LMFDB - Embedded newform 966.2.be.a.493.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, 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:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.1
Character	$\chi$	$=$	966.493
Dual form			966.2.be.a.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-3.21613 + 0.307103i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-1.21317 - 2.35122i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-3.21613 + 0.307103i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-1.21317 - 2.35122i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(-0.761680 + 3.13969i) q^{10} +(-2.74441 + 0.949850i) q^{11} +(-0.189251 + 0.981929i) q^{12} +(-0.686910 - 2.33940i) q^{13} +(-2.61869 + 0.377436i) q^{14} +(1.74668 + 2.71789i) q^{15} +(0.235759 + 0.971812i) q^{16} +(4.72354 + 1.89102i) q^{17} +(0.580057 + 0.814576i) q^{18} +(0.963139 - 0.385583i) q^{19} +(2.71789 + 1.74668i) q^{20} +(-1.53394 + 2.15570i) q^{21} +2.90414i q^{22} +(1.87717 + 4.41319i) q^{23} +(0.866025 + 0.500000i) q^{24} +(5.33952 - 1.02911i) q^{25} +(-2.43540 - 0.116012i) q^{26} +(0.989821 + 0.142315i) q^{27} +(-0.499812 + 2.59811i) q^{28} +(0.239249 + 1.66401i) q^{29} +(3.13969 - 0.761680i) q^{30} +(-0.745370 + 0.0355064i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(2.10182 + 2.00408i) q^{33} +(3.33194 - 3.84526i) q^{34} +(4.62377 + 7.18925i) q^{35} +(0.959493 - 0.281733i) q^{36} +(-0.593418 - 0.422571i) q^{37} +(-0.0493640 - 1.03628i) q^{38} +(-1.76458 + 1.68252i) q^{39} +(2.53955 - 1.99712i) q^{40} +(3.59395 + 1.64130i) q^{41} +(1.53543 + 2.15463i) q^{42} +(-2.41425 + 3.75665i) q^{43} +(2.74441 + 0.949850i) q^{44} +(1.61538 - 2.79792i) q^{45} +(4.78443 - 0.330520i) q^{46} +(-5.91488 + 3.41495i) q^{47} +(0.755750 - 0.654861i) q^{48} +(-4.05645 + 5.70484i) q^{49} +(0.773878 - 5.38244i) q^{50} +(-0.483646 - 5.06497i) q^{51} +(-0.906174 + 2.26351i) q^{52} +(0.642892 + 0.674245i) q^{53} +(0.458227 - 0.888835i) q^{54} +(8.53468 - 3.89766i) q^{55} +(2.29175 + 1.32208i) q^{56} +(-0.784055 - 0.679388i) q^{57} +(1.65074 + 0.318155i) q^{58} +(0.988538 + 0.239817i) q^{59} +(0.307103 - 3.21613i) q^{60} +(-12.6186 - 6.50534i) q^{61} +(-0.210233 + 0.715988i) q^{62} +(2.61895 + 0.375623i) q^{63} +(0.415415 - 0.909632i) q^{64} +(2.92763 + 7.31286i) q^{65} +(2.58130 - 1.33075i) q^{66} +(2.29520 + 11.9086i) q^{67} +(-2.54400 - 4.40634i) q^{68} +(3.06243 - 3.69074i) q^{69} +(8.30613 - 2.01809i) q^{70} +(4.31962 + 4.98511i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(7.23495 - 9.19998i) q^{73} +(-0.593418 + 0.422571i) q^{74} +(-3.36142 - 4.27439i) q^{75} +(-0.995429 - 0.292284i) q^{76} +(5.56274 + 5.30038i) q^{77} +(1.01285 + 2.21783i) q^{78} +(-8.18996 + 8.58939i) q^{79} +(-1.05668 - 3.05307i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(2.72650 - 2.85947i) q^{82} +(-1.30946 - 2.86731i) q^{83} +(2.53832 - 0.746273i) q^{84} +(-15.7722 - 4.63115i) q^{85} +(2.76041 + 3.51015i) q^{86} +(1.36940 - 0.975147i) q^{87} +(1.79522 - 2.28281i) q^{88} +(-0.271899 + 5.70786i) q^{89} +(-2.11570 - 2.44164i) q^{90} +(-4.66710 + 4.45316i) q^{91} +(1.25249 - 4.62939i) q^{92} +(0.373108 + 0.646241i) q^{93} +(1.29257 + 6.70648i) q^{94} +(-2.97916 + 1.53587i) q^{95} +(-0.371662 - 0.928368i) q^{96} +(-2.97464 + 6.51355i) q^{97} +(4.06435 + 5.69922i) q^{98} +(0.818190 - 2.78650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$

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
$3$	−0.458227	−	0.888835i	−0.264557	−	0.513169i
$3$	−0.458227	−	0.888835i	−0.264557	−	0.513169i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−3.21613	+	0.307103i	−1.43830	+	0.137341i	−0.784875	−	0.619654i	$-0.787273\pi$
$5$	−3.21613	+	0.307103i	−1.43830	+	0.137341i	−0.653421	+	0.756995i	$0.726667\pi$
$6$	−0.989821	+	0.142315i	−0.404093	+	0.0580998i
$7$	−1.21317	−	2.35122i	−0.458534	−	0.888677i
$7$	−1.21317	−	2.35122i	−0.458534	−	0.888677i
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	−0.580057	+	0.814576i	−0.193352	+	0.271525i
$10$	−0.761680	+	3.13969i	−0.240864	+	0.992856i
$11$	−2.74441	+	0.949850i	−0.827471	+	0.286391i	−0.707791	−	0.706422i	$-0.750308\pi$
$11$	−2.74441	+	0.949850i	−0.827471	+	0.286391i	−0.119680	+	0.992812i	$0.538187\pi$
$12$	−0.189251	+	0.981929i	−0.0546321	+	0.283458i
$13$	−0.686910	−	2.33940i	−0.190515	−	0.648833i	−0.998242	−	0.0592763i	$-0.981121\pi$
$13$	−0.686910	−	2.33940i	−0.190515	−	0.648833i	0.807727	−	0.589557i	$-0.200697\pi$
$14$	−2.61869	+	0.377436i	−0.699875	+	0.100874i
$15$	1.74668	+	2.71789i	0.450991	+	0.701755i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	4.72354	+	1.89102i	1.14563	+	0.458640i	0.865295	−	0.501263i	$-0.167131\pi$
$17$	4.72354	+	1.89102i	1.14563	+	0.458640i	0.280332	+	0.959903i	$0.409555\pi$
$18$	0.580057	+	0.814576i	0.136721	+	0.191997i
$19$	0.963139	−	0.385583i	0.220959	−	0.0884587i	−0.258542	−	0.966000i	$-0.583242\pi$
$19$	0.963139	−	0.385583i	0.220959	−	0.0884587i	0.479501	+	0.877541i	$0.340818\pi$
$20$	2.71789	+	1.74668i	0.607738	+	0.390569i
$21$	−1.53394	+	2.15570i	−0.334733	+	0.470412i
$22$			2.90414i			0.619164i
$23$	1.87717	+	4.41319i	0.391418	+	0.920213i
$23$	1.87717	+	4.41319i	0.391418	+	0.920213i
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	5.33952	−	1.02911i	1.06790	−	0.205822i
$26$	−2.43540	−	0.116012i	−0.477621	−	0.0227519i
$27$	0.989821	+	0.142315i	0.190491	+	0.0273885i
$28$	−0.499812	+	2.59811i	−0.0944556	+	0.490997i
$29$	0.239249	+	1.66401i	0.0444274	+	0.308999i	0.999903	+	0.0139291i	$0.00443391\pi$
$29$	0.239249	+	1.66401i	0.0444274	+	0.308999i	−0.955476	+	0.295070i	$0.904657\pi$
$30$	3.13969	−	0.761680i	0.573226	−	0.139063i
$31$	−0.745370	+	0.0355064i	−0.133872	+	0.00637713i	−0.114411	−	0.993433i	$-0.536498\pi$
$31$	−0.745370	+	0.0355064i	−0.133872	+	0.00637713i	−0.0194613	+	0.999811i	$0.506195\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	2.10182	+	2.00408i	0.365880	+	0.348866i
$34$	3.33194	−	3.84526i	0.571422	−	0.659456i
$35$	4.62377	+	7.18925i	0.781559	+	1.21520i
$36$	0.959493	−	0.281733i	0.159915	−	0.0469554i
$37$	−0.593418	−	0.422571i	−0.0975574	−	0.0694703i	0.530237	−	0.847849i	$-0.322103\pi$
$37$	−0.593418	−	0.422571i	−0.0975574	−	0.0694703i	−0.627795	+	0.778379i	$0.716042\pi$
$38$	−0.0493640	−	1.03628i	−0.00800790	−	0.168107i
$39$	−1.76458	+	1.68252i	−0.282559	+	0.269420i
$40$	2.53955	−	1.99712i	0.401537	−	0.315773i
$41$	3.59395	+	1.64130i	0.561281	+	0.256328i	0.675790	−	0.737094i	$-0.263802\pi$
$41$	3.59395	+	1.64130i	0.561281	+	0.256328i	−0.114510	+	0.993422i	$0.536530\pi$
$42$	1.53543	+	2.15463i	0.236922	+	0.332467i
$43$	−2.41425	+	3.75665i	−0.368170	+	0.572883i	−0.975071	−	0.221894i	$-0.928776\pi$
$43$	−2.41425	+	3.75665i	−0.368170	+	0.572883i	0.606901	+	0.794777i	$0.292412\pi$
$44$	2.74441	+	0.949850i	0.413736	+	0.143195i
$45$	1.61538	−	2.79792i	0.240806	−	0.417089i
$46$	4.78443	−	0.330520i	0.705426	−	0.0487325i
$47$	−5.91488	+	3.41495i	−0.862773	+	0.498122i	−0.864940	−	0.501875i	$-0.832644\pi$
$47$	−5.91488	+	3.41495i	−0.862773	+	0.498122i	0.00216678	+	0.999998i	$0.499310\pi$
$48$	0.755750	−	0.654861i	0.109083	−	0.0945210i
$49$	−4.05645	+	5.70484i	−0.579493	+	0.814977i
$50$	0.773878	−	5.38244i	0.109443	−	0.761192i
$51$	−0.483646	−	5.06497i	−0.0677239	−	0.709237i
$52$	−0.906174	+	2.26351i	−0.125664	+	0.313893i
$53$	0.642892	+	0.674245i	0.0883079	+	0.0926147i	0.766405	−	0.642358i	$-0.222044\pi$
$53$	0.642892	+	0.674245i	0.0883079	+	0.0926147i	−0.678097	+	0.734972i	$0.737195\pi$
$54$	0.458227	−	0.888835i	0.0623567	−	0.120955i
$55$	8.53468	−	3.89766i	1.15082	−	0.525560i
$56$	2.29175	+	1.32208i	0.306247	+	0.176671i
$57$	−0.784055	−	0.679388i	−0.103851	−	0.0899871i
$58$	1.65074	+	0.318155i	0.216753	+	0.0417757i
$59$	0.988538	+	0.239817i	0.128697	+	0.0312215i	0.299590	−	0.954068i	$-0.403150\pi$
$59$	0.988538	+	0.239817i	0.128697	+	0.0312215i	−0.170893	+	0.985290i	$0.554665\pi$
$60$	0.307103	−	3.21613i	0.0396468	−	0.415200i
$61$	−12.6186	−	6.50534i	−1.61565	−	0.832923i	−0.998954	−	0.0457187i	$-0.985442\pi$
$61$	−12.6186	−	6.50534i	−1.61565	−	0.832923i	−0.616692	−	0.787205i	$-0.711527\pi$
$62$	−0.210233	+	0.715988i	−0.0266996	+	0.0909306i
$63$	2.61895	+	0.375623i	0.329957	+	0.0473240i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	2.92763	+	7.31286i	0.363127	+	0.907048i
$66$	2.58130	−	1.33075i	0.317736	−	0.163804i
$67$	2.29520	+	11.9086i	0.280403	+	1.45487i	0.799763	+	0.600315i	$0.204958\pi$
$67$	2.29520	+	11.9086i	0.280403	+	1.45487i	−0.519360	+	0.854556i	$0.673830\pi$
$68$	−2.54400	−	4.40634i	−0.308506	−	0.534347i
$69$	3.06243	−	3.69074i	0.368673	−	0.444313i
$70$	8.30613	−	2.01809i	0.992773	−	0.241208i
$71$	4.31962	+	4.98511i	0.512645	+	0.591624i	0.951774	−	0.306800i	$-0.0992584\pi$
$71$	4.31962	+	4.98511i	0.512645	+	0.591624i	−0.439129	+	0.898424i	$0.644713\pi$
$72$	0.0475819	−	0.998867i	0.00560758	−	0.117718i
$73$	7.23495	−	9.19998i	0.846786	−	1.07678i	−0.149335	−	0.988787i	$-0.547713\pi$
$73$	7.23495	−	9.19998i	0.846786	−	1.07678i	0.996121	−	0.0879897i	$-0.0280443\pi$
$74$	−0.593418	+	0.422571i	−0.0689835	+	0.0491229i
$75$	−3.36142	−	4.27439i	−0.388143	−	0.493564i
$76$	−0.995429	−	0.292284i	−0.114184	−	0.0335273i
$77$	5.56274	+	5.30038i	0.633933	+	0.604035i
$78$	1.01285	+	2.21783i	0.114683	+	0.251120i
$79$	−8.18996	+	8.58939i	−0.921443	+	0.966381i	−0.999533	−	0.0305650i	$-0.990269\pi$
