LMFDB - Embedded newform 546.2.bw.a.527.8

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			527.8
Character	$\chi$	$=$	546.527
Dual form			546.2.bw.a.431.8

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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	−0.714293	−	0.699847i	$-0.753251\pi$
$5$	−0.996438	−	3.71876i	−0.445621	−	1.66308i	0.268672	−	0.963232i	$-0.413415\pi$
$6$	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	0.133908	−	0.990994i	$-0.457247\pi$
$11$	−2.84263	−	2.84263i	−0.857086	−	0.857086i	−0.990994	+	0.133908i	$0.957247\pi$
$12$	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	−0.417362	−	0.908740i	$-0.637045\pi$
$17$	2.38444	−	4.12997i	0.578311	−	1.00166i	0.995673	−	0.0929237i	$-0.0296213\pi$
$18$	2.52248	−	1.62391i	0.594555	−	0.382759i
$19$	−1.21321	−	1.21321i	−0.278331	−	0.278331i	0.554112	−	0.832442i	$-0.313058\pi$
$19$	−1.21321	−	1.21321i	−0.278331	−	0.278331i	−0.832442	+	0.554112i	$0.813058\pi$
$20$	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	0.981142	+	0.193289i	$0.0619153\pi$
$23$	3.15548	+	5.46546i	0.657964	+	1.13963i	−0.323178	+	0.946338i	$0.604751\pi$
$24$	−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	0.993917	−	0.110135i	$-0.0351284\pi$
$29$	7.51497	+	4.33877i	1.39550	+	0.805689i	0.401578	+	0.915825i	$0.368462\pi$
$30$	6.09717	−	2.70013i	1.11319	−	0.492974i
$31$	−0.191374	+	0.714216i	−0.0343717	+	0.128277i	−0.980980	−	0.194109i	$-0.937818\pi$
$31$	−0.191374	+	0.714216i	−0.0343717	+	0.128277i	0.946608	+	0.322386i	$0.104485\pi$
$32$	−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	−0.0280970	−	0.999605i	$-0.508945\pi$
$37$	−3.35910	−	0.900068i	−0.552232	−	0.147970i	−0.524135	+	0.851635i	$0.675611\pi$
$38$	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	0.932130	−	0.362123i	$-0.117948\pi$
$41$	−0.359724	−	1.34251i	−0.0561795	−	0.209665i	−0.988310	+	0.152458i	$0.951281\pi$
$42$	4.47658	+	0.979929i	0.690751	+	0.151206i
$43$	3.59149	−	2.07355i	0.547696	−	0.316213i	−0.200496	−	0.979695i	$-0.564255\pi$
$43$	3.59149	−	2.07355i	0.547696	−	0.316213i	0.748192	+	0.663482i	$0.230922\pi$
$44$	−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	−0.729475	−	0.684008i	$-0.760235\pi$
$47$	−6.98738	+	1.87226i	−1.01921	+	0.273098i	−0.289740	+	0.957105i	$0.593569\pi$
$48$	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	−0.797769	−	0.602963i	$-0.793987\pi$
$53$	−4.91024	+	2.83493i	−0.674473	+	0.389407i	0.123296	+	0.992370i	$0.460653\pi$
$54$	−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	−0.563002	−	0.826455i	$-0.690354\pi$
$59$	−4.89557	+	1.31176i	−0.637349	+	0.170777i	−0.0743468	+	0.997232i	$0.523687\pi$
$60$	−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	0.988554	−	0.150864i	$-0.0482057\pi$
$67$	6.85679	+	6.85679i	0.837690	+	0.837690i	−0.150864	+	0.988554i	$0.548206\pi$
$68$	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	−0.341302	−	0.939954i	$-0.610868\pi$
$71$	−9.32653	−	2.49904i	−1.10686	−	0.296581i	−0.765553	+	0.643373i	$0.777535\pi$
$72$	2.99649	−	0.145103i	0.353140	−	0.0171005i
$73$	9.57915	+	2.56673i	1.12115	+	0.300413i	0.771351	−	0.636410i	$-0.219581\pi$
$73$	9.57915	+	2.56673i	1.12115	+	0.300413i	0.349804	+	0.936823i	$0.386248\pi$
$74$	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	−0.733428	−	0.679768i	$-0.762081\pi$
$79$	1.97302	−	3.41737i	0.221982	−	0.384485i	0.955410	+	0.295283i	$0.0954140\pi$
$80$	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	−0.158215	−	0.987405i	$-0.550574\pi$
$83$	7.55428	−	7.55428i	0.829190	−	0.829190i	0.987405	+	0.158215i	$0.0505738\pi$
