LMFDB - Embedded newform 260.2.o.a.27.15

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			27.15
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.487116 - 1.32767i) q^{2} +(-0.396814 - 0.396814i) q^{3} +(-1.52544 + 1.29346i) q^{4} +(2.02359 - 0.951360i) q^{5} +(-0.333545 + 0.720134i) q^{6} +(-0.477103 + 0.477103i) q^{7} +(2.46036 + 1.39521i) q^{8} -2.68508i q^{9} +O(q^{10})$	\(q+(-0.487116 - 1.32767i) 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} +(2.46036 + 1.39521i) q^{8} -2.68508i q^{9} +(-2.24882 - 2.22324i) q^{10} -4.12967i q^{11} +(1.11858 + 0.0920497i) 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} +(-3.56491 + 1.30795i) q^{18} -6.79601 q^{19} +(-1.85630 + 4.06868i) q^{20} +0.378643 q^{21} +(-5.48285 + 2.01163i) 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} +(0.110675 - 1.34491i) q^{28} -2.26050i q^{29} +(0.0101492 + 1.77458i) q^{30} -6.38658i q^{31} +(-5.55778 + 1.05408i) 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} +(3.31045 + 9.02288i) q^{38} -0.561180 q^{39} +(6.30611 + 0.482647i) q^{40} +3.13240 q^{41} +(-0.184443 - 0.502714i) 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} +(-1.82538 + 1.30642i) q^{48} +6.54474i q^{49} +(-6.66579 - 2.35949i) q^{50} +0.224322i q^{51} +(-0.164029 + 1.99326i) 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} +(-3.00120 + 1.10113i) q^{58} +11.1882 q^{59} +(2.35112 - 0.877900i) q^{60} +1.24825 q^{61} +(-8.47930 + 3.11101i) 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} +(0.796772 + 0.0655677i) q^{68} -3.32204i q^{69} +(2.13364 - 0.0122027i) q^{70} +14.8287i q^{71} +(3.74626 - 6.60626i) 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} +(0.273360 + 0.745063i) q^{78} +10.1932 q^{79} +(-2.43101 - 8.60757i) q^{80} -6.26487 q^{81} +(-1.52584 - 4.15881i) 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} +(5.76177 - 10.1605i) q^{88} +16.9524i q^{89} +(-5.96958 + 6.03826i) q^{90} +0.674726i q^{91} +(-11.7996 - 0.971008i) 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} +(8.68929 - 3.18805i) 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 $

$2$	−0.487116	−	1.32767i	−0.344443	−	0.938807i
$2$	−0.487116	−	1.32767i	−0.344443	−	0.938807i
$3$	−0.396814	−	0.396814i	−0.229101	−	0.229101i	0.583216	−	0.812317i	$-0.301794\pi$
$3$	−0.396814	−	0.396814i	−0.229101	−	0.229101i	−0.812317	+	0.583216i	$0.801794\pi$
$4$	−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	−0.791499	−	0.611171i	$-0.790699\pi$
$7$	−0.477103	+	0.477103i	−0.180328	+	0.180328i	0.611171	+	0.791499i	$0.290699\pi$
$8$	2.46036	+	1.39521i	0.869869	+	0.493282i
$9$		−	2.68508i		−	0.895026i
$10$	−2.24882	−	2.22324i	−0.711139	−	0.703051i
$11$		−	4.12967i		−	1.24514i	−0.782563	−	0.622571i	$-0.786088\pi$
$11$		−	4.12967i		−	1.24514i	0.782563	−	0.622571i	$-0.213912\pi$
$12$	1.11858	+	0.0920497i	0.322906	+	0.0265725i
$13$	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	$0.765436\pi$
$18$	−3.56491	+	1.30795i	−0.840257	+	0.308286i
$19$	−6.79601			−1.55911			−0.779555	−	0.626333i	$-0.784555\pi$
$19$	−6.79601			−1.55911			−0.779555	+	0.626333i	$0.784555\pi$
$20$	−1.85630	+	4.06868i	−0.415082	+	0.909784i
$21$	0.378643			0.0826266
$22$	−5.48285	+	2.01163i	−1.16895	+	0.428881i
$23$	4.18589	+	4.18589i	0.872818	+	0.872818i	0.992779	−	0.119961i	$-0.0382768\pi$
$23$	4.18589	+	4.18589i	0.872818	+	0.872818i	−0.119961	+	0.992779i	$0.538277\pi$
$24$	−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
$28$	0.110675	−	1.34491i	0.0209155	−	0.254163i
$29$		−	2.26050i		−	0.419764i	−0.977727	−	0.209882i	$-0.932692\pi$
$29$		−	2.26050i		−	0.419764i	0.977727	−	0.209882i	$-0.0673080\pi$
$30$	0.0101492	+	1.77458i	0.00185298	+	0.323992i
$31$		−	6.38658i		−	1.14706i	−0.819183	−	0.573532i	$-0.805573\pi$
$31$		−	6.38658i		−	1.14706i	0.819183	−	0.573532i	$-0.194427\pi$
$32$	−5.55778	+	1.05408i	−0.982486	+	0.186337i
$33$	−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	$0.617001\pi$
$38$	3.31045	+	9.02288i	0.537025	+	1.46370i
$39$	−0.561180			−0.0898607
$40$	6.30611	+	0.482647i	0.997084	+	0.0763133i
$41$	3.13240			0.489199			0.244599	−	0.969624i	$-0.421344\pi$
$41$	3.13240			0.489199			0.244599	+	0.969624i	$0.421344\pi$
$42$	−0.184443	−	0.502714i	−0.0284602	−	0.0775704i
$43$	3.14184	+	3.14184i	0.479126	+	0.479126i	0.904852	−	0.425726i	$-0.139981\pi$
$43$	3.14184	+	3.14184i	0.479126	+	0.479126i	−0.425726	+	0.904852i	$0.639981\pi$
$44$	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	−0.536894	−	0.843650i	$-0.680402\pi$
