LMFDB - Embedded newform 570.2.bi.a.263.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(17,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("570.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bi (of order $36$, degree $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$40$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			263.9
Character	$\chi$	$=$	570.263
Dual form			570.2.bi.a.557.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(-0.695277 - 1.58638i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-2.04009 - 0.915434i) q^{5} +(-1.51974 + 0.830893i) q^{6} +(-0.956140 - 0.256197i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.03318 + 2.20594i) q^{9} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.695277 - 1.58638i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-2.04009 - 0.915434i) q^{5} +(-1.51974 + 0.830893i) q^{6} +(-0.956140 - 0.256197i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.03318 + 2.20594i) q^{9} +(-0.734145 + 2.11212i) q^{10} +(-1.68727 - 0.974147i) q^{11} +(0.960186 + 1.44154i) q^{12} +(2.53459 + 5.43545i) q^{13} +(-0.171889 + 0.974830i) q^{14} +(-0.0337921 + 3.87284i) q^{15} +(0.939693 - 0.342020i) q^{16} +(-0.249112 - 2.84737i) q^{17} +(2.37475 + 1.83318i) q^{18} +(-4.19757 - 1.17490i) q^{19} +(2.16806 + 0.547268i) q^{20} +(0.258358 + 1.69493i) q^{21} +(-0.823385 + 1.76575i) q^{22} +(2.28307 + 1.59862i) q^{23} +(1.35237 - 1.08217i) q^{24} +(3.32396 + 3.73514i) q^{25} +(5.19386 - 2.99868i) q^{26} +(4.91308 + 1.69164i) q^{27} +(0.986102 + 0.0862727i) q^{28} +(0.831703 - 0.697882i) q^{29} +(3.86104 - 0.303876i) q^{30} +(0.207050 + 0.358622i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-0.372241 + 3.35395i) q^{33} +(-2.81482 + 0.496329i) q^{34} +(1.71608 + 1.39795i) q^{35} +(1.61923 - 2.52549i) q^{36} +(-6.98105 + 6.98105i) q^{37} +(-0.804584 + 4.28400i) q^{38} +(6.86042 - 7.79996i) q^{39} +(0.356226 - 2.20751i) q^{40} +(-0.231277 - 0.635428i) q^{41} +(1.66596 - 0.405097i) q^{42} +(-0.540510 + 0.378469i) q^{43} +(1.83080 + 0.666356i) q^{44} +(6.16727 - 2.63909i) q^{45} +(1.39356 - 2.41371i) q^{46} +(-9.29672 - 0.813358i) q^{47} +(-1.19592 - 1.25291i) q^{48} +(-5.21361 - 3.01008i) q^{49} +(3.43123 - 3.63685i) q^{50} +(-4.34379 + 2.37490i) q^{51} +(-3.43994 - 4.91274i) q^{52} +(7.05061 + 4.93689i) q^{53} +(1.25700 - 5.04182i) q^{54} +(2.55043 + 3.53194i) q^{55} -0.989869i q^{56} +(1.05465 + 7.47581i) q^{57} +(-0.767714 - 0.767714i) q^{58} +(0.996800 + 0.836415i) q^{59} +(-0.639232 - 3.81987i) q^{60} +(1.19209 + 6.76066i) q^{61} +(0.339211 - 0.237518i) q^{62} +(2.50916 - 1.58830i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-0.195008 - 13.4091i) q^{65} +(3.37363 + 0.0785089i) q^{66} +(-1.15572 + 13.2100i) q^{67} +(0.739768 + 2.76085i) q^{68} +(0.948649 - 4.73329i) q^{69} +(1.24306 - 1.83139i) q^{70} +(-8.83250 - 1.55741i) q^{71} +(-2.65700 - 1.39296i) q^{72} +(5.75154 + 2.68199i) q^{73} +(7.56293 + 6.34605i) q^{74} +(3.61426 - 7.87001i) q^{75} +(4.33782 + 0.428147i) q^{76} +(1.36369 + 1.36369i) q^{77} +(-8.36820 - 6.15450i) q^{78} +(-3.54991 - 9.75331i) q^{79} +(-2.23016 - 0.162474i) q^{80} +(-0.732369 - 8.97015i) q^{81} +(-0.612853 + 0.285778i) q^{82} +(-6.81831 - 1.82696i) q^{83} +(-0.548753 - 1.62431i) q^{84} +(-2.09836 + 6.03694i) q^{85} +(0.424137 + 0.505467i) q^{86} +(-1.68537 - 0.834173i) q^{87} +(0.504256 - 1.88191i) q^{88} +(-15.9299 - 5.79801i) q^{89} +(-3.16656 - 5.91379i) q^{90} +(-1.03088 - 5.84640i) q^{91} +(-2.52598 - 1.17788i) q^{92} +(0.424952 - 0.577801i) q^{93} +9.33223i q^{94} +(7.48790 + 6.23950i) q^{95} +(-1.14391 + 1.30057i) q^{96} +(-10.1176 + 0.885172i) q^{97} +(-2.54423 + 5.45612i) q^{98} +(5.57944 - 1.74141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q+O(q^{10}) $ 480 * q	$ 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) $ 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$3$	−0.695277	−	1.58638i	−0.401419	−	0.915895i
$3$	−0.695277	−	1.58638i	−0.401419	−	0.915895i
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$	−2.04009	−	0.915434i	−0.912357	−	0.409395i
$5$	−2.04009	−	0.915434i	−0.912357	−	0.409395i
$6$	−1.51974	+	0.830893i	−0.620432	+	0.339211i
$7$	−0.956140	−	0.256197i	−0.361387	−	0.0968333i	0.0735567	−	0.997291i	$-0.476565\pi$
$7$	−0.956140	−	0.256197i	−0.361387	−	0.0968333i	−0.434944	+	0.900458i	$0.643232\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	−2.03318	+	2.20594i	−0.677726	+	0.735314i
$10$	−0.734145	+	2.11212i	−0.232157	+	0.667910i
$11$	−1.68727	−	0.974147i	−0.508732	−	0.293716i	0.223580	−	0.974685i	$-0.428225\pi$
$11$	−1.68727	−	0.974147i	−0.508732	−	0.293716i	−0.732312	+	0.680969i	$0.761559\pi$
$12$	0.960186	+	1.44154i	0.277182	+	0.416137i
$13$	2.53459	+	5.43545i	0.702969	+	1.50752i	0.854712	+	0.519102i	$0.173734\pi$
$13$	2.53459	+	5.43545i	0.702969	+	1.50752i	−0.151743	+	0.988420i	$0.548489\pi$
$14$	−0.171889	+	0.974830i	−0.0459392	+	0.260534i
$15$	−0.0337921	+	3.87284i	−0.00872507	+	0.999962i
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−0.249112	−	2.84737i	−0.0604186	−	0.690588i	−0.964648	−	0.263541i	$-0.915110\pi$
$17$	−0.249112	−	2.84737i	−0.0604186	−	0.690588i	0.904230	−	0.427047i	$-0.140446\pi$
$18$	2.37475	+	1.83318i	0.559734	+	0.432085i
$19$	−4.19757	−	1.17490i	−0.962989	−	0.269540i
$19$	−4.19757	−	1.17490i	−0.962989	−	0.269540i
$20$	2.16806	+	0.547268i	0.484794	+	0.122373i
$21$	0.258358	+	1.69493i	0.0563783	+	0.369863i
$22$	−0.823385	+	1.76575i	−0.175546	+	0.376460i
$23$	2.28307	+	1.59862i	0.476053	+	0.333336i	0.786854	−	0.617139i	$-0.211708\pi$
$23$	2.28307	+	1.59862i	0.476053	+	0.333336i	−0.310801	+	0.950475i	$0.600597\pi$
$24$	1.35237	−	1.08217i	0.276052	−	0.220897i
$25$	3.32396	+	3.73514i	0.664792	+	0.747028i
$26$	5.19386	−	2.99868i	1.01860	−	0.588089i
$27$	4.91308	+	1.69164i	0.945522	+	0.325557i
$28$	0.986102	+	0.0862727i	0.186356	+	0.0163040i
$29$	0.831703	−	0.697882i	0.154443	−	0.129593i	−0.562292	−	0.826939i	$-0.690080\pi$
$29$	0.831703	−	0.697882i	0.154443	−	0.129593i	0.716735	+	0.697346i	$0.245636\pi$
$30$	3.86104	−	0.303876i	0.704927	−	0.0554800i
$31$	0.207050	+	0.358622i	0.0371873	+	0.0644104i	0.884020	−	0.467449i	$-0.154827\pi$
$31$	0.207050	+	0.358622i	0.0371873	+	0.0644104i	−0.846833	+	0.531859i	$0.821494\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$	−0.372241	+	3.35395i	−0.0647989	+	0.583848i
$34$	−2.81482	+	0.496329i	−0.482738	+	0.0851197i
$35$	1.71608	+	1.39795i	0.290071	+	0.236296i
$36$	1.61923	−	2.52549i	0.269872	−	0.420915i
$37$	−6.98105	+	6.98105i	−1.14768	+	1.14768i	−0.160670	+	0.987008i	$0.551366\pi$
$37$	−6.98105	+	6.98105i	−1.14768	+	1.14768i	−0.987008	+	0.160670i	$0.948634\pi$
$38$	−0.804584	+	4.28400i	−0.130521	+	0.694956i
$39$	6.86042	−	7.79996i	1.09855	−	1.24899i
$40$	0.356226	−	2.20751i	0.0563243	−	0.349038i
$41$	−0.231277	−	0.635428i	−0.0361194	−	0.0992372i	0.920322	−	0.391162i	$-0.127927\pi$
$41$	−0.231277	−	0.635428i	−0.0361194	−	0.0992372i	−0.956441	+	0.291924i	$0.905704\pi$
$42$	1.66596	−	0.405097i	0.257063	−	0.0625078i
$43$	−0.540510	+	0.378469i	−0.0824270	+	0.0577160i	−0.614064	−	0.789257i	$-0.710466\pi$
$43$	−0.540510	+	0.378469i	−0.0824270	+	0.0577160i	0.531637	+	0.846973i	$0.321577\pi$
$44$	1.83080	+	0.666356i	0.276003	+	0.100457i
$45$	6.16727	−	2.63909i	0.919362	−	0.393412i
$46$	1.39356	−	2.41371i	0.205469	−	0.355882i
$47$	−9.29672	−	0.813358i	−1.35607	−	0.118640i	−0.614180	−	0.789166i	$-0.710513\pi$
$47$	−9.29672	−	0.813358i	−1.35607	−	0.118640i	−0.741886	+	0.670526i	$0.766069\pi$
$48$	−1.19592	−	1.25291i	−0.172616	−	0.180842i
$49$	−5.21361	−	3.01008i	−0.744802	−	0.430011i
$50$	3.43123	−	3.63685i	0.485249	−	0.514328i
$51$	−4.34379	+	2.37490i	−0.608253	+	0.332552i
$52$	−3.43994	−	4.91274i	−0.477034	−	0.681275i
$53$	7.05061	+	4.93689i	0.968476	+	0.678134i	0.946865	−	0.321632i	$-0.104232\pi$
$53$	7.05061	+	4.93689i	0.968476	+	0.678134i	0.0216112	+	0.999766i	$0.493120\pi$
$54$	1.25700	−	5.04182i	0.171057	−	0.686105i
$55$	2.55043	+	3.53194i	0.343899	+	0.476246i
$56$		−	0.989869i		−	0.132277i
$57$	1.05465	+	7.47581i	0.139692	+	0.990195i
$58$	−0.767714	−	0.767714i	−0.100806	−	0.100806i
$59$	0.996800	+	0.836415i	0.129772	+	0.108892i	0.705364	−	0.708846i	$-0.250784\pi$
$59$	0.996800	+	0.836415i	0.129772	+	0.108892i	−0.575591	+	0.817737i	$0.695228\pi$
$60$	−0.639232	−	3.81987i	−0.0825245	−	0.493143i
$61$	1.19209	+	6.76066i	0.152631	+	0.865613i	0.960920	+	0.276827i	$0.0892829\pi$
$61$	1.19209	+	6.76066i	0.152631	+	0.865613i	−0.808289	+	0.588786i	$0.799606\pi$
$62$	0.339211	−	0.237518i	0.0430799	−	0.0301649i
$63$	2.50916	−	1.58830i	0.316124	−	0.200106i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$	−0.195008	−	13.4091i	−0.0241877	−	1.66319i
$66$	3.37363	+	0.0785089i	0.415265	+	0.00966377i
$67$	−1.15572	+	13.2100i	−0.141194	+	1.61386i	0.513588	+	0.858037i	$0.328316\pi$
$67$	−1.15572	+	13.2100i	−0.141194	+	1.61386i	−0.654782	+	0.755818i	$0.727239\pi$
$68$	0.739768	+	2.76085i	0.0897100	+	0.334802i
$69$	0.948649	−	4.73329i	0.114204	−	0.569821i
$70$	1.24306	−	1.83139i	0.148574	−	0.218893i
$71$	−8.83250	−	1.55741i	−1.04822	−	0.184830i	−0.377098	−	0.926173i	$-0.623078\pi$
$71$	−8.83250	−	1.55741i	−1.04822	−	0.184830i	−0.671126	+	0.741343i	$0.734189\pi$
$72$	−2.65700	−	1.39296i	−0.313131	−	0.164162i
$73$	5.75154	+	2.68199i	0.673167	+	0.313903i	0.728977	−	0.684538i	$-0.239996\pi$
$73$	5.75154	+	2.68199i	0.673167	+	0.313903i	−0.0558096	+	0.998441i	$0.517774\pi$
