LMFDB - Embedded newform 888.2.bo.c.625.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [888,2,Mod(49,888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(888, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 14]))

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

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

chi := DirichletCharacter("888.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.bo (of order $9$, degree $6$, 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:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			625.1
Character	$\chi$	$=$	888.625
Dual form			888.2.bo.c.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{3} +(-2.76055 + 2.31638i) q^{5} +(3.79688 - 3.18596i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{3} +(-2.76055 + 2.31638i) q^{5} +(3.79688 - 3.18596i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(2.83834 - 4.91615i) q^{11} +(-3.96848 - 1.44441i) q^{13} +(-2.76055 - 2.31638i) q^{15} +(4.82179 - 1.75499i) q^{17} +(-0.568725 - 3.22540i) q^{19} +(3.79688 + 3.18596i) q^{21} +(2.47824 + 4.29244i) q^{23} +(1.38679 - 7.86490i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-1.80144 + 3.12018i) q^{29} +1.15272 q^{31} +(5.33433 + 1.94154i) q^{33} +(-3.10159 + 17.5900i) q^{35} +(4.68119 - 3.88413i) q^{37} +(0.733346 - 4.15901i) q^{39} +(0.720927 + 0.262396i) q^{41} +1.10293 q^{43} +(1.80182 - 3.12084i) q^{45} +(2.10668 + 3.64888i) q^{47} +(3.05042 - 17.2998i) q^{49} +(2.56562 + 4.44378i) q^{51} +(8.30367 + 6.96760i) q^{53} +(3.55227 + 20.1459i) q^{55} +(3.07764 - 1.12017i) q^{57} +(-1.62090 - 1.36010i) q^{59} +(2.44183 + 0.888755i) q^{61} +(-2.47824 + 4.29244i) q^{63} +(14.3010 - 5.20513i) q^{65} +(6.19508 - 5.19829i) q^{67} +(-3.79688 + 3.18596i) q^{69} +(-0.923700 - 5.23856i) q^{71} -12.4580 q^{73} +7.98622 q^{75} +(-4.88582 - 27.7089i) q^{77} +(7.81821 - 6.56026i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-14.6427 + 5.32950i) q^{83} +(-9.24557 + 16.0138i) q^{85} +(-3.38559 - 1.23226i) q^{87} +(8.40074 + 7.04906i) q^{89} +(-19.6697 + 7.15918i) q^{91} +(0.200168 + 1.13521i) q^{93} +(9.04122 + 7.58649i) q^{95} +(0.354561 + 0.614118i) q^{97} +(-0.985745 + 5.59044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) $ 24 * q + 3 * q^5 + 15 * q^7	$ 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$		0			0
$5$	−2.76055	+	2.31638i	−1.23455	+	1.03591i	−0.236625	+	0.971601i	$0.576041\pi$
$5$	−2.76055	+	2.31638i	−1.23455	+	1.03591i	−0.997930	+	0.0643136i	$0.979514\pi$
$6$		0			0
$7$	3.79688	−	3.18596i	1.43509	−	1.20418i	0.492459	−	0.870336i	$-0.336098\pi$
$7$	3.79688	−	3.18596i	1.43509	−	1.20418i	0.942628	−	0.333845i	$-0.108346\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	2.83834	−	4.91615i	0.855791	−	1.48227i	−0.0201175	−	0.999798i	$-0.506404\pi$
$11$	2.83834	−	4.91615i	0.855791	−	1.48227i	0.875909	−	0.482477i	$-0.160263\pi$
$12$		0			0
$13$	−3.96848	−	1.44441i	−1.10066	−	0.400607i	−0.273100	−	0.961986i	$-0.588049\pi$
$13$	−3.96848	−	1.44441i	−1.10066	−	0.400607i	−0.827559	+	0.561379i	$0.810271\pi$
$14$		0			0
$15$	−2.76055	−	2.31638i	−0.712771	−	0.598086i
$16$		0			0
$17$	4.82179	−	1.75499i	1.16946	−	0.425647i	0.316989	−	0.948429i	$-0.397328\pi$
$17$	4.82179	−	1.75499i	1.16946	−	0.425647i	0.852466	+	0.522782i	$0.175106\pi$
$18$		0			0
$19$	−0.568725	−	3.22540i	−0.130474	−	0.739957i	−0.977905	−	0.209051i	$-0.932963\pi$
$19$	−0.568725	−	3.22540i	−0.130474	−	0.739957i	0.847430	−	0.530906i	$-0.178148\pi$
$20$		0			0
$21$	3.79688	+	3.18596i	0.828548	+	0.695234i
$22$		0			0
$23$	2.47824	+	4.29244i	0.516749	+	0.895035i	0.999811	+	0.0194489i	$0.00619117\pi$
$23$	2.47824	+	4.29244i	0.516749	+	0.895035i	−0.483062	+	0.875586i	$0.660476\pi$
$24$		0			0
$25$	1.38679	−	7.86490i	0.277359	−	1.57298i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	−1.80144	+	3.12018i	−0.334519	+	0.579403i	−0.983392	−	0.181493i	$-0.941907\pi$
$29$	−1.80144	+	3.12018i	−0.334519	+	0.579403i	0.648874	+	0.760896i	$0.275240\pi$
$30$		0			0
$31$	1.15272			0.207035			0.103518	−	0.994628i	$-0.466990\pi$
$31$	1.15272			0.207035			0.103518	+	0.994628i	$0.466990\pi$
$32$		0			0
$33$	5.33433	+	1.94154i	0.928588	+	0.337978i
$34$		0			0
$35$	−3.10159	+	17.5900i	−0.524265	+	2.97326i
$36$		0			0
$37$	4.68119	−	3.88413i	0.769582	−	0.638548i
$37$	4.68119	−	3.88413i	0.769582	−	0.638548i
$38$		0			0
$39$	0.733346	−	4.15901i	0.117429	−	0.665974i
$40$		0			0
$41$	0.720927	+	0.262396i	0.112590	+	0.0409794i	0.397701	−	0.917515i	$-0.369808\pi$
$41$	0.720927	+	0.262396i	0.112590	+	0.0409794i	−0.285111	+	0.958495i	$0.592030\pi$
$42$		0			0
$43$	1.10293			0.168195			0.0840976	−	0.996458i	$-0.473199\pi$
$43$	1.10293			0.168195			0.0840976	+	0.996458i	$0.473199\pi$
$44$		0			0
$45$	1.80182	−	3.12084i	0.268599	−	0.465228i
$46$		0			0
$47$	2.10668	+	3.64888i	0.307291	+	0.532244i	0.977769	−	0.209686i	$-0.0672440\pi$
$47$	2.10668	+	3.64888i	0.307291	+	0.532244i	−0.670477	+	0.741930i	$0.733911\pi$
$48$		0			0
$49$	3.05042	−	17.2998i	0.435775	−	2.47140i
$50$		0			0
$51$	2.56562	+	4.44378i	0.359259	+	0.622254i
$52$		0			0
$53$	8.30367	+	6.96760i	1.14060	+	0.957074i	0.999458	−	0.0329160i	$-0.0104794\pi$
$53$	8.30367	+	6.96760i	1.14060	+	0.957074i	0.141138	+	0.989990i	$0.454924\pi$
$54$		0			0
$55$	3.55227	+	20.1459i	0.478988	+	2.71648i
$56$		0			0
$57$	3.07764	−	1.12017i	0.407643	−	0.148370i
$58$		0			0
$59$	−1.62090	−	1.36010i	−0.211024	−	0.177070i	0.531149	−	0.847278i	$-0.321760\pi$
$59$	−1.62090	−	1.36010i	−0.211024	−	0.177070i	−0.742173	+	0.670208i	$0.766205\pi$
$60$		0			0
$61$	2.44183	+	0.888755i	0.312645	+	0.113793i	0.493577	−	0.869702i	$-0.335689\pi$
$61$	2.44183	+	0.888755i	0.312645	+	0.113793i	−0.180932	+	0.983496i	$0.557911\pi$
$62$		0			0
$63$	−2.47824	+	4.29244i	−0.312229	+	0.540796i
$64$		0			0
$65$	14.3010	−	5.20513i	1.77382	−	0.645617i
$66$		0			0
$67$	6.19508	−	5.19829i	0.756849	−	0.635072i	−0.180455	−	0.983583i	$-0.557757\pi$
$67$	6.19508	−	5.19829i	0.756849	−	0.635072i	0.937305	+	0.348511i	$0.113313\pi$
$68$		0			0
$69$	−3.79688	+	3.18596i	−0.457091	+	0.383545i
$70$		0			0
$71$	−0.923700	−	5.23856i	−0.109623	−	0.621703i	−0.989273	−	0.146081i	$-0.953334\pi$
$71$	−0.923700	−	5.23856i	−0.109623	−	0.621703i	0.879650	−	0.475622i	$-0.157777\pi$
$72$		0			0
$73$	−12.4580			−1.45810			−0.729048	−	0.684462i	$-0.760037\pi$
$73$	−12.4580			−1.45810			−0.729048	+	0.684462i	$0.760037\pi$
$74$		0			0
$75$	7.98622			0.922170
$76$		0			0
$77$	−4.88582	−	27.7089i	−0.556791	−	3.15772i
$78$		0			0
$79$	7.81821	−	6.56026i	0.879617	−	0.738087i	−0.0864829	−	0.996253i	$-0.527563\pi$
