LMFDB - Embedded newform 260.2.o.a.27.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.o (of order $4$, degree $2$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.13
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.516756 + 1.31642i) q^{2} +(-2.23963 - 2.23963i) q^{3} +(-1.46593 - 1.36054i) q^{4} +(-2.20168 - 0.390628i) q^{5} +(4.10564 - 1.79095i) q^{6} +(0.918543 - 0.918543i) q^{7} +(2.54856 - 1.22671i) q^{8} +7.03189i q^{9} +O(q^{10})$	\(q+(-0.516756 + 1.31642i) q^{2} +(-2.23963 - 2.23963i) q^{3} +(-1.46593 - 1.36054i) q^{4} +(-2.20168 - 0.390628i) q^{5} +(4.10564 - 1.79095i) q^{6} +(0.918543 - 0.918543i) q^{7} +(2.54856 - 1.22671i) q^{8} +7.03189i q^{9} +(1.65196 - 2.69648i) q^{10} +3.84514i q^{11} +(0.236035 + 6.33023i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(0.734526 + 1.68385i) q^{14} +(4.05610 + 5.80582i) q^{15} +(0.297882 + 3.98889i) q^{16} +(-1.82590 - 1.82590i) q^{17} +(-9.25693 - 3.63377i) q^{18} -2.11964 q^{19} +(2.69604 + 3.56810i) q^{20} -4.11439 q^{21} +(-5.06183 - 1.98700i) q^{22} +(4.88785 + 4.88785i) q^{23} +(-8.45522 - 2.96046i) q^{24} +(4.69482 + 1.72008i) q^{25} +(-0.565448 - 1.29625i) q^{26} +(9.02994 - 9.02994i) q^{27} +(-2.59623 + 0.0968054i) q^{28} +8.40499i q^{29} +(-9.73891 + 2.33934i) q^{30} -2.11067i q^{31} +(-5.40499 - 1.66915i) q^{32} +(8.61170 - 8.61170i) q^{33} +(3.34719 - 1.46011i) q^{34} +(-2.38115 + 1.66353i) q^{35} +(9.56714 - 10.3082i) q^{36} +(-4.85589 - 4.85589i) q^{37} +(1.09534 - 2.79033i) q^{38} +3.16732 q^{39} +(-6.09032 + 1.70529i) q^{40} +1.76398 q^{41} +(2.12614 - 5.41627i) q^{42} +(-0.980214 - 0.980214i) q^{43} +(5.23146 - 5.63670i) q^{44} +(2.74685 - 15.4820i) q^{45} +(-8.96029 + 3.90864i) q^{46} +(-6.80504 + 6.80504i) q^{47} +(8.26650 - 9.60079i) q^{48} +5.31256i q^{49} +(-4.69042 + 5.29150i) q^{50} +8.17867i q^{51} +(1.99861 - 0.0745222i) q^{52} +(-2.86242 + 2.86242i) q^{53} +(7.22093 + 16.5535i) q^{54} +(1.50202 - 8.46579i) q^{55} +(1.21418 - 3.46775i) q^{56} +(4.74721 + 4.74721i) q^{57} +(-11.0645 - 4.34333i) q^{58} -8.24159 q^{59} +(1.95309 - 14.0294i) q^{60} +2.94727 q^{61} +(2.77852 + 1.09070i) q^{62} +(6.45909 + 6.45909i) q^{63} +(4.99036 - 6.25270i) q^{64} +(1.83304 - 1.28061i) q^{65} +(6.88647 + 15.7868i) q^{66} +(1.81327 - 1.81327i) q^{67} +(0.192432 + 5.16083i) q^{68} -21.8940i q^{69} +(-0.959435 - 3.99423i) q^{70} -3.60503i q^{71} +(8.62610 + 17.9212i) q^{72} +(-11.5580 + 11.5580i) q^{73} +(8.90171 - 3.88309i) q^{74} +(-6.66232 - 14.3670i) q^{75} +(3.10723 + 2.88384i) q^{76} +(3.53193 + 3.53193i) q^{77} +(-1.63673 + 4.16952i) q^{78} +4.41904 q^{79} +(0.902332 - 8.89864i) q^{80} -19.3518 q^{81} +(-0.911545 + 2.32213i) q^{82} +(4.20776 + 4.20776i) q^{83} +(6.03140 + 5.59778i) q^{84} +(3.30680 + 4.73329i) q^{85} +(1.79691 - 0.783843i) q^{86} +(18.8241 - 18.8241i) q^{87} +(4.71688 + 9.79960i) q^{88} +9.46948i q^{89} +(18.9614 + 11.6164i) q^{90} +1.29902i q^{91} +(-0.515132 - 13.8153i) q^{92} +(-4.72711 + 4.72711i) q^{93} +(-5.44175 - 12.4748i) q^{94} +(4.66677 + 0.827990i) q^{95} +(8.36692 + 15.8435i) q^{96} +(2.33396 + 2.33396i) q^{97} +(-6.99356 - 2.74530i) q^{98} -27.0386 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.516756	+	1.31642i	−0.365402	+	0.930850i
$2$	−0.516756	+	1.31642i	−0.365402	+	0.930850i
$3$	−2.23963	−	2.23963i	−1.29305	−	1.29305i	−0.932890	−	0.360161i	$-0.882722\pi$
$3$	−2.23963	−	2.23963i	−1.29305	−	1.29305i	−0.360161	−	0.932890i	$-0.617278\pi$
$4$	−1.46593	−	1.36054i	−0.732963	−	0.680268i
$5$	−2.20168	−	0.390628i	−0.984623	−	0.174694i
$5$	−2.20168	−	0.390628i	−0.984623	−	0.174694i
$6$	4.10564	−	1.79095i	1.67612	−	0.731154i
$7$	0.918543	−	0.918543i	0.347177	−	0.347177i	−0.511880	−	0.859057i	$-0.671051\pi$
$7$	0.918543	−	0.918543i	0.347177	−	0.347177i	0.859057	+	0.511880i	$0.171051\pi$
$8$	2.54856	−	1.22671i	0.901054	−	0.433708i
$9$			7.03189i			2.34396i
$10$	1.65196	−	2.69648i	0.522397	−	0.852703i
$11$			3.84514i			1.15935i	0.814846	+	0.579677i	$0.196821\pi$
$11$			3.84514i			1.15935i	−0.814846	+	0.579677i	$0.803179\pi$
$12$	0.236035	+	6.33023i	0.0681375	+	1.82738i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$14$	0.734526	+	1.68385i	0.196310	+	0.450028i
$15$	4.05610	+	5.80582i	1.04728	+	1.49906i
$16$	0.297882	+	3.98889i	0.0744704	+	0.997223i
$17$	−1.82590	−	1.82590i	−0.442845	−	0.442845i	0.450122	−	0.892967i	$-0.351380\pi$
$17$	−1.82590	−	1.82590i	−0.442845	−	0.442845i	−0.892967	+	0.450122i	$0.851380\pi$
$18$	−9.25693	−	3.63377i	−2.18188	−	0.856488i
$19$	−2.11964			−0.486278			−0.243139	−	0.969991i	$-0.578177\pi$
$19$	−2.11964			−0.486278			−0.243139	+	0.969991i	$0.578177\pi$
$20$	2.69604	+	3.56810i	0.602853	+	0.797852i
$21$	−4.11439			−0.897834
$22$	−5.06183	−	1.98700i	−1.07919	−	0.423630i
$23$	4.88785	+	4.88785i	1.01919	+	1.01919i	0.999812	+	0.0193750i	$0.00616763\pi$
$23$	4.88785	+	4.88785i	1.01919	+	1.01919i	0.0193750	+	0.999812i	$0.493832\pi$
$24$	−8.45522	−	2.96046i	−1.72591	−	0.604302i
$25$	4.69482	+	1.72008i	0.938964	+	0.344016i
$26$	−0.565448	−	1.29625i	−0.110894	−	0.254216i
$27$	9.02994	−	9.02994i	1.73781	−	1.73781i
$28$	−2.59623	+	0.0968054i	−0.490641	+	0.0182945i
$29$			8.40499i			1.56077i	0.625301	+	0.780383i	$0.284976\pi$
$29$			8.40499i			1.56077i	−0.625301	+	0.780383i	$0.715024\pi$
$30$	−9.73891	+	2.33934i	−1.77807	+	0.427102i
$31$		−	2.11067i		−	0.379087i	−0.981872	−	0.189543i	$-0.939299\pi$
$31$		−	2.11067i		−	0.379087i	0.981872	−	0.189543i	$-0.0607008\pi$
$32$	−5.40499	−	1.66915i	−0.955477	−	0.295066i
$33$	8.61170	−	8.61170i	1.49910	−	1.49910i
$34$	3.34719	−	1.46011i	0.574038	−	0.250406i
$35$	−2.38115	+	1.66353i	−0.402488	+	0.281188i
$36$	9.56714	−	10.3082i	1.59452	−	1.71804i
$37$	−4.85589	−	4.85589i	−0.798304	−	0.798304i	0.184524	−	0.982828i	$-0.440926\pi$
$37$	−4.85589	−	4.85589i	−0.798304	−	0.798304i	−0.982828	+	0.184524i	$0.940926\pi$
$38$	1.09534	−	2.79033i	0.177687	−	0.452652i
$39$	3.16732			0.507176
$40$	−6.09032	+	1.70529i	−0.962964	+	0.269630i
$41$	1.76398			0.275487			0.137743	−	0.990468i	$-0.456015\pi$
$41$	1.76398			0.275487			0.137743	+	0.990468i	$0.456015\pi$
$42$	2.12614	−	5.41627i	0.328070	−	0.835749i
$43$	−0.980214	−	0.980214i	−0.149481	−	0.149481i	0.628405	−	0.777886i	$-0.283708\pi$
$43$	−0.980214	−	0.980214i	−0.149481	−	0.149481i	−0.777886	+	0.628405i	$0.783708\pi$
$44$	5.23146	−	5.63670i	0.788672	−	0.849764i
$45$	2.74685	−	15.4820i	0.409477	−	2.30792i
$46$	−8.96029	+	3.90864i	−1.32112	+	0.576298i
$47$	−6.80504	+	6.80504i	−0.992617	+	0.992617i	−0.999973	−	0.00735546i	$-0.997659\pi$
$47$	−6.80504	+	6.80504i	−0.992617	+	0.992617i	0.00735546	+	0.999973i	$0.497659\pi$
$48$	8.26650	−	9.60079i	1.19317	−	1.38575i
$49$			5.31256i			0.758937i
$50$	−4.69042	+	5.29150i	−0.663326	+	0.748331i
$51$			8.17867i			1.14524i
$52$	1.99861	−	0.0745222i	0.277157	−	0.0103344i
