LMFDB - Embedded newform 390.2.x.b.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(49,390)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("390.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.x (of order $6$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.3
Root			$-0.330925 - 1.46916i$ of defining polynomial
Character	$\chi$	$=$	390.199
Dual form			390.2.x.b.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.571769 + 2.16173i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.603137 + 1.04466i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.571769 + 2.16173i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.603137 + 1.04466i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.15800 + 0.585699i) q^{10} +(4.46182 + 2.57603i) q^{11} +1.00000i q^{12} +(2.24511 - 2.82126i) q^{13} +1.20627 q^{14} +(0.585699 - 2.15800i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.10150 - 2.36800i) q^{17} +1.00000 q^{18} +(-1.84474 + 1.06506i) q^{19} +(1.58623 - 1.57603i) q^{20} -1.20627i q^{21} +(4.46182 - 2.57603i) q^{22} +(-1.88293 - 1.08711i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.34616 + 2.47202i) q^{25} +(-1.32073 - 3.35495i) q^{26} -1.00000i q^{27} +(0.603137 - 1.04466i) q^{28} +(2.38346 - 4.12828i) q^{29} +(-1.57603 - 1.58623i) q^{30} +5.91046i q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.57603 - 4.46182i) q^{33} -4.73601i q^{34} +(-1.91343 + 1.90113i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.20034 + 3.81110i) q^{37} +2.13012i q^{38} +(-3.35495 + 1.32073i) q^{39} +(-0.571769 - 2.16173i) q^{40} +(4.10150 + 2.36800i) q^{41} +(-1.04466 - 0.603137i) q^{42} +(1.70944 - 0.986944i) q^{43} -5.15206i q^{44} +(-1.58623 + 1.57603i) q^{45} +(-1.88293 + 1.08711i) q^{46} +0.852296 q^{47} +(0.866025 - 0.500000i) q^{48} +(2.77245 - 4.80203i) q^{49} +(-0.0322474 + 4.99990i) q^{50} -4.73601 q^{51} +(-3.56583 - 0.533691i) q^{52} -4.48042i q^{53} +(-0.866025 - 0.500000i) q^{54} +(-3.01756 + 11.1181i) q^{55} +(-0.603137 - 1.04466i) q^{56} +2.13012 q^{57} +(-2.38346 - 4.12828i) q^{58} +(1.68133 - 0.970715i) q^{59} +(-2.16173 + 0.571769i) q^{60} +(-1.53795 - 2.66381i) q^{61} +(5.11861 + 2.95523i) q^{62} +(-0.603137 + 1.04466i) q^{63} +1.00000 q^{64} +(7.38248 + 3.24021i) q^{65} -5.15206 q^{66} +(-7.02765 + 12.1723i) q^{67} +(-4.10150 - 2.36800i) q^{68} +(1.08711 + 1.88293i) q^{69} +(0.689710 + 2.60764i) q^{70} +(-0.298707 + 0.172459i) q^{71} +(-0.500000 - 0.866025i) q^{72} -15.7228 q^{73} +(2.20034 + 3.81110i) q^{74} +(4.99990 + 0.0322474i) q^{75} +(1.84474 + 1.06506i) q^{76} +6.21480i q^{77} +(-0.533691 + 3.56583i) q^{78} -13.5863 q^{79} +(-2.15800 - 0.585699i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.10150 - 2.36800i) q^{82} -10.2045 q^{83} +(-1.04466 + 0.603137i) q^{84} +(7.46410 + 7.51240i) q^{85} -1.97389i q^{86} +(-4.12828 + 2.38346i) q^{87} +(-4.46182 - 2.57603i) q^{88} +(14.1941 + 8.19497i) q^{89} +(0.571769 + 2.16173i) q^{90} +(4.30137 + 0.643777i) q^{91} +2.17422i q^{92} +(2.95523 - 5.11861i) q^{93} +(0.426148 - 0.738110i) q^{94} +(-3.35713 - 3.37886i) q^{95} -1.00000i q^{96} +(-4.24139 - 7.34631i) q^{97} +(-2.77245 - 4.80203i) q^{98} +5.15206i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9	$ 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9} + 4 q^{10} + 6 q^{11} + 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} - 18 q^{17} + 12 q^{18} - 6 q^{19} + 2 q^{20} + 6 q^{22} - 6 q^{23} - 10 q^{25} - 2 q^{26} + 2 q^{28} + 14 q^{29} + 6 q^{30} + 6 q^{32} - 6 q^{33} - 22 q^{35} + 6 q^{36} + 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} + 12 q^{42} + 36 q^{43} - 2 q^{45} - 6 q^{46} - 16 q^{47} + 8 q^{49} - 20 q^{50} + 16 q^{51} - 10 q^{52} + 8 q^{55} - 2 q^{56} + 8 q^{57} - 14 q^{58} - 36 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{63} + 12 q^{64} - 44 q^{65} - 12 q^{66} - 4 q^{67} + 18 q^{68} + 16 q^{69} + 4 q^{70} - 12 q^{71} - 6 q^{72} - 28 q^{73} - 12 q^{74} + 16 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} - 4 q^{80} - 6 q^{81} - 18 q^{82} - 72 q^{83} + 12 q^{84} + 48 q^{85} - 6 q^{87} - 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{93} - 8 q^{94} + 18 q^{95} + 48 q^{97} - 8 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9 + 4 * q^10 + 6 * q^11 + 8 * q^13 + 4 * q^14 + 6 * q^15 - 6 * q^16 - 18 * q^17 + 12 * q^18 - 6 * q^19 + 2 * q^20 + 6 * q^22 - 6 * q^23 - 10 * q^25 - 2 * q^26 + 2 * q^28 + 14 * q^29 + 6 * q^30 + 6 * q^32 - 6 * q^33 - 22 * q^35 + 6 * q^36 + 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 + 12 * q^42 + 36 * q^43 - 2 * q^45 - 6 * q^46 - 16 * q^47 + 8 * q^49 - 20 * q^50 + 16 * q^51 - 10 * q^52 + 8 * q^55 - 2 * q^56 + 8 * q^57 - 14 * q^58 - 36 * q^59 + 10 * q^61 - 6 * q^62 - 2 * q^63 + 12 * q^64 - 44 * q^65 - 12 * q^66 - 4 * q^67 + 18 * q^68 + 16 * q^69 + 4 * q^70 - 12 * q^71 - 6 * q^72 - 28 * q^73 - 12 * q^74 + 16 * q^75 + 6 * q^76 + 2 * q^78 + 4 * q^79 - 4 * q^80 - 6 * q^81 - 18 * q^82 - 72 * q^83 + 12 * q^84 + 48 * q^85 - 6 * q^87 - 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^93 - 8 * q^94 + 18 * q^95 + 48 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.571769	+	2.16173i	0.255703	+	0.966755i
$5$	0.571769	+	2.16173i	0.255703	+	0.966755i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	0.603137	+	1.04466i	0.227964	+	0.394846i	0.957205	−	0.289412i	$-0.0934597\pi$
$7$	0.603137	+	1.04466i	0.227964	+	0.394846i	−0.729240	+	0.684258i	$0.760126\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.15800	+	0.585699i	0.682419	+	0.185214i
$11$	4.46182	+	2.57603i	1.34529	+	0.776703i	0.987578	−	0.157130i	$-0.0502240\pi$
$11$	4.46182	+	2.57603i	1.34529	+	0.776703i	0.357711	+	0.933832i	$0.383557\pi$
$12$			1.00000i			0.288675i
$13$	2.24511	−	2.82126i	0.622681	−	0.782476i
$13$	2.24511	−	2.82126i	0.622681	−	0.782476i
$14$	1.20627			0.322390
$15$	0.585699	−	2.15800i	0.151227	−	0.557193i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.10150	−	2.36800i	0.994761	−	0.574326i	0.0880670	−	0.996115i	$-0.471931\pi$
$17$	4.10150	−	2.36800i	0.994761	−	0.574326i	0.906694	+	0.421789i	$0.138598\pi$
$18$	1.00000			0.235702
$19$	−1.84474	+	1.06506i	−0.423212	+	0.244341i	−0.696450	−	0.717605i	$-0.745238\pi$
$19$	−1.84474	+	1.06506i	−0.423212	+	0.244341i	0.273239	+	0.961946i	$0.411905\pi$
$20$	1.58623	−	1.57603i	0.354692	−	0.352411i
$21$		−	1.20627i		−	0.263231i
$22$	4.46182	−	2.57603i	0.951263	−	0.549212i
$23$	−1.88293	−	1.08711i	−0.392618	−	0.226678i	0.290676	−	0.956822i	$-0.406120\pi$
$23$	−1.88293	−	1.08711i	−0.392618	−	0.226678i	−0.683294	+	0.730144i	$0.739453\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−4.34616	+	2.47202i	−0.869232	+	0.494404i
$26$	−1.32073	−	3.35495i	−0.259016	−	0.657960i
$27$		−	1.00000i		−	0.192450i
$28$	0.603137	−	1.04466i	0.113982	−	0.197423i
$29$	2.38346	−	4.12828i	0.442598	−	0.766602i	−0.555283	−	0.831661i	$-0.687390\pi$
$29$	2.38346	−	4.12828i	0.442598	−	0.766602i	0.997881	+	0.0650589i	$0.0207235\pi$
$30$	−1.57603	−	1.58623i	−0.287743	−	0.289605i
$31$			5.91046i			1.06155i	0.847513	+	0.530775i	$0.178099\pi$
$31$			5.91046i			1.06155i	−0.847513	+	0.530775i	$0.821901\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.57603	−	4.46182i	−0.448430	−	0.776703i
$34$		−	4.73601i		−	0.812219i
$35$	−1.91343	+	1.90113i	−0.323428	+	0.321349i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.20034	+	3.81110i	−0.361734	+	0.626541i	−0.988246	−	0.152870i	$-0.951148\pi$
$37$	−2.20034	+	3.81110i	−0.361734	+	0.626541i	0.626513	+	0.779411i	$0.284482\pi$
$38$			2.13012i			0.345551i
$39$	−3.35495	+	1.32073i	−0.537222	+	0.211486i
$40$	−0.571769	−	2.16173i	−0.0904046	−	0.341800i
$41$	4.10150	+	2.36800i	0.640547	+	0.369820i	0.784825	−	0.619717i	$-0.212753\pi$
$41$	4.10150	+	2.36800i	0.640547	+	0.369820i	−0.144278	+	0.989537i	$0.546086\pi$
$42$	−1.04466	−	0.603137i	−0.161195	−	0.0930660i
$43$	1.70944	−	0.986944i	0.260687	−	0.150508i	−0.363961	−	0.931414i	$-0.618576\pi$
$43$	1.70944	−	0.986944i	0.260687	−	0.150508i	0.624648	+	0.780907i	$0.285243\pi$
$44$		−	5.15206i		−	0.776703i
$45$	−1.58623	+	1.57603i	−0.236461	+	0.234941i
$46$	−1.88293	+	1.08711i	−0.277623	+	0.160285i
$47$	0.852296			0.124320			0.0621600	−	0.998066i	$-0.480201\pi$
$47$	0.852296			0.124320			0.0621600	+	0.998066i	$0.480201\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	2.77245	−	4.80203i	0.396065	−	0.686004i
$50$	−0.0322474	+	4.99990i	−0.00456046	+	0.707092i
$51$	−4.73601			−0.663174
$52$	−3.56583	−	0.533691i	−0.494492	−	0.0740096i
$53$		−	4.48042i		−	0.615433i	−0.951478	−	0.307716i	$-0.900435\pi$
$53$		−	4.48042i		−	0.615433i	0.951478	−	0.307716i	$-0.0995648\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−3.01756	+	11.1181i	−0.406888	+	1.49917i
$56$	−0.603137	−	1.04466i	−0.0805976	−	0.139599i
$57$	2.13012			0.282141
$58$	−2.38346	−	4.12828i	−0.312964	−	0.542070i
$59$	1.68133	−	0.970715i	0.218890	−	0.126376i	−0.386546	−	0.922270i	$-0.626332\pi$
$59$	1.68133	−	0.970715i	0.218890	−	0.126376i	0.605436	+	0.795894i	$0.292999\pi$
$60$	−2.16173	+	0.571769i	−0.279078	+	0.0738150i