$47$	2.10301	−	2.10301i	0.306756	−	0.306756i	0.843650	+	0.536894i	$0.180402\pi$
$48$	−1.82538	+	1.30642i	−0.263471	+	0.188566i
$49$			6.54474i			0.934964i
$50$	−6.66579	−	2.35949i	−0.942685	−	0.333683i
$51$			0.224322i			0.0314113i
$52$	−0.164029	+	1.99326i	−0.0227467	+	0.276416i
$53$	−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
$58$	−3.00120	+	1.10113i	−0.394077	+	0.144585i
$59$	11.1882			1.45658			0.728291	−	0.685268i	$-0.240315\pi$
$59$	11.1882			1.45658			0.728291	+	0.685268i	$0.240315\pi$
$60$	2.35112	−	0.877900i	0.303528	−	0.113336i
$61$	1.24825			0.159821			0.0799107	−	0.996802i	$-0.474536\pi$
$61$	1.24825			0.159821			0.0799107	+	0.996802i	$0.474536\pi$
$62$	−8.47930	+	3.11101i	−1.07687	+	0.395099i
$63$	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	$-0.490005\pi$
$67$	8.43829	−	8.43829i	1.03090	−	1.03090i	0.999507	−	0.0313946i	$-0.00999484\pi$
$68$	0.796772	+	0.0655677i	0.0966228	+	0.00795125i
$69$		−	3.32204i		−	0.399926i
$70$	2.13364	−	0.0122027i	0.255018	−	0.00145851i
$71$			14.8287i			1.75985i	0.475116	+	0.879923i	$0.342406\pi$
$71$			14.8287i			1.75985i	−0.475116	+	0.879923i	$0.657594\pi$
$72$	3.74626	−	6.60626i	0.441500	−	0.778555i
$73$	−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
$78$	0.273360	+	0.745063i	0.0309519	+	0.0843618i
$79$	10.1932			1.14683			0.573415	−	0.819265i	$-0.305618\pi$
$79$	10.1932			1.14683			0.573415	+	0.819265i	$0.305618\pi$
$80$	−2.43101	−	8.60757i	−0.271795	−	0.962355i
$81$	−6.26487			−0.696097
$82$	−1.52584	−	4.15881i	−0.168501	−	0.459263i
$83$	−0.412265	−	0.412265i	−0.0452520	−	0.0452520i	0.684119	−	0.729371i	$-0.260187\pi$
$83$	−0.412265	−	0.412265i	−0.0452520	−	0.0452520i	−0.729371	+	0.684119i	$0.760187\pi$
$84$	−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
$88$	5.76177	−	10.1605i	0.614207	−	1.08311i
$89$			16.9524i			1.79696i	0.439020	+	0.898478i	$0.355326\pi$
$89$			16.9524i			1.79696i	−0.439020	+	0.898478i	$0.644674\pi$
$90$	−5.96958	+	6.03826i	−0.629249	+	0.636488i
$91$			0.674726i			0.0707305i
$92$	−11.7996	−	0.971008i	−1.23019	−	0.101235i
$93$	−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	$0.809709\pi$
$98$	8.68929	−	3.18805i	0.877750	−	0.322042i
$99$	−11.0885			−1.11443
$100$	0.114381	+	9.99935i	0.0114381	+	0.999935i
$101$	−12.5028			−1.24407			−0.622036	−	0.782989i	$-0.713694\pi$
$101$	−12.5028			−1.24407			−0.622036	+	0.782989i	$0.713694\pi$
$102$	0.297826	−	0.109271i	0.0294892	−	0.0108194i
$103$	3.40360	+	3.40360i	0.335367	+	0.335367i	0.854620	−	0.519253i	$-0.173790\pi$
$103$	3.40360	+	3.40360i	0.335367	+	0.335367i	−0.519253	+	0.854620i	$0.673790\pi$
$104$	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	−0.870857	−	0.491537i	$-0.836435\pi$
$107$	−3.92371	+	3.92371i	−0.379319	+	0.379319i	0.491537	+	0.870857i	$0.336435\pi$
$108$	0.523310	−	6.35920i	0.0503555	−	0.611915i
$109$		−	14.3064i		−	1.37030i	−0.728401	−	0.685151i	$-0.759736\pi$
$109$		−	14.3064i		−	1.37030i	0.728401	−	0.685151i	$-0.240264\pi$
$110$	−9.18126	+	9.28688i	−0.875399	+	0.885469i
$111$		−	2.77025i		−	0.262940i
$112$	1.57076	+	2.19472i	0.148423	+	0.207382i
$113$	−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
$118$	−5.44996	−	14.8543i	−0.501710	−	1.36745i
$119$	0.269710			0.0247243
$120$	−2.31083	−	2.69387i	−0.210949	−	0.245916i
$121$	−6.05417			−0.550379
$122$	−0.608041	−	1.65726i	−0.0550494	−	0.150041i
$123$	−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	−0.988976	−	0.148079i	$-0.952691\pi$
$127$	−9.47642	+	9.47642i	−0.840896	+	0.840896i	0.148079	+	0.988976i	$0.452691\pi$
$128$	7.11462	−	8.79672i	0.628849	−	0.777527i
$129$		−	2.49345i		−	0.219536i
$130$	−3.16223	+	0.0180855i	−0.277346	+	0.00158620i
$131$			0.403054i			0.0352150i	0.999845	+	0.0176075i	$0.00560493\pi$
$131$			0.403054i			0.0352150i	−0.999845	+	0.0176075i	$0.994395\pi$
$132$	0.380135	−	4.61936i	0.0330865	−	0.402063i
$133$	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	$0.385890\pi$
$138$	−4.41058	+	1.61822i	−0.375454	+	0.137752i
$139$	−8.60240			−0.729646			−0.364823	−	0.931077i	$-0.618871\pi$
$139$	−8.60240			−0.729646			−0.364823	+	0.931077i	$0.618871\pi$
$140$	−1.05553	−	2.82683i	−0.0892086	−	0.238911i
$141$	−1.66901			−0.140556
$142$	19.6877	−	7.22332i	1.65216	−	0.606167i
$143$	−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
$148$	−9.83969	−	0.809725i	−0.808818	−	0.0665590i
$149$		−	13.3726i		−	1.09553i	−0.836632	−	0.547765i	$-0.815479\pi$
$149$		−	13.3726i		−	1.09553i	0.836632	−	0.547765i	$-0.184521\pi$
$150$	1.70880	+	3.58136i	0.139523	+	0.292417i
