LMFDB - Embedded newform 672.2.bd.a.431.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,2,Mod(431,672)] 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("672.431"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bd (of order $6$, degree $2$, not 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.16
Character	$\chi$	$=$	672.431
Dual form			672.2.bd.a.527.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.316681 - 1.70285i) q^{3} +(1.86088 + 3.22314i) q^{5} +(-2.46429 + 0.962962i) q^{7} +(-2.79943 - 1.07852i) q^{9} +(2.26958 + 1.31034i) q^{11} +3.57182i q^{13} +(6.07784 - 2.14810i) q^{15} +(0.186192 + 0.107498i) q^{17} +(1.14103 + 1.97631i) q^{19} +(0.859391 + 4.50127i) q^{21} +(2.33586 + 4.04583i) q^{23} +(-4.42574 + 7.66560i) q^{25} +(-2.72309 + 4.42547i) q^{27} +2.57415 q^{29} +(-4.26196 - 2.46064i) q^{31} +(2.95006 - 3.44980i) q^{33} +(-7.68949 - 6.15077i) q^{35} +(7.31104 - 4.22103i) q^{37} +(6.08229 + 1.13113i) q^{39} +0.909442i q^{41} -3.73541 q^{43} +(-1.73317 - 11.0299i) q^{45} +(0.586728 + 1.01624i) q^{47} +(5.14541 - 4.74603i) q^{49} +(0.242017 - 0.283015i) q^{51} +(-1.06171 + 1.83894i) q^{53} +9.75355i q^{55} +(3.72672 - 1.31714i) q^{57} +(6.79199 + 3.92136i) q^{59} +(-0.301301 + 0.173956i) q^{61} +(7.93716 - 0.0379510i) q^{63} +(-11.5125 + 6.64673i) q^{65} +(4.98736 - 8.63836i) q^{67} +(7.62919 - 2.69640i) q^{69} -10.0808 q^{71} +(4.45173 - 7.71062i) q^{73} +(11.6519 + 9.96394i) q^{75} +(-6.85470 - 1.04354i) q^{77} +(9.70950 - 5.60578i) q^{79} +(6.67358 + 6.03849i) q^{81} +1.73937i q^{83} +0.800163i q^{85} +(0.815185 - 4.38341i) q^{87} +(15.4694 - 8.93127i) q^{89} +(-3.43953 - 8.80199i) q^{91} +(-5.53980 + 6.47826i) q^{93} +(-4.24662 + 7.35536i) q^{95} -8.88553 q^{97} +(-4.94029 - 6.11600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.316681	−	1.70285i	0.182836	−	0.983143i
$3$	0.316681	−	1.70285i	0.182836	−	0.983143i
$4$		0			0
$5$	1.86088	+	3.22314i	0.832210	+	1.44143i	0.896282	+	0.443485i	$0.146258\pi$
$5$	1.86088	+	3.22314i	0.832210	+	1.44143i	−0.0640716	+	0.997945i	$0.520409\pi$
$6$		0			0
$7$	−2.46429	+	0.962962i	−0.931412	+	0.363965i
$7$	−2.46429	+	0.962962i	−0.931412	+	0.363965i
$8$		0			0
$9$	−2.79943	−	1.07852i	−0.933142	−	0.359508i
$10$		0			0
$11$	2.26958	+	1.31034i	0.684304	+	0.395083i	0.801475	−	0.598029i	$-0.204049\pi$
$11$	2.26958	+	1.31034i	0.684304	+	0.395083i	−0.117171	+	0.993112i	$0.537382\pi$
$12$		0			0
$13$			3.57182i			0.990645i	0.868709	+	0.495323i	$0.164950\pi$
$13$			3.57182i			0.990645i	−0.868709	+	0.495323i	$0.835050\pi$
$14$		0			0
$15$	6.07784	−	2.14810i	1.56929	−	0.554637i
$16$		0			0
$17$	0.186192	+	0.107498i	0.0451582	+	0.0260721i	0.522409	−	0.852695i	$-0.325033\pi$
$17$	0.186192	+	0.107498i	0.0451582	+	0.0260721i	−0.477251	+	0.878767i	$0.658367\pi$
$18$		0			0
$19$	1.14103	+	1.97631i	0.261769	+	0.453398i	0.966712	−	0.255866i	$-0.0823607\pi$
$19$	1.14103	+	1.97631i	0.261769	+	0.453398i	−0.704943	+	0.709264i	$0.749027\pi$
$20$		0			0
$21$	0.859391	+	4.50127i	0.187535	+	0.982258i
$22$		0			0
$23$	2.33586	+	4.04583i	0.487061	+	0.843615i	0.999889	−	0.0148767i	$-0.00473557\pi$
$23$	2.33586	+	4.04583i	0.487061	+	0.843615i	−0.512828	+	0.858491i	$0.671402\pi$
$24$		0			0
$25$	−4.42574	+	7.66560i	−0.885148	+	1.53312i
$26$		0			0
$27$	−2.72309	+	4.42547i	−0.524060	+	0.851682i
$28$		0			0
$29$	2.57415			0.478008			0.239004	−	0.971019i	$-0.423179\pi$
$29$	2.57415			0.478008			0.239004	+	0.971019i	$0.423179\pi$
$30$		0			0
$31$	−4.26196	−	2.46064i	−0.765471	−	0.441945i	0.0657857	−	0.997834i	$-0.479045\pi$
$31$	−4.26196	−	2.46064i	−0.765471	−	0.441945i	−0.831257	+	0.555889i	$0.812378\pi$
$32$		0			0
$33$	2.95006	−	3.44980i	0.513539	−	0.600534i
$34$		0			0
$35$	−7.68949	−	6.15077i	−1.29976	−	1.03967i
$36$		0			0
$37$	7.31104	−	4.22103i	1.20193	−	0.693933i	0.240944	−	0.970539i	$-0.422543\pi$
$37$	7.31104	−	4.22103i	1.20193	−	0.693933i	0.960983	+	0.276606i	$0.0892098\pi$
$38$		0			0
$39$	6.08229	+	1.13113i	0.973946	+	0.181125i
$40$		0			0
$41$			0.909442i			0.142031i	0.997475	+	0.0710155i	$0.0226240\pi$
$41$			0.909442i			0.142031i	−0.997475	+	0.0710155i	$0.977376\pi$
$42$		0			0
$43$	−3.73541			−0.569644			−0.284822	−	0.958580i	$-0.591935\pi$
$43$	−3.73541			−0.569644			−0.284822	+	0.958580i	$0.591935\pi$
$44$		0			0
$45$	−1.73317	−	11.0299i	−0.258365	−	1.64425i
$46$		0			0
$47$	0.586728	+	1.01624i	0.0855831	+	0.148234i	0.905640	−	0.424048i	$-0.139391\pi$
$47$	0.586728	+	1.01624i	0.0855831	+	0.148234i	−0.820056	+	0.572283i	$0.806058\pi$
$48$		0			0
$49$	5.14541	−	4.74603i	0.735058	−	0.678004i
$50$		0			0
$51$	0.242017	−	0.283015i	0.0338891	−	0.0396301i
$52$		0			0
$53$	−1.06171	+	1.83894i	−0.145837	+	0.252598i	−0.929685	−	0.368355i	$-0.879921\pi$
$53$	−1.06171	+	1.83894i	−0.145837	+	0.252598i	0.783848	+	0.620953i	$0.213254\pi$
$54$		0			0
$55$			9.75355i			1.31517i
$56$		0			0
$57$	3.72672	−	1.31714i	0.493616	−	0.174459i
$58$		0			0
$59$	6.79199	+	3.92136i	0.884242	+	0.510517i	0.872055	−	0.489408i	$-0.162787\pi$
$59$	6.79199	+	3.92136i	0.884242	+	0.510517i	0.0121872	+	0.999926i	$0.496121\pi$
$60$		0			0
$61$	−0.301301	+	0.173956i	−0.0385776	+	0.0222728i	−0.519165	−	0.854674i	$-0.673757\pi$
$61$	−0.301301	+	0.173956i	−0.0385776	+	0.0222728i	0.480587	+	0.876947i	$0.340424\pi$
$62$		0			0
$63$	7.93716	−	0.0379510i	0.999989	−	0.00478137i
$64$		0			0
$65$	−11.5125	+	6.64673i	−1.42795	+	0.824425i
$66$		0			0
$67$	4.98736	−	8.63836i	0.609303	−	1.05534i	−0.382053	−	0.924140i	$-0.624783\pi$
$67$	4.98736	−	8.63836i	0.609303	−	1.05534i	0.991356	−	0.131203i	$-0.0418839\pi$
$68$		0			0
$69$	7.62919	−	2.69640i	0.918446	−	0.324608i
$70$		0			0
$71$	−10.0808			−1.19637			−0.598183	−	0.801359i	$-0.704111\pi$
$71$	−10.0808			−1.19637			−0.598183	+	0.801359i	$0.704111\pi$
$72$		0			0
$73$	4.45173	−	7.71062i	0.521036	−	0.902460i	−0.478665	−	0.877998i	$-0.658879\pi$
$73$	4.45173	−	7.71062i	0.521036	−	0.902460i	0.999701	−	0.0244626i	$-0.00778746\pi$
$74$		0			0
$75$	11.6519	+	9.96394i	1.34544	+	1.15054i
$76$		0			0
$77$	−6.85470	−	1.04354i	−0.781166	−	0.118922i
$78$		0			0
$79$	9.70950	−	5.60578i	1.09240	−	0.630700i	0.158189	−	0.987409i	$-0.449434\pi$
$79$	9.70950	−	5.60578i	1.09240	−	0.630700i	0.934216	+	0.356709i	$0.116101\pi$
$80$		0			0
$81$	6.67358	+	6.03849i	0.741508	+	0.670944i
$82$		0			0
$83$			1.73937i			0.190921i	0.995433	+	0.0954603i	$0.0304323\pi$
$83$			1.73937i			0.190921i	−0.995433	+	0.0954603i	$0.969568\pi$
$84$		0			0
$85$			0.800163i			0.0867898i
$86$		0			0
