LMFDB - Embedded newform 260.2.o.a.27.20

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			27.20
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.203483 - 1.39950i) q^{2} +(-0.0775283 - 0.0775283i) q^{3} +(-1.91719 - 0.569548i) q^{4} +(0.871245 + 2.05935i) q^{5} +(-0.124276 + 0.0927250i) q^{6} +(2.89635 - 2.89635i) q^{7} +(-1.18720 + 2.56721i) q^{8} -2.98798i q^{9} +O(q^{10})$	\(q+(0.203483 - 1.39950i) q^{2} +(-0.0775283 - 0.0775283i) q^{3} +(-1.91719 - 0.569548i) q^{4} +(0.871245 + 2.05935i) q^{5} +(-0.124276 + 0.0927250i) q^{6} +(2.89635 - 2.89635i) q^{7} +(-1.18720 + 2.56721i) q^{8} -2.98798i q^{9} +(3.05934 - 0.800263i) q^{10} -3.20102i q^{11} +(0.104480 + 0.192792i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(-3.46408 - 4.64280i) q^{14} +(0.0921119 - 0.227204i) q^{15} +(3.35123 + 2.18386i) q^{16} +(-0.217815 - 0.217815i) q^{17} +(-4.18167 - 0.608002i) q^{18} +5.01907 q^{19} +(-0.497443 - 4.44438i) q^{20} -0.449098 q^{21} +(-4.47983 - 0.651354i) q^{22} +(-4.02311 - 4.02311i) q^{23} +(0.291073 - 0.106990i) q^{24} +(-3.48186 + 3.58840i) q^{25} +(0.845710 + 1.13348i) q^{26} +(-0.464238 + 0.464238i) q^{27} +(-7.20247 + 3.90325i) q^{28} +9.89914i q^{29} +(-0.299229 - 0.175143i) q^{30} +2.20528i q^{31} +(3.73823 - 4.24566i) q^{32} +(-0.248170 + 0.248170i) q^{33} +(-0.349153 + 0.260510i) q^{34} +(8.48804 + 3.44118i) q^{35} +(-1.70180 + 5.72852i) q^{36} +(0.278378 + 0.278378i) q^{37} +(1.02129 - 7.02418i) q^{38} +0.109642 q^{39} +(-6.32113 - 0.208186i) q^{40} +5.39487 q^{41} +(-0.0913838 + 0.628512i) q^{42} +(1.36242 + 1.36242i) q^{43} +(-1.82314 + 6.13697i) q^{44} +(6.15330 - 2.60326i) q^{45} +(-6.44897 + 4.81170i) q^{46} +(-4.21558 + 4.21558i) q^{47} +(-0.0905041 - 0.429126i) q^{48} -9.77772i q^{49} +(4.31346 + 5.60304i) q^{50} +0.0337736i q^{51} +(1.75839 - 0.952927i) q^{52} +(-0.797227 + 0.797227i) q^{53} +(0.555235 + 0.744164i) q^{54} +(6.59204 - 2.78888i) q^{55} +(3.99701 + 10.8741i) q^{56} +(-0.389120 - 0.389120i) q^{57} +(13.8538 + 2.01431i) q^{58} -9.66566 q^{59} +(-0.305999 + 0.383131i) q^{60} +10.8601 q^{61} +(3.08629 + 0.448738i) q^{62} +(-8.65424 - 8.65424i) q^{63} +(-5.18113 - 6.09556i) q^{64} +(-2.07225 - 0.840119i) q^{65} +(0.296815 + 0.397812i) q^{66} +(-3.68797 + 3.68797i) q^{67} +(0.293537 + 0.541649i) q^{68} +0.623810i q^{69} +(6.54309 - 11.1788i) q^{70} +11.8869i q^{71} +(7.67077 + 3.54732i) q^{72} +(0.326289 - 0.326289i) q^{73} +(0.446235 - 0.332945i) q^{74} +(0.548145 - 0.00825971i) q^{75} +(-9.62250 - 2.85860i) q^{76} +(-9.27130 - 9.27130i) q^{77} +(0.0223102 - 0.153443i) q^{78} +6.73412 q^{79} +(-1.57760 + 8.80404i) q^{80} -8.89195 q^{81} +(1.09776 - 7.55010i) q^{82} +(2.35855 + 2.35855i) q^{83} +(0.861007 + 0.255783i) q^{84} +(0.258788 - 0.638328i) q^{85} +(2.18393 - 1.62947i) q^{86} +(0.767463 - 0.767463i) q^{87} +(8.21770 + 3.80024i) q^{88} +16.4054i q^{89} +(-2.39117 - 9.14125i) q^{90} +4.09606i q^{91} +(5.42171 + 10.0044i) q^{92} +(0.170972 - 0.170972i) q^{93} +(5.04189 + 6.75749i) q^{94} +(4.37284 + 10.3360i) q^{95} +(-0.618977 + 0.0393405i) q^{96} +(-11.5449 - 11.5449i) q^{97} +(-13.6839 - 1.98960i) q^{98} -9.56459 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 $

$2$	0.203483	−	1.39950i	0.143884	−	0.989595i
$2$	0.203483	−	1.39950i	0.143884	−	0.989595i
$3$	−0.0775283	−	0.0775283i	−0.0447610	−	0.0447610i	0.684372	−	0.729133i	$-0.260076\pi$
$3$	−0.0775283	−	0.0775283i	−0.0447610	−	0.0447610i	−0.729133	+	0.684372i	$0.760076\pi$
$4$	−1.91719	−	0.569548i	−0.958595	−	0.284774i
$5$	0.871245	+	2.05935i	0.389633	+	0.920970i
$5$	0.871245	+	2.05935i	0.389633	+	0.920970i
$6$	−0.124276	+	0.0927250i	−0.0507356	+	0.0378548i
$7$	2.89635	−	2.89635i	1.09472	−	1.09472i	0.0997009	−	0.995017i	$-0.468211\pi$
$7$	2.89635	−	2.89635i	1.09472	−	1.09472i	0.995017	−	0.0997009i	$-0.0317886\pi$
$8$	−1.18720	+	2.56721i	−0.419737	+	0.907646i
$9$		−	2.98798i		−	0.995993i
$10$	3.05934	−	0.800263i	0.967449	−	0.253065i
$11$		−	3.20102i		−	0.965145i	−0.875856	−	0.482573i	$-0.839702\pi$
$11$		−	3.20102i		−	0.965145i	0.875856	−	0.482573i	$-0.160298\pi$
$12$	0.104480	+	0.192792i	0.0301609	+	0.0556544i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$14$	−3.46408	−	4.64280i	−0.925815	−	1.24084i
$15$	0.0921119	−	0.227204i	0.0237832	−	0.0586639i
$16$	3.35123	+	2.18386i	0.837808	+	0.545965i
$17$	−0.217815	−	0.217815i	−0.0528279	−	0.0528279i	0.680199	−	0.733027i	$-0.261893\pi$
$17$	−0.217815	−	0.217815i	−0.0528279	−	0.0528279i	−0.733027	+	0.680199i	$0.761893\pi$
$18$	−4.18167	−	0.608002i	−0.985629	−	0.143308i
$19$	5.01907			1.15145			0.575727	−	0.817642i	$-0.304719\pi$
$19$	5.01907			1.15145			0.575727	+	0.817642i	$0.304719\pi$
$20$	−0.497443	−	4.44438i	−0.111232	−	0.993795i
$21$	−0.449098			−0.0980013
$22$	−4.47983	−	0.651354i	−0.955102	−	0.138869i
$23$	−4.02311	−	4.02311i	−0.838877	−	0.838877i	0.149834	−	0.988711i	$-0.452126\pi$
$23$	−4.02311	−	4.02311i	−0.838877	−	0.838877i	−0.988711	+	0.149834i	$0.952126\pi$
$24$	0.291073	−	0.106990i	0.0594149	−	0.0218393i
$25$	−3.48186	+	3.58840i	−0.696373	+	0.717680i
$26$	0.845710	+	1.13348i	0.165857	+	0.222293i
$27$	−0.464238	+	0.464238i	−0.0893426	+	0.0893426i
$28$	−7.20247	+	3.90325i	−1.36114	+	0.737644i
$29$			9.89914i			1.83822i	0.393995	+	0.919112i	$0.371093\pi$
$29$			9.89914i			1.83822i	−0.393995	+	0.919112i	$0.628907\pi$
$30$	−0.299229	−	0.175143i	−0.0546314	−	0.0319765i
$31$			2.20528i			0.396081i	0.980194	+	0.198040i	$0.0634577\pi$
$31$			2.20528i			0.396081i	−0.980194	+	0.198040i	$0.936542\pi$
$32$	3.73823	−	4.24566i	0.660832	−	0.750534i
$33$	−0.248170	+	0.248170i	−0.0432008	+	0.0432008i
$34$	−0.349153	+	0.260510i	−0.0598793	+	0.0446771i
$35$	8.48804	+	3.44118i	1.43474	+	0.581665i
$36$	−1.70180	+	5.72852i	−0.283633	+	0.954754i
$37$	0.278378	+	0.278378i	0.0457651	+	0.0457651i	0.729619	−	0.683854i	$-0.239697\pi$
$37$	0.278378	+	0.278378i	0.0457651	+	0.0457651i	−0.683854	+	0.729619i	$0.739697\pi$
$38$	1.02129	−	7.02418i	0.165676	−	1.13947i
$39$	0.109642			0.0175567
$40$	−6.32113	−	0.208186i	−0.999458	−	0.0329171i
$41$	5.39487			0.842537			0.421268	−	0.906936i	$-0.361585\pi$
$41$	5.39487			0.842537			0.421268	+	0.906936i	$0.361585\pi$
$42$	−0.0913838	+	0.628512i	−0.0141008	+	0.0969815i
$43$	1.36242	+	1.36242i	0.207767	+	0.207767i	0.803318	−	0.595551i	$-0.203066\pi$
$43$	1.36242	+	1.36242i	0.207767	+	0.207767i	−0.595551	+	0.803318i	$0.703066\pi$
$44$	−1.82314	+	6.13697i	−0.274848	+	0.925183i
$45$	6.15330	−	2.60326i	0.917280	−	0.388071i
$46$	−6.44897	+	4.81170i	−0.950849	+	0.709447i
$47$	−4.21558	+	4.21558i	−0.614905	+	0.614905i	−0.944220	−	0.329315i	$-0.893182\pi$
$47$	−4.21558	+	4.21558i	−0.614905	+	0.614905i	0.329315	+	0.944220i	$0.393182\pi$
$48$	−0.0905041	−	0.429126i	−0.0130631	−	0.0619390i
$49$		−	9.77772i		−	1.39682i
$50$	4.31346	+	5.60304i	0.610016	+	0.792389i
$51$			0.0337736i			0.00472926i
$52$	1.75839	−	0.952927i	0.243845	−	0.132147i
$53$	−0.797227	+	0.797227i	−0.109508	+	0.109508i	−0.759737	−	0.650230i	$-0.774673\pi$