$79$	7.81821	−	6.56026i	0.879617	−	0.738087i	0.966100	+	0.258167i	$0.0831184\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	−14.6427	+	5.32950i	−1.60724	+	0.584988i	−0.980892	−	0.194553i	$-0.937674\pi$
$83$	−14.6427	+	5.32950i	−1.60724	+	0.584988i	−0.626351	+	0.779542i	$0.715452\pi$
$84$		0			0
$85$	−9.24557	+	16.0138i	−1.00282	+	1.73694i
$86$		0			0
$87$	−3.38559	−	1.23226i	−0.362974	−	0.132112i
$88$		0			0
$89$	8.40074	+	7.04906i	0.890476	+	0.747198i	0.968306	−	0.249768i	$-0.0803545\pi$
$89$	8.40074	+	7.04906i	0.890476	+	0.747198i	−0.0778293	+	0.996967i	$0.524799\pi$
$90$		0			0
$91$	−19.6697	+	7.15918i	−2.06194	+	0.750486i
$92$		0			0
$93$	0.200168	+	1.13521i	0.0207565	+	0.117716i
$94$		0			0
$95$	9.04122	+	7.58649i	0.927610	+	0.778357i
$96$		0			0
$97$	0.354561	+	0.614118i	0.0360002	+	0.0623542i	0.883464	−	0.468499i	$-0.155205\pi$
$97$	0.354561	+	0.614118i	0.0360002	+	0.0623542i	−0.847464	+	0.530853i	$0.821872\pi$
$98$		0			0
$99$	−0.985745	+	5.59044i	−0.0990711	+	0.561860i
$100$		0			0
$101$	−7.31910	−	12.6770i	−0.728277	−	1.26141i	−0.957611	−	0.288066i	$-0.906988\pi$
$101$	−7.31910	−	12.6770i	−0.728277	−	1.26141i	0.229333	−	0.973348i	$-0.426345\pi$
$102$		0			0
$103$	4.62687	−	8.01398i	0.455899	−	0.789641i	−0.542840	−	0.839836i	$-0.682651\pi$
$103$	4.62687	−	8.01398i	0.455899	−	0.789641i	0.998739	+	0.0501954i	$0.0159844\pi$
$104$		0			0
$105$	−17.8614			−1.74309
$106$		0			0
$107$	−12.3325	−	4.48867i	−1.19223	−	0.433936i	−0.331724	−	0.943377i	$-0.607630\pi$
$107$	−12.3325	−	4.48867i	−1.19223	−	0.433936i	−0.860506	+	0.509440i	$0.829852\pi$
$108$		0			0
$109$	−3.29924	+	18.7109i	−0.316010	+	1.79218i	0.250489	+	0.968119i	$0.419409\pi$
$109$	−3.29924	+	18.7109i	−0.316010	+	1.79218i	−0.566499	+	0.824062i	$0.691702\pi$
$110$		0			0
$111$	4.63800	+	3.93560i	0.440220	+	0.373550i
$112$		0			0
$113$	0.178090	−	1.01000i	0.0167533	−	0.0950125i	−0.975285	−	0.220952i	$-0.929084\pi$
$113$	0.178090	−	1.01000i	0.0167533	−	0.0950125i	0.992038	+	0.125940i	$0.0401946\pi$
$114$		0			0
$115$	−16.7842	−	6.10895i	−1.56513	−	0.569662i
$116$		0			0
$117$	4.22317			0.390432
$118$		0			0
$119$	12.7164	−	22.0255i	1.16571	−	2.01908i
$120$		0			0
$121$	−10.6123	−	18.3811i	−0.964758	−	1.67101i
$122$		0			0
$123$	−0.133222	+	0.755539i	−0.0120122	+	0.0681247i
$124$		0			0
$125$	5.38064	+	9.31954i	0.481259	+	0.833565i
$126$		0			0
$127$	5.17655	+	4.34364i	0.459344	+	0.385436i	0.842890	−	0.538086i	$-0.180853\pi$
$127$	5.17655	+	4.34364i	0.459344	+	0.385436i	−0.383545	+	0.923522i	$0.625297\pi$
$128$		0			0
$129$	0.191522	+	1.08617i	0.0168625	+	0.0956322i
$130$		0			0
$131$	6.31546	−	2.29864i	0.551784	−	0.200833i	−0.0510547	−	0.998696i	$-0.516258\pi$
$131$	6.31546	−	2.29864i	0.551784	−	0.200833i	0.602839	+	0.797863i	$0.294036\pi$
$132$		0			0
$133$	−12.4354	−	10.4345i	−1.07828	−	0.904788i
$134$		0			0
$135$	3.38631	+	1.23252i	0.291448	+	0.106078i
$136$		0			0
$137$	4.59867	−	7.96512i	0.392890	−	0.680506i	−0.599939	−	0.800046i	$-0.704808\pi$
$137$	4.59867	−	7.96512i	0.392890	−	0.680506i	0.992829	+	0.119539i	$0.0381418\pi$
$138$		0			0
$139$	7.85332	−	2.85838i	0.666110	−	0.242444i	0.0132379	−	0.999912i	$-0.495786\pi$
$139$	7.85332	−	2.85838i	0.666110	−	0.242444i	0.652872	+	0.757468i	$0.273564\pi$
$140$		0			0
$141$	−3.22763	+	2.70830i	−0.271815	+	0.228080i
$142$		0			0
$143$	−18.3648	+	15.4099i	−1.53574	+	1.28864i
$144$		0			0
$145$	−2.25455	−	12.7862i	−0.187231	−	1.06184i
$146$		0			0
$147$	17.5667			1.44888
$148$		0			0
$149$	−10.3072			−0.844400			−0.422200	−	0.906503i	$-0.638742\pi$
$149$	−10.3072			−0.844400			−0.422200	+	0.906503i	$0.638742\pi$
$150$		0			0
$151$	2.76498	+	15.6810i	0.225011	+	1.27610i	0.862665	+	0.505776i	$0.168794\pi$
$151$	2.76498	+	15.6810i	0.225011	+	1.27610i	−0.637655	+	0.770322i	$0.720095\pi$
$152$		0			0
$153$	−3.93076	+	3.29830i	−0.317783	+	0.266651i
$154$		0			0
$155$	−3.18215	+	2.67014i	−0.255597	+	0.214471i
$156$		0			0
$157$	4.00595	−	1.45805i	0.319710	−	0.116365i	−0.177180	−	0.984178i	$-0.556698\pi$
$157$	4.00595	−	1.45805i	0.319710	−	0.116365i	0.496890	+	0.867814i	$0.334475\pi$
$158$		0			0
$159$	−5.41983	+	9.38743i	−0.429821	+	0.744471i
$160$		0			0
$161$	23.0851	+	8.40230i	1.81936	+	0.662194i
$162$		0			0
$163$	8.84145	+	7.41886i	0.692516	+	0.581090i	0.919634	−	0.392778i	$-0.128486\pi$
$163$	8.84145	+	7.41886i	0.692516	+	0.581090i	−0.227118	+	0.973867i	$0.572930\pi$
$164$		0			0
$165$	−19.2230	+	6.99661i	−1.49651	+	0.544685i
$166$		0			0
$167$	−0.329248	−	1.86726i	−0.0254780	−	0.144493i	0.969415	−	0.245427i	$-0.0789281\pi$
$167$	−0.329248	−	1.86726i	−0.0254780	−	0.144493i	−0.994893	+	0.100934i	$0.967817\pi$
$168$		0			0
$169$	3.70394	+	3.10798i	0.284919	+	0.239075i
$170$		0			0
$171$	1.63758	+	2.83637i	0.125229	+	0.216902i
$172$		0			0
$173$	−0.639830	+	3.62866i	−0.0486454	+	0.275882i	−0.999422	−	0.0339954i	$-0.989177\pi$
$173$	−0.639830	+	3.62866i	−0.0486454	+	0.275882i	0.950777	+	0.309877i	$0.100288\pi$
$174$		0			0
$175$	−19.7918	−	34.2804i	−1.49612	−	2.59135i
$176$		0			0
$177$	1.05797	−	1.83246i	0.0795219	−	0.137736i
$178$		0			0
$179$	8.11540			0.606574			0.303287	−	0.952899i	$-0.401916\pi$
$179$	8.11540			0.606574			0.303287	+	0.952899i	$0.401916\pi$
$180$		0			0
$181$	3.31816	+	1.20771i	0.246637	+	0.0897684i	0.462380	−	0.886682i	$-0.346995\pi$
$181$	3.31816	+	1.20771i	0.246637	+	0.0897684i	−0.215744	+	0.976450i	$0.569218\pi$
$182$		0			0
$183$	−0.451233	+	2.55907i	−0.0333561	+	0.189172i
$184$		0			0
$185$	−3.92553	+	21.5657i	−0.288611	+	1.58554i
$186$		0			0
$187$	5.05809	−	28.6859i	0.369884	−	2.09772i
$188$		0			0
$189$	−4.65757	−	1.69522i	−0.338788	−	0.123309i
$190$		0			0
$191$	−13.3234			−0.964048			−0.482024	−	0.876158i	$-0.660098\pi$
$191$	−13.3234			−0.964048			−0.482024	+	0.876158i	$0.660098\pi$
$192$		0			0
$193$	1.44888	−	2.50954i	0.104293	−	0.180641i	−0.809156	−	0.587594i	$-0.800075\pi$
$193$	1.44888	−	2.50954i	0.104293	−	0.180641i	0.913449	+	0.406953i	$0.133409\pi$
$194$		0			0
$195$	7.60939	+	13.1799i	0.544920	+	0.943829i
$196$		0			0
$197$	−1.08560	+	6.15676i	−0.0773460	+	0.438651i	0.921401	+	0.388612i	$0.127045\pi$
$197$	−1.08560	+	6.15676i	−0.0773460	+	0.438651i	−0.998747	+	0.0500384i	$0.984066\pi$
$198$		0			0
$199$	5.43467	+	9.41312i	0.385254	+	0.667279i	0.991804	−	0.127766i	$-0.0407807\pi$
$199$	5.43467	+	9.41312i	0.385254	+	0.667279i	−0.606551	+	0.795045i	$0.707447\pi$
$200$		0			0
$201$	6.19508	+	5.19829i	0.436967	+	0.366659i
$202$		0			0
$203$	3.10093	+	17.5863i	0.217643	+	1.23431i
$204$		0			0
$205$	−2.59796	+	0.945581i	−0.181450	+	0.0660422i
$206$		0			0
$207$	−3.79688	−	3.18596i	−0.263902	−	0.221440i