$87$	0.815185	−	4.38341i	0.0873970	−	0.469950i
$88$		0			0
$89$	15.4694	−	8.93127i	1.63975	−	0.946712i	0.658837	−	0.752286i	$-0.271049\pi$
$89$	15.4694	−	8.93127i	1.63975	−	0.946712i	0.980917	−	0.194426i	$-0.0622845\pi$
$90$		0			0
$91$	−3.43953	−	8.80199i	−0.360560	−	0.922699i
$92$		0			0
$93$	−5.53980	+	6.47826i	−0.574451	+	0.671764i
$94$		0			0
$95$	−4.24662	+	7.35536i	−0.435694	+	0.754644i
$96$		0			0
$97$	−8.88553			−0.902189			−0.451094	−	0.892476i	$-0.648966\pi$
$97$	−8.88553			−0.902189			−0.451094	+	0.892476i	$0.648966\pi$
$98$		0			0
$99$	−4.94029	−	6.11600i	−0.496518	−	0.614681i
$100$		0			0
$101$	−7.38721	+	12.7950i	−0.735055	+	1.27315i	0.219644	+	0.975580i	$0.429510\pi$
$101$	−7.38721	+	12.7950i	−0.735055	+	1.27315i	−0.954699	+	0.297573i	$0.903823\pi$
$102$		0			0
$103$	−6.50151	+	3.75365i	−0.640613	+	0.369858i	−0.784851	−	0.619685i	$-0.787260\pi$
$103$	−6.50151	+	3.75365i	−0.640613	+	0.369858i	0.144238	+	0.989543i	$0.453927\pi$
$104$		0			0
$105$	−12.9090	+	11.1463i	−1.25979	+	1.08776i
$106$		0			0
$107$	−10.9396	+	6.31597i	−1.05757	+	0.610588i	−0.924759	−	0.380554i	$-0.875733\pi$
$107$	−10.9396	+	6.31597i	−1.05757	+	0.610588i	−0.132810	+	0.991141i	$0.542400\pi$
$108$		0			0
$109$	−11.2275	−	6.48219i	−1.07540	−	0.620881i	−0.145747	−	0.989322i	$-0.546558\pi$
$109$	−11.2275	−	6.48219i	−1.07540	−	0.620881i	−0.929651	+	0.368441i	$0.879892\pi$
$110$		0			0
$111$	−4.87253	−	13.7864i	−0.462480	−	1.30854i
$112$		0			0
$113$		−	7.10498i		−	0.668380i	−0.942506	−	0.334190i	$-0.891537\pi$
$113$		−	7.10498i		−	0.668380i	0.942506	−	0.334190i	$-0.108463\pi$
$114$		0			0
$115$	−8.69351	+	15.0576i	−0.810674	+	1.40413i
$116$		0			0
$117$	3.85229	−	9.99905i	0.356145	−	0.924413i
$118$		0			0
$119$	−0.562347	−	0.0856100i	−0.0515502	−	0.00784786i
$120$		0			0
$121$	−2.06600	−	3.57842i	−0.187819	−	0.325311i
$122$		0			0
$123$	1.54865	+	0.288003i	0.139637	+	0.0259684i
$124$		0			0
$125$	−14.3343			−1.28210
$126$		0			0
$127$		−	2.53093i		−	0.224584i	−0.993675	−	0.112292i	$-0.964181\pi$
$127$		−	2.53093i		−	0.224584i	0.993675	−	0.112292i	$-0.0358192\pi$
$128$		0			0
$129$	−1.18293	+	6.36086i	−0.104151	+	0.560042i
$130$		0			0
$131$	5.04824	−	2.91460i	0.441067	−	0.254650i	−0.262983	−	0.964800i	$-0.584706\pi$
$131$	5.04824	−	2.91460i	0.441067	−	0.254650i	0.704050	+	0.710150i	$0.251373\pi$
$132$		0			0
$133$	−4.71493	−	3.77144i	−0.408836	−	0.327025i
$134$		0			0
$135$	−19.3312	−	0.541642i	−1.66377	−	0.0466171i
$136$		0			0
$137$	−8.15158	−	4.70632i	−0.696437	−	0.402088i	0.109582	−	0.993978i	$-0.465049\pi$
$137$	−8.15158	−	4.70632i	−0.696437	−	0.402088i	−0.806019	+	0.591890i	$0.798382\pi$
$138$		0			0
$139$	7.53929			0.639474			0.319737	−	0.947506i	$-0.396405\pi$
$139$	7.53929			0.639474			0.319737	+	0.947506i	$0.396405\pi$
$140$		0			0
$141$	1.91632	−	0.677288i	0.161383	−	0.0570379i
$142$		0			0
$143$	−4.68031	+	8.10654i	−0.391387	+	0.677903i
$144$		0			0
$145$	4.79018	+	8.29684i	0.397803	+	0.689015i
$146$		0			0
$147$	−6.45234	−	10.2649i	−0.532180	−	0.846631i
$148$		0			0
$149$	−7.38721	−	12.7950i	−0.605184	−	1.04821i	−0.992022	−	0.126062i	$-0.959766\pi$
$149$	−7.38721	−	12.7950i	−0.605184	−	1.04821i	0.386838	−	0.922148i	$-0.373567\pi$
$150$		0			0
$151$	−3.18729	−	1.84018i	−0.259378	−	0.149752i	0.364673	−	0.931136i	$-0.381181\pi$
$151$	−3.18729	−	1.84018i	−0.259378	−	0.149752i	−0.624051	+	0.781384i	$0.714514\pi$
$152$		0			0
$153$	−0.405292	−	0.501745i	−0.0327659	−	0.0405637i
$154$		0			0
$155$		−	18.3158i		−	1.47116i
$156$		0			0
$157$	18.5989	+	10.7381i	1.48436	+	0.856993i	0.999842	−	0.0177905i	$-0.00566318\pi$
$157$	18.5989	+	10.7381i	1.48436	+	0.856993i	0.484514	+	0.874784i	$0.338997\pi$
$158$		0			0
$159$	2.79522	+	2.39030i	0.221676	+	0.189563i
$160$		0			0
$161$	−9.65222	−	7.72074i	−0.760701	−	0.608480i
$162$		0			0
$163$	0.756294	+	1.30994i	0.0592375	+	0.102602i	0.894123	−	0.447821i	$-0.147800\pi$
$163$	0.756294	+	1.30994i	0.0592375	+	0.102602i	−0.834886	+	0.550423i	$0.814466\pi$
$164$		0			0
$165$	16.6089	+	3.08877i	1.29300	+	0.240460i
$166$		0			0
$167$	−7.21687			−0.558459			−0.279229	−	0.960224i	$-0.590079\pi$
$167$	−7.21687			−0.558459			−0.279229	+	0.960224i	$0.590079\pi$
$168$		0			0
$169$	0.242090			0.0186223
$170$		0			0
$171$	−1.06272	−	6.76317i	−0.0812680	−	0.517193i
$172$		0			0
$173$	1.33696	+	2.31567i	0.101647	+	0.176057i	0.912363	−	0.409382i	$-0.134256\pi$
$173$	1.33696	+	2.31567i	0.101647	+	0.176057i	−0.810716	+	0.585439i	$0.800922\pi$
$174$		0			0
$175$	3.52460	−	23.1521i	0.266435	−	1.75013i
$176$		0			0
$177$	8.82840	−	10.3240i	0.663583	−	0.775996i
$178$		0			0
$179$	7.29346	+	4.21088i	0.545139	+	0.314736i	0.747159	−	0.664645i	$-0.231417\pi$
$179$	7.29346	+	4.21088i	0.545139	+	0.314736i	−0.202020	+	0.979381i	$0.564751\pi$
$180$		0			0
$181$		−	6.12284i		−	0.455107i	−0.973766	−	0.227553i	$-0.926927\pi$
$181$		−	6.12284i		−	0.455107i	0.973766	−	0.227553i	$-0.0730726\pi$
$182$		0			0
$183$	0.200806	+	0.568160i	0.0148440	+	0.0419996i
$184$		0			0
$185$	27.2099	+	15.7096i	2.00051	+	1.15500i
$186$		0			0
$187$	0.281718	+	0.487951i	0.0206013	+	0.0356825i
$188$		0			0
$189$	2.44892	−	13.5279i	0.178133	−	0.984006i
$190$		0			0
$191$	−7.56478	−	13.1026i	−0.547368	−	0.948069i	−0.998454	−	0.0555887i	$-0.982296\pi$
$191$	−7.56478	−	13.1026i	−0.547368	−	0.948069i	0.451086	−	0.892481i	$-0.351037\pi$
$192$		0			0
$193$	−1.52962	+	2.64937i	−0.110104	+	0.190706i	−0.915812	−	0.401607i	$-0.868452\pi$
$193$	−1.52962	+	2.64937i	−0.110104	+	0.190706i	0.805708	+	0.592313i	$0.201785\pi$
$194$		0			0
$195$	7.67263	+	21.7089i	0.549448	+	1.55461i
$196$		0			0
$197$	−14.5736			−1.03833			−0.519163	−	0.854675i	$-0.673756\pi$
$197$	−14.5736			−1.03833			−0.519163	+	0.854675i	$0.673756\pi$
$198$		0			0
$199$	15.0386	+	8.68255i	1.06606	+	0.615490i	0.927102	−	0.374809i	$-0.122292\pi$
$199$	15.0386	+	8.68255i	1.06606	+	0.615490i	0.138957	+	0.990298i	$0.455625\pi$
$200$		0			0
$201$	−13.1305	−	11.2283i	−0.926151	−	0.791987i
$202$		0			0
$203$	−6.34345	+	2.47881i	−0.445223	+	0.173978i
$204$		0			0
$205$	−2.93126	+	1.69236i	−0.204728	+	0.118200i
$206$		0			0
$207$	−2.17555	−	13.8453i	−0.151211	−	0.962314i
$208$		0			0
$209$			5.98054i			0.413683i
$210$		0			0
$211$	21.2686			1.46419			0.732097	−	0.681201i	$-0.238542\pi$
$211$	21.2686			1.46419			0.732097	+	0.681201i	$0.238542\pi$
$212$		0			0
$213$	−3.19239	+	17.1661i	−0.218739	+	1.17620i
$214$		0			0
$215$	−6.95114	−	12.0397i	−0.474064	−	0.821103i
$216$		0			0
$217$	12.8722	+	1.95963i	0.873822	+	0.133028i
$218$		0			0
