LMFDB - Embedded newform 888.2.bo.c.49.1

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			49.1
Character	$\chi$	$=$	888.49
Dual form			888.2.bo.c.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{3} +(-2.56352 + 0.933046i) q^{5} +(-1.16825 + 0.425209i) q^{7} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{3} +(-2.56352 + 0.933046i) q^{5} +(-1.16825 + 0.425209i) q^{7} +(0.173648 + 0.984808i) q^{9} +(-1.02342 - 1.77261i) q^{11} +(-0.543311 + 3.08127i) q^{13} +(-2.56352 - 0.933046i) q^{15} +(-1.15171 - 6.53170i) q^{17} +(-2.48196 - 2.08261i) q^{19} +(-1.16825 - 0.425209i) q^{21} +(0.621614 - 1.07667i) q^{23} +(1.87086 - 1.56984i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-2.29924 - 3.98239i) q^{29} -0.430705 q^{31} +(0.355429 - 2.01574i) q^{33} +(2.59810 - 2.18007i) q^{35} +(-5.89561 - 1.49724i) q^{37} +(-2.39680 + 2.01116i) q^{39} +(0.763342 - 4.32913i) q^{41} -7.14236 q^{43} +(-1.36402 - 2.36256i) q^{45} +(0.610114 - 1.05675i) q^{47} +(-4.17830 + 3.50601i) q^{49} +(3.31623 - 5.74388i) q^{51} +(-6.90819 - 2.51437i) q^{53} +(4.27748 + 3.58923i) q^{55} +(-0.562615 - 3.19075i) q^{57} +(2.29845 + 0.836566i) q^{59} +(-1.85680 + 10.5304i) q^{61} +(-0.621614 - 1.07667i) q^{63} +(-1.48218 - 8.40585i) q^{65} +(11.1010 - 4.04044i) q^{67} +(1.16825 - 0.425209i) q^{69} +(4.61368 + 3.87134i) q^{71} -4.77058 q^{73} +2.44223 q^{75} +(1.94934 + 1.63569i) q^{77} +(3.91478 - 1.42486i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(1.09598 + 6.21564i) q^{83} +(9.04683 + 15.6696i) q^{85} +(0.798516 - 4.52861i) q^{87} +(-12.0659 - 4.39164i) q^{89} +(-0.675460 - 3.83072i) q^{91} +(-0.329939 - 0.276852i) q^{93} +(8.30574 + 3.02304i) q^{95} +(4.10447 - 7.10915i) q^{97} +(1.56797 - 1.31568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$1$	$1$

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
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$4$		0			0
$5$	−2.56352	+	0.933046i	−1.14644	+	0.417271i	−0.844236	−	0.535971i	$-0.819945\pi$
$5$	−2.56352	+	0.933046i	−1.14644	+	0.417271i	−0.302207	+	0.953242i	$0.597723\pi$
$6$		0			0
$7$	−1.16825	+	0.425209i	−0.441558	+	0.160714i	−0.553225	−	0.833032i	$-0.686603\pi$
$7$	−1.16825	+	0.425209i	−0.441558	+	0.160714i	0.111667	+	0.993746i	$0.464381\pi$
$8$		0			0
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$		0			0
$11$	−1.02342	−	1.77261i	−0.308572	−	0.534462i	0.669478	−	0.742832i	$-0.266518\pi$
$11$	−1.02342	−	1.77261i	−0.308572	−	0.534462i	−0.978050	+	0.208369i	$0.933184\pi$
$12$		0			0
$13$	−0.543311	+	3.08127i	−0.150687	+	0.854591i	0.811936	+	0.583747i	$0.198414\pi$
$13$	−0.543311	+	3.08127i	−0.150687	+	0.854591i	−0.962623	+	0.270844i	$0.912697\pi$
$14$		0			0
$15$	−2.56352	−	0.933046i	−0.661899	−	0.240912i
$16$		0			0
$17$	−1.15171	−	6.53170i	−0.279332	−	1.58417i	−0.724856	−	0.688900i	$-0.758094\pi$
$17$	−1.15171	−	6.53170i	−0.279332	−	1.58417i	0.445524	−	0.895270i	$-0.353017\pi$
$18$		0			0
$19$	−2.48196	−	2.08261i	−0.569401	−	0.477784i	0.312046	−	0.950067i	$-0.398986\pi$
$19$	−2.48196	−	2.08261i	−0.569401	−	0.477784i	−0.881447	+	0.472283i	$0.843430\pi$
$20$		0			0
$21$	−1.16825	−	0.425209i	−0.254934	−	0.0927883i
$22$		0			0
$23$	0.621614	−	1.07667i	0.129616	−	0.224501i	−0.793912	−	0.608033i	$-0.791959\pi$
$23$	0.621614	−	1.07667i	0.129616	−	0.224501i	0.923528	+	0.383532i	$0.125292\pi$
$24$		0			0
$25$	1.87086	−	1.56984i	0.374171	−	0.313967i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	−2.29924	−	3.98239i	−0.426957	−	0.739512i	0.569644	−	0.821892i	$-0.307081\pi$
$29$	−2.29924	−	3.98239i	−0.426957	−	0.739512i	−0.996601	+	0.0823801i	$0.973748\pi$
$30$		0			0
$31$	−0.430705			−0.0773568			−0.0386784	−	0.999252i	$-0.512315\pi$
$31$	−0.430705			−0.0773568			−0.0386784	+	0.999252i	$0.512315\pi$
$32$		0			0
$33$	0.355429	−	2.01574i	0.0618723	−	0.350895i
$34$		0			0
$35$	2.59810	−	2.18007i	0.439160	−	0.368499i
$36$		0			0
$37$	−5.89561	−	1.49724i	−0.969233	−	0.246145i
$37$	−5.89561	−	1.49724i	−0.969233	−	0.246145i
$38$		0			0
$39$	−2.39680	+	2.01116i	−0.383796	+	0.322043i
$40$		0			0
$41$	0.763342	−	4.32913i	0.119214	−	0.676097i	−0.865363	−	0.501145i	$-0.832912\pi$
$41$	0.763342	−	4.32913i	0.119214	−	0.676097i	0.984577	−	0.174951i	$-0.0559767\pi$
$42$		0			0
$43$	−7.14236			−1.08920			−0.544600	−	0.838696i	$-0.683319\pi$
$43$	−7.14236			−1.08920			−0.544600	+	0.838696i	$0.683319\pi$
$44$		0			0
$45$	−1.36402	−	2.36256i	−0.203336	−	0.352189i
$46$		0			0
$47$	0.610114	−	1.05675i	0.0889942	−	0.154143i	−0.818092	−	0.575087i	$-0.804968\pi$
$47$	0.610114	−	1.05675i	0.0889942	−	0.154143i	0.907086	+	0.420945i	$0.138301\pi$
$48$		0			0
$49$	−4.17830	+	3.50601i	−0.596900	+	0.500859i
$50$		0			0
$51$	3.31623	−	5.74388i	0.464365	−	0.804304i
$52$		0			0
$53$	−6.90819	−	2.51437i	−0.948912	−	0.345376i	−0.179233	−	0.983807i	$-0.557362\pi$
$53$	−6.90819	−	2.51437i	−0.948912	−	0.345376i	−0.769679	+	0.638431i	$0.779584\pi$
$54$		0			0
$55$	4.27748	+	3.58923i	0.576776	+	0.483972i
$56$		0			0
$57$	−0.562615	−	3.19075i	−0.0745201	−	0.422625i
$58$		0			0
$59$	2.29845	+	0.836566i	0.299232	+	0.108912i	0.487273	−	0.873250i	$-0.337992\pi$
$59$	2.29845	+	0.836566i	0.299232	+	0.108912i	−0.188041	+	0.982161i	$0.560214\pi$
$60$		0			0
$61$	−1.85680	+	10.5304i	−0.237738	+	1.34828i	0.599031	+	0.800726i	$0.295553\pi$
$61$	−1.85680	+	10.5304i	−0.237738	+	1.34828i	−0.836769	+	0.547555i	$0.815559\pi$
$62$		0			0
$63$	−0.621614	−	1.07667i	−0.0783160	−	0.135647i
$64$		0			0
$65$	−1.48218	−	8.40585i	−0.183842	−	1.04262i
$66$		0			0
$67$	11.1010	−	4.04044i	1.35621	−	0.493619i	0.441327	−	0.897346i	$-0.354508\pi$
$67$	11.1010	−	4.04044i	1.35621	−	0.493619i	0.914879	+	0.403728i	$0.132286\pi$
$68$		0			0
$69$	1.16825	−	0.425209i	0.140641	−	0.0511892i
$70$		0			0
$71$	4.61368	+	3.87134i	0.547543	+	0.459443i	0.874108	−	0.485732i	$-0.161447\pi$
$71$	4.61368	+	3.87134i	0.547543	+	0.459443i	−0.326565	+	0.945175i	$0.605891\pi$
$72$		0			0
$73$	−4.77058			−0.558354			−0.279177	−	0.960240i	$-0.590062\pi$
$73$	−4.77058			−0.558354			−0.279177	+	0.960240i	$0.590062\pi$
$74$		0			0
$75$	2.44223			0.282004
$76$		0			0
$77$	1.94934	+	1.63569i	0.222148	+	0.186404i
$78$		0			0
$79$	3.91478	−	1.42486i	0.440447	−	0.160309i	−0.112272	−	0.993678i	$-0.535813\pi$
$79$	3.91478	−	1.42486i	0.440447	−	0.160309i	0.552718	+	0.833368i	$0.313590\pi$
$80$		0			0
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$		0			0
$83$	1.09598	+	6.21564i	0.120300	+	0.682255i	0.983989	+	0.178230i	$0.0570370\pi$
$83$	1.09598	+	6.21564i	0.120300	+	0.682255i	−0.863689	+	0.504025i	$0.831852\pi$
$84$		0			0
