151i	−1.29099	+	1.13919i
$846$	−14.5852	−	16.0696i	−0.501449	−	0.552485i
$847$	12.7280	−	4.94545i	0.437340	−	0.169928i
$848$	−4.91024	+	2.83493i	−0.168618	+	0.0973518i
$849$	−28.3434	−	12.5519i	−0.972743	−	0.430779i
$850$	12.1231	+	45.2441i	0.415819	+	1.55186i
$851$	−5.68030	+	21.1992i	−0.194718	+	0.726698i
$852$	−6.02431	−	15.6011i	−0.206389	−	0.534486i
$853$	20.9347	+	20.9347i	0.716791	+	0.716791i	0.967947	−	0.251156i	$-0.0808106\pi$
$853$	20.9347	+	20.9347i	0.716791	+	0.716791i	−0.251156	+	0.967947i	$0.580811\pi$
$854$	−10.4898	−	14.3149i	−0.358953	−	0.489846i
$855$	−6.04872	+	18.8708i	−0.206862	+	0.645369i
$856$	2.91474	−	0.781003i	0.0996238	−	0.0266941i
$857$	3.66436	−	6.34685i	0.125172	−	0.216804i	−0.796628	−	0.604470i	$-0.793385\pi$
$857$	3.66436	−	6.34685i	0.125172	−	0.216804i	0.921800	+	0.387665i	$0.126718\pi$
$858$	8.30877	+	23.6907i	0.283657	+	0.808786i
$859$	22.8218	+	39.5285i	0.778670	+	1.34870i	0.932708	+	0.360632i	$0.117439\pi$
$859$	22.8218	+	39.5285i	0.778670	+	1.34870i	−0.154038	+	0.988065i	$0.549228\pi$
$860$	−4.13232	+	15.4220i	−0.140911	+	0.525887i
$861$	1.93142	−	6.06927i	0.0658227	−	0.206840i
$862$	20.4370	+	11.7993i	0.696086	+	0.401886i
$863$	−3.83050	+	14.2956i	−0.130392	+	0.486628i	−0.999974	−	0.00715898i	$-0.997721\pi$
$863$	−3.83050	+	14.2956i	−0.130392	+	0.486628i	0.869583	+	0.493787i	$0.164388\pi$
$864$	0.302868	+	5.18732i	0.0103038	+	0.176476i
$865$	3.04699	−	11.3715i	0.103601	−	0.386644i
$866$	−0.183334	−	0.0491241i	−0.00622993	−	0.00166931i
$867$	−5.86192	−	8.03462i	−0.199081	−	0.272870i
$868$	0.788407	−	1.79040i	0.0267603	−	0.0607700i
$869$	−15.3229	−	4.10576i	−0.519794	−	0.139278i
$870$	57.5353	−	6.16279i	1.95063	−	0.208938i
$871$	30.8092	−	16.5287i	1.04393	−	0.560053i
$872$	−12.9996	−	7.50534i	−0.440223	−	0.254163i
$873$	−7.14341	+	11.0962i	−0.241768	+	0.375548i
$874$	−5.41400	−	9.37733i	−0.183131	−	0.317193i
$875$	44.9519	+	19.7947i	1.51965	+	0.669184i
$876$	6.18748	+	16.0237i	0.209056	+	0.541391i
$877$	−23.9697	+	23.9697i	−0.809401	+	0.809401i	−0.984543	−	0.175142i	$-0.943961\pi$
$877$	−23.9697	+	23.9697i	−0.809401	+	0.809401i	0.175142	+	0.984543i	$0.443961\pi$
$878$	−17.1920	−	4.60659i	−0.580203	−	0.155465i
$879$	−40.8876	−	6.39272i	−1.37910	−	0.215621i
$880$	−15.4771			−0.521733
$881$	17.4587	+	30.2394i	0.588199	+	1.01879i	0.994468	+	0.105037i	$0.0334960\pi$
$881$	17.4587	+	30.2394i	0.588199	+	1.01879i	−0.406270	+	0.913753i	$0.633171\pi$
$882$	−20.7001	+	3.53638i	−0.697009	+	0.119076i
$883$			56.9398i			1.91618i	0.286475	+	0.958088i	$0.407517\pi$
$883$			56.9398i			1.91618i	−0.286475	+	0.958088i	$0.592483\pi$
$884$	11.7732	+	12.5315i	0.395976	+	0.421481i
$885$	19.9195	+	27.3026i	0.669586	+	0.917767i