$61$	−1.53795	−	2.66381i	−0.196915	−	0.341066i	0.750612	−	0.660744i	$-0.229759\pi$
$61$	−1.53795	−	2.66381i	−0.196915	−	0.341066i	−0.947527	+	0.319677i	$0.896426\pi$
$62$	5.11861	+	2.95523i	0.650064	+	0.375315i
$63$	−0.603137	+	1.04466i	−0.0759881	+	0.131615i
$64$	1.00000			0.125000
$65$	7.38248	+	3.24021i	0.915684	+	0.401899i
$66$	−5.15206			−0.634175
$67$	−7.02765	+	12.1723i	−0.858564	+	1.48708i	0.0147340	+	0.999891i	$0.495310\pi$
$67$	−7.02765	+	12.1723i	−0.858564	+	1.48708i	−0.873298	+	0.487186i	$0.838023\pi$
$68$	−4.10150	−	2.36800i	−0.497380	−	0.287163i
$69$	1.08711	+	1.88293i	0.130873	+	0.226678i
$70$	0.689710	+	2.60764i	0.0824361	+	0.311673i
$71$	−0.298707	+	0.172459i	−0.0354500	+	0.0204671i	−0.517620	−	0.855610i	$-0.673182\pi$
$71$	−0.298707	+	0.172459i	−0.0354500	+	0.0204671i	0.482170	+	0.876078i	$0.339849\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−15.7228			−1.84022			−0.920109	−	0.391662i	$-0.871900\pi$
$73$	−15.7228			−1.84022			−0.920109	+	0.391662i	$0.871900\pi$
$74$	2.20034	+	3.81110i	0.255784	+	0.443031i
$75$	4.99990	+	0.0322474i	0.577338	+	0.00372360i
$76$	1.84474	+	1.06506i	0.211606	+	0.122171i
$77$			6.21480i			0.708242i
$78$	−0.533691	+	3.56583i	−0.0604286	+	0.403751i
$79$	−13.5863			−1.52858			−0.764290	−	0.644873i	$-0.776910\pi$
$79$	−13.5863			−1.52858			−0.764290	+	0.644873i	$0.776910\pi$
$80$	−2.15800	−	0.585699i	−0.241272	−	0.0654831i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.10150	−	2.36800i	0.452935	−	0.261502i
$83$	−10.2045			−1.12009			−0.560046	−	0.828462i	$-0.689216\pi$
$83$	−10.2045			−1.12009			−0.560046	+	0.828462i	$0.689216\pi$
$84$	−1.04466	+	0.603137i	−0.113982	+	0.0658076i
$85$	7.46410	+	7.51240i	0.809595	+	0.814834i
$86$		−	1.97389i		−	0.212850i
$87$	−4.12828	+	2.38346i	−0.442598	+	0.255534i
$88$	−4.46182	−	2.57603i	−0.475631	−	0.274606i
$89$	14.1941	+	8.19497i	1.50457	+	0.868665i	0.999986	+	0.00530346i	$0.00168815\pi$
$89$	14.1941	+	8.19497i	1.50457	+	0.868665i	0.504586	+	0.863361i	$0.331645\pi$
$90$	0.571769	+	2.16173i	0.0602697	+	0.227866i
$91$	4.30137	+	0.643777i	0.450906	+	0.0674862i
$92$			2.17422i			0.226678i
$93$	2.95523	−	5.11861i	0.306443	−	0.530775i
$94$	0.426148	−	0.738110i	0.0439538	−	0.0761302i
$95$	−3.35713	−	3.37886i	−0.344435	−	0.346663i
$96$		−	1.00000i		−	0.102062i
$97$	−4.24139	−	7.34631i	−0.430648	−	0.745904i	0.566281	−	0.824212i	$-0.308382\pi$
$97$	−4.24139	−	7.34631i	−0.430648	−	0.745904i	−0.996929	+	0.0783078i	$0.975048\pi$
$98$	−2.77245	−	4.80203i	−0.280060	−	0.485078i
$99$			5.15206i			0.517802i
$100$	4.31391	+	2.52788i	0.431391	+	0.252788i
$101$	6.79121	−	11.7627i	0.675751	−	1.17044i	−0.300498	−	0.953783i	$-0.597153\pi$
$101$	6.79121	−	11.7627i	0.675751	−	1.17044i	0.976249	−	0.216653i	$-0.0695139\pi$
$102$	−2.36800	+	4.10150i	−0.234467	+	0.406109i
$103$		−	2.15696i		−	0.212531i	−0.994338	−	0.106266i	$-0.966111\pi$
$103$		−	2.15696i		−	0.212531i	0.994338	−	0.106266i	$-0.0338894\pi$
$104$	−2.24511	+	2.82126i	−0.220151	+	0.276647i
$105$	2.60764	−	0.689710i	0.254480	−	0.0673088i
$106$	−3.88016	−	2.24021i	−0.376874	−	0.217588i
$107$	−7.00959	−	4.04699i	−0.677642	−	0.391237i	0.121324	−	0.992613i	$-0.461286\pi$
$107$	−7.00959	−	4.04699i	−0.677642	−	0.391237i	−0.798966	+	0.601376i	$0.794619\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$		−	16.8839i		−	1.61718i	−0.588370	−	0.808592i	$-0.700230\pi$
$109$		−	16.8839i		−	1.61718i	0.588370	−	0.808592i	$-0.299770\pi$
$110$	8.11982	+	8.17235i	0.774194	+	0.779203i
$111$	3.81110	−	2.20034i	0.361734	−	0.208847i
$112$	−1.20627			−0.113982
$113$	−4.28771	+	2.47551i	−0.403354	+	0.232876i	−0.687930	−	0.725777i	$-0.741480\pi$
$113$	−4.28771	+	2.47551i	−0.403354	+	0.232876i	0.284576	+	0.958653i	$0.408147\pi$
$114$	1.06506	−	1.84474i	0.0997519	−	0.172775i
$115$	1.27344	−	4.69196i	0.118749	−	0.437527i
$116$	−4.76693			−0.442598
$117$	3.56583	+	0.533691i	0.329661	+	0.0493397i
$118$		−	1.94143i		−	0.178723i
$119$	4.94754	+	2.85646i	0.453540	+	0.261851i
$120$	−0.585699	+	2.15800i	−0.0534668	+	0.196997i
$121$	7.77188	+	13.4613i	0.706535	+	1.22375i
$122$	−3.07591			−0.278480
$123$	−2.36800	−	4.10150i	−0.213516	−	0.369820i
$124$	5.11861	−	2.95523i	0.459665	−	0.265388i
$125$	−7.82884	−	7.98180i	−0.700233	−	0.713914i
$126$	0.603137	+	1.04466i	0.0537317	+	0.0930660i
$127$	1.04089	+	0.600957i	0.0923639	+	0.0533263i	0.545471	−	0.838130i	$-0.316351\pi$
$127$	1.04089	+	0.600957i	0.0923639	+	0.0533263i	−0.453107	+	0.891456i	$0.649684\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.97389			−0.173791
$130$	6.49734	−	4.77331i	0.569855	−	0.418647i
$131$	−6.65149			−0.581143			−0.290572	−	0.956853i	$-0.593845\pi$
$131$	−6.65149			−0.581143			−0.290572	+	0.956853i	$0.593845\pi$
$132$	−2.57603	+	4.46182i	−0.224215	+	0.388351i
$133$	−2.22526	−	1.28475i	−0.192954	−	0.111402i
$134$	7.02765	+	12.1723i	0.607097	+	1.05152i
$135$	2.16173	−	0.571769i	0.186052	−	0.0492100i
$136$	−4.10150	+	2.36800i	−0.351701	+	0.203055i
$137$	7.35746	+	12.7435i	0.628590	+	1.08875i	0.987835	+	0.155507i	$0.0497010\pi$
$137$	7.35746	+	12.7435i	0.628590	+	1.08875i	−0.359245	+	0.933243i	$0.616966\pi$
$138$	2.17422			0.185082
$139$	−7.82540	−	13.5540i	−0.663742	−	1.14963i	−0.979625	−	0.200837i	$-0.935634\pi$
$139$	−7.82540	−	13.5540i	−0.663742	−	1.14963i	0.315883	−	0.948798i	$-0.397699\pi$
$140$	2.60314	+	0.706513i	0.220005	+	0.0597113i
$141$	−0.738110	−	0.426148i	−0.0621600	−	0.0358881i
$142$			0.344918i			0.0289448i
$143$	17.2849	−	6.80447i	1.44544	−	0.569018i
$144$	−1.00000			−0.0833333
$145$	10.2870	+	2.79198i	0.854290	+	0.231862i
$146$	−7.86142	+	13.6164i	−0.650615	+	1.12690i
$147$	−4.80203	+	2.77245i	−0.396065	+	0.228668i
$148$	4.40068			0.361734
$149$	−19.7555	+	11.4058i	−1.61843	+	0.934401i	−0.631103	+	0.775699i	$0.717398\pi$
$149$	−19.7555	+	11.4058i	−1.61843	+	0.934401i	−0.987327	+	0.158702i	$0.949269\pi$
$150$	2.52788	−	4.31391i	0.206400	−	0.352230i
$151$		−	19.8995i		−	1.61940i	−0.586845	−	0.809699i	$-0.699630\pi$
$151$		−	19.8995i		−	1.61940i	0.586845	−	0.809699i	$-0.300370\pi$
$152$	1.84474	−	1.06506i	0.149628	−	0.0863877i
$153$	4.10150	+	2.36800i	0.331587	+	0.191442i
$154$	5.38217	+	3.10740i	0.433708	+	0.250401i
$155$	−12.7768	+	3.37942i	−1.02626	+	0.271442i
$156$	2.82126	+	2.24511i	0.225881	+	0.179752i
$157$			4.74392i			0.378606i	0.981919	+	0.189303i	$0.0606228\pi$
$157$			4.74392i			0.378606i	−0.981919	+	0.189303i	$0.939377\pi$
$158$	−6.79315	+	11.7661i	−0.540434	+	0.936060i
$159$	−2.24021	+	3.88016i	−0.177660	+	0.307716i
$160$	−1.58623	+	1.57603i	−0.125402	+	0.124596i
$161$		−	2.62270i		−	0.206698i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−1.93329	−	3.34855i	−0.151427	−	0.262279i	0.780325	−	0.625374i	$-0.215053\pi$
$163$	−1.93329	−	3.34855i	−0.151427	−	0.262279i	−0.931752	+	0.363095i	$0.881720\pi$
$164$		−	4.73601i		−	0.369820i
$165$	8.17235	−	8.11982i	0.636217	−	0.632127i
$166$	−5.10226	+	8.83737i	−0.396012	+	0.685913i
$167$	11.3614	−	19.6785i	0.879173	−	1.52277i	0.0269225	−	0.999638i	$-0.491429\pi$
$167$	11.3614	−	19.6785i	0.879173	−	1.52277i	0.852250	−	0.523134i	$-0.175237\pi$
$168$			1.20627i			0.0930660i
$169$	−2.91899	−	12.6681i	−0.224538	−	0.974465i
$170$	10.2380	−	2.70790i	0.785217	−	0.207687i
$171$	−1.84474	−	1.06506i	−0.141071	−	0.0814471i
$172$	−1.70944	−	0.986944i	−0.130343	−	0.0752538i
$173$	4.06859	−	2.34900i	0.309329	−	0.178591i	−0.337297	−	0.941398i	$-0.609513\pi$
$173$	4.06859	−	2.34900i	0.309329	−	0.178591i	0.646626	+	0.762807i	$0.276179\pi$
$174$			4.76693i			0.361380i
$175$	−5.20376	−	3.04931i	−0.393367	−	0.230506i
$176$	−4.46182	+	2.57603i	−0.336322	+	0.194176i
$177$	−1.94143			−0.145927
$178$	14.1941	−	8.19497i	1.06389	−	0.614239i
$179$	−4.34913	+	7.53292i	−0.325069	+	0.563037i	−0.981526	−	0.191327i	$-0.938721\pi$
$179$	−4.34913	+	7.53292i	−0.325069	+	0.563037i	0.656457	+	0.754363i	$0.272054\pi$
$180$	2.15800	+	0.585699i	0.160848	+	0.0436554i
$181$	9.75480			0.725069			0.362534	−	0.931970i	$-0.381912\pi$
$181$	9.75480			0.725069			0.362534	+	0.931970i	$0.381912\pi$
$182$	2.70821	−	3.40321i	0.200746	−	0.252263i
$183$			3.07591i			0.227378i
$184$	1.88293	+	1.08711i	0.138811	+	0.0801427i
$185$	−9.49666	−	2.57747i	−0.698208	−	0.189500i
$186$	−2.95523	−	5.11861i	−0.216688	−	0.375315i
$187$	24.4002			1.78432
$188$	−0.426148	−	0.738110i	−0.0310800	−	0.0538322i
$189$	1.04466	−	0.603137i	0.0759881	−	0.0438718i
$190$	−4.60474	+	1.21794i	−0.334063	+	0.0883583i
$191$	−5.77729	−	10.0066i	−0.418030	−	0.724049i	0.577711	−	0.816241i	$-0.303946\pi$
$191$	−5.77729	−	10.0066i	−0.418030	−	0.724049i	−0.995741	+	0.0921920i	$0.970613\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−5.23154	+	9.06130i	−0.376575	+	0.652247i	−0.990561	−	0.137070i	$-0.956232\pi$
$193$	−5.23154	+	9.06130i	−0.376575	+	0.652247i	0.613987	+	0.789316i	$0.289565\pi$
$194$	−8.48278			−0.609028
$195$	−4.77331	−	6.49734i	−0.341824	−	0.465285i
$196$	−5.54490			−0.396065
$197$	8.79472	−	15.2329i	0.626598	−	1.08530i	−0.361632	−	0.932321i	$-0.617780\pi$
$197$	8.79472	−	15.2329i	0.626598	−	1.08530i	0.988230	−	0.152978i	$-0.0488865\pi$