$79$	−8.18996	+	8.58939i	−0.921443	+	0.966381i	0.0780900	+	0.996946i	$0.475118\pi$
$80$	−1.05668	−	3.05307i	−0.118140	−	0.341343i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	2.72650	−	2.85947i	0.301091	−	0.315775i
$83$	−1.30946	−	2.86731i	−0.143732	−	0.314728i	0.824051	−	0.566516i	$-0.191709\pi$
$83$	−1.30946	−	2.86731i	−0.143732	−	0.314728i	−0.967783	+	0.251787i	$0.918982\pi$
$84$	2.53832	−	0.746273i	0.276954	−	0.0814251i
$85$	−15.7722	−	4.63115i	−1.71074	−	0.502319i
$86$	2.76041	+	3.51015i	0.297663	+	0.378509i
$87$	1.36940	−	0.975147i	0.146815	−	0.104547i
$88$	1.79522	−	2.28281i	0.191371	−	0.243348i
$89$	−0.271899	+	5.70786i	−0.0288212	+	0.605032i	0.937545	+	0.347863i	$0.113093\pi$
$89$	−0.271899	+	5.70786i	−0.0288212	+	0.605032i	−0.966367	+	0.257169i	$0.917210\pi$
$90$	−2.11570	−	2.44164i	−0.223014	−	0.257372i
$91$	−4.66710	+	4.45316i	−0.489245	+	0.466818i
$92$	1.25249	−	4.62939i	0.130581	−	0.482647i
$93$	0.373108	+	0.646241i	0.0386895	+	0.0670121i
$94$	1.29257	+	6.70648i	0.133318	+	0.691721i
$95$	−2.97916	+	1.53587i	−0.305656	+	0.157576i
$96$	−0.371662	−	0.928368i	−0.0379326	−	0.0947512i
$97$	−2.97464	+	6.51355i	−0.302029	+	0.661351i	−0.998413	−	0.0563185i	$-0.982064\pi$
$97$	−2.97464	+	6.51355i	−0.302029	+	0.661351i	0.696384	+	0.717669i	$0.254791\pi$
$98$	4.06435	+	5.69922i	0.410561	+	0.575708i
$99$	0.818190	−	2.78650i	0.0822312	−	0.280054i
$100$	−4.83330	−	2.49174i	−0.483330	−	0.249174i
$101$	1.67418	−	17.5328i	0.166587	−	1.74458i	−0.396364	−	0.918093i	$-0.629728\pi$
$101$	1.67418	−	17.5328i	0.166587	−	1.74458i	0.562952	−	0.826490i	$-0.309666\pi$
$102$	−4.94458	−	1.19954i	−0.489587	−	0.118772i
$103$	−4.82857	−	0.930630i	−0.475773	−	0.0916977i	−0.0542729	−	0.998526i	$-0.517284\pi$
$103$	−4.82857	−	0.930630i	−0.475773	−	0.0916977i	−0.421500	+	0.906828i	$0.638496\pi$
$104$	1.84264	+	1.59666i	0.180686	+	0.156565i
$105$	4.27133	−	7.40407i	0.416839	−	0.722563i
$106$	0.847432	−	0.387009i	0.0823098	−	0.0375896i
$107$	−4.80676	+	9.32381i	−0.464687	+	0.901367i	0.533759	+	0.845637i	$0.320779\pi$
$107$	−4.80676	+	9.32381i	−0.464687	+	0.901367i	−0.998446	+	0.0557300i	$0.982251\pi$
$108$	−0.690079	−	0.723734i	−0.0664029	−	0.0696413i
$109$	4.68019	−	11.6906i	0.448281	−	1.11975i	−0.516404	−	0.856345i	$-0.672730\pi$
$109$	4.68019	−	11.6906i	0.448281	−	1.11975i	0.964685	−	0.263407i	$-0.0848462\pi$
$110$	−0.891869	−	9.34007i	−0.0850364	−	0.890541i
$111$	−0.103676	+	0.721085i	−0.00984052	+	0.0684423i
$112$	1.99893	−	1.73329i	0.188881	−	0.163781i
$113$	−8.50996	+	7.37393i	−0.800550	+	0.693681i	−0.955743	−	0.294204i	$-0.904946\pi$
$113$	−8.50996	+	7.37393i	−0.800550	+	0.693681i	0.155193	+	0.987884i	$0.450400\pi$
$114$	−0.898461	+	0.518727i	−0.0841486	+	0.0485832i
$115$	−7.39253	−	13.6169i	−0.689357	−	1.26978i
$116$	0.840561	−	1.45590i	0.0780442	−	0.135176i
$117$	2.30407	+	0.797445i	0.213011	+	0.0737238i
$118$	0.549946	−	0.855733i	0.0506266	−	0.0787766i
$119$	−1.28425	−	13.4002i	−0.117727	−	1.22839i
$120$	−2.93880	−	1.34210i	−0.268274	−	0.122517i
$121$	−2.01700	+	1.58619i	−0.183364	+	0.144199i
$122$	−10.2747	+	9.79690i	−0.930227	+	0.886970i
$123$	−0.187996	−	3.94652i	−0.0169510	−	0.355846i
$124$	0.607849	+	0.432847i	0.0545865	+	0.0388708i
$125$	−1.35709	+	0.398477i	−0.121382	+	0.0356409i
$126$	1.21154	−	2.35206i	0.107932	−	0.209538i
$127$	−0.898783	+	1.03725i	−0.0797541	+	0.0920412i	−0.794224	−	0.607625i	$-0.792122\pi$
$127$	−0.898783	+	1.03725i	−0.0797541	+	0.0920412i	0.714470	+	0.699666i	$0.246668\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	4.44532	+	0.424476i	0.391388	+	0.0373730i
$130$	7.86819	−	0.374808i	0.690086	−	0.0328728i
$131$	−9.85422	+	2.39061i	−0.860967	+	0.208868i	−0.641850	−	0.766830i	$-0.721833\pi$
$131$	−9.85422	+	2.39061i	−0.860967	+	0.208868i	−0.219117	+	0.975699i	$0.570318\pi$
$132$	−0.413302	−	2.87458i	−0.0359733	−	0.250200i
$133$	−2.07504	−	1.79677i	−0.179929	−	0.155800i
$134$	12.0044	+	1.72597i	1.03702	+	0.149101i
$135$	−3.22710	−	0.153726i	−0.277744	−	0.0132306i
$136$	−4.99606	+	0.962911i	−0.428409	+	0.0825690i
$137$	6.75157	+	3.89802i	0.576825	+	0.333030i	0.759871	−	0.650074i	$-0.225262\pi$
$137$	6.75157	+	3.89802i	0.576825	+	0.333030i	−0.183046	+	0.983104i	$0.558596\pi$
$138$	−2.48613	−	4.10112i	−0.211633	−	0.349110i
$139$		−	9.25696i		−	0.785165i	−0.919717	−	0.392583i	$-0.871582\pi$
$139$		−	9.25696i		−	0.785165i	0.919717	−	0.392583i	$-0.128418\pi$
$140$	0.809571	−	8.50935i	0.0684213	−	0.719172i
$141$	5.74569	+	3.69253i	0.483874	+	0.310967i
$142$	6.12374	−	2.45158i	0.513893	−	0.205732i
$143$	4.10724	+	5.76782i	0.343465	+	0.482329i
$144$	−0.928368	−	0.371662i	−0.0773640	−	0.0309719i
$145$	−1.28048	−	5.27820i	−0.106338	−	0.438331i
$146$	−6.32767	−	9.84605i	−0.523682	−	0.814865i
$147$	6.92944	+	0.991405i	0.571530	+	0.0817697i
$148$	0.205242	+	0.698991i	0.0168708	+	0.0574567i
$149$	−1.64384	+	8.52903i	−0.134668	+	0.698725i	0.850342	+	0.526230i	$0.176395\pi$
$149$	−1.64384	+	8.52903i	−0.134668	+	0.698725i	−0.985010	+	0.172495i	$0.944817\pi$
$150$	−5.13871	+	1.77853i	−0.419574	+	0.145216i
$151$	−0.532955	+	2.19687i	−0.0433713	+	0.178779i	−0.989377	−	0.145370i	$-0.953563\pi$
$151$	−0.532955	+	2.19687i	−0.0433713	+	0.178779i	0.946006	+	0.324149i	$0.105078\pi$
$152$	−0.601782	+	0.845085i	−0.0488110	+	0.0685454i
$153$	−4.28030	+	2.75078i	−0.346042	+	0.222388i
$154$	6.82826	−	3.52321i	0.550237	−	0.283908i
$155$	2.38630	−	0.343098i	0.191672	−	0.0275583i
$156$	2.42712	−	0.231762i	0.194325	−	0.0185558i
$157$	−11.0862	−	8.71830i	−0.884777	−	0.695796i	0.0685790	−	0.997646i	$-0.478153\pi$
$157$	−11.0862	−	8.71830i	−0.884777	−	0.695796i	−0.953356	+	0.301850i	$0.902396\pi$
$158$	5.43830	+	10.5488i	0.432648	+	0.839220i
$159$	0.304703	−	0.880382i	0.0241645	−	0.0698188i
$160$	−3.23076			−0.255414
$161$	8.09903	−	9.76758i	0.638293	−	0.769793i
$162$	−1.00000			−0.0785674
$163$	−3.72005	+	10.7484i	−0.291377	+	0.841878i	0.700383	+	0.713767i	$0.253013\pi$
$163$	−3.72005	+	10.7484i	−0.291377	+	0.841878i	−0.991760	+	0.128111i	$0.959109\pi$
$164$	−1.81045	−	3.51178i	−0.141372	−	0.274224i
$165$	−7.37519	−	5.79991i	−0.574158	−	0.451523i
$166$	−3.13789	+	0.299632i	−0.243548	+	0.0232560i
$167$	8.91650	−	1.28200i	0.689979	−	0.0992041i	0.211599	−	0.977357i	$-0.432133\pi$
$167$	8.91650	−	1.28200i	0.689979	−	0.0992041i	0.478381	+	0.878153i	$0.341224\pi$
$168$	0.124975	−	2.64280i	0.00964201	−	0.203896i
$169$	5.93535	−	3.81442i	0.456565	−	0.293417i
$170$	−9.53504	+	13.3901i	−0.731304	+	1.02697i
$171$	−0.244589	+	1.00821i	−0.0187042	+	0.0770997i
$172$	4.21994	−	1.46053i	0.321767	−	0.111365i
$173$	−4.48153	+	23.2524i	−0.340724	+	1.76785i	0.257263	+	0.966341i	$0.417179\pi$
$173$	−4.48153	+	23.2524i	−0.340724	+	1.76785i	−0.597988	+	0.801505i	$0.704033\pi$
$174$	−0.473627	−	1.61303i	−0.0359056	−	0.122283i
$175$	−8.89739	−	11.3059i	−0.672579	−	0.854645i
$176$	−1.57009	−	2.44312i	−0.118350	−	0.184157i
$177$	−0.239817	−	0.988538i	−0.0180257	−	0.0743031i
$178$	5.30500	+	2.12380i	0.397626	+	0.159186i
$179$	−3.26850	−	4.58996i	−0.244299	−	0.343070i	0.674161	−	0.738585i	$-0.264506\pi$
$179$	−3.26850	−	4.58996i	−0.244299	−	0.343070i	−0.918460	+	0.395515i	$0.870566\pi$
$180$	−2.99933	+	1.20075i	−0.223557	+	0.0894987i
$181$	13.8836	+	8.92246i	1.03196	+	0.663201i	0.942986	−	0.332833i	$-0.108004\pi$
$181$	13.8836	+	8.92246i	1.03196	+	0.663201i	0.0889753	+	0.996034i	$0.471641\pi$
$182$	2.68178	+	5.86690i	0.198787	+	0.434884i
$183$			14.1968i			1.04946i
$184$	−3.96513	−	2.69773i	−0.292313	−	0.198879i
$185$	2.03828	+	1.17680i	0.149857	+	0.0865203i
$186$	0.732730	−	0.141222i	0.0537264	−	0.0103549i
$187$	−14.7595	−	0.703083i	−1.07932	−	0.0514145i
$188$	6.76039	+	0.971997i	0.493052	+	0.0708902i
$189$	−0.866206	−	2.49994i	−0.0630072	−	0.181844i
$190$	0.477005	+	3.31764i	0.0346056	+	0.240687i
$191$	−11.5259	+	2.79616i	−0.833986	+	0.202323i	−0.629945	−	0.776640i	$-0.716923\pi$
$191$	−11.5259	+	2.79616i	−0.833986	+	0.202323i	−0.204041	+	0.978962i	$0.565408\pi$
$192$	−0.998867	+	0.0475819i	−0.0720870	+	0.00343393i
$193$	10.9250	+	1.04321i	0.786397	+	0.0750918i	0.480525	−	0.876981i	$-0.340446\pi$
$193$	10.9250	+	1.04321i	0.786397	+	0.0750918i	0.305872	+	0.952073i	$0.401052\pi$
$194$	5.18240	+	4.94141i	0.372075	+	0.354773i
$195$	5.15841	−	5.95312i	0.369401	−	0.426312i
$196$	6.71508	−	1.97678i	0.479649	−	0.141198i
$197$	−21.9648	+	6.44944i	−1.56493	+	0.459504i	−0.945519	−	0.325567i	$-0.894445\pi$
$197$	−21.9648	+	6.44944i	−1.56493	+	0.459504i	−0.619407	+	0.785070i	$0.712627\pi$
$198$	−2.36564	−	1.68456i	−0.168119	−	0.119717i
$199$	0.928678	+	19.4953i	0.0658322	+	1.38199i	0.754209	+	0.656635i	$0.228021\pi$
$199$	0.928678	+	19.4953i	0.0658322	+	1.38199i	−0.688376	+	0.725354i	$0.741676\pi$
$200$	−3.93551	+	3.75250i	−0.278283	+	0.265342i
$201$	9.53309	−	7.49691i	0.672412	−	0.528791i
$202$	−16.0210	−	7.31654i	−1.12723	−	0.514790i
$203$	3.62220	−	2.58125i	0.254229	−	0.181168i
$204$	−2.75078	+	4.28030i	−0.192593	+	0.299681i
$205$	−12.0626	−	4.17492i	−0.842492	−	0.291589i
$206$	−2.45872	+	4.25862i	−0.171307	+	0.296712i
$207$	−4.68374	−	1.03080i	−0.325543	−	0.0716454i
$208$	2.11151	−	1.21908i	0.146407	−	0.0845281i
$209$	−2.27700	+	1.97303i	−0.157504	+	0.136478i
$210$	−5.59984	−	6.45804i	−0.386426	−	0.445647i
$211$	−0.329389	+	2.29095i	−0.0226760	+	0.157715i	−0.998013	−	0.0630048i	$-0.979932\pi$