$53$	−2.86242	+	2.86242i	−0.393183	+	0.393183i	−0.875820	−	0.482637i	$-0.839679\pi$
$53$	−2.86242	+	2.86242i	−0.393183	+	0.393183i	0.482637	+	0.875820i	$0.339679\pi$
$54$	7.22093	+	16.5535i	0.982644	+	2.25264i
$55$	1.50202	−	8.46579i	0.202532	−	1.14153i
$56$	1.21418	−	3.46775i	0.162252	−	0.463398i
$57$	4.74721	+	4.74721i	0.628783	+	0.628783i
$58$	−11.0645	−	4.34333i	−1.45284	−	0.570307i
$59$	−8.24159			−1.07296			−0.536482	−	0.843912i	$-0.680247\pi$
$59$	−8.24159			−1.07296			−0.536482	+	0.843912i	$0.680247\pi$
$60$	1.95309	−	14.0294i	0.252143	−	1.81118i
$61$	2.94727			0.377359			0.188679	−	0.982039i	$-0.439579\pi$
$61$	2.94727			0.377359			0.188679	+	0.982039i	$0.439579\pi$
$62$	2.77852	+	1.09070i	0.352873	+	0.138519i
$63$	6.45909	+	6.45909i	0.813769	+	0.813769i
$64$	4.99036	−	6.25270i	0.623795	−	0.781588i
$65$	1.83304	−	1.28061i	0.227361	−	0.158840i
$66$	6.88647	+	15.7868i	0.847666	+	1.94322i
$67$	1.81327	−	1.81327i	0.221526	−	0.221526i	−0.587615	−	0.809141i	$-0.699933\pi$
$67$	1.81327	−	1.81327i	0.221526	−	0.221526i	0.809141	+	0.587615i	$0.199933\pi$
$68$	0.192432	+	5.16083i	0.0233358	+	0.625842i
$69$		−	21.8940i		−	2.63572i
$70$	−0.959435	−	3.99423i	−0.114674	−	0.477402i
$71$		−	3.60503i		−	0.427839i	−0.976851	−	0.213919i	$-0.931377\pi$
$71$		−	3.60503i		−	0.427839i	0.976851	−	0.213919i	$-0.0686230\pi$
$72$	8.62610	+	17.9212i	1.01660	+	2.11204i
$73$	−11.5580	+	11.5580i	−1.35276	+	1.35276i	−0.470201	+	0.882559i	$0.655819\pi$
$73$	−11.5580	+	11.5580i	−1.35276	+	1.35276i	−0.882559	+	0.470201i	$0.844181\pi$
$74$	8.90171	−	3.88309i	1.03480	−	0.451400i
$75$	−6.66232	−	14.3670i	−0.769299	−	1.65896i
$76$	3.10723	+	2.88384i	0.356424	+	0.330800i
$77$	3.53193	+	3.53193i	0.402501	+	0.402501i
$78$	−1.63673	+	4.16952i	−0.185323	+	0.472105i
$79$	4.41904			0.497181			0.248590	−	0.968609i	$-0.420033\pi$
$79$	4.41904			0.497181			0.248590	+	0.968609i	$0.420033\pi$
$80$	0.902332	−	8.89864i	0.100884	−	0.994898i
$81$	−19.3518			−2.15020
$82$	−0.911545	+	2.32213i	−0.100663	+	0.256437i
$83$	4.20776	+	4.20776i	0.461861	+	0.461861i	0.899265	−	0.437404i	$-0.144102\pi$
$83$	4.20776	+	4.20776i	0.461861	+	0.461861i	−0.437404	+	0.899265i	$0.644102\pi$
$84$	6.03140	+	5.59778i	0.658079	+	0.610768i
$85$	3.30680	+	4.73329i	0.358673	+	0.513398i
$86$	1.79691	−	0.783843i	0.193765	−	0.0845239i
$87$	18.8241	−	18.8241i	2.01815	−	2.01815i
$88$	4.71688	+	9.79960i	0.502821	+	1.04464i
$89$			9.46948i			1.00376i	0.864936	+	0.501882i	$0.167359\pi$
$89$			9.46948i			1.00376i	−0.864936	+	0.501882i	$0.832641\pi$
$90$	18.9614	+	11.6164i	1.99870	+	1.22448i
$91$			1.29902i			0.136174i
$92$	−0.515132	−	13.8153i	−0.0537062	−	1.44035i
$93$	−4.72711	+	4.72711i	−0.490179	+	0.490179i
$94$	−5.44175	−	12.4748i	−0.561274	−	1.28668i
$95$	4.66677	+	0.827990i	0.478801	+	0.0849500i
$96$	8.36692	+	15.8435i	0.853945	+	1.61702i
$97$	2.33396	+	2.33396i	0.236977	+	0.236977i	0.815597	−	0.578620i	$-0.196409\pi$
$97$	2.33396	+	2.33396i	0.236977	+	0.236977i	−0.578620	+	0.815597i	$0.696409\pi$
$98$	−6.99356	−	2.74530i	−0.706456	−	0.277317i
$99$	−27.0386			−2.71748
$100$	−4.54203	−	8.90898i	−0.454203	−	0.890898i
$101$	3.70148			0.368311			0.184155	−	0.982897i	$-0.441045\pi$
$101$	3.70148			0.368311			0.184155	+	0.982897i	$0.441045\pi$
$102$	−10.7666	−	4.22637i	−1.06605	−	0.418473i
$103$	−11.8324	−	11.8324i	−1.16588	−	1.16588i	−0.983167	−	0.182711i	$-0.941513\pi$
$103$	−11.8324	−	11.8324i	−1.16588	−	1.16588i	−0.182711	−	0.983167i	$-0.558487\pi$
$104$	−0.934692	+	2.66952i	−0.0916541	+	0.261768i
$105$	9.05859	+	1.60720i	0.884028	+	0.156846i
$106$	−2.28897	−	5.24732i	−0.222325	−	0.509664i
$107$	−5.22115	+	5.22115i	−0.504748	+	0.504748i	−0.912910	−	0.408162i	$-0.866170\pi$
$107$	−5.22115	+	5.22115i	−0.504748	+	0.504748i	0.408162	+	0.912910i	$0.366170\pi$
$108$	−25.5228	+	0.951668i	−2.45593	+	0.0915743i
$109$		−	8.97655i		−	0.859797i	−0.902877	−	0.429899i	$-0.858549\pi$
$109$		−	8.97655i		−	0.859797i	0.902877	−	0.429899i	$-0.141451\pi$
$110$	10.3684	+	6.35204i	0.988584	+	0.605643i
$111$			21.7508i			2.06450i
$112$	3.93759	+	3.39035i	0.372067	+	0.320358i
$113$	−3.62969	+	3.62969i	−0.341452	+	0.341452i	−0.856913	−	0.515461i	$-0.827621\pi$
$113$	−3.62969	+	3.62969i	−0.341452	+	0.341452i	0.515461	+	0.856913i	$0.327621\pi$
$114$	−8.70247	+	3.79617i	−0.815061	+	0.355544i
$115$	−8.85217	−	12.6708i	−0.825469	−	1.18156i
$116$	11.4353	−	12.3211i	1.06174	−	1.14398i
$117$	−4.97230	−	4.97230i	−0.459689	−	0.459689i
$118$	4.25889	−	10.8494i	0.392063	−	0.998768i
$119$	−3.35433			−0.307491
$120$	17.4593	+	9.82085i	1.59381	+	0.896517i
$121$	−3.78513			−0.344103
$122$	−1.52302	+	3.87984i	−0.137888	+	0.351264i
$123$	−3.95065	−	3.95065i	−0.356219	−	0.356219i
$124$	−2.87164	+	3.09408i	−0.257881	+	0.277857i
$125$	−9.66460	−	5.62100i	−0.864428	−	0.502757i
$126$	−11.8407	+	5.16511i	−1.05485	+	0.460144i
$127$	−4.53841	+	4.53841i	−0.402719	+	0.402719i	−0.879190	−	0.476471i	$-0.841916\pi$
$127$	−4.53841	+	4.53841i	−0.402719	+	0.402719i	0.476471	+	0.879190i	$0.341916\pi$
$128$	5.65239	+	9.80054i	0.499605	+	0.866253i
$129$			4.39063i			0.386574i
$130$	0.738586	+	3.07482i	0.0647783	+	0.269679i
$131$			17.3332i			1.51441i	0.653180	+	0.757203i	$0.273435\pi$
$131$			17.3332i			1.51441i	−0.653180	+	0.757203i	$0.726565\pi$
$132$	−24.3407	+	0.907589i	−2.11858	+	0.0789955i
$133$	−1.94698	+	1.94698i	−0.168824	+	0.168824i
$134$	1.45001	+	3.32404i	0.125261	+	0.287153i
$135$	−23.4084	+	16.3537i	−2.01468	+	1.40750i
$136$	−6.89326	−	2.41357i	−0.591092	−	0.206962i
$137$	−5.36795	−	5.36795i	−0.458615	−	0.458615i	0.439586	−	0.898201i	$-0.355125\pi$
$137$	−5.36795	−	5.36795i	−0.458615	−	0.458615i	−0.898201	+	0.439586i	$0.855125\pi$
$138$	28.8217	+	11.3138i	2.45346	+	0.963097i
$139$	−16.6018			−1.40815			−0.704073	−	0.710128i	$-0.748637\pi$
$139$	−16.6018			−1.40815			−0.704073	+	0.710128i	$0.748637\pi$
$140$	5.75389	+	0.801024i	0.486292	+	0.0676989i
$141$	30.4816			2.56701
$142$	4.74574	+	1.86292i	0.398254	+	0.156333i
$143$	−2.71893	−	2.71893i	−0.227368	−	0.227368i
$144$	−28.0495	+	2.09467i	−2.33745	+	0.174556i
$145$	3.28322	−	18.5051i	0.272657	−	1.53677i
$146$	−9.24252	−	21.1878i	−0.764916	−	1.75352i
$147$	11.8982	−	11.8982i	0.981344	−	0.981344i
$148$	0.511764	+	13.7250i	0.0420667	+	1.12819i
$149$		−	14.1914i		−	1.16260i	−0.813688	−	0.581302i	$-0.802543\pi$
$149$		−	14.1914i		−	1.16260i	0.813688	−	0.581302i	$-0.197457\pi$
$150$	22.3558	−	1.34618i	1.82534	−	0.109916i
$151$		−	4.46986i		−	0.363752i	−0.983321	−	0.181876i	$-0.941783\pi$
$151$		−	4.46986i		−	0.363752i	0.983321	−	0.181876i	$-0.0582169\pi$
$152$	−5.40203	+	2.60018i	−0.438163	+	0.210903i
$153$	12.8395	−	12.8395i	1.03801	−	1.03801i
$154$	−6.47465	+	2.82436i	−0.521742	+	0.227593i
$155$	−0.824485	+	4.64702i	−0.0662242	+	0.373257i
$156$	−4.64305	−	4.30925i	−0.371742	−	0.345016i
$157$	13.1851	+	13.1851i	1.05229	+	1.05229i	0.998555	+	0.0537332i	$0.0171121\pi$
