LMFDB - Embedded newform 966.2.y.a.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			151.1
Character	$\chi$	$=$	966.151
Dual form			966.2.y.a.499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-4.11027 + 0.392484i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.51634 + 0.817338i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-4.11027 + 0.392484i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.51634 + 0.817338i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(-0.973442 + 4.01258i) q^{10} +(0.767303 + 2.21698i) q^{11} +(-0.981929 - 0.189251i) q^{12} +(6.58648 - 1.93396i) q^{13} +(-0.0506289 + 2.64527i) q^{14} +(-3.47351 + 2.23229i) q^{15} +(0.235759 + 0.971812i) q^{16} +(6.59644 + 2.64082i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(-4.80281 + 1.92275i) q^{19} +(3.47351 + 2.23229i) q^{20} +(-1.86209 + 1.87953i) q^{21} +2.34600 q^{22} +(-4.79391 + 0.135764i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(11.8307 - 2.28018i) q^{25} +(0.326628 - 6.85676i) q^{26} +(0.142315 - 0.989821i) q^{27} +(2.48322 + 0.913026i) q^{28} +(0.847547 + 5.89482i) q^{29} +(0.973442 + 4.01258i) q^{30} +(0.165193 + 3.46782i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(1.69788 + 1.61893i) q^{33} +(4.65306 - 5.36992i) q^{34} +(10.0221 - 4.34710i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(2.87110 - 4.03189i) q^{37} +(0.246160 + 5.16753i) q^{38} +(4.96810 - 4.73707i) q^{39} +(3.24559 - 2.55236i) q^{40} +(-1.60836 + 3.52182i) q^{41} +(1.16713 + 2.37441i) q^{42} +(3.03880 + 1.95292i) q^{43} +(0.767303 - 2.21698i) q^{44} +(-2.06449 + 3.57579i) q^{45} +(-1.43964 + 4.57465i) q^{46} +(3.14672 + 5.45028i) q^{47} +(0.654861 + 0.755750i) q^{48} +(5.66392 - 4.11340i) q^{49} +(1.71467 - 11.9258i) q^{50} +(7.07325 - 0.675413i) q^{51} +(-6.37282 - 2.55129i) q^{52} +(1.11984 - 1.06777i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(-4.02395 - 8.81122i) q^{55} +(1.67499 - 2.04802i) q^{56} +(-3.38785 + 3.90979i) q^{57} +(5.84781 + 1.12707i) q^{58} +(-2.38028 + 9.81164i) q^{59} +(4.11027 + 0.392484i) q^{60} +(3.92395 + 2.02294i) q^{61} +(3.33113 + 0.978107i) q^{62} +(-0.793836 + 2.52385i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-26.3132 + 10.5342i) q^{65} +(2.08521 - 1.07500i) q^{66} +(-2.75263 + 0.530525i) q^{67} +(-3.55271 - 6.15347i) q^{68} +(-4.19879 + 2.31737i) q^{69} +(-0.830125 - 10.8926i) q^{70} +(-6.51062 - 7.51365i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(4.38612 + 3.44928i) q^{73} +(-2.87110 - 4.03189i) q^{74} +(9.47068 - 7.44783i) q^{75} +(4.96383 + 1.45751i) q^{76} +(-3.74281 - 4.95151i) q^{77} +(-2.85163 - 6.24420i) q^{78} +(-3.42856 - 3.26913i) q^{79} +(-1.35045 - 3.90188i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(2.80208 + 2.67178i) q^{82} +(5.16495 + 11.3097i) q^{83} +(2.62555 - 0.326347i) q^{84} +(-28.1497 - 8.26549i) q^{85} +(2.83940 - 2.23293i) q^{86} +(3.45449 + 4.85116i) q^{87} +(-1.84408 - 1.45020i) q^{88} +(-0.139073 + 2.91949i) q^{89} +(2.70390 + 3.12047i) q^{90} +(-14.9931 + 10.2499i) q^{91} +(3.85219 + 2.85668i) q^{92} +(1.73588 + 3.00663i) q^{93} +(6.17971 - 1.19104i) q^{94} +(18.9862 - 9.78807i) q^{95} +(0.928368 - 0.371662i) q^{96} +(-7.24552 + 15.8655i) q^{97} +(-2.03468 - 6.69777i) q^{98} +(2.25097 + 0.660946i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	0.888835	−	0.458227i	0.513169	−	0.264557i
$3$	0.888835	−	0.458227i	0.513169	−	0.264557i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−4.11027	+	0.392484i	−1.83817	+	0.175524i	−0.955602	−	0.294660i	$-0.904794\pi$
$5$	−4.11027	+	0.392484i	−1.83817	+	0.175524i	−0.882569	+	0.470184i	$0.844188\pi$
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	−2.51634	+	0.817338i	−0.951087	+	0.308925i
$7$	−2.51634	+	0.817338i	−0.951087	+	0.308925i
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	0.580057	−	0.814576i	0.193352	−	0.271525i
$10$	−0.973442	+	4.01258i	−0.307829	+	1.26889i
$11$	0.767303	+	2.21698i	0.231350	+	0.668443i	0.999600	+	0.0282923i	$0.00900693\pi$
$11$	0.767303	+	2.21698i	0.231350	+	0.668443i	−0.768249	+	0.640151i	$0.778872\pi$
$12$	−0.981929	−	0.189251i	−0.283458	−	0.0546321i
$13$	6.58648	−	1.93396i	1.82676	−	0.536385i	0.827090	−	0.562070i	$-0.189995\pi$
$13$	6.58648	−	1.93396i	1.82676	−	0.536385i	0.999670	+	0.0256848i	$0.00817663\pi$
$14$	−0.0506289	+	2.64527i	−0.0135312	+	0.706977i
$15$	−3.47351	+	2.23229i	−0.896857	+	0.576375i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	6.59644	+	2.64082i	1.59987	+	0.640492i	0.988551	−	0.150889i	$-0.0482137\pi$
$17$	6.59644	+	2.64082i	1.59987	+	0.640492i	0.611322	+	0.791382i	$0.290638\pi$
$18$	−0.580057	−	0.814576i	−0.136721	−	0.191997i
$19$	−4.80281	+	1.92275i	−1.10184	+	0.441110i	−0.850066	−	0.526676i	$-0.823438\pi$
$19$	−4.80281	+	1.92275i	−1.10184	+	0.441110i	−0.251774	+	0.967786i	$0.581014\pi$
$20$	3.47351	+	2.23229i	0.776701	+	0.499155i
$21$	−1.86209	+	1.87953i	−0.406340	+	0.410147i
$22$	2.34600			0.500170
$23$	−4.79391	+	0.135764i	−0.999599	+	0.0283087i
$23$	−4.79391	+	0.135764i	−0.999599	+	0.0283087i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	11.8307	−	2.28018i	2.36613	−	0.456035i
$26$	0.326628	−	6.85676i	0.0640570	−	1.34472i
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$	2.48322	+	0.913026i	0.469285	+	0.172546i
$29$	0.847547	+	5.89482i	0.157386	+	1.09464i	0.903427	+	0.428741i	$0.141043\pi$
$29$	0.847547	+	5.89482i	0.157386	+	1.09464i	−0.746042	+	0.665899i	$0.768048\pi$
$30$	0.973442	+	4.01258i	0.177725	+	0.732594i
$31$	0.165193	+	3.46782i	0.0296695	+	0.622839i	0.963915	+	0.266209i	$0.0857713\pi$
$31$	0.165193	+	3.46782i	0.0296695	+	0.622839i	−0.934246	+	0.356630i	$0.883926\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	1.69788	+	1.61893i	0.295563	+	0.281819i
$34$	4.65306	−	5.36992i	0.797993	−	0.920933i
$35$	10.0221	−	4.34710i	1.69404	−	0.734795i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	2.87110	−	4.03189i	0.472005	−	0.662839i	−0.508104	−	0.861295i	$-0.669654\pi$
$37$	2.87110	−	4.03189i	0.472005	−	0.662839i	0.980110	+	0.198457i	$0.0635930\pi$
$38$	0.246160	+	5.16753i	0.0399324	+	0.838284i
$39$	4.96810	−	4.73707i	0.795533	−	0.758539i
$40$	3.24559	−	2.55236i	0.513173	−	0.403564i
$41$	−1.60836	+	3.52182i	−0.251184	+	0.550016i	−0.992657	−	0.120967i	$-0.961400\pi$
$41$	−1.60836	+	3.52182i	−0.251184	+	0.550016i	0.741473	+	0.670983i	$0.234128\pi$
$42$	1.16713	+	2.37441i	0.180092	+	0.366379i
$43$	3.03880	+	1.95292i	0.463412	+	0.297817i	0.751436	−	0.659806i	$-0.229362\pi$
$43$	3.03880	+	1.95292i	0.463412	+	0.297817i	−0.288023	+	0.957623i	$0.592998\pi$
$44$	0.767303	−	2.21698i	0.115675	−	0.334222i
$45$	−2.06449	+	3.57579i	−0.307755	+	0.533048i
$46$	−1.43964	+	4.57465i	−0.212263	+	0.674496i
$47$	3.14672	+	5.45028i	0.458996	+	0.795005i	0.998908	−	0.0467168i	$-0.0148758\pi$
$47$	3.14672	+	5.45028i	0.458996	+	0.795005i	−0.539912	+	0.841721i	$0.681542\pi$
$48$	0.654861	+	0.755750i	0.0945210	+	0.109083i
$49$	5.66392	−	4.11340i	0.809131	−	0.587628i
$50$	1.71467	−	11.9258i	0.242490	−	1.68656i
$51$	7.07325	−	0.675413i	0.990453	−	0.0945768i
$52$	−6.37282	−	2.55129i	−0.883751	−	0.353800i
$53$	1.11984	−	1.06777i	0.153822	−	0.146669i	−0.609260	−	0.792970i	$-0.708534\pi$
$53$	1.11984	−	1.06777i	0.153822	−	0.146669i	0.763082	+	0.646301i	$0.223685\pi$
$54$	−0.888835	−	0.458227i	−0.120955	−	0.0623567i
$55$	−4.02395	−	8.81122i	−0.542589	−	1.18811i
$56$	1.67499	−	2.04802i	0.223830	−	0.273679i
$57$	−3.38785	+	3.90979i	−0.448732	+	0.517864i
$58$	5.84781	+	1.12707i	0.767856	+	0.147992i
$59$	−2.38028	+	9.81164i	−0.309886	+	1.27737i	0.577520	+	0.816377i	$0.304021\pi$
$59$	−2.38028	+	9.81164i	−0.309886	+	1.27737i	−0.887406	+	0.460990i	$0.847495\pi$
$60$	4.11027	+	0.392484i	0.530634	+	0.0506694i
$61$	3.92395	+	2.02294i	0.502410	+	0.259010i	0.690750	−	0.723094i	$-0.257280\pi$
$61$	3.92395	+	2.02294i	0.502410	+	0.259010i	−0.188340	+	0.982104i	$0.560311\pi$
$62$	3.33113	+	0.978107i	0.423053	+	0.124220i
$63$	−0.793836	+	2.52385i	−0.100014	+	0.317975i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−26.3132	+	10.5342i	−3.26375	+	1.30661i
$66$	2.08521	−	1.07500i	0.256672	−	0.132323i
$67$	−2.75263	+	0.530525i	−0.336287	+	0.0648140i	−0.354599	−	0.935018i	$-0.615383\pi$
$67$	−2.75263	+	0.530525i	−0.336287	+	0.0648140i	0.0183125	+	0.999832i	$0.494171\pi$
$68$	−3.55271	−	6.15347i	−0.430829	−	0.746218i
$69$	−4.19879	+	2.31737i	−0.505474	+	0.278978i
$70$	−0.830125	−	10.8926i	−0.0992189	−	1.30192i
$71$	−6.51062	−	7.51365i	−0.772668	−	0.891707i	0.223889	−	0.974615i	$-0.428125\pi$
$71$	−6.51062	−	7.51365i	−0.772668	−	0.891707i	−0.996557	+	0.0829079i	$0.973579\pi$
$72$	−0.0475819	+	0.998867i	−0.00560758	+	0.117718i
$73$	4.38612	+	3.44928i	0.513356	+	0.403708i	0.840952	−	0.541110i	$-0.181996\pi$
$73$	4.38612	+	3.44928i	0.513356	+	0.403708i	−0.327595	+	0.944818i	$0.606238\pi$
$74$	−2.87110	−	4.03189i	−0.333758	−	0.468698i
$75$	9.47068	−	7.44783i	1.09358	−	0.860001i
$76$	4.96383	+	1.45751i	0.569390	+	0.167188i
$77$	−3.74281	−	4.95151i	−0.426533	−	0.564277i
$78$	−2.85163	−	6.24420i	−0.322884	−	0.707017i
$79$	−3.42856	−	3.26913i	−0.385743	−	0.367806i	0.472251	−	0.881464i	$-0.343441\pi$
$79$	−3.42856	−	3.26913i	−0.385743	−	0.367806i	−0.857995	+	0.513658i	$0.828290\pi$