$85$	9.04683	+	15.6696i	0.981266	+	1.69960i
$86$		0			0
$87$	0.798516	−	4.52861i	0.0856099	−	0.485518i
$88$		0			0
$89$	−12.0659	−	4.39164i	−1.27899	−	0.465513i	−0.388890	−	0.921284i	$-0.627141\pi$
$89$	−12.0659	−	4.39164i	−1.27899	−	0.465513i	−0.890097	+	0.455771i	$0.849364\pi$
$90$		0			0
$91$	−0.675460	−	3.83072i	−0.0708075	−	0.401569i
$92$		0			0
$93$	−0.329939	−	0.276852i	−0.0342131	−	0.0287082i
$94$		0			0
$95$	8.30574	+	3.02304i	0.852151	+	0.310157i
$96$		0			0
$97$	4.10447	−	7.10915i	0.416746	−	0.721825i	−0.578864	−	0.815424i	$-0.696504\pi$
$97$	4.10447	−	7.10915i	0.416746	−	0.721825i	0.995610	+	0.0935990i	$0.0298372\pi$
$98$		0			0
$99$	1.56797	−	1.31568i	0.157587	−	0.132231i
$100$		0			0
$101$	−5.87953	+	10.1836i	−0.585035	+	1.01331i	0.409836	+	0.912159i	$0.365586\pi$
$101$	−5.87953	+	10.1836i	−0.585035	+	1.01331i	−0.994871	+	0.101151i	$0.967747\pi$
$102$		0			0
$103$	4.29551	+	7.44004i	0.423249	+	0.733089i	0.996255	−	0.0864623i	$-0.0275562\pi$
$103$	4.29551	+	7.44004i	0.423249	+	0.733089i	−0.573006	+	0.819551i	$0.694223\pi$
$104$		0			0
$105$	3.39158			0.330985
$106$		0			0
$107$	0.000390860	−	0.00221668i	3.77859e−5	−	0.000214294i	−0.984789	−	0.173755i	$-0.944410\pi$
$107$	0.000390860	−	0.00221668i	3.77859e−5	−	0.000214294i	0.984827	+	0.173541i	$0.0555209\pi$
$108$		0			0
$109$	−10.5647	+	8.86485i	−1.01192	+	0.849098i	−0.988590	−	0.150630i	$-0.951870\pi$
$109$	−10.5647	+	8.86485i	−1.01192	+	0.849098i	−0.0233257	+	0.999728i	$0.507425\pi$
$110$		0			0
$111$	−3.55390	−	4.93658i	−0.337321	−	0.468560i
$112$		0			0
$113$	−9.33816	+	7.83565i	−0.878460	+	0.737116i	−0.965862	−	0.259057i	$-0.916588\pi$
$113$	−9.33816	+	7.83565i	−0.878460	+	0.737116i	0.0874015	+	0.996173i	$0.472144\pi$
$114$		0			0
$115$	−0.588942	+	3.34006i	−0.0549192	+	0.311462i
$116$		0			0
$117$	−3.12880			−0.289258
$118$		0			0
$119$	4.12283	+	7.14096i	0.377939	+	0.654610i
$120$		0			0
$121$	3.40523	−	5.89804i	0.309567	−	0.536185i
$122$		0			0
$123$	3.36747	−	2.82564i	0.303634	−	0.254779i
$124$		0			0
$125$	3.48886	−	6.04287i	0.312053	−	0.540491i
$126$		0			0
$127$	3.18985	+	1.16101i	0.283053	+	0.103023i	0.479646	−	0.877462i	$-0.340765\pi$
$127$	3.18985	+	1.16101i	0.283053	+	0.103023i	−0.196592	+	0.980485i	$0.562987\pi$
$128$		0			0
$129$	−5.47137	−	4.59102i	−0.481727	−	0.404217i
$130$		0			0
$131$	−1.49827	−	8.49714i	−0.130905	−	0.742398i	−0.977624	−	0.210359i	$-0.932537\pi$
$131$	−1.49827	−	8.49714i	−0.130905	−	0.742398i	0.846719	−	0.532040i	$-0.178574\pi$
$132$		0			0
$133$	3.78510	+	1.37766i	0.328210	+	0.119459i
$134$		0			0
$135$	0.473720	−	2.68660i	0.0407713	−	0.231226i
$136$		0			0
$137$	−6.32461	−	10.9545i	−0.540348	−	0.935910i	−0.998884	−	0.0472342i	$-0.984959\pi$
$137$	−6.32461	−	10.9545i	−0.540348	−	0.935910i	0.458536	−	0.888676i	$-0.348374\pi$
$138$		0			0
$139$	2.21816	+	12.5798i	0.188142	+	1.06701i	0.921851	+	0.387544i	$0.126676\pi$
$139$	2.21816	+	12.5798i	0.188142	+	1.06701i	−0.733709	+	0.679464i	$0.762213\pi$
$140$		0			0
$141$	1.14664	−	0.417342i	0.0965644	−	0.0351466i
$142$		0			0
$143$	6.01793	−	2.19035i	0.503244	−	0.183166i
$144$		0			0
$145$	9.60990	+	8.06366i	0.798059	+	0.669651i
$146$		0			0
$147$	−5.45438			−0.449870
$148$		0			0
$149$	0.168765			0.0138258			0.00691288	−	0.999976i	$-0.497800\pi$
$149$	0.168765			0.0138258			0.00691288	+	0.999976i	$0.497800\pi$
$150$		0			0
$151$	6.48184	+	5.43891i	0.527484	+	0.442612i	0.867232	−	0.497905i	$-0.165897\pi$
$151$	6.48184	+	5.43891i	0.527484	+	0.442612i	−0.339747	+	0.940517i	$0.610342\pi$
$152$		0			0
$153$	6.23248	−	2.26844i	0.503866	−	0.183392i
$154$		0			0
$155$	1.10412	−	0.401867i	0.0886852	−	0.0322788i
$156$		0			0
$157$	−0.858891	−	4.87102i	−0.0685470	−	0.388749i	−0.999709	−	0.0241424i	$-0.992314\pi$
$157$	−0.858891	−	4.87102i	−0.0685470	−	0.388749i	0.931162	−	0.364607i	$-0.118797\pi$
$158$		0			0
$159$	−3.67577	−	6.36662i	−0.291507	−	0.504906i
$160$		0			0
$161$	−0.268394	+	1.52214i	−0.0211524	+	0.119961i
$162$		0			0
$163$	−19.0374	−	6.92903i	−1.49112	−	0.542724i	−0.537377	−	0.843342i	$-0.680585\pi$
$163$	−19.0374	−	6.92903i	−1.49112	−	0.542724i	−0.953745	+	0.300618i	$0.902807\pi$
$164$		0			0
$165$	0.969627	+	5.49903i	0.0754853	+	0.428099i
$166$		0			0
$167$	7.23871	+	6.07399i	0.560148	+	0.470020i	0.878360	−	0.478000i	$-0.158638\pi$
$167$	7.23871	+	6.07399i	0.560148	+	0.470020i	−0.318212	+	0.948020i	$0.603082\pi$
$168$		0			0
$169$	3.01696	+	1.09808i	0.232074	+	0.0844679i
$170$		0			0
$171$	1.61998	−	2.80589i	0.123883	−	0.214572i
$172$		0			0
$173$	0.135391	−	0.113607i	0.0102936	−	0.00863736i	−0.637626	−	0.770346i	$-0.720084\pi$
$173$	0.135391	−	0.113607i	0.0102936	−	0.00863736i	0.647920	+	0.761708i	$0.275639\pi$
$174$		0			0
$175$	−1.51813	+	2.62947i	−0.114759	+	0.198769i
$176$		0			0
$177$	1.22298	+	2.11826i	0.0919247	+	0.159218i
$178$		0			0
$179$	17.1380			1.28095			0.640476	−	0.767978i	$-0.278737\pi$
$179$	17.1380			1.28095			0.640476	+	0.767978i	$0.278737\pi$
$180$		0			0
$181$	−0.549581	+	3.11683i	−0.0408500	+	0.231672i	−0.998397	−	0.0566068i	$-0.981972\pi$
$181$	−0.549581	+	3.11683i	−0.0408500	+	0.231672i	0.957547	+	0.288279i	$0.0930830\pi$
$182$		0			0
$183$	−8.19121	+	6.87324i	−0.605511	+	0.508084i
$184$		0			0
$185$	16.5105	−	1.66267i	1.21388	−	0.122242i
$186$		0			0
$187$	−10.3995	+	8.72620i	−0.760485	+	0.638123i
$188$		0			0
$189$	0.215884	−	1.22434i	0.0157033	−	0.0890577i
$190$		0			0
$191$	−22.1475			−1.60254			−0.801268	−	0.598305i	$-0.795841\pi$
$191$	−22.1475			−1.60254			−0.801268	+	0.598305i	$0.795841\pi$
$192$		0			0
$193$	−6.16746	−	10.6823i	−0.443943	−	0.768932i	0.554035	−	0.832494i	$-0.313087\pi$
$193$	−6.16746	−	10.6823i	−0.443943	−	0.768932i	−0.997978	+	0.0635614i	$0.979754\pi$
$194$		0			0
$195$	4.26776	−	7.39198i	0.305621	−	0.529351i
$196$		0			0
$197$	−19.9287	+	16.7222i	−1.41986	+	1.19141i	−0.468452	+	0.883489i	$0.655188\pi$
$197$	−19.9287	+	16.7222i	−1.41986	+	1.19141i	−0.951413	+	0.307919i	$0.900367\pi$
$198$		0			0
$199$	1.39542	−	2.41695i	0.0989190	−	0.171333i	−0.812318	−	0.583214i	$-0.801795\pi$
$199$	1.39542	−	2.41695i	0.0989190	−	0.171333i	0.911237	+	0.411881i	$0.135128\pi$
$200$		0			0
$201$	11.1010	+	4.04044i	0.783006	+	0.284991i
$202$		0			0
$203$	4.37944	+	3.67478i	0.307376	+	0.257919i
$204$		0			0
$205$	2.08243	+	11.8101i	0.145443	+	0.824851i
$206$		0			0
$207$	1.16825	+	0.425209i	0.0811992	+	0.0295541i
$208$		0			0
$209$	−1.15158	+	6.53093i	−0.0796564	+	0.451754i
$210$		0			0
$211$	8.01544	+	13.8831i	0.551806	+	0.955755i	0.998144	+	0.0608912i	$0.0193943\pi$
$211$	8.01544	+	13.8831i	0.551806	+	0.955755i	−0.446339	+	0.894864i	$0.647272\pi$
