LMFDB - Embedded newform 888.2.br.a.569.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [888,2,Mod(473,888)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("888.473"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(888, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 6, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.br (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			569.37
Character	$\chi$	$=$	888.569
Dual form			888.2.br.a.785.37

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72010 - 0.203120i) q^{3} +(0.272728 - 1.01783i) q^{5} +(-0.338361 - 0.586058i) q^{7} +(2.91748 - 0.698774i) q^{9} +6.32941 q^{11} +(-3.74925 - 1.00461i) q^{13} +(0.262377 - 1.80617i) q^{15} +(2.40377 - 0.644088i) q^{17} +(-5.39309 - 1.44507i) q^{19} +(-0.701055 - 0.939351i) q^{21} +(0.0101113 + 0.0101113i) q^{23} +(3.36852 + 1.94482i) q^{25} +(4.87643 - 1.79456i) q^{27} +(-4.64952 + 4.64952i) q^{29} +(-1.74098 - 1.74098i) q^{31} +(10.8872 - 1.28563i) q^{33} +(-0.688791 + 0.184561i) q^{35} +(4.57479 - 4.00890i) q^{37} +(-6.65314 - 0.966478i) q^{39} +(-2.38864 - 4.13724i) q^{41} +(4.64758 - 4.64758i) q^{43} +(0.0844435 - 3.16009i) q^{45} +2.77052i q^{47} +(3.27102 - 5.66558i) q^{49} +(4.00390 - 1.59615i) q^{51} +(9.01397 + 5.20422i) q^{53} +(1.72621 - 6.44229i) q^{55} +(-9.57018 - 1.39023i) q^{57} +(-0.306327 + 0.0820801i) q^{59} +(-1.49014 + 5.56128i) q^{61} +(-1.39669 - 1.47338i) q^{63} +(-2.04505 + 3.54213i) q^{65} +(-7.70626 + 4.44921i) q^{67} +(0.0194463 + 0.0153386i) q^{69} +(-4.32903 + 2.49937i) q^{71} +16.2965i q^{73} +(6.18922 + 2.66106i) q^{75} +(-2.14162 - 3.70940i) q^{77} +(-2.45694 - 0.658334i) q^{79} +(8.02343 - 4.07732i) q^{81} +(-3.12080 - 1.80180i) q^{83} -2.62230i q^{85} +(-7.05323 + 8.94205i) q^{87} +(-1.49214 - 5.56874i) q^{89} +(0.679840 + 2.53720i) q^{91} +(-3.34828 - 2.64103i) q^{93} +(-2.94170 + 5.09517i) q^{95} +(-4.85415 + 4.85415i) q^{97} +(18.4659 - 4.42282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) $ 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Character values

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

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$-1$

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
$3$	1.72010	−	0.203120i	0.993100	−	0.117271i
$3$	1.72010	−	0.203120i	0.993100	−	0.117271i
$4$		0			0
$5$	0.272728	−	1.01783i	0.121968	−	0.455190i	−0.877746	−	0.479127i	$-0.840953\pi$
$5$	0.272728	−	1.01783i	0.121968	−	0.455190i	0.999713	+	0.0239370i	$0.00762012\pi$
$6$		0			0
$7$	−0.338361	−	0.586058i	−0.127888	−	0.221509i	0.794970	−	0.606649i	$-0.207487\pi$
$7$	−0.338361	−	0.586058i	−0.127888	−	0.221509i	−0.922858	+	0.385140i	$0.874153\pi$
$8$		0			0
$9$	2.91748	−	0.698774i	0.972495	−	0.232925i
$10$		0			0
$11$	6.32941			1.90839			0.954194	−	0.299188i	$-0.0967158\pi$
$11$	6.32941			1.90839			0.954194	+	0.299188i	$0.0967158\pi$
$12$		0			0
$13$	−3.74925	−	1.00461i	−1.03985	−	0.278628i	−0.301801	−	0.953371i	$-0.597588\pi$
$13$	−3.74925	−	1.00461i	−1.03985	−	0.278628i	−0.738053	+	0.674743i	$0.764255\pi$
$14$		0			0
$15$	0.262377	−	1.80617i	0.0677453	−	0.466352i
$16$		0			0
$17$	2.40377	−	0.644088i	0.583000	−	0.156214i	0.0447480	−	0.998998i	$-0.485752\pi$
$17$	2.40377	−	0.644088i	0.583000	−	0.156214i	0.538252	+	0.842784i	$0.319085\pi$
$18$		0			0
$19$	−5.39309	−	1.44507i	−1.23726	−	0.331523i	−0.419858	−	0.907590i	$-0.637920\pi$
$19$	−5.39309	−	1.44507i	−1.23726	−	0.331523i	−0.817402	+	0.576067i	$0.804587\pi$
$20$		0			0
$21$	−0.701055	−	0.939351i	−0.152983	−	0.204983i
$22$		0			0
$23$	0.0101113	+	0.0101113i	0.00210835	+	0.00210835i	0.708160	−	0.706052i	$-0.249525\pi$
$23$	0.0101113	+	0.0101113i	0.00210835	+	0.00210835i	−0.706052	+	0.708160i	$0.749525\pi$
$24$		0			0
$25$	3.36852	+	1.94482i	0.673704	+	0.388963i
$26$		0			0
$27$	4.87643	−	1.79456i	0.938469	−	0.345363i
$28$		0			0
$29$	−4.64952	+	4.64952i	−0.863395	+	0.863395i	−0.991731	−	0.128336i	$-0.959036\pi$
$29$	−4.64952	+	4.64952i	−0.863395	+	0.863395i	0.128336	+	0.991731i	$0.459036\pi$
$30$		0			0
$31$	−1.74098	−	1.74098i	−0.312689	−	0.312689i	0.533261	−	0.845950i	$-0.320966\pi$
$31$	−1.74098	−	1.74098i	−0.312689	−	0.312689i	−0.845950	+	0.533261i	$0.820966\pi$
$32$		0			0
$33$	10.8872	−	1.28563i	1.89522	−	0.223800i
$34$		0			0
$35$	−0.688791	+	0.184561i	−0.116427	+	0.0311965i
$36$		0			0
$37$	4.57479	−	4.00890i	0.752091	−	0.659059i
$37$	4.57479	−	4.00890i	0.752091	−	0.659059i
$38$		0			0
$39$	−6.65314	−	0.966478i	−1.06535	−	0.154760i
$40$		0			0
$41$	−2.38864	−	4.13724i	−0.373043	−	0.646129i	0.616989	−	0.786972i	$-0.288352\pi$
$41$	−2.38864	−	4.13724i	−0.373043	−	0.646129i	−0.990032	+	0.140843i	$0.955019\pi$
$42$		0			0
$43$	4.64758	−	4.64758i	0.708750	−	0.708750i	−0.257522	−	0.966272i	$-0.582906\pi$
$43$	4.64758	−	4.64758i	0.708750	−	0.708750i	0.966272	+	0.257522i	$0.0829061\pi$
$44$		0			0
$45$	0.0844435	−	3.16009i	0.0125881	−	0.471079i
$46$		0			0
$47$			2.77052i			0.404122i	0.979373	+	0.202061i	$0.0647639\pi$
$47$			2.77052i			0.404122i	−0.979373	+	0.202061i	$0.935236\pi$
$48$		0			0
$49$	3.27102	−	5.66558i	0.467289	−	0.809368i
$50$		0			0
$51$	4.00390	−	1.59615i	0.560658	−	0.223506i
$52$		0			0
$53$	9.01397	+	5.20422i	1.23816	+	0.714854i	0.968719	−	0.248161i	$-0.0798263\pi$
$53$	9.01397	+	5.20422i	1.23816	+	0.714854i	0.269446	+	0.963016i	$0.413160\pi$
$54$		0			0
$55$	1.72621	−	6.44229i	0.232762	−	0.868679i
$56$		0			0
$57$	−9.57018	−	1.39023i	−1.26760	−	0.184140i
$58$		0			0
$59$	−0.306327	+	0.0820801i	−0.0398804	+	0.0106859i	−0.278704	−	0.960377i	$-0.589905\pi$
$59$	−0.306327	+	0.0820801i	−0.0398804	+	0.0106859i	0.238824	+	0.971063i	$0.423238\pi$
$60$		0			0
$61$	−1.49014	+	5.56128i	−0.190793	+	0.712049i	0.802523	+	0.596621i	$0.203490\pi$
$61$	−1.49014	+	5.56128i	−0.190793	+	0.712049i	−0.993316	+	0.115428i	$0.963176\pi$
$62$		0			0
$63$	−1.39669	−	1.47338i	−0.175966	−	0.185628i
$64$		0			0
$65$	−2.04505	+	3.54213i	−0.253657	+	0.439347i
$66$		0			0
$67$	−7.70626	+	4.44921i	−0.941469	+	0.543558i	−0.890421	−	0.455139i	$-0.849590\pi$
$67$	−7.70626	+	4.44921i	−0.941469	+	0.543558i	−0.0510488	+	0.998696i	$0.516256\pi$
$68$		0			0
$69$	0.0194463	+	0.0153386i	0.00234106	+	0.00184656i
$70$		0			0
$71$	−4.32903	+	2.49937i	−0.513761	+	0.296620i	−0.734378	−	0.678740i	$-0.762526\pi$
$71$	−4.32903	+	2.49937i	−0.513761	+	0.296620i	0.220617	+	0.975360i	$0.429193\pi$
$72$		0			0
$73$			16.2965i			1.90736i	0.300822	+	0.953680i	$0.402739\pi$
$73$			16.2965i			1.90736i	−0.300822	+	0.953680i	$0.597261\pi$
$74$		0			0
$75$	6.18922	+	2.66106i	0.714670	+	0.307273i
$76$		0			0
$77$	−2.14162	−	3.70940i	−0.244061	−	0.422726i
$78$		0			0