$53$	−0.797227	+	0.797227i	−0.109508	+	0.109508i	0.650230	+	0.759737i	$0.274673\pi$
$54$	0.555235	+	0.744164i	0.0755579	+	0.101268i
$55$	6.59204	−	2.78888i	0.888870	−	0.376052i
$56$	3.99701	+	10.8741i	0.534122	+	1.45311i
$57$	−0.389120	−	0.389120i	−0.0515401	−	0.0515401i
$58$	13.8538	+	2.01431i	1.81910	+	0.264491i
$59$	−9.66566			−1.25836			−0.629181	−	0.777259i	$-0.716610\pi$
$59$	−9.66566			−1.25836			−0.629181	+	0.777259i	$0.716610\pi$
$60$	−0.305999	+	0.383131i	−0.0395044	+	0.0494620i
$61$	10.8601			1.39049			0.695244	−	0.718774i	$-0.255296\pi$
$61$	10.8601			1.39049			0.695244	+	0.718774i	$0.255296\pi$
$62$	3.08629	+	0.448738i	0.391959	+	0.0569897i
$63$	−8.65424	−	8.65424i	−1.09033	−	1.09033i
$64$	−5.18113	−	6.09556i	−0.647641	−	0.761945i
$65$	−2.07225	−	0.840119i	−0.257030	−	0.104204i
$66$	0.296815	+	0.397812i	0.0365354	+	0.0489672i
$67$	−3.68797	+	3.68797i	−0.450557	+	0.450557i	−0.895539	−	0.444982i	$-0.853210\pi$
$67$	−3.68797	+	3.68797i	−0.450557	+	0.450557i	0.444982	+	0.895539i	$0.353210\pi$
$68$	0.293537	+	0.541649i	0.0355966	+	0.0656846i
$69$			0.623810i			0.0750979i
$70$	6.54309	−	11.1788i	0.782049	−	1.33612i
$71$			11.8869i			1.41071i	0.708854	+	0.705356i	$0.249213\pi$
$71$			11.8869i			1.41071i	−0.708854	+	0.705356i	$0.750787\pi$
$72$	7.67077	+	3.54732i	0.904009	+	0.418055i
$73$	0.326289	−	0.326289i	0.0381893	−	0.0381893i	−0.687754	−	0.725944i	$-0.741403\pi$
$73$	0.326289	−	0.326289i	0.0381893	−	0.0381893i	0.725944	+	0.687754i	$0.241403\pi$
$74$	0.446235	−	0.332945i	0.0518738	−	0.0387040i
$75$	0.548145	−	0.00825971i	0.0632944	−	0.000953749i
$76$	−9.62250	−	2.85860i	−1.10378	−	0.327904i
$77$	−9.27130	−	9.27130i	−1.05656	−	1.05656i
$78$	0.0223102	−	0.153443i	0.00252613	−	0.0173740i
$79$	6.73412			0.757647			0.378824	−	0.925469i	$-0.376329\pi$
$79$	6.73412			0.757647			0.378824	+	0.925469i	$0.376329\pi$
$80$	−1.57760	+	8.80404i	−0.176381	+	0.984322i
$81$	−8.89195			−0.987995
$82$	1.09776	−	7.55010i	0.121228	−	0.833770i
$83$	2.35855	+	2.35855i	0.258885	+	0.258885i	0.824600	−	0.565716i	$-0.191400\pi$
$83$	2.35855	+	2.35855i	0.258885	+	0.258885i	−0.565716	+	0.824600i	$0.691400\pi$
$84$	0.861007	+	0.255783i	0.0939435	+	0.0279082i
$85$	0.258788	−	0.638328i	0.0280695	−	0.0692364i
$86$	2.18393	−	1.62947i	0.235499	−	0.175710i
$87$	0.767463	−	0.767463i	0.0822807	−	0.0822807i
$88$	8.21770	+	3.80024i	0.876010	+	0.405107i
$89$			16.4054i			1.73897i	0.493961	+	0.869484i	$0.335549\pi$
$89$			16.4054i			1.73897i	−0.493961	+	0.869484i	$0.664451\pi$
$90$	−2.39117	−	9.14125i	−0.252051	−	0.963573i
$91$			4.09606i			0.429384i
$92$	5.42171	+	10.0044i	0.565253	+	1.04303i
$93$	0.170972	−	0.170972i	0.0177290	−	0.0177290i
$94$	5.04189	+	6.75749i	0.520032	+	0.696982i
$95$	4.37284	+	10.3360i	0.448644	+	1.06045i
$96$	−0.618977	+	0.0393405i	−0.0631741	+	0.00401517i
$97$	−11.5449	−	11.5449i	−1.17221	−	1.17221i	−0.981682	−	0.190525i	$-0.938981\pi$
$97$	−11.5449	−	11.5449i	−1.17221	−	1.17221i	−0.190525	−	0.981682i	$-0.561019\pi$
$98$	−13.6839	−	1.98960i	−1.38228	−	0.200980i
$99$	−9.56459			−0.961278
$100$	8.71916	−	4.89656i	0.871916	−	0.489656i
$101$	7.98198			0.794236			0.397118	−	0.917767i	$-0.370010\pi$
$101$	7.98198			0.794236			0.397118	+	0.917767i	$0.370010\pi$
$102$	0.0472662	+	0.00687236i	0.00468005	+	0.000680465i
$103$	−4.94955	−	4.94955i	−0.487694	−	0.487694i	0.419884	−	0.907578i	$-0.362071\pi$
$103$	−4.94955	−	4.94955i	−0.487694	−	0.487694i	−0.907578	+	0.419884i	$0.862071\pi$
$104$	−0.975817	−	2.65477i	−0.0956867	−	0.260321i
$105$	−0.391275	−	0.924852i	−0.0381845	−	0.0902563i
$106$	0.953495	+	1.27794i	0.0926117	+	0.124124i
$107$	−10.5156	+	10.5156i	−1.01658	+	1.01658i	−0.0167221	+	0.999860i	$0.505323\pi$
$107$	−10.5156	+	10.5156i	−1.01658	+	1.01658i	−0.999860	+	0.0167221i	$0.994677\pi$
$108$	1.15444	−	0.625626i	0.111086	−	0.0602009i
$109$		−	0.690455i		−	0.0661336i	−0.999453	−	0.0330668i	$-0.989473\pi$
$109$		−	0.690455i		−	0.0661336i	0.999453	−	0.0330668i	$-0.0105274\pi$
$110$	−2.56166	−	9.79303i	−0.244245	−	0.933729i
$111$		−	0.0431643i		−	0.00409698i
$112$	16.0316	−	3.38111i	1.51484	−	0.319485i
$113$	−3.03257	+	3.03257i	−0.285280	+	0.285280i	−0.835210	−	0.549931i	$-0.814654\pi$
$113$	−3.03257	+	3.03257i	−0.285280	+	0.285280i	0.549931	+	0.835210i	$0.314654\pi$
$114$	−0.623751	+	0.465393i	−0.0584197	+	0.0435880i
$115$	4.77989	−	11.7901i	0.445727	−	1.09943i
$116$	5.63803	−	18.9785i	0.523478	−	1.76211i
$117$	2.11282	+	2.11282i	0.195330	+	0.195330i
$118$	−1.96680	+	13.5271i	−0.181058	+	1.24527i
$119$	−1.26174			−0.115663
$120$	0.473926	+	0.506206i	0.0432633	+	0.0462101i
$121$	0.753441			0.0684947
$122$	2.20984	−	15.1986i	0.200069	−	1.37602i
$123$	−0.418255	−	0.418255i	−0.0377127	−	0.0377127i
$124$	1.25601	−	4.22795i	0.112793	−	0.379681i
$125$	−10.4233	−	4.04401i	−0.932292	−	0.361707i
$126$	−13.8726	+	10.3506i	−1.23587	+	0.922105i
$127$	−0.806054	+	0.806054i	−0.0715257	+	0.0715257i	−0.741965	−	0.670439i	$-0.766106\pi$
$127$	−0.806054	+	0.806054i	−0.0715257	+	0.0715257i	0.670439	+	0.741965i	$0.266106\pi$
$128$	−9.58500	+	6.01064i	−0.847202	+	0.531271i
$129$		−	0.211252i		−	0.0185997i
$130$	−1.59741	+	2.72915i	−0.140102	+	0.239363i
$131$		−	19.2242i		−	1.67962i	−0.542877	−	0.839812i	$-0.682665\pi$
$131$		−	19.2242i		−	1.67962i	0.542877	−	0.839812i	$-0.317335\pi$
$132$	0.617133	−	0.334444i	0.0537146	−	0.0291096i
$133$	14.5370	−	14.5370i	1.26052	−	1.26052i
$134$	4.41087	+	5.91175i	0.381041	+	0.510697i
$135$	−1.36049	−	0.551564i	−0.117093	−	0.0474711i
$136$	0.817766	−	0.300588i	0.0701229	−	0.0257752i
$137$	−3.52426	−	3.52426i	−0.301097	−	0.301097i	0.540346	−	0.841443i	$-0.318293\pi$
$137$	−3.52426	−	3.52426i	−0.301097	−	0.301097i	−0.841443	+	0.540346i	$0.818293\pi$
$138$	0.873021	+	0.126935i	0.0743164	+	0.0108054i
$139$	−5.61731			−0.476454			−0.238227	−	0.971209i	$-0.576566\pi$
$139$	−5.61731			−0.476454			−0.238227	+	0.971209i	$0.576566\pi$
$140$	−14.3133	−	11.4317i	−1.20969	−	0.966158i
$141$	0.653652			0.0550475
$142$	16.6356	+	2.41877i	1.39603	+	0.202979i
$143$	2.26347	+	2.26347i	0.189281	+	0.189281i
$144$	6.52533	−	10.0134i	0.543778	−	0.834451i
$145$	−20.3858	+	8.62458i	−1.69295	+	0.716232i
$146$	−0.390247	−	0.523035i	−0.0322971	−	0.0432867i
$147$	−0.758049	+	0.758049i	−0.0625229	+	0.0625229i
$148$	−0.375154	−	0.692253i	−0.0308375	−	0.0569029i
$149$		−	5.19488i		−	0.425581i	−0.977098	−	0.212791i	$-0.931745\pi$
$149$		−	5.19488i		−	0.425581i	0.977098	−	0.212791i	$-0.0682552\pi$
$150$	0.0999787	−	0.768809i	0.00816323	−	0.0627730i
$151$		−	2.67892i		−	0.218008i	−0.994041	−	0.109004i	$-0.965234\pi$
$151$		−	2.67892i		−	0.218008i	0.994041	−	0.109004i	$-0.0347661\pi$
$152$	−5.95862	+	12.8850i	−0.483308	+	1.04511i
$153$	−0.650827	+	0.650827i	−0.0526162	+	0.0526162i
$154$	−14.8617	+	11.0886i	−1.19759	+	0.893546i
$155$	−4.54146	+	1.92134i	−0.364779	+	0.154326i
$156$	−0.210204	−	0.0624461i	−0.0168298	−	0.00499969i
$157$	12.4188	+	12.4188i	0.991132	+	0.991132i	0.999961	−	0.00882890i	$-0.00281036\pi$