$886$	−20.2757	+	20.2757i	−0.681176	+	0.681176i
$887$	13.7619	+	7.94546i	0.462081	+	0.266782i	0.712919	−	0.701247i	$-0.247373\pi$
$887$	13.7619	+	7.94546i	0.462081	+	0.266782i	−0.250838	+	0.968029i	$0.580706\pi$
$888$	3.55012	+	4.86596i	0.119134	+	0.163291i
$889$	−35.1967	−	28.2649i	−1.18046	−	0.947976i
$890$	−41.4380	+	11.1033i	−1.38901	+	0.372183i
$891$	−22.9920	−	27.9359i	−0.770263	−	0.935889i
$892$	−16.0081	+	4.28935i	−0.535990	+	0.143618i
$893$	10.7487	−	6.20574i	0.359690	−	0.207667i
$894$	26.6596	−	19.4504i	0.891630	−	0.650518i
$895$	22.0279	−	82.2093i	0.736312	−	2.74795i
$896$	−2.13410	+	1.56385i	−0.0712953	+	0.0522444i
$897$	13.0436	+	37.1910i	0.435513	+	1.24177i
$898$	8.90777	+	15.4287i	0.297256	+	0.514862i
$899$	−4.53699	−	4.53699i	−0.151317	−	0.151317i
$900$	19.8035	+	21.8191i	0.660118	+	0.727303i
$901$		−	27.0388i		−	0.900794i
$902$	3.95088	+	3.95088i	0.131550	+	0.131550i
$903$	−16.0009	−	10.2537i	−0.532475	−	0.341222i
$904$	−9.26628	+	2.48289i	−0.308192	+	0.0825798i
$905$	30.3900	+	8.14297i	1.01020	+	0.270681i
$906$	−1.20359	−	11.2366i	−0.0399864	−	0.373310i
$907$		−	10.9422i		−	0.363330i	−0.983360	−	0.181665i	$-0.941851\pi$
$907$		−	10.9422i		−	0.363330i	0.983360	−	0.181665i	$-0.0581487\pi$
$908$	−5.98213	−	22.3256i	−0.198524	−	0.740901i
$909$	−36.6331	−	40.3615i	−1.21504	−	1.33871i
$910$	36.6156	−	2.84728i	1.21379	−	0.0943863i
$911$			22.4731i			0.744568i	0.928119	+	0.372284i	$0.121425\pi$
$911$			22.4731i			0.744568i	−0.928119	+	0.372284i	$0.878575\pi$
$912$	−2.93609	−	0.459053i	−0.0972236	−	0.0152008i
$913$	−42.9481			−1.42137
$914$	13.2258	+	22.9078i	0.437471	+	0.757722i
$915$	−34.8167	−	28.0797i	−1.15100	−	0.928285i
$916$	2.65046	+	9.89167i	0.0875738	+	0.326830i
$917$	−11.3563	−	9.11976i	−0.375018	−	0.301161i
$918$	−22.1456	−	11.1180i	−0.730914	−	0.366949i
$919$	−34.1228			−1.12561			−0.562804	−	0.826590i	$-0.690278\pi$
$919$	−34.1228			−1.12561			−0.562804	+	0.826590i	$0.690278\pi$
$920$	−24.2968			−0.801043
$921$	2.70985	−	1.04640i	0.0892926	−	0.0344799i
$922$	−1.04915	+	0.605726i	−0.0345519	+	0.0199485i
$923$	−34.7966	−	1.08568i	−1.14534	−	0.0357355i
$924$	5.58650	−	17.5549i	0.183782	−	0.577514i
$925$	32.9932	+	8.84050i	1.08481	+	0.290674i
$926$	−15.9517	−	9.20974i	−0.524207	−	0.302651i
$927$	17.2604	+	5.53252i	0.566906	+	0.181712i
$928$	2.24591	+	8.38186i	0.0737257	+	0.275148i
$929$	6.34084	+	6.34084i	0.208036	+	0.208036i	0.803432	−	0.595396i	$-0.203005\pi$
$929$	6.34084	+	6.34084i	0.208036	+	0.208036i	−0.595396	+	0.803432i	$0.703005\pi$
$930$	0.761641	−	4.87143i	0.0249752	−	0.159740i
$931$	0.530772	−	11.9985i	0.0173953	−	0.393234i
$932$	−5.67905	−	3.27880i	−0.186024	−	0.107401i
$933$	−5.16293	−	7.07655i	−0.169027	−	0.231676i
