LMFDB - Embedded newform 280.2.br.a.107.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(67,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 3, 8]))

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

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

chi := DirichletCharacter("280.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.br (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	280.107
Dual form			280.2.br.a.123.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38577 + 0.282211i) q^{2} +(2.74353 + 0.735128i) q^{3} +(1.84071 - 0.782158i) q^{4} +(1.86498 - 1.23363i) q^{5} +(-4.00937 - 0.244463i) q^{6} +(-0.517846 + 2.59458i) q^{7} +(-2.33007 + 1.60336i) q^{8} +(4.38849 + 2.53369i) q^{9} +O(q^{10})$	\(q+(-1.38577 + 0.282211i) q^{2} +(2.74353 + 0.735128i) q^{3} +(1.84071 - 0.782158i) q^{4} +(1.86498 - 1.23363i) q^{5} +(-4.00937 - 0.244463i) q^{6} +(-0.517846 + 2.59458i) q^{7} +(-2.33007 + 1.60336i) q^{8} +(4.38849 + 2.53369i) q^{9} +(-2.23629 + 2.23585i) q^{10} +(1.41212 + 2.44587i) q^{11} +(5.62505 - 0.792716i) q^{12} +(-4.50461 - 4.50461i) q^{13} +(-0.0146028 - 3.74163i) q^{14} +(6.02351 - 2.01351i) q^{15} +(2.77646 - 2.87946i) q^{16} +(0.0288924 - 0.107828i) q^{17} +(-6.79647 - 2.27264i) q^{18} +(-3.58952 - 2.07241i) q^{19} +(2.46800 - 3.72947i) q^{20} +(-3.32807 + 6.73763i) q^{21} +(-2.64712 - 2.99089i) q^{22} +(-4.50099 + 1.20604i) q^{23} +(-7.57131 + 2.68597i) q^{24} +(1.95630 - 4.60140i) q^{25} +(7.51359 + 4.97110i) q^{26} +(4.15215 + 4.15215i) q^{27} +(1.07616 + 5.18091i) q^{28} +5.85829 q^{29} +(-7.77896 + 4.49017i) q^{30} +(2.21278 - 1.27755i) q^{31} +(-3.03492 + 4.77381i) q^{32} +(2.07618 + 7.74840i) q^{33} +(-0.00960804 + 0.157579i) q^{34} +(2.23498 + 5.47767i) q^{35} +(10.0597 + 1.23132i) q^{36} +(-0.282780 - 1.05535i) q^{37} +(5.55911 + 1.85888i) q^{38} +(-9.04708 - 15.6700i) q^{39} +(-2.36758 + 5.86469i) q^{40} -5.98706 q^{41} +(2.71051 - 10.2760i) q^{42} +(3.01075 - 3.01075i) q^{43} +(4.51236 + 3.39764i) q^{44} +(11.3101 - 0.688491i) q^{45} +(5.89697 - 2.94151i) q^{46} +(2.16967 + 8.09731i) q^{47} +(9.73408 - 5.85884i) q^{48} +(-6.46367 - 2.68718i) q^{49} +(-1.41242 + 6.92857i) q^{50} +(0.158535 - 0.274590i) q^{51} +(-11.8150 - 4.76838i) q^{52} +(-1.53592 + 5.73213i) q^{53} +(-6.92571 - 4.58215i) q^{54} +(5.65088 + 2.81945i) q^{55} +(-2.95342 - 6.87585i) q^{56} +(-8.32449 - 8.32449i) q^{57} +(-8.11824 + 1.65327i) q^{58} +(4.70005 - 2.71358i) q^{59} +(9.51268 - 8.41764i) q^{60} +(0.201399 + 0.116278i) q^{61} +(-2.70586 + 2.39486i) q^{62} +(-8.84643 + 10.0742i) q^{63} +(2.85848 - 7.47189i) q^{64} +(-13.9580 - 2.84397i) q^{65} +(-5.06379 - 10.1516i) q^{66} +(-0.423542 + 1.58068i) q^{67} +(-0.0311558 - 0.221079i) q^{68} -13.2352 q^{69} +(-4.64303 - 6.96005i) q^{70} -0.772704i q^{71} +(-14.2879 + 1.13263i) q^{72} +(-12.4038 - 3.32360i) q^{73} +(0.689698 + 1.38267i) q^{74} +(8.74979 - 11.1860i) q^{75} +(-8.22824 - 1.00714i) q^{76} +(-7.07725 + 2.39728i) q^{77} +(16.9594 + 19.1618i) q^{78} +(5.36423 - 9.29113i) q^{79} +(1.62585 - 8.79526i) q^{80} +(0.738128 + 1.27847i) q^{81} +(8.29668 - 1.68961i) q^{82} +(2.37696 - 2.37696i) q^{83} +(-0.856142 + 15.0051i) q^{84} +(-0.0791364 - 0.236740i) q^{85} +(-3.32254 + 5.02187i) q^{86} +(16.0724 + 4.30659i) q^{87} +(-7.21195 - 3.43491i) q^{88} +(-7.48263 - 4.32010i) q^{89} +(-15.4789 + 4.14592i) q^{90} +(14.0202 - 9.35486i) q^{91} +(-7.34172 + 5.74045i) q^{92} +(7.01000 - 1.87832i) q^{93} +(-5.29181 - 10.6087i) q^{94} +(-9.25098 + 0.563145i) q^{95} +(-11.8358 + 10.8661i) q^{96} +(3.14144 + 3.14144i) q^{97} +(9.71551 + 1.89970i) q^{98} +14.3115i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.38577	+	0.282211i	−0.979887	+	0.199553i
$2$	−1.38577	+	0.282211i	−0.979887	+	0.199553i
$3$	2.74353	+	0.735128i	1.58398	+	0.424426i	0.940155	−	0.340747i	$-0.110680\pi$
$3$	2.74353	+	0.735128i	1.58398	+	0.424426i	0.643825	+	0.765173i	$0.277347\pi$
$4$	1.84071	−	0.782158i	0.920357	−	0.391079i
$5$	1.86498	−	1.23363i	0.834044	−	0.551697i
$5$	1.86498	−	1.23363i	0.834044	−	0.551697i
$6$	−4.00937	−	0.244463i	−1.63682	−	0.0998016i
$7$	−0.517846	+	2.59458i	−0.195727	+	0.980658i
$7$	−0.517846	+	2.59458i	−0.195727	+	0.980658i
$8$	−2.33007	+	1.60336i	−0.823805	+	0.566873i
$9$	4.38849	+	2.53369i	1.46283	+	0.844565i
$10$	−2.23629	+	2.23585i	−0.707176	+	0.707037i
$11$	1.41212	+	2.44587i	0.425771	+	0.737456i	0.996492	−	0.0836875i	$-0.0266697\pi$
$11$	1.41212	+	2.44587i	0.425771	+	0.737456i	−0.570721	+	0.821144i	$0.693336\pi$
$12$	5.62505	−	0.792716i	1.62381	−	0.228837i
$13$	−4.50461	−	4.50461i	−1.24935	−	1.24935i	−0.956006	−	0.293347i	$-0.905231\pi$
$13$	−4.50461	−	4.50461i	−1.24935	−	1.24935i	−0.293347	−	0.956006i	$-0.594769\pi$
$14$	−0.0146028	−	3.74163i	−0.00390275	−	0.999992i
$15$	6.02351	−	2.01351i	1.55526	−	0.519887i
$16$	2.77646	−	2.87946i	0.694115	−	0.719865i
$17$	0.0288924	−	0.107828i	0.00700745	−	0.0261521i	−0.962334	−	0.271871i	$-0.912357\pi$
$17$	0.0288924	−	0.107828i	0.00700745	−	0.0261521i	0.969341	+	0.245719i	$0.0790241\pi$
$18$	−6.79647	−	2.27264i	−1.60194	−	0.535666i
$19$	−3.58952	−	2.07241i	−0.823493	−	0.475444i	0.0281267	−	0.999604i	$-0.491046\pi$
$19$	−3.58952	−	2.07241i	−0.823493	−	0.475444i	−0.851619	+	0.524161i	$0.824379\pi$
$20$	2.46800	−	3.72947i	0.551862	−	0.833936i
$21$	−3.32807	+	6.73763i	−0.726245	+	1.47027i
$22$	−2.64712	−	2.99089i	−0.564369	−	0.637660i
$23$	−4.50099	+	1.20604i	−0.938521	+	0.251476i	−0.695484	−	0.718541i	$-0.744810\pi$
$23$	−4.50099	+	1.20604i	−0.938521	+	0.251476i	−0.243036	+	0.970017i	$0.578143\pi$
$24$	−7.57131	+	2.68597i	−1.54549	+	0.548271i
$25$	1.95630	−	4.60140i	0.391260	−	0.920280i
$26$	7.51359	+	4.97110i	1.47354	+	0.974913i
$27$	4.15215	+	4.15215i	0.799082	+	0.799082i
$28$	1.07616	+	5.18091i	0.203376	+	0.979101i
$29$	5.85829			1.08786			0.543928	−	0.839132i	$-0.316936\pi$
$29$	5.85829			1.08786			0.543928	+	0.839132i	$0.316936\pi$
$30$	−7.77896	+	4.49017i	−1.42024	+	0.819788i
$31$	2.21278	−	1.27755i	0.397427	−	0.229455i	−0.287946	−	0.957647i	$-0.592972\pi$
$31$	2.21278	−	1.27755i	0.397427	−	0.229455i	0.685373	+	0.728192i	$0.259639\pi$
$32$	−3.03492	+	4.77381i	−0.536503	+	0.843899i
$33$	2.07618	+	7.74840i	0.361416	+	1.34882i
$34$	−0.00960804	+	0.157579i	−0.00164777	+	0.0270245i
$35$	2.23498	+	5.47767i	0.377781	+	0.925895i
$36$	10.0597	+	1.23132i	1.67662	+	0.205220i
$37$	−0.282780	−	1.05535i	−0.0464887	−	0.173498i	0.938778	−	0.344522i	$-0.111959\pi$
$37$	−0.282780	−	1.05535i	−0.0464887	−	0.173498i	−0.985267	+	0.171024i	$0.945292\pi$
$38$	5.55911	+	1.85888i	0.901806	+	0.301551i
$39$	−9.04708	−	15.6700i	−1.44869	−	2.50921i
$40$	−2.36758	+	5.86469i	−0.374348	+	0.927288i
$41$	−5.98706			−0.935022			−0.467511	−	0.883987i	$-0.654849\pi$
$41$	−5.98706			−0.935022			−0.467511	+	0.883987i	$0.654849\pi$
$42$	2.71051	−	10.2760i	0.418241	−	1.58562i
$43$	3.01075	−	3.01075i	0.459135	−	0.459135i	−0.439237	−	0.898371i	$-0.644751\pi$
$43$	3.01075	−	3.01075i	0.459135	−	0.459135i	0.898371	+	0.439237i	$0.144751\pi$
$44$	4.51236	+	3.39764i	0.680265	+	0.512213i
$45$	11.3101	−	0.688491i	1.68601	−	0.102634i
$46$	5.89697	−	2.94151i	0.869461	−	0.433703i
$47$	2.16967	+	8.09731i	0.316479	+	1.18111i	0.922605	+	0.385746i	$0.126056\pi$
$47$	2.16967	+	8.09731i	0.316479	+	1.18111i	−0.606127	+	0.795368i	$0.707278\pi$
$48$	9.73408	−	5.85884i	1.40499	−	0.845650i
$49$	−6.46367	−	2.68718i	−0.923382	−	0.383883i
$50$	−1.41242	+	6.92857i	−0.199746	+	0.979848i
$51$	0.158535	−	0.274590i	0.0221993	−	0.0384503i
$52$	−11.8150	−	4.76838i	−1.63845	−	0.661255i
$53$	−1.53592	+	5.73213i	−0.210975	+	0.787368i	0.776570	+	0.630031i	$0.216958\pi$
$53$	−1.53592	+	5.73213i	−0.210975	+	0.787368i	−0.987545	+	0.157338i	$0.949709\pi$
$54$	−6.92571	−	4.58215i	−0.942470	−	0.623551i
$55$	5.65088	+	2.81945i	0.761964	+	0.380175i
$56$	−2.95342	−	6.87585i	−0.394668	−	0.918824i
$57$	−8.32449	−	8.32449i	−1.10261	−	1.10261i
$58$	−8.11824	+	1.65327i	−1.06598	+	0.217085i
$59$	4.70005	−	2.71358i	0.611895	−	0.353278i	−0.161812	−	0.986822i	$-0.551734\pi$
$59$	4.70005	−	2.71358i	0.611895	−	0.353278i	0.773707	+	0.633544i	$0.218400\pi$
$60$	9.51268	−	8.41764i	1.22808	−	1.08671i
$61$	0.201399	+	0.116278i	0.0257865	+	0.0148879i	0.512838	−	0.858485i	$-0.328594\pi$
$61$	0.201399	+	0.116278i	0.0257865	+	0.0148879i	−0.487051	+	0.873373i	$0.661928\pi$
$62$	−2.70586	+	2.39486i	−0.343645	+	0.304147i
$63$	−8.84643	+	10.0742i	−1.11454	+	1.26923i
$64$	2.85848	−	7.47189i	0.357310	−	0.933986i
$65$	−13.9580	−	2.84397i	−1.73128	−	0.352751i
$66$	−5.06379	−	10.1516i	−0.623309	−	1.24957i
$67$	−0.423542	+	1.58068i	−0.0517439	+	0.193111i	−0.986960	−	0.160967i	$-0.948539\pi$
$67$	−0.423542	+	1.58068i	−0.0517439	+	0.193111i	0.935216	+	0.354078i	$0.115205\pi$
$68$	−0.0311558	−	0.221079i	−0.00377820	−	0.0268098i
$69$	−13.2352			−1.59333
$70$	−4.64303	−	6.96005i	−0.554948	−	0.831885i
$71$		−	0.772704i		−	0.0917030i	−0.998948	−	0.0458515i	$-0.985400\pi$
$71$		−	0.772704i		−	0.0917030i	0.998948	−	0.0458515i	$-0.0146001\pi$
$72$	−14.2879	+	1.13263i	−1.68385	+	0.133482i
$73$	−12.4038	−	3.32360i	−1.45176	−	0.388998i	−0.555125	−	0.831767i	$-0.687329\pi$
$73$	−12.4038	−	3.32360i	−1.45176	−	0.388998i	−0.896636	+	0.442769i	$0.853996\pi$
