LMFDB - Embedded newform 151.2.h.a.148.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(9,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("151.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.h (of order $25$, 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:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			148.8
Character	$\chi$	$=$	151.148
Dual form			151.2.h.a.50.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.398915 - 0.289829i) q^{2} +(0.0979358 + 0.0919678i) q^{3} +(-0.542901 + 1.67088i) q^{4} +(0.126803 + 2.01548i) q^{5} +(0.0657230 + 0.00830275i) q^{6} +(-2.56949 + 4.04886i) q^{7} +(0.572442 + 1.76179i) q^{8} +(-0.187238 - 2.97607i) q^{9} +O(q^{10})$	\(q+(0.398915 - 0.289829i) q^{2} +(0.0979358 + 0.0919678i) q^{3} +(-0.542901 + 1.67088i) q^{4} +(0.126803 + 2.01548i) q^{5} +(0.0657230 + 0.00830275i) q^{6} +(-2.56949 + 4.04886i) q^{7} +(0.572442 + 1.76179i) q^{8} +(-0.187238 - 2.97607i) q^{9} +(0.634728 + 0.767255i) q^{10} +(2.84414 - 2.67082i) q^{11} +(-0.206836 + 0.113709i) q^{12} +(2.78163 - 5.91127i) q^{13} +(0.148470 + 2.35987i) q^{14} +(-0.172941 + 0.209049i) q^{15} +(-2.10369 - 1.52842i) q^{16} +(2.84160 + 4.47765i) q^{17} +(-0.937243 - 1.13293i) q^{18} +(0.212225 - 0.653161i) q^{19} +(-3.43646 - 0.882334i) q^{20} +(-0.624010 + 0.160218i) q^{21} +(0.360489 - 1.88975i) q^{22} +(-0.988811 + 3.04325i) q^{23} +(-0.105966 + 0.225189i) q^{24} +(0.914492 - 0.115527i) q^{25} +(-0.603621 - 3.16429i) q^{26} +(0.512276 - 0.619235i) q^{27} +(-5.37018 - 6.49143i) q^{28} +(0.520768 - 2.72996i) q^{29} +(-0.00840013 + 0.133516i) q^{30} +(5.43332 + 2.15120i) q^{31} -4.98710 q^{32} +0.524173 q^{33} +(2.43131 + 0.962624i) q^{34} +(-8.48622 - 4.66534i) q^{35} +(5.07430 + 1.30286i) q^{36} +(-0.715776 + 1.52110i) q^{37} +(-0.104645 - 0.322065i) q^{38} +(0.816067 - 0.323104i) q^{39} +(-3.47827 + 1.37715i) q^{40} +(-9.74434 - 1.23100i) q^{41} +(-0.202491 + 0.244770i) q^{42} +(1.49327 + 2.35301i) q^{43} +(2.91854 + 6.20220i) q^{44} +(5.97446 - 0.754750i) q^{45} +(0.487569 + 1.50058i) q^{46} +(5.31046 + 0.670867i) q^{47} +(-0.0654611 - 0.343159i) q^{48} +(-6.81058 - 14.4732i) q^{49} +(0.331322 - 0.311132i) q^{50} +(-0.133505 + 0.699858i) q^{51} +(8.36686 + 7.85700i) q^{52} +(-4.84496 - 2.66354i) q^{53} +(0.0248824 - 0.395495i) q^{54} +(5.74364 + 5.39364i) q^{55} +(-8.60414 - 2.20917i) q^{56} +(0.0808542 - 0.0444500i) q^{57} +(-0.583479 - 1.23996i) q^{58} +(-5.09967 - 3.70513i) q^{59} +(-0.255406 - 0.402456i) q^{60} +(0.927010 - 0.870521i) q^{61} +(2.79092 - 0.716586i) q^{62} +(12.5308 + 6.88886i) q^{63} +(2.21796 - 1.61144i) q^{64} +(12.2668 + 4.85675i) q^{65} +(0.209101 - 0.151920i) q^{66} +(0.686507 - 10.9117i) q^{67} +(-9.02431 + 2.31705i) q^{68} +(-0.376721 + 0.207104i) q^{69} +(-4.73744 + 0.598477i) q^{70} +(-6.85597 + 10.8033i) q^{71} +(5.13603 - 2.03350i) q^{72} +(3.47538 - 5.47632i) q^{73} +(0.155325 + 0.814244i) q^{74} +(0.100186 + 0.0727896i) q^{75} +(0.976136 + 0.709204i) q^{76} +(3.50583 + 18.3782i) q^{77} +(0.231897 - 0.365411i) q^{78} +(-8.69389 + 3.44215i) q^{79} +(2.81375 - 4.43376i) q^{80} +(-8.76819 + 1.10768i) q^{81} +(-4.24395 + 2.33313i) q^{82} +(4.14726 - 1.06483i) q^{83} +(0.0710701 - 1.12963i) q^{84} +(-8.66428 + 6.29497i) q^{85} +(1.27766 + 0.505861i) q^{86} +(0.302070 - 0.219467i) q^{87} +(6.33355 + 3.48190i) q^{88} +(5.55963 - 1.42747i) q^{89} +(2.16456 - 2.03265i) q^{90} +(16.7865 + 26.4514i) q^{91} +(-4.54807 - 3.30437i) q^{92} +(0.334275 + 0.710370i) q^{93} +(2.31286 - 1.27151i) q^{94} +(1.34334 + 0.344912i) q^{95} +(-0.488415 - 0.458652i) q^{96} +(1.06299 - 16.8958i) q^{97} +(-6.91160 - 3.79968i) q^{98} +(-8.48108 - 7.96427i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 15 q^{2} - 20 q^{3} - 55 q^{4} - 20 q^{5} - 20 q^{7} + 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q - 15 * q^2 - 20 * q^3 - 55 * q^4 - 20 * q^5 - 20 * q^7 + 5 * q^8 - 20 * q^9	\( 220 q - 15 q^{2} - 20 q^{3} - 55 q^{4} - 20 q^{5} - 20 q^{7} + 5 q^{8} - 20 q^{9} - 50 q^{10} - 10 q^{11} + 5 q^{12} - 20 q^{13} + 5 q^{14} - 60 q^{15} - 5 q^{16} - 10 q^{17} + 30 q^{18} - 15 q^{19} - 130 q^{20} - 20 q^{21} + 15 q^{22} + 35 q^{23} - 95 q^{24} + 10 q^{25} + 5 q^{26} + 25 q^{27} + 50 q^{28} + 15 q^{29} + 75 q^{30} + 20 q^{31} + 80 q^{32} - 100 q^{33} - 50 q^{34} + 15 q^{35} + 100 q^{36} + 20 q^{37} + 40 q^{38} - 5 q^{39} + 105 q^{40} - 10 q^{41} - 110 q^{42} - 10 q^{43} + 90 q^{44} + 5 q^{45} + 25 q^{46} - 75 q^{47} - 145 q^{48} - 10 q^{49} + 50 q^{50} - 80 q^{51} + 85 q^{52} - 95 q^{53} + 20 q^{54} + 80 q^{55} - 65 q^{56} + 55 q^{57} - 105 q^{58} - 15 q^{59} - 70 q^{62} + 95 q^{63} + 45 q^{64} - 30 q^{65} - 5 q^{66} - 50 q^{67} + 95 q^{68} + 45 q^{69} + 25 q^{71} - 25 q^{72} + 20 q^{73} - 140 q^{74} + 55 q^{75} + 15 q^{76} - 45 q^{77} + 110 q^{78} - 130 q^{79} + 145 q^{80} - 160 q^{81} - 10 q^{82} - 55 q^{83} + 140 q^{84} + 25 q^{85} - 150 q^{86} + 125 q^{87} - 35 q^{88} + 5 q^{89} + 120 q^{90} - 70 q^{91} + 45 q^{92} - 40 q^{93} + 65 q^{94} + 135 q^{96} - 270 q^{97} + 135 q^{98} + 60 q^{99}+O(q^{100}) \) 220 * q - 15 * q^2 - 20 * q^3 - 55 * q^4 - 20 * q^5 - 20 * q^7 + 5 * q^8 - 20 * q^9 - 50 * q^10 - 10 * q^11 + 5 * q^12 - 20 * q^13 + 5 * q^14 - 60 * q^15 - 5 * q^16 - 10 * q^17 + 30 * q^18 - 15 * q^19 - 130 * q^20 - 20 * q^21 + 15 * q^22 + 35 * q^23 - 95 * q^24 + 10 * q^25 + 5 * q^26 + 25 * q^27 + 50 * q^28 + 15 * q^29 + 75 * q^30 + 20 * q^31 + 80 * q^32 - 100 * q^33 - 50 * q^34 + 15 * q^35 + 100 * q^36 + 20 * q^37 + 40 * q^38 - 5 * q^39 + 105 * q^40 - 10 * q^41 - 110 * q^42 - 10 * q^43 + 90 * q^44 + 5 * q^45 + 25 * q^46 - 75 * q^47 - 145 * q^48 - 10 * q^49 + 50 * q^50 - 80 * q^51 + 85 * q^52 - 95 * q^53 + 20 * q^54 + 80 * q^55 - 65 * q^56 + 55 * q^57 - 105 * q^58 - 15 * q^59 - 70 * q^62 + 95 * q^63 + 45 * q^64 - 30 * q^65 - 5 * q^66 - 50 * q^67 + 95 * q^68 + 45 * q^69 + 25 * q^71 - 25 * q^72 + 20 * q^73 - 140 * q^74 + 55 * q^75 + 15 * q^76 - 45 * q^77 + 110 * q^78 - 130 * q^79 + 145 * q^80 - 160 * q^81 - 10 * q^82 - 55 * q^83 + 140 * q^84 + 25 * q^85 - 150 * q^86 + 125 * q^87 - 35 * q^88 + 5 * q^89 + 120 * q^90 - 70 * q^91 + 45 * q^92 - 40 * q^93 + 65 * q^94 + 135 * q^96 - 270 * q^97 + 135 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{1}{25}\right)$

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 $

$2$	0.398915	−	0.289829i	0.282076	−	0.204940i	−0.437747	−	0.899098i	$-0.644223\pi$
$2$	0.398915	−	0.289829i	0.282076	−	0.204940i	0.719822	+	0.694158i	$0.244223\pi$
$3$	0.0979358	+	0.0919678i	0.0565432	+	0.0530976i	0.712304	−	0.701871i	$-0.247652\pi$
$3$	0.0979358	+	0.0919678i	0.0565432	+	0.0530976i	−0.655760	+	0.754969i	$0.727652\pi$
$4$	−0.542901	+	1.67088i	−0.271451	+	0.835439i
$5$	0.126803	+	2.01548i	0.0567081	+	0.901350i	0.918831	+	0.394651i	$0.129135\pi$
$5$	0.126803	+	2.01548i	0.0567081	+	0.901350i	−0.862123	+	0.506699i	$0.830865\pi$
$6$	0.0657230	+	0.00830275i	0.0268313	+	0.00338958i
$7$	−2.56949	+	4.04886i	−0.971175	+	1.53033i	−0.128635	+	0.991692i	$0.541060\pi$
$7$	−2.56949	+	4.04886i	−0.971175	+	1.53033i	−0.842539	+	0.538635i	$0.818940\pi$
$8$	0.572442	+	1.76179i	0.202389	+	0.622888i
$9$	−0.187238	−	2.97607i	−0.0624127	−	0.992022i
$10$	0.634728	+	0.767255i	0.200719	+	0.242627i
$11$	2.84414	−	2.67082i	0.857540	−	0.805284i	−0.124840	−	0.992177i	$-0.539842\pi$
$11$	2.84414	−	2.67082i	0.857540	−	0.805284i	0.982380	+	0.186893i	$0.0598418\pi$
$12$	−0.206836	+	0.113709i	−0.0597086	+	0.0328251i
$13$	2.78163	−	5.91127i	0.771486	−	1.63949i	0.00268984	−	0.999996i	$-0.499144\pi$
$13$	2.78163	−	5.91127i	0.771486	−	1.63949i	0.768796	−	0.639494i	$-0.220856\pi$
$14$	0.148470	+	2.35987i	0.0396803	+	0.630701i
$15$	−0.172941	+	0.209049i	−0.0446531	+	0.0539763i
$16$	−2.10369	−	1.52842i	−0.525923	−	0.382106i
$17$	2.84160	+	4.47765i	0.689189	+	1.08599i	0.991160	+	0.132672i	$0.0423556\pi$
$17$	2.84160	+	4.47765i	0.689189	+	1.08599i	−0.301971	+	0.953317i	$0.597644\pi$
$18$	−0.937243	−	1.13293i	−0.220910	−	0.267035i
$19$	0.212225	−	0.653161i	0.0486877	−	0.149845i	−0.923757	−	0.382979i	$-0.874898\pi$
$19$	0.212225	−	0.653161i	0.0486877	−	0.149845i	0.972445	+	0.233134i	$0.0748980\pi$
$20$	−3.43646	−	0.882334i	−0.768417	−	0.197296i
$21$	−0.624010	+	0.160218i	−0.136170	+	0.0349625i
$22$	0.360489	−	1.88975i	0.0768564	−	0.402895i
$23$	−0.988811	+	3.04325i	−0.206181	+	0.634561i	0.793481	+	0.608594i	$0.208266\pi$
$23$	−0.988811	+	3.04325i	−0.206181	+	0.634561i	−0.999663	+	0.0259666i	$0.991734\pi$
$24$	−0.105966	+	0.225189i	−0.0216302	+	0.0459665i
$25$	0.914492	−	0.115527i	0.182898	−	0.0231054i
$26$	−0.603621	−	3.16429i	−0.118380	−	0.620569i
$27$	0.512276	−	0.619235i	0.0985875	−	0.119172i
$28$	−5.37018	−	6.49143i	−1.01487	−	1.22677i
$29$	0.520768	−	2.72996i	0.0967041	−	0.506941i	−0.900669	−	0.434506i	$-0.856923\pi$
$29$	0.520768	−	2.72996i	0.0967041	−	0.506941i	0.997373	−	0.0724349i	$-0.0230770\pi$
$30$	−0.00840013	+	0.133516i	−0.00153365	+	0.0243766i
$31$	5.43332	+	2.15120i	0.975853	+	0.386368i	0.801289	−	0.598278i	$-0.204148\pi$
$31$	5.43332	+	2.15120i	0.975853	+	0.386368i	0.174565	+	0.984646i	$0.444148\pi$
$32$	−4.98710			−0.881603
$33$	0.524173			0.0912468
$34$	2.43131	+	0.962624i	0.416966	+	0.165089i
$35$	−8.48622	−	4.66534i	−1.43443	−	0.788587i
$36$	5.07430	+	1.30286i	0.845716	+	0.217143i
$37$	−0.715776	+	1.52110i	−0.117673	+	0.250068i	−0.954983	−	0.296661i	$-0.904127\pi$
$37$	−0.715776	+	1.52110i	−0.117673	+	0.250068i	0.837310	+	0.546728i	$0.184127\pi$
$38$	−0.104645	−	0.322065i	−0.0169757	−	0.0522458i
$39$	0.816067	−	0.323104i	0.130675	−	0.0517380i
$40$	−3.47827	+	1.37715i	−0.549963	+	0.217746i
$41$	−9.74434	−	1.23100i	−1.52181	−	0.192249i	−0.680479	−	0.732768i	$-0.738228\pi$
$41$	−9.74434	−	1.23100i	−1.52181	−	0.192249i	−0.841332	+	0.540519i	$0.818228\pi$
$42$	−0.202491	+	0.244770i	−0.0312451	+	0.0377688i
$43$	1.49327	+	2.35301i	0.227721	+	0.358831i	0.938906	−	0.344174i	$-0.111841\pi$
$43$	1.49327	+	2.35301i	0.227721	+	0.358831i	−0.711185	+	0.703005i	$0.751841\pi$
$44$	2.91854	+	6.20220i	0.439986	+	0.935018i
$45$	5.97446	−	0.754750i	0.890620	−	0.112511i