$80$	−1.35045	−	3.90188i	−0.150985	−	0.436244i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	2.80208	+	2.67178i	0.309438	+	0.295049i
$83$	5.16495	+	11.3097i	0.566927	+	1.24140i	0.948417	+	0.317025i	$0.102684\pi$
$83$	5.16495	+	11.3097i	0.566927	+	1.24140i	−0.381490	+	0.924373i	$0.624589\pi$
$84$	2.62555	−	0.326347i	0.286471	−	0.0356074i
$85$	−28.1497	−	8.26549i	−3.05326	−	0.896518i
$86$	2.83940	−	2.23293i	0.306180	−	0.240783i
$87$	3.45449	+	4.85116i	0.370360	+	0.520098i
$88$	−1.84408	−	1.45020i	−0.196580	−	0.154592i
$89$	−0.139073	+	2.91949i	−0.0147417	+	0.309466i	0.979439	+	0.201740i	$0.0646597\pi$
$89$	−0.139073	+	2.91949i	−0.0147417	+	0.309466i	−0.994181	+	0.107725i	$0.965643\pi$
$90$	2.70390	+	3.12047i	0.285016	+	0.328926i
$91$	−14.9931	+	10.2499i	−1.57170	+	1.07448i
$92$	3.85219	+	2.85668i	0.401619	+	0.297830i
$93$	1.73588	+	3.00663i	0.180002	+	0.311773i
$94$	6.17971	−	1.19104i	0.637388	−	0.122847i
$95$	18.9862	−	9.78807i	1.94794	−	1.00423i
$96$	0.928368	−	0.371662i	0.0947512	−	0.0379326i
$97$	−7.24552	+	15.8655i	−0.735671	+	1.61089i	0.0548767	+	0.998493i	$0.482523\pi$
$97$	−7.24552	+	15.8655i	−0.735671	+	1.61089i	−0.790547	+	0.612401i	$0.790204\pi$
$98$	−2.03468	−	6.69777i	−0.205533	−	0.676577i
$99$	2.25097	+	0.660946i	0.226231	+	0.0664275i
$100$	−10.7090	−	5.52090i	−1.07090	−	0.552090i
$101$	−10.9837	−	1.04882i	−1.09292	−	0.104361i	−0.467007	−	0.884254i	$-0.654668\pi$
$101$	−10.9837	−	1.04882i	−1.09292	−	0.104361i	−0.625913	+	0.779892i	$0.715274\pi$
$102$	1.67517	−	6.90513i	0.165866	−	0.683710i
$103$	3.18678	+	0.614201i	0.314003	+	0.0605191i	0.343818	−	0.939036i	$-0.388280\pi$
$103$	3.18678	+	0.614201i	0.314003	+	0.0605191i	−0.0298151	+	0.999555i	$0.509492\pi$
$104$	−4.49532	+	5.18787i	−0.440802	+	0.508713i
$105$	6.91600	−	8.45623i	0.674932	−	0.825244i
$106$	−0.642777	−	1.40748i	−0.0624320	−	0.136707i
$107$	−4.63219	−	2.38806i	−0.447810	−	0.230862i	0.219544	−	0.975603i	$-0.429543\pi$
$107$	−4.63219	−	2.38806i	−0.447810	−	0.230862i	−0.667354	+	0.744740i	$0.732573\pi$
$108$	−0.723734	+	0.690079i	−0.0696413	+	0.0664029i
$109$	−13.4569	−	5.38732i	−1.28894	−	0.516012i	−0.376950	−	0.926234i	$-0.623027\pi$
$109$	−13.4569	−	5.38732i	−1.28894	−	0.516012i	−0.911986	+	0.410222i	$0.865451\pi$
$110$	−9.64272	+	0.920768i	−0.919397	+	0.0877918i
$111$	0.704413	−	4.89930i	0.0668599	−	0.465021i
$112$	−1.38755	−	2.25271i	−0.131111	−	0.212861i
$113$	9.09898	+	10.5008i	0.855960	+	0.987831i	0.999998	−	0.00174153i	$-0.000554345\pi$
$113$	9.09898	+	10.5008i	0.855960	+	0.987831i	−0.144038	+	0.989572i	$0.546009\pi$
$114$	2.58669	+	4.48029i	0.242266	+	0.419617i
$115$	19.6510	−	2.43956i	1.83247	−	0.227490i
$116$	2.97772	−	5.15756i	0.276474	−	0.478867i
$117$	2.24517	−	6.48699i	0.207566	−	0.599723i
$118$	8.49349	+	5.45844i	0.781889	+	0.502490i
$119$	−18.7573	−	1.25367i	−1.71948	−	0.114924i
$120$	1.71524	−	3.75584i	0.156579	−	0.342860i
$121$	4.32036	−	3.39757i	0.392760	−	0.308870i
$122$	3.19507	−	3.04650i	0.289268	−	0.275817i
$123$	0.184223	+	3.86731i	0.0166108	+	0.348704i
$124$	2.01382	−	2.82801i	0.180846	−	0.253963i
$125$	−27.9238	+	8.19916i	−2.49758	+	0.733356i
$126$	2.12540	+	1.57565i	0.189346	+	0.140370i
$127$	0.678886	−	0.783477i	0.0602414	−	0.0695223i	−0.724829	−	0.688929i	$-0.758081\pi$
$127$	0.678886	−	0.783477i	0.0602414	−	0.0695223i	0.785070	+	0.619407i	$0.212627\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	3.59587	+	0.343364i	0.316599	+	0.0302315i
$130$	1.34864	+	28.3114i	0.118283	+	2.48307i
$131$	1.66554	+	6.86543i	0.145519	+	0.599836i	0.997133	+	0.0756671i	$0.0241086\pi$
$131$	1.66554	+	6.86543i	0.145519	+	0.599836i	−0.851615	+	0.524168i	$0.824376\pi$
$132$	−0.333871	−	2.32212i	−0.0290597	−	0.202115i
$133$	10.5140	−	8.76382i	0.911675	−	0.759919i
$134$	−0.398949	+	2.77475i	−0.0344640	+	0.239702i
$135$	−0.196464	+	4.12429i	−0.0169090	+	0.354963i
$136$	−6.97702	+	1.34471i	−0.598274	+	0.115308i
$137$	0.498192	−	0.862894i	0.0425634	−	0.0737220i	−0.843959	−	0.536408i	$-0.819781\pi$
$137$	0.498192	−	0.862894i	0.0425634	−	0.0737220i	0.886522	+	0.462686i	$0.153114\pi$
$138$	0.816626	+	4.72579i	0.0695159	+	0.402286i
$139$	7.09839			0.602077			0.301039	−	0.953612i	$-0.402667\pi$
$139$	7.09839			0.602077			0.301039	+	0.953612i	$0.402667\pi$
$140$	−10.5651	−	2.77817i	−0.892911	−	0.234798i
$141$	5.29438	+	3.40249i	0.445867	+	0.286541i
$142$	−9.22982	+	3.69506i	−0.774550	+	0.310083i
$143$	9.34137	+	13.1181i	0.781165	+	1.09699i
$144$	0.928368	+	0.371662i	0.0773640	+	0.0309719i
$145$	−5.79727	−	23.8967i	−0.481437	−	1.98451i
$146$	4.69413	−	3.01674i	0.388489	−	0.249667i
$147$	3.14942	−	6.25149i	0.259760	−	0.515614i
$148$	−4.74918	+	1.39449i	−0.390380	+	0.114626i
$149$	0.0953618	+	0.0183795i	0.00781234	+	0.00150571i	0.193156	−	0.981168i	$-0.438128\pi$
$149$	0.0953618	+	0.0183795i	0.00781234	+	0.00150571i	−0.185344	+	0.982674i	$0.559340\pi$
$150$	−3.94065	−	11.3858i	−0.321752	−	0.929643i
$151$	0.969952	−	3.99819i	0.0789335	−	0.325368i	−0.918631	−	0.395116i	$-0.870704\pi$
$151$	0.969952	−	3.99819i	0.0789335	−	0.325368i	0.997565	+	0.0697478i	$0.0222195\pi$
$152$	3.00086	−	4.21412i	0.243402	−	0.341810i
$153$	5.97746	−	3.84148i	0.483249	−	0.310565i
$154$	−5.90334	+	1.91748i	−0.475705	+	0.154515i
$155$	−2.04005	−	14.1889i	−0.163861	−	1.13968i
$156$	−6.83346	+	0.652516i	−0.547114	+	0.0522431i
$157$	−13.9923	−	11.0037i	−1.11671	−	0.878188i	−0.123248	−	0.992376i	$-0.539331\pi$
$157$	−13.9923	−	11.0037i	−1.11671	−	0.878188i	−0.993459	+	0.114188i	$0.963573\pi$
$158$	−4.21070	+	2.17077i	−0.334985	+	0.172697i
$159$	0.506076	−	1.46221i	0.0401345	−	0.115961i
$160$	−4.12897			−0.326424
$161$	11.9521	−	4.25987i	0.941960	−	0.335725i
$162$	−1.00000			−0.0785674
$163$	3.42722	−	9.90230i	0.268441	−	0.775608i	−0.727542	−	0.686063i	$-0.759337\pi$
$163$	3.42722	−	9.90230i	0.268441	−	0.775608i	0.995983	−	0.0895451i	$-0.0285413\pi$
$164$	3.44130	−	1.77412i	0.268721	−	0.138535i
$165$	−7.61417	−	5.98785i	−0.592762	−	0.466153i
$166$	12.3769	−	1.18185i	0.960637	−	0.0917297i
$167$	−1.37609	−	9.57092i	−0.106485	−	0.740620i	−0.971184	−	0.238330i	$-0.923400\pi$
$167$	−1.37609	−	9.57092i	−0.106485	−	0.740620i	0.864699	−	0.502290i	$-0.167509\pi$
$168$	0.550334	−	2.58788i	0.0424592	−	0.199659i
$169$	28.7052	−	18.4477i	2.20809	−	1.41905i
$170$	−17.0178	+	23.8981i	−1.30520	+	1.83290i
$171$	−1.21967	+	5.02756i	−0.0932707	+	0.384467i
$172$	−1.18144	−	3.41356i	−0.0900842	−	0.260281i
$173$	6.20982	+	1.19684i	0.472124	+	0.0909944i	0.419763	−	0.907634i	$-0.362113\pi$
$173$	6.20982	+	1.19684i	0.472124	+	0.0909944i	0.0523611	+	0.998628i	$0.483325\pi$
$174$	5.71420	−	1.67784i	0.433192	−	0.127197i
$175$	−27.9063	+	15.4073i	−2.10952	+	1.16469i
$176$	−1.97358	+	1.26835i	−0.148764	+	0.0956051i
$177$	2.38028	+	9.81164i	0.178913	+	0.737488i
$178$	2.71344	+	1.08630i	0.203381	+	0.0814213i
$179$	−4.75973	−	6.68410i	−0.355759	−	0.499593i	0.597450	−	0.801906i	$-0.296181\pi$
$179$	−4.75973	−	6.68410i	−0.355759	−	0.499593i	−0.953209	+	0.302313i	$0.902241\pi$
$180$	3.83320	−	1.53458i	0.285710	−	0.114381i
$181$	18.8612	+	12.1214i	1.40194	+	0.900975i	0.999893	−	0.0146423i	$-0.00466095\pi$
$181$	18.8612	+	12.1214i	1.40194	+	0.900975i	0.402051	+	0.915617i	$0.368297\pi$
$182$	4.78238	+	17.5209i	0.354494	+	1.29874i
$183$	4.41471			0.326344
$184$	3.95949	−	2.70599i	0.291898	−	0.199489i
$185$	−10.2185	+	17.6990i	−0.751282	+	1.30126i
$186$	3.40902	−	0.657034i	0.249961	−	0.0481761i
$187$	−0.793159	+	16.6505i	−0.0580015	+	1.21760i
$188$	0.895650	−	6.22938i	0.0653220	−	0.454324i
$189$	0.450906	+	2.60705i	0.0327986	+	0.189635i
$190$	−3.03995	−	21.1433i	−0.220541	−	1.53390i
$191$	5.26331	+	21.6956i	0.380839	+	1.56984i	0.763409	+	0.645915i	$0.223524\pi$
$191$	5.26331	+	21.6956i	0.380839	+	1.56984i	−0.382570	+	0.923927i	$0.624961\pi$
$192$	−0.0475819	−	0.998867i	−0.00343393	−	0.0720870i
$193$	12.2926	+	1.17381i	0.884844	+	0.0844924i	0.527574	−	0.849509i	$-0.323102\pi$
$193$	12.2926	+	1.17381i	0.884844	+	0.0844924i	0.357270	+	0.934001i	$0.383708\pi$
$194$	12.6231	+	12.0361i	0.906286	+	0.864142i
$195$	−18.5610	+	21.4206i	−1.32918	+	1.53396i
$196$	−6.99487	−	0.267854i	−0.499634	−	0.0191324i
$197$	−0.461218	+	0.135426i	−0.0328604	+	0.00964869i	−0.298121	−	0.954528i	$-0.596360\pi$
$197$	−0.461218	+	0.135426i	−0.0328604	+	0.00964869i	0.265261	+	0.964177i	$0.414542\pi$
$198$	1.36082	−	1.91100i	0.0967089	−	0.135809i
$199$	0.402565	+	8.45088i	0.0285371	+	0.599067i	0.967167	+	0.254141i	$0.0817928\pi$
$199$	0.402565	+	8.45088i	0.0285371	+	0.599067i	−0.938630	+	0.344926i	$0.887904\pi$
$200$	−8.71984	+	8.31435i	−0.616586	+	0.587913i
$201$	−2.20353	+	1.73288i	−0.155425	+	0.122228i
$202$	−4.58355	+	10.0366i	−0.322498	+	0.706172i
$203$	−6.95077	−	14.1406i	−0.487849	−	0.992477i
$204$	−5.97746	−	3.84148i	−0.418506	−	0.268957i
$205$	5.22855	−	15.1069i	0.365178	−	1.05511i
$206$	1.62271	−	2.81062i	0.113060	−	0.195825i
$207$	−2.67015	+	3.98375i	−0.185588	+	0.276890i
$208$	3.43227	+	5.94486i	0.237985	+	0.412202i
$209$	−7.94790	−	9.17237i	−0.549768	−	0.634466i
$210$	−5.72914	−	9.30138i	−0.395348	−	0.641856i
$211$	−2.14028	+	14.8859i	−0.147343	+	1.02479i	0.773204	+	0.634158i	$0.218653\pi$
$211$	−2.14028	+	14.8859i	−0.147343	+	1.02479i	−0.920546	+	0.390633i	$0.872256\pi$
$212$	−1.54031	+	0.147081i	−0.105789	+	0.0101016i