$74$	0.689698	+	1.38267i	0.0801758	+	0.160732i
$75$	8.74979	−	11.1860i	1.01034	−	1.29164i
$76$	−8.22824	−	1.00714i	−0.943843	−	0.115527i
$77$	−7.07725	+	2.39728i	−0.806528	+	0.273195i
$78$	16.9594	+	19.1618i	1.92027	+	2.16965i
$79$	5.36423	−	9.29113i	0.603524	−	1.04533i	−0.388759	−	0.921339i	$-0.627096\pi$
$79$	5.36423	−	9.29113i	0.603524	−	1.04533i	0.992283	−	0.123994i	$-0.0395704\pi$
$80$	1.62585	−	8.79526i	0.181775	−	0.983340i
$81$	0.738128	+	1.27847i	0.0820142	+	0.142053i
$82$	8.29668	−	1.68961i	0.916215	−	0.186586i
$83$	2.37696	−	2.37696i	0.260906	−	0.260906i	−0.564516	−	0.825422i	$-0.690937\pi$
$83$	2.37696	−	2.37696i	0.260906	−	0.260906i	0.825422	+	0.564516i	$0.190937\pi$
$84$	−0.856142	+	15.0051i	−0.0934128	+	1.63719i
$85$	−0.0791364	−	0.236740i	−0.00858355	−	0.0256780i
$86$	−3.32254	+	5.02187i	−0.358278	+	0.541522i
$87$	16.0724	+	4.30659i	1.72314	+	0.461715i
$88$	−7.21195	−	3.43491i	−0.768796	−	0.366162i
$89$	−7.48263	−	4.32010i	−0.793157	−	0.457929i	0.0479159	−	0.998851i	$-0.484742\pi$
$89$	−7.48263	−	4.32010i	−0.793157	−	0.457929i	−0.841073	+	0.540922i	$0.818075\pi$
$90$	−15.4789	+	4.14592i	−1.63162	+	0.437018i
$91$	14.0202	−	9.35486i	1.46972	−	0.980656i
$92$	−7.34172	+	5.74045i	−0.765427	+	0.598483i
$93$	7.01000	−	1.87832i	0.726903	−	0.194773i
$94$	−5.29181	−	10.6087i	−0.545808	−	1.09420i
$95$	−9.25098	+	0.563145i	−0.949131	+	0.0577775i
$96$	−11.8358	+	10.8661i	−1.20798	+	1.10901i
$97$	3.14144	+	3.14144i	0.318965	+	0.318965i	0.848370	−	0.529405i	$-0.177585\pi$
$97$	3.14144	+	3.14144i	0.318965	+	0.318965i	−0.529405	+	0.848370i	$0.677585\pi$
$98$	9.71551	+	1.89970i	0.981415	+	0.191899i
$99$			14.3115i			1.43836i
$100$	0.00197061	−	10.0000i	0.000197061	−	1.00000i
$101$	3.65439	−	2.10987i	0.363626	−	0.209939i	−0.307044	−	0.951695i	$-0.599340\pi$
$101$	3.65439	−	2.10987i	0.363626	−	0.209939i	0.670670	+	0.741756i	$0.266007\pi$
$102$	−0.142200	+	0.425259i	−0.0140799	+	0.0421069i
$103$	−9.54265	+	2.55695i	−0.940266	+	0.251943i	−0.696227	−	0.717822i	$-0.745139\pi$
$103$	−9.54265	+	2.55695i	−0.940266	+	0.251943i	−0.244039	+	0.969765i	$0.578472\pi$
$104$	17.7186	+	3.27356i	1.73745	+	0.320999i
$105$	2.10497	+	16.6712i	0.205424	+	1.62694i
$106$	0.510762	−	8.37686i	0.0496096	−	0.813633i
$107$	7.67972	−	2.05777i	0.742427	−	0.198933i	0.132270	−	0.991214i	$-0.457773\pi$
$107$	7.67972	−	2.05777i	0.742427	−	0.198933i	0.610156	+	0.792281i	$0.291107\pi$
$108$	10.8906	+	4.39529i	1.04795	+	0.422937i
$109$	6.56913	+	11.3781i	0.629208	+	1.08982i	0.987711	+	0.156292i	$0.0499540\pi$
$109$	6.56913	+	11.3781i	0.629208	+	1.08982i	−0.358503	+	0.933529i	$0.616713\pi$
$110$	−8.62649	−	2.31237i	−0.822504	−	0.220476i
$111$		−	3.10326i		−	0.294549i
$112$	6.03320	+	8.69485i	0.570084	+	0.821586i
$113$	5.64901	−	5.64901i	0.531414	−	0.531414i	−0.389579	−	0.920993i	$-0.627379\pi$
$113$	5.64901	−	5.64901i	0.531414	−	0.531414i	0.920993	+	0.389579i	$0.127379\pi$
$114$	13.8851	+	9.18656i	1.30046	+	0.860400i
$115$	−6.90645	+	7.80180i	−0.644029	+	0.727521i
$116$	10.7834	−	4.58210i	1.00122	−	0.425438i
$117$	−8.35511	−	31.1817i	−0.772430	−	2.88275i
$118$	−5.74739	+	5.08680i	−0.529090	+	0.468278i
$119$	0.264807	+	0.130802i	0.0242748	+	0.0119906i
$120$	−10.8068	+	14.3495i	−0.986524	+	1.30992i
$121$	1.51183	−	2.61856i	0.137439	−	0.238051i
$122$	−0.311908	−	0.104297i	−0.0282388	−	0.00944264i
$123$	−16.4257	−	4.40125i	−1.48106	−	0.396848i
$124$	3.07385	−	4.08235i	0.276040	−	0.366605i
$125$	−2.02797	−	10.9949i	−0.181388	−	0.983412i
$126$	9.41606	−	16.4571i	0.838849	−	1.46611i
$127$	−1.99713	+	1.99713i	−0.177217	+	0.177217i	−0.790141	−	0.612925i	$-0.789993\pi$
$127$	−1.99713	+	1.99713i	−0.177217	+	0.177217i	0.612925	+	0.790141i	$0.289993\pi$
$128$	−1.85254	+	11.1610i	−0.163743	+	0.986503i
$129$	10.4734	−	6.04680i	0.922129	−	0.532391i
$130$	20.1452	+	0.00198492i	1.76685	+	0.000174089i
$131$	−10.3779	+	17.9751i	−0.906723	+	1.57049i	−0.0881358	+	0.996108i	$0.528091\pi$
$131$	−10.3779	+	17.9751i	−0.906723	+	1.57049i	−0.818587	+	0.574382i	$0.805242\pi$
$132$	9.88213	+	12.6387i	0.860129	+	1.10006i
$133$	7.23585	−	8.24010i	0.627428	−	0.714508i
$134$	0.140847	−	2.30999i	0.0121673	−	0.199552i
$135$	12.8659	+	2.62145i	1.10732	+	0.225619i
$136$	0.105566	+	0.297572i	0.00905218	+	0.0255166i
$137$	−2.52954	+	9.44036i	−0.216113	+	0.806544i	0.769659	+	0.638455i	$0.220426\pi$
$137$	−2.52954	+	9.44036i	−0.216113	+	0.806544i	−0.985772	+	0.168089i	$0.946240\pi$
$138$	18.3409	−	3.73511i	1.56128	−	0.317954i
$139$			2.01917i			0.171264i	0.996327	+	0.0856321i	$0.0272910\pi$
$139$			2.01917i			0.171264i	−0.996327	+	0.0856321i	$0.972709\pi$
$140$	8.39837	+	8.33471i	0.709792	+	0.704412i
$141$			23.8102i			2.00518i
$142$	0.218065	+	1.07079i	0.0182996	+	0.0898586i
$143$	4.65661	−	17.3787i	0.389405	−	1.45328i
$144$	19.4801	−	5.60177i	1.62334	−	0.466814i
$145$	10.9256	−	7.22697i	0.907321	−	0.600168i
$146$	18.1268	+	1.10525i	1.50019	+	0.0914709i
$147$	−15.7579	−	12.1240i	−1.29969	−	0.999970i
$148$	−1.34597	−	1.72142i	−0.110638	−	0.141500i
$149$	−10.8817	+	18.8477i	−0.891464	+	1.54406i	−0.0533439	+	0.998576i	$0.516988\pi$
$149$	−10.8817	+	18.8477i	−0.891464	+	1.54406i	−0.838120	+	0.545485i	$0.816345\pi$
$150$	−8.96840	+	17.9705i	−0.732267	+	1.46728i
$151$	−12.9172	+	7.45773i	−1.05118	+	0.606901i	−0.922981	−	0.384847i	$-0.874254\pi$
$151$	−12.9172	+	7.45773i	−1.05118	+	0.606901i	−0.128203	+	0.991748i	$0.540921\pi$
$152$	11.6867	−	0.926425i	0.947914	−	0.0751430i
$153$	0.399997	−	0.399997i	0.0323379	−	0.0323379i
$154$	9.13090	−	5.31935i	0.735789	−	0.428645i
$155$	2.55076	−	5.11236i	0.204882	−	0.410635i
$156$	−28.9095	−	21.7677i	−2.31461	−	1.74281i
$157$	−12.3568	−	3.31101i	−0.986184	−	0.264247i	−0.270537	−	0.962710i	$-0.587201\pi$
$157$	−12.3568	−	3.31101i	−0.986184	−	0.264247i	−0.715647	+	0.698463i	$0.753868\pi$
$158$	−4.81154	+	14.3892i	−0.382785	+	1.14474i
$159$	−8.42769	+	14.5972i	−0.668359	+	1.15763i
$160$	0.229068	+	12.6470i	0.0181094	+	0.999836i
$161$	−0.798337	−	12.3027i	−0.0629178	−	0.969589i
$162$	−1.38367	−	1.56336i	−0.108712	−	0.122829i
$163$	3.85202	+	14.3759i	0.301714	+	1.12601i	0.935738	+	0.352697i	$0.114735\pi$
$163$	3.85202	+	14.3759i	0.301714	+	1.12601i	−0.634024	+	0.773313i	$0.718598\pi$
$164$	−11.0205	+	4.68282i	−0.860554	+	0.365667i
$165$	13.4307	+	11.8894i	1.04558	+	0.925587i
$166$	−2.62312	+	3.96473i	−0.203594	+	0.307723i
$167$	10.8781	−	10.8781i	0.841775	−	0.841775i	−0.147315	−	0.989090i	$-0.547063\pi$
$167$	10.8781	−	10.8781i	0.841775	−	0.841775i	0.989090	+	0.147315i	$0.0470630\pi$
$168$	−3.04819	−	21.0353i	−0.235173	−	1.62291i
$169$			27.5830i			2.12177i
$170$	0.176475	+	0.305734i	0.0135350	+	0.0234487i
$171$	−10.5017	−	18.1895i	−0.803086	−	1.39099i
$172$	3.18705	−	7.89681i	0.243010	−	0.602126i
$173$	16.0764	−	4.30766i	1.22227	−	0.327506i	0.410704	−	0.911769i	$-0.365283\pi$
$173$	16.0764	−	4.30766i	1.22227	−	0.327506i	0.811564	+	0.584263i	$0.198616\pi$
$174$	−23.4880	−	1.43213i	−1.78062	−	0.108570i
$175$	10.9256	+	7.45859i	0.825900	+	0.563817i
$176$	10.9635	+	2.72470i	0.826402	+	0.205382i
$177$	14.8896	−	3.98965i	1.11917	−	0.299880i
$178$	11.5884	+	3.87498i	0.868585	+	0.290442i
$179$	5.66778	−	3.27230i	0.423630	−	0.244583i	−0.272999	−	0.962014i	$-0.588016\pi$
$179$	5.66778	−	3.27230i	0.423630	−	0.244583i	0.696629	+	0.717431i	$0.254682\pi$
$180$	20.2801	−	10.1136i	1.51159	−	0.753822i
$181$			0.223222i			0.0165919i	0.999966	+	0.00829597i	$0.00264072\pi$
$181$			0.223222i			0.0165919i	−0.999966	+	0.00829597i	$0.997359\pi$
$182$	−16.7888	+	16.9203i	−1.24447	+	1.25422i
$183$	0.467067	+	0.467067i	0.0345266	+	0.0345266i
$184$	8.55392	−	10.0269i	0.630603	−	0.739189i
$185$	−1.82929	−	1.61936i	−0.134492	−	0.119058i
$186$	−9.18416	+	4.58122i	−0.673415	+	0.335911i
$187$	0.304533	−	0.0815993i	0.0222696	−	0.00596713i
$188$	10.3271	+	13.2078i	0.753182	+	0.963279i
$189$	−12.9233	+	8.62291i	−0.940029	+	0.627225i
$190$	12.6608	−	3.39111i	0.918511	−	0.246017i
$191$	14.3858	+	8.30567i	1.04092	+	0.600977i	0.920095	−	0.391696i	$-0.128112\pi$
$191$	14.3858	+	8.30567i	1.04092	+	0.600977i	0.120828	+	0.992673i	$0.461445\pi$
$192$	13.3351	−	18.3980i	0.962379	−	1.32776i
$193$	−3.04551	−	0.816042i	−0.219221	−	0.0587400i	0.147537	−	0.989057i	$-0.452865\pi$
$193$	−3.04551	−	0.816042i	−0.219221	−	0.0587400i	−0.366758	+	0.930317i	$0.619532\pi$
$194$	−5.23986	−	3.46676i	−0.376200	−	0.248899i
$195$	−36.2036	−	18.0635i	−2.59260	−	1.29355i
$196$	−13.9996	+	0.109276i	−0.999970	+	0.00780545i
$197$	6.07147	−	6.07147i	0.432575	−	0.432575i	−0.456929	−	0.889503i	$-0.651051\pi$
$197$	6.07147	−	6.07147i	0.432575	−	0.432575i	0.889503	+	0.456929i	$0.151051\pi$
$198$	−4.03887	−	19.8325i	−0.287030	−	1.40943i
$199$	−3.99326	−	6.91653i	−0.283075	−	0.490300i	0.689066	−	0.724699i	$-0.258021\pi$
$199$	−3.99326	−	6.91653i	−0.283075	−	0.490300i	−0.972140	+	0.234399i	$0.924688\pi$
$200$	2.81938	+	13.8583i	0.199360	+	0.979926i
$201$	−2.32400	+	4.02529i	−0.163923	+	0.283922i
$202$	−4.46872	+	3.95510i	−0.314418	+	0.278280i
$203$	−3.03369	+	15.1998i	−0.212923	+	1.06682i
$204$	0.0770443	−	0.629441i	0.00539418	−	0.0440697i
$205$	−11.1657	+	7.38583i	−0.779850	+	0.515849i
$206$	12.5023	−	6.23638i	0.871078	−	0.434509i
$207$	−22.8082	−	6.11145i	−1.58528	−	0.424775i
$208$	−25.4777	+	0.463973i	−1.76656	+	0.0321708i