$157$	12.4188	+	12.4188i	0.991132	+	0.991132i	−0.00882890	+	0.999961i	$0.502810\pi$
$158$	1.37028	−	9.42438i	0.109013	−	0.749764i
$159$	0.123615			0.00980332
$160$	12.0002	+	3.99932i	0.948701	+	0.316174i
$161$	−23.3047			−1.83667
$162$	−1.80936	+	12.4443i	−0.142157	+	0.977714i
$163$	−16.7392	−	16.7392i	−1.31112	−	1.31112i	−0.920594	−	0.390522i	$-0.872295\pi$
$163$	−16.7392	−	16.7392i	−1.31112	−	1.31112i	−0.390522	−	0.920594i	$-0.627705\pi$
$164$	−10.3430	−	3.07263i	−0.807651	−	0.239932i
$165$	−0.727286	−	0.294852i	−0.0566191	−	0.0229542i
$166$	3.78071	−	2.82086i	0.293440	−	0.218941i
$167$	1.96065	−	1.96065i	0.151720	−	0.151720i	−0.627166	−	0.778886i	$-0.715785\pi$
$167$	1.96065	−	1.96065i	0.151720	−	0.151720i	0.778886	+	0.627166i	$0.215785\pi$
$168$	0.533168	−	1.15293i	0.0411348	−	0.0889504i
$169$		−	1.00000i		−	0.0769231i
$170$	−0.840680	−	0.492062i	−0.0644772	−	0.0377394i
$171$		−	14.9969i		−	1.14684i
$172$	−1.83605	−	3.38797i	−0.139998	−	0.258331i
$173$	9.64751	−	9.64751i	0.733486	−	0.733486i	−0.237822	−	0.971309i	$-0.576434\pi$
$173$	9.64751	−	9.64751i	0.733486	−	0.733486i	0.971309	+	0.237822i	$0.0764336\pi$
$174$	−0.917898	−	1.23023i	−0.0695857	−	0.0932634i
$175$	0.308572	+	20.4780i	0.0233258	+	1.54799i
$176$	6.99060	−	10.7274i	0.526936	−	0.808606i
$177$	0.749362	+	0.749362i	0.0563255	+	0.0563255i
$178$	22.9593	+	3.33822i	1.72087	+	0.250210i
$179$	23.7480			1.77501			0.887503	−	0.460801i	$-0.152438\pi$
$179$	23.7480			1.77501			0.887503	+	0.460801i	$0.152438\pi$
$180$	−13.2797	+	1.48635i	−0.989812	+	0.110786i
$181$	7.42358			0.551791			0.275895	−	0.961188i	$-0.411026\pi$
$181$	7.42358			0.551791			0.275895	+	0.961188i	$0.411026\pi$
$182$	5.73243	+	0.833478i	0.424916	+	0.0617815i
$183$	−0.841961	−	0.841961i	−0.0622396	−	0.0622396i
$184$	15.1044	−	5.55195i	1.11351	−	0.409295i
$185$	−0.330743	+	0.815814i	−0.0243167	+	0.0599799i
$186$	−0.204485	−	0.274065i	−0.0149936	−	0.0200954i
$187$	−0.697231	+	0.697231i	−0.0509866	+	0.0509866i
$188$	10.4830	−	5.68109i	0.764553	−	0.414336i
$189$			2.68919i			0.195610i
$190$	15.3550	−	4.01657i	1.11397	−	0.291393i
$191$		−	12.9193i		−	0.934807i	−0.884044	−	0.467404i	$-0.845189\pi$
$191$		−	12.9193i		−	0.934807i	0.884044	−	0.467404i	$-0.154811\pi$
$192$	−0.0708943	+	0.874262i	−0.00511636	+	0.0630945i
$193$	15.4343	−	15.4343i	1.11098	−	1.11098i	0.117964	−	0.993018i	$-0.462363\pi$
$193$	15.4343	−	15.4343i	1.11098	−	1.11098i	0.993018	−	0.117964i	$-0.0376368\pi$
$194$	−18.5063	+	13.8079i	−1.32867	+	0.991348i
$195$	0.0955246	+	0.225790i	0.00684066	+	0.0161692i
$196$	−5.56888	+	18.7457i	−0.397777	+	1.33898i
$197$	3.46048	+	3.46048i	0.246549	+	0.246549i	0.819553	−	0.573004i	$-0.194222\pi$
$197$	3.46048	+	3.46048i	0.246549	+	0.246549i	−0.573004	+	0.819553i	$0.694222\pi$
$198$	−1.94623	+	13.3856i	−0.138313	+	0.951275i
$199$	16.8046			1.19125			0.595624	−	0.803263i	$-0.296905\pi$
$199$	16.8046			1.19125			0.595624	+	0.803263i	$0.296905\pi$
$200$	−5.07852	−	13.1988i	−0.359106	−	0.933297i
$201$	0.571844			0.0403348
$202$	1.62420	−	11.1708i	0.114278	−	0.785972i
$203$	28.6714	+	28.6714i	2.01234	+	2.01234i
$204$	0.0192357	−	0.0647505i	0.00134677	−	0.00453344i
$205$	4.70025	+	11.1099i	0.328280	+	0.775951i
$206$	−7.93403	+	5.91974i	−0.552790	+	0.412448i
$207$	−12.0210	+	12.0210i	−0.835515	+	0.835515i
$208$	−3.91390	+	0.825455i	−0.271380	+	0.0572350i
$209$		−	16.0662i		−	1.11132i
$210$	−1.37395	+	0.359397i	−0.0948113	+	0.0248007i
$211$			15.2868i			1.05239i	0.850365	+	0.526193i	$0.176381\pi$
$211$			15.2868i			1.05239i	−0.850365	+	0.526193i	$0.823619\pi$
$212$	1.98249	−	1.07438i	0.136158	−	0.0737885i
$213$	0.921568	−	0.921568i	0.0631448	−	0.0631448i
$214$	12.5768	+	16.8563i	0.859734	+	1.15227i
$215$	−1.61870	+	3.99270i	−0.110394	+	0.272300i
$216$	−0.640654	−	1.74294i	−0.0435910	−	0.118592i
$217$	6.38728	+	6.38728i	0.433597	+	0.433597i
$218$	−0.966291	−	0.140496i	−0.0654455	−	0.00951558i
$219$	−0.0505933			−0.00341878
$220$	−14.2266	+	1.59233i	−0.959156	+	0.107355i
$221$	0.308037			0.0207208
$222$	−0.0604084	−	0.00878321i	−0.00405435	−	0.000589490i
$223$	−2.51119	−	2.51119i	−0.168162	−	0.168162i	0.618009	−	0.786171i	$-0.287940\pi$
$223$	−2.51119	−	2.51119i	−0.168162	−	0.168162i	−0.786171	+	0.618009i	$0.787940\pi$
$224$	−1.46971	−	23.1242i	−0.0981990	−	1.54505i
$225$	10.7221	+	10.4037i	0.714805	+	0.693582i
$226$	3.62700	+	4.86115i	0.241264	+	0.323359i
$227$	2.16630	−	2.16630i	0.143783	−	0.143783i	−0.631551	−	0.775334i	$-0.717582\pi$
$227$	2.16630	−	2.16630i	0.143783	−	0.143783i	0.775334	+	0.631551i	$0.217582\pi$
$228$	0.524394	+	0.967638i	0.0347288	+	0.0640834i
$229$			18.7200i			1.23705i	0.785764	+	0.618526i	$0.212270\pi$
$229$			18.7200i			1.23705i	−0.785764	+	0.618526i	$0.787730\pi$
$230$	−15.5276	−	9.08853i	−1.02386	−	0.599280i
$231$			1.43757i			0.0945855i
$232$	−25.4132	−	11.7522i	−1.66846	−	0.771571i
$233$	−14.6417	+	14.6417i	−0.959209	+	0.959209i	−0.999200	−	0.0399907i	$-0.987267\pi$
$233$	−14.6417	+	14.6417i	−0.959209	+	0.959209i	0.0399907	+	0.999200i	$0.487267\pi$
$234$	3.38681	−	2.52696i	0.221403	−	0.165193i
$235$	−12.3542	−	5.00856i	−0.805896	−	0.326722i
$236$	18.5309	+	5.50505i	1.20626	+	0.358349i
$237$	−0.522084	−	0.522084i	−0.0339130	−	0.0339130i
$238$	−0.256742	+	1.76580i	−0.0166421	+	0.114460i
$239$	−18.2418			−1.17997			−0.589983	−	0.807416i	$-0.700865\pi$
$239$	−18.2418			−1.17997			−0.589983	+	0.807416i	$0.700865\pi$
$240$	0.804871	−	0.560254i	0.0519542	−	0.0361642i
$241$	−5.90974			−0.380680			−0.190340	−	0.981718i	$-0.560959\pi$
$241$	−5.90974			−0.380680			−0.190340	+	0.981718i	$0.560959\pi$
$242$	0.153312	−	1.05444i	0.00985529	−	0.0677819i
$243$	2.08209	+	2.08209i	0.133566	+	0.133566i
$244$	−20.8208	−	6.18532i	−1.33291	−	0.395975i
$245$	20.1358	−	8.51879i	1.28643	−	0.544245i
$246$	−0.670454	+	0.500239i	−0.0427466	+	0.0318941i
$247$	−3.54902	+	3.54902i	−0.225819	+	0.225819i
$248$	−5.66143	−	2.61811i	−0.359501	−	0.166250i
$249$		−	0.365709i		−	0.0231759i
$250$	−7.78055	+	13.7646i	−0.492085	+	0.870547i
$251$		−	8.09939i		−	0.511229i	−0.966779	−	0.255615i	$-0.917722\pi$
$251$		−	8.09939i		−	0.511229i	0.966779	−	0.255615i	$-0.0822778\pi$
$252$	11.6628	+	21.5208i	0.734688	+	1.35568i
$253$	−12.8781	+	12.8781i	−0.809638	+	0.809638i
$254$	0.964053	+	1.29209i	0.0604901	+	0.0810729i
$255$	−0.0695518	+	0.0294251i	−0.00435551	+	0.00184267i
$256$	6.46150	+	14.6372i	0.403843	+	0.914828i
$257$	1.70618	+	1.70618i	0.106429	+	0.106429i	0.758316	−	0.651887i	$-0.226022\pi$
$257$	1.70618	+	1.70618i	0.106429	+	0.106429i	−0.651887	+	0.758316i	$0.726022\pi$
$258$	−0.295646	−	0.0429861i	−0.0184061	−	0.00267620i
$259$	1.61256			0.100200
$260$	3.49440	+	2.79091i	0.216713	+	0.173085i
$261$	29.5784			1.83086
$262$	−26.9042	−	3.91179i	−1.66215	−	0.241671i
$263$	15.3744	+	15.3744i	0.948026	+	0.948026i	0.998715	−	0.0506886i	$-0.0161416\pi$
$263$	15.3744	+	15.3744i	0.948026	+	0.948026i	−0.0506886	+	0.998715i	$0.516142\pi$