$157$	13.1851	+	13.1851i	1.05229	+	1.05229i	0.0537332	+	0.998555i	$0.482888\pi$
$158$	−2.28357	+	5.81732i	−0.181671	+	0.462801i
$159$	12.8215			1.01681
$160$	11.2481	+	5.78627i	0.889238	+	0.457445i
$161$	8.97940			0.707676
$162$	10.0002	−	25.4751i	0.785687	−	2.00151i
$163$	12.3293	+	12.3293i	0.965704	+	0.965704i	0.999431	−	0.0337267i	$-0.0107376\pi$
$163$	12.3293	+	12.3293i	0.965704	+	0.965704i	−0.0337267	+	0.999431i	$0.510738\pi$
$164$	−2.58586	−	2.39995i	−0.201922	−	0.187405i
$165$	−22.3242	+	15.5963i	−1.73794	+	1.21417i
$166$	−7.71356	+	3.36479i	−0.598688	+	0.261159i
$167$	4.32625	−	4.32625i	0.334776	−	0.334776i	−0.519621	−	0.854397i	$-0.673927\pi$
$167$	4.32625	−	4.32625i	0.334776	−	0.334776i	0.854397	+	0.519621i	$0.173927\pi$
$168$	−10.4858	+	5.04717i	−0.808997	+	0.389398i
$169$		−	1.00000i		−	0.0769231i
$170$	−7.93981	+	1.90718i	−0.608956	+	0.146274i
$171$		−	14.9051i		−	1.13982i
$172$	0.103305	+	2.77054i	0.00787693	+	0.211252i
$173$	7.96635	−	7.96635i	0.605670	−	0.605670i	−0.336141	−	0.941812i	$-0.609122\pi$
$173$	7.96635	−	7.96635i	0.605670	−	0.605670i	0.941812	+	0.336141i	$0.109122\pi$
$174$	15.0529	+	34.5078i	1.14116	+	2.61603i
$175$	5.89236	−	2.73243i	0.445420	−	0.206552i
$176$	−15.3379	+	1.14540i	−1.15614	+	0.0863376i
$177$	18.4581	+	18.4581i	1.38740	+	1.38740i
$178$	−12.4658	−	4.89341i	−0.934353	−	0.366777i
$179$	11.8615			0.886572			0.443286	−	0.896380i	$-0.353813\pi$
$179$	11.8615			0.886572			0.443286	+	0.896380i	$0.353813\pi$
$180$	−25.0905	+	18.9583i	−1.87014	+	1.41307i
$181$	2.12699			0.158098			0.0790488	−	0.996871i	$-0.474812\pi$
$181$	2.12699			0.158098			0.0790488	+	0.996871i	$0.474812\pi$
$182$	−1.71005	−	0.671274i	−0.126757	−	0.0497581i
$183$	−6.60079	−	6.60079i	−0.487944	−	0.487944i
$184$	18.4530	+	6.46102i	1.36037	+	0.476313i
$185$	8.79429	+	12.5880i	0.646569	+	0.925487i
$186$	−3.78010	−	8.66563i	−0.277171	−	0.635395i
$187$	7.02083	−	7.02083i	0.513414	−	0.513414i
$188$	19.2342	−	0.717185i	1.40280	−	0.0523061i
$189$		−	16.5888i		−	1.20666i
$190$	−3.50156	+	5.71557i	−0.254030	+	0.414651i
$191$		−	18.0502i		−	1.30607i	−0.757330	−	0.653033i	$-0.773496\pi$
$191$		−	18.0502i		−	1.30607i	0.757330	−	0.653033i	$-0.226504\pi$
$192$	−25.1803	+	2.82718i	−1.81723	+	0.204034i
$193$	−15.6724	+	15.6724i	−1.12812	+	1.12812i	−0.137642	+	0.990482i	$0.543952\pi$
$193$	−15.6724	+	15.6724i	−1.12812	+	1.12812i	−0.990482	+	0.137642i	$0.956048\pi$
$194$	−4.27855	+	1.86638i	−0.307182	+	0.133998i
$195$	−6.97343	−	1.23724i	−0.499377	−	0.0886008i
$196$	7.22793	−	7.78782i	0.516281	−	0.556273i
$197$	3.07519	+	3.07519i	0.219098	+	0.219098i	0.808118	−	0.589020i	$-0.200486\pi$
$197$	3.07519	+	3.07519i	0.219098	+	0.219098i	−0.589020	+	0.808118i	$0.700486\pi$
$198$	13.9724	−	35.5942i	0.992973	−	2.52957i
$199$	8.16946			0.579117			0.289559	−	0.957160i	$-0.406491\pi$
$199$	8.16946			0.579117			0.289559	+	0.957160i	$0.406491\pi$
$200$	14.0751	−	1.37546i	0.995259	−	0.0972594i
$201$	−8.12210			−0.572889
$202$	−1.91276	+	4.87270i	−0.134581	+	0.342842i
$203$	7.72034	+	7.72034i	0.541862	+	0.541862i
$204$	11.1274	−	11.9893i	0.779072	−	0.839421i
$205$	−3.88372	−	0.689058i	−0.271251	−	0.0481259i
$206$	21.6908	−	9.46193i	1.51127	−	0.659244i
$207$	−34.3708	+	34.3708i	−2.38894	+	2.38894i
$208$	−3.03121	−	2.60994i	−0.210176	−	0.180967i
$209$		−	8.15031i		−	0.563769i
$210$	−6.79683	+	11.0944i	−0.469026	+	0.765585i
$211$			18.9671i			1.30575i	0.757467	+	0.652873i	$0.226437\pi$
$211$			18.9671i			1.30575i	−0.757467	+	0.652873i	$0.773563\pi$
$212$	8.09052	−	0.301671i	0.555659	−	0.0207188i
$213$	−8.07394	+	8.07394i	−0.553217	+	0.553217i
$214$	−4.17517	−	9.57130i	−0.285409	−	0.654280i
$215$	1.77522	+	2.54102i	0.121069	+	0.173296i
$216$	11.9363	−	34.0905i	0.812160	−	2.31957i
$217$	−1.93874	−	1.93874i	−0.131610	−	0.131610i
$218$	11.8169	+	4.63868i	0.800342	+	0.314171i
$219$	51.7713			3.49838
$220$	−13.7199	+	10.3667i	−0.924993	+	0.698921i
$221$	2.58221			0.173698
$222$	−28.6332	−	11.2399i	−1.92174	−	0.754370i
$223$	0.848283	+	0.848283i	0.0568052	+	0.0568052i	0.734939	−	0.678134i	$-0.237211\pi$
$223$	0.848283	+	0.848283i	0.0568052	+	0.0568052i	−0.678134	+	0.734939i	$0.737211\pi$
$224$	−6.49790	+	3.43153i	−0.434159	+	0.229279i
$225$	−12.0954	+	33.0135i	−0.806360	+	2.20090i
$226$	−2.90253	−	6.65385i	−0.193073	−	0.442608i
$227$	−9.33049	+	9.33049i	−0.619286	+	0.619286i	−0.945348	−	0.326062i	$-0.894278\pi$
$227$	−9.33049	+	9.33049i	−0.619286	+	0.619286i	0.326062	+	0.945348i	$0.394278\pi$
$228$	−0.500309	−	13.4178i	−0.0331338	−	0.888616i
$229$		−	0.978640i		−	0.0646704i	−0.999477	−	0.0323352i	$-0.989706\pi$
$229$		−	0.978640i		−	0.0646704i	0.999477	−	0.0323352i	$-0.0102944\pi$
$230$	21.2546	−	5.10545i	1.40148	−	0.336643i
$231$		−	15.8204i		−	1.04091i
$232$	10.3105	+	21.4206i	0.676917	+	1.40633i
$233$	9.95655	−	9.95655i	0.652275	−	0.652275i	−0.301265	−	0.953540i	$-0.597409\pi$
$233$	9.95655	−	9.95655i	0.652275	−	0.652275i	0.953540	+	0.301265i	$0.0974090\pi$
$234$	9.11510	−	3.97617i	0.595873	−	0.259930i
$235$	17.6408	−	12.3243i	1.15076	−	0.803949i
$236$	12.0816	+	11.2130i	0.786443	+	0.729903i
$237$	−9.89702	−	9.89702i	−0.642881	−	0.642881i
$238$	1.73337	−	4.41571i	0.112358	−	0.286228i
$239$	−7.98982			−0.516819			−0.258409	−	0.966036i	$-0.583198\pi$
$239$	−7.98982			−0.516819			−0.258409	+	0.966036i	$0.583198\pi$
$240$	−21.9506	+	17.9088i	−1.41690	+	1.15601i
$241$	17.0010			1.09513			0.547565	−	0.836763i	$-0.315555\pi$
$241$	17.0010			1.09513			0.547565	+	0.836763i	$0.315555\pi$
$242$	1.95599	−	4.98282i	0.125736	−	0.320308i
$243$	16.2511	+	16.2511i	1.04251	+	1.04251i
$244$	−4.32048	−	4.00986i	−0.276590	−	0.256705i
$245$	2.07523	−	11.6966i	0.132582	−	0.747267i
$246$	7.24225	−	3.15920i	0.461749	−	0.201423i
$247$	1.49881	−	1.49881i	0.0953670	−	0.0953670i
$248$	−2.58918	−	5.37917i	−0.164413	−	0.341578i
$249$		−	18.8476i		−	1.19442i
$250$	12.3938	−	9.81799i	0.783855	−	0.620944i
$251$			1.82190i			0.114997i	0.998346	+	0.0574985i	$0.0183125\pi$
$251$			1.82190i			0.114997i	−0.998346	+	0.0574985i	$0.981688\pi$
$252$	−0.680725	−	18.2564i	−0.0428817	−	1.15004i
$253$	−18.7945	+	18.7945i	−1.18160	+	1.18160i
$254$	−3.62921	−	8.31970i	−0.227717	−	0.522025i
$255$	3.19482	−	18.0068i	0.200067	−	1.12763i
$256$	−15.8225	+	2.37644i	−0.988908	+	0.148527i
$257$	−17.1141	−	17.1141i	−1.06755	−	1.06755i	−0.997547	−	0.0700002i	$-0.977700\pi$
$257$	−17.1141	−	17.1141i	−1.06755	−	1.06755i	−0.0700002	−	0.997547i	$-0.522300\pi$
$258$	−5.77992	−	2.26889i	−0.359842	−	0.141255i
$259$	−8.92069			−0.554305
$260$	−4.42942	−	0.616639i	−0.274701	−	0.0382423i
$261$	−59.1029			−3.65838
$262$	−22.8177	−	8.95702i	−1.40968	−	0.553366i
$263$	−5.80407	−	5.80407i	−0.357895	−	0.357895i	0.505142	−	0.863036i	$-0.331440\pi$
$263$	−5.80407	−	5.80407i	−0.357895	−	0.357895i	−0.863036	+	0.505142i	$0.831440\pi$
