LMFDB - Embedded newform 380.2.bh.a.357.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(13,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("380.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bh (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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			357.4
Character	$\chi$	$=$	380.357
Dual form			380.2.bh.a.33.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.886233 + 1.26567i) q^{3} +(-2.22818 + 0.187668i) q^{5} +(0.477272 - 0.127885i) q^{7} +(0.209544 + 0.575718i) q^{9} +O(q^{10})$	\(q+(-0.886233 + 1.26567i) q^{3} +(-2.22818 + 0.187668i) q^{5} +(0.477272 - 0.127885i) q^{7} +(0.209544 + 0.575718i) q^{9} +(-1.30958 - 2.26826i) q^{11} +(-3.24748 + 2.27391i) q^{13} +(1.73716 - 2.98646i) q^{15} +(-3.14733 - 6.74948i) q^{17} +(-3.99559 + 1.74219i) q^{19} +(-0.261114 + 0.717405i) q^{21} +(-6.95648 + 0.608613i) q^{23} +(4.92956 - 0.836317i) q^{25} +(-5.39173 - 1.44471i) q^{27} +(7.14293 - 2.59981i) q^{29} +(-4.18291 - 2.41501i) q^{31} +(4.03147 + 0.352708i) q^{33} +(-1.03945 + 0.374519i) q^{35} +(-2.46586 + 2.46586i) q^{37} -6.12545i q^{39} +(7.64737 - 1.34844i) q^{41} +(-0.596842 + 6.82194i) q^{43} +(-0.574946 - 1.24348i) q^{45} +(3.78481 + 1.76489i) q^{47} +(-5.85074 + 3.37793i) q^{49} +(11.3319 + 1.99812i) q^{51} +(1.10972 + 12.6842i) q^{53} +(3.34367 + 4.80833i) q^{55} +(1.33598 - 6.60110i) q^{57} +(-9.64613 - 3.51090i) q^{59} +(4.23307 + 3.55197i) q^{61} +(0.173635 + 0.247977i) q^{63} +(6.80922 - 5.67612i) q^{65} +(-2.96957 + 6.36826i) q^{67} +(5.39476 - 9.34399i) q^{69} +(2.25576 + 2.68831i) q^{71} +(-7.90574 - 5.53566i) q^{73} +(-3.31024 + 6.98038i) q^{75} +(-0.915103 - 0.915103i) q^{77} +(2.00528 + 11.3725i) q^{79} +(5.19887 - 4.36237i) q^{81} +(-0.901564 - 3.36468i) q^{83} +(8.27949 + 14.4484i) q^{85} +(-3.03979 + 11.3446i) q^{87} +(1.27414 - 7.22603i) q^{89} +(-1.25913 + 1.50057i) q^{91} +(6.76364 - 3.15394i) q^{93} +(8.57594 - 4.63176i) q^{95} +(1.27464 - 0.594373i) q^{97} +(1.03146 - 1.22925i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−0.886233	+	1.26567i	−0.511667	+	0.730736i	−0.988988	−	0.147993i	$-0.952719\pi$
$3$	−0.886233	+	1.26567i	−0.511667	+	0.730736i	0.477322	+	0.878729i	$0.341608\pi$
$4$		0			0
$5$	−2.22818	+	0.187668i	−0.996472	+	0.0839278i
$5$	−2.22818	+	0.187668i	−0.996472	+	0.0839278i
$6$		0			0
$7$	0.477272	−	0.127885i	0.180392	−	0.0483359i	−0.167492	−	0.985873i	$-0.553567\pi$
$7$	0.477272	−	0.127885i	0.180392	−	0.0483359i	0.347884	+	0.937538i	$0.386900\pi$
$8$		0			0
$9$	0.209544	+	0.575718i	0.0698481	+	0.191906i
$10$		0			0
$11$	−1.30958	−	2.26826i	−0.394854	−	0.683907i	0.598229	−	0.801326i	$-0.295871\pi$
$11$	−1.30958	−	2.26826i	−0.394854	−	0.683907i	−0.993083	+	0.117418i	$0.962538\pi$
$12$		0			0
$13$	−3.24748	+	2.27391i	−0.900688	+	0.630668i	−0.929462	−	0.368918i	$-0.879728\pi$
$13$	−3.24748	+	2.27391i	−0.900688	+	0.630668i	0.0287743	+	0.999586i	$0.490840\pi$
$14$		0			0
$15$	1.73716	−	2.98646i	0.448532	−	0.771101i
$16$		0			0
$17$	−3.14733	−	6.74948i	−0.763341	−	1.63699i	−0.770849	−	0.637018i	$-0.780168\pi$
$17$	−3.14733	−	6.74948i	−0.763341	−	1.63699i	0.00750861	−	0.999972i	$-0.497610\pi$
$18$		0			0
$19$	−3.99559	+	1.74219i	−0.916652	+	0.399686i
$19$	−3.99559	+	1.74219i	−0.916652	+	0.399686i
$20$		0			0
$21$	−0.261114	+	0.717405i	−0.0569798	+	0.156551i
$22$		0			0
$23$	−6.95648	+	0.608613i	−1.45053	+	0.126905i	−0.785012	−	0.619480i	$-0.787343\pi$
$23$	−6.95648	+	0.608613i	−1.45053	+	0.126905i	−0.665514	+	0.746385i	$0.731788\pi$
$24$		0			0
$25$	4.92956	−	0.836317i	0.985912	−	0.167263i
$26$		0			0
$27$	−5.39173	−	1.44471i	−1.03764	−	0.278035i
$28$		0			0
$29$	7.14293	−	2.59981i	1.32641	−	0.482773i	0.420902	−	0.907106i	$-0.361714\pi$
$29$	7.14293	−	2.59981i	1.32641	−	0.482773i	0.905506	+	0.424333i	$0.139491\pi$
$30$		0			0
$31$	−4.18291	−	2.41501i	−0.751274	−	0.433748i	0.0748803	−	0.997193i	$-0.476143\pi$
$31$	−4.18291	−	2.41501i	−0.751274	−	0.433748i	−0.826154	+	0.563445i	$0.809476\pi$
$32$		0			0
$33$	4.03147	+	0.352708i	0.701789	+	0.0613986i
$34$		0			0
$35$	−1.03945	+	0.374519i	−0.175699	+	0.0633052i
$36$		0			0
$37$	−2.46586	+	2.46586i	−0.405384	+	0.405384i	−0.880125	−	0.474741i	$-0.842542\pi$
$37$	−2.46586	+	2.46586i	−0.405384	+	0.405384i	0.474741	+	0.880125i	$0.342542\pi$
$38$		0			0
$39$		−	6.12545i		−	0.980857i
$40$		0			0
$41$	7.64737	−	1.34844i	1.19432	−	0.210591i	0.459078	−	0.888396i	$-0.348180\pi$
$41$	7.64737	−	1.34844i	1.19432	−	0.210591i	0.735241	+	0.677805i	$0.237069\pi$
$42$		0			0
$43$	−0.596842	+	6.82194i	−0.0910176	+	1.04034i	0.804097	+	0.594499i	$0.202649\pi$
$43$	−0.596842	+	6.82194i	−0.0910176	+	1.04034i	−0.895114	+	0.445837i	$0.852906\pi$
$44$		0			0
$45$	−0.574946	−	1.24348i	−0.0857079	−	0.185367i
$46$		0			0
$47$	3.78481	+	1.76489i	0.552071	+	0.257435i	0.678575	−	0.734531i	$-0.262598\pi$
$47$	3.78481	+	1.76489i	0.552071	+	0.257435i	−0.126504	+	0.991966i	$0.540376\pi$
$48$		0			0
$49$	−5.85074	+	3.37793i	−0.835821	+	0.482561i
$50$		0			0
$51$	11.3319	+	1.99812i	1.58678	+	0.279793i
$52$		0			0
$53$	1.10972	+	12.6842i	0.152432	+	1.74230i	0.559432	+	0.828877i	$0.311019\pi$
$53$	1.10972	+	12.6842i	0.152432	+	1.74230i	−0.407000	+	0.913428i	$0.633425\pi$
$54$		0			0
$55$	3.34367	+	4.80833i	0.450860	+	0.648355i
$56$		0			0
$57$	1.33598	−	6.60110i	0.176955	−	0.874337i
$58$		0			0
$59$	−9.64613	−	3.51090i	−1.25582	−	0.457081i	−0.373455	−	0.927648i	$-0.621827\pi$
$59$	−9.64613	−	3.51090i	−1.25582	−	0.457081i	−0.882364	+	0.470568i	$0.844049\pi$
$60$		0			0
$61$	4.23307	+	3.55197i	0.541989	+	0.454783i	0.872218	−	0.489118i	$-0.162681\pi$
$61$	4.23307	+	3.55197i	0.541989	+	0.454783i	−0.330228	+	0.943901i	$0.607126\pi$
$62$		0			0
$63$	0.173635	+	0.247977i	0.0218760	+	0.0312421i
$64$		0			0
$65$	6.80922	−	5.67612i	0.844579	−	0.704036i
$66$		0			0
$67$	−2.96957	+	6.36826i	−0.362790	+	0.778006i	0.637183	+	0.770713i	$0.280100\pi$
$67$	−2.96957	+	6.36826i	−0.362790	+	0.778006i	−0.999973	+	0.00729393i	$0.997678\pi$
$68$		0			0
$69$	5.39476	−	9.34399i	0.649453	−	1.12488i
$70$		0			0
$71$	2.25576	+	2.68831i	0.267709	+	0.319043i	0.883105	−	0.469175i	$-0.155449\pi$
$71$	2.25576	+	2.68831i	0.267709	+	0.319043i	−0.615396	+	0.788218i	$0.711004\pi$
$72$		0			0
$73$	−7.90574	−	5.53566i	−0.925296	−	0.647900i	0.0106872	−	0.999943i	$-0.496598\pi$
$73$	−7.90574	−	5.53566i	−0.925296	−	0.647900i	−0.935984	+	0.352043i	$0.885487\pi$
$74$		0			0
$75$	−3.31024	+	6.98038i	−0.382233	+	0.806025i
$76$		0			0
$77$	−0.915103	−	0.915103i	−0.104286	−	0.104286i
$78$		0			0
$79$	2.00528	+	11.3725i	0.225612	+	1.27951i	0.861512	+	0.507738i	$0.169518\pi$
$79$	2.00528	+	11.3725i	0.225612	+	1.27951i	−0.635899	+	0.771772i	$0.719371\pi$
$80$		0			0
$81$	5.19887	−	4.36237i	0.577652	−	0.484708i