$212$		0			0
$213$	1.04584	+	5.93123i	0.0716595	+	0.406401i
$214$		0			0
$215$	18.3096	−	6.66416i	1.24871	−	0.454492i
$216$		0			0
$217$	0.503172	−	0.183140i	0.0341575	−	0.0124323i
$218$		0			0
$219$	−3.65448	−	3.06647i	−0.246947	−	0.207213i
$220$		0			0
$221$	20.7517			1.39591
$222$		0			0
$223$	7.50009			0.502243			0.251122	−	0.967956i	$-0.419201\pi$
$223$	7.50009			0.502243			0.251122	+	0.967956i	$0.419201\pi$
$224$		0			0
$225$	1.87086	+	1.56984i	0.124724	+	0.104656i
$226$		0			0
$227$	−16.5258	+	6.01489i	−1.09685	+	0.399222i	−0.826156	−	0.563442i	$-0.809477\pi$
$227$	−16.5258	+	6.01489i	−1.09685	+	0.399222i	−0.270698	+	0.962664i	$0.587255\pi$
$228$		0			0
$229$	5.91590	−	2.15321i	0.390934	−	0.142288i	−0.139072	−	0.990282i	$-0.544412\pi$
$229$	5.91590	−	2.15321i	0.390934	−	0.142288i	0.530006	+	0.847994i	$0.322190\pi$
$230$		0			0
$231$	0.441880	+	2.50602i	0.0290735	+	0.164884i
$232$		0			0
$233$	7.55360	+	13.0832i	0.494853	+	0.857110i	0.999982	−	0.00593363i	$-0.00188874\pi$
$233$	7.55360	+	13.0832i	0.494853	+	0.857110i	−0.505130	+	0.863043i	$0.668555\pi$
$234$		0			0
$235$	−0.578046	+	3.27826i	−0.0377076	+	0.213850i
$236$		0			0
$237$	3.91478	+	1.42486i	0.254292	+	0.0925547i
$238$		0			0
$239$	−5.29487	−	30.0287i	−0.342497	−	1.94239i	−0.334411	−	0.942427i	$-0.608537\pi$
$239$	−5.29487	−	30.0287i	−0.342497	−	1.94239i	−0.00808552	−	0.999967i	$-0.502574\pi$
$240$		0			0
$241$	17.3350	+	14.5458i	1.11665	+	0.936978i	0.998430	−	0.0560100i	$-0.0178379\pi$
$241$	17.3350	+	14.5458i	1.11665	+	0.936978i	0.118217	+	0.992988i	$0.462282\pi$
$242$		0			0
$243$	−0.939693	−	0.342020i	−0.0602813	−	0.0219406i
$244$		0			0
$245$	7.43990	−	12.8863i	0.475318	−	0.823275i
$246$		0			0
$247$	7.76557	−	6.51609i	0.494111	−	0.414609i
$248$		0			0
$249$	−3.15576	+	5.46594i	−0.199988	+	0.346390i
$250$		0			0
$251$	4.47518	+	7.75123i	0.282471	+	0.489253i	0.971993	−	0.235011i	$-0.0755127\pi$
$251$	4.47518	+	7.75123i	0.282471	+	0.489253i	−0.689522	+	0.724265i	$0.742179\pi$
$252$		0			0
$253$	−2.54468			−0.159983
$254$		0			0
$255$	−3.14193	+	17.8188i	−0.196755	+	1.11585i
$256$		0			0
$257$	14.4721	−	12.1435i	0.902745	−	0.757493i	−0.0679801	−	0.997687i	$-0.521655\pi$
$257$	14.4721	−	12.1435i	0.902745	−	0.757493i	0.970725	+	0.240194i	$0.0772110\pi$
$258$		0			0
$259$	7.52421	−	0.757714i	0.467532	−	0.0470821i
$260$		0			0
$261$	3.52263	−	2.95584i	0.218045	−	0.182962i
$262$		0			0
$263$	−1.37393	+	7.79194i	−0.0847201	+	0.480472i	0.912697	+	0.408638i	$0.133996\pi$
$263$	−1.37393	+	7.79194i	−0.0847201	+	0.480472i	−0.997417	+	0.0718336i	$0.977115\pi$
$264$		0			0
$265$	20.0553			1.23199
$266$		0			0
$267$	−6.42015	−	11.1200i	−0.392907	−	0.680535i
$268$		0			0
$269$	0.697189	−	1.20757i	0.0425084	−	0.0736266i	−0.843988	−	0.536361i	$-0.819798\pi$
$269$	0.697189	−	1.20757i	0.0425084	−	0.0736266i	0.886497	+	0.462735i	$0.153132\pi$
$270$		0			0
$271$	−11.3805	+	9.54940i	−0.691318	+	0.580085i	−0.919289	−	0.393583i	$-0.871235\pi$
$271$	−11.3805	+	9.54940i	−0.691318	+	0.580085i	0.227971	+	0.973668i	$0.426791\pi$
$272$		0			0
$273$	1.94491	−	3.36868i	0.117711	−	0.203882i
$274$		0			0
$275$	−4.69737	−	1.70970i	−0.283262	−	0.103099i
$276$		0			0
$277$	4.90551	+	4.11621i	0.294744	+	0.247319i	0.778152	−	0.628075i	$-0.216157\pi$
$277$	4.90551	+	4.11621i	0.294744	+	0.247319i	−0.483409	+	0.875395i	$0.660602\pi$
$278$		0			0
$279$	−0.0747911	−	0.424161i	−0.00447762	−	0.0253939i
$280$		0			0
$281$	1.00397	+	0.365415i	0.0598918	+	0.0217988i	0.371792	−	0.928316i	$-0.378743\pi$
$281$	1.00397	+	0.365415i	0.0598918	+	0.0217988i	−0.311901	+	0.950115i	$0.600966\pi$
$282$		0			0
$283$	2.32494	−	13.1854i	0.138203	−	0.783789i	−0.834372	−	0.551201i	$-0.814170\pi$
$283$	2.32494	−	13.1854i	0.138203	−	0.783789i	0.972575	−	0.232588i	$-0.0747193\pi$
$284$		0			0
$285$	4.41939	+	7.65461i	0.261782	+	0.453420i
$286$		0			0
$287$	0.949009	+	5.38210i	0.0560182	+	0.317695i
$288$		0			0
$289$	−25.3619	+	9.23097i	−1.49188	+	0.542998i
$290$		0			0
$291$	7.71388	−	2.80762i	0.452196	−	0.164586i
$292$		0			0
$293$	−9.54048	−	8.00542i	−0.557361	−	0.467681i	0.320064	−	0.947396i	$-0.396296\pi$
$293$	−9.54048	−	8.00542i	−0.557361	−	0.467681i	−0.877425	+	0.479715i	$0.840740\pi$
$294$		0			0
$295$	−6.67268			−0.388498
$296$		0			0
$297$	2.04683			0.118769
$298$		0			0
$299$	2.97977	+	2.50033i	0.172325	+	0.144598i
$300$		0			0
$301$	8.34408	−	3.03700i	0.480945	−	0.175050i
$302$		0			0
$303$	−11.0499	+	4.02184i	−0.634800	+	0.231048i
$304$		0			0
$305$	−5.06542	−	28.7274i	−0.290045	−	1.64493i
$306$		0			0
$307$	13.6714	+	23.6795i	0.780265	+	1.35146i	0.931787	+	0.363005i	$0.118249\pi$
$307$	13.6714	+	23.6795i	0.780265	+	1.35146i	−0.151522	+	0.988454i	$0.548417\pi$
$308$		0			0
$309$	−1.49181	+	8.46050i	−0.0848664	+	0.481301i
$310$		0			0
$311$	29.7899	+	10.8426i	1.68923	+	0.614830i	0.994528	−	0.104467i	$-0.0333136\pi$
$311$	29.7899	+	10.8426i	1.68923	+	0.614830i	0.694703	+	0.719297i	$0.255536\pi$
$312$		0			0
$313$	−1.89573	−	10.7512i	−0.107153	−	0.607694i	−0.990339	−	0.138670i	$-0.955717\pi$
$313$	−1.89573	−	10.7512i	−0.107153	−	0.607694i	0.883186	−	0.469023i	$-0.155394\pi$
$314$		0			0
$315$	2.59810	+	2.18007i	0.146387	+	0.122833i
$316$		0			0
$317$	−10.9430	−	3.98291i	−0.614618	−	0.223703i	0.0159045	−	0.999874i	$-0.494937\pi$
$317$	−10.9430	−	3.98291i	−0.614618	−	0.223703i	−0.630523	+	0.776171i	$0.717159\pi$
$318$		0			0
$319$	−4.70615	+	8.15130i	−0.263494	+	0.456385i
$320$		0			0
$321$	0.00172427	−	0.00144683i	9.62393e−5	−	8.07544e-5i
$322$		0			0
$323$	−10.7445	+	18.6100i	−0.597839	+	1.03549i
$324$		0			0
$325$	3.82063	+	6.61753i	0.211930	+	0.367074i
$326$		0			0
$327$	−13.7913			−0.762658
$328$		0			0
$329$	−0.263428	+	1.49397i	−0.0145233	+	0.0823655i
$330$		0			0
$331$	−5.81834	+	4.88216i	−0.319805	+	0.268348i	−0.788530	−	0.614996i	$-0.789158\pi$
$331$	−5.81834	+	4.88216i	−0.319805	+	0.268348i	0.468726	+	0.883344i	$0.344713\pi$
$332$		0			0
$333$	0.450731	−	6.06604i	0.0246999	−	0.332417i
$334$		0			0
$335$	−24.6878	+	20.7155i	−1.34884	+	1.13181i
$336$		0			0
$337$	1.49546	−	8.48116i	0.0814627	−	0.461998i	−0.916601	−	0.399803i	$-0.869079\pi$
$337$	1.49546	−	8.48116i	0.0814627	−	0.461998i	0.998064	−	0.0621954i	$-0.0198102\pi$
$338$		0			0
$339$	−12.1901			−0.662076
$340$		0			0
$341$	0.440791	+	0.763472i	0.0238701	+	0.0413443i
$342$		0			0
$343$	7.74182	−	13.4092i	0.418019	−	0.724030i
$344$		0			0
$345$	−2.59810	+	2.18007i	−0.139877	+	0.117371i
$346$		0			0
$347$	3.54065	−	6.13259i	0.190072	−	0.329215i	−0.755202	−	0.655492i	$-0.772461\pi$