$209$		−	11.7060i		−	0.809720i
$210$	−7.62178	−	22.5083i	−0.525953	−	1.55322i
$211$	−8.95907			−0.616767			−0.308384	−	0.951262i	$-0.599788\pi$
$211$	−8.95907			−0.616767			−0.308384	+	0.951262i	$0.599788\pi$
$212$	1.65624	+	11.7525i	0.113751	+	0.807168i
$213$	0.568036	−	2.11994i	0.0389212	−	0.145256i
$214$	−10.0616	+	5.01890i	−0.687797	+	0.343085i
$215$	1.90083	−	9.32914i	0.129635	−	0.636242i
$216$	−16.3322	−	3.01742i	−1.11127	−	0.205310i
$217$	2.16882	+	6.40280i	0.147229	+	0.434651i
$218$	−12.3143	−	13.9135i	−0.834030	−	0.942341i
$219$	−31.5871	−	18.2368i	−2.13446	−	1.23233i
$220$	12.6069	+	0.769928i	0.849958	+	0.0519085i
$221$	−0.615872	+	0.355574i	−0.0414280	+	0.0239185i
$222$	0.875774	+	4.30041i	0.0587781	+	0.288625i
$223$	−11.5085	−	11.5085i	−0.770669	−	0.770669i	0.207555	−	0.978223i	$-0.433450\pi$
$223$	−11.5085	−	11.5085i	−0.770669	−	0.770669i	−0.978223	+	0.207555i	$0.933450\pi$
$224$	−10.8144	−	10.3464i	−0.722568	−	0.691300i
$225$	20.2437	−	15.2365i	1.34958	−	1.01577i
$226$	−6.23402	+	9.42244i	−0.414681	+	0.626771i
$227$	−4.26615	+	15.9215i	−0.283154	+	1.05675i	0.667023	+	0.745037i	$0.267568\pi$
$227$	−4.26615	+	15.9215i	−0.283154	+	1.05675i	−0.950178	+	0.311709i	$0.899099\pi$
$228$	−21.8341	−	8.81194i	−1.44600	−	0.583585i
$229$	7.87641	−	13.6423i	0.520488	−	0.901511i	−0.479229	−	0.877690i	$-0.659084\pi$
$229$	7.87641	−	13.6423i	0.520488	−	0.901511i	0.999716	−	0.0238210i	$-0.00758317\pi$
$230$	7.36899	−	12.7606i	0.485897	−	0.841407i
$231$	−21.1790	+	1.37433i	−1.39347	+	0.0904243i
$232$	−13.6502	+	9.39294i	−0.896182	+	0.616677i
$233$	−1.23815	−	4.62083i	−0.0811138	−	0.302721i	0.913436	−	0.406982i	$-0.133419\pi$
$233$	−1.23815	−	4.62083i	−0.0811138	−	0.302721i	−0.994550	+	0.104261i	$0.966752\pi$
$234$	20.3781	+	40.8528i	1.33216	+	2.67063i
$235$	14.0355	+	12.4247i	0.915574	+	0.810501i
$236$	6.52901	−	8.67110i	0.425002	−	0.564441i
$237$	21.5471	−	21.5471i	1.39964	−	1.39964i
$238$	−0.403875	−	0.106530i	−0.0261793	−	0.00690533i
$239$	−0.799039			−0.0516855			−0.0258428	−	0.999666i	$-0.508227\pi$
$239$	−0.799039			−0.0516855			−0.0258428	+	0.999666i	$0.508227\pi$
$240$	10.9262	−	22.9349i	0.705283	−	1.48044i
$241$	13.2249	+	22.9061i	0.851888	+	1.47551i	0.879502	+	0.475894i	$0.157876\pi$
$241$	13.2249	+	22.9061i	0.851888	+	1.47551i	−0.0276146	+	0.999619i	$0.508791\pi$
$242$	−1.35606	+	4.05538i	−0.0871707	+	0.260690i
$243$	−3.47415	−	12.9657i	−0.222867	−	0.831749i
$244$	0.461666	+	0.0565084i	0.0295552	+	0.00361758i
$245$	−15.3696	+	2.96225i	−0.981929	+	0.189252i
$246$	24.0043	+	1.46361i	1.53046	+	0.0933167i
$247$	6.83399	+	25.5048i	0.434836	+	1.62283i
$248$	−3.10757	+	6.52466i	−0.197331	+	0.414317i
$249$	8.26865	−	4.77391i	0.524004	−	0.302534i
$250$	5.91318	+	14.6640i	0.373982	+	0.927436i
$251$	12.5433			0.791725			0.395862	−	0.918310i	$-0.370446\pi$
$251$	12.5433			0.791725			0.395862	+	0.918310i	$0.370446\pi$
$252$	−8.40412	+	25.4630i	−0.529410	+	1.60402i
$253$	−9.30574	−	9.30574i	−0.585047	−	0.585047i
$254$	2.20395	−	3.33117i	0.138288	−	0.209016i
$255$	−0.0430793	−	0.707679i	−0.00269773	−	0.0443166i
$256$	−0.582558	−	15.9894i	−0.0364099	−	0.999337i
$257$	0.371361	−	0.0995060i	0.0231649	−	0.00620701i	−0.247218	−	0.968960i	$-0.579516\pi$
$257$	0.371361	−	0.0995060i	0.0231649	−	0.00620701i	0.270383	+	0.962753i	$0.412850\pi$
$258$	−12.8072	+	11.3352i	−0.797342	+	0.705697i
$259$	2.88462	−	0.187187i	0.179242	−	0.0116312i
$260$	−27.9172	+	5.68244i	−1.73135	+	0.352410i
$261$	25.7090	+	14.8431i	1.59135	+	0.918765i
$262$	9.30865	−	27.8381i	0.575090	−	1.71984i
$263$	−0.651311	+	2.43073i	−0.0401615	+	0.149885i	−0.983095	−	0.183096i	$-0.941388\pi$
$263$	−0.651311	+	2.43073i	−0.0401615	+	0.149885i	0.942933	+	0.332981i	$0.108055\pi$
$264$	−17.2611	−	14.7255i	−1.06235	−	0.906291i
$265$	4.20688	+	12.5851i	0.258427	+	0.773094i
$266$	−7.70178	+	13.4609i	−0.472226	+	0.825342i
$267$	−17.3530	−	17.3530i	−1.06199	−	1.06199i
$268$	0.456722	+	3.24086i	0.0278987	+	0.197967i
$269$	−7.78768	−	13.4887i	−0.474823	−	0.822418i	0.524761	−	0.851250i	$-0.324155\pi$
$269$	−7.78768	−	13.4887i	−0.474823	−	0.822418i	−0.999584	+	0.0288315i	$0.990821\pi$
$270$	−18.5690	−	0.00182961i	−1.13007	−	0.000111347i
$271$	5.32459	+	3.07416i	0.323446	+	0.186742i	0.652928	−	0.757420i	$-0.273541\pi$
$271$	5.32459	+	3.07416i	0.323446	+	0.186742i	−0.329481	+	0.944162i	$0.606874\pi$
$272$	−0.230268	−	0.382575i	−0.0139620	−	0.0231970i
$273$	45.3420	−	15.3587i	2.74422	−	0.929551i
$274$	0.841185	−	13.7960i	0.0508178	−	0.833448i
$275$	14.0169	−	1.71288i	0.845253	−	0.103291i
$276$	−24.3622	+	10.3520i	−1.46643	+	0.623118i
$277$	24.6584	+	6.60720i	1.48158	+	0.396988i	0.906885	−	0.421379i	$-0.138454\pi$
$277$	24.6584	+	6.60720i	1.48158	+	0.396988i	0.574696	+	0.818367i	$0.305120\pi$
$278$	−0.569833	−	2.79811i	−0.0341763	−	0.167820i
$279$	12.9477			0.775157
$280$	−13.9903	−	9.17988i	−0.836083	−	0.548603i
$281$	7.48146			0.446306			0.223153	−	0.974783i	$-0.428365\pi$
$281$	7.48146			0.446306			0.223153	+	0.974783i	$0.428365\pi$
$282$	−6.71950	−	32.9955i	−0.400140	−	1.96485i
$283$	8.16739	+	2.18845i	0.485501	+	0.130090i	0.493263	−	0.869880i	$-0.335804\pi$
$283$	8.16739	+	2.18845i	0.485501	+	0.130090i	−0.00776182	+	0.999970i	$0.502471\pi$
$284$	−0.604376	−	1.42233i	−0.0358631	−	0.0843996i
$285$	−25.7944	−	5.25564i	−1.52793	−	0.311317i
$286$	−1.54853	+	25.3970i	−0.0915667	+	1.50176i
$287$	3.10037	−	15.5339i	0.183009	−	0.916937i
$288$	−25.4141	+	13.2603i	−1.49754	+	0.781368i
$289$	14.7116	+	8.49377i	0.865391	+	0.499633i
$290$	−13.1008	+	13.0982i	−0.769307	+	0.769155i
$291$	6.30929	+	10.9280i	0.369857	+	0.640611i
$292$	−25.4315	+	3.58397i	−1.48827	+	0.209736i
$293$	0.850178	+	0.850178i	0.0496679	+	0.0496679i	0.731505	−	0.681837i	$-0.238818\pi$
$293$	0.850178	+	0.850178i	0.0496679	+	0.0496679i	−0.681837	+	0.731505i	$0.738818\pi$
$294$	25.2583	+	12.3540i	1.47309	+	0.720501i
$295$	5.41795	−	10.8589i	0.315445	−	0.632230i
$296$	2.35100	+	2.00564i	0.136649	+	0.116576i
$297$	−4.29227	+	16.0190i	−0.249063	+	0.929514i
$298$	9.76053	−	29.1895i	0.565412	−	1.69090i
$299$	25.7079	+	14.8425i	1.48673	+	0.858362i
$300$	7.35668	−	27.4339i	0.424738	−	1.58390i
$301$	6.25252	+	9.37072i	0.360389	+	0.540120i
$302$	15.7956	−	13.9801i	0.908933	−	0.804462i
$303$	11.5770	−	3.10204i	0.665080	−	0.178208i
$304$	−15.9336	+	4.58191i	−0.913853	+	0.262791i
$305$	0.519050	−	0.0315967i	0.0297207	−	0.00180922i
$306$	−0.441421	+	0.667188i	−0.0252343	+	0.0381406i
$307$	13.7449	+	13.7449i	0.784465	+	0.784465i	0.980581	−	0.196116i	$-0.0628328\pi$
$307$	13.7449	+	13.7449i	0.784465	+	0.784465i	−0.196116	+	0.980581i	$0.562833\pi$
$308$	−11.1521	+	9.94823i	−0.635453	+	0.566853i
$309$	−28.0603			−1.59629
$310$	−2.09201	+	7.80441i	−0.118818	+	0.443260i
$311$	−13.6973	+	7.90812i	−0.776701	+	0.448429i	−0.835260	−	0.549855i	$-0.814683\pi$
$311$	−13.6973	+	7.90812i	−0.776701	+	0.448429i	0.0585588	+	0.998284i	$0.481349\pi$
$312$	46.2050	+	22.0065i	2.61584	+	1.24587i
$313$	0.886390	+	3.30805i	0.0501018	+	0.186982i	0.986442	−	0.164113i	$-0.0524761\pi$
$313$	0.886390	+	3.30805i	0.0501018	+	0.186982i	−0.936340	+	0.351095i	$0.885809\pi$
$314$	18.0581	+	1.10106i	1.01908	+	0.0621363i
$315$	−4.07054	+	29.7014i	−0.229349	+	1.67349i
$316$	2.60690	−	21.2980i	0.146649	−	1.19811i
$317$	−1.71990	−	6.41877i	−0.0965994	−	0.360514i	0.900658	−	0.434529i	$-0.143085\pi$
$317$	−1.71990	−	6.41877i	−0.0965994	−	0.360514i	−0.997257	+	0.0740154i	$0.976419\pi$
$318$	7.55935	−	22.6067i	0.423908	−	1.26772i
$319$	8.27261	+	14.3286i	0.463177	+	0.802247i
$320$	−3.88656	−	17.4612i	−0.217266	−	0.976113i
$321$	22.5823			1.26042
$322$	4.57827	+	16.8234i	0.255137	+	0.937532i
$323$	−0.327174	+	0.327174i	−0.0182045	+	0.0182045i
$324$	2.35865	+	1.77597i	0.131036	+	0.0986652i
$325$	−29.5399	+	11.9151i	−1.63858	+	0.660933i
$326$	−9.39505	−	18.8347i	−0.520344	−	1.04315i
$327$	9.65829	+	36.0452i	0.534105	+	1.99331i
$328$	13.9503	−	9.59941i	0.770275	−	0.530039i
$329$	−22.1327	+	1.43621i	−1.22021	+	0.0791811i
$330$	−21.9672	−	12.6856i	−1.20925	−	0.698322i
$331$	−0.873426	+	1.51282i	−0.0480078	+	0.0831520i	−0.889031	−	0.457847i	$-0.848621\pi$
$331$	−0.873426	+	1.51282i	−0.0480078	+	0.0831520i	0.841023	+	0.540999i	$0.181954\pi$
$332$	2.51615	−	6.23447i	0.138092	−	0.342161i
$333$	1.43296	−	5.34786i	0.0785255	−	0.293061i
$334$	−12.0047	+	18.1445i	−0.656866	+	0.992823i
$335$	1.16008	+	3.47043i	0.0633820	+	0.189610i
$336$	10.1605	+	28.2898i	0.554299	+	1.54333i
$337$	−3.13920	−	3.13920i	−0.171003	−	0.171003i	0.616417	−	0.787420i	$-0.288584\pi$
$337$	−3.13920	−	3.13920i	−0.171003	−	0.171003i	−0.787420	+	0.616417i	$0.788584\pi$
$338$	−7.78421	−	38.2236i	−0.423405	−	2.07909i
$339$	19.6510	−	11.3455i	1.06730	−	0.616203i
$340$	−0.330835	−	0.373873i	−0.0179421	−	0.0202761i
$341$	6.24943	+	3.60811i	0.338425	+	0.195390i
$342$	19.6862	+	22.2428i	1.06451	+	1.20275i
$343$	10.3193	−	15.3790i	0.557189	−	0.830386i
$344$	−2.18795	+	11.8426i	−0.117966	+	0.638509i
$345$	−24.6834	+	16.3274i	−1.32891	+	0.879036i
$346$	−21.0626	+	10.5064i	−1.13233	+	0.564826i
$347$	7.79397	−	29.0875i	0.418402	−	1.56150i	−0.359519	−	0.933138i	$-0.617059\pi$
$347$	7.79397	−	29.0875i	0.418402	−	1.56150i	0.777922	−	0.628361i	$-0.216274\pi$