$934$	−13.4636	−	13.4636i	−0.440542	−	0.440542i
$935$	36.9042	−	63.9199i	1.20690	−	2.09041i
$936$	10.1925	+	3.62125i	0.333152	+	0.118364i
$937$	−25.3471			−0.828053			−0.414027	−	0.910265i	$-0.635878\pi$
$937$	−25.3471			−0.828053			−0.414027	+	0.910265i	$0.635878\pi$
$938$	−25.3560	−	3.91012i	−0.827904	−	0.127670i
$939$	28.3790	−	3.03976i	0.926112	−	0.0991989i
$940$		−	27.8500i		−	0.908366i
$941$	3.71927	−	0.996574i	0.121245	−	0.0324874i	−0.197687	−	0.980265i	$-0.563343\pi$
$941$	3.71927	−	0.996574i	0.121245	−	0.0324874i	0.318931	+	0.947778i	$0.396676\pi$
$942$	−16.2373	−	13.0954i	−0.529039	−	0.426670i
$943$	6.20233	+	6.20233i	0.201975	+	0.201975i
$944$	−3.58381	+	3.58381i	−0.116643	+	0.116643i
$945$	−48.1336	+	22.0119i	−1.56579	+	0.716048i
$946$	14.4381	−	8.33584i	0.469423	−	0.271021i
$947$	−2.67298	−	9.97571i	−0.0868603	−	0.324167i	0.908800	−	0.417233i	$-0.137000\pi$
$947$	−2.67298	−	9.97571i	−0.0868603	−	0.324167i	−0.995660	+	0.0930657i	$0.970333\pi$
$948$	−5.52143	+	4.02834i	−0.179328	+	0.130834i
$949$	35.7391	+	1.11509i	1.16014	+	0.0361972i
$950$	−14.5944	+	8.42606i	−0.473504	+	0.273378i
$951$	28.1472	+	22.7007i	0.912736	+	0.736121i
$952$	−1.37000	−	12.5427i	−0.0444019	−	0.406510i
$953$	−5.03077	+	8.71354i	−0.162962	+	0.282259i	−0.935930	−	0.352186i	$-0.885438\pi$
$953$	−5.03077	+	8.71354i	−0.162962	+	0.282259i	0.772967	+	0.634446i	$0.218772\pi$
$954$	−7.78234	−	15.1248i	−0.251963	−	0.489684i
$955$	−5.03212	−	1.34835i	−0.162836	−	0.0436317i
$956$	−17.9792	−	4.81751i	−0.581489	−	0.155809i
$957$	−47.0319	−	37.9313i	−1.52033	−	1.22614i
$958$	−15.3855	+	26.6484i	−0.497082	+	0.860971i
$959$	2.90763	+	26.6200i	0.0938922	+	0.859606i
$960$	−4.18619	+	5.19056i	−0.135109	+	0.167525i
$961$	26.3733	−	15.2266i	0.850752	−	0.491182i
$962$	12.2067	−	2.86596i	0.393560	−	0.0924023i
$963$	1.91733	+	8.84732i	0.0617851	+	0.285101i
$964$	3.42723	+	12.7906i	0.110383	+	0.411957i
$965$	79.9442	−	46.1558i	2.57349	−	1.48581i
$966$	8.77000	−	27.5587i	0.282170	−	0.886686i
$967$	32.9135	−	32.9135i	1.05843	−	1.05843i	0.0602436	−	0.998184i	$-0.480812\pi$
$967$	32.9135	−	32.9135i	1.05843	−	1.05843i	0.998184	−	0.0602436i	$-0.0191878\pi$
$968$	3.64946	+	3.64946i	0.117298	+	0.117298i
$969$	8.89679	−	11.0314i	0.285806	−	0.354378i
$970$	−16.3584	+	4.38323i	−0.525238	+	0.140737i
$971$		−	31.0312i		−	0.995839i	−0.867223	−	0.497920i	$-0.834097\pi$
$971$		−	31.0312i		−	0.995839i	0.867223	−	0.497920i	$-0.165903\pi$
$972$	−15.5877	+	0.154847i	−0.499975	+	0.00496671i
$973$	−18.4001	−	2.83746i	−0.589881	−	0.0909648i
$974$	−12.7619			−0.408917
$975$	57.8820	−	20.3003i	1.85371	−	0.650131i
$976$	3.35385	−	5.80903i	0.107354	−	0.185943i
$977$	34.4868	+	34.4868i	1.10333	+	1.10333i	0.994006	+	0.109326i	$0.0348692\pi$