$151$		−	13.1674i		−	1.07155i	−0.844362	−	0.535774i	$-0.820020\pi$
$151$		−	13.1674i		−	1.07155i	0.844362	−	0.535774i	$-0.179980\pi$
$152$	−16.7206	−	9.48188i	−1.35622	−	0.769082i
$153$	−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	$0.696442\pi$
$158$	−4.96530	−	13.5333i	−0.395018	−	1.07665i
$159$	2.81888			0.223552
$160$	−10.2439	+	7.42048i	−0.809848	+	0.586640i
$161$	−3.99420			−0.314787
$162$	3.05172	+	8.31771i	0.239766	+	0.653501i
$163$	−6.43698	−	6.43698i	−0.504183	−	0.504183i	0.408552	−	0.912735i	$-0.366034\pi$
$163$	−6.43698	−	6.43698i	−0.504183	−	0.504183i	−0.912735	+	0.408552i	$0.866034\pi$
$164$	−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	$-0.345893\pi$
$167$	17.4526	−	17.4526i	1.35052	−	1.35052i	0.885075	−	0.465448i	$-0.154107\pi$
$168$	0.931598	+	0.528287i	0.0718743	+	0.0407582i
$169$		−	1.00000i		−	0.0769231i
$170$	0.00722935	+	1.26404i	0.000554466	+	0.0969478i
$171$			18.2478i			1.39544i
$172$	−8.85652	−	0.728818i	−0.675304	−	0.0555719i
$173$	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
$178$	22.5073	−	8.25781i	1.68699	−	0.618949i
$179$	11.6248			0.868879			0.434439	−	0.900701i	$-0.356947\pi$
$179$	11.6248			0.868879			0.434439	+	0.900701i	$0.356947\pi$
$180$	10.9247	+	4.98432i	0.814280	+	0.371509i
$181$	6.67011			0.495786			0.247893	−	0.968787i	$-0.420262\pi$
$181$	6.67011			0.495786			0.247893	+	0.968787i	$0.420262\pi$
$182$	0.895816	−	0.328670i	0.0664023	−	0.0243627i
$183$	−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
$188$	−0.487840	+	5.92818i	−0.0355794	+	0.432357i
$189$		−	2.15261i		−	0.156579i
$190$	15.2830	+	15.1092i	1.10874	+	1.09613i
$191$			2.00979i			0.145423i	0.997353	+	0.0727116i	$0.0231653\pi$
$191$			2.00979i			0.145423i	−0.997353	+	0.0727116i	$0.976835\pi$
$192$	1.09469	−	4.35393i	0.0790024	−	0.314218i
$193$	−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	$0.676488\pi$
$198$	5.40138	+	14.7219i	0.383859	+	1.04624i
$199$	−9.96517			−0.706412			−0.353206	−	0.935546i	$-0.614909\pi$
$199$	−9.96517			−0.706412			−0.353206	+	0.935546i	$0.614909\pi$
$200$	13.2202	−	5.02271i	0.934806	−	0.355159i
$201$	−6.69686			−0.472360
$202$	6.09030	+	16.5996i	0.428512	+	1.16794i
$203$	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
$208$	−2.32800	−	3.25276i	−0.161417	−	0.225538i
$209$			28.0653i			1.94131i
$210$	−0.851499	−	0.841814i	−0.0587590	−	0.0580907i
$211$			13.5418i			0.932253i	0.884718	+	0.466127i	$0.154351\pi$
$211$			13.5418i			0.932253i	−0.884718	+	0.466127i	$0.845649\pi$
$212$	0.823940	−	10.0124i	0.0565884	−	0.687656i
$213$	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
$218$	−18.9942	+	6.96887i	−1.28645	+	0.471992i
$219$	2.69086			0.181831
$220$	16.8023	+	7.66592i	1.13281	+	0.516836i
$221$	−0.399733			−0.0268889
$222$	−3.67799	+	1.34943i	−0.246850	+	0.0905681i
$223$	−4.34527	−	4.34527i	−0.290981	−	0.290981i	0.546487	−	0.837468i	$-0.315965\pi$
$223$	−4.34527	−	4.34527i	−0.290981	−	0.290981i	−0.837468	+	0.546487i	$0.815965\pi$
$224$	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	−0.746065	−	0.665873i	$-0.768059\pi$
$227$	−1.20822	+	1.20822i	−0.0801924	+	0.0801924i	0.665873	+	0.746065i	$0.268059\pi$
$228$	−7.60186	−	0.625570i	−0.503446	−	0.0414294i
$229$		−	28.9612i		−	1.91381i	−0.290401	−	0.956905i	$-0.593789\pi$
$229$		−	28.9612i		−	1.91381i	0.290401	−	0.956905i	$-0.406211\pi$
$230$	−0.107061	−	18.7196i	−0.00705941	−	1.23433i
$231$		−	1.56367i		−	0.102882i
$232$	3.15388	−	5.56164i	0.207062	−	0.365140i
$233$	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
$238$	−0.131380	−	0.358087i	−0.00851611	−	0.0232113i
$239$	3.91031			0.252937			0.126468	−	0.991971i	$-0.459636\pi$
$239$	3.91031			0.252937			0.126468	+	0.991971i	$0.459636\pi$
$240$	−2.45094	+	4.38026i	−0.158208	+	0.282745i
$241$	−4.12175			−0.265505			−0.132753	−	0.991149i	$-0.542382\pi$
$241$	−4.12175			−0.265505			−0.132753	+	0.991149i	$0.542382\pi$
$242$	2.94908	+	8.03796i	0.189574	+	0.516700i
$243$	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
$248$	8.91065	−	15.7133i	0.565827	−	0.997796i
$249$			0.327185i			0.0207345i
$250$	−15.7336	+	1.56693i	−0.995077	+	0.0991012i
$251$		−	10.0017i		−	0.631302i	−0.948875	−	0.315651i	$-0.897777\pi$
$251$		−	10.0017i		−	0.631302i	0.948875	−	0.315651i	$-0.102223\pi$
$252$	−3.61118	−	0.297170i	−0.227483	−	0.0187199i
$253$	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	$0.691984\pi$
$258$	−3.31049	+	1.21460i	−0.206102	+	0.0756177i
$259$	−3.33077			−0.206964
$260$	1.56438	+	4.18959i	0.0970190	+	0.259828i
$261$	−6.06961			−0.375699