$348$	32.9531	−	4.64396i	1.76647	−	0.248942i
$349$	35.2950			1.88930			0.944649	−	0.328084i	$-0.106403\pi$
$349$	35.2950			1.88930			0.944649	+	0.328084i	$0.106403\pi$
$350$	−17.2453	−	7.25256i	−0.921800	−	0.387666i
$351$		−	37.4076i		−	1.99667i
$352$	−15.9618	−	0.681801i	−0.850765	−	0.0363401i
$353$	−15.4975	−	4.15255i	−0.824851	−	0.221018i	−0.178385	−	0.983961i	$-0.557087\pi$
$353$	−15.4975	−	4.15255i	−0.824851	−	0.221018i	−0.646466	+	0.762943i	$0.723754\pi$
$354$	−19.5076	+	9.73073i	−1.03682	+	0.517183i
$355$	−0.953232	−	1.44108i	−0.0505923	−	0.0764844i
$356$	−17.1524	−	2.09947i	−0.909074	−	0.111272i
$357$	0.630349	+	0.553526i	0.0333616	+	0.0292957i
$358$	−6.93076	+	6.13416i	−0.366302	+	0.324200i
$359$	−15.0010	+	25.9825i	−0.791723	+	1.37130i	0.133176	+	0.991092i	$0.457482\pi$
$359$	−15.0010	+	25.9825i	−0.791723	+	1.37130i	−0.924899	+	0.380212i	$0.875851\pi$
$360$	−25.2494	+	19.7384i	−1.33076	+	1.04030i
$361$	−0.910223	−	1.57655i	−0.0479065	−	0.0829765i
$362$	−0.0629955	−	0.309334i	−0.00331097	−	0.0162582i
$363$	6.07273	−	6.07273i	0.318735	−	0.318735i
$364$	18.4903	−	28.1857i	0.969154	−	1.47733i
$365$	−27.2330	+	9.10334i	−1.42544	+	0.476491i
$366$	−0.779058	−	0.515436i	−0.0407220	−	0.0269422i
$367$	−11.7959	−	3.16071i	−0.615744	−	0.164988i	−0.0625515	−	0.998042i	$-0.519924\pi$
$367$	−11.7959	−	3.16071i	−0.615744	−	0.164988i	−0.553192	+	0.833054i	$0.686590\pi$
$368$	−9.02407	+	16.3089i	−0.470412	+	0.850161i
$369$	−26.2741	−	15.1694i	−1.36778	−	0.789686i
$370$	2.99198	+	1.72781i	0.155545	+	0.0898247i
$371$	−14.0771	−	6.95342i	−0.730846	−	0.361004i
$372$	11.4343	−	8.94038i	0.592838	−	0.463537i
$373$	18.0750	−	4.84319i	0.935891	−	0.250771i	0.241526	−	0.970394i	$-0.422352\pi$
$373$	18.0750	−	4.84319i	0.935891	−	0.250771i	0.694365	+	0.719623i	$0.255685\pi$
$374$	−0.398984	+	0.199020i	−0.0206310	+	0.0102911i
$375$	2.51882	−	31.6556i	0.130071	−	1.63469i
$376$	−18.0384	−	15.3886i	−0.930258	−	0.793604i
$377$	−26.3893	−	26.3893i	−1.35912	−	1.35912i
$378$	15.4752	−	15.5965i	0.795958	−	0.802195i
$379$			1.25847i			0.0646431i	0.999478	+	0.0323216i	$0.0102901\pi$
$379$			1.25847i			0.0646431i	−0.999478	+	0.0323216i	$0.989710\pi$
$380$	−16.5879	+	8.27232i	−0.850944	+	0.424361i
$381$	−6.94734	+	4.01105i	−0.355923	+	0.205492i
$382$	−22.2794	−	7.44991i	−1.13991	−	0.381170i
$383$	−0.106103	+	0.0284302i	−0.00542161	+	0.00145272i	−0.261529	−	0.965196i	$-0.584227\pi$
$383$	−0.106103	+	0.0284302i	−0.00542161	+	0.00145272i	0.256107	+	0.966648i	$0.417560\pi$
$384$	−13.2873	+	29.2587i	−0.678063	+	1.49310i
$385$	−10.2416	+	13.2016i	−0.521959	+	0.672816i
$386$	4.45067	+	0.271371i	0.226533	+	0.0138124i
$387$	20.8409	−	5.58431i	1.05940	−	0.283867i
$388$	8.23960	+	3.32539i	0.418302	+	0.168821i
$389$	5.32592	+	9.22476i	0.270035	+	0.467714i	0.968870	−	0.247568i	$-0.0796315\pi$
$389$	5.32592	+	9.22476i	0.270035	+	0.467714i	−0.698836	+	0.715282i	$0.746298\pi$
$390$	55.2676	+	14.8147i	2.79858	+	0.750174i
$391$			0.520178i			0.0263065i
$392$	19.3693	−	4.10226i	0.978300	−	0.207195i
$393$	−41.6862	+	41.6862i	−2.10279	+	2.10279i
$394$	−6.70023	+	10.1271i	−0.337553	+	0.510196i
$395$	−1.45765	−	23.9453i	−0.0733421	−	1.20482i
$396$	11.1939	+	26.3434i	0.562513	+	1.32381i
$397$	4.97993	+	18.5853i	0.249935	+	0.932771i	0.970838	+	0.239735i	$0.0770606\pi$
$397$	4.97993	+	18.5853i	0.249935	+	0.932771i	−0.720903	+	0.693036i	$0.756273\pi$
$398$	7.48566	+	8.45777i	0.375222	+	0.423950i
$399$	25.9093	−	17.2877i	1.29709	−	0.865469i
$400$	−7.81795	−	18.4087i	−0.390898	−	0.920434i
$401$	−3.22837	+	5.59170i	−0.161217	+	0.279236i	−0.935305	−	0.353841i	$-0.884875\pi$
$401$	−3.22837	+	5.59170i	−0.161217	+	0.279236i	0.774088	+	0.633078i	$0.218209\pi$
$402$	2.08455	−	6.23398i	0.103968	−	0.310923i
$403$	−15.7226	−	4.21285i	−0.783196	−	0.209857i
$404$	5.07645	−	6.74197i	0.252563	−	0.335426i
$405$	2.95376	+	1.47375i	0.146774	+	0.0732313i
$406$	−0.0855472	−	21.9195i	−0.00424564	−	1.08785i
$407$	2.18192	−	2.18192i	0.108154	−	0.108154i
$408$	0.0708694	+	0.894003i	0.00350856	+	0.0442598i
$409$	27.3763	−	15.8057i	1.35367	−	0.781541i	0.364908	−	0.931044i	$-0.381101\pi$
$409$	27.3763	−	15.8057i	1.35367	−	0.781541i	0.988761	+	0.149503i	$0.0477672\pi$
$410$	13.3888	−	13.3862i	0.661225	−	0.661095i
$411$	−13.8797	+	24.0404i	−0.684637	+	1.18583i
$412$	−15.5654	+	12.1705i	−0.766850	+	0.599596i
$413$	4.60669	+	13.5999i	0.226680	+	0.669206i
$414$	33.3317	+	2.03233i	1.63816	+	0.0998837i
$415$	1.50069	−	7.36529i	0.0736660	−	0.361548i
$416$	35.1753	−	7.83303i	1.72461	−	0.384046i
$417$	−1.48435	+	5.53967i	−0.0726890	+	0.271279i
$418$	3.30355	+	16.2218i	0.161582	+	0.793434i
$419$			18.7965i			0.918271i	0.888366	+	0.459136i	$0.151841\pi$
$419$			18.7965i			0.918271i	−0.888366	+	0.459136i	$0.848159\pi$
$420$	16.9141	+	29.0404i	0.825325	+	1.41703i
$421$		−	28.3453i		−	1.38147i	−0.723109	−	0.690733i	$-0.757288\pi$
$421$		−	28.3453i		−	1.38147i	0.723109	−	0.690733i	$-0.242712\pi$
$422$	12.4152	−	2.52834i	0.604362	−	0.123078i
$423$	−10.9945	+	41.0322i	−0.534573	+	1.99505i
$424$	−5.61186	−	15.8189i	−0.272536	−	0.768234i
$425$	−0.439638	−	0.343890i	−0.0213256	−	0.0166811i
$426$	−0.188897	+	3.09805i	−0.00915211	+	0.150101i
$427$	−0.405986	+	0.462332i	−0.0196470	+	0.0223738i
$428$	12.5267	−	9.79453i	0.605499	−	0.473436i
$429$	25.5511	−	44.2559i	1.23362	−	2.13669i
$430$	−0.00132666	+	13.4645i	−6.39772e−5	+	0.649315i
$431$	−25.6417	+	14.8042i	−1.23512	+	0.713095i	−0.968092	−	0.250594i	$-0.919374\pi$
$431$	−25.6417	+	14.8042i	−1.23512	+	0.713095i	−0.267025	+	0.963690i	$0.586041\pi$
$432$	23.4842	−	0.427671i	1.12989	−	0.0205763i
$433$	−3.19372	+	3.19372i	−0.153480	+	0.153480i	−0.779670	−	0.626190i	$-0.784613\pi$
$433$	−3.19372	+	3.19372i	−0.153480	+	0.153480i	0.626190	+	0.779670i	$0.284613\pi$
$434$	−4.81243	−	8.26074i	−0.231004	−	0.396528i
$435$	35.2875	−	11.7957i	1.69190	−	0.565563i
$436$	20.9913	+	15.8057i	1.00530	+	0.756954i
$437$	18.6558	+	4.99880i	0.892428	+	0.239125i
$438$	48.9191	+	16.3578i	2.33744	+	0.781606i
$439$	10.2663	−	17.7817i	0.489983	−	0.848675i	−0.509951	−	0.860204i	$-0.670336\pi$
$439$	10.2663	−	17.7817i	0.489983	−	0.848675i	0.999934	+	0.0115285i	$0.00366971\pi$
$440$	−17.6875	+	2.49086i	−0.843221	+	0.118747i
$441$	−21.5572	−	28.1696i	−1.02654	−	1.34141i
$442$	0.753110	−	0.666549i	0.0358218	−	0.0317045i
$443$	8.46657	+	31.5977i	0.402259	+	1.50125i	0.809055	+	0.587732i	$0.199979\pi$
$443$	8.46657	+	31.5977i	0.402259	+	1.50125i	−0.406796	+	0.913519i	$0.633354\pi$
$444$	−2.42724	−	5.71222i	−0.115192	−	0.271090i
$445$	−19.2844	+	1.17392i	−0.914166	+	0.0556491i
$446$	19.1960	+	12.7004i	0.908958	+	0.601379i
$447$	−43.7098	+	43.7098i	−2.06740	+	2.06740i
$448$	17.9061	+	11.2858i	0.845986	+	0.533205i
$449$		−	14.3769i		−	0.678486i	−0.940699	−	0.339243i	$-0.889829\pi$
$449$		−	14.3769i		−	0.678486i	0.940699	−	0.339243i	$-0.110171\pi$
$450$	−23.7533	+	26.8273i	−1.11974	+	1.26465i
$451$	−8.45445	−	14.6435i	−0.398105	−	0.689537i
$452$	5.97980	−	14.8166i	0.281266	−	0.696916i
$453$	−40.9211	+	10.9648i	−1.92264	+	0.515170i
$454$	1.41869	−	23.2675i	0.0665823	−	1.09200i
$455$	14.6070	−	34.7425i	0.684787	−	1.62875i
$456$	32.7438	+	6.04951i	1.53337	+	0.283294i
$457$	32.8377	−	8.79885i	1.53608	−	0.411593i	0.611086	−	0.791564i	$-0.290733\pi$
$457$	32.8377	−	8.79885i	1.53608	−	0.411593i	0.924998	+	0.379971i	$0.124066\pi$
$458$	−7.06487	+	21.1279i	−0.330120	+	0.987244i
$459$	0.567685	−	0.327753i	0.0264972	−	0.0152982i
$460$	−6.61056	+	19.7628i	−0.308219	+	0.921446i
$461$		−	36.8978i		−	1.71850i	−0.511553	−	0.859252i	$-0.670930\pi$
$461$		−	36.8978i		−	1.71850i	0.511553	−	0.859252i	$-0.329070\pi$
$462$	28.9613	−	7.88144i	1.34740	−	0.366678i
$463$	−9.48101	−	9.48101i	−0.440620	−	0.440620i	0.451600	−	0.892220i	$-0.350853\pi$
$463$	−9.48101	−	9.48101i	−0.440620	−	0.440620i	−0.892220	+	0.451600i	$0.850853\pi$
$464$	16.2653	−	16.8687i	0.755097	−	0.783109i
$465$	10.7563	−	12.1508i	0.498813	−	0.563480i
$466$	3.01984	+	6.05399i	0.139891	+	0.280446i
$467$	8.79527	−	2.35668i	0.406996	−	0.109054i	−0.0495119	−	0.998774i	$-0.515767\pi$
$467$	8.79527	−	2.35668i	0.406996	−	0.109054i	0.456508	+	0.889719i	$0.349100\pi$
$468$	−39.7684	−	50.8616i	−1.83829	−	2.35108i
$469$	−3.88187	−	1.91746i	−0.179248	−	0.0885401i
$470$	−22.9564	−	13.2569i	−1.05890	−	0.611494i
$471$	−31.4674	−	18.1677i	−1.44994	−	0.837124i
$472$	−6.60063	+	13.8587i	−0.303818	+	0.637899i
$473$	11.6154	+	3.11234i	0.534078	+	0.143106i
$474$	−23.7785	+	35.9402i	−1.09218	+	1.65079i
$475$	−16.5582	+	12.4626i	−0.759741	+	0.571822i
$476$	0.589741	+	0.0336486i	0.0270307	+	0.00154228i
$477$	−21.2638	+	21.2638i	−0.973603	+	0.973603i
$478$	1.10728	−	0.225497i	0.0506460	−	0.0103140i
$479$	20.1954	+	34.9794i	0.922750	+	1.59825i	0.795141	+	0.606425i	$0.207397\pi$
$479$	20.1954	+	34.9794i	0.922750	+	1.59825i	0.127609	+	0.991825i	$0.459270\pi$
$480$	−8.66873	+	34.8660i	−0.395672	+	1.59141i
$481$	−3.48012	+	6.02774i	−0.158680	+	0.274841i
$482$	−24.7910	−	28.0104i	−1.12920	−	1.27584i
$483$	6.85379	−	34.3398i	0.311858	−	1.56251i
$484$	0.734714	−	6.00251i	0.0333961	−	0.272841i
$485$	9.73411	+	1.98334i	0.442003	+	0.0900589i
$486$	8.47342	+	16.9870i	0.384362	+	0.770546i
$487$	1.89260	+	0.507120i	0.0857618	+	0.0229798i	0.301445	−	0.953484i	$-0.402531\pi$
