LMFDB - Embedded newform 260.2.o.a.27.2

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			27.2
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41202 - 0.0788259i) q^{2} +(-1.63309 - 1.63309i) q^{3} +(1.98757 + 0.222607i) q^{4} +(-0.963620 + 2.01778i) q^{5} +(2.17721 + 2.43467i) q^{6} +(3.04756 - 3.04756i) q^{7} +(-2.78894 - 0.470996i) q^{8} +2.33394i q^{9} +O(q^{10})$	\(q+(-1.41202 - 0.0788259i) q^{2} +(-1.63309 - 1.63309i) q^{3} +(1.98757 + 0.222607i) q^{4} +(-0.963620 + 2.01778i) q^{5} +(2.17721 + 2.43467i) q^{6} +(3.04756 - 3.04756i) q^{7} +(-2.78894 - 0.470996i) q^{8} +2.33394i q^{9} +(1.51970 - 2.77318i) q^{10} -0.497041i q^{11} +(-2.88234 - 3.60941i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-4.54342 + 4.06297i) q^{14} +(4.86888 - 1.72154i) q^{15} +(3.90089 + 0.884894i) q^{16} +(-2.41342 - 2.41342i) q^{17} +(0.183975 - 3.29556i) q^{18} -5.62862 q^{19} +(-2.36444 + 3.79598i) q^{20} -9.95385 q^{21} +(-0.0391797 + 0.701829i) q^{22} +(-4.41675 - 4.41675i) q^{23} +(3.78540 + 5.32375i) q^{24} +(-3.14287 - 3.88875i) q^{25} +(-1.05418 + 0.942707i) q^{26} +(-1.08773 + 1.08773i) q^{27} +(6.73565 - 5.37884i) q^{28} -5.13981i q^{29} +(-7.01064 + 2.04704i) q^{30} -3.14912i q^{31} +(-5.43837 - 1.55698i) q^{32} +(-0.811710 + 0.811710i) q^{33} +(3.21754 + 3.59802i) q^{34} +(3.21261 + 9.08599i) q^{35} +(-0.519552 + 4.63888i) q^{36} +(4.40088 + 4.40088i) q^{37} +(7.94770 + 0.443681i) q^{38} -2.30953 q^{39} +(3.63784 - 5.17360i) q^{40} +8.49850 q^{41} +(14.0550 + 0.784621i) q^{42} +(-5.16698 - 5.16698i) q^{43} +(0.110645 - 0.987905i) q^{44} +(-4.70939 - 2.24903i) q^{45} +(5.88836 + 6.58467i) q^{46} +(0.110788 - 0.110788i) q^{47} +(-4.92539 - 7.81560i) q^{48} -11.5752i q^{49} +(4.13125 + 5.73871i) q^{50} +7.88265i q^{51} +(1.56283 - 1.24802i) q^{52} +(0.203180 - 0.203180i) q^{53} +(1.62163 - 1.45015i) q^{54} +(1.00292 + 0.478958i) q^{55} +(-9.93483 + 7.06405i) q^{56} +(9.19203 + 9.19203i) q^{57} +(-0.405150 + 7.25749i) q^{58} +7.36019 q^{59} +(10.0605 - 2.33783i) q^{60} -6.43106 q^{61} +(-0.248232 + 4.44661i) q^{62} +(7.11283 + 7.11283i) q^{63} +(7.55632 + 2.62716i) q^{64} +(0.745404 + 2.10817i) q^{65} +(1.21013 - 1.08216i) q^{66} +(7.40905 - 7.40905i) q^{67} +(-4.25960 - 5.33409i) q^{68} +14.4259i q^{69} +(-3.82005 - 13.0828i) q^{70} +0.618858i q^{71} +(1.09928 - 6.50922i) q^{72} +(-11.5363 + 11.5363i) q^{73} +(-5.86720 - 6.56101i) q^{74} +(-1.21807 + 11.4832i) q^{75} +(-11.1873 - 1.25297i) q^{76} +(-1.51476 - 1.51476i) q^{77} +(3.26110 + 0.182051i) q^{78} +2.69514 q^{79} +(-5.54450 + 7.01844i) q^{80} +10.5545 q^{81} +(-12.0000 - 0.669902i) q^{82} +(5.93375 + 5.93375i) q^{83} +(-19.7840 - 2.21579i) q^{84} +(7.19537 - 2.54413i) q^{85} +(6.88856 + 7.70314i) q^{86} +(-8.39376 + 8.39376i) q^{87} +(-0.234104 + 1.38621i) q^{88} -12.7437i q^{89} +(6.47244 + 3.54689i) q^{90} -4.30990i q^{91} +(-7.79541 - 9.76181i) q^{92} +(-5.14279 + 5.14279i) q^{93} +(-0.165168 + 0.147702i) q^{94} +(5.42385 - 11.3573i) q^{95} +(6.33865 + 11.4240i) q^{96} +(8.15212 + 8.15212i) q^{97} +(-0.912426 + 16.3444i) q^{98} +1.16007 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 $

$2$	−1.41202	−	0.0788259i	−0.998445	−	0.0557383i
$2$	−1.41202	−	0.0788259i	−0.998445	−	0.0557383i
$3$	−1.63309	−	1.63309i	−0.942863	−	0.942863i	0.0555906	−	0.998454i	$-0.482296\pi$
$3$	−1.63309	−	1.63309i	−0.942863	−	0.942863i	−0.998454	+	0.0555906i	$0.982296\pi$
$4$	1.98757	+	0.222607i	0.993786	+	0.111303i
$5$	−0.963620	+	2.01778i	−0.430944	+	0.902379i
$5$	−0.963620	+	2.01778i	−0.430944	+	0.902379i
$6$	2.17721	+	2.43467i	0.888844	+	0.993951i
$7$	3.04756	−	3.04756i	1.15187	−	1.15187i	0.165690	−	0.986178i	$-0.447015\pi$
$7$	3.04756	−	3.04756i	1.15187	−	1.15187i	0.986178	−	0.165690i	$-0.0529853\pi$
$8$	−2.78894	−	0.470996i	−0.986038	−	0.166522i
$9$			2.33394i			0.777981i
$10$	1.51970	−	2.77318i	0.480571	−	0.876956i
$11$		−	0.497041i		−	0.149863i	−0.997189	−	0.0749317i	$-0.976126\pi$
$11$		−	0.497041i		−	0.149863i	0.997189	−	0.0749317i	$-0.0238739\pi$
$12$	−2.88234	−	3.60941i	−0.832061	−	1.04195i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$	−4.54342	+	4.06297i	−1.21428	+	1.08587i
$15$	4.86888	−	1.72154i	1.25714	−	0.444499i
$16$	3.90089	+	0.884894i	0.975223	+	0.221224i
$17$	−2.41342	−	2.41342i	−0.585340	−	0.585340i	0.351026	−	0.936366i	$-0.385833\pi$
$17$	−2.41342	−	2.41342i	−0.585340	−	0.585340i	−0.936366	+	0.351026i	$0.885833\pi$
$18$	0.183975	−	3.29556i	0.0433634	−	0.776772i
$19$	−5.62862			−1.29129			−0.645647	−	0.763636i	$-0.723412\pi$
$19$	−5.62862			−1.29129			−0.645647	+	0.763636i	$0.723412\pi$
$20$	−2.36444	+	3.79598i	−0.528704	+	0.848806i
$21$	−9.95385			−2.17211
$22$	−0.0391797	+	0.701829i	−0.00835314	+	0.149630i
$23$	−4.41675	−	4.41675i	−0.920956	−	0.920956i	0.0761410	−	0.997097i	$-0.475740\pi$
$23$	−4.41675	−	4.41675i	−0.920956	−	0.920956i	−0.997097	+	0.0761410i	$0.975740\pi$
$24$	3.78540	+	5.32375i	0.772691	+	1.08671i
$25$	−3.14287	−	3.88875i	−0.628575	−	0.777749i
$26$	−1.05418	+	0.942707i	−0.206742	+	0.184880i
$27$	−1.08773	+	1.08773i	−0.209333	+	0.209333i
$28$	6.73565	−	5.37884i	1.27292	−	1.01650i
$29$		−	5.13981i		−	0.954439i	−0.878784	−	0.477220i	$-0.841645\pi$
$29$		−	5.13981i		−	0.954439i	0.878784	−	0.477220i	$-0.158355\pi$
$30$	−7.01064	+	2.04704i	−1.27996	+	0.373737i
$31$		−	3.14912i		−	0.565599i	−0.959179	−	0.282800i	$-0.908737\pi$
$31$		−	3.14912i		−	0.565599i	0.959179	−	0.282800i	$-0.0912631\pi$
$32$	−5.43837	−	1.55698i	−0.961376	−	0.275237i
$33$	−0.811710	+	0.811710i	−0.141301	+	0.141301i
$34$	3.21754	+	3.59802i	0.551804	+	0.617056i
$35$	3.21261	+	9.08599i	0.543031	+	1.53581i
$36$	−0.519552	+	4.63888i	−0.0865919	+	0.773147i
$37$	4.40088	+	4.40088i	0.723500	+	0.723500i	0.969316	−	0.245817i	$-0.0790561\pi$
$37$	4.40088	+	4.40088i	0.723500	+	0.723500i	−0.245817	+	0.969316i	$0.579056\pi$
$38$	7.94770	+	0.443681i	1.28929	+	0.0719746i
$39$	−2.30953			−0.369821
$40$	3.63784	−	5.17360i	0.575193	−	0.818018i
$41$	8.49850			1.32724			0.663621	−	0.748069i	$-0.269019\pi$
$41$	8.49850			1.32724			0.663621	+	0.748069i	$0.269019\pi$
$42$	14.0550	+	0.784621i	2.16873	+	0.121070i
$43$	−5.16698	−	5.16698i	−0.787957	−	0.787957i	0.193202	−	0.981159i	$-0.438113\pi$
$43$	−5.16698	−	5.16698i	−0.787957	−	0.787957i	−0.981159	+	0.193202i	$0.938113\pi$
$44$	0.110645	−	0.987905i	0.0166803	−	0.148932i
$45$	−4.70939	−	2.24903i	−0.702034	−	0.335266i
$46$	5.88836	+	6.58467i	0.868192	+	0.970857i
$47$	0.110788	−	0.110788i	0.0161601	−	0.0161601i	−0.698981	−	0.715141i	$-0.746363\pi$
$47$	0.110788	−	0.110788i	0.0161601	−	0.0161601i	0.715141	+	0.698981i	$0.246363\pi$
$48$	−4.92539	−	7.81560i	−0.710918	−	1.12809i
$49$		−	11.5752i		−	1.65360i
$50$	4.13125	+	5.73871i	0.584247	+	0.811576i
$51$			7.88265i			1.10379i
$52$	1.56283	−	1.24802i	0.216726	−	0.173069i
$53$	0.203180	−	0.203180i	0.0279090	−	0.0279090i	−0.693015	−	0.720924i	$-0.743718\pi$