$74$	7.56293	+	6.34605i	0.879173	+	0.737713i
$75$	3.61426	−	7.87001i	0.417339	−	0.908751i
$76$	4.33782	+	0.428147i	0.497582	+	0.0491119i
$77$	1.36369	+	1.36369i	0.155407	+	0.155407i
$78$	−8.36820	−	6.15450i	−0.947512	−	0.696860i
$79$	−3.54991	−	9.75331i	−0.399396	−	1.09733i	−0.962579	−	0.271000i	$-0.912646\pi$
$79$	−3.54991	−	9.75331i	−0.399396	−	1.09733i	0.563183	−	0.826332i	$-0.309577\pi$
$80$	−2.23016	−	0.162474i	−0.249339	−	0.0181651i
$81$	−0.732369	−	8.97015i	−0.0813743	−	0.996684i
$82$	−0.612853	+	0.285778i	−0.0676783	+	0.0315589i
$83$	−6.81831	−	1.82696i	−0.748407	−	0.200535i	−0.135596	−	0.990764i	$-0.543295\pi$
$83$	−6.81831	−	1.82696i	−0.748407	−	0.200535i	−0.612811	+	0.790229i	$0.709961\pi$
$84$	−0.548753	−	1.62431i	−0.0598739	−	0.177227i
$85$	−2.09836	+	6.03694i	−0.227600	+	0.654798i
$86$	0.424137	+	0.505467i	0.0457359	+	0.0545059i
$87$	−1.68537	−	0.834173i	−0.180690	−	0.0894327i
$88$	0.504256	−	1.88191i	0.0537538	−	0.200612i
$89$	−15.9299	−	5.79801i	−1.68857	−	0.614588i	−0.694123	−	0.719856i	$-0.744208\pi$
$89$	−15.9299	−	5.79801i	−1.68857	−	0.614588i	−0.994444	+	0.105268i	$0.966430\pi$
$90$	−3.16656	−	5.91379i	−0.333785	−	0.623368i
$91$	−1.03088	−	5.84640i	−0.108065	−	0.612869i
$92$	−2.52598	−	1.17788i	−0.263352	−	0.122803i
$93$	0.424952	−	0.577801i	0.0440654	−	0.0599152i
$94$			9.33223i			0.962547i
$95$	7.48790	+	6.23950i	0.768242	+	0.640159i
$96$	−1.14391	+	1.30057i	−0.116750	+	0.132739i
$97$	−10.1176	+	0.885172i	−1.02728	+	0.0898756i	−0.588319	−	0.808629i	$-0.700210\pi$
$97$	−10.1176	+	0.885172i	−1.02728	+	0.0898756i	−0.438964	+	0.898505i	$0.644654\pi$
$98$	−2.54423	+	5.45612i	−0.257006	+	0.551151i
$99$	5.57944	−	1.74141i	0.560755	−	0.175018i
$100$	−3.92206	−	3.10120i	−0.392206	−	0.310120i
$101$	−5.27281	+	14.4869i	−0.524664	+	1.44150i	0.340611	+	0.940204i	$0.389366\pi$
$101$	−5.27281	+	14.4869i	−0.524664	+	1.44150i	−0.865275	+	0.501298i	$0.832856\pi$
$102$	2.74445	+	4.12028i	0.271741	+	0.407968i
$103$	0.0930424	−	0.0249306i	0.00916774	−	0.00245649i	−0.254232	−	0.967143i	$-0.581823\pi$
$103$	0.0930424	−	0.0249306i	0.00916774	−	0.00245649i	0.263400	+	0.964687i	$0.415156\pi$
$104$	−4.59424	+	3.85502i	−0.450502	+	0.378016i
$105$	1.02452	−	3.69431i	0.0999828	−	0.360528i
$106$	4.30360	−	7.45406i	0.418003	−	0.724002i
$107$	1.51693	−	5.66126i	0.146647	−	0.547295i	−0.853029	−	0.521863i	$-0.825237\pi$
$107$	1.51693	−	5.66126i	0.146647	−	0.547295i	0.999677	−	0.0254320i	$-0.00809612\pi$
$108$	−5.13219	−	0.812797i	−0.493845	−	0.0782114i
$109$	10.3517	+	1.82529i	0.991518	+	0.174831i	0.645799	−	0.763507i	$-0.276524\pi$
$109$	10.3517	+	1.82529i	0.991518	+	0.174831i	0.345718	+	0.938338i	$0.387635\pi$
$110$	3.29621	−	2.84855i	0.314282	−	0.271598i
$111$	15.9283	+	6.22081i	1.51185	+	0.590453i
$112$	−0.986102	+	0.0862727i	−0.0931779	+	0.00815201i
$113$	−9.80637	+	9.80637i	−0.922506	+	0.922506i	−0.997206	−	0.0747004i	$-0.976200\pi$
$113$	−9.80637	+	9.80637i	−0.922506	+	0.922506i	0.0747004	+	0.997206i	$0.476200\pi$
$114$	7.35544	−	1.70219i	0.688900	−	0.159425i
$115$	−3.19424	−	5.35134i	−0.297864	−	0.499015i
$116$	−0.697882	+	0.831703i	−0.0647967	+	0.0772217i
$117$	−17.1436	−	5.46007i	−1.58492	−	0.504784i
$118$	0.746355	−	1.06591i	0.0687075	−	0.0981245i
$119$	−0.491300	+	2.78630i	−0.0450374	+	0.255420i
$120$	−3.74962	+	0.969723i	−0.342292	+	0.0885232i
$121$	−3.60207	−	6.23898i	−0.327461	−	0.567180i
$122$	6.63103	−	1.77678i	0.600346	−	0.160862i
$123$	−0.847226	+	0.808691i	−0.0763918	+	0.0729172i
$124$	−0.266179	−	0.317220i	−0.0239036	−	0.0284872i
$125$	−3.36191	−	10.6629i	−0.300699	−	0.953719i
$126$	−1.80094	−	2.36118i	−0.160440	−	0.210351i
$127$	13.0867	−	6.10243i	1.16126	−	0.541503i	0.256129	−	0.966643i	$-0.417553\pi$
$127$	13.0867	−	6.10243i	1.16126	−	0.541503i	0.905128	+	0.425140i	$0.139775\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$	0.976198	+	0.594311i	0.0859495	+	0.0523262i
$130$	−13.3411	+	1.36294i	−1.17009	+	0.119538i
$131$	−1.84166	+	2.19480i	−0.160906	+	0.191761i	−0.840474	−	0.541853i	$-0.817723\pi$
$131$	−1.84166	+	2.19480i	−0.160906	+	0.191761i	0.679567	+	0.733613i	$0.262168\pi$
$132$	−0.215821	−	3.36764i	−0.0187848	−	0.293115i
$133$	3.71246	+	2.19877i	0.321911	+	0.190658i
$134$	13.2604			1.14553
$135$	−8.47455	−	7.94871i	−0.729373	−	0.684116i
$136$	2.68587	−	0.977577i	0.230312	−	0.0838265i
$137$	−6.76863	+	9.66661i	−0.578283	+	0.825874i	−0.996597	−	0.0824285i	$-0.973732\pi$
$137$	−6.76863	+	9.66661i	−0.578283	+	0.825874i	0.418314	+	0.908303i	$0.362621\pi$
$138$	−4.79796	−	0.532506i	−0.408429	−	0.0453299i
$139$	1.70250	−	4.67758i	0.144404	−	0.396747i	−0.846313	−	0.532686i	$-0.821183\pi$
$139$	1.70250	−	4.67758i	0.144404	−	0.396747i	0.990717	+	0.135939i	$0.0434050\pi$
$140$	−1.93276	−	1.07872i	−0.163348	−	0.0911681i
$141$	5.17351	+	15.3136i	0.435688	+	1.28964i
$142$	−0.781678	+	8.93462i	−0.0655970	+	0.749777i
$143$	1.01838	−	11.6401i	0.0851613	−	0.973398i
$144$	−1.15609	+	2.76830i	−0.0963405	+	0.230691i
$145$	−2.33562	+	0.662375i	−0.193962	+	0.0550072i
$146$	2.17050	−	5.96341i	0.179632	−	0.493535i
$147$	−1.15021	+	10.3636i	−0.0948680	+	0.854774i
$148$	5.66275	−	8.08724i	0.465475	−	0.664767i
$149$	−8.46674	+	3.08164i	−0.693622	+	0.252458i	−0.664685	−	0.747123i	$-0.731434\pi$
$149$	−8.46674	+	3.08164i	−0.693622	+	0.252458i	−0.0289370	+	0.999581i	$0.509212\pi$
$150$	−8.15507	−	2.91459i	−0.665859	−	0.237976i
$151$	−18.9891			−1.54531			−0.772656	−	0.634824i	$-0.781072\pi$
$151$	−18.9891			−1.54531			−0.772656	+	0.634824i	$0.781072\pi$
$152$	0.0484520	−	4.35863i	0.00392998	−	0.353532i
$153$	6.78762	+	5.23968i	0.548747	+	0.423603i
$154$	1.23965	−	1.47736i	0.0998940	−	0.119049i
$155$	−0.0941075	−	0.921163i	−0.00755889	−	0.0739896i
$156$	−5.40175	+	8.87276i	−0.432486	+	0.710389i
$157$	−6.89192	−	9.84268i	−0.550035	−	0.785531i	0.443833	−	0.896110i	$-0.353619\pi$
$157$	−6.89192	−	9.84268i	−0.550035	−	0.785531i	−0.993867	+	0.110579i	$0.964730\pi$
$158$	−9.40680	+	4.38646i	−0.748365	+	0.348968i
$159$	2.92964	−	14.6174i	0.232335	−	1.15924i
$160$	0.0325156	+	2.23583i	0.00257059	+	0.176758i
$161$	−1.77337	−	2.11342i	−0.139761	−	0.166561i
$162$	−8.87219	+	1.51138i	−0.697065	+	0.118745i
$163$	4.87656	−	1.30667i	0.381962	−	0.102346i	−0.0627289	−	0.998031i	$-0.519980\pi$
$163$	4.87656	−	1.30667i	0.381962	−	0.102346i	0.444691	+	0.895684i	$0.353314\pi$
$164$	0.338104	+	0.585614i	0.0264015	+	0.0457287i
$165$	3.82973	−	6.50161i	0.298144	−	0.506150i
$166$	−1.22575	+	6.95160i	−0.0951370	+	0.539549i
$167$	9.62203	−	13.7417i	0.744575	−	1.06336i	−0.250870	−	0.968021i	$-0.580717\pi$
$167$	9.62203	−	13.7417i	0.744575	−	1.06336i	0.995445	−	0.0953423i	$-0.0303946\pi$
$168$	−1.57030	+	0.688233i	−0.121152	+	0.0530984i
$169$	−14.7637	+	17.5947i	−1.13567	+	1.35344i
$170$	6.19685	+	1.56423i	0.475277	+	0.119971i
$171$	11.1262	−	6.87083i	0.850840	−	0.525425i
$172$	0.466578	−	0.466578i	0.0355762	−	0.0355762i
$173$	−14.1724	+	1.23993i	−1.07751	+	0.0942698i	−0.612065	−	0.790807i	$-0.709661\pi$
$173$	−14.1724	+	1.23993i	−1.07751	+	0.0942698i	−0.465444	+	0.885077i	$0.654105\pi$
$174$	−0.684109	+	1.75166i	−0.0518622	+	0.132793i
$175$	−2.22124	−	4.42291i	−0.167910	−	0.334340i
$176$	−1.91870	−	0.338318i	−0.144627	−	0.0255017i
$177$	0.633816	−	2.16284i	0.0476405	−	0.162569i
$178$	−4.38757	+	16.3746i	−0.328862	+	1.22733i
$179$	11.9567	−	20.7095i	0.893682	−	1.54790i	0.0582551	−	0.998302i	$-0.481446\pi$
$179$	11.9567	−	20.7095i	0.893682	−	1.54790i	0.835427	−	0.549601i	$-0.185220\pi$
$180$	−5.61530	+	3.66993i	−0.418540	+	0.273540i
$181$	13.2459	−	11.1147i	0.984563	−	0.826147i	−0.000208366	−	1.00000i	$-0.500066\pi$
$181$	13.2459	−	11.1147i	0.984563	−	0.826147i	0.984772	+	0.173853i	$0.0556219\pi$
$182$	−5.73431	+	1.53650i	−0.425055	+	0.113893i
$183$	9.89611	−	6.59163i	0.731542	−	0.487267i
$184$	−0.953248	+	2.61903i	−0.0702744	+	0.193077i
$185$	20.6327	−	7.85131i	1.51695	−	0.577240i
$186$	−0.612640	−	0.372976i	−0.0449209	−	0.0273479i
$187$	−2.35343	+	5.04696i	−0.172100	+	0.369070i
$188$	9.29672	−	0.813358i	0.678033	−	0.0593202i
$189$	−4.26420	−	2.87616i	−0.310175	−	0.209210i
$190$	5.56314	−	8.00321i	0.403593	−	0.580614i
$191$			1.77826i			0.128671i	0.997928	+	0.0643354i	$0.0204927\pi$
$191$			1.77826i			0.128671i	−0.997928	+	0.0643354i	$0.979507\pi$
$192$	1.39532	+	1.02620i	0.100698	+	0.0740598i
$193$	−6.51188	−	3.03654i	−0.468735	−	0.218575i	0.173876	−	0.984768i	$-0.444371\pi$
$193$	−6.51188	−	3.03654i	−0.468735	−	0.218575i	−0.642611	+	0.766193i	$0.722149\pi$
$194$	1.76361	+	10.0019i	0.126620	+	0.718096i
$195$	−21.1362	+	9.63238i	−1.51360	+	0.689789i
$196$	5.65710	+	2.05902i	0.404079	+	0.147073i
$197$	0.610076	−	2.27684i	0.0434661	−	0.162218i	−0.940781	−	0.339014i	$-0.889907\pi$
$197$	0.610076	−	2.27684i	0.0434661	−	0.162218i	0.984248	+	0.176796i	$0.0565733\pi$
$198$	−2.22107	−	5.40643i	−0.157844	−	0.384219i
$199$	−4.03872	−	4.81316i	−0.286298	−	0.341196i	0.603658	−	0.797243i	$-0.293709\pi$
$199$	−4.03872	−	4.81316i	−0.286298	−	0.341196i	−0.889956	+	0.456047i	$0.849265\pi$
$200$	−2.74757	+	4.17743i	−0.194282	+	0.295389i
$201$	21.7595	−	7.35119i	1.53480	−	0.518513i
$202$	14.8914	+	3.99013i	1.04775	+	0.280744i
$203$	−0.974020	+	0.454193i	−0.0683628	+	0.0318781i
$204$	3.86541	−	3.09311i	0.270632	−	0.216561i
$205$	−0.109866	+	1.50805i	−0.00767338	+	0.105327i
$206$	−0.0329449	−	0.0905155i	−0.00229538	−	0.00630651i
$207$	−8.16835	+	1.78604i	−0.567740	+	0.124138i
$208$	4.24077	+	4.24077i	0.294044	+	0.294044i