$84$	−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	0.626632	+	0.779315i	$0.284433\pi$
$89$	−2.88401	+	10.7633i	−0.305705	+	1.14091i	−0.932337	+	0.361591i	$0.882234\pi$
$90$	−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	−0.999331	−	0.0365717i	$-0.988356\pi$
$97$	−1.13852	+	4.24901i	−0.115599	+	0.431422i	0.883732	+	0.467993i	$0.155023\pi$
$98$	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	0.219556	−	0.975600i	$-0.429539\pi$
$103$	−5.23236	−	3.02090i	−0.515559	−	0.297658i	−0.735116	+	0.677941i	$0.762872\pi$
$104$	−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	−0.620971	−	0.783834i	$-0.713261\pi$
$107$	−2.61329	+	1.50878i	−0.252636	+	0.145859i	0.368335	+	0.929693i	$0.379928\pi$
$108$	3.45383	+	3.88215i	0.332345	+	0.373560i
$109$	3.88505	−	14.4992i	0.372120	−	1.38877i	−0.485386	−	0.874300i	$-0.661321\pi$
$109$	3.88505	−	14.4992i	0.372120	−	1.38877i	0.857507	−	0.514473i	$-0.172012\pi$
$110$	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	−0.0554335	−	0.998462i	$-0.517654\pi$
$113$	8.30792	−	4.79658i	0.781544	−	0.451224i	0.836977	+	0.547238i	$0.184321\pi$
$114$	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	−0.328860	−	0.944379i	$-0.606664\pi$
$127$	−14.7759	−	8.53085i	−1.31115	−	0.756991i	−0.982286	+	0.187388i	$0.939998\pi$
$128$	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	0.277058	−	0.960853i	$-0.410641\pi$
$131$	−4.76748	−	2.75250i	−0.416536	−	0.240487i	−0.693594	+	0.720366i	$0.743974\pi$
$132$	−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	0.184249	−	0.982880i	$-0.441015\pi$
$137$	9.77639	−	2.61958i	0.835254	−	0.223806i	0.651004	+	0.759074i	$0.274348\pi$
$138$	−8.50857	+	6.86216i	−0.724297	+	0.584146i
$139$	−3.51840	−	6.09405i	−0.298427	−	0.516890i	0.677349	−	0.735661i	$-0.263129\pi$
$139$	−3.51840	−	6.09405i	−0.298427	−	0.516890i	−0.975776	+	0.218771i	$0.929795\pi$
$140$	−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	0.109752	−	0.993959i	$-0.464994\pi$
$149$	13.4725	−	13.4725i	1.10371	−	1.10371i	0.993959	−	0.109752i	$-0.0350055\pi$
$150$	−10.6799	−	13.2423i	−0.872009	−	1.08123i
$151$	6.30222	+	1.68868i	0.512868	+	0.137422i	0.505965	−	0.862554i	$-0.331136\pi$
$151$	6.30222	+	1.68868i	0.512868	+	0.137422i	0.00690207	+	0.999976i	$0.497803\pi$
$152$			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	0.999752	−	0.0222723i	$-0.00709009\pi$
$157$	6.02174	+	10.4300i	0.480588	+	0.832402i	−0.519164	+	0.854674i	$0.673757\pi$
$158$	−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	−0.399333	−	0.916806i	$-0.630758\pi$
$163$	6.60665	−	6.60665i	0.517473	−	0.517473i	0.916806	+	0.399333i	$0.130758\pi$
$164$	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	−0.313535	−	0.949577i	$-0.601513\pi$
$167$	−1.42509	+	0.381851i	−0.110277	+	0.0295485i	0.203259	+	0.979125i	$0.434847\pi$
$168$	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	$0.0982263\pi$
$181$			8.17207i			0.607426i	−0.952764	+	0.303713i	$0.901774\pi$
$182$	−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	$-0.984411\pi$
$191$		−	1.35317i		−	0.0979122i	0.998801	−	0.0489561i	$-0.0155894\pi$
$192$	1.58370	−	0.701344i	0.114294	−	0.0506151i
$193$	−16.9546	+	16.9546i	−1.22042	+	1.22042i	−0.252934	+	0.967483i	$0.581396\pi$
$193$	−16.9546	+	16.9546i	−1.22042	+	1.22042i	−0.967483	+	0.252934i	$0.918604\pi$
$194$	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	0.999035	+	0.0439145i	$0.0139829\pi$
$197$	2.18679	+	8.16122i	0.155803	+	0.581463i	−0.843233	+	0.537549i	$0.819350\pi$
$198$	−11.7867	−	2.55432i	−0.837642	−	0.181528i
$199$	−2.84037	−	1.63989i	−0.201348	−	0.116249i	0.395936	−	0.918278i	$-0.370420\pi$