$219$	−11.7203	−	10.0225i	−0.791984	−	0.677255i
$220$		0			0
$221$	−0.383964	+	0.665045i	−0.0258282	+	0.0447357i
$222$		0			0
$223$		−	6.68788i		−	0.447854i	−0.974606	−	0.223927i	$-0.928112\pi$
$223$		−	6.68788i		−	0.447854i	0.974606	−	0.223927i	$-0.0718877\pi$
$224$		0			0
$225$	20.6571	−	16.6860i	1.37714	−	1.11240i
$226$		0			0
$227$	20.7637	+	11.9879i	1.37813	+	0.795666i	0.991935	−	0.126749i	$-0.0404544\pi$
$227$	20.7637	+	11.9879i	1.37813	+	0.795666i	0.386199	+	0.922415i	$0.373788\pi$
$228$		0			0
$229$	−14.3077	+	8.26054i	−0.945478	+	0.545872i	−0.891673	−	0.452680i	$-0.850468\pi$
$229$	−14.3077	+	8.26054i	−0.945478	+	0.545872i	−0.0538045	+	0.998551i	$0.517135\pi$
$230$		0			0
$231$	−3.94775	+	11.3421i	−0.259743	+	0.746255i
$232$		0			0
$233$	−13.4061	+	7.74002i	−0.878264	+	0.507066i	−0.870086	−	0.492901i	$-0.835937\pi$
$233$	−13.4061	+	7.74002i	−0.878264	+	0.507066i	−0.00817827	+	0.999967i	$0.502603\pi$
$234$		0			0
$235$	−2.18366	+	3.78221i	−0.142446	+	0.246724i
$236$		0			0
$237$	−6.47102	−	18.3091i	−0.420338	−	1.18930i
$238$		0			0
$239$	20.5460			1.32901			0.664505	−	0.747284i	$-0.268642\pi$
$239$	20.5460			1.32901			0.664505	+	0.747284i	$0.268642\pi$
$240$		0			0
$241$	−6.16667	+	10.6810i	−0.397230	+	0.688023i	−0.993383	−	0.114848i	$-0.963362\pi$
$241$	−6.16667	+	10.6810i	−0.397230	+	0.688023i	0.596153	+	0.802871i	$0.296695\pi$
$242$		0			0
$243$	12.3961	−	9.45185i	0.795208	−	0.606337i
$244$		0			0
$245$	24.8721	+	7.75258i	1.58902	+	0.495294i
$246$		0			0
$247$	−7.05904	+	4.07554i	−0.449156	+	0.259320i
$248$		0			0
$249$	2.96189	+	0.550825i	0.187702	+	0.0349071i
$250$		0			0
$251$		−	21.2978i		−	1.34430i	−0.740413	−	0.672152i	$-0.765370\pi$
$251$		−	21.2978i		−	1.34430i	0.740413	−	0.672152i	$-0.234630\pi$
$252$		0			0
$253$			12.2431i			0.769719i
$254$		0			0
$255$	1.36256	+	0.253396i	0.0853269	+	0.0158683i
$256$		0			0
$257$	−13.2299	+	7.63828i	−0.825258	+	0.476463i	−0.852226	−	0.523173i	$-0.824748\pi$
$257$	−13.2299	+	7.63828i	−0.825258	+	0.476463i	0.0269684	+	0.999636i	$0.491415\pi$
$258$		0			0
$259$	−13.9518	+	17.4421i	−0.866922	+	1.08380i
$260$		0			0
$261$	−7.20615	−	2.77628i	−0.446049	−	0.171848i
$262$		0			0
$263$	−0.249921	+	0.432876i	−0.0154108	+	0.0266923i	−0.873628	−	0.486594i	$-0.838239\pi$
$263$	−0.249921	+	0.432876i	−0.0154108	+	0.0266923i	0.858217	+	0.513287i	$0.171572\pi$
$264$		0			0
$265$	−7.90287			−0.485470
$266$		0			0
$267$	−10.3098	−	29.1705i	−0.630948	−	1.78521i
$268$		0			0
$269$	10.9207	−	18.9153i	0.665849	−	1.15328i	−0.313205	−	0.949685i	$-0.601403\pi$
$269$	10.9207	−	18.9153i	0.665849	−	1.15328i	0.979054	−	0.203599i	$-0.0652638\pi$
$270$		0			0
$271$	13.6308	−	7.86975i	0.828013	−	0.478053i	−0.0251590	−	0.999683i	$-0.508009\pi$
$271$	13.6308	−	7.86975i	0.828013	−	0.478053i	0.853172	+	0.521630i	$0.174676\pi$
$272$		0			0
$273$	−16.0777	+	3.06959i	−0.973069	+	0.185780i
$274$		0			0
$275$	−20.0891	+	11.5985i	−1.21142	+	0.699414i
$276$		0			0
$277$	−10.8672	−	6.27417i	−0.652945	−	0.376978i	0.136639	−	0.990621i	$-0.456370\pi$
$277$	−10.8672	−	6.27417i	−0.652945	−	0.376978i	−0.789584	+	0.613643i	$0.789703\pi$
$278$		0			0
$279$	9.27718	+	11.4850i	0.555411	+	0.687590i
$280$		0			0
$281$		−	22.7512i		−	1.35722i	−0.734498	−	0.678610i	$-0.762582\pi$
$281$		−	22.7512i		−	1.35722i	0.734498	−	0.678610i	$-0.237418\pi$
$282$		0			0
$283$	−0.440379	+	0.762759i	−0.0261778	+	0.0453413i	−0.878818	−	0.477158i	$-0.841667\pi$
$283$	−0.440379	+	0.762759i	−0.0261778	+	0.0453413i	0.852640	+	0.522499i	$0.175000\pi$
$284$		0			0
$285$	11.1803	+	9.56068i	0.662263	+	0.566326i
$286$		0			0
$287$	−0.875758	−	2.24113i	−0.0516944	−	0.132289i
$288$		0			0
$289$	−8.47689	−	14.6824i	−0.498640	−	0.863671i
$290$		0			0
$291$	−2.81388	+	15.1308i	−0.164952	+	0.886981i
$292$		0			0
$293$	22.1280			1.29273			0.646366	−	0.763028i	$-0.276288\pi$
$293$	22.1280			1.29273			0.646366	+	0.763028i	$0.276288\pi$
$294$		0			0
$295$			29.1887i			1.69943i
$296$		0			0
$297$	−11.9792	+	6.47577i	−0.695101	+	0.375762i
$298$		0			0
$299$	−14.4510	+	8.34329i	−0.835723	+	0.482505i
$300$		0			0
$301$	9.20511	−	3.59705i	0.530574	−	0.207331i
$302$		0			0
$303$	19.4487	+	16.6313i	1.11730	+	0.955442i
$304$		0			0
$305$	−1.12137	−	0.647422i	−0.0642094	−	0.0370713i
$306$		0			0
$307$	−9.96754			−0.568878			−0.284439	−	0.958694i	$-0.591807\pi$
$307$	−9.96754			−0.568878			−0.284439	+	0.958694i	$0.591807\pi$
$308$		0			0
$309$	4.33301	+	12.2598i	0.246496	+	0.697438i
$310$		0			0
$311$	−5.87187	+	10.1704i	−0.332963	+	0.576709i	−0.983091	−	0.183115i	$-0.941382\pi$
$311$	−5.87187	+	10.1704i	−0.332963	+	0.576709i	0.650128	+	0.759825i	$0.274715\pi$
$312$		0			0
$313$	−0.343520	−	0.594993i	−0.0194169	−	0.0336310i	0.856154	−	0.516721i	$-0.172848\pi$
$313$	−0.343520	−	0.594993i	−0.0194169	−	0.0336310i	−0.875571	+	0.483090i	$0.839514\pi$
$314$		0			0
$315$	14.8924	+	25.5119i	0.839093	+	1.43743i
$316$		0			0
$317$	16.4535	+	28.4983i	0.924120	+	1.60062i	0.792970	+	0.609261i	$0.208534\pi$
$317$	16.4535	+	28.4983i	0.924120	+	1.60062i	0.131150	+	0.991363i	$0.458133\pi$
$318$		0			0
$319$	5.84224	+	3.37302i	0.327103	+	0.188853i
$320$		0			0
$321$	7.29082	+	20.6287i	0.406934	+	1.15138i
$322$		0			0
$323$			0.490632i			0.0272995i
$324$		0			0
$325$	−27.3802	−	15.8079i	−1.51878	−	0.876867i
$326$		0			0
$327$	−14.5938	+	17.0660i	−0.807037	+	0.943751i
$328$		0			0
$329$	−2.42447	−	1.93932i	−0.133665	−	0.106918i
$330$		0			0
$331$	0.833276	+	1.44328i	0.0458010	+	0.0793297i	0.888017	−	0.459810i	$-0.152083\pi$
$331$	0.833276	+	1.44328i	0.0458010	+	0.0793297i	−0.842216	+	0.539140i	$0.818749\pi$
$332$		0			0
$333$	−25.0192	+	3.93134i	−1.37104	+	0.215436i
$334$		0			0
$335$	37.1235			2.02827
$336$		0			0
$337$	9.04814			0.492884			0.246442	−	0.969158i	$-0.420739\pi$
$337$	9.04814			0.492884			0.246442	+	0.969158i	$0.420739\pi$
$338$		0			0
$339$	−12.0987	−	2.25001i	−0.657113	−	0.122204i
$340$		0			0
$341$	−6.44858	−	11.1693i	−0.349210	−	0.604849i
$342$		0			0
$343$	−8.10952	+	16.6504i	−0.437873	+	0.899037i
$344$		0			0
$345$	22.8878	+	19.5722i	1.23224	+	1.05373i
$346$		0			0
$347$	−4.59168	−	2.65101i	−0.246494	−	0.142313i	0.371664	−	0.928367i	$-0.378787\pi$
$347$	−4.59168	−	2.65101i	−0.246494	−	0.142313i	−0.618158	+	0.786054i	$0.712121\pi$
$348$		0			0
$349$			10.7938i			0.577779i	0.957362	+	0.288890i	$0.0932861\pi$
$349$			10.7938i			0.577779i	−0.957362	+	0.288890i	$0.906714\pi$
$350$		0			0
$351$	−15.8070	−	9.72640i	−0.843714	−	0.519157i
$352$		0			0