$262$	0.535124	−	0.196334i	0.0330601	−	0.0121296i
$263$	−0.476830	−	0.476830i	−0.0294026	−	0.0294026i	0.692253	−	0.721655i	$-0.256618\pi$
$263$	−0.476830	−	0.476830i	−0.0294026	−	0.0294026i	−0.721655	+	0.692253i	$0.756618\pi$
$264$	−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
$268$	−1.95745	+	23.7867i	−0.119570	+	1.45300i
$269$			4.67122i			0.284810i	0.989809	+	0.142405i	$0.0454835\pi$
$269$			4.67122i			0.284810i	−0.989809	+	0.142405i	$0.954517\pi$
$270$	10.0886	−	0.0576989i	0.613973	−	0.00351145i
$271$			23.3689i			1.41956i	0.704423	+	0.709781i	$0.251206\pi$
$271$			23.3689i			1.41956i	−0.704423	+	0.709781i	$0.748794\pi$
$272$	−1.30023	+	0.930576i	−0.0788382	+	0.0564245i
$273$	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	$0.661144\pi$
$278$	4.19037	+	11.4212i	0.251322	+	0.684997i
$279$	−17.1485			−1.02665
$280$	−3.23894	+	2.77840i	−0.193564	+	0.166041i
$281$	22.1253			1.31988			0.659942	−	0.751317i	$-0.270581\pi$
$281$	22.1253			1.31988			0.659942	+	0.751317i	$0.270581\pi$
$282$	0.813001	+	2.21590i	0.0484135	+	0.131955i
$283$	−12.3982	−	12.3982i	−0.736994	−	0.736994i	0.235001	−	0.971995i	$-0.424491\pi$
$283$	−12.3982	−	12.3982i	−0.736994	−	0.736994i	−0.971995	+	0.235001i	$0.924491\pi$
$284$	−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
$288$	2.83029	+	14.9231i	0.166776	+	0.879350i
$289$		−	16.8402i		−	0.990601i
$290$	−5.02564	+	5.08345i	−0.295115	+	0.298511i
$291$			2.06138i			0.120841i
$292$	0.786520	−	9.55770i	0.0460276	−	0.559322i
$293$	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
$298$	−17.7545	+	6.51404i	−1.02849	+	0.377348i
$299$	5.91974			0.342347
$300$	3.92249	−	4.01327i	0.226465	−	0.231706i
$301$	−2.99796			−0.172800
$302$	−17.4820	+	6.41405i	−1.00598	+	0.369087i
$303$	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	$0.504245\pi$
$307$	−17.7535	+	17.7535i	−1.01325	+	1.01325i	−0.999911	+	0.0133370i	$0.995755\pi$
$308$	−5.55402	−	0.457049i	−0.316470	−	0.0260428i
$309$		−	2.70119i		−	0.153665i
$310$	−14.1989	+	14.3623i	−0.806445	+	0.815722i
$311$		−	2.76330i		−	0.156692i	−0.996926	−	0.0783462i	$-0.975036\pi$
$311$		−	2.76330i		−	0.156692i	0.996926	−	0.0783462i	$-0.0249639\pi$
$312$	−1.38070	−	0.782965i	−0.0781670	−	0.0443267i
$313$	−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	$0.651114\pi$
$318$	−1.37312	−	3.74256i	−0.0770009	−	0.209872i
$319$	−9.33511			−0.522666
$320$	14.8419	+	9.98586i	0.829689	+	0.558226i
$321$	3.11396			0.173805
$322$	1.94564	+	5.30300i	0.108426	+	0.295525i
$323$	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
$328$	7.70684	+	4.37037i	0.425539	+	0.241313i
$329$			2.00671i			0.110633i
$330$	7.32841	−	0.0419128i	0.403416	−	0.00230722i
$331$		−	20.5227i		−	1.12803i	−0.825764	−	0.564016i	$-0.809256\pi$
$331$		−	20.5227i		−	1.12803i	0.825764	−	0.564016i	$-0.190744\pi$
$332$	1.16213	+	0.0956339i	0.0637804	+	0.00524859i
$333$	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	$-0.563172\pi$
$338$	−1.32767	+	0.487116i	−0.0722159	+	0.0264956i
$339$	8.91446			0.484167
$340$	1.67472	−	0.625335i	0.0908243	−	0.0339136i
$341$	−26.3745			−1.42826
$342$	24.2271	−	8.88880i	1.31005	−	0.480651i
$343$	−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	−0.854642	−	0.519218i	$-0.826223\pi$
$347$	−6.24824	+	6.24824i	−0.335423	+	0.335423i	0.519218	+	0.854642i	$0.326223\pi$
$348$	0.208078	−	2.52854i	0.0111542	−	0.135544i
$349$			3.89984i			0.208753i	0.994538	+	0.104377i	$0.0332848\pi$
$349$			3.89984i			0.208753i	−0.994538	+	0.104377i	$0.966715\pi$
$350$	4.30599	−	2.05455i	0.230165	−	0.109820i
$351$			3.19035i			0.170288i
$352$	4.35300	+	22.9518i	0.232016	+	1.22333i
$353$	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
$358$	−5.66263	−	15.4339i	−0.299279	−	0.815709i
$359$	−24.5997			−1.29832			−0.649162	−	0.760650i	$-0.724880\pi$
$359$	−24.5997			−1.29832			−0.649162	+	0.760650i	$0.724880\pi$
$360$	1.29595	−	16.9324i	0.0683023	−	0.892416i
$361$	27.1857			1.43083
$362$	−3.24912	−	8.85574i	−0.170770	−	0.465447i
$363$	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	−0.890626	−	0.454736i	$-0.849734\pi$
$367$	−8.35046	+	8.35046i	−0.435891	+	0.435891i	0.454736	+	0.890626i	$0.349734\pi$
$368$	19.2555	−	13.7811i	1.00376	−	0.718391i
$369$		−	8.41074i		−	0.437846i
$370$	−0.0892784	−	15.6103i	−0.00464136	−	0.811538i
$371$		−	3.38924i		−	0.175961i
$372$	0.587883	−	7.14389i	0.0304803	−	0.370394i
$373$	−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
$378$	−2.85797	+	1.04857i	−0.146998	+	0.0539328i
$379$	13.3405			0.685256			0.342628	−	0.939471i	$-0.388683\pi$