$199$	−2.84037	−	1.63989i	−0.201348	−	0.116249i	−0.597284	+	0.802030i	$0.703754\pi$
$200$	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	−0.754083	−	0.656779i	$-0.771918\pi$
$211$	2.78527	−	4.82423i	0.191746	−	0.332113i	0.945829	+	0.324666i	$0.105252\pi$
$212$	−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	−0.751307	−	0.659953i	$-0.770576\pi$
$223$	−16.0081	+	4.28935i	−1.07198	+	0.287236i	−0.320674	+	0.947190i	$0.603909\pi$
$224$	−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	0.818264	+	0.574842i	$0.194937\pi$
$227$	5.98213	+	22.3256i	0.397048	+	1.48180i	−0.421217	+	0.906960i	$0.638397\pi$
$228$	−2.31320	+	1.86560i	−0.153195	+	0.123552i
$229$	−2.65046	−	9.89167i	−0.175148	−	0.653660i	−0.996526	−	0.0832768i	$-0.973461\pi$
$229$	−2.65046	−	9.89167i	−0.175148	−	0.653660i	0.821379	−	0.570383i	$-0.193205\pi$
$230$	−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	−0.953211	−	0.302305i	$-0.902244\pi$
$233$	−3.27880	+	5.67905i	−0.214801	+	0.372047i	0.738410	+	0.674352i	$0.235577\pi$
$234$	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	−0.990301	−	0.138942i	$-0.955630\pi$
$239$	−13.1617	+	13.1617i	−0.851359	+	0.851359i	0.138942	+	0.990301i	$0.455630\pi$
$240$	−6.22063	−	2.40207i	−0.401540	−	0.155053i
$241$	−3.42723	−	12.7906i	−0.220767	−	0.823914i	−0.984056	−	0.177857i	$-0.943084\pi$
$241$	−3.42723	−	12.7906i	−0.220767	−	0.823914i	0.763289	−	0.646057i	$-0.223583\pi$
$242$	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	−0.993872	−	0.110540i	$-0.964742\pi$
$251$	−9.38960	−	16.2633i	−0.592666	−	1.02653i	0.401206	−	0.915988i	$-0.368591\pi$
$252$	−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	−0.998594	−	0.0530159i	$-0.983117\pi$
$257$	−8.74038	−	15.1388i	−0.545210	−	0.944331i	0.453384	−	0.891315i	$-0.350217\pi$
$258$	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	$0.105936\pi$
$263$			10.5963i			0.653395i	−0.945129	+	0.326698i	$0.894064\pi$
$264$	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	0.530260	−	0.847835i	$-0.322094\pi$
$269$	1.00283	+	0.578986i	0.0611438	+	0.0353014i	−0.469116	+	0.883136i	$0.655428\pi$
$270$	−6.29513	+	18.9886i	−0.383110	+	1.15561i
$271$	−0.518337	−	0.138888i	−0.0314867	−	0.00843684i	0.243041	−	0.970016i	$-0.421855\pi$
$271$	−0.518337	−	0.138888i	−0.0314867	−	0.00843684i	−0.274528	+	0.961579i	$0.588522\pi$
$272$	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	−0.0391996	−	0.999231i	$-0.512481\pi$
$277$	−15.3811	−	8.88027i	−0.924159	−	0.533564i	−0.884960	+	0.465668i	$0.845814\pi$
$278$	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	0.920728	−	0.390206i	$-0.127596\pi$
$281$	8.89317	+	8.89317i	0.530522	+	0.530522i	−0.390206	+	0.920728i	$0.627596\pi$
$282$	−5.07343	−	11.4563i	−0.302118	−	0.682213i
$283$		−	17.8969i		−	1.06386i	−0.846788	−	0.531930i	$-0.821467\pi$
$283$		−	17.8969i		−	1.06386i	0.846788	−	0.531930i	$-0.178533\pi$
$284$	−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	−0.511126	−	0.859506i	$-0.670772\pi$
$293$	6.18403	−	23.0791i	0.361275	−	1.34830i	0.872401	−	0.488791i	$-0.162562\pi$
$294$	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	−0.740138	−	0.672455i	$-0.765240\pi$
$307$	−1.18591	+	1.18591i	−0.0676832	+	0.0676832i	0.672455	+	0.740138i	$0.265240\pi$
$308$	−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	0.785381	−	0.619013i	$-0.212467\pi$
$311$	−2.52872	−	4.37988i	−0.143391	−	0.248360i	−0.928771	+	0.370653i	$0.879134\pi$
$312$	−0.471148	+	6.22720i	−0.0266735	+	0.352546i
$313$	−8.23916	+	14.2706i	−0.465705	+	0.806624i	−0.999233	−	0.0391578i	$-0.987532\pi$