$264$	−0.342478	−	0.931730i	−0.0210780	−	0.0573440i
$265$	−2.33635	−	0.947191i	−0.143521	−	0.0581855i
$266$	−17.3865	−	23.3025i	−1.06603	−	1.42877i
$267$	1.27188	−	1.27188i	0.0778379	−	0.0778379i
$268$	9.17101	−	4.97006i	0.560209	−	0.303595i
$269$			3.62354i			0.220931i	0.993880	+	0.110466i	$0.0352342\pi$
$269$			3.62354i			0.220931i	−0.993880	+	0.110466i	$0.964766\pi$
$270$	−1.04875	+	1.79177i	−0.0638249	+	0.109044i
$271$		−	31.3377i		−	1.90363i	−0.306669	−	0.951816i	$-0.599215\pi$
$271$		−	31.3377i		−	1.90363i	0.306669	−	0.951816i	$-0.400785\pi$
$272$	−0.254271	−	1.20563i	−0.0154174	−	0.0731019i
$273$	0.317560	−	0.317560i	0.0192196	−	0.0192196i
$274$	−5.64931	+	4.21506i	−0.341288	+	0.254641i
$275$	11.4866	+	11.1455i	0.692666	+	0.672101i
$276$	0.355289	−	1.19596i	0.0213859	−	0.0719884i
$277$	−17.8280	−	17.8280i	−1.07118	−	1.07118i	−0.997264	−	0.0739185i	$-0.976450\pi$
$277$	−17.8280	−	17.8280i	−1.07118	−	1.07118i	−0.0739185	−	0.997264i	$-0.523550\pi$
$278$	−1.14303	+	7.86142i	−0.0685542	+	0.471497i
$279$	6.58934			0.394494
$280$	−18.9112	+	17.7052i	−1.13016	+	1.05809i
$281$	−22.1766			−1.32294			−0.661472	−	0.749970i	$-0.730068\pi$
$281$	−22.1766			−1.32294			−0.661472	+	0.749970i	$0.730068\pi$
$282$	0.133007	−	0.914785i	0.00792046	−	0.0544747i
$283$	−1.53553	−	1.53553i	−0.0912776	−	0.0912776i	0.659994	−	0.751271i	$-0.270559\pi$
$283$	−1.53553	−	1.53553i	−0.0912776	−	0.0912776i	−0.751271	+	0.659994i	$0.770559\pi$
$284$	6.77014	−	22.7894i	0.401734	−	1.35230i
$285$	0.462316	−	1.14035i	0.0273852	−	0.0675487i
$286$	3.62829	−	2.70714i	0.214545	−	0.160077i
$287$	15.6254	−	15.6254i	0.922340	−	0.922340i
$288$	−12.6859	−	11.1697i	−0.747527	−	0.658184i
$289$		−	16.9051i		−	0.994418i
$290$	7.92192	+	30.2849i	0.465191	+	1.77839i
$291$			1.79011i			0.104938i
$292$	−0.811396	+	0.439721i	−0.0474833	+	0.0257327i
$293$	−16.3496	+	16.3496i	−0.955155	+	0.955155i	−0.999037	−	0.0438817i	$-0.986028\pi$
$293$	−16.3496	+	16.3496i	−0.955155	+	0.955155i	0.0438817	+	0.999037i	$0.486028\pi$
$294$	0.906638	+	1.21514i	0.0528762	+	0.0708683i
$295$	−8.42116	−	19.9050i	−0.490299	−	1.15891i
$296$	−1.04514	+	0.384166i	−0.0607478	+	0.0223292i
$297$	1.48604	+	1.48604i	0.0862285	+	0.0862285i
$298$	−7.27023	−	1.05707i	−0.421153	−	0.0612344i
$299$	5.68954			0.329035
$300$	−1.05560	−	0.296360i	−0.0609453	−	0.0171103i
$301$	7.89208			0.454892
$302$	−3.74915	−	0.545115i	−0.215739	−	0.0313678i
$303$	−0.618829	−	0.618829i	−0.0355508	−	0.0355508i
$304$	16.8201	+	10.9610i	0.964696	+	0.628654i
$305$	9.46177	+	22.3647i	0.541779	+	1.28060i
$306$	0.778399	+	1.04326i	0.0444981	+	0.0596394i
$307$	−13.1429	+	13.1429i	−0.750106	+	0.750106i	−0.974499	−	0.224393i	$-0.927960\pi$
$307$	−13.1429	+	13.1429i	−0.750106	+	0.750106i	0.224393	+	0.974499i	$0.427960\pi$
$308$	12.4944	+	23.0553i	0.711934	+	1.31370i
$309$			0.767460i			0.0436593i
$310$	1.76481	+	6.74672i	0.100234	+	0.383188i
$311$		−	6.77287i		−	0.384054i	−0.981390	−	0.192027i	$-0.938494\pi$
$311$		−	6.77287i		−	0.384054i	0.981390	−	0.192027i	$-0.0615062\pi$
$312$	−0.130166	+	0.281473i	−0.00736920	+	0.0159353i
$313$	−3.60255	+	3.60255i	−0.203628	+	0.203628i	−0.801553	−	0.597924i	$-0.795992\pi$
$313$	−3.60255	+	3.60255i	−0.203628	+	0.203628i	0.597924	+	0.801553i	$0.295992\pi$
$314$	19.9072	−	14.8531i	1.12343	−	0.838211i
$315$	10.2822	−	25.3621i	0.579334	−	1.42899i
$316$	−12.9106	−	3.83540i	−0.726277	−	0.215758i
$317$	7.62038	+	7.62038i	0.428003	+	0.428003i	0.887948	−	0.459944i	$-0.152131\pi$
$317$	7.62038	+	7.62038i	0.428003	+	0.428003i	−0.459944	+	0.887948i	$0.652131\pi$
$318$	0.0251536	−	0.172999i	0.00141054	−	0.00970132i
$319$	31.6874			1.77415
$320$	8.03888	−	15.9805i	0.449387	−	0.893337i
$321$	1.63051			0.0910064
$322$	−4.74211	+	32.6149i	−0.264267	+	1.81756i
$323$	−1.09323	−	1.09323i	−0.0608289	−	0.0608289i
$324$	17.0476	+	5.06439i	0.947087	+	0.281355i
$325$	−0.0753338	−	4.99943i	−0.00417877	−	0.277319i
$326$	−26.8326	+	20.0203i	−1.48612	+	1.10882i
$327$	−0.0535298	+	0.0535298i	−0.00296020	+	0.00296020i
$328$	−6.40476	+	13.8498i	−0.353644	+	0.764725i
$329$			24.4196i			1.34630i
$330$	−0.560636	+	0.957838i	−0.0308620	+	0.0527272i
$331$			29.2597i			1.60826i	0.594454	+	0.804129i	$0.297368\pi$
$331$			29.2597i			1.60826i	−0.594454	+	0.804129i	$0.702632\pi$
$332$	−3.17848	−	5.86510i	−0.174442	−	0.321889i
$333$	0.831788	−	0.831788i	0.0455817	−	0.0455817i
$334$	−2.34497	−	3.14289i	−0.128311	−	0.171971i
$335$	−10.8080	−	4.38170i	−0.590502	−	0.239398i
$336$	−1.50503	−	0.980769i	−0.0821062	−	0.0535053i
$337$	−4.14129	−	4.14129i	−0.225591	−	0.225591i	0.585257	−	0.810848i	$-0.300994\pi$
$337$	−4.14129	−	4.14129i	−0.225591	−	0.225591i	−0.810848	+	0.585257i	$0.800994\pi$
$338$	−1.39950	−	0.203483i	−0.0761227	−	0.0110680i
$339$	0.470219			0.0255388
$340$	−0.859703	+	1.07640i	−0.0466240	+	0.0583762i
$341$	7.05917			0.382275
$342$	−20.9881	−	3.05161i	−1.13491	−	0.165012i
$343$	−8.04525	−	8.04525i	−0.434403	−	0.434403i
$344$	−5.11507	+	1.88015i	−0.275786	+	0.101371i
$345$	−1.28464	+	0.543491i	−0.0691629	+	0.0292606i
$346$	−11.5386	−	15.4648i	−0.620317	−	0.831391i
$347$	12.3111	−	12.3111i	0.660893	−	0.660893i	−0.294698	−	0.955591i	$-0.595219\pi$
$347$	12.3111	−	12.3111i	0.660893	−	0.660893i	0.955591	+	0.294698i	$0.0952189\pi$
$348$	−1.90848	+	1.03427i	−0.102305	+	0.0554425i
$349$			3.85153i			0.206167i	0.994673	+	0.103084i	$0.0328710\pi$
$349$			3.85153i			0.206167i	−0.994673	+	0.103084i	$0.967129\pi$
$350$	28.7217	+	3.73507i	1.53524	+	0.199648i
$351$		−	0.656531i		−	0.0350430i
$352$	−13.5905	−	11.9662i	−0.724374	−	0.637799i
$353$	13.2758	−	13.2758i	0.706599	−	0.706599i	−0.259219	−	0.965818i	$-0.583465\pi$
$353$	13.2758	−	13.2758i	0.706599	−	0.706599i	0.965818	+	0.259219i	$0.0834653\pi$
$354$	1.20121	−	0.896248i	0.0638437	−	0.0476350i
$355$	−24.4792	+	10.3564i	−1.29922	+	0.549659i
$356$	9.34365	−	31.4522i	0.495213	−	1.66697i
$357$	0.0978204	+	0.0978204i	0.00517720	+	0.00517720i
$358$	4.83230	−	33.2352i	0.255395	−	1.75654i
$359$	−8.57461			−0.452550			−0.226275	−	0.974063i	$-0.572655\pi$
$359$	−8.57461			−0.452550			−0.226275	+	0.974063i	$0.572655\pi$
$360$	−0.622055	+	18.8874i	−0.0327852	+	0.995453i
$361$	6.19104			0.325844
$362$	1.51057	−	10.3893i	0.0793939	−	0.546049i
$363$	−0.0584130	−	0.0584130i	−0.00306589	−	0.00306589i
$364$	2.33290	−	7.85293i	0.122277	−	0.411605i
$365$	0.956222	+	0.387667i	0.0500510	+	0.0202914i
$366$	−1.34965	+	1.00700i	−0.0705472	+	0.0526366i
$367$	4.72502	−	4.72502i	0.246644	−	0.246644i	−0.572948	−	0.819592i	$-0.694200\pi$
$367$	4.72502	−	4.72502i	0.246644	−	0.246644i	0.819592	+	0.572948i	$0.194200\pi$
$368$	−4.69646	−	22.2683i	−0.244820	−	1.16082i
$369$		−	16.1197i		−	0.839160i
$370$	1.07443	+	0.628878i	0.0558570	+	0.0326938i
$371$			4.61810i			0.239760i
$372$	−0.425162	+	0.230409i	−0.0220436	+	0.0119461i
$373$	14.0378	−	14.0378i	0.726850	−	0.726850i	−0.243141	−	0.969991i	$-0.578178\pi$
$373$	14.0378	−	14.0378i	0.726850	−	0.726850i	0.969991	+	0.243141i	$0.0781777\pi$