$198$	4.46182	+	2.57603i	0.317088	+	0.183071i
$199$	12.7858	+	22.1457i	0.906362	+	1.56986i	0.819079	+	0.573681i	$0.194485\pi$
$199$	12.7858	+	22.1457i	0.906362	+	1.56986i	0.0872828	+	0.996184i	$0.472182\pi$
$200$	4.34616	−	2.47202i	0.307320	−	0.174798i
$201$	12.1723	−	7.02765i	0.858564	−	0.495692i
$202$	−6.79121	−	11.7627i	−0.477828	−	0.827623i
$203$	5.75022			0.403586
$204$	2.36800	+	4.10150i	0.165793	+	0.287163i
$205$	−2.77388	+	10.2203i	−0.193736	+	0.713817i
$206$	−1.86798	−	1.07848i	−0.130148	−	0.0751412i
$207$		−	2.17422i		−	0.151119i
$208$	1.32073	+	3.35495i	0.0915760	+	0.232624i
$209$	−10.9745			−0.759122
$210$	0.706513	−	2.60314i	0.0487541	−	0.179634i
$211$	−6.45984	+	11.1888i	−0.444714	+	0.770267i	−0.998032	−	0.0627029i	$-0.980028\pi$
$211$	−6.45984	+	11.1888i	−0.444714	+	0.770267i	0.553318	+	0.832970i	$0.313361\pi$
$212$	−3.88016	+	2.24021i	−0.266490	+	0.153858i
$213$	0.344918			0.0236334
$214$	−7.00959	+	4.04699i	−0.479165	+	0.276646i
$215$	3.11091	+	3.13104i	0.212162	+	0.213535i
$216$			1.00000i			0.0680414i
$217$	−6.17445	+	3.56482i	−0.419149	+	0.241996i
$218$	−14.6219	−	8.44195i	−0.990319	−	0.571761i
$219$	13.6164	+	7.86142i	0.920109	+	0.531225i
$220$	11.1374	−	2.94579i	0.750882	−	0.198605i
$221$	2.52757	−	16.8878i	0.170022	−	1.13600i
$222$		−	4.40068i		−	0.295354i
$223$	3.57679	−	6.19518i	0.239519	−	0.414860i	−0.721057	−	0.692876i	$-0.756343\pi$
$223$	3.57679	−	6.19518i	0.239519	−	0.414860i	0.960576	+	0.278016i	$0.0896768\pi$
$224$	−0.603137	+	1.04466i	−0.0402988	+	0.0697995i
$225$	−4.31391	−	2.52788i	−0.287594	−	0.168525i
$226$			4.95102i			0.329337i
$227$	−12.9192	−	22.3768i	−0.857480	−	1.48520i	−0.874325	−	0.485340i	$-0.838696\pi$
$227$	−12.9192	−	22.3768i	−0.857480	−	1.48520i	0.0168460	−	0.999858i	$-0.494638\pi$
$228$	−1.06506	−	1.84474i	−0.0705353	−	0.122171i
$229$		−	8.95153i		−	0.591533i	−0.955260	−	0.295767i	$-0.904425\pi$
$229$		−	8.95153i		−	0.591533i	0.955260	−	0.295767i	$-0.0955751\pi$
$230$	−3.42664	−	3.44881i	−0.225946	−	0.227408i
$231$	3.10740	−	5.38217i	0.204452	−	0.354121i
$232$	−2.38346	+	4.12828i	−0.156482	+	0.271035i
$233$		−	3.86657i		−	0.253308i	−0.991947	−	0.126654i	$-0.959576\pi$
$233$		−	3.86657i		−	0.253308i	0.991947	−	0.126654i	$-0.0404237\pi$
$234$	2.24511	−	2.82126i	0.146767	−	0.184431i
$235$	0.487316	+	1.84243i	0.0317890	+	0.120187i
$236$	−1.68133	−	0.970715i	−0.109445	−	0.0631882i
$237$	11.7661	+	6.79315i	0.764290	+	0.441263i
$238$	4.94754	−	2.85646i	0.320701	−	0.185157i
$239$			15.4177i			0.997286i	0.866807	+	0.498643i	$0.166168\pi$
$239$			15.4177i			0.997286i	−0.866807	+	0.498643i	$0.833832\pi$
$240$	1.57603	+	1.58623i	0.101732	+	0.102391i
$241$	9.76603	−	5.63842i	0.629085	−	0.363203i	−0.151312	−	0.988486i	$-0.548350\pi$
$241$	9.76603	−	5.63842i	0.629085	−	0.363203i	0.780398	+	0.625283i	$0.215017\pi$
$242$	15.5438			0.999191
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−1.53795	+	2.66381i	−0.0984574	+	0.170533i
$245$	11.9659	+	3.24764i	0.764473	+	0.207484i
$246$	−4.73601			−0.301957
$247$	−1.13682	+	7.59565i	−0.0723344	+	0.483299i
$248$		−	5.91046i		−	0.375315i
$249$	8.83737	+	5.10226i	0.560046	+	0.323342i
$250$	−10.8269	+	2.78907i	−0.684751	+	0.176397i
$251$	6.15329	+	10.6578i	0.388392	+	0.672715i	0.992233	−	0.124390i	$-0.0396973\pi$
$251$	6.15329	+	10.6578i	0.388392	+	0.672715i	−0.603841	+	0.797104i	$0.706364\pi$
$252$	1.20627			0.0759881
$253$	−5.60085	−	9.70096i	−0.352123	−	0.609894i
$254$	1.04089	−	0.600957i	0.0653112	−	0.0377074i
$255$	−2.70790	−	10.2380i	−0.169575	−	0.641127i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	24.3239	+	14.0434i	1.51728	+	0.876004i	0.999794	+	0.0203154i	$0.00646704\pi$
$257$	24.3239	+	14.0434i	1.51728	+	0.876004i	0.517490	+	0.855689i	$0.326866\pi$
$258$	−0.986944	+	1.70944i	−0.0614444	+	0.106425i
$259$	−5.30842			−0.329849
$260$	−0.885137	−	8.01352i	−0.0548939	−	0.496978i
$261$	4.76693			0.295065
$262$	−3.32575	+	5.76036i	−0.205465	+	0.355876i
$263$	6.56756	+	3.79178i	0.404973	+	0.233811i	0.688628	−	0.725115i	$-0.258213\pi$
$263$	6.56756	+	3.79178i	0.404973	+	0.233811i	−0.283654	+	0.958927i	$0.591547\pi$
$264$	2.57603	+	4.46182i	0.158544	+	0.274606i
$265$	9.68546	−	2.56176i	0.594973	−	0.157368i
$266$	−2.22526	+	1.28475i	−0.136439	+	0.0787732i
$267$	−8.19497	−	14.1941i	−0.501524	−	0.868665i
$268$	14.0553			0.858564
$269$	−12.2355	−	21.1924i	−0.746010	−	1.29213i	−0.949722	−	0.313096i	$-0.898634\pi$
$269$	−12.2355	−	21.1924i	−0.746010	−	1.29213i	0.203712	−	0.979031i	$-0.434699\pi$
$270$	0.585699	−	2.15800i	0.0356445	−	0.131332i
$271$	10.0199	+	5.78497i	0.608664	+	0.351412i	0.772442	−	0.635085i	$-0.219035\pi$
$271$	10.0199	+	5.78497i	0.608664	+	0.351412i	−0.163779	+	0.986497i	$0.552368\pi$
$272$			4.73601i			0.287163i
$273$	−3.40321	−	2.70821i	−0.205972	−	0.163909i
$274$	14.7149			0.888961
$275$	−25.7598	−	0.166140i	−1.55337	−	0.0100186i
$276$	1.08711	−	1.88293i	0.0654363	−	0.113339i
$277$	−11.2111	+	6.47271i	−0.673608	+	0.388908i	−0.797442	−	0.603395i	$-0.793814\pi$
$277$	−11.2111	+	6.47271i	−0.673608	+	0.388908i	0.123835	+	0.992303i	$0.460481\pi$
$278$	−15.6508			−0.938673
$279$	−5.11861	+	2.95523i	−0.306443	+	0.176925i
$280$	1.91343	−	1.90113i	0.114349	−	0.113614i
$281$			2.57187i			0.153425i	0.997053	+	0.0767124i	$0.0244423\pi$
$281$			2.57187i			0.153425i	−0.997053	+	0.0767124i	$0.975558\pi$
$282$	−0.738110	+	0.426148i	−0.0439538	+	0.0253767i
$283$	−4.80517	−	2.77427i	−0.285638	−	0.164913i	0.350335	−	0.936624i	$-0.386068\pi$
$283$	−4.80517	−	2.77427i	−0.285638	−	0.164913i	−0.635973	+	0.771711i	$0.719401\pi$
$284$	0.298707	+	0.172459i	0.0177250	+	0.0102335i
$285$	1.21794	+	4.60474i	0.0721443	+	0.272761i
$286$	2.74961	−	18.3714i	0.162588	−	1.08632i
$287$			5.71292i			0.337223i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	2.71489	−	4.70233i	0.159700	−	0.276608i
$290$	7.56144	−	7.51283i	0.444023	−	0.441168i
$291$			8.48278i			0.497270i
$292$	7.86142	+	13.6164i	0.460055	+	0.796838i
$293$	12.0658	+	20.8986i	0.704891	+	1.22091i	0.966731	+	0.255795i	$0.0823374\pi$
$293$	12.0658	+	20.8986i	0.704891	+	1.22091i	−0.261840	+	0.965111i	$0.584329\pi$
$294$			5.54490i			0.323385i
$295$	3.05976	+	3.07955i	0.178146	+	0.179299i
$296$	2.20034	−	3.81110i	0.127892	−	0.221516i
$297$	2.57603	−	4.46182i	0.149477	−	0.258901i
$298$			22.8116i			1.32144i
$299$	−7.29439	+	2.87155i	−0.421845	+	0.166066i
$300$	−2.47202	−	4.34616i	−0.142722	−	0.250926i
$301$	2.06205	+	1.19052i	0.118855	+	0.0686207i
$302$	−17.2335	−	9.94975i	−0.991675	−	0.572544i
$303$	−11.7627	+	6.79121i	−0.675751	+	0.390145i
$304$		−	2.13012i		−	0.122171i
$305$	4.87910	−	4.84773i	0.279376	−	0.277580i
$306$	4.10150	−	2.36800i	0.234467	−	0.135370i
$307$	30.3243			1.73070			0.865348	−	0.501171i	$-0.167097\pi$
$307$	30.3243			1.73070			0.865348	+	0.501171i	$0.167097\pi$
$308$	5.38217	−	3.10740i	0.306678	−	0.177061i
$309$	−1.07848	+	1.86798i	−0.0613525	+	0.106266i
$310$	−3.46175	+	12.7548i	−0.196614	+	0.724422i
$311$	8.76406			0.496964			0.248482	−	0.968636i	$-0.420068\pi$
$311$	8.76406			0.496964			0.248482	+	0.968636i	$0.420068\pi$
$312$	3.35495	−	1.32073i	0.189937	−	0.0747715i
$313$			29.0155i			1.64005i	0.572326	+	0.820026i	$0.306041\pi$
$313$			29.0155i			1.64005i	−0.572326	+	0.820026i	$0.693959\pi$
$314$	4.10836	+	2.37196i	0.231848	+	0.133857i
$315$	−2.60314	−	0.706513i	−0.146670	−	0.0398075i
$316$	6.79315	+	11.7661i	0.382145	+	0.661894i
$317$	−25.9970			−1.46014			−0.730068	−	0.683375i	$-0.760511\pi$
$317$	−25.9970			−1.46014			−0.730068	+	0.683375i	$0.760511\pi$
$318$	2.24021	+	3.88016i	0.125625	+	0.217588i
$319$	21.2692	−	12.2798i	1.19084	−	0.687534i
$320$	0.571769	+	2.16173i	0.0319629	+	0.120844i
$321$	4.04699	+	7.00959i	0.225881	+	0.391237i
$322$	−2.27133	−	1.31135i	−0.126576	−	0.0730787i
$323$	−5.04413	+	8.73669i	−0.280663	+	0.486122i
$324$	1.00000			0.0555556
$325$	−2.78339	+	17.8116i	−0.154395	+	0.988009i
$326$	−3.86657			−0.214150
$327$	−8.44195	+	14.6219i	−0.466841	+	0.808592i
$328$	−4.10150	−	2.36800i	−0.226468	−	0.130751i
$329$	0.514051	+	0.890362i	0.0283405	+	0.0490873i
$330$	−2.94579	−	11.1374i	−0.162160	−	0.613092i
$331$	−9.56025	+	5.51961i	−0.525479	+	0.303385i	−0.739173	−	0.673515i	$-0.764784\pi$
$331$	−9.56025	+	5.51961i	−0.525479	+	0.303385i	0.213694	+	0.976901i	$0.431450\pi$
$332$	5.10226	+	8.83737i	0.280023	+	0.485014i
$333$	−4.40068			−0.241156
$334$	−11.3614	−	19.6785i	−0.621669	−	1.07676i
$335$	−30.3313	−	8.23218i	−1.65718	−	0.449772i
$336$	1.04466	+	0.603137i	0.0569911	+	0.0329038i
$337$		−	17.7108i		−	0.964769i	−0.875960	−	0.482384i	$-0.839771\pi$
$337$		−	17.7108i		−	0.964769i	0.875960	−	0.482384i	$-0.160229\pi$
$338$	−12.4303	−	3.80611i	−0.676122	−	0.207025i
$339$	4.95102			0.268902
$340$	2.77388	−	10.2203i	0.150435	−	0.554274i
$341$	−15.2255	+	26.3714i	−0.824509	+	1.42809i
$342$	−1.84474	+	1.06506i	−0.0997519	+	0.0575918i
$343$	15.1326			0.817083
$344$	−1.70944	+	0.986944i	−0.0921667	+	0.0532124i
$345$	−3.44881	+	3.42664i	−0.185678	+	0.184484i
$346$		−	4.69800i		−	0.252566i
$347$	−30.0526	+	17.3509i	−1.61331	+	0.931443i	−0.624710	+	0.780857i	$0.714783\pi$