$82$		0			0
$83$	−0.901564	−	3.36468i	−0.0989596	−	0.369322i	0.898630	−	0.438706i	$-0.144563\pi$
$83$	−0.901564	−	3.36468i	−0.0989596	−	0.369322i	−0.997590	+	0.0693843i	$0.977897\pi$
$84$		0			0
$85$	8.27949	+	14.4484i	0.898036	+	1.56715i
$86$		0			0
$87$	−3.03979	+	11.3446i	−0.325899	+	1.21627i
$88$		0			0
$89$	1.27414	−	7.22603i	0.135059	−	0.765958i	−0.839760	−	0.542958i	$-0.817304\pi$
$89$	1.27414	−	7.22603i	0.135059	−	0.765958i	0.974819	−	0.222999i	$-0.0715848\pi$
$90$		0			0
$91$	−1.25913	+	1.50057i	−0.131993	+	0.157303i
$92$		0			0
$93$	6.76364	−	3.15394i	0.701357	−	0.327048i
$94$		0			0
$95$	8.57594	−	4.63176i	0.879873	−	0.475209i
$96$		0			0
$97$	1.27464	−	0.594373i	0.129420	−	0.0603494i	−0.356830	−	0.934169i	$-0.616142\pi$
$97$	1.27464	−	0.594373i	0.129420	−	0.0603494i	0.486250	+	0.873820i	$0.338365\pi$
$98$		0			0
$99$	1.03146	−	1.22925i	0.103666	−	0.123544i
$100$		0			0
$101$	−1.89117	+	10.7254i	−0.188179	+	1.06721i	0.733624	+	0.679555i	$0.237827\pi$
$101$	−1.89117	+	10.7254i	−0.188179	+	1.06721i	−0.921803	+	0.387659i	$0.873284\pi$
$102$		0			0
$103$	0.606523	−	2.26357i	0.0597624	−	0.223036i	−0.929585	−	0.368607i	$-0.879835\pi$
$103$	0.606523	−	2.26357i	0.0597624	−	0.223036i	0.989348	+	0.145570i	$0.0465016\pi$
$104$		0			0
$105$	0.447175	−	1.64751i	0.0436398	−	0.160781i
$106$		0			0
$107$	−1.81117	−	6.75938i	−0.175093	−	0.653454i	−0.996536	−	0.0831640i	$-0.973497\pi$
$107$	−1.81117	−	6.75938i	−0.175093	−	0.653454i	0.821443	−	0.570290i	$-0.193169\pi$
$108$		0			0
$109$	11.8380	−	9.93326i	1.13388	−	0.951434i	0.134654	−	0.990893i	$-0.457008\pi$
$109$	11.8380	−	9.93326i	1.13388	−	0.951434i	0.999221	+	0.0394585i	$0.0125633\pi$
$110$		0			0
$111$	−0.935641	−	5.30629i	−0.0888072	−	0.503650i
$112$		0			0
$113$	4.92042	+	4.92042i	0.462874	+	0.462874i	0.899596	−	0.436722i	$-0.143861\pi$
$113$	4.92042	+	4.92042i	0.462874	+	0.462874i	−0.436722	+	0.899596i	$0.643861\pi$
$114$		0			0
$115$	15.3861	−	2.66161i	1.43476	−	0.248196i
$116$		0			0
$117$	−1.98962	−	1.39315i	−0.183940	−	0.128796i
$118$		0			0
$119$	−2.36529	−	2.81884i	−0.216826	−	0.258403i
$120$		0			0
$121$	2.06999	−	3.58532i	0.188181	−	0.325938i
$122$		0			0
$123$	−5.07067	+	10.8741i	−0.457207	+	0.980484i
$124$		0			0
$125$	−10.8270	+	2.78859i	−0.968396	+	0.249419i
$126$		0			0
$127$	−4.44110	−	6.34255i	−0.394084	−	0.562810i	0.572257	−	0.820074i	$-0.306068\pi$
$127$	−4.44110	−	6.34255i	−0.394084	−	0.562810i	−0.966341	+	0.257264i	$0.917179\pi$
$128$		0			0
$129$	−8.10539	−	6.80123i	−0.713640	−	0.598815i
$130$		0			0
$131$	−15.4866	−	5.63667i	−1.35307	−	0.492478i	−0.439167	−	0.898405i	$-0.644726\pi$
$131$	−15.4866	−	5.63667i	−1.35307	−	0.492478i	−0.913905	+	0.405927i	$0.866949\pi$
$132$		0			0
$133$	−1.68418	+	1.34247i	−0.146037	+	0.116407i
$134$		0			0
$135$	12.2849	+	2.20722i	1.05731	+	0.189967i
$136$		0			0
$137$	0.639108	+	7.30503i	0.0546026	+	0.624111i	0.973359	+	0.229286i	$0.0736392\pi$
$137$	0.639108	+	7.30503i	0.0546026	+	0.624111i	−0.918756	+	0.394825i	$0.870805\pi$
$138$		0			0
$139$	10.2337	+	1.80447i	0.868010	+	0.153054i	0.589881	−	0.807490i	$-0.299175\pi$
$139$	10.2337	+	1.80447i	0.868010	+	0.153054i	0.278129	+	0.960544i	$0.410286\pi$
$140$		0			0
$141$	−5.58799	+	3.22623i	−0.470594	+	0.271697i
$142$		0			0
$143$	9.41066	+	4.38826i	0.786959	+	0.366965i
$144$		0			0
$145$	−15.4278	+	7.13335i	−1.28121	+	0.592392i
$146$		0			0
$147$	0.909773	−	10.3988i	0.0750368	−	0.857675i
$148$		0			0
$149$	−14.0270	+	2.47333i	−1.14913	+	0.202623i	−0.715598	−	0.698512i	$-0.753846\pi$
$149$	−14.0270	+	2.47333i	−1.14913	+	0.202623i	−0.433537	+	0.901136i	$0.642735\pi$
$150$		0			0
$151$			0.293600i			0.0238929i	0.999929	+	0.0119464i	$0.00380276\pi$
$151$			0.293600i			0.0238929i	−0.999929	+	0.0119464i	$0.996197\pi$
$152$		0			0
$153$	3.22629	−	3.22629i	0.260830	−	0.260830i
$154$		0			0
$155$	9.77350	+	4.59607i	0.785027	+	0.369165i
$156$		0			0
$157$	−0.786873	−	0.0688424i	−0.0627993	−	0.00549422i	0.0557128	−	0.998447i	$-0.482257\pi$
$157$	−0.786873	−	0.0688424i	−0.0627993	−	0.00549422i	−0.118512	+	0.992953i	$0.537812\pi$
$158$		0			0
$159$	−17.0375	−	9.83659i	−1.35116	−	0.780092i
$160$		0			0
$161$	−3.24230	+	1.18010i	−0.255529	+	0.0930050i
$162$		0			0
$163$	−11.9964	−	3.21443i	−0.939631	−	0.251773i	−0.243674	−	0.969857i	$-0.578353\pi$
$163$	−11.9964	−	3.21443i	−0.939631	−	0.251773i	−0.695957	+	0.718084i	$0.745019\pi$
$164$		0			0
$165$	−9.04903	−	0.0293173i	−0.704466	−	0.00228235i
$166$		0			0
$167$	14.2939	−	1.25055i	1.10609	−	0.0967705i	0.480555	−	0.876965i	$-0.340435\pi$
$167$	14.2939	−	1.25055i	1.10609	−	0.0967705i	0.625537	+	0.780194i	$0.284880\pi$
$168$		0			0
$169$	0.929186	−	2.55292i	0.0714758	−	0.196378i
$170$		0			0
$171$	−1.84027	−	1.93527i	−0.140729	−	0.147994i
$172$		0			0
$173$	−3.17974	−	6.81897i	−0.241751	−	0.518437i	0.747571	−	0.664182i	$-0.231220\pi$
$173$	−3.17974	−	6.81897i	−0.241751	−	0.518437i	−0.989322	+	0.145745i	$0.953442\pi$
$174$		0			0
$175$	2.24579	−	1.02957i	0.169766	−	0.0778279i
$176$		0			0
$177$	12.9924	−	9.09735i	0.976566	−	0.683799i
$178$		0			0
$179$	−6.89499	−	11.9425i	−0.515356	−	0.892622i	−0.999841	−	0.0178228i	$-0.994327\pi$
$179$	−6.89499	−	11.9425i	−0.515356	−	0.892622i	0.484486	−	0.874799i	$-0.339007\pi$
$180$		0			0
$181$	−2.81051	−	7.72180i	−0.208903	−	0.573957i	0.790348	−	0.612659i	$-0.209900\pi$
$181$	−2.81051	−	7.72180i	−0.208903	−	0.573957i	−0.999251	+	0.0387019i	$0.987678\pi$
$182$		0			0
$183$	−8.24712	+	2.20981i	−0.609644	+	0.163354i
$184$		0			0
$185$	5.03160	−	5.95713i	0.369931	−	0.437977i
$186$		0			0
$187$	−11.1879	+	15.9780i	−0.818141	+	1.16843i
$188$		0			0
$189$	−2.75808			−0.200621
$190$		0			0
$191$	−11.3833			−0.823668			−0.411834	−	0.911259i	$-0.635112\pi$
$191$	−11.3833			−0.823668			−0.411834	+	0.911259i	$0.635112\pi$
$192$		0			0
$193$	−7.34591	+	10.4911i	−0.528770	+	0.755162i	−0.991326	−	0.131428i	$-0.958044\pi$
$193$	−7.34591	+	10.4911i	−0.528770	+	0.755162i	0.462555	+	0.886590i	$0.346933\pi$
$194$		0			0
$195$	1.14955	+	13.6486i	0.0823212	+	0.977396i
$196$		0			0
$197$	−13.0874	+	3.50677i	−0.932441	+	0.249847i	−0.692895	−	0.721038i	$-0.743665\pi$
$197$	−13.0874	+	3.50677i	−0.932441	+	0.249847i	−0.239546	+	0.970885i	$0.576999\pi$
$198$		0			0
$199$	8.51151	+	23.3852i	0.603365	+	1.65773i	0.744406	+	0.667728i	$0.232733\pi$
$199$	8.51151	+	23.3852i	0.603365	+	1.65773i	−0.141041	+	0.990004i	$0.545045\pi$
$200$		0			0
$201$	−5.42840	−	9.40226i	−0.382889	−	0.663184i
$202$		0			0
$203$	3.07664	−	2.15429i	0.215938	−	0.151201i
$204$		0			0
$205$	−16.7867	+	4.43973i	−1.17243	+	0.310084i
$206$		0			0
$207$	−1.80808	−	3.87744i	−0.125670	−	0.269501i
$208$		0			0
$209$	9.18431	+	6.78151i	0.635292	+	0.469087i
$210$		0			0