$79$	−2.45694	−	0.658334i	−0.276427	−	0.0740684i	0.117942	−	0.993020i	$-0.462370\pi$
$79$	−2.45694	−	0.658334i	−0.276427	−	0.0740684i	−0.394369	+	0.918952i	$0.629037\pi$
$80$		0			0
$81$	8.02343	−	4.07732i	0.891492	−	0.453036i
$82$		0			0
$83$	−3.12080	−	1.80180i	−0.342553	−	0.197773i	0.318848	−	0.947806i	$-0.396704\pi$
$83$	−3.12080	−	1.80180i	−0.342553	−	0.197773i	−0.661400	+	0.750033i	$0.730037\pi$
$84$		0			0
$85$		−	2.62230i		−	0.284429i
$86$		0			0
$87$	−7.05323	+	8.94205i	−0.756186	+	0.958689i
$88$		0			0
$89$	−1.49214	−	5.56874i	−0.158166	−	0.590285i	−0.998813	−	0.0487017i	$-0.984492\pi$
$89$	−1.49214	−	5.56874i	−0.158166	−	0.590285i	0.840647	−	0.541584i	$-0.182175\pi$
$90$		0			0
$91$	0.679840	+	2.53720i	0.0712666	+	0.265971i
$92$		0			0
$93$	−3.34828	−	2.64103i	−0.347201	−	0.273862i
$94$		0			0
$95$	−2.94170	+	5.09517i	−0.301812	+	0.522753i
$96$		0			0
$97$	−4.85415	+	4.85415i	−0.492864	+	0.492864i	−0.909207	−	0.416343i	$-0.863311\pi$
$97$	−4.85415	+	4.85415i	−0.492864	+	0.492864i	0.416343	+	0.909207i	$0.363311\pi$
$98$		0			0
$99$	18.4659	−	4.42282i	1.85590	−	0.444511i
$100$		0			0
$101$	6.22502			0.619412			0.309706	−	0.950832i	$-0.399769\pi$
$101$	6.22502			0.619412			0.309706	+	0.950832i	$0.399769\pi$
$102$		0			0
$103$	−12.7993	−	12.7993i	−1.26115	−	1.26115i	−0.950535	−	0.310616i	$-0.899465\pi$
$103$	−12.7993	−	12.7993i	−1.26115	−	1.26115i	−0.310616	−	0.950535i	$-0.600535\pi$
$104$		0			0
$105$	−1.14730	+	0.457371i	−0.111965	+	0.0446348i
$106$		0			0
$107$	−14.2518	+	8.22829i	−1.37778	+	0.795459i	−0.991891	−	0.127088i	$-0.959437\pi$
$107$	−14.2518	+	8.22829i	−1.37778	+	0.795459i	−0.385884	+	0.922547i	$0.626104\pi$
$108$		0			0
$109$	4.25712	+	15.8878i	0.407758	+	1.52177i	0.798912	+	0.601448i	$0.205409\pi$
$109$	4.25712	+	15.8878i	0.407758	+	1.52177i	−0.391154	+	0.920325i	$0.627924\pi$
$110$		0			0
$111$	7.05481	−	7.82494i	0.669613	−	0.742710i
$112$		0			0
$113$	0.838296	+	3.12856i	0.0788602	+	0.294310i	0.994081	−	0.108643i	$-0.0346504\pi$
$113$	0.838296	+	3.12856i	0.0788602	+	0.294310i	−0.915221	+	0.402953i	$0.867984\pi$
$114$		0			0
$115$	0.0130493	−	0.00753401i	0.00121685	−	0.000702550i
$116$		0			0
$117$	−11.6404	−	0.311052i	−1.07615	−	0.0287568i
$118$		0			0
$119$	−1.19082	−	1.19082i	−0.109162	−	0.109162i
$120$		0			0
$121$	29.0614			2.64195
$122$		0			0
$123$	−4.94906	−	6.63129i	−0.446241	−	0.597923i
$124$		0			0
$125$	6.62373	−	6.62373i	0.592444	−	0.592444i
$126$		0			0
$127$	3.93940	−	6.82325i	0.349566	−	0.605465i	−0.636607	−	0.771189i	$-0.719663\pi$
$127$	3.93940	−	6.82325i	0.349566	−	0.605465i	0.986172	+	0.165723i	$0.0529958\pi$
$128$		0			0
$129$	7.05029	−	8.93832i	0.620743	−	0.786976i
$130$		0			0
$131$	−0.567492	−	2.11791i	−0.0495820	−	0.185043i	0.936694	−	0.350150i	$-0.113869\pi$
$131$	−0.567492	−	2.11791i	−0.0495820	−	0.185043i	−0.986276	+	0.165108i	$0.947203\pi$
$132$		0			0
$133$	0.977914	+	3.64962i	0.0847959	+	0.316463i
$134$		0			0
$135$	−0.496627	−	5.45283i	−0.0427429	−	0.469305i
$136$		0			0
$137$			12.6181i			1.07804i	0.842293	+	0.539020i	$0.181205\pi$
$137$			12.6181i			1.07804i	−0.842293	+	0.539020i	$0.818795\pi$
$138$		0			0
$139$	−11.5879	−	6.69027i	−0.982871	−	0.567461i	−0.0797354	−	0.996816i	$-0.525408\pi$
$139$	−11.5879	−	6.69027i	−0.982871	−	0.567461i	−0.903136	+	0.429355i	$0.858741\pi$
$140$		0			0
$141$	0.562748	+	4.76557i	0.0473920	+	0.401333i
$142$		0			0
$143$	−23.7305	−	6.35857i	−1.98445	−	0.531731i
$144$		0			0
$145$	3.46439	+	6.00050i	0.287702	+	0.498315i
$146$		0			0
$147$	4.47569	−	10.4098i	0.369149	−	0.858583i
$148$		0			0
$149$			23.1104i			1.89328i	0.322291	+	0.946641i	$0.395547\pi$
$149$			23.1104i			1.89328i	−0.322291	+	0.946641i	$0.604453\pi$
$150$		0			0
$151$	4.99696	−	2.88499i	0.406647	−	0.234778i	−0.282701	−	0.959208i	$-0.591231\pi$
$151$	4.99696	−	2.88499i	0.406647	−	0.234778i	0.689348	+	0.724430i	$0.257897\pi$
$152$		0			0
$153$	6.56289	−	3.55881i	0.530578	−	0.287713i
$154$		0			0
$155$	−2.24684	+	1.29722i	−0.180471	+	0.104195i
$156$		0			0
$157$	2.36133	−	4.08995i	0.188455	−	0.326414i	−0.756280	−	0.654248i	$-0.772985\pi$
$157$	2.36133	−	4.08995i	0.188455	−	0.326414i	0.944735	+	0.327834i	$0.106319\pi$
$158$		0			0
$159$	16.5620	+	7.12086i	1.31345	+	0.564721i
$160$		0			0
$161$	0.00250454	−	0.00934709i	0.000197386	−	0.000736654i
$162$		0			0
$163$	−18.2222	+	4.88262i	−1.42727	+	0.382436i	−0.888058	−	0.459732i	$-0.847945\pi$
$163$	−18.2222	+	4.88262i	−1.42727	+	0.382436i	−0.539214	+	0.842168i	$0.681279\pi$
$164$		0			0
$165$	1.66069	−	11.4320i	0.129284	−	0.889981i
$166$		0			0
$167$	−0.930683	+	3.47336i	−0.0720184	+	0.268776i	−0.992541	−	0.121914i	$-0.961097\pi$
$167$	−0.930683	+	3.47336i	−0.0720184	+	0.268776i	0.920522	+	0.390690i	$0.127764\pi$
$168$		0			0
$169$	1.78929	+	1.03305i	0.137638	+	0.0794652i
$170$		0			0
$171$	−16.7440	−	0.447432i	−1.28045	−	0.0342160i
$172$		0			0
$173$	−6.04334	+	10.4674i	−0.459467	+	0.795819i	−0.998933	−	0.0461879i	$-0.985293\pi$
$173$	−6.04334	+	10.4674i	−0.459467	+	0.795819i	0.539466	+	0.842007i	$0.318626\pi$
$174$		0			0
$175$		−	2.63220i		−	0.198976i
$176$		0			0
$177$	−0.510241	+	0.203407i	−0.0383521	+	0.0152890i
$178$		0			0
$179$	−4.21960	+	4.21960i	−0.315388	+	0.315388i	−0.846993	−	0.531605i	$-0.821589\pi$
$179$	−4.21960	+	4.21960i	−0.315388	+	0.315388i	0.531605	+	0.846993i	$0.321589\pi$
$180$		0			0
$181$	−8.29355	−	14.3648i	−0.616454	−	1.06773i	−0.990127	−	0.140170i	$-0.955235\pi$
$181$	−8.29355	−	14.3648i	−0.616454	−	1.06773i	0.373673	−	0.927561i	$-0.378098\pi$
$182$		0			0
$183$	−1.43358	+	9.86863i	−0.105973	+	0.729510i
$184$		0			0
$185$	−2.83272	−	5.74972i	−0.208266	−	0.422728i
$186$		0			0
$187$	15.2144	−	4.07670i	1.11259	−	0.298118i
$188$		0			0
$189$	−2.70171	−	2.25066i	−0.196520	−	0.163712i
$190$		0			0
$191$	14.0751	+	14.0751i	1.01844	+	1.01844i	0.999827	+	0.0186138i	$0.00592529\pi$
$191$	14.0751	+	14.0751i	1.01844	+	1.01844i	0.0186138	+	0.999827i	$0.494075\pi$
$192$		0			0
$193$	−10.1730	+	10.1730i	−0.732268	+	0.732268i	−0.971069	−	0.238800i	$-0.923246\pi$
$193$	−10.1730	+	10.1730i	−0.732268	+	0.732268i	0.238800	+	0.971069i	$0.423246\pi$
$194$		0			0
$195$	−2.79821	+	6.50821i	−0.200384	+	0.466062i
$196$		0			0
$197$	−7.06926	−	4.08144i	−0.503664	−	0.290791i	0.226561	−	0.973997i	$-0.427252\pi$
$197$	−7.06926	−	4.08144i	−0.503664	−	0.290791i	−0.730225	+	0.683206i	$0.760585\pi$
$198$		0			0
$199$	11.4955	+	11.4955i	0.814894	+	0.814894i	0.985363	−	0.170469i	$-0.0545283\pi$
$199$	11.4955	+	11.4955i	0.814894	+	0.814894i	−0.170469	+	0.985363i	$0.554528\pi$
$200$		0			0
$201$	−12.3518	+	9.21838i	−0.871229	+	0.650215i
$202$		0			0
$203$	4.29811	+	1.15167i	0.301668	+	0.0808317i
