LMFDB - Embedded newform 260.2.o.a.27.3

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			27.3
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39950 + 0.203483i) q^{2} +(0.0775283 + 0.0775283i) q^{3} +(1.91719 - 0.569548i) q^{4} +(0.871245 + 2.05935i) q^{5} +(-0.124276 - 0.0927250i) q^{6} +(-2.89635 + 2.89635i) q^{7} +(-2.56721 + 1.18720i) q^{8} -2.98798i q^{9} +O(q^{10})$	\(q+(-1.39950 + 0.203483i) 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} +(-2.56721 + 1.18720i) q^{8} -2.98798i q^{9} +(-1.63835 - 2.70478i) q^{10} +3.20102i q^{11} +(0.192792 + 0.104480i) 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} +(0.608002 + 4.18167i) q^{18} -5.01907 q^{19} +(2.84324 + 3.45195i) q^{20} -0.449098 q^{21} +(-0.651354 - 4.47983i) 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} +(-3.90325 + 7.20247i) q^{28} +9.89914i q^{29} +(0.0826782 - 0.336715i) q^{30} -2.20528i q^{31} +(-4.24566 + 3.73823i) 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} +(7.02418 - 1.02129i) q^{38} -0.109642 q^{39} +(-4.68152 - 4.25245i) q^{40} +5.39487 q^{41} +(0.628512 - 0.0913838i) 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} +(0.429126 + 0.0905041i) q^{48} -9.77772i q^{49} +(4.14268 - 5.73046i) q^{50} -0.0337736i q^{51} +(-0.952927 + 1.75839i) 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} +(-2.01431 - 13.8538i) q^{58} +9.66566 q^{59} +(-0.0471923 + 0.488055i) q^{60} +10.8601 q^{61} +(0.448738 + 3.08629i) 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} +(-0.541649 - 0.293537i) q^{68} +0.623810i q^{69} +(12.5792 + 3.08875i) q^{70} -11.8869i q^{71} +(3.54732 + 7.67077i) 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} +(0.153443 - 0.0223102i) q^{78} -6.73412 q^{79} +(7.41708 + 4.99869i) q^{80} -8.89195 q^{81} +(-7.55010 + 1.09776i) 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} +(-3.80024 - 8.21770i) q^{88} +16.4054i q^{89} +(-8.08181 + 4.89535i) q^{90} -4.09606i q^{91} +(10.0044 + 5.42171i) 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} +(1.98960 + 13.6839i) 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 $

$2$	−1.39950	+	0.203483i	−0.989595	+	0.143884i
$2$	−1.39950	+	0.203483i	−0.989595	+	0.143884i
$3$	0.0775283	+	0.0775283i	0.0447610	+	0.0447610i	0.729133	−	0.684372i	$-0.239924\pi$
$3$	0.0775283	+	0.0775283i	0.0447610	+	0.0447610i	−0.684372	+	0.729133i	$0.739924\pi$
$4$	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	$0.531789\pi$
$7$	−2.89635	+	2.89635i	−1.09472	+	1.09472i	−0.995017	+	0.0997009i	$0.968211\pi$
$8$	−2.56721	+	1.18720i	−0.907646	+	0.419737i
$9$		−	2.98798i		−	0.995993i
$10$	−1.63835	−	2.70478i	−0.518091	−	0.855325i
$11$			3.20102i			0.965145i	0.875856	+	0.482573i	$0.160298\pi$
$11$			3.20102i			0.965145i	−0.875856	+	0.482573i	$0.839702\pi$
$12$	0.192792	+	0.104480i	0.0556544	+	0.0301609i
$13$	−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	$0.761893\pi$
$18$	0.608002	+	4.18167i	0.143308	+	0.985629i
$19$	−5.01907			−1.15145			−0.575727	−	0.817642i	$-0.695281\pi$
$19$	−5.01907			−1.15145			−0.575727	+	0.817642i	$0.695281\pi$
$20$	2.84324	+	3.45195i	0.635768	+	0.771880i
$21$	−0.449098			−0.0980013
$22$	−0.651354	−	4.47983i	−0.138869	−	0.955102i
$23$	4.02311	+	4.02311i	0.838877	+	0.838877i	0.988711	−	0.149834i	$-0.0478740\pi$
$23$	4.02311	+	4.02311i	0.838877	+	0.838877i	−0.149834	+	0.988711i	$0.547874\pi$
$24$	−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
$28$	−3.90325	+	7.20247i	−0.737644	+	1.36114i
$29$			9.89914i			1.83822i	0.393995	+	0.919112i	$0.371093\pi$
$29$			9.89914i			1.83822i	−0.393995	+	0.919112i	$0.628907\pi$
$30$	0.0826782	−	0.336715i	0.0150949	−	0.0614754i
$31$		−	2.20528i		−	0.396081i	−0.980194	−	0.198040i	$-0.936542\pi$
$31$		−	2.20528i		−	0.396081i	0.980194	−	0.198040i	$-0.0634577\pi$
$32$	−4.24566	+	3.73823i	−0.750534	+	0.660832i
$33$	−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	$0.739697\pi$
$38$	7.02418	−	1.02129i	1.13947	−	0.165676i
$39$	−0.109642			−0.0175567
$40$	−4.68152	−	4.25245i	−0.740214	−	0.672371i
$41$	5.39487			0.842537			0.421268	−	0.906936i	$-0.361585\pi$
$41$	5.39487			0.842537			0.421268	+	0.906936i	$0.361585\pi$
$42$	0.628512	−	0.0913838i	0.0969815	−	0.0141008i
$43$	−1.36242	−	1.36242i	−0.207767	−	0.207767i	0.595551	−	0.803318i	$-0.296934\pi$
$43$	−1.36242	−	1.36242i	−0.207767	−	0.207767i	−0.803318	+	0.595551i	$0.796934\pi$
$44$	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	−0.329315	−	0.944220i	$-0.606818\pi$
$47$	4.21558	−	4.21558i	0.614905	−	0.614905i	0.944220	+	0.329315i	$0.106818\pi$
$48$	0.429126	+	0.0905041i	0.0619390	+	0.0130631i
$49$		−	9.77772i		−	1.39682i
$50$	4.14268	−	5.73046i	0.585864	−	0.810410i
$51$		−	0.0337736i		−	0.00472926i
$52$	−0.952927	+	1.75839i	−0.132147	+	0.243845i
$53$	−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
$58$	−2.01431	−	13.8538i	−0.264491	−	1.81910i
$59$	9.66566			1.25836			0.629181	−	0.777259i	$-0.283390\pi$
$59$	9.66566			1.25836			0.629181	+	0.777259i	$0.283390\pi$
$60$	−0.0471923	+	0.488055i	−0.00609250	+	0.0630077i
$61$	10.8601			1.39049			0.695244	−	0.718774i	$-0.255296\pi$
$61$	10.8601			1.39049			0.695244	+	0.718774i	$0.255296\pi$
$62$	0.448738	+	3.08629i	0.0569897	+	0.391959i
$63$	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	−0.444982	−	0.895539i	$-0.646790\pi$
$67$	3.68797	−	3.68797i	0.450557	−	0.450557i	0.895539	+	0.444982i	$0.146790\pi$
$68$	−0.541649	−	0.293537i	−0.0656846	−	0.0355966i
$69$			0.623810i			0.0750979i
$70$	12.5792	+	3.08875i	1.50350	+	0.369176i
$71$		−	11.8869i		−	1.41071i	−0.708854	−	0.705356i	$-0.750787\pi$
$71$		−	11.8869i		−	1.41071i	0.708854	−	0.705356i	$-0.249213\pi$
$72$	3.54732	+	7.67077i	0.418055	+	0.904009i
$73$	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
$78$	0.153443	−	0.0223102i	0.0173740	−	0.00252613i
$79$	−6.73412			−0.757647			−0.378824	−	0.925469i	$-0.623671\pi$
$79$	−6.73412			−0.757647			−0.378824	+	0.925469i	$0.623671\pi$
$80$	7.41708	+	4.99869i	0.829255	+	0.558870i
$81$	−8.89195			−0.987995
$82$	−7.55010	+	1.09776i	−0.833770	+	0.121228i
$83$	−2.35855	−	2.35855i	−0.258885	−	0.258885i	0.565716	−	0.824600i	$-0.308600\pi$
$83$	−2.35855	−	2.35855i	−0.258885	−	0.258885i	−0.824600	+	0.565716i	$0.808600\pi$
$84$	−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
$88$	−3.80024	−	8.21770i	−0.405107	−	0.876010i
