LMFDB - Embedded newform 672.2.bk.a.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(529,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("672.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bk (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.1
Character	$\chi$	$=$	672.529
Dual form			672.2.bk.a.625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(-3.09843 + 1.78888i) q^{5} +(-0.993295 + 2.45222i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{3} +(-3.09843 + 1.78888i) q^{5} +(-0.993295 + 2.45222i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-0.815768 - 0.470984i) q^{11} -6.15117i q^{13} +3.57776 q^{15} +(1.89187 - 3.27682i) q^{17} +(2.09110 - 1.20730i) q^{19} +(2.08633 - 1.62703i) q^{21} +(1.49371 + 2.58719i) q^{23} +(3.90019 - 6.75532i) q^{25} -1.00000i q^{27} +2.68125i q^{29} +(5.35686 - 9.27835i) q^{31} +(0.470984 + 0.815768i) q^{33} +(-1.30906 - 9.37491i) q^{35} +(1.47851 - 0.853618i) q^{37} +(-3.07558 + 5.32707i) q^{39} -4.56000 q^{41} +3.50672i q^{43} +(-3.09843 - 1.78888i) q^{45} +(-3.42292 - 5.92866i) q^{47} +(-5.02673 - 4.87155i) q^{49} +(-3.27682 + 1.89187i) q^{51} +(-6.57466 - 3.79588i) q^{53} +3.37013 q^{55} -2.41460 q^{57} +(0.100623 + 0.0580947i) q^{59} +(7.06184 - 4.07716i) q^{61} +(-2.62033 + 0.365889i) q^{63} +(11.0037 + 19.0590i) q^{65} +(-3.44314 - 1.98790i) q^{67} -2.98743i q^{69} +3.92572 q^{71} +(-3.11438 + 5.39427i) q^{73} +(-6.75532 + 3.90019i) q^{75} +(1.96525 - 1.53261i) q^{77} +(-2.73628 - 4.73937i) q^{79} +(-0.500000 + 0.866025i) q^{81} -1.19560i q^{83} +13.5373i q^{85} +(1.34063 - 2.32203i) q^{87} +(0.910509 + 1.57705i) q^{89} +(15.0840 + 6.10992i) q^{91} +(-9.27835 + 5.35686i) q^{93} +(-4.31942 + 7.48146i) q^{95} +12.0241 q^{97} -0.941967i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^9	$ 32 q + 16 q^{9} + 8 q^{23} + 16 q^{25} + 24 q^{31} + 24 q^{47} + 8 q^{49} + 64 q^{55} - 16 q^{57} + 80 q^{71} + 8 q^{73} - 8 q^{79} - 16 q^{81} - 24 q^{87} - 24 q^{95} - 48 q^{97}+O(q^{100}) $ 32 * q + 16 * q^9 + 8 * q^23 + 16 * q^25 + 24 * q^31 + 24 * q^47 + 8 * q^49 + 64 * q^55 - 16 * q^57 + 80 * q^71 + 8 * q^73 - 8 * q^79 - 16 * q^81 - 24 * q^87 - 24 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$	−3.09843	+	1.78888i	−1.38566	+	0.800012i	−0.992823	−	0.119596i	$-0.961840\pi$
$5$	−3.09843	+	1.78888i	−1.38566	+	0.800012i	−0.392838	+	0.919608i	$0.628507\pi$
$6$		0			0
$7$	−0.993295	+	2.45222i	−0.375430	+	0.926851i
$7$	−0.993295	+	2.45222i	−0.375430	+	0.926851i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−0.815768	−	0.470984i	−0.245963	−	0.142007i	0.371951	−	0.928252i	$-0.378689\pi$
$11$	−0.815768	−	0.470984i	−0.245963	−	0.142007i	−0.617914	+	0.786245i	$0.712022\pi$
$12$		0			0
$13$		−	6.15117i		−	1.70603i	−0.521889	−	0.853013i	$-0.674772\pi$
$13$		−	6.15117i		−	1.70603i	0.521889	−	0.853013i	$-0.325228\pi$
$14$		0			0
$15$	3.57776			0.923774
$16$		0			0
$17$	1.89187	−	3.27682i	0.458847	−	0.794746i	−0.540053	−	0.841631i	$-0.681596\pi$
$17$	1.89187	−	3.27682i	0.458847	−	0.794746i	0.998900	+	0.0468845i	$0.0149293\pi$
$18$		0			0
$19$	2.09110	−	1.20730i	0.479731	−	0.276973i	−0.240573	−	0.970631i	$-0.577335\pi$
$19$	2.09110	−	1.20730i	0.479731	−	0.276973i	0.720305	+	0.693658i	$0.244002\pi$
$20$		0			0
$21$	2.08633	−	1.62703i	0.455274	−	0.355048i
$22$		0			0
$23$	1.49371	+	2.58719i	0.311461	+	0.539466i	0.978679	−	0.205396i	$-0.0658483\pi$
$23$	1.49371	+	2.58719i	0.311461	+	0.539466i	−0.667218	+	0.744863i	$0.732515\pi$
$24$		0			0