$204$		0			0
$205$	−4.86248	+	1.30290i	−0.339610	+	0.0909983i
$206$		0			0
$207$	0.0365651	+	0.0224341i	0.00254145	+	0.00155928i
$208$		0			0
$209$	−34.1351	−	9.14647i	−2.36117	−	0.632674i
$210$		0			0
$211$	−4.46448			−0.307348			−0.153674	−	0.988122i	$-0.549111\pi$
$211$	−4.46448			−0.307348			−0.153674	+	0.988122i	$0.549111\pi$
$212$		0			0
$213$	−6.93869	+	5.17847i	−0.475431	+	0.354823i
$214$		0			0
$215$	−3.46295	−	5.99800i	−0.236171	−	0.409060i
$216$		0			0
$217$	−0.431236	+	1.60939i	−0.0292742	+	0.109253i
$218$		0			0
$219$	3.31015	+	28.0316i	0.223679	+	1.89420i
$220$		0			0
$221$	−9.65939			−0.649761
$222$		0			0
$223$	−6.97846			−0.467312			−0.233656	−	0.972319i	$-0.575069\pi$
$223$	−6.97846			−0.467312			−0.233656	+	0.972319i	$0.575069\pi$
$224$		0			0
$225$	11.1866	+	3.32014i	0.745773	+	0.221342i
$226$		0			0
$227$	−4.40962	+	16.4569i	−0.292677	+	1.09229i	0.650368	+	0.759620i	$0.274615\pi$
$227$	−4.40962	+	16.4569i	−0.292677	+	1.09229i	−0.943045	+	0.332666i	$0.892052\pi$
$228$		0			0
$229$	−3.66668	−	6.35087i	−0.242301	−	0.419677i	0.719068	−	0.694939i	$-0.244569\pi$
$229$	−3.66668	−	6.35087i	−0.242301	−	0.419677i	−0.961369	+	0.275262i	$0.911235\pi$
$230$		0			0
$231$	−4.43726	−	5.94553i	−0.291950	−	0.391187i
$232$		0			0
$233$	−15.7016			−1.02864			−0.514322	−	0.857597i	$-0.671956\pi$
$233$	−15.7016			−1.02864			−0.514322	+	0.857597i	$0.671956\pi$
$234$		0			0
$235$	2.81993	+	0.755598i	0.183952	+	0.0492898i
$236$		0			0
$237$	−4.35990	−	0.633347i	−0.283206	−	0.0411403i
$238$		0			0
$239$	−9.35787	+	2.50743i	−0.605310	+	0.162192i	−0.548441	−	0.836189i	$-0.684779\pi$
$239$	−9.35787	+	2.50743i	−0.605310	+	0.162192i	−0.0568694	+	0.998382i	$0.518112\pi$
$240$		0			0
$241$	19.7145	+	5.28248i	1.26992	+	0.340274i	0.830000	−	0.557763i	$-0.188340\pi$
$241$	19.7145	+	5.28248i	1.26992	+	0.340274i	0.439920	+	0.898037i	$0.355007\pi$
$242$		0			0
$243$	12.9729	−	8.64312i	0.832213	−	0.554457i
$244$		0			0
$245$	−4.87452	−	4.87452i	−0.311422	−	0.311422i
$246$		0			0
$247$	18.7683	+	10.8359i	1.19420	+	0.689471i
$248$		0			0
$249$	−5.73407	−	2.46537i	−0.363382	−	0.156236i
$250$		0			0
$251$	15.2217	−	15.2217i	0.960787	−	0.960787i	−0.0384723	−	0.999260i	$-0.512249\pi$
$251$	15.2217	−	15.2217i	0.960787	−	0.960787i	0.999260	+	0.0384723i	$0.0122491\pi$
$252$		0			0
$253$	0.0639986	+	0.0639986i	0.00402356	+	0.00402356i
$254$		0			0
$255$	−0.532643	−	4.51062i	−0.0333554	−	0.282466i
$256$		0			0
$257$	11.5529	−	3.09559i	0.720650	−	0.193097i	0.120188	−	0.992751i	$-0.461650\pi$
$257$	11.5529	−	3.09559i	0.720650	−	0.193097i	0.600461	+	0.799654i	$0.294984\pi$
$258$		0			0
$259$	−3.89738	−	1.32464i	−0.242171	−	0.0823091i
$260$		0			0
$261$	−10.3159	+	16.8139i	−0.638541	+	1.04075i
$262$		0			0
$263$	−7.82699	−	13.5567i	−0.482633	−	0.835945i	0.517168	−	0.855884i	$-0.326986\pi$
$263$	−7.82699	−	13.5567i	−0.482633	−	0.835945i	−0.999801	+	0.0199391i	$0.993653\pi$
$264$		0			0
$265$	7.75540	−	7.75540i	0.476410	−	0.476410i
$266$		0			0
$267$	−3.69775	−	9.27570i	−0.226299	−	0.567664i
$268$		0			0
$269$		−	25.6103i		−	1.56148i	−0.624853	−	0.780742i	$-0.714841\pi$
$269$		−	25.6103i		−	1.56148i	0.624853	−	0.780742i	$-0.285159\pi$
$270$		0			0
$271$	1.49553	−	2.59034i	0.0908471	−	0.157352i	−0.817021	−	0.576608i	$-0.804376\pi$
$271$	1.49553	−	2.59034i	0.0908471	−	0.157352i	0.907868	+	0.419257i	$0.137709\pi$
$272$		0			0
$273$	1.68475	+	4.22614i	0.101966	+	0.255778i
$274$		0			0
$275$	21.3207	+	12.3095i	1.28569	+	0.742293i
$276$		0			0
$277$	−1.46879	+	5.48160i	−0.0882510	+	0.329357i	−0.995910	−	0.0903513i	$-0.971201\pi$
$277$	−1.46879	+	5.48160i	−0.0882510	+	0.329357i	0.907659	+	0.419708i	$0.137868\pi$
$278$		0			0
$279$	−6.29583	−	3.86273i	−0.376921	−	0.231256i
$280$		0			0
$281$	26.3734	−	7.06674i	1.57331	−	0.421567i	0.636462	−	0.771308i	$-0.280397\pi$
$281$	26.3734	−	7.06674i	1.57331	−	0.421567i	0.936846	+	0.349742i	$0.113731\pi$
$282$		0			0
$283$	−2.71321	+	10.1258i	−0.161284	+	0.601919i	0.837201	+	0.546895i	$0.184190\pi$
$283$	−2.71321	+	10.1258i	−0.161284	+	0.601919i	−0.998485	+	0.0550242i	$0.982476\pi$
$284$		0			0
$285$	−4.02508	+	9.36171i	−0.238425	+	0.554540i
$286$		0			0
$287$	−1.61644	+	2.79976i	−0.0954157	+	0.165265i
$288$		0			0
$289$	−9.35917	+	5.40352i	−0.550539	+	0.317854i
$290$		0			0
$291$	−7.36364	+	9.33559i	−0.431664	+	0.547262i
$292$		0			0
$293$	−29.4345	+	16.9940i	−1.71958	+	0.992802i	−0.799908	+	0.600123i	$0.795118\pi$
$293$	−29.4345	+	16.9940i	−1.71958	+	0.992802i	−0.919676	+	0.392679i	$0.871548\pi$
$294$		0			0
$295$			0.334176i			0.0194565i
$296$		0			0
$297$	30.8649	−	11.3585i	1.79096	−	0.659087i
$298$		0			0
$299$	−0.0277519	−	0.0480677i	−0.00160493	−	0.00277983i
$300$		0			0
$301$	−4.29632	−	1.15119i	−0.247636	−	0.0663537i
$302$		0			0
$303$	10.7076	−	1.26443i	0.615138	−	0.0726394i
$304$		0			0
$305$	5.25406	+	3.03343i	0.300847	+	0.173694i
$306$		0			0
$307$		−	2.13249i		−	0.121707i	−0.998147	−	0.0608537i	$-0.980618\pi$
$307$		−	2.13249i		−	0.121707i	0.998147	−	0.0608537i	$-0.0193823\pi$
$308$		0			0
$309$	−24.6158	−	19.4163i	−1.40035	−	1.10455i
$310$		0			0
$311$	5.20792	+	19.4362i	0.295314	+	1.10213i	0.940968	+	0.338496i	$0.109918\pi$
$311$	5.20792	+	19.4362i	0.295314	+	1.10213i	−0.645654	+	0.763630i	$0.723415\pi$
$312$		0			0
$313$	−2.85943	−	10.6715i	−0.161624	−	0.603190i	−0.998447	−	0.0557156i	$-0.982256\pi$
$313$	−2.85943	−	10.6715i	−0.161624	−	0.603190i	0.836822	−	0.547474i	$-0.184411\pi$
$314$		0			0
$315$	−1.88057	+	1.01976i	−0.105958	+	0.0574571i
$316$		0			0
$317$	−5.49309	+	9.51431i	−0.308523	+	0.534377i	−0.978039	−	0.208420i	$-0.933168\pi$
$317$	−5.49309	+	9.51431i	−0.308523	+	0.534377i	0.669517	+	0.742797i	$0.266501\pi$
$318$		0			0
$319$	−29.4287	+	29.4287i	−1.64769	+	1.64769i
$320$		0			0
$321$	−22.8432	+	17.0483i	−1.27498	+	0.951544i
$322$		0			0
$323$	−13.8945			−0.773111
$324$		0			0
$325$	−10.6756	−	10.6756i	−0.592178	−	0.592178i
$326$		0			0
$327$	10.5498	+	26.4639i	0.583405	+	1.46345i
$328$		0			0
$329$	1.62369	−	0.937436i	0.0895167	−	0.0516825i
$330$		0			0
$331$	−2.16389	−	8.07576i	−0.118938	−	0.443884i	0.880613	−	0.473836i	$-0.157131\pi$
$331$	−2.16389	−	8.07576i	−0.118938	−	0.443884i	−0.999551	+	0.0299524i	$0.990464\pi$
$332$		0			0
$333$	10.5456	−	14.8926i	0.577894	−	0.816112i
$334$		0			0
$335$	2.42685	+	9.05713i	0.132593	+	0.494844i
$336$		0			0
$337$	1.06618	−	0.615557i	0.0580783	−	0.0335315i	−0.470680	−	0.882304i	$-0.655991\pi$
$337$	1.06618	−	0.615557i	0.0580783	−	0.0335315i	0.528758	+	0.848773i	$0.322658\pi$
$338$		0			0
$339$	2.07743	+	5.21116i	0.112830	+	0.283032i
$340$		0			0
$341$	−11.0194	−	11.0194i	−0.596732	−	0.596732i