$313$	−8.23916	+	14.2706i	−0.465705	+	0.806624i	0.533528	+	0.845782i	$0.320866\pi$
$314$	−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	0.934239	+	0.356647i	$0.116080\pi$
$317$	5.40345	+	20.1659i	0.303488	+	1.13263i	−0.630751	+	0.775985i	$0.717253\pi$
$318$	−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	0.790063	−	0.613025i	$-0.210048\pi$
$331$	3.22092	+	3.22092i	0.177038	+	0.177038i	−0.613025	+	0.790063i	$0.710048\pi$
$332$	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	$0.193175\pi$
$337$			20.9388i			1.14061i	−0.821434	+	0.570304i	$0.806825\pi$
$338$	−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	0.596348	−	0.802726i	$-0.296618\pi$
$347$	3.71329	+	2.14387i	0.199340	+	0.115089i	−0.397008	+	0.917815i	$0.629951\pi$
$348$	8.85852	−	12.1419i	0.474866	−	0.650874i
$349$	0.480623	+	1.79371i	0.0257272	+	0.0960151i	0.977596	−	0.210492i	$-0.0675065\pi$
$349$	0.480623	+	1.79371i	0.0257272	+	0.0960151i	−0.951868	+	0.306507i	$0.900840\pi$
$350$	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	0.300325	−	0.953837i	$-0.402905\pi$
$353$	23.5636	−	23.5636i	1.25416	−	1.25416i	0.953837	−	0.300325i	$-0.0970952\pi$
$354$	−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	−0.256411	−	0.966568i	$-0.582540\pi$
$359$	0.0912401	−	0.0244477i	0.00481547	−	0.00129030i	0.261226	+	0.965278i	$0.415873\pi$
$360$	−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	−0.730291	−	0.683136i	$-0.760616\pi$
$379$	−19.8801	+	5.32687i	−1.02117	+	0.273623i	−0.290883	+	0.956759i	$0.593949\pi$
$380$	−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	−0.129242	−	0.991613i	$-0.541255\pi$
$383$	16.8769	−	16.8769i	0.862371	−	0.862371i	0.991613	+	0.129242i	$0.0412546\pi$
$384$	−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	0.630265	−	0.776380i	$-0.282946\pi$
$389$	−7.04572	−	12.2036i	−0.357232	−	0.618745i	−0.987497	+	0.157635i	$0.949613\pi$
$390$	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	−0.743863	−	0.668332i	$-0.767008\pi$
$397$	−1.50493	+	1.50493i	−0.0755302	+	0.0755302i	0.668332	+	0.743863i	$0.267008\pi$
$398$	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	0.360537	+	0.932745i	$0.382593\pi$
$401$	−8.37184	+	31.2441i	−0.418070	+	1.56026i	−0.778607	+	0.627512i	$0.784073\pi$
$402$	−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	−0.859417	−	0.511276i	$-0.829173\pi$
$409$	−27.2627	+	7.30503i	−1.34806	+	0.361210i	−0.488639	+	0.872486i	$0.662506\pi$
$410$	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	0.841586	−	0.540122i	$-0.181622\pi$
$419$	16.2655	+	9.39087i	0.794620	+	0.458774i	−0.0469666	+	0.998896i	$0.514955\pi$
$420$	−3.77267	+	17.2346i	−0.184087	+	0.840960i
$421$	6.36724	+	6.36724i	0.310320	+	0.310320i	0.845034	−	0.534713i	$-0.179580\pi$
$421$	6.36724	+	6.36724i	0.310320	+	0.310320i	−0.534713	+	0.845034i	$0.679580\pi$
$422$	−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	−0.983683	−	0.179912i	$-0.942419\pi$
$431$	−16.6867	+	16.6867i	−0.803771	+	0.803771i	0.179912	+	0.983683i	$0.442419\pi$
$432$	1.05003	+	5.08895i	0.0505195	+	0.244842i
$433$	0.164373	−	0.0949005i	0.00789924	−	0.00456063i	−0.496045	−	0.868297i	$-0.665215\pi$
$433$	0.164373	−	0.0949005i	0.00789924	−	0.00456063i	0.503944	+	0.863736i	$0.331882\pi$
$434$	−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	−0.0848241	−	0.996396i	$-0.527033\pi$
$439$	15.4140	−	8.89925i	0.735668	−	0.424738i	0.820492	+	0.571658i	$0.193700\pi$
$440$	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	0.955975	−	0.293447i	$-0.0948023\pi$
$443$	24.8326	+	14.3371i	1.17983	+	0.681176i	0.223855	+	0.974622i	$0.428136\pi$