$353$	24.5717	+	14.1865i	1.30782	+	0.755071i	0.981732	−	0.190268i	$-0.0609357\pi$
$353$	24.5717	+	14.1865i	1.30782	+	0.755071i	0.326089	+	0.945339i	$0.394269\pi$
$354$		0			0
$355$	−18.7591	−	32.4917i	−0.995628	−	1.72448i
$356$		0			0
$357$	−0.323866	+	0.930483i	−0.0171408	+	0.0492464i
$358$		0			0
$359$	0.0586851	+	0.101646i	0.00309728	+	0.00536465i	0.867570	−	0.497315i	$-0.165681\pi$
$359$	0.0586851	+	0.101646i	0.00309728	+	0.00536465i	−0.864473	+	0.502680i	$0.832347\pi$
$360$		0			0
$361$	6.89612	−	11.9444i	0.362954	−	0.628654i
$362$		0			0
$363$	−6.74780	+	2.38489i	−0.354168	+	0.125174i
$364$		0			0
$365$	33.1365			1.73444
$366$		0			0
$367$	−7.31080	−	4.22089i	−0.381621	−	0.220329i	0.296902	−	0.954908i	$-0.404046\pi$
$367$	−7.31080	−	4.22089i	−0.381621	−	0.220329i	−0.678523	+	0.734579i	$0.737380\pi$
$368$		0			0
$369$	0.980855	−	2.54592i	0.0510613	−	0.132535i
$370$		0			0
$371$	0.845534	−	5.55406i	0.0438980	−	0.288353i
$372$		0			0
$373$	0.0783826	−	0.0452542i	0.00405850	−	0.00234318i	−0.497969	−	0.867195i	$-0.665921\pi$
$373$	0.0783826	−	0.0452542i	0.00405850	−	0.00234318i	0.502028	+	0.864851i	$0.332587\pi$
$374$		0			0
$375$	−4.53939	+	24.4092i	−0.234413	+	1.26048i
$376$		0			0
$377$			9.19441i			0.473536i
$378$		0			0
$379$	19.7881			1.01645			0.508224	−	0.861225i	$-0.330302\pi$
$379$	19.7881			1.01645			0.508224	+	0.861225i	$0.330302\pi$
$380$		0			0
$381$	−4.30981	−	0.801498i	−0.220798	−	0.0410620i
$382$		0			0
$383$	12.4851	+	21.6249i	0.637961	+	1.10498i	0.985880	+	0.167456i	$0.0535551\pi$
$383$	12.4851	+	21.6249i	0.637961	+	1.10498i	−0.347919	+	0.937525i	$0.613112\pi$
$384$		0			0
$385$	−9.39230	−	24.0355i	−0.478676	−	1.22496i
$386$		0			0
$387$	10.4570	+	4.02872i	0.531559	+	0.204792i
$388$		0			0
$389$	15.0483	−	26.0644i	0.762979	−	1.32152i	−0.178329	−	0.983971i	$-0.557069\pi$
$389$	15.0483	−	26.0644i	0.762979	−	1.32152i	0.941308	−	0.337548i	$-0.109597\pi$
$390$		0			0
$391$			1.00440i			0.0507948i
$392$		0			0
$393$	−3.36446	−	9.51942i	−0.169715	−	0.480191i
$394$		0			0
$395$	36.1364	+	20.8634i	1.81822	+	1.04975i
$396$		0			0
$397$	4.91661	−	2.83861i	0.246758	−	0.142466i	−0.371521	−	0.928425i	$-0.621164\pi$
$397$	4.91661	−	2.83861i	0.246758	−	0.142466i	0.618279	+	0.785959i	$0.287830\pi$
$398$		0			0
$399$	−7.91534	+	6.83449i	−0.396263	+	0.342153i
$400$		0			0
$401$	−0.897563	+	0.518208i	−0.0448222	+	0.0258781i	−0.522244	−	0.852796i	$-0.674905\pi$
$401$	−0.897563	+	0.518208i	−0.0448222	+	0.0258781i	0.477421	+	0.878674i	$0.341572\pi$
$402$		0			0
$403$	8.78898	−	15.2230i	0.437810	−	0.758310i
$404$		0			0
$405$	−7.04417	+	32.7467i	−0.350028	+	1.62720i
$406$		0			0
$407$	22.1240			1.09664
$408$		0			0
$409$	1.83983	−	3.18669i	0.0909739	−	0.157571i	−0.816947	−	0.576712i	$-0.804335\pi$
$409$	1.83983	−	3.18669i	0.0909739	−	0.157571i	0.907921	+	0.419141i	$0.137669\pi$
$410$		0			0
$411$	−10.5956	+	12.3906i	−0.522644	+	0.611181i
$412$		0			0
$413$	−20.5135	−	3.12292i	−1.00940	−	0.153669i
$414$		0			0
$415$	−5.60623	+	3.23676i	−0.275199	+	0.158886i
$416$		0			0
$417$	2.38755	−	12.8383i	0.116919	−	0.628695i
$418$		0			0
$419$		−	9.81445i		−	0.479467i	−0.970839	−	0.239734i	$-0.922940\pi$
$419$		−	9.81445i		−	0.479467i	0.970839	−	0.239734i	$-0.0770601\pi$
$420$		0			0
$421$		−	33.0188i		−	1.60924i	−0.593790	−	0.804620i	$-0.702369\pi$
$421$		−	33.0188i		−	1.60924i	0.593790	−	0.804620i	$-0.297631\pi$
$422$		0			0
$423$	−0.546461	−	3.47770i	−0.0265698	−	0.169091i
$424$		0			0
$425$	−1.64807	+	0.951516i	−0.0799433	+	0.0461553i
$426$		0			0
$427$	0.574978	−	0.718819i	0.0278252	−	0.0347861i
$428$		0			0
$429$	12.3221	+	10.5371i	0.594916	+	0.508735i
$430$		0			0
$431$	5.27304	−	9.13317i	0.253993	−	0.439929i	−0.710628	−	0.703568i	$-0.751589\pi$
$431$	5.27304	−	9.13317i	0.253993	−	0.439929i	0.964622	+	0.263638i	$0.0849226\pi$
$432$		0			0
$433$	13.7135			0.659026			0.329513	−	0.944151i	$-0.393115\pi$
$433$	13.7135			0.659026			0.329513	+	0.944151i	$0.393115\pi$
$434$		0			0
$435$	15.6453	−	5.52953i	0.750133	−	0.265121i
$436$		0			0
$437$	−5.33056	+	9.23280i	−0.254995	+	0.441665i
$438$		0			0
$439$	8.62149	−	4.97762i	0.411481	−	0.237569i	−0.279945	−	0.960016i	$-0.590316\pi$
$439$	8.62149	−	4.97762i	0.411481	−	0.237569i	0.691426	+	0.722447i	$0.256983\pi$
$440$		0			0
$441$	−19.5229	+	7.73671i	−0.929662	+	0.368415i
$442$		0			0
$443$	0.202164	−	0.116720i	0.00960512	−	0.00554552i	−0.495190	−	0.868785i	$-0.664901\pi$
$443$	0.202164	−	0.116720i	0.00960512	−	0.00554552i	0.504795	+	0.863239i	$0.331568\pi$
$444$		0			0
$445$	57.5734	+	33.2400i	2.72924	+	1.57573i
$446$		0			0
$447$	−24.1275	+	8.52740i	−1.14119	+	0.403332i
$448$		0			0
$449$			5.83932i			0.275575i	0.990462	+	0.137787i	$0.0439990\pi$
$449$			5.83932i			0.275575i	−0.990462	+	0.137787i	$0.956001\pi$
$450$		0			0
$451$	−1.19168	+	2.06405i	−0.0561141	+	0.0971924i
$452$		0			0
$453$	−4.14292	+	4.84475i	−0.194651	+	0.227626i
$454$		0			0
$455$	21.9695	−	27.4655i	1.02994	−	1.28760i
$456$		0			0
$457$	8.93416	+	15.4744i	0.417923	+	0.723863i	0.995730	−	0.0923098i	$-0.0294250\pi$
$457$	8.93416	+	15.4744i	0.417923	+	0.723863i	−0.577808	+	0.816173i	$0.696092\pi$
$458$		0			0
$459$	−0.982747	+	0.531260i	−0.0458707	+	0.0247971i
$460$		0			0
$461$	−0.400330			−0.0186452			−0.00932262	−	0.999957i	$-0.502968\pi$
$461$	−0.400330			−0.0186452			−0.00932262	+	0.999957i	$0.502968\pi$
$462$		0			0
$463$		−	29.4293i		−	1.36769i	−0.729626	−	0.683847i	$-0.760306\pi$
$463$		−	29.4293i		−	1.36769i	0.729626	−	0.683847i	$-0.239694\pi$
$464$		0			0
$465$	−31.1892	−	5.80028i	−1.44637	−	0.268982i
$466$		0			0
$467$	6.75074	−	3.89754i	0.312387	−	0.180357i	−0.335607	−	0.942002i	$-0.608941\pi$
$467$	6.75074	−	3.89754i	0.312387	−	0.180357i	0.647994	+	0.761645i	$0.275608\pi$
$468$		0			0
$469$	−3.97187	+	26.0900i	−0.183404	+	1.20472i
$470$		0			0
$471$	24.1753	−	28.2707i	1.11394	−	1.30265i
$472$		0			0
$473$	−8.47781	−	4.89466i	−0.389810	−	0.225057i
$474$		0			0
$475$	−20.1995			−0.926818
$476$		0			0
$477$	4.95553	−	4.00290i	0.226898	−	0.183280i
$478$		0			0
$479$	19.3422	−	33.5016i	0.883765	−	1.53073i	0.0366434	−	0.999328i	$-0.488333\pi$
$479$	19.3422	−	33.5016i	0.883765	−	1.53073i	0.847122	−	0.531398i	$-0.178333\pi$
$480$		0			0
$481$	15.0768	+	26.1137i	0.687441	+	1.19068i
$482$		0			0
$483$	−16.2040	+	13.9913i	−0.737306	+	0.636627i
$484$		0			0
$485$	−16.5349	−	28.6393i	−0.750811	−	1.30044i
$486$		0			0
$487$	−8.63096	−	4.98308i	−0.391106	−	0.225805i	0.291533	−	0.956561i	$-0.405835\pi$
$487$	−8.63096	−	4.98308i	−0.391106	−	0.225805i	−0.682639	+	0.730756i	$0.739168\pi$