$342$		0			0
$343$	−9.16420			−0.494820
$344$		0			0
$345$	0.0209158	−	0.0156098i	0.00112607	−	0.000840404i
$346$		0			0
$347$	11.4401	−	11.4401i	0.614136	−	0.614136i	−0.329885	−	0.944021i	$-0.607010\pi$
$347$	11.4401	−	11.4401i	0.614136	−	0.614136i	0.944021	+	0.329885i	$0.107010\pi$
$348$		0			0
$349$	7.96710	−	13.7994i	0.426469	−	0.738666i	−0.570087	−	0.821584i	$-0.693091\pi$
$349$	7.96710	−	13.7994i	0.426469	−	0.738666i	0.996556	+	0.0829178i	$0.0264239\pi$
$350$		0			0
$351$	−20.0858	+	1.82935i	−1.07210	+	0.0976436i
$352$		0			0
$353$	6.44304	+	24.0458i	0.342928	+	1.27983i	0.895014	+	0.446039i	$0.147166\pi$
$353$	6.44304	+	24.0458i	0.342928	+	1.27983i	−0.552085	+	0.833788i	$0.686168\pi$
$354$		0			0
$355$	1.36329	+	5.08789i	0.0723562	+	0.270037i
$356$		0			0
$357$	−2.29020	−	1.80644i	−0.121210	−	0.0956071i
$358$		0			0
$359$		−	28.4023i		−	1.49902i	−0.661995	−	0.749508i	$-0.730290\pi$
$359$		−	28.4023i		−	1.49902i	0.661995	−	0.749508i	$-0.269710\pi$
$360$		0			0
$361$	10.5427	+	6.08684i	0.554880	+	0.320360i
$362$		0			0
$363$	49.9885	−	5.90296i	2.62372	−	0.309825i
$364$		0			0
$365$	16.5871	+	4.44451i	0.868211	+	0.232636i
$366$		0			0
$367$	0.929286	+	1.60957i	0.0485083	+	0.0840189i	0.889260	−	0.457402i	$-0.151220\pi$
$367$	0.929286	+	1.60957i	0.0485083	+	0.0840189i	−0.840752	+	0.541421i	$0.817887\pi$
$368$		0			0
$369$	−9.85982	−	10.4012i	−0.513282	−	0.541466i
$370$		0			0
$371$		−	7.04362i		−	0.365686i
$372$		0			0
$373$	−6.49613	+	3.75054i	−0.336357	+	0.194196i	−0.658660	−	0.752441i	$-0.728876\pi$
$373$	−6.49613	+	3.75054i	−0.336357	+	0.194196i	0.322303	+	0.946637i	$0.395543\pi$
$374$		0			0
$375$	10.0481	−	12.7389i	0.518879	−	0.657833i
$376$		0			0
$377$	22.1032	−	12.7613i	1.13837	−	0.657239i
$378$		0			0
$379$	−6.13655	+	10.6288i	−0.315214	+	0.545966i	−0.979483	−	0.201527i	$-0.935410\pi$
$379$	−6.13655	+	10.6288i	−0.315214	+	0.545966i	0.664269	+	0.747493i	$0.268743\pi$
$380$		0			0
$381$	5.39023	−	12.5368i	0.276150	−	0.642282i
$382$		0			0
$383$	6.32191	−	23.5937i	0.323035	−	1.20558i	−0.593238	−	0.805027i	$-0.702151\pi$
$383$	6.32191	−	23.5937i	0.323035	−	1.20558i	0.916273	−	0.400555i	$-0.131183\pi$
$384$		0			0
$385$	−4.35964	+	1.16816i	−0.222188	+	0.0595351i
$386$		0			0
$387$	10.3116	−	16.8069i	0.524170	−	0.854341i
$388$		0			0
$389$	−0.785586	+	2.93185i	−0.0398308	+	0.148651i	−0.982977	−	0.183726i	$-0.941184\pi$
$389$	−0.785586	+	2.93185i	−0.0398308	+	0.148651i	0.943147	+	0.332377i	$0.107851\pi$
$390$		0			0
$391$	0.0308178	+	0.0177927i	0.00155853	+	0.000899815i
$392$		0			0
$393$	−1.40633	−	3.52774i	−0.0709401	−	0.177951i
$394$		0			0
$395$	−1.34015	+	2.32121i	−0.0674303	+	0.116793i
$396$		0			0
$397$		−	26.0070i		−	1.30525i	−0.757679	−	0.652627i	$-0.773667\pi$
$397$		−	26.0070i		−	1.30525i	0.757679	−	0.652627i	$-0.226333\pi$
$398$		0			0
$399$	2.42342	+	6.07908i	0.121323	+	0.304335i
$400$		0			0
$401$	3.79949	−	3.79949i	0.189738	−	0.189738i	−0.605845	−	0.795583i	$-0.707165\pi$
$401$	3.79949	−	3.79949i	0.189738	−	0.189738i	0.795583	+	0.605845i	$0.207165\pi$
$402$		0			0
$403$	4.77836	+	8.27636i	0.238027	+	0.412275i
$404$		0			0
$405$	−1.96183	−	9.27853i	−0.0974840	−	0.461054i
$406$		0			0
$407$	28.9557	−	25.3740i	1.43528	−	1.25774i
$408$		0			0
$409$	21.5118	−	5.76407i	1.06369	−	0.285015i	0.315792	−	0.948828i	$-0.397730\pi$
$409$	21.5118	−	5.76407i	1.06369	−	0.285015i	0.747898	+	0.663813i	$0.231063\pi$
$410$		0			0
$411$	2.56300	+	21.7044i	0.126423	+	1.07060i
$412$		0			0
$413$	0.151753	+	0.151753i	0.00746727	+	0.00746727i
$414$		0			0
$415$	−2.68506	+	2.68506i	−0.131804	+	0.131804i
$416$		0			0
$417$	−21.2912	−	9.15419i	−1.04264	−	0.448283i
$418$		0			0
$419$	11.1310	+	6.42647i	0.543784	+	0.313954i	0.746611	−	0.665261i	$-0.231680\pi$
$419$	11.1310	+	6.42647i	0.543784	+	0.313954i	−0.202827	+	0.979215i	$0.565013\pi$
$420$		0			0
$421$	−24.7153	−	24.7153i	−1.20455	−	1.20455i	−0.972768	−	0.231780i	$-0.925545\pi$
$421$	−24.7153	−	24.7153i	−1.20455	−	1.20455i	−0.231780	−	0.972768i	$-0.574455\pi$
$422$		0			0
$423$	1.93597	+	8.08295i	0.0941299	+	0.393006i
$424$		0			0
$425$	9.34978	+	2.50527i	0.453531	+	0.121523i
$426$		0			0
$427$	3.76344	−	1.00841i	0.182126	−	0.0488004i
$428$		0			0
$429$	−42.1104	−	6.11723i	−2.03311	−	0.295343i
$430$		0			0
$431$	39.4346	+	10.5665i	1.89950	+	0.508968i	0.996919	+	0.0784403i	$0.0249940\pi$
$431$	39.4346	+	10.5665i	1.89950	+	0.508968i	0.902577	+	0.430528i	$0.141673\pi$
$432$		0			0
$433$	20.7222			0.995845			0.497923	−	0.867221i	$-0.334096\pi$
$433$	20.7222			0.995845			0.497923	+	0.867221i	$0.334096\pi$
$434$		0			0
$435$	7.17792	+	9.61777i	0.344155	+	0.461137i
$436$		0			0
$437$	−0.0399196	−	0.0691428i	−0.00190961	−	0.00330755i
$438$		0			0
$439$	5.50156	−	20.5321i	0.262575	−	0.979943i	−0.701143	−	0.713021i	$-0.747327\pi$
$439$	5.50156	−	20.5321i	0.262575	−	0.979943i	0.963718	−	0.266923i	$-0.0860068\pi$
$440$		0			0
$441$	5.58420	−	18.8149i	0.265914	−	0.895950i
$442$		0			0
$443$	19.4221			0.922770			0.461385	−	0.887200i	$-0.347353\pi$
$443$	19.4221			0.922770			0.461385	+	0.887200i	$0.347353\pi$
$444$		0			0
$445$	−6.07501			−0.287983
$446$		0			0
$447$	4.69420	+	39.7523i	0.222028	+	1.88022i
$448$		0			0
$449$	2.44638	−	9.13000i	0.115452	−	0.430871i	−0.883869	−	0.467735i	$-0.845070\pi$
$449$	2.44638	−	9.13000i	0.115452	−	0.430871i	0.999320	+	0.0368638i	$0.0117368\pi$
$450$		0			0
$451$	−15.1187	−	26.1863i	−0.711910	−	1.23307i
$452$		0			0
$453$	8.00926	−	5.97746i	0.376308	−	0.280846i
$454$		0			0
$455$	2.76786			0.129759
$456$		0			0
$457$	14.2379	+	3.81504i	0.666021	+	0.178460i	0.575962	−	0.817477i	$-0.304628\pi$
$457$	14.2379	+	3.81504i	0.666021	+	0.178460i	0.0900593	+	0.995936i	$0.471294\pi$
$458$		0			0
$459$	10.5660	−	7.45456i	0.493177	−	0.347949i
$460$		0			0
$461$	23.9417	−	6.41516i	1.11508	−	0.298784i	0.346187	−	0.938165i	$-0.387476\pi$
$461$	23.9417	−	6.41516i	1.11508	−	0.298784i	0.768890	+	0.639381i	$0.220809\pi$
$462$		0			0
$463$	27.1649	+	7.27882i	1.26246	+	0.338276i	0.827138	−	0.561999i	$-0.189967\pi$
$463$	27.1649	+	7.27882i	1.26246	+	0.338276i	0.435323	+	0.900274i	$0.356634\pi$
$464$		0			0
$465$	−3.60130	+	2.68772i	−0.167006	+	0.124640i
$466$		0			0
$467$	−16.0372	−	16.0372i	−0.742111	−	0.742111i	0.230873	−	0.972984i	$-0.425842\pi$
$467$	−16.0372	−	16.0372i	−0.742111	−	0.742111i	−0.972984	+	0.230873i	$0.925842\pi$
$468$		0			0
$469$	5.21499	+	3.01088i	0.240806	+	0.139029i
$470$		0			0
$471$	3.23098	−	7.51475i	0.148876	−	0.346262i
$472$		0			0
$473$	29.4165	−	29.4165i	1.35257	−	1.35257i
$474$		0			0
$475$	−15.3563	−	15.3563i	−0.704597	−	0.704597i
$476$		0			0
$477$	29.9347	+	8.88450i	1.37062	+	0.406793i