$211$	0.326590	−	0.897298i	0.0224834	−	0.0617725i	−0.927943	−	0.372722i	$-0.878425\pi$
$211$	0.326590	−	0.897298i	0.0224834	−	0.0617725i	0.950427	+	0.310949i	$0.100647\pi$
$212$		0			0
$213$	−5.40164	+	0.472582i	−0.370114	+	0.0323808i
$214$		0			0
$215$	0.0496098	−	15.3125i	0.00338336	−	1.04430i
$216$		0			0
$217$	−2.30523	−	0.617685i	−0.156489	−	0.0419312i
$218$		0			0
$219$	14.0126	−	5.10019i	0.946887	−	0.344639i
$220$		0			0
$221$	25.5686	+	14.7620i	1.71993	+	0.993002i
$222$		0			0
$223$	5.95774	+	0.521235i	0.398960	+	0.0349045i	0.284871	−	0.958566i	$-0.408049\pi$
$223$	5.95774	+	0.521235i	0.398960	+	0.0349045i	0.114089	+	0.993470i	$0.463605\pi$
$224$		0			0
$225$	1.51444	+	2.66279i	0.100963	+	0.177519i
$226$		0			0
$227$	−7.52394	+	7.52394i	−0.499382	+	0.499382i	−0.911245	−	0.411864i	$-0.864878\pi$
$227$	−7.52394	+	7.52394i	−0.499382	+	0.499382i	0.411864	+	0.911245i	$0.364878\pi$
$228$		0			0
$229$			12.5028i			0.826206i	0.910684	+	0.413103i	$0.135555\pi$
$229$			12.5028i			0.826206i	−0.910684	+	0.413103i	$0.864445\pi$
$230$		0			0
$231$	1.96921	−	0.347226i	0.129565	−	0.0228458i
$232$		0			0
$233$	0.251393	−	2.87344i	0.0164693	−	0.188245i	−0.983504	−	0.180888i	$-0.942103\pi$
$233$	0.251393	−	2.87344i	0.0164693	−	0.188245i	0.999973	−	0.00735679i	$-0.00234176\pi$
$234$		0			0
$235$	−8.76444	−	3.22219i	−0.571729	−	0.210193i
$236$		0			0
$237$	−16.1710	−	7.54068i	−1.05042	−	0.489820i
$238$		0			0
$239$	6.72844	−	3.88466i	0.435226	−	0.251278i	−0.266344	−	0.963878i	$-0.585816\pi$
$239$	6.72844	−	3.88466i	0.435226	−	0.251278i	0.701571	+	0.712600i	$0.252482\pi$
$240$		0			0
$241$	3.78997	+	0.668274i	0.244134	+	0.0430473i	0.294376	−	0.955690i	$-0.404888\pi$
$241$	3.78997	+	0.668274i	0.244134	+	0.0430473i	−0.0502423	+	0.998737i	$0.515999\pi$
$242$		0			0
$243$	−0.545573	−	6.23593i	−0.0349986	−	0.400035i
$244$		0			0
$245$	12.4026	−	8.62463i	0.792371	−	0.551007i
$246$		0			0
$247$	9.01401	−	14.7433i	0.573548	−	0.938096i
$248$		0			0
$249$	5.05758	+	1.84081i	0.320511	+	0.116657i
$250$		0			0
$251$	−22.6524	−	19.0076i	−1.42981	−	1.19975i	−0.945827	−	0.324672i	$-0.894746\pi$
$251$	−22.6524	−	19.0076i	−1.42981	−	1.19975i	−0.483981	−	0.875079i	$-0.660810\pi$
$252$		0			0
$253$	10.4906	+	14.9821i	0.659537	+	0.941917i
$254$		0			0
$255$	−25.6245	−	2.32553i	−1.60467	−	0.145630i
$256$		0			0
$257$	7.27154	−	15.5939i	0.453586	−	0.972719i	−0.537961	−	0.842970i	$-0.680805\pi$
$257$	7.27154	−	15.5939i	0.453586	−	0.972719i	0.991547	−	0.129749i	$-0.0414171\pi$
$258$		0			0
$259$	−0.861539	+	1.49223i	−0.0535334	+	0.0927226i
$260$		0			0
$261$	2.99352	+	3.56754i	0.185294	+	0.220825i
$262$		0			0
$263$	−13.1509	−	9.20834i	−0.810917	−	0.567810i	0.0929266	−	0.995673i	$-0.470378\pi$
$263$	−13.1509	−	9.20834i	−0.810917	−	0.567810i	−0.903844	+	0.427863i	$0.859267\pi$
$264$		0			0
$265$	−4.85307	−	28.0543i	−0.298122	−	1.72336i
$266$		0			0
$267$	8.01659	+	8.01659i	0.490608	+	0.490608i
$268$		0			0
$269$	2.29086	+	12.9921i	0.139676	+	0.792142i	0.971489	+	0.237085i	$0.0761921\pi$
$269$	2.29086	+	12.9921i	0.139676	+	0.792142i	−0.831813	+	0.555056i	$0.812697\pi$
$270$		0			0
$271$	−1.56103	+	1.30986i	−0.0948258	+	0.0795683i	−0.688968	−	0.724792i	$-0.741936\pi$
$271$	−1.56103	+	1.30986i	−0.0948258	+	0.0795683i	0.594142	+	0.804360i	$0.297492\pi$
$272$		0			0
$273$	−0.783351	−	2.92351i	−0.0474106	−	0.176939i
$274$		0			0
$275$	−8.35265	−	10.0863i	−0.503684	−	0.608228i
$276$		0			0
$277$	1.94512	−	7.25930i	0.116871	−	0.436169i	−0.882549	−	0.470220i	$-0.844174\pi$
$277$	1.94512	−	7.25930i	0.116871	−	0.436169i	0.999420	+	0.0340517i	$0.0108411\pi$
$278$		0			0
$279$	0.513857	−	2.91423i	0.0307638	−	0.174470i
$280$		0			0
$281$	−6.40308	+	7.63090i	−0.381976	+	0.455221i	−0.922437	−	0.386148i	$-0.873805\pi$
$281$	−6.40308	+	7.63090i	−0.381976	+	0.455221i	0.540461	+	0.841369i	$0.318250\pi$
$282$		0			0
$283$	6.03842	−	2.81576i	0.358947	−	0.167380i	−0.234776	−	0.972050i	$-0.575436\pi$
$283$	6.03842	−	2.81576i	0.358947	−	0.167380i	0.593722	+	0.804670i	$0.297658\pi$
$284$		0			0
$285$	−1.73799	+	14.9591i	−0.102950	+	0.886103i
$286$		0			0
$287$	3.47743	−	1.62155i	0.205266	−	0.0957173i
$288$		0			0
$289$	−24.7224	+	29.4630i	−1.45426	+	1.73312i
$290$		0			0
$291$	−0.377344	+	2.14003i	−0.0221203	+	0.125450i
$292$		0			0
$293$	4.51637	−	16.8553i	0.263849	−	0.984698i	−0.699102	−	0.715022i	$-0.746417\pi$
$293$	4.51637	−	16.8553i	0.263849	−	0.984698i	0.962951	−	0.269676i	$-0.0869165\pi$
$294$		0			0
$295$	22.1522	+	6.01265i	1.28975	+	0.350070i
$296$		0			0
$297$	3.78393	+	14.1218i	0.219566	+	0.819432i
$298$		0			0
$299$	21.2071	−	17.7949i	1.22644	−	1.02910i
$300$		0			0
$301$	0.587565	+	3.33225i	0.0338667	+	0.192068i
$302$		0			0
$303$	−11.8988	−	11.8988i	−0.683567	−	0.683567i
$304$		0			0
$305$	−10.0986	−	7.12001i	−0.578246	−	0.407691i
$306$		0			0
$307$	22.7303	+	15.9159i	1.29728	+	0.908368i	0.998937	−	0.0460895i	$-0.0146760\pi$
$307$	22.7303	+	15.9159i	1.29728	+	0.908368i	0.298347	+	0.954458i	$0.403565\pi$
$308$		0			0
$309$	2.32742	+	2.77371i	0.132402	+	0.157791i
$310$		0			0
$311$	−9.60521	+	16.6367i	−0.544661	+	0.943381i	0.453967	+	0.891019i	$0.350008\pi$
$311$	−9.60521	+	16.6367i	−0.544661	+	0.943381i	−0.998628	+	0.0523626i	$0.983325\pi$
$312$		0			0
$313$	11.5340	−	24.7348i	0.651943	−	1.39810i	−0.250853	−	0.968025i	$-0.580711\pi$
$313$	11.5340	−	24.7348i	0.651943	−	1.39810i	0.902795	−	0.430070i	$-0.141511\pi$
$314$		0			0
$315$	−0.433427	−	0.519950i	−0.0244209	−	0.0292959i
$316$		0			0
$317$	−4.21121	−	6.01423i	−0.236525	−	0.337793i	0.683289	−	0.730148i	$-0.260549\pi$
$317$	−4.21121	−	6.01423i	−0.236525	−	0.337793i	−0.919814	+	0.392356i	$0.871660\pi$
$318$		0			0
$319$	−15.2513	−	12.7974i	−0.853909	−	0.716515i
$320$		0			0
$321$	10.1603	+	3.69804i	0.567091	+	0.206404i
$322$		0			0
$323$	24.3344	+	21.4849i	1.35400	+	1.19545i
$324$		0			0
$325$	−14.1069	+	13.9253i	−0.782511	+	0.772436i
$326$		0			0
$327$	2.08102	+	23.7862i	0.115081	+	1.31538i
$328$		0			0
$329$	2.03209	+	0.358311i	0.112032	+	0.0197543i
$330$		0			0
$331$	21.1146	−	12.1905i	1.16057	−	0.670053i	0.209126	−	0.977889i	$-0.432938\pi$
$331$	21.1146	−	12.1905i	1.16057	−	0.670053i	0.951440	+	0.307836i	$0.0996047\pi$
$332$		0			0
$333$	−1.93634	−	0.902932i	−0.106111	−	0.0494804i
$334$		0			0
$335$	5.42161	−	14.7469i	0.296214	−	0.805710i
$336$		0			0
$337$	0.506382	−	5.78797i	0.0275844	−	0.315291i	−0.969850	−	0.243703i	$-0.921638\pi$
$337$	0.506382	−	5.78797i	0.0275844	−	0.315291i	0.997434	−	0.0715879i	$-0.0228067\pi$
$338$		0			0
$339$	−10.5883	+	1.86700i	−0.575076	+	0.101401i
$340$		0			0
$341$			12.6506i			0.685069i
$342$		0			0
$343$	−4.80612	+	4.80612i	−0.259506	+	0.259506i
$344$		0			0
$345$	−10.2669	+	21.8325i	−0.552752	+	1.17542i
$346$		0			0
