LMFDB - Embedded newform 260.2.o.a.27.5

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			27.5
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32767 - 0.487116i) q^{2} +(0.396814 + 0.396814i) q^{3} +(1.52544 + 1.29346i) q^{4} +(2.02359 - 0.951360i) q^{5} +(-0.333545 - 0.720134i) q^{6} +(0.477103 - 0.477103i) q^{7} +(-1.39521 - 2.46036i) q^{8} -2.68508i q^{9} +O(q^{10})$	\(q+(-1.32767 - 0.487116i) q^{2} +(0.396814 + 0.396814i) q^{3} +(1.52544 + 1.29346i) q^{4} +(2.02359 - 0.951360i) q^{5} +(-0.333545 - 0.720134i) q^{6} +(0.477103 - 0.477103i) q^{7} +(-1.39521 - 2.46036i) q^{8} -2.68508i q^{9} +(-3.15009 + 0.277373i) q^{10} +4.12967i q^{11} +(0.0920497 + 1.11858i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-0.865843 + 0.401033i) q^{14} +(1.18050 + 0.425475i) q^{15} +(0.653905 + 3.94619i) q^{16} +(-0.282654 - 0.282654i) q^{17} +(-1.30795 + 3.56491i) q^{18} +6.79601 q^{19} +(4.31740 + 1.16620i) q^{20} +0.378643 q^{21} +(2.01163 - 5.48285i) q^{22} +(-4.18589 - 4.18589i) q^{23} +(0.422666 - 1.52995i) q^{24} +(3.18983 - 3.85033i) q^{25} +(-1.28325 + 0.594364i) q^{26} +(2.25592 - 2.25592i) q^{27} +(1.34491 - 0.110675i) q^{28} -2.26050i q^{29} +(-1.36006 - 1.13993i) q^{30} +6.38658i q^{31} +(1.05408 - 5.55778i) q^{32} +(-1.63871 + 1.63871i) q^{33} +(0.237587 + 0.512957i) q^{34} +(0.511564 - 1.41936i) q^{35} +(3.47305 - 4.09591i) q^{36} +(3.49062 + 3.49062i) q^{37} +(-9.02288 - 3.31045i) q^{38} +0.561180 q^{39} +(-5.16403 - 3.65141i) q^{40} +3.13240 q^{41} +(-0.502714 - 0.184443i) q^{42} +(-3.14184 - 3.14184i) q^{43} +(-5.34158 + 6.29954i) q^{44} +(-2.55448 - 5.43349i) q^{45} +(3.51848 + 7.59651i) q^{46} +(-2.10301 + 2.10301i) q^{47} +(-1.30642 + 1.82538i) q^{48} +6.54474i q^{49} +(-6.11061 + 3.55816i) q^{50} -0.224322i q^{51} +(1.99326 - 0.164029i) q^{52} +(-3.55189 + 3.55189i) q^{53} +(-4.09402 + 1.89623i) q^{54} +(3.92880 + 8.35675i) q^{55} +(-1.83951 - 0.508186i) q^{56} +(2.69675 + 2.69675i) q^{57} +(-1.10113 + 3.00120i) q^{58} -11.1882 q^{59} +(1.25044 + 2.17597i) q^{60} +1.24825 q^{61} +(3.11101 - 8.47930i) q^{62} +(-1.28106 - 1.28106i) q^{63} +(-4.10676 + 6.86546i) q^{64} +(0.758180 - 2.10361i) q^{65} +(2.97391 - 1.37743i) q^{66} +(-8.43829 + 8.43829i) q^{67} +(-0.0655677 - 0.796772i) q^{68} -3.32204i q^{69} +(-1.37058 + 1.63525i) q^{70} -14.8287i q^{71} +(-6.60626 + 3.74626i) q^{72} +(-3.39058 + 3.39058i) q^{73} +(-2.93406 - 6.33473i) q^{74} +(2.79363 - 0.262095i) q^{75} +(10.3669 + 8.79039i) q^{76} +(1.97028 + 1.97028i) q^{77} +(-0.745063 - 0.273360i) q^{78} -10.1932 q^{79} +(5.07748 + 7.36337i) q^{80} -6.26487 q^{81} +(-4.15881 - 1.52584i) q^{82} +(0.412265 + 0.412265i) q^{83} +(0.577595 + 0.489760i) q^{84} +(-0.840880 - 0.303069i) q^{85} +(2.64090 + 5.70178i) q^{86} +(0.896997 - 0.896997i) q^{87} +(10.1605 - 5.76177i) q^{88} +16.9524i q^{89} +(0.744767 + 8.45823i) q^{90} -0.674726i q^{91} +(-0.971008 - 11.7996i) q^{92} +(-2.53429 + 2.53429i) q^{93} +(3.81652 - 1.76770i) q^{94} +(13.7523 - 6.46545i) q^{95} +(2.62368 - 1.78713i) q^{96} +(-2.59742 - 2.59742i) q^{97} +(3.18805 - 8.68929i) q^{98} +11.0885 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 $

$2$	−1.32767	−	0.487116i	−0.938807	−	0.344443i
$2$	−1.32767	−	0.487116i	−0.938807	−	0.344443i
$3$	0.396814	+	0.396814i	0.229101	+	0.229101i	0.812317	−	0.583216i	$-0.198206\pi$
$3$	0.396814	+	0.396814i	0.229101	+	0.229101i	−0.583216	+	0.812317i	$0.698206\pi$
$4$	1.52544	+	1.29346i	0.762718	+	0.646732i
$5$	2.02359	−	0.951360i	0.904977	−	0.425461i
$5$	2.02359	−	0.951360i	0.904977	−	0.425461i
$6$	−0.333545	−	0.720134i	−0.136169	−	0.293993i
$7$	0.477103	−	0.477103i	0.180328	−	0.180328i	−0.611171	−	0.791499i	$-0.709301\pi$
$7$	0.477103	−	0.477103i	0.180328	−	0.180328i	0.791499	+	0.611171i	$0.209301\pi$
$8$	−1.39521	−	2.46036i	−0.493282	−	0.869869i
$9$		−	2.68508i		−	0.895026i
$10$	−3.15009	+	0.277373i	−0.996146	+	0.0877130i
$11$			4.12967i			1.24514i	0.782563	+	0.622571i	$0.213912\pi$
$11$			4.12967i			1.24514i	−0.782563	+	0.622571i	$0.786088\pi$
$12$	0.0920497	+	1.11858i	0.0265725	+	0.322906i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$	−0.865843	+	0.401033i	−0.231406	+	0.107181i
$15$	1.18050	+	0.425475i	0.304804	+	0.109857i
$16$	0.653905	+	3.94619i	0.163476	+	0.986547i
$17$	−0.282654	−	0.282654i	−0.0685536	−	0.0685536i	0.671999	−	0.740552i	$-0.265436\pi$
$17$	−0.282654	−	0.282654i	−0.0685536	−	0.0685536i	−0.740552	+	0.671999i	$0.765436\pi$
$18$	−1.30795	+	3.56491i	−0.308286	+	0.840257i
$19$	6.79601			1.55911			0.779555	−	0.626333i	$-0.215445\pi$
$19$	6.79601			1.55911			0.779555	+	0.626333i	$0.215445\pi$
$20$	4.31740	+	1.16620i	0.965401	+	0.260770i
$21$	0.378643			0.0826266
$22$	2.01163	−	5.48285i	0.428881	−	1.16895i
$23$	−4.18589	−	4.18589i	−0.872818	−	0.872818i	0.119961	−	0.992779i	$-0.461723\pi$
$23$	−4.18589	−	4.18589i	−0.872818	−	0.872818i	−0.992779	+	0.119961i	$0.961723\pi$
$24$	0.422666	−	1.52995i	0.0862763	−	0.312299i
$25$	3.18983	−	3.85033i	0.637965	−	0.770065i
$26$	−1.28325	+	0.594364i	−0.251666	+	0.116564i
$27$	2.25592	−	2.25592i	0.434152	−	0.434152i
$28$	1.34491	−	0.110675i	0.254163	−	0.0209155i
$29$		−	2.26050i		−	0.419764i	−0.977727	−	0.209882i	$-0.932692\pi$
$29$		−	2.26050i		−	0.419764i	0.977727	−	0.209882i	$-0.0673080\pi$
$30$	−1.36006	−	1.13993i	−0.248313	−	0.208123i
$31$			6.38658i			1.14706i	0.819183	+	0.573532i	$0.194427\pi$
$31$			6.38658i			1.14706i	−0.819183	+	0.573532i	$0.805573\pi$
$32$	1.05408	−	5.55778i	0.186337	−	0.982486i
$33$	−1.63871	+	1.63871i	−0.285263	+	0.285263i
$34$	0.237587	+	0.512957i	0.0407458	+	0.0879714i
$35$	0.511564	−	1.41936i	0.0864701	−	0.239915i
$36$	3.47305	−	4.09591i	0.578842	−	0.682652i
$37$	3.49062	+	3.49062i	0.573854	+	0.573854i	0.933203	−	0.359349i	$-0.117001\pi$
$37$	3.49062	+	3.49062i	0.573854	+	0.573854i	−0.359349	+	0.933203i	$0.617001\pi$
$38$	−9.02288	−	3.31045i	−1.46370	−	0.537025i
$39$	0.561180			0.0898607
$40$	−5.16403	−	3.65141i	−0.816505	−	0.577339i
$41$	3.13240			0.489199			0.244599	−	0.969624i	$-0.421344\pi$
$41$	3.13240			0.489199			0.244599	+	0.969624i	$0.421344\pi$
$42$	−0.502714	−	0.184443i	−0.0775704	−	0.0284602i
$43$	−3.14184	−	3.14184i	−0.479126	−	0.479126i	0.425726	−	0.904852i	$-0.360019\pi$
$43$	−3.14184	−	3.14184i	−0.479126	−	0.479126i	−0.904852	+	0.425726i	$0.860019\pi$
$44$	−5.34158	+	6.29954i	−0.805273	+	0.949692i
$45$	−2.55448	−	5.43349i	−0.380799	−	0.809977i
$46$	3.51848	+	7.59651i	0.518771	+	1.12004i
$47$	−2.10301	+	2.10301i	−0.306756	+	0.306756i	−0.843650	−	0.536894i	$-0.819598\pi$
$47$	−2.10301	+	2.10301i	−0.306756	+	0.306756i	0.536894	+	0.843650i	$0.319598\pi$
$48$	−1.30642	+	1.82538i	−0.188566	+	0.263471i
$49$			6.54474i			0.934964i
$50$	−6.11061	+	3.55816i	−0.864170	+	0.503200i
$51$		−	0.224322i		−	0.0314113i
$52$	1.99326	−	0.164029i	0.276416	−	0.0227467i
$53$	−3.55189	+	3.55189i	−0.487890	+	0.487890i	−0.907640	−	0.419750i	$-0.862118\pi$