$487$	1.89260	+	0.507120i	0.0857618	+	0.0229798i	−0.215683	+	0.976463i	$0.569198\pi$
$488$	−0.655710	+	0.0519795i	−0.0296826	+	0.00235300i
$489$			42.2726i			1.91163i
$490$	20.4628	−	8.44247i	0.924413	−	0.381392i
$491$	−6.84926			−0.309103			−0.154551	−	0.987985i	$-0.549393\pi$
$491$	−6.84926			−0.309103			−0.154551	+	0.987985i	$0.549393\pi$
$492$	−33.6775	+	4.74604i	−1.51830	+	0.213968i
$493$	0.169260	−	0.631688i	0.00762310	−	0.0284498i
$494$	−16.6680	−	33.4151i	−0.749931	−	1.50342i
$495$	17.6552	+	26.6907i	0.793541	+	1.19966i
$496$	2.46504	−	9.91867i	0.110684	−	0.445361i
$497$	2.00484	+	0.400141i	0.0899294	+	0.0179488i
$498$	−10.1112	+	8.94904i	−0.453094	+	0.401016i
$499$	−33.2941	−	19.2224i	−1.49045	−	0.860512i	−0.490510	−	0.871435i	$-0.663190\pi$
$499$	−33.2941	−	19.2224i	−1.49045	−	0.860512i	−0.999940	+	0.0109234i	$0.996523\pi$
$500$	−12.3327	−	18.6522i	−0.551533	−	0.834153i
$501$	37.8413	−	21.8477i	1.69063	−	0.976083i
$502$	−17.3821	+	3.53985i	−0.775801	+	0.157991i
$503$	−3.54943	−	3.54943i	−0.158261	−	0.158261i	0.623534	−	0.781796i	$-0.285696\pi$
$503$	−3.54943	−	3.54943i	−0.158261	−	0.158261i	−0.781796	+	0.623534i	$0.785696\pi$
$504$	4.46023	−	37.6576i	0.198675	−	1.67740i
$505$	4.21257	−	8.44304i	0.187457	−	0.375710i
$506$	15.5218	+	10.2694i	0.690028	+	0.456532i
$507$	−20.2770	+	75.6748i	−0.900533	+	3.36084i
$508$	−2.11408	+	5.23822i	−0.0937969	+	0.232408i
$509$	−10.2620	+	17.7744i	−0.454856	+	0.787835i	−0.998680	−	0.0513651i	$-0.983643\pi$
$509$	−10.2620	+	17.7744i	−0.454856	+	0.787835i	0.543823	+	0.839200i	$0.316976\pi$
$510$	0.259413	+	0.968523i	0.0114870	+	0.0428869i
$511$	15.0466	−	30.4616i	0.665623	−	1.34754i
$512$	5.31967	+	21.9932i	0.235098	+	0.971972i
$513$	−6.29928	−	23.5092i	−0.278120	−	1.03796i
$514$	−0.486540	+	0.242694i	−0.0214603	+	0.0107048i
$515$	−14.6425	+	16.5408i	−0.645227	+	0.728874i
$516$	14.5489	−	19.3223i	0.640481	−	0.850615i
$517$	−16.7411	+	16.7411i	−0.736273	+	0.736273i
$518$	−3.94459	+	1.07347i	−0.173316	+	0.0471655i
$519$	47.2729			2.07505
$520$	37.0831	−	15.7531i	1.62620	−	0.690818i
$521$	−18.6704	−	32.3381i	−0.817966	−	1.41676i	−0.907179	−	0.420746i	$-0.861768\pi$
$521$	−18.6704	−	32.3381i	−0.817966	−	1.41676i	0.0892128	−	0.996013i	$-0.471565\pi$
$522$	−39.8157	−	13.3138i	−1.74268	−	0.582728i
$523$	−5.49403	−	20.5040i	−0.240237	−	0.896577i	−0.975718	−	0.219031i	$-0.929710\pi$
$523$	−5.49403	−	20.5040i	−0.240237	−	0.896577i	0.735481	−	0.677546i	$-0.236956\pi$
$524$	−5.04343	+	41.2042i	−0.220323	+	1.80001i
$525$	24.4918	+	28.4946i	1.06891	+	1.24361i
$526$	0.216590	−	3.55223i	0.00944378	−	0.154885i
$527$	−0.0738230	−	0.275511i	−0.00321578	−	0.0120015i
$528$	28.0756	+	15.5349i	1.22183	+	0.676068i
$529$	−1.11422	+	0.643297i	−0.0484444	+	0.0279694i
$530$	−9.38141	−	16.2528i	−0.407502	−	0.705975i
$531$	27.5015			1.19346
$532$	6.87407	−	20.8273i	0.298029	−	0.902976i
$533$	26.9693	+	26.9693i	1.16817	+	1.16817i
$534$	28.9445	+	19.1501i	1.25255	+	0.828705i
$535$	11.7840	−	13.3117i	0.509466	−	0.575513i
$536$	−1.54752	−	4.36219i	−0.0668425	−	0.188418i
$537$	17.9553	−	4.81111i	0.774829	−	0.207615i
$538$	14.5986	+	16.4944i	0.629389	+	0.711124i
$539$	−2.55500	−	19.6039i	−0.110052	−	0.844400i
$540$	25.7329	−	5.23783i	1.10737	−	0.225400i
$541$	−20.3561	−	11.7526i	−0.875179	−	0.505285i	−0.00611324	−	0.999981i	$-0.501946\pi$
$541$	−20.3561	−	11.7526i	−0.875179	−	0.505285i	−0.869066	+	0.494696i	$0.835279\pi$
$542$	−8.24622	−	2.75741i	−0.354205	−	0.118441i
$543$	−0.164096	+	0.612416i	−0.00704205	+	0.0262813i
$544$	0.427065	+	0.465176i	0.0183102	+	0.0199443i
$545$	26.2876	+	13.1160i	1.12604	+	0.561826i
$546$	−58.4992	+	34.0796i	−2.50354	+	1.45847i
$547$	12.8073	+	12.8073i	0.547601	+	0.547601i	0.925746	−	0.378145i	$-0.123438\pi$
$547$	12.8073	+	12.8073i	0.547601	+	0.547601i	−0.378145	+	0.925746i	$0.623438\pi$
$548$	2.72770	+	19.3555i	0.116521	+	0.826826i
$549$	0.589225	+	1.02057i	0.0251475	+	0.0435568i
$550$	−18.9409	+	6.32939i	−0.807641	+	0.269886i
$551$	−21.0284	−	12.1408i	−0.895842	−	0.517215i
$552$	30.8390	−	21.2208i	1.31259	−	0.903216i
$553$	21.3287	+	18.7293i	0.906989	+	0.796451i
$554$	−36.0355	−	2.19719i	−1.53100	−	0.0933498i
$555$	−3.82829	−	5.78753i	−0.162502	−	0.245667i
$556$	1.57931	+	3.71672i	0.0669778	+	0.157624i
$557$	−22.1000	−	5.92167i	−0.936406	−	0.250909i	−0.241822	−	0.970321i	$-0.577745\pi$
$557$	−22.1000	−	5.92167i	−0.936406	−	0.250909i	−0.694584	+	0.719411i	$0.744412\pi$
$558$	−17.9425	+	3.65397i	−0.759566	+	0.154685i
$559$	−27.1245			−1.14724
$560$	21.9781	+	8.77297i	0.928742	+	0.370726i
$561$	0.895481			0.0378072
$562$	−10.3676	+	2.11135i	−0.437330	+	0.0890618i
$563$	−7.23262	−	1.93797i	−0.304819	−	0.0816759i	0.103168	−	0.994664i	$-0.467102\pi$
$563$	−7.23262	−	1.93797i	−0.304819	−	0.0816759i	−0.407986	+	0.912988i	$0.633769\pi$
$564$	18.6233	+	43.8278i	0.784184	+	1.84548i
$565$	3.56649	−	17.5041i	0.150043	−	0.736403i
$566$	−11.9357	−	0.727757i	−0.501696	−	0.0305899i
$567$	−3.69934	+	1.25308i	−0.155358	+	0.0526243i
$568$	1.23892	+	1.80046i	0.0519840	+	0.0755454i
$569$	−9.21123	−	5.31811i	−0.386155	−	0.222947i	0.294338	−	0.955701i	$-0.404901\pi$
$569$	−9.21123	−	5.31811i	−0.386155	−	0.222947i	−0.680493	+	0.732755i	$0.738234\pi$
$570$	37.2282	+	0.00366811i	1.55932	+	0.000153640i
$571$	11.9184	+	20.6433i	0.498771	+	0.863896i	0.999999	−	0.00141881i	$-0.000451623\pi$
$571$	11.9184	+	20.6433i	0.498771	+	0.863896i	−0.501228	+	0.865315i	$0.667118\pi$
$572$	−5.02140	−	35.6315i	−0.209955	−	1.48983i
$573$	33.3623	+	33.3623i	1.39373	+	1.39373i
$574$	0.0874276	+	22.4014i	0.00364916	+	0.935014i
$575$	−3.25583	+	23.0702i	−0.135778	+	0.962094i
$576$	31.4759	−	25.5478i	1.31149	−	1.06449i
$577$	−7.59867	+	28.3586i	−0.316337	+	1.18058i	0.606402	+	0.795158i	$0.292612\pi$
$577$	−7.59867	+	28.3586i	−0.316337	+	1.18058i	−0.922739	+	0.385426i	$0.874054\pi$
$578$	−22.7840	−	7.61863i	−0.947688	−	0.316893i
$579$	−7.75556	−	4.47768i	−0.322310	−	0.186086i
$580$	14.4583	−	21.8483i	0.600346	−	0.907202i
$581$	4.93632	+	7.39812i	0.204793	+	0.306926i
$582$	−11.8272	−	13.3631i	−0.490254	−	0.553920i
$583$	−16.1889	+	4.33781i	−0.670476	+	0.179654i
$584$	34.2308	−	12.1436i	1.41648	−	0.502506i
$585$	−54.0489	−	47.8461i	−2.23465	−	1.97819i
$586$	−1.41808	−	0.938222i	−0.0585804	−	0.0387576i
$587$	−16.0781	−	16.0781i	−0.663615	−	0.663615i	0.292615	−	0.956230i	$-0.405474\pi$
$587$	−16.0781	−	16.0781i	−0.663615	−	0.663615i	−0.956230	+	0.292615i	$0.905474\pi$
$588$	−38.4886	−	9.99167i	−1.58724	−	0.412049i
$589$	−10.5904			−0.436371
$590$	−4.44353	+	16.5769i	−0.182937	+	0.682462i
$591$	21.1206	−	12.1940i	0.868785	−	0.501593i
$592$	−3.82396	−	2.11588i	−0.157164	−	0.0869621i
$593$	−6.91320	−	25.8004i	−0.283891	−	1.05950i	−0.949646	−	0.313326i	$-0.898557\pi$
$593$	−6.91320	−	25.8004i	−0.283891	−	1.05950i	0.665754	−	0.746171i	$-0.268110\pi$
$594$	1.42737	−	23.4099i	0.0585658	−	0.960520i
$595$	0.655221	−	0.0827308i	0.0268614	−	0.00339163i
$596$	−5.28826	+	43.2044i	−0.216616	+	1.76972i
$597$	−5.87111	−	21.9113i	−0.240289	−	0.896769i
$598$	−39.8139	−	13.3132i	−1.62811	−	0.544417i
$599$	−6.19066	−	10.7225i	−0.252944	−	0.438111i	0.711391	−	0.702796i	$-0.248065\pi$
$599$	−6.19066	−	10.7225i	−0.252944	−	0.438111i	−0.964335	+	0.264685i	$0.914732\pi$
$600$	−2.45253	+	40.0932i	−0.100124	+	1.63680i
$601$	−20.0975			−0.819792			−0.409896	−	0.912132i	$-0.634435\pi$
$601$	−20.0975			−0.819792			−0.409896	+	0.912132i	$0.634435\pi$
$602$	−11.3091	−	11.2211i	−0.460923	−	0.457339i
$603$	−5.86367	+	5.86367i	−0.238787	+	0.238787i
$604$	−17.9437	+	23.8308i	−0.730118	+	0.969662i
$605$	−0.410815	−	6.74861i	−0.0167020	−	0.274370i
$606$	−15.1676	+	7.56586i	−0.616141	+	0.307342i
$607$	−8.03071	−	29.9710i	−0.325956	−	1.21649i	−0.913347	−	0.407182i	$-0.866511\pi$
$607$	−8.03071	−	29.9710i	−0.325956	−	1.21649i	0.587390	−	0.809304i	$-0.300155\pi$
$608$	20.7872	−	10.8461i	0.843032	−	0.439867i
$609$	−19.4968	+	39.4710i	−0.790050	+	1.59944i
$610$	−0.710367	+	0.190267i	−0.0287619	+	0.00770369i
$611$	26.7017	−	46.2487i	1.08023	−	1.87102i
$612$	0.423420	−	1.04914i	0.0171157	−	0.0424091i
$613$	−1.06608	+	3.97867i	−0.0430586	+	0.160697i	−0.984108	−	0.177574i	$-0.943175\pi$
$613$	−1.06608	+	3.97867i	−0.0430586	+	0.160697i	0.941049	+	0.338270i	$0.109842\pi$
$614$	−22.9263	−	15.1684i	−0.925230	−	0.612145i
$615$	−36.0631	+	12.0550i	−1.45421	+	0.486106i
$616$	12.6468	−	16.9332i	0.509554	−	0.682258i
$617$	−4.32992	−	4.32992i	−0.174316	−	0.174316i	0.614557	−	0.788873i	$-0.289335\pi$
$617$	−4.32992	−	4.32992i	−0.174316	−	0.174316i	−0.788873	+	0.614557i	$0.789335\pi$
$618$	38.8851	−	7.91891i	1.56419	−	0.318545i
$619$	−5.60482	+	3.23595i	−0.225277	+	0.130064i	−0.608391	−	0.793637i	$-0.708185\pi$
$619$	−5.60482	+	3.23595i	−0.225277	+	0.130064i	0.383114	+	0.923701i	$0.374852\pi$
$620$	0.696555	−	11.4055i	0.0279743	−	0.458056i
$621$	−23.6964	−	13.6811i	−0.950905	−	0.549005i
$622$	16.7495	−	14.8244i	0.671594	−	0.594402i
$623$	15.0837	−	17.1771i	0.604315	−	0.688187i
$624$	−70.2399	−	17.4564i	−2.81185	−	0.698816i
$625$	−17.3458	−	18.0035i	−0.693831	−	0.720138i
$626$	−2.16190	−	4.33405i	−0.0864069	−	0.173224i
$627$	8.60539	−	32.1158i	0.343666	−	1.28258i
$628$	−25.3351	+	3.57039i	−1.01098	+	0.142474i