$347$	−30.0526	+	17.3509i	−1.61331	+	0.931443i	−0.988597	+	0.150587i	$0.951884\pi$
$348$	4.12828	+	2.38346i	0.221299	+	0.127767i
$349$	−30.4563	−	17.5840i	−1.63029	−	0.941249i	−0.984002	−	0.178156i	$-0.942987\pi$
$349$	−30.4563	−	17.5840i	−1.63029	−	0.941249i	−0.646288	−	0.763093i	$-0.723680\pi$
$350$	−5.24266	+	2.98193i	−0.280232	+	0.159391i
$351$	−2.82126	−	2.24511i	−0.150588	−	0.119835i
$352$			5.15206i			0.274606i
$353$	5.54542	−	9.60495i	0.295153	−	0.511220i	−0.679868	−	0.733335i	$-0.737963\pi$
$353$	5.54542	−	9.60495i	0.295153	−	0.511220i	0.975020	+	0.222115i	$0.0712961\pi$
$354$	−0.970715	+	1.68133i	−0.0515929	+	0.0893616i
$355$	−0.543601	−	0.547118i	−0.0288513	−	0.0290380i
$356$		−	16.3899i		−	0.868665i
$357$	−2.85646	−	4.94754i	−0.151180	−	0.261851i
$358$	4.34913	+	7.53292i	0.229859	+	0.398127i
$359$			26.1575i			1.38054i	0.723552	+	0.690270i	$0.242508\pi$
$359$			26.1575i			1.38054i	−0.723552	+	0.690270i	$0.757492\pi$
$360$	1.58623	−	1.57603i	0.0836016	−	0.0830642i
$361$	−7.23130	+	12.5250i	−0.380595	+	0.659209i
$362$	4.87740	−	8.44791i	0.256351	−	0.444012i
$363$		−	15.5438i		−	0.815836i
$364$	−1.59316	−	4.04699i	−0.0835042	−	0.212120i
$365$	−8.98983	−	33.9885i	−0.470549	−	1.77904i
$366$	2.66381	+	1.53795i	0.139240	+	0.0803901i
$367$	−13.4988	−	7.79352i	−0.704630	−	0.406818i	0.104440	−	0.994531i	$-0.466695\pi$
$367$	−13.4988	−	7.79352i	−0.704630	−	0.406818i	−0.809070	+	0.587713i	$0.800028\pi$
$368$	1.88293	−	1.08711i	0.0981544	−	0.0566695i
$369$			4.73601i			0.246547i
$370$	−6.98049	+	6.93561i	−0.362898	+	0.360565i
$371$	4.68053	−	2.70231i	0.243001	−	0.140297i
$372$	−5.91046			−0.306443
$373$	−0.860358	+	0.496728i	−0.0445476	+	0.0257196i	−0.522108	−	0.852879i	$-0.674854\pi$
$373$	−0.860358	+	0.496728i	−0.0445476	+	0.0257196i	0.477561	+	0.878599i	$0.341521\pi$
$374$	12.2001	−	21.1312i	0.630853	−	1.09267i
$375$	2.78907	+	10.8269i	0.144027	+	0.559097i
$376$	−0.852296			−0.0439538
$377$	−6.29581	−	15.9928i	−0.324251	−	0.823671i
$378$		−	1.20627i		−	0.0620440i
$379$	23.7856	+	13.7326i	1.22178	+	0.705398i	0.965298	−	0.261150i	$-0.0841018\pi$
$379$	23.7856	+	13.7326i	1.22178	+	0.705398i	0.256486	+	0.966548i	$0.417435\pi$
$380$	−1.24761	+	4.59679i	−0.0640009	+	0.235810i
$381$	−0.600957	−	1.04089i	−0.0307880	−	0.0533263i
$382$	−11.5546			−0.591184
$383$	16.2851	+	28.2067i	0.832132	+	1.44130i	0.896344	+	0.443359i	$0.146213\pi$
$383$	16.2851	+	28.2067i	0.832132	+	1.44130i	−0.0642122	+	0.997936i	$0.520453\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	−13.4347	+	3.55343i	−0.684697	+	0.181100i
$386$	5.23154	+	9.06130i	0.266279	+	0.461208i
$387$	1.70944	+	0.986944i	0.0868956	+	0.0501692i
$388$	−4.24139	+	7.34631i	−0.215324	+	0.372952i
$389$	−16.9110			−0.857421			−0.428710	−	0.903442i	$-0.641032\pi$
$389$	−16.9110			−0.857421			−0.428710	+	0.903442i	$0.641032\pi$
$390$	−8.01352	+	0.885137i	−0.405780	+	0.0448207i
$391$	−10.2971			−0.520747
$392$	−2.77245	+	4.80203i	−0.140030	+	0.242539i
$393$	5.76036	+	3.32575i	0.290572	+	0.167762i
$394$	−8.79472	−	15.2329i	−0.443072	−	0.767423i
$395$	−7.76823	−	29.3699i	−0.390862	−	1.47776i
$396$	4.46182	−	2.57603i	0.224215	−	0.129450i
$397$	−16.1198	−	27.9204i	−0.809031	−	1.40128i	−0.913536	−	0.406759i	$-0.866659\pi$
$397$	−16.1198	−	27.9204i	−0.809031	−	1.40128i	0.104504	−	0.994524i	$-0.466674\pi$
$398$	25.5716			1.28179
$399$	1.28475	+	2.22526i	0.0643181	+	0.111402i
$400$	0.0322474	−	4.99990i	0.00161237	−	0.249995i
$401$	28.0082	+	16.1705i	1.39866	+	0.807518i	0.994253	−	0.107060i	$-0.0341437\pi$
$401$	28.0082	+	16.1705i	1.39866	+	0.807518i	0.404410	+	0.914578i	$0.367477\pi$
$402$		−	14.0553i		−	0.701015i
$403$	16.6749	+	13.2696i	0.830638	+	0.661007i
$404$	−13.5824			−0.675751
$405$	−2.15800	−	0.585699i	−0.107232	−	0.0291036i
$406$	2.87511	−	4.97984i	0.142689	−	0.247145i
$407$	−19.6350	+	11.3363i	−0.973272	+	0.561919i
$408$	4.73601			0.234467
$409$	1.00971	−	0.582957i	0.0499270	−	0.0288254i	−0.474829	−	0.880078i	$-0.657490\pi$
$409$	1.00971	−	0.582957i	0.0499270	−	0.0288254i	0.524756	+	0.851253i	$0.324157\pi$
$410$	7.46410	+	7.51240i	0.368626	+	0.371011i
$411$		−	14.7149i		−	0.725833i
$412$	−1.86798	+	1.07848i	−0.0920288	+	0.0531328i
$413$	2.02814	+	1.17095i	0.0997984	+	0.0576186i
$414$	−1.88293	−	1.08711i	−0.0925408	−	0.0534285i
$415$	−5.83462	−	22.0594i	−0.286410	−	1.08285i
$416$	3.56583	+	0.533691i	0.174829	+	0.0261663i
$417$			15.6508i			0.766423i
$418$	−5.48725	+	9.50420i	−0.268390	+	0.464866i
$419$	5.91396	−	10.2433i	0.288916	−	0.500417i	−0.684635	−	0.728886i	$-0.740039\pi$
$419$	5.91396	−	10.2433i	0.288916	−	0.500417i	0.973551	+	0.228469i	$0.0733719\pi$
$420$	−1.90113	−	1.91343i	−0.0927654	−	0.0933657i
$421$		−	23.9102i		−	1.16531i	−0.812719	−	0.582655i	$-0.802014\pi$
$421$		−	23.9102i		−	1.16531i	0.812719	−	0.582655i	$-0.197986\pi$
$422$	6.45984	+	11.1888i	0.314460	+	0.544661i
$423$	0.426148	+	0.738110i	0.0207200	+	0.0358881i
$424$			4.48042i			0.217588i
$425$	−11.9720	+	20.4307i	−0.580729	+	0.991036i
$426$	0.172459	−	0.298707i	0.00835566	−	0.0144724i
$427$	1.85519	−	3.21329i	0.0897791	−	0.155502i
$428$			8.09397i			0.391237i
$429$	−18.3714	−	2.74961i	−0.886980	−	0.132752i
$430$	4.26701	−	1.12861i	0.205774	−	0.0544263i
$431$	−22.8082	−	13.1683i	−1.09863	−	0.634294i	−0.162769	−	0.986664i	$-0.552043\pi$
$431$	−22.8082	−	13.1683i	−1.09863	−	0.634294i	−0.935861	+	0.352370i	$0.885376\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−11.2232	+	6.47972i	−0.539353	+	0.311396i	−0.744817	−	0.667269i	$-0.767463\pi$
$433$	−11.2232	+	6.47972i	−0.539353	+	0.311396i	0.205464	+	0.978665i	$0.434130\pi$
$434$			7.12964i			0.342234i
$435$	−7.51283	−	7.56144i	−0.360213	−	0.362543i
$436$	−14.6219	+	8.44195i	−0.700261	+	0.404296i
$437$	4.63134			0.221547
$438$	13.6164	−	7.86142i	0.650615	−	0.375633i
$439$	11.6234	−	20.1324i	0.554756	−	0.960865i	−0.443167	−	0.896439i	$-0.646145\pi$
$439$	11.6234	−	20.1324i	0.554756	−	0.960865i	0.997922	−	0.0644259i	$-0.0205216\pi$
$440$	3.01756	−	11.1181i	0.143856	−	0.530037i
$441$	5.54490			0.264043
$442$	−13.3615	−	10.6328i	−0.635542	−	0.505753i
$443$			23.3728i			1.11047i	0.831692	+	0.555237i	$0.187373\pi$
$443$			23.3728i			1.11047i	−0.831692	+	0.555237i	$0.812627\pi$
$444$	−3.81110	−	2.20034i	−0.180867	−	0.104423i
$445$	−9.59957	+	35.3695i	−0.455063	+	1.67667i
$446$	−3.57679	−	6.19518i	−0.169366	−	0.293350i
$447$	22.8116			1.07895
$448$	0.603137	+	1.04466i	0.0284955	+	0.0493557i
$449$	1.20931	−	0.698196i	0.0570709	−	0.0329499i	−0.471193	−	0.882030i	$-0.656176\pi$
$449$	1.20931	−	0.698196i	0.0570709	−	0.0329499i	0.528264	+	0.849080i	$0.322843\pi$
$450$	−4.34616	+	2.47202i	−0.204880	+	0.116532i
$451$	12.2001	+	21.1312i	0.574481	+	0.995030i
$452$	4.28771	+	2.47551i	0.201677	+	0.116438i
$453$	−9.94975	+	17.2335i	−0.467480	+	0.809699i
$454$	−25.8385			−1.21266
$455$	1.06772	+	9.66650i	0.0500554	+	0.453173i
$456$	−2.13012			−0.0997519
$457$	−3.60093	+	6.23699i	−0.168444	+	0.291754i	−0.937873	−	0.346979i	$-0.887208\pi$
$457$	−3.60093	+	6.23699i	−0.168444	+	0.291754i	0.769429	+	0.638733i	$0.220541\pi$
$458$	−7.75225	−	4.47576i	−0.362239	−	0.209139i
$459$	−2.36800	−	4.10150i	−0.110529	−	0.191442i
$460$	−4.70007	+	1.24315i	−0.219142	+	0.0579622i
$461$	−4.10920	+	2.37245i	−0.191384	+	0.110496i	−0.592630	−	0.805474i	$-0.701911\pi$
$461$	−4.10920	+	2.37245i	−0.191384	+	0.110496i	0.401246	+	0.915970i	$0.368577\pi$
$462$	−3.10740	−	5.38217i	−0.144569	−	0.250401i
$463$	−15.7510			−0.732012			−0.366006	−	0.930612i	$-0.619275\pi$
$463$	−15.7510			−0.732012			−0.366006	+	0.930612i	$0.619275\pi$
$464$	2.38346	+	4.12828i	0.110650	+	0.191651i
$465$	12.7548	+	3.46175i	0.591488	+	0.160535i
$466$	−3.34855	−	1.93329i	−0.155119	−	0.0895578i
$467$		−	17.9789i		−	0.831962i	−0.909373	−	0.415981i	$-0.863438\pi$
$467$		−	17.9789i		−	0.831962i	0.909373	−	0.415981i	$-0.136562\pi$
$468$	−1.32073	−	3.35495i	−0.0610506	−	0.155083i
$469$	−16.9545			−0.782888
$470$	1.83925	+	0.499189i	0.0848384	+	0.0230259i
$471$	2.37196	−	4.10836i	0.109294	−	0.189303i
$472$	−1.68133	+	0.970715i	−0.0773894	+	0.0446808i
$473$	10.1696			0.467598
$474$	11.7661	−	6.79315i	0.540434	−	0.312020i
$475$	5.38467	−	9.18914i	0.247066	−	0.421627i
$476$		−	5.71292i		−	0.261851i
$477$	3.88016	−	2.24021i	0.177660	−	0.102572i
$478$	13.3521	+	7.70884i	0.610711	+	0.352594i
$479$	2.83964	+	1.63947i	0.129747	+	0.0749093i	0.563468	−	0.826138i	$-0.309467\pi$
$479$	2.83964	+	1.63947i	0.129747	+	0.0749093i	−0.433722	+	0.901047i	$0.642800\pi$
$480$	2.16173	−	0.571769i	0.0986691	−	0.0260976i
$481$	5.81210	+	14.7640i	0.265009	+	0.673183i
$482$		−	11.2768i		−	0.513646i
$483$	−1.31135	+	2.27133i	−0.0596685	+	0.103349i
$484$	7.77188	−	13.4613i	0.353267	−	0.611877i
$485$	13.4556	−	13.3691i	0.610989	−	0.607061i
$486$		−	1.00000i		−	0.0453609i
$487$	4.98852	+	8.64037i	0.226052	+	0.391533i	0.956634	−	0.291291i	$-0.0940849\pi$
$487$	4.98852	+	8.64037i	0.226052	+	0.391533i	−0.730583	+	0.682824i	$0.760752\pi$
$488$	1.53795	+	2.66381i	0.0696199	+	0.120585i
$489$			3.86657i			0.174852i