$53$	−3.55189	+	3.55189i	−0.487890	+	0.487890i	0.419750	+	0.907640i	$0.362118\pi$
$54$	−4.09402	+	1.89623i	−0.557125	+	0.258044i
$55$	3.92880	+	8.35675i	0.529760	+	1.12682i
$56$	−1.83951	−	0.508186i	−0.245815	−	0.0679092i
$57$	2.69675	+	2.69675i	0.357193	+	0.357193i
$58$	−1.10113	+	3.00120i	−0.144585	+	0.394077i
$59$	−11.1882			−1.45658			−0.728291	−	0.685268i	$-0.759685\pi$
$59$	−11.1882			−1.45658			−0.728291	+	0.685268i	$0.759685\pi$
$60$	1.25044	+	2.17597i	0.161431	+	0.280917i
$61$	1.24825			0.159821			0.0799107	−	0.996802i	$-0.474536\pi$
$61$	1.24825			0.159821			0.0799107	+	0.996802i	$0.474536\pi$
$62$	3.11101	−	8.47930i	0.395099	−	1.07687i
$63$	−1.28106	−	1.28106i	−0.161398	−	0.161398i
$64$	−4.10676	+	6.86546i	−0.513345	+	0.858182i
$65$	0.758180	−	2.10361i	0.0940407	−	0.260920i
$66$	2.97391	−	1.37743i	0.366064	−	0.169550i
$67$	−8.43829	+	8.43829i	−1.03090	+	1.03090i	−0.0313946	+	0.999507i	$0.509995\pi$
$67$	−8.43829	+	8.43829i	−1.03090	+	1.03090i	−0.999507	+	0.0313946i	$0.990005\pi$
$68$	−0.0655677	−	0.796772i	−0.00795125	−	0.0966228i
$69$		−	3.32204i		−	0.399926i
$70$	−1.37058	+	1.63525i	−0.163816	+	0.195450i
$71$		−	14.8287i		−	1.75985i	−0.475116	−	0.879923i	$-0.657594\pi$
$71$		−	14.8287i		−	1.75985i	0.475116	−	0.879923i	$-0.342406\pi$
$72$	−6.60626	+	3.74626i	−0.778555	+	0.441500i
$73$	−3.39058	+	3.39058i	−0.396837	+	0.396837i	−0.877116	−	0.480279i	$-0.840536\pi$
$73$	−3.39058	+	3.39058i	−0.396837	+	0.396837i	0.480279	+	0.877116i	$0.340536\pi$
$74$	−2.93406	−	6.33473i	−0.341078	−	0.736398i
$75$	2.79363	−	0.262095i	0.322581	−	0.0302641i
$76$	10.3669	+	8.79039i	1.18916	+	1.00833i
$77$	1.97028	+	1.97028i	0.224534	+	0.224534i
$78$	−0.745063	−	0.273360i	−0.0843618	−	0.0309519i
$79$	−10.1932			−1.14683			−0.573415	−	0.819265i	$-0.694382\pi$
$79$	−10.1932			−1.14683			−0.573415	+	0.819265i	$0.694382\pi$
$80$	5.07748	+	7.36337i	0.567680	+	0.823249i
$81$	−6.26487			−0.696097
$82$	−4.15881	−	1.52584i	−0.459263	−	0.168501i
$83$	0.412265	+	0.412265i	0.0452520	+	0.0452520i	0.729371	−	0.684119i	$-0.239813\pi$
$83$	0.412265	+	0.412265i	0.0452520	+	0.0452520i	−0.684119	+	0.729371i	$0.739813\pi$
$84$	0.577595	+	0.489760i	0.0630207	+	0.0534372i
$85$	−0.840880	−	0.303069i	−0.0912063	−	0.0328725i
$86$	2.64090	+	5.70178i	0.284775	+	0.614838i
$87$	0.896997	−	0.896997i	0.0961682	−	0.0961682i
$88$	10.1605	−	5.76177i	1.08311	−	0.614207i
$89$			16.9524i			1.79696i	0.439020	+	0.898478i	$0.355326\pi$
$89$			16.9524i			1.79696i	−0.439020	+	0.898478i	$0.644674\pi$
$90$	0.744767	+	8.45823i	0.0785054	+	0.891576i
$91$		−	0.674726i		−	0.0707305i
$92$	−0.971008	−	11.7996i	−0.101235	−	1.23019i
$93$	−2.53429	+	2.53429i	−0.262793	+	0.262793i
$94$	3.81652	−	1.76770i	0.393644	−	0.182325i
$95$	13.7523	−	6.46545i	1.41096	−	0.663341i
$96$	2.62368	−	1.78713i	0.267778	−	0.182398i
$97$	−2.59742	−	2.59742i	−0.263728	−	0.263728i	0.562839	−	0.826567i	$-0.309709\pi$
$97$	−2.59742	−	2.59742i	−0.263728	−	0.263728i	−0.826567	+	0.562839i	$0.809709\pi$
$98$	3.18805	−	8.68929i	0.322042	−	0.877750i
$99$	11.0885			1.11443
$100$	9.84613	−	1.74750i	0.984613	−	0.174750i
$101$	−12.5028			−1.24407			−0.622036	−	0.782989i	$-0.713694\pi$
$101$	−12.5028			−1.24407			−0.622036	+	0.782989i	$0.713694\pi$
$102$	−0.109271	+	0.297826i	−0.0108194	+	0.0294892i
$103$	−3.40360	−	3.40360i	−0.335367	−	0.335367i	0.519253	−	0.854620i	$-0.326210\pi$
$103$	−3.40360	−	3.40360i	−0.335367	−	0.335367i	−0.854620	+	0.519253i	$0.826210\pi$
$104$	−2.72630	−	0.753174i	−0.267336	−	0.0738548i
$105$	0.766217	−	0.360226i	0.0747751	−	0.0351544i
$106$	6.44594	−	2.98557i	0.626085	−	0.289984i
$107$	3.92371	−	3.92371i	0.379319	−	0.379319i	−0.491537	−	0.870857i	$-0.663565\pi$
$107$	3.92371	−	3.92371i	0.379319	−	0.379319i	0.870857	+	0.491537i	$0.163565\pi$
$108$	6.35920	−	0.523310i	0.611915	−	0.0503555i
$109$		−	14.3064i		−	1.37030i	−0.728401	−	0.685151i	$-0.759736\pi$
$109$		−	14.3064i		−	1.37030i	0.728401	−	0.685151i	$-0.240264\pi$
$110$	−1.14546	−	13.0088i	−0.109215	−	1.24034i
$111$			2.77025i			0.262940i
$112$	2.19472	+	1.57076i	0.207382	+	0.148423i
$113$	−11.2325	+	11.2325i	−1.05667	+	1.05667i	−0.0583738	+	0.998295i	$0.518592\pi$
$113$	−11.2325	+	11.2325i	−1.05667	+	1.05667i	−0.998295	+	0.0583738i	$0.981408\pi$
$114$	−2.26677	−	4.89403i	−0.212303	−	0.458368i
$115$	−12.4528	−	4.48823i	−1.16123	−	0.418530i
$116$	2.92387	−	3.44824i	0.271475	−	0.320161i
$117$	−1.89864	−	1.89864i	−0.175529	−	0.175529i
$118$	14.8543	+	5.44996i	1.36745	+	0.501710i
$119$	−0.269710			−0.0247243
$120$	−0.600228	−	3.49809i	−0.0547931	−	0.319330i
$121$	−6.05417			−0.550379
$122$	−1.65726	−	0.608041i	−0.150041	−	0.0550494i
$123$	1.24298	+	1.24298i	0.112076	+	0.112076i
$124$	−8.26081	+	9.74232i	−0.741843	+	0.874886i
$125$	2.79185	−	10.8262i	0.249711	−	0.968320i
$126$	1.07680	+	2.32485i	0.0959293	+	0.207114i
$127$	9.47642	−	9.47642i	0.840896	−	0.840896i	−0.148079	−	0.988976i	$-0.547309\pi$
$127$	9.47642	−	9.47642i	0.840896	−	0.840896i	0.988976	+	0.148079i	$0.0473090\pi$
$128$	8.79672	−	7.11462i	0.777527	−	0.628849i
$129$		−	2.49345i		−	0.219536i
$130$	−2.03132	+	2.42358i	−0.178158	+	0.212562i
$131$		−	0.403054i		−	0.0352150i	−0.999845	−	0.0176075i	$-0.994395\pi$
$131$		−	0.403054i		−	0.0352150i	0.999845	−	0.0176075i	$-0.00560493\pi$
$132$	−4.61936	+	0.380135i	−0.402063	+	0.0330865i
$133$	3.24240	−	3.24240i	0.281152	−	0.281152i
$134$	15.3137	−	7.09287i	1.32290	−	0.612731i
$135$	2.41886	−	6.71124i	0.208182	−	0.577612i
$136$	−0.301068	+	1.08979i	−0.0258164	+	0.0934489i
$137$	15.0673	+	15.0673i	1.28729	+	1.28729i	0.936429	+	0.350857i	$0.114110\pi$
$137$	15.0673	+	15.0673i	1.28729	+	1.28729i	0.350857	+	0.936429i	$0.385890\pi$
$138$	−1.61822	+	4.41058i	−0.137752	+	0.375454i
$139$	8.60240			0.729646			0.364823	−	0.931077i	$-0.381129\pi$
$139$	8.60240			0.729646			0.364823	+	0.931077i	$0.381129\pi$
$140$	2.61625	−	1.50345i	0.221113	−	0.127065i
$141$	−1.66901			−0.140556
$142$	−7.22332	+	19.6877i	−0.606167	+	1.65216i
$143$	2.92012	+	2.92012i	0.244192	+	0.244192i
$144$	10.5958	−	1.75579i	0.882985	−	0.146316i
$145$	−2.15055	−	4.57432i	−0.178593	−	0.379876i
$146$	6.15319	−	2.84998i	0.509242	−	0.235866i
$147$	−2.59705	+	2.59705i	−0.214201	+	0.214201i
$148$	0.809725	+	9.83969i	0.0665590	+	0.808818i
$149$		−	13.3726i		−	1.09553i	−0.836632	−	0.547765i	$-0.815479\pi$
$149$		−	13.3726i		−	1.09553i	0.836632	−	0.547765i	$-0.184521\pi$
$150$	−3.83670	−	1.01285i	−0.313265	−	0.0826986i
$151$			13.1674i			1.07155i	0.844362	+	0.535774i	$0.179980\pi$
$151$			13.1674i			1.07155i	−0.844362	+	0.535774i	$0.820020\pi$
$152$	−9.48188	−	16.7206i	−0.769082	−	1.35622i
$153$	−0.758947	+	0.758947i	−0.0613572	+	0.0613572i
$154$	−1.65613	−	3.57564i	−0.133455	−	0.288134i
$155$	6.07594	+	12.9238i	0.488031	+	1.03807i
$156$	0.856043	+	0.725865i	0.0685383	+	0.0581157i
$157$	2.96750	+	2.96750i	0.236832	+	0.236832i	0.815537	−	0.578705i	$-0.196442\pi$