$347$	3.54065	−	6.13259i	0.190072	−	0.329215i	0.945274	+	0.326278i	$0.105794\pi$
$348$		0			0
$349$	−4.02741	−	1.46586i	−0.215583	−	0.0784656i	0.231971	−	0.972723i	$-0.425482\pi$
$349$	−4.02741	−	1.46586i	−0.215583	−	0.0784656i	−0.447554	+	0.894257i	$0.647705\pi$
$350$		0			0
$351$	−2.39680	−	2.01116i	−0.127932	−	0.107348i
$352$		0			0
$353$	−3.45872	−	19.6154i	−0.184089	−	1.04402i	−0.927120	−	0.374764i	$-0.877724\pi$
$353$	−3.45872	−	19.6154i	−0.184089	−	1.04402i	0.743031	−	0.669257i	$-0.233387\pi$
$354$		0			0
$355$	−15.4394	−	5.61948i	−0.819439	−	0.298251i
$356$		0			0
$357$	−1.43184	+	8.12040i	−0.0757813	+	0.429777i
$358$		0			0
$359$	−8.08014	−	13.9952i	−0.426453	−	0.738639i	0.570102	−	0.821574i	$-0.306904\pi$
$359$	−8.08014	−	13.9952i	−0.426453	−	0.738639i	−0.996555	+	0.0829354i	$0.973570\pi$
$360$		0			0
$361$	−1.47646	−	8.37343i	−0.0777085	−	0.440707i
$362$		0			0
$363$	6.39975	−	2.32932i	0.335900	−	0.122257i
$364$		0			0
$365$	12.2295	−	4.45117i	0.640121	−	0.232985i
$366$		0			0
$367$	−18.8541	−	15.8204i	−0.984174	−	0.825820i	0.000540026	−	1.00000i	$-0.499828\pi$
$367$	−18.8541	−	15.8204i	−0.984174	−	0.825820i	−0.984714	+	0.174180i	$0.944273\pi$
$368$		0			0
$369$	4.39591			0.228842
$370$		0			0
$371$	9.13964			0.474507
$372$		0			0
$373$	−8.57141	−	7.19227i	−0.443811	−	0.372401i	0.393322	−	0.919401i	$-0.371326\pi$
$373$	−8.57141	−	7.19227i	−0.443811	−	0.372401i	−0.837133	+	0.546999i	$0.815770\pi$
$374$		0			0
$375$	6.55690	−	2.38652i	0.338597	−	0.123239i
$376$		0			0
$377$	13.5200	−	4.92089i	0.696317	−	0.253439i
$378$		0			0
$379$	−5.67385	−	32.1780i	−0.291446	−	1.65287i	−0.681307	−	0.731998i	$-0.738588\pi$
$379$	−5.67385	−	32.1780i	−0.291446	−	1.65287i	0.389861	−	0.920874i	$-0.372523\pi$
$380$		0			0
$381$	1.69728	+	2.93978i	0.0869545	+	0.150610i
$382$		0			0
$383$	4.15578	−	23.5686i	0.212351	−	1.20430i	−0.673095	−	0.739556i	$-0.735035\pi$
$383$	4.15578	−	23.5686i	0.212351	−	1.20430i	0.885445	−	0.464744i	$-0.153854\pi$
$384$		0			0
$385$	−6.52336	−	2.37431i	−0.332461	−	0.121006i
$386$		0			0
$387$	−1.24026	−	7.03385i	−0.0630459	−	0.357551i
$388$		0			0
$389$	11.6702	+	9.79244i	0.591701	+	0.496496i	0.888766	−	0.458361i	$-0.151563\pi$
$389$	11.6702	+	9.79244i	0.591701	+	0.496496i	−0.297065	+	0.954857i	$0.596008\pi$
$390$		0			0
$391$	−7.74839	−	2.82018i	−0.391853	−	0.142623i
$392$		0			0
$393$	4.31411	−	7.47226i	0.217618	−	0.376926i
$394$		0			0
$395$	−8.70616	+	7.30534i	−0.438054	+	0.367571i
$396$		0			0
$397$	−4.48885	+	7.77491i	−0.225289	+	0.390212i	−0.956406	−	0.292040i	$-0.905666\pi$
$397$	−4.48885	+	7.77491i	−0.225289	+	0.390212i	0.731117	+	0.682252i	$0.238999\pi$
$398$		0			0
$399$	2.01401	+	3.48837i	0.100827	+	0.174637i
$400$		0			0
$401$	−31.9257			−1.59429			−0.797147	−	0.603785i	$-0.793658\pi$
$401$	−31.9257			−1.59429			−0.797147	+	0.603785i	$0.793658\pi$
$402$		0			0
$403$	0.234007	−	1.32712i	0.0116567	−	0.0661085i
$404$		0			0
$405$	2.08980	−	1.75355i	0.103843	−	0.0871348i
$406$		0			0
$407$	3.37965	+	11.9829i	0.167523	+	0.593972i
$408$		0			0
$409$	−3.93157	+	3.29898i	−0.194403	+	0.163124i	−0.734794	−	0.678291i	$-0.762721\pi$
$409$	−3.93157	+	3.29898i	−0.194403	+	0.163124i	0.540390	+	0.841414i	$0.318277\pi$
$410$		0			0
$411$	2.19651	−	12.4571i	0.108346	−	0.614461i
$412$		0			0
$413$	−3.04088			−0.149632
$414$		0			0
$415$	−8.60906	−	14.9113i	−0.422602	−	0.731969i
$416$		0			0
$417$	−6.38695	+	11.0625i	−0.312770	+	0.541734i
$418$		0			0
$419$	−21.3001	+	17.8729i	−1.04058	+	0.873150i	−0.992072	−	0.125673i	$-0.959891\pi$
$419$	−21.3001	+	17.8729i	−1.04058	+	0.873150i	−0.0485081	+	0.998823i	$0.515447\pi$
$420$		0			0
$421$	18.1115	−	31.3701i	0.882701	−	1.52888i	0.0343750	−	0.999409i	$-0.489056\pi$
$421$	18.1115	−	31.3701i	0.882701	−	1.52888i	0.848326	−	0.529474i	$-0.177611\pi$
$422$		0			0
$423$	1.14664	+	0.417342i	0.0557515	+	0.0202919i
$424$		0			0
$425$	−12.4084	−	10.4119i	−0.601895	−	0.505050i
$426$		0			0
$427$	−2.30842	−	13.0917i	−0.111712	−	0.633552i
$428$		0			0
$429$	6.01793	+	2.19035i	0.290548	+	0.105751i
$430$		0			0
$431$	6.54540	−	37.1208i	0.315281	−	1.78805i	−0.255360	−	0.966846i	$-0.582194\pi$
$431$	6.54540	−	37.1208i	0.315281	−	1.78805i	0.570641	−	0.821200i	$-0.306695\pi$
$432$		0			0
$433$	−1.03623	−	1.79481i	−0.0497982	−	0.0862529i	0.840052	−	0.542506i	$-0.182524\pi$
$433$	−1.03623	−	1.79481i	−0.0497982	−	0.0862529i	−0.889850	+	0.456253i	$0.849191\pi$
$434$		0			0
$435$	2.17839	+	12.3543i	0.104446	+	0.592341i
$436$		0			0
$437$	−3.78510	+	1.37766i	−0.181066	+	0.0659026i
$438$		0			0
$439$	−14.1572	+	5.15280i	−0.675686	+	0.245930i	−0.656994	−	0.753896i	$-0.728172\pi$
$439$	−14.1572	+	5.15280i	−0.675686	+	0.245930i	−0.0186918	+	0.999825i	$0.505950\pi$
$440$		0			0
$441$	−4.17830	−	3.50601i	−0.198967	−	0.166953i
$442$		0			0
$443$	0.191197			0.00908403			0.00454201	−	0.999990i	$-0.498554\pi$
$443$	0.191197			0.00908403			0.00454201	+	0.999990i	$0.498554\pi$
$444$		0			0
$445$	35.0289			1.66053
$446$		0			0
$447$	0.129281	+	0.108480i	0.00611480	+	0.00513092i
$448$		0			0
$449$	−29.2800	+	10.6571i	−1.38181	+	0.502938i	−0.922726	−	0.385456i	$-0.874044\pi$
$449$	−29.2800	+	10.6571i	−1.38181	+	0.502938i	−0.459083	+	0.888393i	$0.651822\pi$
$450$		0			0
$451$	−8.45508	+	3.07740i	−0.398134	+	0.144909i
$452$		0			0
$453$	1.46931	+	8.33289i	0.0690344	+	0.391513i
$454$		0			0
$455$	5.30580	+	9.18992i	0.248740	+	0.430830i
$456$		0			0
$457$	1.73087	−	9.81627i	0.0809668	−	0.459186i	−0.917187	−	0.398456i	$-0.869546\pi$
$457$	1.73087	−	9.81627i	0.0809668	−	0.459186i	0.998154	−	0.0607296i	$-0.0193427\pi$
$458$		0			0
$459$	6.23248	+	2.26844i	0.290907	+	0.105881i
$460$		0			0
$461$	−0.228273	−	1.29460i	−0.0106317	−	0.0602956i	0.979030	−	0.203715i	$-0.0653015\pi$
$461$	−0.228273	−	1.29460i	−0.0106317	−	0.0602956i	−0.989662	+	0.143419i	$0.954190\pi$
$462$		0			0
$463$	−31.3166	−	26.2777i	−1.45540	−	1.22123i	−0.928515	−	0.371295i	$-0.878914\pi$
$463$	−31.3166	−	26.2777i	−1.45540	−	1.22123i	−0.526889	−	0.849934i	$-0.676642\pi$
$464$		0			0
$465$	1.10412	+	0.401867i	0.0512024	+	0.0186362i
$466$		0			0
$467$	−18.1618	+	31.4572i	−0.840428	+	1.45566i	0.0491057	+	0.998794i	$0.484363\pi$
$467$	−18.1618	+	31.4572i	−0.840428	+	1.45566i	−0.889533	+	0.456870i	$0.848970\pi$
$468$		0			0
$469$	−11.2508	+	9.44052i	−0.519512	+	0.435923i
$470$		0			0
$471$	2.47308	−	4.28350i	0.113953	−	0.197373i
$472$		0			0
$473$	7.30962	+	12.6606i	0.336097	+	0.582136i
$474$		0			0
$475$	−7.91275			−0.363062
$476$		0			0
$477$	1.27658	−	7.23985i	0.0584506	−	0.331490i
$478$		0			0
$479$	−14.4947	+	12.1625i	−0.662282	+	0.555720i	−0.910770	−	0.412915i	$-0.864511\pi$