$89$			16.4054i			1.73897i	0.493961	+	0.869484i	$0.335549\pi$
$89$			16.4054i			1.73897i	−0.493961	+	0.869484i	$0.664451\pi$
$90$	−8.08181	+	4.89535i	−0.851898	+	0.516015i
$91$		−	4.09606i		−	0.429384i
$92$	10.0044	+	5.42171i	1.04303	+	0.565253i
$93$	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	$-0.561019\pi$
$98$	1.98960	+	13.6839i	0.200980	+	1.38228i
$99$	9.56459			0.961278
$100$	−4.63163	+	8.86273i	−0.463163	+	0.886273i
$101$	7.98198			0.794236			0.397118	−	0.917767i	$-0.370010\pi$
$101$	7.98198			0.794236			0.397118	+	0.917767i	$0.370010\pi$
$102$	0.00687236	+	0.0472662i	0.000680465	+	0.00468005i
$103$	4.94955	+	4.94955i	0.487694	+	0.487694i	0.907578	−	0.419884i	$-0.137929\pi$
$103$	4.94955	+	4.94955i	0.487694	+	0.487694i	−0.419884	+	0.907578i	$0.637929\pi$
$104$	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	$-0.494677\pi$
$107$	10.5156	−	10.5156i	1.01658	−	1.01658i	0.999860	−	0.0167221i	$-0.00532305\pi$
$108$	0.625626	−	1.15444i	0.0602009	−	0.111086i
$109$		−	0.690455i		−	0.0661336i	−0.999453	−	0.0330668i	$-0.989473\pi$
$109$		−	0.690455i		−	0.0661336i	0.999453	−	0.0330668i	$-0.0105274\pi$
$110$	8.65805	−	5.24440i	0.825513	−	0.500033i
$111$			0.0431643i			0.00409698i
$112$	−3.38111	+	16.0316i	−0.319485	+	1.51484i
$113$	−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
$118$	−13.5271	+	1.96680i	−1.24527	+	0.181058i
$119$	1.26174			0.115663
$120$	−0.0332654	−	0.692635i	−0.00303670	−	0.0632287i
$121$	0.753441			0.0684947
$122$	−15.1986	+	2.20984i	−1.37602	+	0.200069i
$123$	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	−0.670439	−	0.741965i	$-0.733894\pi$
$127$	0.806054	−	0.806054i	0.0715257	−	0.0715257i	0.741965	+	0.670439i	$0.233894\pi$
$128$	−6.01064	+	9.58500i	−0.531271	+	0.847202i
$129$		−	0.211252i		−	0.0185997i
$130$	3.07105	+	0.754078i	0.269349	+	0.0661370i
$131$			19.2242i			1.67962i	0.542877	+	0.839812i	$0.317335\pi$
$131$			19.2242i			1.67962i	−0.542877	+	0.839812i	$0.682665\pi$
$132$	−0.334444	+	0.617133i	−0.0291096	+	0.0537146i
$133$	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	$0.818293\pi$
$138$	−0.126935	−	0.873021i	−0.0108054	−	0.0743164i
$139$	5.61731			0.476454			0.238227	−	0.971209i	$-0.423434\pi$
$139$	5.61731			0.476454			0.238227	+	0.971209i	$0.423434\pi$
$140$	−18.2331	−	1.76304i	−1.54098	−	0.149004i
$141$	0.653652			0.0550475
$142$	2.41877	+	16.6356i	0.202979	+	1.39603i
$143$	−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
$148$	0.692253	+	0.375154i	0.0569029	+	0.0308375i
$149$		−	5.19488i		−	0.425581i	−0.977098	−	0.212791i	$-0.931745\pi$
$149$		−	5.19488i		−	0.425581i	0.977098	−	0.212791i	$-0.0682552\pi$
$150$	0.765448	−	0.123098i	0.0624985	−	0.0100509i
$151$			2.67892i			0.218008i	0.994041	+	0.109004i	$0.0347661\pi$
$151$			2.67892i			0.218008i	−0.994041	+	0.109004i	$0.965234\pi$
$152$	12.8850	−	5.95862i	1.04511	−	0.483308i
$153$	−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	$0.502810\pi$
$158$	9.42438	−	1.37028i	0.749764	−	0.109013i
$159$	−0.123615			−0.00980332
$160$	−11.3973	−	5.48640i	−0.901039	−	0.433738i
$161$	−23.3047			−1.83667
$162$	12.4443	−	1.80936i	0.977714	−	0.142157i
$163$	16.7392	+	16.7392i	1.31112	+	1.31112i	0.920594	+	0.390522i	$0.127705\pi$
$163$	16.7392	+	16.7392i	1.31112	+	1.31112i	0.390522	+	0.920594i	$0.372295\pi$
$164$	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	−0.778886	−	0.627166i	$-0.784215\pi$
$167$	−1.96065	+	1.96065i	−0.151720	+	0.151720i	0.627166	+	0.778886i	$0.284215\pi$
$168$	1.15293	−	0.533168i	0.0889504	−	0.0411348i
$169$		−	1.00000i		−	0.0769231i
$170$	−0.232284	+	0.945998i	−0.0178154	+	0.0725547i
$171$			14.9969i			1.14684i
$172$	−3.38797	−	1.83605i	−0.258331	−	0.139998i
$173$	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
$178$	−3.33822	−	22.9593i	−0.250210	−	1.72087i
$179$	−23.7480			−1.77501			−0.887503	−	0.460801i	$-0.847562\pi$
$179$	−23.7480			−1.77501			−0.887503	+	0.460801i	$0.847562\pi$
$180$	10.3144	−	8.49555i	0.768787	−	0.633221i
$181$	7.42358			0.551791			0.275895	−	0.961188i	$-0.411026\pi$
$181$	7.42358			0.551791			0.275895	+	0.961188i	$0.411026\pi$
$182$	0.833478	+	5.73243i	0.0617815	+	0.424916i
$183$	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
$188$	5.68109	−	10.4830i	0.414336	−	0.764553i
$189$			2.68919i			0.195610i
$190$	8.22298	+	13.5755i	0.596558	+	0.984867i
$191$			12.9193i			0.934807i	0.884044	+	0.467404i	$0.154811\pi$
$191$			12.9193i			0.934807i	−0.884044	+	0.467404i	$0.845189\pi$
$192$	0.874262	−	0.0708943i	0.0630945	−	0.00511636i
$193$	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	$0.694222\pi$
$198$	−13.3856	+	1.94623i	−0.951275	+	0.138313i
$199$	−16.8046			−1.19125			−0.595624	−	0.803263i	$-0.703095\pi$
$199$	−16.8046			−1.19125			−0.595624	+	0.803263i	$0.703095\pi$
$200$	4.67854	−	13.3458i	0.330823	−	0.943693i
$201$	0.571844			0.0403348
$202$	−11.1708	+	1.62420i	−0.785972	+	0.114278i
$203$	−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
$208$	−0.825455	+	3.91390i	−0.0572350	+	0.271380i
$209$		−	16.0662i		−	1.11132i
$210$	0.735780	+	1.21471i	0.0507736	+	0.0838230i
$211$		−	15.2868i		−	1.05239i	−0.850365	−	0.526193i	$-0.823619\pi$
$211$		−	15.2868i		−	1.05239i	0.850365	−	0.526193i	$-0.176381\pi$
$212$	−1.07438	+	1.98249i	−0.0737885	+	0.136158i
$213$	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
$218$	0.140496	+	0.966291i	0.00951558	+	0.0654455i
$219$	0.0505933			0.00341878
$220$	−11.0498	+	9.10129i	−0.744976	+	0.613609i
$221$	0.308037			0.0207208
$222$	−0.00878321	−	0.0604084i	−0.000589490	−	0.00405435i
$223$	2.51119	+	2.51119i	0.168162	+	0.168162i	0.786171	−	0.618009i	$-0.212060\pi$
$223$	2.51119	+	2.51119i	0.168162	+	0.168162i	−0.618009	+	0.786171i	$0.712060\pi$
$224$	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	−0.775334	−	0.631551i	$-0.782418\pi$
$227$	−2.16630	+	2.16630i	−0.143783	+	0.143783i	0.631551	+	0.775334i	$0.282418\pi$
$228$	−0.967638	−	0.524394i	−0.0640834	−	0.0347288i
$229$			18.7200i			1.23705i	0.785764	+	0.618526i	$0.212270\pi$
$229$			18.7200i			1.23705i	−0.785764	+	0.618526i	$0.787730\pi$
$230$	4.29036	−	17.4729i	0.282898	−	1.15213i
$231$		−	1.43757i		−	0.0945855i
$232$	−11.7522	−	25.4132i	−0.771571	−	1.66846i
$233$	−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
$238$	−1.76580	+	0.256742i	−0.114460	+	0.0166421i