$157$	2.96750	+	2.96750i	0.236832	+	0.236832i	−0.578705	+	0.815537i	$0.696442\pi$
$158$	13.5333	+	4.96530i	1.07665	+	0.395018i
$159$	−2.81888			−0.223552
$160$	−3.15443	−	12.2495i	−0.249379	−	0.968406i
$161$	−3.99420			−0.314787
$162$	8.31771	+	3.05172i	0.653501	+	0.239766i
$163$	6.43698	+	6.43698i	0.504183	+	0.504183i	0.912735	−	0.408552i	$-0.133966\pi$
$163$	6.43698	+	6.43698i	0.504183	+	0.504183i	−0.408552	+	0.912735i	$0.633966\pi$
$164$	4.77828	+	4.05165i	0.373121	+	0.316380i
$165$	−1.75707	+	4.87508i	−0.136788	+	0.379524i
$166$	−0.346533	−	0.748175i	−0.0268961	−	0.0580696i
$167$	−17.4526	+	17.4526i	−1.35052	+	1.35052i	−0.465448	+	0.885075i	$0.654107\pi$
$167$	−17.4526	+	17.4526i	−1.35052	+	1.35052i	−0.885075	+	0.465448i	$0.845893\pi$
$168$	−0.528287	−	0.931598i	−0.0407582	−	0.0718743i
$169$		−	1.00000i		−	0.0769231i
$170$	0.968785	+	0.811984i	0.0743024	+	0.0622763i
$171$		−	18.2478i		−	1.39544i
$172$	−0.728818	−	8.85652i	−0.0555719	−	0.675304i
$173$	4.74226	−	4.74226i	0.360547	−	0.360547i	−0.503467	−	0.864014i	$-0.667942\pi$
$173$	4.74226	−	4.74226i	0.360547	−	0.360547i	0.864014	+	0.503467i	$0.167942\pi$
$174$	−1.62786	+	0.753977i	−0.123408	+	0.0571589i
$175$	−0.315126	−	3.35888i	−0.0238213	−	0.253908i
$176$	−16.2965	+	2.70041i	−1.22839	+	0.203551i
$177$	−4.43964	−	4.43964i	−0.333704	−	0.333704i
$178$	8.25781	−	22.5073i	0.618949	−	1.68699i
$179$	−11.6248			−0.868879			−0.434439	−	0.900701i	$-0.643053\pi$
$179$	−11.6248			−0.868879			−0.434439	+	0.900701i	$0.643053\pi$
$180$	3.13134	−	11.5926i	0.233396	−	0.864059i
$181$	6.67011			0.495786			0.247893	−	0.968787i	$-0.420262\pi$
$181$	6.67011			0.495786			0.247893	+	0.968787i	$0.420262\pi$
$182$	−0.328670	+	0.895816i	−0.0243627	+	0.0664023i
$183$	0.495321	+	0.495321i	0.0366152	+	0.0366152i
$184$	−4.45859	+	16.1390i	−0.328692	+	1.18978i
$185$	10.3844	+	3.74274i	0.763477	+	0.275172i
$186$	4.59920	−	2.13021i	0.337229	−	0.156195i
$187$	1.16727	−	1.16727i	0.0853589	−	0.0853589i
$188$	−5.92818	+	0.487840i	−0.432357	+	0.0355794i
$189$		−	2.15261i		−	0.156579i
$190$	−21.4080	+	1.88503i	−1.55310	+	0.136754i
$191$		−	2.00979i		−	0.145423i	−0.997353	−	0.0727116i	$-0.976835\pi$
$191$		−	2.00979i		−	0.145423i	0.997353	−	0.0727116i	$-0.0231653\pi$
$192$	−4.35393	+	1.09469i	−0.314218	+	0.0790024i
$193$	−13.8316	+	13.8316i	−0.995621	+	0.995621i	−0.999990	−	0.00436966i	$-0.998609\pi$
$193$	−13.8316	+	13.8316i	−0.995621	+	0.995621i	0.00436966	+	0.999990i	$0.498609\pi$
$194$	2.18328	+	4.71377i	0.156750	+	0.338429i
$195$	1.13560	−	0.533884i	0.0813218	−	0.0382322i
$196$	−8.46539	+	9.98358i	−0.604671	+	0.713113i
$197$	4.54345	+	4.54345i	0.323708	+	0.323708i	0.850188	−	0.526480i	$-0.176488\pi$
$197$	4.54345	+	4.54345i	0.323708	+	0.323708i	−0.526480	+	0.850188i	$0.676488\pi$
$198$	−14.7219	−	5.40138i	−1.04624	−	0.383859i
$199$	9.96517			0.706412			0.353206	−	0.935546i	$-0.385091\pi$
$199$	9.96517			0.706412			0.353206	+	0.935546i	$0.385091\pi$
$200$	−13.9237	−	2.47610i	−0.984553	−	0.175087i
$201$	−6.69686			−0.472360
$202$	16.5996	+	6.09030i	1.16794	+	0.428512i
$203$	−1.07849	−	1.07849i	−0.0756952	−	0.0756952i
$204$	0.290152	−	0.342188i	0.0203147	−	0.0239580i
$205$	6.33869	−	2.98004i	0.442714	−	0.208135i
$206$	2.86092	+	6.17682i	0.199330	+	0.430360i
$207$	−11.2394	+	11.2394i	−0.781195	+	0.781195i
$208$	3.25276	+	2.32800i	0.225538	+	0.161417i
$209$			28.0653i			1.94131i
$210$	−1.19276	+	0.105025i	−0.0823081	+	0.00724742i
$211$		−	13.5418i		−	0.932253i	−0.884718	−	0.466127i	$-0.845649\pi$
$211$		−	13.5418i		−	0.932253i	0.884718	−	0.466127i	$-0.154351\pi$
$212$	−10.0124	+	0.823940i	−0.687656	+	0.0565884i
$213$	5.88425	−	5.88425i	0.403182	−	0.403182i
$214$	−7.12071	+	3.29810i	−0.486762	+	0.225454i
$215$	−9.34681	−	3.36877i	−0.637447	−	0.229748i
$216$	−8.69786	−	2.40289i	−0.591814	−	0.163496i
$217$	3.04706	+	3.04706i	0.206848	+	0.206848i
$218$	−6.96887	+	18.9942i	−0.471992	+	1.28645i
$219$	−2.69086			−0.181831
$220$	−4.81602	+	17.8295i	−0.324696	+	1.20206i
$221$	−0.399733			−0.0268889
$222$	1.34943	−	3.67799i	0.0905681	−	0.246850i
$223$	4.34527	+	4.34527i	0.290981	+	0.290981i	0.837468	−	0.546487i	$-0.184035\pi$
$223$	4.34527	+	4.34527i	0.290981	+	0.290981i	−0.546487	+	0.837468i	$0.684035\pi$
$224$	−2.14873	−	3.15454i	−0.143568	−	0.210772i
$225$	−10.3384	−	8.56493i	−0.689228	−	0.570995i
$226$	20.3847	−	9.44159i	1.35597	−	0.628046i
$227$	1.20822	−	1.20822i	0.0801924	−	0.0801924i	−0.665873	−	0.746065i	$-0.731941\pi$
$227$	1.20822	−	1.20822i	0.0801924	−	0.0801924i	0.746065	+	0.665873i	$0.231941\pi$
$228$	0.625570	+	7.60186i	0.0414294	+	0.503446i
$229$		−	28.9612i		−	1.91381i	−0.290401	−	0.956905i	$-0.593789\pi$
$229$		−	28.9612i		−	1.91381i	0.290401	−	0.956905i	$-0.406211\pi$
$230$	14.3470	+	12.0249i	0.946012	+	0.792897i
$231$			1.56367i			0.102882i
$232$	−5.56164	+	3.15388i	−0.365140	+	0.207062i
$233$	4.66377	−	4.66377i	0.305534	−	0.305534i	−0.537640	−	0.843174i	$-0.680684\pi$
$233$	4.66377	−	4.66377i	0.305534	−	0.305534i	0.843174	+	0.537640i	$0.180684\pi$
$234$	1.59591	+	3.44563i	0.104328	+	0.225248i
$235$	−2.25491	+	6.25635i	−0.147094	+	0.408120i
$236$	−17.0669	−	14.4715i	−1.11096	−	0.942017i
$237$	−4.04482	−	4.04482i	−0.262739	−	0.262739i
$238$	0.358087	+	0.131380i	0.0232113	+	0.00851611i
$239$	−3.91031			−0.252937			−0.126468	−	0.991971i	$-0.540364\pi$
$239$	−3.91031			−0.252937			−0.126468	+	0.991971i	$0.540364\pi$
$240$	−0.907070	+	4.93670i	−0.0585511	+	0.318663i
$241$	−4.12175			−0.265505			−0.132753	−	0.991149i	$-0.542382\pi$
$241$	−4.12175			−0.265505			−0.132753	+	0.991149i	$0.542382\pi$
$242$	8.03796	+	2.94908i	0.516700	+	0.189574i
$243$	−9.25374	−	9.25374i	−0.593628	−	0.593628i
$244$	1.90412	+	1.61456i	0.121899	+	0.103362i
$245$	6.22641	+	13.2439i	0.397791	+	0.846120i
$246$	−1.04480	−	2.25575i	−0.0666138	−	0.143821i
$247$	4.80550	−	4.80550i	0.305767	−	0.305767i
$248$	15.7133	−	8.91065i	0.997796	−	0.565827i
$249$			0.327185i			0.0207345i
$250$	−8.98026	+	13.0136i	−0.567962	+	0.823055i
$251$			10.0017i			0.631302i	0.948875	+	0.315651i	$0.102223\pi$
$251$			10.0017i			0.631302i	−0.948875	+	0.315651i	$0.897777\pi$
$252$	−0.297170	−	3.61118i	−0.0187199	−	0.227483i
$253$	17.2863	−	17.2863i	1.08678	−	1.08678i
$254$	−17.1977	+	7.96548i	−1.07908	+	0.499798i
$255$	−0.213411	−	0.453935i	−0.0133643	−	0.0284265i
$256$	−15.1448	+	5.16087i	−0.946551	+	0.322554i
$257$	4.10932	+	4.10932i	0.256332	+	0.256332i	0.823561	−	0.567228i	$-0.191984\pi$
$257$	4.10932	+	4.10932i	0.256332	+	0.256332i	−0.567228	+	0.823561i	$0.691984\pi$
$258$	−1.21460	+	3.31049i	−0.0756177	+	0.206102i
$259$	3.33077			0.206964
$260$	3.87749	−	2.22824i	0.240472	−	0.138189i
$261$	−6.06961			−0.375699
$262$	−0.196334	+	0.535124i	−0.0121296	+	0.0330601i
$263$	0.476830	+	0.476830i	0.0294026	+	0.0294026i	0.721655	−	0.692253i	$-0.243382\pi$
$263$	0.476830	+	0.476830i	0.0294026	+	0.0294026i	−0.692253	+	0.721655i	$0.743382\pi$