$479$	−14.4947	+	12.1625i	−0.662282	+	0.555720i	0.248488	+	0.968635i	$0.420066\pi$
$480$		0			0
$481$	7.81656	−	17.3525i	0.356404	−	0.791207i
$482$		0			0
$483$	−1.18401	+	0.993504i	−0.0538744	+	0.0452060i
$484$		0			0
$485$	−3.88874	+	22.0541i	−0.176579	+	1.00143i
$486$		0			0
$487$	−18.8310			−0.853314			−0.426657	−	0.904413i	$-0.640309\pi$
$487$	−18.8310			−0.853314			−0.426657	+	0.904413i	$0.640309\pi$
$488$		0			0
$489$	−10.1296	−	17.5449i	−0.458075	−	0.793409i
$490$		0			0
$491$	1.36452	−	2.36342i	0.0615801	−	0.106660i	−0.833592	−	0.552381i	$-0.813719\pi$
$491$	1.36452	−	2.36342i	0.0615801	−	0.106660i	0.895172	+	0.445721i	$0.147053\pi$
$492$		0			0
$493$	−23.3637	+	19.6045i	−1.05225	+	0.882942i
$494$		0			0
$495$	−2.79193	+	4.83576i	−0.125488	+	0.217351i
$496$		0			0
$497$	−7.03607	−	2.56092i	−0.315611	−	0.114873i
$498$		0			0
$499$	−16.7817	−	14.0815i	−0.751250	−	0.630374i	0.184583	−	0.982817i	$-0.440907\pi$
$499$	−16.7817	−	14.0815i	−0.751250	−	0.630374i	−0.935833	+	0.352443i	$0.885351\pi$
$500$		0			0
$501$	1.64088	+	9.30590i	0.0733092	+	0.415757i
$502$		0			0
$503$	−4.97590	−	1.81108i	−0.221864	−	0.0807520i	0.228696	−	0.973498i	$-0.426554\pi$
$503$	−4.97590	−	1.81108i	−0.221864	−	0.0807520i	−0.450561	+	0.892746i	$0.648776\pi$
$504$		0			0
$505$	5.57050	−	31.5919i	0.247884	−	1.40582i
$506$		0			0
$507$	1.60529	+	2.78044i	0.0712934	+	0.123484i
$508$		0			0
$509$	0.258591	+	1.46655i	0.0114619	+	0.0650035i	0.990002	−	0.141052i	$-0.0450484\pi$
$509$	0.258591	+	1.46655i	0.0114619	+	0.0650035i	−0.978540	+	0.206055i	$0.933937\pi$
$510$		0			0
$511$	5.57324	−	2.02849i	0.246546	−	0.0897353i
$512$		0			0
$513$	3.04457	−	1.10813i	0.134421	−	0.0489253i
$514$		0			0
$515$	−17.9535	−	15.0648i	−0.791128	−	0.663835i
$516$		0			0
$517$	−2.49760			−0.109844
$518$		0			0
$519$	0.176741			0.00775806
$520$		0			0
$521$	20.5940	+	17.2804i	0.902238	+	0.757068i	0.970627	−	0.240591i	$-0.0773412\pi$
$521$	20.5940	+	17.2804i	0.902238	+	0.757068i	−0.0683881	+	0.997659i	$0.521786\pi$
$522$		0			0
$523$	13.4888	−	4.90951i	0.589822	−	0.214678i	−0.0298291	−	0.999555i	$-0.509496\pi$
$523$	13.4888	−	4.90951i	0.589822	−	0.214678i	0.619651	+	0.784877i	$0.287274\pi$
$524$		0			0
$525$	−2.85314	+	1.03846i	−0.124521	+	0.0453221i
$526$		0			0
$527$	0.496049	+	2.81323i	0.0216082	+	0.122546i
$528$		0			0
$529$	10.7272	+	18.5800i	0.466400	+	0.807828i
$530$		0			0
$531$	−0.424736	+	2.40880i	−0.0184320	+	0.104533i
$532$		0			0
$533$	12.9245	+	4.70413i	0.559822	+	0.203759i
$534$		0			0
$535$	0.00106628	+	0.00604720i	4.60995e−5	+	0.000261443i
$536$		0			0
$537$	13.1285	+	11.0161i	0.566535	+	0.475379i
$538$		0			0
$539$	10.4909	+	3.81839i	0.451877	+	0.164470i
$540$		0			0
$541$	2.02182	−	3.50189i	0.0869248	−	0.150558i	−0.819285	−	0.573387i	$-0.805629\pi$
$541$	2.02182	−	3.50189i	0.0869248	−	0.150558i	0.906210	+	0.422828i	$0.138963\pi$
$542$		0			0
$543$	−2.42446	+	2.03436i	−0.104044	+	0.0873029i
$544$		0			0
$545$	18.8116	−	32.5826i	0.805800	−	1.39569i
$546$		0			0
$547$	−15.5145	−	26.8719i	−0.663353	−	1.14896i	−0.979729	−	0.200327i	$-0.935800\pi$
$547$	−15.5145	−	26.8719i	−0.663353	−	1.14896i	0.316376	−	0.948634i	$-0.397534\pi$
$548$		0			0
$549$	−10.6929			−0.456360
$550$		0			0
$551$	−2.58717	+	14.6726i	−0.110217	+	0.625072i
$552$		0			0
$553$	−3.96758	+	3.32920i	−0.168719	+	0.141572i
$554$		0			0
$555$	13.7166	+	9.33909i	0.582235	+	0.396422i
$556$		0			0
$557$	−24.9919	+	20.9707i	−1.05894	+	0.888556i	−0.994005	−	0.109333i	$-0.965129\pi$
$557$	−24.9919	+	20.9707i	−1.05894	+	0.888556i	−0.0649352	+	0.997889i	$0.520684\pi$
$558$		0			0
$559$	3.88053	−	22.0076i	0.164129	−	0.930820i
$560$		0			0
$561$	−13.5756			−0.573160
$562$		0			0
$563$	13.8888	+	24.0561i	0.585342	+	1.01384i	0.994833	+	0.101528i	$0.0323731\pi$
$563$	13.8888	+	24.0561i	0.585342	+	1.01384i	−0.409491	+	0.912314i	$0.634294\pi$
$564$		0			0
$565$	16.6276	−	28.7998i	0.699528	−	1.21162i
$566$		0			0
$567$	0.952368	−	0.799132i	0.0399957	−	0.0335604i
$568$		0			0
$569$	−10.8095	+	18.7226i	−0.453159	+	0.784894i	−0.998580	−	0.0532680i	$-0.983036\pi$
$569$	−10.8095	+	18.7226i	−0.453159	+	0.784894i	0.545422	+	0.838162i	$0.316370\pi$
$570$		0			0
$571$	35.8618	+	13.0526i	1.50077	+	0.546236i	0.956260	−	0.292518i	$-0.0944931\pi$
$571$	35.8618	+	13.0526i	1.50077	+	0.546236i	0.544511	+	0.838754i	$0.316715\pi$
$572$		0			0
$573$	−16.9660	−	14.2361i	−0.708763	−	0.594723i
$574$		0			0
$575$	−0.527239	−	2.99012i	−0.0219874	−	0.124697i
$576$		0			0
$577$	29.9188	+	10.8895i	1.24553	+	0.453337i	0.878890	−	0.477024i	$-0.158285\pi$
$577$	29.9188	+	10.8895i	1.24553	+	0.453337i	0.366644	+	0.930361i	$0.380507\pi$
$578$		0			0
$579$	2.14193	−	12.1475i	0.0890158	−	0.504834i
$580$		0			0
$581$	−3.92333	−	6.79541i	−0.162767	−	0.281921i
$582$		0			0
$583$	2.61295	+	14.8188i	0.108217	+	0.613731i
$584$		0			0
$585$	8.02077	−	2.91932i	0.331618	−	0.120699i
$586$		0			0
$587$	−4.90212	+	1.78423i	−0.202332	+	0.0736429i	−0.441198	−	0.897410i	$-0.645446\pi$
$587$	−4.90212	+	1.78423i	−0.202332	+	0.0736429i	0.238866	+	0.971052i	$0.423224\pi$
$588$		0			0
$589$	1.06899	+	0.896990i	0.0440470	+	0.0369598i
$590$		0			0
$591$	−26.0151			−1.07012
$592$		0			0
$593$	33.3236			1.36844			0.684219	−	0.729276i	$-0.260143\pi$
$593$	33.3236			1.36844			0.684219	+	0.729276i	$0.260143\pi$
$594$		0			0
$595$	−17.2318	−	14.4592i	−0.706436	−	0.592770i
$596$		0			0
$597$	2.62254	−	0.954527i	0.107333	−	0.0390662i
$598$		0			0
$599$	38.6393	−	14.0635i	1.57876	−	0.574621i	0.603824	−	0.797117i	$-0.293643\pi$
$599$	38.6393	−	14.0635i	1.57876	−	0.574621i	0.974933	+	0.222497i	$0.0714206\pi$
$600$		0			0
$601$	−5.41507	−	30.7104i	−0.220885	−	1.25270i	−0.870397	−	0.492351i	$-0.836138\pi$
$601$	−5.41507	−	30.7104i	−0.220885	−	1.25270i	0.649511	−	0.760352i	$-0.274973\pi$
$602$		0			0
$603$	5.90673	+	10.2308i	0.240541	+	0.416629i
$604$		0			0
$605$	−3.22626	+	18.2970i	−0.131166	+	0.743879i
$606$		0			0
$607$	−21.8502	−	7.95284i	−0.886874	−	0.322796i	−0.141893	−	0.989882i	$-0.545319\pi$
$607$	−21.8502	−	7.95284i	−0.886874	−	0.322796i	−0.744980	+	0.667086i	$0.767541\pi$
$608$		0			0
$609$	0.992738	+	5.63010i	0.0402278	+	0.228143i
$610$		0			0
$611$	2.92465	+	2.45407i	0.118319	+	0.0992810i
$612$		0			0
$613$	−15.3073	−	5.57141i	−0.618257	−	0.225027i	0.0138554	−	0.999904i	$-0.495590\pi$
$613$	−15.3073	−	5.57141i	−0.618257	−	0.225027i	−0.632112	+	0.774877i	$0.717812\pi$
$614$		0			0
$615$	−5.99613	+	10.3856i	−0.241787	+	0.418788i
$616$		0			0
$617$	13.7358	−	11.5257i	0.552984	−	0.464009i	−0.322966	−	0.946411i	$-0.604680\pi$