$208$		0			0
$209$	−17.4708	−	6.35884i	−1.20848	−	0.439850i
$210$		0			0
$211$	8.23255	−	14.2592i	0.566752	−	0.981644i	−0.430132	−	0.902766i	$-0.641533\pi$
$211$	8.23255	−	14.2592i	0.566752	−	0.981644i	0.996884	−	0.0788779i	$-0.0251337\pi$
$212$		0			0
$213$	4.99858	−	1.81933i	0.342497	−	0.124659i
$214$		0			0
$215$	−3.04469	+	2.55480i	−0.207646	+	0.174236i
$216$		0			0
$217$	4.37676	−	3.67254i	0.297114	−	0.249308i
$218$		0			0
$219$	−2.16331	−	12.2687i	−0.146183	−	0.829043i
$220$		0			0
$221$	−21.6701			−1.45769
$222$		0			0
$223$	−23.2841			−1.55922			−0.779608	−	0.626268i	$-0.784582\pi$
$223$	−23.2841			−1.55922			−0.779608	+	0.626268i	$0.784582\pi$
$224$		0			0
$225$	1.38679	+	7.86490i	0.0924529	+	0.524326i
$226$		0			0
$227$	−5.19178	+	4.35642i	−0.344591	+	0.289146i	−0.798614	−	0.601844i	$-0.794433\pi$
$227$	−5.19178	+	4.35642i	−0.344591	+	0.289146i	0.454023	+	0.890990i	$0.349988\pi$
$228$		0			0
$229$	−9.20691	+	7.72551i	−0.608410	+	0.510516i	−0.894136	−	0.447795i	$-0.852209\pi$
$229$	−9.20691	+	7.72551i	−0.608410	+	0.510516i	0.285727	+	0.958311i	$0.407765\pi$
$230$		0			0
$231$	26.4395	−	9.62319i	1.73959	−	0.633160i
$232$		0			0
$233$	9.18640	−	15.9113i	0.601821	−	1.04238i	−0.390724	−	0.920508i	$-0.627775\pi$
$233$	9.18640	−	15.9113i	0.601821	−	1.04238i	0.992545	−	0.121877i	$-0.0388913\pi$
$234$		0			0
$235$	−14.2678	−	5.19305i	−0.930728	−	0.338757i
$236$		0			0
$237$	7.81821	+	6.56026i	0.507847	+	0.426135i
$238$		0			0
$239$	−27.2477	+	9.91734i	−1.76250	+	0.641499i	−0.999985	−	0.00546571i	$-0.998260\pi$
$239$	−27.2477	+	9.91734i	−1.76250	+	0.641499i	−0.762520	+	0.646965i	$0.776038\pi$
$240$		0			0
$241$	0.532097	+	3.01767i	0.0342754	+	0.194385i	0.997138	−	0.0756077i	$-0.0240897\pi$
$241$	0.532097	+	3.01767i	0.0342754	+	0.194385i	−0.962862	+	0.269993i	$0.912979\pi$
$242$		0			0
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$		0			0
$245$	31.6520	+	54.8229i	2.02217	+	3.50251i
$246$		0			0
$247$	−2.40182	+	13.6214i	−0.152824	+	0.866709i
$248$		0			0
$249$	−7.79121	−	13.4948i	−0.493748	−	0.855196i
$250$		0			0
$251$	−7.34606	+	12.7238i	−0.463679	+	0.803116i	−0.999141	−	0.0414435i	$-0.986804\pi$
$251$	−7.34606	+	12.7238i	−0.463679	+	0.803116i	0.535462	+	0.844560i	$0.320138\pi$
$252$		0			0
$253$	28.1363			1.76892
$254$		0			0
$255$	−17.3760	−	6.32434i	−1.08813	−	0.396046i
$256$		0			0
$257$	−1.64854	+	9.34931i	−0.102833	+	0.583194i	0.889231	+	0.457458i	$0.151240\pi$
$257$	−1.64854	+	9.34931i	−0.102833	+	0.583194i	−0.992064	+	0.125735i	$0.959871\pi$
$258$		0			0
$259$	5.39921	−	29.6617i	0.335491	−	1.84309i
$260$		0			0
$261$	0.625633	−	3.54814i	0.0387257	−	0.219624i
$262$		0			0
$263$	19.6275	+	7.14381i	1.21028	+	0.440506i	0.866801	−	0.498654i	$-0.166172\pi$
$263$	19.6275	+	7.14381i	1.21028	+	0.440506i	0.343480	+	0.939160i	$0.388394\pi$
$264$		0			0
$265$	−39.0623			−2.39958
$266$		0			0
$267$	−5.48319	+	9.49717i	−0.335566	+	0.581217i
$268$		0			0
$269$	−6.57099	−	11.3813i	−0.400640	−	0.693929i	0.593163	−	0.805082i	$-0.297879\pi$
$269$	−6.57099	−	11.3813i	−0.400640	−	0.693929i	−0.993803	+	0.111153i	$0.964546\pi$
$270$		0			0
$271$	−4.25240	+	24.1166i	−0.258315	+	1.46498i	0.529102	+	0.848558i	$0.322529\pi$
$271$	−4.25240	+	24.1166i	−0.258315	+	1.46498i	−0.787417	+	0.616420i	$0.788582\pi$
$272$		0			0
$273$	−10.4660	−	18.1277i	−0.633433	−	1.09714i
$274$		0			0
$275$	−34.7288	−	29.1409i	−2.09423	−	1.75726i
$276$		0			0
$277$	−5.05180	−	28.6502i	−0.303533	−	1.72142i	−0.630330	−	0.776327i	$-0.717080\pi$
$277$	−5.05180	−	28.6502i	−0.303533	−	1.72142i	0.326797	−	0.945095i	$-0.394031\pi$
$278$		0			0
$279$	−1.08321	+	0.394255i	−0.0648499	+	0.0236034i
$280$		0			0
$281$	−21.4707	−	18.0160i	−1.28083	−	1.07475i	−0.993129	−	0.117027i	$-0.962664\pi$
$281$	−21.4707	−	18.0160i	−1.28083	−	1.07475i	−0.287704	−	0.957719i	$-0.592892\pi$
$282$		0			0
$283$	13.7413	+	5.00143i	0.816836	+	0.297304i	0.716445	−	0.697644i	$-0.245768\pi$
$283$	13.7413	+	5.00143i	0.816836	+	0.297304i	0.100392	+	0.994948i	$0.467990\pi$
$284$		0			0
$285$	−5.90124	+	10.2212i	−0.349559	+	0.605454i
$286$		0			0
$287$	3.57326	−	1.30056i	0.210923	−	0.0767696i
$288$		0			0
$289$	7.14689	−	5.99695i	0.420405	−	0.352762i
$290$		0			0
$291$	−0.543219	+	0.455815i	−0.0318441	+	0.0267204i
$292$		0			0
$293$	−0.941072	−	5.33708i	−0.0549780	−	0.311796i	0.944901	−	0.327356i	$-0.106158\pi$
$293$	−0.941072	−	5.33708i	−0.0549780	−	0.311796i	−0.999879	+	0.0155607i	$0.995047\pi$
$294$		0			0
$295$	7.62509			0.443950
$296$		0			0
$297$	−5.67668			−0.329394
$298$		0			0
$299$	−3.63481	−	20.6140i	−0.210207	−	1.19214i
$300$		0			0
$301$	4.18769	−	3.51389i	0.241375	−	0.202537i
$302$		0			0
$303$	11.2135	−	9.40925i	0.644199	−	0.540547i
$304$		0			0
$305$	−8.79949	+	3.20275i	−0.503857	+	0.183389i
$306$		0			0
$307$	−10.6785	+	18.4958i	−0.609457	+	1.05561i	0.381873	+	0.924215i	$0.375279\pi$
$307$	−10.6785	+	18.4958i	−0.609457	+	1.05561i	−0.991330	+	0.131396i	$0.958054\pi$
$308$		0			0
$309$	8.69567	+	3.16497i	0.494680	+	0.180049i
$310$		0			0
$311$	−10.5070	−	8.81643i	−0.595798	−	0.499934i	0.294294	−	0.955715i	$-0.404916\pi$
$311$	−10.5070	−	8.81643i	−0.595798	−	0.499934i	−0.890092	+	0.455781i	$0.849360\pi$
$312$		0			0
$313$	−15.4958	+	5.64003i	−0.875877	+	0.318793i	−0.740545	−	0.672007i	$-0.765432\pi$
$313$	−15.4958	+	5.64003i	−0.875877	+	0.318793i	−0.135332	+	0.990800i	$0.543210\pi$
$314$		0			0
$315$	−3.10159	−	17.5900i	−0.174755	−	0.991085i
$316$		0			0
$317$	20.4677	+	17.1744i	1.14958	+	0.964613i	0.999710	−	0.0240930i	$-0.00766977\pi$
$317$	20.4677	+	17.1744i	1.14958	+	0.964613i	0.149871	+	0.988706i	$0.452114\pi$
$318$		0			0
$319$	10.2262	+	17.7123i	0.572556	+	0.991696i
$320$		0			0
$321$	2.27896	−	12.9246i	0.127199	−	0.721381i
$322$		0			0
$323$	−8.40280	−	14.5541i	−0.467544	−	0.809810i
$324$		0			0
$325$	−16.8636	+	29.2086i	−0.935423	+	1.62020i
$326$		0			0
$327$	−18.9996			−1.05068
$328$		0			0
$329$	19.6240	+	7.14257i	1.08191	+	0.393782i
$330$		0			0
$331$	−3.45571	+	19.5983i	−0.189943	+	1.07722i	0.729496	+	0.683986i	$0.239755\pi$
$331$	−3.45571	+	19.5983i	−0.189943	+	1.07722i	−0.919438	+	0.393234i	$0.871356\pi$
$332$		0			0
$333$	−3.07042	+	5.25095i	−0.168258	+	0.287750i
$334$		0			0
$335$	−5.06063	+	28.7003i	−0.276492	+	1.56806i
$336$		0			0
$337$	11.7796	+	4.28741i	0.641673	+	0.233550i	0.642304	−	0.766450i	$-0.277979\pi$
$337$	11.7796	+	4.28741i	0.641673	+	0.233550i	−0.000630994		1.00000i	$0.500201\pi$
$338$		0			0
$339$	1.02558			0.0557017
$340$		0			0
$341$	3.27182	−	5.66696i	0.177179	−	0.306883i
$342$		0			0
$343$	−26.1868	−	45.3568i	−1.41395	−	2.44904i