$209$	5.93793	+	6.07143i	0.410735	+	0.419969i
$210$	−3.76955	−	0.698639i	−0.260124	−	0.0482107i
$211$	11.3522	+	9.52562i	0.781517	+	0.655770i	0.943630	−	0.331002i	$-0.107387\pi$
$211$	11.3522	+	9.52562i	0.781517	+	0.655770i	−0.162113	+	0.986772i	$0.551831\pi$
$212$	−7.80078	−	3.63756i	−0.535760	−	0.249829i
$213$	3.67040	+	15.0945i	0.251492	+	1.03426i
$214$	−5.77193	−	1.01775i	−0.394561	−	0.0695717i
$215$	1.44915	−	0.277311i	0.0988315	−	0.0189125i
$216$	−0.362404	+	5.18350i	−0.0246585	+	0.352692i
$217$	−0.106091	−	0.395938i	−0.00720195	−	0.0268780i
$218$	0.916132	−	10.4714i	0.0620483	−	0.709216i
$219$	0.255725	−	10.9888i	0.0172803	−	0.742557i
$220$	−3.12499	−	3.03540i	−0.210687	−	0.204647i
$221$	14.8453	−	8.57095i	0.998604	−	0.576544i
$222$	4.80889	−	16.4099i	0.322752	−	1.10136i
$223$	14.0901	−	9.86602i	0.943546	−	0.660678i	0.00287403	−	0.999996i	$-0.499085\pi$
$223$	14.0901	−	9.86602i	0.943546	−	0.660678i	0.940672	+	0.339318i	$0.110196\pi$
$224$	0.171889	+	0.974830i	0.0114848	+	0.0651336i
$225$	−14.9977	−	0.261742i	−0.999848	−	0.0174495i
$226$	10.6237	+	8.91437i	0.706680	+	0.592975i
$227$	17.2331	+	17.2331i	1.14380	+	1.14380i	0.987749	+	0.156051i	$0.0498764\pi$
$227$	17.2331	+	17.2331i	1.14380	+	1.14380i	0.156051	+	0.987749i	$0.450124\pi$
$228$	−2.33679	−	7.17910i	−0.154757	−	0.475447i
$229$			8.52084i			0.563073i	0.959551	+	0.281536i	$0.0908440\pi$
$229$			8.52084i			0.563073i	−0.959551	+	0.281536i	$0.909156\pi$
$230$	−5.05258	+	3.64848i	−0.333157	+	0.240574i
$231$	1.21519	−	3.11148i	0.0799534	−	0.204720i
$232$	0.889363	+	0.622739i	0.0583895	+	0.0408848i
$233$	11.4867	+	16.4047i	0.752518	+	1.07471i	0.994532	+	0.104435i	$0.0333033\pi$
$233$	11.4867	+	16.4047i	0.752518	+	1.07471i	−0.242013	+	0.970273i	$0.577808\pi$
$234$	−3.94514	+	17.5542i	−0.257902	+	1.14755i
$235$	18.2216	+	10.1699i	1.18865	+	0.663409i
$236$	−1.12690	−	0.650615i	−0.0733548	−	0.0423514i
$237$	−13.0042	+	12.4128i	−0.844716	+	0.806295i
$238$	2.81852	+	0.246589i	0.182698	+	0.0159840i
$239$	−8.58302	+	14.8662i	−0.555190	+	0.961617i	0.442699	+	0.896670i	$0.354021\pi$
$239$	−8.58302	+	14.8662i	−0.555190	+	0.961617i	−0.997889	+	0.0649463i	$0.979312\pi$
$240$	1.29283	+	3.65083i	0.0834521	+	0.235660i
$241$	−3.85394	−	1.40272i	−0.248254	−	0.0903571i	0.214896	−	0.976637i	$-0.431059\pi$
$241$	−3.85394	−	1.40272i	−0.248254	−	0.0903571i	−0.463150	+	0.886280i	$0.653281\pi$
$242$	−5.90129	+	4.13213i	−0.379350	+	0.265623i
$243$	−13.7208	+	7.39856i	−0.880192	+	0.474618i
$244$	−2.34795	−	6.45094i	−0.150312	−	0.412979i
$245$	7.88072	+	10.9136i	0.503481	+	0.697242i
$246$	0.879454	+	0.773520i	0.0560719	+	0.0493178i
$247$	−4.25304	−	25.7936i	−0.270614	−	1.64121i
$248$	−0.292813	+	0.292813i	−0.0185937	+	0.0185937i
$249$	1.84237	+	12.0867i	0.116755	+	0.765960i
$250$	−10.3293	+	4.27845i	−0.653283	+	0.270593i
$251$	−11.9820	+	2.11275i	−0.756297	+	0.133356i	−0.538485	−	0.842635i	$-0.681003\pi$
$251$	−11.9820	+	2.11275i	−0.756297	+	0.133356i	−0.217812	+	0.975991i	$0.569892\pi$
$252$	−2.19523	+	1.99988i	−0.138287	+	0.125980i
$253$	−2.29487	−	4.92135i	−0.144277	−	0.309403i
$254$	−7.21978	−	12.5050i	−0.453010	−	0.784636i
$255$	11.0358	−	0.868553i	0.691089	−	0.0543909i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	6.04376	+	0.528760i	0.376999	+	0.0329832i	0.274081	−	0.961707i	$-0.411626\pi$
$257$	6.04376	+	0.528760i	0.376999	+	0.0329832i	0.102918	+	0.994690i	$0.467182\pi$
$258$	0.506968	−	1.02428i	0.0315625	−	0.0637690i
$259$	8.46339	−	4.88634i	0.525889	−	0.303622i
$260$	2.52051	+	13.1715i	0.156315	+	0.816861i
$261$	−0.151514	+	3.25361i	−0.00937846	+	0.201393i
$262$	2.34696	+	1.64336i	0.144996	+	0.101527i
$263$	5.44933	−	11.6861i	0.336020	−	0.720598i	−0.663602	−	0.748086i	$-0.730973\pi$
$263$	5.44933	−	11.6861i	0.336020	−	0.720598i	0.999622	+	0.0274880i	$0.00875080\pi$
$264$	−3.33601	+	0.508509i	−0.205317	+	0.0312966i
$265$	−9.86450	−	16.5261i	−0.605972	−	1.01519i
$266$	1.86684	−	3.88997i	0.114463	−	0.238509i
$267$	1.87788	+	29.3021i	0.114924	+	1.79326i
$268$	−1.15572	−	13.2100i	−0.0705970	−	0.806928i
$269$	3.57049	−	1.29955i	0.217697	−	0.0792351i	−0.230869	−	0.972985i	$-0.574157\pi$
$269$	3.57049	−	1.29955i	0.217697	−	0.0792351i	0.448566	+	0.893750i	$0.351935\pi$
$270$	−7.17986	+	9.13508i	−0.436952	+	0.555943i
$271$	0.469395	−	2.66207i	0.0285137	−	0.161709i	−0.967226	−	0.253917i	$-0.918281\pi$
$271$	0.469395	−	2.66207i	0.0285137	−	0.161709i	0.995740	+	0.0922072i	$0.0293922\pi$
$272$	−1.20795	−	2.59045i	−0.0732425	−	0.157069i
$273$	−8.55785	+	5.70023i	−0.517944	+	0.344994i
$274$	10.2198	+	5.90038i	0.617398	+	0.356455i
$275$	−1.96985	−	9.54023i	−0.118786	−	0.575297i
$276$	−0.112310	+	4.82611i	−0.00676027	+	0.290498i
$277$	2.13084	+	7.95241i	0.128030	+	0.477814i	0.999930	−	0.0118706i	$-0.00377863\pi$
$277$	2.13084	+	7.95241i	0.128030	+	0.477814i	−0.871900	+	0.489685i	$0.837112\pi$
$278$	−4.80816	−	1.28834i	−0.288374	−	0.0772697i
$279$	−1.21207	−	0.272401i	−0.0725647	−	0.0163082i
$280$	−0.906160	+	2.01942i	−0.0541534	+	0.120684i
$281$	−5.75773	+	1.01524i	−0.343477	+	0.0605643i	−0.342726	−	0.939435i	$-0.611350\pi$
$281$	−5.75773	+	1.01524i	−0.343477	+	0.0605643i	−0.000751340		1.00000i	$0.500239\pi$
$282$	14.8044	−	6.48849i	0.881591	−	0.386384i
$283$	−1.30076	−	14.8678i	−0.0773224	−	0.883799i	−0.931482	−	0.363788i	$-0.881483\pi$
$283$	−1.30076	−	14.8678i	−0.0773224	−	0.883799i	0.854160	−	0.520011i	$-0.174072\pi$
$284$	8.96875			0.532198
$285$	4.69203	−	16.2168i	0.277932	−	0.960601i
$286$	−11.6846			−0.690925
$287$	0.0583383	+	0.666810i	0.00344360	+	0.0393606i
$288$	2.85852	+	0.910414i	0.168440	+	0.0536467i
$289$	8.69629	−	1.53339i	0.511546	−	0.0901994i
$290$	0.863417	+	2.26900i	0.0507016	+	0.133240i
$291$	8.43873	+	15.4348i	0.494687	+	0.904805i
$292$	−6.12989	−	1.64250i	−0.358724	−	0.0961199i
$293$	4.10815	+	15.3318i	0.240001	+	0.895695i	0.975831	+	0.218528i	$0.0701256\pi$
$293$	4.10815	+	15.3318i	0.240001	+	0.895695i	−0.735830	+	0.677166i	$0.763208\pi$
$294$	10.4244	+	0.242590i	0.607963	+	0.0141481i
$295$	−1.26788	−	2.61887i	−0.0738190	−	0.152476i
$296$	−8.55001	−	4.93635i	−0.496959	−	0.286920i
$297$	−6.64179	−	7.64033i	−0.385396	−	0.443337i
$298$	3.80784	+	8.16594i	0.220582	+	0.473040i
$299$	−2.90258	+	16.4614i	−0.167861	+	0.951985i
$300$	−2.19274	+	8.37806i	−0.126598	+	0.483707i
$301$	0.613765	−	0.223392i	0.0353769	−	0.0128761i
$302$	1.65501	+	18.9169i	0.0952352	+	1.08854i
$303$	26.6478	−	1.70777i	1.53087	−	0.0981089i
$304$	−4.34627	+	0.331612i	−0.249275	+	0.0190192i
$305$	3.75697	−	14.8836i	0.215123	−	0.852235i
$306$	4.62816	−	7.21846i	0.264574	−	0.412652i
$307$	12.6496	−	27.1272i	0.721952	−	1.54823i	−0.110341	−	0.993894i	$-0.535194\pi$
$307$	12.6496	−	27.1272i	0.721952	−	1.54823i	0.832293	−	0.554337i	$-0.187028\pi$
$308$	−1.57978	−	1.10617i	−0.0900163	−	0.0630301i
$309$	−0.104240	−	0.130267i	−0.00592999	−	0.00741060i
$310$	−0.909455	+	0.174034i	−0.0516536	+	0.00988447i
$311$	20.0600	−	11.5817i	1.13750	−	0.656735i	0.191689	−	0.981456i	$-0.438604\pi$
$311$	20.0600	−	11.5817i	1.13750	−	0.656735i	0.945810	+	0.324721i	$0.105270\pi$
$312$	9.30979	+	4.60788i	0.527063	+	0.260870i
$313$	−6.29186	−	0.550466i	−0.355637	−	0.0311142i	−0.0920624	−	0.995753i	$-0.529346\pi$
$313$	−6.29186	−	0.550466i	−0.355637	−	0.0311142i	−0.263575	+	0.964639i	$0.584901\pi$
$314$	−9.20455	+	7.72354i	−0.519443	+	0.435864i
$315$	−6.57290	+	0.943302i	−0.370341	+	0.0531491i
$316$	5.18963	+	8.98870i	0.291939	+	0.505654i
$317$	−1.05257	−	2.25724i	−0.0591181	−	0.126779i	0.874529	−	0.484973i	$-0.161171\pi$
$317$	−1.05257	−	2.25724i	−0.0591181	−	0.126779i	−0.933647	+	0.358194i	$0.883393\pi$
$318$	−14.8171	−	1.64449i	−0.830904	−	0.0922187i
$319$	−2.08315	+	0.367316i	−0.116634	+	0.0205657i
$320$	2.22449	−	0.227257i	0.124353	−	0.0127041i
$321$	−10.0356	+	1.52973i	−0.560132	+	0.0853809i
$322$	−1.95082	+	1.95082i	−0.108715	+	0.108715i
$323$	−2.29970	+	12.2447i	−0.127959	+	0.681314i
$324$	2.27889	+	8.70670i	0.126605	+	0.483706i
$325$	−11.8773	+	27.5343i	−0.658833	+	1.52733i
$326$	−1.72672	−	4.74412i	−0.0956341	−	0.262752i
$327$	−4.30174	−	17.6909i	−0.237887	−	0.978306i
$328$	0.553917	−	0.387857i	0.0305850	−	0.0214158i
$329$	8.68059	+	3.15948i	0.478576	+	0.174188i
$330$	−6.81065	−	3.24850i	−0.374914	−	0.178824i
$331$	−15.9880	+	27.6920i	−0.878779	+	1.52209i	−0.0260966	+	0.999659i	$0.508308\pi$
$331$	−15.9880	+	27.6920i	−0.878779	+	1.52209i	−0.852682	+	0.522430i	$0.825026\pi$
$332$	7.03197	+	0.615218i	0.385930	+	0.0337645i
$333$	−1.20608	−	29.5935i	−0.0660926	−	1.62172i
$334$	−14.5280	−	8.38775i	−0.794937	−	0.458957i
$335$	14.4506	−	25.8916i	0.789523	−	1.41461i
$336$	0.822475	+	1.50435i	0.0448697	+	0.0820688i
$337$	4.22875	+	6.03928i	0.230354	+	0.328980i	0.917644	−	0.397403i	$-0.130089\pi$
$337$	4.22875	+	6.03928i	0.230354	+	0.328980i	−0.687290	+	0.726383i	$0.741200\pi$
$338$	18.8145	+	13.1740i	1.02337	+	0.716574i
$339$	22.3747	+	8.73844i	1.21523	+	0.474607i
$340$	1.01818	−	6.30960i	0.0552187	−	0.342186i
$341$		−	0.806790i		−	0.0436901i
$342$	−7.81439	−	10.4850i	−0.422554	−	0.566964i
$343$	9.11337	+	9.11337i	0.492076	+	0.492076i
$344$	−0.505467	−	0.424137i	−0.0272530	−	0.0228680i
$345$	−6.26835	+	8.78793i	−0.337477	+	0.473126i
$346$	2.47042	+	14.0104i	0.132810	+	0.753205i
$347$	−21.9095	+	15.3412i	−1.17616	+	0.823558i	−0.987366	−	0.158458i	$-0.949348\pi$
$347$	−21.9095	+	15.3412i	−1.17616	+	0.823558i	−0.188798	+	0.982016i	$0.560459\pi$
$348$	1.80462	+	0.528839i	0.0967376	+	0.0283487i