$213$	−9.22982	−	3.69506i	−0.632417	−	0.253182i
$214$	−3.77176	+	3.59636i	−0.257832	+	0.245842i
$215$	−13.2568	−	6.83434i	−0.904105	−	0.466098i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	−3.25006	−	8.59120i	−0.220629	−	0.583209i
$218$	−9.49234	+	10.9547i	−0.642902	+	0.741949i
$219$	5.47909	+	1.05601i	0.370243	+	0.0713584i
$220$	−2.28370	+	9.41353i	−0.153967	+	0.634660i
$221$	48.5546	+	4.63640i	3.26613	+	0.311878i
$222$	−4.39945	−	2.26807i	−0.295272	−	0.152223i
$223$	7.32942	+	2.15211i	0.490814	+	0.144116i	0.517769	−	0.855521i	$-0.326763\pi$
$223$	7.32942	+	2.15211i	0.490814	+	0.144116i	−0.0269544	+	0.999637i	$0.508581\pi$
$224$	−2.58264	+	0.574444i	−0.172560	+	0.0383816i
$225$	5.00509	−	10.9596i	0.333672	−	0.730641i
$226$	12.8992	−	5.16407i	0.858044	−	0.343509i
$227$	2.76554	−	1.42574i	0.183556	−	0.0946295i	−0.363999	−	0.931399i	$-0.618589\pi$
$227$	2.76554	−	1.42574i	0.183556	−	0.0946295i	0.547555	+	0.836770i	$0.315559\pi$
$228$	5.07990	−	0.979070i	0.336424	−	0.0648405i
$229$	6.39040	+	11.0685i	0.422290	+	0.731427i	0.996163	−	0.0875171i	$-0.0278932\pi$
$229$	6.39040	+	11.0685i	0.422290	+	0.731427i	−0.573874	+	0.818944i	$0.694560\pi$
$230$	4.12183	−	19.3681i	0.271785	−	1.27710i
$231$	−5.59566	−	2.68603i	−0.368167	−	0.176728i
$232$	−3.89998	−	4.50082i	−0.256046	−	0.295493i
$233$	0.308698	−	6.48037i	0.0202235	−	0.424543i	−0.965940	−	0.258767i	$-0.916684\pi$
$233$	0.308698	−	6.48037i	0.0202235	−	0.424543i	0.986163	−	0.165776i	$-0.0530130\pi$
$234$	−5.39589	−	4.24338i	−0.352740	−	0.277398i
$235$	−15.0730	−	21.1671i	−0.983256	−	1.38079i
$236$	7.93617	−	6.24108i	0.516601	−	0.406260i
$237$	−4.54543	−	1.33466i	−0.295257	−	0.0866954i
$238$	−7.31964	+	17.3157i	−0.474462	+	1.12241i
$239$	−4.19859	−	9.19363i	−0.271584	−	0.594686i	0.723869	−	0.689937i	$-0.242362\pi$
$239$	−4.19859	−	9.19363i	−0.271584	−	0.594686i	−0.995453	+	0.0952509i	$0.969635\pi$
$240$	−2.98828	−	2.84932i	−0.192892	−	0.183923i
$241$	−5.85081	−	16.9048i	−0.376884	−	1.08893i	−0.960829	−	0.277141i	$-0.910613\pi$
$241$	−5.85081	−	16.9048i	−0.376884	−	1.08893i	0.583946	−	0.811793i	$-0.301508\pi$
$242$	−1.79765	−	5.19398i	−0.115558	−	0.333882i
$243$	−0.723734	−	0.690079i	−0.0464276	−	0.0442686i
$244$	−1.83394	−	4.01576i	−0.117406	−	0.257083i
$245$	−21.6658	+	19.1302i	−1.38418	+	1.22218i
$246$	3.71487	+	1.09078i	0.236851	+	0.0695458i
$247$	−27.9150	+	21.9526i	−1.77619	+	1.39681i
$248$	−2.01382	−	2.82801i	−0.127877	−	0.179579i
$249$	9.77319	+	7.68572i	0.619351	+	0.487063i
$250$	−1.38476	+	29.0697i	−0.0875799	+	1.83853i
$251$	−16.6020	−	19.1597i	−1.04791	−	1.20935i	−0.977303	−	0.211844i	$-0.932053\pi$
$251$	−16.6020	−	19.1597i	−1.04791	−	1.20935i	−0.0706031	−	0.997504i	$-0.522492\pi$
$252$	2.18414	−	1.49316i	0.137588	−	0.0940605i
$253$	−3.97936	−	10.5238i	−0.250180	−	0.661626i
$254$	−0.518344	−	0.897798i	−0.0325238	−	0.0563329i
$255$	−28.8079	+	5.55227i	−1.80402	+	0.347696i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−9.15380	+	3.66463i	−0.570999	+	0.228593i	−0.639151	−	0.769082i	$-0.720714\pi$
$257$	−9.15380	+	3.66463i	−0.570999	+	0.228593i	0.0681520	+	0.997675i	$0.478290\pi$
$258$	1.50057	−	3.28580i	0.0934216	−	0.204565i
$259$	−3.92923	+	12.4923i	−0.244151	+	0.776231i
$260$	27.1954	+	7.98528i	1.68659	+	0.495226i
$261$	5.29340	+	2.72894i	0.327653	+	0.168917i
$262$	7.03258	+	0.671530i	0.434474	+	0.0414873i
$263$	6.40486	−	26.4012i	0.394941	−	1.62797i	−0.333423	−	0.942777i	$-0.608204\pi$
$263$	6.40486	−	26.4012i	0.394941	−	1.62797i	0.728364	−	0.685191i	$-0.240281\pi$
$264$	−2.30361	−	0.443984i	−0.141777	−	0.0273253i
$265$	−4.18378	+	4.82834i	−0.257007	+	0.296602i
$266$	−4.84304	−	12.8021i	−0.296946	−	0.784944i
$267$	1.21418	+	2.65867i	0.0743064	+	0.162708i
$268$	2.49166	+	1.28454i	0.152202	+	0.0784658i
$269$	2.31419	−	2.20657i	0.141099	−	0.134537i	−0.616243	−	0.787556i	$-0.711346\pi$
$269$	2.31419	−	2.20657i	0.141099	−	0.134537i	0.757342	+	0.653019i	$0.226498\pi$
$270$	3.83320	+	1.53458i	0.233281	+	0.0933918i
$271$	−9.46113	+	0.903429i	−0.574723	+	0.0548794i	−0.378371	−	0.925654i	$-0.623516\pi$
$271$	−9.46113	+	0.903429i	−0.574723	+	0.0548794i	−0.196352	+	0.980533i	$0.562910\pi$
$272$	−1.01121	+	7.03310i	−0.0613134	+	0.426444i
$273$	−8.62963	+	15.9807i	−0.522289	+	0.967196i
$274$	−0.652493	−	0.753017i	−0.0394185	−	0.0454914i
$275$	14.1328	+	24.4787i	0.852240	+	1.47612i
$276$	4.73297	+	0.773943i	0.284891	+	0.0465859i
$277$	−12.4860	+	21.6263i	−0.750208	+	1.29940i	0.197513	+	0.980300i	$0.436714\pi$
$277$	−12.4860	+	21.6263i	−0.750208	+	1.29940i	−0.947721	+	0.319099i	$0.896620\pi$
$278$	2.32165	−	6.70798i	0.139244	−	0.402318i
$279$	2.92063	+	1.87697i	0.174853	+	0.112371i
$280$	−6.08086	+	9.07535i	−0.363401	+	0.542356i
$281$	3.36953	−	7.37824i	0.201009	−	0.440149i	−0.782104	−	0.623148i	$-0.785853\pi$
$281$	3.36953	−	7.37824i	0.201009	−	0.440149i	0.983113	+	0.182999i	$0.0585806\pi$
$282$	4.94698	−	3.89035i	0.294588	−	0.231667i
$283$	23.2253	−	22.1453i	1.38060	−	1.31640i	0.482982	−	0.875630i	$-0.339554\pi$
$283$	23.2253	−	22.1453i	1.38060	−	1.31640i	0.897620	−	0.440771i	$-0.145295\pi$
$284$	0.473059	+	9.93073i	0.0280709	+	0.589280i
$285$	12.3905	−	17.4000i	0.733948	−	1.03069i
$286$	15.4519	−	4.53709i	0.913690	−	0.268284i
$287$	1.16867	−	10.1767i	0.0689842	−	0.600710i
$288$	0.654861	−	0.755750i	0.0385880	−	0.0445330i
$289$	24.2357	+	23.1087i	1.42563	+	1.35933i
$290$	−24.4785	−	2.33741i	−1.43743	−	0.137258i
$291$	0.829906	+	17.4219i	0.0486500	+	1.02129i
$292$	−1.31552	−	5.42264i	−0.0769849	−	0.317336i
$293$	−1.09314	−	7.60293i	−0.0638617	−	0.444168i	−0.996516	−	0.0833976i	$-0.973423\pi$
$293$	−1.09314	−	7.60293i	−0.0638617	−	0.444168i	0.932655	−	0.360771i	$-0.117486\pi$
$294$	−4.87759	−	5.02087i	−0.284467	−	0.292823i
$295$	5.93269	−	41.2627i	0.345414	−	2.40241i
$296$	−0.235515	+	4.94407i	−0.0136890	+	0.287368i
$297$	2.30361	−	0.443984i	0.133669	−	0.0257626i
$298$	0.0485584	−	0.0841056i	0.00281291	−	0.00487211i
$299$	−31.3124	+	10.1655i	−1.81084	+	0.587883i
$300$	−12.0484			−0.695615
$301$	−9.24283	−	2.43048i	−0.532748	−	0.140090i
$302$	−3.46106	−	2.22429i	−0.199161	−	0.127993i
$303$	−10.2433	+	4.10080i	−0.588463	+	0.235585i
$304$	−3.00086	−	4.21412i	−0.172111	−	0.241696i
$305$	−16.9225	−	6.77473i	−0.968978	−	0.387920i
$306$	−1.67517	−	6.90513i	−0.0957629	−	0.394740i
$307$	10.6796	−	6.86337i	0.609518	−	0.391713i	−0.199158	−	0.979967i	$-0.563821\pi$
$307$	10.6796	−	6.86337i	0.609518	−	0.391713i	0.808676	+	0.588254i	$0.200184\pi$
$308$	−0.118776	+	6.20580i	−0.00676787	+	0.353609i
$309$	3.11397	−	0.914343i	0.177147	−	0.0520152i
$310$	−14.0757	−	2.71287i	−0.799448	−	0.154081i
$311$	5.91766	+	17.0980i	0.335560	+	0.969537i	0.978968	+	0.204013i	$0.0653986\pi$
$311$	5.91766	+	17.0980i	0.335560	+	0.969537i	−0.643408	+	0.765523i	$0.722480\pi$
$312$	−1.61838	+	6.67104i	−0.0916225	+	0.377673i
$313$	−0.401796	+	0.564243i	−0.0227108	+	0.0318929i	−0.825775	−	0.563999i	$-0.809262\pi$
$313$	−0.401796	+	0.564243i	−0.0227108	+	0.0318929i	0.803064	+	0.595892i	$0.203201\pi$
$314$	−14.9749	+	9.62379i	−0.845083	+	0.543102i
$315$	2.27231	−	10.6853i	0.128030	−	0.602048i
$316$	0.674192	+	4.68911i	0.0379262	+	0.263783i
$317$	−14.9915	+	1.43152i	−0.842008	+	0.0804020i	−0.507141	−	0.861863i	$-0.669298\pi$
$317$	−14.9915	+	1.43152i	−0.842008	+	0.0804020i	−0.334867	+	0.942265i	$0.608692\pi$
$318$	−1.21627	−	0.956485i	−0.0682050	−	0.0536370i
$319$	−12.4183	+	6.40210i	−0.695294	+	0.358449i
$320$	−1.35045	+	3.90188i	−0.0754927	+	0.218122i
$321$	−5.21152			−0.290879
$322$	−0.116421	−	12.6880i	−0.00648789	−	0.707077i
$323$	−36.7591			−2.04533
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	73.5127	−	37.8984i	4.07775	−	2.10223i
$326$	−8.23675	−	6.47745i	−0.456191	−	0.358753i
$327$	−14.4296	+	1.37786i	−0.797957	+	0.0761957i
$328$	−0.551000	−	3.83229i	−0.0304239	−	0.211603i
$329$	−12.3729	−	11.1428i	−0.682142	−	0.614323i
$330$	−8.14887	+	5.23696i	−0.448581	+	0.288285i
$331$	−2.40209	+	3.37326i	−0.132031	+	0.185411i	−0.875299	−	0.483583i	$-0.839335\pi$
$331$	−2.40209	+	3.37326i	−0.132031	+	0.185411i	0.743268	+	0.668994i	$0.233275\pi$
$332$	2.93125	−	12.0828i	0.160873	−	0.663128i
$333$	−1.61888	−	4.67745i	−0.0887142	−	0.256323i
$334$	−9.49460	−	1.82993i	−0.519521	−	0.100130i
$335$	11.1058	−	3.26097i	0.606776	−	0.178166i
$336$	−2.26555	−	1.36648i	−0.123596	−	0.0745476i
$337$	4.88505	−	3.13943i	0.266106	−	0.171016i	−0.400783	−	0.916173i	$-0.631262\pi$
$337$	4.88505	−	3.13943i	0.266106	−	0.171016i	0.666889	+	0.745157i	$0.267626\pi$
$338$	−8.04454	−	33.1600i	−0.437565	−	1.80367i
$339$	12.8992	+	5.16407i	0.700590	+	0.280474i
$340$	17.0178	+	23.8981i	0.922917	+	1.29606i
$341$	−7.56133	+	3.02710i	−0.409469	+	0.163927i
$342$	4.35213	+	2.79694i	0.235336	+	0.151241i
$343$	−10.8903	+	14.9800i	−0.588021	+	0.808846i
$344$	−3.61223			−0.194758
$345$	16.3486	−	11.1730i	0.880181	−	0.601533i
$346$	3.16205	−	5.47684i	0.169993	−	0.294437i
$347$	−21.7208	+	4.18635i	−1.16604	+	0.224735i	−0.735299	−	0.677743i	$-0.762958\pi$
$347$	−21.7208	+	4.18635i	−1.16604	+	0.224735i	−0.430737	+	0.902478i	$0.641746\pi$
$348$	0.283371	−	5.94869i	0.0151903	−	0.318883i
$349$	−1.55632	+	10.8245i	−0.0833081	+	0.579421i	0.904821	+	0.425793i	$0.140005\pi$
$349$	−1.55632	+	10.8245i	−0.0833081	+	0.579421i	−0.988129	+	0.153628i	$0.950904\pi$