$239$	18.2418			1.17997			0.589983	−	0.807416i	$-0.299135\pi$
$239$	18.2418			1.17997			0.589983	+	0.807416i	$0.299135\pi$
$240$	0.187494	+	0.962573i	0.0121027	+	0.0621338i
$241$	−5.90974			−0.380680			−0.190340	−	0.981718i	$-0.560959\pi$
$241$	−5.90974			−0.380680			−0.190340	+	0.981718i	$0.560959\pi$
$242$	−1.05444	+	0.153312i	−0.0677819	+	0.00985529i
$243$	−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
$248$	2.61811	+	5.66143i	0.166250	+	0.359501i
$249$		−	0.365709i		−	0.0231759i
$250$	15.4103	+	3.53861i	0.974635	+	0.223801i
$251$			8.09939i			0.511229i	0.966779	+	0.255615i	$0.0822778\pi$
$251$			8.09939i			0.511229i	−0.966779	+	0.255615i	$0.917722\pi$
$252$	21.5208	+	11.6628i	1.35568	+	0.734688i
$253$	−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	$0.726022\pi$
$258$	0.0429861	+	0.295646i	0.00267620	+	0.0184061i
$259$	−1.61256			−0.100200
$260$	−4.45137	−	0.430424i	−0.276063	−	0.0266937i
$261$	29.5784			1.83086
$262$	−3.91179	−	26.9042i	−0.241671	−	1.66215i
$263$	−15.3744	−	15.3744i	−0.948026	−	0.948026i	0.0506886	−	0.998715i	$-0.483858\pi$
$263$	−15.3744	−	15.3744i	−0.948026	−	0.948026i	−0.998715	+	0.0506886i	$0.983858\pi$
$264$	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
$268$	4.97006	−	9.17101i	0.303595	−	0.560209i
$269$			3.62354i			0.220931i	0.993880	+	0.110466i	$0.0352342\pi$
$269$			3.62354i			0.220931i	−0.993880	+	0.110466i	$0.964766\pi$
$270$	−2.01624	−	0.495076i	−0.122705	−	0.0301293i
$271$			31.3377i			1.90363i	0.306669	+	0.951816i	$0.400785\pi$
$271$			31.3377i			1.90363i	−0.306669	+	0.951816i	$0.599215\pi$
$272$	−1.20563	−	0.254271i	−0.0731019	−	0.0154174i
$273$	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	$-0.523550\pi$
$278$	−7.86142	+	1.14303i	−0.471497	+	0.0685542i
$279$	−6.58934			−0.394494
$280$	25.8759	−	1.24275i	1.54638	−	0.0742685i
$281$	−22.1766			−1.32294			−0.661472	−	0.749970i	$-0.730068\pi$
$281$	−22.1766			−1.32294			−0.661472	+	0.749970i	$0.730068\pi$
$282$	−0.914785	+	0.133007i	−0.0544747	+	0.00792046i
$283$	1.53553	+	1.53553i	0.0912776	+	0.0912776i	0.751271	−	0.659994i	$-0.229441\pi$
$283$	1.53553	+	1.53553i	0.0912776	+	0.0912776i	−0.659994	+	0.751271i	$0.729441\pi$
$284$	−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
$288$	11.1697	+	12.6859i	0.658184	+	0.747527i
$289$		−	16.9051i		−	0.994418i
$290$	26.7750	−	16.2183i	1.57228	−	0.952368i
$291$		−	1.79011i		−	0.104938i
$292$	0.439721	−	0.811396i	0.0257327	−	0.0474833i
$293$	−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
$298$	1.05707	+	7.27023i	0.0612344	+	0.421153i
$299$	−5.68954			−0.329035
$300$	−1.04619	+	0.328030i	−0.0604020	+	0.0189388i
$301$	7.89208			0.454892
$302$	−0.545115	−	3.74915i	−0.0313678	−	0.215739i
$303$	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	−0.224393	−	0.974499i	$-0.572040\pi$
$307$	13.1429	−	13.1429i	0.750106	−	0.750106i	0.974499	+	0.224393i	$0.0720399\pi$
$308$	−23.0553	−	12.4944i	−1.31370	−	0.711934i
$309$			0.767460i			0.0436593i
$310$	−5.96480	+	3.61303i	−0.338778	+	0.205206i
$311$			6.77287i			0.384054i	0.981390	+	0.192027i	$0.0615062\pi$
$311$			6.77287i			0.384054i	−0.981390	+	0.192027i	$0.938494\pi$
$312$	0.281473	−	0.130166i	0.0159353	−	0.00736920i
$313$	−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	$0.652131\pi$
$318$	0.172999	−	0.0251536i	0.00970132	−	0.00141054i
$319$	−31.6874			−1.77415
$320$	17.0669	+	5.35904i	0.954071	+	0.299580i
$321$	1.63051			0.0910064
$322$	32.6149	−	4.74211i	1.81756	−	0.264267i
$323$	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
$328$	−13.8498	+	6.40476i	−0.764725	+	0.353644i
$329$			24.4196i			1.34630i
$330$	1.07783	+	0.264655i	0.0593327	+	0.0145688i
$331$		−	29.2597i		−	1.60826i	−0.594454	−	0.804129i	$-0.702632\pi$
$331$		−	29.2597i		−	1.60826i	0.594454	−	0.804129i	$-0.297368\pi$
$332$	−5.86510	−	3.17848i	−0.321889	−	0.174442i
$333$	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	$0.800994\pi$
$338$	0.203483	+	1.39950i	0.0110680	+	0.0761227i
$339$	−0.470219			−0.0255388
$340$	0.132586	−	1.37119i	0.00719051	−	0.0743631i
$341$	7.05917			0.382275
$342$	−3.05161	−	20.9881i	−0.165012	−	1.13491i
$343$	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	−0.955591	−	0.294698i	$-0.904781\pi$
$347$	−12.3111	+	12.3111i	−0.660893	+	0.660893i	0.294698	+	0.955591i	$0.404781\pi$
$348$	−1.03427	+	1.90848i	−0.0554425	+	0.102305i
$349$			3.85153i			0.206167i	0.994673	+	0.103084i	$0.0328710\pi$
$349$			3.85153i			0.206167i	−0.994673	+	0.103084i	$0.967129\pi$
$350$	4.59876	+	28.5961i	0.245814	+	1.52853i
$351$			0.656531i			0.0350430i
$352$	−11.9662	−	13.5905i	−0.637799	−	0.724374i
$353$	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
$358$	33.2352	−	4.83230i	1.75654	−	0.255395i
$359$	8.57461			0.452550			0.226275	−	0.974063i	$-0.427345\pi$
$359$	8.57461			0.452550			0.226275	+	0.974063i	$0.427345\pi$
$360$	−12.7062	+	13.9883i	−0.669677	+	0.737248i
$361$	6.19104			0.325844
$362$	−10.3893	+	1.51057i	−0.546049	+	0.0793939i
$363$	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	−0.819592	−	0.572948i	$-0.805800\pi$
$367$	−4.72502	+	4.72502i	−0.246644	+	0.246644i	0.572948	+	0.819592i	$0.305800\pi$
$368$	22.2683	+	4.69646i	1.16082	+	0.244820i
$369$		−	16.1197i		−	0.839160i
$370$	0.296870	−	1.20903i	0.0154335	−	0.0628545i
$371$		−	4.61810i		−	0.239760i
$372$	0.230409	−	0.425162i	0.0119461	−	0.0220436i
$373$	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
$378$	−0.547204	−	3.76352i	−0.0281452	−	0.193574i
$379$	−4.73069			−0.242999			−0.121500	−	0.992591i	$-0.538770\pi$
$379$	−4.73069			−0.242999			−0.121500	+	0.992591i	$0.538770\pi$
$380$	−14.2704	−	17.3256i	−0.732057	−	0.888784i
$381$	0.124984			0.00640312
$382$	−2.62885	−	18.0805i	−0.134504	−	0.925080i
$383$	16.3407	+	16.3407i	0.834968	+	0.834968i	0.988192	−	0.153223i	$-0.0489654\pi$
$383$	16.3407	+	16.3407i	0.834968	+	0.834968i	−0.153223	+	0.988192i	$0.548965\pi$
$384$	−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
$388$	−28.7091	−	15.5584i	−1.45749	−	0.789858i
$389$		−	6.94354i		−	0.352051i	−0.984386	−	0.176026i	$-0.943676\pi$
$389$		−	6.94354i		−	0.352051i	0.984386	−	0.176026i	$-0.0563242\pi$
$390$	0.179631	+	0.296556i	0.00909597	+	0.0150167i
$391$		−	1.75259i		−	0.0886322i
$392$	11.6081	+	25.1014i	0.586296	+	1.26781i