$53$	0.203180	−	0.203180i	0.0279090	−	0.0279090i	0.720924	+	0.693015i	$0.243718\pi$
$54$	1.62163	−	1.45015i	0.220676	−	0.197340i
$55$	1.00292	+	0.478958i	0.135234	+	0.0645827i
$56$	−9.93483	+	7.06405i	−1.32760	+	0.943974i
$57$	9.19203	+	9.19203i	1.21751	+	1.21751i
$58$	−0.405150	+	7.25749i	−0.0531988	+	0.952955i
$59$	7.36019			0.958216			0.479108	−	0.877756i	$-0.340960\pi$
$59$	7.36019			0.958216			0.479108	+	0.877756i	$0.340960\pi$
$60$	10.0605	−	2.33783i	1.29880	−	0.301813i
$61$	−6.43106			−0.823413			−0.411707	−	0.911316i	$-0.635067\pi$
$61$	−6.43106			−0.823413			−0.411707	+	0.911316i	$0.635067\pi$
$62$	−0.248232	+	4.44661i	−0.0315256	+	0.564720i
$63$	7.11283	+	7.11283i	0.896132	+	0.896132i
$64$	7.55632	+	2.62716i	0.944541	+	0.328395i
$65$	0.745404	+	2.10817i	0.0924560	+	0.261486i
$66$	1.21013	−	1.08216i	0.148957	−	0.133205i
$67$	7.40905	−	7.40905i	0.905159	−	0.905159i	−0.0907174	−	0.995877i	$-0.528916\pi$
$67$	7.40905	−	7.40905i	0.905159	−	0.905159i	0.995877	+	0.0907174i	$0.0289160\pi$
$68$	−4.25960	−	5.33409i	−0.516553	−	0.646853i
$69$			14.4259i			1.73667i
$70$	−3.82005	−	13.0828i	−0.456583	−	1.56369i
$71$			0.618858i			0.0734449i	0.999326	+	0.0367225i	$0.0116917\pi$
$71$			0.618858i			0.0734449i	−0.999326	+	0.0367225i	$0.988308\pi$
$72$	1.09928	−	6.50922i	0.129551	−	0.767119i
$73$	−11.5363	+	11.5363i	−1.35023	+	1.35023i	−0.464820	+	0.885405i	$0.653881\pi$
$73$	−11.5363	+	11.5363i	−1.35023	+	1.35023i	−0.885405	+	0.464820i	$0.846119\pi$
$74$	−5.86720	−	6.56101i	−0.682048	−	0.762701i
$75$	−1.21807	+	11.4832i	−0.140651	+	1.32597i
$76$	−11.1873	−	1.25297i	−1.28327	−	0.143725i
$77$	−1.51476	−	1.51476i	−0.172623	−	0.172623i
$78$	3.26110	+	0.182051i	0.369246	+	0.0206132i
$79$	2.69514			0.303227			0.151613	−	0.988440i	$-0.451553\pi$
$79$	2.69514			0.303227			0.151613	+	0.988440i	$0.451553\pi$
$80$	−5.54450	+	7.01844i	−0.619894	+	0.784686i
$81$	10.5545			1.17273
$82$	−12.0000	−	0.669902i	−1.32518	−	0.0739783i
$83$	5.93375	+	5.93375i	0.651314	+	0.651314i	0.953309	−	0.301995i	$-0.0976527\pi$
$83$	5.93375	+	5.93375i	0.651314	+	0.651314i	−0.301995	+	0.953309i	$0.597653\pi$
$84$	−19.7840	−	2.21579i	−2.15861	−	0.241763i
$85$	7.19537	−	2.54413i	0.780447	−	0.275950i
$86$	6.88856	+	7.70314i	0.742812	+	0.830651i
$87$	−8.39376	+	8.39376i	−0.899905	+	0.899905i
$88$	−0.234104	+	1.38621i	−0.0249556	+	0.147771i
$89$		−	12.7437i		−	1.35083i	−0.737440	−	0.675413i	$-0.763965\pi$
$89$		−	12.7437i		−	1.35083i	0.737440	−	0.675413i	$-0.236035\pi$
$90$	6.47244	+	3.54689i	0.682255	+	0.373875i
$91$		−	4.30990i		−	0.451800i
$92$	−7.79541	−	9.76181i	−0.812728	−	1.01774i
$93$	−5.14279	+	5.14279i	−0.533282	+	0.533282i
$94$	−0.165168	+	0.147702i	−0.0170357	+	0.0152343i
$95$	5.42385	−	11.3573i	0.556476	−	1.16524i
$96$	6.33865	+	11.4240i	0.646936	+	1.16596i
$97$	8.15212	+	8.15212i	0.827723	+	0.827723i	0.987201	−	0.159479i	$-0.0509814\pi$
$97$	8.15212	+	8.15212i	0.827723	+	0.827723i	−0.159479	+	0.987201i	$0.550981\pi$
$98$	−0.912426	+	16.3444i	−0.0921690	+	1.65103i
$99$	1.16007			0.116591
$100$	−5.38103	−	8.42879i	−0.538103	−	0.842879i
$101$	−4.18013			−0.415938			−0.207969	−	0.978135i	$-0.566685\pi$
$101$	−4.18013			−0.415938			−0.207969	+	0.978135i	$0.566685\pi$
$102$	0.621357	−	11.1304i	0.0615235	−	1.10208i
$103$	−3.46965	−	3.46965i	−0.341875	−	0.341875i	0.515197	−	0.857072i	$-0.327719\pi$
$103$	−3.46965	−	3.46965i	−0.341875	−	0.341875i	−0.857072	+	0.515197i	$0.827719\pi$
$104$	−2.30512	+	1.63903i	−0.226036	+	0.160720i
$105$	9.59172	−	20.0847i	0.936056	−	1.96006i
$106$	−0.302910	+	0.270878i	−0.0294212	+	0.0263100i
$107$	−9.43408	+	9.43408i	−0.912027	+	0.912027i	−0.996432	−	0.0844046i	$-0.973101\pi$
$107$	−9.43408	+	9.43408i	−0.912027	+	0.912027i	0.0844046	+	0.996432i	$0.473101\pi$
$108$	−2.40407	+	1.91980i	−0.231332	+	0.184733i
$109$		−	10.2008i		−	0.977061i	−0.872547	−	0.488531i	$-0.837533\pi$
$109$		−	10.2008i		−	0.977061i	0.872547	−	0.488531i	$-0.162467\pi$
$110$	−1.37838	−	0.755352i	−0.131424	−	0.0720200i
$111$		−	14.3740i		−	1.36432i
$112$	14.5850	−	9.19143i	1.37815	−	0.868508i
$113$	9.50714	−	9.50714i	0.894357	−	0.894357i	−0.100573	−	0.994930i	$-0.532068\pi$
$113$	9.50714	−	9.50714i	0.894357	−	0.894357i	0.994930	+	0.100573i	$0.0320676\pi$
$114$	−12.2547	−	13.7039i	−1.14776	−	1.28348i
$115$	13.1681	−	4.65596i	1.22793	−	0.434171i
$116$	1.14416	−	10.2158i	0.106232	−	0.948509i
$117$	1.65035	+	1.65035i	0.152575	+	0.152575i
$118$	−10.3927	−	0.580174i	−0.956726	−	0.0534093i
$119$	−14.7101			−1.34847
$120$	−14.3898	+	2.50803i	−1.31361	+	0.228950i
$121$	10.7530			0.977541
$122$	9.08076	+	0.506934i	0.822133	+	0.0458957i
$123$	−13.8788	−	13.8788i	−1.25141	−	1.25141i
$124$	0.701016	−	6.25911i	0.0629531	−	0.562085i
$125$	10.8752	−	2.59436i	0.972705	−	0.232046i
$126$	−9.48274	−	10.6041i	−0.844790	−	0.944688i
$127$	0.0846773	−	0.0846773i	0.00751389	−	0.00751389i	−0.703340	−	0.710854i	$-0.748309\pi$
$127$	0.0846773	−	0.0846773i	0.00751389	−	0.00751389i	0.710854	+	0.703340i	$0.248309\pi$
$128$	−10.4626	−	4.30522i	−0.924768	−	0.380531i
$129$			16.8762i			1.48587i
$130$	−0.886344	−	3.03552i	−0.0777375	−	0.266233i
$131$			12.2879i			1.07360i	0.843709	+	0.536801i	$0.180367\pi$
$131$			12.2879i			1.07360i	−0.843709	+	0.536801i	$0.819633\pi$
$132$	−1.79403	+	1.43264i	−0.156150	+	0.124695i
$133$	−17.1536	+	17.1536i	−1.48740	+	1.48740i
$134$	−11.0457	+	9.87766i	−0.954204	+	0.853300i
$135$	−1.14664	−	3.24295i	−0.0986870	−	0.279109i
$136$	5.59416	+	7.86758i	0.479695	+	0.674640i
$137$	−2.43793	−	2.43793i	−0.208286	−	0.208286i	0.595253	−	0.803539i	$-0.297052\pi$
$137$	−2.43793	−	2.43793i	−0.208286	−	0.208286i	−0.803539	+	0.595253i	$0.797052\pi$
$138$	1.13713	−	20.3695i	0.0967991	−	1.73397i
$139$	−2.17145			−0.184180			−0.0920899	−	0.995751i	$-0.529355\pi$
$139$	−2.17145			−0.184180			−0.0920899	+	0.995751i	$0.529355\pi$
$140$	4.36270	+	18.7742i	0.368716	+	1.58671i
$141$	−0.361854			−0.0304736
$142$	0.0487820	−	0.873837i	0.00409370	−	0.0733307i
$143$	−0.351461	−	0.351461i	−0.0293906	−	0.0293906i
$144$	−2.06529	+	9.10446i	−0.172108	+	0.758705i
$145$	10.3710	+	4.95282i	0.861266	+	0.411310i
$146$	17.1988	−	15.3801i	1.42339	−	1.27287i
$147$	−18.9033	+	18.9033i	−1.55912	+	1.55912i
$148$	7.76740	+	9.72673i	0.638476	+	0.799532i
$149$			0.402191i			0.0329488i	0.999864	+	0.0164744i	$0.00524420\pi$
$149$			0.402191i			0.0329488i	−0.999864	+	0.0164744i	$0.994756\pi$
$150$	2.62511	−	16.1185i	0.214340	−	1.31607i
$151$			11.5532i			0.940189i	0.882616	+	0.470095i	$0.155780\pi$
$151$			11.5532i			0.940189i	−0.882616	+	0.470095i	$0.844220\pi$
$152$	15.6979	+	2.65106i	1.27327	+	0.215029i
$153$	5.63279	−	5.63279i	0.455384	−	0.455384i
$154$	2.01946	+	2.25827i	0.162733	+	0.181976i
$155$	6.35424	+	3.03456i	0.510385	+	0.243741i
$156$	−4.59037	−	0.514118i	−0.367523	−	0.0411624i
$157$	10.9364	+	10.9364i	0.872818	+	0.872818i	0.992779	−	0.119960i	$-0.0382767\pi$