$490$	8.79549	−	8.73894i	0.397340	−	0.394785i
$491$	10.0376	−	17.3857i	0.452992	−	0.784605i	−0.545578	−	0.838060i	$-0.683690\pi$
$491$	10.0376	−	17.3857i	0.452992	−	0.784605i	0.998570	+	0.0534548i	$0.0170233\pi$
$492$	−2.36800	+	4.10150i	−0.106758	+	0.184910i
$493$		−	22.5762i		−	1.01678i
$494$	6.00961	+	4.78234i	0.270385	+	0.215168i
$495$	−11.1374	+	2.94579i	−0.500588	+	0.132403i
$496$	−5.11861	−	2.95523i	−0.229832	−	0.132694i
$497$	−0.360323	−	0.208033i	−0.0161627	−	0.00933153i
$498$	8.83737	−	5.10226i	0.396012	−	0.228638i
$499$			23.9474i			1.07203i	0.844208	+	0.536016i	$0.180071\pi$
$499$			23.9474i			1.07203i	−0.844208	+	0.536016i	$0.819929\pi$
$500$	−2.99802	+	10.7709i	−0.134076	+	0.481688i
$501$	−19.6785	+	11.3614i	−0.879173	+	0.507591i
$502$	12.3066			0.549269
$503$	−10.5377	+	6.08395i	−0.469853	+	0.271270i	−0.716178	−	0.697917i	$-0.754110\pi$
$503$	−10.5377	+	6.08395i	−0.469853	+	0.271270i	0.246325	+	0.969187i	$0.420777\pi$
$504$	0.603137	−	1.04466i	0.0268659	−	0.0465330i
$505$	29.3109	+	7.95522i	1.30432	+	0.354002i
$506$	−11.2017			−0.497977
$507$	−3.80611	+	12.4303i	−0.169035	+	0.552051i
$508$		−	1.20191i		−	0.0533263i
$509$	34.9666	+	20.1880i	1.54987	+	0.894817i	0.998151	+	0.0607857i	$0.0193606\pi$
$509$	34.9666	+	20.1880i	1.54987	+	0.894817i	0.551717	+	0.834031i	$0.313973\pi$
$510$	−10.2203	−	2.77388i	−0.452563	−	0.122829i
$511$	−9.48302	−	16.4251i	−0.419504	−	0.726602i
$512$	−1.00000			−0.0441942
$513$	1.06506	+	1.84474i	0.0470235	+	0.0814471i
$514$	24.3239	−	14.0434i	1.07288	−	0.619429i
$515$	4.66276	−	1.23328i	0.205466	−	0.0543449i
$516$	0.986944	+	1.70944i	0.0434478	+	0.0752538i
$517$	3.80279	+	2.19554i	0.167246	+	0.0965598i
$518$	−2.65421	+	4.59723i	−0.116619	+	0.201991i
$519$	−4.69800			−0.206219
$520$	−7.38248	−	3.24021i	−0.323743	−	0.142093i
$521$	−0.259356			−0.0113626			−0.00568129	−	0.999984i	$-0.501808\pi$
$521$	−0.259356			−0.0113626			−0.00568129	+	0.999984i	$0.501808\pi$
$522$	2.38346	−	4.12828i	0.104321	−	0.180690i
$523$	33.4527	+	19.3139i	1.46278	+	0.844539i	0.999139	−	0.0414825i	$-0.0132081\pi$
$523$	33.4527	+	19.3139i	1.46278	+	0.844539i	0.463645	+	0.886021i	$0.346541\pi$
$524$	3.32575	+	5.76036i	0.145286	+	0.251642i
$525$	2.98193	+	5.24266i	0.130142	+	0.228808i
$526$	6.56756	−	3.79178i	0.286359	−	0.165330i
$527$	13.9960	+	24.2418i	0.609676	+	1.05599i
$528$	5.15206			0.224215
$529$	−9.13639	−	15.8247i	−0.397234	−	0.688030i
$530$	2.62418	−	9.66874i	0.113987	−	0.419983i
$531$	1.68133	+	0.970715i	0.0729634	+	0.0421255i
$532$			2.56951i			0.111402i
$533$	15.8891	−	6.25498i	0.688232	−	0.270933i
$534$	−16.3899			−0.709262
$535$	4.74063	−	17.4668i	0.204955	−	0.755155i
$536$	7.02765	−	12.1723i	0.303548	−	0.525761i
$537$	7.53292	−	4.34913i	0.325069	−	0.187679i
$538$	−24.4709			−1.05502
$539$	24.7403	−	14.2838i	1.06564	−	0.615249i
$540$	−1.57603	−	1.58623i	−0.0678216	−	0.0682604i
$541$			19.4443i			0.835975i	0.908453	+	0.417988i	$0.137264\pi$
$541$			19.4443i			0.835975i	−0.908453	+	0.417988i	$0.862736\pi$
$542$	10.0199	−	5.78497i	0.430390	−	0.248486i
$543$	−8.44791	−	4.87740i	−0.362534	−	0.209309i
$544$	4.10150	+	2.36800i	0.175851	+	0.101527i
$545$	36.4984	−	9.65369i	1.56342	−	0.413518i
$546$	−4.04699	+	1.59316i	−0.173195	+	0.0681809i
$547$		−	25.2121i		−	1.07799i	−0.842308	−	0.538997i	$-0.818803\pi$
$547$		−	25.2121i		−	1.07799i	0.842308	−	0.538997i	$-0.181197\pi$
$548$	7.35746	−	12.7435i	0.314295	−	0.544375i
$549$	1.53795	−	2.66381i	0.0656383	−	0.113689i
$550$	−13.0238	+	22.2256i	−0.555336	+	0.947701i
$551$			10.1541i			0.432580i
$552$	−1.08711	−	1.88293i	−0.0462704	−	0.0801427i
$553$	−8.19440	−	14.1931i	−0.348462	−	0.603553i
$554$			12.9454i			0.549998i
$555$	6.93561	+	6.98049i	0.294400	+	0.296305i
$556$	−7.82540	+	13.5540i	−0.331871	+	0.574817i
$557$	−5.63445	+	9.75916i	−0.238739	+	0.413509i	−0.960353	−	0.278787i	$-0.910067\pi$
$557$	−5.63445	+	9.75916i	−0.238739	+	0.413509i	0.721613	+	0.692296i	$0.243401\pi$
$558$			5.91046i			0.250210i
$559$	1.05345	−	7.03856i	0.0445560	−	0.297699i
$560$	−0.689710	−	2.60764i	−0.0291456	−	0.110193i
$561$	−21.1312	−	12.2001i	−0.892160	−	0.515089i
$562$	2.22730	+	1.28593i	0.0939531	+	0.0542439i
$563$	14.2495	−	8.22694i	0.600544	−	0.346724i	−0.168712	−	0.985665i	$-0.553961\pi$
$563$	14.2495	−	8.22694i	0.600544	−	0.346724i	0.769256	+	0.638941i	$0.220627\pi$
$564$			0.852296i			0.0358881i
$565$	−7.80296	−	7.85345i	−0.328273	−	0.330397i
$566$	−4.80517	+	2.77427i	−0.201976	+	0.116611i
$567$	−1.20627			−0.0506587
$568$	0.298707	−	0.172459i	0.0125335	−	0.00723621i
$569$	15.2444	−	26.4040i	0.639077	−	1.10691i	−0.346558	−	0.938028i	$-0.612650\pi$
$569$	15.2444	−	26.4040i	0.639077	−	1.10691i	0.985636	−	0.168886i	$-0.0540170\pi$
$570$	4.59679	+	1.24761i	0.192538	+	0.0522565i
$571$	13.0909			0.547836			0.273918	−	0.961753i	$-0.411680\pi$
$571$	13.0909			0.547836			0.273918	+	0.961753i	$0.411680\pi$
$572$	−14.5353	−	11.5669i	−0.607751	−	0.483638i
$573$			11.5546i			0.482699i
$574$	4.94754	+	2.85646i	0.206506	+	0.119226i
$575$	10.8709	+	0.0701128i	0.453346	+	0.00292390i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−13.1315			−0.546670			−0.273335	−	0.961919i	$-0.588127\pi$
$577$	−13.1315			−0.546670			−0.273335	+	0.961919i	$0.588127\pi$
$578$	−2.71489	−	4.70233i	−0.112925	−	0.195591i
$579$	9.06130	−	5.23154i	0.376575	−	0.217416i
$580$	−2.72558	−	10.3048i	−0.113174	−	0.427884i
$581$	−6.15472	−	10.6603i	−0.255341	−	0.442263i
$582$	7.34631	+	4.24139i	0.304514	+	0.175811i
$583$	11.5417	−	19.9908i	0.478009	−	0.827935i
$584$	15.7228			0.650615
$585$	0.885137	+	8.01352i	0.0365959	+	0.331318i
$586$	24.1316			0.996866
$587$	3.03785	−	5.26171i	0.125386	−	0.217174i	−0.796498	−	0.604641i	$-0.793317\pi$
$587$	3.03785	−	5.26171i	0.125386	−	0.217174i	0.921884	+	0.387467i	$0.126650\pi$
$588$	4.80203	+	2.77245i	0.198032	+	0.114334i
$589$	−6.29499	−	10.9032i	−0.259381	−	0.449260i
$590$	4.19685	−	1.11005i	0.172782	−	0.0457000i
$591$	−15.2329	+	8.79472i	−0.626598	+	0.361767i
$592$	−2.20034	−	3.81110i	−0.0904334	−	0.156635i
$593$	18.3609			0.753990			0.376995	−	0.926215i	$-0.376957\pi$
$593$	18.3609			0.753990			0.376995	+	0.926215i	$0.376957\pi$
$594$	−2.57603	−	4.46182i	−0.105696	−	0.183071i
$595$	−3.34605	+	12.3285i	−0.137175	+	0.505418i
$596$	19.7555	+	11.4058i	0.809215	+	0.467200i
$597$		−	25.5716i		−	1.04658i
$598$	−1.16036	+	7.75290i	−0.0474507	+	0.317040i
$599$	22.1098			0.903382			0.451691	−	0.892174i	$-0.350821\pi$
$599$	22.1098			0.903382			0.451691	+	0.892174i	$0.350821\pi$
$600$	−4.99990	−	0.0322474i	−0.204120	−	0.00131649i
$601$	−5.90349	+	10.2251i	−0.240808	+	0.417092i	−0.960945	−	0.276740i	$-0.910746\pi$
$601$	−5.90349	+	10.2251i	−0.240808	+	0.417092i	0.720136	+	0.693832i	$0.244079\pi$
$602$	2.06205	−	1.19052i	0.0840428	−	0.0485222i
$603$	−14.0553			−0.572376
$604$	−17.2335	+	9.94975i	−0.701220	+	0.404850i
$605$	−24.6560	+	24.4975i	−1.00241	+	0.995963i
$606$			13.5824i			0.551748i
$607$	22.3119	−	12.8818i	0.905612	−	0.522856i	0.0265955	−	0.999646i	$-0.491533\pi$
$607$	22.3119	−	12.8818i	0.905612	−	0.522856i	0.879017	+	0.476791i	$0.158200\pi$
$608$	−1.84474	−	1.06506i	−0.0748139	−	0.0431938i
$609$	−4.97984	−	2.87511i	−0.201793	−	0.116505i
$610$	−1.75871	−	6.64928i	−0.0712080	−	0.269222i
$611$	1.91349	−	2.40455i	0.0774117	−	0.0972775i
$612$		−	4.73601i		−	0.191442i
$613$	6.54178	−	11.3307i	0.264220	−	0.457642i	−0.703139	−	0.711052i	$-0.748219\pi$
$613$	6.54178	−	11.3307i	0.264220	−	0.457642i	0.967359	+	0.253410i	$0.0815522\pi$
$614$	15.1621	−	26.2616i	0.611894	−	1.05983i
$615$	7.51240	−	7.46410i	0.302929	−	0.300982i
$616$		−	6.21480i		−	0.250401i
$617$	−2.20914	−	3.82634i	−0.0889366	−	0.154043i	0.818125	−	0.575040i	$-0.195014\pi$
$617$	−2.20914	−	3.82634i	−0.0889366	−	0.154043i	−0.907062	+	0.420997i	$0.861680\pi$
$618$	1.07848	+	1.86798i	0.0433828	+	0.0751412i
$619$		−	1.12760i		−	0.0453220i	−0.999743	−	0.0226610i	$-0.992786\pi$
$619$		−	1.12760i		−	0.0453220i	0.999743	−	0.0226610i	$-0.00721383\pi$
$620$	9.31508	+	9.37535i	0.374103	+	0.376523i
$621$	−1.08711	+	1.88293i	−0.0436242	+	0.0755593i
$622$	4.38203	−	7.58990i	0.175703	−	0.304327i
$623$			19.7708i			0.792099i
$624$	0.533691	−	3.56583i	0.0213647	−	0.142748i
$625$	12.7782	−	21.4876i	0.511129	−	0.859504i
$626$	25.1282	+	14.5077i	1.00432	+	0.579846i
$627$	9.50420	+	5.48725i	0.379561	+	0.219140i
$628$	4.10836	−	2.37196i	0.163941	−	0.0946515i
$629$			20.8417i			0.831011i
$630$	−1.91343	+	1.90113i	−0.0762328	+	0.0757427i
$631$	−14.3916	+	8.30898i	−0.572920	+	0.330775i	−0.758315	−	0.651889i	$-0.773977\pi$
$631$	−14.3916	+	8.30898i	−0.572920	+	0.330775i	0.185395	+	0.982664i	$0.440644\pi$
$632$	13.5863			0.540434
$633$	11.1888	−	6.45984i	0.444714	−	0.256756i
$634$	−12.9985	+	22.5140i	−0.516236	+	0.894147i
$635$	−0.703960	+	2.59373i	−0.0279358	+	0.102929i
$636$	4.48042			0.177660
$637$	−7.32331	−	18.6029i	−0.290160	−	0.737072i
$638$		−	24.5595i		−	0.972320i
$639$	−0.298707	−	0.172459i	−0.0118167	−	0.00682236i
$640$	2.15800	+	0.585699i	0.0853024	+	0.0231518i
$641$	5.05184	+	8.75005i	0.199536	+	0.345606i	0.948378	−	0.317142i	$-0.102723\pi$