$347$	32.6777	+	2.85893i	1.75423	+	0.153475i	0.918436	−	0.395569i	$-0.129453\pi$
$347$	32.6777	+	2.85893i	1.75423	+	0.153475i	0.835793	+	0.549044i	$0.185008\pi$
$348$		0			0
$349$	−9.20005	−	5.31165i	−0.492467	−	0.284326i	0.233130	−	0.972446i	$-0.425103\pi$
$349$	−9.20005	−	5.31165i	−0.492467	−	0.284326i	−0.725597	+	0.688119i	$0.758437\pi$
$350$		0			0
$351$	20.7947	−	7.56864i	1.10994	−	0.403984i
$352$		0			0
$353$	−3.09233	−	0.828587i	−0.164588	−	0.0441012i	0.175584	−	0.984464i	$-0.443819\pi$
$353$	−3.09233	−	0.828587i	−0.164588	−	0.0441012i	−0.340172	+	0.940363i	$0.610485\pi$
$354$		0			0
$355$	−5.53074	−	5.56669i	−0.293541	−	0.295449i
$356$		0			0
$357$	5.66393	−	0.495529i	0.299767	−	0.0262262i
$358$		0			0
$359$	−4.53462	+	12.4588i	−0.239328	+	0.657548i	0.760637	+	0.649177i	$0.224887\pi$
$359$	−4.53462	+	12.4588i	−0.239328	+	0.657548i	−0.999965	+	0.00837080i	$0.997335\pi$
$360$		0			0
$361$	12.9295	−	13.9222i	0.680502	−	0.732747i
$362$		0			0
$363$	2.70335	+	5.79736i	0.141889	+	0.304282i
$364$		0			0
$365$	18.6543	+	10.8508i	0.976409	+	0.567956i
$366$		0			0
$367$	−24.3395	+	17.0427i	−1.27051	+	0.889620i	−0.997379	−	0.0723565i	$-0.976948\pi$
$367$	−24.3395	+	17.0427i	−1.27051	+	0.889620i	−0.273131	+	0.961977i	$0.588059\pi$
$368$		0			0
$369$	2.37878	+	4.12017i	0.123835	+	0.214488i
$370$		0			0
$371$	2.15175	+	5.91188i	0.111713	+	0.306930i
$372$		0			0
$373$	25.3739	−	6.79892i	1.31381	−	0.352035i	0.467156	−	0.884175i	$-0.345279\pi$
$373$	25.3739	−	6.79892i	1.31381	−	0.352035i	0.846656	+	0.532140i	$0.178612\pi$
$374$		0			0
$375$	6.06580	−	16.1748i	0.313237	−	0.835261i
$376$		0			0
$377$	−17.2847	+	24.6852i	−0.890210	+	1.27135i
$378$		0			0
$379$	37.5940			1.93107			0.965537	−	0.260264i	$-0.0838096\pi$
$379$	37.5940			1.93107			0.965537	+	0.260264i	$0.0838096\pi$
$380$		0			0
$381$	11.9634			0.612905
$382$		0			0
$383$	−0.538068	+	0.768441i	−0.0274940	+	0.0392655i	−0.832664	−	0.553779i	$-0.813185\pi$
$383$	−0.538068	+	0.768441i	−0.0274940	+	0.0392655i	0.805170	+	0.593044i	$0.202074\pi$
$384$		0			0
$385$	2.21075	+	1.86728i	0.112670	+	0.0951653i
$386$		0			0
$387$	−4.05258	+	1.08588i	−0.206004	+	0.0551986i
$388$		0			0
$389$	10.6622	+	29.2941i	0.540595	+	1.48527i	0.846070	+	0.533072i	$0.178963\pi$
$389$	10.6622	+	29.2941i	0.540595	+	1.48527i	−0.305475	+	0.952200i	$0.598815\pi$
$390$		0			0
$391$	26.0022	+	45.0371i	1.31499	+	2.27763i
$392$		0			0
$393$	20.8589	−	14.6056i	1.05219	−	0.736754i
$394$		0			0
$395$	−6.60240	−	24.9637i	−0.332203	−	1.25606i
$396$		0			0
$397$	−0.762993	−	1.63624i	−0.0382935	−	0.0821207i	0.886230	−	0.463245i	$-0.153315\pi$
$397$	−0.762993	−	1.63624i	−0.0382935	−	0.0821207i	−0.924524	+	0.381124i	$0.875537\pi$
$398$		0			0
$399$	−0.206552	−	3.32137i	−0.0103405	−	0.166277i
$400$		0			0
$401$	6.16526	−	16.9389i	0.307879	−	0.845889i	−0.685191	−	0.728363i	$-0.740281\pi$
$401$	6.16526	−	16.9389i	0.307879	−	0.845889i	0.993070	−	0.117526i	$-0.0374964\pi$
$402$		0			0
$403$	19.0754	−	1.66888i	0.950214	−	0.0831330i
$404$		0			0
$405$	−10.7653	+	10.6958i	−0.534934	+	0.531479i
$406$		0			0
$407$	8.82245	+	2.36397i	0.437313	+	0.117178i
$408$		0			0
$409$	−26.1564	+	9.52016i	−1.29335	+	0.470742i	−0.894826	−	0.446415i	$-0.852700\pi$
$409$	−26.1564	+	9.52016i	−1.29335	+	0.470742i	−0.398526	+	0.917157i	$0.630478\pi$
$410$		0			0
$411$	−9.81217	−	5.66506i	−0.483999	−	0.279437i
$412$		0			0
$413$	−5.05282	−	0.442064i	−0.248633	−	0.0217526i
$414$		0			0
$415$	2.64029	+	7.32792i	0.129607	+	0.359714i
$416$		0			0
$417$	−11.3533	+	11.3533i	−0.555974	+	0.555974i
$418$		0			0
$419$			18.1585i			0.887103i	0.896249	+	0.443551i	$0.146282\pi$
$419$			18.1585i			0.887103i	−0.896249	+	0.443551i	$0.853718\pi$
$420$		0			0
$421$	−29.5610	+	5.21240i	−1.44071	+	0.254037i	−0.838763	−	0.544496i	$-0.816721\pi$
$421$	−29.5610	+	5.21240i	−1.44071	+	0.254037i	−0.601951	+	0.798533i	$0.705610\pi$
$422$		0			0
$423$	−0.222992	+	2.54880i	−0.0108422	+	0.123927i
$424$		0			0
$425$	−21.1597	−	30.6398i	−1.02640	−	1.48625i
$426$		0			0
$427$	2.47457	+	1.15391i	0.119753	+	0.0558416i
$428$		0			0
$429$	−13.8941	+	8.02178i	−0.670815	+	0.387295i
$430$		0			0
$431$	−22.3234	−	3.93622i	−1.07528	−	0.189601i	−0.392153	−	0.919900i	$-0.628269\pi$
$431$	−22.3234	−	3.93622i	−1.07528	−	0.189601i	−0.683127	+	0.730299i	$0.739381\pi$
$432$		0			0
$433$	0.651368	+	7.44518i	0.0313028	+	0.357792i	0.995651	+	0.0931573i	$0.0296959\pi$
$433$	0.651368	+	7.44518i	0.0313028	+	0.357792i	−0.964349	+	0.264635i	$0.914749\pi$
$434$		0			0
$435$	4.64416	−	25.8484i	0.222670	−	1.23933i
$436$		0			0
$437$	26.7349	−	14.5513i	1.27891	−	0.696083i
$438$		0			0
$439$	21.2933	+	7.75013i	1.01627	+	0.369894i	0.795839	−	0.605508i	$-0.207030\pi$
$439$	21.2933	+	7.75013i	1.01627	+	0.369894i	0.220435	+	0.975402i	$0.429252\pi$
$440$		0			0
$441$	−3.17072	−	2.66055i	−0.150987	−	0.126693i
$442$		0			0
$443$	−10.5613	−	15.0831i	−0.501783	−	0.716620i	0.485739	−	0.874104i	$-0.338551\pi$
$443$	−10.5613	−	15.0831i	−0.501783	−	0.716620i	−0.987522	+	0.157484i	$0.949662\pi$
$444$		0			0
$445$	−1.48292	+	16.3400i	−0.0702973	+	0.774590i
$446$		0			0
$447$	9.30074	−	19.9455i	0.439910	−	0.943390i
$448$		0			0
$449$	−1.67194	+	2.89589i	−0.0789039	+	0.136666i	−0.902777	−	0.430108i	$-0.858475\pi$
$449$	−1.67194	+	2.89589i	−0.0789039	+	0.136666i	0.823873	+	0.566774i	$0.191809\pi$
$450$		0			0
$451$	−13.0735	−	15.5804i	−0.615606	−	0.733651i
$452$		0			0
$453$	−0.371602	−	0.260198i	−0.0174594	−	0.0122252i
$454$		0			0
$455$	2.52396	−	3.57985i	0.118325	−	0.167826i
$456$		0			0
$457$	−7.43344	−	7.43344i	−0.347721	−	0.347721i	0.511539	−	0.859260i	$-0.329076\pi$
$457$	−7.43344	−	7.43344i	−0.347721	−	0.347721i	−0.859260	+	0.511539i	$0.829076\pi$
$458$		0			0
$459$	7.21854	+	40.9384i	0.336933	+	1.91084i
$460$		0			0
$461$	−0.317855	+	0.266712i	−0.0148040	+	0.0124220i	−0.650160	−	0.759798i	$-0.725298\pi$
$461$	−0.317855	+	0.266712i	−0.0148040	+	0.0124220i	0.635356	+	0.772220i	$0.280854\pi$
$462$		0			0
$463$	−6.79649	−	25.3649i	−0.315860	−	1.17881i	−0.923186	−	0.384353i	$-0.874425\pi$
$463$	−6.79649	−	25.3649i	−0.315860	−	1.17881i	0.607326	−	0.794452i	$-0.292242\pi$
$464$		0			0
$465$	−14.4787	+	8.29686i	−0.671434	+	0.384758i
$466$		0			0
$467$	−0.670696	+	2.50307i	−0.0310361	+	0.115828i	−0.979706	−	0.200439i	$-0.935763\pi$
$467$	−0.670696	+	2.50307i	−0.0310361	+	0.115828i	0.948670	+	0.316268i	$0.102430\pi$
$468$		0			0
$469$	−0.602889	+	3.41915i	−0.0278388	+	0.157882i
$470$		0			0
$471$	0.784484	−	0.934912i	0.0361471	−	0.0430785i
$472$		0			0
$473$	16.2556	−	7.58010i	0.747432	−	0.348533i
$474$		0			0
$475$	−18.2395	+	11.9298i	−0.836885	+	0.547378i
$476$		0			0
$477$	−7.06997	+	3.29678i	−0.323712	+	0.150949i
$478$		0			0
$479$	16.3953	−	19.5392i	0.749120	−	0.892767i	−0.247988	−	0.968763i	$-0.579769\pi$