$211$	−0.329389	+	2.29095i	−0.0226760	+	0.157715i	0.975337	+	0.220720i	$0.0708408\pi$
$212$	−0.0885561	−	0.927402i	−0.00608206	−	0.0636942i
$213$	2.45158	−	6.12374i	0.167979	−	0.419592i
$214$	7.23887	+	7.59191i	0.494839	+	0.518972i
$215$	6.61086	−	12.8233i	0.450857	−	0.874541i
$216$	−0.909632	+	0.415415i	−0.0618926	+	0.0282654i
$217$	0.987742	+	1.70945i	0.0670523	+	0.116045i
$218$	−9.51684	−	8.24639i	−0.644562	−	0.558516i
$219$	−11.4925	−	2.21500i	−0.776592	−	0.149676i
$220$	−9.11808	−	2.21202i	−0.614741	−	0.149134i
$221$	1.17921	−	12.3492i	0.0793220	−	0.830698i
$222$	0.647517	+	0.333818i	0.0434585	+	0.0224044i
$223$	0.214381	−	0.730113i	0.0143560	−	0.0488920i	−0.952004	−	0.306087i	$-0.900980\pi$
$223$	0.214381	−	0.730113i	0.0143560	−	0.0488920i	0.966359	+	0.257195i	$0.0827983\pi$
$224$	−0.984177	−	2.45589i	−0.0657581	−	0.164091i
$225$	−2.25894	+	4.94638i	−0.150596	+	0.329759i
$226$	4.18503	+	10.4537i	0.278384	+	0.695370i
$227$	−22.6465	+	11.6751i	−1.50310	+	0.774901i	−0.996199	−	0.0871037i	$-0.972239\pi$
$227$	−22.6465	+	11.6751i	−1.50310	+	0.774901i	−0.506900	+	0.862005i	$0.669209\pi$
$228$	0.196339	+	1.01871i	0.0130029	+	0.0674654i
$229$	−2.37846	−	4.11961i	−0.157173	−	0.272232i	0.776675	−	0.629901i	$-0.216905\pi$
$229$	−2.37846	−	4.11961i	−0.157173	−	0.272232i	−0.933848	+	0.357670i	$0.883571\pi$
$230$	−15.2858	+	2.53231i	−1.00792	+	0.166975i
$231$	2.16217	−	7.37313i	0.142261	−	0.485117i
$232$	−1.10090	−	1.27051i	−0.0722777	−	0.0834129i
$233$	−0.833315	+	17.4934i	−0.0545923	+	1.14603i	0.790865	+	0.611990i	$0.209631\pi$
$233$	−0.833315	+	17.4934i	−0.0545923	+	1.14603i	−0.845458	+	0.534043i	$0.820672\pi$
$234$	1.50717	−	1.91653i	0.0985269	−	0.125287i
$235$	17.9742	−	12.7994i	1.17251	−	0.834941i
$236$	−0.628799	−	0.799582i	−0.0409313	−	0.0520484i
$237$	11.3874	+	3.34364i	0.739692	+	0.217193i
$238$	−13.0832	−	3.16916i	−0.848060	−	0.205426i
$239$	−1.97919	−	4.33382i	−0.128023	−	0.280332i	0.834756	−	0.550619i	$-0.185608\pi$
$239$	−1.97919	−	4.33382i	−0.128023	−	0.280332i	−0.962780	+	0.270288i	$0.912881\pi$
$240$	−2.22948	+	2.33821i	−0.143912	+	0.150931i
$241$	8.72158	+	25.1993i	0.561806	+	1.62323i	0.764955	+	0.644084i	$0.222761\pi$
$241$	8.72158	+	25.1993i	0.561806	+	1.62323i	−0.203149	+	0.979148i	$0.565117\pi$
$242$	0.839253	+	2.42486i	0.0539492	+	0.155876i
$243$	−0.690079	+	0.723734i	−0.0442686	+	0.0464276i
$244$	5.89755	+	12.9138i	0.377552	+	0.826724i
$245$	11.2941	−	19.5932i	0.721552	−	1.25177i
$246$	−3.79095	−	1.11312i	−0.241702	−	0.0709702i
$247$	−1.56362	−	1.98831i	−0.0994908	−	0.126513i
$248$	0.607849	−	0.432847i	0.0385985	−	0.0274858i
$249$	−1.94854	+	2.47777i	−0.123484	+	0.157022i
$250$	−0.0672989	+	1.41278i	−0.00425636	+	0.0893519i
$251$	−19.6335	−	22.6583i	−1.23926	−	1.43018i	−0.864176	−	0.503189i	$-0.832160\pi$
$251$	−19.6335	−	22.6583i	−1.23926	−	1.43018i	−0.375082	−	0.926992i	$-0.622386\pi$
$252$	−1.82644	−	1.91419i	−0.115055	−	0.120583i
$253$	−9.34361	−	10.3286i	−0.587427	−	0.649351i
$254$	0.686240	+	1.18860i	0.0430585	+	0.0745796i
$255$	3.11093	+	16.1410i	0.194814	+	1.01079i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−3.50528	−	8.75577i	−0.218653	−	0.546170i	0.777968	−	0.628304i	$-0.216251\pi$
$257$	−3.50528	−	8.75577i	−0.218653	−	0.546170i	−0.996621	+	0.0821342i	$0.973826\pi$
$258$	1.85505	−	4.06199i	0.115490	−	0.252889i
$259$	−0.273641	+	1.90791i	−0.0170032	+	0.118552i
$260$	2.21924	−	7.55803i	0.137631	−	0.468729i
$261$	−1.49424	−	0.770335i	−0.0924912	−	0.0476825i
$262$	−0.963873	+	10.0941i	−0.0595483	+	0.623618i
$263$	−17.4793	−	4.24043i	−1.07782	−	0.261476i	−0.342721	−	0.939437i	$-0.611349\pi$
$263$	−17.4793	−	4.24043i	−1.07782	−	0.261476i	−0.735098	+	0.677961i	$0.762864\pi$
$264$	−2.85166	−	0.549612i	−0.175507	−	0.0338263i
$265$	−2.27468	−	1.97102i	−0.139733	−	0.121079i
$266$	−2.37663	+	1.37325i	−0.145720	+	0.0841991i
$267$	5.19794	−	2.37382i	0.318109	−	0.145275i
$268$	5.55728	−	10.7796i	0.339465	−	0.658470i
$269$	16.0300	+	16.8118i	0.977369	+	1.02503i	0.999680	+	0.0252839i	$0.00804898\pi$
$269$	16.0300	+	16.8118i	0.977369	+	1.02503i	−0.0223114	+	0.999751i	$0.507103\pi$
$270$	−1.20075	+	2.99933i	−0.0730754	+	0.182533i
$271$	−1.58283	−	16.5761i	−0.0961498	−	1.00693i	−0.906847	−	0.421461i	$-0.861518\pi$
$271$	−1.58283	−	16.5761i	−0.0961498	−	1.00693i	0.810697	−	0.585466i	$-0.199088\pi$
$272$	−0.724099	+	5.03622i	−0.0439049	+	0.305366i
$273$	6.09672	+	2.10773i	0.368990	+	0.127566i
$274$	5.89185	−	5.10532i	0.355940	−	0.308424i
$275$	−13.6763	+	7.89604i	−0.824714	+	0.476149i
$276$	−4.68869	+	1.00805i	−0.282226	+	0.0606775i
$277$	12.0921	−	20.9441i	0.726541	−	1.25841i	−0.231795	−	0.972765i	$-0.574460\pi$
$277$	12.0921	−	20.9441i	0.726541	−	1.25841i	0.958336	−	0.285642i	$-0.0922067\pi$
$278$	−8.74783	−	3.02766i	−0.524660	−	0.181587i
$279$	0.403435	−	0.627756i	0.0241530	−	0.0375828i
$280$	−7.77656	−	3.54818i	−0.464738	−	0.212044i
$281$	−2.25280	−	1.02882i	−0.134391	−	0.0613743i	0.347084	−	0.937834i	$-0.387172\pi$
$281$	−2.25280	−	1.02882i	−0.134391	−	0.0613743i	−0.481476	+	0.876460i	$0.659899\pi$
$282$	5.36867	−	4.22197i	0.319700	−	0.251415i
$283$	16.9268	−	16.1397i	1.00619	−	0.959403i	0.00701649	−	0.999975i	$-0.497767\pi$
$283$	16.9268	−	16.1397i	1.00619	−	0.959403i	0.999177	+	0.0405722i	$0.0129181\pi$
$284$	−0.313862	−	6.58877i	−0.0186243	−	0.390972i
$285$	2.73026	+	1.94421i	0.161727	+	0.115165i
$286$	6.79394	−	1.99488i	0.401734	−	0.117960i
$287$	−0.501006	−	10.4413i	−0.0295734	−	0.616332i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	6.43240	+	6.13329i	0.378377	+	0.360781i
$290$	−5.40671	−	0.516278i	−0.317493	−	0.0303169i
$291$	7.15253	−	0.340717i	0.419289	−	0.0199732i
$292$	−11.3741	+	2.75933i	−0.665619	+	0.161477i
$293$	2.08651	+	14.5120i	0.121895	+	0.847801i	0.955405	+	0.295297i	$0.0954186\pi$
$293$	2.08651	+	14.5120i	0.121895	+	0.847801i	−0.833510	+	0.552504i	$0.813672\pi$
$294$	3.20328	−	6.22407i	0.186819	−	0.362995i
$295$	−3.25291	−	0.467698i	−0.189392	−	0.0272304i
$296$	0.727675	+	0.0346634i	0.0422952	+	0.00201477i
$297$	−2.85166	+	0.549612i	−0.165470	+	0.0318917i
$298$	7.52229	+	4.34300i	0.435755	+	0.251583i
$299$	9.03476	−	7.42292i	0.522494	−	0.429279i
$300$			5.43779i			0.313951i
$301$	11.7616	+	1.11899i	0.677927	+	0.0644973i
$302$	1.90173	+	1.22217i	0.109432	+	0.0703280i
$303$	−16.3510	+	6.54594i	−0.939338	+	0.376054i
$304$	0.601782	+	0.845085i	0.0345146	+	0.0484689i
$305$	42.5808	+	17.0468i	2.43817	+	0.976096i
$306$	1.19954	+	4.94458i	0.0685733	+	0.282663i
$307$	−4.72714	−	7.35558i	−0.269792	−	0.419805i	0.679750	−	0.733444i	$-0.262088\pi$
$307$	−4.72714	−	7.35558i	−0.269792	−	0.419805i	−0.949542	+	0.313639i	$0.898452\pi$
$308$	−1.09613	−	7.60504i	−0.0624576	−	0.433337i
$309$	1.38540	+	4.71824i	0.0788127	+	0.268411i
$310$	0.456254	−	2.36727i	0.0259135	−	0.134452i
$311$	−0.852237	+	0.294962i	−0.0483259	+	0.0167258i	−0.351124	−	0.936329i	$-0.614200\pi$
$311$	−0.852237	+	0.294962i	−0.0483259	+	0.0167258i	0.302798	+	0.953055i	$0.402079\pi$
$312$	0.574819	−	2.36943i	0.0325427	−	0.134143i
$313$	7.23529	−	10.1605i	0.408963	−	0.574308i	−0.557802	−	0.829974i	$-0.688355\pi$
$313$	7.23529	−	10.1605i	0.408963	−	0.574308i	0.966765	+	0.255666i	$0.0822947\pi$
$314$	−11.8647	+	7.62501i	−0.669566	+	0.430304i
$315$	−8.53824	−	0.403763i	−0.481075	−	0.0227495i
$316$	11.7474	−	1.68901i	0.660840	−	0.0950145i
$317$	6.91490	−	0.660293i	0.388379	−	0.0370857i	0.100960	−	0.994891i	$-0.467809\pi$
$317$	6.91490	−	0.660293i	0.388379	−	0.0370857i	0.287420	+	0.957805i	$0.407203\pi$
$318$	−0.732303	−	0.575889i	−0.0410655	−	0.0322943i
$319$	−2.23716	−	4.33948i	−0.125257	−	0.242964i
$320$	−1.05668	+	3.05307i	−0.0590700	+	0.170672i
$321$	10.4899			0.585490
$322$	−6.58144	−	10.8483i	−0.366769	−	0.604550i
$323$	5.27857			0.293707
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	−6.07526	−	11.7844i	−0.336995	−	0.653679i
$326$	8.94052	+	7.03090i	0.495170	+	0.389406i
$327$	−12.5356	+	1.19700i	−0.693219	+	0.0661943i
$328$	−3.91078	+	0.562285i	−0.215937	+	0.0310470i
$329$	15.2050	+	9.76425i	0.838281	+	0.538320i
$330$	−7.89311	+	5.07259i	−0.434501	+	0.279237i
$331$	7.44499	−	10.4550i	0.409213	−	0.574660i	−0.557611	−	0.830103i	$-0.688282\pi$
$331$	7.44499	−	10.4550i	0.409213	−	0.574660i	0.966824	+	0.255443i	$0.0822212\pi$
$332$	−0.743151	+	3.06331i	−0.0407857	+	0.168121i
$333$	0.688433	−	0.238269i	0.0377259	−	0.0130571i
$334$	1.70481	−	8.84540i	0.0932831	−	0.483999i
$335$	−11.0388	−	37.5948i	−0.603116	−	2.05402i
$336$	−2.45657	−	0.982476i	−0.134017	−	0.0535985i
$337$	−16.7843	−	26.1169i	−0.914299	−	1.42268i	−0.906266	−	0.422709i	$-0.861079\pi$
$337$	−16.7843	−	26.1169i	−0.914299	−	1.42268i	−0.00803315	−	0.999968i	$-0.502557\pi$
$338$	−1.66336	−	6.85648i	−0.0904751	−	0.372944i
$339$	10.4537	+	4.18503i	0.567767	+	0.227300i
$340$	9.53504	+	13.3901i	0.517110	+	0.726179i
$341$	2.01188	−	0.805434i	0.108949	−	0.0436167i
$342$	0.872761	+	0.560890i	0.0471935	+	0.0303294i
$343$	18.3345	+	2.61666i	0.989969	+	0.141287i
$344$		−	4.46554i		−	0.240766i
$345$	−8.71571	+	12.8104i	−0.469238	+	0.689687i
$346$	20.5078	+	11.8402i	1.10250	+	0.636531i
$347$	−34.8428	+	6.71539i	−1.87046	+	0.360501i	−0.992898	−	0.118968i	$-0.962041\pi$
$347$	−34.8428	+	6.71539i	−1.87046	+	0.360501i	−0.877559	+	0.479469i	$0.840829\pi$
$348$	−1.67922	−	0.0799910i	−0.0900156	−	0.00428797i
$349$	3.68939	+	0.530454i	0.197488	+	0.0283946i	0.240349	−	0.970687i	$-0.422738\pi$