$393$	−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	$0.565458\pi$
$398$	23.5180	−	3.41945i	1.17885	−	0.171402i
$399$	2.25405			0.112844
$400$	−3.83195	+	19.6295i	−0.191598	+	0.981474i
$401$	−2.06489			−0.103116			−0.0515578	−	0.998670i	$-0.516419\pi$
$401$	−2.06489			−0.103116			−0.0515578	+	0.998670i	$0.516419\pi$
$402$	−0.800294	+	0.116360i	−0.0399151	+	0.00580353i
$403$	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
$408$	0.0400959	+	0.0867040i	0.00198505	+	0.00429249i
$409$		−	5.10061i		−	0.252209i	−0.992017	−	0.126104i	$-0.959753\pi$
$409$		−	5.10061i		−	0.252209i	0.992017	−	0.126104i	$-0.0402474\pi$
$410$	−8.83867	−	14.5919i	−0.436511	−	0.720643i
$411$		−	0.546459i		−	0.0269548i
$412$	12.3082	+	6.67022i	0.606383	+	0.328618i
$413$	−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
$418$	3.26919	+	22.4846i	0.159901	+	1.09976i
$419$	14.0619			0.686969			0.343484	−	0.939158i	$-0.388393\pi$
$419$	14.0619			0.686969			0.343484	+	0.939158i	$0.388393\pi$
$420$	−1.27690	−	1.55027i	−0.0623061	−	0.0756452i
$421$	4.35784			0.212388			0.106194	−	0.994345i	$-0.466133\pi$
$421$	4.35784			0.212388			0.106194	+	0.994345i	$0.466133\pi$
$422$	3.11060	+	21.3938i	0.151422	+	1.04143i
$423$	−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
$428$	14.1713	−	26.1496i	0.684994	−	1.26399i
$429$		−	0.350965i		−	0.0169448i
$430$	−1.45292	+	5.91715i	−0.0700660	+	0.285350i
$431$		−	27.0992i		−	1.30532i	−0.757649	−	0.652662i	$-0.773652\pi$
$431$		−	27.0992i		−	1.30532i	0.757649	−	0.652662i	$-0.226348\pi$
$432$	0.541937	−	2.56960i	0.0260739	−	0.123630i
$433$	−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
$438$	−0.0708052	+	0.0102949i	−0.00338320	+	0.000491908i
$439$	25.2613			1.20566			0.602829	−	0.797870i	$-0.294040\pi$
$439$	25.2613			1.20566			0.602829	+	0.797870i	$0.294040\pi$
$440$	13.6122	−	14.9857i	0.648936	−	0.714414i
$441$	−29.2156			−1.39122
$442$	−0.431097	+	0.0626803i	−0.0205052	+	0.00298140i
$443$	4.83303	+	4.83303i	0.229624	+	0.229624i	0.812536	−	0.582912i	$-0.198087\pi$
$443$	4.83303	+	4.83303i	0.229624	+	0.229624i	−0.582912	+	0.812536i	$0.698087\pi$
$444$	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
$448$	2.64852	+	32.6613i	0.125131	+	1.54310i
$449$		−	30.4670i		−	1.43783i	−0.695099	−	0.718914i	$-0.744640\pi$
$449$		−	30.4670i		−	1.43783i	0.695099	−	0.718914i	$-0.255360\pi$
$450$	−17.1225	−	12.3782i	−0.807162	−	0.583516i
$451$			17.2691i			0.813170i
$452$	−4.08681	+	7.54120i	−0.192228	+	0.354708i
$453$	−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	$0.730524\pi$
$458$	−3.80920	−	26.1986i	−0.177992	−	1.22418i
$459$	−0.202236			−0.00943956
$460$	−2.44891	+	25.3263i	−0.114181	+	1.18084i
$461$	−20.6755			−0.962955			−0.481477	−	0.876458i	$-0.659900\pi$
$461$	−20.6755			−0.962955			−0.481477	+	0.876458i	$0.659900\pi$
$462$	0.292522	+	2.01188i	0.0136093	+	0.0936013i
$463$	−15.8454	−	15.8454i	−0.736400	−	0.736400i	0.235479	−	0.971879i	$-0.424334\pi$
$463$	−15.8454	−	15.8454i	−0.736400	−	0.736400i	−0.971879	+	0.235479i	$0.924334\pi$
$464$	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	−0.00105852	−	0.999999i	$-0.500337\pi$
$467$	21.5873	−	21.5873i	0.998941	−	0.998941i	0.999999	+	0.00105852i	$0.000336938\pi$
$468$	5.25403	+	2.84732i	0.242868	+	0.131618i
$469$			21.3633i			0.986467i
$470$	−18.3088	−	4.49560i	−0.844521	−	0.207367i
$471$			1.92562i			0.0887281i
$472$	−24.8138	+	11.4750i	−1.14215	+	0.528181i
$473$	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
$478$	−25.5294	+	3.71190i	−1.16769	+	0.169778i
$479$	26.2847			1.20098			0.600488	−	0.799634i	$-0.294973\pi$
$479$	26.2847			1.20098			0.600488	+	0.799634i	$0.294973\pi$
$480$	−0.458265	−	1.30897i	−0.0209168	−	0.0597459i
$481$	−0.393686			−0.0179505
$482$	8.27067	−	1.20253i	0.376719	−	0.0547738i
$483$	−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	−0.928635	−	0.370996i	$-0.879016\pi$
$487$	−12.3060	+	12.3060i	−0.557639	+	0.557639i	0.370996	+	0.928635i	$0.379016\pi$
$488$	−27.8800	+	12.8930i	−1.26207	+	0.583639i
$489$			2.59552i			0.117374i
$490$	−26.4465	+	16.0193i	−1.19473	+	0.723679i
$491$			8.98739i			0.405595i	0.979221	+	0.202798i	$0.0650034\pi$
$491$			8.98739i			0.405595i	−0.979221	+	0.202798i	$0.934997\pi$
$492$	1.04009	+	0.563657i	0.0468908	+	0.0254116i
$493$	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
$498$	0.0744155	+	0.511809i	0.00333464	+	0.0229347i
$499$	−1.43936			−0.0644347			−0.0322173	−	0.999481i	$-0.510257\pi$
$499$	−1.43936			−0.0644347			−0.0322173	+	0.999481i	$0.510257\pi$
$500$	−22.2868	−	1.81654i	−0.996695	−	0.0812379i
$501$	−0.304012			−0.0135823
$502$	−1.64809	−	11.3351i	−0.0735578	−	0.505910i
$503$	−22.4761	−	22.4761i	−1.00216	−	1.00216i	−0.999998	−	0.00216153i	$-0.999312\pi$
$503$	−22.4761	−	22.4761i	−1.00216	−	1.00216i	−0.00216153	−	0.999998i	$-0.500688\pi$
$504$	−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
$508$	1.08627	−	2.00445i	0.0481955	−	0.0889329i
$509$		−	25.4007i		−	1.12587i	−0.826502	−	0.562934i	$-0.809673\pi$
$509$		−	25.4007i		−	1.12587i	0.826502	−	0.562934i	$-0.190327\pi$
$510$	−0.0913502	+	0.0553330i	−0.00404505	+	0.00245019i
$511$			1.89010i			0.0836130i
$512$	−6.06442	+	21.7996i	−0.268012	+	0.963416i
$513$	−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
$518$	2.25678	−	0.328129i	0.0991571	−	0.0144172i
$519$	1.49591			0.0656631
$520$	6.31727	−	0.303401i	0.277031	−	0.0133050i
$521$	−9.27032			−0.406140			−0.203070	−	0.979164i	$-0.565092\pi$
$521$	−9.27032			−0.406140			−0.203070	+	0.979164i	$0.565092\pi$
$522$	−41.3950	+	6.01870i	−1.81181	+	0.263432i
$523$	16.5690	+	16.5690i	0.724513	+	0.724513i	0.969521	−	0.245008i	$-0.0787907\pi$
$523$	16.5690	+	16.5690i	0.724513	+	0.724513i	−0.245008	+	0.969521i	$0.578791\pi$
$524$	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
$528$	−0.289706	+	1.37364i	−0.0126078	+	0.0597801i
$529$			9.37086i			0.407429i
$530$	3.46246	+	0.850184i	0.150399	+	0.0369296i
$531$		−	28.8808i		−	1.25332i
$532$	19.5907	−	36.1497i	0.849363	−	1.56729i
$533$	−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
$538$	−0.737329	−	5.07114i	−0.0317885	−	0.218632i
$539$	31.2987			1.34813
$540$	2.92247	+	0.282587i	0.125763	+	0.0121606i
$541$	−12.4118			−0.533626			−0.266813	−	0.963748i	$-0.585971\pi$
$541$	−12.4118			−0.533626			−0.266813	+	0.963748i	$0.585971\pi$