$488$		0			0
$489$	2.47014	−	0.873026i	0.111704	−	0.0394796i
$490$		0			0
$491$			15.5075i			0.699845i	0.936779	+	0.349923i	$0.113792\pi$
$491$			15.5075i			0.699845i	−0.936779	+	0.349923i	$0.886208\pi$
$492$		0			0
$493$	0.479286	+	0.276716i	0.0215860	+	0.0124627i
$494$		0			0
$495$	10.5194	−	27.3044i	0.472813	−	1.22724i
$496$		0			0
$497$	24.8419	−	9.70739i	1.11431	−	0.435436i
$498$		0			0
$499$	0.275544	+	0.477256i	0.0123350	+	0.0213649i	0.872127	−	0.489279i	$-0.162740\pi$
$499$	0.275544	+	0.477256i	0.0123350	+	0.0213649i	−0.859792	+	0.510644i	$0.829407\pi$
$500$		0			0
$501$	−2.28545	+	12.2893i	−0.102106	+	0.549045i
$502$		0			0
$503$	−32.2097			−1.43616			−0.718079	−	0.695962i	$-0.754978\pi$
$503$	−32.2097			−1.43616			−0.718079	+	0.695962i	$0.754978\pi$
$504$		0			0
$505$	−54.9868			−2.44688
$506$		0			0
$507$	0.0766652	−	0.412243i	0.00340482	−	0.0183084i
$508$		0			0
$509$	−0.906135	−	1.56947i	−0.0401637	−	0.0695656i	0.845245	−	0.534379i	$-0.179455\pi$
$509$	−0.906135	−	1.56947i	−0.0401637	−	0.0695656i	−0.885408	+	0.464814i	$0.846121\pi$
$510$		0			0
$511$	−3.54530	+	23.2880i	−0.156835	+	1.03020i
$512$		0			0
$513$	−11.8532	−	0.332116i	−0.523333	−	0.0146633i
$514$		0			0
$515$	−24.1970	−	13.9702i	−1.06625	−	0.615599i
$516$		0			0
$517$			3.07526i			0.135250i
$518$		0			0
$519$	4.36664	−	1.54331i	0.191674	−	0.0677438i
$520$		0			0
$521$	6.65560	+	3.84261i	0.291587	+	0.168348i	0.638657	−	0.769491i	$-0.279490\pi$
$521$	6.65560	+	3.84261i	0.291587	+	0.168348i	−0.347070	+	0.937839i	$0.612823\pi$
$522$		0			0
$523$	4.33611	+	7.51035i	0.189605	+	0.328405i	0.945118	−	0.326728i	$-0.105946\pi$
$523$	4.33611	+	7.51035i	0.189605	+	0.328405i	−0.755514	+	0.655133i	$0.772613\pi$
$524$		0			0
$525$	−38.3084	−	13.3337i	−1.67192	−	0.581930i
$526$		0			0
$527$	−0.529029	−	0.916305i	−0.0230449	−	0.0399149i
$528$		0			0
$529$	0.587489	−	1.01756i	0.0255430	−	0.0442417i
$530$		0			0
$531$	−14.7844	−	18.3029i	−0.641588	−	0.794277i
$532$		0			0
$533$	−3.24837			−0.140702
$534$		0			0
$535$	−40.7145	−	23.5065i	−1.76024	−	1.01627i
$536$		0			0
$537$	9.48022	−	11.0862i	0.409102	−	0.478405i
$538$		0			0
$539$	17.8968	−	4.02924i	0.770871	−	0.173551i
$540$		0			0
$541$	10.0751	−	5.81687i	0.433163	−	0.250087i	−0.267530	−	0.963549i	$-0.586208\pi$
$541$	10.0751	−	5.81687i	0.433163	−	0.250087i	0.700693	+	0.713463i	$0.252874\pi$
$542$		0			0
$543$	−10.4263	−	1.93899i	−0.447435	−	0.0832098i
$544$		0			0
$545$		−	48.2503i		−	2.06681i
$546$		0			0
$547$	27.7574			1.18682			0.593410	−	0.804900i	$-0.297781\pi$
$547$	27.7574			1.18682			0.593410	+	0.804900i	$0.297781\pi$
$548$		0			0
$549$	1.03109	−	0.162017i	0.0440056	−	0.00691473i
$550$		0			0
$551$	2.93717	+	5.08733i	0.125128	+	0.216728i
$552$		0			0
$553$	−18.5288	+	23.1641i	−0.787926	+	0.985039i
$554$		0			0
$555$	35.3681	−	41.3596i	1.50129	−	1.75562i
$556$		0			0
$557$	−7.71096	+	13.3558i	−0.326724	+	0.565902i	−0.981860	−	0.189609i	$-0.939278\pi$
$557$	−7.71096	+	13.3558i	−0.326724	+	0.565902i	0.655136	+	0.755511i	$0.272611\pi$
$558$		0			0
$559$		−	13.3422i		−	0.564315i
$560$		0			0
$561$	0.920124	−	0.325201i	0.0388476	−	0.0137300i
$562$		0			0
$563$	−11.5626	−	6.67567i	−0.487305	−	0.281346i	0.236151	−	0.971716i	$-0.424114\pi$
$563$	−11.5626	−	6.67567i	−0.487305	−	0.281346i	−0.723456	+	0.690371i	$0.757447\pi$
$564$		0			0
$565$	22.9003	−	13.2215i	0.963423	−	0.556233i
$566$		0			0
$567$	−22.2604	−	8.45417i	−0.934850	−	0.355042i
$568$		0			0
$569$	−39.4279	+	22.7637i	−1.65290	+	0.954305i	−0.677034	+	0.735951i	$0.736735\pi$
$569$	−39.4279	+	22.7637i	−1.65290	+	0.954305i	−0.975870	+	0.218353i	$0.929931\pi$
$570$		0			0
$571$	−20.3243	+	35.2028i	−0.850546	+	1.47319i	0.0301698	+	0.999545i	$0.490395\pi$
$571$	−20.3243	+	35.2028i	−0.850546	+	1.47319i	−0.880716	+	0.473645i	$0.842938\pi$
$572$		0			0
$573$	−24.7074	+	8.73238i	−1.03217	+	0.364800i
$574$		0			0
$575$	−41.3517			−1.72448
$576$		0			0
$577$	−8.50680	+	14.7342i	−0.354143	+	0.613393i	−0.986971	−	0.160899i	$-0.948561\pi$
$577$	−8.50680	+	14.7342i	−0.354143	+	0.613393i	0.632828	+	0.774292i	$0.281894\pi$
$578$		0			0
$579$	4.02710	+	3.44372i	0.167360	+	0.143116i
$580$		0			0
$581$	−1.67495	−	4.28630i	−0.0694885	−	0.177826i
$582$		0			0
$583$	−4.81928	+	2.78241i	−0.199594	+	0.115236i
$584$		0			0
$585$	39.3970	−	6.19056i	1.62886	−	0.255948i
$586$		0			0
$587$			28.5925i			1.18014i	0.807352	+	0.590070i	$0.200900\pi$
$587$			28.5925i			1.18014i	−0.807352	+	0.590070i	$0.799100\pi$
$588$		0			0
$589$		−	11.2306i		−	0.462750i
$590$		0			0
$591$	−4.61518	+	24.8167i	−0.189843	+	1.02082i
$592$		0			0
$593$	−4.49943	+	2.59775i	−0.184770	+	0.106677i	−0.589532	−	0.807745i	$-0.700688\pi$
$593$	−4.49943	+	2.59775i	−0.184770	+	0.106677i	0.404762	+	0.914422i	$0.367354\pi$
$594$		0			0
$595$	−0.770526	−	1.97183i	−0.0315885	−	0.0808371i
$596$		0			0
$597$	19.5476	−	22.8590i	0.800029	−	0.935556i
$598$		0			0
$599$	22.7140	−	39.3418i	0.928069	−	1.60746i	0.141519	−	0.989936i	$-0.454801\pi$
$599$	22.7140	−	39.3418i	0.928069	−	1.60746i	0.786550	−	0.617527i	$-0.211865\pi$
$600$		0			0
$601$	45.5994			1.86004			0.930019	−	0.367511i	$-0.119790\pi$
$601$	45.5994			1.86004			0.930019	+	0.367511i	$0.119790\pi$
$602$		0			0
$603$	−23.2784	+	18.8035i	−0.947970	+	0.765736i
$604$		0			0
$605$	7.68917	−	13.3180i	0.312609	−	0.541455i
$606$		0			0
$607$	−18.3382	+	10.5876i	−0.744324	+	0.429736i	−0.823639	−	0.567114i	$-0.808060\pi$
$607$	−18.3382	+	10.5876i	−0.744324	+	0.429736i	0.0793155	+	0.996850i	$0.474727\pi$
$608$		0			0
$609$	2.21220	+	11.5870i	0.0896430	+	0.469527i
$610$		0			0
$611$	−3.62984	+	2.09569i	−0.146848	+	0.0847825i
$612$		0			0
$613$	−22.2592	−	12.8513i	−0.899039	−	0.519060i	−0.0221508	−	0.999755i	$-0.507051\pi$
$613$	−22.2592	−	12.8513i	−0.899039	−	0.519060i	−0.876888	+	0.480694i	$0.840385\pi$
$614$		0			0
$615$	1.95357	+	5.52744i	0.0787756	+	0.222888i
$616$		0			0
$617$			16.9888i			0.683941i	0.939711	+	0.341971i	$0.111094\pi$
$617$			16.9888i			0.683941i	−0.939711	+	0.341971i	$0.888906\pi$
$618$		0			0
$619$	11.6456	−	20.1708i	0.468076	−	0.810732i	−0.531258	−	0.847210i	$-0.678281\pi$
$619$	11.6456	−	20.1708i	0.468076	−	0.810732i	0.999334	+	0.0364781i	$0.0116139\pi$
$620$		0			0
$621$	−24.2655	−	0.679895i	−0.973740	−	0.0272832i
$622$		0			0
$623$	−29.5206	+	36.9056i	−1.18272	+	1.47859i
$624$		0			0
$625$	−4.54562	−	7.87325i	−0.181825	−	0.314930i
$626$		0			0
$627$	10.1840	+	1.89392i	0.406709	+	0.0756360i
$628$		0			0
$629$	1.81501			0.0723691