$349$	3.68939	+	0.530454i	0.197488	+	0.0283946i	−0.0428607	+	0.999081i	$0.513647\pi$
$350$	−13.5941	+	4.71024i	−0.726637	+	0.251773i
$351$	−0.346987	−	2.41335i	−0.0185208	−	0.128815i
$352$	−2.82227	+	0.684676i	−0.150428	+	0.0364934i
$353$	−5.06158	+	0.241113i	−0.269401	+	0.0128331i	−0.181848	−	0.983327i	$-0.558208\pi$
$353$	−5.06158	+	0.241113i	−0.269401	+	0.0128331i	−0.0875532	+	0.996160i	$0.527905\pi$
$354$	−1.01261	−	0.0966921i	−0.0538194	−	0.00513913i
$355$	−15.4234	−	14.7062i	−0.818589	−	0.780523i
$356$	3.74209	−	4.31860i	0.198330	−	0.228885i
$357$	−11.3221	+	7.28181i	−0.599229	+	0.385394i
$358$	−5.40654	+	1.58750i	−0.285744	+	0.0839021i
$359$	−17.1787	−	12.2329i	−0.906658	−	0.645628i	0.0286016	−	0.999591i	$-0.490895\pi$
$359$	−17.1787	−	12.2329i	−0.906658	−	0.645628i	−0.935260	+	0.353963i	$0.884834\pi$
$360$	0.153726	+	3.22710i	0.00810205	+	0.170083i
$361$	−12.9720	+	12.3688i	−0.682736	+	0.650987i
$362$	12.9726	−	10.2018i	0.681826	−	0.536194i
$363$	2.33411	+	1.06595i	0.122509	+	0.0559479i
$364$	6.42135	−	0.615408i	0.336570	−	0.0322562i
$365$	−20.4432	+	31.8102i	−1.07004	+	1.66502i
$366$	13.4160	+	4.64331i	0.701264	+	0.242710i
$367$	−13.7065	+	23.7404i	−0.715474	+	1.23924i	0.247302	+	0.968938i	$0.420456\pi$
$367$	−13.7065	+	23.7404i	−0.715474	+	1.23924i	−0.962776	+	0.270299i	$0.912877\pi$
$368$	−3.84623	+	2.86471i	−0.200498	+	0.149333i
$369$	−3.42166	+	1.97550i	−0.178125	+	0.102840i
$370$	1.77874	−	1.54128i	0.0924721	−	0.0801275i
$371$	0.805362	−	2.32955i	0.0418123	−	0.120944i
$372$	0.106198	−	0.738620i	0.00550609	−	0.0382957i
$373$	−0.103574	−	1.08467i	−0.00536285	−	0.0561623i	0.992394	−	0.123099i	$-0.0392834\pi$
$373$	−0.103574	−	1.08467i	−0.00536285	−	0.0561623i	−0.997757	+	0.0669371i	$0.978677\pi$
$374$	−5.49178	+	13.7178i	−0.283973	+	0.709331i
$375$	0.976034	+	1.02364i	0.0504022	+	0.0528603i
$376$	3.12965	−	6.07067i	0.161399	−	0.313071i
$377$	3.72845	−	1.70272i	0.192025	−	0.0876948i
$378$	−2.64575		0.000916166i	−0.136083		4.71225e-5i
$379$	23.9389	+	20.7432i	1.22966	+	1.06551i	0.995641	+	0.0932732i	$0.0297330\pi$
$379$	23.9389	+	20.7432i	1.22966	+	1.06551i	0.234018	+	0.972232i	$0.424812\pi$
$380$	3.29119	+	0.634325i	0.168834	+	0.0325402i
$381$	1.33379	+	0.323574i	0.0683322	+	0.0165772i
$382$	−1.12739	+	11.8065i	−0.0576821	+	0.604075i
$383$	16.4441	+	8.47752i	0.840254	+	0.433181i	0.823934	−	0.566686i	$-0.191775\pi$
$383$	16.4441	+	8.47752i	0.840254	+	0.433181i	0.0163198	+	0.999867i	$0.494805\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	−19.5182	−	15.3384i	−0.994741	−	0.781716i
$386$	4.55904	−	9.98292i	0.232049	−	0.508117i
$387$	−1.65967	−	4.14566i	−0.0843659	−	0.210736i
$388$	6.36463	−	3.28120i	0.323115	−	0.166578i
$389$	6.37635	+	33.0836i	0.323294	+	1.67741i	0.672293	+	0.740285i	$0.265309\pi$
$389$	6.37635	+	33.0836i	0.323294	+	1.67741i	−0.349000	+	0.937123i	$0.613479\pi$
$390$	−3.93855	−	6.82178i	−0.199436	−	0.345434i
$391$	0.521485	+	24.3956i	0.0263726	+	1.23374i
$392$	0.328231	−	6.99230i	0.0165782	−	0.353165i
$393$	6.64032	+	7.66334i	0.334960	+	0.386564i
$394$	−1.08925	+	22.8661i	−0.0548756	+	1.15198i
$395$	23.7021	−	30.1397i	1.19258	−	1.51649i
$396$	−2.36564	+	1.68456i	−0.118878	+	0.0846526i
$397$	10.1543	+	12.9123i	0.509631	+	0.648048i	0.970977	−	0.239172i	$-0.0768759\pi$
$397$	10.1543	+	12.9123i	0.509631	+	0.648048i	−0.461347	+	0.887220i	$0.652633\pi$
$398$	18.7269	+	5.49870i	0.938693	+	0.275625i
$399$	−0.646198	+	2.66770i	−0.0323504	+	0.133552i
$400$	2.25894	+	4.94638i	0.112947	+	0.247319i
$401$	2.49449	−	2.61615i	0.124569	−	0.130644i	−0.658496	−	0.752585i	$-0.728807\pi$
$401$	2.49449	−	2.61615i	0.124569	−	0.130644i	0.783065	+	0.621940i	$0.213655\pi$
$402$	−3.96661	−	11.4608i	−0.197837	−	0.571612i
$403$	0.595066	+	1.71933i	0.0296423	+	0.0856459i
$404$	−12.1541	+	12.7468i	−0.604688	+	0.634179i
$405$	1.34210	+	2.93880i	0.0666897	+	0.146030i
$406$	−1.25458	−	4.26723i	−0.0622636	−	0.211779i
$407$	2.02996	+	0.596051i	0.100622	+	0.0295452i
$408$	3.14520	+	3.99944i	0.155710	+	0.198002i
$409$	26.6454	−	18.9741i	1.31753	−	0.938209i	0.317580	−	0.948231i	$-0.397130\pi$
$409$	26.6454	−	18.9741i	1.31753	−	0.938209i	0.999950	+	0.0100225i	$0.00319031\pi$
$410$	−7.89061	+	10.0337i	−0.389690	+	0.495531i
$411$	0.370950	−	7.78721i	0.0182976	−	0.384115i
$412$	3.22023	+	3.71635i	0.158649	+	0.183091i
$413$	−0.635401	−	2.61521i	−0.0312660	−	0.128686i
$414$	−2.50601	+	4.08900i	−0.123164	+	0.200963i
$415$	5.09194	+	8.81950i	0.249954	+	0.432932i
$416$	−0.461425	−	2.39410i	−0.0226232	−	0.117381i
$417$	−8.22791	+	4.24178i	−0.402923	+	0.207721i
$418$	1.11978	+	2.79709i	0.0547704	+	0.136810i
$419$	−12.7779	+	27.9796i	−0.624240	+	1.36689i	0.288156	+	0.957584i	$0.406958\pi$
$419$	−12.7779	+	27.9796i	−0.624240	+	1.36689i	−0.912395	+	0.409310i	$0.865769\pi$
$420$	−7.93438	+	3.17964i	−0.387158	+	0.155150i
$421$	6.59403	−	22.4572i	0.321373	−	1.09450i	−0.627441	−	0.778664i	$-0.715898\pi$
$421$	6.59403	−	22.4572i	0.321373	−	1.09450i	0.948815	−	0.315833i	$-0.102284\pi$
$422$	2.05722	+	1.06057i	0.100144	+	0.0516277i
$423$	0.649224	−	6.79898i	0.0315664	−	0.330578i
$424$	−0.905359	−	0.219638i	−0.0439681	−	0.0106666i
$425$	27.1675	+	5.23611i	1.31782	+	0.253988i
$426$	−4.98511	−	4.31962i	−0.241529	−	0.209286i
$427$	0.0130066	+	37.5611i	0.000629434	+	1.81771i
$428$	9.54196	−	4.35767i	0.461228	−	0.210636i
$429$	3.24459	−	6.29363i	0.156650	−	0.303859i
$430$	−9.95581	−	10.4414i	−0.480112	−	0.503527i
$431$	4.26355	−	10.6498i	0.205368	−	0.512984i	−0.789549	−	0.613688i	$-0.789685\pi$
$431$	4.26355	−	10.6498i	0.205368	−	0.512984i	0.994916	+	0.100704i	$0.0321095\pi$
$432$	0.0950560	+	0.995472i	0.00457339	+	0.0478947i
$433$	−2.26876	+	15.7796i	−0.109030	+	0.758319i	0.859807	+	0.510619i	$0.170584\pi$
$433$	−2.26876	+	15.7796i	−0.109030	+	0.758319i	−0.968837	+	0.247700i	$0.920325\pi$
$434$	1.93849	−	0.374310i	0.0930506	−	0.0179675i
$435$	−4.10470	+	3.55674i	−0.196805	+	0.170533i
$436$	−10.9055	+	6.29629i	−0.522279	+	0.301538i
$437$	3.50963	+	3.52670i	0.167888	+	0.168705i
$438$	−5.85201	+	10.1360i	−0.279620	+	0.484316i
$439$	−35.2689	−	12.2067i	−1.68329	−	0.582593i	−0.692920	−	0.721015i	$-0.743676\pi$
$439$	−35.2689	−	12.2067i	−1.68329	−	0.582593i	−0.990373	+	0.138421i	$0.955797\pi$
$440$	−5.07259	+	7.89311i	−0.241826	+	0.376289i
$441$	−2.29406	−	6.61342i	−0.109241	−	0.314925i
$442$	−11.2843	−	5.15338i	−0.536741	−	0.245121i
$443$	12.5213	−	9.84689i	0.594907	−	0.467840i	−0.274737	−	0.961519i	$-0.588591\pi$
$443$	12.5213	−	9.84689i	0.594907	−	0.467840i	0.869644	+	0.493679i	$0.164348\pi$
$444$	0.527240	−	0.502722i	0.0250217	−	0.0238582i
$445$	−0.878438	−	18.4407i	−0.0416420	−	0.874173i
$446$	−0.619841	−	0.441386i	−0.0293503	−	0.0209003i
$447$	8.33415	−	2.44713i	0.394192	−	0.115745i
$448$	−2.64271	+	0.126805i	−0.124856	+	0.00599097i
$449$	21.4019	−	24.6991i	1.01002	−	1.16562i	0.0238755	−	0.999715i	$-0.492399\pi$
$449$	21.4019	−	24.6991i	1.01002	−	1.16562i	0.986141	−	0.165907i	$-0.0530551\pi$
$450$	3.93551	+	3.75250i	0.185522	+	0.176895i
$451$	−11.4223	−	1.09069i	−0.537854	−	0.0513588i
$452$	11.2475	−	0.535786i	0.529040	−	0.0252013i
$453$	2.19687	−	0.532955i	0.103218	−	0.0250404i
$454$	3.62601	+	25.2195i	0.170177	+	1.18361i
$455$	13.6424	−	15.7552i	0.639566	−	0.738615i
$456$	1.02689	+	0.147645i	0.0480887	+	0.00691411i
$457$	39.1373	+	1.86434i	1.83077	+	0.0872101i	0.934426	−	0.356158i	$-0.115913\pi$
$457$	39.1373	+	1.86434i	1.83077	+	0.0872101i	0.896340	+	0.443368i	$0.146216\pi$
$458$	−4.67095	+	0.900252i	−0.218259	+	0.0420660i
$459$	4.40634	+	2.54400i	0.205670	+	0.118744i
$460$	−2.60647	+	15.2734i	−0.121527	+	0.712124i
$461$		−	26.0444i		−	1.21301i	−0.795079	−	0.606505i	$-0.792571\pi$
$461$		−	26.0444i		−	1.21301i	0.795079	−	0.606505i	$-0.207429\pi$
$462$	−6.26044	−	4.45477i	−0.291262	−	0.207255i
$463$	13.1324	+	8.43967i	0.610313	+	0.392225i	0.808975	−	0.587844i	$-0.200023\pi$
$463$	13.1324	+	8.43967i	0.610313	+	0.392225i	−0.198661	+	0.980068i	$0.563659\pi$
$464$	−1.56070	+	0.624810i	−0.0724537	+	0.0290061i
$465$	−1.39842	−	1.96381i	−0.0648504	−	0.0910696i
$466$	16.2588	+	6.50902i	0.753172	+	0.301525i
$467$	3.43668	+	14.1662i	0.159031	+	0.655533i	0.994385	+	0.105822i	$0.0337472\pi$
$467$	3.43668	+	14.1662i	0.159031	+	0.655533i	−0.835355	+	0.549712i	$0.814738\pi$
$468$	−1.31817	−	2.05111i	−0.0609324	−	0.0948127i
$469$	25.2153	−	19.8437i	1.16434	−	0.916296i
$470$	−6.21665	−	21.1720i	−0.286753	−	0.976589i
$471$	−2.66913	+	13.8488i	−0.122987	+	0.638118i
$472$	−0.961266	+	0.332697i	−0.0442459	+	0.0153136i
$473$	3.05745	−	12.6030i	0.140582	−	0.579485i
$474$	6.88420	−	9.66751i	0.316202	−	0.444043i
$475$	4.74589	−	3.05000i	0.217756	−	0.139944i
$476$	−7.27397	+	11.3271i	−0.333402	+	0.519178i
$477$	−0.922138	+	0.132583i	−0.0422218	+	0.00607058i
$478$	−4.74279	+	0.452882i	−0.216930	+	0.0207143i
$479$	−12.5192	−	9.84522i	−0.572018	−	0.449840i	0.289779	−	0.957094i	$-0.406418\pi$
$479$	−12.5192	−	9.84522i	−0.572018	−	0.449840i	−0.861797	+	0.507254i	$0.830661\pi$
$480$	1.48042	+	2.87161i	0.0675715	+	0.131070i
$481$	−0.580939	+	1.67851i	−0.0264885	+	0.0765335i
$482$	26.6659			1.21460
$483$	−12.3930	−	2.72294i	−0.563899	−	0.123898i
$484$	2.56599			0.116636
$485$	7.56649	−	21.8619i	0.343576	−	0.992699i
$486$	0.458227	+	0.888835i	0.0207856	+	0.0403184i
$487$	9.52432	+	7.49001i	0.431588	+	0.339405i	0.810203	−	0.586150i	$-0.199357\pi$