$157$	10.9364	+	10.9364i	0.872818	+	0.872818i	−0.119960	+	0.992779i	$0.538277\pi$
$158$	−3.80557	−	0.212447i	−0.302755	−	0.0169013i
$159$	−0.663622			−0.0526287
$160$	8.38215	−	9.47310i	0.662667	−	0.748914i
$161$	−26.9206			−2.12164
$162$	−14.9032	−	0.831971i	−1.17090	−	0.0653658i
$163$	5.15794	+	5.15794i	0.404001	+	0.404001i	0.879640	−	0.475639i	$-0.157783\pi$
$163$	5.15794	+	5.15794i	0.404001	+	0.404001i	−0.475639	+	0.879640i	$0.657783\pi$
$164$	16.8914	+	1.89182i	1.31900	+	0.147727i
$165$	−0.855673	−	2.42003i	−0.0666141	−	0.188399i
$166$	−7.91081	−	8.84628i	−0.613998	−	0.686605i
$167$	−4.88399	+	4.88399i	−0.377935	+	0.377935i	−0.870357	−	0.492422i	$-0.836112\pi$
$167$	−4.88399	+	4.88399i	−0.377935	+	0.377935i	0.492422	+	0.870357i	$0.336112\pi$
$168$	27.7606	+	4.68823i	2.14178	+	0.361705i
$169$		−	1.00000i		−	0.0769231i
$170$	−10.3605	+	3.02517i	−0.794615	+	0.232020i
$171$		−	13.1369i		−	1.00460i
$172$	−9.11954	−	11.4200i	−0.695359	−	0.870763i
$173$	11.3759	−	11.3759i	0.864896	−	0.864896i	−0.127006	−	0.991902i	$-0.540537\pi$
$173$	11.3759	−	11.3759i	0.864896	−	0.864896i	0.991902	+	0.127006i	$0.0405367\pi$
$174$	12.5138	−	11.1905i	0.948666	−	0.848347i
$175$	−21.4293	−	2.27308i	−1.61990	−	0.171829i
$176$	0.439828	−	1.93890i	0.0331533	−	0.146150i
$177$	−12.0198	−	12.0198i	−0.903466	−	0.903466i
$178$	−1.00453	+	17.9942i	−0.0752928	+	1.34873i
$179$	14.2199			1.06285			0.531423	−	0.847106i	$-0.321657\pi$
$179$	14.2199			1.06285			0.531423	+	0.847106i	$0.321657\pi$
$180$	−8.85960	−	5.51846i	−0.660355	−	0.411322i
$181$	−10.4080			−0.773624			−0.386812	−	0.922159i	$-0.626424\pi$
$181$	−10.4080			−0.773624			−0.386812	+	0.922159i	$0.626424\pi$
$182$	−0.339732	+	6.08564i	−0.0251826	+	0.451098i
$183$	10.5025	+	10.5025i	0.776366	+	0.776366i
$184$	10.2378	+	14.3983i	0.754738	+	1.06146i
$185$	−13.1208	+	4.63923i	−0.964658	+	0.341083i
$186$	7.66708	−	6.85631i	0.562178	−	0.502729i
$187$	−1.19957	+	1.19957i	−0.0877211	+	0.0877211i
$188$	0.244862	−	0.195538i	0.0178584	−	0.0142610i
$189$			6.62982i			0.482249i
$190$	−8.55381	+	15.6092i	−0.620559	+	1.13241i
$191$			7.07244i			0.511744i	0.966711	+	0.255872i	$0.0823626\pi$
$191$			7.07244i			0.511744i	−0.966711	+	0.255872i	$0.917637\pi$
$192$	−8.04976	−	16.6305i	−0.580941	−	1.20020i
$193$	15.3297	−	15.3297i	1.10345	−	1.10345i	0.109464	−	0.993991i	$-0.465087\pi$
$193$	15.3297	−	15.3297i	1.10345	−	1.10345i	0.993991	−	0.109464i	$-0.0349134\pi$
$194$	−10.8683	−	12.1535i	−0.780300	−	0.872572i
$195$	2.22551	−	4.66013i	0.159372	−	0.333719i
$196$	2.57672	−	23.0066i	0.184051	−	1.64333i
$197$	−3.85661	−	3.85661i	−0.274772	−	0.274772i	0.556246	−	0.831018i	$-0.312241\pi$
$197$	−3.85661	−	3.85661i	−0.274772	−	0.274772i	−0.831018	+	0.556246i	$0.812241\pi$
$198$	−1.63803	−	0.0914432i	−0.116410	−	0.00649858i
$199$	−3.17819			−0.225296			−0.112648	−	0.993635i	$-0.535933\pi$
$199$	−3.17819			−0.225296			−0.112648	+	0.993635i	$0.535933\pi$
$200$	6.93369	+	12.3257i	0.490286	+	0.871562i
$201$	−24.1992			−1.70688
$202$	5.90240	+	0.329502i	0.415292	+	0.0231837i
$203$	−15.6639	−	15.6639i	−1.09939	−	1.09939i
$204$	−1.75473	+	15.6673i	−0.122856	+	1.09693i
$205$	−8.18932	+	17.1481i	−0.571967	+	1.19768i
$206$	4.62570	+	5.17269i	0.322288	+	0.360399i
$207$	10.3084	−	10.3084i	0.716487	−	0.716487i
$208$	3.38406	−	2.13263i	0.234642	−	0.147871i
$209$			2.79766i			0.193518i
$210$	−15.1269	+	27.6038i	−1.04385	+	1.90484i
$211$		−	10.6465i		−	0.732937i	−0.930430	−	0.366469i	$-0.880567\pi$
$211$		−	10.6465i		−	0.732937i	0.930430	−	0.366469i	$-0.119433\pi$
$212$	0.449065	−	0.358606i	0.0308419	−	0.0246292i
$213$	1.01065	−	1.01065i	0.0692485	−	0.0692485i
$214$	14.0647	−	12.5774i	0.961444	−	0.859774i
$215$	15.4048	−	5.44683i	1.05060	−	0.371470i
$216$	3.54592	−	2.52129i	0.241269	−	0.171552i
$217$	−9.59713	−	9.59713i	−0.651496	−	0.651496i
$218$	−0.804089	+	14.4037i	−0.0544598	+	0.975542i
$219$	37.6796			2.54615
$220$	1.88676	+	1.17522i	0.127205	+	0.0792334i
$221$	−3.41309			−0.229589
$222$	−1.13305	+	20.2963i	−0.0760450	+	1.36220i
$223$	13.3536	+	13.3536i	0.894220	+	0.894220i	0.994917	−	0.100697i	$-0.0321072\pi$
$223$	13.3536	+	13.3536i	0.894220	+	0.894220i	−0.100697	+	0.994917i	$0.532107\pi$
$224$	−21.3187	+	11.8288i	−1.42442	+	0.790342i
$225$	9.07611	−	7.33529i	0.605074	−	0.489020i
$226$	−14.1736	+	12.6748i	−0.942816	+	0.843116i
$227$	5.71415	−	5.71415i	0.379262	−	0.379262i	−0.491574	−	0.870836i	$-0.663578\pi$
$227$	5.71415	−	5.71415i	0.379262	−	0.379262i	0.870836	+	0.491574i	$0.163578\pi$
$228$	16.2236	+	20.3160i	1.07444	+	1.34546i
$229$			12.9982i			0.858948i	0.903079	+	0.429474i	$0.141301\pi$
$229$			12.9982i			0.858948i	−0.903079	+	0.429474i	$0.858699\pi$
$230$	−18.9606	+	5.53630i	−1.25022	+	0.365053i
$231$			4.94747i			0.325519i
$232$	−2.42083	+	14.3346i	−0.158935	+	0.941113i
$233$	0.881833	−	0.881833i	0.0577708	−	0.0577708i	−0.677631	−	0.735402i	$-0.736993\pi$
$233$	0.881833	−	0.881833i	0.0577708	−	0.0577708i	0.735402	+	0.677631i	$0.236993\pi$
$234$	−2.20023	−	2.46041i	−0.143833	−	0.160842i
$235$	0.116789	+	0.330304i	0.00761845	+	0.0215467i
$236$	14.6289	+	1.63843i	0.952262	+	0.106653i
$237$	−4.40139	−	4.40139i	−0.285901	−	0.285901i
$238$	20.7708	+	1.15953i	1.34637	+	0.0751614i
$239$	−6.13684			−0.396960			−0.198480	−	0.980105i	$-0.563600\pi$
$239$	−6.13684			−0.396960			−0.198480	+	0.980105i	$0.563600\pi$
$240$	20.5164	−	2.40708i	1.32433	−	0.155376i
$241$	23.7790			1.53174			0.765869	−	0.642997i	$-0.222309\pi$
$241$	23.7790			1.53174			0.765869	+	0.642997i	$0.222309\pi$
$242$	−15.1833	−	0.847611i	−0.976021	−	0.0544865i
$243$	−13.9733	−	13.9733i	−0.896387	−	0.896387i
$244$	−12.7822	−	1.43160i	−0.818297	−	0.0916487i
$245$	23.3562	+	11.1541i	1.49217	+	0.712609i
$246$	18.5030	+	20.6911i	1.17971	+	1.31921i
$247$	−3.98004	+	3.98004i	−0.253244	+	0.253244i
$248$	−1.48323	+	8.78270i	−0.0941849	+	0.557702i
$249$		−	19.3807i		−	1.22820i
$250$	−15.5604	+	2.80603i	−0.984126	+	0.177469i
$251$		−	21.3919i		−	1.35025i	−0.737705	−	0.675124i	$-0.764090\pi$
$251$		−	21.3919i		−	1.35025i	0.737705	−	0.675124i	$-0.235910\pi$
$252$	12.5539	+	15.7206i	0.790821	+	0.990306i
$253$	−2.19530	+	2.19530i	−0.138018	+	0.138018i
$254$	−0.126240	+	0.112891i	−0.00792103	+	0.00708340i
$255$	−15.9054	−	7.59587i	−0.996038	−	0.475672i
$256$	14.4339	+	6.90375i	0.902120	+	0.431485i
$257$	11.7799	+	11.7799i	0.734811	+	0.734811i	0.971569	−	0.236758i	$-0.0760847\pi$
$257$	11.7799	+	11.7799i	0.734811	+	0.734811i	−0.236758	+	0.971569i	$0.576085\pi$
$258$	1.33029	−	23.8295i	0.0828200	−	1.48356i
$259$	26.8238			1.66675
$260$	1.01225	+	4.35607i	0.0627772	+	0.270152i
$261$	11.9960			0.742536
$262$	0.968608	−	17.3508i	0.0598408	−	1.07193i
$263$	11.1802	+	11.1802i	0.689398	+	0.689398i	0.962099	−	0.272701i	$-0.0879169\pi$
$263$	11.1802	+	11.1802i	0.689398	+	0.689398i	−0.272701	+	0.962099i	$0.587917\pi$
$264$	2.64612	−	1.88150i	0.162857	−	0.115798i