$349$	21.7920	−	12.5816i	1.16650	−	0.673480i	0.213648	−	0.976911i	$-0.431466\pi$
$349$	21.7920	−	12.5816i	1.16650	−	0.673480i	0.952853	+	0.303431i	$0.0981322\pi$
$350$	−4.21248	+	2.59827i	−0.225167	+	0.138883i
$351$	3.25780	+	30.9924i	0.173889	+	1.65425i
$352$	−0.169805	+	1.94088i	−0.00905064	+	0.103449i
$353$	1.58505	+	5.91549i	0.0843638	+	0.314850i	0.995193	−	0.0979336i	$-0.0312233\pi$
$353$	1.58505	+	5.91549i	0.0843638	+	0.314850i	−0.910829	+	0.412784i	$0.864557\pi$
$354$	−2.20985	−	0.442900i	−0.117452	−	0.0235399i
$355$	16.5934	+	11.2628i	0.880687	+	0.597769i
$356$	16.6947	+	2.94373i	0.884818	+	0.156017i
$357$	4.76171	−	1.15787i	0.252017	−	0.0612808i
$358$	−21.6728	−	10.1062i	−1.14544	−	0.534129i
$359$	−8.35473	−	7.01045i	−0.440946	−	0.369998i	0.395117	−	0.918631i	$-0.370704\pi$
$359$	−8.35473	−	7.01045i	−0.440946	−	0.369998i	−0.836063	+	0.548633i	$0.815148\pi$
$360$	4.14537	+	5.27408i	0.218480	+	0.277968i
$361$	16.2392	+	9.86343i	0.854696	+	0.519128i
$362$	−12.2268	−	12.2268i	−0.642628	−	0.642628i
$363$	−7.39292	+	10.0521i	−0.388028	+	0.527597i
$364$	2.03043	+	5.57857i	0.106424	+	0.292397i
$365$	−9.27850	−	10.7367i	−0.485659	−	0.561983i
$366$	−7.42905	−	9.28396i	−0.388323	−	0.485280i
$367$	−24.0552	+	11.2171i	−1.25567	+	0.585529i	−0.932622	−	0.360854i	$-0.882485\pi$
$367$	−24.0552	+	11.2171i	−1.25567	+	0.585529i	−0.323048	+	0.946383i	$0.604707\pi$
$368$	2.69214	+	0.721358i	0.140338	+	0.0376034i
$369$	1.87194	+	0.781755i	0.0974496	+	0.0406965i
$370$	−9.61969	−	19.8699i	−0.500104	−	1.03299i
$371$	−5.47655	−	6.52670i	−0.284328	−	0.338849i
$372$	−0.318161	+	0.642815i	−0.0164959	+	0.0333284i
$373$	4.92284	−	18.3723i	0.254895	−	0.951281i	−0.713254	−	0.700906i	$-0.752779\pi$
$373$	4.92284	−	18.3723i	0.254895	−	0.951281i	0.968149	−	0.250375i	$-0.0805540\pi$
$374$	5.23287	+	1.90461i	0.270585	+	0.0984849i
$375$	−14.5779	+	12.7469i	−0.752800	+	0.658249i
$376$	−1.62053	−	9.19046i	−0.0835722	−	0.473962i
$377$	5.90133	+	2.75183i	0.303934	+	0.141727i
$378$	−2.49357	+	4.49864i	−0.128255	+	0.231385i
$379$			30.1362i			1.54799i	0.633191	+	0.773995i	$0.281745\pi$
$379$			30.1362i			1.54799i	−0.633191	+	0.773995i	$0.718255\pi$
$380$	−8.45762	−	4.84445i	−0.433867	−	0.248515i
$381$	−18.7796	−	16.5175i	−0.962109	−	0.846219i
$382$	1.77150	−	0.154986i	0.0906377	−	0.00792977i
$383$	1.72926	−	3.70840i	0.0883609	−	0.189491i	−0.857161	−	0.515048i	$-0.827774\pi$
$383$	1.72926	−	3.70840i	0.0883609	−	0.189491i	0.945522	+	0.325557i	$0.105552\pi$
$384$	0.900689	−	1.47945i	0.0459631	−	0.0754977i
$385$	−1.53369	−	4.03044i	−0.0781642	−	0.205410i
$386$	−2.45744	+	6.75175i	−0.125080	+	0.343655i
$387$	0.264072	−	1.96183i	0.0134235	−	0.0997254i
$388$	9.81015	−	2.62862i	0.498035	−	0.133448i
$389$	−6.57884	+	5.52031i	−0.333561	+	0.279891i	−0.794149	−	0.607723i	$-0.792083\pi$
$389$	−6.57884	+	5.52031i	−0.333561	+	0.279891i	0.460588	+	0.887614i	$0.347639\pi$
$390$	11.4379	+	20.2163i	0.579179	+	1.02369i
$391$	3.98312	−	6.89897i	0.201435	−	0.348896i
$392$	1.55813	−	5.81503i	0.0786976	−	0.293703i
$393$	4.76224	+	1.39556i	0.240223	+	0.0703969i
$394$	−2.32134	−	0.409315i	−0.116948	−	0.0206210i
$395$	−1.68636	+	23.1474i	−0.0848497	+	1.16467i
$396$	−5.19228	+	2.68382i	−0.260922	+	0.134867i
$397$	30.0571	−	2.62965i	1.50852	−	0.131978i	0.697326	−	0.716754i	$-0.254373\pi$
$397$	30.0571	−	2.62965i	1.50852	−	0.131978i	0.811195	+	0.584776i	$0.198818\pi$
$398$	−4.44285	+	4.44285i	−0.222700	+	0.222700i
$399$	0.906888	−	7.41812i	0.0454012	−	0.371370i
$400$	4.40100	+	2.37302i	0.220050	+	0.118651i
$401$	−14.1302	+	16.8397i	−0.705630	+	0.840937i	−0.993151	−	0.116837i	$-0.962724\pi$
$401$	−14.1302	+	16.8397i	−0.705630	+	0.840937i	0.287521	+	0.957774i	$0.407169\pi$
$402$	−9.21968	−	21.0360i	−0.459836	−	1.04918i
$403$	−1.42448	+	2.03437i	−0.0709585	+	0.101339i
$404$	2.67708	−	15.1824i	0.133189	−	0.755355i
$405$	−6.71748	+	18.9704i	−0.333794	+	0.942646i
$406$	0.537356	+	0.930728i	0.0266685	+	0.0461912i
$407$	18.5795	−	4.97837i	0.920952	−	0.246768i
$408$	−3.41823	−	3.58111i	−0.169228	−	0.177292i
$409$	−21.9670	−	26.1793i	−1.08620	−	1.29448i	−0.952860	−	0.303412i	$-0.901874\pi$
$409$	−21.9670	−	26.1793i	−1.08620	−	1.29448i	−0.133340	−	0.991070i	$-0.542570\pi$
$410$	1.51189	−	0.0219873i	0.0746668	−	0.00108588i
$411$	20.0410	+	4.01662i	0.988547	+	0.198125i
$412$	−0.0872997	+	0.0407085i	−0.00430095	+	0.00200556i
$413$	−0.738793	−	1.05511i	−0.0363536	−	0.0519184i
$414$	2.49116	+	7.98161i	0.122434	+	0.392275i
$415$	12.2375	+	9.96889i	0.600717	+	0.489353i
$416$	3.85502	−	4.59424i	0.189008	−	0.225251i
$417$	−8.60411	+	0.551410i	−0.421345	+	0.0270027i
$418$	5.53080	−	6.44449i	0.270520	−	0.315210i
$419$	−39.1047			−1.91039			−0.955194	−	0.295979i	$-0.904354\pi$
$419$	−39.1047			−1.91039			−0.955194	+	0.295979i	$0.904354\pi$
$420$	−0.367443	+	3.81610i	−0.0179294	+	0.186206i
$421$	−18.0729	+	6.57799i	−0.880818	+	0.320592i	−0.742540	−	0.669802i	$-0.766379\pi$
$421$	−18.0729	+	6.57799i	−0.880818	+	0.320592i	−0.138278	+	0.990393i	$0.544157\pi$
$422$	8.49996	−	12.1392i	0.413772	−	0.590927i
$423$	20.6961	−	18.8543i	1.00628	−	0.916729i
$424$	−2.94384	+	8.08813i	−0.142965	+	0.392794i
$425$	9.80728	−	10.3950i	0.475723	−	0.504232i
$426$	14.7172	−	4.97201i	0.713049	−	0.240894i
$427$	0.592258	−	6.76954i	0.0286614	−	0.327601i
$428$	−0.510817	+	5.83867i	−0.0246913	+	0.282223i
$429$	−19.1737	+	6.47760i	−0.925715	+	0.312741i
$430$	−0.402558	−	1.41947i	−0.0194131	−	0.0684529i
$431$	4.32017	−	11.8696i	0.208095	−	0.571737i	−0.791107	−	0.611678i	$-0.790495\pi$
$431$	4.32017	−	11.8696i	0.208095	−	0.571737i	0.999202	+	0.0399412i	$0.0127171\pi$
$432$	5.19536	−	0.0907466i	0.249962	−	0.00436605i
$433$	6.76713	−	9.66447i	0.325208	−	0.464445i	−0.622942	−	0.782268i	$-0.714063\pi$
$433$	6.76713	−	9.66447i	0.325208	−	0.464445i	0.948150	+	0.317823i	$0.102952\pi$
$434$	−0.385185	+	0.140196i	−0.0184895	+	0.00672962i
$435$	2.67468	+	3.24463i	0.128241	+	0.155568i
$436$	−10.5114			−0.503407
$437$	−7.70513	−	9.39270i	−0.368586	−	0.449314i
$438$	−10.9693	+	0.702989i	−0.524134	+	0.0335901i
$439$	20.9543	−	24.9724i	1.00010	−	1.19187i	0.0187100	−	0.999825i	$-0.494044\pi$
$439$	20.9543	−	24.9724i	1.00010	−	1.19187i	0.981386	−	0.192044i	$-0.0615115\pi$
$440$	−2.75149	+	3.37765i	−0.131172	+	0.161023i
$441$	17.2403	−	5.38090i	0.820965	−	0.256233i
$442$	−9.83219	−	14.0418i	−0.467670	−	0.667901i
$443$	4.56049	−	2.12659i	0.216675	−	0.101037i	−0.311250	−	0.950328i	$-0.600748\pi$
$443$	4.56049	−	2.12659i	0.216675	−	0.101037i	0.527926	+	0.849291i	$0.322970\pi$
$444$	−16.7666	−	3.36037i	−0.795707	−	0.159476i
$445$	27.1908	+	26.4113i	1.28897	+	1.25201i
$446$	−11.0565	−	13.1766i	−0.523541	−	0.623932i
$447$	10.7754	+	11.2888i	0.509658	+	0.533944i
$448$	0.956140	−	0.256197i	0.0451734	−	0.0121042i
$449$	−15.2377	−	26.3924i	−0.719110	−	1.24554i	−0.961353	−	0.275320i	$-0.911216\pi$
$449$	−15.2377	−	26.3924i	−0.719110	−	1.24554i	0.242242	−	0.970216i	$-0.422117\pi$
$450$	1.04639	+	14.9635i	0.0493273	+	0.705384i
$451$	−0.228773	+	1.29744i	−0.0107725	+	0.0610940i
$452$	7.95453	−	11.3602i	0.374150	−	0.534341i
$453$	13.2027	+	30.1239i	0.620317	+	1.41534i
$454$	15.6655	−	18.6695i	0.735220	−	0.876202i
$455$	−3.24891	+	12.8709i	−0.152311	+	0.603397i
$456$	−6.94811	+	2.95359i	−0.325375	+	0.138315i
$457$	−2.25517	+	2.25517i	−0.105492	+	0.105492i	−0.757883	−	0.652391i	$-0.773766\pi$
$457$	−2.25517	+	2.25517i	−0.105492	+	0.105492i	0.652391	+	0.757883i	$0.273766\pi$
$458$	8.48841	−	0.742640i	0.396638	−	0.0347013i
$459$	3.59282	−	14.4107i	0.167699	−	0.672636i
$460$	4.07496	+	4.71536i	0.189996	+	0.219855i
$461$	−22.0568	−	3.88920i	−1.02729	−	0.181138i	−0.365484	−	0.930817i	$-0.619097\pi$
$461$	−22.0568	−	3.88920i	−1.02729	−	0.181138i	−0.661801	+	0.749679i	$0.730208\pi$
$462$	−3.20555	−	0.939379i	−0.149136	−	0.0437039i
$463$	−3.58939	+	13.3958i	−0.166813	+	0.622556i	0.830989	+	0.556289i	$0.187775\pi$
$463$	−3.58939	+	13.3958i	−0.166813	+	0.622556i	−0.997802	+	0.0662664i	$0.978891\pi$
$464$	0.542856	−	0.940254i	0.0252014	−	0.0436502i
$465$	−1.39588	+	0.789754i	−0.0647324	+	0.0366239i
$466$	15.3411	−	12.8727i	0.710665	−	0.596318i
$467$	−17.6671	+	4.73387i	−0.817534	+	0.219057i	−0.643268	−	0.765641i	$-0.722422\pi$
$467$	−17.6671	+	4.73387i	−0.817534	+	0.219057i	−0.174266	+	0.984699i	$0.555755\pi$
$468$	17.8312	+	2.40017i	0.824250	+	0.110948i
$469$	4.48939	−	12.3345i	0.207301	−	0.569554i
$470$	8.54305	−	19.0386i	0.394061	−	0.878186i
$471$	−10.8224	+	17.7766i	−0.498670	+	0.819101i
$472$	−0.549924	+	1.17931i	−0.0253123	+	0.0542824i
$473$	1.28067	−	0.112044i	0.0588853	−	0.00515180i
$474$	13.4989	+	11.8729i	0.620025	+	0.545341i
$475$	−9.56416	−	19.5838i	−0.438834	−	0.898568i
$476$		−	2.82929i		−	0.129680i
$477$	−25.2256	+	5.51566i	−1.15500	+	0.252545i
$478$	15.5577	+	7.25468i	0.711594	+	0.331822i
$479$	0.0425891	+	0.241535i	0.00194594	+	0.0110360i	0.985765	−	0.168127i	$-0.0537720\pi$
$479$	0.0425891	+	0.241535i	0.00194594	+	0.0110360i	−0.983819	+	0.179163i	$0.942661\pi$
$480$	3.52426	−	1.60611i	0.160860	−	0.0733083i
$481$	−55.6393	−	20.2510i	−2.53693	−	0.923368i
$482$	−1.06149	+	3.96153i	−0.0483495	+	0.180443i
$483$	−2.11970	+	4.28265i	−0.0964495	+	0.194867i
$484$	4.63074	+	5.51870i	0.210488	+	0.250850i
$485$	21.4511	+	7.45613i	0.974044	+	0.338565i
$486$	8.56625	+	13.0238i	0.388573	+	0.590771i
$487$	−3.73107	−	0.999737i	−0.169071	−	0.0453024i	0.173290	−	0.984871i	$-0.444560\pi$