$487$	9.52432	+	7.49001i	0.431588	+	0.339405i	−0.378615	+	0.925554i	$0.623599\pi$
$488$	14.1325	−	1.34949i	0.639748	−	0.0610885i
$489$	11.2582	−	1.61868i	0.509112	−	0.0731993i
$490$	−14.8217	−	17.0812i	−0.669576	−	0.771652i
$491$	35.9742	−	23.1192i	1.62349	−	1.04335i	0.669812	−	0.742530i	$-0.266375\pi$
$491$	35.9742	−	23.1192i	1.62349	−	1.04335i	0.953680	−	0.300825i	$-0.0972619\pi$
$492$	−2.29180	+	3.21838i	−0.103322	+	0.145096i
$493$	−2.01658	+	8.31245i	−0.0908221	+	0.374374i
$494$	−2.39036	+	0.827312i	−0.107547	+	0.0372225i
$495$	−1.77566	+	9.21300i	−0.0798100	+	0.414094i
$496$	−0.210233	−	0.715988i	−0.00943975	−	0.0321488i
$497$	6.48065	−	16.2041i	0.290697	−	0.726855i
$498$	1.70419	+	2.65177i	0.0763666	+	0.118829i
$499$	3.06456	+	12.6323i	0.137189	+	0.565500i	0.998363	+	0.0571904i	$0.0182142\pi$
$499$	3.06456	+	12.6323i	0.137189	+	0.565500i	−0.861175	+	0.508309i	$0.830271\pi$
$500$	1.31307	+	0.525672i	0.0587221	+	0.0235088i
$501$	−5.22526	−	7.33785i	−0.233447	−	0.327831i
$502$	−27.8336	+	11.1429i	−1.24228	+	0.497332i
$503$	−27.4472	−	17.6392i	−1.22381	−	0.786494i	−0.240894	−	0.970552i	$-0.577441\pi$
$503$	−27.4472	−	17.6392i	−1.22381	−	0.786494i	−0.982916	+	0.184057i	$0.941077\pi$
$504$	−2.40628	+	1.09992i	−0.107184	+	0.0489942i
$505$			56.9020i			2.53211i
$506$	−12.8165	+	5.45157i	−0.569763	+	0.242352i
$507$	−6.11012	−	3.52768i	−0.271360	−	0.156670i
$508$	1.34768	−	0.259744i	0.0597935	−	0.0115243i
$509$	17.8215	+	0.848944i	0.789926	+	0.0376288i	0.438667	−	0.898650i	$-0.355451\pi$
$509$	17.8215	+	0.848944i	0.789926	+	0.0376288i	0.351259	+	0.936278i	$0.385754\pi$
$510$	16.2708	+	2.33939i	0.720483	+	0.103590i
$511$	−30.4084	−	5.84981i	−1.34519	−	0.258780i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	1.00821	−	0.244589i	0.0445135	−	0.0107989i
$514$	−9.42068	+	0.448762i	−0.415528	+	0.0197940i
$515$	15.8151	+	1.51016i	0.696896	+	0.0665455i
$516$	−3.23186	−	3.08157i	−0.142275	−	0.135659i
$517$	12.9892	−	14.9903i	0.571263	−	0.659272i
$518$	1.71347	+	0.882606i	0.0752857	+	0.0387795i
$519$	22.7211	−	6.67152i	0.997346	−	0.292847i
$520$	−6.41650	−	4.56917i	−0.281382	−	0.200371i
$521$	1.45012	+	30.4418i	0.0635310	+	1.33368i	0.775446	+	0.631414i	$0.217525\pi$
$521$	1.45012	+	30.4418i	0.0635310	+	1.33368i	−0.711915	+	0.702266i	$0.752172\pi$
$522$	−1.21669	+	1.16011i	−0.0532529	+	0.0507765i
$523$	−11.1941	+	8.80315i	−0.489485	+	0.384935i	−0.832175	−	0.554513i	$-0.812904\pi$
$523$	−11.1941	+	8.80315i	−0.489485	+	0.384935i	0.342690	+	0.939449i	$0.388662\pi$
$524$	9.22371	+	4.21233i	0.402940	+	0.184016i
$525$	−5.97206	+	13.0890i	−0.260642	+	0.571250i
$526$	−9.72412	+	15.1310i	−0.423992	+	0.659744i
$527$	−3.58793	−	1.24179i	−0.156293	−	0.0540934i
$528$	−1.45207	+	2.51506i	−0.0631932	+	0.109454i
$529$	−15.9524	+	16.5686i	−0.693584	+	0.720376i
$530$	−2.60660	+	1.50492i	−0.113223	+	0.0653695i
$531$	−0.768757	+	0.666132i	−0.0333612	+	0.0289077i
$532$	0.520398	+	2.69506i	0.0225621	+	0.116846i
$533$	1.37094	−	9.53511i	0.0593821	−	0.413012i
$534$	−0.543181	−	5.68845i	−0.0235058	−	0.246163i
$535$	12.5958	−	31.4627i	0.544563	−	1.36025i
$536$	−8.36914	−	8.77730i	−0.361492	−	0.379122i
$537$	−2.58201	+	5.00840i	−0.111422	+	0.216128i
$538$	21.1301	−	9.64979i	0.910983	−	0.416032i
$539$	5.71382	−	19.5095i	0.246112	−	0.840332i
$540$	2.44164	+	2.11570i	0.105072	+	0.0910450i
$541$	−16.9584	−	3.26846i	−0.729098	−	0.140522i	−0.188824	−	0.982011i	$-0.560467\pi$
$541$	−16.9584	−	3.26846i	−0.729098	−	0.140522i	−0.540275	+	0.841489i	$0.681680\pi$
$542$	−16.1821	−	3.92574i	−0.695082	−	0.168625i
$543$	1.56876	−	16.4288i	0.0673218	−	0.705026i
$544$	4.52240	+	2.33146i	0.193896	+	0.0999605i
$545$	−11.4619	+	39.0356i	−0.490973	+	1.67210i
$546$	3.98585	−	5.07203i	0.170578	−	0.217063i
$547$	−8.58369	+	18.7957i	−0.367012	+	0.803644i	0.632563	+	0.774509i	$0.282003\pi$
$547$	−8.58369	+	18.7957i	−0.367012	+	0.803644i	−0.999575	+	0.0291357i	$0.990725\pi$
$548$	−2.89749	−	7.23759i	−0.123775	−	0.309175i
$549$	12.6186	−	6.50534i	0.538549	−	0.277641i
$550$	2.98867	+	15.5067i	0.127437	+	0.661208i
$551$	0.872043	+	1.51042i	0.0371503	+	0.0643462i
$552$	−0.580912	+	4.76052i	−0.0247253	+	0.202621i
$553$	30.1313	+	8.83602i	1.28131	+	0.375746i
$554$	−15.8372	−	18.2771i	−0.672859	−	0.776521i
$555$	0.111989	−	2.35094i	0.00475367	−	0.0997918i
$556$	−5.72227	+	7.27646i	−0.242678	+	0.308591i
$557$	5.14559	−	3.66416i	0.218026	−	0.155255i	−0.465826	−	0.884876i	$-0.654243\pi$
$557$	5.14559	−	3.66416i	0.218026	−	0.155255i	0.683852	+	0.729621i	$0.260303\pi$
$558$	−0.461280	−	0.586565i	−0.0195275	−	0.0248313i
$559$	10.4467	+	3.06742i	0.441847	+	0.129738i
$560$	−5.89650	+	6.18836i	−0.249173	+	0.261506i
$561$	6.13828	+	13.4410i	0.259158	+	0.567478i
$562$	−1.70906	+	1.79241i	−0.0720922	+	0.0756082i
$563$	10.8217	+	31.2673i	0.456082	+	1.31776i	0.905465	+	0.424422i	$0.139523\pi$
$563$	10.8217	+	31.2673i	0.456082	+	1.31776i	−0.449383	+	0.893339i	$0.648356\pi$
$564$	−2.23384	−	6.45427i	−0.0940618	−	0.271774i
$565$	25.1046	−	26.3289i	1.05616	−	1.10767i
$566$	−9.71578	−	21.2746i	−0.408385	−	0.894238i
$567$	−1.82511	+	1.91545i	−0.0766476	+	0.0804414i
$568$	−6.32905	−	1.85838i	−0.265561	−	0.0779758i
$569$	3.65741	+	4.65077i	0.153327	+	0.194971i	0.856648	−	0.515901i	$-0.172543\pi$
$569$	3.65741	+	4.65077i	0.153327	+	0.194971i	−0.703321	+	0.710872i	$0.748301\pi$
$570$	2.73026	−	1.94421i	0.114358	−	0.0814340i
$571$	−9.77217	+	12.4263i	−0.408952	+	0.520025i	−0.946280	−	0.323348i	$-0.895191\pi$
$571$	−9.77217	+	12.4263i	−0.408952	+	0.520025i	0.537328	+	0.843374i	$0.319434\pi$
$572$	0.336916	−	7.07274i	0.0140872	−	0.295726i
$573$	7.76680	+	8.96337i	0.324463	+	0.374450i
$574$	−10.0309	−	2.94157i	−0.418683	−	0.122779i
$575$	14.5649	+	21.6325i	0.607396	+	0.902137i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	0.175449	+	0.910314i	0.00730402	+	0.0378969i	0.985398	−	0.170268i	$-0.0544632\pi$
$577$	0.175449	+	0.910314i	0.00730402	+	0.0378969i	−0.978094	+	0.208164i	$0.933251\pi$
$578$	7.89979	−	4.07263i	0.328588	−	0.169399i
$579$	−4.07887	−	10.1885i	−0.169512	−	0.423421i
$580$	−2.25624	+	4.94048i	−0.0936854	+	0.205142i
$581$	−5.15308	+	6.55735i	−0.213786	+	0.272045i
$582$	2.01739	−	6.87059i	0.0836234	−	0.284795i
$583$	−2.40479	−	1.23976i	−0.0995963	−	0.0513454i
$584$	−1.11254	+	11.6510i	−0.0460371	+	0.482123i
$585$	−7.65507	−	1.85710i	−0.316498	−	0.0767816i
$586$	14.3963	+	2.77466i	0.594706	+	0.114620i
$587$	−30.4642	−	26.3974i	−1.25739	−	1.08954i	−0.992111	−	0.125365i	$-0.959990\pi$
$587$	−30.4642	−	26.3974i	−1.25739	−	1.08954i	−0.265281	−	0.964171i	$-0.585465\pi$
$588$	−4.83406	−	5.06279i	−0.199353	−	0.208786i
$589$	−0.704204	+	0.321599i	−0.0290162	+	0.0132513i
$590$	−1.50590	+	2.92104i	−0.0619969	+	0.120257i
$591$	15.7973	+	16.5678i	0.649816	+	0.681507i
$592$	0.270756	−	0.676316i	0.0111280	−	0.0277964i
$593$	−0.558733	−	5.85131i	−0.0229444	−	0.240285i	−0.999668	−	0.0257811i	$-0.991793\pi$
$593$	−0.558733	−	5.85131i	−0.0229444	−	0.240285i	0.976723	−	0.214504i	$-0.0688134\pi$
$594$	−0.413302	+	2.87458i	−0.0169580	+	0.117945i
$595$	8.24554	+	42.7023i	0.338034	+	1.75063i
$596$	6.56444	−	5.68812i	0.268890	−	0.232994i
$597$	16.9026	−	9.75873i	0.691778	−	0.399398i
$598$	−4.05969	−	10.9657i	−0.166013	−	0.448419i
$599$	8.46508	−	14.6619i	0.345874	−	0.599071i	−0.639638	−	0.768676i	$-0.720916\pi$
$599$	8.46508	−	14.6619i	0.345874	−	0.599071i	0.985512	+	0.169605i	$0.0542492\pi$
$600$	5.13871	+	1.77853i	0.209787	+	0.0726080i
$601$	−3.58792	+	5.58291i	−0.146354	+	0.227732i	−0.906689	−	0.421800i	$-0.861399\pi$
$601$	−3.58792	+	5.58291i	−0.146354	+	0.227732i	0.760335	+	0.649531i	$0.225035\pi$
$602$	4.90428	−	10.7487i	0.199884	−	0.438085i
$603$	−11.0318	−	5.03807i	−0.449251	−	0.205166i
$604$	1.77695	−	1.39741i	0.0723030	−	0.0568597i
$605$	5.99982	−	5.72081i	0.243927	−	0.232584i
$606$	0.838041	+	17.5926i	0.0340431	+	0.714652i
$607$	−12.9054	−	9.18992i	−0.523815	−	0.373007i	0.287348	−	0.957826i	$-0.407226\pi$
$607$	−12.9054	−	9.18992i	−0.523815	−	0.373007i	−0.811164	+	0.584819i	$0.801166\pi$
$608$	0.995429	−	0.292284i	0.0403700	−	0.0118537i
$609$	−3.95410	−	2.03675i	−0.160228	−	0.0825331i
$610$	30.0361	−	34.6635i	1.21612	−	1.40348i
$611$	12.0519	+	11.4915i	0.487569	+	0.464896i
$612$	5.06497	+	0.483646i	0.204739	+	0.0195502i
$613$	−43.3272	+	2.06393i	−1.74997	+	0.0833613i	−0.897936	−	0.440127i	$-0.854934\pi$
$613$	−43.3272	+	2.06393i	−1.74997	+	0.0833613i	−0.852033	+	0.523488i	$0.824631\pi$
$614$	−8.49712	+	2.06138i	−0.342916	+	0.0831905i
$615$	1.81661	+	12.6348i	0.0732526	+	0.509483i
$616$	−7.54527	−	1.45152i	−0.304008	−	0.0584835i
$617$	−2.95692	−	0.425141i	−0.119041	−	0.0171155i	0.0825367	−	0.996588i	$-0.473698\pi$
$617$	−2.95692	−	0.425141i	−0.119041	−	0.0171155i	−0.201578	+	0.979472i	$0.564607\pi$
$618$	4.91186	+	0.233981i	0.197584	+	0.00941209i
$619$	1.40125	−	0.270069i	0.0563209	−	0.0108550i	−0.161013	−	0.986952i	$-0.551476\pi$
$619$	1.40125	−	0.270069i	0.0563209	−	0.0108550i	0.217334	+	0.976097i	$0.430264\pi$
$620$	−2.08785	−	1.20542i	−0.0838500	−	0.0484108i
$621$	1.23001	+	4.63542i	0.0493584	+	0.186013i
$622$			0.901837i			0.0361604i
$623$	13.7503	−	6.28529i	0.550893	−	0.251815i
$624$	−2.05111	−	1.31817i	−0.0821102	−	0.0527690i
$625$	−20.9991	+	8.40679i	−0.839966	+	0.336271i
$626$	−7.23529	−	10.1605i	−0.289180	−	0.406097i