$264$	6.31817	+	1.74547i	0.388856	+	0.107426i
$265$	−3.80844	+	10.5667i	−0.233951	+	0.649108i
$266$	−5.88427	+	2.72542i	−0.360788	+	0.167106i
$267$	−6.72696	+	6.72696i	−0.411683	+	0.411683i
$268$	−23.7867	+	1.95745i	−1.45300	+	0.119570i
$269$			4.67122i			0.284810i	0.989809	+	0.142405i	$0.0454835\pi$
$269$			4.67122i			0.284810i	−0.989809	+	0.142405i	$0.954517\pi$
$270$	−6.48061	+	7.73207i	−0.394398	+	0.470559i
$271$		−	23.3689i		−	1.41956i	−0.704423	−	0.709781i	$-0.748794\pi$
$271$		−	23.3689i		−	1.41956i	0.704423	−	0.709781i	$-0.251206\pi$
$272$	0.930576	−	1.30023i	0.0564245	−	0.0788382i
$273$	0.267741	−	0.267741i	0.0162044	−	0.0162044i
$274$	−12.6649	−	27.3440i	−0.765116	−	1.65191i
$275$	15.9006	+	13.1729i	0.958840	+	0.794358i
$276$	4.29693	−	5.06755i	0.258645	−	0.305031i
$277$	6.48537	+	6.48537i	0.389668	+	0.389668i	0.874569	−	0.484901i	$-0.161144\pi$
$277$	6.48537	+	6.48537i	0.389668	+	0.389668i	−0.484901	+	0.874569i	$0.661144\pi$
$278$	−11.4212	−	4.19037i	−0.684997	−	0.251322i
$279$	17.1485			1.02665
$280$	−4.20588	+	0.721675i	−0.251349	+	0.0431283i
$281$	22.1253			1.31988			0.659942	−	0.751317i	$-0.270581\pi$
$281$	22.1253			1.31988			0.659942	+	0.751317i	$0.270581\pi$
$282$	2.21590	+	0.813001i	0.131955	+	0.0484135i
$283$	12.3982	+	12.3982i	0.736994	+	0.736994i	0.971995	−	0.235001i	$-0.0755093\pi$
$283$	12.3982	+	12.3982i	0.736994	+	0.736994i	−0.235001	+	0.971995i	$0.575509\pi$
$284$	19.1804	−	22.6203i	1.13815	−	1.34227i
$285$	8.02269	+	2.89153i	0.475223	+	0.171280i
$286$	−2.45453	−	5.29940i	−0.145139	−	0.313360i
$287$	1.49448	−	1.49448i	0.0882163	−	0.0882163i
$288$	−14.9231	−	2.83029i	−0.879350	−	0.166776i
$289$		−	16.8402i		−	0.990601i
$290$	0.627000	+	7.12077i	0.0368187	+	0.418146i
$291$		−	2.06138i		−	0.120841i
$292$	−9.55770	+	0.786520i	−0.559322	+	0.0460276i
$293$	18.7805	−	18.7805i	1.09717	−	1.09717i	0.102425	−	0.994741i	$-0.467340\pi$
$293$	18.7805	−	18.7805i	1.09717	−	1.09717i	0.994741	−	0.102425i	$-0.0326602\pi$
$294$	4.71309	−	2.18297i	0.274873	−	0.127313i
$295$	−22.6403	+	10.6440i	−1.31817	+	0.619719i
$296$	3.71802	−	13.4583i	0.216106	−	0.782249i
$297$	9.31619	+	9.31619i	0.540580	+	0.540580i
$298$	−6.51404	+	17.7545i	−0.377348	+	1.02849i
$299$	−5.91974			−0.342347
$300$	4.60051	+	3.21365i	0.265611	+	0.185540i
$301$	−2.99796			−0.172800
$302$	6.41405	−	17.4820i	0.369087	−	1.00598i
$303$	−4.96127	−	4.96127i	−0.285018	−	0.285018i
$304$	4.44394	+	26.8183i	0.254878	+	1.53814i
$305$	2.52594	−	1.18753i	0.144635	−	0.0679978i
$306$	1.37733	−	0.637938i	0.0787367	−	0.0364685i
$307$	17.7535	−	17.7535i	1.01325	−	1.01325i	0.0133370	−	0.999911i	$-0.495755\pi$
$307$	17.7535	−	17.7535i	1.01325	−	1.01325i	0.999911	−	0.0133370i	$-0.00424541\pi$
$308$	0.457049	+	5.55402i	0.0260428	+	0.316470i
$309$		−	2.70119i		−	0.153665i
$310$	−1.77146	−	20.1183i	−0.100612	−	1.14264i
$311$			2.76330i			0.156692i	0.996926	+	0.0783462i	$0.0249639\pi$
$311$			2.76330i			0.156692i	−0.996926	+	0.0783462i	$0.975036\pi$
$312$	−0.782965	−	1.38070i	−0.0443267	−	0.0781670i
$313$	−15.3877	+	15.3877i	−0.869762	+	0.869762i	−0.992446	−	0.122684i	$-0.960850\pi$
$313$	−15.3877	+	15.3877i	−0.869762	+	0.869762i	0.122684	+	0.992446i	$0.460850\pi$
$314$	−2.49436	−	5.38539i	−0.140765	−	0.303915i
$315$	−3.81109	−	1.37359i	−0.214730	−	0.0773930i
$316$	−15.5491	−	13.1846i	−0.874707	−	0.741691i
$317$	7.69697	+	7.69697i	0.432305	+	0.432305i	0.889412	−	0.457107i	$-0.151114\pi$
$317$	7.69697	+	7.69697i	0.432305	+	0.432305i	−0.457107	+	0.889412i	$0.651114\pi$
$318$	3.74256	+	1.37312i	0.209872	+	0.0770009i
$319$	9.33511			0.522666
$320$	−1.77887	+	17.7999i	−0.0994419	+	0.995043i
$321$	3.11396			0.173805
$322$	5.30300	+	1.94564i	0.295525	+	0.108426i
$323$	−1.92092	−	1.92092i	−0.106883	−	0.106883i
$324$	−9.55666	−	8.10338i	−0.530925	−	0.450188i
$325$	−0.467043	−	4.97814i	−0.0259069	−	0.276137i
$326$	−5.41065	−	11.6818i	−0.299668	−	0.646993i
$327$	5.67697	−	5.67697i	0.313937	−	0.313937i
$328$	−4.37037	−	7.70684i	−0.241313	−	0.425539i
$329$			2.00671i			0.110633i
$330$	4.70755	−	5.61662i	0.259142	−	0.309185i
$331$			20.5227i			1.12803i	0.825764	+	0.564016i	$0.190744\pi$
$331$			20.5227i			1.12803i	−0.825764	+	0.564016i	$0.809256\pi$
$332$	0.0956339	+	1.16213i	0.00524859	+	0.0637804i
$333$	9.37257	−	9.37257i	0.513614	−	0.513614i
$334$	31.6728	−	14.6699i	1.73306	−	0.802702i
$335$	−9.04778	+	25.1035i	−0.494333	+	1.37155i
$336$	0.247596	+	1.49420i	0.0135075	+	0.0815150i
$337$	−21.6166	−	21.6166i	−1.17753	−	1.17753i	−0.980371	−	0.197160i	$-0.936828\pi$
$337$	−21.6166	−	21.6166i	−1.17753	−	1.17753i	−0.197160	−	0.980371i	$-0.563172\pi$
$338$	−0.487116	+	1.32767i	−0.0264956	+	0.0722159i
$339$	−8.91446			−0.484167
$340$	−0.890699	−	1.54996i	−0.0483050	−	0.0840584i
$341$	−26.3745			−1.42826
$342$	−8.88880	+	24.2271i	−0.480651	+	1.31005i
$343$	6.46224	+	6.46224i	0.348928	+	0.348928i
$344$	−3.34653	+	12.1136i	−0.180433	+	0.653121i
$345$	−3.16045	−	6.72244i	−0.170153	−	0.361924i
$346$	−8.60621	+	3.98614i	−0.462673	+	0.214296i
$347$	6.24824	−	6.24824i	0.335423	−	0.335423i	−0.519218	−	0.854642i	$-0.673777\pi$
$347$	6.24824	−	6.24824i	0.335423	−	0.335423i	0.854642	+	0.519218i	$0.173777\pi$
$348$	2.52854	−	0.208078i	0.135544	−	0.0111542i
$349$			3.89984i			0.208753i	0.994538	+	0.104377i	$0.0332848\pi$
$349$			3.89984i			0.208753i	−0.994538	+	0.104377i	$0.966715\pi$
$350$	−1.21778	+	4.61300i	−0.0650931	+	0.246575i
$351$		−	3.19035i		−	0.170288i
$352$	22.9518	+	4.35300i	1.22333	+	0.232016i
$353$	14.6707	−	14.6707i	0.780840	−	0.780840i	−0.199133	−	0.979973i	$-0.563812\pi$
$353$	14.6707	−	14.6707i	0.780840	−	0.780840i	0.979973	+	0.199133i	$0.0638124\pi$
$354$	3.73177	+	8.05701i	0.198341	+	0.428225i
$355$	−14.1075	−	30.0073i	−0.748747	−	1.59262i
$356$	−21.9274	+	25.8598i	−1.16215	+	1.37057i
$357$	−0.107025	−	0.107025i	−0.00566435	−	0.00566435i
$358$	15.4339	+	5.66263i	0.815709	+	0.299279i
$359$	24.5997			1.29832			0.649162	−	0.760650i	$-0.275120\pi$
$359$	24.5997			1.29832			0.649162	+	0.760650i	$0.275120\pi$
$360$	−9.80432	+	13.8658i	−0.516733	+	0.730793i
$361$	27.1857			1.43083
$362$	−8.85574	−	3.24912i	−0.465447	−	0.170770i
$363$	−2.40238	−	2.40238i	−0.126092	−	0.126092i
$364$	0.872734	−	1.02925i	0.0457437	−	0.0539474i
$365$	−3.63548	+	10.0868i	−0.190290	+	0.527968i
$366$	−0.416346	−	0.898904i	−0.0217627	−	0.0469864i
$367$	8.35046	−	8.35046i	0.435891	−	0.435891i	−0.454736	−	0.890626i	$-0.650266\pi$
$367$	8.35046	−	8.35046i	0.435891	−	0.435891i	0.890626	+	0.454736i	$0.150266\pi$
$368$	13.7811	−	19.2555i	0.718391	−	1.00376i
$369$		−	8.41074i		−	0.437846i
$370$	−11.9640	−	10.0275i	−0.621976	−	0.521307i
$371$			3.38924i			0.175961i
$372$	−7.14389	+	0.587883i	−0.370394	+	0.0304803i
$373$	−14.7736	+	14.7736i	−0.764948	+	0.764948i	−0.977212	−	0.212264i	$-0.931916\pi$
$373$	−14.7736	+	14.7736i	−0.764948	+	0.764948i	0.212264	+	0.977212i	$0.431916\pi$