$641$	5.05184	+	8.75005i	0.199536	+	0.345606i	−0.748842	+	0.662748i	$0.769390\pi$
$642$	8.09397			0.319444
$643$	−17.5208	−	30.3469i	−0.690951	−	1.19676i	−0.971526	−	0.236931i	$-0.923858\pi$
$643$	−17.5208	−	30.3469i	−0.690951	−	1.19676i	0.280575	−	0.959832i	$-0.409475\pi$
$644$	−2.27133	+	1.31135i	−0.0895028	+	0.0516745i
$645$	−1.12861	−	4.26701i	−0.0444389	−	0.168014i
$646$	5.04413	+	8.73669i	0.198459	+	0.343740i
$647$	−17.2864	−	9.98031i	−0.679598	−	0.392366i	0.120105	−	0.992761i	$-0.461677\pi$
$647$	−17.2864	−	9.98031i	−0.679598	−	0.392366i	−0.799704	+	0.600395i	$0.795010\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	10.0024			0.392628
$650$	14.0336	+	11.3163i	0.550443	+	0.443861i
$651$	7.12964			0.279433
$652$	−1.93329	+	3.34855i	−0.0757133	+	0.131139i
$653$	4.51410	+	2.60621i	0.176650	+	0.101989i	0.585718	−	0.810515i	$-0.300813\pi$
$653$	4.51410	+	2.60621i	0.176650	+	0.101989i	−0.409068	+	0.912504i	$0.634146\pi$
$654$	8.44195	+	14.6219i	0.330106	+	0.571761i
$655$	−3.80312	−	14.3787i	−0.148600	−	0.561824i
$656$	−4.10150	+	2.36800i	−0.160137	+	0.0924551i
$657$	−7.86142	−	13.6164i	−0.306703	−	0.531225i
$658$	1.02810			0.0400796
$659$	3.66183	+	6.34248i	0.142645	+	0.247068i	0.928492	−	0.371353i	$-0.121106\pi$
$659$	3.66183	+	6.34248i	0.142645	+	0.247068i	−0.785847	+	0.618421i	$0.787773\pi$
$660$	−11.1181	−	3.01756i	−0.432773	−	0.117458i
$661$	−31.7189	−	18.3129i	−1.23372	−	0.712289i	−0.265917	−	0.963996i	$-0.585675\pi$
$661$	−31.7189	−	18.3129i	−1.23372	−	0.712289i	−0.967803	+	0.251707i	$0.919008\pi$
$662$			11.0392i			0.429052i
$663$	−10.6328	+	13.3615i	−0.412946	+	0.518918i
$664$	10.2045			0.396012
$665$	1.50496	−	5.54499i	0.0583597	−	0.215025i
$666$	−2.20034	+	3.81110i	−0.0852614	+	0.147677i
$667$	−8.97578	+	5.18217i	−0.347543	+	0.200654i
$668$	−22.7228			−0.879173
$669$	−6.19518	+	3.57679i	−0.239519	+	0.138287i
$670$	−22.2949	+	22.1516i	−0.861329	+	0.855791i
$671$		−	15.8473i		−	0.611777i
$672$	1.04466	−	0.603137i	0.0402988	−	0.0232665i
$673$	29.4292	+	16.9909i	1.13441	+	0.654952i	0.945041	−	0.326953i	$-0.106022\pi$
$673$	29.4292	+	16.9909i	1.13441	+	0.654952i	0.189370	+	0.981906i	$0.439355\pi$
$674$	−15.3380	−	8.85540i	−0.590798	−	0.341097i
$675$	2.47202	+	4.34616i	0.0951481	+	0.167284i
$676$	−9.51136	+	8.86194i	−0.365822	+	0.340844i
$677$			41.7902i			1.60613i	0.595894	+	0.803063i	$0.296798\pi$
$677$			41.7902i			1.60613i	−0.595894	+	0.803063i	$0.703202\pi$
$678$	2.47551	−	4.28771i	0.0950713	−	0.164668i
$679$	5.11628	−	8.86166i	0.196345	−	0.340079i
$680$	−7.46410	−	7.51240i	−0.286235	−	0.288087i
$681$			25.8385i			0.990132i
$682$	15.2255	+	26.3714i	0.583016	+	1.00981i
$683$	24.2071	+	41.9280i	0.926260	+	1.60433i	0.789523	+	0.613721i	$0.210328\pi$
$683$	24.2071	+	41.9280i	0.926260	+	1.60433i	0.136737	+	0.990607i	$0.456338\pi$
$684$			2.13012i			0.0814471i
$685$	−23.3412	+	23.1912i	−0.891823	+	0.886089i
$686$	7.56629	−	13.1052i	0.288882	−	0.500359i
$687$	−4.47576	+	7.75225i	−0.170761	+	0.295767i
$688$			1.97389i			0.0752538i
$689$	−12.6404	−	10.0590i	−0.481562	−	0.383218i
$690$	1.24315	+	4.70007i	0.0473259	+	0.178929i
$691$	−23.8905	−	13.7932i	−0.908837	−	0.524717i	−0.0287804	−	0.999586i	$-0.509162\pi$
$691$	−23.8905	−	13.7932i	−0.908837	−	0.524717i	−0.880057	+	0.474868i	$0.842496\pi$
$692$	−4.06859	−	2.34900i	−0.154664	−	0.0892955i
$693$	−5.38217	+	3.10740i	−0.204452	+	0.118040i
$694$			34.7017i			1.31726i
$695$	24.8258	−	24.6662i	0.941695	−	0.935641i
$696$	4.12828	−	2.38346i	0.156482	−	0.0903449i
$697$	22.4298			0.849589
$698$	−30.4563	+	17.5840i	−1.15279	+	0.665563i
$699$	−1.93329	+	3.34855i	−0.0731236	+	0.126654i
$700$	−0.0388991	+	6.03124i	−0.00147025	+	0.227960i
$701$	−19.7883			−0.747392			−0.373696	−	0.927551i	$-0.621910\pi$
$701$	−19.7883			−0.747392			−0.373696	+	0.927551i	$0.621910\pi$
$702$	−3.35495	+	1.32073i	−0.126624	+	0.0498476i
$703$		−	9.37396i		−	0.353546i
$704$	4.46182	+	2.57603i	0.168161	+	0.0970879i
$705$	0.499189	−	1.83925i	0.0188005	−	0.0692703i
$706$	−5.54542	−	9.60495i	−0.208705	−	0.361487i
$707$	16.3841			0.616189
$708$	0.970715	+	1.68133i	0.0364817	+	0.0631882i
$709$	−6.09389	+	3.51831i	−0.228861	+	0.132133i	−0.610046	−	0.792366i	$-0.708849\pi$
$709$	−6.09389	+	3.51831i	−0.228861	+	0.132133i	0.381186	+	0.924499i	$0.375516\pi$
$710$	−0.745619	+	0.197213i	−0.0279826	+	0.00740128i
$711$	−6.79315	−	11.7661i	−0.254763	−	0.441263i
$712$	−14.1941	−	8.19497i	−0.531946	−	0.307119i
$713$	6.42532	−	11.1290i	0.240630	−	0.416783i
$714$	−5.71292			−0.213801
$715$	24.5924	+	33.4747i	0.919704	+	1.25188i
$716$	8.69827			0.325069
$717$	7.70884	−	13.3521i	0.287892	−	0.498643i
$718$	22.6531	+	13.0788i	0.845405	+	0.488095i
$719$	−5.52118	−	9.56296i	−0.205905	−	0.356638i	0.744516	−	0.667605i	$-0.232681\pi$
$719$	−5.52118	−	9.56296i	−0.205905	−	0.356638i	−0.950421	+	0.310967i	$0.899347\pi$
$720$	−0.571769	−	2.16173i	−0.0213086	−	0.0805630i
$721$	2.25330	−	1.30094i	0.0839171	−	0.0484496i
$722$	7.23130	+	12.5250i	0.269121	+	0.466131i
$723$	−11.2768			−0.419390
$724$	−4.87740	−	8.44791i	−0.181267	−	0.313964i
$725$	−0.153721	+	23.8341i	−0.00570905	+	0.885178i
$726$	−13.4613	−	7.77188i	−0.499595	−	0.288442i
$727$		−	14.1056i		−	0.523147i	−0.965184	−	0.261573i	$-0.915759\pi$
$727$		−	14.1056i		−	0.523147i	0.965184	−	0.261573i	$-0.0842414\pi$
$728$	−4.30137	−	0.643777i	−0.159419	−	0.0238600i
$729$	−1.00000			−0.0370370
$730$	−33.9298	−	9.20885i	−1.25580	−	0.340835i
$731$	4.67418	−	8.09591i	0.172881	−	0.299438i
$732$	2.66381	−	1.53795i	0.0984574	−	0.0568444i
$733$	−11.3855			−0.420535			−0.210267	−	0.977644i	$-0.567433\pi$
$733$	−11.3855			−0.420535			−0.210267	+	0.977644i	$0.567433\pi$
$734$	−13.4988	+	7.79352i	−0.498249	+	0.287664i
$735$	−8.73894	−	8.79549i	−0.322341	−	0.324426i
$736$		−	2.17422i		−	0.0801427i
$737$	−62.7122	+	36.2069i	−2.31003	+	1.33370i
$738$	4.10150	+	2.36800i	0.150978	+	0.0871675i
$739$	−7.93251	−	4.57983i	−0.291802	−	0.168472i	0.346952	−	0.937883i	$-0.387217\pi$
$739$	−7.93251	−	4.57983i	−0.291802	−	0.168472i	−0.638754	+	0.769411i	$0.720550\pi$
$740$	2.51617	+	9.51308i	0.0924963	+	0.349708i
$741$	4.78234	−	6.00961i	0.175684	−	0.220769i
$742$		−	5.40461i		−	0.198410i
$743$	19.9566	−	34.5658i	0.732135	−	1.26809i	−0.223834	−	0.974627i	$-0.571857\pi$
$743$	19.9566	−	34.5658i	0.732135	−	1.26809i	0.955969	−	0.293468i	$-0.0948093\pi$
$744$	−2.95523	+	5.11861i	−0.108344	+	0.187657i
$745$	−35.9519	−	36.1845i	−1.31717	−	1.32570i
$746$			0.993455i			0.0363730i
$747$	−5.10226	−	8.83737i	−0.186682	−	0.323342i
$748$	−12.2001	−	21.1312i	−0.446080	−	0.772634i
$749$		−	9.76355i		−	0.356752i
$750$	10.7709	+	2.99802i	0.393297	+	0.109472i
$751$	8.79993	−	15.2419i	0.321114	−	0.556186i	−0.659604	−	0.751613i	$-0.729276\pi$
$751$	8.79993	−	15.2419i	0.321114	−	0.556186i	0.980718	+	0.195427i	$0.0626094\pi$
$752$	−0.426148	+	0.738110i	−0.0155400	+	0.0269161i
$753$		−	12.3066i		−	0.448476i
$754$	−16.9981	−	2.54407i	−0.619033	−	0.0926494i
$755$	43.0174	−	11.3779i	1.56556	−	0.414085i
$756$	−1.04466	−	0.603137i	−0.0379941	−	0.0219359i
$757$	19.1099	+	11.0331i	0.694560	+	0.401004i	0.805318	−	0.592843i	$-0.201995\pi$
$757$	19.1099	+	11.0331i	0.694560	+	0.401004i	−0.110758	+	0.993847i	$0.535328\pi$
$758$	23.7856	−	13.7326i	0.863932	−	0.498791i
$759$			11.2017i			0.406596i
$760$	3.35713	+	3.37886i	0.121776	+	0.122564i
$761$	−17.4454	+	10.0721i	−0.632394	+	0.365113i	−0.781678	−	0.623682i	$-0.785636\pi$
$761$	−17.4454	+	10.0721i	−0.632394	+	0.365113i	0.149285	+	0.988794i	$0.452303\pi$
$762$	−1.20191			−0.0435408
$763$	17.6380	−	10.1833i	0.638538	−	0.368660i
$764$	−5.77729	+	10.0066i	−0.209015	+	0.362025i
$765$	−2.77388	+	10.2203i	−0.100290	+	0.369516i
$766$	32.5703			1.17681
$767$	1.03612	−	6.92282i	0.0374123	−	0.249969i
$768$			1.00000i			0.0360844i
$769$	26.9356	+	15.5513i	0.971323	+	0.560794i	0.899639	−	0.436634i	$-0.143829\pi$
$769$	26.9356	+	15.5513i	0.971323	+	0.560794i	0.0716840	+	0.997427i	$0.477163\pi$
$770$	−3.64000	+	13.4115i	−0.131177	+	0.483318i
$771$	−14.0434	−	24.3239i	−0.505761	−	0.876004i
$772$	10.4631			0.376575
$773$	0.416119	+	0.720739i	0.0149668	+	0.0259232i	0.873412	−	0.486982i	$-0.161902\pi$
$773$	0.416119	+	0.720739i	0.0149668	+	0.0259232i	−0.858445	+	0.512906i	$0.828569\pi$
$774$	1.70944	−	0.986944i	0.0614444	−	0.0354750i
$775$	−14.6108	−	25.6878i	−0.524835	−	0.922734i
$776$	4.24139	+	7.34631i	0.152257	+	0.263717i
$777$	4.59723	+	2.65421i	0.164925	+	0.0952193i
$778$	−8.45549	+	14.6453i	−0.303144	+	0.525061i
$779$	−10.0883			−0.361449
$780$	−3.24021	+	7.38248i	−0.116018	+	0.264335i
$781$	−1.77704			−0.0635874
$782$	−5.14856	+	8.91756i	−0.184112	+	0.318891i
$783$	−4.12828	−	2.38346i	−0.147533	−	0.0851780i
$784$	2.77245	+	4.80203i	0.0990161	+	0.171501i
$785$	−10.2551	+	2.71243i	−0.366019	+	0.0968106i
$786$	5.76036	−	3.32575i	0.205465	−	0.118625i
$787$	12.4115	+	21.4974i	0.442422	+	0.766298i	0.997869	−	0.0652545i	$-0.0207859\pi$
$787$	12.4115	+	21.4974i	0.442422	+	0.766298i	−0.555446	+	0.831552i	$0.687453\pi$
$788$	−17.5894			−0.626598
$789$	−3.79178	−	6.56756i	−0.134991	−	0.233811i