$379$	13.3405			0.685256			0.342628	+	0.939471i	$0.388683\pi$
$380$	12.6155	−	27.6508i	0.647159	−	1.41845i
$381$	7.52075			0.385300
$382$	2.66834	−	0.979001i	0.136524	−	0.0500900i
$383$	−23.6943	−	23.6943i	−1.21072	−	1.21072i	−0.970789	−	0.239933i	$-0.922875\pi$
$383$	−23.6943	−	23.6943i	−1.21072	−	1.21072i	−0.239933	−	0.970789i	$-0.577125\pi$
$384$	−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
$388$	7.32186	+	0.602528i	0.371711	+	0.0305887i
$389$			2.92067i			0.148084i	0.997255	+	0.0740418i	$0.0235898\pi$
$389$			2.92067i			0.148084i	−0.997255	+	0.0740418i	$0.976410\pi$
$390$	1.26199	+	1.24764i	0.0639034	+	0.0631766i
$391$		−	2.36631i		−	0.119670i
$392$	−9.13131	+	16.1024i	−0.461201	+	0.813296i
$393$	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	$0.983207\pi$
$398$	4.85420	+	13.2305i	0.243319	+	0.663185i
$399$	−2.57326			−0.128824
$400$	−13.1083	−	15.1054i	−0.655413	−	0.755270i
$401$	−4.36969			−0.218212			−0.109106	−	0.994030i	$-0.534799\pi$
$401$	−4.36969			−0.218212			−0.109106	+	0.994030i	$0.534799\pi$
$402$	3.26215	+	8.89125i	0.162701	+	0.443455i
$403$	−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
$408$	−0.312977	+	0.551913i	−0.0154947	+	0.0273238i
$409$		−	4.50695i		−	0.222854i	−0.993773	−	0.111427i	$-0.964458\pi$
$409$		−	4.50695i		−	0.222854i	0.993773	−	0.111427i	$-0.0355422\pi$
$410$	−7.04421	−	6.96409i	−0.347889	−	0.343932i
$411$		−	11.9578i		−	0.589836i
$412$	−9.59441	−	0.789540i	−0.472682	−	0.0388978i
$413$	−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
$418$	37.2615	−	13.6710i	1.82252	−	0.668673i
$419$	−18.5650			−0.906962			−0.453481	−	0.891266i	$-0.649818\pi$
$419$	−18.5650			−0.906962			−0.453481	+	0.891266i	$0.649818\pi$
$420$	−0.702876	+	1.54057i	−0.0342968	+	0.0751723i
$421$	−12.6368			−0.615881			−0.307940	−	0.951406i	$-0.599640\pi$
$421$	−12.6368			−0.615881			−0.307940	+	0.951406i	$0.599640\pi$
$422$	17.9790	−	6.59641i	0.875206	−	0.321108i
$423$	−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
$428$	0.910190	−	11.0605i	0.0439957	−	0.534631i
$429$			2.31749i			0.111889i
$430$	−0.0803579	−	14.0505i	−0.00387520	−	0.677575i
$431$			12.4884i			0.601544i	0.953696	+	0.300772i	$0.0972443\pi$
$431$			12.4884i			0.601544i	−0.953696	+	0.300772i	$0.902756\pi$
$432$	7.42712	+	10.3774i	0.357338	+	0.499285i
$433$	−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
$438$	−1.31076	−	3.57258i	−0.0626306	−	0.170705i
$439$	15.6930			0.748987			0.374494	−	0.927229i	$-0.377817\pi$
$439$	15.6930			0.748987			0.374494	+	0.927229i	$0.377817\pi$
$440$	1.99317	−	26.0422i	0.0950208	−	1.24151i
$441$	17.5731			0.836816
$442$	0.194716	+	0.530714i	0.00926171	+	0.0252435i
$443$	25.4951	+	25.4951i	1.21131	+	1.21131i	0.970597	+	0.240712i	$0.0773810\pi$
$443$	25.4951	+	25.4951i	1.21131	+	1.21131i	0.240712	+	0.970597i	$0.422619\pi$
$444$	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
$448$	−5.23488	−	1.31618i	−0.247325	−	0.0621839i
$449$			18.4241i			0.869486i	0.900555	+	0.434743i	$0.143161\pi$
$449$			18.4241i			0.869486i	−0.900555	+	0.434743i	$0.856839\pi$
$450$	−6.33542	+	17.8982i	−0.298655	+	0.843728i
$451$		−	12.9358i		−	0.609122i
$452$	2.60563	−	31.6634i	0.122559	−	1.48932i
$453$	−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	$0.858876\pi$
$458$	−38.4510	+	14.1075i	−1.79670	+	0.659199i
$459$	1.27529			0.0595253
$460$	−24.8013	+	9.26075i	−1.15637	+	0.431784i
$461$	−10.3914			−0.483976			−0.241988	−	0.970279i	$-0.577799\pi$
$461$	−10.3914			−0.483976			−0.241988	+	0.970279i	$0.577799\pi$
$462$	−2.07604	+	0.761689i	−0.0965862	+	0.0354370i
$463$	28.6939	+	28.6939i	1.33352	+	1.33352i	0.902198	+	0.431323i	$0.141953\pi$
$463$	28.6939	+	28.6939i	1.33352	+	1.33352i	0.431323	+	0.902198i	$0.358047\pi$
$464$	−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	−0.999701	−	0.0244401i	$-0.992220\pi$
$467$	−21.0756	+	21.0756i	−0.975261	+	0.975261i	0.0244401	+	0.999701i	$0.492220\pi$
$468$	5.35206	+	0.440430i	0.247399	+	0.0203589i
$469$			8.05188i			0.371801i
$470$	−9.40480	+	0.0537881i	−0.433811	+	0.00248106i
$471$		−	2.35509i		−	0.108517i
$472$	27.5271	+	15.6099i	1.26704	+	0.718506i
$473$	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
$478$	−1.90478	−	5.19162i	−0.0871224	−	0.237459i
$479$	−2.23544			−0.102140			−0.0510700	−	0.998695i	$-0.516263\pi$
$479$	−2.23544			−0.102140			−0.0510700	+	0.998695i	$0.516263\pi$
$480$	7.00945	+	1.12035i	0.319936	+	0.0511369i
$481$	4.93648			0.225084
$482$	2.00777	+	5.47234i	0.0914515	+	0.249258i