$374$	0.833899	+	1.11765i	0.0431199	+	0.0577922i
$375$	0.494579	+	1.12163i	0.0255399	+	0.0579206i
$376$	−5.81755	−	15.8270i	−0.300017	−	0.816214i
$377$	−6.99975	−	6.99975i	−0.360506	−	0.360506i
$378$	3.76352	+	0.547204i	0.193574	+	0.0281452i
$379$	4.73069			0.242999			0.121500	−	0.992591i	$-0.461230\pi$
$379$	4.73069			0.242999			0.121500	+	0.992591i	$0.461230\pi$
$380$	−2.49670	−	22.3067i	−0.128078	−	1.14431i
$381$	0.124984			0.00640312
$382$	−18.0805	−	2.62885i	−0.925080	−	0.134504i
$383$	−16.3407	−	16.3407i	−0.834968	−	0.834968i	0.153223	−	0.988192i	$-0.451035\pi$
$383$	−16.3407	−	16.3407i	−0.834968	−	0.834968i	−0.988192	+	0.153223i	$0.951035\pi$
$384$	1.20910	+	0.277114i	0.0617018	+	0.0141414i
$385$	11.0153	−	27.1704i	0.561391	−	1.38473i
$386$	−18.4596	−	24.7408i	−0.939569	−	1.25927i
$387$	4.07087	−	4.07087i	0.206934	−	0.206934i
$388$	15.5584	+	28.7091i	0.789858	+	1.45749i
$389$		−	6.94354i		−	0.352051i	−0.984386	−	0.176026i	$-0.943676\pi$
$389$		−	6.94354i		−	0.352051i	0.984386	−	0.176026i	$-0.0563242\pi$
$390$	0.335431	−	0.0877421i	0.0169852	−	0.00444299i
$391$			1.75259i			0.0886322i
$392$	25.1014	+	11.6081i	1.26781	+	0.586296i
$393$	−1.49042	+	1.49042i	−0.0751816	+	0.0751816i
$394$	5.54708	−	4.13879i	0.279458	−	0.208509i
$395$	5.86707	+	13.8679i	0.295204	+	0.697771i
$396$	18.3371	+	5.44749i	0.921476	+	0.273747i
$397$	15.4365	+	15.4365i	0.774734	+	0.774734i	0.978930	−	0.204196i	$-0.0654581\pi$
$397$	15.4365	+	15.4365i	0.774734	+	0.774734i	−0.204196	+	0.978930i	$0.565458\pi$
$398$	3.41945	−	23.5180i	0.171402	−	1.17885i
$399$	−2.25405			−0.112844
$400$	−19.5051	+	4.42165i	−0.975255	+	0.221083i
$401$	−2.06489			−0.103116			−0.0515578	−	0.998670i	$-0.516419\pi$
$401$	−2.06489			−0.103116			−0.0515578	+	0.998670i	$0.516419\pi$
$402$	0.116360	−	0.800294i	0.00580353	−	0.0399151i
$403$	−1.55937	−	1.55937i	−0.0776778	−	0.0776778i
$404$	−15.3030	−	4.54612i	−0.761351	−	0.226178i
$405$	−7.74707	−	18.3117i	−0.384955	−	0.909914i
$406$	45.9597	−	34.2914i	2.28094	−	1.70186i
$407$	0.891095	−	0.891095i	0.0441700	−	0.0441700i
$408$	−0.0867040	−	0.0400959i	−0.00429249	−	0.00198505i
$409$		−	5.10061i		−	0.252209i	−0.992017	−	0.126104i	$-0.959753\pi$
$409$		−	5.10061i		−	0.252209i	0.992017	−	0.126104i	$-0.0402474\pi$
$410$	16.5047	−	4.31731i	0.815111	−	0.213217i
$411$			0.546459i			0.0269548i
$412$	6.67022	+	12.3082i	0.328618	+	0.606383i
$413$	−27.9952	+	27.9952i	−1.37755	+	1.37755i
$414$	14.3773	+	19.2694i	0.706604	+	0.947039i
$415$	−2.80221	+	6.91197i	−0.137555	+	0.339295i
$416$	0.358810	+	5.64546i	0.0175921	+	0.276792i
$417$	0.435500	+	0.435500i	0.0213266	+	0.0213266i
$418$	−22.4846	−	3.26919i	−1.09976	−	0.159901i
$419$	−14.0619			−0.686969			−0.343484	−	0.939158i	$-0.611607\pi$
$419$	−14.0619			−0.686969			−0.343484	+	0.939158i	$0.611607\pi$
$420$	0.223401	+	1.99597i	0.0109008	+	0.0973931i
$421$	4.35784			0.212388			0.106194	−	0.994345i	$-0.466133\pi$
$421$	4.35784			0.212388			0.106194	+	0.994345i	$0.466133\pi$
$422$	21.3938	+	3.11060i	1.04143	+	0.151422i
$423$	12.5961	+	12.5961i	0.612441	+	0.612441i
$424$	−1.10018	−	2.99311i	−0.0534297	−	0.145358i
$425$	1.54001	−	0.0232056i	0.0747015	−	0.00112564i
$426$	−1.10221	−	1.47726i	−0.0534022	−	0.0715733i
$427$	31.4546	−	31.4546i	1.52219	−	1.52219i
$428$	26.1496	−	14.1713i	1.26399	−	0.684994i
$429$		−	0.350965i		−	0.0169448i
$430$	5.25839	+	3.07781i	0.253582	+	0.148425i
$431$			27.0992i			1.30532i	0.757649	+	0.652662i	$0.226348\pi$
$431$			27.0992i			1.30532i	−0.757649	+	0.652662i	$0.773652\pi$
$432$	−2.56960	+	0.541937i	−0.123630	+	0.0260739i
$433$	−6.46531	+	6.46531i	−0.310703	+	0.310703i	−0.845182	−	0.534479i	$-0.820508\pi$
$433$	−6.46531	+	6.46531i	−0.310703	+	0.310703i	0.534479	+	0.845182i	$0.320508\pi$
$434$	10.2387	−	7.63929i	0.491473	−	0.366697i
$435$	2.24913	+	0.911829i	0.107837	+	0.0437188i
$436$	−0.393247	+	1.32373i	−0.0188331	+	0.0633953i
$437$	−20.1923	−	20.1923i	−0.965927	−	0.965927i
$438$	−0.0102949	+	0.0708052i	−0.000491908	+	0.00338320i
$439$	−25.2613			−1.20566			−0.602829	−	0.797870i	$-0.705960\pi$
$439$	−25.2613			−1.20566			−0.602829	+	0.797870i	$0.705960\pi$
$440$	−0.666408	+	20.2341i	−0.0317698	+	0.964622i
$441$	−29.2156			−1.39122
$442$	0.0626803	−	0.431097i	0.00298140	−	0.0205052i
$443$	−4.83303	−	4.83303i	−0.229624	−	0.229624i	0.582912	−	0.812536i	$-0.301913\pi$
$443$	−4.83303	−	4.83303i	−0.229624	−	0.229624i	−0.812536	+	0.582912i	$0.801913\pi$
$444$	−0.0245842	+	0.0827542i	−0.00116671	+	0.00392734i
$445$	−33.7845	+	14.2931i	−1.60154	+	0.677559i
$446$	−4.02540	+	3.00343i	−0.190608	+	0.142216i
$447$	−0.402750	+	0.402750i	−0.0190494	+	0.0190494i
$448$	−32.6613	−	2.64852i	−1.54310	−	0.125131i
$449$		−	30.4670i		−	1.43783i	−0.695099	−	0.718914i	$-0.744640\pi$
$449$		−	30.4670i		−	1.43783i	0.695099	−	0.718914i	$-0.255360\pi$
$450$	16.7418	−	12.8885i	0.789214	−	0.607571i
$451$		−	17.2691i		−	0.813170i
$452$	7.54120	−	4.08681i	0.354708	−	0.192228i
$453$	−0.207692	+	0.207692i	−0.00975823	+	0.00975823i
$454$	−2.59093	−	3.47254i	−0.121599	−	0.162975i
$455$	−8.43523	+	3.56867i	−0.395450	+	0.167302i
$456$	1.46091	−	0.536990i	0.0684135	−	0.0251469i
$457$	1.84860	+	1.84860i	0.0864737	+	0.0864737i	0.749021	−	0.662547i	$-0.230524\pi$
$457$	1.84860	+	1.84860i	0.0864737	+	0.0864737i	−0.662547	+	0.749021i	$0.730524\pi$
$458$	26.1986	+	3.80920i	1.22418	+	0.177992i
$459$	0.202236			0.00943956
$460$	−15.8790	+	19.8815i	−0.740362	+	0.926981i
$461$	−20.6755			−0.962955			−0.481477	−	0.876458i	$-0.659900\pi$
$461$	−20.6755			−0.962955			−0.481477	+	0.876458i	$0.659900\pi$
$462$	2.01188	+	0.292522i	0.0936013	+	0.0136093i
$463$	15.8454	+	15.8454i	0.736400	+	0.736400i	0.971879	−	0.235479i	$-0.0756660\pi$
$463$	15.8454	+	15.8454i	0.736400	+	0.736400i	−0.235479	+	0.971879i	$0.575666\pi$
$464$	−21.6184	+	33.1743i	−1.00361	+	1.54008i
$465$	0.501050	+	0.203133i	0.0232356	+	0.00942006i
$466$	17.5117	+	23.4704i	0.811213	+	1.08724i
$467$	−21.5873	+	21.5873i	−0.998941	+	0.998941i	−0.999999	−	0.00105852i	$-0.999663\pi$
$467$	−21.5873	+	21.5873i	−0.998941	+	0.998941i	0.00105852	+	0.999999i	$0.499663\pi$
$468$	−2.84732	−	5.25403i	−0.131618	−	0.242868i
$469$			21.3633i			0.986467i
$470$	−9.52332	+	16.2705i	−0.439278	+	0.750500i
$471$		−	1.92562i		−	0.0887281i
$472$	11.4750	−	24.8138i	0.528181	−	1.14215i
$473$	4.36113	−	4.36113i	0.200525	−	0.200525i
$474$	−0.836891	+	0.624421i	−0.0384397	+	0.0286806i
$475$	−17.4757	+	18.0104i	−0.801841	+	0.826375i
$476$	2.41899	+	0.718620i	0.110874	+	0.0329379i
$477$	2.38210	+	2.38210i	0.109069	+	0.109069i
$478$	−3.71190	+	25.5294i	−0.169778	+	1.16769i
$479$	−26.2847			−1.20098			−0.600488	−	0.799634i	$-0.705027\pi$
$479$	−26.2847			−1.20098			−0.600488	+	0.799634i	$0.705027\pi$
$480$	−0.620297	−	1.24042i	−0.0283125	−	0.0566170i
$481$	−0.393686			−0.0179505
$482$	−1.20253	+	8.27067i	−0.0547738	+	0.376719i
$483$	1.80677	+	1.80677i	0.0822110	+	0.0822110i
$484$	−1.44449	−	0.429121i	−0.0656586	−	0.0195055i