$630$		0			0
$631$			15.0554i			0.599347i	0.954042	+	0.299674i	$0.0968778\pi$
$631$			15.0554i			0.599347i	−0.954042	+	0.299674i	$0.903122\pi$
$632$		0			0
$633$	6.73537	−	36.2174i	0.267707	−	1.43951i
$634$		0			0
$635$	8.15754	−	4.70976i	0.323722	−	0.186901i
$636$		0			0
$637$	16.9520	+	18.3785i	0.671661	+	0.728182i
$638$		0			0
$639$	28.2204	+	10.8723i	1.11638	+	0.430103i
$640$		0			0
$641$	22.9318	+	13.2397i	0.905752	+	0.522936i	0.879062	−	0.476707i	$-0.158170\pi$
$641$	22.9318	+	13.2397i	0.905752	+	0.522936i	0.0266904	+	0.999644i	$0.491503\pi$
$642$		0			0
$643$	29.9973			1.18298			0.591490	−	0.806312i	$-0.298540\pi$
$643$	29.9973			1.18298			0.591490	+	0.806312i	$0.298540\pi$
$644$		0			0
$645$	−22.7032	+	8.02403i	−0.893937	+	0.315946i
$646$		0			0
$647$	−9.22707	+	15.9817i	−0.362753	+	0.628307i	−0.988413	−	0.151789i	$-0.951497\pi$
$647$	−9.22707	+	15.9817i	−0.362753	+	0.628307i	0.625659	+	0.780096i	$0.284830\pi$
$648$		0			0
$649$	10.2766	+	17.7997i	0.403394	+	0.698698i
$650$		0			0
$651$	7.41334	−	21.2989i	0.290552	−	0.834770i
$652$		0			0
$653$	−8.95898	−	15.5174i	−0.350592	−	0.607243i	0.635761	−	0.771886i	$-0.280686\pi$
$653$	−8.95898	−	15.5174i	−0.350592	−	0.607243i	−0.986353	+	0.164643i	$0.947353\pi$
$654$		0			0
$655$	18.7883	+	10.8474i	0.734121	+	0.423845i
$656$		0			0
$657$	−20.7784	+	16.7840i	−0.810642	+	0.654807i
$658$		0			0
$659$			30.7250i			1.19687i	0.801170	+	0.598437i	$0.204211\pi$
$659$			30.7250i			1.19687i	−0.801170	+	0.598437i	$0.795789\pi$
$660$		0			0
$661$	−13.0311	−	7.52352i	−0.506852	−	0.292631i	0.224687	−	0.974431i	$-0.427864\pi$
$661$	−13.0311	−	7.52352i	−0.506852	−	0.292631i	−0.731539	+	0.681800i	$0.761197\pi$
$662$		0			0
$663$	1.01088	+	0.864441i	0.0392593	+	0.0335721i
$664$		0			0
$665$	3.38195	−	22.2151i	0.131147	−	0.861463i
$666$		0			0
$667$	6.01287	+	10.4146i	0.232819	+	0.403254i
$668$		0			0
$669$	−11.3885	−	2.11793i	−0.440304	−	0.0818837i
$670$		0			0
$671$	−0.911768			−0.0351984
$672$		0			0
$673$	20.6079			0.794376			0.397188	−	0.917737i	$-0.369986\pi$
$673$	20.6079			0.794376			0.397188	+	0.917737i	$0.369986\pi$
$674$		0			0
$675$	−21.8722	−	40.4601i	−0.841861	−	1.55731i
$676$		0			0
$677$	5.13682	+	8.89723i	0.197424	+	0.341948i	0.947692	−	0.319185i	$-0.103409\pi$
$677$	5.13682	+	8.89723i	0.197424	+	0.341948i	−0.750268	+	0.661133i	$0.770076\pi$
$678$		0			0
$679$	21.8965	−	8.55642i	0.840310	−	0.328365i
$680$		0			0
$681$	26.9891	−	31.5612i	1.03423	−	1.20943i
$682$		0			0
$683$	−30.7725	−	17.7665i	−1.17748	−	0.679817i	−0.222048	−	0.975036i	$-0.571274\pi$
$683$	−30.7725	−	17.7665i	−1.17748	−	0.679817i	−0.955430	+	0.295218i	$0.904608\pi$
$684$		0			0
$685$		−	35.0316i		−	1.33849i
$686$		0			0
$687$	9.53553	+	26.9798i	0.363803	+	1.02935i
$688$		0			0
$689$	−6.56837	−	3.79225i	−0.250235	−	0.144473i
$690$		0			0
$691$	−17.0490	−	29.5298i	−0.648576	−	1.12337i	−0.983463	−	0.181109i	$-0.942031\pi$
$691$	−17.0490	−	29.5298i	−0.648576	−	1.12337i	0.334887	−	0.942258i	$-0.391302\pi$
$692$		0			0
$693$	18.0638	+	10.3143i	0.686185	+	0.391807i
$694$		0			0
$695$	14.0297	+	24.3002i	0.532177	+	0.921758i
$696$		0			0
$697$	−0.0977632	+	0.169331i	−0.00370305	+	0.00641386i
$698$		0			0
$699$	8.93467	+	25.2798i	0.337940	+	0.956169i
$700$		0			0
$701$	−42.6496			−1.61085			−0.805426	−	0.592696i	$-0.798063\pi$
$701$	−42.6496			−1.61085			−0.805426	+	0.592696i	$0.798063\pi$
$702$		0			0
$703$	16.6842	+	9.63261i	0.629255	+	0.363301i
$704$		0			0
$705$	5.74903	+	4.91621i	0.216521	+	0.185155i
$706$		0			0
$707$	5.88308	−	38.6442i	0.221256	−	1.45336i
$708$		0			0
$709$	−24.7114	+	14.2671i	−0.928054	+	0.535812i	−0.886196	−	0.463311i	$-0.846661\pi$
$709$	−24.7114	+	14.2671i	−0.928054	+	0.535812i	−0.0418586	+	0.999124i	$0.513328\pi$
$710$		0			0
$711$	−33.2270	+	5.22106i	−1.24611	+	0.195805i
$712$		0			0
$713$		−	22.9909i		−	0.861017i
$714$		0			0
$715$	−34.8380			−1.30287
$716$		0			0
$717$	6.50653	−	34.9869i	0.242991	−	1.30661i
$718$		0			0
$719$	−25.0072	−	43.3138i	−0.932612	−	1.61533i	−0.778837	−	0.627226i	$-0.784190\pi$
$719$	−25.0072	−	43.3138i	−0.932612	−	1.61533i	−0.153775	−	0.988106i	$-0.549143\pi$
$720$		0			0
$721$	12.4070	−	15.5108i	0.462059	−	0.577651i
$722$		0			0
$723$	16.2353	+	13.8834i	0.603797	+	0.516329i
$724$		0			0
$725$	−11.3925	+	19.7324i	−0.423108	+	0.732844i
$726$		0			0
$727$		−	27.7338i		−	1.02859i	−0.857614	−	0.514295i	$-0.828054\pi$
$727$		−	27.7338i		−	1.02859i	0.857614	−	0.514295i	$-0.171946\pi$
$728$		0			0
$729$	−12.1695	−	24.1019i	−0.450723	−	0.892664i
$730$		0			0
$731$	−0.695503	−	0.401549i	−0.0257241	−	0.0148518i
$732$		0			0
$733$	−24.4018	+	14.0884i	−0.901300	+	0.520366i	−0.877622	−	0.479354i	$-0.840871\pi$
$733$	−24.4018	+	14.0884i	−0.901300	+	0.520366i	−0.0236782	+	0.999720i	$0.507538\pi$
$734$		0			0
$735$	21.0780	−	39.8984i	0.777475	−	1.47168i
$736$		0			0
$737$	22.6384	−	13.0703i	0.833897	−	0.481450i
$738$		0			0
$739$	−15.9133	+	27.5626i	−0.585379	+	1.01391i	0.409449	+	0.912333i	$0.365721\pi$
$739$	−15.9133	+	27.5626i	−0.585379	+	1.01391i	−0.994828	+	0.101573i	$0.967612\pi$
$740$		0			0
$741$	4.70459	+	13.3112i	0.172827	+	0.488998i
$742$		0			0
$743$	−30.9943			−1.13707			−0.568535	−	0.822659i	$-0.692490\pi$
$743$	−30.9943			−1.13707			−0.568535	+	0.822659i	$0.692490\pi$
$744$		0			0
$745$	27.4934	−	47.6200i	1.00728	−	1.74466i
$746$		0			0
$747$	1.87595	−	4.86924i	0.0686375	−	0.178156i
$748$		0			0
$749$	20.8762	−	26.0988i	0.762800	−	0.953628i
$750$		0			0
$751$	−32.0364	+	18.4962i	−1.16902	+	0.674936i	−0.953450	−	0.301551i	$-0.902496\pi$
$751$	−32.0364	+	18.4962i	−1.16902	+	0.674936i	−0.215574	+	0.976488i	$0.569162\pi$
$752$		0			0
$753$	−36.2670	−	6.74460i	−1.32164	−	0.245787i
$754$		0			0
$755$		−	13.6974i		−	0.498501i
$756$		0			0
$757$		−	2.01191i		−	0.0731242i	−0.999331	−	0.0365621i	$-0.988359\pi$
$757$		−	2.01191i		−	0.0731242i	0.999331	−	0.0365621i	$-0.0116407\pi$
$758$		0			0
$759$	20.8483	+	3.87716i	0.756744	+	0.140732i
$760$		0			0
$761$	−35.5006	+	20.4963i	−1.28689	+	0.742989i	−0.978099	−	0.208140i	$-0.933259\pi$
$761$	−35.5006	+	20.4963i	−1.28689	+	0.742989i	−0.308795	+	0.951129i	$0.599926\pi$
$762$		0			0
$763$	33.9098	+	5.16233i	1.22762	+	0.186889i
$764$		0			0
$765$	0.862994	−	2.24000i	0.0312016	−	0.0809873i
$766$		0			0
$767$	−14.0064	+	24.2598i	−0.505741	+	0.875970i
$768$		0			0
$769$	−46.8470			−1.68935			−0.844673	−	0.535282i	$-0.820205\pi$
$769$	−46.8470			−1.68935			−0.844673	+	0.535282i	$0.820205\pi$
$770$		0			0
$771$	8.81723	+	24.9475i	0.317545	+	0.898461i