$264$	11.3834	−	32.5115i	0.700600	−	2.00095i
$265$	7.42028	−	5.18400i	0.455824	−	0.318450i
$266$	−1.55693	−	3.56915i	−0.0954615	−	0.218839i
$267$	21.2081	−	21.2081i	1.29792	−	1.29792i
$268$	−5.12513	+	0.191101i	−0.313067	+	0.0116733i
$269$			2.30491i			0.140533i	0.997528	+	0.0702664i	$0.0223849\pi$
$269$			2.30491i			0.140533i	−0.997528	+	0.0702664i	$0.977615\pi$
$270$	−9.43194	−	39.2662i	−0.574010	−	2.38967i
$271$		−	17.1855i		−	1.04394i	−0.852963	−	0.521971i	$-0.825197\pi$
$271$		−	17.1855i		−	1.04394i	0.852963	−	0.521971i	$-0.174803\pi$
$272$	6.73940	−	7.82721i	0.408636	−	0.474594i
$273$	2.90932	−	2.90932i	0.176080	−	0.176080i
$274$	9.84041	−	4.29256i	0.594481	−	0.259323i
$275$	−6.61395	+	18.0523i	−0.398836	+	1.08859i
$276$	−29.7875	+	32.0949i	−1.79300	+	1.93189i
$277$	1.69205	+	1.69205i	0.101666	+	0.101666i	0.756110	−	0.654444i	$-0.227097\pi$
$277$	1.69205	+	1.69205i	0.101666	+	0.101666i	−0.654444	+	0.756110i	$0.727097\pi$
$278$	8.57907	−	21.8549i	0.514538	−	1.31077i
$279$	14.8420			0.888566
$280$	−4.02784	+	7.16060i	−0.240709	+	0.427928i
$281$	−12.7153			−0.758532			−0.379266	−	0.925288i	$-0.623823\pi$
$281$	−12.7153			−0.758532			−0.379266	+	0.925288i	$0.623823\pi$
$282$	−15.7515	+	40.1266i	−0.937990	+	2.38950i
$283$	12.4780	+	12.4780i	0.741737	+	0.741737i	0.972912	−	0.231175i	$-0.0742569\pi$
$283$	12.4780	+	12.4780i	0.741737	+	0.741737i	−0.231175	+	0.972912i	$0.574257\pi$
$284$	−4.90478	+	5.28471i	−0.291045	+	0.313590i
$285$	−8.59745	−	12.3062i	−0.509269	−	0.728958i
$286$	4.98427	−	2.17423i	0.294726	−	0.128565i
$287$	1.62029	−	1.62029i	0.0956425	−	0.0956425i
$288$	11.7373	−	38.0073i	0.691624	−	2.23960i
$289$		−	10.3322i		−	0.607777i
$290$	22.6639	+	13.8847i	1.33087	+	0.815339i
$291$		−	10.4544i		−	0.612848i
$292$	32.6682	−	1.21810i	1.91176	−	0.0712839i
$293$	−1.44715	+	1.44715i	−0.0845432	+	0.0845432i	−0.748114	−	0.663571i	$-0.769040\pi$
$293$	−1.44715	+	1.44715i	−0.0845432	+	0.0845432i	0.663571	+	0.748114i	$0.269040\pi$
$294$	9.51454	+	21.8114i	0.554900	+	1.27207i
$295$	18.1454	+	3.21940i	1.05646	+	0.187440i
$296$	−18.3323	−	6.41878i	−1.06555	−	0.373084i
$297$	34.7214	+	34.7214i	2.01474	+	2.01474i
$298$	18.6818	+	7.33349i	1.08221	+	0.424817i
$299$	−6.91246			−0.399758
$300$	−9.78035	+	30.1253i	−0.564669	+	1.73929i
$301$	−1.80074			−0.103793
$302$	5.88421	+	2.30982i	0.338598	+	0.132915i
$303$	−8.28995	−	8.28995i	−0.476245	−	0.476245i
$304$	−0.631401	−	8.45501i	−0.0362133	−	0.484928i
$305$	−6.48895	−	1.15128i	−0.371556	−	0.0659224i
$306$	10.2673	+	23.5371i	0.586942	+	1.34553i
$307$	2.02392	−	2.02392i	0.115511	−	0.115511i	−0.646988	−	0.762500i	$-0.723972\pi$
$307$	2.02392	−	2.02392i	0.115511	−	0.115511i	0.762500	+	0.646988i	$0.223972\pi$
$308$	−0.372231	−	9.98287i	−0.0212098	−	0.568827i
$309$			53.0003i			3.01508i
$310$	−5.69137	−	3.48674i	−0.323248	−	0.198034i
$311$			21.9636i			1.24544i	0.782444	+	0.622722i	$0.213973\pi$
$311$			21.9636i			1.24544i	−0.782444	+	0.622722i	$0.786027\pi$
$312$	8.07211	−	3.88538i	0.456993	−	0.219966i
$313$	9.29451	−	9.29451i	0.525357	−	0.525357i	−0.393827	−	0.919184i	$-0.628849\pi$
$313$	9.29451	−	9.29451i	0.525357	−	0.525357i	0.919184	+	0.393827i	$0.128849\pi$
$314$	−24.1707	+	10.5437i	−1.36403	+	0.595015i
$315$	−11.6978	−	16.7440i	−0.659095	−	0.943416i
$316$	−6.47799	−	6.01227i	−0.364415	−	0.338216i
$317$	−24.5364	−	24.5364i	−1.37810	−	1.37810i	−0.847823	−	0.530279i	$-0.822087\pi$
$317$	−24.5364	−	24.5364i	−1.37810	−	1.37810i	−0.530279	−	0.847823i	$-0.677913\pi$
$318$	−6.62559	+	16.8785i	−0.371545	+	0.946500i
$319$	−32.3184			−1.80948
$320$	−13.4297	+	11.8171i	−0.750742	+	0.660596i
$321$	23.3869			1.30533
$322$	−4.64016	+	11.8207i	−0.258586	+	0.658740i
$323$	3.87024	+	3.87024i	0.215346	+	0.215346i
$324$	28.3683	+	26.3288i	1.57602	+	1.46271i
$325$	−4.53602	+	2.10346i	−0.251613	+	0.116679i
$326$	−22.6018	+	9.85930i	−1.25180	+	0.546056i
$327$	−20.1042	+	20.1042i	−1.11176	+	1.11176i
$328$	4.49561	−	2.16389i	0.248228	−	0.119481i
$329$			12.5014i			0.689227i
$330$	−8.99508	−	37.4475i	−0.495163	−	2.06142i
$331$		−	8.67620i		−	0.476887i	−0.971156	−	0.238444i	$-0.923363\pi$
$331$		−	8.67620i		−	0.476887i	0.971156	−	0.238444i	$-0.0766372\pi$
$332$	−0.443456	−	11.8931i	−0.0243378	−	0.652717i
$333$	34.1461	−	34.1461i	1.87120	−	1.87120i
$334$	3.45955	+	7.93079i	0.189298	+	0.433953i
$335$	−4.70056	+	3.28393i	−0.256819	+	0.179420i
$336$	−1.22560	−	16.4119i	−0.0668621	−	0.895341i
$337$	−5.34559	−	5.34559i	−0.291193	−	0.291193i	0.546358	−	0.837551i	$-0.316014\pi$
$337$	−5.34559	−	5.34559i	−0.291193	−	0.291193i	−0.837551	+	0.546358i	$0.816014\pi$
$338$	1.31642	+	0.516756i	0.0716038	+	0.0281078i
$339$	16.2583			0.883030
$340$	1.59229	−	11.4377i	0.0863541	−	0.620295i
$341$	8.11581			0.439496
$342$	19.6213	+	7.70228i	1.06100	+	0.416491i
$343$	11.3096	+	11.3096i	0.610662	+	0.610662i
$344$	−3.70058	−	1.29570i	−0.199522	−	0.0698594i
$345$	−8.55239	+	48.2036i	−0.460445	+	2.59519i
$346$	6.37041	+	14.6037i	0.342475	+	0.785101i
$347$	−4.16909	+	4.16909i	−0.223809	+	0.223809i	−0.810100	−	0.586292i	$-0.800587\pi$
$347$	−4.16909	+	4.16909i	−0.223809	+	0.223809i	0.586292	+	0.810100i	$0.300587\pi$
$348$	−53.2055	+	1.98387i	−2.85211	+	0.106347i
$349$		−	2.32016i		−	0.124195i	−0.998070	−	0.0620976i	$-0.980221\pi$
$349$		−	2.32016i		−	0.124195i	0.998070	−	0.0620976i	$-0.0197790\pi$
$350$	0.552113	+	9.16882i	0.0295117	+	0.490094i
$351$			12.7703i			0.681627i
$352$	6.41811	−	20.7830i	0.342086	−	1.10774i
$353$	−20.9071	+	20.9071i	−1.11277	+	1.11277i	−0.119997	+	0.992774i	$0.538288\pi$
$353$	−20.9071	+	20.9071i	−1.11277	+	1.11277i	−0.992774	+	0.119997i	$0.961712\pi$
$354$	−33.8370	+	14.7603i	−1.79842	+	0.784501i
$355$	−1.40823	+	7.93714i	−0.0747409	+	0.421260i
$356$	12.8836	−	13.8816i	0.682828	−	0.735722i
$357$	7.51246	+	7.51246i	0.397601	+	0.397601i
$358$	−6.12951	+	15.6147i	−0.323955	+	0.825265i
$359$	−1.85375			−0.0978370			−0.0489185	−	0.998803i	$-0.515577\pi$
$359$	−1.85375			−0.0978370			−0.0489185	+	0.998803i	$0.515577\pi$
$360$	−11.9914	−	42.8265i	−0.632002	−	2.25715i
$361$	−14.5071			−0.763533
$362$	−1.09913	+	2.80001i	−0.0577692	+	0.147165i
$363$	8.47729	+	8.47729i	0.444942	+	0.444942i
$364$	1.76736	−	1.90426i	0.0926347	−	0.0998104i
$365$	29.9619	−	20.9322i	1.56828	−	1.09564i
$366$	12.1004	−	5.27842i	0.632499	−	0.275907i
$367$	−2.30679	+	2.30679i	−0.120414	+	0.120414i	−0.764746	−	0.644332i	$-0.777135\pi$
$367$	−2.30679	+	2.30679i	−0.120414	+	0.120414i	0.644332	+	0.764746i	$0.277135\pi$
$368$	−18.0411	+	20.9531i	−0.940458	+	1.09226i
$369$			12.4041i			0.645731i
$370$	−21.1156	+	5.07207i	−1.09775	+	0.263684i
$371$			5.25851i			0.273008i
$372$	13.3610	−	0.498191i	0.692736	−	0.0258300i
$373$	23.9386	−	23.9386i	1.23949	−	1.23949i	0.279284	−	0.960209i	$-0.409903\pi$
$373$	23.9386	−	23.9386i	1.23949	−	1.23949i	0.960209	−	0.279284i	$-0.0900970\pi$