$483$	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	−0.0148107	−	0.999890i	$-0.504715\pi$
$487$	21.7388	−	21.7388i	0.985080	−	0.985080i	0.999890	+	0.0148107i	$0.00471458\pi$
$488$	3.07113	+	1.74157i	0.139024	+	0.0788371i
$489$			5.10857i			0.231017i
$490$	14.5506	−	14.7180i	0.657327	−	0.664889i
$491$			28.0576i			1.26622i	0.774061	+	0.633111i	$0.218222\pi$
$491$			28.0576i			1.26622i	−0.774061	+	0.633111i	$0.781778\pi$
$492$	3.50384	+	0.288337i	0.157965	+	0.0129992i
$493$	−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
$498$	0.434395	−	0.159377i	0.0194657	−	0.00714186i
$499$	−27.1042			−1.21335			−0.606676	−	0.794949i	$-0.707497\pi$
$499$	−27.1042			−1.21335			−0.606676	+	0.794949i	$0.707497\pi$
$500$	9.74444	+	20.1258i	0.435785	+	0.900051i
$501$	−13.8509			−0.618811
$502$	−13.2790	+	4.87199i	−0.592670	+	0.217448i
$503$	13.4274	+	13.4274i	0.598699	+	0.598699i	0.939966	−	0.341268i	$-0.110856\pi$
$503$	13.4274	+	13.4274i	0.598699	+	0.598699i	−0.341268	+	0.939966i	$0.610856\pi$
$504$	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
$508$	2.19826	−	26.7131i	0.0975322	−	1.18520i
$509$			20.6331i			0.914546i	0.889326	+	0.457273i	$0.151174\pi$
$509$			20.6331i			0.914546i	−0.889326	+	0.457273i	$0.848826\pi$
$510$	0.498722	−	0.504459i	0.0220838	−	0.0223378i
$511$		−	3.23532i		−	0.143122i
$512$	0.525340	+	22.6213i	0.0232170	+	0.999730i
$513$	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
$518$	1.62247	+	4.42217i	0.0712873	+	0.194299i
$519$	−3.76359			−0.165203
$520$	4.80038	−	4.11781i	0.210510	−	0.180578i
$521$	12.9140			0.565771			0.282886	−	0.959154i	$-0.408708\pi$
$521$	12.9140			0.565771			0.282886	+	0.959154i	$0.408708\pi$
$522$	2.95661	+	8.05846i	0.129407	+	0.352709i
$523$	3.59192	+	3.59192i	0.157064	+	0.157064i	0.781264	−	0.624200i	$-0.214575\pi$
$523$	3.59192	+	3.59192i	0.157064	+	0.157064i	−0.624200	+	0.781264i	$0.714575\pi$
$524$	−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
$528$	5.39510	+	7.53822i	0.234792	+	0.328059i
$529$			12.0433i			0.523623i
$530$	15.8843	−	0.0908457i	0.689970	−	0.00394609i
$531$		−	30.0412i		−	1.30368i
$532$	−0.752145	+	9.13999i	−0.0326096	+	0.396269i
$533$	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
$538$	6.20186	−	2.27543i	0.267381	−	0.0981007i
$539$	27.0276			1.16416
$540$	−4.99093	−	13.3663i	−0.214775	−	0.575193i
$541$	26.0058			1.11808			0.559038	−	0.829142i	$-0.311170\pi$
$541$	26.0058			1.11808			0.559038	+	0.829142i	$0.311170\pi$
$542$	31.0263	−	11.3834i	1.33269	−	0.488958i
$543$	−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	−0.533291	−	0.845932i	$-0.679045\pi$
$547$	7.31204	−	7.31204i	0.312640	−	0.312640i	0.845932	+	0.533291i	$0.179045\pi$
$548$	−42.4732	−	3.49519i	−1.81436	−	0.149307i
$549$		−	3.35163i		−	0.143044i
$550$	−9.74392	+	27.5275i	−0.415482	+	1.17378i
$551$			15.3624i			0.654458i
$552$	4.63495	−	8.17341i	0.197277	−	0.347884i
$553$	−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	$0.644981\pi$
$558$	8.35330	+	22.7676i	0.353623	+	0.963828i
$559$	4.44323			0.187929
$560$	5.26654	+	2.94685i	0.222552	+	0.124527i
$561$	0.926375			0.0391116
$562$	−10.7776	−	29.3751i	−0.454625	−	1.23912i
$563$	−31.4173	−	31.4173i	−1.32408	−	1.32408i	−0.910438	−	0.413645i	$-0.864255\pi$
$563$	−31.4173	−	31.4173i	−1.32408	−	1.32408i	−0.413645	−	0.910438i	$-0.635745\pi$
$564$	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
$568$	−20.6892	+	36.4840i	−0.868101	+	1.53084i
$569$			27.9496i			1.17171i	0.810417	+	0.585853i	$0.199241\pi$
$569$			27.9496i			1.17171i	−0.810417	+	0.585853i	$0.800759\pi$
$570$	−0.0689740	−	12.0600i	−0.00288900	−	0.505139i
$571$		−	16.2190i		−	0.678744i	−0.940652	−	0.339372i	$-0.889785\pi$
$571$		−	16.2190i		−	0.678744i	0.940652	−	0.339372i	$-0.110215\pi$
$572$	8.23151	+	0.677385i	0.344177	+	0.0283229i
$573$	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	$-0.506314\pi$
$578$	−22.3583	+	8.20314i	−0.929983	+	0.341206i
$579$	10.9771			0.456195
$580$	9.19723	+	4.19617i	0.381894	+	0.174237i
$581$	0.393386			0.0163204
$582$	2.73685	−	1.00413i	0.113446	−	0.0416227i
$583$	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	−0.841884	−	0.539658i	$-0.818554\pi$
$587$	−7.32237	+	7.32237i	−0.302227	+	0.302227i	0.539658	+	0.841884i	$0.318554\pi$
$588$	−0.602442	+	7.32081i	−0.0248443	+	0.301905i
$589$			43.4033i			1.78840i
$590$	−25.1603	−	24.8741i	−1.03583	−	1.02405i
$591$		−	3.60581i		−	0.148323i
$592$	16.0572	−	11.4921i	0.659945	−	0.472322i
$593$	−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