$629$	−0.121966			−0.00486312
$630$	−2.74124	−	42.3081i	−0.109214	−	1.68559i
$631$			38.4848i			1.53206i	0.642808	+	0.766028i	$0.277770\pi$
$631$			38.4848i			1.53206i	−0.642808	+	0.766028i	$0.722230\pi$
$632$	2.39796	+	30.2498i	0.0953858	+	1.20327i
$633$	−24.5795	−	6.58606i	−0.976947	−	0.261772i
$634$	4.19484	+	8.40956i	0.166598	+	0.333986i
$635$	−1.26088	+	6.18833i	−0.0500366	+	0.245577i
$636$	−4.09567	+	33.4610i	−0.162404	+	1.32682i
$637$	17.0116	+	41.2210i	0.674024	+	1.63324i
$638$	−15.5076	−	17.5215i	−0.613952	−	0.693683i
$639$	1.95779	−	3.39100i	0.0774491	−	0.134146i
$640$	10.3136	+	23.1004i	0.407682	+	0.913124i
$641$	11.3786	+	19.7084i	0.449429	+	0.778434i	0.998349	−	0.0574407i	$-0.0182940\pi$
$641$	11.3786	+	19.7084i	0.449429	+	0.778434i	−0.548920	+	0.835875i	$0.684961\pi$
$642$	−31.2939	+	6.37296i	−1.23507	+	0.251521i
$643$	32.1875	−	32.1875i	1.26935	−	1.26935i	0.322928	−	0.946423i	$-0.395333\pi$
$643$	32.1875	−	32.1875i	1.26935	−	1.26935i	0.946423	−	0.322928i	$-0.104667\pi$
$644$	−11.0922	−	22.0213i	−0.437093	−	0.867762i
$645$	12.0731	−	24.1975i	0.475378	−	0.952774i
$646$	0.361056	−	0.545720i	0.0142056	−	0.0214711i
$647$	33.4732	+	8.96912i	1.31597	+	0.352612i	0.847466	−	0.530850i	$-0.178127\pi$
$647$	33.4732	+	8.96912i	1.31597	+	0.352612i	0.468502	+	0.883463i	$0.344794\pi$
$648$	−3.76975	−	1.79545i	−0.148090	−	0.0705321i
$649$	13.2741	+	7.66380i	0.521054	+	0.300830i
$650$	37.5729	−	24.8481i	1.47373	−	0.974622i
$651$	1.24336	+	19.1607i	0.0487311	+	0.750966i
$652$	18.3347	+	23.4491i	0.718043	+	0.918338i
$653$	−25.9512	+	6.95360i	−1.01555	+	0.272115i	−0.727946	−	0.685634i	$-0.759525\pi$
$653$	−25.9512	+	6.95360i	−1.01555	+	0.272115i	−0.287603	+	0.957750i	$0.592858\pi$
$654$	−23.5565	−	47.2247i	−0.921133	−	1.84663i
$655$	2.82004	+	46.3257i	0.110188	+	1.81010i
$656$	−16.6228	+	17.2395i	−0.649012	+	0.673089i
$657$	−46.0131	−	46.0131i	−1.79514	−	1.79514i
$658$	30.2654	−	8.23633i	1.17987	−	0.321086i
$659$			29.9105i			1.16515i	0.812778	+	0.582574i	$0.197954\pi$
$659$			29.9105i			1.16515i	−0.812778	+	0.582574i	$0.802046\pi$
$660$	34.0215	+	11.3800i	1.32428	+	0.442966i
$661$	3.93564	−	2.27224i	0.153079	−	0.0883800i	−0.421504	−	0.906826i	$-0.638498\pi$
$661$	3.93564	−	2.27224i	0.153079	−	0.0883800i	0.574583	+	0.818447i	$0.305164\pi$
$662$	0.783433	−	2.34291i	0.0304490	−	0.0910596i
$663$	−1.95106	+	0.522784i	−0.0757728	+	0.0203033i
$664$	−1.72737	+	9.34963i	−0.0670350	+	0.362836i
$665$	3.32946	−	24.2940i	0.129111	−	0.942081i
$666$	−0.476522	+	7.81530i	−0.0184649	+	0.302837i
$667$	−26.3681	+	7.06530i	−1.02098	+	0.273570i
$668$	11.5151	−	28.5319i	0.445533	−	1.10393i
$669$	−23.1138	−	40.0343i	−0.893632	−	1.54782i
$670$	−2.58700	−	4.48183i	−0.0999445	−	0.173148i
$671$			0.656794i			0.0253553i
$672$	−22.0637	−	36.3357i	−0.851127	−	1.40168i
$673$	3.36196	−	3.36196i	0.129594	−	0.129594i	−0.639335	−	0.768929i	$-0.720790\pi$
$673$	3.36196	−	3.36196i	0.129594	−	0.129594i	0.768929	+	0.639335i	$0.220790\pi$
$674$	5.23613	+	3.46430i	0.201688	+	0.133440i
$675$	27.2286	−	10.9829i	1.04803	−	0.422730i
$676$	21.5742	+	50.7724i	0.829778	+	1.95278i
$677$	−8.12079	−	30.3072i	−0.312107	−	1.16480i	−0.926652	−	0.375919i	$-0.877327\pi$
$677$	−8.12079	−	30.3072i	−0.312107	−	1.16480i	0.614545	−	0.788882i	$-0.289340\pi$
$678$	−24.0299	+	21.2680i	−0.922864	+	0.816792i
$679$	−9.77749	+	6.52393i	−0.375226	+	0.250366i
$680$	0.563973	+	0.424737i	0.0216274	+	0.0162879i
$681$	−23.4086	+	40.5450i	−0.897021	+	1.55369i
$682$	−9.67851	−	3.23635i	−0.370609	−	0.123926i
$683$	11.8796	+	3.18313i	0.454560	+	0.121799i	0.478833	−	0.877906i	$-0.341060\pi$
$683$	11.8796	+	3.18313i	0.454560	+	0.121799i	−0.0242720	+	0.999705i	$0.507727\pi$
$684$	−33.5577	−	25.2677i	−1.28311	−	0.966134i
$685$	6.92840	+	20.7266i	0.264721	+	0.791923i
$686$	−9.96005	+	24.2239i	−0.380277	+	0.924873i
$687$	31.6380	−	31.6380i	1.20707	−	1.20707i
$688$	−0.310106	−	17.0285i	−0.0118227	−	0.649207i
$689$	32.7397	−	18.9023i	1.24728	−	0.720119i
$690$	29.5977	−	29.5919i	1.12677	−	1.12654i
$691$	6.42537	−	11.1291i	0.244433	−	0.423370i	−0.717539	−	0.696518i	$-0.754732\pi$
$691$	6.42537	−	11.1291i	0.244433	−	0.423370i	0.961972	+	0.273148i	$0.0880649\pi$
$692$	26.2228	−	20.5035i	0.996842	−	0.779425i
$693$	−37.1324	−	7.41116i	−1.41054	−	0.281527i
$694$	−2.59185	+	42.5081i	−0.0983852	+	1.61359i
$695$	2.49092	+	3.76572i	0.0944860	+	0.142842i
$696$	−44.3549	+	15.7352i	−1.68127	+	0.596441i
$697$	−0.172981	+	0.645573i	−0.00655211	+	0.0244528i
$698$	−48.9107	+	9.96062i	−1.85130	+	0.377015i
$699$		−	13.5876i		−	0.513931i
$700$	25.9448	+	5.18357i	0.980620	+	0.195921i
$701$		−	22.2614i		−	0.840802i	−0.907338	−	0.420401i	$-0.861889\pi$
$701$		−	22.2614i		−	0.840802i	0.907338	−	0.420401i	$-0.138111\pi$
$702$	10.5568	+	51.8384i	0.398442	+	1.95651i
$703$	−1.17207	+	4.37423i	−0.0442056	+	0.164977i
$704$	22.3117	−	3.55976i	0.840906	−	0.134164i
$705$	29.3731	+	44.4056i	1.10625	+	1.67241i
$706$	22.6479	+	1.38091i	0.852366	+	0.0519713i
$707$	3.58180	+	10.5742i	0.134707	+	0.397684i
$708$	24.2869	−	18.9898i	0.912758	−	0.713681i
$709$	−1.75277	+	3.03588i	−0.0658265	+	0.114015i	−0.897060	−	0.441908i	$-0.854302\pi$
$709$	−1.75277	+	3.03588i	−0.0658265	+	0.114015i	0.831234	+	0.555923i	$0.187635\pi$
$710$	1.72765	+	1.72799i	0.0648375	+	0.0648502i
$711$	47.0817	−	27.1827i	1.76570	−	1.01943i
$712$	24.3617	−	1.93120i	0.912994	−	0.0723749i
$713$	−8.41892	+	8.41892i	−0.315291	+	0.315291i
$714$	−1.02973	−	0.589168i	−0.0385367	−	0.0220491i
$715$	−12.7545	−	38.1555i	−0.476990	−	1.42693i
$716$	7.87332	−	10.4565i	0.294240	−	0.390776i
$717$	−2.19219	−	0.587395i	−0.0818688	−	0.0219367i
$718$	13.4554	−	40.2392i	0.502151	−	1.50171i
$719$	−5.49540	+	9.51831i	−0.204944	+	0.354973i	−0.950115	−	0.311900i	$-0.899035\pi$
$719$	−5.49540	+	9.51831i	−0.204944	+	0.354973i	0.745171	+	0.666873i	$0.232368\pi$
$720$	29.4195	−	34.4785i	1.09640	−	1.28494i
$721$	−1.69257	−	26.0833i	−0.0630348	−	0.971391i
$722$	1.70628	+	1.92786i	0.0635012	+	0.0717477i
$723$	19.4439	+	72.5657i	0.723127	+	2.69875i
$724$	0.174595	+	0.410887i	0.00648875	+	0.0152705i
$725$	11.4606	−	26.9563i	0.425635	−	1.00113i
$726$	−6.70161	+	10.1292i	−0.248720	+	0.375929i
$727$	−5.57756	+	5.57756i	−0.206860	+	0.206860i	−0.802932	−	0.596071i	$-0.796728\pi$
$727$	−5.57756	+	5.57756i	−0.206860	+	0.206860i	0.596071	+	0.802932i	$0.296728\pi$
$728$	−17.6690	+	44.2770i	−0.654856	+	1.64102i
$729$		−	42.5545i		−	1.57609i
$730$	35.1696	−	20.3006i	1.30169	−	0.751358i
$731$	−0.237655	−	0.411631i	−0.00879000	−	0.0152247i
$732$	1.22506	+	0.494416i	0.0452794	+	0.0182742i
$733$	42.8456	−	11.4804i	1.58254	−	0.424040i	0.642828	−	0.766011i	$-0.277761\pi$
$733$	42.8456	−	11.4804i	1.58254	−	0.424040i	0.939710	+	0.341971i	$0.111095\pi$
$734$	17.2385	+	1.05108i	0.636283	+	0.0387961i
$735$	−44.3447	−	3.17158i	−1.63568	−	0.116986i
$736$	7.90274	−	25.1471i	0.291299	−	0.926934i
$737$	−4.46422	+	1.19619i	−0.164442	+	0.0440620i
$738$	40.6908	+	13.6064i	1.49785	+	0.500859i
$739$	−38.5836	+	22.2763i	−1.41932	+	0.819446i	−0.996239	−	0.0866458i	$-0.972385\pi$
$739$	−38.5836	+	22.2763i	−1.41932	+	0.819446i	−0.423082	+	0.906091i	$0.639052\pi$
$740$	−4.63380	−	1.54998i	−0.170342	−	0.0569784i
$741$			74.9971i			2.75509i
$742$	21.4699	+	5.66313i	0.788186	+	0.207900i
$743$	9.00133	+	9.00133i	0.330227	+	0.330227i	0.852672	−	0.522446i	$-0.174980\pi$
$743$	9.00133	+	9.00133i	0.330227	+	0.330227i	−0.522446	+	0.852672i	$0.674980\pi$
$744$	−13.3222	+	15.6162i	−0.488415	+	0.572517i
$745$	2.95693	+	48.5746i	0.108334	+	1.77963i
$746$	−23.6811	+	11.8125i	−0.867025	+	0.432487i
$747$	16.4538	−	4.40878i	0.602012	−	0.161309i
$748$	0.496734	−	0.388393i	0.0181624	−	0.0142011i
$749$	1.36215	+	20.9912i	0.0497718	+	0.767003i
$750$	5.44305	+	44.5782i	0.198752	+	1.62777i
$751$	−11.8548	−	6.84435i	−0.432586	−	0.249754i	0.267862	−	0.963457i	$-0.413683\pi$
$751$	−11.8548	−	6.84435i	−0.432586	−	0.249754i	−0.700448	+	0.713704i	$0.747016\pi$
$752$	29.3399	+	16.2344i	1.06991	+	0.592007i
$753$	34.4129	+	9.22091i	1.25408	+	0.336029i
$754$	44.0168	+	29.1221i	1.60300	+	1.06057i
$755$	−14.8902	+	29.8436i	−0.541908	+	1.08612i
$756$	−17.0436	+	25.9803i	−0.619868	+	0.944896i
$757$	−14.4439	+	14.4439i	−0.524971	+	0.524971i	−0.919069	−	0.394098i	$-0.871057\pi$
$757$	−14.4439	+	14.4439i	−0.524971	+	0.524971i	0.394098	+	0.919069i	$0.371057\pi$
$758$	−0.355153	−	1.74395i	−0.0128997	−	0.0633430i
$759$	−18.6897	−	32.3715i	−0.678393	−	1.17501i
$760$	20.6525	−	16.1448i	0.749146	−	0.585634i
$761$	−17.4803	+	30.2767i	−0.633659	+	1.09753i	0.353138	+	0.935571i	$0.385115\pi$
$761$	−17.4803	+	30.2767i	−0.633659	+	1.09753i	−0.986797	+	0.161959i	$0.948219\pi$
$762$	8.49545	−	7.51900i	0.307758	−	0.272385i
$763$	−32.9231	+	11.1520i	−1.19189	+	0.403731i
$764$	32.9766	+	4.03637i	1.19305	+	0.146031i
$765$	0.252537	−	1.23944i	0.00913051	−	0.0448119i
$766$	0.139011	−	0.0693412i	0.00502268	−	0.00250540i
$767$	−33.3955	−	8.94829i	−1.20584	−	0.323104i
$768$	10.1560	−	44.2957i	0.366472	−	1.59838i
$769$		−	33.8840i		−	1.22189i	−0.791674	−	0.610943i	$-0.790790\pi$
$769$		−	33.8840i		−	1.22189i	0.791674	−	0.610943i	$-0.209210\pi$
$770$	10.4668	−	21.1847i	0.377198	−	0.763442i
$771$	1.09199			0.0393271
$772$	−6.24419	+	0.879969i	−0.224733	+	0.0316708i