$478$		0			0
$479$	−18.7274	+	5.01798i	−0.855675	+	0.229277i	−0.659883	−	0.751368i	$-0.729394\pi$
$479$	−18.7274	+	5.01798i	−0.855675	+	0.229277i	−0.195792	+	0.980645i	$0.562728\pi$
$480$		0			0
$481$	−21.1794	+	10.4345i	−0.965698	+	0.475772i
$482$		0			0
$483$	0.00240948	−	0.0165866i	0.000109635	−	0.000754718i
$484$		0			0
$485$	3.61686	+	6.26458i	0.164233	+	0.284460i
$486$		0			0
$487$	25.5679	−	25.5679i	1.15859	−	1.15859i	0.173812	−	0.984779i	$-0.444392\pi$
$487$	25.5679	−	25.5679i	1.15859	−	1.15859i	0.984779	−	0.173812i	$-0.0556084\pi$
$488$		0			0
$489$	−30.3522	+	12.0999i	−1.37257	+	0.547176i
$490$		0			0
$491$			30.3318i			1.36885i	0.729081	+	0.684427i	$0.239948\pi$
$491$			30.3318i			1.36885i	−0.729081	+	0.684427i	$0.760052\pi$
$492$		0			0
$493$	−8.18168	+	14.1711i	−0.368485	+	0.638234i
$494$		0			0
$495$	0.534477	−	20.0015i	0.0240230	−	0.899001i
$496$		0			0
$497$	2.92955	+	1.69138i	0.131408	+	0.0758686i
$498$		0			0
$499$	−4.85357	+	18.1138i	−0.217276	+	0.810883i	0.768078	+	0.640357i	$0.221214\pi$
$499$	−4.85357	+	18.1138i	−0.217276	+	0.810883i	−0.985353	+	0.170527i	$0.945453\pi$
$500$		0			0
$501$	−0.895359	+	6.16356i	−0.0400017	+	0.275368i
$502$		0			0
$503$	7.25712	−	1.94454i	0.323579	−	0.0867027i	−0.0933732	−	0.995631i	$-0.529765\pi$
$503$	7.25712	−	1.94454i	0.323579	−	0.0867027i	0.416952	+	0.908928i	$0.363098\pi$
$504$		0			0
$505$	1.69774	−	6.33604i	0.0755483	−	0.281950i
$506$		0			0
$507$	3.28759	+	1.41350i	0.146007	+	0.0627759i
$508$		0			0
$509$	−5.88287	+	10.1894i	−0.260754	+	0.451639i	−0.966442	−	0.256883i	$-0.917304\pi$
$509$	−5.88287	+	10.1894i	−0.260754	+	0.451639i	0.705689	+	0.708522i	$0.250638\pi$
$510$		0			0
$511$	9.55070	−	5.51410i	0.422498	−	0.243929i
$512$		0			0
$513$	−28.8923	+	2.63143i	−1.27563	+	0.116180i
$514$		0			0
$515$	−16.5183	+	9.53684i	−0.727883	+	0.420243i
$516$		0			0
$517$			17.5357i			0.771221i
$518$		0			0
$519$	−8.26901	+	19.2324i	−0.362969	+	0.844210i
$520$		0			0
$521$	9.16727	+	15.8782i	0.401625	+	0.695635i	0.993922	−	0.110084i	$-0.0351121\pi$
$521$	9.16727	+	15.8782i	0.401625	+	0.695635i	−0.592297	+	0.805720i	$0.701779\pi$
$522$		0			0
$523$	−3.95846	−	1.06066i	−0.173091	−	0.0463796i	0.171232	−	0.985231i	$-0.445225\pi$
$523$	−3.95846	−	1.06066i	−0.173091	−	0.0463796i	−0.344324	+	0.938851i	$0.611892\pi$
$524$		0			0
$525$	−0.534653	−	4.52764i	−0.0233342	−	0.197603i
$526$		0			0
$527$	−5.30626	−	3.06357i	−0.231144	−	0.133451i
$528$		0			0
$529$		−	22.9998i		−	0.999991i
$530$		0			0
$531$	−0.836349	+	0.453521i	−0.0362945	+	0.0196811i
$532$		0			0
$533$	4.79929	+	17.9112i	0.207880	+	0.775820i
$534$		0			0
$535$	4.48817	+	16.7501i	0.194041	+	0.724169i
$536$		0			0
$537$	−6.40105	+	8.11523i	−0.276226	+	0.350198i
$538$		0			0
$539$	20.7036	−	35.8598i	0.891769	−	1.54459i
$540$		0			0
$541$	21.7995	−	21.7995i	0.937234	−	0.937234i	−0.0609093	−	0.998143i	$-0.519400\pi$
$541$	21.7995	−	21.7995i	0.937234	−	0.937234i	0.998143	+	0.0609093i	$0.0194000\pi$
$542$		0			0
$543$	−17.1835	−	23.0244i	−0.737415	−	0.988070i
$544$		0			0
$545$	17.3322			0.742429
$546$		0			0
$547$	−24.2405	−	24.2405i	−1.03645	−	1.03645i	−0.999310	−	0.0371406i	$-0.988175\pi$
$547$	−24.2405	−	24.2405i	−1.03645	−	1.03645i	−0.0371406	−	0.999310i	$-0.511825\pi$
$548$		0			0
$549$	−0.461385	+	17.2662i	−0.0196914	+	0.736904i
$550$		0			0
$551$	31.7942	−	18.3564i	1.35448	−	0.782009i
$552$		0			0
$553$	0.445509	+	1.66266i	0.0189450	+	0.0707036i
$554$		0			0
$555$	−6.04045	−	9.31471i	−0.256403	−	0.395387i
$556$		0			0
$557$	−3.12090	−	11.6473i	−0.132237	−	0.493514i	0.867757	−	0.496988i	$-0.165561\pi$
$557$	−3.12090	−	11.6473i	−0.132237	−	0.493514i	−0.999994	+	0.00347431i	$0.998894\pi$
$558$		0			0
$559$	−22.0939	+	12.7559i	−0.934474	+	0.539519i
$560$		0			0
$561$	25.3423	−	10.1027i	1.06995	−	0.426536i
$562$		0			0
$563$	−22.4940	−	22.4940i	−0.948011	−	0.948011i	0.0507028	−	0.998714i	$-0.483854\pi$
$563$	−22.4940	−	22.4940i	−0.948011	−	0.948011i	−0.998714	+	0.0507028i	$0.983854\pi$
$564$		0			0
$565$	3.41299			0.143585
$566$		0			0
$567$	−5.10436	−	3.32259i	−0.214363	−	0.139536i
$568$		0			0
$569$	2.83892	−	2.83892i	0.119014	−	0.119014i	−0.645092	−	0.764105i	$-0.723181\pi$
$569$	2.83892	−	2.83892i	0.119014	−	0.119014i	0.764105	+	0.645092i	$0.223181\pi$
$570$		0			0
$571$	9.71471	−	16.8264i	0.406548	−	0.704162i	−0.587952	−	0.808896i	$-0.700066\pi$
$571$	9.71471	−	16.8264i	0.406548	−	0.704162i	0.994500	+	0.104734i	$0.0333991\pi$
$572$		0			0
$573$	27.0696	+	21.3517i	1.13085	+	0.891979i
$574$		0			0
$575$	0.0143955	+	0.0537248i	0.000600334	+	0.00224048i
$576$		0			0
$577$	2.79471	+	10.4300i	0.116345	+	0.434207i	0.999384	−	0.0350934i	$-0.0111729\pi$
$577$	2.79471	+	10.4300i	0.116345	+	0.434207i	−0.883039	+	0.469300i	$0.844506\pi$
$578$		0			0
$579$	−15.4322	+	19.5649i	−0.641341	+	0.813090i
$580$		0			0
$581$			2.43863i			0.101171i
$582$		0			0
$583$	57.0531	+	32.9396i	2.36290	+	1.36422i
$584$		0			0
$585$	−3.49125	+	11.7631i	−0.144346	+	0.486346i
$586$		0			0
$587$	−32.9659	−	8.83319i	−1.36065	−	0.364585i	−0.496595	−	0.867983i	$-0.665416\pi$
$587$	−32.9659	−	8.83319i	−1.36065	−	0.364585i	−0.864055	+	0.503398i	$0.832083\pi$
$588$		0			0
$589$	6.87342	+	11.9051i	0.283214	+	0.490541i
$590$		0			0
$591$	−12.9889	−	5.58457i	−0.534290	−	0.229719i
$592$		0			0
$593$		−	15.9280i		−	0.654084i	−0.945010	−	0.327042i	$-0.893948\pi$
$593$		−	15.9280i		−	0.654084i	0.945010	−	0.327042i	$-0.106052\pi$
$594$		0			0
$595$	−1.53682	+	0.887285i	−0.0630036	+	0.0363751i
$596$		0			0
$597$	22.1084	+	17.4384i	0.904835	+	0.713707i
$598$		0			0
$599$	29.4343	−	16.9939i	1.20265	−	0.694352i	0.241509	−	0.970399i	$-0.422358\pi$
$599$	29.4343	−	16.9939i	1.20265	−	0.694352i	0.961144	+	0.276046i	$0.0890243\pi$
$600$		0			0
$601$	−7.04148	+	12.1962i	−0.287228	+	0.497493i	−0.973147	−	0.230184i	$-0.926067\pi$
$601$	−7.04148	+	12.1962i	−0.287228	+	0.497493i	0.685919	+	0.727678i	$0.259400\pi$
$602$		0			0
$603$	−19.3739	+	18.3654i	−0.788966	+	0.747898i
$604$		0			0
$605$	7.92586	−	29.5797i	0.322232	−	1.20259i
$606$		0			0
$607$	29.7139	−	7.96182i	1.20605	−	0.323160i	0.400840	−	0.916148i	$-0.368718\pi$
$607$	29.7139	−	7.96182i	1.20605	−	0.323160i	0.805211	+	0.592988i	$0.202052\pi$
$608$		0			0
$609$	7.62710	+	1.10796i	0.309066	+	0.0448969i
$610$		0			0
$611$	2.78329	−	10.3874i	0.112600	−	0.420228i
$612$		0			0
$613$	−39.0127	−	22.5240i	−1.57571	−	0.909734i	−0.995448	−	0.0953016i	$-0.969618\pi$
$613$	−39.0127	−	22.5240i	−1.57571	−	0.909734i	−0.580258	−	0.814433i	$-0.697048\pi$
$614$		0			0
$615$	−8.09931	+	3.22878i	−0.326596	+	0.130197i
$616$		0			0
$617$	−8.84886	+	15.3267i	−0.356242	+	0.617029i	−0.987330	−	0.158683i	$-0.949275\pi$