$350$	5.43270	+	31.4107i	0.290390	+	1.67897i
$351$	−0.976926	−	6.79467i	−0.0521444	−	0.362673i
$352$	0.553091	+	2.27987i	0.0294799	+	0.121518i
$353$	−0.365329	−	7.66921i	−0.0194445	−	0.408191i	−0.987516	−	0.157517i	$-0.949651\pi$
$353$	−0.365329	−	7.66921i	−0.0194445	−	0.408191i	0.968072	−	0.250673i	$-0.0806520\pi$
$354$	10.0505	+	0.959708i	0.534179	+	0.0510079i
$355$	29.7094	+	28.3279i	1.57681	+	1.50349i
$356$	1.91403	−	2.20891i	0.101443	−	0.117072i
$357$	−17.2466	+	7.48080i	−0.912789	+	0.395926i
$358$	−7.87323	+	2.31179i	−0.416113	+	0.122182i
$359$	11.1109	−	15.6031i	0.586411	−	0.823499i	−0.409643	−	0.912246i	$-0.634347\pi$
$359$	11.1109	−	15.6031i	0.586411	−	0.823499i	0.996054	+	0.0887467i	$0.0282862\pi$
$360$	−0.196464	−	4.12429i	−0.0103546	−	0.217369i
$361$	5.61903	−	5.35774i	0.295739	−	0.281986i
$362$	17.6236	−	13.8594i	0.926277	−	0.728432i
$363$	2.28323	−	4.99958i	0.119839	−	0.262410i
$364$	18.1214	+	1.21117i	0.949821	+	0.0634825i
$365$	−19.3819	−	12.4560i	−1.01450	−	0.651978i
$366$	1.44391	−	4.17190i	0.0754743	−	0.218069i
$367$	−8.88293	+	15.3857i	−0.463685	+	0.803126i	−0.999141	−	0.0414371i	$-0.986806\pi$
$367$	−8.88293	+	15.3857i	−0.463685	+	0.803126i	0.535456	+	0.844563i	$0.320140\pi$
$368$	−1.26214	−	4.62677i	−0.0657938	−	0.241187i
$369$	1.93585	+	3.35299i	0.100776	+	0.174550i
$370$	13.3834	+	15.4453i	0.695772	+	0.802964i
$371$	−1.94518	+	3.60215i	−0.100989	+	0.187015i
$372$	0.494082	−	3.43642i	0.0256170	−	0.178170i
$373$	−1.39564	+	0.133268i	−0.0722635	+	0.00690033i	−0.131125	−	0.991366i	$-0.541859\pi$
$373$	−1.39564	+	0.133268i	−0.0722635	+	0.00690033i	0.0588616	+	0.998266i	$0.481253\pi$
$374$	15.4753	+	6.19537i	0.800208	+	0.320355i
$375$	−21.0626	+	20.0831i	−1.08767	+	1.03709i
$376$	−5.59383	−	2.88382i	−0.288480	−	0.148722i
$377$	16.9827	+	37.1870i	0.874654	+	1.91523i
$378$	2.61114	+	0.426574i	0.134302	+	0.0219406i
$379$	14.0628	−	16.2294i	0.722359	−	0.833647i	−0.269230	−	0.963076i	$-0.586769\pi$
$379$	14.0628	−	16.2294i	0.722359	−	0.833647i	0.991589	+	0.129429i	$0.0413145\pi$
$380$	−20.9748	−	4.04255i	−1.07598	−	0.207379i
$381$	0.244409	−	1.00747i	0.0125214	−	0.0516140i
$382$	22.2239	+	2.12212i	1.13707	+	0.108577i
$383$	0.343480	+	0.177076i	0.0175510	+	0.00904818i	0.466980	−	0.884268i	$-0.345342\pi$
$383$	0.343480	+	0.177076i	0.0175510	+	0.00904818i	−0.449429	+	0.893316i	$0.648372\pi$
$384$	−0.959493	−	0.281733i	−0.0489639	−	0.0143771i
$385$	17.3274	+	18.8831i	0.883084	+	0.962372i
$386$	5.12978	−	11.2326i	0.261099	−	0.571727i
$387$	3.35347	−	1.34253i	0.170467	−	0.0682446i
$388$	15.5027	−	7.99222i	0.787032	−	0.405743i
$389$	−14.4281	+	2.78079i	−0.731533	+	0.140991i	−0.541398	−	0.840766i	$-0.682105\pi$
$389$	−14.4281	+	2.78079i	−0.731533	+	0.140991i	−0.190135	+	0.981758i	$0.560893\pi$
$390$	14.1717	+	24.5462i	0.717614	+	1.24294i
$391$	−31.9813	−	11.7643i	−1.61736	−	0.594945i
$392$	−2.54092	+	6.52255i	−0.128336	+	0.329439i
$393$	4.62631	+	5.33905i	0.233366	+	0.269319i
$394$	−0.0228721	+	0.480145i	−0.00115228	+	0.0241894i
$395$	15.3754	+	12.0914i	0.773621	+	0.608382i
$396$	−1.36082	−	1.91100i	−0.0683835	−	0.0960313i
$397$	−2.82762	+	2.22366i	−0.141914	+	0.111602i	−0.686592	−	0.727043i	$-0.740894\pi$
$397$	−2.82762	+	2.22366i	−0.141914	+	0.111602i	0.544678	+	0.838645i	$0.316652\pi$
$398$	8.11775	+	2.38359i	0.406906	+	0.119478i
$399$	5.32936	−	12.6074i	0.266802	−	0.631158i
$400$	5.00509	+	10.9596i	0.250254	+	0.547981i
$401$	12.9839	+	12.3801i	0.648386	+	0.618235i	0.941166	−	0.337945i	$-0.109732\pi$
$401$	12.9839	+	12.3801i	0.648386	+	0.618235i	−0.292780	+	0.956180i	$0.594580\pi$
$402$	0.916865	+	2.64911i	0.0457291	+	0.132125i
$403$	7.79468	+	22.5213i	0.388281	+	1.12186i
$404$	7.98545	+	7.61411i	0.397291	+	0.378816i
$405$	1.71524	+	3.75584i	0.0852308	+	0.186629i
$406$	−15.6363	+	1.94354i	−0.776015	+	0.0964562i
$407$	11.1416	+	3.27147i	0.552268	+	0.162161i
$408$	−5.58524	+	4.39228i	−0.276510	+	0.217450i
$409$	−1.47431	−	2.07038i	−0.0728999	−	0.102374i	0.776516	−	0.630097i	$-0.216985\pi$
$409$	−1.47431	−	2.07038i	−0.0728999	−	0.102374i	−0.849416	+	0.527724i	$0.823046\pi$
$410$	−12.5659	−	9.88197i	−0.620588	−	0.488036i
$411$	0.0474099	−	0.995256i	0.00233856	−	0.0490924i
$412$	−2.12530	−	2.45273i	−0.104706	−	0.120837i
$413$	−2.02984	−	26.6349i	−0.0998817	−	1.31062i
$414$	2.89133	+	3.82625i	0.142101	+	0.188050i
$415$	−25.6682	−	44.4587i	−1.26000	−	2.18239i
$416$	6.74049	−	1.29912i	0.330480	−	0.0636947i
$417$	6.30930	−	3.25267i	0.308968	−	0.159284i
$418$	−11.2674	+	4.51079i	−0.551107	+	0.220630i
$419$	5.30923	−	11.6256i	0.259373	−	0.567947i	−0.734483	−	0.678627i	$-0.762575\pi$
$419$	5.30923	−	11.6256i	0.259373	−	0.567947i	0.993856	+	0.110680i	$0.0353028\pi$
$420$	−10.6636	+	2.37186i	−0.520332	+	0.115735i
$421$	1.21452	+	0.356615i	0.0591921	+	0.0173804i	0.311195	−	0.950346i	$-0.399271\pi$
$421$	1.21452	+	0.356615i	0.0591921	+	0.0173804i	−0.252002	+	0.967727i	$0.581089\pi$
$422$	13.3672	+	6.89128i	0.650706	+	0.335462i
$423$	6.26494	+	0.598229i	0.304612	+	0.0290869i
$424$	−0.364793	+	1.50370i	−0.0177159	+	0.0730259i
$425$	84.0619	+	16.2016i	4.07760	+	0.785893i
$426$	−6.51062	+	7.51365i	−0.315441	+	0.364038i
$427$	−11.5274	−	1.88320i	−0.557850	−	0.0911344i
$428$	2.16495	+	4.74057i	0.104647	+	0.229144i
$429$	14.3140	+	7.37939i	0.691087	+	0.356280i
$430$	−10.7943	+	10.2924i	−0.520549	+	0.496342i
$431$	19.5147	+	7.81250i	0.939990	+	0.376315i	0.790510	−	0.612450i	$-0.209816\pi$
$431$	19.5147	+	7.81250i	0.939990	+	0.376315i	0.149480	+	0.988765i	$0.452240\pi$
$432$	0.995472	−	0.0950560i	0.0478947	−	0.00457339i
$433$	1.63764	−	11.3901i	0.0787001	−	0.547371i	−0.911882	−	0.410452i	$-0.865371\pi$
$433$	1.63764	−	11.3901i	0.0787001	−	0.547371i	0.990582	−	0.136919i	$-0.0437200\pi$
$434$	−9.18168	+	0.261407i	−0.440735	+	0.0125479i
$435$	−16.1029	−	18.5837i	−0.772075	−	0.891023i
$436$	7.24760	+	12.5532i	0.347097	+	0.601190i
$437$	22.7632	−	9.86956i	1.08891	−	0.472125i
$438$	2.78996	−	4.83236i	0.133310	−	0.230899i
$439$	−4.36124	+	12.6010i	−0.208151	+	0.601412i	−0.999956	−	0.00936154i	$-0.997020\pi$
$439$	−4.36124	+	12.6010i	−0.208151	+	0.601412i	0.791806	+	0.610773i	$0.209141\pi$
$440$	8.14887	+	5.23696i	0.388482	+	0.249662i
$441$	−0.0652788	−	6.99970i	−0.00310851	−	0.333319i
$442$	20.2620	−	44.3677i	0.963767	−	2.11036i
$443$	−18.1773	+	14.2948i	−0.863631	+	0.679167i	−0.948346	−	0.317238i	$-0.897244\pi$
$443$	−18.1773	+	14.2948i	−0.863631	+	0.679167i	0.0847148	+	0.996405i	$0.473002\pi$
$444$	−3.58225	+	3.41567i	−0.170006	+	0.162101i
$445$	−0.574227	−	12.0545i	−0.0272209	−	0.571438i
$446$	4.43097	−	6.22242i	0.209812	−	0.294640i
$447$	0.0931829	−	0.0273610i	0.00440740	−	0.00129413i
$448$	−0.301848	+	2.62848i	−0.0142610	+	0.124184i
$449$	14.0304	−	16.1919i	0.662134	−	0.764144i	−0.320990	−	0.947083i	$-0.604016\pi$
$449$	14.0304	−	16.1919i	0.662134	−	0.764144i	0.983124	+	0.182939i	$0.0585611\pi$
$450$	−8.71984	−	8.31435i	−0.411057	−	0.391942i
$451$	−9.04189	−	0.863396i	−0.425766	−	0.0406557i
$452$	−0.661128	−	13.8788i	−0.0310969	−	0.652803i
$453$	−0.969952	−	3.99819i	−0.0455723	−	0.187852i
$454$	−0.442802	−	3.07975i	−0.0207817	−	0.144540i
$455$	57.6029	−	48.0144i	2.70046	−	2.25095i
$456$	0.736250	−	5.12073i	0.0344781	−	0.239800i
$457$	−1.08923	+	22.8658i	−0.0509520	+	1.06962i	0.818157	+	0.574995i	$0.194996\pi$
$457$	−1.08923	+	22.8658i	−0.0509520	+	1.06962i	−0.869109	+	0.494620i	$0.835307\pi$
$458$	12.5498	−	2.41878i	0.586415	−	0.113022i
$459$	3.55271	−	6.15347i	0.165826	−	0.287220i
$460$	−16.9548	−	10.2298i	−0.790520	−	0.476968i
$461$	11.3786			0.529953			0.264976	−	0.964255i	$-0.414636\pi$
$461$	11.3786			0.529953			0.264976	+	0.964255i	$0.414636\pi$
$462$	−4.36846	+	4.40939i	−0.203239	+	0.205143i
$463$	−4.43630	−	2.85104i	−0.206172	−	0.132499i	0.433480	−	0.901163i	$-0.357285\pi$
$463$	−4.43630	−	2.85104i	−0.206172	−	0.132499i	−0.639653	+	0.768664i	$0.720922\pi$
$464$	−5.52884	+	2.21341i	−0.256670	+	0.102755i
$465$	−8.31499	−	11.6768i	−0.385598	−	0.541497i
$466$	−6.02299	−	2.41124i	−0.279010	−	0.111699i
$467$	−7.83094	−	32.2796i	−0.362373	−	1.49372i	−0.802972	−	0.596016i	$-0.796749\pi$
$467$	−7.83094	−	32.2796i	−0.362373	−	1.49372i	0.440600	−	0.897704i	$-0.354766\pi$
$468$	−5.77482	+	3.71125i	−0.266941	+	0.171553i
$469$	6.49292	−	3.58481i	0.299815	−	0.165531i
$470$	−24.9328	+	7.32094i	−1.15007	+	0.337690i
$471$	−17.4790	−	3.36881i	−0.805391	−	0.155226i
$472$	−3.30215	−	9.54095i	−0.151994	−	0.439158i
$473$	−1.99789	+	8.23542i	−0.0918631	+	0.378665i
$474$	−2.74792	+	3.85891i	−0.126216	+	0.177246i
$475$	−52.4362	+	33.6987i	−2.40594	+	1.54620i
$476$	13.9693	+	12.5805i	0.640281	+	0.576624i
$477$	−0.220205	−	1.53156i	−0.0100825	−	0.0701254i
$478$	−10.0612	+	0.960729i	−0.460189	+	0.0439427i
$479$	31.3897	+	24.6851i	1.43423	+	1.12789i	0.970267	+	0.242036i	$0.0778153\pi$
$479$	31.3897	+	24.6851i	1.43423	+	1.12789i	0.463963	+	0.885855i	$0.346427\pi$
$480$	−3.66998	+	1.89200i	−0.167511	+	0.0863578i
$481$	11.1129	−	32.1085i	0.506703	−	1.46402i
$482$	−17.8887			−0.814806
$483$	8.67149	−	9.26311i	0.394567	−	0.421486i
$484$	−5.49627			−0.249830
$485$	23.5541	−	68.0552i	1.06954	−	3.09023i
$486$	−0.888835	+	0.458227i	−0.0403184	+	0.0207856i
$487$	−0.0530122	−	0.0416893i	−0.00240221	−	0.00188912i	0.616957	−	0.786997i	$-0.288365\pi$