$627$	2.79709	+	1.11978i	0.111705	+	0.0447199i
$628$	3.32506	+	13.7061i	0.132684	+	0.546933i
$629$	−2.00395	−	3.11820i	−0.0799025	−	0.124331i
$630$	−3.17414	+	7.93658i	−0.126461	+	0.316201i
$631$	9.12510	+	31.0772i	0.363264	+	1.23717i	0.915105	+	0.403215i	$0.132107\pi$
$631$	9.12510	+	31.0772i	0.363264	+	1.23717i	−0.551841	+	0.833950i	$0.686074\pi$
$632$	2.24606	−	11.6537i	0.0893436	−	0.463558i
$633$	2.18721	−	0.757001i	0.0869338	−	0.0300881i
$634$	1.63766	−	6.75055i	0.0650400	−	0.268098i
$635$	2.57206	−	3.61195i	0.102069	−	0.143336i
$636$	−0.783729	+	0.503672i	−0.0310769	+	0.0199719i
$637$	16.1323	+	5.57094i	0.639186	+	0.220729i
$638$	−4.83252	+	0.694811i	−0.191321	+	0.0275078i
$639$	−6.56638	+	0.627013i	−0.259762	+	0.0248042i
$640$	2.53955	+	1.99712i	0.100384	+	0.0789431i
$641$	−20.1777	−	39.1394i	−0.796973	−	1.54591i	−0.837312	−	0.546725i	$-0.815874\pi$
$641$	−20.1777	−	39.1394i	−0.796973	−	1.54591i	0.0403392	−	0.999186i	$-0.487156\pi$
$642$	3.43092	−	9.91298i	0.135407	−	0.391234i
$643$	19.7656			0.779479			0.389740	−	0.920925i	$-0.372565\pi$
$643$	19.7656			0.779479			0.389740	+	0.920925i	$0.372565\pi$
$644$	−12.4042	+	2.67135i	−0.488794	+	0.105266i
$645$	−14.4271			−0.568065
$646$	1.72645	−	4.98825i	0.0679263	−	0.196260i
$647$	−2.35000	−	4.55836i	−0.0923880	−	0.179208i	0.838113	−	0.545496i	$-0.183659\pi$
$647$	−2.35000	−	4.55836i	−0.0923880	−	0.179208i	−0.930501	+	0.366288i	$0.880628\pi$
$648$	0.786053	+	0.618159i	0.0308791	+	0.0242836i
$649$	−2.94075	+	0.280807i	−0.115434	+	0.0110226i
$650$	−13.1233	+	1.88684i	−0.514737	+	0.0740079i
$651$	1.06681	−	1.66126i	0.0418117	−	0.0651098i
$652$	9.56837	−	6.14922i	0.374726	−	0.240822i
$653$	10.5677	−	14.8403i	0.413548	−	0.580746i	−0.554290	−	0.832324i	$-0.687010\pi$
$653$	10.5677	−	14.8403i	0.413548	−	0.580746i	0.967837	+	0.251578i	$0.0809494\pi$
$654$	−2.96882	+	12.2376i	−0.116090	+	0.478529i
$655$	30.9583	−	10.7148i	1.20964	−	0.418660i
$656$	−0.747730	+	3.87959i	−0.0291940	+	0.151473i
$657$	3.29740	+	11.2299i	0.128644	+	0.438121i
$658$	14.2003	−	11.1752i	0.553585	−	0.435655i
$659$	20.1301	+	31.3230i	0.784156	+	1.22017i	0.971305	+	0.237839i	$0.0764390\pi$
$659$	20.1301	+	31.3230i	0.784156	+	1.22017i	−0.187149	+	0.982332i	$0.559925\pi$
$660$	2.21202	+	9.11808i	0.0861028	+	0.354921i
$661$	−43.4404	−	17.3909i	−1.68964	−	0.676428i	−0.690726	−	0.723117i	$-0.742709\pi$
$661$	−43.4404	−	17.3909i	−1.68964	−	0.676428i	−0.998909	+	0.0466888i	$0.985133\pi$
$662$	−7.44499	−	10.4550i	−0.289358	−	0.406346i
$663$	−11.5168	+	4.61062i	−0.447274	+	0.179061i
$664$	2.65177	+	1.70419i	0.102909	+	0.0661354i
$665$	7.22538	+	5.14140i	0.280188	+	0.199375i
$666$		−	0.728500i		−	0.0282288i
$667$	−6.89448	+	4.17949i	−0.266955	+	0.161830i
$668$	−7.80132	−	4.50409i	−0.301842	−	0.174269i
$669$	−0.747185	+	0.144008i	−0.0288879	+	0.00556768i
$670$	−39.1376	−	1.86435i	−1.51202	−	0.0720262i
$671$	40.8097	+	5.86755i	1.57544	+	0.226514i
$672$	−1.73191	+	2.00013i	−0.0668097	+	0.0771565i
$673$	5.98766	+	41.6451i	0.230807	+	1.60530i	0.694627	+	0.719370i	$0.255570\pi$
$673$	5.98766	+	41.6451i	0.230807	+	1.60530i	−0.463820	+	0.885930i	$0.653521\pi$
$674$	−30.1701	+	7.31918i	−1.16211	+	0.281924i
$675$	5.43163	−	0.258740i	0.209063	−	0.00995892i
$676$	−7.02342	−	0.670655i	−0.270131	−	0.0257944i
$677$	−25.8825	−	24.6789i	−0.994746	−	0.948488i	0.00392686	−	0.999992i	$-0.498750\pi$
$677$	−25.8825	−	24.6789i	−0.994746	−	0.948488i	−0.998673	+	0.0515040i	$0.983599\pi$
$678$	7.37393	−	8.50996i	0.283194	−	0.326823i
$679$	18.9235	−	0.908006i	0.726218	−	0.0348461i
$680$	15.7722	−	4.63115i	0.604838	−	0.177596i
$681$	20.7544	+	14.7792i	0.795311	+	0.566339i
$682$	−0.103115	−	2.16466i	−0.00394849	−	0.0828890i
$683$	−7.50577	+	7.15674i	−0.287200	+	0.273845i	−0.819959	−	0.572422i	$-0.806004\pi$
$683$	−7.50577	+	7.15674i	−0.287200	+	0.273845i	0.532759	+	0.846267i	$0.321155\pi$
$684$	0.815494	−	0.641311i	0.0311812	−	0.0245211i
$685$	−22.9110	−	10.4631i	−0.875384	−	0.399774i
$686$	8.46937	−	16.4703i	0.323362	−	0.628838i
$687$	−2.57178	+	4.00177i	−0.0981196	+	0.152677i
$688$	−4.21994	−	1.46053i	−0.160884	−	0.0556823i
$689$	1.13572	−	1.96713i	0.0432675	−	0.0749415i
$690$	9.25517	+	12.4262i	0.352338	+	0.473058i
$691$	−25.8990	+	14.9528i	−0.985243	+	0.568830i	−0.903849	−	0.427852i	$-0.859271\pi$
$691$	−25.8990	+	14.9528i	−0.985243	+	0.568830i	−0.0813942	+	0.996682i	$0.525937\pi$
$692$	17.8964	−	15.5073i	0.680319	−	0.589500i
$693$	−7.54427	+	1.45675i	−0.286583	+	0.0553373i
$694$	−5.04990	+	35.1228i	−0.191692	+	1.33324i
$695$	2.84284	+	29.7716i	0.107835	+	1.12930i
$696$	−0.624810	+	1.56070i	−0.0236834	+	0.0591582i
$697$	13.8724	+	14.5490i	0.525456	+	0.551082i
$698$	1.70796	−	3.31298i	0.0646473	−	0.125398i
$699$	15.9306	−	7.27528i	0.602552	−	0.275176i
$700$	0.00498192	+	14.3870i	0.000188299	+	0.543779i
$701$	−21.9296	−	19.0021i	−0.828269	−	0.717699i	0.133652	−	0.991028i	$-0.457330\pi$
$701$	−21.9296	−	19.0021i	−0.828269	−	0.717699i	−0.961920	+	0.273329i	$0.911875\pi$
$702$	−2.39410	−	0.461425i	−0.0903596	−	0.0174154i
$703$	−0.734480	−	0.178183i	−0.0277015	−	0.00672030i
$704$	−0.276056	+	2.89099i	−0.0104042	+	0.108958i
$705$	−19.6128	−	10.1111i	−0.738662	−	0.380807i
$706$	−1.42763	+	4.86206i	−0.0537296	+	0.182986i
$707$	−43.2546	+	17.3339i	−1.62676	+	0.651909i
$708$	−0.422565	+	0.925288i	−0.0158810	+	0.0347745i
$709$	0.429104	+	1.07185i	0.0161153	+	0.0402541i	0.936207	−	0.351448i	$-0.114311\pi$
$709$	0.429104	+	1.07185i	0.0161153	+	0.0402541i	−0.920092	+	0.391702i	$0.871886\pi$
$710$	−18.9418	+	9.76520i	−0.710875	+	0.366481i
$711$	−2.24606	−	11.6537i	−0.0842339	−	0.437047i
$712$	−2.85716	−	4.94875i	−0.107077	−	0.185462i
$713$	−1.55589	−	3.22281i	−0.0582684	−	0.120695i
$714$	3.17822	+	13.0810i	0.118942	+	0.489545i
$715$	−14.9807	−	17.2887i	−0.560247	−	0.646560i
$716$	−0.268114	+	5.62840i	−0.0100199	+	0.210343i
$717$	−2.94514	+	3.74505i	−0.109988	+	0.139861i
$718$	−17.1787	+	12.2329i	−0.641104	+	0.456528i
$719$	17.9565	+	22.8336i	0.669666	+	0.851549i	0.995587	−	0.0938479i	$-0.0299167\pi$
$719$	17.9565	+	22.8336i	0.669666	+	0.851549i	−0.325921	+	0.945397i	$0.605674\pi$
$720$	3.09989	+	0.910209i	0.115526	+	0.0339215i
$721$	3.66975	+	12.4820i	0.136669	+	0.464855i
$722$	7.44577	+	16.3040i	0.277103	+	0.606771i
$723$	18.4016	−	19.2991i	0.684363	−	0.717739i
$724$	−5.39776	−	15.5958i	−0.200606	−	0.579614i
$725$	2.98992	+	8.63881i	0.111043	+	0.320837i
$726$	1.77073	−	1.85709i	0.0657181	−	0.0689232i
$727$	−3.29859	−	7.22291i	−0.122338	−	0.267883i	0.838548	−	0.544828i	$-0.183405\pi$
$727$	−3.29859	−	7.22291i	−0.122338	−	0.267883i	−0.960886	+	0.276945i	$0.910678\pi$
$728$	1.51866	−	6.26946i	0.0562851	−	0.232362i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	23.3743	+	29.7229i	0.865123	+	1.10009i
$731$	−18.5077	+	13.1793i	−0.684533	+	0.487453i
$732$	8.77587	−	11.1594i	0.324365	−	0.412464i
$733$	1.40266	−	29.4454i	0.0518083	−	1.08759i	−0.811964	−	0.583707i	$-0.801602\pi$
$733$	1.40266	−	29.4454i	0.0518083	−	1.08759i	0.863773	−	0.503882i	$-0.168095\pi$
$734$	17.9517	+	20.7174i	0.662610	+	0.764693i
$735$	−22.5904	−	1.06043i	−0.833260	−	0.0391147i
$736$	1.44917	+	4.57164i	0.0534173	+	0.168513i
$737$	−17.6104	−	30.5021i	−0.648687	−	1.12356i
$738$	0.747730	+	3.87959i	0.0275243	+	0.142810i
$739$	21.1529	−	10.9051i	0.778121	−	0.401149i	−0.0229363	−	0.999737i	$-0.507301\pi$
$739$	21.1529	−	10.9051i	0.778121	−	0.401149i	0.801057	+	0.598588i	$0.204271\pi$
$740$	−0.874747	−	2.18501i	−0.0321563	−	0.0803226i
$741$	−1.05078	+	2.30090i	−0.0386015	+	0.0845255i
$742$	−1.93802	−	1.52299i	−0.0711469	−	0.0559107i
$743$	2.78805	−	9.49522i	0.102284	−	0.348346i	−0.892410	−	0.451225i	$-0.850987\pi$
$743$	2.78805	−	9.49522i	0.102284	−	0.348346i	0.994694	+	0.102879i	$0.0328055\pi$
$744$	−0.663263	−	0.341936i	−0.0243164	−	0.0125360i
$745$	2.66749	−	27.9353i	0.0977295	−	1.02347i
$746$	−1.05889	−	0.256885i	−0.0387689	−	0.00940523i
$747$	3.09520	+	0.596551i	0.113248	+	0.0218267i
$748$	11.1672	+	9.67640i	0.408312	+	0.353804i
$749$	27.7537	−	0.00961051i	1.01410	−	0.000351160i
$750$	1.28657	−	0.587555i	0.0469787	−	0.0214545i
$751$	6.52216	−	12.6512i	0.237997	−	0.461650i	−0.739342	−	0.673330i	$-0.764863\pi$
$751$	6.52216	−	12.6512i	0.237997	−	0.461650i	0.977339	+	0.211680i	$0.0678936\pi$
$752$	−4.71318	−	4.94304i	−0.171872	−	0.180254i
$753$	−11.1429	+	27.8336i	−0.406070	+	1.01431i
$754$	−0.389621	−	4.08029i	−0.0141891	−	0.148595i
$755$	1.03939	−	7.22909i	0.0378271	−	0.263094i
$756$	−0.864475	+	2.50054i	−0.0314406	+	0.0909436i
$757$	−13.8444	+	11.9962i	−0.503183	+	0.436010i	−0.869100	−	0.494637i	$-0.835301\pi$
$757$	−13.8444	+	11.9962i	−0.503183	+	0.436010i	0.365917	+	0.930648i	$0.380755\pi$
$758$	27.4320	−	15.8379i	0.996374	−	0.575257i
$759$	−4.89891	+	13.0378i	−0.177819	+	0.473240i
$760$	1.67588	−	2.90271i	0.0607905	−	0.105292i
$761$	−7.38289	−	2.55524i	−0.267629	−	0.0926275i	0.189958	−	0.981792i	$-0.439165\pi$
$761$	−7.38289	−	2.55524i	−0.267629	−	0.0926275i	−0.457587	+	0.889165i	$0.651286\pi$
$762$	0.742019	−	1.15460i	0.0268805	−	0.0418269i
$763$	−33.1649	+	3.17845i	−1.20065	+	0.115068i
$764$	10.7885	+	4.92692i	0.390312	+	0.178250i
$765$	12.9212	−	10.1614i	0.467168	−	0.367385i
$766$	13.3896	−	12.7670i	0.483786	−	0.461289i
$767$	−0.118009	−	2.47732i	−0.00426107	−	0.0894508i
$768$	0.814576	+	0.580057i	0.0293935	+	0.0209310i