$46$	0.487569	+	1.50058i	0.0718882	+	0.221249i
$47$	5.31046	+	0.670867i	0.774610	+	0.0978560i	0.502693	−	0.864465i	$-0.332342\pi$
$47$	5.31046	+	0.670867i	0.774610	+	0.0978560i	0.271917	+	0.962321i	$0.412342\pi$
$48$	−0.0654611	−	0.343159i	−0.00944850	−	0.0495308i
$49$	−6.81058	−	14.4732i	−0.972940	−	2.06760i
$50$	0.331322	−	0.311132i	0.0468560	−	0.0440007i
$51$	−0.133505	+	0.699858i	−0.0186944	+	0.0979997i
$52$	8.36686	+	7.85700i	1.16027	+	1.08957i
$53$	−4.84496	−	2.66354i	−0.665506	−	0.365865i	0.112918	−	0.993604i	$-0.463980\pi$
$53$	−4.84496	−	2.66354i	−0.665506	−	0.365865i	−0.778424	+	0.627739i	$0.783980\pi$
$54$	0.0248824	−	0.395495i	0.00338607	−	0.0538200i
$55$	5.74364	+	5.39364i	0.774472	+	0.727278i
$56$	−8.60414	−	2.20917i	−1.14978	−	0.295213i
$57$	0.0808542	−	0.0444500i	0.0107094	−	0.00588754i
$58$	−0.583479	−	1.23996i	−0.0766146	−	0.162814i
$59$	−5.09967	−	3.70513i	−0.663921	−	0.482367i	0.204064	−	0.978958i	$-0.434585\pi$
$59$	−5.09967	−	3.70513i	−0.663921	−	0.482367i	−0.867985	+	0.496591i	$0.834585\pi$
$60$	−0.255406	−	0.402456i	−0.0329728	−	0.0519569i
$61$	0.927010	−	0.870521i	0.118692	−	0.111459i	−0.622929	−	0.782278i	$-0.714057\pi$
$61$	0.927010	−	0.870521i	0.118692	−	0.111459i	0.741621	+	0.670820i	$0.234057\pi$
$62$	2.79092	−	0.716586i	0.354447	−	0.0910065i
$63$	12.5308	+	6.88886i	1.57873	+	0.867915i
$64$	2.21796	−	1.61144i	0.277245	−	0.201430i
$65$	12.2668	+	4.85675i	1.52150	+	0.602406i
$66$	0.209101	−	0.151920i	0.0257385	−	0.0187001i
$67$	0.686507	−	10.9117i	0.0838702	−	1.33308i	−0.700886	−	0.713273i	$-0.747212\pi$
$67$	0.686507	−	10.9117i	0.0838702	−	1.33308i	0.784756	−	0.619805i	$-0.212788\pi$
$68$	−9.02431	+	2.31705i	−1.09436	+	0.280984i
$69$	−0.376721	+	0.207104i	−0.0453519	+	0.0249324i
$70$	−4.73744	+	0.598477i	−0.566232	+	0.0715317i
$71$	−6.85597	+	10.8033i	−0.813653	+	1.28211i	0.142661	+	0.989772i	$0.454434\pi$
$71$	−6.85597	+	10.8033i	−0.813653	+	1.28211i	−0.956314	+	0.292341i	$0.905566\pi$
$72$	5.13603	−	2.03350i	0.605287	−	0.239650i
$73$	3.47538	−	5.47632i	0.406762	−	0.640954i	−0.577762	−	0.816205i	$-0.696074\pi$
$73$	3.47538	−	5.47632i	0.406762	−	0.640954i	0.984524	+	0.175251i	$0.0560737\pi$
$74$	0.155325	+	0.814244i	0.0180562	+	0.0946539i
$75$	0.100186	+	0.0727896i	0.0115685	+	0.00840502i
$76$	0.976136	+	0.709204i	0.111970	+	0.0813513i
$77$	3.50583	+	18.3782i	0.399526	+	2.09439i
$78$	0.231897	−	0.365411i	0.0262572	−	0.0413747i
$79$	−8.69389	+	3.44215i	−0.978139	+	0.387272i	−0.802152	−	0.597120i	$-0.796312\pi$
$79$	−8.69389	+	3.44215i	−0.978139	+	0.387272i	−0.175987	+	0.984393i	$0.556312\pi$
$80$	2.81375	−	4.43376i	0.314587	−	0.495710i
$81$	−8.76819	+	1.10768i	−0.974243	+	0.123076i
$82$	−4.24395	+	2.33313i	−0.468666	+	0.257651i
$83$	4.14726	−	1.06483i	0.455220	−	0.116881i	−0.0141156	−	0.999900i	$-0.504493\pi$
$83$	4.14726	−	1.06483i	0.455220	−	0.116881i	0.469336	+	0.883020i	$0.344493\pi$
$84$	0.0710701	−	1.12963i	0.00775439	−	0.123252i
$85$	−8.66428	+	6.29497i	−0.939774	+	0.682785i
$86$	1.27766	+	0.505861i	0.137773	+	0.0545484i
$87$	0.302070	−	0.219467i	0.0323853	−	0.0235293i
$88$	6.33355	+	3.48190i	0.675158	+	0.371171i
$89$	5.55963	−	1.42747i	0.589320	−	0.151312i	0.0577572	−	0.998331i	$-0.481605\pi$
$89$	5.55963	−	1.42747i	0.589320	−	0.151312i	0.531562	+	0.847019i	$0.321605\pi$
$90$	2.16456	−	2.03265i	0.228164	−	0.214260i
$91$	16.7865	+	26.4514i	1.75971	+	2.77286i
$92$	−4.54807	−	3.30437i	−0.474169	−	0.344504i
$93$	0.334275	+	0.710370i	0.0346627	+	0.0736620i
$94$	2.31286	−	1.27151i	0.238553	−	0.131146i
$95$	1.34334	+	0.344912i	0.137824	+	0.0353872i
$96$	−0.488415	−	0.458652i	−0.0498487	−	0.0468110i
$97$	1.06299	−	16.8958i	0.107930	−	1.71550i	−0.456249	−	0.889852i	$-0.650807\pi$
$97$	1.06299	−	16.8958i	0.107930	−	1.71550i	0.564179	−	0.825652i	$-0.309193\pi$
$98$	−6.91160	−	3.79968i	−0.698177	−	0.383826i
$99$	−8.48108	−	7.96427i	−0.852381	−	0.800439i
$100$	−0.303447	+	1.59073i	−0.0303447	+	0.159073i
$101$	0.407683	−	0.382840i	0.0405660	−	0.0380940i	−0.663999	−	0.747733i	$-0.731142\pi$
$101$	0.407683	−	0.382840i	0.0405660	−	0.0380940i	0.704565	+	0.709639i	$0.251142\pi$
$102$	0.149582	+	0.317878i	0.0148108	+	0.0314746i
$103$	−1.26197	−	6.61547i	−0.124345	−	0.651842i	−0.988814	−	0.149155i	$-0.952345\pi$
$103$	−1.26197	−	6.61547i	−0.124345	−	0.651842i	0.864468	−	0.502687i	$-0.167655\pi$
$104$	12.0068	+	1.51681i	1.17736	+	0.148735i
$105$	−0.402044	−	1.23736i	−0.0392354	−	0.120754i
$106$	−2.70470	+	0.341683i	−0.262704	+	0.0331872i
$107$	2.33542	+	4.96302i	0.225773	+	0.479793i	0.985333	−	0.170645i	$-0.0545852\pi$
$107$	2.33542	+	4.96302i	0.225773	+	0.479793i	−0.759559	+	0.650438i	$0.774585\pi$
$108$	0.756551	+	1.19213i	0.0727992	+	0.114713i
$109$	7.19111	−	8.69255i	0.688783	−	0.832596i	−0.303981	−	0.952678i	$-0.598316\pi$
$109$	7.19111	−	8.69255i	0.688783	−	0.832596i	0.992764	+	0.120083i	$0.0383159\pi$
$110$	3.85446	+	0.486931i	0.367508	+	0.0464271i
$111$	−0.209992	+	0.0831419i	−0.0199316	+	0.00789148i
$112$	11.5938	−	4.59031i	1.09551	−	0.433743i
$113$	1.89702	+	5.83843i	0.178457	+	0.549234i	0.999774	−	0.0212376i	$-0.00676063\pi$
$113$	1.89702	+	5.83843i	0.178457	+	0.549234i	−0.821318	+	0.570471i	$0.806761\pi$
$114$	0.0193711	−	0.0411657i	0.00181427	−	0.00385552i
$115$	−6.25899	−	1.60704i	−0.583654	−	0.149857i
$116$	4.27871	+	2.35224i	0.397268	+	0.218400i
$117$	−18.1132	−	7.17150i	−1.67456	−	0.663006i
$118$	−3.10819			−0.286132
$119$	−25.4308			−2.33124
$120$	−0.467300	−	0.185017i	−0.0426585	−	0.0168897i
$121$	0.265129	−	4.21410i	0.0241026	−	0.383100i
$122$	0.117497	−	0.615939i	0.0106376	−	0.0557645i
$123$	−0.841108	−	1.01672i	−0.0758401	−	0.0916750i
$124$	−6.54416	+	7.91053i	−0.587683	+	0.710386i
$125$	2.24085	+	11.7470i	0.200428	+	1.05068i
$126$	6.99532	−	0.883714i	0.623192	−	0.0787275i
$127$	−3.09261	+	6.57213i	−0.274425	+	0.583183i	−0.993767	−	0.111473i	$-0.964443\pi$
$127$	−3.09261	+	6.57213i	−0.274425	+	0.583183i	0.719343	+	0.694655i	$0.244443\pi$
$128$	3.49993	−	10.7717i	0.309353	−	0.952091i
$129$	−0.0701571	+	0.367777i	−0.00617699	+	0.0323809i
$130$	6.30103	−	1.61783i	0.552637	−	0.141893i
$131$	−15.6035	−	4.00629i	−1.36328	−	0.350031i	−0.504960	−	0.863143i	$-0.668493\pi$
$131$	−15.6035	−	4.00629i	−1.36328	−	0.350031i	−0.858322	+	0.513112i	$0.828493\pi$
$132$	−0.284574	+	0.875829i	−0.0247690	+	0.0762311i
$133$	2.09925	+	2.53756i	0.182028	+	0.220034i
$134$	−2.88867	−	4.55182i	−0.249543	−	0.393217i
$135$	1.31301	+	0.953960i	0.113006	+	0.0821038i
$136$	−6.26204	+	7.56951i	−0.536966	+	0.649080i
$137$	−0.104422	−	1.65974i	−0.00892138	−	0.141801i	−0.999966	−	0.00826880i	$-0.997368\pi$
$137$	−0.104422	−	1.65974i	−0.00892138	−	0.141801i	0.991044	−	0.133533i	$-0.0426321\pi$
$138$	−0.0902550	+	0.191802i	−0.00768301	+	0.0163272i
$139$	−5.07842	+	2.79188i	−0.430746	+	0.236804i	−0.682350	−	0.731026i	$-0.739042\pi$
$139$	−5.07842	+	2.79188i	−0.430746	+	0.236804i	0.251604	+	0.967830i	$0.419042\pi$
$140$	12.4024	−	11.6466i	1.04819	−	0.984320i
$141$	0.458386	+	0.554093i	0.0386030	+	0.0466631i
$142$	0.396152	+	6.29665i	0.0332443	+	0.528403i
$143$	−7.87661	−	24.2417i	−0.658675	−	2.02719i
$144$	−4.15480	+	6.54691i	−0.346233	+	0.545576i
$145$	5.56821	+	0.703429i	0.462415	+	0.0584166i
$146$	−0.200814	−	3.19185i	−0.0166195	−	0.264160i
$147$	0.664071	−	2.04380i	0.0547716	−	0.168570i
$148$	−2.15298	−	2.02178i	−0.176974	−	0.166190i
$149$	3.84200	−	2.79138i	0.314749	−	0.228679i	−0.419183	−	0.907902i	$-0.637683\pi$
$149$	3.84200	−	2.79138i	0.314749	−	0.228679i	0.733932	+	0.679223i	$0.237683\pi$
$150$	0.0610624			0.00498572
$151$	7.02733	−	10.0805i	0.571876	−	0.820340i
$151$	7.02733	−	10.0805i	0.571876	−	0.820340i
$152$	1.27222			0.103191
$153$	12.7937	−	9.29518i	1.03431	−	0.751471i
$154$	6.72506	+	6.31525i	0.541921	+	0.508897i
$155$	−3.64675	+	11.2235i	−0.292914	+	0.901496i
$156$	0.0968234	+	1.53896i	0.00775207	+	0.123216i
$157$	8.32810	+	1.05208i	0.664654	+	0.0839654i	0.450420	−	0.892817i	$-0.351274\pi$
$157$	8.32810	+	1.05208i	0.664654	+	0.0839654i	0.214235	+	0.976782i	$0.431274\pi$
$158$	−2.47049	+	3.89287i	−0.196542	+	0.309700i
$159$	−0.229535	−	0.706436i	−0.0182033	−	0.0560240i
$160$	−0.632380	−	10.0514i	−0.0499940	−	0.794633i
$161$	−9.78096	−	11.8231i	−0.770847	−	0.931794i
$162$	−3.17673	+	2.98315i	−0.249587	+	0.234378i
$163$	−10.5761	+	5.81424i	−0.828381	+	0.455406i	−0.838735	−	0.544540i	$-0.816704\pi$
$163$	−10.5761	+	5.81424i	−0.828381	+	0.455406i	0.0103538	+	0.999946i	$0.496704\pi$
$164$	7.34706	−	15.6133i	0.573709	−	1.21919i
$165$	0.0664668	+	1.05646i	0.00517444	+	0.0822453i
$166$	1.34578	−	1.62677i	0.104453	−	0.126262i
$167$	7.51188	+	5.45770i	0.581287	+	0.422329i	0.839188	−	0.543842i	$-0.183031\pi$
$167$	7.51188	+	5.45770i	0.581287	+	0.422329i	−0.257901	+	0.966171i	$0.583031\pi$
$168$	−0.639481	−	1.00766i	−0.0493370	−	0.0777427i
$169$	−18.9191	−	22.8693i	−1.45532	−	1.75917i
$170$	−1.63185	+	5.02232i	−0.125157	+	0.385194i
$171$	−1.98359	−	0.509299i	−0.151689	−	0.0389471i
$172$	−4.74229	+	1.21761i	−0.361597	+	0.0928422i
$173$	−0.885892	+	4.64401i	−0.0673531	+	0.353077i	−0.999970	−	0.00779151i	$-0.997520\pi$
$173$	−0.885892	+	4.64401i	−0.0673531	+	0.353077i	0.932617	+	0.360869i	$0.117520\pi$
$174$	0.0568926	−	0.175097i	0.00431302	−	0.0132741i
$175$	−1.88202	+	3.99950i	−0.142267	+	0.302334i
$176$	−10.0653	+	1.27155i	−0.758704	+	0.0958466i
$177$	−0.158688	−	0.831870i	−0.0119277	−	0.0625272i
$178$	1.80410	−	2.18078i	0.135223	−	0.163457i
$179$	0.864533	+	1.04504i	0.0646183	+	0.0781101i	0.801832	−	0.597550i	$-0.203859\pi$
$179$	0.864533	+	1.04504i	0.0646183	+	0.0781101i	−0.737214	+	0.675660i	$0.763859\pi$
$180$	−1.98245	+	10.3924i	−0.147763	+	0.774600i
$181$	0.690468	−	10.9747i	0.0513221	−	0.815742i	−0.885217	−	0.465178i	$-0.845990\pi$
$181$	0.690468	−	10.9747i	0.0513221	−	0.815742i	0.936539	−	0.350563i	$-0.114010\pi$
$182$	14.3628	+	5.68663i	1.06464	+	0.421521i
$183$	0.170847			0.0126294
$184$	−5.92761			−0.436989
$185$	−3.15651	−	1.24975i	−0.232071	−	0.0918836i
$186$	0.339233	+	0.186495i	0.0248738	+	0.0136745i
$187$	20.0409	+	5.14563i	1.46554	+	0.376286i