$617$	13.7358	−	11.5257i	0.552984	−	0.464009i	0.875950	+	0.482402i	$0.160236\pi$
$618$		0			0
$619$	14.1291	−	24.4723i	0.567895	−	0.983624i	−0.428878	−	0.903362i	$-0.641091\pi$
$619$	14.1291	−	24.4723i	0.567895	−	0.983624i	0.996774	−	0.0802615i	$-0.0255755\pi$
$620$		0			0
$621$	0.621614	+	1.07667i	0.0249445	+	0.0432052i
$622$		0			0
$623$	15.9634			0.639562
$624$		0			0
$625$	−5.42593	+	30.7720i	−0.217037	+	1.23088i
$626$		0			0
$627$	−5.08016	+	4.26276i	−0.202882	+	0.170238i
$628$		0			0
$629$	−2.98946	+	40.2328i	−0.119198	+	1.60419i
$630$		0			0
$631$	12.6272	−	10.5955i	0.502680	−	0.421799i	−0.355864	−	0.934538i	$-0.615813\pi$
$631$	12.6272	−	10.5955i	0.502680	−	0.421799i	0.858545	+	0.512739i	$0.171369\pi$
$632$		0			0
$633$	−2.78373	+	15.7873i	−0.110643	+	0.627490i
$634$		0			0
$635$	−9.26053			−0.367493
$636$		0			0
$637$	−8.53285	−	14.7793i	−0.338084	−	0.585578i
$638$		0			0
$639$	−3.01136	+	5.21584i	−0.119128	+	0.206335i
$640$		0			0
$641$	9.21503	−	7.73233i	0.363972	−	0.305409i	−0.442400	−	0.896818i	$-0.645873\pi$
$641$	9.21503	−	7.73233i	0.363972	−	0.305409i	0.806372	+	0.591409i	$0.201428\pi$
$642$		0			0
$643$	15.2920	−	26.4866i	0.603059	−	1.04453i	−0.389295	−	0.921113i	$-0.627281\pi$
$643$	15.2920	−	26.4866i	0.603059	−	1.04453i	0.992355	−	0.123417i	$-0.0393852\pi$
$644$		0			0
$645$	18.3096	+	6.66416i	0.720940	+	0.262401i
$646$		0			0
$647$	−4.21610	−	3.53773i	−0.165752	−	0.139082i	0.556139	−	0.831089i	$-0.312282\pi$
$647$	−4.21610	−	3.53773i	−0.165752	−	0.139082i	−0.721891	+	0.692007i	$0.756727\pi$
$648$		0			0
$649$	−0.869364	−	4.93041i	−0.0341255	−	0.193535i
$650$		0			0
$651$	0.503172	+	0.183140i	0.0197209	+	0.00717781i
$652$		0			0
$653$	−5.48307	+	31.0960i	−0.214569	+	1.21688i	0.667084	+	0.744983i	$0.267542\pi$
$653$	−5.48307	+	31.0960i	−0.214569	+	1.21688i	−0.881653	+	0.471899i	$0.843569\pi$
$654$		0			0
$655$	11.7691	+	20.3847i	0.459856	+	0.796494i
$656$		0			0
$657$	−0.828402	−	4.69810i	−0.0323191	−	0.183290i
$658$		0			0
$659$	−14.0626	+	5.11837i	−0.547802	+	0.199384i	−0.601070	−	0.799197i	$-0.705259\pi$
$659$	−14.0626	+	5.11837i	−0.547802	+	0.199384i	0.0532678	+	0.998580i	$0.483036\pi$
$660$		0			0
$661$	−1.59641	+	0.581047i	−0.0620933	+	0.0226001i	−0.372880	−	0.927880i	$-0.621630\pi$
$661$	−1.59641	+	0.581047i	−0.0620933	+	0.0226001i	0.310787	+	0.950480i	$0.399407\pi$
$662$		0			0
$663$	15.8967	+	13.3389i	0.617377	+	0.518041i
$664$		0			0
$665$	−10.9886			−0.426121
$666$		0			0
$667$	−5.71695			−0.221361
$668$		0			0
$669$	5.74541	+	4.82097i	0.222130	+	0.186389i
$670$		0			0
$671$	20.5666	−	7.48563i	0.793965	−	0.288980i
$672$		0			0
$673$	11.7072	−	4.26108i	0.451280	−	0.164253i	−0.106374	−	0.994326i	$-0.533924\pi$
$673$	11.7072	−	4.26108i	0.451280	−	0.164253i	0.557654	+	0.830074i	$0.311702\pi$
$674$		0			0
$675$	0.424089	+	2.40513i	0.0163232	+	0.0925734i
$676$		0			0
$677$	−13.2071	−	22.8754i	−0.507591	−	0.879174i	−0.999961	−	0.00878820i	$-0.997203\pi$
$677$	−13.2071	−	22.8754i	−0.507591	−	0.879174i	0.492370	−	0.870386i	$-0.336131\pi$
$678$		0			0
$679$	−1.77218	+	10.0505i	−0.0680101	+	0.385704i
$680$		0			0
$681$	−16.5258	−	6.01489i	−0.633269	−	0.230491i
$682$		0			0
$683$	−2.22149	−	12.5987i	−0.0850030	−	0.482076i	−0.997356	−	0.0726714i	$-0.976848\pi$
$683$	−2.22149	−	12.5987i	−0.0850030	−	0.482076i	0.912353	−	0.409405i	$-0.134264\pi$
$684$		0			0
$685$	26.4344	+	22.1811i	1.01001	+	0.847496i
$686$		0			0
$687$	5.91590	+	2.15321i	0.225706	+	0.0821502i
$688$		0			0
$689$	11.5008	−	19.9199i	0.438144	−	0.758888i
$690$		0			0
$691$	36.5084	−	30.6342i	1.38885	−	1.16538i	0.423040	−	0.906111i	$-0.360963\pi$
$691$	36.5084	−	30.6342i	1.38885	−	1.16538i	0.965805	−	0.259269i	$-0.0834816\pi$
$692$		0			0
$693$	−1.27234	+	2.20376i	−0.0483323	+	0.0837139i
$694$		0			0
$695$	−17.4239	−	30.1790i	−0.660925	−	1.14476i
$696$		0			0
$697$	−29.1557			−1.10435
$698$		0			0
$699$	−2.62334	+	14.8777i	−0.0992237	+	0.562726i
$700$		0			0
$701$	14.6060	−	12.2559i	0.551662	−	0.462899i	−0.323842	−	0.946111i	$-0.604975\pi$
$701$	14.6060	−	12.2559i	0.551662	−	0.462899i	0.875503	+	0.483212i	$0.160530\pi$
$702$		0			0
$703$	11.5145	+	15.9944i	0.434278	+	0.603239i
$704$		0			0
$705$	−2.55004	+	2.13973i	−0.0960399	+	0.0805871i
$706$		0			0
$707$	2.53860	−	14.3971i	0.0954738	−	0.541459i
$708$		0			0
$709$	−50.7711			−1.90675			−0.953375	−	0.301788i	$-0.902417\pi$
$709$	−50.7711			−1.90675			−0.953375	+	0.301788i	$0.902417\pi$
$710$		0			0
$711$	2.08301	+	3.60788i	0.0781189	+	0.135306i
$712$		0			0
$713$	−0.267732	+	0.463726i	−0.0100266	+	0.0173667i
$714$		0			0
$715$	−13.3834	+	11.2300i	−0.500511	+	0.419979i
$716$		0			0
$717$	15.2460	−	26.4068i	0.569371	−	0.986180i
$718$		0			0
$719$	−33.3218	−	12.1281i	−1.24269	−	0.452303i	−0.364766	−	0.931099i	$-0.618851\pi$
$719$	−33.3218	−	12.1281i	−1.24269	−	0.452303i	−0.877926	+	0.478796i	$0.841073\pi$
$720$		0			0
$721$	−8.18181	−	6.86536i	−0.304707	−	0.255679i
$722$		0			0
$723$	3.92953	+	22.2855i	0.146141	+	0.828806i
$724$		0			0
$725$	−10.5532	−	3.84107i	−0.391938	−	0.142654i
$726$		0			0
$727$	1.48111	−	8.39978i	0.0549312	−	0.311531i	−0.944946	−	0.327228i	$-0.893886\pi$
$727$	1.48111	−	8.39978i	0.0549312	−	0.311531i	0.999877	+	0.0156971i	$0.00499674\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	8.22596	+	46.6518i	0.304248	+	1.72548i
$732$		0			0
$733$	−45.0317	+	16.3902i	−1.66328	+	0.605386i	−0.990874	−	0.134792i	$-0.956963\pi$
$733$	−45.0317	+	16.3902i	−1.66328	+	0.605386i	−0.672411	+	0.740178i	$0.734741\pi$
$734$		0			0
$735$	13.9824	−	5.08919i	0.515750	−	0.187718i
$736$		0			0
$737$	−18.5231	−	15.5427i	−0.682308	−	0.572524i
$738$		0			0
$739$	43.7552			1.60956			0.804780	−	0.593573i	$-0.202283\pi$
$739$	43.7552			1.60956			0.804780	+	0.593573i	$0.202283\pi$
$740$		0			0
$741$	10.1372			0.372400
$742$		0			0
$743$	24.1107	+	20.2313i	0.884535	+	0.742213i	0.967106	−	0.254372i	$-0.0818688\pi$
$743$	24.1107	+	20.2313i	0.884535	+	0.742213i	−0.0825714	+	0.996585i	$0.526313\pi$
$744$		0			0
$745$	−0.432633	+	0.157465i	−0.0158504	+	0.00576909i
$746$		0			0
$747$	−5.93089	+	2.15867i	−0.217000	+	0.0789816i
$748$		0			0
$749$	0.000485928		0.00275584i	1.77554e−5		0.000100696i
$750$		0			0
$751$	24.3532	+	42.1809i	0.888659	+	1.53920i	0.841461	+	0.540318i	$0.181696\pi$
$751$	24.3532	+	42.1809i	0.888659	+	1.53920i	0.0471985	+	0.998886i	$0.484971\pi$
$752$		0			0
$753$	−1.55421	+	8.81438i	−0.0566386	+	0.321214i
$754$		0			0
$755$	−21.6911	−	7.89491i	−0.789420	−	0.287325i
$756$		0			0
$757$	0.423954	+	2.40436i	0.0154089	+	0.0873880i	0.991542	−	0.129783i	$-0.0414281\pi$