$265$	0.214185	+	0.605762i	0.0131573	+	0.0372117i
$266$	25.5732	−	22.8689i	1.56799	−	1.40218i
$267$	−20.8115	+	20.8115i	−1.27364	+	1.27364i
$268$	16.3753	−	13.0767i	1.00028	−	0.798788i
$269$		−	1.87020i		−	0.114028i	−0.998373	−	0.0570141i	$-0.981842\pi$
$269$		−	1.87020i		−	0.114028i	0.998373	−	0.0570141i	$-0.0181580\pi$
$270$	1.36344	+	4.66948i	0.0829765	+	0.284175i
$271$			23.6707i			1.43789i	0.695066	+	0.718946i	$0.255375\pi$
$271$			23.6707i			1.43789i	−0.695066	+	0.718946i	$0.744625\pi$
$272$	−7.27887	−	11.5501i	−0.441346	−	0.700328i
$273$	−7.03843	+	7.03843i	−0.425985	+	0.425985i
$274$	3.25022	+	3.63456i	0.196353	+	0.219572i
$275$	−1.93286	+	1.56214i	−0.116556	+	0.0942004i
$276$	−3.21130	+	28.6725i	−0.193297	+	1.72588i
$277$	−11.2334	−	11.2334i	−0.674949	−	0.674949i	0.283903	−	0.958853i	$-0.408370\pi$
$277$	−11.2334	−	11.2334i	−0.674949	−	0.674949i	−0.958853	+	0.283903i	$0.908370\pi$
$278$	3.06612	+	0.171166i	0.183893	+	0.0102659i
$279$	7.34988			0.440026
$280$	−4.68031	−	26.8534i	−0.279702	−	1.60480i
$281$	5.48143			0.326995			0.163497	−	0.986544i	$-0.447723\pi$
$281$	5.48143			0.326995			0.163497	+	0.986544i	$0.447723\pi$
$282$	0.510943	+	0.0285234i	0.0304262	+	0.00169855i
$283$	−7.89795	−	7.89795i	−0.469484	−	0.469484i	0.432263	−	0.901747i	$-0.357715\pi$
$283$	−7.89795	−	7.89795i	−0.469484	−	0.469484i	−0.901747	+	0.432263i	$0.857715\pi$
$284$	−0.137762	+	1.23003i	−0.00817467	+	0.0729886i
$285$	−27.4051	+	9.68988i	−1.62334	+	0.573979i
$286$	0.468564	+	0.523972i	0.0277068	+	0.0309831i
$287$	25.8997	−	25.8997i	1.52881	−	1.52881i
$288$	3.63389	−	12.6928i	0.214129	−	0.747933i
$289$		−	5.35082i		−	0.314754i
$290$	−14.2536	−	7.81097i	−0.837001	−	0.458676i
$291$		−	26.6262i		−	1.56086i
$292$	−25.4974	+	20.3612i	−1.49212	+	1.19155i
$293$	−12.2389	+	12.2389i	−0.715005	+	0.715005i	−0.967578	−	0.252573i	$-0.918723\pi$
$293$	−12.2389	+	12.2389i	−0.715005	+	0.715005i	0.252573	+	0.967578i	$0.418723\pi$
$294$	28.1818	−	25.2017i	1.64360	−	1.46979i
$295$	−7.09243	+	14.8513i	−0.412937	+	0.864673i
$296$	−10.2010	−	14.3466i	−0.592919	−	0.833877i
$297$	0.540645	+	0.540645i	0.0313714	+	0.0313714i
$298$	0.0317031	−	0.567900i	0.00183651	−	0.0328976i
$299$	−6.24623			−0.361229
$300$	−4.97725	+	22.5526i	−0.287362	+	1.30208i
$301$	−31.4933			−1.81524
$302$	0.910695	−	16.3133i	0.0524046	−	0.938728i
$303$	6.82651	+	6.82651i	0.392173	+	0.392173i
$304$	−21.9567	−	4.98074i	−1.25930	−	0.285665i
$305$	6.19710	−	12.9765i	0.354845	−	0.743031i
$306$	−8.39759	+	7.50957i	−0.480058	+	0.429293i
$307$	4.60280	−	4.60280i	0.262696	−	0.262696i	−0.563453	−	0.826148i	$-0.690527\pi$
$307$	4.60280	−	4.60280i	0.262696	−	0.262696i	0.826148	+	0.563453i	$0.190527\pi$
$308$	−2.67350	−	3.34789i	−0.152337	−	0.190764i
$309$			11.3325i			0.644682i
$310$	−8.73308	−	4.78572i	−0.496005	−	0.271810i
$311$		−	32.5052i		−	1.84320i	−0.388141	−	0.921600i	$-0.626882\pi$
$311$		−	32.5052i		−	1.84320i	0.388141	−	0.921600i	$-0.373118\pi$
$312$	6.44114	+	1.08778i	0.364658	+	0.0615835i
$313$	−19.2039	+	19.2039i	−1.08547	+	1.08547i	−0.0894769	+	0.995989i	$0.528520\pi$
$313$	−19.2039	+	19.2039i	−1.08547	+	1.08547i	−0.995989	+	0.0894769i	$0.971480\pi$
$314$	−14.5803	−	16.3044i	−0.822812	−	0.920111i
$315$	−21.2062	+	7.49806i	−1.19483	+	0.422468i
$316$	5.35678	+	0.599956i	0.301342	+	0.0337501i
$317$	−8.28473	−	8.28473i	−0.465317	−	0.465317i	0.435077	−	0.900393i	$-0.356721\pi$
$317$	−8.28473	−	8.28473i	−0.465317	−	0.465317i	−0.900393	+	0.435077i	$0.856721\pi$
$318$	0.937045	+	0.0523106i	0.0525469	+	0.00293343i
$319$	−2.55470			−0.143035
$320$	−12.5824	+	12.7154i	−0.703380	+	0.710814i
$321$	30.8133			1.71983
$322$	38.0123	+	2.12204i	2.11834	+	0.118257i
$323$	13.5842	+	13.5842i	0.755847	+	0.755847i
$324$	20.9779	+	2.34951i	1.16544	+	0.130528i
$325$	−4.97211	−	0.527410i	−0.275803	−	0.0292555i
$326$	−6.87651	−	7.68967i	−0.380855	−	0.425891i
$327$	−16.6588	+	16.6588i	−0.921235	+	0.921235i
$328$	−23.7018	−	4.00276i	−1.30871	−	0.221015i
$329$		−	0.675267i		−	0.0372287i
$330$	1.01746	+	3.48457i	0.0560094	+	0.191819i
$331$		−	2.91495i		−	0.160220i	−0.996786	−	0.0801102i	$-0.974473\pi$
$331$		−	2.91495i		−	0.160220i	0.996786	−	0.0801102i	$-0.0255272\pi$
$332$	10.4729	+	13.1147i	0.574774	+	0.719760i
$333$	−10.2714	+	10.2714i	−0.562869	+	0.562869i
$334$	7.28126	−	6.51129i	0.398413	−	0.356282i
$335$	7.81033	+	22.0893i	0.426724	+	1.20687i
$336$	−38.8289	−	8.80810i	−2.11829	−	0.480521i
$337$	−4.32305	−	4.32305i	−0.235492	−	0.235492i	0.579489	−	0.814980i	$-0.303252\pi$
$337$	−4.32305	−	4.32305i	−0.235492	−	0.235492i	−0.814980	+	0.579489i	$0.803252\pi$
$338$	−0.0788259	+	1.41202i	−0.00428756	+	0.0768035i
$339$	−31.0520			−1.68651
$340$	14.8677	−	3.45491i	0.806312	−	0.187369i
$341$	−1.56524			−0.0847626
$342$	−1.03553	+	18.5495i	−0.0559949	+	1.00304i
$343$	−13.9432	−	13.9432i	−0.752862	−	0.752862i
$344$	11.9767	+	16.8440i	0.645743	+	0.908168i
$345$	−29.1082	−	13.9011i	−1.56713	−	0.748408i
$346$	−16.9597	+	15.1663i	−0.911760	+	0.815344i
$347$	16.3762	−	16.3762i	0.879119	−	0.879119i	−0.114324	−	0.993443i	$-0.536470\pi$
$347$	16.3762	−	16.3762i	0.879119	−	0.879119i	0.993443	+	0.114324i	$0.0364703\pi$
$348$	−18.5517	+	14.8147i	−0.994476	+	0.794151i
$349$		−	24.6174i		−	1.31774i	−0.752258	−	0.658869i	$-0.771035\pi$
$349$		−	24.6174i		−	1.31774i	0.752258	−	0.658869i	$-0.228965\pi$
$350$	30.0793	+	4.89881i	1.60780	+	0.261852i
$351$			1.53828i			0.0821072i
$352$	−0.773880	+	2.70309i	−0.0412479	+	0.144075i
$353$	5.78094	−	5.78094i	0.307688	−	0.307688i	−0.536324	−	0.844012i	$-0.680187\pi$
$353$	5.78094	−	5.78094i	0.307688	−	0.307688i	0.844012	+	0.536324i	$0.180187\pi$
$354$	16.0247	+	17.9197i	0.851704	+	0.952419i
$355$	−1.24872	−	0.596344i	−0.0662751	−	0.0316506i
$356$	2.83683	−	25.3290i	0.150351	−	1.34243i
$357$	24.0228	+	24.0228i	1.27142	+	1.27142i
$358$	−20.0787	−	1.12090i	−1.06119	−	0.0592413i
$359$	−6.42788			−0.339251			−0.169625	−	0.985509i	$-0.554256\pi$
$359$	−6.42788			−0.339251			−0.169625	+	0.985509i	$0.554256\pi$
$360$	12.0749	+	8.49052i	0.636402	+	0.447489i
$361$	12.6814			0.667443
$362$	14.6963	+	0.820424i	0.772422	+	0.0431205i
$363$	−17.5605	−	17.5605i	−0.921687	−	0.921687i
$364$	0.959412	−	8.56623i	0.0502869	−	0.448993i
$365$	−12.1611	−	34.3944i	−0.636543	−	1.80029i
$366$	−14.0018	−	15.6575i	−0.731886	−	0.818432i
$367$	11.7313	−	11.7313i	0.612371	−	0.612371i	−0.331192	−	0.943563i	$-0.607451\pi$
$367$	11.7313	−	11.7313i	0.612371	−	0.612371i	0.943563	+	0.331192i	$0.107451\pi$
$368$	−13.3209	−	21.1376i	−0.694400	−	1.10187i
$369$			19.8350i			1.03257i
$370$	18.8924	−	5.51641i	0.982170	−	0.286784i
$371$		−	1.23841i		−	0.0642949i
$372$	−11.3665	+	9.07685i	−0.589325	+	0.470613i
$373$	15.7227	−	15.7227i	0.814091	−	0.814091i	−0.171154	−	0.985244i	$-0.554749\pi$
$373$	15.7227	−	15.7227i	0.814091	−	0.814091i	0.985244	+	0.171154i	$0.0547494\pi$
$374$	1.78836	−	1.59925i	0.0924741	−	0.0826953i