$542$	−6.37669	−	43.8571i	−0.273902	−	1.88382i
$543$	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	−0.468334	−	0.883551i	$-0.655146\pi$
$547$	9.71112	−	9.71112i	0.415217	−	0.415217i	0.883551	+	0.468334i	$0.155146\pi$
$548$	−8.76390	−	4.74943i	−0.374375	−	0.202886i
$549$		−	32.4496i		−	1.38492i
$550$	18.3433	+	13.2608i	0.782163	+	0.565444i
$551$		−	49.6845i		−	2.11663i
$552$	−0.740585	−	1.60145i	−0.0315214	−	0.0681623i
$553$	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	$0.722680\pi$
$558$	9.22177	−	1.34082i	0.390389	−	0.0567614i
$559$	1.92675			0.0814928
$560$	−35.9604	+	7.00454i	−1.51961	+	0.295996i
$561$	0.108110			0.00456442
$562$	31.0361	−	4.51256i	1.30918	−	0.190351i
$563$	12.8341	+	12.8341i	0.540893	+	0.540893i	0.923791	−	0.382898i	$-0.125074\pi$
$563$	12.8341	+	12.8341i	0.540893	+	0.540893i	−0.382898	+	0.923791i	$0.625074\pi$
$564$	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
$568$	14.1120	+	30.5161i	0.592128	+	1.28043i
$569$		−	12.1495i		−	0.509334i	−0.967029	−	0.254667i	$-0.918034\pi$
$569$		−	12.1495i		−	0.509334i	0.967029	−	0.254667i	$-0.0819658\pi$
$570$	−0.414968	+	1.68999i	−0.0173811	+	0.0707861i
$571$		−	19.5871i		−	0.819695i	−0.912154	−	0.409848i	$-0.865582\pi$
$571$		−	19.5871i		−	0.819695i	0.912154	−	0.409848i	$-0.134418\pi$
$572$	−5.62865	−	3.05034i	−0.235345	−	0.127541i
$573$	−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	$0.782028\pi$
$578$	3.43990	+	23.6587i	0.143081	+	0.984071i
$579$	2.39318			0.0994572
$580$	−34.1714	+	28.1457i	−1.41889	+	1.16868i
$581$	13.6624			0.566812
$582$	0.364257	+	2.50526i	0.0150989	+	0.103846i
$583$	−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	−0.951894	−	0.306427i	$-0.900867\pi$
$587$	−15.6384	+	15.6384i	−0.645467	+	0.645467i	0.306427	+	0.951894i	$0.400867\pi$
$588$	1.02158	−	1.88507i	0.0421292	−	0.0777390i
$589$			11.0685i			0.456068i
$590$	−15.8357	−	26.1434i	−0.651946	−	1.07631i
$591$			0.536570i			0.0220715i
$592$	1.54085	+	0.324970i	0.0633285	+	0.0133562i
$593$	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
$598$	7.96250	−	1.15772i	0.325611	−	0.0473428i
$599$	−24.3473			−0.994804			−0.497402	−	0.867520i	$-0.665713\pi$
$599$	−24.3473			−0.994804			−0.497402	+	0.867520i	$0.665713\pi$
$600$	1.39740	−	0.671960i	0.0570485	−	0.0274327i
$601$	−25.3047			−1.03220			−0.516099	−	0.856529i	$-0.672617\pi$
$601$	−25.3047			−1.03220			−0.516099	+	0.856529i	$0.672617\pi$
$602$	−11.0450	+	1.60590i	−0.450159	+	0.0654517i
$603$	−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	$-0.405927\pi$
$607$	30.7450	−	30.7450i	1.24790	−	1.24790i	0.956646	−	0.291255i	$-0.0940728\pi$
$608$	21.3093	−	18.7624i	0.864205	−	0.760917i
$609$		−	4.44569i		−	0.180148i
$610$	−17.7926	−	29.3740i	−0.720400	−	1.18932i
$611$			5.96172i			0.241186i
$612$	−0.877081	+	1.61844i	−0.0354539	+	0.0654214i
$613$	−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	$0.638603\pi$
$618$	−0.156165	−	1.07406i	−0.00628188	−	0.0432050i
$619$	7.68371			0.308834			0.154417	−	0.988006i	$-0.450650\pi$
$619$	7.68371			0.308834			0.154417	+	0.988006i	$0.450650\pi$
$620$	7.61254	−	6.27016i	0.305727	−	0.251816i
$621$	3.73536			0.149895
$622$	−1.37816	−	9.47862i	−0.0552593	−	0.380058i
$623$	−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
$628$	30.8824	+	16.7362i	1.23234	+	0.667845i
$629$		−	0.121270i		−	0.00483535i
$630$	9.22912	−	37.5864i	0.367697	−	1.49748i
$631$		−	26.5327i		−	1.05625i	−0.849166	−	0.528126i	$-0.822895\pi$
$631$		−	26.5327i		−	1.05625i	0.849166	−	0.528126i	$-0.177105\pi$
$632$	17.2879	−	7.99472i	0.687675	−	0.318013i
$633$	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
$638$	44.3465	−	6.44784i	1.75569	−	0.255273i
$639$	−35.5177			−1.40506
$640$	−24.9756	−	4.02714i	−0.987249	−	0.159187i
$641$	1.48587			0.0586882			0.0293441	−	0.999569i	$-0.490658\pi$
$641$	1.48587			0.0586882			0.0293441	+	0.999569i	$0.490658\pi$
$642$	−2.28190	+	0.331782i	−0.0900594	+	0.0130944i
$643$	15.8763	+	15.8763i	0.626098	+	0.626098i	0.947084	−	0.320986i	$-0.104014\pi$
$643$	15.8763	+	15.8763i	0.626098	+	0.626098i	−0.320986	+	0.947084i	$0.604014\pi$
$644$	−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	−0.954481	−	0.298272i	$-0.903590\pi$
$647$	−16.6915	+	16.6915i	−0.656209	+	0.656209i	0.298272	+	0.954481i	$0.403590\pi$
$648$	22.8275	−	10.5565i	0.896749	−	0.414698i
$649$			30.9400i			1.21450i
$650$	1.12273	+	6.98137i	0.0440370	+	0.273832i
$651$			0.990390i			0.0388164i
$652$	41.6260	+	22.5584i	1.63020	+	0.883457i
$653$	−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
$658$	−4.96897	−	34.1752i	−0.193711	−	1.33229i
$659$	17.4766			0.680792			0.340396	−	0.940282i	$-0.389439\pi$
$659$	17.4766			0.680792			0.340396	+	0.940282i	$0.389439\pi$
$660$	−1.56228	−	0.151064i	−0.0608116	−	0.00588015i
$661$	−6.43375			−0.250244			−0.125122	−	0.992141i	$-0.539932\pi$
$661$	−6.43375			−0.250244			−0.125122	+	0.992141i	$0.539932\pi$
$662$	5.95385	+	40.9489i	0.231403	+	1.59152i
$663$	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
$668$	−2.64226	+	4.87563i	−0.102232	+	0.188644i
$669$			0.389377i			0.0150542i
$670$	−16.0173	−	3.93295i	−0.618803	−	0.151943i
$671$			34.7633i			1.34202i
$672$	1.90672	−	1.67883i	0.0735533	−	0.0647624i
$673$	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	$0.949216\pi$
$678$	0.658071	−	0.0956815i	0.0252731	−	0.00367463i
$679$	66.8762			2.56647
$680$	0.0934588	+	1.94595i	0.00358398	+	0.0746239i
$681$	−0.335900			−0.0128717
$682$	−9.87929	+	1.43642i	−0.378298	+	0.0550034i
$683$	7.68769	+	7.68769i	0.294161	+	0.294161i	0.838722	−	0.544560i	$-0.183303\pi$
$683$	7.68769	+	7.68769i	0.294161	+	0.294161i	−0.544560	+	0.838722i	$0.683303\pi$
$684$	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
$688$	−7.54110	−	1.59044i	−0.287502	−	0.0606351i
$689$		−	1.12745i		−	0.0429524i
$690$	1.68727	−	1.02202i	0.0642331	−	0.0389076i
$691$		−	29.0242i		−	1.10413i	−0.833800	−	0.552067i	$-0.813839\pi$
$691$		−	29.0242i		−	1.10413i	0.833800	−	0.552067i	$-0.186161\pi$
$692$	13.0014	−	23.9908i	0.494238	−	0.911994i
$693$	−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
$698$	−0.783720	−	5.39020i	−0.0296642	−	0.204022i
$699$	−2.27029			−0.0858703
$700$	−12.2548	−	39.0844i	−0.463187	−	1.47725i
$701$	28.0124			1.05801			0.529007	−	0.848617i	$-0.322565\pi$
$701$	28.0124			1.05801			0.529007	+	0.848617i	$0.322565\pi$