$25$	3.90019	−	6.75532i	0.780037	−	1.35106i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			2.68125i			0.497897i	0.968517	+	0.248948i	$0.0800849\pi$
$29$			2.68125i			0.497897i	−0.968517	+	0.248948i	$0.919915\pi$
$30$		0			0
$31$	5.35686	−	9.27835i	0.962120	−	1.66644i	0.244960	−	0.969533i	$-0.421225\pi$
$31$	5.35686	−	9.27835i	0.962120	−	1.66644i	0.717160	−	0.696908i	$-0.245441\pi$
$32$		0			0
$33$	0.470984	+	0.815768i	0.0819877	+	0.142007i
$34$		0			0
$35$	−1.30906	−	9.37491i	−0.221272	−	1.58465i
$36$		0			0
$37$	1.47851	−	0.853618i	0.243065	−	0.140334i	−0.373519	−	0.927622i	$-0.621849\pi$
$37$	1.47851	−	0.853618i	0.243065	−	0.140334i	0.616585	+	0.787288i	$0.288516\pi$
$38$		0			0
$39$	−3.07558	+	5.32707i	−0.492488	+	0.853013i
$40$		0			0
$41$	−4.56000			−0.712152			−0.356076	−	0.934457i	$-0.615886\pi$
$41$	−4.56000			−0.712152			−0.356076	+	0.934457i	$0.615886\pi$
$42$		0			0
$43$			3.50672i			0.534770i	0.963590	+	0.267385i	$0.0861596\pi$
$43$			3.50672i			0.534770i	−0.963590	+	0.267385i	$0.913840\pi$
$44$		0			0
$45$	−3.09843	−	1.78888i	−0.461887	−	0.266671i
$46$		0			0
$47$	−3.42292	−	5.92866i	−0.499284	−	0.864785i	0.500716	−	0.865612i	$-0.333070\pi$
$47$	−3.42292	−	5.92866i	−0.499284	−	0.864785i	−1.00000		0.000827022i	$0.999737\pi$
$48$		0			0
$49$	−5.02673	−	4.87155i	−0.718104	−	0.695936i
$50$		0			0
$51$	−3.27682	+	1.89187i	−0.458847	+	0.264915i
$52$		0			0
$53$	−6.57466	−	3.79588i	−0.903099	−	0.521404i	−0.0248947	−	0.999690i	$-0.507925\pi$
$53$	−6.57466	−	3.79588i	−0.903099	−	0.521404i	−0.878204	+	0.478286i	$0.841258\pi$
$54$		0			0
$55$	3.37013			0.454429
$56$		0			0
$57$	−2.41460			−0.319821
$58$		0			0
$59$	0.100623	+	0.0580947i	0.0131000	+	0.00756328i	0.506536	−	0.862219i	$-0.330926\pi$
$59$	0.100623	+	0.0580947i	0.0131000	+	0.00756328i	−0.493436	+	0.869782i	$0.664259\pi$
$60$		0			0
$61$	7.06184	−	4.07716i	0.904176	−	0.522027i	0.0256236	−	0.999672i	$-0.491843\pi$
$61$	7.06184	−	4.07716i	0.904176	−	0.522027i	0.878553	+	0.477645i	$0.158510\pi$
$62$		0			0
$63$	−2.62033	+	0.365889i	−0.330130	+	0.0460977i
$64$		0			0
$65$	11.0037	+	19.0590i	1.36484	+	2.36397i
$66$		0			0
$67$	−3.44314	−	1.98790i	−0.420647	−	0.242861i	0.274707	−	0.961528i	$-0.411419\pi$
$67$	−3.44314	−	1.98790i	−0.420647	−	0.242861i	−0.695354	+	0.718667i	$0.744752\pi$
$68$		0			0
$69$		−	2.98743i		−	0.359644i
$70$		0			0
$71$	3.92572			0.465897			0.232949	−	0.972489i	$-0.425163\pi$
$71$	3.92572			0.465897			0.232949	+	0.972489i	$0.425163\pi$
$72$		0			0
$73$	−3.11438	+	5.39427i	−0.364511	+	0.631351i	−0.988698	−	0.149924i	$-0.952097\pi$
$73$	−3.11438	+	5.39427i	−0.364511	+	0.631351i	0.624187	+	0.781275i	$0.285430\pi$
$74$		0			0
$75$	−6.75532	+	3.90019i	−0.780037	+	0.450355i
$76$		0			0
$77$	1.96525	−	1.53261i	0.223961	−	0.174657i
$78$		0			0
$79$	−2.73628	−	4.73937i	−0.307855	−	0.533221i	0.670038	−	0.742327i	$-0.266278\pi$
$79$	−2.73628	−	4.73937i	−0.307855	−	0.533221i	−0.977893	+	0.209106i	$0.932945\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	1.19560i		−	0.131234i	−0.997845	−	0.0656172i	$-0.979098\pi$
$83$		−	1.19560i		−	0.131234i	0.997845	−	0.0656172i	$-0.0209016\pi$
$84$		0			0
$85$			13.5373i			1.46833i
$86$		0			0
$87$	1.34063	−	2.32203i	0.143730	−	0.248948i
$88$		0			0
$89$	0.910509	+	1.57705i	0.0965138	+	0.167167i	0.910239	−	0.414082i	$-0.135897\pi$
$89$	0.910509	+	1.57705i	0.0965138	+	0.167167i	−0.813726	+	0.581249i	$0.802564\pi$
$90$		0			0
$91$	15.0840	+	6.10992i	1.58123	+	0.640494i
$92$		0			0
$93$	−9.27835	+	5.35686i	−0.962120	+	0.555480i
$94$		0			0
$95$	−4.31942	+	7.48146i	−0.443163	+	0.767581i
$96$		0			0