$487$	−0.0530122	−	0.0416893i	−0.00240221	−	0.00188912i	−0.619359	+	0.785108i	$0.712608\pi$
$488$	−4.39472	+	0.419644i	−0.198939	+	0.0189964i
$489$	−1.49126	−	10.3720i	−0.0674372	−	0.469036i
$490$	10.9918	+	26.7311i	0.496561	+	1.20759i
$491$	11.3213	−	7.27579i	0.510925	−	0.328352i	−0.259648	−	0.965703i	$-0.583607\pi$
$491$	11.3213	−	7.27579i	0.510925	−	0.328352i	0.770573	+	0.637352i	$0.219970\pi$
$492$	2.24581	−	3.15379i	0.101249	−	0.142184i
$493$	−9.97635	+	41.1231i	−0.449312	+	1.85209i
$494$	11.6151	+	33.5597i	0.522590	+	1.50992i
$495$	−9.51153	−	1.83320i	−0.427512	−	0.0823961i
$496$	−3.33113	+	0.978107i	−0.149572	+	0.0439183i
$497$	22.5241	+	13.5855i	1.01034	+	0.609394i
$498$	10.4595	−	6.72192i	0.468702	−	0.301216i
$499$	1.27674	+	5.26278i	0.0571545	+	0.235594i	0.993223	−	0.116223i	$-0.0370789\pi$
$499$	1.27674	+	5.26278i	0.0571545	+	0.235594i	−0.936069	+	0.351818i	$0.885564\pi$
$500$	27.0180	+	10.8164i	1.20828	+	0.483722i
$501$	−5.60877	−	7.87641i	−0.250581	−	0.351892i
$502$	−23.5359	+	9.42235i	−1.05046	+	0.420540i
$503$	26.6249	+	17.1108i	1.18714	+	0.762931i	0.976686	−	0.214672i	$-0.0688682\pi$
$503$	26.6249	+	17.1108i	1.18714	+	0.762931i	0.210458	+	0.977603i	$0.432505\pi$
$504$	−0.696680	−	2.55238i	−0.0310326	−	0.113692i
$505$	45.5577			2.02729
$506$	−11.2465	+	0.318502i	−0.499969	+	0.0141592i
$507$	17.0609	−	29.5504i	0.757703	−	1.31238i
$508$	−1.01795	+	0.196195i	−0.0451644	+	0.00870472i
$509$	−0.605306	+	12.7069i	−0.0268297	+	0.563225i	0.944933	+	0.327264i	$0.106127\pi$
$509$	−0.605306	+	12.7069i	−0.0268297	+	0.563225i	−0.971763	+	0.235961i	$0.924176\pi$
$510$	−4.17524	+	29.0395i	−0.184883	+	1.28589i
$511$	−13.8562	−	5.09462i	−0.612962	−	0.225373i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	1.21967	+	5.02756i	0.0538499	+	0.221972i
$514$	0.469163	+	9.84894i	0.0206939	+	0.434418i
$515$	−13.3396	−	1.27378i	−0.587813	−	0.0561294i
$516$	−2.61429	−	2.49272i	−0.115088	−	0.109736i
$517$	−9.66864	+	11.1582i	−0.425226	+	0.490738i
$518$	10.5201	+	7.79894i	0.462225	+	0.342666i
$519$	6.06794	−	1.78171i	0.266353	−	0.0782082i
$520$	16.4408	−	23.0879i	0.720978	−	1.01247i
$521$	−0.459950	−	9.65555i	−0.0201508	−	0.423017i	−0.986293	−	0.165006i	$-0.947236\pi$
$521$	−0.459950	−	9.65555i	−0.0201508	−	0.423017i	0.966142	−	0.258012i	$-0.0830673\pi$
$522$	4.31015	−	4.10972i	0.188650	−	0.179878i
$523$	19.6973	−	15.4902i	0.861304	−	0.677337i	−0.0864786	−	0.996254i	$-0.527561\pi$
$523$	19.6973	−	15.4902i	0.861304	−	0.677337i	0.947783	+	0.318917i	$0.103319\pi$
$524$	2.93473	−	6.42616i	0.128204	−	0.280728i
$525$	−17.7441	+	26.4820i	−0.774414	+	1.15577i
$526$	−22.8543	−	14.6876i	−0.996497	−	0.640409i
$527$	−8.06821	+	23.3115i	−0.351457	+	1.01547i
$528$	−1.17300	+	2.03170i	−0.0510483	+	0.0884183i
$529$	22.9631	−	1.30168i	0.998397	−	0.0565947i
$530$	3.19440	+	5.53287i	0.138756	+	0.240332i
$531$	6.61163	+	7.63022i	0.286920	+	0.331123i
$532$	−13.6820	+	0.389532i	−0.593188	+	0.0168883i
$533$	−3.78236	+	26.3069i	−0.163832	+	1.13948i
$534$	2.90957	−	0.277830i	0.125909	−	0.0120229i
$535$	19.9768	+	7.99752i	0.863674	+	0.345763i
$536$	2.02883	−	1.93449i	0.0876323	−	0.0835572i
$537$	−7.29344	−	3.76003i	−0.314735	−	0.162257i
$538$	−1.32832	−	2.90861i	−0.0572678	−	0.125399i
$539$	13.4652	+	9.40055i	0.579989	+	0.404910i
$540$	2.70390	−	3.12047i	0.116357	−	0.134284i
$541$	−29.1924	−	5.62637i	−1.25508	−	0.241896i	−0.481979	−	0.876183i	$-0.660082\pi$
$541$	−29.1924	−	5.62637i	−1.25508	−	0.241896i	−0.773098	+	0.634286i	$0.781294\pi$
$542$	−2.24069	+	9.23626i	−0.0962460	+	0.396731i
$543$	22.3189	+	2.13119i	0.957794	+	0.0914583i
$544$	6.31555	+	3.25589i	0.270777	+	0.139595i
$545$	57.4259	+	16.8618i	2.45986	+	0.722279i
$546$	12.2793	+	13.3818i	0.525505	+	0.572687i
$547$	−17.8942	+	39.1828i	−0.765100	+	1.67534i	−0.0279475	+	0.999609i	$0.508897\pi$
$547$	−17.8942	+	39.1828i	−0.765100	+	1.67534i	−0.737153	+	0.675726i	$0.763830\pi$
$548$	−0.925011	+	0.370319i	−0.0395145	+	0.0158192i
$549$	3.92395	−	2.02294i	0.167470	−	0.0863368i
$550$	27.7548	−	5.34930i	1.18347	−	0.228095i
$551$	−15.4049	−	26.6821i	−0.656271	−	1.13669i
$552$	2.27938	−	4.21953i	0.0970168	−	0.179595i
$553$	11.2994	+	5.42394i	0.480500	+	0.230649i
$554$	16.3531	+	18.8725i	0.694778	+	0.801816i
$555$	−0.972435	+	20.4139i	−0.0412776	+	0.866523i
$556$	−5.57971	−	4.38793i	−0.236632	−	0.186090i
$557$	−26.1654	−	36.7442i	−1.10866	−	1.55690i	−0.794225	−	0.607624i	$-0.792123\pi$
$557$	−26.1654	−	36.7442i	−1.10866	−	1.55690i	−0.314439	−	0.949278i	$-0.601817\pi$
$558$	2.72898	−	2.14610i	0.115527	−	0.0908515i
$559$	23.7918	+	6.98591i	1.00629	+	0.295473i
$560$	6.58735	+	8.71468i	0.278367	+	0.368262i
$561$	6.92469	+	15.1630i	0.292361	+	0.640181i
$562$	−5.87038	−	5.59739i	−0.247627	−	0.236112i
$563$	5.08099	+	14.6806i	0.214138	+	0.618712i	1.00000		0.000309465i	$9.85059e-5\pi$
$563$	5.08099	+	14.6806i	0.214138	+	0.618712i	−0.785862	+	0.618402i	$0.787780\pi$
$564$	−2.05838	−	5.94730i	−0.0866735	−	0.250427i
$565$	−41.5207	−	39.5899i	−1.74679	−	1.66556i
$566$	−13.3311	−	29.1910i	−0.560346	−	1.22699i
$567$	1.59540	+	2.11062i	0.0670004	+	0.0886376i
$568$	9.53927	+	2.80098i	0.400259	+	0.117527i
$569$	14.6784	−	11.5432i	0.615351	−	0.483917i	−0.261162	−	0.965295i	$-0.584106\pi$
$569$	14.6784	−	11.5432i	0.615351	−	0.483917i	0.876513	+	0.481378i	$0.159863\pi$
$570$	−12.3905	−	17.4000i	−0.518979	−	0.728805i
$571$	−29.4132	−	23.1308i	−1.23091	−	0.967995i	−0.230918	−	0.972973i	$-0.574173\pi$
$571$	−29.4132	−	23.1308i	−1.23091	−	0.967995i	−0.999988	+	0.00497791i	$0.998415\pi$
$572$	0.766270	−	16.0860i	0.0320394	−	0.672589i
$573$	14.6197	+	16.8721i	0.610748	+	0.704841i
$574$	−9.23473	−	4.43285i	−0.385450	−	0.185024i
$575$	−56.4056	+	12.5371i	−2.35228	+	0.522834i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−31.6985	+	6.10939i	−1.31963	+	0.254337i	−0.799971	−	0.600039i	$-0.795152\pi$
$577$	−31.6985	+	6.10939i	−1.31963	+	0.254337i	−0.519655	+	0.854376i	$0.673940\pi$
$578$	29.7644	−	15.3446i	1.23804	−	0.638252i
$579$	11.4640	−	4.58950i	0.476428	−	0.190733i
$580$	−10.2150	+	22.3677i	−0.424154	+	0.928768i
$581$	−22.2406	−	24.2375i	−0.922695	−	1.00554i
$582$	16.7351	+	4.91388i	0.693693	+	0.203687i
$583$	3.22647	+	1.66336i	0.133627	+	0.0688894i
$584$	−5.55466	−	0.530406i	−0.229854	−	0.0219484i
$585$	−6.68223	+	27.5445i	−0.276276	+	1.13883i
$586$	−7.54231	−	1.45366i	−0.311570	−	0.0600502i
$587$	0.868865	−	1.00272i	0.0358619	−	0.0413868i	−0.737535	−	0.675309i	$-0.764010\pi$
$587$	0.868865	−	1.00272i	0.0358619	−	0.0413868i	0.773397	+	0.633922i	$0.218556\pi$
$588$	−6.34003	+	2.96716i	−0.261458	+	0.122364i
$589$	−7.46116	−	16.3377i	−0.307432	−	0.673182i
$590$	−37.0529	−	19.1021i	−1.52545	−	0.786422i
$591$	−0.347891	+	0.331714i	−0.0143103	+	0.0136449i
$592$	4.59512	+	1.83961i	0.188858	+	0.0756075i
$593$	33.2926	−	3.17905i	1.36716	−	0.130548i	0.614480	−	0.788933i	$-0.289366\pi$
$593$	33.2926	−	3.17905i	1.36716	−	0.130548i	0.752682	+	0.658384i	$0.228760\pi$
$594$	0.333871	−	2.32212i	0.0136989	−	0.0952779i
$595$	77.5898	−	2.20902i	3.18087	−	0.0905609i
$596$	−0.0635980	−	0.0733960i	−0.00260507	−	0.00300642i
$597$	4.23023	+	7.32697i	0.173132	+	0.299873i
$598$	−0.634924	+	32.9150i	−0.0259640	+	1.34600i
$599$	13.6915	−	23.7143i	0.559419	−	0.968941i	−0.438126	−	0.898913i	$-0.644358\pi$
$599$	13.6915	−	23.7143i	0.559419	−	0.968941i	0.997545	−	0.0700281i	$-0.0223089\pi$
$600$	−3.94065	+	11.3858i	−0.160876	+	0.464821i
$601$	−27.9229	−	17.9450i	−1.13900	−	0.731991i	−0.171581	−	0.985170i	$-0.554888\pi$
$601$	−27.9229	−	17.9450i	−1.13900	−	0.731991i	−0.967420	+	0.253179i	$0.918524\pi$
$602$	−5.31984	+	7.93956i	−0.216820	+	0.323592i
$603$	−1.16453	+	2.54996i	−0.0474232	+	0.103842i
$604$	−3.23395	+	2.54321i	−0.131588	+	0.103482i
$605$	−16.4244	+	15.6606i	−0.667746	+	0.636694i
$606$	0.525003	+	11.0212i	0.0213268	+	0.447705i
$607$	3.35628	−	4.71324i	0.136227	−	0.191304i	−0.740827	−	0.671696i	$-0.765566\pi$
$607$	3.35628	−	4.71324i	0.136227	−	0.191304i	0.877054	+	0.480392i	$0.159505\pi$
$608$	−4.96383	+	1.45751i	−0.201310	+	0.0591099i
$609$	−12.6577	−	9.38366i	−0.512916	−	0.380245i
$610$	−11.9369	+	13.7759i	−0.483312	+	0.557772i
$611$	31.2664	+	29.8125i	1.26490	+	1.20608i
$612$	−7.07325	−	0.675413i	−0.285919	−	0.0273020i
$613$	−1.09061	−	22.8947i	−0.0440493	−	0.924709i	−0.907442	−	0.420177i	$-0.861968\pi$
$613$	−1.09061	−	22.8947i	−0.0440493	−	0.924709i	0.863393	−	0.504532i	$-0.168335\pi$
$614$	−2.99293	−	12.3370i	−0.120785	−	0.497882i
$615$	−2.27506	−	15.8234i	−0.0917394	−	0.638062i
$616$	5.82564	+	2.14196i	0.234722	+	0.0863022i
$617$	−4.51604	+	31.4098i	−0.181809	+	1.26451i	0.670673	+	0.741753i	$0.266005\pi$
$617$	−4.51604	+	31.4098i	−0.181809	+	1.26451i	−0.852482	+	0.522756i	$0.824904\pi$
$618$	0.154424	−	3.24175i	0.00621183	−	0.130402i
$619$	−29.3381	+	5.65446i	−1.17920	+	0.227272i	−0.740936	−	0.671575i	$-0.765618\pi$
$619$	−29.3381	+	5.65446i	−1.17920	+	0.227272i	−0.438262	+	0.898847i	$0.644406\pi$
$620$	−7.16739	+	12.4143i	−0.287849	+	0.498570i
$621$	−0.547862	+	4.76444i	−0.0219850	+	0.191190i
$622$	18.0931			0.725466
$623$	−2.03626	−	7.46010i	−0.0815809	−	0.298883i
$624$	5.77482	+	3.71125i	0.231178	+	0.148569i
$625$	55.6297	−	22.2708i	2.22519	−	0.890830i
$626$	0.401796	+	0.564243i	0.0160590	+	0.0225517i