$374$	5.61431	+	12.8704i	0.290309	+	0.665514i
$375$	9.05617	+	34.2341i	0.467659	+	1.76784i
$376$	−8.99527	+	25.6909i	−0.463896	+	1.32491i
$377$	−5.94322	−	5.94322i	−0.306092	−	0.306092i
$378$	21.8378	+	8.57235i	1.12322	+	0.440914i
$379$	20.2186			1.03856			0.519279	−	0.854605i	$-0.326201\pi$
$379$	20.2186			1.03856			0.519279	+	0.854605i	$0.326201\pi$
$380$	−5.71463	−	7.56308i	−0.293155	−	0.387978i
$381$	20.3287			1.04147
$382$	23.7616	+	9.32754i	1.21575	+	0.477239i
$383$	−3.38104	−	3.38104i	−0.172763	−	0.172763i	0.615429	−	0.788192i	$-0.288983\pi$
$383$	−3.38104	−	3.38104i	−0.172763	−	0.172763i	−0.788192	+	0.615429i	$0.788983\pi$
$384$	9.29032	−	34.6088i	0.474095	−	1.76613i
$385$	−6.39652	−	9.15586i	−0.325997	−	0.466626i
$386$	−12.5327	−	28.7303i	−0.637896	−	1.46233i
$387$	6.89276	−	6.89276i	0.350379	−	0.350379i
$388$	−0.245976	−	6.59684i	−0.0124875	−	0.334904i
$389$			3.25593i			0.165082i	0.996588	+	0.0825410i	$0.0263035\pi$
$389$			3.25593i			0.165082i	−0.996588	+	0.0825410i	$0.973696\pi$
$390$	5.23229	−	8.54061i	0.264947	−	0.432471i
$391$		−	17.8494i		−	0.902684i
$392$	6.51697	+	13.5394i	0.329157	+	0.683843i
$393$	38.8199	−	38.8199i	1.95820	−	1.95820i
$394$	−5.63737	+	2.45912i	−0.284007	+	0.123889i
$395$	−9.72933	−	1.72620i	−0.489536	−	0.0868546i
$396$	39.6366	+	36.7870i	1.99182	+	1.84862i
$397$	4.48113	+	4.48113i	0.224901	+	0.224901i	0.810559	−	0.585657i	$-0.199164\pi$
$397$	4.48113	+	4.48113i	0.224901	+	0.224901i	−0.585657	+	0.810559i	$0.699164\pi$
$398$	−4.22161	+	10.7544i	−0.211610	+	0.539071i
$399$	8.72102			0.436597
$400$	−5.46271	+	19.2395i	−0.273135	+	0.961976i
$401$	−15.9771			−0.797860			−0.398930	−	0.916981i	$-0.630618\pi$
$401$	−15.9771			−0.797860			−0.398930	+	0.916981i	$0.630618\pi$
$402$	4.19714	−	10.6921i	0.209335	−	0.533274i
$403$	1.49247	+	1.49247i	0.0743450	+	0.0743450i
$404$	−5.42610	−	5.03600i	−0.269958	−	0.250550i
$405$	42.6066	+	7.55936i	2.11714	+	0.375627i
$406$	−14.1527	+	6.17368i	−0.702389	+	0.306395i
$407$	18.6716	−	18.6716i	0.925517	−	0.925517i
$408$	10.0329	+	20.8439i	0.496701	+	1.03192i
$409$		−	8.03499i		−	0.397305i	−0.980070	−	0.198652i	$-0.936344\pi$
$409$		−	8.03499i		−	0.397305i	0.980070	−	0.198652i	$-0.0636565\pi$
$410$	2.91402	−	4.75653i	0.143913	−	0.234908i
$411$			24.0445i			1.18603i
$412$	1.24702	+	33.4437i	0.0614361	+	1.64765i
$413$	−7.57025	+	7.57025i	−0.372508	+	0.372508i
$414$	−27.4851	−	63.0078i	−1.35082	−	3.09666i
$415$	−7.62048	−	10.9078i	−0.374075	−	0.535443i
$416$	5.00217	−	2.64164i	0.245252	−	0.129517i
$417$	37.1819	+	37.1819i	1.82080	+	1.82080i
$418$	10.7292	+	4.21172i	0.524784	+	0.206002i
$419$	−10.1291			−0.494838			−0.247419	−	0.968909i	$-0.579582\pi$
$419$	−10.1291			−0.494838			−0.247419	+	0.968909i	$0.579582\pi$
$420$	−11.0926	−	14.6806i	−0.541262	−	0.716339i
$421$	6.38901			0.311381			0.155691	−	0.987806i	$-0.450240\pi$
$421$	6.38901			0.311381			0.155691	+	0.987806i	$0.450240\pi$
$422$	−24.9686	−	9.80134i	−1.21545	−	0.477122i
$423$	−47.8523	−	47.8523i	−2.32666	−	2.32666i
$424$	−3.78370	+	10.8064i	−0.183753	+	0.524806i
$425$	−5.43157	−	11.7129i	−0.263470	−	0.568161i
$426$	−6.45645	−	14.8010i	−0.312816	−	0.717109i
$427$	2.70719	−	2.70719i	0.131010	−	0.131010i
$428$	14.7574	−	0.550259i	0.713326	−	0.0265978i
$429$			12.1788i			0.587997i
$430$	−4.26241	+	1.02385i	−0.205552	+	0.0493745i
$431$		−	20.5386i		−	0.989310i	−0.869089	−	0.494655i	$-0.835294\pi$
$431$		−	20.5386i		−	0.989310i	0.869089	−	0.494655i	$-0.164706\pi$
$432$	38.7093	+	33.3296i	1.86240	+	1.60357i
$433$	−16.7017	+	16.7017i	−0.802631	+	0.802631i	−0.983506	−	0.180875i	$-0.942107\pi$
$433$	−16.7017	+	16.7017i	−0.802631	+	0.802631i	0.180875	+	0.983506i	$0.442107\pi$
$434$	3.55405	−	1.55034i	0.170600	−	0.0744187i
$435$	−48.7978	+	34.0914i	−2.33968	+	1.63456i
$436$	−12.2129	+	13.1590i	−0.584893	+	0.630200i
$437$	−10.3605	−	10.3605i	−0.495609	−	0.495609i
$438$	−26.7531	+	68.1527i	−1.27831	+	3.25646i
$439$	26.9755			1.28747			0.643735	−	0.765249i	$-0.277384\pi$
$439$	26.9755			1.28747			0.643735	+	0.765249i	$0.277384\pi$
$440$	−6.55708	−	23.4182i	−0.312596	−	1.11642i
$441$	−37.3573			−1.77892
$442$	−1.33437	+	3.39927i	−0.0634696	+	0.161687i
$443$	−20.1664	−	20.1664i	−0.958132	−	0.958132i	0.0410258	−	0.999158i	$-0.486937\pi$
$443$	−20.1664	−	20.1664i	−0.958132	−	0.958132i	−0.999158	+	0.0410258i	$0.986937\pi$
$444$	29.5928	−	31.8851i	1.40441	−	1.51320i
$445$	3.69904	−	20.8488i	0.175352	−	0.988328i
$446$	−1.55505	+	0.678342i	−0.0736338	+	0.0321204i
$447$	−31.7835	+	31.7835i	−1.50331	+	1.50331i
$448$	−1.15951	−	10.3272i	−0.0547819	−	0.487916i
$449$			18.7329i			0.884062i	0.897000	+	0.442031i	$0.145742\pi$
$449$			18.7329i			0.884062i	−0.897000	+	0.442031i	$0.854258\pi$
$450$	−37.2092	−	32.9825i	−1.75406	−	1.55481i
$451$			6.78274i			0.319387i
$452$	10.2592	−	0.382533i	0.482551	−	0.0179929i
$453$	−10.0108	+	10.0108i	−0.470350	+	0.470350i
$454$	−7.46126	−	17.1044i	−0.350174	−	0.802751i
$455$	0.507432	−	2.86002i	0.0237888	−	0.134080i
$456$	17.9220	+	6.27511i	0.839275	+	0.293859i
$457$	−0.912019	−	0.912019i	−0.0426624	−	0.0426624i	0.685454	−	0.728116i	$-0.259604\pi$
$457$	−0.912019	−	0.912019i	−0.0426624	−	0.0426624i	−0.728116	+	0.685454i	$0.759604\pi$
$458$	1.28830	+	0.505718i	0.0601984	+	0.0236307i
$459$	−32.9755			−1.53916
$460$	−4.26250	+	30.6182i	−0.198740	+	1.42758i
$461$	−13.6853			−0.637387			−0.318693	−	0.947858i	$-0.603244\pi$
$461$	−13.6853			−0.637387			−0.318693	+	0.947858i	$0.603244\pi$
$462$	20.8263	+	8.17530i	0.968929	+	0.380349i
$463$	−2.10470	−	2.10470i	−0.0978137	−	0.0978137i	0.656507	−	0.754320i	$-0.272033\pi$
$463$	−2.10470	−	2.10470i	−0.0978137	−	0.0978137i	−0.754320	+	0.656507i	$0.772033\pi$
$464$	−33.5266	+	2.50369i	−1.55643	+	0.116231i
$465$	12.2541	−	8.56106i	0.568272	−	0.397010i
$466$	7.96190	+	18.2521i	0.368828	+	0.845513i
$467$	28.5364	−	28.5364i	1.32051	−	1.32051i	0.407143	−	0.913365i	$-0.366525\pi$
$467$	28.5364	−	28.5364i	1.32051	−	1.32051i	0.913365	−	0.407143i	$-0.133475\pi$
$468$	0.524032	+	14.0540i	0.0242234	+	0.649647i
$469$		−	3.33113i		−	0.153817i
$470$	7.10799	+	29.5914i	0.327867	+	1.36495i
$471$		−	59.0597i		−	2.72133i
$472$	−21.0042	+	10.1100i	−0.966798	+	0.465353i
$473$	3.76906	−	3.76906i	0.173302	−	0.173302i
$474$	18.1430	−	7.91430i	0.833335	−	0.363516i
$475$	−9.95132	−	3.64594i	−0.456598	−	0.167287i
$476$	4.91720	+	4.56369i	0.225379	+	0.209176i
$477$	−20.1282	−	20.1282i	−0.921607	−	0.921607i
$478$	4.12879	−	10.5180i	0.188846	−	0.481081i
$479$	−19.8088			−0.905086			−0.452543	−	0.891743i	$-0.649483\pi$
$479$	−19.8088			−0.905086			−0.452543	+	0.891743i	$0.649483\pi$
$480$	−12.2324	−	38.1506i	−0.558330	−	1.74133i
$481$	6.86727			0.313121
$482$	−8.78536	+	22.3804i	−0.400162	+	1.01940i
$483$	−20.1105	−	20.1105i	−0.915061	−	0.915061i
$484$	5.54872	+	5.14981i	0.252215	+	0.234082i