$188$	−4.00399	+	8.50892i	−0.292021	+	0.620577i
$189$	1.19091	+	3.66525i	0.0866261	+	0.266608i
$190$	0.635846	−	0.251749i	0.0461291	−	0.0182638i
$191$	−13.1552	+	5.20852i	−0.951878	+	0.376875i	−0.792178	−	0.610290i	$-0.791053\pi$
$191$	−13.1552	+	5.20852i	−0.951878	+	0.376875i	−0.159700	+	0.987166i	$0.551053\pi$
$192$	0.365418	+	0.0461630i	0.0263718	+	0.00333153i
$193$	−3.36390	+	4.06626i	−0.242139	+	0.292696i	−0.877557	−	0.479473i	$-0.840828\pi$
$193$	−3.36390	+	4.06626i	−0.242139	+	0.292696i	0.635418	+	0.772169i	$0.280828\pi$
$194$	−4.47284	−	7.04806i	−0.321131	−	0.506022i
$195$	0.754690	+	1.60380i	0.0540445	+	0.114850i
$196$	27.8805	−	3.52212i	1.99146	−	0.251580i
$197$	8.38076	+	25.7933i	0.597105	+	1.83770i	0.543959	+	0.839112i	$0.316925\pi$
$197$	8.38076	+	25.7933i	0.597105	+	1.83770i	0.0531458	+	0.998587i	$0.483075\pi$
$198$	−5.69151	−	0.719005i	−0.404478	−	0.0510974i
$199$	2.23405	+	11.7113i	0.158368	+	0.830194i	0.969455	+	0.245269i	$0.0788762\pi$
$199$	2.23405	+	11.7113i	0.158368	+	0.830194i	−0.811087	+	0.584925i	$0.801124\pi$
$200$	0.727028	+	1.54501i	0.0514087	+	0.109249i
$201$	1.07076	−	1.00551i	0.0755256	−	0.0709232i
$202$	0.0516730	−	0.270879i	0.00363570	−	0.0190590i
$203$	9.71513	+	9.12311i	0.681868	+	0.640317i
$204$	−1.09690	−	0.603024i	−0.0767981	−	0.0422201i
$205$	1.24544	−	19.7956i	0.0869850	−	1.38259i
$206$	−2.42077	−	2.27326i	−0.168663	−	0.158385i
$207$	9.24205	+	2.37296i	0.642367	+	0.164932i
$208$	−14.8866	+	8.18399i	−1.03220	+	0.567457i
$209$	−1.14088	−	2.42450i	−0.0789164	−	0.167706i
$210$	−0.519005	−	0.377079i	−0.0358148	−	0.0260209i
$211$	0.219273	+	0.345519i	0.0150954	+	0.0237865i	0.851792	−	0.523880i	$-0.175516\pi$
$211$	0.219273	+	0.345519i	0.0150954	+	0.0237865i	−0.836696	+	0.547667i	$0.815516\pi$
$212$	7.08078	−	6.64930i	0.486310	−	0.456676i
$213$	−1.66500	+	0.427499i	−0.114084	+	0.0292917i
$214$	2.37006	+	1.30295i	0.162014	+	0.0890680i
$215$	−4.55310	+	3.30802i	−0.310519	+	0.225605i
$216$	1.38421	+	0.548048i	0.0941837	+	0.0372900i
$217$	−22.6708	+	16.4713i	−1.53899	+	1.11814i
$218$	0.349289	−	5.55178i	0.0236568	−	0.376014i
$219$	0.844008	−	0.216705i	0.0570328	−	0.0146435i
$220$	−12.1303	+	6.66871i	−0.817827	+	0.449604i
$221$	34.3729	−	4.34230i	2.31217	−	0.292095i
$222$	−0.0596723	+	0.0940285i	−0.00400494	+	0.00631078i
$223$	0.610048	−	0.241535i	0.0408518	−	0.0161744i	−0.347610	−	0.937639i	$-0.613007\pi$
$223$	0.610048	−	0.241535i	0.0408518	−	0.0161744i	0.388462	+	0.921465i	$0.373007\pi$
$224$	12.8143	−	20.1921i	0.856190	−	1.34914i
$225$	−0.515045	−	2.69996i	−0.0343363	−	0.179997i
$226$	2.44890	+	1.77923i	0.162898	+	0.118353i
$227$	15.5827	+	11.3215i	1.03426	+	0.751435i	0.969157	−	0.246443i	$-0.0792619\pi$
$227$	15.5827	+	11.3215i	1.03426	+	0.751435i	0.0651047	+	0.997878i	$0.479262\pi$
$228$	0.0303747	+	0.159230i	0.00201161	+	0.0105452i
$229$	−0.705865	+	1.11227i	−0.0466449	+	0.0735006i	−0.866850	−	0.498569i	$-0.833859\pi$
$229$	−0.705865	+	1.11227i	−0.0466449	+	0.0735006i	0.820205	+	0.572069i	$0.193859\pi$
$230$	−2.96257	+	1.17297i	−0.195346	+	0.0773431i
$231$	−1.34686	+	2.12230i	−0.0886166	+	0.139637i
$232$	5.10774	−	0.645257i	0.335339	−	0.0423632i
$233$	−25.0477	+	13.7701i	−1.64093	+	0.902108i	−0.651240	+	0.758872i	$0.725751\pi$
$233$	−25.0477	+	13.7701i	−1.64093	+	0.902108i	−0.989689	+	0.143236i	$0.954249\pi$
$234$	−9.30413	+	2.38889i	−0.608230	+	0.156167i
$235$	−0.678736	+	10.7882i	−0.0442758	+	0.703744i
$236$	8.95944	−	6.50941i	0.583210	−	0.423727i
$237$	−1.16801	−	0.462448i	−0.0758704	−	0.0300392i
$238$	−10.1448	+	7.37059i	−0.657587	+	0.477765i
$239$	14.1875	+	7.79962i	0.917711	+	0.504516i	0.869285	−	0.494311i	$-0.164580\pi$
$239$	14.1875	+	7.79962i	0.917711	+	0.504516i	0.0484255	+	0.998827i	$0.484580\pi$
$240$	0.683330	−	0.175449i	0.0441088	−	0.0113252i
$241$	−3.97255	+	3.73047i	−0.255894	+	0.240301i	−0.801867	−	0.597502i	$-0.796160\pi$
$241$	−3.97255	+	3.73047i	−0.255894	+	0.240301i	0.545973	+	0.837803i	$0.316160\pi$
$242$	−1.11560	−	1.75791i	−0.0717137	−	0.113003i
$243$	−2.91113	−	2.11506i	−0.186749	−	0.135681i
$244$	0.951259	+	2.02153i	0.0608981	+	0.129415i
$245$	28.3069	−	15.5618i	1.80846	−	0.994209i
$246$	−0.630207	−	0.161810i	−0.0401805	−	0.0103166i
$247$	−3.27068	−	3.07137i	−0.208108	−	0.195427i
$248$	−0.679719	+	10.8038i	−0.0431622	+	0.686044i
$249$	0.504095	+	0.277129i	0.0319457	+	0.0175623i
$250$	4.29852	+	4.03658i	0.271862	+	0.255296i
$251$	0.598794	−	3.13899i	0.0377955	−	0.198131i	−0.958381	−	0.285491i	$-0.907843\pi$
$251$	0.598794	−	3.13899i	0.0377955	−	0.198131i	0.996177	+	0.0873604i	$0.0278432\pi$
$252$	−18.3134	+	17.1975i	−1.15364	+	1.08334i
$253$	5.31566	+	11.2964i	0.334193	+	0.710196i
$254$	0.671105	+	3.51805i	0.0421089	+	0.220742i
$255$	−1.42748	−	0.180332i	−0.0893921	−	0.0112929i
$256$	−0.0314000	−	0.0966394i	−0.00196250	−	0.00603996i
$257$	−1.98132	+	0.250299i	−0.123591	+	0.0156132i	−0.186885	−	0.982382i	$-0.559839\pi$
$257$	−1.98132	+	0.250299i	−0.123591	+	0.0156132i	0.0632943	+	0.997995i	$0.479839\pi$
$258$	0.0786056	+	0.167045i	0.00489377	+	0.0103998i
$259$	−4.31956	−	6.80653i	−0.268404	−	0.422937i
$260$	−14.7747	+	17.8595i	−0.916287	+	1.10760i
$261$	−8.22205	−	1.03869i	−0.508932	−	0.0642931i
$262$	−7.38560	+	2.92417i	−0.456284	+	0.180656i
$263$	−12.4684	+	4.93658i	−0.768833	+	0.304403i	−0.719604	−	0.694385i	$-0.755677\pi$
$263$	−12.4684	+	4.93658i	−0.768833	+	0.304403i	−0.0492293	+	0.998788i	$0.515677\pi$
$264$	0.300058	+	0.923485i	0.0184673	+	0.0568365i
$265$	4.75395	−	10.1027i	0.292033	−	0.620602i
$266$	1.57288	+	0.403847i	0.0964396	+	0.0247615i
$267$	0.675768	+	0.371507i	0.0413563	+	0.0227358i
$268$	17.8594	+	7.07105i	1.09094	+	0.431933i
$269$	21.1952			1.29229			0.646146	−	0.763214i	$-0.276380\pi$
$269$	21.1952			1.29229			0.646146	+	0.763214i	$0.276380\pi$
$270$	0.800267			0.0487027
$271$	−7.17740	−	2.84173i	−0.435996	−	0.172623i	0.139865	−	0.990171i	$-0.455333\pi$
$271$	−7.17740	−	2.84173i	−0.435996	−	0.172623i	−0.575861	+	0.817547i	$0.695333\pi$
$272$	0.865880	−	13.7628i	0.0525017	−	0.834490i
$273$	−0.788671	+	4.13436i	−0.0477325	+	0.250223i
$274$	−0.522697	−	0.631832i	−0.0315773	−	0.0381704i
$275$	2.29239	−	2.77102i	0.138236	−	0.167099i
$276$	−0.141523	−	0.741892i	−0.00851871	−	0.0446566i
$277$	−12.0668	+	1.52439i	−0.725025	+	0.0915919i	−0.479179	−	0.877717i	$-0.659066\pi$
$277$	−12.0668	+	1.52439i	−0.725025	+	0.0915919i	−0.245845	+	0.969309i	$0.579066\pi$
$278$	−1.21669	+	2.58560i	−0.0729722	+	0.155074i
$279$	5.38480	−	16.5727i	0.322380	−	0.992182i
$280$	3.36150	−	17.6216i	0.200888	−	1.05309i
$281$	2.16613	−	0.556168i	0.129220	−	0.0331782i	−0.183526	−	0.983015i	$-0.558751\pi$
$281$	2.16613	−	0.556168i	0.129220	−	0.0331782i	0.312746	+	0.949837i	$0.398751\pi$
$282$	0.343449	+	0.0881828i	0.0204521	+	0.00525121i
$283$	2.61847	−	8.05882i	0.155652	−	0.479047i	−0.842575	−	0.538580i	$-0.818961\pi$
$283$	2.61847	−	8.05882i	0.155652	−	0.479047i	0.998226	+	0.0595328i	$0.0189611\pi$
$284$	−14.3288	−	17.3206i	−0.850260	−	1.02779i
$285$	0.0998406	+	0.157324i	0.00591405	+	0.00931905i
$286$	−10.1681	−	7.38752i	−0.601250	−	0.436833i
$287$	30.0221	−	36.2905i	1.77215	−	2.14216i
$288$	0.933775	+	14.8419i	0.0550232	+	0.874569i
$289$	−4.73637	+	10.0653i	−0.278610	+	0.592077i
$290$	2.42512	−	1.33322i	0.142408	−	0.0782895i
$291$	1.65797	−	1.55694i	0.0971920	−	0.0912693i
$292$	7.26347	+	8.78003i	0.425063	+	0.513812i
$293$	−1.65618	−	26.3242i	−0.0967551	−	1.53788i	−0.684609	−	0.728911i	$-0.740027\pi$
$293$	−1.65618	−	26.3242i	−0.0967551	−	1.53788i	0.587854	−	0.808967i	$-0.299973\pi$
$294$	−0.327444	−	1.00777i	−0.0190969	−	0.0587743i
$295$	6.82096	−	10.7481i	0.397132	−	0.625779i
$296$	−3.08961	−	0.390308i	−0.179580	−	0.0226862i
$297$	−0.196884	−	3.12939i	−0.0114244	−	0.181586i
$298$	0.723611	−	2.22705i	0.0419177	−	0.129009i
$299$	15.2389	+	14.3103i	0.881291	+	0.827587i
$300$	−0.176014	+	0.127882i	−0.0101622	+	0.00738324i
$301$	−13.3640			−0.770286
$302$	−0.118312	−	6.05799i	−0.00680808	−	0.348598i
$303$	0.0751357			0.00431644
$304$	−1.44476	+	1.04968i	−0.0828628	+	0.0602034i
$305$	1.87207	+	1.75799i	0.107194	+	0.100662i
$306$	2.40960	−	7.41598i	0.137748	−	0.423943i
$307$	0.812766	+	12.9186i	0.0463870	+	0.737301i	0.950639	+	0.310301i	$0.100430\pi$
$307$	0.812766	+	12.9186i	0.0463870	+	0.737301i	−0.904251	+	0.427000i	$0.859570\pi$
$308$	−32.6110	−	4.11973i	−1.85819	−	0.234743i
$309$	0.484819	−	0.763952i	0.0275804	−	0.0434597i
$310$	1.79816	+	5.53417i	0.102129	+	0.314320i
$311$	−2.05432	−	32.6526i	−0.116490	−	1.85156i	−0.431061	−	0.902323i	$-0.641861\pi$
$311$	−2.05432	−	32.6526i	−0.116490	−	1.85156i	0.314571	−	0.949234i	$-0.398139\pi$
$312$	1.03639	+	1.25278i	0.0586742	+	0.0709250i
$313$	−8.62744	+	8.10171i	−0.487652	+	0.457935i	−0.888945	−	0.458014i	$-0.848561\pi$
$313$	−8.62744	+	8.10171i	−0.487652	+	0.457935i	0.401293	+	0.915950i	$0.368561\pi$
$314$	3.62713	−	1.99403i	0.204691	−	0.112530i
$315$	−12.2954	+	26.1291i	−0.692768	+	1.47221i
$316$	−1.03150	−	16.3952i	−0.0580262	−	0.922301i
$317$	−17.5239	+	21.1828i	−0.984242	+	1.18974i	−0.00240918	+	0.999997i	$0.500767\pi$
$317$	−17.5239	+	21.1828i	−0.984242	+	1.18974i	−0.981833	+	0.189747i	$0.939233\pi$
$318$	−0.296311	−	0.215282i	−0.0166163	−	0.0120724i
$319$	−5.81011	−	9.15526i	−0.325304	−	0.512596i
$320$	3.52907	+	4.26591i	0.197281	+	0.238472i
$321$	−0.227717	+	0.700840i	−0.0127099	+	0.0391171i
$322$	−7.32847	−	1.88163i	−0.408399	−	0.104859i
$323$	3.52768	−	0.905755i	0.196286	−	0.0503976i
$324$	2.90946	−	15.2519i	0.161637	−	0.847330i
$325$	1.86087	−	5.72716i	0.103222	−	0.317686i
$326$	−2.53382	+	5.38464i	−0.140335	+	0.298228i
$327$	1.50370	−	0.189962i	0.0831549	−	0.0105049i
$328$	−3.40930	−	17.8722i	−0.188247	−	0.986827i
$329$	−16.3614	+	19.7775i	−0.902034	+	1.09037i
$330$	0.332707	+	0.402174i	0.0183149	+	0.0221390i
$331$	1.27538	−	6.68577i	0.0701011	−	0.367483i	−0.929899	−	0.367815i	$-0.880106\pi$
$331$	1.27538	−	6.68577i	0.0701011	−	0.367483i	1.00000		0.000332398i	$0.000105806\pi$
$332$	−0.472342	+	7.50766i	−0.0259231	+	0.412036i
$333$	4.66092	+	1.84539i	0.255417	+	0.101127i