$344$		0			0
$345$	3.10159	−	17.5900i	0.166984	−	0.947015i
$346$		0			0
$347$	9.33602	+	16.1705i	0.501184	+	0.868076i	0.999999	+	0.00136771i	$0.000435356\pi$
$347$	9.33602	+	16.1705i	0.501184	+	0.868076i	−0.498815	+	0.866708i	$0.666231\pi$
$348$		0			0
$349$	14.8767	+	12.4830i	0.796332	+	0.668202i	0.947304	−	0.320336i	$-0.103796\pi$
$349$	14.8767	+	12.4830i	0.796332	+	0.668202i	−0.150972	+	0.988538i	$0.548240\pi$
$350$		0			0
$351$	0.733346	+	4.15901i	0.0391431	+	0.221991i
$352$		0			0
$353$	2.22037	−	0.808149i	0.118178	−	0.0430135i	−0.282254	−	0.959340i	$-0.591082\pi$
$353$	2.22037	−	0.808149i	0.118178	−	0.0430135i	0.400433	+	0.916326i	$0.368860\pi$
$354$		0			0
$355$	14.6844	+	12.3217i	0.779367	+	0.653966i
$356$		0			0
$357$	23.8991	+	8.69856i	1.26487	+	0.460376i
$358$		0			0
$359$	2.66085	−	4.60872i	0.140434	−	0.243239i	−0.787226	−	0.616665i	$-0.788483\pi$
$359$	2.66085	−	4.60872i	0.140434	−	0.243239i	0.927660	+	0.373425i	$0.121817\pi$
$360$		0			0
$361$	7.77442	−	2.82966i	0.409180	−	0.148929i
$362$		0			0
$363$	16.2590	−	13.6430i	0.853378	−	0.716069i
$364$		0			0
$365$	34.3909	−	28.8574i	1.80010	−	1.51046i
$366$		0			0
$367$	0.348423	+	1.97600i	0.0181875	+	0.103147i	0.992550	−	0.121837i	$-0.0388784\pi$
$367$	0.348423	+	1.97600i	0.0181875	+	0.103147i	−0.974363	+	0.224983i	$0.927767\pi$
$368$		0			0
$369$	−0.767194			−0.0399386
$370$		0			0
$371$	53.7266			2.78935
$372$		0			0
$373$	0.505379	+	2.86614i	0.0261675	+	0.148403i	0.995092	−	0.0989529i	$-0.0315493\pi$
$373$	0.505379	+	2.86614i	0.0261675	+	0.148403i	−0.968925	+	0.247356i	$0.920438\pi$
$374$		0			0
$375$	−8.24362	+	6.91722i	−0.425699	+	0.357204i
$376$		0			0
$377$	11.6558	−	9.78037i	0.600304	−	0.503714i
$378$		0			0
$379$	11.1665	−	4.06426i	0.573583	−	0.208767i	−0.0389107	−	0.999243i	$-0.512389\pi$
$379$	11.1665	−	4.06426i	0.573583	−	0.208767i	0.612493	+	0.790476i	$0.290167\pi$
$380$		0			0
$381$	−3.37875	+	5.85217i	−0.173099	+	0.299816i
$382$		0			0
$383$	−10.8389	−	3.94505i	−0.553844	−	0.201583i	0.0499095	−	0.998754i	$-0.484107\pi$
$383$	−10.8389	−	3.94505i	−0.553844	−	0.201583i	−0.603754	+	0.797171i	$0.706329\pi$
$384$		0			0
$385$	77.6717	+	65.1743i	3.95852	+	3.32159i
$386$		0			0
$387$	−1.03641	+	0.377224i	−0.0526839	+	0.0191754i
$388$		0			0
$389$	0.147333	+	0.835565i	0.00747006	+	0.0423648i	0.988315	−	0.152426i	$-0.0487084\pi$
$389$	0.147333	+	0.835565i	0.00747006	+	0.0423648i	−0.980845	+	0.194790i	$0.937597\pi$
$390$		0			0
$391$	19.4827	+	16.3479i	0.985283	+	0.826751i
$392$		0			0
$393$	3.36039	+	5.82036i	0.169509	+	0.293598i
$394$		0			0
$395$	−6.38653	+	36.2198i	−0.321341	+	1.82242i
$396$		0			0
$397$	14.7400	+	25.5304i	0.739778	+	1.28133i	0.952595	+	0.304242i	$0.0984030\pi$
$397$	14.7400	+	25.5304i	0.739778	+	1.28133i	−0.212816	+	0.977092i	$0.568264\pi$
$398$		0			0
$399$	8.11662	−	14.0584i	0.406339	−	0.703800i
$400$		0			0
$401$	16.1916			0.808568			0.404284	−	0.914634i	$-0.367521\pi$
$401$	16.1916			0.808568			0.404284	+	0.914634i	$0.367521\pi$
$402$		0			0
$403$	−4.57456	−	1.66500i	−0.227875	−	0.0829398i
$404$		0			0
$405$	−0.625766	+	3.54889i	−0.0310945	+	0.176346i
$406$		0			0
$407$	−5.80818	−	34.0379i	−0.287901	−	1.68720i
$408$		0			0
$409$	−1.89630	+	10.7545i	−0.0937661	+	0.531774i	0.901352	+	0.433086i	$0.142576\pi$
$409$	−1.89630	+	10.7545i	−0.0937661	+	0.531774i	−0.995118	+	0.0986875i	$0.968536\pi$
$410$		0			0
$411$	8.64266	+	3.14567i	0.426311	+	0.155165i
$412$		0			0
$413$	−10.4876			−0.516062
$414$		0			0
$415$	28.0767	−	48.6303i	1.37823	−	2.38717i
$416$		0			0
$417$	4.17866	+	7.23766i	0.204630	+	0.354430i
$418$		0			0
$419$	3.54292	−	20.0929i	0.173083	−	0.981601i	−0.767251	−	0.641347i	$-0.778376\pi$
$419$	3.54292	−	20.0929i	0.173083	−	0.981601i	0.940334	−	0.340254i	$-0.110513\pi$
$420$		0			0
$421$	1.17107	+	2.02834i	0.0570742	+	0.0988554i	0.893151	−	0.449757i	$-0.148490\pi$
$421$	1.17107	+	2.02834i	0.0570742	+	0.0988554i	−0.836077	+	0.548613i	$0.815156\pi$
$422$		0			0
$423$	−3.22763	−	2.70830i	−0.156933	−	0.131682i
$424$		0			0
$425$	−7.11597	−	40.3567i	−0.345175	−	1.95759i
$426$		0			0
$427$	12.1029	−	4.40509i	0.585700	−	0.213177i
$428$		0			0
$429$	−18.3648	−	15.4099i	−0.886662	−	0.743998i
$430$		0			0
$431$	29.0677	+	10.5798i	1.40014	+	0.509610i	0.928221	−	0.372030i	$-0.121338\pi$
$431$	29.0677	+	10.5798i	1.40014	+	0.509610i	0.471922	+	0.881640i	$0.343560\pi$
$432$		0			0
$433$	−14.4519	+	25.0314i	−0.694512	+	1.20293i	0.275833	+	0.961206i	$0.411046\pi$
$433$	−14.4519	+	25.0314i	−0.694512	+	1.20293i	−0.970345	+	0.241725i	$0.922287\pi$
$434$		0			0
$435$	12.2005	−	4.44061i	0.584968	−	0.212911i
$436$		0			0
$437$	12.4354	−	10.4345i	0.594865	−	0.499151i
$438$		0			0
$439$	−7.95754	+	6.67717i	−0.379793	+	0.318684i	−0.812621	−	0.582792i	$-0.801960\pi$
$439$	−7.95754	+	6.67717i	−0.379793	+	0.318684i	0.432828	+	0.901476i	$0.357516\pi$
$440$		0			0
$441$	3.05042	+	17.2998i	0.145258	+	0.823800i
$442$		0			0
$443$	31.5669			1.49979			0.749894	−	0.661558i	$-0.230105\pi$
$443$	31.5669			1.49979			0.749894	+	0.661558i	$0.230105\pi$
$444$		0			0
$445$	−39.5189			−1.87338
$446$		0			0
$447$	−1.78983	−	10.1506i	−0.0846560	−	0.480108i
$448$		0			0
$449$	−19.3078	+	16.2011i	−0.911190	+	0.764579i	−0.972345	−	0.233549i	$-0.924966\pi$
$449$	−19.3078	+	16.2011i	−0.911190	+	0.764579i	0.0611551	+	0.998128i	$0.480522\pi$
$450$		0			0
$451$	3.33621	−	2.79941i	0.157096	−	0.131819i
$452$		0			0
$453$	−14.9626	+	5.44594i	−0.703004	+	0.255873i
$454$		0			0
$455$	37.7158	−	65.3257i	1.76814	−	3.06251i
$456$		0			0
$457$	−30.0185	−	10.9258i	−1.40421	−	0.511089i	−0.474782	−	0.880103i	$-0.657473\pi$
$457$	−30.0185	−	10.9258i	−1.40421	−	0.511089i	−0.929424	+	0.369014i	$0.879695\pi$
$458$		0			0
$459$	−3.93076	−	3.29830i	−0.183472	−	0.153951i
$460$		0			0
$461$	−21.8038	+	7.93594i	−1.01551	+	0.369614i	−0.795545	−	0.605895i	$-0.792815\pi$
$461$	−21.8038	+	7.93594i	−1.01551	+	0.369614i	−0.219961	+	0.975509i	$0.570593\pi$
$462$		0			0
$463$	−4.30235	−	24.3998i	−0.199947	−	1.13396i	−0.905195	−	0.424996i	$-0.860276\pi$
$463$	−4.30235	−	24.3998i	−0.199947	−	1.13396i	0.705248	−	0.708960i	$-0.250835\pi$
$464$		0			0
$465$	−3.18215	−	2.67014i	−0.147569	−	0.123825i
$466$		0			0
$467$	−14.5460	−	25.1944i	−0.673108	−	1.16586i	−0.977018	−	0.213157i	$-0.931625\pi$
$467$	−14.5460	−	25.1944i	−0.673108	−	1.16586i	0.303909	−	0.952701i	$-0.401708\pi$
$468$		0			0
$469$	6.96043	−	39.4746i	0.321403	−	1.82277i
$470$		0			0
$471$	2.13152	+	3.69190i	0.0982153	+	0.170114i
$472$		0			0
$473$	3.13049	−	5.42216i	0.143940	−	0.249311i
$474$		0			0
$475$	−26.1561			−1.20012
$476$		0			0