$485$	−4.22692	−	6.05034i	−0.191935	−	0.274732i
$486$	−29.7911	+	12.9954i	−1.35135	+	0.589484i
$487$	−9.20752	+	9.20752i	−0.417232	+	0.417232i	−0.884249	−	0.467016i	$-0.845329\pi$
$487$	−9.20752	+	9.20752i	−0.417232	+	0.417232i	0.467016	+	0.884249i	$0.345329\pi$
$488$	7.51130	−	3.61544i	0.340020	−	0.163663i
$489$		−	55.2261i		−	2.49741i
$490$	14.3252	+	8.77615i	0.647147	+	0.396466i
$491$			23.5043i			1.06073i	0.847768	+	0.530367i	$0.177946\pi$
$491$			23.5043i			1.06073i	−0.847768	+	0.530367i	$0.822054\pi$
$492$	0.416360	+	11.1664i	0.0187710	+	0.503419i
$493$	15.3466	−	15.3466i	0.691178	−	0.691178i
$494$	1.19855	+	2.74758i	0.0539251	+	0.123620i
$495$	59.5305	+	10.5620i	2.67570	+	0.474729i
$496$	8.41922	−	0.628729i	0.378034	−	0.0282307i
$497$	−3.31138	−	3.31138i	−0.148536	−	0.148536i
$498$	24.8114	+	9.73963i	1.11183	+	0.436443i
$499$	−22.4244			−1.00386			−0.501928	−	0.864910i	$-0.667376\pi$
$499$	−22.4244			−1.00386			−0.501928	+	0.864910i	$0.667376\pi$
$500$	6.52002	+	21.3890i	0.291584	+	0.956545i
$501$	−19.3784			−0.865764
$502$	−2.39838	−	0.941476i	−0.107045	−	0.0420201i
$503$	24.2077	+	24.2077i	1.07937	+	1.07937i	0.996566	+	0.0828029i	$0.0263872\pi$
$503$	24.2077	+	24.2077i	1.07937	+	1.07937i	0.0828029	+	0.996566i	$0.473613\pi$
$504$	24.3848	+	8.53797i	1.08619	+	0.380312i
$505$	−8.14949	−	1.44590i	−0.362647	−	0.0643418i
$506$	−15.0293	−	34.4536i	−0.668133	−	1.53165i
$507$	−2.23963	+	2.23963i	−0.0994655	+	0.0994655i
$508$	12.8276	−	0.478304i	0.569135	−	0.0212213i
$509$			42.3216i			1.87587i	0.346808	+	0.937936i	$0.387266\pi$
$509$			42.3216i			1.87587i	−0.346808	+	0.937936i	$0.612734\pi$
$510$	22.0536	+	13.5109i	0.976551	+	0.598271i
$511$			21.2330i			0.939293i
$512$	5.04800	−	22.0571i	0.223092	−	0.974797i
$513$	−19.1402	+	19.1402i	−0.845061	+	0.845061i
$514$	31.3731	−	13.6855i	1.38381	−	0.603643i
$515$	21.4291	+	30.6732i	0.944278	+	1.35162i
$516$	5.97362	−	6.43635i	0.262974	−	0.283344i
$517$	−26.1664	−	26.1664i	−1.15080	−	1.15080i
$518$	4.60982	−	11.7434i	0.202544	−	0.515975i
$519$	−35.6834			−1.56633
$520$	3.10069	−	5.51233i	0.135974	−	0.241732i
$521$	−13.0136			−0.570136			−0.285068	−	0.958507i	$-0.592016\pi$
$521$	−13.0136			−0.570136			−0.285068	+	0.958507i	$0.592016\pi$
$522$	30.5418	−	77.8043i	1.33678	−	3.40540i
$523$	24.0226	+	24.0226i	1.05043	+	1.05043i	0.998659	+	0.0517748i	$0.0164878\pi$
$523$	24.0226	+	24.0226i	1.05043	+	1.05043i	0.0517748	+	0.998659i	$0.483512\pi$
$524$	23.5824	−	25.4092i	1.03020	−	1.11000i
$525$	−19.3163	−	7.07708i	−0.843034	−	0.308869i
$526$	10.6399	−	4.64131i	0.463921	−	0.202371i
$527$	−3.85386	+	3.85386i	−0.167877	+	0.167877i
$528$	36.9164	+	31.7859i	1.60658	+	1.38330i
$529$			24.7822i			1.07749i
$530$	2.98985	+	12.4471i	0.129871	+	0.540666i
$531$		−	57.9539i		−	2.51499i
$532$	5.50306	−	0.205192i	0.238588	−	0.00889622i
$533$	−1.24732	+	1.24732i	−0.0540274	+	0.0540274i
$534$	16.9594	+	38.8783i	0.733905	+	1.68243i
$535$	13.5349	−	9.45580i	0.585163	−	0.408810i
$536$	2.39687	−	6.84559i	0.103529	−	0.295684i
$537$	−26.5654	−	26.5654i	−1.14638	−	1.14638i
$538$	−3.03423	−	1.19108i	−0.130815	−	0.0513509i
$539$	−20.4275			−0.879877
$540$	56.5649	+	7.87465i	2.43416	+	0.338871i
$541$	27.8612			1.19785			0.598923	−	0.800807i	$-0.295596\pi$
$541$	27.8612			1.19785			0.598923	+	0.800807i	$0.295596\pi$
$542$	22.6233	+	8.88069i	0.971754	+	0.381458i
$543$	−4.76366	−	4.76366i	−0.204428	−	0.204428i
$544$	6.82127	+	12.9166i	0.292459	+	0.553797i
$545$	−3.50649	+	19.7635i	−0.150202	+	0.846576i
$546$	2.32648	+	5.33329i	0.0995640	+	0.228244i
$547$	−15.6942	+	15.6942i	−0.671038	+	0.671038i	−0.957955	−	0.286918i	$-0.907369\pi$
$547$	−15.6942	+	15.6942i	−0.671038	+	0.671038i	0.286918	+	0.957955i	$0.407369\pi$
$548$	0.565730	+	15.1723i	0.0241668	+	0.648129i
$549$			20.7249i			0.884515i
$550$	−20.3466	−	18.0353i	−0.867580	−	0.769030i
$551$		−	17.8155i		−	0.758967i
$552$	−26.8576	−	55.7982i	−1.14313	−	2.37493i
$553$	4.05908	−	4.05908i	0.172610	−	0.172610i
$554$	−3.10183	+	1.35308i	−0.131784	+	0.0574867i
$555$	8.49648	−	47.8884i	0.360655	−	2.03275i
$556$	24.3370	+	22.5873i	1.03212	+	0.957916i
$557$	−26.1672	−	26.1672i	−1.10874	−	1.10874i	−0.993317	−	0.115422i	$-0.963178\pi$
$557$	−26.1672	−	26.1672i	−1.10874	−	1.10874i	−0.115422	−	0.993317i	$-0.536822\pi$
$558$	−7.66968	+	19.5383i	−0.324683	+	0.827121i
$559$	1.38623			0.0586314
$560$	−7.34495	−	9.00261i	−0.310381	−	0.380430i
$561$	−31.4482			−1.32774
$562$	6.57072	−	16.7387i	0.277169	−	0.706080i
$563$	−27.4350	−	27.4350i	−1.15625	−	1.15625i	−0.985276	−	0.170971i	$-0.945310\pi$
$563$	−27.4350	−	27.4350i	−1.15625	−	1.15625i	−0.170971	−	0.985276i	$-0.554690\pi$
$564$	−44.6837	−	41.4713i	−1.88152	−	1.74626i
$565$	9.40927	−	6.57356i	0.395851	−	0.276552i
$566$	−22.8743	+	9.97818i	−0.961478	+	0.419414i
$567$	−17.7755	+	17.7755i	−0.746499	+	0.746499i
$568$	−4.42233	−	9.18766i	−0.185557	−	0.385506i
$569$		−	9.90886i		−	0.415401i	−0.978192	−	0.207701i	$-0.933402\pi$
$569$		−	9.90886i		−	0.415401i	0.978192	−	0.207701i	$-0.0665980\pi$
$570$	20.6430	−	4.95854i	0.864639	−	0.207691i
$571$		−	23.0063i		−	0.962784i	−0.876505	−	0.481392i	$-0.840131\pi$
$571$		−	23.0063i		−	0.962784i	0.876505	−	0.481392i	$-0.159869\pi$
$572$	0.286548	+	7.68495i	0.0119812	+	0.321324i
$573$	−40.4257	+	40.4257i	−1.68881	+	1.68881i
$574$	1.29569	+	2.97027i	0.0540809	+	0.123977i
$575$	14.5401	+	31.3551i	0.606364	+	1.30760i
$576$	43.9683	+	35.0917i	1.83201	+	1.46215i
$577$	14.0786	+	14.0786i	0.586101	+	0.586101i	0.936573	−	0.350472i	$-0.113979\pi$
$577$	14.0786	+	14.0786i	0.586101	+	0.586101i	−0.350472	+	0.936573i	$0.613979\pi$
$578$	13.6015	+	5.33923i	0.565749	+	0.222083i
$579$	70.2008			2.91745
$580$	−29.9898	+	22.6602i	−1.24526	+	0.940914i
$581$	7.73001			0.320695
$582$	13.7624	+	5.40237i	0.570469	+	0.223935i
$583$	−11.0064	−	11.0064i	−0.455839	−	0.455839i
$584$	−15.2780	+	43.6346i	−0.632207	+	1.80561i
$585$	9.00511	+	12.8897i	0.372315	+	0.532925i
$586$	−1.15723	−	2.65287i	−0.0478048	−	0.109589i
$587$	8.08122	−	8.08122i	0.333547	−	0.333547i	−0.520385	−	0.853932i	$-0.674211\pi$
$587$	8.08122	−	8.08122i	0.333547	−	0.333547i	0.853932	+	0.520385i	$0.174211\pi$
$588$	−33.6297	+	1.25395i	−1.38687	+	0.0517121i
$589$			4.47385i			0.184342i
$590$	−13.6148	+	22.2233i	−0.560513	+	0.914919i
$591$		−	13.7746i		−	0.566611i
$592$	17.9232	−	20.8161i	0.736637	−	0.855537i
$593$	9.04916	−	9.04916i	0.371605	−	0.371605i	−0.496457	−	0.868061i	$-0.665366\pi$
$593$	9.04916	−	9.04916i	0.371605	−	0.371605i	0.868061	+	0.496457i	$0.165366\pi$
$594$	−63.6505	+	27.7655i	−2.61161	+	1.13923i
$595$	7.38517	+	1.31029i	0.302762	+	0.0537168i
$596$	−19.3079	+	20.8035i	−0.790883	+	0.852146i
$597$	−18.2966	−	18.2966i	−0.748828	−	0.748828i
$598$	3.57206	−	9.09971i	0.146072	−	0.372115i
$599$	−9.45761			−0.386428			−0.193214	−	0.981157i	$-0.561891\pi$