$617$	−8.84886	+	15.3267i	−0.356242	+	0.617029i	0.631088	+	0.775711i	$0.282609\pi$
$618$		0			0
$619$			24.0819i			0.967935i	0.875086	+	0.483968i	$0.160805\pi$
$619$			24.0819i			0.967935i	−0.875086	+	0.483968i	$0.839195\pi$
$620$		0			0
$621$	0.0674524	+	0.0311617i	0.00270677	+	0.00125048i
$622$		0			0
$623$	−2.75873	+	2.75873i	−0.110526	+	0.110526i
$624$		0			0
$625$	4.78869	+	8.29426i	0.191548	+	0.331770i
$626$		0			0
$627$	−60.5736	−	8.79931i	−2.41908	−	0.351411i
$628$		0			0
$629$	8.41467	−	12.5830i	0.335515	−	0.501719i
$630$		0			0
$631$	5.62001	−	1.50588i	0.223729	−	0.0599480i	−0.145213	−	0.989400i	$-0.546387\pi$
$631$	5.62001	−	1.50588i	0.223729	−	0.0599480i	0.368942	+	0.929452i	$0.379720\pi$
$632$		0			0
$633$	−7.67936	+	0.906827i	−0.305227	+	0.0360431i
$634$		0			0
$635$	−5.87056	−	5.87056i	−0.232966	−	0.232966i
$636$		0			0
$637$	−17.9556	+	17.9556i	−0.711425	+	0.711425i
$638$		0			0
$639$	−10.8834	+	10.3169i	−0.430540	+	0.408129i
$640$		0			0
$641$	10.1966	+	5.88701i	0.402742	+	0.232523i	0.687666	−	0.726027i	$-0.258635\pi$
$641$	10.1966	+	5.88701i	0.402742	+	0.232523i	−0.284925	+	0.958550i	$0.591969\pi$
$642$		0			0
$643$	−19.7367	−	19.7367i	−0.778341	−	0.778341i	0.201207	−	0.979549i	$-0.435513\pi$
$643$	−19.7367	−	19.7367i	−0.778341	−	0.778341i	−0.979549	+	0.201207i	$0.935513\pi$
$644$		0			0
$645$	−7.17493	−	9.61376i	−0.282512	−	0.378542i
$646$		0			0
$647$	−1.12927	−	0.302586i	−0.0443960	−	0.0118959i	0.236553	−	0.971619i	$-0.423982\pi$
$647$	−1.12927	−	0.302586i	−0.0443960	−	0.0118959i	−0.280949	+	0.959723i	$0.590649\pi$
$648$		0			0
$649$	−1.93887	+	0.519518i	−0.0761073	+	0.0203929i
$650$		0			0
$651$	−0.414868	+	2.85591i	−0.0162600	+	0.111932i
$652$		0			0
$653$	−13.3675	−	3.58182i	−0.523113	−	0.140168i	−0.0124066	−	0.999923i	$-0.503949\pi$
$653$	−13.3675	−	3.58182i	−0.523113	−	0.140168i	−0.510706	+	0.859755i	$0.670616\pi$
$654$		0			0
$655$	−2.31045			−0.0902769
$656$		0			0
$657$	11.3876	+	47.5448i	0.444271	+	1.85490i
$658$		0			0
$659$	−0.260848	−	0.451802i	−0.0101612	−	0.0175997i	0.860900	−	0.508774i	$-0.169901\pi$
$659$	−0.260848	−	0.451802i	−0.0101612	−	0.0175997i	−0.871061	+	0.491174i	$0.836568\pi$
$660$		0			0
$661$	−9.88587	+	36.8946i	−0.384516	+	1.43503i	0.454413	+	0.890791i	$0.349849\pi$
$661$	−9.88587	+	36.8946i	−0.384516	+	1.43503i	−0.838929	+	0.544241i	$0.816818\pi$
$662$		0			0
$663$	−16.6151	+	1.96202i	−0.645277	+	0.0761984i
$664$		0			0
$665$	3.98142			0.154393
$666$		0			0
$667$	−0.0940255			−0.00364068
$668$		0			0
$669$	−12.0036	+	1.41747i	−0.464088	+	0.0548024i
$670$		0			0
$671$	−9.43170	+	35.1996i	−0.364107	+	1.35887i
$672$		0			0
$673$	−15.7794	−	27.3306i	−0.608249	−	1.05352i	−0.991529	−	0.129886i	$-0.958539\pi$
$673$	−15.7794	−	27.3306i	−0.608249	−	1.05352i	0.383279	−	0.923632i	$-0.374795\pi$
$674$		0			0
$675$	19.9164	+	3.43874i	0.766584	+	0.132357i
$676$		0			0
$677$	−8.95857			−0.344306			−0.172153	−	0.985070i	$-0.555072\pi$
$677$	−8.95857			−0.344306			−0.172153	+	0.985070i	$0.555072\pi$
$678$		0			0
$679$	4.48727	+	1.20236i	0.172206	+	0.0461423i
$680$		0			0
$681$	−4.24226	+	29.2033i	−0.162564	+	1.11907i
$682$		0			0
$683$	3.73186	−	0.999949i	0.142796	−	0.0382620i	−0.186713	−	0.982414i	$-0.559784\pi$
$683$	3.73186	−	0.999949i	0.142796	−	0.0382620i	0.329509	+	0.944152i	$0.393117\pi$
$684$		0			0
$685$	12.8432	+	3.44132i	0.490713	+	0.131486i
$686$		0			0
$687$	−7.59704	−	10.1794i	−0.289845	−	0.388366i
$688$		0			0
$689$	−28.5674	−	28.5674i	−1.08833	−	1.08833i
$690$		0			0
$691$	−4.62569	−	2.67064i	−0.175969	−	0.101596i	0.409428	−	0.912342i	$-0.365728\pi$
$691$	−4.62569	−	2.67064i	−0.175969	−	0.101596i	−0.585398	+	0.810746i	$0.699062\pi$
$692$		0			0
$693$	−8.84019	−	9.32561i	−0.335811	−	0.354251i
$694$		0			0
$695$	−9.96993	+	9.96993i	−0.378181	+	0.378181i
$696$		0			0
$697$	−8.40649	−	8.40649i	−0.318419	−	0.318419i
$698$		0			0
$699$	−27.0082	+	3.18930i	−1.02155	+	0.120631i
$700$		0			0
$701$	9.32708	−	2.49918i	0.352279	−	0.0943929i	−0.0783399	−	0.996927i	$-0.524962\pi$
$701$	9.32708	−	2.49918i	0.352279	−	0.0943929i	0.430619	+	0.902534i	$0.358295\pi$
$702$		0			0
$703$	−30.4654	+	15.0095i	−1.14903	+	0.566092i
$704$		0			0
$705$	5.00404	+	0.726919i	0.188463	+	0.0273774i
$706$		0			0
$707$	−2.10630	−	3.64822i	−0.0792157	−	0.137206i
$708$		0			0
$709$	−14.0024	+	14.0024i	−0.525873	+	0.525873i	−0.919339	−	0.393466i	$-0.871276\pi$
$709$	−14.0024	+	14.0024i	−0.525873	+	0.525873i	0.393466	+	0.919339i	$0.371276\pi$
$710$		0			0
$711$	−7.62810	−	0.203837i	−0.286076	−	0.00764448i
$712$		0			0
$713$		−	0.0352071i		−	0.00131852i
$714$		0			0
$715$	−12.9440	+	22.4196i	−0.484077	+	0.838445i
$716$		0			0
$717$	−15.5872	+	6.21381i	−0.582113	+	0.232059i
$718$		0			0
$719$	3.78714	+	2.18651i	0.141236	+	0.0815429i	0.568953	−	0.822370i	$-0.307349\pi$
$719$	3.78714	+	2.18651i	0.141236	+	0.0815429i	−0.427717	+	0.903913i	$0.640682\pi$
$720$		0			0
$721$	−3.17035	+	11.8319i	−0.118070	+	0.440643i
$722$		0			0
$723$	34.9838	+	5.08198i	1.30106	+	0.189001i
$724$		0			0
$725$	−24.7045	+	6.61954i	−0.917501	+	0.245844i
$726$		0			0
$727$	−9.48763	+	35.4083i	−0.351877	+	1.31322i	0.532493	+	0.846434i	$0.321255\pi$
$727$	−9.48763	+	35.4083i	−0.351877	+	1.31322i	−0.884370	+	0.466787i	$0.845411\pi$
$728$		0			0
$729$	20.5591	−	17.5021i	0.761448	−	0.648226i
$730$		0			0
$731$	8.17827	−	14.1652i	0.302484	−	0.523918i
$732$		0			0
$733$	26.8999	−	15.5307i	0.993572	−	0.573639i	0.0872321	−	0.996188i	$-0.472198\pi$
$733$	26.8999	−	15.5307i	0.993572	−	0.573639i	0.906340	+	0.422549i	$0.138864\pi$
$734$		0			0
$735$	−9.37478	−	7.39455i	−0.345794	−	0.272752i
$736$		0			0
$737$	−48.7761	+	28.1609i	−1.79669	+	1.03732i
$738$		0			0
$739$		−	3.04296i		−	0.111937i	−0.998433	−	0.0559686i	$-0.982175\pi$
$739$		−	3.04296i		−	0.111937i	0.998433	−	0.0559686i	$-0.0178247\pi$
$740$		0			0
$741$	34.4843	+	14.8266i	1.26681	+	0.544668i
$742$		0			0
$743$	−3.20824	−	5.55684i	−0.117699	−	0.203861i	0.801156	−	0.598455i	$-0.204218\pi$
$743$	−3.20824	−	5.55684i	−0.117699	−	0.203861i	−0.918855	+	0.394594i	$0.870885\pi$
$744$		0			0
$745$	23.5226	+	6.30287i	0.861802	+	0.230919i
$746$		0			0
$747$	−10.3639	−	3.07598i	−0.379197	−	0.112544i
$748$		0			0
$749$	9.64452	+	5.56827i	0.352403	+	0.203460i
$750$		0			0
$751$		−	44.2837i		−	1.61593i	−0.589227	−	0.807967i	$-0.700568\pi$
$751$		−	44.2837i		−	1.61593i	0.589227	−	0.807967i	$-0.299432\pi$
$752$		0			0
$753$	23.0911	−	29.2747i	0.841485	−	1.06683i
$754$		0			0
$755$	−1.57364	−	5.87290i	−0.0572705	−	0.213737i
$756$		0			0
$757$	2.02860	+	7.57083i	0.0737306	+	0.275166i	0.992942	−	0.118597i	$-0.0378396\pi$