$627$	−11.2674	−	4.51079i	−0.449977	−	0.180144i
$628$	4.19668	+	17.2989i	0.167466	+	0.690303i
$629$	29.5865	−	19.0141i	1.17969	−	0.758142i
$630$	−9.35441	−	5.64215i	−0.372688	−	0.224789i
$631$	−16.3431	+	4.79877i	−0.650609	+	0.191036i	−0.590351	−	0.807147i	$-0.701011\pi$
$631$	−16.3431	+	4.79877i	−0.650609	+	0.191036i	−0.0602582	+	0.998183i	$0.519192\pi$
$632$	4.65171	+	0.896544i	0.185035	+	0.0356626i
$633$	4.91878	+	14.2119i	0.195504	+	0.564872i
$634$	−3.55046	+	14.6352i	−0.141007	+	0.581239i
$635$	−2.48291	+	3.48676i	−0.0985312	+	0.138368i
$636$	−1.30168	+	0.836540i	−0.0516150	+	0.0331710i
$637$	29.3501	−	38.0466i	1.16289	−	1.50746i
$638$	1.98835	+	13.8293i	0.0787195	+	0.547506i
$639$	−9.89697	+	0.945046i	−0.391518	+	0.0373854i
$640$	3.24559	+	2.55236i	0.128293	+	0.100891i
$641$	1.38577	−	0.714412i	0.0547345	−	0.0282176i	−0.430642	−	0.902523i	$-0.641713\pi$
$641$	1.38577	−	0.714412i	0.0547345	−	0.0282176i	0.485377	+	0.874305i	$0.338683\pi$
$642$	−1.70452	+	4.92489i	−0.0672721	+	0.194370i
$643$	6.27964			0.247645			0.123822	−	0.992304i	$-0.460485\pi$
$643$	6.27964			0.247645			0.123822	+	0.992304i	$0.460485\pi$
$644$	−12.0283	−	4.03983i	−0.473981	−	0.159192i
$645$	−14.9148			−0.587269
$646$	−12.0227	+	34.7374i	−0.473028	+	1.36672i
$647$	−4.47247	+	2.30572i	−0.175831	+	0.0906471i	−0.543895	−	0.839153i	$-0.683051\pi$
$647$	−4.47247	+	2.30572i	−0.175831	+	0.0906471i	0.368064	+	0.929800i	$0.380021\pi$
$648$	0.786053	+	0.618159i	0.0308791	+	0.0242836i
$649$	−23.5785	+	2.25148i	−0.925539	+	0.0883782i
$650$	−11.7704	−	81.8649i	−0.461673	−	3.21100i
$651$	−6.82549	−	6.14690i	−0.267512	−	0.240916i
$652$	−8.81517	+	5.66517i	−0.345229	+	0.221865i
$653$	−17.8427	+	25.0566i	−0.698238	+	0.980539i	0.301396	+	0.953499i	$0.402547\pi$
$653$	−17.8427	+	25.0566i	−0.698238	+	0.980539i	−0.999634	+	0.0270397i	$0.991392\pi$
$654$	−3.41737	+	14.0866i	−0.133630	+	0.550830i
$655$	−9.54038	−	27.5651i	−0.372773	−	1.07706i
$656$	−3.80173	−	0.732724i	−0.148433	−	0.0286081i
$657$	5.35390	−	1.57205i	0.208876	−	0.0613314i
$658$	−14.5768	+	8.04797i	−0.568261	+	0.313743i
$659$	−21.0477	+	13.5265i	−0.819900	+	0.526918i	−0.882054	−	0.471149i	$-0.843840\pi$
$659$	−21.0477	+	13.5265i	−0.819900	+	0.526918i	0.0621536	+	0.998067i	$0.480203\pi$
$660$	2.28370	+	9.41353i	0.0888928	+	0.366421i
$661$	−13.4598	−	5.38849i	−0.523526	−	0.209588i	0.0948198	−	0.995494i	$-0.469772\pi$
$661$	−13.4598	−	5.38849i	−0.523526	−	0.209588i	−0.618345	+	0.785906i	$0.712197\pi$
$662$	2.40209	+	3.37326i	0.0933598	+	0.131105i
$663$	45.2815	−	18.1280i	1.75859	−	0.704033i
$664$	−10.4595	−	6.72192i	−0.405908	−	0.260861i
$665$	−39.7756	+	40.1482i	−1.54243	+	1.55688i
$666$	−4.94968			−0.191796
$667$	−4.86337	−	28.1442i	−0.188310	−	1.08975i
$668$	−4.83467	+	8.37389i	−0.187059	+	0.323996i
$669$	7.50081	−	1.44566i	0.289998	−	0.0558925i
$670$	0.550746	−	11.5616i	0.0212772	−	0.446663i
$671$	−1.47394	+	10.2515i	−0.0569009	+	0.395755i
$672$	−2.03231	+	1.69402i	−0.0783982	+	0.0653482i
$673$	−0.119304	−	0.829776i	−0.00459882	−	0.0319855i	0.987393	−	0.158289i	$-0.0505978\pi$
$673$	−0.119304	−	0.829776i	−0.00459882	−	0.0319855i	−0.991992	+	0.126304i	$0.959689\pi$
$674$	−1.36902	−	5.64319i	−0.0527328	−	0.217367i
$675$	−0.573286	−	12.0348i	−0.0220658	−	0.463218i
$676$	−33.9674	−	3.24349i	−1.30644	−	0.124750i
$677$	−35.3423	−	33.6988i	−1.35831	−	1.29515i	−0.917602	−	0.397500i	$-0.869878\pi$
$677$	−35.3423	−	33.6988i	−1.35831	−	1.29515i	−0.440711	−	0.897649i	$-0.645274\pi$
$678$	9.09898	−	10.5008i	0.349444	−	0.403280i
$679$	5.26473	−	45.8449i	0.202042	−	1.75937i
$680$	28.1497	−	8.26549i	1.07949	−	0.316967i
$681$	1.80480	−	2.53449i	0.0691602	−	0.0971219i
$682$	0.387543	+	8.13553i	0.0148398	+	0.311525i
$683$	−23.6227	+	22.5242i	−0.903896	+	0.861863i	−0.990935	−	0.134342i	$-0.957108\pi$
$683$	−23.6227	+	22.5242i	−0.903896	+	0.861863i	0.0870392	+	0.996205i	$0.472259\pi$
$684$	4.06656	−	3.19798i	0.155489	−	0.122278i
$685$	−1.70904	+	3.74226i	−0.0652989	+	0.142985i
$686$	10.5943	+	15.1908i	0.404491	+	0.579989i
$687$	10.7519	+	6.90982i	0.410210	+	0.263626i
$688$	−1.18144	+	3.41356i	−0.0450421	+	0.130141i
$689$	5.31079	−	9.19856i	0.202325	−	0.350437i
$690$	−5.21136	−	19.1038i	−0.198393	−	0.727269i
$691$	11.2833	+	19.5433i	0.429238	+	0.743461i	0.996806	−	0.0798651i	$-0.0254490\pi$
$691$	11.2833	+	19.5433i	0.429238	+	0.743461i	−0.567568	+	0.823326i	$0.692116\pi$
$692$	−4.14141	−	4.77944i	−0.157433	−	0.181687i
$693$	−6.20443	+	0.176643i	−0.235687	+	0.00671011i
$694$	−3.14809	+	21.8954i	−0.119500	+	0.831139i
$695$	−29.1763	+	2.78600i	−1.10672	+	0.105679i
$696$	−5.52884	−	2.21341i	−0.209570	−	0.0838992i
$697$	−19.9100	+	18.9841i	−0.754143	+	0.719074i
$698$	9.72011	+	5.01107i	0.367912	+	0.189672i
$699$	−2.69509	−	5.90143i	−0.101938	−	0.223213i
$700$	31.4600	+	5.13954i	1.18908	+	0.194256i
$701$	28.4944	−	32.8843i	1.07622	−	1.24202i	0.107411	−	0.994215i	$-0.465744\pi$
$701$	28.4944	−	32.8843i	1.07622	−	1.24202i	0.968809	−	0.247809i	$-0.0797105\pi$
$702$	−6.74049	−	1.29912i	−0.254403	−	0.0490322i
$703$	−6.03699	+	24.8848i	−0.227689	+	0.938548i
$704$	2.33538	+	0.223002i	0.0880180	+	0.00840470i
$705$	−23.0968	−	11.9072i	−0.869875	−	0.448452i
$706$	−7.36690	−	2.16312i	−0.277257	−	0.0814099i
$707$	28.4960	−	6.33822i	1.07170	−	0.238373i
$708$	4.19413	−	9.18386i	0.157625	−	0.345150i
$709$	35.3323	−	14.1449i	1.32693	−	0.531224i	0.403498	−	0.914980i	$-0.367794\pi$
$709$	35.3323	−	14.1449i	1.32693	−	0.531224i	0.923434	+	0.383757i	$0.125370\pi$
$710$	36.4869	−	18.8103i	1.36933	−	0.705937i
$711$	−4.65171	+	0.896544i	−0.174453	+	0.0336230i
$712$	−1.46140	−	2.53122i	−0.0547683	−	0.0948615i
$713$	−1.26272	−	16.6020i	−0.0472894	−	0.621750i
$714$	1.42854	+	18.7448i	0.0534617	+	0.701507i
$715$	−43.5442	−	50.2527i	−1.62846	−	1.87935i
$716$	−0.390439	+	8.19632i	−0.0145914	+	0.306311i
$717$	−7.94462	−	6.24772i	−0.296697	−	0.233325i
$718$	−11.1109	−	15.6031i	−0.414655	−	0.582302i
$719$	17.4845	−	13.7499i	0.652061	−	0.512787i	−0.236449	−	0.971644i	$-0.575984\pi$
$719$	17.4845	−	13.7499i	0.652061	−	0.512787i	0.888510	+	0.458857i	$0.151741\pi$
$720$	−3.96172	−	1.16327i	−0.147645	−	0.0433523i
$721$	−8.52103	+	1.05914i	−0.317340	+	0.0394443i
$722$	−3.22526	−	7.06233i	−0.120032	−	0.262833i
$723$	−12.9466	−	12.3446i	−0.481490	−	0.459100i
$724$	−7.33299	−	21.1873i	−0.272528	−	0.787419i
$725$	23.4683	+	67.8071i	0.871590	+	2.51829i
$726$	−3.97784	−	3.79286i	−0.147631	−	0.140766i
$727$	−0.162304	−	0.355397i	−0.00601953	−	0.0131809i	0.906598	−	0.421995i	$-0.138670\pi$
$727$	−0.162304	−	0.355397i	−0.00601953	−	0.0131809i	−0.912618	+	0.408814i	$0.865943\pi$
$728$	7.07149	−	16.7286i	0.262087	−	0.620004i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−18.1102	+	14.2420i	−0.670287	+	0.527120i
$731$	14.8880	+	20.9072i	0.550651	+	0.773281i
$732$	−3.47019	−	2.72899i	−0.128262	−	0.100866i
$733$	−1.40986	+	29.5967i	−0.0520745	+	1.09318i	0.810011	+	0.586415i	$0.199461\pi$
$733$	−1.40986	+	29.5967i	−0.0520745	+	1.09318i	−0.862086	+	0.506763i	$0.830842\pi$
$734$	11.6342	+	13.4265i	0.429425	+	0.495582i
$735$	−10.4914	+	26.9314i	−0.386981	+	0.993381i
$736$	−4.78511	−	0.320541i	−0.176381	−	0.0118153i
$737$	−3.28826	−	5.69543i	−0.121125	−	0.209794i
$738$	3.80173	−	0.732724i	0.139944	−	0.0269719i
$739$	−22.6865	+	11.6957i	−0.834535	+	0.430233i	−0.821862	−	0.569687i	$-0.807064\pi$
$739$	−22.6865	+	11.6957i	−0.834535	+	0.430233i	−0.0126732	+	0.999920i	$0.504034\pi$
$740$	18.9731	−	7.59570i	0.697466	−	0.279223i
$741$	−14.7526	+	32.3037i	−0.541950	+	1.18671i
$742$	2.76783	+	3.01634i	0.101610	+	0.110733i
$743$	−22.6592	−	6.65335i	−0.831286	−	0.244088i	−0.161717	−	0.986837i	$-0.551703\pi$
$743$	−22.6592	−	6.65335i	−0.831286	−	0.244088i	−0.669569	+	0.742750i	$0.733521\pi$
$744$	−3.08582	−	1.59085i	−0.113132	−	0.0583234i
$745$	−0.399177	−	0.0381168i	−0.0146247	−	0.00139649i
$746$	−0.330531	+	1.36247i	−0.0121016	+	0.0498835i
$747$	12.2086	+	2.35301i	0.446688	+	0.0860920i
$748$	10.9161	−	12.5978i	0.399132	−	0.460623i
$749$	13.6080	+	2.22310i	0.497226	+	0.0812304i
$750$	12.0897	+	26.4727i	0.441453	+	0.966646i
$751$	20.6234	+	10.6321i	0.752560	+	0.387972i	0.791420	−	0.611273i	$-0.209342\pi$
$751$	20.6234	+	10.6321i	0.752560	+	0.387972i	−0.0388598	+	0.999245i	$0.512373\pi$
$752$	−4.55478	+	4.34297i	−0.166096	+	0.158372i
$753$	−23.5359	−	9.42235i	−0.857695	−	0.343369i
$754$	40.6962	−	3.88602i	1.48207	−	0.141520i
$755$	−2.41754	+	16.8144i	−0.0879833	+	0.611938i
$756$	1.25713	−	2.32801i	0.0457215	−	0.0846688i
$757$	15.3831	+	17.7531i	0.559109	+	0.645246i	0.962981	−	0.269570i	$-0.0868814\pi$
$757$	15.3831	+	17.7531i	0.559109	+	0.645246i	−0.403872	+	0.914815i	$0.632336\pi$
$758$	−10.7373	−	18.5975i	−0.389995	−	0.675491i
$759$	−8.35929	−	7.53048i	−0.303423	−	0.273339i
$760$	−10.6804	+	18.4990i	−0.387418	+	0.671028i
$761$	11.3037	−	32.6598i	0.409758	−	1.18392i	−0.531743	−	0.846906i	$-0.678463\pi$
$761$	11.3037	−	32.6598i	0.409758	−	1.18392i	0.941501	−	0.337011i	$-0.109416\pi$
$762$	−0.872118	−	0.560476i	−0.0315935	−	0.0203039i
$763$	38.2653	+	2.55751i	1.38530	+	0.0925881i
$764$	9.27412	−	20.3075i	0.335526	−	0.734699i
$765$	−23.0613	+	18.1356i	−0.833783	+	0.655694i
$766$	0.279679	−	0.266673i	0.0101052	−	0.00963529i
$767$	3.29771	+	69.2275i	0.119073	+	2.49966i