$97$	12.0241			1.22086			0.610431	−	0.792069i	$-0.290996\pi$
$97$	12.0241			1.22086			0.610431	+	0.792069i	$0.290996\pi$
$98$		0			0
$99$		−	0.941967i		−	0.0946713i
$100$		0			0
$101$	−1.54240	−	0.890504i	−0.153474	−	0.0886085i	0.421296	−	0.906923i	$-0.361575\pi$
$101$	−1.54240	−	0.890504i	−0.153474	−	0.0886085i	−0.574770	+	0.818315i	$0.694909\pi$
$102$		0			0
$103$	−6.21150	−	10.7586i	−0.612037	−	1.06008i	−0.990897	−	0.134625i	$-0.957017\pi$
$103$	−6.21150	−	10.7586i	−0.612037	−	1.06008i	0.378859	−	0.925454i	$-0.376316\pi$
$104$		0			0
$105$	−3.55377	+	8.77344i	−0.346813	+	0.856200i
$106$		0			0
$107$	8.41266	−	4.85705i	0.813283	−	0.469549i	−0.0348118	−	0.999394i	$-0.511083\pi$
$107$	8.41266	−	4.85705i	0.813283	−	0.469549i	0.848095	+	0.529845i	$0.177750\pi$
$108$		0			0
$109$	12.3647	+	7.13874i	1.18432	+	0.683767i	0.957010	−	0.290055i	$-0.0936738\pi$
$109$	12.3647	+	7.13874i	1.18432	+	0.683767i	0.227309	+	0.973823i	$0.427007\pi$
$110$		0			0
$111$	−1.70724			−0.162044
$112$		0			0
$113$	−13.8775			−1.30549			−0.652743	−	0.757580i	$-0.726382\pi$
$113$	−13.8775			−1.30549			−0.652743	+	0.757580i	$0.726382\pi$
$114$		0			0
$115$	−9.25634	−	5.34415i	−0.863159	−	0.498345i
$116$		0			0
$117$	5.32707	−	3.07558i	0.492488	−	0.284338i
$118$		0			0
$119$	6.15629	+	7.89414i	0.564346	+	0.723654i
$120$		0			0
$121$	−5.05635	−	8.75785i	−0.459668	−	0.796168i
$122$		0			0
$123$	3.94907	+	2.28000i	0.356076	+	0.205581i
$124$		0			0
$125$			10.0191i			0.896131i
$126$		0			0
$127$	−7.77389			−0.689822			−0.344911	−	0.938635i	$-0.612091\pi$
$127$	−7.77389			−0.689822			−0.344911	+	0.938635i	$0.612091\pi$
$128$		0			0
$129$	1.75336	−	3.03691i	0.154375	−	0.267385i
$130$		0			0
$131$	−6.10134	+	3.52261i	−0.533076	+	0.307772i	−0.742268	−	0.670103i	$-0.766250\pi$
$131$	−6.10134	+	3.52261i	−0.533076	+	0.307772i	0.209192	+	0.977875i	$0.432917\pi$
$132$		0			0
$133$	0.883475	+	6.32703i	0.0766070	+	0.548623i
$134$		0			0
$135$	1.78888	+	3.09843i	0.153962	+	0.266671i
$136$		0			0
$137$	9.05379	−	15.6816i	0.773518	−	1.33977i	−0.162106	−	0.986773i	$-0.551829\pi$
$137$	9.05379	−	15.6816i	0.773518	−	1.33977i	0.935624	−	0.352999i	$-0.114838\pi$
$138$		0			0
$139$			8.32721i			0.706305i	0.935566	+	0.353152i	$0.114890\pi$
$139$			8.32721i			0.706305i	−0.935566	+	0.353152i	$0.885110\pi$
$140$		0			0
$141$			6.84583i			0.576523i
$142$		0			0
$143$	−2.89710	+	5.01792i	−0.242268	+	0.419620i
$144$		0			0
$145$	−4.79644	−	8.30768i	−0.398323	−	0.689916i
$146$		0			0
$147$	1.91750	+	6.73225i	0.158153	+	0.555267i
$148$		0			0
$149$	17.9316	−	10.3528i	1.46901	−	0.848134i	0.469614	−	0.882872i	$-0.344393\pi$
$149$	17.9316	−	10.3528i	1.46901	−	0.848134i	0.999396	+	0.0347378i	$0.0110596\pi$
$150$		0			0
$151$	1.97783	−	3.42570i	0.160954	−	0.278780i	−0.774257	−	0.632871i	$-0.781876\pi$
$151$	1.97783	−	3.42570i	0.160954	−	0.278780i	0.935211	+	0.354091i	$0.115210\pi$
$152$		0			0
$153$	3.78375			0.305898
$154$		0			0
$155$			38.3311i			3.07883i
$156$		0			0
$157$	−10.2803	−	5.93532i	−0.820456	−	0.473690i	0.0301179	−	0.999546i	$-0.490412\pi$
$157$	−10.2803	−	5.93532i	−0.820456	−	0.473690i	−0.850574	+	0.525856i	$0.823745\pi$
$158$		0			0
$159$	3.79588	+	6.57466i	0.301033	+	0.521404i
$160$		0			0
$161$	−7.82805	+	1.09307i	−0.616937	+	0.0861459i
$162$		0			0
$163$	14.7683	−	8.52649i	1.15674	−	0.667846i	0.206222	−	0.978505i	$-0.433883\pi$
$163$	14.7683	−	8.52649i	1.15674	−	0.667846i	0.950522	+	0.310659i	$0.100550\pi$
$164$		0			0
$165$	−2.91862	−	1.68507i	−0.227214	−	0.131182i
$166$		0			0