$485$	13.7166	−	33.8335i	0.622838	−	1.53630i
$486$	3.33755	−	2.49021i	0.151394	−	0.112958i
$487$	12.3060	−	12.3060i	0.557639	−	0.557639i	−0.370996	−	0.928635i	$-0.620984\pi$
$487$	12.3060	−	12.3060i	0.557639	−	0.557639i	0.928635	+	0.370996i	$0.120984\pi$
$488$	−12.8930	+	27.8800i	−0.583639	+	1.26207i
$489$			2.59552i			0.117374i
$490$	−7.82475	−	29.9134i	−0.353486	−	1.35135i
$491$		−	8.98739i		−	0.405595i	−0.979221	−	0.202798i	$-0.934997\pi$
$491$		−	8.98739i		−	0.405595i	0.979221	−	0.202798i	$-0.0650034\pi$
$492$	0.563657	+	1.04009i	0.0254116	+	0.0468908i
$493$	2.15618	−	2.15618i	0.0971096	−	0.0971096i
$494$	4.24468	+	5.68901i	0.190977	+	0.255960i
$495$	−8.33311	−	19.6969i	−0.374545	−	0.885308i
$496$	−4.81604	+	7.39042i	−0.216246	+	0.331840i
$497$	34.4286	+	34.4286i	1.54433	+	1.54433i
$498$	−0.511809	−	0.0744155i	−0.0229347	−	0.00333464i
$499$	1.43936			0.0644347			0.0322173	−	0.999481i	$-0.489743\pi$
$499$	1.43936			0.0644347			0.0322173	+	0.999481i	$0.489743\pi$
$500$	17.6803	+	13.6897i	0.790685	+	0.612223i
$501$	−0.304012			−0.0135823
$502$	−11.3351	−	1.64809i	−0.505910	−	0.0735578i
$503$	22.4761	+	22.4761i	1.00216	+	1.00216i	0.999998	+	0.00216153i	$0.000688036\pi$
$503$	22.4761	+	22.4761i	1.00216	+	1.00216i	0.00216153	+	0.999998i	$0.499312\pi$
$504$	32.4915	−	11.9430i	1.44729	−	0.531982i
$505$	6.95426	+	16.4377i	0.309460	+	0.731468i
$506$	15.4024	+	20.6433i	0.684719	+	0.917707i
$507$	−0.0775283	+	0.0775283i	−0.00344315	+	0.00344315i
$508$	2.00445	−	1.08627i	0.0889329	−	0.0481955i
$509$		−	25.4007i		−	1.12587i	−0.826502	−	0.562934i	$-0.809673\pi$
$509$		−	25.4007i		−	1.12587i	0.826502	−	0.562934i	$-0.190327\pi$
$510$	0.0270278	+	0.103325i	0.00119681	+	0.00457532i
$511$		−	1.89010i		−	0.0836130i
$512$	21.7996	−	6.06442i	0.963416	−	0.268012i
$513$	−2.33004	+	2.33004i	−0.102874	+	0.102874i
$514$	2.73497	−	2.04062i	0.120635	−	0.0900078i
$515$	5.88060	−	14.5051i	0.259130	−	0.639173i
$516$	−0.120318	+	0.405009i	−0.00529670	+	0.0178295i
$517$	13.4942	+	13.4942i	0.593473	+	0.593473i
$518$	0.328129	−	2.25678i	0.0144172	−	0.0991571i
$519$	−1.49591			−0.0656631
$520$	4.61692	−	4.32250i	0.202465	−	0.189554i
$521$	−9.27032			−0.406140			−0.203070	−	0.979164i	$-0.565092\pi$
$521$	−9.27032			−0.406140			−0.203070	+	0.979164i	$0.565092\pi$
$522$	6.01870	−	41.3950i	0.263432	−	1.81181i
$523$	−16.5690	−	16.5690i	−0.724513	−	0.724513i	0.245008	−	0.969521i	$-0.421209\pi$
$523$	−16.5690	−	16.5690i	−0.724513	−	0.724513i	−0.969521	+	0.245008i	$0.921209\pi$
$524$	−10.9491	+	36.8564i	−0.478313	+	1.61008i
$525$	1.56370	−	1.61155i	0.0682454	−	0.0703336i
$526$	24.6449	−	18.3880i	1.07457	−	0.801755i
$527$	0.480344	−	0.480344i	0.0209241	−	0.0209241i
$528$	−1.37364	+	0.289706i	−0.0597801	+	0.0126078i
$529$			9.37086i			0.407429i
$530$	−1.80100	+	3.07698i	−0.0782304	+	0.133656i
$531$			28.8808i			1.25332i
$532$	−36.1497	+	19.5907i	−1.56729	+	0.849363i
$533$	−3.81475	+	3.81475i	−0.165235	+	0.165235i
$534$	−1.52119	−	2.03880i	−0.0658283	−	0.0882276i
$535$	−30.8170	−	12.4937i	−1.33234	−	0.540148i
$536$	−5.08945	−	13.8461i	−0.219831	−	0.598062i
$537$	−1.84114	−	1.84114i	−0.0794510	−	0.0794510i
$538$	5.07114	+	0.737329i	0.218632	+	0.0317885i
$539$	−31.2987			−1.34813
$540$	2.29418	+	1.83232i	0.0987259	+	0.0788504i
$541$	−12.4118			−0.533626			−0.266813	−	0.963748i	$-0.585971\pi$
$541$	−12.4118			−0.533626			−0.266813	+	0.963748i	$0.585971\pi$
$542$	−43.8571	−	6.37669i	−1.88382	−	0.273902i
$543$	−0.575537	−	0.575537i	−0.0246987	−	0.0246987i
$544$	−1.73901	+	0.110527i	−0.0745595	+	0.00473880i
$545$	1.42189	−	0.601556i	0.0609071	−	0.0257678i
$546$	−0.379807	−	0.509043i	−0.0162542	−	0.0217850i
$547$	−9.71112	+	9.71112i	−0.415217	+	0.415217i	−0.883551	−	0.468334i	$-0.844854\pi$
$547$	−9.71112	+	9.71112i	−0.415217	+	0.415217i	0.468334	+	0.883551i	$0.344854\pi$
$548$	4.74943	+	8.76390i	0.202886	+	0.374375i
$549$		−	32.4496i		−	1.38492i
$550$	17.9355	−	13.8075i	0.764771	−	0.588754i
$551$			49.6845i			2.11663i
$552$	−1.60145	−	0.740585i	−0.0681623	−	0.0315214i
$553$	19.5044	−	19.5044i	0.829410	−	0.829410i
$554$	−28.5780	+	21.3226i	−1.21416	+	0.905910i
$555$	0.0888906	−	0.0376067i	0.00377320	−	0.00159632i
$556$	10.7695	+	3.19933i	0.456727	+	0.135682i
$557$	2.86118	+	2.86118i	0.121232	+	0.121232i	0.765120	−	0.643888i	$-0.222680\pi$
$557$	2.86118	+	2.86118i	0.121232	+	0.121232i	−0.643888	+	0.765120i	$0.722680\pi$
$558$	1.34082	−	9.22177i	0.0567614	−	0.390389i
$559$	−1.92675			−0.0814928
$560$	20.9303	+	30.0689i	0.884468	+	1.27064i
$561$	0.108110			0.00456442
$562$	−4.51256	+	31.0361i	−0.190351	+	1.30918i
$563$	−12.8341	−	12.8341i	−0.540893	−	0.540893i	0.382898	−	0.923791i	$-0.374926\pi$
$563$	−12.8341	−	12.8341i	−0.540893	−	0.540893i	−0.923791	+	0.382898i	$0.874926\pi$
$564$	−1.25318	−	0.372286i	−0.0527682	−	0.0156761i
$565$	−8.88723	−	3.60301i	−0.373889	−	0.151580i
$566$	−2.46142	+	1.83651i	−0.103461	+	0.0771945i
$567$	−25.7542	+	25.7542i	−1.08158	+	1.08158i
$568$	−30.5161	−	14.1120i	−1.28043	−	0.592128i
$569$		−	12.1495i		−	0.509334i	−0.967029	−	0.254667i	$-0.918034\pi$
$569$		−	12.1495i		−	0.509334i	0.967029	−	0.254667i	$-0.0819658\pi$
$570$	−1.50185	−	0.879052i	−0.0629055	−	0.0368194i
$571$			19.5871i			0.819695i	0.912154	+	0.409848i	$0.134418\pi$
$571$			19.5871i			0.819695i	−0.912154	+	0.409848i	$0.865582\pi$
$572$	−3.05034	−	5.62865i	−0.127541	−	0.235345i
$573$	−1.00161	+	1.00161i	−0.0418429	+	0.0418429i
$574$	−18.6883	−	25.0473i	−0.780033	−	1.04545i
$575$	28.4445	−	0.428615i	1.18622	−	0.0178745i
$576$	−18.2134	+	15.4811i	−0.758892	+	0.645046i
$577$	−3.41237	−	3.41237i	−0.142059	−	0.142059i	0.632501	−	0.774560i	$-0.282028\pi$
$577$	−3.41237	−	3.41237i	−0.142059	−	0.142059i	−0.774560	+	0.632501i	$0.782028\pi$
$578$	−23.6587	−	3.43990i	−0.984071	−	0.143081i
$579$	−2.39318			−0.0994572
$580$	43.9956	−	4.92426i	1.82682	−	0.204469i
$581$	13.6624			0.566812
$582$	2.50526	+	0.364257i	0.103846	+	0.0150989i
$583$	2.55194	+	2.55194i	0.105691	+	0.105691i
$584$	0.450284	+	1.22502i	0.0186329	+	0.0506918i
$585$	−2.51026	+	6.19183i	−0.103786	+	0.256000i
$586$	19.5544	+	26.2081i	0.807785	+	1.08265i
$587$	15.6384	−	15.6384i	0.645467	−	0.645467i	−0.306427	−	0.951894i	$-0.599133\pi$
$587$	15.6384	−	15.6384i	0.645467	−	0.645467i	0.951894	+	0.306427i	$0.0991335\pi$
$588$	1.88507	−	1.02158i	0.0777390	−	0.0421292i
$589$			11.0685i			0.456068i
$590$	−29.5706	+	7.73507i	−1.21740	+	0.318448i
$591$		−	0.536570i		−	0.0220715i
$592$	0.324970	+	1.54085i	0.0133562	+	0.0633285i
$593$	10.9939	−	10.9939i	0.451467	−	0.451467i	−0.444374	−	0.895841i	$-0.646574\pi$
$593$	10.9939	−	10.9939i	0.451467	−	0.451467i	0.895841	+	0.444374i	$0.146574\pi$
$594$	2.38209	−	1.77732i	0.0977382	−	0.0729244i
$595$	−1.09928	−	2.59836i	−0.0450662	−	0.106523i
$596$	−2.95873	+	9.95957i	−0.121194	+	0.407960i
$597$	−1.30283	−	1.30283i	−0.0533214	−	0.0533214i
$598$	1.15772	−	7.96250i	0.0473428	−	0.325611i
$599$	24.3473			0.994804			0.497402	−	0.867520i	$-0.334287\pi$