$375$	−21.9969	−	13.5233i	−1.13592	−	0.698339i
$376$	−0.361162	+	0.256800i	−0.0186255	+	0.0132435i
$377$	−3.63440	−	3.63440i	−0.187181	−	0.187181i
$378$	0.522602	−	9.36141i	0.0268797	−	0.481499i
$379$	−28.9807			−1.48864			−0.744319	−	0.667825i	$-0.767226\pi$
$379$	−28.9807			−1.48864			−0.744319	+	0.667825i	$0.767226\pi$
$380$	13.3085	−	21.3661i	0.682713	−	1.09606i
$381$	−0.276571			−0.0141691
$382$	0.557492	−	9.98640i	0.0285238	−	0.510948i
$383$	22.7875	+	22.7875i	1.16439	+	1.16439i	0.983505	+	0.180882i	$0.0578953\pi$
$383$	22.7875	+	22.7875i	1.16439	+	1.16439i	0.180882	+	0.983505i	$0.442105\pi$
$384$	10.0555	+	24.1171i	0.513141	+	1.23072i
$385$	4.51610	−	1.59680i	0.230162	−	0.0813805i
$386$	−22.8541	+	20.4374i	−1.16324	+	1.04023i
$387$	12.0594	−	12.0594i	0.613016	−	0.613016i
$388$	14.3882	+	18.0177i	0.730451	+	0.914708i
$389$		−	1.60674i		−	0.0814649i	−0.999170	−	0.0407324i	$-0.987031\pi$
$389$		−	1.60674i		−	0.0814649i	0.999170	−	0.0407324i	$-0.0129691\pi$
$390$	−3.50979	+	6.40475i	−0.177725	+	0.324317i
$391$			21.3189i			1.07815i
$392$	−5.45188	+	32.2825i	−0.275362	+	1.63051i
$393$	20.0673	−	20.0673i	1.01226	−	1.01226i
$394$	5.14160	+	5.74960i	0.259030	+	0.289661i
$395$	−2.59709	+	5.43819i	−0.130674	+	0.273625i
$396$	2.30571	+	0.258238i	0.115866	+	0.0129770i
$397$	−12.8728	−	12.8728i	−0.646069	−	0.646069i	0.305971	−	0.952041i	$-0.401019\pi$
$397$	−12.8728	−	12.8728i	−0.646069	−	0.646069i	−0.952041	+	0.305971i	$0.901019\pi$
$398$	4.48766	+	0.250524i	0.224946	+	0.0125576i
$399$	56.0265			2.80483
$400$	−8.81889	−	17.9507i	−0.440944	−	0.897534i
$401$	−9.91973			−0.495367			−0.247684	−	0.968841i	$-0.579669\pi$
$401$	−9.91973			−0.495367			−0.247684	+	0.968841i	$0.579669\pi$
$402$	34.1697	+	1.90753i	1.70423	+	0.0951388i
$403$	−2.22677	−	2.22677i	−0.110923	−	0.110923i
$404$	−8.30831	−	0.930524i	−0.413354	−	0.0462953i
$405$	−10.1706	+	21.2967i	−0.505379	+	1.05824i
$406$	20.8829	+	23.3523i	1.03640	+	1.15896i
$407$	2.18741	−	2.18741i	0.108426	−	0.108426i
$408$	3.71270	−	21.9842i	0.183806	−	1.08838i
$409$			22.7557i			1.12520i	0.826730	+	0.562599i	$0.190198\pi$
$409$			22.7557i			1.12520i	−0.826730	+	0.562599i	$0.809802\pi$
$410$	12.9152	−	23.5678i	0.637834	−	1.16393i
$411$			7.96269i			0.392770i
$412$	−6.12381	−	7.66855i	−0.301699	−	0.377802i
$413$	22.4306	−	22.4306i	1.10374	−	1.10374i
$414$	−15.3683	+	13.7431i	−0.755309	+	0.675437i
$415$	−17.6909	+	6.25513i	−0.868412	+	0.307052i
$416$	−4.94645	+	2.74456i	−0.242520	+	0.134563i
$417$	3.54616	+	3.54616i	0.173656	+	0.173656i
$418$	0.220528	−	3.95033i	0.0107864	−	0.193217i
$419$	−6.93899			−0.338992			−0.169496	−	0.985531i	$-0.554214\pi$
$419$	−6.93899			−0.338992			−0.169496	+	0.985531i	$0.554214\pi$
$420$	23.5352	−	37.7846i	1.14840	−	1.84370i
$421$	−3.45189			−0.168235			−0.0841173	−	0.996456i	$-0.526807\pi$
$421$	−3.45189			−0.168235			−0.0841173	+	0.996456i	$0.526807\pi$
$422$	−0.839222	+	15.0331i	−0.0408527	+	0.731798i
$423$	0.258574	+	0.258574i	0.0125723	+	0.0125723i
$424$	−0.662354	+	0.470960i	−0.0321668	+	0.0228718i
$425$	−1.80010	+	16.9702i	−0.0873176	+	0.823178i
$426$	−1.50672	+	1.34739i	−0.0730006	+	0.0652810i
$427$	−19.5990	+	19.5990i	−0.948463	+	0.948463i
$428$	−20.8510	+	16.6508i	−1.00787	+	0.804848i
$429$			1.14793i			0.0554227i
$430$	−22.1812	+	6.47670i	−1.06967	+	0.312334i
$431$			5.69174i			0.274161i	0.990560	+	0.137081i	$0.0437720\pi$
$431$			5.69174i			0.274161i	−0.990560	+	0.137081i	$0.956228\pi$
$432$	−5.20563	+	3.28058i	−0.250456	+	0.157837i
$433$	−22.4844	+	22.4844i	−1.08053	+	1.08053i	−0.0840698	+	0.996460i	$0.526792\pi$
$433$	−22.4844	+	22.4844i	−1.08053	+	1.08053i	−0.996460	+	0.0840698i	$0.973208\pi$
$434$	12.7948	+	14.3078i	0.614170	+	0.686796i
$435$	−8.84837	−	25.0252i	−0.424247	−	1.19986i
$436$	2.27077	−	20.2749i	0.108750	−	0.970990i
$437$	24.8602	+	24.8602i	1.18923	+	1.18923i
$438$	−53.2042	−	2.97013i	−2.54220	−	0.141918i
$439$	−18.8063			−0.897574			−0.448787	−	0.893639i	$-0.648144\pi$
$439$	−18.8063			−0.897574			−0.448787	+	0.893639i	$0.648144\pi$
$440$	−2.57149	−	1.80815i	−0.122591	−	0.0862004i
$441$	27.0159			1.28647
$442$	4.81933	+	0.269040i	0.229232	+	0.0127969i
$443$	27.8526	+	27.8526i	1.32332	+	1.32332i	0.911073	+	0.412246i	$0.135256\pi$
$443$	27.8526	+	27.8526i	1.32332	+	1.32332i	0.412246	+	0.911073i	$0.364744\pi$
$444$	3.19975	−	28.5694i	0.151854	−	1.35584i
$445$	25.7139	+	12.2800i	1.21896	+	0.582130i
$446$	−17.8028	−	19.9080i	−0.842988	−	0.942672i
$447$	0.656813	−	0.656813i	0.0310662	−	0.0310662i
$448$	31.0347	−	15.0219i	1.46625	−	0.709719i
$449$			18.0953i			0.853970i	0.904259	+	0.426985i	$0.140424\pi$
$449$			18.0953i			0.853970i	−0.904259	+	0.426985i	$0.859576\pi$
$450$	−13.3938	+	9.64211i	−0.631391	+	0.454533i
$451$		−	4.22410i		−	0.198905i
$452$	21.0125	−	16.7798i	0.988344	−	0.789255i
$453$	18.8674	−	18.8674i	0.886470	−	0.886470i
$454$	−8.51890	+	7.61805i	−0.399812	+	0.357533i
$455$	8.69642	+	4.15310i	0.407695	+	0.194700i
$456$	−21.3066	−	29.9654i	−0.997772	−	1.40326i
$457$	19.6055	+	19.6055i	0.917105	+	0.917105i	0.996818	−	0.0797133i	$-0.0254005\pi$
$457$	19.6055	+	19.6055i	0.917105	+	0.917105i	−0.0797133	+	0.996818i	$0.525400\pi$
$458$	1.02460	−	18.3537i	0.0478763	−	0.857613i
$459$	5.25028			0.245062
$460$	27.2090	−	6.32276i	1.26863	−	0.294800i
$461$	−34.9245			−1.62660			−0.813298	−	0.581848i	$-0.802330\pi$
$461$	−34.9245			−1.62660			−0.813298	+	0.581848i	$0.802330\pi$
$462$	0.389989	−	6.98590i	0.0181439	−	0.325013i
$463$	−21.6671	−	21.6671i	−1.00695	−	1.00695i	−0.999976	−	0.00697798i	$-0.997779\pi$
$463$	−21.6671	−	21.6671i	−1.00695	−	1.00695i	−0.00697798	−	0.999976i	$-0.502221\pi$
$464$	4.54819	−	20.0499i	0.211144	−	0.930791i
$465$	−5.42133	−	15.3327i	−0.251408	−	0.711038i
$466$	−1.31467	+	1.17565i	−0.0609010	+	0.0544609i
$467$	−1.42697	+	1.42697i	−0.0660321	+	0.0660321i	−0.739352	−	0.673320i	$-0.764868\pi$
$467$	−1.42697	+	1.42697i	−0.0660321	+	0.0660321i	0.673320	+	0.739352i	$0.264868\pi$
$468$	2.91281	+	3.64756i	0.134645	+	0.168609i
$469$		−	45.1590i		−	2.08525i
$470$	−0.138871	−	0.475600i	−0.00640563	−	0.0219378i
$471$		−	35.7201i		−	1.64590i
$472$	−20.5271	−	3.46662i	−0.944837	−	0.159564i
$473$	−2.56820	+	2.56820i	−0.118086	+	0.118086i
$474$	5.86789	+	6.56178i	0.269521	+	0.301392i
$475$	17.6901	+	21.8883i	0.811676	+	1.00430i
$476$	−29.2373	−	3.27456i	−1.34009	−	0.150089i
$477$	0.474212	+	0.474212i	0.0217127	+	0.0217127i
$478$	8.66532	+	0.483742i	0.396342	+	0.0221259i
$479$	−27.3934			−1.25163			−0.625817	−	0.779970i	$-0.715235\pi$
$479$	−27.3934			−1.25163			−0.625817	+	0.779970i	$0.715235\pi$
$480$	−29.1592	+	1.78161i	−1.33093	+	0.0813189i
$481$	6.22378			0.283780
$482$	−33.5763	−	1.87440i	−1.52936	−	0.0853765i
$483$	43.9637	+	43.9637i	2.00042	+	2.00042i
$484$	21.3723	+	2.39368i	0.971467	+	0.108804i
$485$	−24.3047	+	8.59365i	−1.10362	+	0.390217i
$486$	18.6290	+	20.8320i	0.845030	+	0.944957i