$334$	4.57840			0.250519
$335$	22.0794			1.20633
$336$	1.55761	+	0.616700i	0.0849744	+	0.0336438i
$337$	13.1205	+	7.21305i	0.714718	+	0.392920i	0.797234	−	0.603670i	$-0.206296\pi$
$337$	13.1205	+	7.21305i	0.714718	+	0.392920i	−0.0825161	+	0.996590i	$0.526296\pi$
$338$	−14.1753	−	3.63960i	−0.771034	−	0.197968i
$339$	−0.351162	+	0.746256i	−0.0190725	+	0.0405311i
$340$	−5.81428	−	17.8945i	−0.315324	−	0.970466i
$341$	21.1986	−	8.39312i	1.14797	−	0.454513i
$342$	−0.938893	+	0.371734i	−0.0507695	+	0.0201011i
$343$	42.7969	+	5.40650i	2.31081	+	0.291924i
$344$	−3.29072	+	3.97779i	−0.177423	+	0.214468i
$345$	−0.465183	−	0.733012i	−0.0250446	−	0.0394640i
$346$	0.992573	+	2.10932i	0.0533610	+	0.113398i
$347$	−18.2237	+	2.30219i	−0.978302	+	0.123588i	−0.598192	−	0.801353i	$-0.704114\pi$
$347$	−18.2237	+	2.30219i	−0.978302	+	0.123588i	−0.380110	+	0.924941i	$0.624114\pi$
$348$	0.202708	+	0.623871i	0.0108663	+	0.0334430i
$349$	−13.2741	−	1.67691i	−0.710545	−	0.0897627i	−0.238251	−	0.971204i	$-0.576574\pi$
$349$	−13.2741	−	1.67691i	−0.710545	−	0.0897627i	−0.472294	+	0.881441i	$0.656574\pi$
$350$	0.408404	+	2.14093i	0.0218301	+	0.114437i
$351$	−2.23550	−	4.75068i	−0.119322	−	0.253573i
$352$	−14.1840	+	13.3197i	−0.756010	+	0.709940i
$353$	5.60679	−	29.3918i	0.298419	−	1.56437i	−0.444992	−	0.895534i	$-0.646794\pi$
$353$	5.60679	−	29.3918i	0.298419	−	1.56437i	0.743411	−	0.668834i	$-0.233206\pi$
$354$	−0.304403	−	0.285854i	−0.0161788	−	0.0151929i
$355$	−22.6431	−	12.4482i	−1.20177	−	0.660680i
$356$	−0.633201	+	10.0644i	−0.0335596	+	0.533414i
$357$	−2.49059	−	2.33882i	−0.131816	−	0.123783i
$358$	0.647759	+	0.166316i	0.0342351	+	0.00879009i
$359$	−8.43410	+	4.63668i	−0.445135	+	0.244715i	−0.688524	−	0.725214i	$-0.741741\pi$
$359$	−8.43410	+	4.63668i	−0.445135	+	0.244715i	0.243389	+	0.969929i	$0.421741\pi$
$360$	4.74974	+	10.0937i	0.250333	+	0.531986i
$361$	14.9897	+	10.8907i	0.788934	+	0.573194i
$362$	−2.90534	−	4.57809i	−0.152701	−	0.240619i
$363$	0.413527	−	0.388328i	0.0217045	−	0.0203819i
$364$	−53.3105	+	13.6878i	−2.79423	+	0.717436i
$365$	11.4781	+	6.31014i	0.600791	+	0.330288i
$366$	0.0681536	−	0.0495165i	0.00356245	−	0.00258827i
$367$	−17.1856	−	6.80425i	−0.897079	−	0.355179i	−0.126084	−	0.992020i	$-0.540241\pi$
$367$	−17.1856	−	6.80425i	−0.897079	−	0.355179i	−0.770995	+	0.636841i	$0.780241\pi$
$368$	6.73152	−	4.89074i	0.350905	−	0.254947i
$369$	−1.83901	+	29.2303i	−0.0957353	+	1.52167i
$370$	−1.62140	+	0.416304i	−0.0842924	+	0.0216426i
$371$	23.2334	−	12.7726i	1.20622	−	0.663123i
$372$	−1.36842	+	0.172872i	−0.0709493	+	0.00896298i
$373$	−7.32658	+	11.5448i	−0.379356	+	0.597769i	−0.979335	−	0.202247i	$-0.935176\pi$
$373$	−7.32658	+	11.5448i	−0.379356	+	0.597769i	0.599979	+	0.800016i	$0.295176\pi$
$374$	9.48598	−	3.75577i	0.490509	−	0.194206i
$375$	−0.860883	+	1.35653i	−0.0444558	+	0.0700511i
$376$	1.85800	+	9.73997i	0.0958190	+	0.502301i
$377$	−14.6889	−	10.6721i	−0.756519	−	0.549643i
$378$	1.53737	+	1.11696i	0.0790737	+	0.0574504i
$379$	−4.41755	−	23.1576i	−0.226914	−	1.18953i	−0.895215	−	0.445635i	$-0.852978\pi$
$379$	−4.41755	−	23.1576i	−0.226914	−	1.18953i	0.668300	−	0.743892i	$-0.267022\pi$
$380$	−1.30561	+	2.05731i	−0.0669764	+	0.105538i
$381$	−0.907302	+	0.359226i	−0.0464825	+	0.0184037i
$382$	−3.73824	+	5.89052i	−0.191265	+	0.301385i
$383$	3.33228	−	0.420965i	0.170272	−	0.0215103i	−0.0397352	−	0.999210i	$-0.512651\pi$
$383$	3.33228	−	0.420965i	0.170272	−	0.0215103i	0.210007	+	0.977700i	$0.432651\pi$
$384$	1.33342	−	0.733052i	0.0680456	−	0.0374084i
$385$	−36.5963	+	9.39633i	−1.86512	+	0.478882i
$386$	−0.163393	+	2.59705i	−0.00831646	+	0.132186i
$387$	6.72312	−	4.88464i	0.341756	−	0.248300i
$388$	27.6537	+	10.9489i	1.40390	+	0.555844i
$389$	−6.60144	+	4.79623i	−0.334706	+	0.243178i	−0.742425	−	0.669929i	$-0.766324\pi$
$389$	−6.60144	+	4.79623i	−0.334706	+	0.243178i	0.407719	+	0.913108i	$0.366324\pi$
$390$	0.765884	+	0.421048i	0.0387821	+	0.0213206i
$391$	−16.4364	+	4.22015i	−0.831224	+	0.213422i
$392$	21.6002	−	20.2839i	1.09097	−	1.02449i
$393$	−1.15969	−	1.82738i	−0.0584985	−	0.0921789i
$394$	10.8189	+	7.86037i	0.545047	+	0.396000i
$395$	−8.04000	−	17.0859i	−0.404536	−	0.859684i
$396$	17.9117	−	9.84705i	0.900097	−	0.494833i
$397$	35.1105	+	9.01485i	1.76215	+	0.452443i	0.984372	−	0.176100i	$-0.0563482\pi$
$397$	35.1105	+	9.01485i	1.76215	+	0.452443i	0.777775	+	0.628543i	$0.216348\pi$
$398$	4.28548	+	4.02433i	0.214812	+	0.201722i
$399$	−0.0277819	+	0.441581i	−0.00139084	+	0.0221067i
$400$	−2.10039	−	1.15470i	−0.105019	−	0.0577348i
$401$	0.0402351	+	0.0377833i	0.00200925	+	0.00188681i	0.685551	−	0.728025i	$-0.259561\pi$
$401$	0.0402351	+	0.0377833i	0.00200925	+	0.00188681i	−0.683542	+	0.729911i	$0.739561\pi$
$402$	0.135717	−	0.711451i	0.00676893	−	0.0354839i
$403$	27.8298	−	26.1340i	1.38630	−	1.30183i
$404$	0.418348	+	0.889034i	0.0208136	+	0.0442311i
$405$	−3.34434	−	17.5317i	−0.166182	−	0.871155i
$406$	6.51966	+	0.823624i	0.323565	+	0.0408758i
$407$	2.02683	+	6.23794i	0.100466	+	0.309203i
$408$	−1.30943	+	0.165419i	−0.0648264	+	0.00818948i
$409$	5.58823	+	11.8756i	0.276320	+	0.587210i	0.994027	−	0.109135i	$-0.0348081\pi$
$409$	5.58823	+	11.8756i	0.276320	+	0.587210i	−0.717707	+	0.696346i	$0.754808\pi$
$410$	−5.24052	−	8.25774i	−0.258811	−	0.407821i
$411$	0.142416	−	0.172152i	0.00702487	−	0.00849161i
$412$	11.7388	+	1.48295i	0.578328	+	0.0730598i
$413$	28.1051	−	11.1276i	1.38296	−	0.547553i
$414$	4.37455	−	1.73201i	0.214997	−	0.0851234i
$415$	2.67204	+	8.22369i	0.131165	+	0.403685i
$416$	−13.8723	+	29.4801i	−0.680144	+	1.44538i
$417$	−0.754122	−	0.193626i	−0.0369295	−	0.00948189i
$418$	−1.15780	−	0.636509i	−0.0566301	−	0.0311327i
$419$	24.4709	+	9.68871i	1.19548	+	0.473325i	0.879710	−	0.475511i	$-0.157737\pi$
$419$	24.4709	+	9.68871i	1.19548	+	0.473325i	0.315772	+	0.948835i	$0.397737\pi$
$420$	2.28575			0.111533
$421$	−23.0124			−1.12156			−0.560778	−	0.827966i	$-0.689498\pi$
$421$	−23.0124			−1.12156			−0.560778	+	0.827966i	$0.689498\pi$
$422$	0.187613	+	0.0742812i	0.00913285	+	0.00361595i
$423$	1.00222	−	15.9299i	0.0487298	−	0.774538i
$424$	1.91915	−	10.0605i	0.0932022	−	0.488583i
$425$	3.11591	+	3.76649i	0.151144	+	0.182702i
$426$	−0.540292	+	0.653100i	−0.0261772	+	0.0316428i
$427$	1.14268	+	5.99013i	0.0552981	+	0.289883i
$428$	−9.56050	+	1.20777i	−0.462124	+	0.0583799i
$429$	1.45806	−	3.09853i	0.0703956	−	0.149598i
$430$	−0.857541	+	2.63924i	−0.0413543	+	0.127275i
$431$	−3.76474	+	19.7355i	−0.181341	+	0.950624i	0.768961	+	0.639296i	$0.220774\pi$
$431$	−3.76474	+	19.7355i	−0.181341	+	0.950624i	−0.950302	+	0.311328i	$0.899226\pi$
$432$	−2.02412	+	0.519707i	−0.0973857	+	0.0250044i
$433$	22.9235	+	5.88575i	1.10163	+	0.282851i	0.755378	−	0.655289i	$-0.227453\pi$
$433$	22.9235	+	5.88575i	1.10163	+	0.282851i	0.346255	+	0.938141i	$0.387453\pi$
$434$	−4.26987	+	13.1413i	−0.204960	+	0.630803i
$435$	0.480635	+	0.580987i	0.0230447	+	0.0278562i
$436$	10.6201	+	16.7347i	0.508612	+	0.801445i
$437$	1.77788	+	1.29171i	0.0850476	+	0.0617907i
$438$	0.273881	−	0.331065i	0.0130865	−	0.0158189i
$439$	−0.413432	−	6.57132i	−0.0197320	−	0.313632i	−0.995496	−	0.0948054i	$-0.969777\pi$
$439$	−0.413432	−	6.57132i	−0.0197320	−	0.313632i	0.975764	−	0.218827i	$-0.0702229\pi$
$440$	−6.21458	+	13.2067i	−0.296268	+	0.629602i
$441$	−41.7980	+	22.9787i	−1.99038	+	1.09422i
$442$	12.4533	−	11.6945i	0.592345	−	0.556249i
$443$	−7.48456	−	9.04728i	−0.355602	−	0.429849i	0.562130	−	0.827049i	$-0.309982\pi$
$443$	−7.48456	−	9.04728i	−0.355602	−	0.429849i	−0.917732	+	0.397200i	$0.869982\pi$
$444$	−0.0249148	−	0.396010i	−0.00118241	−	0.0187938i
$445$	3.58202	+	11.0243i	0.169804	+	0.522603i
$446$	0.173354	−	0.273161i	0.00820853	−	0.0129346i
$447$	0.632986	+	0.0799648i	0.0299392	+	0.00378220i
$448$	0.825490	+	13.1208i	0.0390007	+	0.619899i
$449$	−2.40464	+	7.40071i	−0.113482	+	0.349261i	−0.991627	−	0.129133i	$-0.958781\pi$
$449$	−2.40464	+	7.40071i	−0.113482	+	0.349261i	0.878146	+	0.478394i	$0.158781\pi$
$450$	−0.987985	−	0.927780i	−0.0465741	−	0.0437360i
$451$	−31.0020	+	22.5243i	−1.45983	+	1.06063i
$452$	−10.7852			−0.507294
$453$	1.61531	−	0.340954i	0.0758938	−	0.0160194i
$454$	9.49749			0.445739
$455$	−51.1836	+	37.1871i	−2.39953	+	1.74336i
$456$	0.124596	+	0.117003i	0.00583474	+	0.00547919i
$457$	−3.71088	+	11.4209i	−0.173587	+	0.534247i	−0.999566	−	0.0294540i	$-0.990623\pi$
$457$	−3.71088	+	11.4209i	−0.173587	+	0.534247i	0.825979	+	0.563701i	$0.190623\pi$
$458$	0.0407863	+	0.648280i	0.00190582	+	0.0302921i
$459$	4.22840	+	0.534171i	0.197365	+	0.0249330i
$460$	6.08318	−	9.58555i	0.283630	−	0.446929i
$461$	−8.59335	−	26.4476i	−0.400232	−	1.23179i	−0.924811	−	0.380426i	$-0.875777\pi$
$461$	−8.59335	−	26.4476i	−0.400232	−	1.23179i	0.524579	−	0.851362i	$-0.324223\pi$
$462$	0.0778240	+	1.23698i	0.00362070	+	0.0575494i
$463$	−11.4756	−	13.8716i	−0.533315	−	0.644667i	0.433194	−	0.901301i	$-0.357387\pi$
$463$	−11.4756	−	13.8716i	−0.533315	−	0.644667i	−0.966509	+	0.256634i	$0.917387\pi$
$464$	−5.26807	+	4.94704i	−0.244564	+	0.229661i
$465$	−1.38935	+	0.763802i	−0.0644296	+	0.0354205i
$466$	−6.00094	+	12.7526i	−0.277988	+	0.590755i
$467$	1.20998	+	19.2320i	0.0559910	+	0.889952i	0.921334	+	0.388772i	$0.127101\pi$
$467$	1.20998	+	19.2320i	0.0559910	+	0.889952i	−0.865343	+	0.501180i	$0.832899\pi$
$468$	21.8164	−	26.3715i	1.00846	−	1.21902i
$469$	42.4161	+	30.8171i	1.95859	+	1.42300i
$470$	2.85597	+	4.50029i	0.131736	+	0.207583i
$471$	0.718861	+	0.868953i	0.0331234	+	0.0400393i
$472$	3.60841	−	11.1055i	0.166090	−	0.511174i
$473$	10.5315	+	2.70404i	0.484241	+	0.124332i
$474$	−0.599968	+	0.154046i	−0.0275574	+	0.00707555i
$475$	0.118620	−	0.621829i	0.00544267	−	0.0285314i
$476$	13.8064	−	42.4918i	0.632817	−	1.94761i
$477$	−7.01970	+	14.9176i	−0.321410	+	0.683031i
$478$	7.92015	−	1.00055i	0.362259	−	0.0457640i
$479$	−3.35410	−	17.5828i	−0.153253	−	0.803379i	−0.973027	−	0.230692i	$-0.925901\pi$
$479$	−3.35410	−	17.5828i	−0.153253	−	0.803379i	0.819774	−	0.572687i	$-0.194099\pi$
$480$	0.862472	−	1.04255i	0.0393663	−	0.0475857i