$444$	−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	0.767626	+	0.640898i	$0.221438\pi$
$449$	−4.61100	+	17.2085i	−0.217606	+	0.812118i	−0.985233	+	0.171221i	$0.945229\pi$
$450$	−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	0.598750	+	0.800936i	$0.295664\pi$
$457$	−6.84618	+	25.5503i	−0.320251	+	1.19519i	−0.919001	+	0.394256i	$0.871002\pi$
$458$			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	0.285966	−	0.958240i	$-0.407685\pi$
$461$	1.17017	+	0.313547i	0.0545004	+	0.0146033i	−0.231466	+	0.972843i	$0.574352\pi$
$462$	−9.93968	−	15.5108i	−0.462436	−	0.721630i
$463$	13.0245	−	13.0245i	0.605302	−	0.605302i	−0.336413	−	0.941715i	$-0.609214\pi$
$463$	13.0245	−	13.0245i	0.605302	−	0.605302i	0.941715	+	0.336413i	$0.109214\pi$
$464$			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	−0.557187	−	0.830387i	$-0.688119\pi$
$467$	9.52020	−	16.4895i	0.440542	−	0.763042i	0.997730	+	0.0673449i	$0.0214528\pi$
$468$	−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	0.999983	−	0.00581938i	$-0.00185238\pi$
$479$	21.7583	+	21.7583i	0.994164	+	0.994164i	−0.00581938	+	0.999983i	$0.501852\pi$
$480$	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	0.0315322	−	0.999503i	$-0.489961\pi$
$487$	12.3270	−	3.30302i	0.558591	−	0.149674i	0.527059	+	0.849829i	$0.323295\pi$
$488$	−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	−0.899807	−	0.436289i	$-0.856293\pi$
$491$	−1.59689	+	2.76589i	−0.0720664	+	0.124823i	0.827740	+	0.561111i	$0.189626\pi$
$492$	−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	0.504150	−	0.863616i	$-0.331806\pi$
$499$	30.6608	−	8.21553i	1.37256	−	0.367777i	0.868415	+	0.495839i	$0.165139\pi$
$500$	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	0.407735	−	0.913100i	$-0.366319\pi$
$503$	31.4519	−	18.1588i	1.40237	−	0.809659i	0.994636	+	0.103441i	$0.0329853\pi$
$504$	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	−0.641333	−	0.767263i	$-0.721618\pi$
$509$	−35.6549	−	9.55370i	−1.58037	−	0.423460i	−0.939042	+	0.343802i	$0.888285\pi$
$510$	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	−0.463636	−	0.886026i	$-0.653455\pi$
$521$	1.64039	−	0.947080i	0.0718668	−	0.0414923i	0.535503	+	0.844533i	$0.320122\pi$
$522$	26.0022	−	1.25913i	1.13808	−	0.0551108i
$523$	15.2438	+	26.4030i	0.666565	+	1.15452i	0.978858	+	0.204539i	$0.0655694\pi$
$523$	15.2438	+	26.4030i	0.666565	+	1.15452i	−0.312294	+	0.949986i	$0.601097\pi$
$524$	−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	−0.903819	−	0.427916i	$-0.859248\pi$
$541$	−7.79299	−	29.0838i	−0.335047	−	1.25041i	0.568772	−	0.822495i	$-0.307419\pi$
$542$	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	−0.999999	−	0.00145828i	$-0.999536\pi$
$557$	−23.6352	−	23.6352i	−1.00146	−	1.00146i	−0.00145828	−	0.999999i	$-0.500464\pi$
$558$	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	−0.398528	−	0.917156i	$-0.630479\pi$
$563$	14.1183	−	24.4536i	0.595016	−	1.03060i	0.993545	−	0.113442i	$-0.0361877\pi$
$564$	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	−0.998540	−	0.0540133i	$-0.982799\pi$
$569$	−13.0253	−	22.5604i	−0.546047	−	0.945781i	0.452493	−	0.891768i	$-0.350535\pi$
$570$	−10.6730	−	4.12133i	−0.447043	−	0.172624i
$571$	−26.2753	+	15.1701i	−1.09959	+	0.634848i	−0.936113	−	0.351700i	$-0.885604\pi$
$571$	−26.2753	+	15.1701i	−1.09959	+	0.634848i	−0.163475	+	0.986547i	$0.552270\pi$
$572$	−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	0.825359	+	0.564609i	$0.190973\pi$
$577$	−4.12503	+	15.3948i	−0.171727	+	0.640895i	−0.997086	+	0.0762863i	$0.975694\pi$