$477$	−10.1860	−	3.70738i	−0.466383	−	0.169749i
$478$		0			0
$479$	−6.64362	+	37.6779i	−0.303555	+	1.72155i	0.326675	+	0.945137i	$0.394072\pi$
$479$	−6.64362	+	37.6779i	−0.303555	+	1.72155i	−0.630230	+	0.776409i	$0.717039\pi$
$480$		0			0
$481$	−24.1875	+	8.65256i	−1.10285	+	0.394523i
$482$		0			0
$483$	−4.26596	+	24.1935i	−0.194108	+	1.10084i
$484$		0			0
$485$	−2.40131	−	0.874006i	−0.109038	−	0.0396866i
$486$		0			0
$487$	−3.93496			−0.178310			−0.0891550	−	0.996018i	$-0.528417\pi$
$487$	−3.93496			−0.178310			−0.0891550	+	0.996018i	$0.528417\pi$
$488$		0			0
$489$	−5.77085	+	9.99540i	−0.260967	+	0.452008i
$490$		0			0
$491$	−4.08824	−	7.08104i	−0.184500	−	0.319563i	0.758908	−	0.651198i	$-0.225733\pi$
$491$	−4.08824	−	7.08104i	−0.184500	−	0.319563i	−0.943408	+	0.331635i	$0.892400\pi$
$492$		0			0
$493$	−3.21027	+	18.2063i	−0.144583	+	0.819973i
$494$		0			0
$495$	−10.2284	−	17.7160i	−0.459730	−	0.796276i
$496$		0			0
$497$	−20.1971	−	16.9473i	−0.905962	−	0.760192i
$498$		0			0
$499$	3.02698	+	17.1669i	0.135506	+	0.768494i	0.974506	+	0.224362i	$0.0720298\pi$
$499$	3.02698	+	17.1669i	0.135506	+	0.768494i	−0.839000	+	0.544132i	$0.816859\pi$
$500$		0			0
$501$	1.78172	−	0.648492i	0.0796013	−	0.0289725i
$502$		0			0
$503$	−19.7713	−	16.5901i	−0.881560	−	0.739717i	0.0849393	−	0.996386i	$-0.472930\pi$
$503$	−19.7713	−	16.5901i	−0.881560	−	0.739717i	−0.966499	+	0.256670i	$0.917375\pi$
$504$		0			0
$505$	49.5695	+	18.0418i	2.20582	+	0.802851i
$506$		0			0
$507$	−2.41758	+	4.18737i	−0.107368	+	0.185967i
$508$		0			0
$509$	10.4554	−	3.80547i	0.463429	−	0.168674i	−0.0997446	−	0.995013i	$-0.531803\pi$
$509$	10.4554	−	3.80547i	0.463429	−	0.168674i	0.563173	+	0.826339i	$0.309580\pi$
$510$		0			0
$511$	−47.3015	+	39.6907i	−2.09249	+	1.75581i
$512$		0			0
$513$	−2.50891	+	2.10523i	−0.110771	+	0.0929481i
$514$		0			0
$515$	5.79067	+	32.8405i	0.255168	+	1.44713i
$516$		0			0
$517$	23.9179			1.05191
$518$		0			0
$519$	−3.68464			−0.161738
$520$		0			0
$521$	−0.120087	−	0.681048i	−0.00526111	−	0.0298373i	0.982064	−	0.188547i	$-0.0603777\pi$
$521$	−0.120087	−	0.681048i	−0.00526111	−	0.0298373i	−0.987325	+	0.158710i	$0.949267\pi$
$522$		0			0
$523$	11.3798	−	9.54880i	0.497605	−	0.417540i	−0.359138	−	0.933285i	$-0.616929\pi$
$523$	11.3798	−	9.54880i	0.497605	−	0.417540i	0.856742	+	0.515745i	$0.172485\pi$
$524$		0			0
$525$	30.3228	−	25.4438i	1.32339	−	1.11046i
$526$		0			0
$527$	5.55819	−	2.02302i	0.242119	−	0.0881239i
$528$		0			0
$529$	−0.783342	+	1.35679i	−0.0340584	+	0.0589908i
$530$		0			0
$531$	1.98833	+	0.723694i	0.0862863	+	0.0314057i
$532$		0			0
$533$	−2.48198	−	2.08263i	−0.107506	−	0.0902086i
$534$		0			0
$535$	44.4420	−	16.1756i	1.92139	−	0.699330i
$536$		0			0
$537$	1.40922	+	7.99211i	0.0608125	+	0.344885i
$538$		0			0
$539$	−76.3903	−	64.0990i	−3.29036	−	2.76094i
$540$		0			0
$541$	−16.2771	−	28.1928i	−0.699809	−	1.21210i	−0.968533	−	0.248887i	$-0.919935\pi$
$541$	−16.2771	−	28.1928i	−0.699809	−	1.21210i	0.268724	−	0.963217i	$-0.413398\pi$
$542$		0			0
$543$	−0.613170	+	3.47746i	−0.0263137	+	0.149232i
$544$		0			0
$545$	−34.2338	−	59.2947i	−1.46642	−	2.53991i
$546$		0			0
$547$	19.9329	−	34.5248i	0.852269	−	1.47617i	−0.0268862	−	0.999639i	$-0.508559\pi$
$547$	19.9329	−	34.5248i	0.852269	−	1.47617i	0.879155	−	0.476535i	$-0.158108\pi$
$548$		0			0
$549$	−2.59854			−0.110903
$550$		0			0
$551$	11.0883	+	4.03583i	0.472379	+	0.171932i
$552$		0			0
$553$	8.78409	−	49.8171i	0.373538	−	2.11844i
$554$		0			0
$555$	−21.9198	−	0.121044i	−0.930442	−	0.00513803i
$556$		0			0
$557$	−6.63437	+	37.6254i	−0.281107	+	1.59424i	0.437760	+	0.899092i	$0.355772\pi$
$557$	−6.63437	+	37.6254i	−0.281107	+	1.59424i	−0.718867	+	0.695148i	$0.755339\pi$
$558$		0			0
$559$	−4.37695	−	1.59308i	−0.185125	−	0.0673802i
$560$		0			0
$561$	29.1284			1.22980
$562$		0			0
$563$	−17.7352	+	30.7182i	−0.747449	+	1.29462i	0.201593	+	0.979469i	$0.435388\pi$
$563$	−17.7352	+	30.7182i	−0.747449	+	1.29462i	−0.949042	+	0.315150i	$0.897945\pi$
$564$		0			0
$565$	1.84791	+	3.20067i	0.0777420	+	0.134653i
$566$		0			0
$567$	0.860684	−	4.88118i	0.0361453	−	0.204990i
$568$		0			0
$569$	6.80107	+	11.7798i	0.285116	+	0.493835i	0.972637	−	0.232329i	$-0.0746347\pi$
$569$	6.80107	+	11.7798i	0.285116	+	0.493835i	−0.687522	+	0.726164i	$0.741301\pi$
$570$		0			0
$571$	18.5217	+	15.5415i	0.775108	+	0.650393i	0.942012	−	0.335580i	$-0.108932\pi$
$571$	18.5217	+	15.5415i	0.775108	+	0.650393i	−0.166903	+	0.985973i	$0.553377\pi$
$572$		0			0
$573$	−2.31358	−	13.1210i	−0.0966514	−	0.548137i
$574$		0			0
$575$	37.1964	−	13.5384i	1.55120	−	0.564589i
$576$		0			0
$577$	−15.4667	−	12.9781i	−0.643885	−	0.540284i	0.261323	−	0.965251i	$-0.415841\pi$
$577$	−15.4667	−	12.9781i	−0.643885	−	0.540284i	−0.905209	+	0.424968i	$0.860286\pi$
$578$		0			0
$579$	2.72301	+	0.991094i	0.113164	+	0.0411885i
$580$		0			0
$581$	−38.6169	+	66.8865i	−1.60210	+	2.77492i
$582$		0			0
$583$	57.8224	−	21.0456i	2.39476	−	0.871621i
$584$		0			0
$585$	−11.6583	+	9.78244i	−0.482010	+	0.404454i
$586$		0			0
$587$	−9.58512	+	8.04287i	−0.395620	+	0.331965i	−0.818798	−	0.574082i	$-0.805359\pi$
$587$	−9.58512	+	8.04287i	−0.395620	+	0.331965i	0.423178	+	0.906047i	$0.360915\pi$
$588$		0			0
$589$	−0.655583	−	3.71799i	−0.0270128	−	0.153197i
$590$		0			0
$591$	−6.25173			−0.257162
$592$		0			0
$593$	25.4114			1.04352			0.521760	−	0.853092i	$-0.325276\pi$
$593$	25.4114			1.04352			0.521760	+	0.853092i	$0.325276\pi$
$594$		0			0
$595$	15.9150	+	90.2585i	0.652452	+	3.70024i
$596$		0			0
$597$	−8.32640	+	6.98668i	−0.340777	+	0.285946i
$598$		0			0
$599$	−8.98951	+	7.54309i	−0.367301	+	0.308202i	−0.807693	−	0.589603i	$-0.799284\pi$
$599$	−8.98951	+	7.54309i	−0.367301	+	0.308202i	0.440392	+	0.897806i	$0.354840\pi$
$600$		0			0
$601$	41.8889	−	15.2463i	1.70868	−	0.621910i	0.711918	−	0.702263i	$-0.247827\pi$
$601$	41.8889	−	15.2463i	1.70868	−	0.621910i	0.996766	+	0.0803528i	$0.0256047\pi$
$602$		0			0
$603$	−4.04355	+	7.00363i	−0.164666	+	0.285210i
$604$		0			0
$605$	71.8734	+	26.1598i	2.92207	+	1.06355i
$606$		0			0
$607$	25.9712	+	21.7924i	1.05414	+	0.884526i	0.993523	−	0.113635i	$-0.0362494\pi$
$607$	25.9712	+	21.7924i	1.05414	+	0.884526i	0.0606150	+	0.998161i	$0.480694\pi$
$608$		0			0
$609$	−16.7806	+	6.10765i	−0.679985	+	0.247494i
$610$		0			0
$611$	−3.08985	−	17.5234i	−0.125002	−	0.708922i
$612$		0			0
$613$	−11.1746	−	9.37662i	−0.451339	−	0.378718i	0.388594	−	0.921409i	$-0.372961\pi$
$613$	−11.1746	−	9.37662i	−0.451339	−	0.378718i	−0.839932	+	0.542691i	$0.817405\pi$
$614$		0			0
$615$	−1.38235	−	2.39429i	−0.0557416	−	0.0965473i
$616$		0			0