$599$	24.3473			0.994804			0.497402	+	0.867520i	$0.334287\pi$
$600$	−0.629552	+	1.41701i	−0.0257013	+	0.0578492i
$601$	−25.3047			−1.03220			−0.516099	−	0.856529i	$-0.672617\pi$
$601$	−25.3047			−1.03220			−0.516099	+	0.856529i	$0.672617\pi$
$602$	1.60590	−	11.0450i	0.0654517	−	0.450159i
$603$	11.0196	+	11.0196i	0.448752	+	0.448752i
$604$	−1.52577	+	5.13600i	−0.0620829	+	0.208981i
$605$	0.656432	+	1.55160i	0.0266878	+	0.0630816i
$606$	−0.991971	+	0.740129i	−0.0402961	+	0.0300657i
$607$	−30.7450	+	30.7450i	−1.24790	+	1.24790i	−0.291255	+	0.956646i	$0.594073\pi$
$607$	−30.7450	+	30.7450i	−1.24790	+	1.24790i	−0.956646	+	0.291255i	$0.905927\pi$
$608$	18.7624	−	21.3093i	0.760917	−	0.864205i
$609$		−	4.44569i		−	0.180148i
$610$	33.2246	−	8.69090i	1.34523	−	0.351884i
$611$		−	5.96172i		−	0.241186i
$612$	1.61844	−	0.877081i	0.0654214	−	0.0354539i
$613$	−20.1332	+	20.1332i	−0.813171	+	0.813171i	−0.985108	−	0.171937i	$-0.944997\pi$
$613$	−20.1332	+	20.1332i	−0.813171	+	0.813171i	0.171937	+	0.985108i	$0.444997\pi$
$614$	15.7191	+	21.0678i	0.634372	+	0.850229i
$615$	0.496931	−	1.22574i	0.0200382	−	0.0494264i
$616$	34.8082	−	12.7945i	1.40246	−	0.515506i
$617$	12.0443	+	12.0443i	0.484885	+	0.484885i	0.906688	−	0.421803i	$-0.138603\pi$
$617$	12.0443	+	12.0443i	0.484885	+	0.484885i	−0.421803	+	0.906688i	$0.638603\pi$
$618$	1.07406	+	0.156165i	0.0432050	+	0.00628188i
$619$	−7.68371			−0.308834			−0.154417	−	0.988006i	$-0.549350\pi$
$619$	−7.68371			−0.308834			−0.154417	+	0.988006i	$0.549350\pi$
$620$	9.80113	−	1.09700i	0.393623	−	0.0440567i
$621$	3.73536			0.149895
$622$	−9.47862	−	1.37816i	−0.380058	−	0.0552593i
$623$	47.5158	+	47.5158i	1.90368	+	1.90368i
$624$	0.367434	+	0.239442i	0.0147091	+	0.00958535i
$625$	−0.753252	−	24.9886i	−0.0301301	−	0.999546i
$626$	4.30870	+	5.77482i	0.172210	+	0.230808i
$627$	−1.24558	+	1.24558i	−0.0497437	+	0.0497437i
$628$	−16.7362	−	30.8824i	−0.667845	−	1.23234i
$629$		−	0.121270i		−	0.00483535i
$630$	−33.4020	−	19.5506i	−1.33077	−	0.778915i
$631$			26.5327i			1.05625i	0.849166	+	0.528126i	$0.177105\pi$
$631$			26.5327i			1.05625i	−0.849166	+	0.528126i	$0.822895\pi$
$632$	−7.99472	+	17.2879i	−0.318013	+	0.687675i
$633$	1.18516	−	1.18516i	0.0471058	−	0.0471058i
$634$	12.2153	−	9.11409i	0.485133	−	0.361967i
$635$	−2.36222	−	0.957679i	−0.0937419	−	0.0380043i
$636$	−0.236994	−	0.0704048i	−0.00939742	−	0.00279173i
$637$	6.91389	+	6.91389i	0.273938	+	0.273938i
$638$	6.44784	−	44.3465i	0.255273	−	1.75569i
$639$	35.5177			1.40506
$640$	−20.7289	−	14.5021i	−0.819382	−	0.573248i
$641$	1.48587			0.0586882			0.0293441	−	0.999569i	$-0.490658\pi$
$641$	1.48587			0.0586882			0.0293441	+	0.999569i	$0.490658\pi$
$642$	0.331782	−	2.28190i	0.0130944	−	0.0900594i
$643$	−15.8763	−	15.8763i	−0.626098	−	0.626098i	0.320986	−	0.947084i	$-0.395986\pi$
$643$	−15.8763	−	15.8763i	−0.626098	−	0.626098i	−0.947084	+	0.320986i	$0.895986\pi$
$644$	44.6795	+	13.2731i	1.76062	+	0.523035i
$645$	0.435042	−	0.184052i	0.0171297	−	0.00724704i
$646$	−1.75242	+	1.30752i	−0.0689482	+	0.0514436i
$647$	16.6915	−	16.6915i	0.656209	−	0.656209i	−0.298272	−	0.954481i	$-0.596410\pi$
$647$	16.6915	−	16.6915i	0.656209	−	0.656209i	0.954481	+	0.298272i	$0.0964103\pi$
$648$	10.5565	−	22.8275i	0.414698	−	0.896749i
$649$			30.9400i			1.21450i
$650$	−7.01202	−	0.911869i	−0.275034	−	0.0357665i
$651$		−	0.990390i		−	0.0388164i
$652$	22.5584	+	41.6260i	0.883457	+	1.63020i
$653$	−7.63408	+	7.63408i	−0.298745	+	0.298745i	−0.840522	−	0.541777i	$-0.817752\pi$
$653$	−7.63408	+	7.63408i	−0.298745	+	0.298745i	0.541777	+	0.840522i	$0.317752\pi$
$654$	0.0640224	+	0.0858072i	0.00250348	+	0.00335533i
$655$	39.5894	−	16.7490i	1.54688	−	0.654437i
$656$	18.0794	+	11.7816i	0.705884	+	0.459996i
$657$	−0.974945	−	0.974945i	−0.0380362	−	0.0380362i
$658$	34.1752	+	4.96897i	1.33229	+	0.193711i
$659$	−17.4766			−0.680792			−0.340396	−	0.940282i	$-0.610561\pi$
$659$	−17.4766			−0.680792			−0.340396	+	0.940282i	$0.610561\pi$
$660$	1.22641	+	0.979512i	0.0477380	+	0.0381274i
$661$	−6.43375			−0.250244			−0.125122	−	0.992141i	$-0.539932\pi$
$661$	−6.43375			−0.250244			−0.125122	+	0.992141i	$0.539932\pi$
$662$	40.9489	+	5.95385i	1.59152	+	0.231403i
$663$	−0.0238816	−	0.0238816i	−0.000927484	−	0.000927484i
$664$	−8.85496	+	3.25483i	−0.343639	+	0.126312i
$665$	42.6021	+	17.2715i	1.65204	+	0.669760i
$666$	−0.994831	−	1.33334i	−0.0385489	−	0.0516659i
$667$	39.8254	−	39.8254i	1.54204	−	1.54204i
$668$	−4.87563	+	2.64226i	−0.188644	+	0.102232i
$669$			0.389377i			0.0150542i
$670$	−8.33142	+	14.2341i	−0.321871	+	0.549912i
$671$		−	34.7633i		−	1.34202i
$672$	−1.67883	+	1.90672i	−0.0647624	+	0.0735533i
$673$	31.2053	−	31.2053i	1.20288	−	1.20288i	0.229589	−	0.973288i	$-0.426262\pi$
$673$	31.2053	−	31.2053i	1.20288	−	1.20288i	0.973288	−	0.229589i	$-0.0737381\pi$
$674$	−6.63841	+	4.95305i	−0.255702	+	0.190784i
$675$	−0.0494590	−	3.28228i	−0.00190368	−	0.126335i
$676$	−0.569548	+	1.91719i	−0.0219057	+	0.0737381i
$677$	−21.5552	−	21.5552i	−0.828434	−	0.828434i	0.158866	−	0.987300i	$-0.449216\pi$
$677$	−21.5552	−	21.5552i	−0.828434	−	0.828434i	−0.987300	+	0.158866i	$0.949216\pi$
$678$	0.0956815	−	0.658071i	0.00367463	−	0.0252731i
$679$	−66.8762			−2.56647
$680$	1.33149	+	1.42218i	0.0510604	+	0.0545382i
$681$	−0.335900			−0.0128717
$682$	1.43642	−	9.87929i	0.0550034	−	0.378298i
$683$	−7.68769	−	7.68769i	−0.294161	−	0.294161i	0.544560	−	0.838722i	$-0.316697\pi$
$683$	−7.68769	−	7.68769i	−0.294161	−	0.294161i	−0.838722	+	0.544560i	$0.816697\pi$
$684$	−8.54143	+	28.7518i	−0.326590	+	1.09935i
$685$	4.18719	−	10.3282i	0.159984	−	0.394619i
$686$	−12.8964	+	9.62224i	−0.492386	+	0.367379i
$687$	1.45133	−	1.45133i	0.0553716	−	0.0553716i
$688$	1.59044	+	7.54110i	0.0606351	+	0.287502i
$689$		−	1.12745i		−	0.0429524i
$690$	0.499212	+	1.90845i	0.0190047	+	0.0726534i
$691$			29.0242i			1.10413i	0.833800	+	0.552067i	$0.186161\pi$
$691$			29.0242i			1.10413i	−0.833800	+	0.552067i	$0.813839\pi$
$692$	−23.9908	+	13.0014i	−0.911994	+	0.494238i
$693$	−27.7024	+	27.7024i	−1.05233	+	1.05233i
$694$	−14.7242	−	19.7344i	−0.558924	−	0.749108i
$695$	−4.89406	−	11.5680i	−0.185642	−	0.438800i
$696$	1.05911	+	2.88137i	0.0401455	+	0.109218i
$697$	−1.17508	−	1.17508i	−0.0445095	−	0.0445095i
$698$	5.39020	+	0.783720i	0.204022	+	0.0296642i
$699$	2.27029			0.0858703
$700$	11.0716	−	39.4359i	0.418467	−	1.49054i
$701$	28.0124			1.05801			0.529007	−	0.848617i	$-0.322565\pi$
$701$	28.0124			1.05801			0.529007	+	0.848617i	$0.322565\pi$
$702$	−0.918814	−	0.133593i	−0.0346784	−	0.00504214i
$703$	1.39720	+	1.39720i	0.0526964	+	0.0526964i
$704$	−19.5120	+	16.5849i	−0.735388	+	0.625068i
$705$	0.569492	+	1.34610i	0.0214483	+	0.0506971i
$706$	−15.8780	−	21.2808i	−0.597578	−	0.800915i
$707$	23.1186	−	23.1186i	0.869465	−	0.869465i
$708$	−1.00987	−	1.86347i	−0.0379533	−	0.0700333i
$709$			13.6438i			0.512402i	0.966624	+	0.256201i	$0.0824709\pi$
$709$			13.6438i			0.512402i	−0.966624	+	0.256201i	$0.917529\pi$