$167$	−10.4339			−0.807396			−0.403698	−	0.914892i	$-0.632275\pi$
$167$	−10.4339			−0.807396			−0.403698	+	0.914892i	$0.632275\pi$
$168$		0			0
$169$	−24.8369			−1.91053
$170$		0			0
$171$	2.09110	+	1.20730i	0.159910	+	0.0923244i
$172$		0			0
$173$	−12.6216	+	7.28708i	−0.959602	+	0.554027i	−0.896051	−	0.443952i	$-0.853576\pi$
$173$	−12.6216	+	7.28708i	−0.959602	+	0.554027i	−0.0635517	+	0.997979i	$0.520243\pi$
$174$		0			0
$175$	12.6915	+	16.2741i	0.959385	+	1.23021i
$176$		0			0
$177$	−0.0580947	−	0.100623i	−0.00436666	−	0.00756328i
$178$		0			0
$179$	3.27323	+	1.88980i	0.244653	+	0.141251i	0.617313	−	0.786717i	$-0.288221\pi$
$179$	3.27323	+	1.88980i	0.244653	+	0.141251i	−0.372660	+	0.927968i	$0.621554\pi$
$180$		0			0
$181$			1.12363i			0.0835189i	0.999128	+	0.0417595i	$0.0132963\pi$
$181$			1.12363i			0.0835189i	−0.999128	+	0.0417595i	$0.986704\pi$
$182$		0			0
$183$	−8.15432			−0.602784
$184$		0			0
$185$	−3.05404	+	5.28975i	−0.224537	+	0.388910i
$186$		0			0
$187$	−3.08666	+	1.78208i	−0.225719	+	0.130319i
$188$		0			0
$189$	2.45222	+	0.993295i	0.178372	+	0.0722516i
$190$		0			0
$191$	7.01502	+	12.1504i	0.507589	+	0.879169i	0.999961	+	0.00878494i	$0.00279637\pi$
$191$	7.01502	+	12.1504i	0.507589	+	0.879169i	−0.492373	+	0.870384i	$0.663870\pi$
$192$		0			0
$193$	−0.390098	+	0.675669i	−0.0280798	+	0.0486357i	−0.879724	−	0.475485i	$-0.842273\pi$
$193$	−0.390098	+	0.675669i	−0.0280798	+	0.0486357i	0.851644	+	0.524121i	$0.175606\pi$
$194$		0			0
$195$		−	22.0074i		−	1.57598i
$196$		0			0
$197$			2.37637i			0.169309i	0.996410	+	0.0846545i	$0.0269787\pi$
$197$			2.37637i			0.169309i	−0.996410	+	0.0846545i	$0.973021\pi$
$198$		0			0
$199$	−6.79196	+	11.7640i	−0.481469	+	0.833929i	−0.999774	−	0.0212671i	$-0.993230\pi$
$199$	−6.79196	+	11.7640i	−0.481469	+	0.833929i	0.518305	+	0.855196i	$0.326563\pi$
$200$		0			0
$201$	1.98790	+	3.44314i	0.140216	+	0.242861i
$202$		0			0
$203$	−6.57502	−	2.66328i	−0.461476	−	0.186925i
$204$		0			0
$205$	14.1288	−	8.15729i	0.986801	−	0.569730i
$206$		0			0
$207$	−1.49371	+	2.58719i	−0.103820	+	0.179822i
$208$		0			0
$209$	−2.27447			−0.157328
$210$		0			0
$211$		−	14.1932i		−	0.977103i	−0.872535	−	0.488551i	$-0.837526\pi$
$211$		−	14.1932i		−	0.977103i	0.872535	−	0.488551i	$-0.162474\pi$
$212$		0			0
$213$	−3.39977	−	1.96286i	−0.232949	−	0.134493i
$214$		0			0
$215$	−6.27311	−	10.8653i	−0.427823	−	0.741010i
$216$		0			0
$217$	17.4316	+	22.3523i	1.18333	+	1.51737i
$218$		0			0
$219$	5.39427	−	3.11438i	0.364511	−	0.210450i
$220$		0			0
$221$	−20.1563	−	11.6372i	−1.35586	−	0.782805i
$222$		0			0
$223$	0.198178			0.0132710			0.00663548	−	0.999978i	$-0.497888\pi$
$223$	0.198178			0.0132710			0.00663548	+	0.999978i	$0.497888\pi$
$224$		0			0
$225$	7.80037			0.520025
$226$		0			0
$227$	−22.3054	−	12.8780i	−1.48046	−	0.854744i	−0.480705	−	0.876882i	$-0.659619\pi$
$227$	−22.3054	−	12.8780i	−1.48046	−	0.854744i	−0.999755	+	0.0221381i	$0.992953\pi$
$228$		0			0
$229$	−13.9965	+	8.08087i	−0.924913	+	0.533999i	−0.885199	−	0.465212i	$-0.845978\pi$
$229$	−13.9965	+	8.08087i	−0.924913	+	0.533999i	−0.0397138	+	0.999211i	$0.512645\pi$
$230$		0			0
$231$	−2.46826	+	0.344656i	−0.162400	+	0.0226767i
$232$		0			0
$233$	−12.5619	−	21.7579i	−0.822959	−	1.42541i	−0.903469	−	0.428654i	$-0.858988\pi$
$233$	−12.5619	−	21.7579i	−0.822959	−	1.42541i	0.0805094	−	0.996754i	$-0.474345\pi$
$234$		0			0
$235$	21.2113	+	12.2464i	1.38368	+	0.798865i
$236$		0			0
$237$			5.47255i			0.355480i
$238$		0			0
$239$	−16.0389			−1.03747			−0.518736	−	0.854935i	$-0.673597\pi$