$374$	−2.11834	+	0.981154i	−0.109537	+	0.0507343i
$375$	5.40381	−	3.18812i	0.279052	−	0.164634i
$376$	8.10832	+	2.24002i	0.418155	+	0.115520i
$377$	−1.59841	−	1.59841i	−0.0823225	−	0.0823225i
$378$	−1.04857	+	2.85797i	−0.0539328	+	0.146998i
$379$	−13.3405			−0.685256			−0.342628	−	0.939471i	$-0.611317\pi$
$379$	−13.3405			−0.685256			−0.342628	+	0.939471i	$0.611317\pi$
$380$	29.3411	+	7.92550i	1.50517	+	0.406570i
$381$	7.52075			0.385300
$382$	−0.979001	+	2.66834i	−0.0500900	+	0.136524i
$383$	23.6943	+	23.6943i	1.21072	+	1.21072i	0.970789	+	0.239933i	$0.0771254\pi$
$383$	23.6943	+	23.6943i	1.21072	+	1.21072i	0.239933	+	0.970789i	$0.422875\pi$
$384$	6.31384	+	0.667480i	0.322202	+	0.0340622i
$385$	5.86148	+	2.11259i	0.298729	+	0.107668i
$386$	25.1015	−	11.6263i	1.27763	−	0.591761i
$387$	−8.43608	+	8.43608i	−0.428830	+	0.428830i
$388$	−0.602528	−	7.32186i	−0.0305887	−	0.371711i
$389$			2.92067i			0.148084i	0.997255	+	0.0740418i	$0.0235898\pi$
$389$			2.92067i			0.148084i	−0.997255	+	0.0740418i	$0.976410\pi$
$390$	−1.76777	+	0.155656i	−0.0895143	+	0.00788194i
$391$			2.36631i			0.119670i
$392$	16.1024	−	9.13131i	0.813296	−	0.461201i
$393$	0.159938	−	0.159938i	0.00806778	−	0.00806778i
$394$	−3.81903	−	8.24541i	−0.192400	−	0.415398i
$395$	−20.6269	+	9.69745i	−1.03785	+	0.487932i
$396$	16.9148	+	14.3425i	0.849999	+	0.720740i
$397$	−18.8464	−	18.8464i	−0.945876	−	0.945876i	0.0527325	−	0.998609i	$-0.483207\pi$
$397$	−18.8464	−	18.8464i	−0.945876	−	0.945876i	−0.998609	+	0.0527325i	$0.983207\pi$
$398$	−13.2305	−	4.85420i	−0.663185	−	0.243319i
$399$	2.57326			0.128824
$400$	17.2800	+	10.0699i	0.863998	+	0.503496i
$401$	−4.36969			−0.218212			−0.109106	−	0.994030i	$-0.534799\pi$
$401$	−4.36969			−0.218212			−0.109106	+	0.994030i	$0.534799\pi$
$402$	8.89125	+	3.26215i	0.443455	+	0.162701i
$403$	4.51600	+	4.51600i	0.224958	+	0.224958i
$404$	−19.0722	−	16.1719i	−0.948876	−	0.804581i
$405$	−12.6775	+	5.96015i	−0.629952	+	0.296162i
$406$	0.906534	+	1.95724i	0.0449905	+	0.0971359i
$407$	−14.4151	+	14.4151i	−0.714529	+	0.714529i
$408$	−0.551913	+	0.312977i	−0.0273238	+	0.0154947i
$409$		−	4.50695i		−	0.222854i	−0.993773	−	0.111427i	$-0.964458\pi$
$409$		−	4.50695i		−	0.222854i	0.993773	−	0.111427i	$-0.0355422\pi$
$410$	−9.86734	+	0.868843i	−0.487313	+	0.0429091i
$411$			11.9578i			0.589836i
$412$	−0.789540	−	9.59441i	−0.0388978	−	0.472682i
$413$	−5.33793	+	5.33793i	−0.262663	+	0.262663i
$414$	20.3972	−	9.44739i	1.00247	−	0.464314i
$415$	1.22647	+	0.442043i	0.0602049	+	0.0216990i
$416$	−3.18460	−	4.67529i	−0.156138	−	0.229225i
$417$	3.41355	+	3.41355i	0.167162	+	0.167162i
$418$	13.6710	−	37.2615i	0.668673	−	1.82252i
$419$	18.5650			0.906962			0.453481	−	0.891266i	$-0.350182\pi$
$419$	18.5650			0.906962			0.453481	+	0.891266i	$0.350182\pi$
$420$	1.63475	+	0.441573i	0.0797678	+	0.0215465i
$421$	−12.6368			−0.615881			−0.307940	−	0.951406i	$-0.599640\pi$
$421$	−12.6368			−0.615881			−0.307940	+	0.951406i	$0.599640\pi$
$422$	−6.59641	+	17.9790i	−0.321108	+	0.875206i
$423$	5.64675	+	5.64675i	0.274554	+	0.274554i
$424$	13.6946	+	3.78330i	0.665068	+	0.183733i
$425$	−1.98992	+	0.186692i	−0.0965255	+	0.00905591i
$426$	−10.6787	+	4.94605i	−0.517383	+	0.239637i
$427$	0.595542	−	0.595542i	0.0288203	−	0.0288203i
$428$	11.0605	−	0.910190i	0.534631	−	0.0439957i
$429$			2.31749i			0.111889i
$430$	10.7685	+	9.02561i	0.519305	+	0.435254i
$431$		−	12.4884i		−	0.601544i	−0.953696	−	0.300772i	$-0.902756\pi$
$431$		−	12.4884i		−	0.601544i	0.953696	−	0.300772i	$-0.0972443\pi$
$432$	10.3774	+	7.42712i	0.499285	+	0.357338i
$433$	−12.5876	+	12.5876i	−0.604921	+	0.604921i	−0.941614	−	0.336694i	$-0.890691\pi$
$433$	−12.5876	+	12.5876i	−0.604921	+	0.604921i	0.336694	+	0.941614i	$0.390691\pi$
$434$	−2.56123	−	5.52978i	−0.122943	−	0.265438i
$435$	0.961786	−	2.66852i	0.0461141	−	0.127946i
$436$	18.5048	−	21.8235i	0.886218	−	1.04515i
$437$	−28.4473	−	28.4473i	−1.36082	−	1.36082i
$438$	3.57258	+	1.31076i	0.170705	+	0.0626306i
$439$	−15.6930			−0.748987			−0.374494	−	0.927229i	$-0.622183\pi$
$439$	−15.6930			−0.748987			−0.374494	+	0.927229i	$0.622183\pi$
$440$	15.0791	−	21.3257i	0.718869	−	1.01666i
$441$	17.5731			0.836816
$442$	0.530714	+	0.194716i	0.0252435	+	0.00926171i
$443$	−25.4951	−	25.4951i	−1.21131	−	1.21131i	−0.970597	−	0.240712i	$-0.922619\pi$
$443$	−25.4951	−	25.4951i	−1.21131	−	1.21131i	−0.240712	−	0.970597i	$-0.577381\pi$
$444$	−3.58322	+	4.22584i	−0.170052	+	0.200549i
$445$	16.1279	+	34.3048i	0.764535	+	1.62620i
$446$	−3.65245	−	7.88575i	−0.172948	−	0.373401i
$447$	5.30645	−	5.30645i	0.250987	−	0.250987i
$448$	1.31618	+	5.23488i	0.0621839	+	0.247325i
$449$			18.4241i			0.869486i	0.900555	+	0.434743i	$0.143161\pi$
$449$			18.4241i			0.869486i	−0.900555	+	0.434743i	$0.856839\pi$
$450$	9.55393	+	16.4075i	0.450377	+	0.773455i
$451$			12.9358i			0.609122i
$452$	−31.6634	+	2.60563i	−1.48932	+	0.122559i
$453$	−5.22500	+	5.22500i	−0.245492	+	0.245492i
$454$	−2.19267	+	1.01558i	−0.102907	+	0.0476635i
$455$	−0.641908	−	1.36537i	−0.0300931	−	0.0640095i
$456$	2.87244	−	10.3975i	0.134514	−	0.486909i
$457$	−10.1404	−	10.1404i	−0.474346	−	0.474346i	0.428972	−	0.903318i	$-0.358876\pi$
$457$	−10.1404	−	10.1404i	−0.474346	−	0.474346i	−0.903318	+	0.428972i	$0.858876\pi$
$458$	−14.1075	+	38.4510i	−0.659199	+	1.79670i
$459$	−1.27529			−0.0595253
$460$	−13.1906	−	22.9538i	−0.615014	−	1.07022i
$461$	−10.3914			−0.483976			−0.241988	−	0.970279i	$-0.577799\pi$
$461$	−10.3914			−0.483976			−0.241988	+	0.970279i	$0.577799\pi$
$462$	0.761689	−	2.07604i	0.0354370	−	0.0965862i
$463$	−28.6939	−	28.6939i	−1.33352	−	1.33352i	−0.902198	−	0.431323i	$-0.858047\pi$
$463$	−28.6939	−	28.6939i	−1.33352	−	1.33352i	−0.431323	−	0.902198i	$-0.641953\pi$
$464$	8.92035	−	1.47815i	0.414117	−	0.0686214i
$465$	−2.71733	+	7.53937i	−0.126013	+	0.349630i
$466$	−8.46377	+	3.92017i	−0.392076	+	0.181598i
$467$	21.0756	−	21.0756i	0.975261	−	0.975261i	−0.0244401	−	0.999701i	$-0.507780\pi$
$467$	21.0756	−	21.0756i	0.975261	−	0.975261i	0.999701	+	0.0244401i	$0.00778029\pi$
$468$	−0.440430	−	5.35206i	−0.0203589	−	0.247399i
$469$			8.05188i			0.371801i
$470$	6.04136	−	7.20799i	0.278667	−	0.332480i
$471$			2.35509i			0.108517i
$472$	15.6099	+	27.5271i	0.718506	+	1.26704i
$473$	12.9748	−	12.9748i	0.596580	−	0.596580i
$474$	3.39991	+	7.34050i	0.156163	+	0.337160i
$475$	21.6781	−	26.1668i	0.994659	−	1.20062i
$476$	−0.411425	−	0.348860i	−0.0188576	−	0.0159900i
$477$	9.53711	+	9.53711i	0.436674	+	0.436674i
$478$	5.19162	+	1.90478i	0.237459	+	0.0871224i
$479$	2.23544			0.102140			0.0510700	−	0.998695i	$-0.483737\pi$
$479$	2.23544			0.102140			0.0510700	+	0.998695i	$0.483737\pi$
$480$	3.60904	−	6.11248i	0.164729	−	0.278995i
$481$	4.93648			0.225084
$482$	5.47234	+	2.00777i	0.249258	+	0.0914515i
$483$	−1.58496	−	1.58496i	−0.0721180	−	0.0721180i
$484$	−9.23524	−	7.83084i	−0.419784	−	0.355947i