$481$	7.00061	+	8.46229i	0.319201	+	0.385847i
$482$	−0.503512	+	2.63950i	−0.0229343	+	0.120226i
$483$	0.129443	−	2.05744i	0.00588987	−	0.0936169i
$484$	6.89731	+	2.73084i	0.313514	+	0.124129i
$485$	34.1879			1.55239
$486$	−1.77430			−0.0804838
$487$	−37.2737	−	14.7577i	−1.68903	−	0.668735i	−0.690523	−	0.723311i	$-0.742619\pi$
$487$	−37.2737	−	14.7577i	−1.68903	−	0.668735i	−0.998510	+	0.0545755i	$0.982619\pi$
$488$	2.06434	+	1.13488i	0.0934482	+	0.0513736i
$489$	−1.57050	−	0.403235i	−0.0710203	−	0.0182349i
$490$	6.78178	−	14.4120i	0.306369	−	0.651068i
$491$	5.44764	+	16.7661i	0.245849	+	0.756644i	0.995496	+	0.0948065i	$0.0302232\pi$
$491$	5.44764	+	16.7661i	0.245849	+	0.756644i	−0.749647	+	0.661838i	$0.769777\pi$
$492$	2.15546	−	0.853408i	0.0971757	−	0.0384746i
$493$	13.7036	−	5.42564i	0.617179	−	0.244359i
$494$	−2.19490	−	0.277280i	−0.0987531	−	0.0124754i
$495$	14.9764	−	18.1033i	0.673139	−	0.813685i
$496$	−8.14209	−	12.8299i	−0.365591	−	0.576079i
$497$	−26.1247	−	55.5177i	−1.17185	−	2.49031i
$498$	0.281411	−	0.0355505i	0.0126103	−	0.00159306i
$499$	−7.41486	−	22.8206i	−0.331935	−	1.02159i	−0.968212	−	0.250130i	$-0.919527\pi$
$499$	−7.41486	−	22.8206i	−0.331935	−	1.02159i	0.636277	−	0.771460i	$-0.280473\pi$
$500$	−20.8443	−	2.63325i	−0.932186	−	0.117762i
$501$	0.233749	+	1.22535i	0.0104431	+	0.0547448i
$502$	−0.670901	−	1.42574i	−0.0299438	−	0.0636338i
$503$	−8.52909	+	8.00935i	−0.380293	+	0.357119i	−0.850996	−	0.525173i	$-0.824001\pi$
$503$	−8.52909	+	8.00935i	−0.380293	+	0.357119i	0.470702	+	0.882292i	$0.344001\pi$
$504$	−4.96361	+	26.0201i	−0.221097	+	1.15903i
$505$	0.823302	+	0.773132i	0.0366365	+	0.0344039i
$506$	5.39451	+	2.96566i	0.239815	+	0.131840i
$507$	0.250379	−	3.97967i	0.0111197	−	0.176743i
$508$	−9.30225	−	8.73540i	−0.412721	−	0.387571i
$509$	22.1944	+	5.69856i	0.983751	+	0.252584i	0.706111	−	0.708101i	$-0.250448\pi$
$509$	22.1944	+	5.69856i	0.983751	+	0.252584i	0.277640	+	0.960685i	$0.410448\pi$
$510$	−0.621708	+	0.341787i	−0.0275297	+	0.0151346i
$511$	13.2429	+	28.1426i	0.585832	+	1.24496i
$512$	18.2853	+	13.2851i	0.808105	+	0.587123i
$513$	−0.295743	−	0.466016i	−0.0130574	−	0.0205751i
$514$	−0.717834	+	0.674091i	−0.0316623	+	0.0297329i
$515$	13.1733	−	3.38234i	0.580486	−	0.149044i
$516$	−0.576422	−	0.316890i	−0.0253755	−	0.0139503i
$517$	16.8955	−	12.2753i	0.743061	−	0.539866i
$518$	−3.69587	−	1.46330i	−0.162387	−	0.0642936i
$519$	−0.513860	+	0.373341i	−0.0225559	+	0.0163879i
$520$	−1.53460	+	24.3917i	−0.0672965	+	1.06965i
$521$	8.18728	−	2.10214i	0.358691	−	0.0920962i	−0.0650440	−	0.997882i	$-0.520719\pi$
$521$	8.18728	−	2.10214i	0.358691	−	0.0920962i	0.423735	+	0.905786i	$0.360719\pi$
$522$	−3.58094	+	1.96864i	−0.156734	+	0.0861650i
$523$	7.39088	−	0.933686i	0.323181	−	0.0408272i	0.0379308	−	0.999280i	$-0.487923\pi$
$523$	7.39088	−	0.933686i	0.323181	−	0.0408272i	0.285250	+	0.958453i	$0.407923\pi$
$524$	15.1652	−	23.8965i	0.662493	−	1.04392i
$525$	−0.552142	+	0.218609i	−0.0240975	+	0.00954086i
$526$	−3.54306	+	5.58297i	−0.154485	+	0.243429i
$527$	5.80700	+	30.4414i	0.252957	+	1.32605i
$528$	−1.10270	−	0.801158i	−0.0479888	−	0.0348659i
$529$	10.3238	+	7.50067i	0.448860	+	0.326116i
$530$	−1.03162	−	5.40794i	−0.0448107	−	0.234906i
$531$	−10.0719	+	15.8707i	−0.437081	+	0.688730i
$532$	−5.37964	+	2.12995i	−0.233237	+	0.0923450i
$533$	−34.3819	+	54.1772i	−1.48925	+	2.34668i
$534$	0.377248	−	0.0476575i	0.0163251	−	0.00206234i
$535$	−9.70673	+	5.33632i	−0.419658	+	0.230709i
$536$	19.6172	−	5.03684i	0.847333	−	0.217558i
$537$	−0.0114414	+	0.181856i	−0.000493734	+	0.00784767i
$538$	8.45508	−	6.14298i	0.364524	−	0.264843i
$539$	−58.0256	−	22.9740i	−2.49934	−	0.989559i
$540$	−2.30679	+	1.67598i	−0.0992684	+	0.0721227i
$541$	−12.2209	−	6.71851i	−0.525419	−	0.288851i	0.196886	−	0.980426i	$-0.436917\pi$
$541$	−12.2209	−	6.71851i	−0.525419	−	0.288851i	−0.722305	+	0.691575i	$0.756917\pi$
$542$	−3.68679	+	0.946608i	−0.158361	+	0.0406603i
$543$	1.07694	−	1.01131i	0.0462159	−	0.0433996i
$544$	−14.1713	−	22.3305i	−0.607591	−	0.957410i
$545$	18.4315	+	13.3913i	0.789520	+	0.573620i
$546$	0.883644	+	1.87784i	0.0378165	+	0.0803641i
$547$	9.78868	−	5.38137i	0.418534	−	0.230091i	−0.258548	−	0.965998i	$-0.583244\pi$
$547$	9.78868	−	5.38137i	0.418534	−	0.230091i	0.677082	+	0.735907i	$0.263244\pi$
$548$	2.82992	+	0.726600i	0.120888	+	0.0310388i
$549$	−2.76430	−	2.59585i	−0.117977	−	0.110788i
$550$	0.111347	−	1.76980i	0.00474784	−	0.0754647i
$551$	−1.67258	−	0.919511i	−0.0712545	−	0.0391725i
$552$	−0.580525	−	0.545150i	−0.0247088	−	0.0232031i
$553$	8.40202	−	44.0449i	0.357290	−	1.87298i
$554$	−4.37183	+	4.10542i	−0.185741	+	0.174422i
$555$	−0.194199	−	0.412693i	−0.00824327	−	0.0175178i
$556$	−1.90782	−	10.0011i	−0.0809095	−	0.424143i
$557$	−3.21764	−	0.406482i	−0.136336	−	0.0172232i	0.0568692	−	0.998382i	$-0.481888\pi$
$557$	−3.21764	−	0.406482i	−0.136336	−	0.0172232i	−0.193205	+	0.981158i	$0.561888\pi$
$558$	−2.65517	−	8.17178i	−0.112402	−	0.345939i
$559$	18.0630	−	2.28189i	0.763984	−	0.0965136i
$560$	10.7218	+	22.7850i	0.453079	+	0.962841i
$561$	1.48949	+	2.34706i	0.0628863	+	0.0990930i
$562$	0.702909	−	0.849671i	0.0296504	−	0.0358412i
$563$	−17.2524	−	2.17948i	−0.727101	−	0.0918542i	−0.246935	−	0.969032i	$-0.579423\pi$
$563$	−17.2524	−	2.17948i	−0.727101	−	0.0918542i	−0.480166	+	0.877178i	$0.659423\pi$
$564$	−1.17468	+	0.465089i	−0.0494630	+	0.0195838i
$565$	−11.5267	+	4.56374i	−0.484932	+	0.191998i
$566$	−1.29113	−	3.97369i	−0.0542703	−	0.167027i
$567$	18.0449	−	38.3474i	0.757815	−	1.61044i
$568$	−22.9578	−	5.89456i	−0.963287	−	0.247330i
$569$	−17.6977	−	9.72938i	−0.741925	−	0.407877i	0.0654955	−	0.997853i	$-0.479137\pi$
$569$	−17.6977	−	9.72938i	−0.741925	−	0.407877i	−0.807421	+	0.589976i	$0.799137\pi$
$570$	0.0854249	+	0.0338221i	0.00357806	+	0.00141665i
$571$	−33.3746			−1.39668			−0.698341	−	0.715765i	$-0.746078\pi$
$571$	−33.3746			−1.39668			−0.698341	+	0.715765i	$0.746078\pi$
$572$	44.7812			1.87240
$573$	−1.76738	−	0.699756i	−0.0738334	−	0.0292327i
$574$	1.45824	−	23.1781i	0.0608659	−	0.967436i
$575$	−0.552682	+	2.89726i	−0.0230484	+	0.120824i
$576$	−5.21104	−	6.29906i	−0.217127	−	0.262461i
$577$	5.80631	−	7.01862i	0.241720	−	0.292189i	−0.635676	−	0.771956i	$-0.719279\pi$
$577$	5.80631	−	7.01862i	0.241720	−	0.292189i	0.877396	+	0.479767i	$0.159279\pi$
$578$	1.02781	+	5.38795i	0.0427511	+	0.224109i
$579$	−0.703412	+	0.0888615i	−0.0292328	+	0.00369296i
$580$	−4.19834	+	8.92192i	−0.174326	+	0.370462i
$581$	−6.34495	+	19.5277i	−0.263233	+	0.810147i
$582$	0.210144	−	1.10161i	0.00871076	−	0.0456634i
$583$	−20.8936	+	5.36456i	−0.865323	+	0.222177i
$584$	11.6376	+	2.98803i	0.481567	+	0.123645i
$585$	12.1572	−	37.4161i	0.502639	−	1.54696i
$586$	−8.29020	−	10.0211i	−0.342465	−	0.413969i
$587$	−2.22192	−	3.50119i	−0.0917086	−	0.144510i	0.795376	−	0.606116i	$-0.207273\pi$
$587$	−2.22192	−	3.50119i	−0.0917086	−	0.144510i	−0.887085	+	0.461606i	$0.847273\pi$
$588$	3.05442	+	2.21916i	0.125962	+	0.0915167i
$589$	2.55817	−	3.09230i	0.105408	−	0.127416i
$590$	−0.394129	−	6.26450i	−0.0162260	−	0.257905i
$591$	−1.55138	+	3.29685i	−0.0638152	+	0.135614i
$592$	3.83066	−	2.10592i	0.157439	−	0.0865529i
$593$	−26.9433	+	25.3015i	−1.10643	+	1.03901i	−0.107434	+	0.994212i	$0.534264\pi$
$593$	−26.9433	+	25.3015i	−1.10643	+	1.03901i	−0.998996	+	0.0447953i	$0.985736\pi$
$594$	−0.985528	−	1.19130i	−0.0404367	−	0.0488796i
$595$	−3.22471	−	51.2553i	−0.132200	−	2.10126i
$596$	2.57822	+	7.93496i	0.105608	+	0.325029i
$597$	−0.858271	+	1.35242i	−0.0351267	+	0.0553508i
$598$	10.2266	+	1.29192i	0.418197	+	0.0528305i
$599$	0.251057	+	3.99043i	0.0102579	+	0.163045i	0.999821	+	0.0189416i	$0.00602965\pi$
$599$	0.251057	+	3.99043i	0.0102579	+	0.163045i	−0.989563	+	0.144103i	$0.953970\pi$
$600$	−0.0708895	+	0.218175i	−0.00289405	+	0.00890697i
$601$	15.9351	+	14.9641i	0.650007	+	0.610398i	0.937750	−	0.347310i	$-0.112905\pi$
$601$	15.9351	+	14.9641i	0.650007	+	0.610398i	−0.287743	+	0.957708i	$0.592905\pi$
$602$	−5.33109	+	3.87326i	−0.217279	+	0.157862i
$603$	−32.6025			−1.32768
$604$	13.0282	+	17.2145i	0.530108	+	0.700450i
$605$	8.52705			0.346674
$606$	0.0299728	−	0.0217765i	0.00121756	−	0.000884611i
$607$	−8.27848	−	7.77401i	−0.336013	−	0.315537i	0.498112	−	0.867113i	$-0.334027\pi$
$607$	−8.27848	−	7.77401i	−0.336013	−	0.315537i	−0.834125	+	0.551576i	$0.814027\pi$
$608$	−1.05839	+	3.25738i	−0.0429232	+	0.132104i
$609$	0.112426	+	1.78696i	0.00455573	+	0.0724112i
$610$	1.25631	+	0.158709i	0.0508665	+	0.00642594i
$611$	18.7374	−	29.5254i	0.758035	−	1.19447i
$612$	8.58539	+	26.4231i	0.347044	+	1.06809i
$613$	2.50264	+	39.7783i	0.101081	+	1.60663i	0.642776	+	0.766054i	$0.277783\pi$
$613$	2.50264	+	39.7783i	0.101081	+	1.60663i	−0.541696	+	0.840575i	$0.682217\pi$
$614$	4.06840	+	4.91785i	0.164187	+	0.198468i
$615$	1.94253	−	1.82416i	0.0783305	−	0.0735572i
$616$	−30.3717	+	16.6970i	−1.22371	+	0.672740i
$617$	7.18680	−	15.2727i	0.289330	−	0.614857i	−0.706334	−	0.707878i	$-0.749652\pi$
$617$	7.18680	−	15.2727i	0.289330	−	0.614857i	0.995664	+	0.0930213i	$0.0296525\pi$
$618$	−0.0280138	−	0.445267i	−0.00112688	−	0.0179112i
$619$	16.2869	−	19.6875i	0.654628	−	0.791309i	−0.333858	−	0.942623i	$-0.608351\pi$
$619$	16.2869	−	19.6875i	0.654628	−	0.791309i	0.988486	+	0.151314i	$0.0483506\pi$
$620$	−16.7733	−	12.1865i	−0.673633	−	0.489423i
$621$	1.37794	+	2.17129i	0.0552949	+	0.0871308i
$622$	−10.2832	−	12.4302i	−0.412317	−	0.498406i
$623$	−8.50576	+	26.1781i	−0.340776	+	1.04880i
$624$	−2.21060	−	0.567584i	−0.0884946	−	0.0227216i
$625$	−18.9276	+	4.85979i	−0.757105	+	0.194391i
$626$	−1.09351	+	5.73238i	−0.0437054	+	0.229112i
$627$	0.111243	−	0.342369i	0.00444260	−	0.0136729i
$628$	−6.27924	+	13.3441i	−0.250569	+	0.532486i
$629$	−8.84491	+	1.11737i	−0.352670	+	0.0445525i
$630$	2.66814	+	13.9869i	0.106301	+	0.557250i
$631$	24.2596	−	29.3249i	0.965761	−	1.16740i	−0.0200928	−	0.999798i	$-0.506396\pi$
$631$	24.2596	−	29.3249i	0.965761	−	1.16740i	0.985854	−	0.167607i	$-0.0536038\pi$
$632$	−11.0411	−	13.3464i	−0.439192	−	0.530891i