$768$	−0.580057	+	0.814576i	−0.0209310	+	0.0293935i
$769$	−45.3888	+	13.3273i	−1.63676	+	0.480596i	−0.965452	−	0.260582i	$-0.916086\pi$
$769$	−45.3888	+	13.3273i	−1.63676	+	0.480596i	−0.671309	+	0.741178i	$0.734268\pi$
$770$	23.5118	−	10.1983i	0.847305	−	0.367522i
$771$	−6.45699	+	7.45177i	−0.232543	+	0.268369i
$772$	−8.93708	−	8.52148i	−0.321652	−	0.306695i
$773$	−6.11048	−	0.583480i	−0.219779	−	0.0209863i	−0.0154142	−	0.999881i	$-0.504907\pi$
$773$	−6.11048	−	0.583480i	−0.219779	−	0.0209863i	−0.204364	+	0.978895i	$0.565513\pi$
$774$	−0.171877	−	3.60813i	−0.00617798	−	0.129692i
$775$	9.86159	+	40.6500i	0.354239	+	1.46019i
$776$	−2.48220	−	17.2641i	−0.0891059	−	0.619745i
$777$	2.23184	+	12.9040i	0.0800668	+	0.462930i
$778$	−2.09112	+	14.5441i	−0.0749703	+	0.521430i
$779$	0.953056	−	20.0071i	0.0341468	−	0.716829i
$780$	27.8313	−	5.36404i	0.996520	−	0.192063i
$781$	11.6620	−	20.1991i	0.417298	−	0.722782i
$782$	−21.5773	+	26.3746i	−0.771603	+	0.943154i
$783$	5.95544			0.212830
$784$	5.33277	+	4.53449i	0.190456	+	0.161946i
$785$	61.8310	+	39.7363i	2.20684	+	1.41825i
$786$	6.55852	−	2.62564i	0.233935	−	0.0936533i
$787$	16.3593	+	22.9734i	0.583145	+	0.818912i	0.995760	−	0.0919935i	$-0.0293239\pi$
$787$	16.3593	+	22.9734i	0.583145	+	0.818912i	−0.412615	+	0.910906i	$0.635385\pi$
$788$	0.446257	+	0.178654i	0.0158972	+	0.00636429i
$789$	−6.40486	−	26.4012i	−0.228019	−	0.939908i
$790$	16.4552	−	10.5751i	0.585448	−	0.376245i
$791$	−31.4788	−	18.9866i	−1.11926	−	0.675085i
$792$	−2.25097	+	0.660946i	−0.0799849	+	0.0234857i
$793$	29.7573	+	5.73524i	1.05671	+	0.203664i
$794$	1.17654	+	3.39939i	0.0417538	+	0.120640i
$795$	−1.50622	+	6.20872i	−0.0534201	+	0.220200i
$796$	4.90755	−	6.89169i	0.173943	−	0.244269i
$797$	15.3812	−	9.88490i	0.544830	−	0.350141i	−0.239095	−	0.970996i	$-0.576851\pi$
$797$	15.3812	−	9.88490i	0.544830	−	0.350141i	0.783926	+	0.620855i	$0.213214\pi$
$798$	−10.1709	−	9.15971i	−0.360046	−	0.324250i
$799$	6.36397	+	44.2624i	0.225141	+	1.56589i
$800$	11.9938	−	1.14527i	0.424047	−	0.0404915i
$801$	2.29748	+	1.80676i	0.0811774	+	0.0638386i
$802$	15.9459	−	8.22067i	0.563068	−	0.290282i
$803$	−4.28149	+	12.3706i	−0.151091	+	0.436548i
$804$	2.80329			0.0988643
$805$	−47.4546	+	22.2003i	−1.67256	+	0.782456i
$806$	23.8320			0.839446
$807$	1.04582	−	3.02170i	0.0368147	−	0.106369i
$808$	9.80712	−	5.05592i	0.345013	−	0.177867i
$809$	23.1554	+	18.2096i	0.814099	+	0.640215i	0.935871	−	0.352343i	$-0.114615\pi$
$809$	23.1554	+	18.2096i	0.814099	+	0.640215i	−0.121772	+	0.992558i	$0.538858\pi$
$810$	4.11027	−	0.392484i	0.144420	−	0.0137905i
$811$	−5.89273	−	40.9849i	−0.206922	−	1.43917i	−0.783124	−	0.621866i	$-0.786375\pi$
$811$	−5.89273	−	40.9849i	−0.206922	−	1.43917i	0.576202	−	0.817307i	$-0.304534\pi$
$812$	−3.27748	+	15.4120i	−0.115017	+	0.540854i
$813$	−7.99542	+	5.13834i	−0.280411	+	0.180210i
$814$	6.73560	−	9.45883i	0.236083	−	0.331532i
$815$	−10.2003	+	42.0463i	−0.357302	+	1.47282i
$816$	2.32396	+	6.71463i	0.0813547	+	0.235059i
$817$	−18.3497	−	3.53662i	−0.641976	−	0.123731i
$818$	−2.43871	+	0.716070i	−0.0852675	+	0.0250368i
$819$	−0.347544	+	18.1585i	−0.0121442	+	0.634511i
$820$	−13.4484	+	8.64276i	−0.469638	+	0.301818i
$821$	2.68239	+	11.0570i	0.0936162	+	0.385891i	0.999273	−	0.0381200i	$-0.0121369\pi$
$821$	2.68239	+	11.0570i	0.0936162	+	0.385891i	−0.905657	+	0.424011i	$0.860622\pi$
$822$	−0.925011	−	0.370319i	−0.0322635	−	0.0129163i
$823$	−24.6321	−	34.5909i	−0.858621	−	1.20576i	−0.977094	−	0.212807i	$-0.931739\pi$
$823$	−24.6321	−	34.5909i	−0.858621	−	1.20576i	0.118473	−	0.992957i	$-0.462200\pi$
$824$	−3.01295	+	1.20620i	−0.104961	+	0.0420201i
$825$	23.7785	+	15.2815i	0.827862	+	0.532035i
$826$	−25.8339	−	6.79322i	−0.898876	−	0.236366i
$827$	−23.0020			−0.799858			−0.399929	−	0.916546i	$-0.630965\pi$
$827$	−23.0020			−0.799858			−0.399929	+	0.916546i	$0.630965\pi$
$828$	4.56147	−	1.48086i	0.158522	−	0.0514636i
$829$	−7.45304	+	12.9090i	−0.258855	+	0.448350i	−0.965935	−	0.258783i	$-0.916678\pi$
$829$	−7.45304	+	12.9090i	−0.258855	+	0.448350i	0.707081	+	0.707133i	$0.250012\pi$
$830$	−50.4088	+	9.71549i	−1.74971	+	0.337230i
$831$	−1.18821	+	24.9436i	−0.0412186	+	0.865285i
$832$	0.976926	−	6.79467i	0.0338688	−	0.235563i
$833$	48.2245	−	12.1764i	1.67088	−	0.421888i
$834$	−1.01021	−	7.02613i	−0.0349806	−	0.243295i
$835$	9.41254	+	38.7990i	0.325734	+	1.34269i
$836$	0.577492	+	12.1230i	0.0199730	+	0.419284i
$837$	3.45604	+	0.330011i	0.119458	+	0.0114069i
$838$	−9.24971	−	8.81958i	−0.319526	−	0.304667i
$839$	15.4082	−	17.7820i	0.531951	−	0.613904i	−0.424631	−	0.905366i	$-0.639596\pi$
$839$	15.4082	−	17.7820i	0.531951	−	0.613904i	0.956582	+	0.291462i	$0.0941418\pi$
$840$	−1.24632	+	10.8529i	−0.0430022	+	0.374461i
$841$	−6.20526	+	1.82203i	−0.213974	+	0.0628285i
$842$	0.734233	−	1.03109i	0.0253033	−	0.0355335i
$843$	−0.385948	−	8.10205i	−0.0132928	−	0.279049i
$844$	10.8843	−	10.3781i	0.374651	−	0.357229i
$845$	−110.746	+	87.0914i	−3.80977	+	2.99603i
$846$	2.61439	−	5.72471i	0.0898845	−	0.196820i
$847$	−8.09452	+	12.0806i	−0.278131	+	0.415095i
$848$	1.30168	+	0.836540i	0.0446999	+	0.0287269i
$849$	10.4959	−	30.3260i	0.360219	−	1.04078i
$850$	42.8045	−	74.1395i	1.46818	−	2.54297i
$851$	−13.2164	+	19.7183i	−0.453052	+	0.675935i
$852$	4.97099	+	8.61002i	0.170303	+	0.294974i
$853$	−12.3009	−	14.1960i	−0.421175	−	0.486062i	0.505019	−	0.863108i	$-0.331485\pi$
$853$	−12.3009	−	14.1960i	−0.421175	−	0.486062i	−0.926195	+	0.377046i	$0.876940\pi$
$854$	−5.54987	+	10.2775i	−0.189913	+	0.351688i
$855$	3.03995	−	21.1433i	0.103964	−	0.723087i
$856$	5.18793	−	0.495387i	0.177320	−	0.0169320i
$857$	14.7560	+	5.90740i	0.504054	+	0.201793i	0.609732	−	0.792608i	$-0.291277\pi$
$857$	14.7560	+	5.90740i	0.504054	+	0.201793i	−0.105678	+	0.994400i	$0.533701\pi$
$858$	11.6552	−	11.1132i	0.397901	−	0.379398i
$859$	−31.4670	−	16.2224i	−1.07364	−	0.553500i	−0.171606	−	0.985166i	$-0.554896\pi$
$859$	−31.4670	−	16.2224i	−1.07364	−	0.553500i	−0.902034	+	0.431666i	$0.857926\pi$
$860$	6.19582	+	13.5670i	0.211276	+	0.462629i
$861$	−3.62447	−	9.58090i	−0.123522	−	0.326516i
$862$	13.7655	−	15.8862i	0.468853	−	0.541085i
$863$	37.6774	+	7.26172i	1.28255	+	0.247192i	0.784595	−	0.620009i	$-0.212871\pi$
$863$	37.6774	+	7.26172i	1.28255	+	0.247192i	0.497959	+	0.867201i	$0.334083\pi$
$864$	0.235759	−	0.971812i	0.00802068	−	0.0330617i
$865$	−25.9938	−	2.48211i	−0.883816	−	0.0843942i
$866$	−10.2280	−	5.27290i	−0.347561	−	0.179180i
$867$	32.1305	+	9.43438i	1.09121	+	0.320408i
$868$	−2.75600	+	8.76219i	−0.0935449	+	0.297408i
$869$	4.61683	−	10.1094i	0.156615	−	0.342940i
$870$	−22.8284	+	9.13911i	−0.773955	+	0.309845i
$871$	−17.1041	+	8.81778i	−0.579550	+	0.298779i
$872$	14.2333	−	2.74324i	0.481999	−	0.0928977i
$873$	8.72082	+	15.1049i	0.295155	+	0.511223i
$874$	−1.88163	−	24.7392i	−0.0636471	−	0.836817i
$875$	63.5642	−	43.4550i	2.14886	−	1.46905i
$876$	−3.65408	−	4.21703i	−0.123460	−	0.142480i
$877$	−1.72690	+	36.2520i	−0.0583132	+	1.22414i	0.760213	+	0.649674i	$0.225095\pi$
$877$	−1.72690	+	36.2520i	−0.0583132	+	1.22414i	−0.818526	+	0.574470i	$0.805208\pi$
$878$	10.4815	+	8.24275i	0.353734	+	0.278179i
$879$	−4.45548	−	6.25685i	−0.150280	−	0.211038i
$880$	7.61417	−	5.98785i	0.256673	−	0.201850i
$881$	−18.1044	−	5.31594i	−0.609954	−	0.179099i	−0.0378550	−	0.999283i	$-0.512053\pi$
$881$	−18.1044	−	5.31594i	−0.609954	−	0.179099i	−0.572099	+	0.820185i	$0.693871\pi$
$882$	−6.63607	−	2.22769i	−0.223448	−	0.0750101i
$883$	−1.88364	−	4.12460i	−0.0633896	−	0.138804i	0.875286	−	0.483606i	$-0.160673\pi$
$883$	−1.88364	−	4.12460i	−0.0633896	−	0.138804i	−0.938675	+	0.344802i	$0.887946\pi$
$884$	−35.3004	−	33.6589i	−1.18728	−	1.13207i
$885$	−13.6345	−	39.3943i	−0.458319	−	1.32422i
$886$	7.56339	+	21.8530i	0.254097	+	0.734165i
$887$	−1.13024	−	1.07768i	−0.0379496	−	0.0361849i	0.670867	−	0.741578i	$-0.265922\pi$
$887$	−1.13024	−	1.07768i	−0.0379496	−	0.0361849i	−0.708817	+	0.705393i	$0.750771\pi$
$888$	2.05617	+	4.50239i	0.0690006	+	0.151090i
$889$	−1.06794	+	2.52637i	−0.0358177	+	0.0847318i
$890$	−11.5793	−	3.40000i	−0.388140	−	0.113968i
$891$	1.84408	−	1.45020i	0.0617791	−	0.0485836i
$892$	−4.43097	−	6.22242i	−0.148360	−	0.208342i
$893$	−25.5926	−	20.1263i	−0.856425	−	0.673500i
$894$	0.00462100	−	0.0970068i	0.000154549	−	0.00324439i
$895$	22.1872	+	25.6054i	0.741636	+	0.855893i
$896$	2.38519	+	1.14494i	0.0796835	+	0.0382497i
$897$	−23.1735	+	23.3836i	−0.773741	+	0.780755i
$898$	−10.7125	−	18.5546i	−0.357480	−	0.619174i
$899$	−20.3022	+	3.91292i	−0.677116	+	0.130503i
$900$	−10.7090	+	5.52090i	−0.356968	+	0.184030i
$901$	10.2068	−	4.08617i	0.340036	−	0.136130i
$902$	−3.77322	+	8.26220i	−0.125635	+	0.275101i
$903$	−9.32907	+	2.07502i	−0.310452	+	0.0690523i
$904$	−13.3317	−	3.91454i	−0.443406	−	0.130196i
$905$	−82.2823	−	42.4195i	−2.73516	−	1.41007i
$906$	−4.09554	−	0.391076i	−0.136065	−	0.0129926i
$907$	4.17749	−	17.2199i	0.138711	−	0.571776i	−0.859453	−	0.511215i	$-0.829196\pi$
$907$	4.17749	−	17.2199i	0.138711	−	0.571776i	0.998164	−	0.0605615i	$-0.0192891\pi$
$908$	−3.05520	−	0.588841i	−0.101390	−	0.0195414i
$909$	−7.22552	+	8.33869i	−0.239655	+	0.276577i
$910$	−26.5336	−	70.1387i	−0.879580	−	2.32508i
$911$	−3.08017	−	6.74462i	−0.102050	−	0.223459i	0.851719	−	0.523999i	$-0.175560\pi$