$487$	−3.73107	−	0.999737i	−0.169071	−	0.0453024i	−0.342361	+	0.939568i	$0.611227\pi$
$488$	−6.22176	+	2.90125i	−0.281646	+	0.131334i
$489$	−5.46343	−	6.82756i	−0.247065	−	0.308753i
$490$	10.1852	−	8.80191i	0.460120	−	0.397630i
$491$	−0.935546	−	2.57039i	−0.0422206	−	0.116000i	0.916791	−	0.399368i	$-0.130770\pi$
$491$	−0.935546	−	2.57039i	−0.0422206	−	0.116000i	−0.959011	+	0.283368i	$0.908548\pi$
$492$	0.693927	−	0.943524i	0.0312847	−	0.0425374i
$493$	−2.19431	−	2.19431i	−0.0988269	−	0.0988269i
$494$	−25.3247	+	6.48491i	−1.13941	+	0.291770i
$495$	−12.9767	−	1.55497i	−0.583260	−	0.0698906i
$496$	0.317220	+	0.266179i	0.0142436	+	0.0119518i
$497$	8.04610	+	3.75196i	0.360917	+	0.168298i
$498$	11.8801	−	2.88878i	0.532359	−	0.129449i
$499$	11.3962	+	2.00945i	0.510162	+	0.0899553i	0.422803	−	0.906222i	$-0.361046\pi$
$499$	11.3962	+	2.00945i	0.510162	+	0.0899553i	0.0873588	+	0.996177i	$0.472157\pi$
$500$	5.16243	+	9.91712i	0.230871	+	0.443507i
$501$	−28.4895	−	5.70988i	−1.27281	−	0.255098i
$502$	3.14901	+	11.7523i	0.140547	+	0.524529i
$503$	1.17659	−	13.4484i	0.0524614	−	0.599637i	−0.923776	−	0.382933i	$-0.874914\pi$
$503$	1.17659	−	13.4484i	0.0524614	−	0.599637i	0.976237	−	0.216704i	$-0.0695305\pi$
$504$	2.18359	+	2.01258i	0.0972650	+	0.0896474i
$505$	24.0188	−	24.7278i	1.06882	−	1.10037i
$506$	−4.70262	+	2.71506i	−0.209057	+	0.120699i
$507$	38.1767	+	11.1876i	1.69549	+	0.496858i
$508$	−11.8282	+	8.28220i	−0.524792	+	0.367463i
$509$	−3.19818	−	18.1378i	−0.141757	−	0.803944i	−0.969914	−	0.243448i	$-0.921722\pi$
$509$	−3.19818	−	18.1378i	−0.141757	−	0.803944i	0.828157	−	0.560496i	$-0.189390\pi$
$510$	−1.82708	−	10.9181i	−0.0809045	−	0.483462i
$511$	−4.81216	−	4.03788i	−0.212878	−	0.178625i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−18.6355	−	12.8732i	−0.822777	−	0.568364i
$514$		−	6.06684i		−	0.267597i
$515$	−0.212637	−	0.0343134i	−0.00936993	−	0.00151203i
$516$	−1.06457	−	0.415767i	−0.0468650	−	0.0183031i
$517$	14.8938	+	10.4287i	0.655027	+	0.458655i
$518$	−5.60538	−	8.00531i	−0.246286	−	0.351733i
$519$	11.8208	+	21.6207i	0.518873	+	0.949043i
$520$	12.9017	−	3.65889i	0.565777	−	0.160453i
$521$	−28.1545	−	16.2550i	−1.23347	−	0.712144i	−0.265718	−	0.964051i	$-0.585609\pi$
$521$	−28.1545	−	16.2550i	−1.23347	−	0.712144i	−0.967752	+	0.251907i	$0.918942\pi$
$522$	3.25443	−	0.132634i	0.142443	−	0.00580522i
$523$	−43.2478	−	3.78369i	−1.89109	−	0.165449i	−0.918110	−	0.396325i	$-0.870285\pi$
$523$	−43.2478	−	3.78369i	−1.89109	−	0.165449i	−0.972983	+	0.230876i	$0.925841\pi$
$524$	1.43255	−	2.48126i	0.0625814	−	0.108394i
$525$	−5.47201	+	6.59887i	−0.238818	+	0.287998i
$526$	−12.1166	−	4.41008i	−0.528309	−	0.192289i
$527$	0.969549	−	0.678886i	0.0422342	−	0.0295727i
$528$	0.797326	+	3.27900i	0.0346992	+	0.142700i
$529$	−5.20965	−	14.3134i	−0.226507	−	0.622322i
$530$	−15.6035	+	11.2673i	−0.677771	+	0.489421i
$531$	−3.87176	+	0.498304i	−0.168020	+	0.0216245i
$532$	−4.03787	−	1.52070i	−0.175064	−	0.0659309i
$533$	2.86764	−	2.86764i	0.124211	−	0.124211i
$534$	29.0269	−	4.42457i	1.25612	−	0.191470i
$535$	−8.27719	+	10.1609i	−0.357854	+	0.439292i
$536$	−13.0590	+	2.30265i	−0.564062	+	0.0994593i
$537$	−41.1663	−	4.56888i	−1.77646	−	0.197162i
$538$	−1.60580	−	3.44364i	−0.0692308	−	0.148466i
$539$	5.86452	+	10.1576i	0.252603	+	0.437521i
$540$	9.72608	+	6.35636i	0.418544	+	0.273534i
$541$	6.27431	−	5.26477i	0.269754	−	0.226350i	−0.497869	−	0.867252i	$-0.665884\pi$
$541$	6.27431	−	5.26477i	0.269754	−	0.226350i	0.767623	+	0.640902i	$0.221439\pi$
$542$	−2.69285	−	0.235594i	−0.115668	−	0.0101196i
$543$	−26.8416	−	13.2853i	−1.15189	−	0.570126i
$544$	−2.47531	+	1.42912i	−0.106128	+	0.0612731i
$545$	−19.4476	−	13.2001i	−0.833044	−	0.565431i
$546$	6.42441	+	8.02847i	0.274939	+	0.343587i
$547$	−12.4039	−	8.68530i	−0.530352	−	0.371357i	0.277515	−	0.960721i	$-0.410489\pi$
$547$	−12.4039	−	8.68530i	−0.530352	−	0.371357i	−0.807867	+	0.589365i	$0.799378\pi$
$548$	4.98721	−	10.6951i	0.213043	−	0.456873i
$549$	−17.3373	−	11.1159i	−0.739940	−	0.474417i
$550$	−9.33224	+	2.79384i	−0.397928	+	0.119130i
$551$	−4.31107	+	1.95224i	−0.183658	+	0.0831684i
$552$	4.81754	−	0.308741i	0.205048	−	0.0131409i
$553$	0.895446	+	10.2350i	0.0380783	+	0.435236i
$554$	7.73643	−	2.81583i	0.328689	−	0.119633i
$555$	−26.8006	−	27.2724i	−1.13762	−	1.15765i
$556$	−0.864381	+	4.90215i	−0.0366579	+	0.207897i
$557$	16.6924	+	35.7970i	0.707280	+	1.51677i	0.849874	+	0.526985i	$0.176678\pi$
$557$	16.6924	+	35.7970i	0.707280	+	1.51677i	−0.142595	+	0.989781i	$0.545545\pi$
$558$	−0.165725	+	1.23120i	−0.00701572	+	0.0521208i
$559$	−3.42712	−	1.97865i	−0.144952	−	0.0836879i
$560$	2.09072	+	0.726707i	0.0883489	+	0.0307090i
$561$	9.64266	+	0.224397i	0.407113	+	0.00947407i
$562$	1.51320	+	5.64734i	0.0638305	+	0.238219i
$563$	−37.0977	−	9.94029i	−1.56348	−	0.418933i	−0.629717	−	0.776824i	$-0.716829\pi$
$563$	−37.0977	−	9.94029i	−1.56348	−	0.418933i	−0.933763	+	0.357891i	$0.883496\pi$
$564$	−7.75409	−	14.1826i	−0.326506	−	0.597195i
$565$	28.9830	−	11.0288i	1.21932	−	0.463986i
$566$	−14.6979	+	2.59163i	−0.617797	+	0.108934i
$567$	−1.59788	+	8.76435i	−0.0671046	+	0.368068i
$568$	−0.781678	−	8.93462i	−0.0327985	−	0.374888i
$569$	34.6147			1.45112			0.725561	−	0.688158i	$-0.241580\pi$
$569$	34.6147			1.45112			0.725561	+	0.688158i	$0.241580\pi$
$570$	−16.5640	−	3.26079i	−0.693791	−	0.136579i
$571$	−17.4318			−0.729498			−0.364749	−	0.931106i	$-0.618845\pi$
$571$	−17.4318			−0.729498			−0.364749	+	0.931106i	$0.618845\pi$
$572$	1.01838	+	11.6401i	0.0425806	+	0.486699i
$573$	2.82100	−	1.23639i	0.117849	−	0.0516508i
$574$	0.659188	−	0.116233i	0.0275140	−	0.00485146i
$575$	1.61775	+	13.8413i	0.0674649	+	0.577224i
$576$	0.657813	−	2.92699i	0.0274089	−	0.121958i
$577$	35.4567	+	9.50061i	1.47608	+	0.395515i	0.905012	−	0.425385i	$-0.139861\pi$
$577$	35.4567	+	9.50061i	1.47608	+	0.395515i	0.571071	+	0.820901i	$0.306528\pi$
$578$	−2.28549	−	8.52955i	−0.0950637	−	0.354783i
$579$	−0.289531	+	12.4415i	−0.0120325	+	0.517052i
$580$	2.18511	−	1.05789i	0.0907319	−	0.0439264i
$581$	6.05120	+	3.49366i	0.251046	+	0.144941i
$582$	14.6406	−	9.75185i	0.606873	−	0.404227i
$583$	−7.08704	−	15.1982i	−0.293515	−	0.629446i
$584$	−1.10199	+	6.24971i	−0.0456008	+	0.258615i
$585$	29.9761	+	26.8329i	1.23936	+	1.10940i
$586$	14.9154	−	5.42877i	0.616151	−	0.224261i
$587$	−1.58604	−	18.1285i	−0.0654629	−	0.748245i	−0.956006	−	0.293346i	$-0.905231\pi$
$587$	−1.58604	−	18.1285i	−0.0654629	−	0.748245i	0.890543	−	0.454899i	$-0.150324\pi$
$588$	−0.666880	−	10.4059i	−0.0275017	−	0.429131i
$589$	−0.447765	−	1.74860i	−0.0184498	−	0.0720500i
$590$	−2.49840	+	1.49131i	−0.102857	+	0.0613962i
$591$	−4.03609	+	0.615222i	−0.166023	+	0.0253068i
$592$	−4.17238	+	8.94771i	−0.171484	+	0.367748i
$593$	−21.2939	−	14.9102i	−0.874436	−	0.612287i	0.0478241	−	0.998856i	$-0.484771\pi$
$593$	−21.2939	−	14.9102i	−0.874436	−	0.612287i	−0.922261	+	0.386569i	$0.873660\pi$
$594$	−7.03238	+	7.28242i	−0.288542	+	0.298801i
$595$	3.55298	−	5.23456i	0.145658	−	0.214596i
$596$	7.80299	−	4.50506i	0.319623	−	0.184534i
$597$	−4.82746	+	9.75342i	−0.197575	+	0.399181i
$598$	16.6517	+	1.45683i	0.680938	+	0.0595744i
$599$	−20.3376	+	17.0653i	−0.830973	+	0.697270i	−0.955514	−	0.294945i	$-0.904699\pi$
$599$	−20.3376	+	17.0653i	−0.830973	+	0.697270i	0.124541	+	0.992214i	$0.460254\pi$
$600$	8.53729	+	1.45420i	0.348533	+	0.0593676i
$601$	10.2267	+	17.7131i	0.417155	+	0.722534i	0.995652	−	0.0931506i	$-0.0296938\pi$
$601$	10.2267	+	17.7131i	0.417155	+	0.722534i	−0.578497	+	0.815685i	$0.696360\pi$
$602$	−0.276035	−	0.591960i	−0.0112504	−	0.0241265i
$603$	−26.7907	−	29.4077i	−1.09100	−	1.19757i
$604$	18.7006	−	3.29743i	0.760918	−	0.134170i
$605$	1.63720	+	16.0256i	0.0665615	+	0.651531i
$606$	−4.02378	−	26.3975i	−0.163455	−	1.07233i
$607$	−7.03076	+	7.03076i	−0.285370	+	0.285370i	−0.835246	−	0.549876i	$-0.814675\pi$
$607$	−7.03076	+	7.03076i	−0.285370	+	0.285370i	0.549876	+	0.835246i	$0.314675\pi$
$608$	0.709152	+	4.30083i	0.0287599	+	0.174422i
$609$	1.39773	+	1.22937i	0.0566391	+	0.0498167i
$610$	−15.1545	−	2.44548i	−0.613586	−	0.0990145i
$611$	−19.1424	−	52.5934i	−0.774420	−	2.12770i
$612$	−7.59436	−	3.98142i	−0.306984	−	0.160939i
$613$	−23.7076	+	16.6002i	−0.957540	+	0.670476i	−0.944179	−	0.329434i	$-0.893142\pi$
$613$	−23.7076	+	16.6002i	−0.957540	+	0.670476i	−0.0133611	+	0.999911i	$0.504253\pi$
$614$	−28.1264	−	10.2372i	−1.13509	−	0.413139i
$615$	2.46872	−	0.874225i	0.0995485	−	0.0352521i
$616$	−0.964278	+	1.67018i	−0.0388519	+	0.0672934i
$617$	47.2470	+	4.13357i	1.90209	+	0.166411i	0.976987	−	0.213301i	$-0.0684214\pi$
$617$	47.2470	+	4.13357i	1.90209	+	0.166411i	0.925105	+	0.379712i	$0.123977\pi$
$618$	−0.120686	+	0.115196i	−0.00485469	+	0.00463388i
$619$	−0.691678	−	0.399341i	−0.0278009	−	0.0160509i	0.486035	−	0.873939i	$-0.338443\pi$
$619$	−0.691678	−	0.399341i	−0.0278009	−	0.0160509i	−0.513836	+	0.857888i	$0.671776\pi$
$620$	0.252636	+	0.890827i	0.0101461	+	0.0357765i
$621$	8.51260	+	11.7163i	0.341599	+	0.470159i
$622$	−13.2859	−	18.9743i	−0.532717	−	0.760799i
$623$	13.7458	+	9.62490i	0.550713	+	0.385614i
$624$	3.77894	−	9.67597i	0.151279	−	0.387349i
$625$	−2.90257	+	24.8309i	−0.116103	+	0.993237i
$626$			6.31589i			0.252434i
$627$	5.50306	−	13.6411i	0.219771	−	0.544773i
$628$	8.49638	+	8.49638i	0.339042	+	0.339042i
$629$	21.6167	+	18.1386i	0.861914	+	0.723232i
$630$	1.51258	+	6.46567i	0.0602626	+	0.257599i
$631$	0.491998	+	2.79026i	0.0195861	+	0.111078i	0.993033	−	0.117833i	$-0.0375946\pi$