$977$	34.4868	+	34.4868i	1.10333	+	1.10333i	0.109326	+	0.994006i	$0.465131\pi$
$978$	13.0733	−	9.53808i	0.418039	−	0.304994i
$979$	38.7943	+	22.3979i	1.23987	+	0.715839i
$980$	−22.7207	−	14.4931i	−0.725787	−	0.462964i
$981$	24.3760	−	37.8642i	0.778265	−	1.20891i
$982$	2.25834	+	2.25834i	0.0720664	+	0.0720664i
$983$	−6.57359	−	24.5330i	−0.209665	−	0.782481i	−0.987977	−	0.154602i	$-0.950590\pi$
$983$	−6.57359	−	24.5330i	−0.209665	−	0.782481i	0.778312	−	0.627878i	$-0.216076\pi$
$984$	2.39363	−	0.256390i	0.0763061	−	0.00817340i
$985$	28.1706	+	16.2643i	0.897590	+	0.518224i
$986$	−39.9720	−	10.7105i	−1.27297	−	0.341091i
$987$	31.5888	+	10.0525i	1.00548	+	0.319975i
$988$	−3.25867	+	5.25834i	−0.103672	+	0.167290i
$989$	22.6657	−	13.0861i	0.720729	−	0.416113i
$990$	2.24577	−	46.3770i	0.0713753	−	1.47396i
$991$	−1.89149			−0.0600853			−0.0300426	−	0.999549i	$-0.509564\pi$
$991$	−1.89149			−0.0600853			−0.0300426	+	0.999549i	$0.509564\pi$
$992$	0.739411			0.0234763
$993$	2.84201	+	7.35996i	0.0901886	+	0.233561i
$994$	19.9184	+	15.9956i	0.631775	+	0.507351i
$995$	−3.26809	−	12.1967i	−0.103605	−	0.386661i
$996$	−11.6164	+	14.4035i	−0.368081	+	0.456393i
$997$	−10.4531	−	18.1052i	−0.331052	−	0.573399i	0.651667	−	0.758506i	$-0.274070\pi$
$997$	−10.4531	−	18.1052i	−0.331052	−	0.573399i	−0.982718	+	0.185107i	$0.940737\pi$
$998$	−31.7424			−1.00479
$999$	−15.0959	+	9.93184i	−0.477614	+	0.314229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.431.8	✓	152
3.2	odd	2	inner	546.2.bw.a.431.27	yes	152
7.2	even	3		546.2.ch.a.275.25	yes	152
13.7	odd	12		546.2.ch.a.137.19	yes	152
21.2	odd	6		546.2.ch.a.275.19	yes	152
39.20	even	12		546.2.ch.a.137.25	yes	152
91.72	odd	12	inner	546.2.bw.a.527.27	yes	152
273.254	even	12	inner	546.2.bw.a.527.8	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.8	✓	152	1.1	even	1	trivial
546.2.bw.a.431.27	yes	152	3.2	odd	2	inner
546.2.bw.a.527.8	yes	152	273.254	even	12	inner
546.2.bw.a.527.27	yes	152	91.72	odd	12	inner
546.2.ch.a.137.19	yes	152	13.7	odd	12
546.2.ch.a.137.25	yes	152	39.20	even	12
546.2.ch.a.275.19	yes	152	21.2	odd	6
546.2.ch.a.275.25	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)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.701344 + 1.58370i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.996438 + 3.71876i) q^{5} +(0.267553 - 1.71126i) q^{6} +(0.958213 + 2.46614i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.01623 - 2.22144i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.701344 + 1.58370i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.996438 + 3.71876i) q^{5} +(0.267553 - 1.71126i) q^{6} +(0.958213 + 2.46614i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.01623 - 2.22144i) q^{9} -3.84994i