$710$	9.51262	+	36.3660i	0.357002	+	1.36479i
$711$		−	20.1214i		−	0.754611i
$712$	−42.1161	−	19.4764i	−1.57837	−	0.729910i
$713$	8.87211	−	8.87211i	0.332263	−	0.332263i
$714$	0.156804	−	0.116995i	0.00586825	−	0.00437842i
$715$	−2.68924	+	6.63331i	−0.100572	+	0.248072i
$716$	−45.5294	−	13.5256i	−1.70151	−	0.505475i
$717$	1.41426	+	1.41426i	0.0528164	+	0.0528164i
$718$	−1.74479	+	12.0001i	−0.0651148	+	0.447841i
$719$	−19.0497			−0.710433			−0.355217	−	0.934784i	$-0.615593\pi$
$719$	−19.0497			−0.710433			−0.355217	+	0.934784i	$0.615593\pi$
$720$	26.3063	+	4.71383i	0.980378	+	0.175674i
$721$	−28.6713			−1.06777
$722$	1.25977	−	8.66435i	0.0468838	−	0.322454i
$723$	0.458172	+	0.458172i	0.0170396	+	0.0170396i
$724$	−14.2324	−	4.22808i	−0.528944	−	0.157136i
$725$	−35.5221	−	34.4675i	−1.31926	−	1.28009i
$726$	−0.0936349	+	0.0698628i	−0.00347512	+	0.00259285i
$727$	28.3966	−	28.3966i	1.05317	−	1.05317i	0.0546675	−	0.998505i	$-0.482590\pi$
$727$	28.3966	−	28.3966i	1.05317	−	1.05317i	0.998505	−	0.0546675i	$-0.0174099\pi$
$728$	−10.5154	−	4.86283i	−0.389728	−	0.180228i
$729$			26.3530i			0.976038i
$730$	0.737113	−	1.25935i	0.0272818	−	0.0466106i
$731$		−	0.593510i		−	0.0219518i
$732$	1.13466	+	2.09374i	0.0419383	+	0.0773867i
$733$	−6.90352	+	6.90352i	−0.254987	+	0.254987i	−0.823012	−	0.568024i	$-0.807708\pi$
$733$	−6.90352	+	6.90352i	−0.254987	+	0.254987i	0.568024	+	0.823012i	$0.307708\pi$
$734$	−5.65120	−	7.57412i	−0.208590	−	0.279566i
$735$	−2.22154	−	0.900644i	−0.0819426	−	0.0332207i
$736$	−32.1201	+	2.04146i	−1.18396	+	0.0752494i
$737$	11.8053	+	11.8053i	0.434853	+	0.434853i
$738$	−22.5596	−	3.28009i	−0.830429	−	0.120742i
$739$	30.9143			1.13720			0.568601	−	0.822614i	$-0.307485\pi$
$739$	30.9143			1.13720			0.568601	+	0.822614i	$0.307485\pi$
$740$	1.09874	−	1.37570i	0.0403906	−	0.0505716i
$741$	0.550298			0.0202157
$742$	6.46302	+	0.939704i	0.237265	+	0.0344976i
$743$	−31.0812	−	31.0812i	−1.14026	−	1.14026i	−0.988402	−	0.151858i	$-0.951475\pi$
$743$	−31.0812	−	31.0812i	−1.14026	−	1.14026i	−0.151858	−	0.988402i	$-0.548525\pi$
$744$	0.235943	+	0.641898i	0.00865011	+	0.0235331i
$745$	10.6981	−	4.52602i	0.391948	−	0.165820i
$746$	−16.7894	−	22.5023i	−0.614705	−	0.823869i
$747$	7.04730	−	7.04730i	0.257847	−	0.257847i
$748$	1.73383	−	0.939618i	0.0633952	−	0.0343558i
$749$			60.9138i			2.22574i
$750$	1.67035	−	0.463930i	0.0609927	−	0.0169403i
$751$		−	1.26768i		−	0.0462582i	−0.999732	−	0.0231291i	$-0.992637\pi$
$751$		−	1.26768i		−	0.0462582i	0.999732	−	0.0231291i	$-0.00736287\pi$
$752$	−23.3336	+	4.92113i	−0.850889	+	0.179455i
$753$	−0.627932	+	0.627932i	−0.0228831	+	0.0228831i
$754$	−11.2205	+	8.37181i	−0.408625	+	0.304883i
$755$	5.51685	−	2.33400i	0.200779	−	0.0849429i
$756$	1.53162	−	5.15569i	0.0557046	−	0.187511i
$757$	−6.66924	−	6.66924i	−0.242398	−	0.242398i	0.575444	−	0.817841i	$-0.304829\pi$
$757$	−6.66924	−	6.66924i	−0.242398	−	0.242398i	−0.817841	+	0.575444i	$0.804829\pi$
$758$	0.962613	−	6.62059i	0.0349637	−	0.240470i
$759$	1.99683			0.0724804
$760$	−31.7262	−	1.04490i	−1.15083	−	0.0379025i
$761$	17.3878			0.630309			0.315155	−	0.949040i	$-0.397944\pi$
$761$	17.3878			0.630309			0.315155	+	0.949040i	$0.397944\pi$
$762$	0.0254321	−	0.174915i	0.000921308	−	0.00633649i
$763$	−1.99980	−	1.99980i	−0.0723977	−	0.0723977i
$764$	−7.35815	+	24.7687i	−0.266209	+	0.896101i
$765$	−1.90731	−	0.773252i	−0.0689590	−	0.0279570i
$766$	−26.1938	+	19.5437i	−0.946419	+	0.706141i
$767$	6.83465	−	6.83465i	0.246785	−	0.246785i
$768$	0.633852	−	1.63575i	0.0228722	−	0.0590250i
$769$			7.24605i			0.261299i	0.991429	+	0.130650i	$0.0417063\pi$
$769$			7.24605i			0.261299i	−0.991429	+	0.130650i	$0.958294\pi$
$770$	−35.7835	−	20.9446i	−1.28955	−	0.754791i
$771$		−	0.264554i		−	0.00952769i
$772$

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)

\(f(q)\)	\(=\)	\(q+(0.203483 - 1.39950i) q^{2} +(-0.0775283 - 0.0775283i) q^{3} +(-1.91719 - 0.569548i) q^{4} +(0.871245 + 2.05935i) q^{5} +(-0.124276 + 0.0927250i) q^{6} +(2.89635 - 2.89635i) q^{7} +(-1.18720 + 2.56721i) q^{8} -2.98798i q^{9} +O(q^{10})\)	\(q+(0.203483 - 1.39950i) q^{2} +(-0.0775283 - 0.0775283i) q^{3} +(-1.91719 - 0.569548i) q^{4} +(0.871245 + 2.05935i) q^{5} +(-0.124276 + 0.0927250i) q^{6} +(2.89635 - 2.89635i) q^{7} +(-1.18720 + 2.56721i) q^{8} -2.98798i q^{9} +(3.05934 - 0.800263i) q^{10} -3.20102i q^{11} +(0.104480 + 0.192792i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(-3.46408 - 4.64280i) q^{14} +(0.0921119 - 0.227204i) q^{15} +(3.35123 + 2.18386i) q^{16} +(-0.217815 - 0.217815i) q^{17} +(-4.18167 - 0.608002i) q^{18} +5.01907 q^{19} +(-0.497443 - 4.44438i) q^{20} -0.449098 q^{21} +(-4.47983 - 0.651354i) q^{22} +(-4.02311 - 4.02311i) q^{23} +(0.291073 - 0.106990i) q^{24} +(-3.48186 + 3.58840i) q^{25} +(0.845710 + 1.13348i) q^{26} +(-0.464238 + 0.464238i) q^{27} +(-7.20247 + 3.90325i) q^{28} +9.89914i q^{29} +(-0.299229 - 0.175143i) q^{30} +2.20528i q^{31} +(3.73823 - 4.24566i) q^{32} +(-0.248170 + 0.248170i) q^{33} +(-0.349153 + 0.260510i) q^{34} +(8.48804 + 3.44118i) q^{35} +(-1.70180 + 5.72852i) q^{36} +(0.278378 + 0.278378i) q^{37} +(1.02129 - 7.02418i) q^{38} +0.109642 q^{39} +(-6.32113 - 0.208186i) q^{40} +5.39487 q^{41} +(-0.0913838 + 0.628512i) q^{42} +(1.36242 + 1.36242i) q^{43} +(-1.82314 + 6.13697i) q^{44} +(6.15330 - 2.60326i) q^{45} +(-6.44897 + 4.81170i) q^{46} +(-4.21558 + 4.21558i) q^{47} +(-0.0905041 - 0.429126i) q^{48} -9.77772i q^{49} +(4.31346 + 5.60304i) q^{50} +0.0337736i q^{51} +(1.75839 - 0.952927i) q^{52} +(-0.797227 + 0.797227i) q^{53} +(0.555235 + 0.744164i) q^{54} +(6.59204 - 2.78888i) q^{55} +(3.99701 + 10.8741i) q^{56} +(-0.389120 - 0.389120i) q^{57} +(13.8538 + 2.01431i) q^{58} -9.66566 q^{59} +(-0.305999 + 0.383131i) q^{60} +10.8601 q^{61} +(3.08629 + 0.448738i) q^{62} +(-8.65424 - 8.65424i) q^{63} +(-5.18113 - 6.09556i) q^{64} +(-2.07225 - 0.840119i) q^{65} +(0.296815 + 0.397812i) q^{66} +(-3.68797 + 3.68797i) q^{67} +(0.293537 + 0.541649i) q^{68} +0.623810i q^{69} +(6.54309 - 11.1788i) q^{70} +11.8869i q^{71} +(7.67077 + 3.54732i) q^{72} +(0.326289 - 0.326289i) q^{73} +(0.446235 - 0.332945i) q^{74} +(0.548145 - 0.00825971i) q^{75} +(-9.62250 - 2.85860i) q^{76} +(-9.27130 - 9.27130i) q^{77} +(0.0223102 - 0.153443i) q^{78} +6.73412 q^{79} +(-1.57760 + 8.80404i) q^{80} -8.89195 q^{81} +(1.09776 - 7.55010i) q^{82} +(2.35855 + 2.35855i) q^{83} +(0.861007 + 0.255783i) q^{84} +(0.258788 - 0.638328i) q^{85} +(2.18393 - 1.62947i) q^{86} +(0.767463 - 0.767463i) q^{87} +(8.21770 + 3.80024i) q^{88} +16.4054i q^{89} +(-2.39117 - 9.14125i) q^{90} +4.09606i q^{91} +(5.42171 + 10.0044i) q^{92} +(0.170972 - 0.170972i) q^{93} +(5.04189 + 6.75749i) q^{94} +(4.37284 + 10.3360i) q^{95} +(-0.618977 + 0.0393405i) q^{96} +(-11.5449 - 11.5449i) q^{97} +(-13.6839 - 1.98960i) q^{98} -9.56459 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

Properties

Related objects

Downloads

Learn more