$631$	0.491998	+	2.79026i	0.0195861	+	0.111078i	−0.973447	+	0.228911i	$0.926484\pi$
$632$	8.50218	−	5.95329i	0.338199	−	0.236809i
$633$	7.21829	−	24.6318i	0.286901	−	0.979026i
$634$	−2.15691	+	1.24529i	−0.0856619	+	0.0494569i
$635$	−32.2844	+	0.469512i	−1.28117	+	0.0186320i
$636$	−0.346838	+	14.9041i	−0.0137530	+	0.590985i
$637$	3.14676	−	35.9676i	0.124679	−	1.42509i
$638$	0.547476	+	2.04321i	0.0216748	+	0.0808914i
$639$	21.3936	−	16.3175i	0.846318	−	0.645510i
$640$	−0.420270	−	2.19622i	−0.0166126	−	0.0868131i
$641$	−7.30973	−	1.28890i	−0.288717	−	0.0509086i	0.0274140	−	0.999624i	$-0.491273\pi$
$641$	−7.30973	−	1.28890i	−0.288717	−	0.0509086i	−0.316131	+	0.948716i	$0.602384\pi$
$642$	2.39856	+	9.86407i	0.0946637	+	0.389304i
$643$	11.1232	+	5.18684i	0.438657	+	0.204549i	0.629385	−	0.777094i	$-0.283307\pi$
$643$	11.1232	+	5.18684i	0.438657	+	0.204549i	−0.190728	+	0.981643i	$0.561085\pi$
$644$	2.11342	+	1.77337i	0.0832804	+	0.0698806i
$645$	−1.44748	−	2.10609i	−0.0569946	−	0.0829274i
$646$	12.3985	+	1.22375i	0.487814	+	0.0481478i
$647$	31.8896	+	31.8896i	1.25371	+	1.25371i	0.954044	+	0.299666i	$0.0968754\pi$
$647$	31.8896	+	31.8896i	1.25371	+	1.25371i	0.299666	+	0.954044i	$0.403125\pi$
$648$	8.47495	−	3.02906i	0.332928	−	0.118993i
$649$	−0.867082	−	2.38229i	−0.0340360	−	0.0935130i
$650$	28.4647	+	9.43232i	1.11648	+	0.369966i
$651$	−0.554344	+	0.443588i	−0.0217265	+	0.0173856i
$652$	−4.57557	+	2.13362i	−0.179193	+	0.0835592i
$653$	34.4800	+	9.23889i	1.34931	+	0.361546i	0.859879	−	0.510498i	$-0.170539\pi$
$653$	34.4800	+	9.23889i	1.34931	+	0.361546i	0.489428	+	0.872044i	$0.337206\pi$
$654$	−17.2486	+	5.82723i	−0.674474	+	0.227863i
$655$	5.76635	−	2.79168i	0.225310	−	0.109080i
$656$	−0.434658	−	0.518006i	−0.0169706	−	0.0202247i
$657$	−17.6102	+	7.23461i	−0.687040	+	0.282249i
$658$	2.39089	−	8.92292i	0.0932066	−	0.347852i
$659$	1.90152	+	0.692096i	0.0740726	+	0.0269602i	0.378791	−	0.925482i	$-0.376340\pi$
$659$	1.90152	+	0.692096i	0.0740726	+	0.0269602i	−0.304718	+	0.952443i	$0.598562\pi$
$660$	−2.64255	+	7.06786i	−0.102861	+	0.275116i
$661$	−6.69202	−	37.9523i	−0.260289	−	1.47617i	−0.782122	−	0.623126i	$-0.785862\pi$
$661$	−6.69202	−	37.9523i	−0.260289	−	1.47617i	0.521832	−	0.853048i	$-0.325249\pi$
$662$	28.9801	+	13.5136i	1.12634	+	0.525222i
$663$	−23.9184	−	17.5911i	−0.928912	−	0.683181i
$664$		−	7.05884i		−	0.273936i
$665$	−5.56094	−	7.88421i	−0.215644	−	0.305737i
$666$	−29.3758	+	3.78073i	−1.13829	+	0.146500i
$667$	3.01448	−	0.263733i	0.116721	−	0.0102118i
$668$	−7.08963	+	15.2038i	−0.274306	+	0.588251i
$669$	−25.4478	−	15.4926i	−0.983868	−	0.598980i
$670$	−27.0525	−	12.1391i	−1.04513	−	0.468973i
$671$	4.57450	−	12.5683i	0.176597	−	0.485195i
$672$	1.42694	−	0.950458i	0.0550453	−	0.0366647i
$673$	−19.9158	+	5.33641i	−0.767696	+	0.205704i	−0.621353	−	0.783530i	$-0.713417\pi$
$673$	−19.9158	+	5.33641i	−0.767696	+	0.205704i	−0.146343	+	0.989234i	$0.546750\pi$
$674$	5.64773	−	4.73901i	0.217543	−	0.182540i
$675$	10.0124	+	23.9740i	0.385376	+	0.922760i
$676$	11.4841	−	19.8911i	0.441697	−	0.765042i
$677$	0.515270	−	1.92301i	0.0198034	−	0.0739074i	−0.955317	−	0.295583i	$-0.904486\pi$
$677$	0.515270	−	1.92301i	0.0198034	−	0.0739074i	0.975120	+	0.221676i	$0.0711527\pi$
$678$	6.75510	−	23.0512i	0.259428	−	0.885276i
$679$	9.90058	+	1.74574i	0.379950	+	0.0669954i
$680$	−6.37433	−	0.464389i	−0.244445	−	0.0178085i
$681$	15.3564	−	39.3199i	0.588458	−	1.50674i
$682$	−0.803720	+	0.0703164i	−0.0307760	+	0.00269255i
$683$	−25.4468	+	25.4468i	−0.973695	+	0.973695i	−0.999663	−	0.0259681i	$-0.991733\pi$
$683$	−25.4468	+	25.4468i	−0.973695	+	0.973695i	0.0259681	+	0.999663i	$0.491733\pi$
$684$	−9.76403	+	8.69849i	−0.373337	+	0.332595i
$685$	22.6578	−	13.5245i	0.865710	−	0.516746i
$686$	8.28441	−	9.87297i	0.316300	−	0.376952i
$687$	13.5173	−	5.92435i	0.515715	−	0.226028i
$688$	−0.378469	+	0.540510i	−0.0144290	+	0.0206067i
$689$	−8.96380	+	50.8362i	−0.341493	+	1.93671i
$690$	9.30081	+	5.47858i	0.354076	+	0.208566i
$691$	0.00818857	+	0.0141830i	0.000311508	+	0.000539548i	0.866181	−	0.499730i	$-0.166568\pi$
$691$	0.00818857	+	0.0141830i	0.000311508	+	0.000539548i	−0.865870	+	0.500270i	$0.833234\pi$
$692$	13.7418	−	3.68210i	0.522385	−	0.139973i
$693$	−5.78087	+	0.235598i	−0.219597	+	0.00894962i
$694$	17.1924	+	20.4891i	0.652613	+	0.777754i
$695$	−7.75527	+	7.98417i	−0.294174	+	0.302857i
$696$	0.369544	−	1.84384i	0.0140075	−	0.0698906i
$697$	−1.75168	+	0.816823i	−0.0663497	+	0.0309394i
$698$	−14.4331	−	20.6126i	−0.546300	−	0.780197i
$699$	18.0376	−	29.6280i	0.682244	−	1.12064i
$700$	2.95552	+	3.97000i	0.111708	+	0.150052i
$701$	6.87555	−	8.19396i	0.259686	−	0.309482i	−0.620410	−	0.784278i	$-0.713034\pi$
$701$	6.87555	−	8.19396i	0.259686	−	0.309482i	0.880096	+	0.474796i	$0.157478\pi$
$702$	30.5905	−	5.94657i	1.15457	−	0.224439i
$703$	37.5055	−	21.1015i	1.41455	−	0.795857i
$704$	1.94829			0.0734291
$705$	3.46416	−	35.9772i	0.130468	−	1.35498i
$706$	5.75484	−	2.09459i	0.216586	−	0.0788309i
$707$	8.75305	−	12.5006i	0.329192	−	0.470135i
$708$	−0.248613	+	2.24004i	−0.00934346	+	0.0841859i
$709$	−14.5263	+	39.9106i	−0.545545	+	1.49887i	0.294121	+	0.955768i	$0.404973\pi$
$709$	−14.5263	+	39.9106i	−0.545545	+	1.49887i	−0.839665	+	0.543104i	$0.817249\pi$
$710$	9.77376	−	17.5119i	0.366803	−	0.657210i
$711$	28.7328	+	11.9993i	1.07757	+	0.450009i
$712$	1.47749	−	16.8877i	0.0553711	−	0.632895i
$713$	−0.100590	+	1.14975i	−0.00376714	+	0.0430586i
$714$	−1.56847	−	4.64268i	−0.0586986	−	0.173748i
$715$	−12.7334	+	22.8147i	−0.476201	+	0.853222i
$716$	−8.17883	+	22.4712i	−0.305657	+	0.839787i
$717$	29.5510	+	3.27975i	1.10360	+	0.122484i
$718$	−6.25561	+	8.93394i	−0.233457	+	0.333412i
$719$	−42.2585	+	15.3808i	−1.57598	+	0.573608i	−0.974324	−	0.225150i	$-0.927713\pi$
$719$	−42.2585	+	15.3808i	−1.57598	+	0.573608i	−0.601652	+	0.798758i	$0.705491\pi$
$720$	4.89272	−	4.58926i	0.182341	−	0.171032i
$721$	−0.0953487			−0.00355097
$722$	8.41056	−	17.0371i	0.313009	−	0.634055i
$723$	0.454317	+	7.08908i	0.0168962	+	0.263646i
$724$	−11.1147	+	13.2459i	−0.413073	+	0.492282i
$725$	5.37124	+	0.786798i	0.199483	+	0.0292209i
$726$	10.6581	+	6.48869i	0.395561	+	0.240818i
$727$	−6.08564	−	8.69119i	−0.225704	−	0.322339i	0.690288	−	0.723534i	$-0.257484\pi$
$727$	−6.08564	−	8.69119i	−0.225704	−	0.322339i	−0.915992	+	0.401196i	$0.868595\pi$
$728$	5.38038	−	2.50891i	0.199410	−	0.0929865i
$729$	21.2767	+	16.6224i	0.788025	+	0.615643i
$730$	−9.88713	+	10.1790i	−0.365939	+	0.376740i
$731$	1.21229	+	1.44475i	0.0448381	+	0.0534360i
$732$	−8.60115	+	8.20993i	−0.317908	+	0.303448i
$733$	−51.1849	+	13.7149i	−1.89056	+	0.506573i	−0.892051	+	0.451936i	$0.850734\pi$
$733$	−51.1849	+	13.7149i	−1.89056	+	0.506573i	−0.998506	+	0.0546376i	$0.982600\pi$
$734$	13.2710	+	22.9860i	0.489841	+	0.848429i
$735$	11.8337	−	20.0897i	0.436494	−	0.741021i
$736$	0.483977	−	2.74477i	0.0178396	−	0.101174i
$737$	14.8185	−	21.1630i	0.545846	−	0.779548i
$738$	0.615629	−	1.93296i	0.0226616	−	0.0711531i
$739$	−30.1451	+	35.9256i	−1.10891	+	1.32154i	−0.166890	+	0.985976i	$0.553372\pi$
$739$	−30.1451	+	35.9256i	−1.10891	+	1.32154i	−0.942016	+	0.335567i	$0.891072\pi$
$740$	−18.9559	+	11.3149i	−0.696832	+	0.415942i
$741$	−37.9613	+	24.6806i	−1.39454	+	0.906665i
$742$	−6.02455	+	6.02455i	−0.221168	+	0.221168i
$743$	28.8612	−	2.52503i	1.05881	−	0.0926342i	0.455577	−	0.890196i	$-0.349433\pi$
$743$	28.8612	−	2.52503i	1.05881	−	0.0926342i	0.603237	+	0.797562i	$0.293877\pi$
$744$	0.668099	+	0.260926i	0.0244937	+	0.00956600i
$745$	20.0940	+	1.46391i	0.736187	+	0.0536334i
$746$	−18.7314	−	3.30286i	−0.685806	−	0.120926i
$747$	17.8930	−	11.3263i	0.654671	−	0.414407i
$748$	1.44129	−	5.37895i	0.0526986	−	0.196674i
$749$	−2.90080	+	5.02433i	−0.105993	+	0.183585i
$750$	13.9690	+	13.4115i	0.510075	+	0.489718i
$751$	−6.27400	+	5.26451i	−0.228942	+	0.192105i	−0.750041	−	0.661391i	$-0.769966\pi$
$751$	−6.27400	+	5.26451i	−0.228942	+	0.192105i	0.521100	+	0.853496i	$0.325522\pi$
$752$	−9.01425	+	2.41536i	−0.328716	+	0.0880791i
$753$	11.6824	+	17.5390i	0.425732	+	0.639157i
$754$	2.22703	−	6.11871i	0.0811036	−	0.222830i
$755$	38.7396	+	17.3833i	1.40988	+	0.632643i
$756$	4.69885	+	2.09200i	0.170896	+	0.0760852i
$757$	0.483510	−	1.03689i	0.0175735	−	0.0376864i	−0.897325	−	0.441370i	$-0.854493\pi$
$757$	0.483510	−	1.03689i	0.0175735	−	0.0376864i	0.914899	+	0.403684i	$0.132270\pi$
$758$	30.0215	−	2.62654i	1.09043	−	0.0954002i
$759$	−6.21155	+	7.06223i	−0.225465	+	0.256343i
$760$	−4.08888	+	8.84766i	−0.148319	+	0.320938i
$761$		−	2.12300i		−	0.0769588i	−0.999259	−	0.0384794i	$-0.987749\pi$
$761$		−	2.12300i		−	0.0769588i	0.999259	−	0.0384794i	$-0.0122514\pi$
$762$	−14.8179	+	20.1478i	−0.536797	+	0.729876i
$763$	−9.43008	−	4.39732i	−0.341392	−	0.159194i
$764$	−0.308792	−	1.75125i	−0.0111717	−	0.0633580i
$765$	−9.05080	−	16.9031i	−0.327232	−	0.611131i
$766$	−3.84501	−	1.39947i	−0.138926	−	0.0505648i
$767$	−2.01981	+	7.53802i	−0.0729310	+	0.272182i
$768$	−1.55232	−	0.768319i	−0.0560144	−	0.0277243i
$769$	17.0304	+	20.2961i	0.614133	+	0.731895i	0.980050	−	0.198752i	$-0.0636889\pi$
$769$	17.0304	+	20.2961i	0.614133	+	0.731895i	−0.365917	+	0.930648i	$0.619244\pi$
$770$	−3.88143	+	1.87913i	−0.139877	+	0.0677192i
$771$	−3.36328	−	9.95531i	−0.121125	−	0.358532i
$772$	6.94024	+	1.85963i	0.249785	+	0.0669296i
$773$	45.2698	−	21.1096i	1.62824	−	0.759261i	0.628414	−	0.777879i	$-0.283704\pi$