$790$	−29.3192	−	7.95749i	−1.04313	−	0.283115i
$791$	−5.17215	−	2.98614i	−0.183900	−	0.106175i
$792$		−	5.15206i		−	0.183071i
$793$	−10.9682	−	1.64158i	−0.389491	−	0.0582944i
$794$	−32.2397			−1.14414
$795$	−9.66874	−	2.62418i	−0.342915	−	0.0930700i
$796$	12.7858	−	22.1457i	0.453181	−	0.784932i
$797$	20.5483	−	11.8636i	0.727858	−	0.420229i	−0.0897802	−	0.995962i	$-0.528616\pi$
$797$	20.5483	−	11.8636i	0.727858	−	0.420229i	0.817638	+	0.575733i	$0.195283\pi$
$798$	2.56951			0.0909595
$799$	3.49569	−	2.01824i	0.123669	−	0.0714002i
$800$	−4.31391	−	2.52788i	−0.152520	−	0.0893739i
$801$			16.3899i			0.579110i
$802$	28.0082	−	16.1705i	0.989003	−	0.571001i
$803$	−70.1524	−	40.5025i	−2.47562	−	1.42930i
$804$	−12.1723	−	7.02765i	−0.429282	−	0.247846i
$805$	5.66958	−	1.49958i	0.199826	−	0.0528532i
$806$	19.8293	−	7.80611i	0.698457	−	0.274959i
$807$			24.4709i			0.861418i
$808$	−6.79121	+	11.7627i	−0.238914	+	0.413811i
$809$	18.7196	−	32.4233i	0.658145	−	1.13994i	−0.322950	−	0.946416i	$-0.604675\pi$
$809$	18.7196	−	32.4233i	0.658145	−	1.13994i	0.981095	−	0.193525i	$-0.0619921\pi$
$810$	−1.58623	+	1.57603i	−0.0557344	+	0.0553761i
$811$		−	40.2205i		−	1.41233i	−0.708046	−	0.706166i	$-0.750423\pi$
$811$		−	40.2205i		−	1.41233i	0.708046	−	0.706166i	$-0.249577\pi$
$812$	−2.87511	−	4.97984i	−0.100897	−	0.174758i
$813$	−5.78497	−	10.0199i	−0.202888	−	0.351412i
$814$			22.6726i			0.794673i
$815$	6.13327	−	6.09384i	0.214839	−	0.213458i
$816$	2.36800	−	4.10150i	0.0828967	−	0.143581i
$817$	−2.10231	+	3.64130i	−0.0735504	+	0.127393i
$818$		−	1.16591i		−	0.0407652i
$819$	1.59316	+	4.04699i	0.0556695	+	0.141413i
$820$	10.2380	−	2.70790i	0.357526	−	0.0945641i
$821$	−24.5442	−	14.1706i	−0.856598	−	0.494557i	0.00627372	−	0.999980i	$-0.498003\pi$
$821$	−24.5442	−	14.1706i	−0.856598	−	0.494557i	−0.862872	+	0.505423i	$0.831336\pi$
$822$	−12.7435	−	7.35746i	−0.444480	−	0.256621i
$823$	−41.0437	+	23.6966i	−1.43069	+	0.826011i	−0.997174	−	0.0751325i	$-0.976062\pi$
$823$	−41.0437	+	23.6966i	−1.43069	+	0.826011i	−0.433520	+	0.901144i	$0.642729\pi$
$824$			2.15696i			0.0751412i
$825$	22.2256	+	13.0238i	0.773795	+	0.453430i
$826$	2.02814	−	1.17095i	0.0705681	−	0.0407425i
$827$	−2.70177			−0.0939496			−0.0469748	−	0.998896i	$-0.514958\pi$
$827$	−2.70177			−0.0939496			−0.0469748	+	0.998896i	$0.514958\pi$
$828$	−1.88293	+	1.08711i	−0.0654363	+	0.0377796i
$829$	−10.4285	+	18.0627i	−0.362197	+	0.627343i	−0.988322	−	0.152379i	$-0.951307\pi$
$829$	−10.4285	+	18.0627i	−0.362197	+	0.627343i	0.626125	+	0.779722i	$0.284640\pi$
$830$	−22.0213	−	5.97677i	−0.764371	−	0.207457i
$831$	12.9454			0.449072
$832$	2.24511	−	2.82126i	0.0778351	−	0.0978095i
$833$		−	26.2607i		−	0.909880i
$834$	13.5540	+	7.82540i	0.469336	+	0.270972i
$835$	49.0358	+	13.3087i	1.69695	+	0.460568i
$836$	5.48725	+	9.50420i	0.189781	+	0.328710i
$837$	5.91046			0.204296
$838$	−5.91396	−	10.2433i	−0.204294	−	0.353848i
$839$	5.34438	−	3.08558i	0.184508	−	0.106526i	−0.404901	−	0.914361i	$-0.632694\pi$
$839$	5.34438	−	3.08558i	0.184508	−	0.106526i	0.589409	+	0.807835i	$0.299361\pi$
$840$	−2.60764	+	0.689710i	−0.0899721	+	0.0237973i
$841$	3.13821	+	5.43553i	0.108214	+	0.187432i
$842$	−20.7068	−	11.9551i	−0.713604	−	0.412000i
$843$	1.28593	−	2.22730i	0.0442899	−	0.0767124i
$844$	12.9197			0.444714
$845$	25.7159	−	13.5533i	0.884655	−	0.466247i
$846$	0.852296			0.0293025
$847$	−9.37502	+	16.2380i	−0.322129	+	0.557944i
$848$	3.88016	+	2.24021i	0.133245	+	0.0769291i
$849$	2.77427	+	4.80517i	0.0952125	+	0.164913i
$850$	11.7075	+	20.5835i	0.401564	+	0.706007i
$851$	8.28616	−	4.78402i	0.284046	−	0.163994i
$852$	−0.172459	−	0.298707i	−0.00590834	−	0.0102335i
$853$	−52.4997			−1.79756			−0.898778	−	0.438405i	$-0.855544\pi$
$853$	−52.4997			−1.79756			−0.898778	+	0.438405i	$0.855544\pi$
$854$	−1.85519	−	3.21329i	−0.0634834	−	0.109956i
$855$	1.24761	−	4.59679i	0.0426673	−	0.157207i
$856$	7.00959	+	4.04699i	0.239583	+	0.138323i
$857$			23.9128i			0.816846i	0.912793	+	0.408423i	$0.133921\pi$
$857$			23.9128i			0.816846i	−0.912793	+	0.408423i	$0.866079\pi$
$858$	−11.5669	+	14.5353i	−0.394889	+	0.496227i
$859$	−35.2521			−1.20279			−0.601393	−	0.798953i	$-0.705387\pi$
$859$	−35.2521			−1.20279			−0.601393	+	0.798953i	$0.705387\pi$
$860$	1.15610	−	4.25965i	0.0394228	−	0.145253i
$861$	2.85646	−	4.94754i	0.0973480	−	0.168612i
$862$	−22.8082	+	13.1683i	−0.776849	+	0.448514i
$863$	−7.68909			−0.261740			−0.130870	−	0.991400i	$-0.541777\pi$
$863$	−7.68909			−0.261740			−0.130870	+	0.991400i	$0.541777\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	7.40419	+	7.45210i	0.251750	+	0.253379i
$866$			12.9594i			0.440380i
$867$	−4.70233	+	2.71489i	−0.159700	+	0.0922026i
$868$	6.17445	+	3.56482i	0.209574	+	0.120998i
$869$	−60.6196	−	34.9988i	−2.05638	−	1.18725i
$870$	−10.3048	+	2.72558i	−0.349366	+	0.0924058i
$871$	18.5632	+	47.1548i	0.628991	+	1.59778i
$872$			16.8839i			0.571761i
$873$	4.24139	−	7.34631i	0.143549	−	0.248635i
$874$	2.31567	−	4.01086i	0.0783287	−	0.135669i
$875$	3.61644	−	12.9926i	0.122258	−	0.439231i
$876$		−	15.7228i		−	0.531225i
$877$	8.42697	+	14.5959i	0.284559	+	0.492870i	0.972502	−	0.232894i	$-0.0748196\pi$
$877$	8.42697	+	14.5959i	0.284559	+	0.492870i	−0.687943	+	0.725764i	$0.741486\pi$
$878$	−11.6234	−	20.1324i	−0.392272	−	0.679434i
$879$		−	24.1316i		−	0.813938i
$880$	−8.11982	−	8.17235i	−0.273719	−	0.275490i
$881$	−24.0475	+	41.6516i	−0.810182	+	1.40328i	0.102554	+	0.994727i	$0.467299\pi$
$881$	−24.0475	+	41.6516i	−0.810182	+	1.40328i	−0.912736	+	0.408550i	$0.866035\pi$
$882$	2.77245	−	4.80203i	0.0933533	−	0.161693i
$883$			38.3641i			1.29105i	0.763737	+	0.645527i	$0.223362\pi$
$883$			38.3641i			1.29105i	−0.763737	+	0.645527i	$0.776638\pi$
$884$	−15.8891	+	6.25498i	−0.534407	+	0.210378i
$885$	−1.11005	−	4.19685i	−0.0373139	−	0.141076i
$886$	20.2414	+	11.6864i	0.680024	+	0.392612i
$887$	−16.2697	−	9.39331i	−0.546283	−	0.315396i	0.201339	−	0.979522i	$-0.435471\pi$
$887$	−16.2697	−	9.39331i	−0.546283	−	0.315396i	−0.747621	+	0.664125i	$0.768804\pi$
$888$	−3.81110	+	2.20034i	−0.127892	+	0.0738385i
$889$			1.44984i			0.0486260i
$890$	25.8311	+	25.9982i	0.865859	+	0.871462i
$891$	−4.46182	+	2.57603i	−0.149477	+	0.0863003i
$892$	−7.15357			−0.239519
$893$	−1.57226	+	0.907745i	−0.0526137	+	0.0303765i
$894$	11.4058	−	19.7555i	0.381468	−	0.660721i
$895$	−18.7708	−	5.09457i	−0.627440	−	0.170293i
$896$	1.20627			0.0402988
$897$	7.75290	+	1.16036i	0.258862	+	0.0387433i
$898$		−	1.39639i		−	0.0465982i
$899$	24.4000	+	14.0874i	0.813787	+	0.469840i
$900$	−0.0322474	+	4.99990i	−0.00107491	+	0.166663i
$901$	−10.6097	−	18.3765i	−0.353459	−	0.612209i
$902$	24.4002			0.812439
$903$	−1.19052	−	2.06205i	−0.0396182	−	0.0686207i
$904$	4.28771	−	2.47551i	0.142607	−	0.0823342i
$905$	5.57749	+	21.0873i	0.185402	+	0.700964i
$906$	9.94975	+	17.2335i	0.330558	+	0.572544i
$907$	18.2967	+	10.5636i	0.607532	+	0.350759i	0.771999	−	0.635624i	$-0.219257\pi$
$907$	18.2967	+	10.5636i	0.607532	+	0.350759i	−0.164467	+	0.986383i	$0.552590\pi$
$908$	−12.9192	+	22.3768i	−0.428740	+	0.742599i
$909$	13.5824			0.450501
$910$	8.90530	+	3.90858i	0.295208	+	0.129568i
$911$	19.2766			0.638664			0.319332	−	0.947643i	$-0.396542\pi$
$911$	19.2766			0.638664			0.319332	+	0.947643i	$0.396542\pi$
$912$	−1.06506	+	1.84474i	−0.0352676	+	0.0610853i
$913$	−45.5307	−	26.2872i	−1.50685	−	0.869978i
$914$	3.60093	+	6.23699i	0.119108	+	0.206301i
$915$	−6.64928	+	1.75871i	−0.219819	+	0.0581411i
$916$	−7.75225	+	4.47576i	−0.256142	+	0.147883i
$917$	−4.01176	−	6.94857i	−0.132480	−	0.229462i
$918$	−4.73601			−0.156312
$919$	17.8995	+	31.0028i	0.590450	+	1.02269i	0.994172	+	0.107807i	$0.0343830\pi$
$919$	17.8995	+	31.0028i	0.590450	+	1.02269i	−0.403722	+	0.914882i	$0.632284\pi$
$920$	−1.27344	+	4.69196i	−0.0419840	+	0.154689i
$921$	−26.2616	−	15.1621i	−0.865348	−	0.499609i
$922$			4.74489i			0.156265i
$923$	−0.184079	+	1.22992i	−0.00605905	+	0.0404833i
$924$	−6.21480			−0.204452
$925$	0.141910	−	22.0029i	0.00466598	−	0.723452i
$926$	−7.87551	+	13.6408i	−0.258805	+	0.448264i
$927$	1.86798	−	1.07848i	0.0613525	−	0.0354219i
$928$	4.76693			0.156482
$929$	−13.4933	+	7.79033i	−0.442699	+	0.255593i	−0.704742	−	0.709464i	$-0.748937\pi$
$929$	−13.4933	+	7.79033i	−0.442699	+	0.255593i	0.262043	+	0.965056i	$0.415604\pi$
$930$	9.37535	−	9.31508i	0.307430	−	0.305454i
$931$			11.8113i			0.387100i
$932$	−3.34855	+	1.93329i	−0.109685	+	0.0633269i
$933$	−7.58990	−	4.38203i	−0.248482	−	0.143461i
$934$	−15.5701	−	8.98943i	−0.509471	−	0.294143i
$935$	13.9513	+	52.7467i	0.456256	+	1.72500i
$936$	−3.56583	−	0.533691i	−0.116553	−	0.0174442i
$937$			27.4692i			0.897381i	0.893687	+	0.448690i	$0.148109\pi$
$937$			27.4692i			0.897381i	−0.893687	+	0.448690i	$0.851891\pi$
$938$	−8.47727	+	14.6831i	−0.276793	+	0.479419i
$939$	14.5077	−	25.1282i	0.473442	−	0.820026i
$940$	1.35194	−	1.34324i	0.0440953	−	0.0438118i
$941$		−	5.01957i		−	0.163633i	−0.996647	−	0.0818167i	$-0.973928\pi$
$941$		−	5.01957i		−	0.163633i	0.996647	−	0.0818167i	$-0.0260722\pi$