$479$	16.3953	−	19.5392i	0.749120	−	0.892767i	0.997108	+	0.0759965i	$0.0242138\pi$
$480$		0			0
$481$	2.40068	−	13.6149i	0.109462	−	0.620788i
$482$		0			0
$483$	1.37981	−	5.14953i	0.0627837	−	0.234312i
$484$		0			0
$485$	−2.72857	+	1.56358i	−0.123898	+	0.0709984i
$486$		0			0
$487$	−7.76189	−	28.9678i	−0.351725	−	1.31265i	−0.884556	−	0.466433i	$-0.845539\pi$
$487$	−7.76189	−	28.9678i	−0.351725	−	1.31265i	0.532831	−	0.846221i	$-0.321128\pi$
$488$		0			0
$489$	14.7000	−	12.3348i	0.664758	−	0.557798i
$490$		0			0
$491$	−1.13753	−	6.45128i	−0.0513362	−	0.291142i	0.948321	−	0.317312i	$-0.102780\pi$
$491$	−1.13753	−	6.45128i	−0.0513362	−	0.291142i	−0.999658	+	0.0261695i	$0.991669\pi$
$492$		0			0
$493$	−40.0286	−	40.0286i	−1.80280	−	1.80280i
$494$		0			0
$495$	−2.06760	+	2.93257i	−0.0929315	+	0.131809i
$496$		0			0
$497$	1.42040	+	0.994576i	0.0637137	+	0.0446128i
$498$		0			0
$499$	−20.9317	−	24.9454i	−0.937032	−	1.11671i	−0.992981	−	0.118277i	$-0.962263\pi$
$499$	−20.9317	−	24.9454i	−0.937032	−	1.11671i	0.0559489	−	0.998434i	$-0.482182\pi$
$500$		0			0
$501$	−11.0849	+	19.1996i	−0.495237	+	0.857775i
$502$		0			0
$503$	−8.37995	+	17.9709i	−0.373643	+	0.801281i	0.626124	+	0.779723i	$0.284640\pi$
$503$	−8.37995	+	17.9709i	−0.373643	+	0.801281i	−0.999768	+	0.0215576i	$0.993137\pi$
$504$		0			0
$505$	2.20106	−	24.2530i	0.0979458	−	1.07924i
$506$		0			0
$507$	2.40768	+	3.43852i	0.106929	+	0.152710i
$508$		0			0
$509$	−30.7769	−	25.8249i	−1.36416	−	1.14467i	−0.974672	−	0.223638i	$-0.928207\pi$
$509$	−30.7769	−	25.8249i	−1.36416	−	1.14467i	−0.389491	−	0.921030i	$-0.627349\pi$
$510$		0			0
$511$	−4.48111	−	1.63099i	−0.198233	−	0.0721508i
$512$		0			0
$513$	24.0601	−	3.62096i	1.06228	−	0.159869i
$514$		0			0
$515$	−0.926640	+	5.15747i	−0.0408326	+	0.227265i
$516$		0			0
$517$	−0.953295	−	10.8962i	−0.0419259	−	0.479215i
$518$		0			0
$519$	11.4486	+	2.01869i	0.502537	+	0.0886107i
$520$		0			0
$521$	−22.0853	+	12.7510i	−0.967576	+	0.558630i	−0.898496	−	0.438981i	$-0.855340\pi$
$521$	−22.0853	+	12.7510i	−0.967576	+	0.558630i	−0.0690794	+	0.997611i	$0.522006\pi$
$522$		0			0
$523$	4.42522	+	2.06351i	0.193501	+	0.0902311i	0.516954	−	0.856013i	$-0.327066\pi$
$523$	4.42522	+	2.06351i	0.193501	+	0.0902311i	−0.323453	+	0.946244i	$0.604844\pi$
$524$		0			0
$525$	−0.687200	+	3.75487i	−0.0299919	+	0.163876i
$526$		0			0
$527$	−3.13501	+	35.8333i	−0.136563	+	1.56092i
$528$		0			0
$529$	25.3716	−	4.47371i	1.10311	−	0.194509i
$530$		0			0
$531$		−	6.28914i		−	0.272925i
$532$		0			0
$533$	−21.7684	+	21.7684i	−0.942896	+	0.942896i
$534$		0			0
$535$	5.30413	+	14.7212i	0.229318	+	0.636453i
$536$		0			0
$537$	21.2258	+	1.85702i	0.915961	+	0.0801362i
$538$		0			0
$539$	15.3241	+	8.84735i	0.660054	+	0.381082i
$540$		0			0
$541$	−21.1925	+	7.71343i	−0.911136	+	0.331626i	−0.754706	−	0.656063i	$-0.772221\pi$
$541$	−21.1925	+	7.71343i	−0.911136	+	0.331626i	−0.156430	+	0.987689i	$0.549998\pi$
$542$		0			0
$543$	12.2640	+	3.28614i	0.526300	+	0.141022i
$544$		0			0
$545$	−24.5130	+	24.3547i	−1.05002	+	1.04324i
$546$		0			0
$547$	36.5018	−	3.19349i	1.56070	−	0.136544i	0.726175	−	0.687510i	$-0.241296\pi$
$547$	36.5018	−	3.19349i	1.56070	−	0.136544i	0.834528	+	0.550966i	$0.185741\pi$
$548$		0			0
$549$	−1.15792	+	3.18135i	−0.0494187	+	0.135777i
$550$		0			0
$551$	−24.0109	+	22.8321i	−1.02290	+	0.972682i
$552$		0			0
$553$	2.41144	+	5.17135i	0.102545	+	0.219908i
$554$		0			0
$555$	3.08060	+	11.6478i	0.130764	+	0.494420i
$556$		0			0
$557$	33.9568	−	23.7768i	1.43880	−	1.00746i	0.445083	−	0.895489i	$-0.353174\pi$
$557$	33.9568	−	23.7768i	1.43880	−	1.00746i	0.993712	−	0.111966i	$-0.0357147\pi$
$558$		0			0
$559$	−13.5742	−	23.5112i	−0.574129	−	0.994420i
$560$		0			0
$561$	−10.3078	−	28.3204i	−0.435195	−	1.19569i
$562$		0			0
$563$	−4.31800	+	1.15700i	−0.181982	+	0.0487619i	−0.348659	−	0.937250i	$-0.613363\pi$
$563$	−4.31800	+	1.15700i	−0.181982	+	0.0487619i	0.166677	+	0.986012i	$0.446696\pi$
$564$		0			0
$565$	−11.8870	−	10.0402i	−0.500089	−	0.422393i
$566$		0			0
$567$	1.92339	−	2.74689i	0.0807750	−	0.115359i
$568$		0			0
$569$	−24.2123			−1.01503			−0.507516	−	0.861642i	$-0.669436\pi$
$569$	−24.2123			−1.01503			−0.507516	+	0.861642i	$0.669436\pi$
$570$		0			0
$571$	−34.3613			−1.43798			−0.718988	−	0.695022i	$-0.755395\pi$
$571$	−34.3613			−1.43798			−0.718988	+	0.695022i	$0.755395\pi$
$572$		0			0
$573$	10.0883	−	14.4075i	0.421444	−	0.601884i
$574$		0			0
$575$	−33.7834	+	8.81802i	−1.40887	+	0.367737i
$576$		0			0
$577$	−11.5754	+	3.10163i	−0.481892	+	0.129122i	−0.491583	−	0.870831i	$-0.663582\pi$
$577$	−11.5754	+	3.10163i	−0.481892	+	0.129122i	0.00969172	+	0.999953i	$0.496915\pi$
$578$		0			0
$579$	−6.76804	−	18.5950i	−0.281270	−	0.772783i
$580$		0			0
$581$	−0.860583	−	1.49057i	−0.0357030	−	0.0618394i
$582$		0			0
$583$	27.3178	−	19.1281i	1.13139	−	0.792205i
$584$		0			0
$585$	4.69468	+	2.73079i	0.194101	+	0.112904i
$586$		0			0
$587$	0.127928	+	0.274343i	0.00528017	+	0.0113234i	0.908930	−	0.416948i	$-0.136900\pi$
$587$	0.127928	+	0.274343i	0.00528017	+	0.0113234i	−0.903650	+	0.428272i	$0.859123\pi$
$588$		0			0
$589$	20.9206	+	2.36194i	0.862020	+	0.0973221i
$590$		0			0
$591$	7.16010	−	19.6722i	0.294527	−	0.809206i
$592$		0			0
$593$	−13.1398	+	1.14958i	−0.539586	+	0.0472077i	−0.353692	−	0.935362i	$-0.615074\pi$
$593$	−13.1398	+	1.14958i	−0.539586	+	0.0472077i	−0.185894	+	0.982570i	$0.559518\pi$
$594$		0			0
$595$	5.79929	+	5.83699i	0.237748	+	0.239293i
$596$		0			0
$597$	−37.1411	−	9.95194i	−1.52009	−	0.407306i
$598$		0			0
$599$	−23.0207	+	8.37884i	−0.940599	+	0.342350i	−0.766403	−	0.642361i	$-0.777955\pi$
$599$	−23.0207	+	8.37884i	−0.940599	+	0.342350i	−0.174197	+	0.984711i	$0.555733\pi$
$600$		0			0
$601$	8.39944	+	4.84942i	0.342620	+	0.197812i	0.661430	−	0.750007i	$-0.269950\pi$
$601$	8.39944	+	4.84942i	0.342620	+	0.197812i	−0.318810	+	0.947819i	$0.603283\pi$
$602$		0			0
$603$	−4.28858	−	0.375202i	−0.174644	−	0.0152794i
$604$		0			0
$605$	−3.93945	+	8.37721i	−0.160161	+	0.340582i
$606$		0			0
$607$	−27.6117	+	27.6117i	−1.12072	+	1.12072i	−0.129090	+	0.991633i	$0.541206\pi$
$607$	−27.6117	+	27.6117i	−1.12072	+	1.12072i	−0.991633	+	0.129090i	$0.958794\pi$
$608$		0			0
$609$			5.80322i			0.235158i
$610$		0			0
$611$	−16.3043	+	2.87488i	−0.659600	+	0.116305i
$612$		0			0
$613$	−0.0548168	+	0.626559i	−0.00221403	+	0.0253065i	−0.997221	−	0.0744955i	$-0.976265\pi$
$613$	−0.0548168	+	0.626559i	−0.00221403	+	0.0253065i	0.995007	+	0.0998020i	$0.0318209\pi$
$614$		0			0
$615$	9.25765	−	25.1810i	0.373304	−	1.01540i
$616$		0			0
$617$	28.5538	+	13.3149i	1.14953	+	0.536037i	0.901528	−	0.432722i	$-0.142447\pi$
$617$	28.5538	+	13.3149i	1.14953	+	0.536037i	0.248007	+	0.968758i	$0.420225\pi$