$485$	−7.72719	−	2.78503i	−0.350874	−	0.126462i
$486$	7.77830	+	16.7936i	0.352831	+	0.761773i
$487$	−21.7388	+	21.7388i	−0.985080	+	0.985080i	−0.999890	−	0.0148107i	$-0.995285\pi$
$487$	−21.7388	+	21.7388i	−0.985080	+	0.985080i	0.0148107	+	0.999890i	$0.495285\pi$
$488$	−1.74157	−	3.07113i	−0.0788371	−	0.139024i
$489$			5.10857i			0.231017i
$490$	−1.81533	−	20.6165i	−0.0820084	−	0.931360i
$491$		−	28.0576i		−	1.26622i	−0.774061	−	0.633111i	$-0.781778\pi$
$491$		−	28.0576i		−	1.26622i	0.774061	−	0.633111i	$-0.218222\pi$
$492$	0.288337	+	3.50384i	0.0129992	+	0.157965i
$493$	−0.638938	+	0.638938i	−0.0287763	+	0.0287763i
$494$	−8.72098	+	4.03930i	−0.392375	+	0.181737i
$495$	22.4385	−	10.5491i	1.00854	−	0.474149i
$496$	−25.2027	+	4.17622i	−1.13163	+	0.187518i
$497$	−7.07484	−	7.07484i	−0.317350	−	0.317350i
$498$	0.159377	−	0.434395i	0.00714186	−	0.0194657i
$499$	27.1042			1.21335			0.606676	−	0.794949i	$-0.292503\pi$
$499$	27.1042			1.21335			0.606676	+	0.794949i	$0.292503\pi$
$500$	18.2620	−	12.9034i	0.816702	−	0.577059i
$501$	−13.8509			−0.618811
$502$	4.87199	−	13.2790i	0.217448	−	0.592670i
$503$	−13.4274	−	13.4274i	−0.598699	−	0.598699i	0.341268	−	0.939966i	$-0.389144\pi$
$503$	−13.4274	−	13.4274i	−0.598699	−	0.598699i	−0.939966	+	0.341268i	$0.889144\pi$
$504$	−1.36452	+	4.93922i	−0.0607805	+	0.220010i
$505$	−25.3005	+	11.8946i	−1.12586	+	0.529305i
$506$	−31.3711	+	14.5302i	−1.39461	+	0.645944i
$507$	0.396814	−	0.396814i	0.0176231	−	0.0176231i
$508$	26.7131	−	2.19826i	1.18520	−	0.0975322i
$509$			20.6331i			0.914546i	0.889326	+	0.457273i	$0.151174\pi$
$509$			20.6331i			0.914546i	−0.889326	+	0.457273i	$0.848826\pi$
$510$	0.0622207	+	0.706634i	0.00275518	+	0.0312903i
$511$			3.23532i			0.143122i
$512$	22.6213	+	0.525340i	0.999730	+	0.0232170i
$513$	15.3312	−	15.3312i	0.676890	−	0.676890i
$514$	−3.45412	−	7.45755i	−0.152355	−	0.328939i
$515$	−10.1255	−	3.64944i	−0.446185	−	0.160814i
$516$	3.22519	−	3.80360i	0.141981	−	0.167444i
$517$	−8.68474	−	8.68474i	−0.381955	−	0.381955i
$518$	−4.42217	−	1.62247i	−0.194299	−	0.0712873i
$519$	3.76359			0.165203
$520$	−6.23346	+	1.06958i	−0.273355	+	0.0469043i
$521$	12.9140			0.565771			0.282886	−	0.959154i	$-0.408708\pi$
$521$	12.9140			0.565771			0.282886	+	0.959154i	$0.408708\pi$
$522$	8.05846	+	2.95661i	0.352709	+	0.129407i
$523$	−3.59192	−	3.59192i	−0.157064	−	0.157064i	0.624200	−	0.781264i	$-0.285425\pi$
$523$	−3.59192	−	3.59192i	−0.157064	−	0.157064i	−0.781264	+	0.624200i	$0.785425\pi$
$524$	0.521336	−	0.614833i	0.0227747	−	0.0268591i
$525$	1.20780	−	1.45790i	0.0527129	−	0.0636278i
$526$	−0.400803	−	0.865346i	−0.0174758	−	0.0377309i
$527$	1.80519	−	1.80519i	0.0786354	−	0.0786354i
$528$	−7.53822	−	5.39510i	−0.328059	−	0.234792i
$529$			12.0433i			0.523623i
$530$	10.2036	−	12.1740i	0.443215	−	0.528804i
$531$			30.0412i			1.30368i
$532$	9.13999	−	0.752145i	0.396269	−	0.0326096i
$533$	2.21494	−	2.21494i	0.0959398	−	0.0959398i
$534$	12.2080	−	5.65440i	0.528293	−	0.244690i
$535$	4.20711	−	11.6728i	0.181889	−	0.504661i
$536$	32.5345	+	8.98804i	1.40528	+	0.388224i
$537$	−4.61288	−	4.61288i	−0.199061	−	0.199061i
$538$	2.27543	−	6.20186i	0.0981007	−	0.267381i
$539$	−27.0276			−1.16416
$540$	12.3706	−	7.10886i	0.532344	−	0.305917i
$541$	26.0058			1.11808			0.559038	−	0.829142i	$-0.311170\pi$
$541$	26.0058			1.11808			0.559038	+	0.829142i	$0.311170\pi$
$542$	−11.3834	+	31.0263i	−0.488958	+	1.33269i
$543$	2.64679	+	2.64679i	0.113585	+	0.113585i
$544$	−1.86887	+	1.27299i	−0.0801270	+	0.0545789i
$545$	−13.6105	−	28.9502i	−0.583011	−	1.24009i
$546$	−0.485893	+	0.225051i	−0.0207943	+	0.00963131i
$547$	−7.31204	+	7.31204i	−0.312640	+	0.312640i	−0.845932	−	0.533291i	$-0.820955\pi$
$547$	−7.31204	+	7.31204i	−0.312640	+	0.312640i	0.533291	+	0.845932i	$0.320955\pi$
$548$	3.49519	+	42.4732i	0.149307	+	1.81436i
$549$		−	3.35163i		−	0.143044i
$550$	−14.6940	−	25.2348i	−0.626555	−	1.07601i
$551$		−	15.3624i		−	0.654458i
$552$	−8.17341	+	4.63495i	−0.347884	+	0.197277i
$553$	−4.86323	+	4.86323i	−0.206806	+	0.206806i
$554$	−5.45132	−	11.7696i	−0.231605	−	0.500042i
$555$	2.63551	+	5.60585i	0.111871	+	0.237955i
$556$	13.1224	+	11.1269i	0.556514	+	0.471885i
$557$	10.8132	+	10.8132i	0.458169	+	0.458169i	0.898054	−	0.439885i	$-0.144981\pi$
$557$	10.8132	+	10.8132i	0.458169	+	0.458169i	−0.439885	+	0.898054i	$0.644981\pi$
$558$	−22.7676	−	8.35330i	−0.963828	−	0.353623i
$559$	−4.44323			−0.187929
$560$	5.93557	+	1.09060i	0.250824	+	0.0460864i
$561$	0.926375			0.0391116
$562$	−29.3751	−	10.7776i	−1.23912	−	0.454625i
$563$	31.4173	+	31.4173i	1.32408	+	1.32408i	0.910438	+	0.413645i	$0.135745\pi$
$563$	31.4173	+	31.4173i	1.32408	+	1.32408i	0.413645	+	0.910438i	$0.364255\pi$
$564$	−2.54596	−	2.15880i	−0.107204	−	0.0909019i
$565$	−12.0439	+	33.4162i	−0.506689	+	1.40583i
$566$	−10.4214	−	22.5001i	−0.438043	−	0.945748i
$567$	−2.98899	+	2.98899i	−0.125526	+	0.125526i
$568$	−36.4840	+	20.6892i	−1.53084	+	0.868101i
$569$			27.9496i			1.17171i	0.810417	+	0.585853i	$0.199241\pi$
$569$			27.9496i			1.17171i	−0.810417	+	0.585853i	$0.800759\pi$
$570$	−9.24301	−	7.74700i	−0.387147	−	0.324486i
$571$			16.2190i			0.678744i	0.940652	+	0.339372i	$0.110215\pi$
$571$			16.2190i			0.678744i	−0.940652	+	0.339372i	$0.889785\pi$
$572$	0.677385	+	8.23151i	0.0283229	+	0.344177i
$573$	0.797512	−	0.797512i	0.0333165	−	0.0333165i
$574$	−2.71217	+	1.25620i	−0.113204	+	0.0524326i
$575$	−29.4693	+	2.76477i	−1.22895	+	0.115299i
$576$	18.4343	+	11.0270i	0.768095	+	0.459457i
$577$	−24.4926	−	24.4926i	−1.01964	−	1.01964i	−0.999803	−	0.0198359i	$-0.993686\pi$
$577$	−24.4926	−	24.4926i	−1.01964	−	1.01964i	−0.0198359	−	0.999803i	$-0.506314\pi$
$578$	−8.20314	+	22.3583i	−0.341206	+	0.929983i
$579$	−10.9771			−0.456195
$580$	2.63619	−	9.75948i	0.109462	−	0.405240i
$581$	0.393386			0.0163204
$582$	−1.00413	+	2.73685i	−0.0416227	+	0.113446i
$583$	−14.6681	−	14.6681i	−0.607493	−	0.607493i
$584$	13.0726	+	3.61147i	0.540950	+	0.149444i
$585$	−5.64835	−	2.03577i	−0.233530	−	0.0841688i
$586$	−34.0826	+	15.7860i	−1.40794	+	0.652116i
$587$	7.32237	−	7.32237i	0.302227	−	0.302227i	−0.539658	−	0.841884i	$-0.681446\pi$
$587$	7.32237	−	7.32237i	0.302227	−	0.302227i	0.841884	+	0.539658i	$0.181446\pi$
$588$	−7.32081	+	0.602442i	−0.301905	+	0.0248443i
$589$			43.4033i			1.78840i
$590$	35.2439	−	3.10331i	1.45097	−	0.127761i
$591$			3.60581i			0.148323i
$592$	−11.4921	+	16.0572i	−0.472322	+	0.659945i
$593$	−31.9155	+	31.9155i	−1.31061	+	1.31061i	−0.389649	+	0.920964i	$0.627404\pi$
$593$	−31.9155	+	31.9155i	−1.31061	+	1.31061i	−0.920964	+	0.389649i	$0.872596\pi$
$594$	−7.83080	−	16.9069i	−0.321301	−	0.693700i
$595$	−0.545782	+	0.256591i	−0.0223749	+	0.0105192i
$596$	17.2970	−	20.3991i	0.708514	−	0.835580i
$597$	3.95432	+	3.95432i	0.161839	+	0.161839i
$598$	7.85948	+	2.88360i	0.321398	+	0.117919i
$599$	−35.5811			−1.45381			−0.726903	−	0.686741i	$-0.759041\pi$