$702$	−0.133593	−	0.918814i	−0.00504214	−	0.0346784i
$703$	−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
$708$	1.86347	+	1.00987i	0.0700333	+	0.0379533i
$709$			13.6438i			0.512402i	0.966624	+	0.256201i	$0.0824709\pi$
$709$			13.6438i			0.512402i	−0.966624	+	0.256201i	$0.917529\pi$
$710$	−32.1513	+	19.4748i	−1.20662	+	0.730877i
$711$			20.1214i			0.754611i
$712$	−19.4764	−	42.1161i	−0.729910	−	1.57837i
$713$	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
$718$	−12.0001	+	1.74479i	−0.447841	+	0.0651148i
$719$	19.0497			0.710433			0.355217	−	0.934784i	$-0.384407\pi$
$719$	19.0497			0.710433			0.355217	+	0.934784i	$0.384407\pi$
$720$	14.9360	−	22.1621i	0.556631	−	0.825932i
$721$	−28.6713			−1.06777
$722$	−8.66435	+	1.25977i	−0.322454	+	0.0468838i
$723$	−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	$0.517410\pi$
$727$	−28.3966	+	28.3966i	−1.05317	+	1.05317i	−0.998505	+	0.0546675i	$0.982590\pi$
$728$	4.86283	+	10.5154i	0.180228	+	0.389728i
$729$			26.3530i			0.976038i
$730$	−1.41711	−	0.347964i	−0.0524498	−	0.0128787i
$731$			0.593510i			0.0219518i
$732$	2.09374	+	1.13466i	0.0773867	+	0.0419383i
$733$	−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
$738$	3.28009	+	22.5596i	0.120742	+	0.830429i
$739$	−30.9143			−1.13720			−0.568601	−	0.822614i	$-0.692515\pi$
$739$	−30.9143			−1.13720			−0.568601	+	0.822614i	$0.692515\pi$
$740$	−0.169452	+	1.75244i	−0.00622918	+	0.0644211i
$741$	0.550298			0.0202157
$742$	0.939704	+	6.46302i	0.0344976	+	0.237265i
$743$	31.0812	+	31.0812i	1.14026	+	1.14026i	0.988402	+	0.151858i	$0.0485255\pi$
$743$	31.0812	+	31.0812i	1.14026	+	1.14026i	0.151858	+	0.988402i	$0.451475\pi$
$744$	−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
$748$	0.939618	−	1.73383i	0.0343558	−	0.0633952i
$749$			60.9138i			2.22574i
$750$	0.920394	+	1.46908i	0.0336080	+	0.0536431i
$751$			1.26768i			0.0462582i	0.999732	+	0.0231291i	$0.00736287\pi$
$751$			1.26768i			0.0462582i	−0.999732	+	0.0231291i	$0.992637\pi$
$752$	4.92113	−	23.3336i	0.179455	−	0.850889i
$753$	−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	$0.804829\pi$
$758$	6.62059	−	0.962613i	0.240470	−	0.0349637i
$759$	−1.99683			−0.0724804
$760$	23.4969	+	21.3433i	0.852322	+	0.774204i
$761$	17.3878			0.630309			0.315155	−	0.949040i	$-0.397944\pi$
$761$	17.3878			0.630309			0.315155	+	0.949040i	$0.397944\pi$
$762$	−0.174915	+	0.0254321i	−0.00633649	+	0.000921308i
$763$	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
$768$	1.63575	−	0.633852i	0.0590250	−	0.0228722i
$769$			7.24605i			0.261299i	0.991429	+	0.130650i	$0.0417063\pi$
$769$			7.24605i			0.261299i	−0.991429	+	0.130650i	$0.958294\pi$
$770$	−9.88716	+	40.2664i	−0.356309	+	1.45110i
$771$			0.264554i			0.00952769i
$772$	20.7998	−	38.3809i	0.748603	−	1.38136i
$773$	24.8969	−	24.8969i	0.895479	−	0.895479i	−0.0995533	−	0.995032i	$-0.531741\pi$
$773$	24.8969	−	24.8969i	0.895479	−	0.895479i	0.995032	+	0.0995533i	$0.0317414\pi$
$774$	4.86883	−	6.52553i	0.175006	−	0.234555i
$775$	7.91345	+	7.67850i	0.284259	+	0.275820i
$776$	43.3443	+	15.9321i	1.55597	+	0.571930i
$777$	−0.125019	−	0.125019i	−0.00448504	−	0.00448504i
$778$	1.41289	+	9.71747i	0.0506546	+	0.348388i
$779$	−27.0772			−0.970141
$780$	−0.311737	−	0.378477i	−0.0111620	−	0.0135517i
$781$	38.0501			1.36154
$782$	0.356622	+	2.45275i	0.0127528	+	0.0877100i
$783$	4.59555	+	4.59555i	0.164232	+	0.164232i
$784$	−21.3532	−	32.7674i	−0.762614	−	1.17026i
$785$	−14.7549	+	36.3947i	−0.526626	+	1.29898i
$786$	1.78256	−	2.38911i	0.0635819	−	0.0852167i
$787$	−21.2409	+	21.2409i	−0.757157	+	0.757157i	−0.975804	−	0.218647i	$-0.929836\pi$
$787$	−21.2409	+	21.2409i	−0.757157	+	0.757157i	0.218647	+	0.975804i	$0.429836\pi$
$788$	8.60531	+	4.66349i	0.306551	+	0.166130i
$789$		−	2.38390i		−	0.0848691i
$790$	11.0328	+	18.2143i	0.392531	+	0.648035i
$791$		−	17.5668i		−	0.624602i
$792$	−24.5543	+	11.3550i	−0.872500	+	0.403484i
$793$	−7.67922	+	7.67922i	−0.272697	+	0.272697i
$794$	−24.7443	−	18.4622i	−0.878144	−	0.655200i
$795$	−0.107699	−	0.254567i	−0.00381970	−	0.00902857i
$796$	−32.2177	+	9.57104i	−1.14192	+	0.339236i
$797$	7.46746	+	7.46746i	0.264511	+	0.264511i	0.826884	−	0.562373i	$-0.190111\pi$
$797$	7.46746	+	7.46746i	0.264511	+	0.264511i	−0.562373	+	0.826884i	$0.690111\pi$
$798$	−3.15455	+	0.458662i	−0.111670	+	0.0162364i
$799$	−1.83643			−0.0649683
$800$	1.36855	−	28.2511i	0.0483856	−	0.998829i
$801$	49.0190			1.73200
$802$	2.88981	−	0.420170i	0.102043	−	0.0148367i
$803$	1.04446	+	1.04446i	0.0368582	+	0.0368582i
$804$	1.09633	−	0.325692i	0.0386647	−	0.0114863i
$805$	−20.3041	−	47.9926i	−0.715626	−	1.69152i
$806$	−2.49964	−	1.86503i	−0.0880462	−	0.0656930i
$807$	−0.280927	+	0.280927i	−0.00988910	+	0.00988910i
$808$	−20.4914	+	9.47617i	−0.720885	+	0.333371i
$809$		−	8.75599i		−	0.307844i	−0.988083	−	0.153922i	$-0.950810\pi$
$809$		−	8.75599i		−	0.307844i	0.988083	−	0.153922i	$-0.0491905\pi$
$810$	14.5681	+	24.0507i	0.511872	+	0.845057i
$811$		−	27.3991i		−	0.962114i	−0.876689	−	0.481057i	$-0.840253\pi$
$811$		−	27.3991i		−	0.962114i	0.876689	−	0.481057i	$-0.159747\pi$
$812$	−71.2983	−	38.6388i	−2.50208	−	1.35596i
$813$	−2.42956	+	2.42956i	−0.0852084	+	0.0852084i
$814$	1.06576	−	1.42841i	0.0373550	−	0.0500657i
$815$	−19.8880	+	49.0559i	−0.696645	+	1.71835i
$816$	−0.0737570	−	0.113183i	−0.00258201	−	0.00396221i
$817$	6.83806	+	6.83806i	0.239234	+	0.239234i
$818$	1.03789	+	7.13829i	0.0362888	+	0.249584i
$819$	−12.2389			−0.427663
$820$	15.3389	+	18.6228i	0.535658	+	0.650337i
$821$	−21.3289			−0.744382			−0.372191	−	0.928156i	$-0.621393\pi$
$821$	−21.3289			−0.744382			−0.372191	+	0.928156i	$0.621393\pi$
$822$	0.111195	+	0.764768i	0.00387837	+	0.0266743i
$823$	19.4695	+	19.4695i	0.678663	+	0.678663i	0.959698	−	0.281035i	$-0.0906775\pi$
$823$	19.4695	+	19.4695i	0.678663	+	0.678663i	−0.281035	+	0.959698i	$0.590678\pi$
$824$	−18.5826	−	6.83045i	−0.647356	−	0.237950i
$825$	−0.0264395	−	1.75463i	−0.000920507	−	0.0610883i
$826$	33.4826	−	44.8757i	1.16501	−	1.56143i
$827$	−5.55378	+	5.55378i	−0.193124	+	0.193124i	−0.797045	−	0.603921i	$-0.793604\pi$
$827$	−5.55378	+	5.55378i	−0.193124	+	0.193124i	0.603921	+	0.797045i	$0.293604\pi$
$828$	16.2000	−	29.8930i	0.562988	−	1.03885i
$829$		−	0.629497i		−	0.0218633i	−0.999940	−	0.0109317i	$-0.996520\pi$