$598$	−2.88360	−	7.85948i	−0.117919	−	0.321398i
$599$	35.5811			1.45381			0.726903	−	0.686741i	$-0.240959\pi$
$599$	35.5811			1.45381			0.726903	+	0.686741i	$0.240959\pi$
$600$	−7.23902	−	3.25286i	−0.295532	−	0.132797i
$601$	13.9106			0.567423			0.283712	−	0.958910i	$-0.408434\pi$
$601$	13.9106			0.567423			0.283712	+	0.958910i	$0.408434\pi$
$602$	1.46036	+	3.98032i	0.0595197	+	0.162226i
$603$	−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	−0.860358	−	0.509690i	$-0.829760\pi$
$607$	−8.63954	+	8.63954i	−0.350668	+	0.350668i	0.509690	+	0.860358i	$0.329760\pi$
$608$	37.7707	−	7.16354i	1.53180	−	0.290520i
$609$		−	0.855920i		−	0.0346836i
$610$	−2.80708	−	2.77515i	−0.113655	−	0.112363i
$611$		−	2.97411i		−	0.120320i
$612$	0.176054	−	2.13939i	0.00711658	−	0.0864799i
$613$	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	$0.632082\pi$
$618$	−3.58630	+	1.31580i	−0.144262	+	0.0529290i
$619$	7.93318			0.318861			0.159431	−	0.987209i	$-0.449034\pi$
$619$	7.93318			0.318861			0.159431	+	0.987209i	$0.449034\pi$
$620$	25.9849	+	11.8554i	1.04358	+	0.476126i
$621$	−18.8860			−0.757871
$622$	−3.66876	+	1.34605i	−0.147104	+	0.0539716i
$623$	−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
$628$	−8.36509	−	0.688377i	−0.333803	−	0.0274692i
$629$		−	1.97327i		−	0.0786794i
$630$	−0.0327653	−	5.72898i	−0.00130540	−	0.228248i
$631$			6.80852i			0.271043i	0.990774	+	0.135521i	$0.0432710\pi$
$631$			6.80852i			0.271043i	−0.990774	+	0.135521i	$0.956729\pi$
$632$	25.0791	+	14.2218i	0.997592	+	0.565711i
$633$	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
$638$	4.54728	+	12.3940i	0.180029	+	0.490682i
$639$	39.8163			1.57511
$640$	6.02822	−	24.5695i	0.238286	−	0.971195i
$641$	38.7376			1.53004			0.765022	−	0.644004i	$-0.222728\pi$
$641$	38.7376			1.53004			0.765022	+	0.644004i	$0.222728\pi$
$642$	−1.51686	−	4.13433i	−0.0598658	−	0.163169i
$643$	28.5706	+	28.5706i	1.12672	+	1.12672i	0.990708	+	0.136008i	$0.0434273\pi$
$643$	28.5706	+	28.5706i	1.12672	+	1.12672i	0.136008	+	0.990708i	$0.456573\pi$
$644$	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	−0.994580	−	0.103976i	$-0.966844\pi$
$647$	−22.6536	+	22.6536i	−0.890604	+	0.890604i	0.103976	+	0.994580i	$0.466844\pi$
$648$	−15.4139	−	8.74083i	−0.605513	−	0.343372i
$649$		−	46.2036i		−	1.81365i
$650$	−6.38184	+	3.04501i	−0.250316	+	0.119435i
$651$		−	2.41823i		−	0.0947780i
$652$	18.1452	+	1.49320i	0.710621	+	0.0584782i
$653$	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
$658$	2.66425	−	0.977500i	0.103863	−	0.0381069i
$659$	39.9047			1.55447			0.777233	−	0.629212i	$-0.216622\pi$
$659$	39.9047			1.55447			0.777233	+	0.629212i	$0.216622\pi$
$660$	−3.62544	−	9.70933i	−0.141120	−	0.377935i
$661$	−22.4907			−0.874787			−0.437393	−	0.899270i	$-0.644098\pi$
$661$	−22.4907			−0.874787			−0.437393	+	0.899270i	$0.644098\pi$
$662$	−27.2475	+	9.99696i	−1.05900	+	0.388543i
$663$	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
$668$	−4.04851	+	49.1971i	−0.156642	+	1.90349i
$669$			3.44852i			0.133328i
$670$	−37.7366	+	0.215824i	−1.45789	+	0.00833800i
$671$		−	5.15484i		−	0.199000i
$672$	−2.10441	+	0.399120i	−0.0811794	+	0.0153964i
$673$	−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	$0.927879\pi$
$678$	−4.34238	−	11.8355i	−0.166768	−	0.454539i
$679$	2.47848			0.0951152
$680$	−1.64602	−	1.91887i	−0.0631221	−	0.0735852i
$681$	0.958877			0.0367443
$682$	12.8474	+	35.0167i	0.491954	+	1.34086i
$683$	−28.7846	−	28.7846i	−1.10141	−	1.10141i	−0.994241	−	0.107171i	$-0.965821\pi$
$683$	−28.7846	−	28.7846i	−1.10141	−	1.10141i	−0.107171	−	0.994241i	$-0.534179\pi$
$684$	−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
$688$	14.4528	−	10.3438i	0.551006	−	0.394355i
$689$			5.02314i			0.191366i
$690$	−7.38570	+	7.47066i	−0.281169	+	0.284403i
$691$		−	22.8571i		−	0.869526i	−0.900545	−	0.434763i	$-0.856832\pi$
$691$		−	22.8571i		−	0.869526i	0.900545	−	0.434763i	$-0.143168\pi$
$692$	−1.10007	+	13.3680i	−0.0418184	+	0.508173i
$693$	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
$698$	5.17771	−	1.89967i	0.195979	−	0.0719037i
$699$	−3.70130			−0.139996
$700$	−4.82529	−	4.71615i	−0.182379	−	0.178254i
$701$	14.5556			0.549756			0.274878	−	0.961479i	$-0.411363\pi$
$701$	14.5556			0.549756			0.274878	+	0.961479i	$0.411363\pi$
$702$	4.23574	−	1.55407i	0.159868	−	0.0586547i
$703$	−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
$708$	12.5149	+	1.02987i	0.470338	+	0.0387049i
$709$		−	15.9737i		−	0.599907i	−0.953954	−	0.299953i	$-0.903029\pi$
$709$		−	15.9737i		−	0.599907i	0.953954	−	0.299953i	$-0.0969711\pi$