$239$	−16.0389			−1.03747			−0.518736	+	0.854935i	$0.673597\pi$
$240$		0			0
$241$	6.58453	−	11.4047i	0.424147	−	0.734643i	−0.572194	−	0.820119i	$-0.693907\pi$
$241$	6.58453	−	11.4047i	0.424147	−	0.734643i	0.996340	+	0.0854750i	$0.0272408\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$	24.2896	+	6.10194i	1.55181	+	0.389839i
$246$		0			0
$247$	−7.42629	−	12.8627i	−0.472523	−	0.818435i
$248$		0			0
$249$	−0.597802	+	1.03542i	−0.0378841	+	0.0656172i
$250$		0			0
$251$			8.64704i			0.545796i	0.962043	+	0.272898i	$0.0879822\pi$
$251$			8.64704i			0.545796i	−0.962043	+	0.272898i	$0.912018\pi$
$252$		0			0
$253$		−	2.81406i		−	0.176918i
$254$		0			0
$255$	6.76867	−	11.7237i	0.423871	−	0.734166i
$256$		0			0
$257$	7.23254	+	12.5271i	0.451154	+	0.781421i	0.998458	−	0.0555126i	$-0.0176793\pi$
$257$	7.23254	+	12.5271i	0.451154	+	0.781421i	−0.547304	+	0.836934i	$0.684346\pi$
$258$		0			0
$259$	0.624659	+	4.47352i	0.0388144	+	0.277971i
$260$		0			0
$261$	−2.32203	+	1.34063i	−0.143730	+	0.0829828i
$262$		0			0
$263$	9.94833	−	17.2310i	0.613440	−	1.06251i	−0.377216	−	0.926125i	$-0.623119\pi$
$263$	9.94833	−	17.2310i	0.613440	−	1.06251i	0.990656	−	0.136384i	$-0.0435481\pi$
$264$		0			0
$265$	27.1615			1.66852
$266$		0			0
$267$		−	1.82102i		−	0.111444i
$268$		0			0
$269$	14.6930	+	8.48299i	0.895847	+	0.517217i	0.875850	−	0.482583i	$-0.160301\pi$
$269$	14.6930	+	8.48299i	0.895847	+	0.517217i	0.0199962	+	0.999800i	$0.493635\pi$
$270$		0			0
$271$	0.538186	+	0.932165i	0.0326925	+	0.0566250i	0.881909	−	0.471420i	$-0.156258\pi$
$271$	0.538186	+	0.932165i	0.0326925	+	0.0566250i	−0.849216	+	0.528045i	$0.822925\pi$
$272$		0			0
$273$	−10.0082	−	12.8333i	−0.605721	−	0.776709i
$274$		0			0
$275$	−6.36329	+	3.67385i	−0.383721	+	0.221541i
$276$		0			0
$277$	4.23611	+	2.44572i	0.254523	+	0.146949i	0.621834	−	0.783149i	$-0.286388\pi$
$277$	4.23611	+	2.44572i	0.254523	+	0.146949i	−0.367311	+	0.930098i	$0.619721\pi$
$278$		0			0
$279$	10.7137			0.641414
$280$		0			0
$281$	−0.754188			−0.0449911			−0.0224956	−	0.999747i	$-0.507161\pi$
$281$	−0.754188			−0.0449911			−0.0224956	+	0.999747i	$0.507161\pi$
$282$		0			0
$283$	−16.8270	−	9.71510i	−1.00026	−	0.577503i	−0.0919376	−	0.995765i	$-0.529306\pi$
$283$	−16.8270	−	9.71510i	−1.00026	−	0.577503i	−0.908326	+	0.418262i	$0.862639\pi$
$284$		0			0
$285$	7.48146	−	4.31942i	0.443163	−	0.255860i
$286$		0			0
$287$	4.52942	−	11.1821i	0.267363	−	0.660058i
$288$		0			0
$289$	1.34162	+	2.32376i	0.0789189	+	0.136691i
$290$		0			0
$291$	−10.4132	−	6.01205i	−0.610431	−	0.352433i
$292$		0			0
$293$		−	21.9433i		−	1.28194i	−0.767564	−	0.640972i	$-0.778532\pi$
$293$		−	21.9433i		−	1.28194i	0.767564	−	0.640972i	$-0.221468\pi$
$294$		0			0
$295$	−0.415698			−0.0242029
$296$		0			0
$297$	−0.470984	+	0.815768i	−0.0273292	+	0.0473356i
$298$		0			0
$299$	15.9142	−	9.18809i	0.920344	−	0.531361i
$300$		0			0
$301$	−8.59925	−	3.48321i	−0.495652	−	0.200769i
$302$		0			0
$303$	0.890504	+	1.54240i	0.0511581	+	0.0886085i
$304$		0			0
$305$	−14.5871	+	25.2656i	−0.835255	+	1.44670i
$306$		0			0
$307$			2.18555i			0.124736i	0.998053	+	0.0623679i	$0.0198652\pi$
$307$			2.18555i			0.124736i	−0.998053	+	0.0623679i	$0.980135\pi$
$308$		0			0
$309$			12.4230i			0.706720i
$310$		0			0
$311$	13.6343	−	23.6152i	0.773129	−	1.33910i	−0.162712	−	0.986674i	$-0.552024\pi$
$311$	13.6343	−	23.6152i	0.773129	−	1.33910i	0.935840	−	0.352424i	$-0.114643\pi$
$312$		0			0
$313$	0.683268	+	1.18346i	0.0386206	+	0.0668929i	0.884690	−	0.466181i	$-0.154370\pi$
$313$	0.683268	+	1.18346i	0.0386206	+	0.0668929i	−0.846069	+	0.533073i	$0.821037\pi$