$757$	2.02860	+	7.57083i	0.0737306	+	0.275166i	−0.919212	+	0.393763i	$0.871173\pi$
$758$		0			0
$759$	0.123083	+	0.0970845i	0.00446764	+	0.00352395i
$760$		0			0
$761$	18.8901	−	32.7186i	0.684765	−	1.18605i	−0.288746	−	0.957406i	$-0.593238\pi$
$761$	18.8901	−	32.7186i	0.684765	−	1.18605i	0.973511	−	0.228641i	$-0.0734283\pi$
$762$		0			0
$763$	7.87072	−	7.87072i	0.284939	−	0.284939i
$764$		0			0
$765$	−1.83240	−	7.65053i	−0.0662504	−	0.276605i
$766$		0			0
$767$	1.23095			0.0444472
$768$		0			0
$769$	15.1774	+	15.1774i	0.547312	+	0.547312i	0.925662	−	0.378350i	$-0.123509\pi$
$769$	15.1774	+	15.1774i	0.547312	+	0.547312i	−0.378350	+	0.925662i	$0.623509\pi$
$770$		0			0
$771$	19.2433	−	7.67134i	0.693032	−	0.276277i
$772$		0			0
$773$	11.7282	−	6.77125i	0.421832	−	0.243545i	−0.274029	−	0.961722i	$-0.588356\pi$
$773$	11.7282	−	6.77125i	0.421832	−	0.243545i	0.695861	+	0.718176i	$0.255023\pi$
$774$		0			0
$775$	−2.47864	−	9.25040i	−0.0890353	−	0.332284i
$776$		0			0
$777$	−6.97294	−	1.48688i	−0.250153	−	0.0533414i
$778$		0			0
$779$	6.90352	+	25.7643i	0.247344	+	0.923102i
$780$		0			0
$781$	−27.4002	+	15.8195i	−0.980456	+	0.566067i
$782$		0			0
$783$	−14.3292	+	31.0169i	−0.512084	+	1.10845i
$784$		0			0
$785$	−3.51889	−	3.51889i	−0.125595	−	0.125595i
$786$		0			0
$787$	−37.1667			−1.32485			−0.662426	−	0.749128i	$-0.730473\pi$
$787$	−37.1667			−1.32485			−0.662426	+	0.749128i	$0.730473\pi$
$788$		0			0
$789$	−16.2168	−	21.7291i	−0.577335	−	0.773577i
$790$		0			0
$791$	1.54987	−	1.54987i	0.0551072	−	0.0551072i
$792$		0			0
$793$	11.1738	−	19.3536i	0.396794	−	0.687267i
$794$		0			0
$795$	11.7648	−	14.9153i	0.417254	−	0.528992i
$796$		0			0
$797$	8.94231	+	33.3732i	0.316753	+	1.18214i	0.922346	+	0.386364i	$0.126269\pi$
$797$	8.94231	+	33.3732i	0.316753	+	1.18214i	−0.605594	+	0.795774i	$0.707064\pi$
$798$		0			0
$799$	1.78446	+	6.65969i	0.0631296	+	0.235603i
$800$		0			0
$801$	−8.24458	−	15.2040i	−0.291308	−	0.537209i
$802$		0			0
$803$			103.147i			3.63999i
$804$		0			0
$805$	−0.00883073	−	0.00509843i	−0.000311242	−	0.000179696i
$806$		0			0
$807$	−5.20196	−	44.0522i	−0.183118	−	1.55071i
$808$		0			0
$809$	−45.0624	−	12.0744i	−1.58431	−	0.424514i	−0.644053	−	0.764981i	$-0.722748\pi$
$809$	−45.0624	−	12.0744i	−1.58431	−	0.424514i	−0.940257	+	0.340467i	$0.889415\pi$
$810$		0			0
$811$	13.9797	+	24.2135i	0.490893	+	0.850252i	0.999945	−	0.0104836i	$-0.00333710\pi$
$811$	13.9797	+	24.2135i	0.490893	+	0.850252i	−0.509052	+	0.860736i	$0.670004\pi$
$812$		0			0
$813$	2.04631	−	4.75941i	0.0717674	−	0.166920i
$814$		0			0
$815$			19.8788i			0.696324i
$816$		0			0
$817$	−31.7810	+	18.3487i	−1.11187	+	0.641941i
$818$		0			0
$819$	3.75635	+	6.92718i	0.131258	+	0.242055i
$820$		0			0
$821$	8.18074	−	4.72315i	0.285510	−	0.164839i	−0.350405	−	0.936598i	$-0.613956\pi$
$821$	8.18074	−	4.72315i	0.285510	−	0.164839i	0.635915	+	0.771759i	$0.280623\pi$
$822$		0			0
$823$	23.0116	−	39.8573i	0.802134	−	1.38934i	−0.116075	−	0.993240i	$-0.537031\pi$
$823$	23.0116	−	39.8573i	0.802134	−	1.38934i	0.918209	−	0.396097i	$-0.129635\pi$
$824$		0			0
$825$	39.1741	+	16.8429i	1.36387	+	0.586396i
$826$		0			0
$827$	10.4453	−	38.9825i	0.363220	−	1.35555i	−0.506599	−	0.862182i	$-0.669097\pi$
$827$	10.4453	−	38.9825i	0.363220	−	1.35555i	0.869818	−	0.493372i	$-0.164236\pi$
$828$		0			0
$829$	−7.99208	+	2.14147i	−0.277576	+	0.0743764i	−0.394922	−	0.918715i	$-0.629228\pi$
$829$	−7.99208	+	2.14147i	−0.277576	+	0.0743764i	0.117345	+	0.993091i	$0.462562\pi$
$830$		0			0
$831$	−1.41304	+	9.72723i	−0.0490178	+	0.337434i
$832$		0			0
$833$	4.21366	−	15.7256i	0.145995	−	0.544859i
$834$		0			0
$835$	3.28148	+	1.89456i	0.113560	+	0.0655641i
$836$		0			0
$837$	−11.6141	−	5.36547i	−0.401440	−	0.185458i
$838$		0			0
$839$	−12.6738	+	21.9517i	−0.437549	+	0.757857i	−0.997500	−	0.0706685i	$-0.977487\pi$
$839$	−12.6738	+	21.9517i	−0.437549	+	0.757857i	0.559951	+	0.828526i	$0.310820\pi$
$840$		0			0
$841$		−	14.2361i		−	0.490901i
$842$		0			0
$843$	43.9296	−	17.5125i	1.51301	−	0.603162i
$844$		0			0
$845$	1.53946	−	1.53946i	0.0529591	−	0.0529591i
$846$		0			0
$847$	−9.83324	−	17.0317i	−0.337874	−	0.585215i
$848$		0			0
$849$	−2.61023	+	17.9686i	−0.0895829	+	0.616680i
$850$		0			0
$851$	0.0867923	+	0.00572191i	0.00297520	+	0.000196144i
$852$		0			0
$853$	−7.21927	+	1.93440i	−0.247183	+	0.0662325i	−0.380283	−	0.924870i	$-0.624173\pi$
$853$	−7.21927	+	1.93440i	−0.247183	+	0.0662325i	0.133100	+	0.991103i	$0.457507\pi$
$854$		0			0
$855$	−5.02198	+	16.9206i	−0.171748	+	0.578674i
$856$		0			0
$857$	−4.01165	−	4.01165i	−0.137035	−	0.137035i	0.635262	−	0.772297i	$-0.280892\pi$
$857$	−4.01165	−	4.01165i	−0.137035	−	0.137035i	−0.772297	+	0.635262i	$0.780892\pi$
$858$		0			0
$859$	−5.07986	+	5.07986i	−0.173322	+	0.173322i	−0.788437	−	0.615115i	$-0.789110\pi$
$859$	−5.07986	+	5.07986i	−0.173322	+	0.173322i	0.615115	+	0.788437i	$0.289110\pi$
$860$		0			0
$861$	−2.21176	+	5.14421i	−0.0753765	+	0.175314i
$862$		0			0
$863$	−34.7787	−	20.0795i	−1.18388	−	0.683514i	−0.226972	−	0.973901i	$-0.572883\pi$
$863$	−34.7787	−	20.0795i	−1.18388	−	0.683514i	−0.956909	+	0.290387i	$0.906216\pi$
$864$		0			0
$865$	9.00587	+	9.00587i	0.306209	+	0.306209i
$866$		0			0
$867$	−15.0011	+	11.1956i	−0.509465	+	0.380223i
$868$		0			0
$869$	−15.5510	−	4.16687i	−0.527530	−	0.141351i
$870$		0			0
$871$	33.3624	−	8.93943i	1.13044	−	0.302901i
$872$		0			0
$873$	−10.7699	+	17.5538i	−0.364507	+	0.594108i
$874$		0			0
$875$	−6.12310	−	1.64068i	−0.206999	−	0.0554651i
$876$		0			0
$877$	41.2247			1.39206			0.696029	−	0.718013i	$-0.254948\pi$
$877$	41.2247			1.39206			0.696029	+	0.718013i	$0.254948\pi$
$878$		0			0
$879$	−47.1785	+	35.2102i	−1.59129	+	1.18761i
$880$		0			0
$881$	−11.6640	−	20.2027i	−0.392971	−	0.680646i	0.599869	−	0.800099i	$-0.295220\pi$
$881$	−11.6640	−	20.2027i	−0.392971	−	0.680646i	−0.992840	+	0.119452i	$0.961886\pi$
$882$		0			0
$883$	−0.678293	+	2.53142i	−0.0228264	+	0.0851891i	−0.976399	−	0.215973i	$-0.930708\pi$
$883$	−0.678293	+	2.53142i	−0.0228264	+	0.0851891i	0.953573	+	0.301162i	$0.0973744\pi$
$884$		0			0
$885$	0.0678779	+	0.574816i	0.00228169	+	0.0193222i
$886$		0			0
$887$	−19.1168			−0.641880			−0.320940	−	0.947100i	$-0.603999\pi$
$887$	−19.1168			−0.641880			−0.320940	+	0.947100i	$0.603999\pi$
$888$		0			0
$889$	−5.33176			−0.178822
$890$		0			0
$891$	50.7836	−	25.8070i	1.70131	−	0.864568i
$892$		0			0
$893$	4.00361	−	14.9417i	0.133976	−	0.500004i
$894$		0			0
$895$	3.14406	+	5.44567i	0.105094	+	0.182029i
$896$		0			0
$897$	−0.0574995	−	0.0770443i	−0.00191985	−	0.00257243i
$898$		0			0
$899$	16.1894			0.539948
$900$		0			0
$901$	25.0195	+	6.70396i	0.833520	+	0.223341i