$710$	32.9679	−	33.3471i	1.23726	−	1.25150i
$711$		−	27.3697i		−	1.02644i
$712$	−23.6523	+	41.7091i	−0.886406	+	1.56312i
$713$	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
$718$	11.9829	+	32.6604i	0.447199	+	1.21888i
$719$	2.30805			0.0860756			0.0430378	−	0.999073i	$-0.486296\pi$
$719$	2.30805			0.0860756			0.0430378	+	0.999073i	$0.486296\pi$
$720$	−23.1120	+	6.52746i	−0.861333	+	0.243264i
$721$	−3.24774			−0.120952
$722$	−13.2426	−	36.0937i	−0.492839	−	1.34327i
$723$	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	$0.651163\pi$
$727$	−36.3079	+	36.3079i	−1.34658	+	1.34658i	−0.889342	+	0.457242i	$0.848837\pi$
$728$	−0.941387	+	1.66007i	−0.0348901	+	0.0615263i
$729$			11.4506i			0.424096i
$730$	15.1629	−	0.0867199i	0.561204	−	0.00320965i
$731$		−	1.77610i		−	0.0656916i
$732$	1.39626	+	0.114901i	0.0516072	+	0.00424685i
$733$	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
$738$	−11.1667	+	4.09701i	−0.411053	+	0.150813i
$739$	−27.4036			−1.00806			−0.504030	−	0.863686i	$-0.668150\pi$
$739$	−27.4036			−1.00806			−0.504030	+	0.863686i	$0.668150\pi$
$740$	−20.6818	+	7.72254i	−0.760279	+	0.283886i
$741$	3.81378			0.140103
$742$	−4.49981	+	1.65096i	−0.165193	+	0.0606085i
$743$	−30.3545	−	30.3545i	−1.11360	−	1.11360i	−0.992660	−	0.120937i	$-0.961410\pi$
$743$	−30.3545	−	30.3545i	−1.11360	−	1.11360i	−0.120937	−	0.992660i	$-0.538590\pi$
$744$	−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
$748$	0.270773	−	3.29040i	0.00990044	−	0.120309i
$749$		−	3.74403i		−	0.136804i
$750$	6.86507	+	5.62151i	0.250677	+	0.205269i
$751$		−	25.9682i		−	0.947594i	−0.880634	−	0.473797i	$-0.842883\pi$
$751$		−	25.9682i		−	0.947594i	0.880634	−	0.473797i	$-0.157117\pi$
$752$	−6.92371	−	9.67405i	−0.252482	−	0.352776i
$753$	−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	$0.527896\pi$
$758$	−6.49838	−	17.7118i	−0.236032	−	0.643323i
$759$	−13.7189			−0.497965
$760$	−42.8564	−	3.28007i	−1.55456	−	0.118981i
$761$	5.38965			0.195375			0.0976873	−	0.995217i	$-0.468855\pi$
$761$	5.38965			0.195375			0.0976873	+	0.995217i	$0.468855\pi$
$762$	−3.66348	−	9.98510i	−0.132714	−	0.361722i
$763$	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
$768$	3.96177	+	8.05758i	0.142958	+	0.290753i
$769$			6.24953i			0.225364i	0.993631	+	0.112682i	$0.0359441\pi$
$769$			6.24953i			0.225364i	−0.993631	+	0.112682i	$0.964056\pi$
$770$	−0.0503932	−	8.81121i	−0.00181605	−	0.317534i
$771$		−	3.26127i		−	0.117452i
$772$	3.20854	−	38.9899i	0.115478	−	1.40328i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.487116 - 1.32767i) q^{2} +(-0.396814 - 0.396814i) q^{3} +(-1.52544 + 1.29346i) q^{4} +(2.02359 - 0.951360i) q^{5} +(-0.333545 + 0.720134i) q^{6} +(-0.477103 + 0.477103i) q^{7} +(2.46036 + 1.39521i) q^{8} -2.68508i q^{9} +O(q^{10})\)	\(q+(-0.487116 - 1.32767i) 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} +(2.46036 + 1.39521i) q^{8} -2.68508i q^{9} +(-2.24882 - 2.22324i) q^{10} -4.12967i q^{11} +(1.11858 + 0.0920497i) 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} +(-3.56491 + 1.30795i) q^{18} -6.79601 q^{19} +(-1.85630 + 4.06868i) q^{20} +0.378643 q^{21} +(-5.48285 + 2.01163i) 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} +(0.110675 - 1.34491i) q^{28} -2.26050i q^{29} +(0.0101492 + 1.77458i) q^{30} -6.38658i q^{31} +(-5.55778 + 1.05408i) 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} +(3.31045 + 9.02288i) q^{38} -0.561180 q^{39} +(6.30611 + 0.482647i) q^{40} +3.13240 q^{41} +(-0.184443 - 0.502714i) 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} +(-1.82538 + 1.30642i) q^{48} +6.54474i q^{49} +(-6.66579 - 2.35949i) q^{50} +0.224322i q^{51} +(-0.164029 + 1.99326i) 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} +(-3.00120 + 1.10113i) q^{58} +11.1882 q^{59} +(2.35112 - 0.877900i) q^{60} +1.24825 q^{61} +(-8.47930 + 3.11101i) 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} +(0.796772 + 0.0655677i) q^{68} -3.32204i q^{69} +(2.13364 - 0.0122027i) q^{70} +14.8287i q^{71} +(3.74626 - 6.60626i) 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} +(0.273360 + 0.745063i) q^{78} +10.1932 q^{79} +(-2.43101 - 8.60757i) q^{80} -6.26487 q^{81} +(-1.52584 - 4.15881i) 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} +(5.76177 - 10.1605i) q^{88} +16.9524i q^{89} +(-5.96958 + 6.03826i) q^{90} +0.674726i q^{91} +(-11.7996 - 0.971008i) 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} +(8.68929 - 3.18805i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more