$829$		−	0.629497i		−	0.0218633i	0.999940	−	0.0109317i	$-0.00347973\pi$
$830$	−2.51522	+	10.2435i	−0.0873047	+	0.355557i
$831$		−	2.76435i		−	0.0958943i
$832$	0.646601	+	7.97383i	0.0224169	+	0.276443i
$833$	−2.12973	+	2.12973i	−0.0737909	+	0.0737909i
$834$	−0.698099	−	0.520865i	−0.0241732	−	0.0180361i
$835$	−5.74589	−	2.32947i	−0.198845	−	0.0806145i
$836$	−9.15044	−	30.8019i	−0.316475	−	1.06530i
$837$	−1.02378	−	1.02378i	−0.0353869	−	0.0353869i
$838$	−19.6796	+	2.86136i	−0.679820	+	0.0988439i
$839$	7.60249			0.262467			0.131234	−	0.991351i	$-0.458106\pi$
$839$	7.60249			0.262467			0.131234	+	0.991351i	$0.458106\pi$
$840$	2.10246	+	1.90977i	0.0725419	+	0.0658933i
$841$	−68.9930			−2.37907
$842$	−6.09879	+	0.886747i	−0.210178	+	0.0305593i
$843$	−1.71931	−	1.71931i	−0.0592163	−	0.0592163i
$844$	−8.70655	−	29.3077i	−0.299692	−	1.00881i
$845$	2.05935	−	0.871245i	0.0708439	−	0.0299717i
$846$	20.1912	+	15.0651i	0.694189	+	0.517948i
$847$	−2.18223	+	2.18223i	−0.0749824	+	0.0749824i
$848$	−0.930658	+	4.41272i	−0.0319589	+	0.151534i
$849$			0.238094i			0.00817135i
$850$	−2.15052	+	0.345842i	−0.0737622	+	0.0118623i
$851$			2.23989i			0.0767825i
$852$	1.24194	−	2.29170i	0.0425483	−	0.0785123i
$853$	−21.0350	+	21.0350i	−0.720225	+	0.720225i	−0.968651	−	0.248426i	$-0.920087\pi$
$853$	−21.0350	+	21.0350i	−0.720225	+	0.720225i	0.248426	+	0.968651i	$0.420087\pi$
$854$	37.6201	−	50.4210i	1.28733	−	1.72537i
$855$	−30.8838	+	13.0659i	−1.05620	+	0.446846i
$856$	−14.5117	+	39.4799i	−0.495999	+	1.34939i
$857$	28.9236	+	28.9236i	0.988013	+	0.988013i	0.999929	−	0.0119161i	$-0.00379310\pi$
$857$	28.9236	+	28.9236i	0.988013	+	0.988013i	−0.0119161	+	0.999929i	$0.503793\pi$
$858$	0.0714154	+	0.491175i	0.00243808	+	0.0167684i
$859$	−4.64140			−0.158362			−0.0791812	−	0.996860i	$-0.525231\pi$
$859$	−4.64140			−0.158362			−0.0791812	+	0.996860i	$0.525231\pi$
$860$	0.829318	−	8.57668i	0.0282795	−	0.292462i
$861$	−2.42283			−0.0825697
$862$	5.51423	+	37.9253i	0.187815	+	1.29174i
$863$	30.7683	+	30.7683i	1.04736	+	1.04736i	0.998821	+	0.0485433i	$0.0154579\pi$
$863$	30.7683	+	30.7683i	1.04736	+	1.04736i	0.0485433	+	0.998821i	$0.484542\pi$
$864$	−0.235570	+	3.70642i	−0.00801425	+	0.126095i
$865$	28.2730	+	11.4623i	0.961309	+	0.389729i
$866$	7.73260	−	10.3638i	0.262765	−	0.352175i
$867$	1.31062	−	1.31062i	0.0445111	−	0.0445111i
$868$	15.8835	+	8.60777i	0.539121	+	0.292167i
$869$		−	21.5561i		−	0.731240i
$870$	3.33319	+	0.818444i	0.113006	+	0.0277478i
$871$			5.21558i			0.176723i
$872$	0.819706	+	1.77254i	0.0277587	+	0.0600259i
$873$	−34.4959	+	34.4959i	−1.16751	+	1.16751i
$874$	32.3678	+	24.1503i	1.09486	+	0.816895i
$875$	41.9025	−	18.4768i	1.41656	−	0.624630i
$876$	0.0969969	−	0.0288153i	0.00327722	−	0.000973578i
$877$	7.68136	+	7.68136i	0.259381	+	0.259381i	0.824802	−	0.565421i	$-0.191286\pi$
$877$	7.68136	+	7.68136i	0.259381	+	0.259381i	−0.565421	+	0.824802i	$0.691286\pi$
$878$	−35.3532	+	5.14025i	−1.19311	+	0.173475i
$879$	−2.53512			−0.0855073
$880$	−16.0009	+	23.7423i	−0.539391	+	0.800352i
$881$	40.9290			1.37893			0.689467	−	0.724317i	$-0.257845\pi$
$881$	40.9290			1.37893			0.689467	+	0.724317i	$0.257845\pi$
$882$	40.8872	−	5.94488i	1.37674	−	0.200174i
$883$	−33.7937	−	33.7937i	−1.13725	−	1.13725i	−0.988942	−	0.148306i	$-0.952618\pi$
$883$	−33.7937	−	33.7937i	−1.13725	−	1.13725i	−0.148306	−	0.988942i	$-0.547382\pi$
$884$	0.590565	−	0.175442i	0.0198629	−	0.00590075i
$885$	−0.890322	+	2.19608i	−0.0299278	+	0.0738203i
$886$	−7.74725	−	5.78037i	−0.260274	−	0.194195i
$887$	−29.9180	+	29.9180i	−1.00455	+	1.00455i	−0.00455987	+	0.999990i	$0.501451\pi$
$887$	−29.9180	+	29.9180i	−1.00455	+	1.00455i	−0.999990	+	0.00455987i	$0.998549\pi$
$888$	−0.0512445	−	0.110812i	−0.00171965	−	0.00371860i
$889$			4.66923i			0.156601i
$890$	44.3729	−	26.8778i	1.48738	−	0.900944i
$891$		−	28.4634i		−	0.953558i
$892$	6.24468	+	3.38419i	0.209087	+	0.113311i
$893$	−21.1583	+	21.1583i	−0.708034	+	0.708034i
$894$	−0.481695	+	0.645601i	−0.0161103	+	0.0215921i
$895$	−20.6903	−	48.9054i	−0.691601	−	1.63473i
$896$	−10.3526	−	45.1705i	−0.345856	−	1.50904i
$897$	−0.441100	−	0.441100i	−0.0147279	−	0.0147279i
$898$	6.19952	+	42.6385i	0.206881	+	1.42287i
$899$	21.8304			0.728086
$900$	26.4817	+	13.8392i	0.882722	+	0.461307i
$901$	0.347296			0.0115701
$902$	−3.51397	−	24.1681i	−0.117002	−	0.804709i
$903$	0.611859	+	0.611859i	0.0203614	+	0.0203614i
$904$	4.18498	−	11.3855i	0.139190	−	0.378676i
$905$	6.46776	+	15.2878i	0.214996	+	0.508183i
$906$	0.248403	−	0.332927i	0.00825264	−	0.0110607i
$907$	41.2581	−	41.2581i	1.36995	−	1.36995i	0.509458	−	0.860496i	$-0.329846\pi$
$907$	41.2581	−	41.2581i	1.36995	−	1.36995i	0.860496	−	0.509458i	$-0.170154\pi$
$908$	−2.91940	+	5.38703i	−0.0968838	+	0.178775i
$909$		−	23.8500i		−	0.791054i
$910$	−11.0789	+	6.71078i	−0.367263	+	0.222460i
$911$			28.0092i			0.927985i	0.885839	+	0.463993i	$0.153584\pi$
$911$			28.0092i			0.927985i	−0.885839	+	0.463993i	$0.846416\pi$
$912$	−2.15381	−	0.454246i	−0.0713199	−	0.0150416i
$913$	7.54978	−	7.54978i	0.249861	−	0.249861i
$914$	−2.96327	−	2.21095i	−0.0980161	−	0.0731317i
$915$	−1.00034	+	2.46745i	−0.0330702	+	0.0815714i
$916$	10.6619	+	35.8898i	0.352280	+	1.18583i
$917$	−55.6800	−	55.6800i	−1.83872	−	1.83872i
$918$	0.283029	−	0.0411515i	0.00934134	−	0.00135820i
$919$	−27.0757			−0.893144			−0.446572	−	0.894748i	$-0.647355\pi$
$919$	−27.0757			−0.893144			−0.446572	+	0.894748i	$0.647355\pi$
$920$	−1.72621	−	35.9424i	−0.0569116	−	1.18499i
$921$	2.03789			0.0671509
$922$	28.9353	−	4.20711i	0.952935	−	0.138554i
$923$	8.40528	+	8.40528i	0.276663	+	0.276663i
$924$	−0.818767	−	2.75610i	−0.0269355	−	0.0906691i
$925$	−1.96821	+	0.0296579i	−0.0647143	+	0.000975145i
$926$	25.3999	+	18.9514i	0.834694	+	0.622781i
$927$	14.7891	−	14.7891i	0.485739	−	0.485739i
$928$	−37.0053	−	42.0284i	−1.21476	−	1.37965i
$929$		−	45.0449i		−	1.47788i	−0.673773	−	0.738938i	$-0.735328\pi$
$929$		−	45.0449i		−	1.47788i	0.673773	−	0.738938i	$-0.264672\pi$
$930$	−0.742552	−	0.182329i	−0.0243492	−	0.00597880i
$931$			49.0750i			1.60837i
$932$	−19.7318	+	36.4100i	−0.646335	+	1.19265i
$933$	−0.525089	+	0.525089i	−0.0171906	+	0.0171906i
$934$	−25.8187	+	34.6040i	−0.844815	+	1.13228i
$935$	2.04330	+	0.828386i	0.0668232	+	0.0270911i
$936$	−7.93238	−	2.91572i	−0.259278	−	0.0953033i