$578$	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	0.957506	+	0.288412i	$0.0931272\pi$
$587$	6.60185	+	24.6384i	0.272487	+	1.01694i	−0.685019	+	0.728525i	$0.740206\pi$
$588$	−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	0.247513	−	0.968885i	$-0.420387\pi$
$593$	23.0441	−	6.17464i	0.946307	−	0.253562i	0.698795	+	0.715322i	$0.253720\pi$
$594$	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	−0.0362029	−	0.999344i	$-0.511526\pi$
$599$	19.8526	−	11.4619i	0.811153	−	0.468320i	0.847356	+	0.531025i	$0.178193\pi$
$600$	−2.62792	−	16.8081i	−0.107284	−	0.686187i
$601$	12.1680	−	21.0756i	0.496343	−	0.859690i	−0.503649	−	0.863909i	$-0.668009\pi$
$601$	12.1680	−	21.0756i	0.496343	−	0.859690i	0.999991	+	0.00421817i	$0.00134269\pi$
$602$	−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	0.592561	−	0.805525i	$-0.298117\pi$
$613$	−5.27274	−	5.27274i	−0.212964	−	0.212964i	−0.805525	+	0.592561i	$0.798117\pi$
$614$	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	0.631492	−	0.775383i	$-0.282443\pi$
$617$	19.6403	+	5.26260i	0.790688	+	0.211864i	0.159196	+	0.987247i	$0.449110\pi$
$618$	3.76962	−	9.76218i	0.151636	−	0.392693i
$619$	−13.3339	−	3.57282i	−0.535936	−	0.143604i	−0.0193082	−	0.999814i	$-0.506146\pi$
$619$	−13.3339	−	3.57282i	−0.535936	−	0.143604i	−0.516628	+	0.856210i	$0.672813\pi$
$620$	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	−0.678579	−	0.734528i	$-0.737404\pi$
$631$	−41.0333	−	10.9948i	−1.63351	−	0.437697i	−0.954930	+	0.296830i	$0.904070\pi$
$632$	−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	−0.882656	−	0.470019i	$-0.844247\pi$
$641$	−0.867888	+	1.50323i	−0.0342795	+	0.0593738i	0.848377	+	0.529393i	$0.177580\pi$
$642$	−3.28111	−	4.06834i	−0.129495	−	0.160564i
$643$	−3.79013	+	14.1449i	−0.149468	+	0.557822i	0.850048	+	0.526706i	$0.176573\pi$
$643$	−3.79013	+	14.1449i	−0.149468	+	0.557822i	−0.999516	+	0.0311165i	$0.990094\pi$
$644$	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	−0.914056	−	0.405589i	$-0.867067\pi$
$653$	−26.0607	+	15.0461i	−1.01983	+	0.588801i	−0.105778	+	0.994390i	$0.533733\pi$
$654$	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	0.185844	−	0.982579i	$-0.440498\pi$
$659$	29.0006	−	16.7435i	1.12970	−	0.652235i	0.943861	+	0.330344i	$0.107165\pi$
$660$	21.6561	+	15.7999i	0.842962	+	0.615010i
$661$	8.95487	−	8.95487i	0.348304	−	0.348304i	−0.511173	−	0.859478i	$-0.670789\pi$
$661$	8.95487	−	8.95487i	0.348304	−	0.348304i	0.859478	+	0.511173i	$0.170789\pi$
$662$	−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	0.759667	−	0.650312i	$-0.225362\pi$
$673$	14.9509	+	8.63190i	0.576315	+	0.332735i	−0.183353	+	0.983047i	$0.558695\pi$
$674$	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	0.456738	−	0.889602i	$-0.349018\pi$
$677$	−2.21973	−	1.28156i	−0.0853113	−	0.0492545i	−0.542049	+	0.840347i	$0.682351\pi$
$678$	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	0.530390	−	0.847754i	$-0.322045\pi$
$683$	36.9434	−	9.89894i	1.41360	−	0.378773i	0.883208	+	0.468981i	$0.155379\pi$
$684$	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	0.756445	+	0.654058i	$0.226935\pi$
$691$	−5.93254	+	22.1405i	−0.225684	+	0.842266i	−0.982129	+	0.188208i	$0.939732\pi$
$692$	−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	−0.138994	−	0.990293i	$-0.544387\pi$
$709$	22.6676	−	22.6676i	0.851299	−	0.851299i	0.990293	+	0.138994i	$0.0443870\pi$
$710$	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	$-0.771798\pi$
$727$		−	35.4327i		−	1.31413i	0.753835	−	0.657064i	$-0.228202\pi$
$728$	−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	0.419374	−	0.907814i	$-0.362250\pi$