$617$	−3.35433	+	19.0234i	−0.135040	+	0.765852i	0.839791	+	0.542909i	$0.182677\pi$
$617$	−3.35433	+	19.0234i	−0.135040	+	0.765852i	−0.974832	+	0.222942i	$0.928434\pi$
$618$		0			0
$619$	10.5345	+	18.2463i	0.423417	+	0.733379i	0.996271	−	0.0862780i	$-0.0274973\pi$
$619$	10.5345	+	18.2463i	0.423417	+	0.733379i	−0.572855	+	0.819657i	$0.694164\pi$
$620$		0			0
$621$	2.47824	−	4.29244i	0.0994483	−	0.172250i
$622$		0			0
$623$	54.3546			2.17767
$624$		0			0
$625$	1.08191	+	0.393783i	0.0432764	+	0.0157513i
$626$		0			0
$627$	3.22847	−	18.3095i	0.128933	−	0.731213i
$628$		0			0
$629$	15.7551	−	26.9439i	0.628196	−	1.07432i
$630$		0			0
$631$	−3.93480	+	22.3154i	−0.156642	+	0.888361i	0.800627	+	0.599163i	$0.204500\pi$
$631$	−3.93480	+	22.3154i	−0.156642	+	0.888361i	−0.957269	+	0.289198i	$0.906611\pi$
$632$		0			0
$633$	15.4721	+	5.63140i	0.614962	+	0.223828i
$634$		0			0
$635$	−24.3516			−0.966364
$636$		0			0
$637$	−37.0935	+	64.2479i	−1.46970	+	2.54559i
$638$		0			0
$639$	2.65969	+	4.60671i	0.105216	+	0.182239i
$640$		0			0
$641$	−5.24493	+	29.7455i	−0.207162	+	1.17487i	0.686839	+	0.726810i	$0.258998\pi$
$641$	−5.24493	+	29.7455i	−0.207162	+	1.17487i	−0.894001	+	0.448065i	$0.852113\pi$
$642$		0			0
$643$	3.97082	+	6.87766i	0.156594	+	0.271229i	0.933638	−	0.358217i	$-0.116615\pi$
$643$	3.97082	+	6.87766i	0.156594	+	0.271229i	−0.777044	+	0.629446i	$0.783282\pi$
$644$		0			0
$645$	−3.04469	−	2.55480i	−0.119885	−	0.100595i
$646$		0			0
$647$	0.666589	+	3.78041i	0.0262063	+	0.148623i	0.995103	−	0.0988414i	$-0.0315136\pi$
$647$	0.666589	+	3.78041i	0.0262063	+	0.148623i	−0.968897	+	0.247465i	$0.920403\pi$
$648$		0			0
$649$	−11.2871	+	4.10818i	−0.443059	+	0.161260i
$650$		0			0
$651$	4.37676	+	3.67254i	0.171539	+	0.143938i
$652$		0			0
$653$	−27.8957	−	10.1532i	−1.09164	−	0.397325i	−0.267413	−	0.963582i	$-0.586169\pi$
$653$	−27.8957	−	10.1532i	−1.09164	−	0.397325i	−0.824229	+	0.566257i	$0.808391\pi$
$654$		0			0
$655$	−12.1096	+	20.9745i	−0.473162	+	0.819541i
$656$		0			0
$657$	11.7067	−	4.26088i	0.456721	−	0.166233i
$658$		0			0
$659$	−8.32492	+	6.98544i	−0.324293	+	0.272114i	−0.790370	−	0.612630i	$-0.790112\pi$
$659$	−8.32492	+	6.98544i	−0.324293	+	0.272114i	0.466077	+	0.884744i	$0.345667\pi$
$660$		0			0
$661$	−19.5700	+	16.4212i	−0.761187	+	0.638711i	−0.938435	−	0.345455i	$-0.887725\pi$
$661$	−19.5700	+	16.4212i	−0.761187	+	0.638711i	0.177249	+	0.984166i	$0.443280\pi$
$662$		0			0
$663$	−3.76297	−	21.3409i	−0.146142	−	0.828811i
$664$		0			0
$665$	58.4987			2.26848
$666$		0			0
$667$	−17.8576			−0.691448
$668$		0			0
$669$	−4.04324	−	22.9303i	−0.156321	−	0.886538i
$670$		0			0
$671$	11.3000	−	9.48183i	0.436232	−	0.366042i
$672$		0			0
$673$	−3.90713	+	3.27847i	−0.150609	+	0.126376i	−0.714979	−	0.699146i	$-0.753564\pi$
$673$	−3.90713	+	3.27847i	−0.150609	+	0.126376i	0.564370	+	0.825522i	$0.309119\pi$
$674$		0			0
$675$	−7.50460	+	2.73145i	−0.288852	+	0.105134i
$676$		0			0
$677$	10.9348	−	18.9397i	0.420260	−	0.727912i	−0.575704	−	0.817658i	$-0.695272\pi$
$677$	10.9348	−	18.9397i	0.420260	−	0.727912i	0.995965	+	0.0897458i	$0.0286055\pi$
$678$		0			0
$679$	3.30278	+	1.20212i	0.126749	+	0.0461329i
$680$		0			0
$681$	−5.19178	−	4.35642i	−0.198949	−	0.166938i
$682$		0			0
$683$	32.1067	−	11.6859i	1.22853	−	0.447148i	0.355435	−	0.934701i	$-0.384333\pi$
$683$	32.1067	−	11.6859i	1.22853	−	0.447148i	0.873093	+	0.487554i	$0.162111\pi$
$684$		0			0
$685$	5.75537	+	32.6403i	0.219901	+	1.24712i
$686$		0			0
$687$	−9.20691	−	7.72551i	−0.351265	−	0.294747i
$688$		0			0
$689$	−22.8889	−	39.6447i	−0.871997	−	1.51034i
$690$		0			0
$691$	−7.35997	+	41.7404i	−0.279986	+	1.58788i	0.442677	+	0.896681i	$0.354029\pi$
$691$	−7.35997	+	41.7404i	−0.279986	+	1.58788i	−0.722663	+	0.691200i	$0.757082\pi$
$692$		0			0
$693$	14.0682	+	24.3668i	0.534405	+	0.925617i
$694$		0			0
$695$	−15.0584	+	26.0819i	−0.571198	+	0.989344i
$696$		0			0
$697$	3.93666			0.149112
$698$		0			0
$699$	17.2648	+	6.28387i	0.653014	+	0.237678i
$700$		0			0
$701$	−3.24563	+	18.4069i	−0.122586	+	0.695217i	0.860127	+	0.510080i	$0.170384\pi$
$701$	−3.24563	+	18.4069i	−0.122586	+	0.695217i	−0.982713	+	0.185137i	$0.940727\pi$
$702$		0			0
$703$	−15.1902	−	12.8897i	−0.572908	−	0.486144i
$704$		0			0
$705$	2.63658	−	14.9528i	0.0992994	−	0.563155i
$706$		0			0
$707$	−68.1784	−	24.8149i	−2.56411	−	0.933260i
$708$		0			0
$709$	−23.4708			−0.881463			−0.440732	−	0.897639i	$-0.645281\pi$
$709$	−23.4708			−0.881463			−0.440732	+	0.897639i	$0.645281\pi$
$710$		0			0
$711$	−5.10297	+	8.83861i	−0.191377	+	0.331474i
$712$		0			0
$713$	2.85673	+	4.94800i	0.106985	+	0.185304i
$714$		0			0
$715$	15.0018	−	85.0796i	0.561037	−	3.18180i
$716$		0			0
$717$	−14.4982	−	25.1116i	−0.541444	−	0.937809i
$718$		0			0
$719$	18.5601	+	15.5738i	0.692176	+	0.580804i	0.919536	−	0.393006i	$-0.128565\pi$
$719$	18.5601	+	15.5738i	0.692176	+	0.580804i	−0.227360	+	0.973811i	$0.573009\pi$
$720$		0			0
$721$	−7.96454	−	45.1692i	−0.296615	−	1.68219i
$722$		0			0
$723$	−2.87943	+	1.04803i	−0.107087	+	0.0389765i
$724$		0			0
$725$	22.0417	+	18.4952i	0.818607	+	0.686893i
$726$		0			0
$727$	−38.0433	−	13.8466i	−1.41095	−	0.513543i	−0.479539	−	0.877521i	$-0.659196\pi$
$727$	−38.0433	−	13.8466i	−1.41095	−	0.513543i	−0.931408	+	0.363978i	$0.881418\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	5.31809	−	1.93563i	0.196697	−	0.0715917i
$732$		0			0
$733$	28.6737	−	24.0601i	1.05909	−	0.888681i	0.0650692	−	0.997881i	$-0.479273\pi$
$733$	28.6737	−	24.0601i	1.05909	−	0.888681i	0.994020	+	0.109200i	$0.0348287\pi$
$734$		0			0
$735$	−48.4937	+	40.6910i	−1.78872	+	1.50091i
$736$		0			0
$737$	−7.97182	−	45.2104i	−0.293646	−	1.66535i
$738$		0			0
$739$	4.21281			0.154971			0.0774854	−	0.996993i	$-0.475311\pi$
$739$	4.21281			0.154971			0.0774854	+	0.996993i	$0.475311\pi$
$740$		0			0
$741$	−13.8315			−0.508114
$742$		0			0
$743$	−2.72745	−	15.4681i	−0.100060	−	0.567471i	−0.993079	−	0.117450i	$-0.962528\pi$
$743$	−2.72745	−	15.4681i	−0.100060	−	0.567471i	0.893018	−	0.450020i	$-0.148583\pi$
$744$		0			0
$745$	28.4536	−	23.8754i	1.04246	−	0.874727i
$746$		0			0
$747$	11.9368	−	10.0162i	0.436745	−	0.366473i
$748$		0			0
$749$	−61.1259	+	22.2480i	−2.23349	+	0.812924i
$750$		0			0
$751$	−15.0497	+	26.0669i	−0.549173	+	0.951195i	0.449159	+	0.893452i	$0.351724\pi$
$751$	−15.0497	+	26.0669i	−0.549173	+	0.951195i	−0.998331	+	0.0577431i	$0.981610\pi$
$752$		0			0
$753$	−13.8061	−	5.02500i	−0.503122	−	0.183121i
$754$		0			0
$755$	−43.9558	−	36.8833i	−1.59972	−	1.34232i
$756$		0			0
$757$	31.0095	−	11.2865i	1.12706	−	0.410216i	0.289836	−	0.957076i	$-0.406399\pi$