$942$	−2.37196	−	4.10836i	−0.0772826	−	0.133857i
$943$	−5.14856	−	8.91756i	−0.167660	−	0.290396i
$944$			1.94143i			0.0631882i
$945$	1.90113	+	1.91343i	0.0618436	+	0.0622438i
$946$	5.08480	−	8.80713i	0.165321	−	0.286344i
$947$	20.0915	−	34.7995i	0.652886	−	1.13083i	−0.329534	−	0.944144i	$-0.606891\pi$
$947$	20.0915	−	34.7995i	0.652886	−	1.13083i	0.982419	−	0.186688i	$-0.0597752\pi$
$948$		−	13.5863i		−	0.441263i
$949$	−35.2994	+	44.3582i	−1.14587	+	1.43993i
$950$	−5.26570	−	9.25783i	−0.170842	−	0.300364i
$951$	22.5140	+	12.9985i	0.730068	+	0.421505i
$952$	−4.94754	−	2.85646i	−0.160351	−	0.0925785i
$953$	−9.42493	+	5.44149i	−0.305304	+	0.176267i	−0.644823	−	0.764332i	$-0.723069\pi$
$953$	−9.42493	+	5.44149i	−0.305304	+	0.176267i	0.339519	+	0.940599i	$0.389736\pi$
$954$		−	4.48042i		−	0.145059i
$955$	18.3282	−	18.2104i	0.593087	−	0.589274i
$956$	13.3521	−	7.70884i	0.431838	−	0.249322i
$957$	−24.5595			−0.793896
$958$	2.83964	−	1.63947i	0.0917447	−	0.0529688i
$959$	−8.87511	+	15.3721i	−0.286592	+	0.496392i
$960$	0.585699	−	2.15800i	0.0189034	−	0.0696491i
$961$	−3.93359			−0.126890
$962$	15.6921	+	2.34860i	0.505933	+	0.0757220i
$963$		−	8.09397i		−	0.260825i
$964$	−9.76603	−	5.63842i	−0.314543	−	0.181601i
$965$	−22.5793	−	6.12822i	−0.726854	−	0.197274i
$966$	1.31135	+	2.27133i	0.0421920	+	0.0730787i
$967$	−2.14376			−0.0689387			−0.0344693	−	0.999406i	$-0.510974\pi$
$967$	−2.14376			−0.0689387			−0.0344693	+	0.999406i	$0.510974\pi$
$968$	−7.77188	−	13.4613i	−0.249798	−	0.432662i
$969$	8.73669	−	5.04413i	0.280663	−	0.162041i
$970$	−4.85019	−	18.3375i	−0.155730	−	0.588781i
$971$	−4.57889	−	7.93087i	−0.146944	−	0.254514i	0.783153	−	0.621829i	$-0.213610\pi$
$971$	−4.57889	−	7.93087i	−0.146944	−	0.254514i	−0.930096	+	0.367316i	$0.880277\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	9.43958	−	16.3498i	0.302619	−	0.524151i
$974$	9.97704			0.319685
$975$	11.3163	−	14.0336i	0.362411	−	0.449435i
$976$	3.07591			0.0984574
$977$	−7.16508	+	12.4103i	−0.229231	+	0.397040i	−0.957581	−	0.288166i	$-0.906955\pi$
$977$	−7.16508	+	12.4103i	−0.229231	+	0.397040i	0.728349	+	0.685206i	$0.240288\pi$
$978$	3.34855	+	1.93329i	0.107075	+	0.0618197i
$979$	42.2210	+	73.1289i	1.34939	+	2.33721i
$980$	−3.17040	−	11.9866i	−0.101275	−	0.382898i
$981$	14.6219	−	8.44195i	0.466841	−	0.269531i
$982$	−10.0376	−	17.3857i	−0.320314	−	0.554800i
$983$	21.6099			0.689250			0.344625	−	0.938740i	$-0.388006\pi$
$983$	21.6099			0.689250			0.344625	+	0.938740i	$0.388006\pi$
$984$	2.36800	+	4.10150i	0.0754892	+	0.130751i
$985$	37.9580	+	10.3021i	1.20944	+	0.328253i
$986$	−19.5516	−	11.2881i	−0.622649	−	0.359486i
$987$		−	1.02810i		−	0.0327248i
$988$	7.14644	−	2.81330i	0.227358	−	0.0895031i
$989$	−4.29166			−0.136467
$990$	−3.01756	+	11.1181i	−0.0959043	+	0.353358i
$991$	−11.9222	+	20.6499i	−0.378722	+	0.655966i	−0.990877	−	0.134772i	$-0.956970\pi$
$991$	−11.9222	+	20.6499i	−0.378722	+	0.655966i	0.612154	+	0.790738i	$0.290303\pi$
$992$	−5.11861	+	2.95523i	−0.162516	+	0.0938287i
$993$	11.0392			0.350319
$994$	−0.360323	+	0.208033i	−0.0114287	+	0.00659839i
$995$	−40.5624	+	40.3017i	−1.28592	+	1.27765i
$996$		−	10.2045i		−	0.323342i
$997$	25.5772	−	14.7670i	0.810037	−	0.467675i	−0.0369315	−	0.999318i	$-0.511758\pi$
$997$	25.5772	−	14.7670i	0.810037	−	0.467675i	0.846969	+	0.531642i	$0.178425\pi$
$998$	20.7390	+	11.9737i	0.656482	+	0.379020i
$999$	3.81110	+	2.20034i	0.120578	+	0.0696157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.x.b.199.3	yes	12
3.2	odd	2		1170.2.bj.c.199.3		12
5.2	odd	4		1950.2.bc.i.901.4		12
5.3	odd	4		1950.2.bc.j.901.3		12
5.4	even	2		390.2.x.a.199.4	yes	12
13.10	even	6		390.2.x.a.49.4	✓	12
15.14	odd	2		1170.2.bj.d.199.4		12
39.23	odd	6		1170.2.bj.d.829.4		12
65.23	odd	12		1950.2.bc.j.751.3		12
65.49	even	6	inner	390.2.x.b.49.3	yes	12
65.62	odd	12		1950.2.bc.i.751.4		12
195.179	odd	6		1170.2.bj.c.829.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.4	✓	12	13.10	even	6
390.2.x.a.199.4	yes	12	5.4	even	2
390.2.x.b.49.3	yes	12	65.49	even	6	inner
390.2.x.b.199.3	yes	12	1.1	even	1	trivial
1170.2.bj.c.199.3		12	3.2	odd	2
1170.2.bj.c.829.3		12	195.179	odd	6
1170.2.bj.d.199.4		12	15.14	odd	2
1170.2.bj.d.829.4		12	39.23	odd	6
1950.2.bc.i.751.4		12	65.62	odd	12
1950.2.bc.i.901.4		12	5.2	odd	4
1950.2.bc.j.751.3		12	65.23	odd	12
1950.2.bc.j.901.3		12	5.3	odd	4

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.571769 + 2.16173i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.603137 + 1.04466i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.571769 + 2.16173i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.603137 + 1.04466i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.15800 + 0.585699i) q^{10} +(4.46182 + 2.57603i) q^{11} +1.00000i q^{12} +(2.24511 - 2.82126i) q^{13} +1.20627 q^{14} +(0.585699 - 2.15800i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.10150 - 2.36800i) q^{17} +1.00000 q^{18} +(-1.84474 + 1.06506i) q^{19} +(1.58623 - 1.57603i) q^{20} -1.20627i q^{21} +(4.46182 - 2.57603i) q^{22} +(-1.88293 - 1.08711i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.34616 + 2.47202i) q^{25} +(-1.32073 - 3.35495i) q^{26} -1.00000i q^{27} +(0.603137 - 1.04466i) q^{28} +(2.38346 - 4.12828i) q^{29} +(-1.57603 - 1.58623i) q^{30} +5.91046i q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.57603 - 4.46182i) q^{33} -4.73601i q^{34} +(-1.91343 + 1.90113i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.20034 + 3.81110i) q^{37} +2.13012i q^{38} +(-3.35495 + 1.32073i) q^{39} +(-0.571769 - 2.16173i) q^{40} +(4.10150 + 2.36800i) q^{41} +(-1.04466 - 0.603137i) q^{42} +(1.70944 - 0.986944i) q^{43} -5.15206i q^{44} +(-1.58623 + 1.57603i) q^{45} +(-1.88293 + 1.08711i) q^{46} +0.852296 q^{47} +(0.866025 - 0.500000i) q^{48} +(2.77245 - 4.80203i) q^{49} +(-0.0322474 + 4.99990i) q^{50} -4.73601 q^{51} +(-3.56583 - 0.533691i) q^{52} -4.48042i q^{53} +(-0.866025 - 0.500000i) q^{54} +(-3.01756 + 11.1181i) q^{55} +(-0.603137 - 1.04466i) q^{56} +2.13012 q^{57} +(-2.38346 - 4.12828i) q^{58} +(1.68133 - 0.970715i) q^{59} +(-2.16173 + 0.571769i) q^{60} +(-1.53795 - 2.66381i) q^{61} +(5.11861 + 2.95523i) q^{62} +(-0.603137 + 1.04466i) q^{63} +1.00000 q^{64} +(7.38248 + 3.24021i) q^{65} -5.15206 q^{66} +(-7.02765 + 12.1723i) q^{67} +(-4.10150 - 2.36800i) q^{68} +(1.08711 + 1.88293i) q^{69} +(0.689710 + 2.60764i) q^{70} +(-0.298707 + 0.172459i) q^{71} +(-0.500000 - 0.866025i) q^{72} -15.7228 q^{73} +(2.20034 + 3.81110i) q^{74} +(4.99990 + 0.0322474i) q^{75} +(1.84474 + 1.06506i) q^{76} +6.21480i q^{77} +(-0.533691 + 3.56583i) q^{78} -13.5863 q^{79} +(-2.15800 - 0.585699i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.10150 - 2.36800i) q^{82} -10.2045 q^{83} +(-1.04466 + 0.603137i) q^{84} +(7.46410 + 7.51240i) q^{85} -1.97389i q^{86} +(-4.12828 + 2.38346i) q^{87} +(-4.46182 - 2.57603i) q^{88} +(14.1941 + 8.19497i) q^{89} +(0.571769 + 2.16173i) q^{90} +(4.30137 + 0.643777i) q^{91} +2.17422i q^{92} +(2.95523 - 5.11861i) q^{93} +(0.426148 - 0.738110i) q^{94} +(-3.35713 - 3.37886i) q^{95} -1.00000i q^{96} +(-4.24139 - 7.34631i) q^{97} +(-2.77245 - 4.80203i) q^{98} +5.15206i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9} + 4 q^{10} + 6 q^{11} + 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} - 18 q^{17} + 12 q^{18} - 6 q^{19} + 2 q^{20} + 6 q^{22} - 6 q^{23} - 10 q^{25} - 2 q^{26} + 2 q^{28} + 14 q^{29} + 6 q^{30} + 6 q^{32} - 6 q^{33} - 22 q^{35} + 6 q^{36} + 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} + 12 q^{42} + 36 q^{43} - 2 q^{45} - 6 q^{46} - 16 q^{47} + 8 q^{49} - 20 q^{50} + 16 q^{51} - 10 q^{52} + 8 q^{55} - 2 q^{56} + 8 q^{57} - 14 q^{58} - 36 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{63} + 12 q^{64} - 44 q^{65} - 12 q^{66} - 4 q^{67} + 18 q^{68} + 16 q^{69} + 4 q^{70} - 12 q^{71} - 6 q^{72} - 28 q^{73} - 12 q^{74} + 16 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} - 4 q^{80} - 6 q^{81} - 18 q^{82} - 72 q^{83} + 12 q^{84} + 48 q^{85} - 6 q^{87} - 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{93} - 8 q^{94} + 18 q^{95} + 48 q^{97} - 8 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9 + 4 * q^10 + 6 * q^11 + 8 * q^13 + 4 * q^14 + 6 * q^15 - 6 * q^16 - 18 * q^17 + 12 * q^18 - 6 * q^19 + 2 * q^20 + 6 * q^22 - 6 * q^23 - 10 * q^25 - 2 * q^26 + 2 * q^28 + 14 * q^29 + 6 * q^30 + 6 * q^32 - 6 * q^33 - 22 * q^35 + 6 * q^36 + 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 + 12 * q^42 + 36 * q^43 - 2 * q^45 - 6 * q^46 - 16 * q^47 + 8 * q^49 - 20 * q^50 + 16 * q^51 - 10 * q^52 + 8 * q^55 - 2 * q^56 + 8 * q^57 - 14 * q^58 - 36 * q^59 + 10 * q^61 - 6 * q^62 - 2 * q^63 + 12 * q^64 - 44 * q^65 - 12 * q^66 - 4 * q^67 + 18 * q^68 + 16 * q^69 + 4 * q^70 - 12 * q^71 - 6 * q^72 - 28 * q^73 - 12 * q^74 + 16 * q^75 + 6 * q^76 + 2 * q^78 + 4 * q^79 - 4 * q^80 - 6 * q^81 - 18 * q^82 - 72 * q^83 + 12 * q^84 + 48 * q^85 - 6 * q^87 - 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^93 - 8 * q^94 + 18 * q^95 + 48 * q^97 - 8 * q^98

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