$599$	−35.5811			−1.45381			−0.726903	+	0.686741i	$0.759041\pi$
$600$	−4.54256	−	6.50766i	−0.185449	−	0.265674i
$601$	13.9106			0.567423			0.283712	−	0.958910i	$-0.408434\pi$
$601$	13.9106			0.567423			0.283712	+	0.958910i	$0.408434\pi$
$602$	3.98032	+	1.46036i	0.162226	+	0.0595197i
$603$	22.6575	+	22.6575i	0.922684	+	0.922684i
$604$	−17.0315	+	20.0860i	−0.693004	+	0.817288i
$605$	−12.2511	+	5.75970i	−0.498080	+	0.234165i
$606$	4.17023	+	9.00367i	0.169404	+	0.365749i
$607$	8.63954	−	8.63954i	0.350668	−	0.350668i	−0.509690	−	0.860358i	$-0.670240\pi$
$607$	8.63954	−	8.63954i	0.350668	−	0.350668i	0.860358	+	0.509690i	$0.170240\pi$
$608$	7.16354	−	37.7707i	0.290520	−	1.53180i
$609$		−	0.855920i		−	0.0346836i
$610$	−3.93208	+	0.346229i	−0.159205	+	0.0140184i
$611$			2.97411i			0.120320i
$612$	−2.13939	+	0.176054i	−0.0864799	+	0.00711658i
$613$	3.62256	−	3.62256i	0.146314	−	0.146314i	−0.630155	−	0.776469i	$-0.717009\pi$
$613$	3.62256	−	3.62256i	0.146314	−	0.146314i	0.776469	+	0.630155i	$0.217009\pi$
$614$	−32.2189	+	14.9229i	−1.30025	+	0.602238i
$615$	3.69780	+	1.33276i	0.149110	+	0.0537420i
$616$	2.09864	−	7.59656i	0.0845566	−	0.306074i
$617$	12.7177	+	12.7177i	0.511995	+	0.511995i	0.915137	−	0.403142i	$-0.132082\pi$
$617$	12.7177	+	12.7177i	0.511995	+	0.511995i	−0.403142	+	0.915137i	$0.632082\pi$
$618$	−1.31580	+	3.58630i	−0.0529290	+	0.144262i
$619$	−7.93318			−0.318861			−0.159431	−	0.987209i	$-0.550966\pi$
$619$	−7.93318			−0.318861			−0.159431	+	0.987209i	$0.550966\pi$
$620$	−7.44803	+	27.5735i	−0.299120	+	1.10738i
$621$	−18.8860			−0.757871
$622$	1.34605	−	3.66876i	0.0539716	−	0.147104i
$623$	8.08807	+	8.08807i	0.324042	+	0.324042i
$624$	0.366958	+	2.21452i	0.0146901	+	0.0886518i
$625$	−4.65001	−	24.5637i	−0.186000	−	0.982550i
$626$	27.9254	−	12.9342i	1.11612	−	0.516955i
$627$	−11.1367	+	11.1367i	−0.444756	+	0.444756i
$628$	0.688377	+	8.36509i	0.0274692	+	0.333803i
$629$		−	1.97327i		−	0.0786794i
$630$	4.39078	+	3.68012i	0.174933	+	0.146620i
$631$		−	6.80852i		−	0.271043i	−0.990774	−	0.135521i	$-0.956729\pi$
$631$		−	6.80852i		−	0.271043i	0.990774	−	0.135521i	$-0.0432710\pi$
$632$	14.2218	+	25.0791i	0.565711	+	0.997592i
$633$	5.37356	−	5.37356i	0.213580	−	0.213580i
$634$	−6.46975	−	13.9684i	−0.256947	−	0.554756i
$635$	10.1609	−	28.1919i	0.403223	−	1.11876i
$636$	−4.30002	−	3.64612i	−0.170507	−	0.144578i
$637$	4.62783	+	4.62783i	0.183361	+	0.183361i
$638$	−12.3940	−	4.54728i	−0.490682	−	0.180029i
$639$	−39.8163			−1.57511
$640$	11.0324	−	22.7659i	0.436093	−	0.899902i
$641$	38.7376			1.53004			0.765022	−	0.644004i	$-0.222728\pi$
$641$	38.7376			1.53004			0.765022	+	0.644004i	$0.222728\pi$
$642$	−4.13433	−	1.51686i	−0.163169	−	0.0598658i
$643$	−28.5706	−	28.5706i	−1.12672	−	1.12672i	−0.990708	−	0.136008i	$-0.956573\pi$
$643$	−28.5706	−	28.5706i	−1.12672	−	1.12672i	−0.136008	−	0.990708i	$-0.543427\pi$
$644$	−6.09290	−	5.16636i	−0.240094	−	0.203583i
$645$	−2.37217	−	5.04572i	−0.0934041	−	0.198675i
$646$	1.61464	+	3.48606i	0.0635272	+	0.137157i
$647$	22.6536	−	22.6536i	0.890604	−	0.890604i	−0.103976	−	0.994580i	$-0.533156\pi$
$647$	22.6536	−	22.6536i	0.890604	−	0.890604i	0.994580	+	0.103976i	$0.0331564\pi$
$648$	8.74083	+	15.4139i	0.343372	+	0.605513i
$649$		−	46.2036i		−	1.81365i
$650$	−1.80485	+	6.83685i	−0.0707921	+	0.268163i
$651$			2.41823i			0.0947780i
$652$	1.49320	+	18.1452i	0.0584782	+	0.710621i
$653$	14.2480	−	14.2480i	0.557567	−	0.557567i	−0.371047	−	0.928614i	$-0.621001\pi$
$653$	14.2480	−	14.2480i	0.557567	−	0.557567i	0.928614	+	0.371047i	$0.121001\pi$
$654$	−10.3025	+	4.77182i	−0.402860	+	0.186593i
$655$	−0.383450	−	0.815616i	−0.0149826	−	0.0318688i
$656$	2.04829	+	12.3610i	0.0799724	+	0.482618i
$657$	9.10397	+	9.10397i	0.355180	+	0.355180i
$658$	0.977500	−	2.66425i	0.0381069	−	0.103863i
$659$	−39.9047			−1.55447			−0.777233	−	0.629212i	$-0.783378\pi$
$659$	−39.9047			−1.55447			−0.777233	+	0.629212i	$0.783378\pi$
$660$	−8.98604	+	5.16391i	−0.349781	+	0.201005i
$661$	−22.4907			−0.874787			−0.437393	−	0.899270i	$-0.644098\pi$
$661$	−22.4907			−0.874787			−0.437393	+	0.899270i	$0.644098\pi$
$662$	9.99696	−	27.2475i	0.388543	−	1.05900i
$663$	−0.158619	−	0.158619i	−0.00616027	−	0.00616027i
$664$	0.439124	−	1.58952i	0.0170413	−	0.0616853i
$665$	3.47659	−	9.64597i	0.134816	−	0.374055i
$666$	−17.0093	+	7.87818i	−0.659095	+	0.305273i
$667$	−9.46219	+	9.46219i	−0.366377	+	0.366377i
$668$	−49.1971	+	4.04851i	−1.90349	+	0.156642i
$669$			3.44852i			0.133328i
$670$	24.2408	−	28.9219i	0.936505	−	1.11735i
$671$			5.15484i			0.199000i
$672$	0.399120	−	2.10441i	0.0153964	−	0.0811794i
$673$	−10.2300	+	10.2300i	−0.394338	+	0.394338i	−0.876231	−	0.481892i	$-0.839950\pi$
$673$	−10.2300	+	10.2300i	−0.394338	+	0.394338i	0.481892	+	0.876231i	$0.339950\pi$
$674$	18.1700	+	39.2296i	0.699882	+	1.51107i
$675$	−1.49003	−	15.8820i	−0.0573513	−	0.611299i
$676$	1.29346	−	1.52544i	0.0497486	−	0.0586706i
$677$	−19.5092	−	19.5092i	−0.749800	−	0.749800i	0.224642	−	0.974441i	$-0.427879\pi$
$677$	−19.5092	−	19.5092i	−0.749800	−	0.749800i	−0.974441	+	0.224642i	$0.927879\pi$
$678$	11.8355	+	4.34238i	0.454539	+	0.166768i
$679$	−2.47848			−0.0951152
$680$	0.427547	+	2.49172i	0.0163957	+	0.0955530i
$681$	0.958877			0.0367443
$682$	35.0167	+	12.8474i	1.34086	+	0.491954i
$683$	28.7846	+	28.7846i	1.10141	+	1.10141i	0.994241	+	0.107171i	$0.0341791\pi$
$683$	28.7846	+	28.7846i	1.10141	+	1.10141i	0.107171	+	0.994241i	$0.465821\pi$
$684$	23.6029	−	27.8358i	0.902478	−	1.06433i
$685$	44.8244	+	16.1556i	1.71265	+	0.617273i
$686$	−5.43189	−	11.7276i	−0.207390	−	0.447763i
$687$	11.4922	−	11.4922i	0.438455	−	0.438455i
$688$	10.3438	−	14.4528i	0.394355	−	0.551006i
$689$			5.02314i			0.191366i
$690$	0.921443	+	10.4647i	0.0350787	+	0.398385i
$691$			22.8571i			0.869526i	0.900545	+	0.434763i	$0.143168\pi$
$691$			22.8571i			0.869526i	−0.900545	+	0.434763i	$0.856832\pi$
$692$	13.3680	−	1.10007i	0.508173	−	0.0418184i
$693$	5.29035	−	5.29035i	0.200964	−	0.200964i
$694$	−11.3392	+	5.25201i	−0.430432	+	0.199363i
$695$	17.4077	−	8.18398i	0.660313	−	0.310436i
$696$	−3.45844	−	0.955435i	−0.131092	−	0.0362157i
$697$	−0.885385	−	0.885385i	−0.0335363	−	0.0335363i
$698$	1.89967	−	5.17771i	0.0719037	−	0.195979i
$699$	3.70130			0.139996
$700$	3.86388	−	5.53136i	0.146041	−	0.209066i
$701$	14.5556			0.549756			0.274878	−	0.961479i	$-0.411363\pi$
$701$	14.5556			0.549756			0.274878	+	0.961479i	$0.411363\pi$
$702$	−1.55407	+	4.23574i	−0.0586547	+	0.159868i
$703$	23.7222	+	23.7222i	0.894701	+	0.894701i
$704$	−28.3521	−	16.9596i	−1.06856	−	0.639188i
$705$	−3.37739	+	1.58783i	−0.127200	+	0.0598011i
$706$	−26.6242	+	12.3315i	−1.00201	+	0.464103i
$707$	−5.96511	+	5.96511i	−0.224341	+	0.224341i
$708$	−1.02987	−	12.5149i	−0.0387049	−	0.470338i
$709$		−	15.9737i		−	0.599907i	−0.953954	−	0.299953i	$-0.903029\pi$
$709$		−	15.9737i		−	0.599907i	0.953954	−	0.299953i	$-0.0969711\pi$