$618$		0			0
$619$	−2.68249	+	1.54874i	−0.107818	+	0.0622490i	−0.552940	−	0.833221i	$-0.686494\pi$
$619$	−2.68249	+	1.54874i	−0.107818	+	0.0622490i	0.445121	+	0.895470i	$0.353161\pi$
$620$		0			0
$621$	38.3867	+	6.76862i	1.54041	+	0.271615i
$622$		0			0
$623$	−0.315985	−	3.61173i	−0.0126597	−	0.144701i
$624$		0			0
$625$	23.6011	−	8.24535i	0.944046	−	0.329814i
$626$		0			0
$627$	−16.7226	+	5.61432i	−0.667837	+	0.224214i
$628$		0			0
$629$	24.4041	+	8.88237i	0.973056	+	0.354163i
$630$		0			0
$631$	−17.0940	−	14.3435i	−0.680500	−	0.571007i	0.235652	−	0.971837i	$-0.424277\pi$
$631$	−17.0940	−	14.3435i	−0.680500	−	0.571007i	−0.916152	+	0.400830i	$0.868722\pi$
$632$		0			0
$633$	0.846250	+	1.20857i	0.0336354	+	0.0480364i
$634$		0			0
$635$	11.0859	+	13.2989i	0.439929	+	0.527750i
$636$		0			0
$637$	11.3191	−	24.2738i	0.448477	−	0.961763i
$638$		0			0
$639$	−1.07503	+	1.86200i	−0.0425273	+	0.0736595i
$640$		0			0
$641$	4.29592	+	5.11968i	0.169679	+	0.202215i	0.844182	−	0.536057i	$-0.180087\pi$
$641$	4.29592	+	5.11968i	0.169679	+	0.202215i	−0.674503	+	0.738272i	$0.735642\pi$
$642$		0			0
$643$	−24.2648	−	16.9904i	−0.956910	−	0.670035i	−0.0128874	−	0.999917i	$-0.504102\pi$
$643$	−24.2648	−	16.9904i	−0.956910	−	0.670035i	−0.944022	+	0.329882i	$0.892991\pi$
$644$		0			0
$645$	19.3366	+	13.6332i	0.761380	+	0.536808i
$646$		0			0
$647$	23.4593	+	23.4593i	0.922281	+	0.922281i	0.997190	−	0.0749093i	$-0.0238667\pi$
$647$	23.4593	+	23.4593i	0.922281	+	0.922281i	−0.0749093	+	0.997190i	$0.523867\pi$
$648$		0			0
$649$	4.66875	+	26.4778i	0.183264	+	1.03934i
$650$		0			0
$651$	2.82476	−	2.37025i	0.110711	−	0.0928975i
$652$		0			0
$653$	6.83610	+	25.5127i	0.267517	+	0.998389i	0.960691	+	0.277618i	$0.0895451\pi$
$653$	6.83610	+	25.5127i	0.267517	+	0.998389i	−0.693174	+	0.720770i	$0.743788\pi$
$654$		0			0
$655$	35.5648	+	9.65316i	1.38963	+	0.377180i
$656$		0			0
$657$	1.53038	−	5.71144i	0.0597056	−	0.222824i
$658$		0			0
$659$	−0.251800	+	1.42803i	−0.00980875	+	0.0556282i	−0.989319	−	0.145765i	$-0.953436\pi$
$659$	−0.251800	+	1.42803i	−0.00980875	+	0.0556282i	0.979511	+	0.201393i	$0.0645468\pi$
$660$		0			0
$661$	−8.82689	+	10.5195i	−0.343326	+	0.409160i	−0.909885	−	0.414861i	$-0.863830\pi$
$661$	−8.82689	+	10.5195i	−0.343326	+	0.409160i	0.566559	+	0.824021i	$0.308274\pi$
$662$		0			0
$663$	−41.3436	+	19.2788i	−1.60565	+	0.748728i
$664$		0			0
$665$	3.50073	−	3.30734i	0.135752	−	0.128253i
$666$		0			0
$667$	−48.1074	+	22.4328i	−1.86272	+	0.868602i
$668$		0			0
$669$	−5.93966	+	7.07861i	−0.229641	+	0.273675i
$670$		0			0
$671$	2.51325	−	14.2533i	0.0970228	−	0.550243i
$672$		0			0
$673$	1.43051	−	5.33875i	0.0551422	−	0.205794i	−0.932858	−	0.360243i	$-0.882694\pi$
$673$	1.43051	−	5.33875i	0.0551422	−	0.205794i	0.988001	+	0.154449i	$0.0493604\pi$
$674$		0			0
$675$	−27.7871	−	2.61259i	−1.06953	−	0.100559i
$676$		0			0
$677$	3.44220	+	12.8465i	0.132294	+	0.493729i	0.999994	−	0.00335887i	$-0.00106916\pi$
$677$	3.44220	+	12.8465i	0.132294	+	0.493729i	−0.867700	+	0.497088i	$0.834402\pi$
$678$		0			0
$679$	0.532337	−	0.446684i	0.0204292	−	0.0171422i
$680$		0			0
$681$	−2.85488	−	16.1908i	−0.109399	−	0.620433i
$682$		0			0
$683$	5.48507	+	5.48507i	0.209880	+	0.209880i	0.804217	−	0.594336i	$-0.202585\pi$
$683$	5.48507	+	5.48507i	0.209880	+	0.209880i	−0.594336	+	0.804217i	$0.702585\pi$
$684$		0			0
$685$	−2.79497	−	16.1570i	−0.106790	−	0.617326i
$686$		0			0
$687$	−15.8244	−	11.0804i	−0.603738	−	0.422742i
$688$		0			0
$689$	−32.4464	−	38.6681i	−1.23611	−	1.47314i
$690$		0			0
$691$	−4.54170	+	7.86646i	−0.172775	+	0.299254i	−0.939389	−	0.342854i	$-0.888607\pi$
$691$	−4.54170	+	7.86646i	−0.172775	+	0.299254i	0.766614	+	0.642108i	$0.221940\pi$
$692$		0			0
$693$	0.335087	−	0.718596i	0.0127289	−	0.0272972i
$694$		0			0
$695$	−23.1411	−	2.10015i	−0.877793	−	0.0796634i
$696$		0			0
$697$	−33.1701	−	47.3718i	−1.25641	−	1.79434i
$698$		0			0
$699$	3.41404	+	2.86472i	0.129131	+	0.108354i
$700$		0			0
$701$	−26.7671	−	9.74244i	−1.01098	−	0.367967i	−0.217171	−	0.976134i	$-0.569683\pi$
$701$	−26.7671	−	9.74244i	−1.01098	−	0.367967i	−0.793809	+	0.608167i	$0.791905\pi$
$702$		0			0
$703$	5.55656	−	14.1486i	0.209570	−	0.533623i
$704$		0			0
$705$	11.8456	−	8.23730i	0.446130	−	0.310235i
$706$		0			0
$707$	0.469007	+	5.36077i	0.0176388	+	0.201613i
$708$		0			0
$709$	16.0271	+	2.82601i	0.601911	+	0.106133i	0.466296	−	0.884629i	$-0.345588\pi$
$709$	16.0271	+	2.82601i	0.601911	+	0.106133i	0.135615	+	0.990762i	$0.456699\pi$
$710$		0			0
$711$	−6.12718	+	3.53753i	−0.229787	+	0.132668i
$712$		0			0
$713$	30.5682	+	14.2542i	1.14479	+	0.533823i
$714$		0			0
$715$	−21.7922	−	8.01175i	−0.814981	−	0.299623i
$716$		0			0
$717$	−1.04625	+	11.9587i	−0.0390730	+	0.446606i
$718$		0			0
$719$	−5.61267	+	0.989666i	−0.209317	+	0.0369083i	−0.277324	−	0.960777i	$-0.589447\pi$
$719$	−5.61267	+	0.989666i	−0.209317	+	0.0369083i	0.0680061	+	0.997685i	$0.478336\pi$
$720$		0			0
$721$		−	1.15790i		−	0.0431226i
$722$		0			0
$723$	−4.20461	+	4.20461i	−0.156371	+	0.156371i
$724$		0			0
$725$	33.0372	−	18.7897i	1.22697	−	0.697831i
$726$		0			0
$727$	9.54101	+	0.834730i	0.353857	+	0.0309584i	0.262698	−	0.964878i	$-0.415388\pi$
$727$	9.54101	+	0.834730i	0.353857	+	0.0309584i	0.0911581	+	0.995836i	$0.470943\pi$
$728$		0			0
$729$	26.0084	+	15.0159i	0.963273	+	0.556146i
$730$		0			0
$731$	47.9230	−	17.4425i	1.77250	−	0.645136i
$732$		0			0
$733$	30.1358	+	8.07486i	1.11309	+	0.298252i	0.768085	−	0.640348i	$-0.221210\pi$
$733$	30.1358	+	8.07486i	1.11309	+	0.298252i	0.345007	+	0.938600i	$0.387877\pi$
$734$		0			0
$735$	−0.0756208	+	23.3410i	−0.00278931	+	0.860946i
$736$		0			0
$737$	18.3338	−	1.60400i	0.675333	−	0.0590840i
$738$		0			0
$739$	14.8938	−	40.9203i	0.547876	−	1.50528i	−0.288697	−	0.957421i	$-0.593222\pi$
$739$	14.8938	−	40.9203i	0.547876	−	1.50528i	0.836573	−	0.547856i	$-0.184556\pi$
$740$		0			0
$741$	10.6717	+	24.4748i	0.392035	+	0.899105i
$742$		0			0
$743$	−1.05126	−	2.25443i	−0.0385669	−	0.0827070i	0.886080	−	0.463532i	$-0.153418\pi$
$743$	−1.05126	−	2.25443i	−0.0385669	−	0.0827070i	−0.924647	+	0.380825i	$0.875640\pi$
$744$		0			0
$745$	30.7904	−	8.14345i	1.12807	−	0.298353i
$746$		0			0
$747$	1.74819	−	1.22410i	0.0639630	−	0.0447874i
$748$		0			0
$749$	−1.72884	−	2.99444i	−0.0631705	−	0.109415i
$750$		0			0
$751$	10.7462	+	29.5249i	0.392134	+	1.07738i	0.966025	+	0.258448i	$0.0832110\pi$
$751$	10.7462	+	29.5249i	0.392134	+	1.07738i	−0.573891	+	0.818932i	$0.694567\pi$
$752$		0			0
$753$	44.1327	−	11.8253i	1.60829	−	0.430939i
$754$		0			0
$755$	−0.0550995	−	0.654194i	−0.00200528	−	0.0238086i
$756$		0			0
$757$	−5.55356	+	7.93130i	−0.201848	+	0.288268i	−0.907296	−	0.420494i	$-0.861857\pi$
$757$	−5.55356	+	7.93130i	−0.201848	+	0.288268i	0.705448	+	0.708762i	$0.250746\pi$