$487$	8.51241	−	8.51241i	0.385734	−	0.385734i	−0.487429	−	0.873163i	$-0.662065\pi$
$487$	8.51241	−	8.51241i	0.385734	−	0.385734i	0.873163	+	0.487429i	$0.162065\pi$
$488$	17.9358	+	3.02901i	0.811916	+	0.137117i
$489$		−	16.8467i		−	0.761835i
$490$	−32.1001	−	17.5908i	−1.45014	−	0.794673i
$491$		−	14.9696i		−	0.675570i	−0.941223	−	0.337785i	$-0.890322\pi$
$491$		−	14.9696i		−	0.675570i	0.941223	−	0.337785i	$-0.109678\pi$
$492$	−24.4956	−	30.6746i	−1.10435	−	1.38292i
$493$	−12.4045	+	12.4045i	−0.558672	+	0.558672i
$494$	5.93360	−	5.30614i	0.266965	−	0.238735i
$495$	−1.11786	+	2.34076i	−0.0502441	+	0.105209i
$496$	2.78664	−	12.2844i	0.125124	−	0.551585i
$497$	1.88600	+	1.88600i	0.0845989	+	0.0845989i
$498$	−1.52770	+	27.3658i	−0.0684578	+	1.22629i
$499$	15.5021			0.693969			0.346984	−	0.937871i	$-0.387206\pi$
$499$	15.5021			0.693969			0.346984	+	0.937871i	$0.387206\pi$
$500$	22.1927	−	2.73559i	0.992488	−	0.122339i
$501$	15.9520			0.712682
$502$	−1.68624	+	30.2057i	−0.0752605	+	1.34815i
$503$	−7.25339	−	7.25339i	−0.323413	−	0.323413i	0.526662	−	0.850075i	$-0.323443\pi$
$503$	−7.25339	−	7.25339i	−0.323413	−	0.323413i	−0.850075	+	0.526662i	$0.823443\pi$
$504$	−16.4871	−	23.1873i	−0.734394	−	1.03285i
$505$	4.02805	−	8.43458i	0.179246	−	0.375334i
$506$	3.27285	−	2.92676i	0.145496	−	0.130110i
$507$	−1.63309	+	1.63309i	−0.0725279	+	0.0725279i
$508$	0.187152	−	0.149453i	0.00830353	−	0.00663089i
$509$		−	3.62150i		−	0.160520i	−0.996774	−	0.0802602i	$-0.974425\pi$
$509$		−	3.62150i		−	0.160520i	0.996774	−	0.0802602i	$-0.0255751\pi$
$510$	21.8600	+	11.9792i	0.967976	+	0.530450i
$511$			70.3152i			3.11056i
$512$	−19.8367	−	10.8860i	−0.876668	−	0.481097i
$513$	6.12241	−	6.12241i	0.270311	−	0.270311i
$514$	−15.7049	−	17.5620i	−0.692712	−	0.774626i
$515$	10.3444	−	3.65757i	0.455829	−	0.161172i
$516$	−3.75677	+	33.5428i	−0.165382	+	1.47664i
$517$	−0.0550663	−	0.0550663i	−0.00242181	−	0.00242181i
$518$	−37.8757	−	2.11441i	−1.66416	−	0.0929020i
$519$	−37.1558			−1.63096
$520$	−1.08594	−	6.23063i	−0.0476218	−	0.273231i
$521$	35.8853			1.57216			0.786082	−	0.618123i	$-0.212107\pi$
$521$	35.8853			1.57216			0.786082	+	0.618123i	$0.212107\pi$
$522$	−16.9386	−	0.945598i	−0.741381	−	0.0413877i
$523$	−18.4185	−	18.4185i	−0.805384	−	0.805384i	0.178548	−	0.983931i	$-0.442860\pi$
$523$	−18.4185	−	18.4185i	−0.805384	−	0.805384i	−0.983931	+	0.178548i	$0.942860\pi$
$524$	−2.73538	+	24.4232i	−0.119496	+	1.06693i
$525$	31.2837	+	38.7080i	1.36533	+	1.68936i
$526$	−14.9053	−	16.6678i	−0.649900	−	0.726752i
$527$	−7.60015	+	7.60015i	−0.331068	+	0.331068i
$528$	−3.88467	+	2.44812i	−0.169059	+	0.106541i
$529$			16.0154i			0.696320i
$530$	−0.254682	−	0.872228i	−0.0110627	−	0.0378872i
$531$			17.1783i			0.745474i
$532$	−37.9124	+	30.2754i	−1.64371	+	1.31261i
$533$	6.00935	−	6.00935i	0.260294	−	0.260294i
$534$	31.0266	−	27.7457i	1.34265	−	1.20067i
$535$	−9.94504	−	28.1268i	−0.429961	−	1.21603i
$536$	−24.1530	+	17.1737i	−1.04325	+	0.741792i
$537$	−23.2224	−	23.2224i	−1.00212	−	1.00212i
$538$	−0.147420	+	2.64075i	−0.00635574	+	0.113851i
$539$	−5.75335			−0.247814
$540$	−1.55713	−	6.70085i	−0.0670081	−	0.288359i
$541$	−0.467513			−0.0200999			−0.0100500	−	0.999949i	$-0.503199\pi$
$541$	−0.467513			−0.0200999			−0.0100500	+	0.999949i	$0.503199\pi$
$542$	1.86586	−	33.4234i	0.0801457	−	1.43566i
$543$	16.9972	+	16.9972i	0.729422	+	0.729422i
$544$	9.36742	+	16.8827i	0.401625	+	0.723839i
$545$	20.5830	+	9.82971i	0.881679	+	0.421058i
$546$	10.4932	−	9.38356i	0.449067	−	0.401579i
$547$	16.7318	−	16.7318i	0.715402	−	0.715402i	−0.252258	−	0.967660i	$-0.581173\pi$
$547$	16.7318	−	16.7318i	0.715402	−	0.715402i	0.967660	+	0.252258i	$0.0811732\pi$
$548$	−4.30286	−	5.38825i	−0.183809	−	0.230175i
$549$		−	15.0097i		−	0.640600i
$550$	2.85237	−	2.05340i	0.121625	−	0.0875573i
$551$			28.9301i			1.23246i
$552$	6.79453	−	40.2328i	0.289194	−	1.71242i
$553$	8.21358	−	8.21358i	0.349277	−	0.349277i
$554$	14.9762	+	16.7472i	0.636280	+	0.711521i
$555$	29.0036	+	13.8511i	1.23114	+	0.587946i
$556$	−4.31591	−	0.483379i	−0.183035	−	0.0204998i
$557$	−26.5909	−	26.5909i	−1.12669	−	1.12669i	−0.990711	−	0.135981i	$-0.956581\pi$
$557$	−26.5909	−	26.5909i	−1.12669	−	1.12669i	−0.135981	−	0.990711i	$-0.543419\pi$
$558$	−10.3781	−	0.579361i	−0.439341	−	0.0245263i
$559$	−7.30721			−0.309062
$560$	4.49193	+	38.2863i	0.189819	+	1.61789i
$561$	3.91800			0.165418
$562$	−7.73986	−	0.432078i	−0.326486	−	0.0182261i
$563$	0.168647	+	0.168647i	0.00710764	+	0.00710764i	0.710652	−	0.703544i	$-0.248400\pi$
$563$	0.168647	+	0.168647i	0.00710764	+	0.00710764i	−0.703544	+	0.710652i	$0.748400\pi$
$564$	−0.719211	−	0.0805511i	−0.0302842	−	0.00339181i
$565$	10.0221	+	28.3446i	0.421631	+	1.19247i
$566$	10.5295	+	11.7746i	0.442586	+	0.494923i
$567$	32.1656	−	32.1656i	1.35083	−	1.35083i
$568$	0.291480	−	1.72595i	0.0122302	−	0.0724194i
$569$		−	3.52360i		−	0.147717i	−0.997269	−	0.0738586i	$-0.976469\pi$
$569$		−	3.52360i		−	0.147717i	0.997269	−	0.0738586i	$-0.0235313\pi$
$570$	39.4603	−	11.5220i	1.65281	−	0.482604i
$571$			29.6178i			1.23947i	0.784812	+	0.619734i	$0.212760\pi$
$571$			29.6178i			1.23947i	−0.784812	+	0.619734i	$0.787240\pi$
$572$	−0.620316	−	0.776792i	−0.0259367	−	0.0324793i
$573$	11.5499	−	11.5499i	0.482505	−	0.482505i
$574$	−38.6123	+	34.5291i	−1.61164	+	1.44122i
$575$	−3.29433	+	31.0569i	−0.137383	+	1.29516i
$576$	−6.13164	+	17.6360i	−0.255485	+	0.734835i
$577$	−6.92290	−	6.92290i	−0.288204	−	0.288204i	0.548166	−	0.836370i	$-0.315326\pi$
$577$	−6.92290	−	6.92290i	−0.288204	−	0.288204i	−0.836370	+	0.548166i	$0.815326\pi$
$578$	−0.421783	+	7.55543i	−0.0175439	+	0.314265i
$579$	−50.0694			−2.08081
$580$	19.5106	+	12.1528i	0.810134	+	0.504616i
$581$	36.1669			1.50046
$582$	−2.09884	+	37.5967i	−0.0869996	+	1.55843i
$583$	−0.100989	−	0.100989i	−0.00418253	−	0.00418253i
$584$	37.6076	−	26.7405i	1.55622	−	1.10653i
$585$	−4.92035	+	1.73973i	−0.203431	+	0.0719290i
$586$	18.2463	−	16.3168i	0.753747	−	0.674040i
$587$	18.1217	−	18.1217i	0.747961	−	0.747961i	−0.226135	−	0.974096i	$-0.572609\pi$
$587$	18.1217	−	18.1217i	0.747961	−	0.747961i	0.974096	+	0.226135i	$0.0726090\pi$
$588$	−41.7797	+	33.3637i	−1.72297	+	1.37590i
$589$			17.7252i			0.730355i
$590$	11.1853	−	20.4111i	0.460491	−	0.840313i
$591$			12.5964i			0.518145i
$592$	13.2730	+	21.0617i	0.545518	+	0.865629i
$593$	−16.4896	+	16.4896i	−0.677147	+	0.677147i	−0.959354	−	0.282206i	$-0.908934\pi$
$593$	−16.4896	+	16.4896i	−0.677147	+	0.677147i	0.282206	+	0.959354i	$0.408934\pi$
$594$	−0.720782	−	0.806015i	−0.0295740	−	0.0330712i
$595$	14.1749	−	29.6817i	0.581115	−	1.21683i
$596$	−0.0895305	+	0.799385i	−0.00366731	+	0.0327441i
$597$	5.19027	+	5.19027i	0.212423	+	0.212423i
$598$	8.81977	+	0.492365i	0.360667	+	0.0201343i
$599$	−6.82062			−0.278683			−0.139341	−	0.990244i	$-0.544499\pi$
$599$	−6.82062			−0.278683			−0.139341	+	0.990244i	$0.544499\pi$