$314$		0			0
$315$	7.46438	−	5.82114i	0.420570	−	0.327984i
$316$		0			0
$317$	7.09368	−	4.09554i	0.398421	−	0.230028i	−0.287382	−	0.957816i	$-0.592785\pi$
$317$	7.09368	−	4.09554i	0.398421	−	0.230028i	0.685802	+	0.727788i	$0.259451\pi$
$318$		0			0
$319$	1.26283	−	2.18728i	0.0707048	−	0.122464i
$320$		0			0
$321$	−9.71411			−0.542189
$322$		0			0
$323$		−	9.13622i		−	0.508353i
$324$		0			0
$325$	−41.5531	−	23.9907i	−2.30495	−	1.33076i
$326$		0			0
$327$	−7.13874	−	12.3647i	−0.394773	−	0.683767i
$328$		0			0
$329$	17.9383	−	2.50482i	0.988972	−	0.138095i
$330$		0			0
$331$	−13.3643	+	7.71590i	−0.734570	+	0.424104i	−0.820092	−	0.572232i	$-0.806078\pi$
$331$	−13.3643	+	7.71590i	−0.734570	+	0.424104i	0.0855218	+	0.996336i	$0.472744\pi$
$332$		0			0
$333$	1.47851	+	0.853618i	0.0810218	+	0.0467780i
$334$		0			0
$335$	14.2245			0.777165
$336$		0			0
$337$	−0.543923			−0.0296294			−0.0148147	−	0.999890i	$-0.504716\pi$
$337$	−0.543923			−0.0296294			−0.0148147	+	0.999890i	$0.504716\pi$
$338$		0			0
$339$	12.0183	+	6.93875i	0.652743	+	0.376861i
$340$		0			0
$341$	−8.73990	+	5.04599i	−0.473292	+	0.273255i
$342$		0			0
$343$	16.9391	−	7.48774i	0.914626	−	0.404300i
$344$		0			0
$345$	5.34415	+	9.25634i	0.287720	+	0.498345i
$346$		0			0
$347$	−9.92740	−	5.73159i	−0.532931	−	0.307688i	0.209278	−	0.977856i	$-0.432889\pi$
$347$	−9.92740	−	5.73159i	−0.532931	−	0.307688i	−0.742209	+	0.670168i	$0.766222\pi$
$348$		0			0
$349$			1.23092i			0.0658899i	0.999457	+	0.0329449i	$0.0104886\pi$
$349$			1.23092i			0.0658899i	−0.999457	+	0.0329449i	$0.989511\pi$
$350$		0			0
$351$	−6.15117			−0.328325
$352$		0			0
$353$	17.1091	−	29.6339i	0.910628	−	1.57725i	0.0974483	−	0.995241i	$-0.468932\pi$
$353$	17.1091	−	29.6339i	0.910628	−	1.57725i	0.813179	−	0.582013i	$-0.197735\pi$
$354$		0			0
$355$	−12.1636	+	7.02264i	−0.645575	+	0.372723i
$356$		0			0
$357$	−1.38443	−	9.91467i	−0.0732720	−	0.524740i
$358$		0			0
$359$	16.9536	+	29.3645i	0.894777	+	1.54980i	0.834080	+	0.551643i	$0.185999\pi$
$359$	16.9536	+	29.3645i	0.894777	+	1.54980i	0.0606972	+	0.998156i	$0.480668\pi$
$360$		0			0
$361$	−6.58487	+	11.4053i	−0.346572	+	0.600280i
$362$		0			0
$363$			10.1127i			0.530779i
$364$		0			0
$365$		−	22.2850i		−	1.16645i
$366$		0			0
$367$	−9.62235	+	16.6664i	−0.502282	+	0.869979i	0.497714	+	0.867341i	$0.334173\pi$
$367$	−9.62235	+	16.6664i	−0.502282	+	0.869979i	−0.999997	+	0.00263748i	$0.999160\pi$
$368$		0			0
$369$	−2.28000	−	3.94907i	−0.118692	−	0.205581i
$370$		0			0
$371$	15.8389	−	12.3521i	0.822315	−	0.641287i
$372$		0			0
$373$	12.8464	−	7.41686i	0.665160	−	0.384030i	−0.129080	−	0.991634i	$-0.541202\pi$
$373$	12.8464	−	7.41686i	0.665160	−	0.384030i	0.794240	+	0.607604i	$0.207869\pi$
$374$		0			0
$375$	5.00953	−	8.67676i	0.258691	−	0.448066i
$376$		0			0
$377$	16.4928			0.849425
$378$		0			0
$379$		−	11.7500i		−	0.603555i	−0.953378	−	0.301778i	$-0.902420\pi$
$379$		−	11.7500i		−	0.603555i	0.953378	−	0.301778i	$-0.0975800\pi$
$380$		0			0
$381$	6.73239	+	3.88695i	0.344911	+	0.199134i
$382$		0			0
$383$	9.53274	+	16.5112i	0.487100	+	0.843682i	0.999890	−	0.0148320i	$-0.00472133\pi$
$383$	9.53274	+	16.5112i	0.487100	+	0.843682i	−0.512790	+	0.858514i	$0.671388\pi$
$384$		0			0
$385$	−3.34754	+	8.26430i	−0.170606	+	0.421188i
$386$		0			0
$387$	−3.03691	+	1.75336i	−0.154375	+	0.0891284i
$388$		0			0
$389$	−1.73492	−	1.00165i	−0.0879638	−	0.0507859i	0.455373	−	0.890301i	$-0.349506\pi$
$389$	−1.73492	−	1.00165i	−0.0879638	−	0.0507859i	−0.543337	+	0.839515i	$0.682839\pi$