$758$		0			0
$759$	−28.2595			−1.02576
$760$		0			0
$761$	7.46577			0.270634			0.135317	−	0.990802i	$-0.456795\pi$
$761$	7.46577			0.270634			0.135317	+	0.990802i	$0.456795\pi$
$762$		0			0
$763$	4.37964	−	6.25477i	0.158553	−	0.226438i
$764$		0			0
$765$	−6.58328	+	7.79423i	−0.238019	+	0.281801i
$766$		0			0
$767$	39.3090	−	10.5328i	1.41937	−	0.380318i
$768$		0			0
$769$	−3.59032	−	9.86433i	−0.129470	−	0.355717i	0.857972	−	0.513696i	$-0.171724\pi$
$769$	−3.59032	−	9.86433i	−0.129470	−	0.355717i	−0.987442	+	0.157980i	$0.949502\pi$
$770$		0			0
$771$	13.2924	+	23.0232i	0.478715	+	0.829160i
$772$		0			0
$773$	−43.1004	+	30.1792i	−1.55021	+	1.08547i	−0.589558	+	0.807726i	$0.700698\pi$
$773$	−43.1004	+	30.1792i	−1.55021	+	1.08547i	−0.960655	+	0.277744i	$0.910413\pi$
$774$		0			0
$775$	−22.6396	−	8.40668i	−0.813240	−	0.301977i
$776$		0			0
$777$	−1.12515	−	2.41289i	−0.0403645	−	0.0865619i
$778$		0			0
$779$	−28.2066	+	18.7110i	−1.01060	+	0.670392i
$780$		0			0
$781$	3.14369	−	8.63721i	0.112490	−	0.309064i
$782$		0			0
$783$	−42.2687	+	3.69803i	−1.51056	+	0.132157i
$784$		0			0
$785$	1.76621	+	0.00572222i	0.0630388	+	0.000204235i
$786$		0			0
$787$	3.80841	+	1.02046i	0.135755	+	0.0363754i	0.326057	−	0.945350i	$-0.394280\pi$
$787$	3.80841	+	1.02046i	0.135755	+	0.0363754i	−0.190302	+	0.981726i	$0.560947\pi$
$788$		0			0
$789$	23.3095	−	8.48395i	0.829839	−	0.302037i
$790$		0			0
$791$	2.97762	+	1.71913i	0.105872	+	0.0611253i
$792$		0			0
$793$	−21.8237	−	1.90932i	−0.774981	−	0.0678020i
$794$		0			0
$795$	39.8085	+	18.7203i	1.41186	+	0.663940i
$796$		0			0
$797$	12.2777	−	12.2777i	0.434898	−	0.434898i	−0.455392	−	0.890291i	$-0.650501\pi$
$797$	12.2777	−	12.2777i	0.434898	−	0.434898i	0.890291	+	0.455392i	$0.150501\pi$
$798$		0			0
$799$		−	31.1002i		−	1.10025i
$800$		0			0
$801$	4.42715	−	0.780625i	0.156426	−	0.0275820i
$802$		0			0
$803$	−2.20311	+	25.1817i	−0.0777462	+	0.888643i
$804$		0			0
$805$	7.00296	−	3.23795i	0.246822	−	0.114123i
$806$		0			0
$807$	−18.4740	−	8.61455i	−0.650314	−	0.303246i
$808$		0			0
$809$	−11.3728	+	6.56609i	−0.399847	+	0.230852i	−0.686418	−	0.727207i	$-0.740818\pi$
$809$	−11.3728	+	6.56609i	−0.399847	+	0.230852i	0.286571	+	0.958059i	$0.407484\pi$
$810$		0			0
$811$	50.7076	+	8.94113i	1.78059	+	0.313965i	0.964523	−	0.263998i	$-0.0850411\pi$
$811$	50.7076	+	8.94113i	1.78059	+	0.313965i	0.816063	+	0.577963i	$0.196152\pi$
$812$		0			0
$813$	−0.274416	−	3.13659i	−0.00962419	−	0.110005i
$814$		0			0
$815$	27.3334	+	4.91097i	0.957447	+	0.172024i
$816$		0			0
$817$	−9.50039	−	28.2975i	−0.332377	−	0.990004i
$818$		0			0
$819$	−1.12775	−	0.410468i	−0.0394068	−	0.0143429i
$820$		0			0
$821$	10.0401	+	8.42464i	0.350402	+	0.294022i	0.800951	−	0.598729i	$-0.204328\pi$
$821$	10.0401	+	8.42464i	0.350402	+	0.294022i	−0.450550	+	0.892751i	$0.648772\pi$
$822$		0			0
$823$	16.8605	+	24.0793i	0.587721	+	0.839352i	0.997339	−	0.0729048i	$-0.0232269\pi$
$823$	16.8605	+	24.0793i	0.587721	+	0.839352i	−0.409618	+	0.912257i	$0.634338\pi$
$824$		0			0
$825$	20.1684	−	1.63289i	0.702172	−	0.0568500i
$826$		0			0
$827$	−12.0095	+	25.7544i	−0.417610	+	0.895568i	0.579156	+	0.815217i	$0.303382\pi$
$827$	−12.0095	+	25.7544i	−0.417610	+	0.895568i	−0.996767	+	0.0803518i	$0.974396\pi$
$828$		0			0
$829$	13.6717	−	23.6801i	0.474837	−	0.822442i	−0.524747	−	0.851258i	$-0.675840\pi$
$829$	13.6717	−	23.6801i	0.474837	−	0.822442i	0.999585	+	0.0288157i	$0.00917358\pi$
$830$		0			0
$831$	7.46405	+	8.89531i	0.258925	+	0.308575i
$832$		0			0
$833$	41.2135	+	28.8580i	1.42796	+	0.999871i
$834$		0			0
$835$	−31.6146	+	5.46895i	−1.09407	+	0.189261i
$836$		0			0
$837$	19.0642	+	19.0642i	0.658954	+	0.658954i
$838$		0			0
$839$	−1.64823	−	9.34760i	−0.0569033	−	0.322715i	0.943047	−	0.332659i	$-0.107946\pi$
$839$	−1.64823	−	9.34760i	−0.0569033	−	0.322715i	−0.999951	+	0.00994405i	$0.996835\pi$
$840$		0			0
$841$	22.0471	−	18.4997i	0.760244	−	0.637920i
$842$		0			0
$843$	−3.98359	−	14.8670i	−0.137202	−	0.512045i
$844$		0			0
$845$	−1.59129	+	5.86273i	−0.0547420	+	0.201684i
$846$		0			0
$847$	0.529439	−	1.97589i	0.0181917	−	0.0678925i
$848$		0			0
$849$	−1.78762	+	10.1381i	−0.0613508	+	0.347938i
$850$		0			0
$851$	15.6529	−	18.6544i	0.536575	−	0.639466i
$852$		0			0
$853$	6.11377	−	2.85090i	0.209332	−	0.0976129i	−0.315125	−	0.949050i	$-0.602046\pi$
$853$	6.11377	−	2.85090i	0.209332	−	0.0976129i	0.524456	+	0.851437i	$0.324269\pi$
$854$		0			0
$855$	4.46363	+	3.96677i	0.152653	+	0.135661i
$856$		0			0
$857$	−16.4626	+	7.67664i	−0.562352	+	0.262229i	−0.682941	−	0.730473i	$-0.739299\pi$
$857$	−16.4626	+	7.67664i	−0.562352	+	0.262229i	0.120589	+	0.992703i	$0.461522\pi$
$858$		0			0
$859$	−5.87826	+	7.00544i	−0.200564	+	0.239022i	−0.856946	−	0.515406i	$-0.827641\pi$
$859$	−5.87826	+	7.00544i	−0.200564	+	0.239022i	0.656383	+	0.754428i	$0.272086\pi$
$860$		0			0
$861$	−1.02946	+	5.83836i	−0.0350839	+	0.198971i
$862$		0			0
$863$	−3.50552	+	13.0828i	−0.119329	+	0.445343i	−0.999574	−	0.0291764i	$-0.990712\pi$
$863$	−3.50552	+	13.0828i	−0.119329	+	0.445343i	0.880245	+	0.474520i	$0.157378\pi$
$864$		0			0
$865$	8.36473	+	14.5972i	0.284409	+	0.496318i
$866$		0			0
$867$	−15.3807	−	57.4015i	−0.522355	−	1.94946i
$868$		0			0
$869$	23.1698	−	19.4418i	0.785982	−	0.659517i
$870$		0			0
$871$	−4.83723	−	27.4333i	−0.163903	−	0.929541i
$872$		0			0
$873$	0.609284	+	0.609284i	0.0206211	+	0.0206211i
$874$		0			0
$875$	−4.81080	+	2.71552i	−0.162635	+	0.0918013i
$876$		0			0
$877$	−29.4789	−	20.6414i	−0.995433	−	0.697009i	−0.0421569	−	0.999111i	$-0.513423\pi$
$877$	−29.4789	−	20.6414i	−0.995433	−	0.697009i	−0.953276	+	0.302102i	$0.902312\pi$
$878$		0			0
$879$	17.3307	+	20.6540i	0.584551	+	0.696641i
$880$		0			0
$881$	−15.2716	+	26.4512i	−0.514514	+	0.891165i	0.485344	+	0.874323i	$0.338694\pi$
$881$	−15.2716	+	26.4512i	−0.514514	+	0.891165i	−0.999858	+	0.0168414i	$0.994639\pi$
$882$		0			0
$883$	12.8611	−	27.5806i	0.432809	−	0.928162i	−0.562070	−	0.827090i	$-0.689995\pi$
$883$	12.8611	−	27.5806i	0.432809	−	0.928162i	0.994879	−	0.101072i	$-0.0322274\pi$
$884$		0			0
$885$	−27.2420	+	22.7088i	−0.915731	+	0.763347i
$886$		0			0
$887$	6.36565	+	9.09110i	0.213738	+	0.305249i	0.911677	−	0.410908i	$-0.134788\pi$
$887$	6.36565	+	9.09110i	0.213738	+	0.305249i	−0.697939	+	0.716157i	$0.745899\pi$
$888$		0			0
$889$	−2.93073	−	2.45917i	−0.0982934	−	0.0824780i
$890$		0			0
$891$	−16.7033	−	6.07952i	−0.559583	−	0.203672i
$892$		0			0
$893$	−18.1973	−	0.457898i	−0.608950	−	0.0153230i
$894$		0			0
$895$	17.6045	+	25.3160i	0.588453	+	0.846220i
$896$		0			0
$897$	3.72803	+	42.6116i	0.124475	+	1.42276i
$898$		0			0
$899$	−36.1568	−	6.37542i	−1.20590	−	0.212632i
$900$		0			0
$901$	82.1189	−	47.4114i	2.73578	−	1.57950i