$937$	13.2385	+	13.2385i	0.432484	+	0.432484i	0.889472	−	0.456989i	$-0.151072\pi$
$937$	13.2385	+	13.2385i	0.432484	+	0.432484i	−0.456989	+	0.889472i	$0.651072\pi$
$938$	−4.34707	−	29.8979i	−0.141937	−	0.976202i
$939$	−0.558599			−0.0182292
$940$	26.5379	+	2.56607i	0.865570	+	0.0836959i
$941$	−7.07176			−0.230533			−0.115266	−	0.993335i	$-0.536772\pi$
$941$	−7.07176			−0.230533			−0.115266	+	0.993335i	$0.536772\pi$
$942$	−0.391831	−	2.69491i	−0.0127666	−	0.0878048i
$943$	21.7042	+	21.7042i	0.706784	+	0.706784i
$944$	32.3919	−	21.1085i	1.05427	−	0.687022i
$945$	−5.53799	+	2.34295i	−0.180151	+	0.0762160i
$946$	−5.21598	+	6.99081i	−0.169586	+	0.227291i
$947$	26.7687	−	26.7687i	0.869867	−	0.869867i	−0.122591	−	0.992457i	$-0.539120\pi$
$947$	26.7687	−	26.7687i	0.869867	−	0.869867i	0.992457	+	0.122591i	$0.0391202\pi$
$948$	−1.29829	−	0.703583i	−0.0421664	−	0.0228513i
$949$			0.461443i			0.0149791i
$950$	−20.7924	+	28.7616i	−0.674595	+	0.933149i
$951$			1.18159i			0.0383157i
$952$	−3.23915	+	1.49793i	−0.104981	+	0.0485482i
$953$	−4.97183	+	4.97183i	−0.161053	+	0.161053i	−0.783033	−	0.621980i	$-0.786329\pi$
$953$	−4.97183	+	4.97183i	−0.161053	+	0.161053i	0.621980	+	0.783033i	$0.286329\pi$
$954$	−3.81846	−	2.84902i	−0.123627	−	0.0922406i
$955$	−26.6054	+	11.2559i	−0.860930	+	0.364231i
$956$	34.9730	−	10.3896i	1.13111	−	0.336023i
$957$	−2.45667	−	2.45667i	−0.0794128	−	0.0794128i
$958$	−36.7853	+	5.34848i	−1.18848	+	0.172801i
$959$	20.4150			0.659234
$960$	0.907693	+	1.73865i	0.0292957	+	0.0561146i
$961$	26.1367			0.843120
$962$	0.550963	−	0.0801084i	0.0177638	−	0.00258280i
$963$	−31.4204	−	31.4204i	−1.01251	−	1.01251i
$964$	−11.3301	+	3.36588i	−0.364918	+	0.108408i
$965$	45.2316	+	18.3375i	1.45606	+	0.590306i
$966$	2.89622	+	2.16093i	0.0931844	+	0.0695267i
$967$	18.2417	−	18.2417i	0.586613	−	0.586613i	−0.350099	−	0.936713i	$-0.613852\pi$
$967$	18.2417	−	18.2417i	0.586613	−	0.586613i	0.936713	+	0.350099i	$0.113852\pi$
$968$	−1.93424	+	0.894483i	−0.0621689	+	0.0287498i
$969$			0.169512i			0.00544552i
$970$	−12.3118	+	50.1410i	−0.395308	+	1.60993i
$971$			11.5273i			0.369928i	0.982745	+	0.184964i	$0.0592169\pi$
$971$			11.5273i			0.369928i	−0.982745	+	0.184964i	$0.940783\pi$
$972$	−5.17761	−	2.80591i	−0.166072	−	0.0899997i
$973$	−16.2697	+	16.2697i	−0.521583	+	0.521583i
$974$	14.7182	−	19.7263i	0.471601	−	0.632072i
$975$	0.381757	−	0.393438i	0.0122260	−	0.0126001i
$976$	36.3946	−	23.7169i	1.16496	−	0.759158i
$977$	3.14585	+	3.14585i	0.100645	+	0.100645i	0.755636	−	0.654992i	$-0.227328\pi$
$977$	3.14585	+	3.14585i	0.100645	+	0.100645i	−0.654992	+	0.755636i	$0.727328\pi$
$978$	−0.528144	−	3.63243i	−0.0168882	−	0.116152i
$979$	−52.5141			−1.67836
$980$	33.7522	−	27.8004i	1.07817	−	0.888052i
$981$	−2.06307			−0.0658686
$982$	−1.82878	−	12.5778i	−0.0583587	−	0.401375i
$983$	−26.9662	−	26.9662i	−0.860088	−	0.860088i	0.131260	−	0.991348i	$-0.458098\pi$
$983$	−26.9662	−	26.9662i	−0.860088	−	0.860088i	−0.991348	+	0.131260i	$0.958098\pi$
$984$	−1.57030	−	0.577197i	−0.0500593	−	0.0184004i
$985$	−4.11142	+	10.1413i	−0.131001	+	0.323128i
$986$	−2.57883	+	3.45632i	−0.0821266	+	0.110072i
$987$	−1.89321	+	1.89321i	−0.0602615	+	0.0602615i
$988$	4.78280	−	8.82547i	0.152161	−	0.280776i
$989$		−	10.9623i		−	0.348581i
$990$	−15.6701	−	25.8701i	−0.498030	−	0.822205i
$991$		−	44.8243i		−	1.42389i	−0.702235	−	0.711945i	$-0.747814\pi$
$991$		−	44.8243i		−	1.42389i	0.702235	−	0.711945i	$-0.252186\pi$
$992$	8.24386	+	9.36289i	0.261743	+	0.297272i
$993$	2.26845	−	2.26845i	0.0719872	−	0.0719872i
$994$	−55.1883	−	41.1771i	−1.75047	−	1.30606i
$995$	−14.6410	−	34.6067i	−0.464149	−	1.09710i
$996$	−0.208289	−	0.701133i	−0.00659988	−	0.0222162i
$997$	−22.3957	−	22.3957i	−0.709279	−	0.709279i	0.257105	−	0.966384i	$-0.417232\pi$
$997$	−22.3957	−	22.3957i	−0.709279	−	0.709279i	−0.966384	+	0.257105i	$0.917232\pi$
$998$	2.01438	−	0.292885i	0.0637642	−	0.00927113i
$999$	0.258467			0.00817754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.o.a.27.3	✓	72
4.3	odd	2	inner	260.2.o.a.27.20	yes	72
5.3	odd	4	inner	260.2.o.a.183.20	yes	72
20.3	even	4	inner	260.2.o.a.183.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.o.a.27.3	✓	72	1.1	even	1	trivial
260.2.o.a.27.20	yes	72	4.3	odd	2	inner
260.2.o.a.183.3	yes	72	20.3	even	4	inner
260.2.o.a.183.20	yes	72	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.39950 + 0.203483i) q^{2} +(0.0775283 + 0.0775283i) q^{3} +(1.91719 - 0.569548i) q^{4} +(0.871245 + 2.05935i) q^{5} +(-0.124276 - 0.0927250i) q^{6} +(-2.89635 + 2.89635i) q^{7} +(-2.56721 + 1.18720i) q^{8} -2.98798i q^{9} +O(q^{10})\)	\(q+(-1.39950 + 0.203483i) 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} +(-2.56721 + 1.18720i) q^{8} -2.98798i q^{9} +(-1.63835 - 2.70478i) q^{10} +3.20102i q^{11} +(0.192792 + 0.104480i) 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} +(0.608002 + 4.18167i) q^{18} -5.01907 q^{19} +(2.84324 + 3.45195i) q^{20} -0.449098 q^{21} +(-0.651354 - 4.47983i) 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} +(-3.90325 + 7.20247i) q^{28} +9.89914i q^{29} +(0.0826782 - 0.336715i) q^{30} -2.20528i q^{31} +(-4.24566 + 3.73823i) 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} +(7.02418 - 1.02129i) q^{38} -0.109642 q^{39} +(-4.68152 - 4.25245i) q^{40} +5.39487 q^{41} +(0.628512 - 0.0913838i) 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} +(0.429126 + 0.0905041i) q^{48} -9.77772i q^{49} +(4.14268 - 5.73046i) q^{50} -0.0337736i q^{51} +(-0.952927 + 1.75839i) 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} +(-2.01431 - 13.8538i) q^{58} +9.66566 q^{59} +(-0.0471923 + 0.488055i) q^{60} +10.8601 q^{61} +(0.448738 + 3.08629i) 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} +(-0.541649 - 0.293537i) q^{68} +0.623810i q^{69} +(12.5792 + 3.08875i) q^{70} -11.8869i q^{71} +(3.54732 + 7.67077i) 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} +(0.153443 - 0.0223102i) q^{78} -6.73412 q^{79} +(7.41708 + 4.99869i) q^{80} -8.89195 q^{81} +(-7.55010 + 1.09776i) 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} +(-3.80024 - 8.21770i) q^{88} +16.4054i q^{89} +(-8.08181 + 4.89535i) q^{90} -4.09606i q^{91} +(10.0044 + 5.42171i) 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} +(1.98960 + 13.6839i) 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