$773$	45.2698	−	21.1096i	1.62824	−	0.759261i	0.999827	+	0.0186177i	$0.00592653\pi$
$774$	−1.97738	−	0.0920823i	−0.0710754	−	0.00330983i
$775$	−0.651276	+	1.96541i	−0.0233945	+	0.0705995i
$776$	−3.47363	−	9.54372i	−0.124696	−	0.342600i
$777$	−13.6360	−	10.0288i	−0.489188	−	0.359780i
$778$	6.07268	+	6.07268i	0.217716	+	0.217716i
$779$	0.224239	+	2.93898i	0.00803419	+	0.105300i
$780$	19.1425	−	13.1563i	0.685411	−	0.471072i
$781$	13.3857	+	11.2319i	0.478977	+	0.401910i
$782$	−7.21987	−	3.36668i	−0.258182	−	0.120392i
$783$	5.26679	−	2.02180i	0.188220	−	0.0722534i
$784$	−5.92870	−	1.04539i	−0.211739	−	0.0373354i
$785$	5.04983	+	26.3891i	0.180236	+	0.941867i
$786$	0.975197	−	4.86575i	0.0347841	−	0.173556i
$787$	2.89392	+	10.8003i	0.103157	+	0.384988i	0.998130	−	0.0611338i	$-0.0194716\pi$
$787$	2.89392	+	10.8003i	0.103157	+	0.384988i	−0.894972	+	0.446121i	$0.852805\pi$
$788$	−0.205439	+	2.34818i	−0.00731848	+	0.0836506i
$789$	−22.3274	−	0.519588i	−0.794877	−	0.0184978i
$790$	23.2063	−	0.337488i	0.825642	−	0.0120073i
$791$	11.8886	−	6.86390i	0.422711	−	0.244052i
$792$	3.12614	+	4.93861i	0.111083	+	0.175486i
$793$	−33.7258	+	23.6150i	−1.19764	+	0.838594i
$794$	−5.23929	−	29.7135i	−0.185935	−	1.05449i
$795$	−19.3580	+	27.1390i	−0.686558	+	0.962522i
$796$	4.81316	+	4.03872i	0.170598	+	0.143149i
$797$	−10.2625	−	10.2625i	−0.363515	−	0.363515i	0.501590	−	0.865105i	$-0.332748\pi$
$797$	−10.2625	−	10.2625i	−0.363515	−	0.363515i	−0.865105	+	0.501590i	$0.832748\pi$
$798$	−7.46893	−	0.256905i	−0.264397	−	0.00909436i
$799$			26.6738i			0.943651i
$800$	1.98042	−	4.59107i	0.0700185	−	0.162319i
$801$	45.1784	−	23.3521i	1.59630	−	0.825105i
$802$	18.0072	+	12.6088i	0.635856	+	0.445231i
$803$	−7.09177	−	10.1281i	−0.250263	−	0.357413i
$804$	−20.1524	+	11.0180i	−0.710722	+	0.388575i
$805$	1.68314	+	5.93498i	0.0593230	+	0.209181i
$806$	2.15078	+	1.24175i	0.0757580	+	0.0437389i
$807$	−4.54406	−	4.76059i	−0.159959	−	0.167581i
$808$	−15.3580	−	1.34365i	−0.540292	−	0.0472695i
$809$	11.6162	−	20.1198i	0.408402	−	0.707374i	−0.586308	−	0.810088i	$-0.699419\pi$
$809$	11.6162	−	20.1198i	0.408402	−	0.707374i	0.994711	+	0.102714i	$0.0327527\pi$
$810$	19.4837	+	5.03854i	0.684586	+	0.177036i
$811$	18.6817	+	6.79958i	0.656003	+	0.238766i	0.648510	−	0.761206i	$-0.275393\pi$
$811$	18.6817	+	6.79958i	0.656003	+	0.238766i	0.00749342	+	0.999972i	$0.497615\pi$
$812$	0.880352	−	0.616429i	0.0308943	−	0.0216324i
$813$	−4.54941	+	1.10624i	−0.159555	+	0.0387976i
$814$	−6.57873	−	18.0749i	−0.230584	−	0.633526i
$815$	−11.1448	−	1.79844i	−0.390386	−	0.0629966i
$816$	−3.26957	+	3.71734i	−0.114458	+	0.130133i
$817$	2.71349	−	0.953608i	0.0949330	−	0.0333625i
$818$	−24.1651	+	24.1651i	−0.844913	+	0.844913i
$819$	14.9928	+	9.61272i	0.523890	+	0.335896i
$820$	−0.153673	−	1.50422i	−0.00536651	−	0.0525296i
$821$	16.5219	−	2.91326i	0.576619	−	0.101673i	0.122269	−	0.992497i	$-0.460983\pi$
$821$	16.5219	−	2.91326i	0.576619	−	0.101673i	0.454350	+	0.890824i	$0.349872\pi$
$822$	2.25465	−	20.3148i	0.0786401	−	0.708559i
$823$	−11.1077	−	23.8204i	−0.387188	−	0.830328i	−0.999220	−	0.0394947i	$-0.987425\pi$
$823$	−11.1077	−	23.8204i	−0.387188	−	0.830328i	0.612031	−	0.790833i	$-0.290353\pi$
$824$	0.0481623	+	0.0834195i	0.00167781	+	0.00290606i
$825$	−13.7648	+	9.75803i	−0.479229	+	0.339731i
$826$	−0.986701	+	0.827941i	−0.0343317	+	0.0288077i
$827$	−21.6162	−	1.89117i	−0.751668	−	0.0657624i	−0.295119	−	0.955461i	$-0.595359\pi$
$827$	−21.6162	−	1.89117i	−0.751668	−	0.0657624i	−0.456549	+	0.889698i	$0.650915\pi$
$828$	7.73412	−	3.17732i	0.268779	−	0.110420i
$829$	0.950996	−	0.549058i	0.0330295	−	0.0190696i	−0.483394	−	0.875403i	$-0.660596\pi$
$829$	0.950996	−	0.549058i	0.0330295	−	0.0190696i	0.516424	+	0.856333i	$0.327263\pi$
$830$	8.86438	−	13.0598i	0.307687	−	0.453313i
$831$	11.1340	−	8.90945i	0.386234	−	0.309065i
$832$	−4.91274	−	3.43994i	−0.170319	−	0.119258i
$833$	−7.27203	+	15.5949i	−0.251961	+	0.540332i
$834$	1.29921	+	8.52331i	0.0449879	+	0.295138i
$835$	−32.2094	+	19.2260i	−1.11465	+	0.665342i
$836$	−6.90201	−	4.94808i	−0.238711	−	0.171133i
$837$	0.410594	+	2.11219i	0.0141922	+	0.0730080i
$838$	3.40820	+	38.9559i	0.117734	+	1.34571i
$839$	28.5912	−	10.4063i	0.987078	−	0.359267i	0.202490	−	0.979284i	$-0.435097\pi$
$839$	28.5912	−	10.4063i	0.987078	−	0.359267i	0.784588	+	0.620017i	$0.212874\pi$
$840$	3.83360	+	0.0334497i	0.132272	+	0.00115412i
$841$	−4.83111	+	27.3986i	−0.166590	+	0.944778i
$842$	8.12811	+	17.4308i	0.280113	+	0.600705i
$843$	5.61378	+	8.42805i	0.193349	+	0.290277i
$844$	−12.8338	−	7.40961i	−0.441759	−	0.255049i
$845$	46.2261	−	22.3796i	1.59023	−	0.769883i
$846$	−20.5864	−	18.9741i	−0.707774	−	0.652343i
$847$	1.84568	+	6.88817i	0.0634183	+	0.236680i
$848$	8.31392	+	2.22771i	0.285501	+	0.0764998i
$849$	−22.6815	+	12.4007i	−0.778428	+	0.425592i
$850$	−11.2102	−	8.86398i	−0.384507	−	0.304032i
$851$	−27.0983	+	4.77816i	−0.928917	+	0.163793i
$852$	−6.23577	−	14.2278i	−0.213634	−	0.487437i
$853$	4.23609	+	48.4187i	0.145041	+	1.65782i	0.625068	+	0.780570i	$0.285071\pi$
$853$	4.23609	+	48.4187i	0.145041	+	1.65782i	−0.480027	+	0.877254i	$0.659373\pi$
$854$	−6.79540			−0.232534
$855$	−28.9882	+	3.83186i	−0.991376	+	0.131047i
$856$	5.86097			0.200324
$857$	2.29778	+	26.2638i	0.0784907	+	0.897153i	0.928730	+	0.370757i	$0.120902\pi$
$857$	2.29778	+	26.2638i	0.0784907	+	0.897153i	−0.850239	+	0.526396i	$0.823543\pi$
$858$	8.12405	+	18.5362i	0.277350	+	0.632815i
$859$	−15.7329	+	2.77414i	−0.536800	+	0.0946524i	−0.435475	−	0.900201i	$-0.643419\pi$
$859$	−15.7329	+	2.77414i	−0.536800	+	0.0946524i	−0.101325	+	0.994853i	$0.532308\pi$
$860$	−1.37898	+	0.524741i	−0.0470229	+	0.0178935i
$861$	1.01725	−	0.556165i	0.0346678	−	0.0189540i
$862$	−12.2009	−	3.26923i	−0.415565	−	0.111350i
$863$	11.4475	+	42.7227i	0.389678	+	1.45430i	0.830659	+	0.556782i	$0.187964\pi$
$863$	11.4475	+	42.7227i	0.389678	+	1.45430i	−0.440981	+	0.897517i	$0.645369\pi$
$864$	−0.543207	−	5.16768i	−0.0184803	−	0.175808i
$865$	30.0481	+	10.4444i	1.02167	+	0.355119i
$866$	−10.2175	−	5.89907i	−0.347204	−	0.200458i
$867$	−8.47887	−	12.7295i	−0.287957	−	0.432315i
$868$	0.173233	+	0.371500i	0.00587993	+	0.0126095i
$869$	−3.51149	+	19.9146i	−0.119119	+	0.675557i
$870$	2.99917	−	2.94729i	0.101681	−	0.0999224i
$871$	−74.7314	+	27.2000i	−2.53218	+	0.921637i
$872$	0.916132	+	10.4714i	0.0310242	+	0.354608i
$873$	18.6182	−	24.1185i	0.630130	−	0.816287i
$874$	−8.68541	+	8.49444i	−0.293788	+	0.287329i
$875$	0.482657	+	11.0565i	0.0163168	+	0.373779i
$876$	1.65635	+	10.8663i	0.0559629	+	0.367138i
$877$	20.8875	−	44.7934i	0.705320	−	1.51256i	−0.146771	−	0.989171i	$-0.546888\pi$
$877$	20.8875	−	44.7934i	0.705320	−	1.51256i	0.852091	−	0.523394i	$-0.175334\pi$
$878$	−26.7037	−	18.6981i	−0.901206	−	0.631031i
$879$	21.4657	−	17.1769i	0.724021	−	0.579364i
$880$	3.60461	+	2.44664i	0.121511	+	0.0824762i
$881$	6.46178	−	3.73071i	0.217703	−	0.125691i	−0.387183	−	0.922003i	$-0.626552\pi$
$881$	6.46178	−	3.73071i	0.217703	−	0.125691i	0.604886	+	0.796312i	$0.293219\pi$
$882$	−6.86301	−	16.7057i	−0.231090	−	0.562510i
$883$	43.7282	+	3.82572i	1.47157	+	0.128746i	0.794542	−	0.607210i	$-0.207711\pi$
$883$	43.7282	+	3.82572i	1.47157	+	0.128746i	0.677030	+	0.735956i	$0.263267\pi$
$884$	−13.1315	+	11.0186i	−0.441659	+	0.370596i
$885$	−3.27298	+	3.83218i	−0.110020	+	0.128817i
$886$	−2.51597	−	4.35779i	−0.0845257	−	0.146403i
$887$	−5.83964	−	12.5232i	−0.196076	−	0.420486i	0.783547	−	0.621333i	$-0.213409\pi$
$887$	−5.83964	−	12.5232i	−0.196076	−	0.420486i	−0.979623	+	0.200847i	$0.935631\pi$
$888$	−1.88628	+	16.9957i	−0.0632994	+	0.570337i
$889$	−14.0761	+	2.48200i	−0.472098	+	0.0832437i
$890$	23.9409	−	29.3892i	0.802502	−	0.985129i
$891$	−7.50254	+	15.8485i	−0.251345	+	0.530946i
$892$	−12.1629	+	12.1629i	−0.407243	+	0.407243i
$893$	38.0681	+	14.3368i	1.27390	+	0.479764i
$894$	10.3067	−	11.7183i	0.344709	−	0.391917i
$895$	−43.3509	+	31.3038i	−1.44906	+	1.04637i
$896$	−0.338555	−	0.930172i	−0.0113103	−	0.0310749i
$897$	28.1320	−	6.84062i	0.939300	−	0.228402i
$898$	−24.9639	+	17.4799i	−0.833058	+	0.583313i
$899$	0.422480	+	0.153770i	0.0140905	+	0.00512852i
$900$	14.8153	−	2.34656i	0.493844	−	0.0782187i
$901$	12.3007	−	21.3055i	0.409797	−	0.709790i
$902$	1.31244	+	0.114824i	0.0436995	+	0.00382321i
$903$	−0.781122	−	0.818343i	−0.0259941	−	0.0272328i
$904$	−12.0103	−	6.93415i	−0.399457	−	0.230626i
$905$	−37.1977	+	10.5492i	−1.23649	+	0.350666i
$906$	28.8586	−	15.7779i	0.958762	−	0.524187i
$907$	14.7228	+	21.0263i	0.488862	+	0.698167i	0.985478	−	0.169803i	$-0.0543132\pi$
$907$	14.7228	+	21.0263i	0.488862	+	0.698167i	−0.496616	+	0.867970i	$0.665424\pi$
$908$	−19.9638	−	13.9788i	−0.662521	−	0.463902i
$909$	−21.2368	−	41.0860i	−0.704379	−	1.36274i
$910$	13.1051	+	2.11477i	0.434430	+	0.0701040i
$911$			26.0118i			0.861809i	0.902398	+	0.430904i	$0.141805\pi$
$911$			26.0118i			0.861809i	−0.902398	+	0.430904i	$0.858195\pi$
$912$	3.54792	+	6.66425i	0.117483	+	0.220675i
$913$	9.72462	+	9.72462i	0.321838	+	0.321838i
$914$	2.44313	+	2.05003i	0.0808117	+	0.0678091i
$915$	−26.2232	+	4.38830i	−0.866912	+	0.145073i
$916$	−1.47963	−	8.39139i	−0.0488883	−	0.277259i
$917$	2.32318	−	1.62671i	0.0767182	−	0.0537187i
$918$	−14.6690	−	2.32317i	−0.484151	−	0.0766761i
$919$	−13.5876	+	7.84479i	−0.448213	+	0.258776i	−0.707075	−	0.707138i	$-0.749986\pi$
$919$	−13.5876	+	7.84479i	−0.448213	+	0.258776i	0.258862	+	0.965914i	$0.416652\pi$