$710$	4.11309	+	46.7118i	0.154361	+	1.75306i
$711$			27.3697i			1.02644i
$712$	41.7091	−	23.6523i	1.56312	−	0.886406i
$713$	26.7335	−	26.7335i	1.00118	−	1.00118i
$714$	0.0899604	+	0.194227i	0.00336668	+	0.00726878i
$715$	8.68720	+	3.13103i	0.324883	+	0.117094i
$716$	−17.7329	−	15.0363i	−0.662709	−	0.561931i
$717$	−1.55167	−	1.55167i	−0.0579480	−	0.0579480i
$718$	−32.6604	−	11.9829i	−1.21888	−	0.447199i
$719$	−2.30805			−0.0860756			−0.0430378	−	0.999073i	$-0.513704\pi$
$719$	−2.30805			−0.0860756			−0.0430378	+	0.999073i	$0.513704\pi$
$720$	19.7712	−	13.6334i	0.736829	−	0.508088i
$721$	−3.24774			−0.120952
$722$	−36.0937	−	13.2426i	−1.34327	−	0.492839i
$723$	−1.63557	−	1.63557i	−0.0608274	−	0.0608274i
$724$	10.1748	+	8.62755i	0.378144	+	0.320640i
$725$	−8.70365	−	7.21060i	−0.323245	−	0.267795i
$726$	2.01934	+	4.35981i	0.0749446	+	0.161808i
$727$	36.3079	−	36.3079i	1.34658	−	1.34658i	0.457242	−	0.889342i	$-0.348837\pi$
$727$	36.3079	−	36.3079i	1.34658	−	1.34658i	0.889342	−	0.457242i	$-0.151163\pi$
$728$	−1.66007	+	0.941387i	−0.0615263	+	0.0348901i
$729$			11.4506i			0.424096i
$730$	9.74018	−	11.6211i	0.360500	−	0.430116i
$731$			1.77610i			0.0656916i
$732$	0.114901	+	1.39626i	0.00424685	+	0.0516072i
$733$	24.2605	−	24.2605i	0.896084	−	0.896084i	−0.0990035	−	0.995087i	$-0.531566\pi$
$733$	24.2605	−	24.2605i	0.896084	−	0.896084i	0.995087	+	0.0990035i	$0.0315655\pi$
$734$	−15.1543	+	7.01904i	−0.559357	+	0.259078i
$735$	−2.78463	+	7.72608i	−0.102713	+	0.284981i
$736$	−27.6765	+	18.8520i	−1.02017	+	0.694893i
$737$	−34.8474	−	34.8474i	−1.28362	−	1.28362i
$738$	−4.09701	+	11.1667i	−0.150813	+	0.411053i
$739$	27.4036			1.00806			0.504030	−	0.863686i	$-0.331850\pi$
$739$	27.4036			1.00806			0.504030	+	0.863686i	$0.331850\pi$
$740$	10.9996	+	19.1412i	0.404355	+	0.703643i
$741$	3.81378			0.140103
$742$	1.65096	−	4.49981i	0.0606085	−	0.165193i
$743$	30.3545	+	30.3545i	1.11360	+	1.11360i	0.992660	+	0.120937i	$0.0385900\pi$
$743$	30.3545	+	30.3545i	1.11360	+	1.11360i	0.120937	+	0.992660i	$0.461410\pi$
$744$	9.77113	+	2.69939i	0.358227	+	0.0989645i
$745$	−12.7222	−	27.0607i	−0.466106	−	0.991429i
$746$	26.8110	−	12.4181i	0.981620	−	0.454658i
$747$	1.10696	−	1.10696i	0.0405017	−	0.0405017i
$748$	3.29040	−	0.270773i	0.120309	−	0.00990044i
$749$		−	3.74403i		−	0.136804i
$750$	−8.72749	+	1.60050i	−0.318683	+	0.0584420i
$751$			25.9682i			0.947594i	0.880634	+	0.473797i	$0.157117\pi$
$751$			25.9682i			0.947594i	−0.880634	+	0.473797i	$0.842883\pi$
$752$	−9.67405	−	6.92371i	−0.352776	−	0.252482i
$753$	−3.96881	+	3.96881i	−0.144632	+	0.144632i
$754$	1.34356	+	2.90078i	0.0489295	+	0.105640i
$755$	12.5269	+	26.6454i	0.455902	+	0.969725i
$756$	2.78432	−	3.28367i	0.101265	−	0.119426i
$757$	24.9999	+	24.9999i	0.908636	+	0.908636i	0.996162	−	0.0875264i	$-0.0278962\pi$
$757$	24.9999	+	24.9999i	0.908636	+	0.908636i	−0.0875264	+	0.996162i	$0.527896\pi$
$758$	17.7118	+	6.49838i	0.643323	+	0.236032i
$759$	13.7189			0.497965
$760$	−35.0948	−	24.8150i	−1.27302	−	0.900135i
$761$	5.38965			0.195375			0.0976873	−	0.995217i	$-0.468855\pi$
$761$	5.38965			0.195375			0.0976873	+	0.995217i	$0.468855\pi$
$762$	−9.98510	−	3.66348i	−0.361722	−	0.132714i
$763$	−6.82562	−	6.82562i	−0.247104	−	0.247104i
$764$	2.59959	−	3.06580i	0.0940498	−	0.110917i
$765$	−0.813765	+	2.25783i	−0.0294217	+	0.0816320i
$766$	−19.9164	−	43.0002i	−0.719610	−	1.55366i
$767$	−7.91126	+	7.91126i	−0.285659	+	0.285659i
$768$	−8.05758	−	3.96177i	−0.290753	−	0.142958i
$769$			6.24953i			0.225364i	0.993631	+	0.112682i	$0.0359441\pi$
$769$			6.24953i			0.225364i	−0.993631	+	0.112682i	$0.964056\pi$
$770$	−6.75306	−	5.66005i	−0.243363	−	0.203974i
$771$			3.26127i			0.117452i
$772$	−38.9899	+	3.20854i	−1.40328	+	0.115478i

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)

\(f(q)\)	\(=\)	\(q+(-1.32767 - 0.487116i) q^{2} +(0.396814 + 0.396814i) q^{3} +(1.52544 + 1.29346i) q^{4} +(2.02359 - 0.951360i) q^{5} +(-0.333545 - 0.720134i) q^{6} +(0.477103 - 0.477103i) q^{7} +(-1.39521 - 2.46036i) q^{8} -2.68508i q^{9} +O(q^{10})\)	\(q+(-1.32767 - 0.487116i) q^{2} +(0.396814 + 0.396814i) q^{3} +(1.52544 + 1.29346i) q^{4} +(2.02359 - 0.951360i) q^{5} +(-0.333545 - 0.720134i) q^{6} +(0.477103 - 0.477103i) q^{7} +(-1.39521 - 2.46036i) q^{8} -2.68508i q^{9} +(-3.15009 + 0.277373i) q^{10} +4.12967i q^{11} +(0.0920497 + 1.11858i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-0.865843 + 0.401033i) q^{14} +(1.18050 + 0.425475i) q^{15} +(0.653905 + 3.94619i) q^{16} +(-0.282654 - 0.282654i) q^{17} +(-1.30795 + 3.56491i) q^{18} +6.79601 q^{19} +(4.31740 + 1.16620i) q^{20} +0.378643 q^{21} +(2.01163 - 5.48285i) q^{22} +(-4.18589 - 4.18589i) q^{23} +(0.422666 - 1.52995i) q^{24} +(3.18983 - 3.85033i) q^{25} +(-1.28325 + 0.594364i) q^{26} +(2.25592 - 2.25592i) q^{27} +(1.34491 - 0.110675i) q^{28} -2.26050i q^{29} +(-1.36006 - 1.13993i) q^{30} +6.38658i q^{31} +(1.05408 - 5.55778i) q^{32} +(-1.63871 + 1.63871i) q^{33} +(0.237587 + 0.512957i) q^{34} +(0.511564 - 1.41936i) q^{35} +(3.47305 - 4.09591i) q^{36} +(3.49062 + 3.49062i) q^{37} +(-9.02288 - 3.31045i) q^{38} +0.561180 q^{39} +(-5.16403 - 3.65141i) q^{40} +3.13240 q^{41} +(-0.502714 - 0.184443i) q^{42} +(-3.14184 - 3.14184i) q^{43} +(-5.34158 + 6.29954i) q^{44} +(-2.55448 - 5.43349i) q^{45} +(3.51848 + 7.59651i) q^{46} +(-2.10301 + 2.10301i) q^{47} +(-1.30642 + 1.82538i) q^{48} +6.54474i q^{49} +(-6.11061 + 3.55816i) q^{50} -0.224322i q^{51} +(1.99326 - 0.164029i) q^{52} +(-3.55189 + 3.55189i) q^{53} +(-4.09402 + 1.89623i) q^{54} +(3.92880 + 8.35675i) q^{55} +(-1.83951 - 0.508186i) q^{56} +(2.69675 + 2.69675i) q^{57} +(-1.10113 + 3.00120i) q^{58} -11.1882 q^{59} +(1.25044 + 2.17597i) q^{60} +1.24825 q^{61} +(3.11101 - 8.47930i) q^{62} +(-1.28106 - 1.28106i) q^{63} +(-4.10676 + 6.86546i) q^{64} +(0.758180 - 2.10361i) q^{65} +(2.97391 - 1.37743i) q^{66} +(-8.43829 + 8.43829i) q^{67} +(-0.0655677 - 0.796772i) q^{68} -3.32204i q^{69} +(-1.37058 + 1.63525i) q^{70} -14.8287i q^{71} +(-6.60626 + 3.74626i) q^{72} +(-3.39058 + 3.39058i) q^{73} +(-2.93406 - 6.33473i) q^{74} +(2.79363 - 0.262095i) q^{75} +(10.3669 + 8.79039i) q^{76} +(1.97028 + 1.97028i) q^{77} +(-0.745063 - 0.273360i) q^{78} -10.1932 q^{79} +(5.07748 + 7.36337i) q^{80} -6.26487 q^{81} +(-4.15881 - 1.52584i) q^{82} +(0.412265 + 0.412265i) q^{83} +(0.577595 + 0.489760i) q^{84} +(-0.840880 - 0.303069i) q^{85} +(2.64090 + 5.70178i) q^{86} +(0.896997 - 0.896997i) q^{87} +(10.1605 - 5.76177i) q^{88} +16.9524i q^{89} +(0.744767 + 8.45823i) q^{90} -0.674726i q^{91} +(-0.971008 - 11.7996i) q^{92} +(-2.53429 + 2.53429i) q^{93} +(3.81652 - 1.76770i) q^{94} +(13.7523 - 6.46545i) q^{95} +(2.62368 - 1.78713i) q^{96} +(-2.59742 - 2.59742i) q^{97} +(3.18805 - 8.68929i) q^{98} +11.0885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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