$599$	−9.45761			−0.386428			−0.193214	+	0.981157i	$0.561891\pi$
$600$	−34.6035	−	28.4425i	−1.41268	−	1.16116i
$601$	36.3082			1.48104			0.740522	−	0.672032i	$-0.234578\pi$
$601$	36.3082			1.48104			0.740522	+	0.672032i	$0.234578\pi$
$602$	0.930542	−	2.37053i	0.0379260	−	0.0966155i
$603$	12.7507	+	12.7507i	0.519249	+	0.519249i
$604$	−6.08140	+	6.55248i	−0.247449	+	0.266617i
$605$	8.33366	+	1.47858i	0.338811	+	0.0601127i
$606$	15.1969	−	6.62918i	0.617333	−	0.269292i
$607$	−8.30758	+	8.30758i	−0.337194	+	0.337194i	−0.855310	−	0.518116i	$-0.826634\pi$
$607$	−8.30758	+	8.30758i	−0.337194	+	0.337194i	0.518116	+	0.855310i	$0.326634\pi$
$608$	11.4566	+	3.53799i	0.464628	+	0.143484i
$609$		−	34.5814i		−	1.40131i
$610$	4.86878	−	7.94725i	0.197131	−	0.321775i
$611$		−	9.62378i		−	0.389337i
$612$	−36.2904	+	1.35316i	−1.46695	+	0.0546982i
$613$	−0.566575	+	0.566575i	−0.0228838	+	0.0228838i	−0.718456	−	0.695572i	$-0.755151\pi$
$613$	−0.566575	+	0.566575i	−0.0228838	+	0.0228838i	0.695572	+	0.718456i	$0.255151\pi$
$614$	1.61846	+	3.71021i	0.0653157	+	0.149732i
$615$	7.15485	+	10.2413i	0.288512	+	0.412970i
$616$	13.3340	+	4.66869i	0.537242	+	0.188107i
$617$	32.2437	+	32.2437i	1.29808	+	1.29808i	0.929657	+	0.368426i	$0.120103\pi$
$617$	32.2437	+	32.2437i	1.29808	+	1.29808i	0.368426	+	0.929657i	$0.379897\pi$
$618$	−69.7706	−	27.3882i	−2.80659	−	1.10171i
$619$	−26.0469			−1.04691			−0.523457	−	0.852052i	$-0.675358\pi$
$619$	−26.0469			−1.04691			−0.523457	+	0.852052i	$0.675358\pi$
$620$	7.53107	−	5.69045i	0.302455	−	0.228534i
$621$	88.2740			3.54231
$622$	−28.9134	−	11.3498i	−1.15932	−	0.455087i
$623$	8.69813	+	8.69813i	0.348483	+	0.348483i
$624$	0.943485	+	12.6341i	0.0377696	+	0.505768i
$625$	19.0827	+	16.1509i	0.763306	+	0.646037i
$626$	7.43250	+	17.0385i	0.297062	+	0.680995i
$627$	−18.2537	+	18.2537i	−0.728982	+	0.728982i
$628$	−1.38958	−	37.2673i	−0.0554505	−	1.48713i
$629$			17.7327i			0.707050i
$630$	28.0870	−	6.74664i	1.11901	−	0.268793i
$631$			36.4532i			1.45118i	0.688128	+	0.725589i	$0.258433\pi$
$631$			36.4532i			1.45118i	−0.688128	+	0.725589i	$0.741567\pi$
$632$	11.2622	−	5.42089i	0.447987	−	0.215631i
$633$	42.4792	−	42.4792i	1.68840	−	1.68840i
$634$	44.9796	−	19.6209i	1.78637	−	0.779246i
$635$	11.7650	−	8.21931i	0.466879	−	0.326173i
$636$	−18.7954	−	17.4441i	−0.745286	−	0.691705i
$637$	−3.75655	−	3.75655i	−0.148840	−	0.148840i
$638$	16.7007	−	42.5446i	0.661188	−	1.68436i
$639$	25.3502			1.00284
$640$	−8.61641	−	23.7857i	−0.340593	−	0.940211i
$641$	40.5177			1.60035			0.800177	−	0.599764i	$-0.204739\pi$
$641$	40.5177			1.60035			0.800177	+	0.599764i	$0.204739\pi$
$642$	−12.0853	+	30.7870i	−0.476970	+	1.21507i
$643$	−0.831375	−	0.831375i	−0.0327862	−	0.0327862i	0.690524	−	0.723310i	$-0.257380\pi$
$643$	−0.831375	−	0.831375i	−0.0327862	−	0.0327862i	−0.723310	+	0.690524i	$0.757380\pi$
$644$	−13.1631	−	12.2168i	−0.518700	−	0.481409i
$645$	1.71510	−	9.66679i	0.0675322	−	0.380629i
$646$	−7.09483	+	3.09489i	−0.279142	+	0.121767i
$647$	18.6491	−	18.6491i	0.733170	−	0.733170i	−0.238076	−	0.971246i	$-0.576517\pi$
$647$	18.6491	−	18.6491i	0.733170	−	0.733170i	0.971246	+	0.238076i	$0.0765168\pi$
$648$	−49.3193	+	23.7391i	−1.93745	+	0.932559i
$649$		−	31.6901i		−	1.24394i
$650$	−0.425024	−	7.05828i	−0.0166708	−	0.276849i
$651$			8.68411i			0.340357i
$652$	−1.29939	−	34.8483i	−0.0508879	−	1.36476i
$653$	−13.4285	+	13.4285i	−0.525499	+	0.525499i	−0.919227	−	0.393728i	$-0.871185\pi$
$653$	−13.4285	+	13.4285i	−0.525499	+	0.525499i	0.393728	+	0.919227i	$0.371185\pi$
$654$	−16.0766	−	36.8545i	−0.628644	−	1.44112i
$655$	6.77082	−	38.1622i	0.264558	−	1.49112i
$656$	0.525456	+	7.03631i	0.0205156	+	0.274722i
$657$	−81.2745	−	81.2745i	−3.17082	−	3.17082i
$658$	−16.4572	−	6.46020i	−0.641567	−	0.251845i
$659$	14.8202			0.577314			0.288657	−	0.957433i	$-0.406791\pi$
$659$	14.8202			0.577314			0.288657	+	0.957433i	$0.406791\pi$
$660$	53.9449	+	7.50992i	2.09980	+	0.292323i
$661$	13.3113			0.517749			0.258874	−	0.965911i	$-0.416648\pi$
$661$	13.3113			0.517749			0.258874	+	0.965911i	$0.416648\pi$
$662$	11.4215	+	4.48348i	0.443910	+	0.174255i
$663$	−5.78319	−	5.78319i	−0.224601	−	0.224601i
$664$	15.8854	+	5.56204i	0.616474	+	0.215849i
$665$	5.04717	−	3.52608i	0.195721	−	0.136736i
$666$	27.3054	+	62.5959i	1.05806	+	2.42554i
$667$	−41.0823	+	41.0823i	−1.59071	+	1.59071i
$668$	−12.2280	+	0.455945i	−0.473115	+	0.0176410i
$669$		−	3.79968i		−	0.146904i
$670$	−1.89399	−	7.88490i	−0.0731713	−	0.304620i
$671$			11.3327i			0.437493i
$672$	22.2383	+	6.86752i	0.857860	+	0.264921i
$673$	−12.2894	+	12.2894i	−0.473722	+	0.473722i	−0.903117	−	0.429395i	$-0.858727\pi$
$673$	−12.2894	+	12.2894i	−0.473722	+	0.473722i	0.429395	+	0.903117i	$0.358727\pi$
$674$	9.79941	−	4.27468i	0.377459	−	0.164655i
$675$	57.9262	−	26.8617i	2.22958	−	1.03391i
$676$	−1.36054	+	1.46593i	−0.0523283	+	0.0563818i
$677$	13.2252	+	13.2252i	0.508286	+	0.508286i	0.914000	−	0.405714i	$-0.132977\pi$
$677$	13.2252	+	13.2252i	0.508286	+	0.508286i	−0.405714	+	0.914000i	$0.632977\pi$
$678$	−8.40158	+	21.4028i	−0.322661	+	0.821968i
$679$	4.28768			0.164546
$680$	14.2340	+	8.00661i	0.545848	+	0.307040i
$681$	41.7937			1.60154
$682$	−4.19389	+	10.6838i	−0.160593	+	0.409105i
$683$	2.26846	+	2.26846i	0.0868002	+	0.0868002i	0.749174	−	0.662374i	$-0.230451\pi$
$683$	2.26846	+	2.26846i	0.0868002	+	0.0868002i	−0.662374	+	0.749174i	$0.730451\pi$
$684$	−20.2789	+	21.8497i	−0.775382	+	0.835445i
$685$	9.72166	+	13.9154i	0.371446	+	0.531680i
$686$	−20.7325	+	9.04390i	−0.791571	+	0.345298i
$687$	−2.19179	+	2.19179i	−0.0836221	+	0.0836221i
$688$	3.61798	−	4.20196i	0.137934	−	0.160198i
$689$		−	4.04807i		−	0.154219i
$690$	−59.0367	−	36.1680i	−2.24749	−	1.37689i
$691$			27.3699i			1.04120i	0.853800	+	0.520601i	$0.174292\pi$
$691$			27.3699i			1.04120i	−0.853800	+	0.520601i	$0.825708\pi$
$692$	−22.5166	+	0.839576i	−0.855953	+	0.0319159i
$693$	−24.8361	+	24.8361i	−0.943447	+	0.943447i
$694$	−3.33388	−	7.64268i	−0.126552	−	0.290112i
$695$	36.5519	+	6.48512i	1.38649	+	0.245995i
$696$	24.8827	−	71.0660i	0.943175	−	2.69375i
$697$	−3.22084	−	3.22084i	−0.121998	−	0.121998i
$698$	3.05430	+	1.19896i	0.115607	+	0.0453811i
$699$	−44.5980			−1.68685
$700$	−12.3553	−	4.01123i	−0.466988	−	0.151610i
$701$	19.5520			0.738467			0.369234	−	0.929337i	$-0.379620\pi$
$701$	19.5520			0.738467			0.369234	+	0.929337i	$0.379620\pi$
$702$	−16.8110	−	6.59911i	−0.634492	−	0.249067i
$703$	10.2927	+	10.2927i	0.388198	+	0.388198i
$704$	24.0425	+	19.1887i	0.906137	+	0.723200i
$705$	−67.1108	−	11.9070i	−2.52754	−	0.448442i
$706$	−16.7186	−	38.3263i	−0.629214	−	1.44243i
$707$	3.39997	−	3.39997i	0.127869	−	0.127869i
$708$	−1.94531	−	52.1712i	−0.0731090	−	1.96071i
$709$			23.8454i			0.895532i	0.894151	+	0.447766i	$0.147780\pi$
$709$			23.8454i			0.895532i	−0.894151	+	0.447766i	$0.852220\pi$