$920$	4.34226	−	4.47043i	0.143160	−	0.147386i
$921$	−51.8289	−	1.20613i	−1.70782	−	0.0397433i
$922$	−1.95203	+	22.3118i	−0.0642866	+	0.734800i
$923$	−13.9216	−	51.9560i	−0.458234	−	1.71015i
$924$	−0.656423	+	3.27522i	−0.0215947	+	0.107747i
$925$	−49.2800	−	2.87048i	−1.62032	−	0.0943807i
$926$	13.6577	+	2.40821i	0.448819	+	0.0791388i
$927$	−0.134176	+	0.255935i	−0.00440693	+	0.00840600i
$928$	−0.983989	−	0.458842i	−0.0323010	−	0.0150622i
$929$	10.7533	+	9.02305i	0.352803	+	0.296037i	0.801914	−	0.597439i	$-0.203815\pi$
$929$	10.7533	+	9.02305i	0.352803	+	0.296037i	−0.449112	+	0.893476i	$0.648259\pi$
$930$	0.908407	+	1.32174i	0.0297878	+	0.0433415i
$931$	18.3480	+	18.7605i	0.601331	+	0.614850i
$932$	−14.1608	−	14.1608i	−0.463853	−	0.463853i
$933$	−32.3201	−	23.7703i	−1.05811	−	0.778203i
$934$	6.25564	+	17.1872i	0.204691	+	0.562384i
$935$	9.42138	−	8.14185i	0.308112	−	0.266267i
$936$	0.836945	−	17.9726i	0.0273564	−	0.587452i
$937$	−6.81373	+	3.17729i	−0.222595	+	0.103798i	−0.530717	−	0.847549i	$-0.678077\pi$
$937$	−6.81373	+	3.17729i	−0.222595	+	0.103798i	0.308122	+	0.951347i	$0.400299\pi$
$938$	−12.6788	−	3.39728i	−0.413978	−	0.110925i
$939$	3.50134	+	10.3640i	0.114262	+	0.338216i
$940$	−19.7108	−	6.85121i	−0.642894	−	0.223462i
$941$	17.9668	+	21.4119i	0.585699	+	0.698009i	0.974773	−	0.223197i	$-0.0716494\pi$
$941$	17.9668	+	21.4119i	0.585699	+	0.698009i	−0.389074	+	0.921207i	$0.627205\pi$
$942$	18.6522	+	9.23188i	0.607720	+	0.300791i
$943$	0.487788	−	1.82045i	0.0158846	−	0.0592820i
$944$	1.22276	+	0.445047i	0.0397973	+	0.0144850i
$945$	6.06642	+	9.77123i	0.197341	+	0.317858i
$946$	−0.223236	−	1.26603i	−0.00725802	−	0.0411623i
$947$	−28.5984	−	13.3356i	−0.929323	−	0.433350i	−0.101814	−	0.994803i	$-0.532465\pi$
$947$	−28.5984	−	13.3356i	−0.929323	−	0.433350i	−0.827509	+	0.561453i	$0.810242\pi$
$948$	10.6512	−	14.4823i	0.345936	−	0.470364i
$949$			38.0600i			1.23548i
$950$	−18.6757	+	11.2346i	−0.605921	+	0.364499i
$951$	−2.84900	+	3.23918i	−0.0923853	+	0.105037i
$952$	−2.81852	+	0.246589i	−0.0913488	+	0.00799198i
$953$	−16.0928	+	34.5112i	−0.521298	+	1.11793i	0.452761	+	0.891632i	$0.350439\pi$
$953$	−16.0928	+	34.5112i	−0.521298	+	1.11793i	−0.974059	+	0.226295i	$0.927339\pi$
$954$	7.69324	+	24.6489i	0.249078	+	0.798039i
$955$	1.62788	−	3.62783i	0.0526771	−	0.117394i
$956$	5.87113	−	16.1308i	0.189886	−	0.521708i
$957$	2.03107	+	3.04927i	0.0656551	+	0.0985690i
$958$	0.236904	−	0.0634781i	0.00765401	−	0.00205088i
$959$	8.94831	−	7.50853i	0.288956	−	0.242463i
$960$	−1.90715	−	3.37087i	−0.0615531	−	0.108794i
$961$	15.4143	−	26.6983i	0.497234	−	0.861235i
$962$	−15.3247	+	57.1925i	−0.494088	+	1.84396i
$963$	9.40423	+	14.8566i	0.303047	+	0.478748i
$964$	4.03897	+	0.712179i	0.130086	+	0.0229377i
$965$	10.5051	+	12.1560i	0.338171	+	0.391316i
$966$	4.45109	+	1.73837i	0.143212	+	0.0559312i
$967$	3.91548	−	0.342560i	0.125913	−	0.0110160i	−0.0240249	−	0.999711i	$-0.507648\pi$
$967$	3.91548	−	0.342560i	0.125913	−	0.0110160i	0.149938	+	0.988695i	$0.452093\pi$
$968$	5.09410	−	5.09410i	0.163731	−	0.163731i
$969$	21.0236	−	4.86529i	0.675377	−	0.156296i
$970$	5.55817	−	22.0193i	0.178462	−	0.706997i
$971$	9.14300	−	10.8962i	0.293413	−	0.349676i	−0.599119	−	0.800660i	$-0.704482\pi$
$971$	9.14300	−	10.8962i	0.293413	−	0.349676i	0.892532	+	0.450984i	$0.148927\pi$
$972$	12.2276	−	9.66875i	0.392202	−	0.310125i
$973$	−2.82621	+	4.03624i	−0.0906040	+	0.129396i
$974$	−0.670749	+	3.80401i	−0.0214922	+	0.121888i
$975$	51.9377	−	0.302112i	1.66334	−	0.00967534i
$976$	3.43248	+	5.94522i	0.109871	+	0.190302i
$977$	15.8016	−	4.23403i	0.505538	−	0.135459i	0.00296924	−	0.999996i	$-0.499055\pi$
$977$	15.8016	−	4.23403i	0.505538	−	0.135459i	0.502569	+	0.864537i	$0.332388\pi$
$978$	−6.32541	+	6.03770i	−0.202264	+	0.193064i
$979$	21.2300	+	25.3009i	0.678513	+	0.808620i
$980$	−9.65612	−	9.37929i	−0.308453	−	0.299610i
$981$	−25.0734	+	19.1242i	−0.800533	+	0.610589i
$982$	−2.47907	+	1.15601i	−0.0791104	+	0.0368898i
$983$	11.6787	+	16.6789i	0.372493	+	0.531975i	0.961011	−	0.276509i	$-0.0891775\pi$
$983$	11.6787	+	16.6789i	0.372493	+	0.531975i	−0.588518	+	0.808484i	$0.700289\pi$
$984$	−1.00041	−	0.609053i	−0.0318920	−	0.0194159i
$985$	−3.32891	+	4.08647i	−0.106068	+	0.130206i
$986$	−1.99472	+	2.37721i	−0.0635247	+	0.0757058i
$987$	−1.02330	−	15.9674i	−0.0325720	−	0.508248i
$988$	8.66743	+	24.6632i	0.275748	+	0.784640i
$989$	−1.83905			−0.0584784
$990$	−0.418054	+	13.0629i	−0.0132866	+	0.415165i
$991$	48.2996	−	17.5796i	1.53429	−	0.558435i	0.569621	−	0.821907i	$-0.307090\pi$
$991$	48.2996	−	17.5796i	1.53429	−	0.558435i	0.964667	+	0.263472i	$0.0848677\pi$
$992$	0.237518	−	0.339211i	0.00754122	−	0.0107700i
$993$	55.0460	+	6.10933i	1.74683	+	0.193874i
$994$	3.03642	−	8.34249i	0.0963093	−	0.264608i
$995$	3.83324	+	13.5165i	0.121522	+	0.428502i
$996$	−3.91321	−	11.5831i	−0.123995	−	0.367025i
$997$	−0.360517	+	4.12073i	−0.0114177	+	0.130505i	−0.999764	−	0.0217161i	$-0.993087\pi$
$997$	−0.360517	+	4.12073i	−0.0114177	+	0.130505i	0.988346	+	0.152221i	$0.0486426\pi$
$998$	1.00856	−	11.5279i	0.0319255	−	0.364910i
$999$	−46.1079	+	22.4890i	−1.45879	+	0.711521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.263.9	✓	480
3.2	odd	2	inner	570.2.bi.a.263.23	yes	480
5.2	odd	4	inner	570.2.bi.a.377.23	yes	480
15.2	even	4	inner	570.2.bi.a.377.13	yes	480
19.6	even	9	inner	570.2.bi.a.443.13	yes	480
57.44	odd	18	inner	570.2.bi.a.443.23	yes	480
95.82	odd	36	inner	570.2.bi.a.557.23	yes	480
285.272	even	36	inner	570.2.bi.a.557.9	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.263.9	✓	480	1.1	even	1	trivial
570.2.bi.a.263.23	yes	480	3.2	odd	2	inner
570.2.bi.a.377.13	yes	480	15.2	even	4	inner
570.2.bi.a.377.23	yes	480	5.2	odd	4	inner
570.2.bi.a.443.13	yes	480	19.6	even	9	inner
570.2.bi.a.443.23	yes	480	57.44	odd	18	inner
570.2.bi.a.557.9	yes	480	285.272	even	36	inner
570.2.bi.a.557.23	yes	480	95.82	odd	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.695277 - 1.58638i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-2.04009 - 0.915434i) q^{5} +(-1.51974 + 0.830893i) q^{6} +(-0.956140 - 0.256197i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.03318 + 2.20594i) q^{9} +O(q^{10})\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-0.695277 - 1.58638i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-2.04009 - 0.915434i) q^{5} +(-1.51974 + 0.830893i) q^{6} +(-0.956140 - 0.256197i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.03318 + 2.20594i) q^{9} +(-0.734145 + 2.11212i) q^{10} +(-1.68727 - 0.974147i) q^{11} +(0.960186 + 1.44154i) q^{12} +(2.53459 + 5.43545i) q^{13} +(-0.171889 + 0.974830i) q^{14} +(-0.0337921 + 3.87284i) q^{15} +(0.939693 - 0.342020i) q^{16} +(-0.249112 - 2.84737i) q^{17} +(2.37475 + 1.83318i) q^{18} +(-4.19757 - 1.17490i) q^{19} +(2.16806 + 0.547268i) q^{20} +(0.258358 + 1.69493i) q^{21} +(-0.823385 + 1.76575i) q^{22} +(2.28307 + 1.59862i) q^{23} +(1.35237 - 1.08217i) q^{24} +(3.32396 + 3.73514i) q^{25} +(5.19386 - 2.99868i) q^{26} +(4.91308 + 1.69164i) q^{27} +(0.986102 + 0.0862727i) q^{28} +(0.831703 - 0.697882i) q^{29} +(3.86104 - 0.303876i) q^{30} +(0.207050 + 0.358622i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-0.372241 + 3.35395i) q^{33} +(-2.81482 + 0.496329i) q^{34} +(1.71608 + 1.39795i) q^{35} +(1.61923 - 2.52549i) q^{36} +(-6.98105 + 6.98105i) q^{37} +(-0.804584 + 4.28400i) q^{38} +(6.86042 - 7.79996i) q^{39} +(0.356226 - 2.20751i) q^{40} +(-0.231277 - 0.635428i) q^{41} +(1.66596 - 0.405097i) q^{42} +(-0.540510 + 0.378469i) q^{43} +(1.83080 + 0.666356i) q^{44} +(6.16727 - 2.63909i) q^{45} +(1.39356 - 2.41371i) q^{46} +(-9.29672 - 0.813358i) q^{47} +(-1.19592 - 1.25291i) q^{48} +(-5.21361 - 3.01008i) q^{49} +(3.43123 - 3.63685i) q^{50} +(-4.34379 + 2.37490i) q^{51} +(-3.43994 - 4.91274i) q^{52} +(7.05061 + 4.93689i) q^{53} +(1.25700 - 5.04182i) q^{54} +(2.55043 + 3.53194i) q^{55} -0.989869i q^{56} +(1.05465 + 7.47581i) q^{57} +(-0.767714 - 0.767714i) q^{58} +(0.996800 + 0.836415i) q^{59} +(-0.639232 - 3.81987i) q^{60} +(1.19209 + 6.76066i) q^{61} +(0.339211 - 0.237518i) q^{62} +(2.50916 - 1.58830i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-0.195008 - 13.4091i) q^{65} +(3.37363 + 0.0785089i) q^{66} +(-1.15572 + 13.2100i) q^{67} +(0.739768 + 2.76085i) q^{68} +(0.948649 - 4.73329i) q^{69} +(1.24306 - 1.83139i) q^{70} +(-8.83250 - 1.55741i) q^{71} +(-2.65700 - 1.39296i) q^{72} +(5.75154 + 2.68199i) q^{73} +(7.56293 + 6.34605i) q^{74} +(3.61426 - 7.87001i) q^{75} +(4.33782 + 0.428147i) q^{76} +(1.36369 + 1.36369i) q^{77} +(-8.36820 - 6.15450i) q^{78} +(-3.54991 - 9.75331i) q^{79} +(-2.23016 - 0.162474i) q^{80} +(-0.732369 - 8.97015i) q^{81} +(-0.612853 + 0.285778i) q^{82} +(-6.81831 - 1.82696i) q^{83} +(-0.548753 - 1.62431i) q^{84} +(-2.09836 + 6.03694i) q^{85} +(0.424137 + 0.505467i) q^{86} +(-1.68537 - 0.834173i) q^{87} +(0.504256 - 1.88191i) q^{88} +(-15.9299 - 5.79801i) q^{89} +(-3.16656 - 5.91379i) q^{90} +(-1.03088 - 5.84640i) q^{91} +(-2.52598 - 1.17788i) q^{92} +(0.424952 - 0.577801i) q^{93} +9.33223i q^{94} +(7.48790 + 6.23950i) q^{95} +(-1.14391 + 1.30057i) q^{96} +(-10.1176 + 0.885172i) q^{97} +(-2.54423 + 5.45612i) q^{98} +(5.57944 - 1.74141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q+O(q^{10}) \) 480 * q	\( 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) \) 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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