q^{10} +(-2.84263 + 2.84263i) q^{11} +(0.184470 + 1.72220i) q^{12} +(3.45190 + 1.04134i) q^{13} +(-1.56385 - 2.13410i) q^{14} +(-5.19056 - 4.18619i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.38444 + 4.12997i) q^{17} +(2.52248 + 1.62391i) q^{18} +(-1.21321 + 1.21321i) q^{19} +(0.996438 + 3.71876i) q^{20} +(-4.57767 - 0.212084i) q^{21} +(2.01004 - 3.48150i) q^{22} +(3.15548 - 5.46546i) q^{23} +(-0.623923 - 1.61577i) q^{24} +(-8.50614 - 4.91102i) q^{25} +(-3.60380 - 0.112441i) q^{26} +(4.93218 - 1.63512i) q^{27} +(2.06290 + 1.65663i) q^{28} +(7.51497 - 4.33877i) q^{29} +(6.09717 + 2.70013i) q^{30} +(-0.191374 - 0.714216i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.50823 - 6.49555i) q^{33} +(-3.37210 - 3.37210i) q^{34} +(-10.1258 + 1.10601i) q^{35} +(-2.85683 - 0.915707i) q^{36} +(-3.35910 + 0.900068i) q^{37} +(0.857872 - 1.48588i) q^{38} +(-4.07014 + 4.73645i) q^{39} +(-1.92497 - 3.33415i) q^{40} +(-0.359724 + 1.34251i) q^{41} +(4.47658 - 0.979929i) q^{42} +(3.59149 + 2.07355i) q^{43} +(-1.04048 + 3.88311i) q^{44} +(10.2701 - 5.28436i) q^{45} +(-1.63340 + 6.09593i) q^{46} +(-6.98738 - 1.87226i) q^{47} +(1.02086 + 1.39923i) q^{48} +(-5.16366 + 4.72617i) q^{49} +(9.48737 + 2.54213i) q^{50} +(-8.21295 + 0.879717i) q^{51} +(3.51010 - 0.824122i) q^{52} +(-4.91024 - 2.83493i) q^{53} +(-4.34092 + 2.85595i) q^{54} +(-7.73855 - 13.4036i) q^{55} +(-2.42138 - 1.06626i) q^{56} +(-1.07049 - 2.77225i) q^{57} +(-6.13595 + 6.13595i) q^{58} +(-4.89557 - 1.31176i) q^{59} +(-6.58826 - 1.03006i) q^{60} +6.70769 q^{61} +(0.369706 + 0.640349i) q^{62} +(3.54639 - 7.10092i) q^{63} -1.00000i q^{64} +(-7.31210 + 11.7991i) q^{65} +(4.10393 + 5.62504i) q^{66} +(6.85679 - 6.85679i) q^{67} +(4.12997 + 2.38444i) q^{68} +(6.44259 + 8.83051i) q^{69} +(9.49448 - 3.68906i) q^{70} +(-9.32653 + 2.49904i) q^{71} +(2.99649 + 0.145103i) q^{72} +(9.57915 - 2.56673i) q^{73} +(3.01168 - 1.73880i) q^{74} +(13.7433 - 10.0269i) q^{75} +(-0.444067 + 1.65728i) q^{76} +(-9.73417 - 4.28647i) q^{77} +(2.70557 - 5.62849i) q^{78} +(1.97302 + 3.41737i) q^{79} +(2.72232 + 2.72232i) q^{80} +(-0.869597 + 8.95789i) q^{81} -1.38987i q^{82} +(7.55428 + 7.55428i) q^{83} +(-4.07042 + 2.10516i) q^{84} +(-17.7343 + 4.75189i) q^{85} +(-4.00578 - 1.07335i) q^{86} +(1.60075 + 14.9445i) q^{87} -4.02009i q^{88} +(-2.88401 - 10.7633i) q^{89} +(-8.55242 + 7.76238i) q^{90} +(0.739564 + 9.51068i) q^{91} -6.31097i q^{92} +(1.26533 + 0.197832i) q^{93} +7.23387 q^{94} +(-3.30276 - 5.72054i) q^{95} +(-1.34822 - 1.08734i) q^{96} +(-1.13852 - 4.24901i) q^{97} +(3.76449 - 5.90158i) q^{98} +(12.0462 + 0.583326i) 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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