$390$		0			0
$391$	11.3037			0.571652
$392$		0			0
$393$	7.04522			0.355384
$394$		0			0
$395$	16.9563	+	9.78974i	0.853165	+	0.492575i
$396$		0			0
$397$	−7.34718	+	4.24190i	−0.368744	+	0.212895i	−0.672910	−	0.739725i	$-0.734956\pi$
$397$	−7.34718	+	4.24190i	−0.368744	+	0.212895i	0.304165	+	0.952619i	$0.401622\pi$
$398$		0			0
$399$	2.39841	−	5.92111i	0.120070	−	0.296426i
$400$		0			0
$401$	7.04632	+	12.2046i	0.351876	+	0.609468i	0.986578	−	0.163289i	$-0.0522104\pi$
$401$	7.04632	+	12.2046i	0.351876	+	0.609468i	−0.634702	+	0.772757i	$0.718877\pi$
$402$		0			0
$403$	−57.0727	−	32.9509i	−2.84299	−	1.64140i
$404$		0			0
$405$		−	3.57776i		−	0.177780i
$406$		0			0
$407$	−1.60816			−0.0797135
$408$		0			0
$409$	−15.1789	+	26.2906i	−0.750547	+	1.29998i	0.197011	+	0.980401i	$0.436876\pi$
$409$	−15.1789	+	26.2906i	−0.750547	+	1.29998i	−0.947558	+	0.319584i	$0.896457\pi$
$410$		0			0
$411$	−15.6816	+	9.05379i	−0.773518	+	0.446591i
$412$		0			0
$413$	−0.242409	+	0.189044i	−0.0119282	+	0.00930225i
$414$		0			0
$415$	2.13879	+	3.70449i	0.104989	+	0.181846i
$416$		0			0
$417$	4.16360	−	7.21157i	0.203893	−	0.353152i
$418$		0			0
$419$		−	30.8896i		−	1.50905i	−0.656269	−	0.754527i	$-0.727866\pi$
$419$		−	30.8896i		−	1.50905i	0.656269	−	0.754527i	$-0.272134\pi$
$420$		0			0
$421$			20.0940i			0.979321i	0.871913	+	0.489661i	$0.162879\pi$
$421$			20.0940i			0.979321i	−0.871913	+	0.489661i	$0.837121\pi$
$422$		0			0
$423$	3.42292	−	5.92866i	0.166428	−	0.288262i
$424$		0			0
$425$	−14.7573	−	25.5604i	−0.715835	−	1.23986i
$426$		0			0
$427$	2.98358	+	21.3670i	0.144385	+	1.03402i
$428$		0			0
$429$	5.01792	−	2.89710i	0.242268	−	0.139873i
$430$		0			0
$431$	4.00873	−	6.94333i	0.193094	−	0.334448i	−0.753180	−	0.657814i	$-0.771481\pi$
$431$	4.00873	−	6.94333i	0.193094	−	0.334448i	0.946274	+	0.323366i	$0.104814\pi$
$432$		0			0
$433$	−26.9812			−1.29663			−0.648316	−	0.761371i	$-0.724527\pi$
$433$	−26.9812			−1.29663			−0.648316	+	0.761371i	$0.724527\pi$
$434$		0			0
$435$			9.59289i			0.459944i
$436$		0			0
$437$	6.24701	+	3.60672i	0.298835	+	0.172533i
$438$		0			0
$439$	18.2576	+	31.6231i	0.871388	+	1.50929i	0.860561	+	0.509347i	$0.170113\pi$
$439$	18.2576	+	31.6231i	0.871388	+	1.50929i	0.0108272	+	0.999941i	$0.496554\pi$
$440$		0			0
$441$	1.70552	−	6.78905i	0.0812153	−	0.323288i
$442$		0			0
$443$	−0.190464	+	0.109964i	−0.00904921	+	0.00522457i	−0.504518	−	0.863401i	$-0.668330\pi$
$443$	−0.190464	+	0.109964i	−0.00904921	+	0.00522457i	0.495469	+	0.868626i	$0.334996\pi$
$444$		0			0
$445$	−5.64230	−	3.25758i	−0.267471	−	0.154424i
$446$		0			0
$447$	−20.7056			−0.979341
$448$		0			0
$449$	20.6799			0.975946			0.487973	−	0.872859i	$-0.337736\pi$
$449$	20.6799			0.975946			0.487973	+	0.872859i	$0.337736\pi$
$450$		0			0
$451$	3.71990	+	2.14768i	0.175163	+	0.101130i
$452$		0			0
$453$	−3.42570	+	1.97783i	−0.160954	+	0.0929266i
$454$		0			0
$455$	−57.6666	+	8.05227i	−2.70345	+	0.377496i
$456$		0			0
$457$	4.29209	+	7.43412i	0.200776	+	0.347753i	0.948779	−	0.315942i	$-0.102320\pi$
$457$	4.29209	+	7.43412i	0.200776	+	0.347753i	−0.748003	+	0.663695i	$0.768987\pi$
$458$		0			0
$459$	−3.27682	−	1.89187i	−0.152949	−	0.0883051i
$460$		0			0
$461$		−	13.8203i		−	0.643676i	−0.946795	−	0.321838i	$-0.895699\pi$
$461$		−	13.8203i		−	0.643676i	0.946795	−	0.321838i	$-0.104301\pi$
$462$		0			0
$463$	−28.8694			−1.34168			−0.670838	−	0.741604i	$-0.734065\pi$
$463$	−28.8694			−1.34168			−0.670838	+	0.741604i	$0.734065\pi$
$464$		0			0
$465$	19.1656	−	33.1957i	0.888782	−	1.53941i
$466$		0			0