$902$		0			0
$903$	−4.73825	−	2.20948i	−0.157679	−	0.0735270i
$904$		0			0
$905$	7.71144	+	16.6781i	0.256337	+	0.554399i
$906$		0			0
$907$	−3.54076	+	40.4711i	−0.117569	+	1.34382i	0.676702	+	0.736257i	$0.263409\pi$
$907$	−3.54076	+	40.4711i	−0.117569	+	1.34382i	−0.794271	+	0.607563i	$0.792147\pi$
$908$		0			0
$909$	−6.57107	+	1.15866i	−0.217949	+	0.0384302i
$910$		0			0
$911$			17.8168i			0.590296i	0.955452	+	0.295148i	$0.0953689\pi$
$911$			17.8168i			0.590296i	−0.955452	+	0.295148i	$0.904631\pi$
$912$		0			0
$913$	−6.45132	+	6.45132i	−0.213507	+	0.213507i
$914$		0			0
$915$	17.9613	−	6.47157i	0.593783	−	0.213943i
$916$		0			0
$917$	−8.11218	−	0.709723i	−0.267888	−	0.0234371i
$918$		0			0
$919$	−4.61864	−	2.66658i	−0.152355	−	0.0879622i	0.421884	−	0.906650i	$-0.361369\pi$
$919$	−4.61864	−	2.66658i	−0.152355	−	0.0879622i	−0.574239	+	0.818687i	$0.694702\pi$
$920$		0			0
$921$	−40.2886	+	14.6638i	−1.32755	+	0.483190i
$922$		0			0
$923$	−13.4385	−	3.60083i	−0.442333	−	0.118523i
$924$		0			0
$925$	−10.0933	+	14.2178i	−0.331867	+	0.467479i
$926$		0			0
$927$	1.43027	−	0.125133i	0.0469763	−	0.00410990i
$928$		0			0
$929$	−2.96996	+	8.15991i	−0.0974413	+	0.267718i	−0.978830	−	0.204673i	$-0.934387\pi$
$929$	−2.96996	+	8.15991i	−0.0974413	+	0.267718i	0.881389	+	0.472391i	$0.156609\pi$
$930$		0			0
$931$	17.4922	−	23.6900i	0.573283	−	0.776407i
$932$		0			0
$933$	−12.5442	−	26.9010i	−0.410677	−	0.880700i
$934$		0			0
$935$	21.9301	−	37.7014i	0.717191	−	1.23297i
$936$		0			0
$937$	−39.1356	+	27.4030i	−1.27850	+	0.895217i	−0.997911	−	0.0646098i	$-0.979420\pi$
$937$	−39.1356	+	27.4030i	−1.27850	+	0.895217i	−0.280592	+	0.959827i	$0.590531\pi$
$938$		0			0
$939$	21.0843	+	36.5191i	0.688061	+	1.19176i
$940$		0			0
$941$	6.10190	+	16.7648i	0.198916	+	0.546518i	0.998542	−	0.0539806i	$-0.0171909\pi$
$941$	6.10190	+	16.7648i	0.198916	+	0.546518i	−0.799626	+	0.600499i	$0.794969\pi$
$942$		0			0
$943$	−52.3781	+	14.0347i	−1.70567	+	0.457032i
$944$		0			0
$945$	6.14549	−	0.517604i	0.199913	−	0.0168377i
$946$		0			0
$947$	5.98940	−	8.55374i	0.194629	−	0.277959i	−0.709961	−	0.704240i	$-0.751288\pi$
$947$	5.98940	−	8.55374i	0.194629	−	0.277959i	0.904591	+	0.426281i	$0.140177\pi$
$948$		0			0
$949$	38.2613			1.24201
$950$		0			0
$951$	11.3441			0.367859
$952$		0			0
$953$	−17.4761	+	24.9585i	−0.566107	+	0.808485i	−0.995513	−	0.0946271i	$-0.969834\pi$
$953$	−17.4761	+	24.9585i	−0.566107	+	0.808485i	0.429406	+	0.903112i	$0.358723\pi$
$954$		0			0
$955$	25.3641	−	2.13629i	0.820762	−	0.0691287i
$956$		0			0
$957$	29.7135	−	7.96170i	0.960500	−	0.257365i
$958$		0			0
$959$	1.23923	+	3.40476i	0.0400168	+	0.109945i
$960$		0			0
$961$	−3.83548	−	6.64325i	−0.123725	−	0.214299i
$962$		0			0
$963$	3.51198	−	2.45911i	0.113172	−	0.0792438i
$964$		0			0
$965$	14.3992	−	24.7545i	0.463526	−	0.796877i
$966$		0			0
$967$	10.9073	+	23.3908i	0.350756	+	0.752198i	0.999965	−	0.00841219i	$-0.00267771\pi$
$967$	10.9073	+	23.3908i	0.350756	+	0.752198i	−0.649209	+	0.760610i	$0.724900\pi$
$968$		0			0
$969$	−48.7588	+	11.7587i	−1.56636	+	0.377743i
$970$		0			0
$971$	−17.2725	+	47.4558i	−0.554301	+	1.52293i	0.273479	+	0.961878i	$0.411826\pi$
$971$	−17.2725	+	47.4558i	−0.554301	+	1.52293i	−0.827780	+	0.561052i	$0.810397\pi$
$972$		0			0
$973$	5.11502	−	0.447506i	0.163980	−	0.0143464i
$974$		0			0
$975$	−5.12282	−	30.1958i	−0.164061	−	0.967039i
$976$		0			0
$977$	−3.14630	−	0.843049i	−0.100659	−	0.0269715i	0.208138	−	0.978099i	$-0.433260\pi$
$977$	−3.14630	−	0.843049i	−0.100659	−	0.0269715i	−0.308797	+	0.951128i	$0.599926\pi$
$978$		0			0
$979$	−18.0591	+	6.57299i	−0.577173	+	0.210074i
$980$		0			0
$981$	8.19934	+	4.73389i	0.261785	+	0.151142i
$982$		0			0
$983$	2.15469	+	0.188511i	0.0687239	+	0.00601256i	0.121466	−	0.992596i	$-0.461241\pi$
$983$	2.15469	+	0.188511i	0.0687239	+	0.00601256i	−0.0527419	+	0.998608i	$0.516796\pi$
$984$		0			0
$985$	28.5030	−	10.2698i	0.908182	−	0.327223i
$986$		0			0
$987$	−2.25441	+	2.25441i	−0.0717585	+	0.0717585i
$988$		0			0
$989$		−	47.8199i		−	1.52059i
$990$		0			0
$991$	44.1414	−	7.78333i	1.40220	−	0.247246i	0.579152	−	0.815219i	$-0.303384\pi$
$991$	44.1414	−	7.78333i	1.40220	−	0.247246i	0.823047	+	0.567974i	$0.192272\pi$
$992$		0			0
$993$	−3.28326	+	37.5279i	−0.104191	+	1.19091i
$994$		0			0
$995$	−23.3538	−	50.5090i	−0.740366	−	1.60124i
$996$		0			0
$997$	−29.0842	−	13.5622i	−0.921107	−	0.429519i	−0.0965694	−	0.995326i	$-0.530787\pi$
$997$	−29.0842	−	13.5622i	−0.921107	−	0.429519i	−0.824538	+	0.565807i	$0.808565\pi$
$998$		0			0
$999$	16.8577	−	9.73278i	0.533353	−	0.307932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.357.4	yes	120
5.3	odd	4	inner	380.2.bh.a.53.4	yes	120
19.14	odd	18	inner	380.2.bh.a.337.4	yes	120
95.33	even	36	inner	380.2.bh.a.33.4	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.33.4	✓	120	95.33	even	36	inner
380.2.bh.a.53.4	yes	120	5.3	odd	4	inner
380.2.bh.a.337.4	yes	120	19.14	odd	18	inner
380.2.bh.a.357.4	yes	120	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.886233 + 1.26567i) q^{3} +(-2.22818 + 0.187668i) q^{5} +(0.477272 - 0.127885i) q^{7} +(0.209544 + 0.575718i) q^{9} +O(q^{10})\)	\(q+(-0.886233 + 1.26567i) q^{3} +(-2.22818 + 0.187668i) q^{5} +(0.477272 - 0.127885i) q^{7} +(0.209544 + 0.575718i) q^{9} +(-1.30958 - 2.26826i) q^{11} +(-3.24748 + 2.27391i) q^{13} +(1.73716 - 2.98646i) q^{15} +(-3.14733 - 6.74948i) q^{17} +(-3.99559 + 1.74219i) q^{19} +(-0.261114 + 0.717405i) q^{21} +(-6.95648 + 0.608613i) q^{23} +(4.92956 - 0.836317i) q^{25} +(-5.39173 - 1.44471i) q^{27} +(7.14293 - 2.59981i) q^{29} +(-4.18291 - 2.41501i) q^{31} +(4.03147 + 0.352708i) q^{33} +(-1.03945 + 0.374519i) q^{35} +(-2.46586 + 2.46586i) q^{37} -6.12545i q^{39} +(7.64737 - 1.34844i) q^{41} +(-0.596842 + 6.82194i) q^{43} +(-0.574946 - 1.24348i) q^{45} +(3.78481 + 1.76489i) q^{47} +(-5.85074 + 3.37793i) q^{49} +(11.3319 + 1.99812i) q^{51} +(1.10972 + 12.6842i) q^{53} +(3.34367 + 4.80833i) q^{55} +(1.33598 - 6.60110i) q^{57} +(-9.64613 - 3.51090i) q^{59} +(4.23307 + 3.55197i) q^{61} +(0.173635 + 0.247977i) q^{63} +(6.80922 - 5.67612i) q^{65} +(-2.96957 + 6.36826i) q^{67} +(5.39476 - 9.34399i) q^{69} +(2.25576 + 2.68831i) q^{71} +(-7.90574 - 5.53566i) q^{73} +(-3.31024 + 6.98038i) q^{75} +(-0.915103 - 0.915103i) q^{77} +(2.00528 + 11.3725i) q^{79} +(5.19887 - 4.36237i) q^{81} +(-0.901564 - 3.36468i) q^{83} +(8.27949 + 14.4484i) q^{85} +(-3.03979 + 11.3446i) q^{87} +(1.27414 - 7.22603i) q^{89} +(-1.25913 + 1.50057i) q^{91} +(6.76364 - 3.15394i) q^{93} +(8.57594 - 4.63176i) q^{95} +(1.27464 - 0.594373i) q^{97} +(1.03146 - 1.22925i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 120 * q + 6 * q^7	\( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more