$772$		0			0
$773$	−11.2358	+	19.4611i	−0.404125	+	0.699966i	−0.994219	−	0.107369i	$-0.965757\pi$
$773$	−11.2358	+	19.4611i	−0.404125	+	0.699966i	0.590094	+	0.807335i	$0.299091\pi$
$774$		0			0
$775$	37.7247	−	21.7803i	1.35511	−	0.782373i
$776$		0			0
$777$	25.2830	+	29.2814i	0.907024	+	1.05047i
$778$		0			0
$779$	−1.79734	+	1.03770i	−0.0643965	+	0.0371794i
$780$		0			0
$781$	−22.8791	−	13.2093i	−0.818679	−	0.472664i
$782$		0			0
$783$	−7.00965	+	11.3918i	−0.250505	+	0.407111i
$784$		0			0
$785$			79.9291i			2.85279i
$786$		0			0
$787$	−11.3998	+	19.7450i	−0.406358	+	0.703833i	−0.994479	−	0.104940i	$-0.966535\pi$
$787$	−11.3998	+	19.7450i	−0.406358	+	0.703833i	0.588120	+	0.808773i	$0.299868\pi$
$788$		0			0
$789$	0.657979	+	0.562662i	0.0234247	+	0.0200313i
$790$		0			0
$791$	6.84182	+	17.5087i	0.243267	+	0.622538i
$792$		0			0
$793$	−0.621340	−	1.07619i	−0.0220644	−	0.0382167i
$794$		0			0
$795$	−2.50269	+	13.4574i	−0.0887612	+	0.477286i
$796$		0			0
$797$	21.8746			0.774837			0.387419	−	0.921904i	$-0.373367\pi$
$797$	21.8746			0.774837			0.387419	+	0.921904i	$0.373367\pi$
$798$		0			0
$799$			0.252288i			0.00892532i
$800$		0			0
$801$	−52.9380	+	8.31831i	−1.87047	+	0.293913i
$802$		0			0
$803$	20.2071	−	11.6666i	0.713094	−	0.411705i
$804$		0			0
$805$	6.92340	−	45.4778i	0.244018	−	1.60288i
$806$		0			0
$807$	−28.7516	−	24.5865i	−1.01210	−	0.865487i
$808$		0			0
$809$	24.0416	+	13.8804i	0.845258	+	0.488010i	0.859048	−	0.511895i	$-0.171056\pi$
$809$	24.0416	+	13.8804i	0.845258	+	0.488010i	−0.0137900	+	0.999905i	$0.504390\pi$
$810$		0			0
$811$	−6.49133			−0.227942			−0.113971	−	0.993484i	$-0.536357\pi$
$811$	−6.49133			−0.227942			−0.113971	+	0.993484i	$0.536357\pi$
$812$		0			0
$813$	−9.08442	−	25.7035i	−0.318605	−	0.901461i
$814$		0			0
$815$	−2.81474	+	4.87528i	−0.0985962	+	0.170774i
$816$		0			0
$817$	−4.26220	−	7.38234i	−0.149115	−	0.258275i
$818$		0			0
$819$	0.135554	+	28.3501i	0.00473664	+	0.990634i
$820$		0			0
$821$	12.8884	+	22.3234i	0.449810	+	0.779094i	0.998373	−	0.0570153i	$-0.0181584\pi$
$821$	12.8884	+	22.3234i	0.449810	+	0.779094i	−0.548563	+	0.836109i	$0.684825\pi$
$822$		0			0
$823$	18.5654	+	10.7188i	0.647151	+	0.373633i	0.787364	−	0.616489i	$-0.211445\pi$
$823$	18.5654	+	10.7188i	0.647151	+	0.373633i	−0.140213	+	0.990121i	$0.544779\pi$
$824$		0			0
$825$	13.3887	+	37.8819i	0.466133	+	1.31888i
$826$		0			0
$827$		−	0.550214i		−	0.0191328i	−0.999954	−	0.00956640i	$-0.996955\pi$
$827$		−	0.550214i		−	0.0191328i	0.999954	−	0.00956640i	$-0.00304513\pi$
$828$		0			0
$829$	40.9798	+	23.6597i	1.42329	+	0.821735i	0.996578	−	0.0826545i	$-0.0263398\pi$
$829$	40.9798	+	23.6597i	1.42329	+	0.821735i	0.426708	+	0.904389i	$0.359673\pi$
$830$		0			0
$831$	−14.1254	+	16.5183i	−0.490005	+	0.573014i
$832$		0			0
$833$	1.46822	−	0.330551i	0.0508709	−	0.0114529i
$834$		0			0
$835$	−13.4297	−	23.2610i	−0.464755	−	0.804979i
$836$		0			0
$837$	22.4952	−	12.1606i	0.777549	−	0.420332i
$838$		0			0
$839$	13.0088			0.449114			0.224557	−	0.974461i	$-0.427906\pi$
$839$	13.0088			0.449114			0.224557	+	0.974461i	$0.427906\pi$
$840$		0			0
$841$	−22.3737			−0.771508
$842$		0			0
$843$	−38.7419	−	7.20486i	−1.33434	−	0.248149i
$844$		0			0
$845$	0.450499	+	0.780288i	0.0154977	+	0.0268427i
$846$		0			0
$847$	8.53711	+	6.82878i	0.293339	+	0.234640i
$848$		0			0
$849$	1.15941	+	0.991453i	0.0397908	+	0.0340266i
$850$		0			0
$851$	34.1552	+	19.7195i	1.17082	+	0.675975i
$852$		0			0
$853$		−	30.6386i		−	1.04904i	−0.851397	−	0.524522i	$-0.824244\pi$
$853$		−	30.6386i		−	1.04904i	0.851397	−	0.524522i	$-0.175756\pi$
$854$		0			0
$855$	19.8210	−	16.0107i	0.677865	−	0.547555i
$856$		0			0
$857$	−37.8255	−	21.8385i	−1.29209	−	0.745991i	−0.313069	−	0.949731i	$-0.601357\pi$
$857$	−37.8255	−	21.8385i	−1.29209	−	0.745991i	−0.979025	+	0.203740i	$0.934690\pi$
$858$		0			0
$859$	10.5500	+	18.2731i	0.359961	+	0.623471i	0.987954	−	0.154748i	$-0.0494567\pi$
$859$	10.5500	+	18.2731i	0.359961	+	0.623471i	−0.627993	+	0.778219i	$0.716123\pi$
$860$		0			0
$861$	−4.09365	+	0.781567i	−0.139511	+	0.0266357i
$862$		0			0
$863$	−23.7379	−	41.1152i	−0.808047	−	1.39958i	−0.914215	−	0.405230i	$-0.867191\pi$
$863$	−23.7379	−	41.1152i	−0.808047	−	1.39958i	0.106168	−	0.994348i	$-0.466142\pi$
$864$		0			0
$865$	−4.97582	+	8.61838i	−0.169183	+	0.293034i
$866$		0			0
$867$	−27.6865	+	9.78527i	−0.940282	+	0.332325i
$868$		0			0
$869$	29.3820			0.996716
$870$		0			0
$871$	30.8547	+	17.8140i	1.04547	+	0.603603i
$872$		0			0
$873$	24.8744	+	9.58325i	0.841870	+	0.324344i
$874$		0			0
$875$	35.3237	−	13.8033i	1.19416	−	0.466638i
$876$		0			0
$877$	−33.6478	+	19.4266i	−1.13621	+	0.655989i	−0.945488	−	0.325656i	$-0.894415\pi$
$877$	−33.6478	+	19.4266i	−1.13621	+	0.655989i	−0.190718	+	0.981645i	$0.561082\pi$
$878$		0			0
$879$	7.00752	−	37.6808i	0.236358	−	1.27094i
$880$		0			0
$881$		−	45.6144i		−	1.53679i	−0.639978	−	0.768393i	$-0.721056\pi$
$881$		−	45.6144i		−	1.53679i	0.639978	−	0.768393i	$-0.278944\pi$
$882$		0			0
$883$	−56.6501			−1.90643			−0.953214	−	0.302295i	$-0.902247\pi$
$883$	−56.6501			−1.90643			−0.953214	+	0.302295i	$0.902247\pi$
$884$		0			0
$885$	49.7041	+	9.24350i	1.67078	+	0.310717i
$886$		0			0
$887$	3.46905	+	6.00857i	0.116479	+	0.201748i	0.918370	−	0.395723i	$-0.129506\pi$
$887$	3.46905	+	6.00857i	0.116479	+	0.201748i	−0.801891	+	0.597471i	$0.796172\pi$
$888$		0			0
$889$	2.43719	+	6.23694i	0.0817407	+	0.209180i
$890$		0			0
$891$	7.23372	+	22.4495i	0.242339	+	0.752087i
$892$		0			0
$893$	−1.33894	+	2.31912i	−0.0448060	+	0.0776064i
$894$		0			0
$895$			31.3438i			1.04771i
$896$		0			0
$897$	9.63105	+	27.2501i	0.321571	+	0.909854i
$898$		0			0
$899$	−10.9709	−	6.33407i	−0.365901	−	0.211253i
$900$		0			0
$901$	−0.395365	+	0.228264i	−0.0131715	+	0.00760457i
$902$		0			0
$903$	−3.21018	−	16.8141i	−0.106828	−	0.559538i
$904$		0			0
$905$	19.7347	−	11.3939i	0.656005	−	0.378745i
$906$		0			0
$907$	23.0866	−	39.9871i	0.766577	−	1.32775i	−0.172832	−	0.984951i	$-0.555292\pi$
$907$	23.0866	−	39.9871i	0.766577	−	1.32775i	0.939409	−	0.342799i	$-0.111375\pi$
$908$		0			0
$909$	34.4797	−	27.8515i	1.14362	−	0.923774i
$910$		0			0
$911$	33.7577			1.11844			0.559221	−	0.829018i	$-0.311100\pi$
$911$	33.7577			1.11844			0.559221	+	0.829018i	$0.311100\pi$
$912$		0			0
$913$	−2.27917	+	3.94764i	−0.0754295	+	0.130648i
$914$		0			0
$915$	−1.45758	+	1.70450i	−0.0481862	+	0.0563491i
$916$		0			0
$917$	−9.63366	+	12.0437i	−0.318131	+	0.397717i
$918$		0			0