$600$	8.80569	−	31.4523i	0.359491	−	1.28404i
$601$	3.24618			0.132415			0.0662073	−	0.997806i	$-0.478910\pi$
$601$	3.24618			0.132415			0.0662073	+	0.997806i	$0.478910\pi$
$602$	44.4690	+	2.48249i	1.81242	+	0.101179i
$603$	17.2923	+	17.2923i	0.704197	+	0.704197i
$604$	−2.57183	+	22.9629i	−0.104646	+	0.934347i
$605$	−10.3618	+	21.6971i	−0.421265	+	0.882112i
$606$	−9.10103	−	10.1772i	−0.369704	−	0.413422i
$607$	6.52615	−	6.52615i	0.264888	−	0.264888i	−0.562148	−	0.827036i	$-0.690025\pi$
$607$	6.52615	−	6.52615i	0.264888	−	0.264888i	0.827036	+	0.562148i	$0.190025\pi$
$608$	30.6105	+	8.76363i	1.24142	+	0.355412i
$609$			51.1609i			2.07314i
$610$	−9.77328	+	17.8345i	−0.395708	+	0.722097i
$611$		−	0.156678i		−	0.00633852i
$612$	12.4495	−	9.94168i	0.503240	−	0.401868i
$613$	−5.59655	+	5.59655i	−0.226042	+	0.226042i	−0.811037	−	0.584995i	$-0.801097\pi$
$613$	−5.59655	+	5.59655i	−0.226042	+	0.226042i	0.584995	+	0.811037i	$0.301097\pi$
$614$	−6.86205	+	6.13641i	−0.276930	+	0.247645i
$615$	41.3782	−	14.6305i	1.66853	−	0.589957i
$616$	3.51112	+	4.93801i	0.141467	+	0.198958i
$617$	−26.4213	−	26.4213i	−1.06368	−	1.06368i	−0.997829	−	0.0658511i	$-0.979024\pi$
$617$	−26.4213	−	26.4213i	−1.06368	−	1.06368i	−0.0658511	−	0.997829i	$-0.520976\pi$
$618$	0.893292	−	16.0016i	0.0359335	−	0.643680i
$619$	18.4631			0.742093			0.371046	−	0.928614i	$-0.378999\pi$
$619$	18.4631			0.742093			0.371046	+	0.928614i	$0.378999\pi$
$620$	11.9540	+	7.44590i	0.480084	+	0.299034i
$621$	9.60844			0.385573
$622$	−2.56225	+	45.8978i	−0.102737	+	1.84033i
$623$	−38.8370	−	38.8370i	−1.55597	−	1.55597i
$624$	−9.00924	−	2.04369i	−0.360658	−	0.0818132i
$625$	−5.24468	+	24.4437i	−0.209787	+	0.977747i
$626$	28.6299	−	25.6024i	1.14428	−	1.02328i
$627$	4.56881	−	4.56881i	0.182461	−	0.182461i
$628$	19.3023	+	24.1714i	0.770248	+	0.964543i
$629$		−	21.2423i		−	0.846987i
$630$	30.5345	−	8.91578i	1.21652	−	0.355213i
$631$		−	23.4935i		−	0.935263i	−0.883923	−	0.467632i	$-0.845107\pi$
$631$		−	23.4935i		−	0.935263i	0.883923	−	0.467632i	$-0.154893\pi$
$632$	−7.51656	−	1.26940i	−0.298993	−	0.0504940i
$633$	−17.3867	+	17.3867i	−0.691059	+	0.691059i
$634$	11.0451	+	12.3512i	0.438657	+	0.490529i
$635$	0.0892635	+	0.252457i	0.00354231	+	0.0100184i
$636$	−1.31900	−	0.147727i	−0.0523017	−	0.00585775i
$637$	−8.18491	−	8.18491i	−0.324298	−	0.324298i
$638$	3.60727	+	0.201376i	0.142813	+	0.00797256i
$639$	−1.44438			−0.0571388
$640$	18.7689	−	16.9625i	0.741906	−	0.670504i
$641$	23.5205			0.929004			0.464502	−	0.885572i	$-0.346233\pi$
$641$	23.5205			0.929004			0.464502	+	0.885572i	$0.346233\pi$
$642$	−43.5089	−	2.42889i	−1.71716	−	0.0958606i
$643$	21.3805	+	21.3805i	0.843165	+	0.843165i	0.989269	−	0.146104i	$-0.0466736\pi$
$643$	21.3805	+	21.3805i	0.843165	+	0.843165i	−0.146104	+	0.989269i	$0.546674\pi$
$644$	−53.5066	−	5.99271i	−2.10846	−	0.236146i
$645$	−34.0526	−	16.2623i	−1.34082	−	0.640327i
$646$	−18.1103	−	20.2519i	−0.712542	−	0.796801i
$647$	−20.7116	+	20.7116i	−0.814255	+	0.814255i	−0.985269	−	0.171013i	$-0.945296\pi$
$647$	−20.7116	+	20.7116i	−0.814255	+	0.814255i	0.171013	+	0.985269i	$0.445296\pi$
$648$	−29.4359	−	4.97115i	−1.15635	−	0.195285i
$649$		−	3.65832i		−	0.143601i
$650$	6.97911	+	1.13664i	0.273743	+	0.0445828i
$651$			31.3459i			1.22854i
$652$	9.10359	+	11.4000i	0.356524	+	0.446457i
$653$	18.3070	−	18.3070i	0.716410	−	0.716410i	−0.251458	−	0.967868i	$-0.580910\pi$
$653$	18.3070	−	18.3070i	0.716410	−	0.716410i	0.967868	+	0.251458i	$0.0809101\pi$
$654$	24.8356	−	22.2094i	0.971151	−	0.868455i
$655$	−24.7944	−	11.8409i	−0.968796	−	0.462662i
$656$	33.1517	+	7.52027i	1.29436	+	0.293617i
$657$	−26.9251	−	26.9251i	−1.05045	−	1.05045i
$658$	−0.0532285	+	0.953487i	−0.00207506	+	0.0371708i
$659$	−21.7960			−0.849050			−0.424525	−	0.905416i	$-0.639559\pi$
$659$	−21.7960			−0.849050			−0.424525	+	0.905416i	$0.639559\pi$
$660$	−1.16200	−	5.00047i	−0.0452307	−	0.194643i
$661$	−8.52927			−0.331750			−0.165875	−	0.986147i	$-0.553045\pi$
$661$	−8.52927			−0.331750			−0.165875	+	0.986147i	$0.553045\pi$
$662$	−0.229774	+	4.11596i	−0.00893042	+	0.159971i
$663$	5.57387	+	5.57387i	0.216471	+	0.216471i
$664$	−13.7541	−	19.3436i	−0.533762	−	0.750678i
$665$	−18.0826	−	51.1416i	−0.701213	−	1.98319i
$666$	15.3130	−	13.6937i	0.593367	−	0.530621i
$667$	−22.7013	+	22.7013i	−0.878997	+	0.878997i
$668$	−10.7945	+	8.62009i	−0.417652	+	0.333521i
$669$		−	43.6150i		−	1.68625i
$670$	−9.28709	−	31.8061i	−0.358791	−	1.22878i
$671$			3.19650i			0.123399i
$672$	54.1327	+	15.4979i	2.08821	+	0.597844i
$673$	12.3291	−	12.3291i	0.475250	−	0.475250i	−0.428358	−	0.903609i	$-0.640908\pi$
$673$	12.3291	−	12.3291i	0.475250	−	0.475250i	0.903609	+	0.428358i	$0.140908\pi$
$674$	5.76344	+	6.44498i	0.222000	+	0.248251i
$675$	7.64848	+	0.811304i	0.294390	+	0.0312271i
$676$	0.222607	−	1.98757i	0.00856180	−	0.0764451i
$677$	18.8117	+	18.8117i	0.722992	+	0.722992i	0.969213	−	0.246222i	$-0.0791892\pi$
$677$	18.8117	+	18.8117i	0.722992	+	0.722992i	−0.246222	+	0.969213i	$0.579189\pi$
$678$	43.8458	+	2.44770i	1.68389	+	0.0940033i
$679$	49.6881			1.90685
$680$	−21.2657	+	3.70643i	−0.815502	+	0.142135i
$681$	−18.6634			−0.715184
$682$	2.21015	+	0.123382i	0.0846308	+	0.00472453i
$683$	29.2411	+	29.2411i	1.11888	+	1.11888i	0.991906	+	0.126973i	$0.0405262\pi$
$683$	29.2411	+	29.2411i	1.11888	+	1.11888i	0.126973	+	0.991906i	$0.459474\pi$
$684$	2.92436	−	26.1105i	0.111816	−	0.998361i
$685$	7.26843	−	2.56996i	0.277712	−	0.0981933i
$686$	18.5889	+	20.7871i	0.709729	+	0.793655i
$687$	21.2273	−	21.2273i	0.809870	−	0.809870i
$688$	−15.5836	−	24.7281i	−0.594119	−	0.942748i
$689$		−	0.287340i		−	0.0109468i
$690$	40.0055	+	21.9230i	1.52298	+	0.834594i
$691$			21.6953i			0.825329i	0.910883	+	0.412664i	$0.135402\pi$
$691$			21.6953i			0.825329i	−0.910883	+	0.412664i	$0.864598\pi$
$692$	25.1429	−	20.0781i	0.955788	−	0.763256i
$693$	3.53536	−	3.53536i	0.134297	−	0.134297i
$694$	−24.4143	+	21.8325i	−0.926753	+	0.828752i
$695$	2.09245	−	4.38150i	0.0793711	−	0.166200i
$696$	27.3631	−	19.4562i	1.03719	−	0.737486i
$697$	−20.5104	−	20.5104i	−0.776888	−	0.776888i
$698$	−1.94049	+	34.7601i	−0.0734485	+	1.31569i
$699$	−2.88022			−0.108940
$700$	−42.0862	−	9.28822i	−1.59071	−	0.351062i
$701$	−1.18461			−0.0447420			−0.0223710	−	0.999750i	$-0.507122\pi$
$701$	−1.18461			−0.0447420			−0.0223710	+	0.999750i	$0.507122\pi$
$702$	0.121256	−	2.17207i	0.00457652	−	0.0819796i
$703$	−24.7709	−	24.7709i	−0.934251	−	0.934251i
$704$	1.30580	−	3.75580i	0.0492143	−	0.141552i
$705$	0.348689	−	0.730141i	0.0131324	−	0.0274987i
$706$	−8.61846	+	7.70709i	−0.324360	+	0.290060i
$707$	−12.7392	+	12.7392i	−0.479106	+	0.479106i
$708$	−21.2146	−	26.5660i	−0.797294	−	0.998411i
$709$			22.7803i			0.855532i	0.903890	+	0.427766i	$0.140699\pi$
$709$			22.7803i			0.855532i	−0.903890	+	0.427766i	$0.859301\pi$
$710$	1.71620	+	0.940477i	0.0644079	+	0.0352955i
$711$			6.29030i			0.235905i