$757$	0.423954	+	2.40436i	0.0154089	+	0.0873880i	−0.976134	+	0.217171i	$0.930317\pi$
$758$		0			0
$759$	−1.94934	−	1.63569i	−0.0707566	−	0.0593718i
$760$		0			0
$761$	34.1072	+	12.4140i	1.23639	+	0.450008i	0.875780	−	0.482710i	$-0.160348\pi$
$761$	34.1072	+	12.4140i	1.23639	+	0.450008i	0.360606	+	0.932718i	$0.382570\pi$
$762$		0			0
$763$	8.57284	−	14.8486i	0.310358	−	0.537555i
$764$		0			0
$765$	−13.8605	+	11.6304i	−0.501129	+	0.420497i
$766$		0			0
$767$	−3.82646	+	6.62762i	−0.138165	+	0.239310i
$768$		0			0
$769$	−8.00473	−	13.8646i	−0.288658	−	0.499970i	0.684832	−	0.728701i	$-0.259876\pi$
$769$	−8.00473	−	13.8646i	−0.288658	−	0.499970i	−0.973490	+	0.228731i	$0.926542\pi$
$770$		0			0
$771$	18.8920			0.680378
$772$		0			0
$773$	3.83118	−	21.7277i	0.137798	−	0.781492i	−0.835072	−	0.550140i	$-0.814574\pi$
$773$	3.83118	−	21.7277i	0.137798	−	0.781492i	0.972870	−	0.231351i	$-0.0743147\pi$
$774$		0			0
$775$	−0.805787	+	0.676135i	−0.0289447	+	0.0242875i
$776$		0			0
$777$	6.25093	+	4.25602i	0.224251	+	0.152684i
$778$		0			0
$779$	−10.9105	+	9.15498i	−0.390909	+	0.328011i
$780$		0			0
$781$	2.14065	−	12.1402i	0.0765986	−	0.434412i
$782$		0			0
$783$	4.59847			0.164336
$784$		0			0
$785$	6.74667	+	11.6856i	0.240799	+	0.417076i
$786$		0			0
$787$	−4.20784	+	7.28819i	−0.149993	+	0.259796i	−0.931225	−	0.364446i	$-0.881258\pi$
$787$	−4.20784	+	7.28819i	−0.149993	+	0.259796i	0.781232	+	0.624241i	$0.214592\pi$
$788$		0			0
$789$	−6.06105	+	5.08583i	−0.215779	+	0.181060i
$790$		0			0
$791$	7.57754	−	13.1247i	0.269426	−	0.466660i
$792$		0			0
$793$	−31.4382	−	11.4426i	−1.11640	−	0.406338i
$794$		0			0
$795$	15.3633	+	12.8913i	0.544879	+	0.457208i
$796$		0			0
$797$	0.273057	+	1.54858i	0.00967217	+	0.0548536i	0.989262	−	0.146154i	$-0.0466895\pi$
$797$	0.273057	+	1.54858i	0.00967217	+	0.0548536i	−0.979590	+	0.201008i	$0.935578\pi$
$798$		0			0
$799$	−7.60504	−	2.76801i	−0.269047	−	0.0979251i
$800$		0			0
$801$	2.22970	−	12.6452i	0.0787824	−	0.446797i
$802$		0			0
$803$	4.88229	+	8.45638i	0.172292	+	0.298419i
$804$		0			0
$805$	−0.732190	−	4.15246i	−0.0258063	−	0.146355i
$806$		0			0
$807$	1.31029	−	0.476905i	0.0461243	−	0.0167879i
$808$		0			0
$809$	−8.08707	+	2.94345i	−0.284326	+	0.103486i	−0.480247	−	0.877134i	$-0.659453\pi$
$809$	−8.08707	+	2.94345i	−0.284326	+	0.103486i	0.195920	+	0.980620i	$0.437231\pi$
$810$		0			0
$811$	30.6957	+	25.7568i	1.07787	+	0.904442i	0.995742	−	0.0921798i	$-0.0293835\pi$
$811$	30.6957	+	25.7568i	1.07787	+	0.904442i	0.0821294	+	0.996622i	$0.473828\pi$
$812$		0			0
$813$	−14.8562			−0.521031
$814$		0			0
$815$	55.2679			1.93595
$816$		0			0
$817$	17.7271	+	14.8748i	0.620191	+	0.520402i
$818$		0			0
$819$	3.65523	−	1.33040i	0.127724	−	0.0464878i
$820$		0			0
$821$	−23.7788	+	8.65478i	−0.829886	+	0.302054i	−0.721812	−	0.692089i	$-0.756691\pi$
$821$	−23.7788	+	8.65478i	−0.829886	+	0.302054i	−0.108074	+	0.994143i	$0.534468\pi$
$822$		0			0
$823$	5.28503	+	29.9729i	0.184225	+	1.04479i	0.926947	+	0.375191i	$0.122423\pi$
$823$	5.28503	+	29.9729i	0.184225	+	1.04479i	−0.742723	+	0.669599i	$0.766466\pi$
$824$		0			0
$825$	−2.49942	−	4.32912i	−0.0870187	−	0.150721i
$826$		0			0
$827$	4.45671	−	25.2753i	0.154975	−	0.878908i	−0.803833	−	0.594855i	$-0.797210\pi$
$827$	4.45671	−	25.2753i	0.154975	−	0.878908i	0.958809	−	0.284053i	$-0.0916793\pi$
$828$		0			0
$829$	45.3967	+	16.5231i	1.57669	+	0.573870i	0.974482	−	0.224467i	$-0.0720640\pi$
$829$	45.3967	+	16.5231i	1.57669	+	0.573870i	0.602212	+	0.798336i	$0.294286\pi$
$830$		0			0
$831$	1.11199	+	6.30640i	0.0385745	+	0.218767i
$832$		0			0
$833$	27.7124	+	23.2535i	0.960178	+	0.805685i
$834$		0			0
$835$	−24.2239	−	8.81678i	−0.838303	−	0.305117i
$836$		0			0
$837$	0.215352	−	0.373001i	0.00744367	−	0.0128928i
$838$		0			0
$839$	13.8288	−	11.6037i	0.477422	−	0.400604i	−0.372071	−	0.928204i	$-0.621352\pi$
$839$	13.8288	−	11.6037i	0.477422	−	0.400604i	0.849493	+	0.527600i	$0.176908\pi$
$840$		0			0
$841$	3.92704	−	6.80182i	0.135415	−	0.234546i
$842$		0			0
$843$	0.534201	+	0.925264i	0.0183989	+	0.0318678i
$844$		0			0
$845$	−8.75861			−0.301305
$846$		0			0
$847$	−1.47027	+	8.33834i	−0.0505192	+	0.286509i
$848$		0			0
$849$	10.2564	−	8.60614i	0.351999	−	0.295362i
$850$		0			0
$851$	−5.27683	+	5.41691i	−0.180887	+	0.185689i
$852$		0			0
$853$	11.3898	−	9.55718i	0.389979	−	0.327232i	−0.426626	−	0.904428i	$-0.640298\pi$
$853$	11.3898	−	9.55718i	0.389979	−	0.327232i	0.816605	+	0.577197i	$0.195853\pi$
$854$		0			0
$855$	−1.53484	+	8.70450i	−0.0524904	+	0.297688i
$856$		0			0
$857$	−4.38078			−0.149645			−0.0748223	−	0.997197i	$-0.523839\pi$
$857$	−4.38078			−0.149645			−0.0748223	+	0.997197i	$0.523839\pi$
$858$		0			0
$859$	24.0689	+	41.6886i	0.821222	+	1.42240i	0.904773	+	0.425894i	$0.140040\pi$
$859$	24.0689	+	41.6886i	0.821222	+	1.42240i	−0.0835512	+	0.996503i	$0.526626\pi$
$860$		0			0
$861$	−2.73256	+	4.73294i	−0.0931255	+	0.161298i
$862$		0			0
$863$	1.92454	−	1.61488i	0.0655120	−	0.0549711i	−0.609444	−	0.792829i	$-0.708607\pi$
$863$	1.92454	−	1.61488i	0.0655120	−	0.0549711i	0.674956	+	0.737858i	$0.264163\pi$
$864$		0			0
$865$	−0.241078	+	0.417560i	−0.00819691	+	0.0141975i
$866$		0			0
$867$	−25.3619	−	9.23097i	−0.861334	−	0.313500i
$868$		0			0
$869$	−6.53218	−	5.48115i	−0.221589	−	0.185935i
$870$		0			0
$871$	6.41839	+	36.4005i	0.217479	+	1.23338i
$872$		0			0
$873$	7.71388	+	2.80762i	0.261075	+	0.0950236i
$874$		0			0
$875$	−1.50638	+	8.54310i	−0.0509249	+	0.288809i
$876$		0			0
$877$	−9.11010	−	15.7792i	−0.307626	−	0.532824i	0.670216	−	0.742166i	$-0.266201\pi$
$877$	−9.11010	−	15.7792i	−0.307626	−	0.532824i	−0.977843	+	0.209342i	$0.932868\pi$
$878$		0			0
$879$	−2.16265	−	12.2650i	−0.0729444	−	0.413688i
$880$		0			0
$881$	18.8641	−	6.86597i	0.635547	−	0.231320i	−0.00409675	−	0.999992i	$-0.501304\pi$
$881$	18.8641	−	6.86597i	0.635547	−	0.231320i	0.639644	+	0.768671i	$0.279082\pi$
$882$		0			0
$883$	−26.8647	+	9.77796i	−0.904070	+	0.329055i	−0.751883	−	0.659297i	$-0.770854\pi$
$883$	−26.8647	+	9.77796i	−0.904070	+	0.329055i	−0.152188	+	0.988352i	$0.548632\pi$
$884$		0			0
$885$	−5.11157	−	4.28912i	−0.171824	−	0.144177i
$886$		0			0
$887$	37.4906			1.25881			0.629406	−	0.777077i	$-0.283298\pi$
$887$	37.4906			1.25881			0.629406	+	0.777077i	$0.283298\pi$
$888$		0			0
$889$	−4.22022			−0.141542
$890$		0			0
$891$	1.56797	+	1.31568i	0.0525288	+	0.0440769i
$892$		0			0
$893$	−3.71507	+	1.35218i	−0.124320	+	0.0452489i
$894$		0			0
$895$	−43.9336	+	15.9905i	−1.46854	+	0.534504i
$896$		0			0
$897$	0.675460	+	3.83072i	0.0225530	+	0.127904i
$898$		0			0
$899$	0.990291	+	1.71523i	0.0330281	+	0.0572063i