$902$		0			0
$903$	−7.62392	−	1.10750i	−0.253708	−	0.0368553i
$904$		0			0
$905$	−16.8829	+	4.52377i	−0.561207	+	0.150375i
$906$		0			0
$907$	6.53083	+	1.74993i	0.216852	+	0.0581054i	0.365610	−	0.930768i	$-0.380861\pi$
$907$	6.53083	+	1.74993i	0.216852	+	0.0581054i	−0.148757	+	0.988874i	$0.547527\pi$
$908$		0			0
$909$	18.1614	−	4.34988i	0.602375	−	0.144276i
$910$		0			0
$911$	18.8036	+	18.8036i	0.622991	+	0.622991i	0.946295	−	0.323304i	$-0.104794\pi$
$911$	18.8036	+	18.8036i	0.622991	+	0.622991i	−0.323304	+	0.946295i	$0.604794\pi$
$912$		0			0
$913$	−19.7528	−	11.4043i	−0.653723	−	0.377427i
$914$		0			0
$915$	9.65366	+	4.15060i	0.319140	+	0.137215i
$916$		0			0
$917$	−1.04920	+	1.04920i	−0.0346477	+	0.0346477i
$918$		0			0
$919$	33.1411	+	33.1411i	1.09322	+	1.09322i	0.995182	+	0.0980403i	$0.0312574\pi$
$919$	33.1411	+	33.1411i	1.09322	+	1.09322i	0.0980403	+	0.995182i	$0.468743\pi$
$920$		0			0
$921$	−0.433151	−	3.66809i	−0.0142728	−	0.120868i
$922$		0			0
$923$	18.7415	−	5.02177i	0.616884	−	0.165293i
$924$		0			0
$925$	23.2068	−	4.60693i	0.763036	−	0.151475i
$926$		0			0
$927$	−46.2855	−	28.3979i	−1.52022	−	0.932710i
$928$		0			0
$929$	11.7383	+	20.3313i	0.385121	+	0.667050i	0.991786	−	0.127908i	$-0.0408263\pi$
$929$	11.7383	+	20.3313i	0.385121	+	0.667050i	−0.606665	+	0.794958i	$0.707493\pi$
$930$		0			0
$931$	−25.8281	+	25.8281i	−0.846482	+	0.846482i
$932$		0			0
$933$	12.9060	+	32.3744i	0.422524	+	1.05989i
$934$		0			0
$935$		−	16.5976i		−	0.542800i
$936$		0			0
$937$	4.38323	−	7.59198i	0.143194	−	0.248019i	−0.785504	−	0.618857i	$-0.787596\pi$
$937$	4.38323	−	7.59198i	0.143194	−	0.248019i	0.928698	+	0.370838i	$0.120929\pi$
$938$		0			0
$939$	−7.08610	−	17.7753i	−0.231246	−	0.580074i
$940$		0			0
$941$	46.0643	+	26.5952i	1.50165	+	0.866980i	0.999998	+	0.00191282i	$0.000608870\pi$
$941$	46.0643	+	26.5952i	1.50165	+	0.866980i	0.501656	+	0.865067i	$0.332724\pi$
$942$		0			0
$943$	0.0176807	−	0.0659852i	0.000575762	−	0.00214877i
$944$		0			0
$945$	−3.02764	+	2.13608i	−0.0984890	+	0.0694866i
$946$		0			0
$947$	−30.2958	+	8.11774i	−0.984481	+	0.263791i	−0.714931	−	0.699195i	$-0.753542\pi$
$947$	−30.2958	+	8.11774i	−0.984481	+	0.263791i	−0.269551	+	0.962986i	$0.586875\pi$
$948$		0			0
$949$	16.3716	−	61.0996i	0.531444	−	1.98338i
$950$		0			0
$951$	−7.51611	+	17.4813i	−0.243727	+	0.566871i
$952$		0			0
$953$	−13.9829	+	24.2191i	−0.452951	+	0.784534i	−0.998568	−	0.0535008i	$-0.982962\pi$
$953$	−13.9829	+	24.2191i	−0.452951	+	0.784534i	0.545617	+	0.838035i	$0.316295\pi$
$954$		0			0
$955$	18.1648	−	10.4875i	0.587800	−	0.339367i
$956$		0			0
$957$	−44.6428	+	56.5979i	−1.44310	+	1.82955i
$958$		0			0
$959$	7.39496	−	4.26948i	0.238796	−	0.137869i
$960$		0			0
$961$		−	24.9380i		−	0.804451i
$962$		0			0
$963$	−35.8298	+	33.9647i	−1.15460	+	1.09450i
$964$		0			0
$965$	7.57997	+	13.1289i	0.244008	+	0.422634i
$966$		0			0
$967$	−41.1436	−	11.0244i	−1.32309	−	0.354520i	−0.472954	−	0.881087i	$-0.656812\pi$
$967$	−41.1436	−	11.0244i	−1.32309	−	0.354520i	−0.850134	+	0.526567i	$0.823479\pi$
$968$		0			0
$969$	−23.8999	+	2.82226i	−0.767777	+	0.0906639i
$970$		0			0
$971$	−23.2319	−	13.4129i	−0.745547	−	0.430442i	0.0785358	−	0.996911i	$-0.474976\pi$
$971$	−23.2319	−	13.4129i	−0.745547	−	0.430442i	−0.824083	+	0.566470i	$0.808309\pi$
$972$		0			0
$973$			9.05490i			0.290287i
$974$		0			0
$975$	−20.5316	−	16.1947i	−0.657537	−	0.518646i
$976$		0			0
$977$	4.98452	+	18.6025i	0.159469	+	0.595146i	0.998681	+	0.0513422i	$0.0163499\pi$
$977$	4.98452	+	18.6025i	0.159469	+	0.595146i	−0.839212	+	0.543804i	$0.816983\pi$
$978$		0			0
$979$	−9.44436	−	35.2468i	−0.301843	−	1.12649i
$980$		0			0
$981$	23.5220	+	43.3776i	0.751001	+	1.38494i
$982$		0			0
$983$	−21.2380	+	36.7854i	−0.677388	+	1.17327i	0.298377	+	0.954448i	$0.403555\pi$
$983$	−21.2380	+	36.7854i	−0.677388	+	1.17327i	−0.975765	+	0.218822i	$0.929778\pi$
$984$		0			0
$985$	−6.08222	+	6.08222i	−0.193796	+	0.193796i
$986$		0			0
$987$	2.60249	−	1.94229i	0.0828382	−	0.0618236i
$988$		0			0
$989$	0.0939863			0.00298859
$990$		0			0
$991$	−13.0352	−	13.0352i	−0.414078	−	0.414078i	0.469078	−	0.883157i	$-0.344586\pi$
$991$	−13.0352	−	13.0352i	−0.414078	−	0.414078i	−0.883157	+	0.469078i	$0.844586\pi$
$992$		0			0
$993$	−5.36246	−	13.4516i	−0.170172	−	0.426873i
$994$		0			0
$995$	14.8357	−	8.56537i	0.470322	−	0.271541i
$996$		0			0
$997$	13.8261	+	51.5997i	0.437877	+	1.63418i	0.734087	+	0.679055i	$0.237610\pi$
$997$	13.8261	+	51.5997i	0.437877	+	1.63418i	−0.296211	+	0.955123i	$0.595723\pi$
$998$		0			0
$999$	15.1144	−	27.7589i	0.478199	−	0.878251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.br.a.569.37	yes	152
3.2	odd	2	inner	888.2.br.a.569.28	✓	152
37.8	odd	12	inner	888.2.br.a.785.28	yes	152
111.8	even	12	inner	888.2.br.a.785.37	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.br.a.569.28	✓	152	3.2	odd	2	inner
888.2.br.a.569.37	yes	152	1.1	even	1	trivial
888.2.br.a.785.28	yes	152	37.8	odd	12	inner
888.2.br.a.785.37	yes	152	111.8	even	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72010 - 0.203120i) q^{3} +(0.272728 - 1.01783i) q^{5} +(-0.338361 - 0.586058i) q^{7} +(2.91748 - 0.698774i) q^{9} +6.32941 q^{11} +(-3.74925 - 1.00461i) q^{13} +(0.262377 - 1.80617i) q^{15} +(2.40377 - 0.644088i) q^{17} +(-5.39309 - 1.44507i) q^{19} +(-0.701055 - 0.939351i) q^{21} +(0.0101113 + 0.0101113i) q^{23} +(3.36852 + 1.94482i) q^{25} +(4.87643 - 1.79456i) q^{27} +(-4.64952 + 4.64952i) q^{29} +(-1.74098 - 1.74098i) q^{31} +(10.8872 - 1.28563i) q^{33} +(-0.688791 + 0.184561i) q^{35} +(4.57479 - 4.00890i) q^{37} +(-6.65314 - 0.966478i) q^{39} +(-2.38864 - 4.13724i) q^{41} +(4.64758 - 4.64758i) q^{43} +(0.0844435 - 3.16009i) q^{45} +2.77052i q^{47} +(3.27102 - 5.66558i) q^{49} +(4.00390 - 1.59615i) q^{51} +(9.01397 + 5.20422i) q^{53} +(1.72621 - 6.44229i) q^{55} +(-9.57018 - 1.39023i) q^{57} +(-0.306327 + 0.0820801i) q^{59} +(-1.49014 + 5.56128i) q^{61} +(-1.39669 - 1.47338i) q^{63} +(-2.04505 + 3.54213i) q^{65} +(-7.70626 + 4.44921i) q^{67} +(0.0194463 + 0.0153386i) q^{69} +(-4.32903 + 2.49937i) q^{71} +16.2965i q^{73} +(6.18922 + 2.66106i) q^{75} +(-2.14162 - 3.70940i) q^{77} +(-2.45694 - 0.658334i) q^{79} +(8.02343 - 4.07732i) q^{81} +(-3.12080 - 1.80180i) q^{83} -2.62230i q^{85} +(-7.05323 + 8.94205i) q^{87} +(-1.49214 - 5.56874i) q^{89} +(0.679840 + 2.53720i) q^{91} +(-3.34828 - 2.64103i) q^{93} +(-2.94170 + 5.09517i) q^{95} +(-4.85415 + 4.85415i) q^{97} +(18.4659 - 4.42282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) \) 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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