$633$	−0.0103020	+	0.0540047i	−0.000409466	+	0.00214649i
$634$	−0.851178	+	13.5291i	−0.0338046	+	0.537309i
$635$	−13.6382	−	5.39973i	−0.541214	−	0.214282i
$636$	1.30498			0.0517459
$637$	−104.500			−4.14042
$638$	−4.97120	−	1.96824i	−0.196812	−	0.0779233i
$639$	33.4350	+	18.3810i	1.32267	+	0.727142i
$640$	22.1539	+	5.68816i	0.875710	+	0.224844i
$641$	10.5850	−	22.4943i	0.418083	−	0.888471i	−0.579227	−	0.815166i	$-0.696645\pi$
$641$	10.5850	−	22.4943i	0.418083	−	0.888471i	0.997310	−	0.0733045i	$-0.0233545\pi$
$642$	0.112284	+	0.345575i	0.00443150	+	0.0136388i
$643$	36.6292	−	14.5025i	1.44451	−	0.571923i	0.490434	−	0.871478i	$-0.336838\pi$
$643$	36.6292	−	14.5025i	1.44451	−	0.571923i	0.954079	+	0.299555i	$0.0968381\pi$
$644$	25.0651	−	9.92399i	0.987705	−	0.391060i
$645$	−0.750143	−	0.0947650i	−0.0295368	−	0.00373137i
$646$	1.14473	−	1.38374i	0.0450389	−	0.0544427i
$647$	−0.378872	−	0.597007i	−0.0148950	−	0.0234708i	0.836799	−	0.547510i	$-0.184424\pi$
$647$	−0.378872	−	0.597007i	−0.0148950	−	0.0234708i	−0.851694	+	0.524040i	$0.824424\pi$
$648$	−6.97078	−	14.8137i	−0.273838	−	0.581936i
$649$	−24.3999	+	3.08243i	−0.957781	+	0.120996i
$650$	−0.917569	−	2.82399i	−0.0359900	−	0.110766i
$651$	−3.73511	−	0.471854i	−0.146390	−	0.0184934i
$652$	−3.97313	−	20.8279i	−0.155600	−	0.815682i
$653$	3.46502	+	7.36355i	0.135597	+	0.288158i	0.961081	−	0.276268i	$-0.0890977\pi$
$653$	3.46502	+	7.36355i	0.135597	+	0.288158i	−0.825484	+	0.564426i	$0.809098\pi$
$654$	0.544793	−	0.511595i	0.0213031	−	0.0200049i
$655$	6.09603	−	31.9565i	0.238191	−	1.24864i
$656$	18.6176	+	17.4831i	0.726896	+	0.682601i
$657$	−16.9486	−	9.31757i	−0.661228	−	0.363513i
$658$	−0.794712	+	12.6316i	−0.0309811	+	0.492430i
$659$	0.227663	+	0.213790i	0.00886848	+	0.00832806i	0.688969	−	0.724791i	$-0.258064\pi$
$659$	0.227663	+	0.213790i	0.00886848	+	0.00832806i	−0.680100	+	0.733119i	$0.738064\pi$
$660$	−1.80130	−	0.462496i	−0.0701155	−	0.0180026i
$661$	1.80906	−	0.994537i	0.0703641	−	0.0386830i	−0.446183	−	0.894942i	$-0.647217\pi$
$661$	1.80906	−	0.994537i	0.0703641	−	0.0386830i	0.516547	+	0.856259i	$0.327217\pi$
$662$	−1.42896	−	3.03670i	−0.0555382	−	0.118025i
$663$	3.76568	+	2.73593i	0.146247	+	0.106255i
$664$	4.25008	+	6.69705i	0.164935	+	0.259896i
$665$	−4.84821	+	4.55277i	−0.188005	+	0.176549i
$666$	2.39416	−	0.614716i	0.0927718	−	0.0238198i
$667$	7.79300	+	4.28424i	0.301746	+	0.165886i
$668$	−13.1974	+	9.58844i	−0.510621	+	0.370988i
$669$	0.0819589	+	0.0324498i	0.00316871	+	0.00125458i
$670$	8.80781	−	6.39925i	0.340275	−	0.247225i
$671$	0.311539	−	4.95176i	0.0120268	−	0.191161i
$672$	3.11200	−	0.799025i	0.120048	−	0.0308231i
$673$	12.9850	−	7.13856i	0.500535	−	0.275171i	−0.211422	−	0.977395i	$-0.567809\pi$
$673$	12.9850	−	7.13856i	0.500535	−	0.275171i	0.711956	+	0.702224i	$0.247809\pi$
$674$	7.32451	−	0.925301i	0.282130	−	0.0356413i
$675$	0.396934	−	0.625467i	0.0152780	−	0.0240742i
$676$	48.4830	−	19.1958i	1.86473	−	0.738299i
$677$	−22.7204	+	35.8016i	−0.873216	+	1.37597i	0.0528482	+	0.998603i	$0.483170\pi$
$677$	−22.7204	+	35.8016i	−0.873216	+	1.37597i	−0.926064	+	0.377366i	$0.876830\pi$
$678$	0.0762030	+	0.399470i	0.00292656	+	0.0153416i
$679$	65.6773	+	47.7173i	2.52046	+	1.83122i
$680$	−16.0502	−	11.6612i	−0.615499	−	0.447186i
$681$	0.484892	+	2.54189i	0.0185811	+	0.0974055i
$682$	6.02388	−	9.49212i	0.230666	−	0.363472i
$683$	35.3656	−	14.0022i	1.35323	−	0.535780i	0.424125	−	0.905604i	$-0.360582\pi$
$683$	35.3656	−	14.0022i	1.35323	−	0.535780i	0.929102	+	0.369824i	$0.120582\pi$
$684$	1.92787	−	3.03784i	0.0737139	−	0.116155i
$685$	3.33194	−	0.420921i	0.127307	−	0.0160826i
$686$	18.6393	−	10.2470i	0.711651	−	0.391234i
$687$	−0.171422	+	0.0440137i	−0.00654016	+	0.00167923i
$688$	0.455022	−	7.23236i	0.0173475	−	0.275731i
$689$	−29.2218	+	21.2309i	−1.11326	+	0.808831i
$690$	−0.398017	−	0.157586i	−0.0151522	−	0.00599920i
$691$	−25.4250	+	18.4724i	−0.967213	+	0.702722i	−0.954815	−	0.297202i	$-0.903947\pi$
$691$	−25.4250	+	18.4724i	−0.967213	+	0.702722i	−0.0123985	+	0.999923i	$0.503947\pi$
$692$	−7.27862	−	4.00146i	−0.276692	−	0.152113i
$693$	54.0383	−	13.8747i	2.05274	−	0.527055i
$694$	−6.60249	+	6.20015i	−0.250627	+	0.235355i
$695$	−6.27094	−	9.88143i	−0.237870	−	0.374824i
$696$	0.559573	+	0.406553i	0.0212106	+	0.0154104i
$697$	−22.1776	−	47.1297i	−0.840035	−	1.78517i
$698$	−5.78125	+	3.17827i	−0.218824	+	0.120299i
$699$	−3.71947	−	0.954997i	−0.140683	−	0.0361213i
$700$	−5.66093	−	5.31596i	−0.213963	−	0.200925i
$701$	−1.23307	+	19.5991i	−0.0465725	+	0.740248i	0.903572	+	0.428437i	$0.140936\pi$
$701$	−1.23307	+	19.5991i	−0.0465725	+	0.740248i	−0.950144	+	0.311811i	$0.899064\pi$
$702$	−2.26866	−	1.24721i	−0.0856251	−	0.0470728i
$703$	0.841619	+	0.790333i	0.0317423	+	0.0298080i
$704$	2.00431	−	10.5069i	0.0755401	−	0.395995i
$705$	−1.05864	+	0.994128i	−0.0398707	+	0.0374410i
$706$	−6.28197	−	13.3499i	−0.236425	−	0.502429i
$707$	0.502530	+	2.63436i	0.0188996	+	0.0990752i
$708$	1.47611	+	0.186476i	0.0554755	+	0.00700818i
$709$	−2.99093	−	9.20515i	−0.112327	−	0.345707i	0.879053	−	0.476724i	$-0.158176\pi$
$709$	−2.99093	−	9.20515i	−0.112327	−	0.345707i	−0.991380	+	0.131017i	$0.958176\pi$
$710$	−12.6405	+	1.59687i	−0.474391	+	0.0599295i
$711$	11.8719	+	25.2291i	0.445231	+	0.946164i
$712$	5.69747	+	8.97778i	0.213522	+	0.336457i
$713$	−11.9192	+	14.4078i	−0.446377	+	0.539577i
$714$	−1.67139	−	0.211146i	−0.0625503	−	0.00790193i
$715$	47.8599	−	18.9491i	1.78986	−	0.708655i
$716$	−2.21549	+	0.877176i	−0.0827969	+	0.0327816i
$717$	0.672146	+	2.06865i	0.0251017	+	0.0772552i
$718$	−2.02065	+	4.29409i	−0.0754098	+	0.160254i
$719$	−30.0361	−	7.71197i	−1.12016	−	0.287608i	−0.357182	−	0.934035i	$-0.616263\pi$
$719$	−30.0361	−	7.71197i	−1.12016	−	0.287608i	−0.762976	+	0.646427i	$0.776263\pi$
$720$	−13.7220	−	7.54374i	−0.511389	−	0.281139i
$721$	30.0278	+	11.8888i	1.11829	+	0.442763i
$722$	9.13608			0.340010
$723$	−0.732138			−0.0272285
$724$	17.9625	+	7.11186i	0.667571	+	0.264310i
$725$	0.160853	−	2.55669i	0.00597394	−	0.0949530i
$726$	0.0524136	−	0.274762i	0.00194525	−	0.0101974i
$727$	28.6740	+	34.6609i	1.06346	+	1.28550i	0.956656	+	0.291222i	$0.0940617\pi$
$727$	28.6740	+	34.6609i	1.06346	+	1.28550i	0.106804	+	0.994280i	$0.465938\pi$
$728$	−36.9925	+	44.7163i	−1.37104	+	1.65730i
$729$	4.87757	+	25.5691i	0.180651	+	0.947005i
$730$	6.40765	−	0.809474i	0.237158	−	0.0299600i
$731$	−6.29269	+	13.3726i	−0.232744	+	0.494605i
$732$	−0.0927533	+	0.285465i	−0.00342826	+	0.0105511i
$733$	0.216581	−	1.13536i	0.00799959	−	0.0419353i	−0.978064	−	0.208306i	$-0.933205\pi$
$733$	0.216581	−	1.13536i	0.00799959	−	0.0419353i	0.986063	+	0.166371i	$0.0532049\pi$
$734$	−8.82765	+	2.26656i	−0.325835	+	0.0836601i
$735$	4.20344	+	1.07926i	0.155046	+	0.0398091i
$736$	4.93130	−	15.1770i	0.181770	−	0.559431i
$737$	−27.1908	−	32.8680i	−1.00158	−	1.21071i
$738$	7.73818	+	12.1934i	0.284846	+	0.448846i
$739$	34.5610	+	25.1101i	1.27135	+	0.923688i	0.999255	−	0.0385830i	$-0.0122844\pi$
$739$	34.5610	+	25.1101i	1.27135	+	0.923688i	0.272092	+	0.962271i	$0.412284\pi$
$740$	3.80186	−	4.59566i	0.139759	−	0.168940i
$741$	−0.0378491	−	0.601594i	−0.00139042	−	0.0221001i
$742$	5.56626	−	11.8289i	0.204344	−	0.434253i
$743$	−11.8471	+	6.51301i	−0.434629	+	0.238939i	−0.684019	−	0.729464i	$-0.739770\pi$
$743$	−11.8471	+	6.51301i	−0.434629	+	0.238939i	0.249391	+	0.968403i	$0.419770\pi$
$744$	−1.06017	+	0.995569i	−0.0388678	+	0.0364993i
$745$	6.11314	+	7.38952i	0.223968	+	0.270731i
$746$	0.423345	+	6.72887i	0.0154998	+	0.246362i
$747$	−3.94554	−	12.1431i	−0.144360	−	0.444294i
$748$	−19.4780	+	30.6924i	−0.712185	+	1.12222i
$749$	−26.0954	−	3.29662i	−0.953506	−	0.120456i
$750$	0.0497436	+	0.790651i	0.00181638	+	0.0288705i
$751$	8.28876	−	25.5102i	0.302461	−	0.930880i	−0.678151	−	0.734922i	$-0.737219\pi$
$751$	8.28876	−	25.5102i	0.302461	−	0.930880i	0.980612	−	0.195957i	$-0.0627814\pi$
$752$	−10.1462	−	9.52793i	−0.369994	−	0.347448i
$753$	0.347329	−	0.252349i	0.0126574	−	0.00919612i
$754$	−8.95274			−0.326039
$755$	21.2081	+	12.8852i	0.771844	+	0.468941i
$756$	−6.77074			−0.246249
$757$	3.33965	−	2.42640i	0.121382	−	0.0881890i	−0.525438	−	0.850832i	$-0.676099\pi$
$757$	3.33965	−	2.42640i	0.121382	−	0.0881890i	0.646820	+	0.762643i	$0.276099\pi$
$758$	−8.47398	−	7.95760i	−0.307789	−	0.289033i
$759$	−0.518308	+	1.59519i	−0.0188134	+	0.0579016i
$760$	0.161322	+	2.56414i	0.00585176	+	0.0930111i
$761$	−34.2631	−	4.32843i	−1.24204	−	0.156906i	−0.523275	−	0.852164i	$-0.675290\pi$
$761$	−34.2631	−	4.32843i	−1.24204	−	0.156906i	−0.718760	+	0.695258i	$0.755290\pi$
$762$	−0.257823	+	0.406263i	−0.00933993	+	0.0147174i
$763$	16.7175	+	51.4512i	0.605214	+	1.86266i
$764$	−1.56082	−	24.8085i	−0.0564684	−	0.897539i
$765$	20.3565	+	24.6068i	0.735992	+	0.889662i
$766$	1.20729	−	1.13372i	0.0436211	−	0.0409630i
$767$	−36.0874	+	19.8392i	−1.30304	+	0.716353i
$768$	0.00581253	−	0.0123522i	0.000209741	−	0.000445723i
$769$	2.71242	+	43.1126i	0.0978122	+	1.55468i	0.674845	+	0.737959i	$0.264210\pi$
$769$	2.71242	+	43.1126i	0.0978122	+	1.55468i	−0.577033	+	0.816721i	$0.695790\pi$
$770$	−11.8755	+	14.3550i	−0.427963	+	0.517319i
$771$	−0.217061	−	0.157704i	−0.00781727	−	0.00567958i
$772$	−4.96796	−	7.82825i	−0.178801	−	0.281745i
$773$	12.5723	+	15.1974i	0.452196	+	0.546611i	0.946511	−	0.322672i	$-0.104581\pi$
$773$	12.5723	+	15.1974i	0.452196	+	0.546611i	−0.494315	+	0.869283i	$0.664581\pi$
$774$	1.26625	−	3.89711i	0.0455144	−	0.140079i
$775$	5.21725	+	1.33956i	0.187409	+	0.0481185i
$776$	30.3754	−	7.79906i	1.09041	−	0.279970i
$777$	0.202943	−	1.06386i	0.00728053	−	0.0381659i
$778$	−1.24333	+	3.82658i	−0.0445756	+	0.137189i
$779$	−2.87203	+	6.10338i	−0.102901	+	0.218676i
$780$	−3.08947	+	0.390291i	−0.110621	+	0.0139747i
$781$	9.35432	+	49.0371i	0.334724	+	1.75468i
$782$	−5.33361	+	6.44723i	−0.190729	+	0.230552i
$783$	−1.42371	−	1.72097i	−0.0508792	−	0.0615024i
$784$	−7.79382	+	40.8566i	−0.278351	+	1.45917i
$785$	−1.06442	+	16.9185i	−0.0379909	+	0.603848i
$786$	−0.992244	−	0.392857i	−0.0353922	−	0.0140127i