$712$	−6.00222	+	35.5413i	−0.224943	+	1.33197i
$713$	−13.9089	+	13.9089i	−0.520892	+	0.520892i
$714$	−32.0270	−	35.8142i	−1.19858	−	1.34031i
$715$	1.04785	−	0.370496i	0.0391872	−	0.0138558i
$716$	28.2631	+	3.16545i	1.05624	+	0.118298i
$717$	10.0220	+	10.0220i	0.374278	+	0.374278i
$718$	9.07627	+	0.506684i	0.338723	+	0.0189093i
$719$	11.1110			0.414370			0.207185	−	0.978302i	$-0.433570\pi$
$719$	11.1110			0.414370			0.207185	+	0.978302i	$0.433570\pi$
$720$	−16.3807	−	12.9405i	−0.610471	−	0.482266i
$721$	−21.1479			−0.787589
$722$	−17.9063	−	0.999624i	−0.666405	−	0.0372021i
$723$	−38.8331	−	38.8331i	−1.44422	−	1.44422i
$724$	−20.6868	−	2.31690i	−0.768817	−	0.0861070i
$725$	−19.9874	+	16.1538i	−0.742314	+	0.599936i
$726$	23.4115	+	26.1799i	0.868881	+	0.971628i
$727$	11.9420	−	11.9420i	0.442904	−	0.442904i	−0.450083	−	0.892987i	$-0.648606\pi$
$727$	11.9420	−	11.9420i	0.442904	−	0.442904i	0.892987	+	0.450083i	$0.148606\pi$
$728$	−2.02995	+	12.0200i	−0.0752348	+	0.445492i
$729$			13.9756i			0.517614i
$730$	14.4605	+	49.5240i	0.535209	+	1.83297i
$731$			24.9402i			0.922445i
$732$	18.5365	+	23.2124i	0.685130	+	0.857954i
$733$	26.1775	−	26.1775i	0.966887	−	0.966887i	−0.0325820	−	0.999469i	$-0.510373\pi$
$733$	26.1775	−	26.1775i	0.966887	−	0.966887i	0.999469	+	0.0325820i	$0.0103730\pi$
$734$	−17.4896	+	15.6401i	−0.645552	+	0.577287i
$735$	−19.9271	−	56.3584i	−0.735023	−	2.07881i
$736$	17.1431	+	30.8967i	0.631904	+	1.13887i
$737$	−3.68260	−	3.68260i	−0.135650	−	0.135650i
$738$	1.56351	−	28.0073i	0.0575537	−	1.03096i
$739$	4.47304			0.164544			0.0822718	−	0.996610i	$-0.473782\pi$
$739$	4.47304			0.164544			0.0822718	+	0.996610i	$0.473782\pi$
$740$	−27.1112	+	6.30004i	−0.996628	+	0.231594i
$741$	12.9995			0.477548
$742$	−0.0976186	+	1.74865i	−0.00358369	+	0.0641950i
$743$	−33.2249	−	33.2249i	−1.21890	−	1.21890i	−0.968017	−	0.250885i	$-0.919278\pi$
$743$	−33.2249	−	33.2249i	−1.21890	−	1.21890i	−0.250885	−	0.968017i	$-0.580722\pi$
$744$	16.7651	−	11.9207i	0.614640	−	0.437033i
$745$	−0.811534	−	0.387560i	−0.0297323	−	0.0141991i
$746$	−23.4401	+	20.9613i	−0.858201	+	0.767449i
$747$	−13.8490	+	13.8490i	−0.506710	+	0.506710i
$748$	−2.65126	+	2.11720i	−0.0969397	+	0.0774124i
$749$			57.5018i			2.10107i
$750$	29.9940	+	20.8290i	1.09523	+	0.760568i
$751$		−	20.1494i		−	0.735264i	−0.929971	−	0.367632i	$-0.880169\pi$
$751$		−	20.1494i		−	0.735264i	0.929971	−	0.367632i	$-0.119831\pi$
$752$	0.530209	−	0.334137i	0.0193347	−	0.0121847i
$753$	−34.9349	+	34.9349i	−1.27310	+	1.27310i
$754$	4.84534	+	5.41831i	0.176457	+	0.197323i
$755$	−23.3119	−	11.1329i	−0.848407	−	0.405169i
$756$	−1.47584	+	13.1773i	−0.0536759	+	0.479252i
$757$	0.215715	+	0.215715i	0.00784030	+	0.00784030i	0.711016	−	0.703176i	$-0.248235\pi$
$757$	0.215715	+	0.215715i	0.00784030	+	0.00784030i	−0.703176	+	0.711016i	$0.748235\pi$
$758$	40.9211	+	2.28443i	1.48632	+	0.0829742i
$759$	7.17024			0.260263
$760$	−20.4760	+	29.1202i	−0.742744	+	1.05630i
$761$	−44.7165			−1.62097			−0.810485	−	0.585759i	$-0.800796\pi$
$761$	−44.7165			−1.62097			−0.810485	+	0.585759i	$0.800796\pi$
$762$	0.390522	+	0.0218009i	0.0141471	+	0.000789765i
$763$	−31.0876	−	31.0876i	−1.12545	−	1.12545i
$764$	−1.57437	+	14.0570i	−0.0569588	+	0.508564i
$765$	5.93786	+	16.7936i	0.214684	+	0.607173i
$766$	−30.3801	−	33.9725i	−1.09768	−	1.22748i
$767$	5.20444	−	5.20444i	0.187922	−	0.187922i
$768$	−12.2974	−	34.8463i	−0.443745	−	1.25741i
$769$		−	10.5286i		−	0.379672i	−0.981816	−	0.189836i	$-0.939204\pi$
$769$		−	10.5286i		−	0.379672i	0.981816	−	0.189836i	$-0.0607956\pi$
$770$	−6.50268	+	1.89872i	−0.234340	+	0.0684251i
$771$		−	38.4753i		−	1.38565i
$772$	33.8814	−	27.0564i	1.21942	−	0.973780i

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)

\(f(q)\)	\(=\)	\(q+(-1.41202 - 0.0788259i) q^{2} +(-1.63309 - 1.63309i) q^{3} +(1.98757 + 0.222607i) q^{4} +(-0.963620 + 2.01778i) q^{5} +(2.17721 + 2.43467i) q^{6} +(3.04756 - 3.04756i) q^{7} +(-2.78894 - 0.470996i) q^{8} +2.33394i q^{9} +O(q^{10})\)	\(q+(-1.41202 - 0.0788259i) q^{2} +(-1.63309 - 1.63309i) q^{3} +(1.98757 + 0.222607i) q^{4} +(-0.963620 + 2.01778i) q^{5} +(2.17721 + 2.43467i) q^{6} +(3.04756 - 3.04756i) q^{7} +(-2.78894 - 0.470996i) q^{8} +2.33394i q^{9} +(1.51970 - 2.77318i) q^{10} -0.497041i q^{11} +(-2.88234 - 3.60941i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-4.54342 + 4.06297i) q^{14} +(4.86888 - 1.72154i) q^{15} +(3.90089 + 0.884894i) q^{16} +(-2.41342 - 2.41342i) q^{17} +(0.183975 - 3.29556i) q^{18} -5.62862 q^{19} +(-2.36444 + 3.79598i) q^{20} -9.95385 q^{21} +(-0.0391797 + 0.701829i) q^{22} +(-4.41675 - 4.41675i) q^{23} +(3.78540 + 5.32375i) q^{24} +(-3.14287 - 3.88875i) q^{25} +(-1.05418 + 0.942707i) q^{26} +(-1.08773 + 1.08773i) q^{27} +(6.73565 - 5.37884i) q^{28} -5.13981i q^{29} +(-7.01064 + 2.04704i) q^{30} -3.14912i q^{31} +(-5.43837 - 1.55698i) q^{32} +(-0.811710 + 0.811710i) q^{33} +(3.21754 + 3.59802i) q^{34} +(3.21261 + 9.08599i) q^{35} +(-0.519552 + 4.63888i) q^{36} +(4.40088 + 4.40088i) q^{37} +(7.94770 + 0.443681i) q^{38} -2.30953 q^{39} +(3.63784 - 5.17360i) q^{40} +8.49850 q^{41} +(14.0550 + 0.784621i) q^{42} +(-5.16698 - 5.16698i) q^{43} +(0.110645 - 0.987905i) q^{44} +(-4.70939 - 2.24903i) q^{45} +(5.88836 + 6.58467i) q^{46} +(0.110788 - 0.110788i) q^{47} +(-4.92539 - 7.81560i) q^{48} -11.5752i q^{49} +(4.13125 + 5.73871i) q^{50} +7.88265i q^{51} +(1.56283 - 1.24802i) q^{52} +(0.203180 - 0.203180i) q^{53} +(1.62163 - 1.45015i) q^{54} +(1.00292 + 0.478958i) q^{55} +(-9.93483 + 7.06405i) q^{56} +(9.19203 + 9.19203i) q^{57} +(-0.405150 + 7.25749i) q^{58} +7.36019 q^{59} +(10.0605 - 2.33783i) q^{60} -6.43106 q^{61} +(-0.248232 + 4.44661i) q^{62} +(7.11283 + 7.11283i) q^{63} +(7.55632 + 2.62716i) q^{64} +(0.745404 + 2.10817i) q^{65} +(1.21013 - 1.08216i) q^{66} +(7.40905 - 7.40905i) q^{67} +(-4.25960 - 5.33409i) q^{68} +14.4259i q^{69} +(-3.82005 - 13.0828i) q^{70} +0.618858i q^{71} +(1.09928 - 6.50922i) q^{72} +(-11.5363 + 11.5363i) q^{73} +(-5.86720 - 6.56101i) q^{74} +(-1.21807 + 11.4832i) q^{75} +(-11.1873 - 1.25297i) q^{76} +(-1.51476 - 1.51476i) q^{77} +(3.26110 + 0.182051i) q^{78} +2.69514 q^{79} +(-5.54450 + 7.01844i) q^{80} +10.5545 q^{81} +(-12.0000 - 0.669902i) q^{82} +(5.93375 + 5.93375i) q^{83} +(-19.7840 - 2.21579i) q^{84} +(7.19537 - 2.54413i) q^{85} +(6.88856 + 7.70314i) q^{86} +(-8.39376 + 8.39376i) q^{87} +(-0.234104 + 1.38621i) q^{88} -12.7437i q^{89} +(6.47244 + 3.54689i) q^{90} -4.30990i q^{91} +(-7.79541 - 9.76181i) q^{92} +(-5.14279 + 5.14279i) q^{93} +(-0.165168 + 0.147702i) q^{94} +(5.42385 - 11.3573i) q^{95} +(6.33865 + 11.4240i) q^{96} +(8.15212 + 8.15212i) q^{97} +(-0.912426 + 16.3444i) q^{98} +1.16007 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

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Groups

Database

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