$710$	−9.72091	−	5.95538i	−0.364819	−	0.223502i
$711$			31.0742i			1.16537i
$712$	11.6163	+	24.1336i	0.435340	+	0.904444i
$713$	10.3166	−	10.3166i	0.386360	−	0.386360i
$714$	−13.7717	+	6.00745i	−0.515391	+	0.224823i
$715$	4.92413	+	7.04831i	0.184152	+	0.263592i
$716$	−17.3881	−	16.1380i	−0.649824	−	0.603106i
$717$	17.8942	+	17.8942i	0.668273	+	0.668273i
$718$	0.957934	−	2.44031i	0.0357498	−	0.0910715i
$719$	15.9103			0.593354			0.296677	−	0.954978i	$-0.404122\pi$
$719$	15.9103			0.593354			0.296677	+	0.954978i	$0.404122\pi$
$720$	62.5743	+	6.34510i	2.33200	+	0.236468i
$721$	−21.7371			−0.809531
$722$	7.49665	−	19.0975i	0.278996	−	0.710735i
$723$	−38.0759	−	38.0759i	−1.41606	−	1.41606i
$724$	−3.11801	−	2.89384i	−0.115880	−	0.107549i
$725$	−14.4572	+	39.4599i	−0.536928	+	1.46550i
$726$	−15.5404	+	6.77899i	−0.576757	+	0.251592i
$727$	8.05611	−	8.05611i	0.298785	−	0.298785i	−0.541753	−	0.840538i	$-0.682239\pi$
$727$	8.05611	−	8.05611i	0.298785	−	0.298785i	0.840538	+	0.541753i	$0.182239\pi$
$728$	1.59352	+	3.31063i	0.0590597	+	0.122700i
$729$		−	14.7373i		−	0.545828i
$730$	12.0725	+	50.2593i	0.446825	+	1.86018i
$731$			3.57954i			0.132394i
$732$	0.695659	+	18.6569i	0.0257123	+	0.689578i
$733$	−1.51240	+	1.51240i	−0.0558618	+	0.0558618i	−0.734486	−	0.678624i	$-0.762577\pi$
$733$	−1.51240	+	1.51240i	−0.0558618	+	0.0558618i	0.678624	+	0.734486i	$0.262577\pi$
$734$	−1.84466	−	4.22876i	−0.0680877	−	0.156086i
$735$	−30.8438	+	21.5482i	−1.13769	+	0.794819i
$736$	−18.2603	−	34.5773i	−0.673082	−	1.27454i
$737$	6.97228	+	6.97228i	0.256827	+	0.256827i
$738$	−16.3290	−	6.40988i	−0.601079	−	0.235951i
$739$	3.38051			0.124354			0.0621771	−	0.998065i	$-0.480196\pi$
$739$	3.38051			0.124354			0.0621771	+	0.998065i	$0.480196\pi$
$740$	4.23463	−	30.4180i	0.155668	−	1.11819i
$741$	−6.71356			−0.246629
$742$	−6.92240	−	2.71736i	−0.254129	−	0.0997576i
$743$	−31.2491	−	31.2491i	−1.14642	−	1.14642i	−0.987252	−	0.159167i	$-0.949119\pi$
$743$	−31.2491	−	31.2491i	−1.14642	−	1.14642i	−0.159167	−	0.987252i	$-0.550881\pi$
$744$	−6.24855	+	17.8461i	−0.229083	+	0.654272i
$745$	−5.54355	+	31.2450i	−0.203100	+	1.14473i
$746$	19.1428	+	43.8836i	0.700869	+	1.60669i
$747$	−29.5885	+	29.5885i	−1.08259	+	1.08259i
$748$	−19.8441	+	0.739927i	−0.725573	+	0.0270544i
$749$			9.59171i			0.350473i
$750$	−49.7463	−	5.76893i	−1.81648	−	0.210652i
$751$			3.27690i			0.119576i	0.998211	+	0.0597879i	$0.0190424\pi$
$751$			3.27690i			0.119576i	−0.998211	+	0.0597879i	$0.980958\pi$
$752$	−29.1717	−	25.1175i	−1.06378	−	0.915941i
$753$	4.08038	−	4.08038i	0.148697	−	0.148697i
$754$	10.8950	−	4.75258i	0.396772	−	0.173079i
$755$	−1.74605	+	9.84121i	−0.0635453	+	0.358158i
$756$	−22.5696	+	24.3179i	−0.820850	+	0.884435i
$757$	31.9796	+	31.9796i	1.16232	+	1.16232i	0.983967	+	0.178353i	$0.0570768\pi$
$757$	31.9796	+	31.9796i	1.16232	+	1.16232i	0.178353	+	0.983967i	$0.442923\pi$
$758$	−10.4481	+	26.6161i	−0.379491	+	0.966741i
$759$	84.1854			3.05574
$760$	12.9093	−	3.61459i	0.468268	−	0.131115i
$761$	28.7698			1.04290			0.521451	−	0.853281i	$-0.325391\pi$
$761$	28.7698			1.04290			0.521451	+	0.853281i	$0.325391\pi$
$762$	−10.5050	+	26.7611i	−0.380555	+	0.969454i
$763$	−8.24534	−	8.24534i	−0.298501	−	0.298501i
$764$	−24.5579	+	26.4602i	−0.888475	+	0.957298i
$765$	−33.2840	+	23.2531i	−1.20339	+	0.840716i
$766$	6.19804	−	2.70370i	0.223944	−	0.0976885i
$767$	5.82768	−	5.82768i	0.210425	−	0.210425i
$768$	40.7590	+	30.1143i	1.47076	+	1.08666i
$769$		−	17.7747i		−	0.640972i	−0.947253	−	0.320486i	$-0.896154\pi$
$769$		−	17.7747i		−	0.640972i	0.947253	−	0.320486i	$-0.103846\pi$
$770$	15.3584	−	3.68916i	0.553478	−	0.132948i
$771$			76.6584i			2.76079i
$772$	44.2975	−	1.65172i	1.59430	−	0.0594467i
$773$	4.56344	−	4.56344i

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.516756 + 1.31642i) q^{2} +(-2.23963 - 2.23963i) q^{3} +(-1.46593 - 1.36054i) q^{4} +(-2.20168 - 0.390628i) q^{5} +(4.10564 - 1.79095i) q^{6} +(0.918543 - 0.918543i) q^{7} +(2.54856 - 1.22671i) q^{8} +7.03189i q^{9} +O(q^{10})\)	\(q+(-0.516756 + 1.31642i) q^{2} +(-2.23963 - 2.23963i) q^{3} +(-1.46593 - 1.36054i) q^{4} +(-2.20168 - 0.390628i) q^{5} +(4.10564 - 1.79095i) q^{6} +(0.918543 - 0.918543i) q^{7} +(2.54856 - 1.22671i) q^{8} +7.03189i q^{9} +(1.65196 - 2.69648i) q^{10} +3.84514i q^{11} +(0.236035 + 6.33023i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(0.734526 + 1.68385i) q^{14} +(4.05610 + 5.80582i) q^{15} +(0.297882 + 3.98889i) q^{16} +(-1.82590 - 1.82590i) q^{17} +(-9.25693 - 3.63377i) q^{18} -2.11964 q^{19} +(2.69604 + 3.56810i) q^{20} -4.11439 q^{21} +(-5.06183 - 1.98700i) q^{22} +(4.88785 + 4.88785i) q^{23} +(-8.45522 - 2.96046i) q^{24} +(4.69482 + 1.72008i) q^{25} +(-0.565448 - 1.29625i) q^{26} +(9.02994 - 9.02994i) q^{27} +(-2.59623 + 0.0968054i) q^{28} +8.40499i q^{29} +(-9.73891 + 2.33934i) q^{30} -2.11067i q^{31} +(-5.40499 - 1.66915i) q^{32} +(8.61170 - 8.61170i) q^{33} +(3.34719 - 1.46011i) q^{34} +(-2.38115 + 1.66353i) q^{35} +(9.56714 - 10.3082i) q^{36} +(-4.85589 - 4.85589i) q^{37} +(1.09534 - 2.79033i) q^{38} +3.16732 q^{39} +(-6.09032 + 1.70529i) q^{40} +1.76398 q^{41} +(2.12614 - 5.41627i) q^{42} +(-0.980214 - 0.980214i) q^{43} +(5.23146 - 5.63670i) q^{44} +(2.74685 - 15.4820i) q^{45} +(-8.96029 + 3.90864i) q^{46} +(-6.80504 + 6.80504i) q^{47} +(8.26650 - 9.60079i) q^{48} +5.31256i q^{49} +(-4.69042 + 5.29150i) q^{50} +8.17867i q^{51} +(1.99861 - 0.0745222i) q^{52} +(-2.86242 + 2.86242i) q^{53} +(7.22093 + 16.5535i) q^{54} +(1.50202 - 8.46579i) q^{55} +(1.21418 - 3.46775i) q^{56} +(4.74721 + 4.74721i) q^{57} +(-11.0645 - 4.34333i) q^{58} -8.24159 q^{59} +(1.95309 - 14.0294i) q^{60} +2.94727 q^{61} +(2.77852 + 1.09070i) q^{62} +(6.45909 + 6.45909i) q^{63} +(4.99036 - 6.25270i) q^{64} +(1.83304 - 1.28061i) q^{65} +(6.88647 + 15.7868i) q^{66} +(1.81327 - 1.81327i) q^{67} +(0.192432 + 5.16083i) q^{68} -21.8940i q^{69} +(-0.959435 - 3.99423i) q^{70} -3.60503i q^{71} +(8.62610 + 17.9212i) q^{72} +(-11.5580 + 11.5580i) q^{73} +(8.90171 - 3.88309i) q^{74} +(-6.66232 - 14.3670i) q^{75} +(3.10723 + 2.88384i) q^{76} +(3.53193 + 3.53193i) q^{77} +(-1.63673 + 4.16952i) q^{78} +4.41904 q^{79} +(0.902332 - 8.89864i) q^{80} -19.3518 q^{81} +(-0.911545 + 2.32213i) q^{82} +(4.20776 + 4.20776i) q^{83} +(6.03140 + 5.59778i) q^{84} +(3.30680 + 4.73329i) q^{85} +(1.79691 - 0.783843i) q^{86} +(18.8241 - 18.8241i) q^{87} +(4.71688 + 9.79960i) q^{88} +9.46948i q^{89} +(18.9614 + 11.6164i) q^{90} +1.29902i q^{91} +(-0.515132 - 13.8153i) q^{92} +(-4.72711 + 4.72711i) q^{93} +(-5.44175 - 12.4748i) q^{94} +(4.66677 + 0.827990i) q^{95} +(8.36692 + 15.8435i) q^{96} +(2.33396 + 2.33396i) q^{97} +(-6.99356 - 2.74530i) q^{98} -27.0386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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