$787$	11.4088			0.406679			0.203340	−	0.979108i	$-0.434820\pi$
$787$	11.4088			0.406679			0.203340	+	0.979108i	$0.434820\pi$
$788$	−47.6474			−1.69737
$789$	−1.67511	−	0.663221i	−0.0596354	−	0.0236113i
$790$	−8.15926	−	4.48559i	−0.290294	−	0.159590i
$791$	−28.5134	−	7.32099i	−1.01382	−	0.260305i
$792$	9.17647	−	19.5010i	0.326072	−	0.692938i
$793$	−2.56728	−	7.90127i	−0.0911668	−	0.280582i
$794$	16.6189	−	6.57989i	0.589783	−	0.233511i
$795$	1.39470	−	0.552201i	0.0494650	−	0.0195846i
$796$	−20.7811	−	2.62526i	−0.736566	−	0.0930499i
$797$	−9.43321	+	11.4028i	−0.334141	+	0.403907i	−0.910647	−	0.413186i	$-0.864416\pi$
$797$	−9.43321	+	11.4028i	−0.334141	+	0.403907i	0.576505	+	0.817093i	$0.304416\pi$
$798$	0.116900	+	0.184206i	0.00413823	+	0.00652081i
$799$	12.0863	+	25.6847i	0.427583	+	0.908659i
$800$	−4.56066	+	0.576145i	−0.161244	+	0.0203698i
$801$	−5.28922	−	16.2786i	−0.186885	−	0.575174i
$802$	0.0270011	+	0.00341103i	0.000953442	+	0.000120448i
$803$	−4.74183	−	24.8575i	−0.167335	−	0.877203i
$804$	1.09877	+	2.33500i	0.0387506	+	0.0823492i
$805$	22.5891	−	21.2125i	0.796160	−	0.747644i
$806$	3.52737	−	18.4911i	0.124246	−	0.651322i
$807$	2.07577	+	1.94927i	0.0730704	+	0.0686177i
$808$	0.907860	+	0.499100i	0.0319384	+	0.0175583i
$809$	−1.60778	+	25.5549i	−0.0565265	+	0.898463i	0.862943	+	0.505301i	$0.168619\pi$
$809$	−1.60778	+	25.5549i	−0.0565265	+	0.898463i	−0.919470	+	0.393161i	$0.871381\pi$
$810$	−6.41529	−	6.02436i	−0.225410	−	0.211674i
$811$	−33.7794	−	8.67307i	−1.18615	−	0.304553i	−0.396460	−	0.918052i	$-0.629761\pi$
$811$	−33.7794	−	8.67307i	−1.18615	−	0.304553i	−0.789695	+	0.613499i	$0.789761\pi$
$812$	−20.5180	+	11.2798i	−0.720040	+	0.395845i
$813$	−0.441576	−	0.938397i	−0.0154868	−	0.0329110i
$814$	2.61647	+	1.90098i	0.0917072	+	0.0666292i
$815$	−13.0596	−	20.5786i	−0.457456	−	0.720836i
$816$	1.35053	−	1.26823i	0.0472781	−	0.0443971i
$817$	1.85381	−	0.475976i	0.0648564	−	0.0166523i
$818$	5.67112	+	3.11773i	0.198286	+	0.109009i
$819$	75.5779	−	54.9106i	2.64091	−	1.91873i
$820$	32.3999	+	12.8280i	1.13145	+	0.447975i
$821$	27.9184	−	20.2839i	0.974358	−	0.707912i	0.0179170	−	0.999839i	$-0.494297\pi$
$821$	27.9184	−	20.2839i	0.974358	−	0.707912i	0.956441	+	0.291927i	$0.0942965\pi$
$822$	0.00691748	−	0.109950i	0.000241275	−	0.00383496i
$823$	20.4694	−	5.25564i	0.713518	−	0.183200i	0.125553	−	0.992087i	$-0.459929\pi$
$823$	20.4694	−	5.25564i	0.713518	−	0.183200i	0.587965	+	0.808887i	$0.299929\pi$
$824$	10.9327	−	6.01030i	0.380858	−	0.209379i
$825$	0.479352	−	0.0605562i	0.0166889	−	0.00210830i
$826$	7.98646	−	12.5846i	0.277884	−	0.437876i
$827$	17.8799	−	7.07916i	0.621746	−	0.246166i	−0.0360656	−	0.999349i	$-0.511483\pi$
$827$	17.8799	−	7.07916i	0.621746	−	0.246166i	0.657811	+	0.753183i	$0.271483\pi$
$828$	−8.98244	+	14.1541i	−0.312161	+	0.491888i
$829$	4.28229	+	22.4485i	0.148730	+	0.779670i	0.975984	+	0.217842i	$0.0699018\pi$
$829$	4.28229	+	22.4485i	0.148730	+	0.779670i	−0.827254	+	0.561828i	$0.810098\pi$
$830$	3.44938	+	2.50612i	0.119730	+	0.0869887i
$831$	−1.32197	−	0.960466i	−0.0458586	−	0.0333182i
$832$	−3.35612	−	17.5934i	−0.116352	−	0.609940i
$833$	45.4530	−	71.6225i	1.57485	−	2.48157i
$834$	−0.356949	+	0.141326i	−0.0123601	+	0.00489373i
$835$	−10.0474	+	15.8321i	−0.347703	+	0.547892i
$836$	4.67043	−	0.590012i	0.161530	−	0.0204060i
$837$	4.11546	−	2.26249i	0.142251	−	0.0782032i
$838$	12.5699	−	3.22740i	0.434220	−	0.111489i
$839$	0.748832	−	11.9023i	0.0258526	−	0.410915i	−0.963723	−	0.266903i	$-0.914000\pi$
$839$	0.748832	−	11.9023i	0.0258526	−	0.410915i	0.989576	−	0.144012i	$-0.0460003\pi$
$840$	1.94983	−	1.41664i	0.0672756	−	0.0488786i
$841$	19.7820	+	7.83226i	0.682139	+	0.270078i
$842$	−9.18000	+	6.66966i	−0.316364	+	0.229852i
$843$	0.263291	+	0.144746i	0.00906823	+	0.00498530i
$844$	−0.696364	+	0.178796i	−0.0239698	+	0.00615441i
$845$	43.6935	−	41.0310i	1.50310	−	1.41151i
$846$	−4.21714	−	6.64515i	−0.144988	−	0.228465i
$847$	16.3811	+	11.9015i	0.562860	+	0.408942i
$848$	6.12129	+	13.0084i	0.210206	+	0.446711i
$849$	0.997593	−	0.548432i	0.0342373	−	0.0188221i
$850$	2.33462	+	0.599429i	0.0800769	+	0.0205603i
$851$	−3.92132	−	3.68237i	−0.134421	−	0.126230i
$852$	0.189631	−	3.01410i	0.00649665	−	0.103261i
$853$	14.0561	+	7.72739i	0.481271	+	0.264581i	0.703870	−	0.710329i	$-0.251454\pi$
$853$	14.0561	+	7.72739i	0.481271	+	0.264581i	−0.222599	+	0.974910i	$0.571454\pi$
$854$	2.19195	+	2.05837i	0.0750068	+	0.0704361i
$855$	0.774956	−	4.06246i	0.0265029	−	0.138933i
$856$	−7.40693	+	6.95557i	−0.253163	+	0.237736i
$857$	7.81724	+	16.6125i	0.267032	+	0.567472i	0.992705	−	0.120568i	$-0.0384715\pi$
$857$	7.81724	+	16.6125i	0.267032	+	0.567472i	−0.725673	+	0.688040i	$0.758472\pi$
$858$	−0.316402	−	1.65864i	−0.0108018	−	0.0566249i
$859$	−44.0504	−	5.56486i	−1.50298	−	0.189871i	−0.669663	−	0.742665i	$-0.733561\pi$
$859$	−44.0504	−	5.56486i	−1.50298	−	0.189871i	−0.833318	+	0.552795i	$0.813561\pi$
$860$	−3.05542	−	9.40360i	−0.104189	−	0.320660i
$861$	6.27779	−	0.793070i	0.213947	−	0.0270277i
$862$	4.21810	+	8.96391i	0.143669	+	0.305312i
$863$	−23.0497	−	36.3206i	−0.784622	−	1.23637i	−0.967410	−	0.253214i	$-0.918512\pi$
$863$	−23.0497	−	36.3206i	−0.784622	−	1.23637i	0.182788	−	0.983152i	$-0.441488\pi$
$864$	−2.55477	+	3.08818i	−0.0869150	+	0.105062i
$865$	−9.47224	−	1.19662i	−0.322066	−	0.0406864i
$866$	10.8504	−	4.29598i	0.368711	−	0.145983i
$867$	−1.38954	+	0.550160i	−0.0471914	+	0.0186844i
$868$	−15.2135	−	46.8224i	−0.516381	−	1.58926i
$869$	−15.5332	+	33.0098i	−0.526929	+	1.11978i
$870$	0.360119	+	0.0924630i	0.0122092	+	0.00313479i
$871$	−62.5925	−	34.4105i	−2.12086	−	1.16596i
$872$	19.4310	+	7.69327i	0.658016	+	0.260527i
$873$	−50.4819			−1.70855
$874$	1.08360			0.0366533
$875$	−53.3197	−	21.1108i	−1.80254	−	0.713674i
$876$	−0.0961264	+	1.52788i	−0.00324781	+	0.0516224i
$877$	4.37595	−	22.9395i	0.147765	−	0.774612i	−0.828826	−	0.559507i	$-0.810991\pi$
$877$	4.37595	−	22.9395i	0.147765	−	0.774612i	0.976591	−	0.215105i	$-0.0690095\pi$
$878$	−2.06948	−	2.50158i	−0.0698417	−	0.0844241i
$879$	2.25878	−	2.73040i	0.0761868	−	0.0920941i
$880$	−3.83910	−	20.1253i	−0.129416	−	0.678423i
$881$	−14.7251	+	1.86021i	−0.496101	+	0.0626721i	−0.369403	−	0.929269i	$-0.620438\pi$
$881$	−14.7251	+	1.86021i	−0.496101	+	0.0626721i	−0.126698	+	0.991941i	$0.540438\pi$
$882$	−10.0140	+	21.2808i	−0.337189	+	0.716563i
$883$	−4.90715	+	15.1027i	−0.165139	+	0.508245i	−0.999046	−	0.0436591i	$-0.986098\pi$
$883$	−4.90715	+	15.1027i	−0.165139	+	0.508245i	0.833908	+	0.551904i	$0.186098\pi$
$884$	−11.4056	+	59.7903i	−0.383612	+	2.01097i
$885$	1.65650	−	0.425316i	0.0556825	−	0.0142968i
$886$	−5.60787	−	1.43986i	−0.188400	−	0.0483729i
$887$	4.76779	−	14.6738i	0.160087	−	0.492697i	−0.838554	−	0.544819i	$-0.816598\pi$
$887$	4.76779	−	14.6738i	0.160087	−	0.492697i	0.998641	+	0.0521221i	$0.0165985\pi$
$888$	−0.266687	−	0.322370i	−0.00894944	−	0.0108180i
$889$	−18.6632	−	29.4086i	−0.625945	−	0.986332i
$890$	4.62409	+	3.35960i	0.155000	+	0.112614i
$891$	−21.9795	+	26.5687i	−0.736342	+	0.890085i
$892$	0.0723799	+	1.15045i	0.00242346	+	0.0385198i
$893$	1.56520	−	3.32621i	0.0523773	−	0.111307i
$894$	0.275684	−	0.151559i	0.00922025	−	0.00506888i
$895$	−1.99663	+	1.87496i	−0.0667401	+	0.0626732i
$896$	34.6200	+	41.8484i	1.15657	+	1.39806i
$897$	0.176349	+	2.80298i	0.00588812	+	0.0935889i
$898$	1.18569	+	3.64919i	0.0395671	+	0.121775i
$899$	8.70220	−	13.7125i	0.290235	−	0.457336i
$900$	4.79092	+	0.605234i	0.159697	+	0.0201745i
$901$	−1.84105	−	29.2627i	−0.0613344	−	0.974882i
$902$	−5.83900	+	17.9706i	−0.194417	+	0.598355i
$903$	−1.30881	−	1.22905i	−0.0435544	−	0.0409003i
$904$	−9.20018	+	6.68432i	−0.305994	+	0.222317i
$905$	22.2068			0.738179
$906$	0.545553	−	0.604175i	0.0181248	−	0.0200724i
$907$	−29.1884			−0.969186			−0.484593	−	0.874740i	$-0.661032\pi$
$907$	−29.1884			−0.969186			−0.484593	+	0.874740i	$0.661032\pi$
$908$	−27.3768	+	19.8904i	−0.908530	+	0.660085i
$909$	−1.21569	−	1.14161i	−0.0403219	−	0.0378648i
$910$	−9.64004	+	29.6690i	−0.319564	+	0.983518i
$911$	−1.37354	−	21.8318i	−0.0455074	−	0.723319i	−0.952947	−	0.303137i	$-0.901966\pi$
$911$	−1.37354	−	21.8318i	−0.0455074	−	0.723319i	0.907440	−	0.420182i	$-0.138034\pi$
$912$	−0.238031	−	0.0300703i	−0.00788199	−	0.000995727i
$913$	8.95139	−	14.1051i	0.296248	−	0.466812i
$914$	1.82978	+	5.63149i	0.0605239	+	0.186273i
$915$	0.0216640	+	0.344339i	0.000716190	+	0.0113835i
$916$	−1.47525	−	1.78327i	−0.0487435	−	0.0589208i
$917$	56.3138	−	52.8822i	1.85965	−	1.74632i
$918$	1.84159	−	1.01242i	0.0607816	−	0.0334149i
$919$	−18.8924	+	40.1484i	−0.623203	+	1.32437i	0.305019	+	0.952346i	$0.401337\pi$
$919$	−18.8924	+	40.1484i	−0.623203	+	1.32437i	−0.928222	+	0.372027i	$0.878663\pi$
$920$	−0.751641	−	11.9470i	−0.0247809	−	0.393880i
$921$	−1.10849	+	1.33994i	−0.0365261	+	0.0441524i
$922$	−11.0933	−	8.05975i	−0.365338	−	0.265434i
$923$	44.7903	+	70.5782i	1.47429	+	2.32311i
$924$	−2.81490	−	3.40263i	−0.0926035	−	0.111938i
$925$	−0.478843	+	1.47373i	−0.0157443	+	0.0484558i
$926$	−8.59817	−	2.20764i	−0.282553	−	0.0725474i
$927$	−19.4518	+	4.99437i	−0.638881	+	0.164037i
$928$	−2.59712	+	13.6146i	−0.0852546	+	0.446920i
$929$	8.21310	−	25.2773i	0.269463	−	0.829322i	−0.721169	−	0.692760i	$-0.756395\pi$
$929$	8.21310	−	25.2773i	0.269463	−	0.829322i	0.990632	−	0.136562i	$-0.0436053\pi$
$930$	−0.332861	+	0.707366i	−0.0109150	+	0.0231955i
$931$	−10.8987	+	1.37683i	−0.357191	+	0.0451237i
$932$	−9.40971	−	49.3274i	−0.308225	−	1.61577i
$933$	2.80179	−	3.38678i	0.0917265	−	0.110878i
$934$	6.05667	+	7.32126i	0.198180	+	0.239559i
$935$	−7.82967	+	41.0446i	−0.256057	+	1.34230i
$936$	2.26599	−	36.0169i	0.0740663	−	1.17725i
$937$	−12.8845	−	5.10133i	−0.420918	−	0.166653i	0.148111	−	0.988971i	$-0.452681\pi$
$937$	−12.8845	−	5.10133i	−0.420918	−	0.166653i	−0.569029	+	0.822318i	$0.692681\pi$
$938$	25.8521			0.844101
$939$	−1.59003			−0.0518887
$940$	−17.6573	−	6.99101i	−0.575917	−	0.228022i
$941$	−36.1576	−	19.8778i	−1.17871	−	0.647999i	−0.232826	−	0.972518i	$-0.574797\pi$