$733$	33.4761	−	8.96990i	1.23647	−	0.331311i	0.817095	+	0.576503i	$0.195583\pi$
$734$	−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	−0.752022	−	0.659138i	$-0.770921\pi$
$739$	−2.52499	+	2.52499i	−0.0928834	+	0.0928834i	0.659138	+	0.752022i	$0.270921\pi$
$740$	−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	0.825354	+	0.564616i	$0.190976\pi$
$743$	10.7093	+	39.9675i	0.392884	+	1.46626i	−0.432469	+	0.901649i	$0.642358\pi$
$744$	−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	−0.718743	−	0.695276i	$-0.755282\pi$
$751$	−13.0442	+	7.53105i	−0.475988	+	0.274812i	0.242755	+	0.970088i	$0.421949\pi$
$752$	−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	0.0334769	+	0.999439i	$0.489342\pi$
$757$	−23.3536	+	40.4496i	−0.848802	+	1.47017i	−0.882278	+	0.470728i	$0.843991\pi$
$758$	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	0.949463	−	0.313880i	$-0.101629\pi$
$761$	17.5333	+	17.5333i	0.635583	+	0.635583i	−0.313880	+	0.949463i	$0.601629\pi$
$762$	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	−0.634568	−	0.772867i	$-0.718822\pi$
$769$	−22.1205	+	5.92717i	−0.797686	+	0.213739i	−0.163118	+	0.986607i	$0.552155\pi$
$770$	−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	0.867749	−	0.497002i	$-0.165566\pi$
$773$	−3.67678	−	13.7219i	−0.132245	−	0.493544i	−0.999994	+	0.00345832i	$0.998899\pi$
$774$	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	0.882461	+	0.470386i	$0.155885\pi$
$787$	9.91468	+	37.0021i	0.353420	+	1.31898i	−0.529041	+	0.848596i	$0.677448\pi$
$788$	−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	0.746798	−	0.665051i	$-0.231590\pi$
$797$	−5.71829	−	9.90437i	−0.202552	−	0.350831i	−0.949350	+	0.314220i	$0.898257\pi$
$798$	−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	$0.129460\pi$
$809$			22.5036i			0.791183i	−0.918427	+	0.395591i	$0.870540\pi$
$810$	34.4873	−	3.34790i	1.21176	−	0.117633i
$811$	−13.3542	−	13.3542i	−0.468928	−	0.468928i	0.432639	−	0.901567i	$-0.357582\pi$
$811$	−13.3542	−	13.3542i	−0.468928	−	0.468928i	−0.901567	+	0.432639i	$0.857582\pi$
$812$	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	0.294066	−	0.955785i	$-0.404991\pi$
$821$	2.02986	+	0.543901i	0.0708428	+	0.0189823i	−0.223224	+	0.974767i	$0.571658\pi$
$822$	7.09849	+	16.0291i	0.247588	+	0.559079i
$823$	38.4146	+	22.1787i	1.33905	+	0.773099i	0.986666	−	0.162757i	$-0.0520387\pi$
$823$	38.4146	+	22.1787i	1.33905	+	0.773099i	0.352381	+	0.935857i	$0.385372\pi$
$824$	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	0.845386	−	0.534156i	$-0.179370\pi$
$827$	8.95024	+	8.95024i	0.311231	+	0.311231i	−0.534156	+	0.845386i	$0.679370\pi$
$828$	−14.0194	−	12.7244i	−0.487209	−	0.442203i
$829$			32.7643i			1.13795i	0.822354	+	0.568976i	$0.192660\pi$
$829$			32.7643i			1.13795i	−0.822354	+	0.568976i	$0.807340\pi$
$830$	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	−0.979457	−	0.201655i	$-0.935368\pi$
$839$	−0.880405	+	3.28572i	−0.0303950	+	0.113436i	0.949062	+	0.315090i	$0.102035\pi$
$840$	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	−0.251156	−	0.967947i	$-0.580811\pi$
$853$	20.9347	−	20.9347i	0.716791	−	0.716791i	0.967947	+	0.251156i	$0.0808106\pi$
$854$	−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	0.921800	−	0.387665i	$-0.126718\pi$
$857$	3.66436	+	6.34685i	0.125172	+	0.216804i	−0.796628	+	0.604470i	$0.793385\pi$
$858$	8.30877	−	23.6907i	0.283657	−	0.808786i
$859$	22.8218	−	39.5285i	0.778670	−	1.34870i	−0.154038	−	0.988065i	$-0.549228\pi$
$859$	22.8218	−	39.5285i	0.778670	−	1.34870i	0.932708	−	0.360632i	$-0.117439\pi$