$769$	4.35594	−	1.27902i	0.157079	−	0.0461226i	−0.202248	−	0.979334i	$-0.564825\pi$
$769$	4.35594	−	1.27902i	0.157079	−	0.0461226i	0.359327	+	0.933212i	$0.383006\pi$
$770$	−20.8786	+	13.4281i	−0.752411	+	0.483913i
$771$	−6.17623	+	7.12775i	−0.222431	+	0.256699i
$772$	−7.94275	−	7.57339i	−0.285866	−	0.272572i
$773$	14.8484	+	1.41785i	0.534061	+	0.0509967i	0.358603	−	0.933490i	$-0.383253\pi$
$773$	14.8484	+	1.41785i	0.534061	+	0.0509967i	0.175458	+	0.984487i	$0.443859\pi$
$774$	−4.46048	+	0.212479i	−0.160329	+	0.00763739i
$775$	−3.94338	+	0.956653i	−0.141650	+	0.0343640i
$776$	−1.01907	−	7.08776i	−0.0365823	−	0.254436i
$777$	1.82120	−	0.631031i	0.0653353	−	0.0226381i
$778$	33.3496	+	4.79495i	1.19564	+	0.171907i
$779$	4.09433	+	0.195037i	0.146695	+	0.00698792i
$780$	−7.73476	+	1.49075i	−0.276949	+	0.0533775i
$781$	−16.5899	−	9.57820i	−0.593634	−	0.342735i
$782$	23.2245	+	7.48623i	0.830505	+	0.267707i
$783$			1.68112i			0.0600784i
$784$	−6.50038	−	2.59714i	−0.232156	−	0.0927549i
$785$	38.3321	+	24.6345i	1.36813	+	0.879245i
$786$	9.41370	−	3.76868i	0.335775	−	0.134424i
$787$	−22.0524	−	30.9683i	−0.786085	−	1.10390i	−0.992112	−	0.125355i	$-0.959993\pi$
$787$	−22.0524	−	30.9683i	−0.786085	−	1.10390i	0.206027	−	0.978546i	$-0.433946\pi$
$788$	21.2523	+	8.50812i	0.757081	+	0.303089i
$789$	4.24043	+	17.4793i	0.150963	+	0.622279i
$790$	−20.7298	−	32.2563i	−0.737535	−	1.14763i
$791$	27.6617	+	11.0630i	0.983537	+	0.393354i
$792$	0.818190	+	2.78650i	0.0290731	+	0.0990139i
$793$	−6.55075	+	33.9885i	−0.232624	+	1.20697i
$794$	15.5233	−	5.37265i	0.550900	−	0.190668i
$795$	−0.709596	+	2.92500i	−0.0251668	+	0.103739i
$796$	11.3212	−	15.8985i	0.401271	−	0.563506i
$797$	−19.1482	+	12.3058i	−0.678263	+	0.435893i	−0.833896	−	0.551922i	$-0.813895\pi$
$797$	−19.1482	+	12.3058i	−0.678263	+	0.435893i	0.155633	+	0.987815i	$0.450258\pi$
$798$	2.30962	+	1.48318i	0.0817598	+	0.0525038i
$799$	−34.3969	+	4.94553i	−1.21688	+	0.174960i
$800$	5.41316	−	0.516894i	0.191384	−	0.0182750i
$801$	−4.49177	−	3.53236i	−0.158709	−	0.124810i
$802$	−1.65639	−	3.21296i	−0.0584893	−	0.113453i
$803$	−11.1171	+	32.1207i	−0.392313	+	1.13351i
$804$	−12.1278			−0.427714
$805$	−23.0479	+	33.9010i	−0.812331	+	1.19485i
$806$	1.81939			0.0640854
$807$	7.59755	−	21.9517i	0.267447	−	0.772736i
$808$	8.07056	+	15.6547i	0.283921	+	0.550730i
$809$	3.03046	+	2.38318i	0.106545	+	0.0837880i	0.670010	−	0.742352i	$-0.266290\pi$
$809$	3.03046	+	2.38318i	0.106545	+	0.0837880i	−0.563465	+	0.826140i	$0.690532\pi$
$810$	3.21613	−	0.307103i	0.113003	−	0.0107905i
$811$	−45.8997	+	6.59938i	−1.61176	+	0.231735i	−0.888511	−	0.458856i	$-0.848259\pi$
$811$	−45.8997	+	6.59938i	−1.61176	+	0.231735i	−0.723245	+	0.690591i	$0.757350\pi$
$812$	−4.44287	−	0.210098i	−0.155914	−	0.00737299i
$813$	−14.0081	+	9.00248i	−0.491287	+	0.315731i
$814$	1.22721	−	1.72337i	0.0430135	−	0.0604040i
$815$	8.66330	−	35.7106i	0.303462	−	1.25089i
$816$	4.80817	−	1.66412i	0.168320	−	0.0582560i
$817$	−0.876761	+	4.54907i	−0.0306740	+	0.159152i
$818$	−9.21569	−	31.3857i	−0.322219	−	1.09738i
$819$	−0.920252	−	6.38479i	−0.0321562	−	0.223103i
$820$	6.90112	+	10.7383i	0.240997	+	0.374999i
$821$	−11.1914	−	46.1317i	−0.390583	−	1.61001i	−0.739707	−	0.672930i	$-0.765036\pi$
$821$	−11.1914	−	46.1317i	−0.390583	−	1.61001i	0.349123	−	0.937077i	$-0.386479\pi$
$822$	−7.23759	−	2.89749i	−0.252440	−	0.101062i
$823$	−10.3841	−	14.5824i	−0.361965	−	0.508309i	0.592929	−	0.805255i	$-0.297971\pi$
$823$	−10.3841	−	14.5824i	−0.361965	−	0.508309i	−0.954894	+	0.296946i	$0.904032\pi$
$824$	4.56518	−	1.82762i	0.159036	−	0.0636683i
$825$	13.2851	+	8.53784i	0.462529	+	0.297249i
$826$	−2.67919	−	0.254896i	−0.0932210	−	0.00886895i
$827$		−	5.31153i		−	0.184700i	−0.995727	−	0.0923501i	$-0.970562\pi$
$827$		−	5.31153i		−	0.184700i	0.995727	−	0.0923501i	$-0.0294379\pi$
$828$	3.04447	+	3.70556i	0.105803	+	0.128777i
$829$	7.11285	+	4.10661i	0.247040	+	0.142628i	0.618408	−	0.785857i	$-0.287778\pi$
$829$	7.11285	+	4.10661i	0.247040	+	0.142628i	−0.371368	+	0.928486i	$0.621111\pi$
$830$	9.99984	−	1.92731i	0.347100	−	0.0668980i
$831$	−24.1567	−	1.15073i	−0.837987	−	0.0399183i
$832$	−2.41335	−	0.346987i	−0.0836677	−	0.0120296i
$833$	−29.9488	+	19.2762i	−1.03766	+	0.667882i
$834$	1.31740	+	9.16274i	0.0456179	+	0.317280i
$835$	−28.2829	+	6.86135i	−0.978770	+	0.237447i
$836$	3.00949	−	0.143360i	0.104086	−	0.00495821i
$837$	−0.742836	−	0.0709323i	−0.0256762	−	0.00245178i
$838$	22.2615	+	21.2263i	0.769012	+	0.733251i
$839$	19.9814	−	23.0598i	0.689834	−	0.796111i	−0.297507	−	0.954720i	$-0.596155\pi$
$839$	19.9814	−	23.0598i	0.689834	−	0.796111i	0.987342	+	0.158608i	$0.0507007\pi$
$840$	0.409676	+	8.53795i	0.0141352	+	0.294587i
$841$	25.1136	−	7.37402i	0.865986	−	0.254277i
$842$	−19.0654	−	13.5764i	−0.657036	−	0.467873i
$843$	0.117842	+	2.47381i	0.00405869	+	0.0852024i
$844$	1.67509	−	1.59719i	0.0576589	−	0.0549776i
$845$	−17.9174	+	14.0904i	−0.616378	+	0.484725i
$846$	−6.21270	−	2.83725i	−0.213597	−	0.0975466i
$847$	6.17644	+	2.81810i	0.212225	+	0.0968311i
$848$	−0.503672	+	0.783729i	−0.0172962	+	0.0269134i
$849$	−22.1018	−	7.64951i	−0.758532	−	0.262530i
$850$	13.8337	−	23.9607i	0.474493	−	0.821847i
$851$	0.750936	−	3.41211i	0.0257418	−	0.116966i
$852$	−5.71252	+	3.29812i	−0.195708	+	0.112992i
$853$	−32.1223	+	27.8341i	−1.09985	+	0.953023i	−0.999122	−	0.0418916i	$-0.986662\pi$
$853$	−32.1223	+	27.8341i	−1.09985	+	0.953023i	−0.100725	+	0.994914i	$0.532116\pi$
$854$	35.4996	+	12.2728i	1.21477	+	0.419965i
$855$	0.477005	−	3.31764i	0.0163132	−	0.113461i
$856$	−0.997130	−	10.4424i	−0.0340812	−	0.356914i
$857$	−17.4775	+	43.6567i	−0.597021	+	1.49129i	0.254557	+	0.967058i	$0.418070\pi$
$857$	−17.4775	+	43.6567i	−0.597021	+	1.49129i	−0.851578	+	0.524228i	$0.824354\pi$
$858$	−4.88628	−	5.12459i	−0.166815	−	0.174950i
$859$	24.5453	−	47.6112i	0.837474	−	1.62447i	0.0577664	−	0.998330i	$-0.481602\pi$
$859$	24.5453	−	47.6112i	0.837474	−	1.62447i	0.779708	−	0.626143i	$-0.215368\pi$
$860$	−13.1233	+	5.99322i	−0.447501	+	0.204367i
$861$	−9.05105	+	5.22981i	−0.308459	+	0.178231i
$862$	−8.66962	−	7.51227i	−0.295288	−	0.255869i
$863$	−2.00295	−	0.386037i	−0.0681813	−	0.0131409i	0.155047	−	0.987907i	$-0.450447\pi$
$863$	−2.00295	−	0.386037i	−0.0681813	−	0.0131409i	−0.223228	+	0.974766i	$0.571659\pi$
$864$	0.971812	+	0.235759i	0.0330617	+	0.00802068i
$865$	7.27230	−	76.1589i	0.247265	−	2.58948i
$866$	14.1697	+	7.30498i	0.481505	+	0.248233i
$867$	2.50398	−	8.52778i	0.0850397	−	0.289619i
$868$	0.280296	−	1.95430i	0.00951385	−	0.0663333i
$869$	14.3180	−	31.3520i	0.485705	−	1.06355i
$870$	2.01861	+	5.04224i	0.0684373	+	0.170948i
$871$	26.2825	−	13.5495i	0.890547	−	0.459109i
$872$	2.38316	+	12.3650i	0.0807041	+	0.418733i
$873$	−3.58032	−	6.20130i	−0.121176	−	0.209882i
$874$	4.48063	−	2.16313i	0.151559	−	0.0731689i
$875$	2.58328	+	2.70739i	0.0873308	+	0.0915265i
$876$	7.66450	+	8.84531i	0.258960	+	0.298855i
$877$	1.25697	−	26.3871i	0.0424450	−	0.891031i	−0.872786	−	0.488102i	$-0.837689\pi$
$877$	1.25697	−	26.3871i	0.0424450	−	0.891031i	0.915231	−	0.402928i	$-0.132008\pi$
$878$	−23.0707	+	29.3367i	−0.778597	+	0.990067i
$879$	11.9427	−	8.50436i	0.402817	−	0.286845i
$880$	5.79991	+	7.37519i	0.195515	+	0.248618i
$881$	−37.8503	−	11.1138i	−1.27521	−	0.374435i	−0.427074	−	0.904217i	$-0.640456\pi$
$881$	−37.8503	−	11.1138i	−1.27521	−	0.374435i	−0.848134	+	0.529782i	$0.822274\pi$
$882$	−7.00000	+	0.00484790i	−0.235702	+	0.000163237i
$883$	21.2174	+	46.4596i	0.714021	+	1.56349i	0.822098	+	0.569346i	$0.192804\pi$
$883$	21.2174	+	46.4596i	0.714021	+	1.56349i	−0.108077	+	0.994143i	$0.534469\pi$
$884$	−8.56070	+	8.97820i	−0.287927	+	0.301970i
$885$	1.07486	+	3.10562i	0.0361312	+	0.104394i
$886$	−5.20999	−	15.0533i	−0.175033	−	0.505725i
$887$	−4.92005	+	5.16000i	−0.165199	+	0.173256i	−0.801130	−	0.598490i	$-0.795768\pi$
$887$	−4.92005	+	5.16000i	−0.165199	+	0.173256i	0.635931	+	0.771746i	$0.280616\pi$
$888$	−0.302630	−	0.662667i	−0.0101556	−	0.0222376i
$889$	3.52918	+	0.854875i	0.118365	+	0.0286716i
$890$	−17.7138	−	5.20123i	−0.593767	−	0.174346i
$891$	1.79522	+	2.28281i	0.0601421	+	0.0764769i
$892$	−0.619841	+	0.441386i	−0.0207538	+	0.0147787i
$893$	−4.38010	+	5.56975i	−0.146574	+	0.186384i
$894$	0.413296	−	8.67616i	0.0138227	−	0.290174i
$895$	11.9215	+	13.7581i	0.398492	+	0.459884i
$896$	−0.744515	+	2.53884i	−0.0248725	+	0.0848166i
$897$	−10.7377	−	4.62903i	−0.358522	−	0.154559i
$898$	−16.3408	−	28.3031i	−0.545299	−	0.944486i
$899$	−0.237412	−	1.23181i	−0.00791813	−	0.0410832i
$900$	4.83330	−	2.49174i	0.161110	−	0.0830579i
$901$	1.76171	+	4.40055i	0.0586912	+	0.146603i
$902$	−4.76657	+	10.4373i	−0.158709	+	0.347525i
$903$	−4.39488	−	10.9669i	−0.146252	−	0.364954i
$904$	3.17239	−	10.8042i	0.105512	−	0.359342i
$905$	−47.3916	−	24.4321i	−1.57535	−	0.812149i
$906$	0.214883	−	2.25036i	0.00713902	−	0.0747632i
$907$	−25.7177	−	6.23903i	−0.853941	−	0.207164i	−0.215185	−	0.976573i	$-0.569035\pi$
$907$	−25.7177	−	6.23903i	−0.853941	−	0.207164i	−0.638756	+	0.769410i	$0.720551\pi$
$908$	25.0184	+	4.82190i	0.830264	+	0.160020i
$909$	13.3107	+	11.5338i	0.441488	+	0.382552i
$910$	−10.4267	−	18.0451i	−0.345641	−	0.598190i
$911$	6.86787	−	3.13645i	0.227543	−	0.103915i	−0.298382	−	0.954447i	$-0.596447\pi$
$911$	6.86787	−	3.13645i	0.227543	−	0.103915i	0.525924	+	0.850531i	$0.323720\pi$