$757$	31.0095	−	11.2865i	1.12706	−	0.410216i	0.837224	+	0.546860i	$0.184177\pi$
$758$		0			0
$759$	4.88582	+	27.7089i	0.177344	+	1.00577i
$760$		0			0
$761$	25.9004	+	21.7330i	0.938888	+	0.787821i	0.977391	−	0.211438i	$-0.0678146\pi$
$761$	25.9004	+	21.7330i	0.938888	+	0.787821i	−0.0385035	+	0.999258i	$0.512259\pi$
$762$		0			0
$763$	47.0855	+	81.5545i	1.70461	+	2.95247i
$764$		0			0
$765$	3.21095	−	18.2102i	0.116092	−	0.658392i
$766$		0			0
$767$	4.46799	+	7.73878i	0.161330	+	0.279431i
$768$		0			0
$769$	−25.1232	+	43.5146i	−0.905965	+	1.56918i	−0.0863490	+	0.996265i	$0.527520\pi$
$769$	−25.1232	+	43.5146i	−0.905965	+	1.56918i	−0.819616	+	0.572913i	$0.805813\pi$
$770$		0			0
$771$	−9.49354			−0.341901
$772$		0			0
$773$	−7.06402	−	2.57109i	−0.254075	−	0.0924758i	0.211843	−	0.977304i	$-0.432054\pi$
$773$	−7.06402	−	2.57109i	−0.254075	−	0.0924758i	−0.465918	+	0.884828i	$0.654276\pi$
$774$		0			0
$775$	1.59859	−	9.06605i	0.0574231	−	0.325662i
$776$		0			0
$777$	30.1486	+	0.166485i	1.08158	+	0.00597261i
$778$		0			0
$779$	0.436322	−	2.47451i	0.0156329	−	0.0886584i
$780$		0			0
$781$	−28.3753	−	10.3278i	−1.01535	−	0.369557i
$782$		0			0
$783$	3.60287			0.128756
$784$		0			0
$785$	−7.68124	+	13.3043i	−0.274155	+	0.474851i
$786$		0			0
$787$	−3.67779	−	6.37012i	−0.131099	−	0.227070i	0.793001	−	0.609220i	$-0.208517\pi$
$787$	−3.67779	−	6.37012i	−0.131099	−	0.227070i	−0.924101	+	0.382149i	$0.875184\pi$
$788$		0			0
$789$	−3.62701	+	20.5698i	−0.129125	+	0.732304i
$790$		0			0
$791$	−2.54163	−	4.40223i	−0.0903698	−	0.156525i
$792$		0			0
$793$	−8.40664	−	7.05401i	−0.298529	−	0.250495i
$794$		0			0
$795$	−6.78309	−	38.4688i	−0.240571	−	1.36435i
$796$		0			0
$797$	17.8513	−	6.49735i	0.632326	−	0.230148i	−0.00591741	−	0.999982i	$-0.501884\pi$
$797$	17.8513	−	6.49735i	0.632326	−	0.230148i	0.638243	+	0.769835i	$0.279661\pi$
$798$		0			0
$799$	16.5617	+	13.8969i	0.585912	+	0.491638i
$800$		0			0
$801$	−10.3050	−	3.75072i	−0.364110	−	0.132525i
$802$		0			0
$803$	−35.3600	+	61.2453i	−1.24783	+	2.16130i
$804$		0			0
$805$	−83.1905	+	30.2789i	−2.93208	+	1.06719i
$806$		0			0
$807$	10.0673	−	8.44750i	0.354387	−	0.297366i
$808$		0			0
$809$	−3.84588	+	3.22707i	−0.135214	+	0.113458i	−0.707886	−	0.706326i	$-0.750351\pi$
$809$	−3.84588	+	3.22707i	−0.135214	+	0.113458i	0.572673	+	0.819784i	$0.305907\pi$
$810$		0			0
$811$	−2.37636	−	13.4770i	−0.0834454	−	0.473242i	−0.997681	−	0.0680598i	$-0.978319\pi$
$811$	−2.37636	−	13.4770i	−0.0834454	−	0.473242i	0.914236	−	0.405182i	$-0.132792\pi$
$812$		0			0
$813$	−24.4886			−0.858853
$814$		0			0
$815$	−41.5921			−1.45691
$816$		0			0
$817$	−0.627263	−	3.55739i	−0.0219452	−	0.124457i
$818$		0			0
$819$	16.0349	−	13.4549i	0.560304	−	0.470151i
$820$		0			0
$821$	−34.5949	+	29.0286i	−1.20737	+	1.01310i	−0.207982	+	0.978133i	$0.566689\pi$
$821$	−34.5949	+	29.0286i	−1.20737	+	1.01310i	−0.999388	+	0.0349710i	$0.988866\pi$
$822$		0			0
$823$	−22.1429	+	8.05936i	−0.771853	+	0.280932i	−0.697771	−	0.716321i	$-0.745825\pi$
$823$	−22.1429	+	8.05936i	−0.771853	+	0.280932i	−0.0740817	+	0.997252i	$0.523603\pi$
$824$		0			0
$825$	22.6676	−	39.2615i	0.789185	−	1.36691i
$826$		0			0
$827$	15.5019	+	5.64224i	0.539055	+	0.196200i	0.597177	−	0.802109i	$-0.296289\pi$
$827$	15.5019	+	5.64224i	0.539055	+	0.196200i	−0.0581218	+	0.998309i	$0.518511\pi$
$828$		0			0
$829$	3.20000	+	2.68512i	0.111141	+	0.0932581i	0.696664	−	0.717397i	$-0.254667\pi$
$829$	3.20000	+	2.68512i	0.111141	+	0.0932581i	−0.585524	+	0.810655i	$0.699111\pi$
$830$		0			0
$831$	27.3377	−	9.95010i	0.948333	−	0.345165i
$832$		0			0
$833$	−15.6524	−	88.7694i	−0.542325	−	3.07568i
$834$		0			0
$835$	5.23418	+	4.39200i	0.181136	+	0.151991i
$836$		0			0
$837$	−0.576362	−	0.998288i	−0.0199220	−	0.0345059i
$838$		0			0
$839$	−4.56781	+	25.9053i	−0.157698	+	0.894351i	0.798579	+	0.601890i	$0.205585\pi$
$839$	−4.56781	+	25.9053i	−0.157698	+	0.894351i	−0.956277	+	0.292461i	$0.905526\pi$
$840$		0			0
$841$	8.00965	+	13.8731i	0.276195	+	0.478383i
$842$		0			0
$843$	14.0140	−	24.2729i	0.482667	−	0.836004i
$844$		0			0
$845$	−17.4242			−0.599409
$846$		0			0
$847$	−98.8553	−	35.9804i	−3.39671	−	1.23630i
$848$		0			0
$849$	−2.53929	+	14.4010i	−0.0871483	+	0.494242i
$850$		0			0
$851$	28.2735	+	10.4679i	0.969203	+	0.358834i
$852$		0			0
$853$	7.76759	−	44.0522i	0.265957	−	1.50832i	−0.500338	−	0.865830i	$-0.666791\pi$
$853$	7.76759	−	44.0522i	0.265957	−	1.50832i	0.766296	−	0.642488i	$-0.222098\pi$
$854$		0			0
$855$	−11.0907	−	4.03669i	−0.379294	−	0.138052i
$856$		0			0
$857$	−25.5651			−0.873286			−0.436643	−	0.899635i	$-0.643833\pi$
$857$	−25.5651			−0.873286			−0.436643	+	0.899635i	$0.643833\pi$
$858$		0			0
$859$	−16.1614	+	27.9924i	−0.551421	+	0.955088i	0.446752	+	0.894658i	$0.352581\pi$
$859$	−16.1614	+	27.9924i	−0.551421	+	0.955088i	−0.998172	+	0.0604304i	$0.980753\pi$
$860$		0			0
$861$	1.90129	+	3.29313i	0.0647958	+	0.112230i
$862$		0			0
$863$	−0.580581	+	3.29264i	−0.0197632	+	0.112083i	−0.993094	−	0.117325i	$-0.962568\pi$
$863$	−0.580581	+	3.29264i	−0.0197632	+	0.112083i	0.973330	+	0.229408i	$0.0736791\pi$
$864$		0			0
$865$	−6.63905	−	11.4992i	−0.225735	−	0.390984i
$866$		0			0
$867$	7.14689	+	5.99695i	0.242721	+	0.203667i
$868$		0			0
$869$	−10.0605	−	57.0557i	−0.341278	−	1.93548i
$870$		0			0
$871$	−32.0935	+	11.6811i	−1.08745	+	0.395798i
$872$		0			0
$873$	−0.543219	−	0.455815i	−0.0183852	−	0.0154270i
$874$		0			0
$875$	50.1214	+	18.2427i	1.69441	+	0.616715i
$876$		0			0
$877$	18.6137	−	32.2399i	0.628541	−	1.08866i	−0.359304	−	0.933220i	$-0.616986\pi$
$877$	18.6137	−	32.2399i	0.628541	−	1.08866i	0.987845	−	0.155444i	$-0.0496807\pi$
$878$		0			0
$879$	5.09259	−	1.85355i	0.171769	−	0.0625187i
$880$		0			0
$881$	−22.5759	+	18.9434i	−0.760600	+	0.638219i	−0.938283	−	0.345868i	$-0.887584\pi$
$881$	−22.5759	+	18.9434i	−0.760600	+	0.638219i	0.177683	+	0.984088i	$0.443140\pi$
$882$		0			0
$883$	−3.65148	+	3.06395i	−0.122882	+	0.103110i	−0.702158	−	0.712021i	$-0.747780\pi$
$883$	−3.65148	+	3.06395i	−0.122882	+	0.103110i	0.579276	+	0.815132i	$0.303335\pi$
$884$		0			0
$885$	1.32408	+	7.50925i	0.0445086	+	0.252421i
$886$		0			0
$887$	3.43777			0.115429			0.0577145	−	0.998333i	$-0.481619\pi$
$887$	3.43777			0.115429			0.0577145	+	0.998333i	$0.481619\pi$
$888$		0			0
$889$	33.4934			1.12333
$890$		0			0
$891$	−0.985745	−	5.59044i	−0.0330237	−	0.187287i
$892$		0			0
$893$	10.5710	−	8.87010i	0.353744	−	0.296827i
$894$		0			0
$895$	−22.4030	+	18.7983i	−0.748848	+	0.628358i
$896$		0			0
$897$	19.6697	−	7.15918i	0.656752	−	0.239038i
$898$		0			0
$899$	−2.07656	+	3.59671i	−0.0692572	+	0.119957i