$860$	−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	0.869583	−	0.493787i	$-0.164388\pi$
$863$	−3.83050	−	14.2956i	−0.130392	−	0.486628i	−0.999974	+	0.00715898i	$0.997721\pi$
$864$	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	0.175142	−	0.984543i	$-0.443961\pi$
$877$	−23.9697	−	23.9697i	−0.809401	−	0.809401i	−0.984543	+	0.175142i	$0.943961\pi$
$878$	−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	−0.406270	−	0.913753i	$-0.633171\pi$
$881$	17.4587	−	30.2394i	0.588199	−	1.01879i	0.994468	−	0.105037i	$-0.0334960\pi$
$882$	−20.7001	−	3.53638i	−0.697009	−	0.119076i
$883$		−	56.9398i		−	1.91618i	−0.286475	−	0.958088i	$-0.592483\pi$
$883$		−	56.9398i		−	1.91618i	0.286475	−	0.958088i	$-0.407517\pi$
$884$	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	−0.250838	−	0.968029i	$-0.580706\pi$
$887$	13.7619	−	7.94546i	0.462081	−	0.266782i	0.712919	+	0.701247i	$0.247373\pi$
$888$	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	$0.0581487\pi$
$907$			10.9422i			0.363330i	−0.983360	+	0.181665i	$0.941851\pi$
$908$	−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	$-0.878575\pi$
$911$		−	22.4731i		−	0.744568i	0.928119	−	0.372284i	$-0.121425\pi$
$912$	−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	−0.595396	−	0.803432i	$-0.703005\pi$
$929$	6.34084	−	6.34084i	0.208036	−	0.208036i	0.803432	+	0.595396i	$0.203005\pi$
$930$	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	0.318931	−	0.947778i	$-0.396676\pi$
$941$	3.71927	+	0.996574i	0.121245	+	0.0324874i	−0.197687	+	0.980265i	$0.563343\pi$
$942$	−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	−0.995660	−	0.0930657i	$-0.970333\pi$
$947$	−2.67298	+	9.97571i	−0.0868603	+	0.324167i	0.908800	+	0.417233i	$0.137000\pi$
$948$	−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	0.772967	−	0.634446i	$-0.218772\pi$
$953$	−5.03077	−	8.71354i	−0.162962	−	0.282259i	−0.935930	+	0.352186i	$0.885438\pi$
$954$	−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	0.998184	+	0.0602436i	$0.0191878\pi$
$967$	32.9135	+	32.9135i	1.05843	+	1.05843i	0.0602436	+	0.998184i	$0.480812\pi$
$968$	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	$0.165903\pi$
$971$			31.0312i			0.995839i	−0.867223	+	0.497920i	$0.834097\pi$
$972$	−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	0.109326	−	0.994006i	$-0.465131\pi$
$977$	34.4868	−	34.4868i	1.10333	−	1.10333i	0.994006	−	0.109326i	$-0.0348692\pi$
$978$	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	0.778312	+	0.627878i	$0.216076\pi$
$983$	−6.57359	+	24.5330i	−0.209665	+	0.782481i	−0.987977	+	0.154602i	$0.950590\pi$
$984$	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	−0.982718	−	0.185107i	$-0.940737\pi$
$997$	−10.4531	+	18.1052i	−0.331052	+	0.573399i	0.651667	+	0.758506i	$0.274070\pi$
$998$	−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.527.8	yes	152
3.2	odd	2	inner	546.2.bw.a.527.27	yes	152
7.4	even	3		546.2.ch.a.137.25	yes	152
13.2	odd	12		546.2.ch.a.275.19	yes	152
21.11	odd	6		546.2.ch.a.137.19	yes	152
39.2	even	12		546.2.ch.a.275.25	yes	152
91.67	odd	12	inner	546.2.bw.a.431.27	yes	152
273.158	even	12	inner	546.2.bw.a.431.8	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.8	✓	152	273.158	even	12	inner
546.2.bw.a.431.27	yes	152	91.67	odd	12	inner
546.2.bw.a.527.8	yes	152	1.1	even	1	trivial
546.2.bw.a.527.27	yes	152	3.2	odd	2	inner
546.2.ch.a.137.19	yes	152	21.11	odd	6
546.2.ch.a.137.25	yes	152	7.4	even	3
546.2.ch.a.275.19	yes	152	13.2	odd	12
546.2.ch.a.275.25	yes	152	39.2	even	12

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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