$919$	−1.09773	+	0.633774i	−0.0362107	+	0.0209063i	−0.517996	−	0.855383i	$-0.673322\pi$
$919$	−1.09773	+	0.633774i	−0.0362107	+	0.0209063i	0.481785	+	0.876289i	$0.339988\pi$
$920$		0			0
$921$	−3.15653	+	16.9733i	−0.104011	+	0.559289i
$922$		0			0
$923$		−	36.0067i		−	1.18517i
$924$		0			0
$925$			74.7247i			2.45693i
$926$		0			0
$927$	22.2489	−	3.49603i	0.730750	−	0.114825i
$928$		0			0
$929$	28.9002	−	16.6855i	0.948183	−	0.547434i	0.0556673	−	0.998449i	$-0.482271\pi$
$929$	28.9002	−	16.6855i	0.948183	−	0.547434i	0.892516	+	0.451015i	$0.148938\pi$
$930$		0			0
$931$	15.2507	+	4.75361i	0.499821	+	0.155793i
$932$		0			0
$933$	15.4592	+	13.2197i	0.506111	+	0.432794i
$934$		0			0
$935$	−1.04849	+	1.81603i	−0.0342892	+	0.0593906i
$936$		0			0
$937$	−9.31498			−0.304307			−0.152154	−	0.988357i	$-0.548621\pi$
$937$	−9.31498			−0.304307			−0.152154	+	0.988357i	$0.548621\pi$
$938$		0			0
$939$	−1.12197	+	0.396541i	−0.0366142	+	0.0129406i
$940$		0			0
$941$	−20.0007	+	34.6422i	−0.652003	+	1.12930i	0.330633	+	0.943759i	$0.392738\pi$
$941$	−20.0007	+	34.6422i	−0.652003	+	1.12930i	−0.982636	+	0.185543i	$0.940596\pi$
$942$		0			0
$943$	−3.67945	+	2.12433i	−0.119819	+	0.0691778i
$944$		0			0
$945$	48.1593	−	17.2805i	1.56662	−	0.562134i
$946$		0			0
$947$	−28.9295	+	16.7025i	−0.940083	+	0.542757i	−0.889986	−	0.455987i	$-0.849286\pi$
$947$	−28.9295	+	16.7025i	−0.940083	+	0.542757i	−0.0500965	+	0.998744i	$0.515953\pi$
$948$		0			0
$949$	27.5410	+	15.9008i	0.894018	+	0.516161i
$950$		0			0
$951$	53.7389	−	18.9930i	1.74260	−	0.615891i
$952$		0			0
$953$			35.4084i			1.14699i	0.819209	+	0.573495i	$0.194413\pi$
$953$			35.4084i			1.14699i	−0.819209	+	0.573495i	$0.805587\pi$
$954$		0			0
$955$	28.1543	−	48.7646i	0.911051	−	1.57799i
$956$		0			0
$957$	7.59389	−	8.88032i	0.245476	−	0.287060i
$958$		0			0
$959$	24.6198	+	3.74805i	0.795016	+	0.121031i
$960$		0			0
$961$	−3.39046	−	5.87244i	−0.109370	−	0.189434i
$962$		0			0
$963$	37.4365	−	5.88250i	1.20637	−	0.189561i
$964$		0			0
$965$	−11.3857			−0.366519
$966$		0			0
$967$		−	59.2726i		−	1.90608i	−0.302849	−	0.953039i	$-0.597938\pi$
$967$		−	59.2726i		−	1.90608i	0.302849	−	0.953039i	$-0.402062\pi$
$968$		0			0
$969$	0.835475	+	0.155374i	0.0268393	+	0.00499133i
$970$		0			0
$971$	−49.2281	+	28.4218i	−1.57980	+	0.912101i	−0.584919	+	0.811092i	$0.698874\pi$
$971$	−49.2281	+	28.4218i	−1.57980	+	0.912101i	−0.994886	+	0.101009i	$0.967793\pi$
$972$		0			0
$973$	−18.5790	+	7.26005i	−0.595614	+	0.232746i
$974$		0			0
$975$	−35.5894	+	41.6184i	−1.13977	+	1.33285i
$976$		0			0
$977$	−31.5116	−	18.1932i	−1.00814	−	0.582052i	−0.0974966	−	0.995236i	$-0.531084\pi$
$977$	−31.5116	−	18.1932i	−1.00814	−	0.582052i	−0.910648	+	0.413183i	$0.864417\pi$
$978$		0			0
$979$	46.8121			1.49612
$980$		0			0
$981$	24.4393	+	30.2555i	0.780287	+	0.965984i
$982$		0			0
$983$	−7.30275	+	12.6487i	−0.232921	+	0.403432i	−0.958667	−	0.284532i	$-0.908162\pi$
$983$	−7.30275	+	12.6487i	−0.232921	+	0.403432i	0.725745	+	0.687964i	$0.241495\pi$
$984$		0			0
$985$	−27.1197	−	46.9727i	−0.864105	−	1.49667i
$986$		0			0
$987$	−4.07016	+	3.51437i	−0.129555	+	0.111864i
$988$		0			0
$989$	−8.72540	−	15.1128i	−0.277452	−	0.480560i
$990$		0			0
$991$	−36.4541	−	21.0468i	−1.15800	−	0.668572i	−0.207177	−	0.978303i	$-0.566428\pi$
$991$	−36.4541	−	21.0468i	−1.15800	−	0.668572i	−0.950824	+	0.309731i	$0.899761\pi$
$992$		0			0
$993$	2.72157	−	0.961890i	0.0863665	−	0.0305246i
$994$		0			0
$995$			64.6287i			2.04887i
$996$		0			0
$997$	11.0158	+	6.36000i	0.348875	+	0.201423i	0.664190	−	0.747564i	$-0.268777\pi$
$997$	11.0158	+	6.36000i	0.348875	+	0.201423i	−0.315315	+	0.948987i	$0.602110\pi$
$998$		0			0
$999$	−1.22861	+	43.8490i	−0.0388714	+	1.38732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bd.a.431.16		56
3.2	odd	2	inner	672.2.bd.a.431.21		56
4.3	odd	2		168.2.v.a.11.6	yes	56
7.2	even	3	inner	672.2.bd.a.527.22		56
8.3	odd	2	inner	672.2.bd.a.431.15		56
8.5	even	2		168.2.v.a.11.3	✓	56
12.11	even	2		168.2.v.a.11.23	yes	56
21.2	odd	6	inner	672.2.bd.a.527.15		56
24.5	odd	2		168.2.v.a.11.26	yes	56
24.11	even	2	inner	672.2.bd.a.431.22		56
28.23	odd	6		168.2.v.a.107.26	yes	56
56.37	even	6		168.2.v.a.107.23	yes	56
56.51	odd	6	inner	672.2.bd.a.527.21		56
84.23	even	6		168.2.v.a.107.3	yes	56
168.107	even	6	inner	672.2.bd.a.527.16		56
168.149	odd	6		168.2.v.a.107.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.3	✓	56	8.5	even	2
168.2.v.a.11.6	yes	56	4.3	odd	2
168.2.v.a.11.23	yes	56	12.11	even	2
168.2.v.a.11.26	yes	56	24.5	odd	2
168.2.v.a.107.3	yes	56	84.23	even	6
168.2.v.a.107.6	yes	56	168.149	odd	6
168.2.v.a.107.23	yes	56	56.37	even	6
168.2.v.a.107.26	yes	56	28.23	odd	6
672.2.bd.a.431.15		56	8.3	odd	2	inner
672.2.bd.a.431.16		56	1.1	even	1	trivial
672.2.bd.a.431.21		56	3.2	odd	2	inner
672.2.bd.a.431.22		56	24.11	even	2	inner
672.2.bd.a.527.15		56	21.2	odd	6	inner
672.2.bd.a.527.16		56	168.107	even	6	inner
672.2.bd.a.527.21		56	56.51	odd	6	inner
672.2.bd.a.527.22		56	7.2	even	3	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bd (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.316681 - 1.70285i) q^{3} +(1.86088 + 3.22314i) q^{5} +(-2.46429 + 0.962962i) q^{7} +(-2.79943 - 1.07852i) q^{9} +(2.26958 + 1.31034i) q^{11} +3.57182i q^{13} +(6.07784 - 2.14810i) q^{15} +(0.186192 + 0.107498i) q^{17} +(1.14103 + 1.97631i) q^{19} +(0.859391 + 4.50127i) q^{21} +(2.33586 + 4.04583i) q^{23} +(-4.42574 + 7.66560i) q^{25} +(-2.72309 + 4.42547i) q^{27} +2.57415 q^{29} +(-4.26196 - 2.46064i) q^{31} +(2.95006 - 3.44980i) q^{33} +(-7.68949 - 6.15077i) q^{35} +(7.31104 - 4.22103i) q^{37} +(6.08229 + 1.13113i) q^{39} +0.909442i q^{41} -3.73541 q^{43} +(-1.73317 - 11.0299i) q^{45} +(0.586728 + 1.01624i) q^{47} +(5.14541 - 4.74603i) q^{49} +(0.242017 - 0.283015i) q^{51} +(-1.06171 + 1.83894i) q^{53} +9.75355i q^{55} +(3.72672 - 1.31714i) q^{57} +(6.79199 + 3.92136i) q^{59} +(-0.301301 + 0.173956i) q^{61} +(7.93716 - 0.0379510i) q^{63} +(-11.5125 + 6.64673i) q^{65} +(4.98736 - 8.63836i) q^{67} +(7.62919 - 2.69640i) q^{69} -10.0808 q^{71} +(4.45173 - 7.71062i) q^{73} +(11.6519 + 9.96394i) q^{75} +(-6.85470 - 1.04354i) q^{77} +(9.70950 - 5.60578i) q^{79} +(6.67358 + 6.03849i) q^{81} +1.73937i q^{83} +0.800163i q^{85} +(0.815185 - 4.38341i) q^{87} +(15.4694 - 8.93127i) q^{89} +(-3.43953 - 8.80199i) q^{91} +(-5.53980 + 6.47826i) q^{93} +(-4.24662 + 7.35536i) q^{95} -8.88553 q^{97} +(-4.94029 - 6.11600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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