$773$	−2.92147	+	10.9031i	−0.105078	+	0.392157i	−0.998354	−	0.0573519i	$-0.981734\pi$
$773$	−2.92147	+	10.9031i	−0.105078	+	0.392157i	0.893276	+	0.449509i	$0.148401\pi$
$774$	−27.3048	+	13.6201i	−0.981450	+	0.489565i
$775$	−1.54965	−	12.6812i	−0.0556651	−	0.455521i
$776$	−12.3566	−	2.28293i	−0.443578	−	0.0819522i
$777$	8.05166	+	1.60701i	0.288852	+	0.0576512i
$778$	−9.98382	−	11.2804i	−0.357937	−	0.404421i
$779$	21.4907	+	12.4076i	0.769983	+	0.444550i
$780$	−80.7690	−	4.93272i	−2.89200	−	0.176620i
$781$	1.88993	−	1.09115i	0.0676270	−	0.0390445i
$782$	−0.146800	−	0.720847i	−0.00524955	−	0.0257774i
$783$	24.3245	+	24.3245i	0.869287	+	0.869287i
$784$	−25.6837	+	11.1510i	−0.917277	+	0.398251i
$785$	−27.1298	+	9.06884i	−0.968305	+	0.323681i
$786$	46.0031	−	69.5317i	1.64088	−	2.48011i
$787$	10.3504	−	38.6284i	0.368953	−	1.37695i	−0.493028	−	0.870013i	$-0.664110\pi$
$787$	10.3504	−	38.6284i	0.368953	−	1.37695i	0.861982	−	0.506940i	$-0.169223\pi$
$788$	6.42700	−	15.9247i	0.228952	−	0.567294i
$789$	−3.57379	+	6.18998i	−0.127230	+	0.220369i
$790$	8.77757	+	32.7712i	0.312292	+	1.16595i
$791$	11.7315	+	17.5821i	0.417124	+	0.625148i
$792$	−22.9465	−	33.3469i	−0.815369	−	1.18493i
$793$	−0.383438	−	1.43101i	−0.0136163	−	0.0508167i
$794$	−12.1460	−	24.3496i	−0.431046	−	0.864135i
$795$	2.29009	+	37.6201i	0.0812212	+	1.33425i
$796$	−12.7603	−	9.60799i	−0.452276	−	0.340546i
$797$	17.6546	−	17.6546i	0.625356	−	0.625356i	−0.321540	−	0.946896i	$-0.604200\pi$
$797$	17.6546	−	17.6546i	0.625356	−	0.625356i	0.946896	+	0.321540i	$0.104200\pi$
$798$	−31.0256	+	31.2687i	−1.09829	+	1.10690i
$799$	0.935804			0.0331064
$800$	16.0290	+	23.3039i	0.566711	+	0.823917i
$801$	−21.8916	−	37.9174i	−0.773502	−	1.33974i
$802$	2.89574	−	8.65989i	0.102252	−	0.305791i
$803$	−9.38665	−	35.0315i	−0.331248	−	1.23623i
$804$	−1.12941	+	9.22715i	−0.0398313	+	0.325416i
$805$	−16.6659	−	21.9594i	−0.587396	−	0.773969i
$806$	22.9768	+	1.40096i	0.809322	+	0.0493468i
$807$	−11.4499	−	42.7315i	−0.403055	−	1.50422i
$808$	−5.13213	+	10.7754i	−0.180548	+	0.379079i
$809$	−32.2619	+	18.6264i	−1.13427	+	0.654869i	−0.945005	−	0.327057i	$-0.893943\pi$
$809$	−32.2619	+	18.6264i	−1.13427	+	0.654869i	−0.189262	+	0.981927i	$0.560610\pi$
$810$	−4.50914	−	1.20870i	−0.158435	−	0.0424693i
$811$	−7.41017			−0.260206			−0.130103	−	0.991500i	$-0.541531\pi$
$811$	−7.41017			−0.260206			−0.130103	+	0.991500i	$0.541531\pi$
$812$	6.30448	+	30.3513i	0.221244	+	1.06512i
$813$	12.3483	+	12.3483i	0.433074	+	0.433074i
$814$	−2.40788	+	3.63940i	−0.0843961	+	0.127561i
$815$	24.9186	+	22.0589i	0.872859	+	0.772688i
$816$	−0.350506	−	1.21888i	−0.0122702	−	0.0426694i
$817$	−17.0467	+	4.56764i	−0.596387	+	0.159801i
$818$	−33.4767	+	29.6289i	−1.17048	+	1.03595i
$819$	85.2300	−	5.53068i	2.97818	−	0.193258i
$820$	−14.7761	+	22.3286i	−0.516002	+	0.779748i
$821$	−29.5491	−	17.0602i	−1.03127	−	0.595405i	−0.113923	−	0.993490i	$-0.536342\pi$
$821$	−29.5491	−	17.0602i	−1.03127	−	0.595405i	−0.917349	+	0.398085i	$0.869675\pi$
$822$	12.4497	−	37.2315i	0.434232	−	1.29860i
$823$	−10.4619	+	39.0443i	−0.364678	+	1.36100i	0.503178	+	0.864183i	$0.332164\pi$
$823$	−10.4619	+	39.0443i	−0.364678	+	1.36100i	−0.867856	+	0.496815i	$0.834503\pi$
$824$	18.1354	−	21.2582i	0.631776	−	0.740564i
$825$	39.7151	+	5.60488i	1.38270	+	0.195137i
$826$	−10.2218	−	17.5462i	−0.355663	−	0.610511i
$827$	23.4820	+	23.4820i	0.816548	+	0.816548i	0.985606	−	0.169058i	$-0.0540726\pi$
$827$	23.4820	+	23.4820i	0.816548	+	0.816548i	−0.169058	+	0.985606i	$0.554073\pi$
$828$	−46.7636	+	6.59021i	−1.62515	+	0.229026i
$829$	12.2338	+	21.1895i	0.424897	+	0.735943i	0.996411	−	0.0846491i	$-0.0269769\pi$
$829$	12.2338	+	21.1895i	0.424897	+	0.735943i	−0.571514	+	0.820593i	$0.693644\pi$
$830$	−0.00104739	+	10.6301i	−3.63554e−5	+	0.368976i
$831$	62.7940	+	36.2542i	2.17830	+	1.25764i
$832$	−46.5342	+	20.7816i	−1.61328	+	0.720473i
$833$	−0.476505	+	0.619326i	−0.0165099	+	0.0214584i
$834$	0.493614	−	8.09561i	0.0170924	−	0.280328i
$835$	6.86788	−	33.7071i	0.237673	−	1.16648i
$836$	−9.15593	−	21.5474i	−0.316664	−	0.745231i
$837$	14.4924	+	3.88322i	0.500930	+	0.134224i
$838$	−5.30459	−	26.0477i	−0.183244	−	0.899802i
$839$	−45.8332			−1.58234			−0.791168	−	0.611598i	$-0.790527\pi$
$839$	−45.8332			−1.58234			−0.791168	+	0.611598i	$0.790527\pi$
$840$	−31.6346	−	35.4700i	−1.09150	−	1.22383i
$841$	5.31953			0.183432
$842$	7.99935	+	39.2801i	0.275676	+	1.35368i
$843$	20.5256	+	5.49983i	0.706940	+	0.189424i
$844$	−16.4911	+	7.00740i	−0.567646	+	0.241205i
$845$	34.0272	+	51.4417i	1.17057	+	1.76965i
$846$	3.65618	−	59.9640i	0.125702	−	2.06160i
$847$	6.01117	+	5.27857i	0.206546	+	0.181374i
$848$	12.2410	+	20.3376i	0.420358	+	0.698397i
$849$	20.7987	+	12.0082i	0.713811	+	0.412119i
$850$	0.706286	+	0.352482i	0.0242254	+	0.0120900i
$851$	2.54558	+	4.40907i	0.0872613	+	0.151141i
$852$	−0.612535	−	4.34649i	−0.0209851	−	0.148908i
$853$	−15.2272	−	15.2272i	−0.521371	−	0.521371i	0.396614	−	0.917985i	$-0.370185\pi$
$853$	−15.2272	−	15.2272i	−0.521371	−	0.521371i	−0.917985	+	0.396614i	$0.870185\pi$
$854$	0.432128	−	0.755259i	0.0147871	−	0.0258444i
$855$	−42.0246	−	20.9678i	−1.43721	−	0.717084i
$856$	−14.5950	+	17.1081i	−0.498845	+	0.584743i
$857$	−9.46893	+	35.3385i	−0.323452	+	1.20714i	0.592406	+	0.805640i	$0.298178\pi$
$857$	−9.46893	+	35.3385i	−0.323452	+	1.20714i	−0.915858	+	0.401501i	$0.868488\pi$
$858$	−22.9185	+	68.5392i	−0.782425	+	2.33989i
$859$	9.77589	+	5.64411i	0.333549	+	0.192575i	0.657416	−	0.753528i	$-0.271650\pi$
$859$	9.77589	+	5.64411i	0.333549	+	0.192575i	−0.323867	+	0.946103i	$0.604983\pi$
$860$	−3.79798	−	18.6590i	−0.129510	−	0.636268i
$861$	19.9254	−	40.3386i	0.679055	−	1.37474i
$862$	31.3556	−	27.7516i	1.06797	−	0.945224i
$863$	32.8266	−	8.79587i	1.11743	−	0.299415i	0.347588	−	0.937647i	$-0.387001\pi$
$863$	32.8266	−	8.79587i	1.11743	−	0.299415i	0.769844	+	0.638233i	$0.220334\pi$
$864$	−32.4230	+	7.22015i	−1.10305	+	0.245635i
$865$	24.6681	−	27.8661i	0.838742	−	0.947476i
$866$	3.52445	−	5.32706i	0.119766	−	0.181021i
$867$	34.1179	+	34.1179i	1.15870	+	1.15870i
$868$	9.00018	+	10.0894i	0.305486	+	0.342456i
$869$	30.2998			1.02785
$870$	−45.5714	+	26.3047i	−1.54502	+	0.891812i
$871$	9.02823	−	5.21245i	0.305910	−	0.176617i
$872$	−33.5497	−	15.9790i	−1.13613	−	0.541118i
$873$	5.82672	+	21.7456i	0.197205	+	0.735978i
$874$	−27.2633	−	1.66233i	−0.922196	−	0.0562291i
$875$	29.5772	+	0.431911i	0.999893	+	0.0146013i
$876$	−72.4069	−	8.86268i	−2.44640	−	0.299442i
$877$	−9.43871	−	35.2257i	−0.318722	−	1.18949i	−0.920474	−	0.390805i	$-0.872197\pi$
$877$	−9.43871	−	35.2257i	−0.318722	−	1.18949i	0.601751	−	0.798684i	$-0.294470\pi$
$878$	−9.20851	+	27.5386i	−0.310772	+	0.929383i
$879$	1.70750	+	2.95748i	0.0575926	+	0.0997534i
$880$	23.8079	−	8.44337i	0.802565	−	0.284626i
$881$	48.2404			1.62526			0.812630	−	0.582780i	$-0.198035\pi$
$881$	48.2404			1.62526			0.812630	+	0.582780i	$0.198035\pi$
$882$	37.8231	+	32.9529i	1.27357	+	1.10958i
$883$	−16.8144	+	16.8144i	−0.565849	+	0.565849i	−0.930963	−	0.365114i	$-0.881030\pi$
$883$	−16.8144	+	16.8144i	−0.565849	+	0.565849i	0.365114	+	0.930963i	$0.381030\pi$
$884$	−0.855530	+	1.13622i	−0.0287746	+	0.0382152i
$885$	22.8470	−	25.8089i	0.767994	−	0.867556i
$886$	−20.6499	−	41.3978i	−0.693748	−	1.39078i
$887$	−8.20910	−	30.6368i	−0.275635	−	1.02868i	−0.955415	−	0.295267i	$-0.904592\pi$
$887$	−8.20910	−	30.6368i	−0.275635	−	1.02868i	0.679780	−	0.733416i	$-0.262075\pi$
$888$	4.97565	+	7.23083i	0.166972	+	0.242651i
$889$	−4.14751	−	6.21592i	−0.139103	−	0.208475i
$890$	26.3924	−	7.06903i	0.884675	−	0.236954i
$891$	−2.08465	+	3.61072i	−0.0698385	+	0.120964i
$892$	−30.1854	−	12.1824i	−1.01068	−	0.407898i
$893$	8.99289	−	33.5619i	0.300935	−	1.12311i
$894$	48.2363	−	72.9070i	1.61326	−	2.43838i
$895$	6.53349	−	13.0947i	0.218391	−	0.437708i
$896$	−27.9988	−	10.5862i	−0.935373	−	0.353662i
$897$	59.6194	+	59.6194i	1.99063	+	1.99063i
$898$	4.05730	+	19.9230i	0.135394	+	0.664840i
$899$	12.9631	−	7.48425i	0.432344	−	0.249614i
$900$	25.3456	−	43.8799i	0.844853	−	1.46266i
$901$	0.573708	+	0.331230i	0.0191130	+	0.0110349i
$902$	15.8485	+	17.9066i	0.527697	+	0.596226i
$903$	10.2653	+	30.3053i	0.341608	+	1.00850i
$904$	−4.10521	+	22.2200i	−0.136537	+	0.739026i
$905$	0.275373	+	0.416304i	0.00915372	+	0.0138384i
$906$	53.6128	−	26.7430i	1.78117	−	0.888476i
$907$	14.3494	−	53.5529i	0.476466	−	1.77819i	−0.139284	−	0.990252i	$-0.544480\pi$
$907$	14.3494	−	53.5529i	0.476466	−	1.77819i	0.615750	−	0.787941i	$-0.288853\pi$
$908$	4.60035	+	32.6437i	0.152668	+	1.08332i
$909$	21.3830			0.709230
$910$	−10.4373	+	52.2673i	−0.345992	+	1.73264i
$911$		−	20.1962i		−	0.669129i	−0.942373	−	0.334564i	$-0.891411\pi$
$911$		−	20.1962i		−	0.669129i	0.942373	−	0.334564i	$-0.108589\pi$
$912$	−47.0826	+	0.857420i	−1.55906	+	0.0283920i
$913$	9.17029	+	2.45717i	0.303492	+	0.0813206i
$914$	−43.0224	+	21.4603i	−1.42305	+	0.709845i
$915$	1.44726	+	0.294881i	0.0478449	+	0.00974848i
$916$	3.82776	−	31.2722i	0.126473	−	1.03326i
$917$	−41.2636	−	36.2346i	−1.36264	−	1.19657i
$918$	−0.694185	+	0.614397i	−0.0229115	+	0.0202781i
$919$	13.3795	−	23.1740i	0.441349	−	0.764439i	−0.556441	−	0.830887i	$-0.687833\pi$