$941$	−36.1576	−	19.8778i	−1.17871	−	0.647999i	−0.945879	+	0.324520i	$0.894797\pi$
$942$	0.538613	+	0.138292i	0.0175489	+	0.00450580i
$943$	13.3815	−	28.4372i	0.435763	−	0.926043i
$944$	5.06514	+	15.5889i	0.164856	+	0.507376i
$945$	−7.23623	+	2.86503i	−0.235394	+	0.0931993i
$946$	4.98490	−	1.97366i	0.162073	−	0.0641693i
$947$	−22.6710	−	2.86402i	−0.736709	−	0.0930680i	−0.251980	−	0.967732i	$-0.581082\pi$
$947$	−22.6710	−	2.86402i	−0.736709	−	0.0930680i	−0.484729	+	0.874664i	$0.661082\pi$
$948$	1.40681	−	1.70054i	0.0456910	−	0.0552309i
$949$	−22.7048	−	35.7770i	−0.737028	−	1.16137i
$950$	−0.132905	−	0.282437i	−0.00431199	−	0.00916345i
$951$	−3.66436	+	0.462916i	−0.118825	+	0.0150111i
$952$	−14.5577	−	44.8039i	−0.471817	−	1.45210i
$953$	58.8098	+	7.42940i	1.90504	+	0.240662i	0.987573	−	0.157161i	$-0.0502342\pi$
$953$	58.8098	+	7.42940i	1.90504	+	0.240662i	0.917462	+	0.397823i	$0.130234\pi$
$954$	1.52329	+	7.98539i	0.0493185	+	0.258536i
$955$	−12.1658	−	25.8536i	−0.393676	−	0.836603i
$956$	−20.7346	+	19.4711i	−0.670605	+	0.629740i
$957$	0.272972	−	1.43097i	0.00882394	−	0.0462567i
$958$	−6.43401	−	6.04194i	−0.207873	−	0.195206i
$959$	6.98838	+	3.84189i	0.225667	+	0.124061i
$960$	−0.0467045	+	0.742346i	−0.00150738	+	0.0239591i
$961$	2.29527	+	2.15540i	0.0740411	+	0.0695292i
$962$	5.24527	+	1.34676i	0.169114	+	0.0434212i
$963$	14.3330	−	7.87963i	0.461874	−	0.253918i
$964$	−4.07646	−	8.66292i	−0.131294	−	0.279014i
$965$	−8.62202	−	6.26427i	−0.277553	−	0.201654i
$966$	−0.544669	−	0.858262i	−0.0175245	−	0.0276141i
$967$	−2.29809	+	2.15805i	−0.0739017	+	0.0693984i	−0.720618	−	0.693332i	$-0.756142\pi$
$967$	−2.29809	+	2.15805i	−0.0739017	+	0.0693984i	0.646716	+	0.762731i	$0.276142\pi$
$968$	7.57614	−	1.94522i	0.243506	−	0.0625218i
$969$	0.428787	+	0.235727i	0.0137746	+	0.00757266i
$970$	13.6381	−	9.90863i	0.437892	−	0.318147i
$971$	51.2804	+	20.3033i	1.64567	+	0.651565i	0.994243	−	0.107149i	$-0.0341723\pi$
$971$	51.2804	+	20.3033i	1.64567	+	0.651565i	0.651423	+	0.758715i	$0.274172\pi$
$972$	5.11446	−	3.71587i	0.164046	−	0.119187i
$973$	1.74497	−	27.7355i	0.0559412	−	0.889160i
$974$	−19.1463	+	4.91592i	−0.613486	+	0.157516i
$975$	0.708960	−	0.389754i	0.0227049	−	0.0124821i
$976$	−3.28067	+	0.414445i	−0.105012	+	0.0132661i
$977$	24.0248	−	37.8570i	0.768621	−	1.21115i	−0.204048	−	0.978961i	$-0.565410\pi$
$977$	24.0248	−	37.8570i	0.768621	−	1.21115i	0.972670	−	0.232193i	$-0.0745900\pi$
$978$	−0.743365	+	0.294319i	−0.0237702	+	0.00941128i
$979$	11.9998	−	18.9087i	0.383517	−	0.604325i
$980$	10.6341	+	55.7459i	0.339694	+	1.78074i
$981$	−27.2161	−	19.7736i	−0.868942	−	0.631323i
$982$	7.03245	+	5.10938i	0.224415	+	0.163047i
$983$	7.96413	+	41.7494i	0.254016	+	1.33160i	0.849226	+	0.528030i	$0.177069\pi$
$983$	7.96413	+	41.7494i	0.254016	+	1.33160i	−0.595209	+	0.803571i	$0.702931\pi$
$984$	1.30977	−	2.06387i	0.0417541	−	0.0657939i
$985$	−50.9232	+	20.1619i	−1.62255	+	0.642413i
$986$	3.89407	−	6.13607i	0.124013	−	0.195412i
$987$	−3.42126	+	0.432206i	−0.108900	+	0.0137573i
$988$	6.90755	−	3.79746i	0.219758	−	0.120813i
$989$	−8.63736	+	2.21770i	−0.274652	+	0.0705187i
$990$	0.727438	−	11.5623i	0.0231195	−	0.367474i
$991$	45.7824	−	33.2629i	1.45433	−	1.05663i	0.469531	−	0.882916i	$-0.344423\pi$
$991$	45.7824	−	33.2629i	1.45433	−	1.05663i	0.984796	−	0.173715i	$-0.0555770\pi$
$992$	−27.0965	−	10.7283i	−0.860315	−	0.340623i
$993$	0.739781	−	0.537482i	0.0234762	−	0.0170565i
$994$	−26.5122	−	14.5752i	−0.840915	−	0.462297i
$995$	−23.3207	+	5.98773i	−0.739315	+	0.189824i
$996$	−0.736722	+	0.691828i	−0.0233439	+	0.0219214i
$997$	7.26024	+	11.4403i	0.229934	+	0.362318i	0.939631	−	0.342189i	$-0.111168\pi$
$997$	7.26024	+	11.4403i	0.229934	+	0.362318i	−0.709697	+	0.704507i	$0.751168\pi$
$998$	−9.57198	−	6.95445i	−0.302996	−	0.220139i
$999$	0.575245	+	1.22246i	0.0181999	+	0.0386768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.h.a.148.8	yes	220
151.50	even	25	inner	151.2.h.a.50.8	✓	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.h.a.50.8	✓	220	151.50	even	25	inner
151.2.h.a.148.8	yes	220	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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.h (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.398915 - 0.289829i) q^{2} +(0.0979358 + 0.0919678i) q^{3} +(-0.542901 + 1.67088i) q^{4} +(0.126803 + 2.01548i) q^{5} +(0.0657230 + 0.00830275i) q^{6} +(-2.56949 + 4.04886i) q^{7} +(0.572442 + 1.76179i) q^{8} +(-0.187238 - 2.97607i) q^{9} +O(q^{10})\)	\(q+(0.398915 - 0.289829i) q^{2} +(0.0979358 + 0.0919678i) q^{3} +(-0.542901 + 1.67088i) q^{4} +(0.126803 + 2.01548i) q^{5} +(0.0657230 + 0.00830275i) q^{6} +(-2.56949 + 4.04886i) q^{7} +(0.572442 + 1.76179i) q^{8} +(-0.187238 - 2.97607i) q^{9} +(0.634728 + 0.767255i) q^{10} +(2.84414 - 2.67082i) q^{11} +(-0.206836 + 0.113709i) q^{12} +(2.78163 - 5.91127i) q^{13} +(0.148470 + 2.35987i) q^{14} +(-0.172941 + 0.209049i) q^{15} +(-2.10369 - 1.52842i) q^{16} +(2.84160 + 4.47765i) q^{17} +(-0.937243 - 1.13293i) q^{18} +(0.212225 - 0.653161i) q^{19} +(-3.43646 - 0.882334i) q^{20} +(-0.624010 + 0.160218i) q^{21} +(0.360489 - 1.88975i) q^{22} +(-0.988811 + 3.04325i) q^{23} +(-0.105966 + 0.225189i) q^{24} +(0.914492 - 0.115527i) q^{25} +(-0.603621 - 3.16429i) q^{26} +(0.512276 - 0.619235i) q^{27} +(-5.37018 - 6.49143i) q^{28} +(0.520768 - 2.72996i) q^{29} +(-0.00840013 + 0.133516i) q^{30} +(5.43332 + 2.15120i) q^{31} -4.98710 q^{32} +0.524173 q^{33} +(2.43131 + 0.962624i) q^{34} +(-8.48622 - 4.66534i) q^{35} +(5.07430 + 1.30286i) q^{36} +(-0.715776 + 1.52110i) q^{37} +(-0.104645 - 0.322065i) q^{38} +(0.816067 - 0.323104i) q^{39} +(-3.47827 + 1.37715i) q^{40} +(-9.74434 - 1.23100i) q^{41} +(-0.202491 + 0.244770i) q^{42} +(1.49327 + 2.35301i) q^{43} +(2.91854 + 6.20220i) q^{44} +(5.97446 - 0.754750i) q^{45} +(0.487569 + 1.50058i) q^{46} +(5.31046 + 0.670867i) q^{47} +(-0.0654611 - 0.343159i) q^{48} +(-6.81058 - 14.4732i) q^{49} +(0.331322 - 0.311132i) q^{50} +(-0.133505 + 0.699858i) q^{51} +(8.36686 + 7.85700i) q^{52} +(-4.84496 - 2.66354i) q^{53} +(0.0248824 - 0.395495i) q^{54} +(5.74364 + 5.39364i) q^{55} +(-8.60414 - 2.20917i) q^{56} +(0.0808542 - 0.0444500i) q^{57} +(-0.583479 - 1.23996i) q^{58} +(-5.09967 - 3.70513i) q^{59} +(-0.255406 - 0.402456i) q^{60} +(0.927010 - 0.870521i) q^{61} +(2.79092 - 0.716586i) q^{62} +(12.5308 + 6.88886i) q^{63} +(2.21796 - 1.61144i) q^{64} +(12.2668 + 4.85675i) q^{65} +(0.209101 - 0.151920i) q^{66} +(0.686507 - 10.9117i) q^{67} +(-9.02431 + 2.31705i) q^{68} +(-0.376721 + 0.207104i) q^{69} +(-4.73744 + 0.598477i) q^{70} +(-6.85597 + 10.8033i) q^{71} +(5.13603 - 2.03350i) q^{72} +(3.47538 - 5.47632i) q^{73} +(0.155325 + 0.814244i) q^{74} +(0.100186 + 0.0727896i) q^{75} +(0.976136 + 0.709204i) q^{76} +(3.50583 + 18.3782i) q^{77} +(0.231897 - 0.365411i) q^{78} +(-8.69389 + 3.44215i) q^{79} +(2.81375 - 4.43376i) q^{80} +(-8.76819 + 1.10768i) q^{81} +(-4.24395 + 2.33313i) q^{82} +(4.14726 - 1.06483i) q^{83} +(0.0710701 - 1.12963i) q^{84} +(-8.66428 + 6.29497i) q^{85} +(1.27766 + 0.505861i) q^{86} +(0.302070 - 0.219467i) q^{87} +(6.33355 + 3.48190i) q^{88} +(5.55963 - 1.42747i) q^{89} +(2.16456 - 2.03265i) q^{90} +(16.7865 + 26.4514i) q^{91} +(-4.54807 - 3.30437i) q^{92} +(0.334275 + 0.710370i) q^{93} +(2.31286 - 1.27151i) q^{94} +(1.34334 + 0.344912i) q^{95} +(-0.488415 - 0.458652i) q^{96} +(1.06299 - 16.8958i) q^{97} +(-6.91160 - 3.79968i) q^{98} +(-8.48108 - 7.96427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 15 q^{2} - 20 q^{3} - 55 q^{4} - 20 q^{5} - 20 q^{7} + 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q - 15 * q^2 - 20 * q^3 - 55 * q^4 - 20 * q^5 - 20 * q^7 + 5 * q^8 - 20 * q^9	\( 220 q - 15 q^{2} - 20 q^{3} - 55 q^{4} - 20 q^{5} - 20 q^{7} + 5 q^{8} - 20 q^{9} - 50 q^{10} - 10 q^{11} + 5 q^{12} - 20 q^{13} + 5 q^{14} - 60 q^{15} - 5 q^{16} - 10 q^{17} + 30 q^{18} - 15 q^{19} - 130 q^{20} - 20 q^{21} + 15 q^{22} + 35 q^{23} - 95 q^{24} + 10 q^{25} + 5 q^{26} + 25 q^{27} + 50 q^{28} + 15 q^{29} + 75 q^{30} + 20 q^{31} + 80 q^{32} - 100 q^{33} - 50 q^{34} + 15 q^{35} + 100 q^{36} + 20 q^{37} + 40 q^{38} - 5 q^{39} + 105 q^{40} - 10 q^{41} - 110 q^{42} - 10 q^{43} + 90 q^{44} + 5 q^{45} + 25 q^{46} - 75 q^{47} - 145 q^{48} - 10 q^{49} + 50 q^{50} - 80 q^{51} + 85 q^{52} - 95 q^{53} + 20 q^{54} + 80 q^{55} - 65 q^{56} + 55 q^{57} - 105 q^{58} - 15 q^{59} - 70 q^{62} + 95 q^{63} + 45 q^{64} - 30 q^{65} - 5 q^{66} - 50 q^{67} + 95 q^{68} + 45 q^{69} + 25 q^{71} - 25 q^{72} + 20 q^{73} - 140 q^{74} + 55 q^{75} + 15 q^{76} - 45 q^{77} + 110 q^{78} - 130 q^{79} + 145 q^{80} - 160 q^{81} - 10 q^{82} - 55 q^{83} + 140 q^{84} + 25 q^{85} - 150 q^{86} + 125 q^{87} - 35 q^{88} + 5 q^{89} + 120 q^{90} - 70 q^{91} + 45 q^{92} - 40 q^{93} + 65 q^{94} + 135 q^{96} - 270 q^{97} + 135 q^{98} + 60 q^{99}+O(q^{100}) \) 220 * q - 15 * q^2 - 20 * q^3 - 55 * q^4 - 20 * q^5 - 20 * q^7 + 5 * q^8 - 20 * q^9 - 50 * q^10 - 10 * q^11 + 5 * q^12 - 20 * q^13 + 5 * q^14 - 60 * q^15 - 5 * q^16 - 10 * q^17 + 30 * q^18 - 15 * q^19 - 130 * q^20 - 20 * q^21 + 15 * q^22 + 35 * q^23 - 95 * q^24 + 10 * q^25 + 5 * q^26 + 25 * q^27 + 50 * q^28 + 15 * q^29 + 75 * q^30 + 20 * q^31 + 80 * q^32 - 100 * q^33 - 50 * q^34 + 15 * q^35 + 100 * q^36 + 20 * q^37 + 40 * q^38 - 5 * q^39 + 105 * q^40 - 10 * q^41 - 110 * q^42 - 10 * q^43 + 90 * q^44 + 5 * q^45 + 25 * q^46 - 75 * q^47 - 145 * q^48 - 10 * q^49 + 50 * q^50 - 80 * q^51 + 85 * q^52 - 95 * q^53 + 20 * q^54 + 80 * q^55 - 65 * q^56 + 55 * q^57 - 105 * q^58 - 15 * q^59 - 70 * q^62 + 95 * q^63 + 45 * q^64 - 30 * q^65 - 5 * q^66 - 50 * q^67 + 95 * q^68 + 45 * q^69 + 25 * q^71 - 25 * q^72 + 20 * q^73 - 140 * q^74 + 55 * q^75 + 15 * q^76 - 45 * q^77 + 110 * q^78 - 130 * q^79 + 145 * q^80 - 160 * q^81 - 10 * q^82 - 55 * q^83 + 140 * q^84 + 25 * q^85 - 150 * q^86 + 125 * q^87 - 35 * q^88 + 5 * q^89 + 120 * q^90 - 70 * q^91 + 45 * q^92 - 40 * q^93 + 65 * q^94 + 135 * q^96 - 270 * q^97 + 135 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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