$912$	0.475389	−	0.922125i	0.0157417	−	0.0305346i
$913$	6.31721	+	6.62529i	0.209069	+	0.219265i
$914$	14.5624	−	36.3750i	0.481680	−	1.20318i
$915$	−4.35987	−	45.6586i	−0.144133	−	1.50943i
$916$	−0.676980	+	4.70850i	−0.0223680	+	0.155573i
$917$	17.5757	+	20.2692i	0.580399	+	0.669348i
$918$	3.84526	−	3.33194i	0.126912	−	0.109970i
$919$	2.55996	−	1.47799i	0.0844452	−	0.0487544i	−0.457183	−	0.889373i	$-0.651141\pi$
$919$	2.55996	−	1.47799i	0.0844452	−	0.0487544i	0.541628	+	0.840618i	$0.317808\pi$
$920$	13.5808	+	7.45854i	0.447747	+	0.245901i
$921$	−4.37179	+	7.57217i	−0.144056	+	0.249512i
$922$	−24.6120	−	8.51830i	−0.810554	−	0.280535i
$923$	8.69497	−	13.5296i	0.286199	−	0.445334i
$924$	−6.25735	+	4.45911i	−0.205852	+	0.146694i
$925$	−3.60344	−	1.64564i	−0.118480	−	0.0541082i
$926$	12.2707	−	9.64977i	0.403239	−	0.317111i
$927$	3.55891	−	3.39342i	0.116890	−	0.111454i
$928$	0.0799910	+	1.67922i	0.00262583	+	0.0551231i
$929$	21.9891	+	15.6583i	0.721438	+	0.513734i	0.880801	−	0.473486i	$-0.157005\pi$
$929$	21.9891	+	15.6583i	0.721438	+	0.513734i	−0.159363	+	0.987220i	$0.550944\pi$
$930$	−2.31318	+	0.679212i	−0.0758523	+	0.0222722i
$931$	−1.70723	+	7.05865i	−0.0559523	+	0.231338i
$932$	11.4688	−	13.2356i	0.375671	−	0.433548i
$933$	0.652690	+	0.622339i	0.0213681	+	0.0203745i
$934$	14.5111	+	1.38564i	0.474817	+	0.0453396i
$935$	47.6844	−	2.27149i	1.55945	−	0.0742857i
$936$	−2.36943	+	0.574819i	−0.0774474	+	0.0187885i
$937$	−2.32188	−	16.1490i	−0.0758526	−	0.527566i	−0.991952	−	0.126615i	$-0.959589\pi$
$937$	−2.32188	−	16.1490i	−0.0758526	−	0.527566i	0.916099	−	0.400951i	$-0.131320\pi$
$938$	−10.5052	−	30.3187i	−0.343006	−	0.989942i
$939$	−12.3465	−	1.77515i	−0.402911	−	0.0579299i
$940$	−22.0408	−	1.04993i	−0.718891	−	0.0342450i
$941$	−29.1924	+	5.62638i	−0.951646	+	0.183415i	−0.641370	−	0.767232i	$-0.721634\pi$
$941$	−29.1924	+	5.62638i	−0.951646	+	0.183415i	−0.310276	+	0.950646i	$0.600421\pi$
$942$	12.2141	+	7.05183i	0.397958	+	0.229761i
$943$	−0.496900	+	18.9418i	−0.0161813	+	0.616829i
$944$			1.01721i			0.0331074i
$945$	3.55357	+	7.77410i	0.115598	+	0.252892i
$946$	−10.9098	−	7.01132i	−0.354709	−	0.227958i
$947$	−28.0689	+	11.2371i	−0.912116	+	0.365156i	−0.779784	−	0.626049i	$-0.784671\pi$
$947$	−28.0689	+	11.2371i	−0.912116	+	0.365156i	−0.132333	+	0.991205i	$0.542247\pi$
$948$	−6.88420	−	9.66751i	−0.223589	−	0.313986i
$949$	−26.4922	−	10.6059i	−0.859973	−	0.344281i
$950$	−1.33002	−	5.48243i	−0.0431516	−	0.177873i
$951$	−3.75548	−	5.84364i	−0.121780	−	0.189493i
$952$	8.32507	+	10.5786i	0.269817	+	0.342856i
$953$	−11.0833	−	37.7462i	−0.359022	−	1.22272i	−0.919016	−	0.394221i	$-0.871014\pi$
$953$	−11.0833	−	37.7462i	−0.359022	−	1.22272i	0.559993	−	0.828497i	$-0.310804\pi$
$954$	−0.176310	+	0.914785i	−0.00570826	+	0.0296172i
$955$	36.2101	−	12.5324i	1.17173	−	0.405540i
$956$	−1.12324	+	4.63007i	−0.0363283	+	0.149747i
$957$	−2.83196	+	3.97693i	−0.0915443	+	0.128556i
$958$	−13.3984	+	8.61062i	−0.432882	+	0.278196i
$959$	0.974308	−	20.6033i	0.0314620	−	0.665317i
$960$	3.19787	−	0.459785i	0.103211	−	0.0148395i
$961$	−30.3053	+	2.89381i	−0.977591	+	0.0933486i
$962$	1.39619	+	1.09797i	0.0450149	+	0.0354001i
$963$	−4.80676	−	9.32381i	−0.154896	−	0.300456i
$964$	8.72158	−	25.1993i	0.280903	−	0.811616i
$965$	−35.4565			−1.14139
$966$	−6.62653	+	10.8208i	−0.213205	+	0.348153i
$967$	−57.1465			−1.83771			−0.918854	−	0.394598i	$-0.870884\pi$
$967$	−57.1465			−1.83771			−0.918854	+	0.394598i	$0.870884\pi$
$968$	0.839253	−	2.42486i	0.0269746	−	0.0779380i
$969$	−2.41878	−	4.69178i	−0.0777024	−	0.150722i
$970$	−18.1848	−	14.3007i	−0.583878	−	0.459167i
$971$	−44.1252	+	4.21345i	−1.41605	+	0.135216i	−0.774842	−	0.632154i	$-0.782171\pi$
$971$	−44.1252	+	4.21345i	−1.41605	+	0.135216i	−0.641204	+	0.767371i	$0.721565\pi$
$972$	0.989821	−	0.142315i	0.0317485	−	0.00456475i
$973$	−21.7651	+	11.2302i	−0.697758	+	0.360025i
$974$	10.1932	−	6.55075i	0.326610	−	0.209900i
$975$	−7.69051	+	10.7998i	−0.246294	+	0.345871i
$976$	3.34702	−	13.7966i	0.107135	−	0.441618i
$977$	15.0351	−	5.20371i	0.481017	−	0.166481i	−0.0757897	−	0.997124i	$-0.524148\pi$
$977$	15.0351	−	5.20371i	0.481017	−	0.166481i	0.556806	+	0.830642i	$0.312027\pi$
$978$	2.15253	−	11.1684i	0.0688304	−	0.357126i
$979$	−4.67541	−	15.9230i	−0.149427	−	0.508900i
$980$	−20.9895	+	8.41979i	−0.670485	+	0.268960i
$981$	6.80807	+	10.5936i	0.217365	+	0.338226i
$982$	−10.0817	−	41.5572i	−0.321719	−	1.32614i
$983$	24.8894	+	9.96423i	0.793850	+	0.317810i	0.732905	−	0.680332i	$-0.238164\pi$
$983$	24.8894	+	9.96423i	0.793850	+	0.317810i	0.0609455	+	0.998141i	$0.480588\pi$
$984$	2.29180	+	3.21838i	0.0730599	+	0.102598i
$985$	68.6609	−	27.4877i	2.18772	−	0.875830i
$986$	7.19572	+	4.62441i	0.229158	+	0.147271i
$987$	1.71146	−	17.9890i	0.0544763	−	0.572597i
$988$			2.52948i			0.0804735i
$989$	−21.1108	−	3.60266i	−0.671283	−	0.114558i
$990$	8.12553	+	4.69128i	0.258246	+	0.149099i
$991$	−2.74663	+	0.529370i	−0.0872497	+	0.0168160i	−0.232689	−	0.972551i	$-0.574753\pi$
$991$	−2.74663	+	0.529370i	−0.0872497	+	0.0168160i	0.145440	+	0.989367i	$0.453540\pi$
$992$	−0.745370	−	0.0355064i	−0.0236655	−	0.00112733i
$993$	−12.7043	−	1.82660i	−0.403158	−	0.0579654i
$994$	−13.1933	−	11.4241i	−0.418467	−	0.362350i
$995$	−8.97382	−	62.4143i	−0.284489	−	1.97867i
$996$	3.06331	−	0.743151i	0.0970647	−	0.0235477i
$997$	−22.7170	+	1.08214i	−0.719453	+	0.0342718i	−0.404116	−	0.914708i	$-0.632421\pi$
$997$	−22.7170	+	1.08214i	−0.719453	+	0.0342718i	−0.315337	+	0.948980i	$0.602118\pi$
$998$	12.9399	+	1.23561i	0.409604	+	0.0391125i
$999$	−0.527240	−	0.502722i	−0.0166811	−	0.0159054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.493.1	yes	320
7.5	odd	6	inner	966.2.be.a.355.1	yes	320
23.7	odd	22	inner	966.2.be.a.283.1	yes	320
161.145	even	66	inner	966.2.be.a.145.1	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.145.1	✓	320	161.145	even	66	inner
966.2.be.a.283.1	yes	320	23.7	odd	22	inner
966.2.be.a.355.1	yes	320	7.5	odd	6	inner
966.2.be.a.493.1	yes	320	1.1	even	1	trivial

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.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-3.21613 + 0.307103i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-1.21317 - 2.35122i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(-0.458227 - 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-3.21613 + 0.307103i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-1.21317 - 2.35122i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(-0.761680 + 3.13969i) q^{10} +(-2.74441 + 0.949850i) q^{11} +(-0.189251 + 0.981929i) q^{12} +(-0.686910 - 2.33940i) q^{13} +(-2.61869 + 0.377436i) q^{14} +(1.74668 + 2.71789i) q^{15} +(0.235759 + 0.971812i) q^{16} +(4.72354 + 1.89102i) q^{17} +(0.580057 + 0.814576i) q^{18} +(0.963139 - 0.385583i) q^{19} +(2.71789 + 1.74668i) q^{20} +(-1.53394 + 2.15570i) q^{21} +2.90414i q^{22} +(1.87717 + 4.41319i) q^{23} +(0.866025 + 0.500000i) q^{24} +(5.33952 - 1.02911i) q^{25} +(-2.43540 - 0.116012i) q^{26} +(0.989821 + 0.142315i) q^{27} +(-0.499812 + 2.59811i) q^{28} +(0.239249 + 1.66401i) q^{29} +(3.13969 - 0.761680i) q^{30} +(-0.745370 + 0.0355064i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(2.10182 + 2.00408i) q^{33} +(3.33194 - 3.84526i) q^{34} +(4.62377 + 7.18925i) q^{35} +(0.959493 - 0.281733i) q^{36} +(-0.593418 - 0.422571i) q^{37} +(-0.0493640 - 1.03628i) q^{38} +(-1.76458 + 1.68252i) q^{39} +(2.53955 - 1.99712i) q^{40} +(3.59395 + 1.64130i) q^{41} +(1.53543 + 2.15463i) q^{42} +(-2.41425 + 3.75665i) q^{43} +(2.74441 + 0.949850i) q^{44} +(1.61538 - 2.79792i) q^{45} +(4.78443 - 0.330520i) q^{46} +(-5.91488 + 3.41495i) q^{47} +(0.755750 - 0.654861i) q^{48} +(-4.05645 + 5.70484i) q^{49} +(0.773878 - 5.38244i) q^{50} +(-0.483646 - 5.06497i) q^{51} +(-0.906174 + 2.26351i) q^{52} +(0.642892 + 0.674245i) q^{53} +(0.458227 - 0.888835i) q^{54} +(8.53468 - 3.89766i) q^{55} +(2.29175 + 1.32208i) q^{56} +(-0.784055 - 0.679388i) q^{57} +(1.65074 + 0.318155i) q^{58} +(0.988538 + 0.239817i) q^{59} +(0.307103 - 3.21613i) q^{60} +(-12.6186 - 6.50534i) q^{61} +(-0.210233 + 0.715988i) q^{62} +(2.61895 + 0.375623i) q^{63} +(0.415415 - 0.909632i) q^{64} +(2.92763 + 7.31286i) q^{65} +(2.58130 - 1.33075i) q^{66} +(2.29520 + 11.9086i) q^{67} +(-2.54400 - 4.40634i) q^{68} +(3.06243 - 3.69074i) q^{69} +(8.30613 - 2.01809i) q^{70} +(4.31962 + 4.98511i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(7.23495 - 9.19998i) q^{73} +(-0.593418 + 0.422571i) q^{74} +(-3.36142 - 4.27439i) q^{75} +(-0.995429 - 0.292284i) q^{76} +(5.56274 + 5.30038i) q^{77} +(1.01285 + 2.21783i) q^{78} +(-8.18996 + 8.58939i) q^{79} +(-1.05668 - 3.05307i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(2.72650 - 2.85947i) q^{82} +(-1.30946 - 2.86731i) q^{83} +(2.53832 - 0.746273i) q^{84} +(-15.7722 - 4.63115i) q^{85} +(2.76041 + 3.51015i) q^{86} +(1.36940 - 0.975147i) q^{87} +(1.79522 - 2.28281i) q^{88} +(-0.271899 + 5.70786i) q^{89} +(-2.11570 - 2.44164i) q^{90} +(-4.66710 + 4.45316i) q^{91} +(1.25249 - 4.62939i) q^{92} +(0.373108 + 0.646241i) q^{93} +(1.29257 + 6.70648i) q^{94} +(-2.97916 + 1.53587i) q^{95} +(-0.371662 - 0.928368i) q^{96} +(-2.97464 + 6.51355i) q^{97} +(4.06435 + 5.69922i) q^{98} +(0.818190 - 2.78650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

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