$919$	13.3795	−	23.1740i	0.441349	−	0.764439i	0.997790	+	0.0664480i	$0.0211666\pi$
$920$	3.58343	−	29.2523i	0.118142	−	0.964419i
$921$	27.6054	+	47.8140i	0.909629	+	1.57552i
$922$	10.4130	+	51.1319i	0.342933	+	1.68394i
$923$	−3.48073	+	3.48073i	−0.114569	+	0.114569i
$924$	−37.9095	+	19.0951i	−1.24713	+	0.628181i
$925$	−5.40929	−	0.763397i	−0.177856	−	0.0251003i
$926$	15.8141	+	10.4629i	0.519685	+	0.343831i
$927$	−48.3563	−	12.9570i	−1.58823	−	0.425565i
$928$	−17.7794	+	27.9664i	−0.583638	+	0.918041i
$929$	−10.9634	−	6.32971i	−0.359697	−	0.207671i	0.309251	−	0.950980i	$-0.399922\pi$
$929$	−10.9634	−	6.32971i	−0.359697	−	0.207671i	−0.668948	+	0.743310i	$0.733255\pi$
$930$	−11.4767	+	19.8738i	−0.376337	+	0.651686i
$931$	17.6325	+	23.0411i	0.577883	+	0.755141i
$932$	−5.89330	−	7.53721i	−0.193041	−	0.246889i
$933$	−43.3924	+	11.6270i	−1.42060	+	0.380650i
$934$	−11.5231	+	5.74794i	−0.377048	+	0.188078i
$935$	0.467284	−	0.527862i	0.0152818	−	0.0172629i
$936$	69.4635	+	59.2594i	2.27049	+	1.93695i
$937$	−11.8896	−	11.8896i	−0.388416	−	0.388416i	0.485706	−	0.874122i	$-0.338563\pi$
$937$	−11.8896	−	11.8896i	−0.388416	−	0.388416i	−0.874122	+	0.485706i	$0.838563\pi$
$938$	5.92050	+	1.56165i	0.193311	+	0.0509898i
$939$			9.72737i			0.317441i
$940$	35.5534	+	11.8924i	1.15963	+	0.387889i
$941$	−27.9945	+	16.1626i	−0.912596	+	0.526887i	−0.881265	−	0.472622i	$-0.843308\pi$
$941$	−27.9945	+	16.1626i	−0.912596	+	0.526887i	−0.0313302	+	0.999509i	$0.509974\pi$
$942$	48.7337	+	16.2958i	1.58783	+	0.530947i
$943$	26.9477	−	7.22061i	0.877537	−	0.235135i
$944$	5.23587	−	21.0677i	0.170413	−	0.685697i
$945$	−13.4641	+	32.0241i	−0.437988	+	1.04174i
$946$	−16.9746	−	1.03499i	−0.551893	−	0.0336506i
$947$	−37.4142	+	10.0251i	−1.21580	+	0.325772i	−0.809034	−	0.587762i	$-0.800009\pi$
$947$	−37.4142	+	10.0251i	−1.21580	+	0.325772i	−0.406763	+	0.913534i	$0.633343\pi$
$948$	22.8088	−	56.5153i	0.740797	−	1.83553i
$949$	40.9029	+	70.8460i	1.32777	+	2.29976i
$950$	19.4288	−	21.9431i	0.630352	−	0.711929i
$951$		−	18.8745i		−	0.612046i
$952$	−0.826741	+	0.119802i	−0.0267948	+	0.00388280i
$953$	34.3020	−	34.3020i	1.11115	−	1.11115i	0.118157	−	0.992995i	$-0.462301\pi$
$953$	34.3020	−	34.3020i	1.11115	−	1.11115i	0.992995	−	0.118157i	$-0.0376987\pi$
$954$	23.4659	−	35.4676i	0.759736	−	1.14831i
$955$	37.0755	−	2.25693i	1.19973	−	0.0730327i
$956$	−1.47080	+	0.624974i	−0.0475691	+	0.0202131i
$957$	12.1628	+	45.3924i	0.393169	+	1.46733i
$958$	−37.8577	−	42.7740i	−1.22313	−	1.38197i
$959$	−23.1838	−	11.4517i	−0.748645	−	0.369796i
$960$	2.17331	−	50.7626i	0.0701434	−	1.63836i
$961$	−12.2357	+	21.1929i	−0.394701	+	0.683643i
$962$	3.12155	−	9.33519i	0.100643	−	0.300979i
$963$	38.9161	+	10.4275i	1.25405	+	0.336023i
$964$	42.2594	+	31.8197i	1.36108	+	1.02484i
$965$	−6.68651	+	2.23514i	−0.215246	+	0.0719517i
$966$	0.193271	+	49.5212i	0.00621838	+	1.59332i
$967$	−27.9338	+	27.9338i	−0.898291	+	0.898291i	−0.995285	−	0.0969936i	$-0.969077\pi$
$967$	−27.9338	+	27.9338i	−0.898291	+	0.898291i	0.0969936	+	0.995285i	$0.469077\pi$
$968$	0.675829	+	8.52544i	0.0217220	+	0.274018i
$969$	−1.13813	+	0.657098i	−0.0365619	+	0.0211090i
$970$	−14.0489	−	0.00138425i	−0.451085	−	4.44455e-5i
$971$	−5.31012	+	9.19740i	−0.170410	+	0.295159i	−0.938563	−	0.345107i	$-0.887843\pi$
$971$	−5.31012	+	9.19740i	−0.170410	+	0.295159i	0.768153	+	0.640266i	$0.221176\pi$
$972$	−16.5361	−	21.1488i	−0.530396	−	0.678348i
$973$	−5.23891	−	1.04562i	−0.167952	−	0.0335211i
$974$	−2.76582	−	0.168640i	−0.0886226	−	0.00540359i
$975$	−89.8028	+	10.9740i	−2.87599	+	0.351449i
$976$	0.893994	−	0.257080i	0.0286161	−	0.00822893i
$977$	5.58345	−	20.8377i	0.178630	−	0.666658i	−0.817274	−	0.576249i	$-0.804516\pi$
$977$	5.58345	−	20.8377i	0.178630	−	0.666658i	0.995905	−	0.0904089i	$-0.0288174\pi$
$978$	−11.9298	−	58.5801i	−0.381472	−	1.87318i
$979$		−	24.4020i		−	0.779891i
$980$	−25.9741	+	17.4741i	−0.829713	+	0.558191i
$981$			66.5766i			2.12563i
$982$	9.49150	−	1.93293i	0.302886	−	0.0616824i
$983$	0.406837	−	1.51834i	0.0129761	−	0.0484274i	−0.959134	−	0.282951i	$-0.908686\pi$
$983$	0.406837	−	1.51834i	0.0129761	−	0.0484274i	0.972110	+	0.234524i	$0.0753532\pi$
$984$	45.3299	−	16.0811i	1.44506	−	0.512645i
$985$	3.83321	−	18.8131i	0.122136	−	0.599437i
$986$	−0.0562867	+	0.923141i	−0.00179253	+	0.0293988i
$987$	−61.7775	−	12.3300i	−1.96640	−	0.392469i
$988$	32.5282	+	41.6018i	1.03486	+	1.32353i
$989$	−9.92027	+	17.1824i	−0.315446	+	0.546369i
$990$	−31.9984	−	32.0047i	−1.01698	−	1.01718i
$991$	37.2008	−	21.4779i	1.18172	−	0.682268i	0.225310	−	0.974287i	$-0.427660\pi$
$991$	37.2008	−	21.4779i	1.18172	−	0.682268i	0.956412	+	0.292019i	$0.0943271\pi$
$992$	−0.616827	+	14.4406i	−0.0195843	+	0.458491i
$993$	−3.50839	+	3.50839i	−0.111335	+	0.111335i
$994$	−2.89117	+	0.0112836i	−0.0917023	+	0.000357894i
$995$	−15.9798	−	7.97297i	−0.506594	−	0.252760i
$996$	11.4863	−	15.2548i	0.363957	−	0.483367i
$997$	−31.2333	−	8.36894i	−0.989168	−	0.265047i	−0.272267	−	0.962222i	$-0.587773\pi$
$997$	−31.2333	−	8.36894i	−0.989168	−	0.265047i	−0.716901	+	0.697175i	$0.754440\pi$
$998$	51.5628	+	17.2418i	1.63219	+	0.545781i
$999$	3.20783	−	5.55612i	0.101491	−	0.175788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.107.4	yes	176
5.3	odd	4	inner	280.2.br.a.163.24	yes	176
7.4	even	3	inner	280.2.br.a.67.27	yes	176
8.3	odd	2	inner	280.2.br.a.107.6	yes	176
35.18	odd	12	inner	280.2.br.a.123.6	yes	176
40.3	even	4	inner	280.2.br.a.163.27	yes	176
56.11	odd	6	inner	280.2.br.a.67.24	✓	176
280.123	even	12	inner	280.2.br.a.123.4	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.24	✓	176	56.11	odd	6	inner
280.2.br.a.67.27	yes	176	7.4	even	3	inner
280.2.br.a.107.4	yes	176	1.1	even	1	trivial
280.2.br.a.107.6	yes	176	8.3	odd	2	inner
280.2.br.a.123.4	yes	176	280.123	even	12	inner
280.2.br.a.123.6	yes	176	35.18	odd	12	inner
280.2.br.a.163.24	yes	176	5.3	odd	4	inner
280.2.br.a.163.27	yes	176	40.3	even	4	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38577 + 0.282211i) q^{2} +(2.74353 + 0.735128i) q^{3} +(1.84071 - 0.782158i) q^{4} +(1.86498 - 1.23363i) q^{5} +(-4.00937 - 0.244463i) q^{6} +(-0.517846 + 2.59458i) q^{7} +(-2.33007 + 1.60336i) q^{8} +(4.38849 + 2.53369i) q^{9} +O(q^{10})\)	\(q+(-1.38577 + 0.282211i) q^{2} +(2.74353 + 0.735128i) q^{3} +(1.84071 - 0.782158i) q^{4} +(1.86498 - 1.23363i) q^{5} +(-4.00937 - 0.244463i) q^{6} +(-0.517846 + 2.59458i) q^{7} +(-2.33007 + 1.60336i) q^{8} +(4.38849 + 2.53369i) q^{9} +(-2.23629 + 2.23585i) q^{10} +(1.41212 + 2.44587i) q^{11} +(5.62505 - 0.792716i) q^{12} +(-4.50461 - 4.50461i) q^{13} +(-0.0146028 - 3.74163i) q^{14} +(6.02351 - 2.01351i) q^{15} +(2.77646 - 2.87946i) q^{16} +(0.0288924 - 0.107828i) q^{17} +(-6.79647 - 2.27264i) q^{18} +(-3.58952 - 2.07241i) q^{19} +(2.46800 - 3.72947i) q^{20} +(-3.32807 + 6.73763i) q^{21} +(-2.64712 - 2.99089i) q^{22} +(-4.50099 + 1.20604i) q^{23} +(-7.57131 + 2.68597i) q^{24} +(1.95630 - 4.60140i) q^{25} +(7.51359 + 4.97110i) q^{26} +(4.15215 + 4.15215i) q^{27} +(1.07616 + 5.18091i) q^{28} +5.85829 q^{29} +(-7.77896 + 4.49017i) q^{30} +(2.21278 - 1.27755i) q^{31} +(-3.03492 + 4.77381i) q^{32} +(2.07618 + 7.74840i) q^{33} +(-0.00960804 + 0.157579i) q^{34} +(2.23498 + 5.47767i) q^{35} +(10.0597 + 1.23132i) q^{36} +(-0.282780 - 1.05535i) q^{37} +(5.55911 + 1.85888i) q^{38} +(-9.04708 - 15.6700i) q^{39} +(-2.36758 + 5.86469i) q^{40} -5.98706 q^{41} +(2.71051 - 10.2760i) q^{42} +(3.01075 - 3.01075i) q^{43} +(4.51236 + 3.39764i) q^{44} +(11.3101 - 0.688491i) q^{45} +(5.89697 - 2.94151i) q^{46} +(2.16967 + 8.09731i) q^{47} +(9.73408 - 5.85884i) q^{48} +(-6.46367 - 2.68718i) q^{49} +(-1.41242 + 6.92857i) q^{50} +(0.158535 - 0.274590i) q^{51} +(-11.8150 - 4.76838i) q^{52} +(-1.53592 + 5.73213i) q^{53} +(-6.92571 - 4.58215i) q^{54} +(5.65088 + 2.81945i) q^{55} +(-2.95342 - 6.87585i) q^{56} +(-8.32449 - 8.32449i) q^{57} +(-8.11824 + 1.65327i) q^{58} +(4.70005 - 2.71358i) q^{59} +(9.51268 - 8.41764i) q^{60} +(0.201399 + 0.116278i) q^{61} +(-2.70586 + 2.39486i) q^{62} +(-8.84643 + 10.0742i) q^{63} +(2.85848 - 7.47189i) q^{64} +(-13.9580 - 2.84397i) q^{65} +(-5.06379 - 10.1516i) q^{66} +(-0.423542 + 1.58068i) q^{67} +(-0.0311558 - 0.221079i) q^{68} -13.2352 q^{69} +(-4.64303 - 6.96005i) q^{70} -0.772704i q^{71} +(-14.2879 + 1.13263i) q^{72} +(-12.4038 - 3.32360i) q^{73} +(0.689698 + 1.38267i) q^{74} +(8.74979 - 11.1860i) q^{75} +(-8.22824 - 1.00714i) q^{76} +(-7.07725 + 2.39728i) q^{77} +(16.9594 + 19.1618i) q^{78} +(5.36423 - 9.29113i) q^{79} +(1.62585 - 8.79526i) q^{80} +(0.738128 + 1.27847i) q^{81} +(8.29668 - 1.68961i) q^{82} +(2.37696 - 2.37696i) q^{83} +(-0.856142 + 15.0051i) q^{84} +(-0.0791364 - 0.236740i) q^{85} +(-3.32254 + 5.02187i) q^{86} +(16.0724 + 4.30659i) q^{87} +(-7.21195 - 3.43491i) q^{88} +(-7.48263 - 4.32010i) q^{89} +(-15.4789 + 4.14592i) q^{90} +(14.0202 - 9.35486i) q^{91} +(-7.34172 + 5.74045i) q^{92} +(7.01000 - 1.87832i) q^{93} +(-5.29181 - 10.6087i) q^{94} +(-9.25098 + 0.563145i) q^{95} +(-11.8358 + 10.8661i) q^{96} +(3.14144 + 3.14144i) q^{97} +(9.71551 + 1.89970i) q^{98} +14.3115i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Introduction

L-functions

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