$900$		0			0
$901$	−8.46687	+	48.0180i	−0.282072	+	1.59971i
$902$		0			0
$903$	8.34408	+	3.03700i	0.277674	+	0.101065i
$904$		0			0
$905$	−1.49928	−	8.50284i	−0.0498378	−	0.282644i
$906$		0			0
$907$	23.9000	+	20.0545i	0.793586	+	0.665898i	0.946630	−	0.322322i	$-0.104463\pi$
$907$	23.9000	+	20.0545i	0.793586	+	0.665898i	−0.153044	+	0.988219i	$0.548908\pi$
$908$		0			0
$909$	−11.0499	−	4.02184i	−0.366502	−	0.133396i
$910$		0			0
$911$	12.4035	−	21.4835i	0.410946	−	0.711779i	−0.584048	−	0.811719i	$-0.698532\pi$
$911$	12.4035	−	21.4835i	0.410946	−	0.711779i	0.994993	+	0.0999406i	$0.0318653\pi$
$912$		0			0
$913$	9.89626	−	8.30395i	0.327518	−	0.274821i
$914$		0			0
$915$	14.5853	−	25.2625i	0.482175	−	0.835152i
$916$		0			0
$917$	5.36342	+	9.28972i	0.177116	+	0.306774i
$918$		0			0
$919$	42.8575			1.41374			0.706869	−	0.707344i	$-0.250107\pi$
$919$	42.8575			1.41374			0.706869	+	0.707344i	$0.250107\pi$
$920$		0			0
$921$	−4.74801	+	26.9273i	−0.156452	+	0.887285i
$922$		0			0
$923$	−14.4353	+	12.1127i	−0.475144	+	0.398693i
$924$		0			0
$925$	−13.3803	+	6.45402i	−0.439941	+	0.212207i
$926$		0			0
$927$	−6.58110	+	5.52220i	−0.216152	+	0.181373i
$928$		0			0
$929$	−7.80702	+	44.2758i	−0.256140	+	1.45264i	0.536989	+	0.843589i	$0.319562\pi$
$929$	−7.80702	+	44.2758i	−0.256140	+	1.45264i	−0.793129	+	0.609053i	$0.791550\pi$
$930$		0			0
$931$	17.6720			0.579177
$932$		0			0
$933$	15.8509	+	27.4545i	0.518935	+	0.898821i
$934$		0			0
$935$	18.5174	−	32.0730i	0.605582	−	1.04890i
$936$		0			0
$937$	−4.05445	+	3.40209i	−0.132453	+	0.111141i	−0.706608	−	0.707606i	$-0.749775\pi$
$937$	−4.05445	+	3.40209i	−0.132453	+	0.111141i	0.574154	+	0.818747i	$0.305331\pi$
$938$		0			0
$939$	5.45853	−	9.45444i	0.178132	−	0.308534i
$940$		0			0
$941$	17.1426	+	6.23940i	0.558833	+	0.203399i	0.605967	−	0.795490i	$-0.292786\pi$
$941$	17.1426	+	6.23940i	0.558833	+	0.203399i	−0.0471337	+	0.998889i	$0.515009\pi$
$942$		0			0
$943$	−4.18653	−	3.51292i	−0.136332	−	0.114396i
$944$		0			0
$945$	0.588942	+	3.34006i	0.0191583	+	0.108652i
$946$		0			0
$947$	−54.1714	−	19.7168i	−1.76033	−	0.640709i	−0.760373	−	0.649487i	$-0.774984\pi$
$947$	−54.1714	−	19.7168i	−1.76033	−	0.640709i	−0.999961	+	0.00877776i	$0.997206\pi$
$948$		0			0
$949$	2.59191	−	14.6995i	0.0841369	−	0.477164i
$950$		0			0
$951$	−5.82263	−	10.0851i	−0.188812	−	0.327032i
$952$		0			0
$953$	4.84843	+	27.4968i	0.157056	+	0.890708i	0.956882	+	0.290477i	$0.0938139\pi$
$953$	4.84843	+	27.4968i	0.157056	+	0.890708i	−0.799826	+	0.600232i	$0.795075\pi$
$954$		0			0
$955$	56.7756	−	20.6646i	1.83722	−	0.668692i
$956$		0			0
$957$	−8.84468	+	3.21920i	−0.285908	+	0.104062i
$958$		0			0
$959$	12.0467	+	10.1084i	0.389009	+	0.326417i
$960$		0			0
$961$	−30.8145			−0.994016
$962$		0			0
$963$	0.00225087			7.25334e−5
$964$		0			0
$965$	25.7775	+	21.6299i	0.829808	+	0.696292i
$966$		0			0
$967$	−46.1652	+	16.8028i	−1.48457	+	0.540340i	−0.952015	−	0.306053i	$-0.900992\pi$
$967$	−46.1652	+	16.8028i	−1.48457	+	0.540340i	−0.532559	+	0.846393i	$0.678769\pi$
$968$		0			0
$969$	−20.1930	+	7.34966i	−0.648693	+	0.236105i
$970$		0			0
$971$	6.04782	+	34.2989i	0.194084	+	1.10070i	0.913718	+	0.406350i	$0.133199\pi$
$971$	6.04782	+	34.2989i	0.194084	+	1.10070i	−0.719634	+	0.694354i	$0.755690\pi$
$972$		0			0
$973$	−7.94044	−	13.7532i	−0.254559	−	0.440909i
$974$		0			0
$975$	−1.32689	+	7.52517i	−0.0424945	+	0.240998i
$976$		0			0
$977$	−30.5326	−	11.1130i	−0.976824	−	0.355535i	−0.196219	−	0.980560i	$-0.562867\pi$
$977$	−30.5326	−	11.1130i	−0.976824	−	0.355535i	−0.780605	+	0.625025i	$0.785089\pi$
$978$		0			0
$979$	4.56382	+	25.8827i	0.145860	+	0.827215i
$980$		0			0
$981$	−10.5647	−	8.86485i	−0.337305	−	0.283033i
$982$		0			0
$983$	−20.4067	−	7.42742i	−0.650872	−	0.236898i	−0.00458145	−	0.999990i	$-0.501458\pi$
$983$	−20.4067	−	7.42742i	−0.650872	−	0.236898i	−0.646290	+	0.763092i	$0.723681\pi$
$984$		0			0
$985$	35.4852	−	61.4622i	1.13065	−	1.95835i
$986$		0			0
$987$	−1.16211	+	0.975123i	−0.0369902	+	0.0310385i
$988$		0			0
$989$	−4.43979	+	7.68995i	−0.141177	+	0.244526i
$990$		0			0
$991$	−29.7905	−	51.5987i	−0.946328	−	1.63909i	−0.753071	−	0.657940i	$-0.771428\pi$
$991$	−29.7905	−	51.5987i	−0.946328	−	1.63909i	−0.193257	−	0.981148i	$-0.561905\pi$
$992$		0			0
$993$	−7.59530			−0.241030
$994$		0			0
$995$	−1.32208	+	7.49790i	−0.0419128	+	0.237699i
$996$		0			0
$997$	−22.6911	+	19.0401i	−0.718633	+	0.603005i	−0.927007	−	0.375045i	$-0.877627\pi$
$997$	−22.6911	+	19.0401i	−0.718633	+	0.603005i	0.208374	+	0.978049i	$0.433183\pi$
$998$		0			0
$999$	4.24446	−	4.35713i	0.134289	−	0.137854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.bo.c.49.1	✓	24
37.34	even	9	inner	888.2.bo.c.145.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.bo.c.49.1	✓	24	1.1	even	1	trivial
888.2.bo.c.145.1	yes	24	37.34	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{3} +(-2.56352 + 0.933046i) q^{5} +(-1.16825 + 0.425209i) q^{7} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{3} +(-2.56352 + 0.933046i) q^{5} +(-1.16825 + 0.425209i) q^{7} +(0.173648 + 0.984808i) q^{9} +(-1.02342 - 1.77261i) q^{11} +(-0.543311 + 3.08127i) q^{13} +(-2.56352 - 0.933046i) q^{15} +(-1.15171 - 6.53170i) q^{17} +(-2.48196 - 2.08261i) q^{19} +(-1.16825 - 0.425209i) q^{21} +(0.621614 - 1.07667i) q^{23} +(1.87086 - 1.56984i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-2.29924 - 3.98239i) q^{29} -0.430705 q^{31} +(0.355429 - 2.01574i) q^{33} +(2.59810 - 2.18007i) q^{35} +(-5.89561 - 1.49724i) q^{37} +(-2.39680 + 2.01116i) q^{39} +(0.763342 - 4.32913i) q^{41} -7.14236 q^{43} +(-1.36402 - 2.36256i) q^{45} +(0.610114 - 1.05675i) q^{47} +(-4.17830 + 3.50601i) q^{49} +(3.31623 - 5.74388i) q^{51} +(-6.90819 - 2.51437i) q^{53} +(4.27748 + 3.58923i) q^{55} +(-0.562615 - 3.19075i) q^{57} +(2.29845 + 0.836566i) q^{59} +(-1.85680 + 10.5304i) q^{61} +(-0.621614 - 1.07667i) q^{63} +(-1.48218 - 8.40585i) q^{65} +(11.1010 - 4.04044i) q^{67} +(1.16825 - 0.425209i) q^{69} +(4.61368 + 3.87134i) q^{71} -4.77058 q^{73} +2.44223 q^{75} +(1.94934 + 1.63569i) q^{77} +(3.91478 - 1.42486i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(1.09598 + 6.21564i) q^{83} +(9.04683 + 15.6696i) q^{85} +(0.798516 - 4.52861i) q^{87} +(-12.0659 - 4.39164i) q^{89} +(-0.675460 - 3.83072i) q^{91} +(-0.329939 - 0.276852i) q^{93} +(8.30574 + 3.02304i) q^{95} +(4.10447 - 7.10915i) q^{97} +(1.56797 - 1.31568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) \) 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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