$911$	−3.08017	−	6.74462i	−0.102050	−	0.223459i	−0.953769	+	0.300540i	$0.902833\pi$
$912$	−4.59829	−	2.37058i	−0.152265	−	0.0784979i
$913$	−21.1102	+	20.1285i	−0.698645	+	0.666157i
$914$	21.2519	+	8.50798i	0.702951	+	0.281419i
$915$	−18.1457	+	1.73270i	−0.599877	+	0.0572813i
$916$	1.81890	−	12.6507i	0.0600981	−	0.417991i
$917$	−9.80243	−	15.9144i	−0.323705	−	0.525541i
$918$	−4.65306	−	5.36992i	−0.153574	−	0.177234i
$919$	−6.10889	−	10.5809i	−0.201514	−	0.349032i	0.747503	−	0.664259i	$-0.231253\pi$
$919$	−6.10889	−	10.5809i	−0.201514	−	0.349032i	−0.949016	+	0.315227i	$0.897919\pi$
$920$	−15.2125	+	12.6764i	−0.501543	+	0.417929i
$921$	6.34744	−	10.9941i	0.209155	−	0.362268i
$922$	3.72156	−	10.7528i	0.122563	−	0.354123i
$923$	−57.4132	−	36.8972i	−1.88978	−	1.21449i
$924$	2.73809	+	5.57037i	0.0900766	+	0.183252i
$925$	24.7736	−	54.2466i	0.814550	−	1.78362i
$926$	−4.14520	+	3.25982i	−0.136220	+	0.107124i
$927$	2.34883	−	2.23960i	0.0771456	−	0.0735582i
$928$	0.283371	+	5.94869i	0.00930211	+	0.195275i
$929$	11.2261	−	15.7649i	0.368317	−	0.517229i	−0.588274	−	0.808661i	$-0.700193\pi$
$929$	11.2261	−	15.7649i	0.368317	−	0.517229i	0.956591	+	0.291433i	$0.0941319\pi$
$930$	−13.7541	+	4.03857i	−0.451015	+	0.132430i
$931$	−19.2937	+	30.6462i	−0.632324	+	1.00439i
$932$	−4.24855	+	4.90309i	−0.139166	+	0.160606i
$933$	13.0946	+	12.4856i	0.428697	+	0.408762i
$934$	−33.0655	−	3.15737i	−1.08194	−	0.103312i
$935$	−3.27493	−	68.7493i	−0.107102	−	2.24834i
$936$	1.61838	+	6.67104i	0.0528983	+	0.218050i
$937$	6.15396	+	42.8018i	0.201041	+	1.39827i	0.801202	+	0.598393i	$0.204194\pi$
$937$	6.15396	+	42.8018i	0.201041	+	1.39827i	−0.600161	+	0.799879i	$0.704897\pi$
$938$	−1.26402	−	7.30829i	−0.0412717	−	0.238624i
$939$	−0.0985792	+	0.685633i	−0.00321701	+	0.0223748i
$940$	−1.23644	+	25.9560i	−0.0403281	+	0.846591i
$941$	9.31984	−	1.79625i	0.303818	−	0.0585562i	−0.0350637	−	0.999385i	$-0.511163\pi$
$941$	9.31984	−	1.79625i	0.303818	−	0.0585562i	0.338882	+	0.940829i	$0.389951\pi$
$942$	−8.90035	+	15.4159i	−0.289989	+	0.502276i
$943$	7.23221	−	17.1016i	0.235513	−	0.556906i
$944$	−10.0962			−0.328604
$945$	−2.87657	−	10.5387i	−0.0935748	−	0.342824i
$946$	7.12903	+	4.58155i	0.231785	+	0.148959i
$947$	−25.8754	+	10.3589i	−0.840837	+	0.336620i	−0.751786	−	0.659407i	$-0.770808\pi$
$947$	−25.8754	+	10.3589i	−0.840837	+	0.336620i	−0.0890507	+	0.996027i	$0.528383\pi$
$948$	2.74792	+	3.85891i	0.0892482	+	0.125332i
$949$	35.5599	+	14.2360i	1.15432	+	0.462121i
$950$	14.6951	+	60.5741i	0.476772	+	1.96528i
$951$	−12.6690	+	8.14190i	−0.410822	+	0.264019i
$952$	16.4575	−	9.08632i	0.533389	−	0.294489i
$953$	−6.06104	+	1.77968i	−0.196336	+	0.0576495i	−0.378422	−	0.925633i	$-0.623533\pi$
$953$	−6.06104	+	1.77968i	−0.196336	+	0.0576495i	0.182086	+	0.983283i	$0.441715\pi$
$954$	−1.51935	−	0.292831i	−0.0491908	−	0.00948075i
$955$	−30.1488	−	87.1093i	−0.975593	−	2.81879i
$956$	−2.38281	+	9.82208i	−0.0770656	+	0.317669i
$957$	−8.10425	+	11.3808i	−0.261973	+	0.367890i
$958$	33.5940	−	21.5895i	1.08537	−	0.697527i
$959$	−0.548344	+	2.57853i	−0.0177070	+	0.0832649i
$960$	0.587614	+	4.08694i	0.0189652	+	0.131906i
$961$	18.8611	−	1.80102i	0.608423	−	0.0580974i
$962$	−26.7079	−	21.0033i	−0.861098	−	0.677175i
$963$	−4.63219	+	2.38806i	−0.149270	+	0.0769541i
$964$	−5.85081	+	16.9048i	−0.188442	+	0.544467i
$965$	−50.9869			−1.64133
$966$	−5.91748	−	11.2242i	−0.190392	−	0.361134i
$967$	29.1809			0.938395			0.469198	−	0.883093i	$-0.344543\pi$
$967$	29.1809			0.938395			0.469198	+	0.883093i	$0.344543\pi$
$968$	−1.79765	+	5.19398i	−0.0577788	+	0.166941i
$969$	−32.6728	+	16.8440i	−1.04960	+	0.541107i
$970$	−56.6084	−	44.5173i	−1.81759	−	1.42937i
$971$	32.8078	−	3.13276i	1.05285	−	0.100535i	0.445748	−	0.895158i	$-0.352938\pi$
$971$	32.8078	−	3.13276i	1.05285	−	0.100535i	0.607103	+	0.794623i	$0.292332\pi$
$972$	0.142315	+	0.989821i	0.00456475	+	0.0317485i
$973$	−17.8619	+	5.80178i	−0.572628	+	0.185996i
$974$	−0.0567350	+	0.0364614i	−0.00181791	+	0.00116830i
$975$	47.9746	−	67.3709i	1.53642	−	2.15760i
$976$	−1.04081	+	4.29026i	−0.0333154	+	0.137328i
$977$	−5.83184	−	16.8500i	−0.186577	−	0.539079i	0.812457	−	0.583021i	$-0.198129\pi$
$977$	−5.83184	−	16.8500i	−0.186577	−	0.539079i	−0.999034	+	0.0439423i	$0.986008\pi$
$978$	−10.2893	−	1.98309i	−0.329014	−	0.0634123i
$979$	−6.57915	+	1.93181i	−0.210271	+	0.0617410i
$980$	28.8560	−	1.64442i	0.921770	−	0.0525291i
$981$	−12.1941	+	7.83670i	−0.389329	+	0.250207i
$982$	−3.17277	−	13.0784i	−0.101247	−	0.417347i
$983$	32.1475	+	12.8699i	1.02535	+	0.410486i	0.822525	−	0.568730i	$-0.192565\pi$
$983$	32.1475	+	12.8699i	1.02535	+	0.410486i	0.202821	+	0.979216i	$0.434989\pi$
$984$	−2.24581	−	3.15379i	−0.0715937	−	0.100539i
$985$	1.84258	−	0.737658i	0.0587095	−	0.0235037i
$986$	35.5984	+	22.8777i	1.13368	+	0.728574i
$987$	−16.1034	−	4.23452i	−0.512578	−	0.134786i
$988$	35.5129			1.12982
$989$	−14.8329	−	8.94955i	−0.471657	−	0.284579i
$990$	−4.84329	+	8.38882i	−0.153930	+	0.266614i
$991$	−3.74687	+	0.722150i	−0.119023	+	0.0229398i	−0.248415	−	0.968654i	$-0.579910\pi$
$991$	−3.74687	+	0.722150i	−0.119023	+	0.0229398i	0.129392	+	0.991594i	$0.458698\pi$
$992$	−0.165193	+	3.46782i	−0.00524488	+	0.110104i
$993$	−0.589343	+	4.09897i	−0.0187023	+	0.130077i
$994$	20.2052	−	16.8419i	0.640872	−	0.534193i
$995$	−4.97148	−	34.5774i	−0.157607	−	1.09618i
$996$	−2.93125	−	12.0828i	−0.0928801	−	0.382857i
$997$	1.70464	+	35.7847i	0.0539864	+	1.13331i	0.849572	+	0.527473i	$0.176860\pi$
$997$	1.70464	+	35.7847i	0.0539864	+	1.13331i	−0.795586	+	0.605841i	$0.792837\pi$
$998$	5.39091	+	0.514769i	0.170646	+	0.0162947i
$999$	−3.58225	−	3.41567i	−0.113337	−	0.108067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.a.151.1	✓	160
7.2	even	3	inner	966.2.y.a.289.8	yes	160
23.16	even	11	inner	966.2.y.a.361.8	yes	160
161.16	even	33	inner	966.2.y.a.499.1	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.a.151.1	✓	160	1.1	even	1	trivial
966.2.y.a.289.8	yes	160	7.2	even	3	inner
966.2.y.a.361.8	yes	160	23.16	even	11	inner
966.2.y.a.499.1	yes	160	161.16	even	33	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-4.11027 + 0.392484i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.51634 + 0.817338i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-4.11027 + 0.392484i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.51634 + 0.817338i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(-0.973442 + 4.01258i) q^{10} +(0.767303 + 2.21698i) q^{11} +(-0.981929 - 0.189251i) q^{12} +(6.58648 - 1.93396i) q^{13} +(-0.0506289 + 2.64527i) q^{14} +(-3.47351 + 2.23229i) q^{15} +(0.235759 + 0.971812i) q^{16} +(6.59644 + 2.64082i) q^{17} +(-0.580057 - 0.814576i) q^{18} +(-4.80281 + 1.92275i) q^{19} +(3.47351 + 2.23229i) q^{20} +(-1.86209 + 1.87953i) q^{21} +2.34600 q^{22} +(-4.79391 + 0.135764i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(11.8307 - 2.28018i) q^{25} +(0.326628 - 6.85676i) q^{26} +(0.142315 - 0.989821i) q^{27} +(2.48322 + 0.913026i) q^{28} +(0.847547 + 5.89482i) q^{29} +(0.973442 + 4.01258i) q^{30} +(0.165193 + 3.46782i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(1.69788 + 1.61893i) q^{33} +(4.65306 - 5.36992i) q^{34} +(10.0221 - 4.34710i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(2.87110 - 4.03189i) q^{37} +(0.246160 + 5.16753i) q^{38} +(4.96810 - 4.73707i) q^{39} +(3.24559 - 2.55236i) q^{40} +(-1.60836 + 3.52182i) q^{41} +(1.16713 + 2.37441i) q^{42} +(3.03880 + 1.95292i) q^{43} +(0.767303 - 2.21698i) q^{44} +(-2.06449 + 3.57579i) q^{45} +(-1.43964 + 4.57465i) q^{46} +(3.14672 + 5.45028i) q^{47} +(0.654861 + 0.755750i) q^{48} +(5.66392 - 4.11340i) q^{49} +(1.71467 - 11.9258i) q^{50} +(7.07325 - 0.675413i) q^{51} +(-6.37282 - 2.55129i) q^{52} +(1.11984 - 1.06777i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(-4.02395 - 8.81122i) q^{55} +(1.67499 - 2.04802i) q^{56} +(-3.38785 + 3.90979i) q^{57} +(5.84781 + 1.12707i) q^{58} +(-2.38028 + 9.81164i) q^{59} +(4.11027 + 0.392484i) q^{60} +(3.92395 + 2.02294i) q^{61} +(3.33113 + 0.978107i) q^{62} +(-0.793836 + 2.52385i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-26.3132 + 10.5342i) q^{65} +(2.08521 - 1.07500i) q^{66} +(-2.75263 + 0.530525i) q^{67} +(-3.55271 - 6.15347i) q^{68} +(-4.19879 + 2.31737i) q^{69} +(-0.830125 - 10.8926i) q^{70} +(-6.51062 - 7.51365i) q^{71} +(-0.0475819 + 0.998867i) q^{72} +(4.38612 + 3.44928i) q^{73} +(-2.87110 - 4.03189i) q^{74} +(9.47068 - 7.44783i) q^{75} +(4.96383 + 1.45751i) q^{76} +(-3.74281 - 4.95151i) q^{77} +(-2.85163 - 6.24420i) q^{78} +(-3.42856 - 3.26913i) q^{79} +(-1.35045 - 3.90188i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(2.80208 + 2.67178i) q^{82} +(5.16495 + 11.3097i) q^{83} +(2.62555 - 0.326347i) q^{84} +(-28.1497 - 8.26549i) q^{85} +(2.83940 - 2.23293i) q^{86} +(3.45449 + 4.85116i) q^{87} +(-1.84408 - 1.45020i) q^{88} +(-0.139073 + 2.91949i) q^{89} +(2.70390 + 3.12047i) q^{90} +(-14.9931 + 10.2499i) q^{91} +(3.85219 + 2.85668i) q^{92} +(1.73588 + 3.00663i) q^{93} +(6.17971 - 1.19104i) q^{94} +(18.9862 - 9.78807i) q^{95} +(0.928368 - 0.371662i) q^{96} +(-7.24552 + 15.8655i) q^{97} +(-2.03468 - 6.69777i) q^{98} +(2.25097 + 0.660946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more