$900$		0			0
$901$	52.2666	+	19.0235i	1.74125	+	0.633764i
$902$		0			0
$903$	4.18769	+	3.51389i	0.139358	+	0.116935i
$904$		0			0
$905$	−11.9574	+	4.35215i	−0.397479	+	0.144670i
$906$		0			0
$907$	−1.12665	−	6.38958i	−0.0374100	−	0.212162i	0.960373	−	0.278719i	$-0.0899098\pi$
$907$	−1.12665	−	6.38958i	−0.0374100	−	0.212162i	−0.997783	+	0.0665566i	$0.978799\pi$
$908$		0			0
$909$	11.2135	+	9.40925i	0.371929	+	0.312085i
$910$		0			0
$911$	−5.24986	−	9.09302i	−0.173935	−	0.301265i	0.765857	−	0.643011i	$-0.222315\pi$
$911$	−5.24986	−	9.09302i	−0.173935	−	0.301265i	−0.939792	+	0.341746i	$0.888982\pi$
$912$		0			0
$913$	−15.3603	+	87.1125i	−0.508351	+	2.88300i
$914$		0			0
$915$	−4.68211	−	8.10965i	−0.154786	−	0.268097i
$916$		0			0
$917$	16.6557	−	28.8485i	0.550019	−	0.952661i
$918$		0			0
$919$	11.5831			0.382091			0.191045	−	0.981581i	$-0.438812\pi$
$919$	11.5831			0.382091			0.191045	+	0.981581i	$0.438812\pi$
$920$		0			0
$921$	−20.0691	−	7.30456i	−0.661299	−	0.240693i
$922$		0			0
$923$	−3.90094	+	22.1233i	−0.128401	+	0.728198i
$924$		0			0
$925$	−24.0565	−	42.2035i	−0.790972	−	1.38764i
$926$		0			0
$927$	−1.60690	+	9.11316i	−0.0527774	+	0.299315i
$928$		0			0
$929$	−0.793149	−	0.288683i	−0.0260224	−	0.00947137i	0.328976	−	0.944338i	$-0.393296\pi$
$929$	−0.793149	−	0.288683i	−0.0260224	−	0.00947137i	−0.354999	+	0.934867i	$0.615519\pi$
$930$		0			0
$931$	−57.5336			−1.88559
$932$		0			0
$933$	6.85796	−	11.8783i	0.224520	−	0.388880i
$934$		0			0
$935$	52.4841	+	90.9052i	1.71641	+	2.97292i
$936$		0			0
$937$	8.02288	−	45.5000i	0.262096	−	1.48642i	−0.515083	−	0.857141i	$-0.672239\pi$
$937$	8.02288	−	45.5000i	0.262096	−	1.48642i	0.777179	−	0.629280i	$-0.216650\pi$
$938$		0			0
$939$	−8.24517	−	14.2810i	−0.269071	−	0.466044i
$940$		0			0
$941$	−12.8822	−	10.8094i	−0.419947	−	0.352378i	0.408196	−	0.912894i	$-0.366158\pi$
$941$	−12.8822	−	10.8094i	−0.419947	−	0.352378i	−0.828143	+	0.560517i	$0.810603\pi$
$942$		0			0
$943$	0.660312	+	3.74481i	0.0215027	+	0.121948i
$944$		0			0
$945$	16.7842	−	6.10895i	0.545990	−	0.198724i
$946$		0			0
$947$	12.4303	+	10.4303i	0.403931	+	0.338938i	0.822011	−	0.569472i	$-0.192852\pi$
$947$	12.4303	+	10.4303i	0.403931	+	0.338938i	−0.418080	+	0.908410i	$0.637297\pi$
$948$		0			0
$949$	49.4393	+	17.9944i	1.60487	+	0.584123i
$950$		0			0
$951$	−13.3593	+	23.1391i	−0.433206	+	0.750335i
$952$		0			0
$953$	−15.1737	+	5.52277i	−0.491524	+	0.178900i	−0.575878	−	0.817536i	$-0.695340\pi$
$953$	−15.1737	+	5.52277i	−0.491524	+	0.178900i	0.0843540	+	0.996436i	$0.473117\pi$
$954$		0			0
$955$	36.7799	−	30.8620i	1.19017	−	0.998671i
$956$		0			0
$957$	−15.6674	+	13.1465i	−0.506456	+	0.424967i
$958$		0			0
$959$	−7.91599	−	44.8938i	−0.255621	−	1.44970i
$960$		0			0
$961$	−29.6712			−0.957136
$962$		0			0
$963$	13.1240			0.422915
$964$		0			0
$965$	1.81332	+	10.2839i	0.0583729	+	0.331049i
$966$		0			0
$967$	−5.01192	+	4.20550i	−0.161173	+	0.135240i	−0.719807	−	0.694174i	$-0.755770\pi$
$967$	−5.01192	+	4.20550i	−0.161173	+	0.135240i	0.558635	+	0.829414i	$0.311325\pi$
$968$		0			0
$969$	12.8738	−	10.8024i	0.413567	−	0.347024i
$970$		0			0
$971$	−22.7326	+	8.27401i	−0.729525	+	0.265525i	−0.679964	−	0.733246i	$-0.738005\pi$
$971$	−22.7326	+	8.27401i	−0.729525	+	0.265525i	−0.0495614	+	0.998771i	$0.515782\pi$
$972$		0			0
$973$	20.7115	−	35.8733i	0.663979	−	1.15005i
$974$		0			0
$975$	−31.6932	−	11.5354i	−1.01499	−	0.369428i
$976$		0			0
$977$	−17.6729	−	14.8293i	−0.565405	−	0.474431i	0.314712	−	0.949187i	$-0.398092\pi$
$977$	−17.6729	−	14.8293i	−0.565405	−	0.474431i	−0.880118	+	0.474756i	$0.842536\pi$
$978$		0			0
$979$	58.4983	−	21.2917i	1.86961	−	0.680484i
$980$		0			0
$981$	−3.29924	−	18.7109i	−0.105337	−	0.597394i
$982$		0			0
$983$	−24.7335	−	20.7539i	−0.788877	−	0.661946i	0.156591	−	0.987664i	$-0.449950\pi$
$983$	−24.7335	−	20.7539i	−0.788877	−	0.661946i	−0.945467	+	0.325718i	$0.894394\pi$
$984$		0			0
$985$	−11.2645	−	19.5107i	−0.358917	−	0.621662i
$986$		0			0
$987$	−3.62638	+	20.5662i	−0.115429	+	0.654629i
$988$		0			0
$989$	2.73332	+	4.73426i	0.0869146	+	0.150541i
$990$		0			0
$991$	−14.7096	+	25.4778i	−0.467266	+	0.809328i	−0.999301	−	0.0373945i	$-0.988094\pi$
$991$	−14.7096	+	25.4778i	−0.467266	+	0.809328i	0.532035	+	0.846722i	$0.321428\pi$
$992$		0			0
$993$	−19.9006			−0.631527
$994$		0			0
$995$	−36.8070	−	13.3967i	−1.16686	−	0.424702i
$996$		0			0
$997$	4.70629	−	26.6907i	0.149050	−	0.845303i	−0.814976	−	0.579494i	$-0.803250\pi$
$997$	4.70629	−	26.6907i	0.149050	−	0.845303i	0.964026	−	0.265808i	$-0.0856388\pi$
$998$		0			0
$999$	−5.70435	−	2.11196i	−0.180478	−	0.0668194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.bo.c.625.1	yes	24
37.9	even	9	inner	888.2.bo.c.601.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.bo.c.601.1	✓	24	37.9	even	9	inner
888.2.bo.c.625.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{3} +(-2.76055 + 2.31638i) q^{5} +(3.79688 - 3.18596i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{3} +(-2.76055 + 2.31638i) q^{5} +(3.79688 - 3.18596i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(2.83834 - 4.91615i) q^{11} +(-3.96848 - 1.44441i) q^{13} +(-2.76055 - 2.31638i) q^{15} +(4.82179 - 1.75499i) q^{17} +(-0.568725 - 3.22540i) q^{19} +(3.79688 + 3.18596i) q^{21} +(2.47824 + 4.29244i) q^{23} +(1.38679 - 7.86490i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-1.80144 + 3.12018i) q^{29} +1.15272 q^{31} +(5.33433 + 1.94154i) q^{33} +(-3.10159 + 17.5900i) q^{35} +(4.68119 - 3.88413i) q^{37} +(0.733346 - 4.15901i) q^{39} +(0.720927 + 0.262396i) q^{41} +1.10293 q^{43} +(1.80182 - 3.12084i) q^{45} +(2.10668 + 3.64888i) q^{47} +(3.05042 - 17.2998i) q^{49} +(2.56562 + 4.44378i) q^{51} +(8.30367 + 6.96760i) q^{53} +(3.55227 + 20.1459i) q^{55} +(3.07764 - 1.12017i) q^{57} +(-1.62090 - 1.36010i) q^{59} +(2.44183 + 0.888755i) q^{61} +(-2.47824 + 4.29244i) q^{63} +(14.3010 - 5.20513i) q^{65} +(6.19508 - 5.19829i) q^{67} +(-3.79688 + 3.18596i) q^{69} +(-0.923700 - 5.23856i) q^{71} -12.4580 q^{73} +7.98622 q^{75} +(-4.88582 - 27.7089i) q^{77} +(7.81821 - 6.56026i) q^{79} +(0.766044 - 0.642788i) q^{81} +(-14.6427 + 5.32950i) q^{83} +(-9.24557 + 16.0138i) q^{85} +(-3.38559 - 1.23226i) q^{87} +(8.40074 + 7.04906i) q^{89} +(-19.6697 + 7.15918i) q^{91} +(0.200168 + 1.13521i) q^{93} +(9.04122 + 7.58649i) q^{95} +(0.354561 + 0.614118i) q^{97} +(-0.985745 + 5.59044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) \) 24 * q + 3 * q^5 + 15 * q^7	\( 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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