$467$	10.7682	−	6.21705i	0.498295	−	0.287691i	−0.229714	−	0.973258i	$-0.573779\pi$
$467$	10.7682	−	6.21705i	0.498295	−	0.287691i	0.728009	+	0.685567i	$0.240446\pi$
$468$		0			0
$469$	8.29482	−	6.46876i	0.383019	−	0.298700i
$470$		0			0
$471$	5.93532	+	10.2803i	0.273485	+	0.473690i
$472$		0			0
$473$	1.65161	−	2.86067i	0.0759411	−	0.131534i
$474$		0			0
$475$		−	18.8347i		−	0.864197i
$476$		0			0
$477$		−	7.59176i		−	0.347603i
$478$		0			0
$479$	19.1410	−	33.1532i	0.874575	−	1.51481i	0.0173596	−	0.999849i	$-0.494474\pi$
$479$	19.1410	−	33.1532i	0.874575	−	1.51481i	0.857215	−	0.514958i	$-0.172193\pi$
$480$		0			0
$481$	−5.25075	−	9.09456i	−0.239413	−	0.414676i
$482$		0			0
$483$	7.32582	+	2.96740i	0.333336	+	0.135021i
$484$		0			0
$485$	−37.2559	+	21.5097i	−1.69170	+	0.976704i
$486$		0			0
$487$	−0.902290	+	1.56281i	−0.0408867	+	0.0708178i	−0.885745	−	0.464173i	$-0.846352\pi$
$487$	−0.902290	+	1.56281i	−0.0408867	+	0.0708178i	0.844858	+	0.534991i	$0.179685\pi$
$488$		0			0
$489$	−17.0530			−0.771163
$490$		0			0
$491$			4.10278i			0.185156i	0.995705	+	0.0925780i	$0.0295108\pi$
$491$			4.10278i			0.185156i	−0.995705	+	0.0925780i	$0.970489\pi$
$492$		0			0
$493$	8.78600	+	5.07260i	0.395701	+	0.228458i
$494$		0			0
$495$	1.68507	+	2.91862i	0.0757381	+	0.131182i
$496$		0			0
$497$	−3.89940	+	9.62671i	−0.174912	+	0.431817i
$498$		0			0
$499$	38.4522	−	22.2004i	1.72135	−	0.993825i	0.805197	−	0.593008i	$-0.202060\pi$
$499$	38.4522	−	22.2004i	1.72135	−	0.993825i	0.916158	−	0.400817i	$-0.131274\pi$
$500$		0			0
$501$	9.03598	+	5.21693i	0.403698	+	0.233075i
$502$		0			0
$503$	−8.88976			−0.396375			−0.198187	−	0.980164i	$-0.563505\pi$
$503$	−8.88976			−0.396375			−0.198187	+	0.980164i	$0.563505\pi$
$504$		0			0
$505$	6.37202			0.283551
$506$		0			0
$507$	21.5094	+	12.4184i	0.955264	+	0.551522i
$508$		0			0
$509$	−9.56641	+	5.52317i	−0.424024	+	0.244810i	−0.696797	−	0.717268i	$-0.745392\pi$
$509$	−9.56641	+	5.52317i	−0.424024	+	0.244810i	0.272774	+	0.962078i	$0.412059\pi$
$510$		0			0
$511$	−10.1344	−	12.9952i	−0.448320	−	0.574875i
$512$		0			0
$513$	−1.20730	−	2.09110i	−0.0533035	−	0.0923244i
$514$		0			0
$515$	38.4918	+	22.2233i	1.69615	+	0.979274i
$516$		0			0
$517$			6.44855i			0.283607i
$518$		0			0
$519$	14.5742			0.639735
$520$		0			0
$521$	16.9975	−	29.4406i	0.744675	−	1.28982i	−0.205671	−	0.978621i	$-0.565938\pi$
$521$	16.9975	−	29.4406i	0.744675	−	1.28982i	0.950346	−	0.311194i	$-0.100729\pi$
$522$		0			0
$523$	−15.7706	+	9.10516i	−0.689601	+	0.398141i	−0.803462	−	0.595356i	$-0.797011\pi$
$523$	−15.7706	+	9.10516i	−0.689601	+	0.398141i	0.113862	+	0.993497i	$0.463678\pi$
$524$		0			0
$525$	−2.85407	−	20.4395i	−0.124562	−	0.892055i
$526$		0			0
$527$	−20.2690	−	35.1070i	−0.882932	−	1.52928i
$528$		0			0
$529$	7.03763	−	12.1895i	0.305984	−	0.529980i
$530$		0			0
$531$			0.116189i			0.00504219i
$532$		0			0
$533$			28.0493i			1.21495i
$534$		0			0
$535$	−17.3774	+	30.0985i	−0.751289	+	1.30127i
$536$		0			0
$537$	−1.88980	−	3.27323i	−0.0815510	−	0.141251i
$538$		0			0
$539$	1.80622	+	6.34156i	0.0777995	+	0.273150i
$540$		0			0
$541$	−26.0940	+	15.0654i	−1.12187	+	0.647712i	−0.941877	−	0.335957i	$-0.890940\pi$
$541$	−26.0940	+	15.0654i	−1.12187	+	0.647712i	−0.179992	+	0.983668i	$0.557607\pi$
$542$		0			0
$543$	0.561816	−	0.973094i	0.0241098	−	0.0417595i
$544$		0			0
$545$	−51.0814			−2.18809
$546$		0			0
$547$			36.0927i			1.54321i	0.636101	+	0.771606i	$0.280546\pi$
$547$			36.0927i			1.54321i	−0.636101	+	0.771606i	$0.719454\pi$
$548$		0			0
$549$	7.06184	+	4.07716i	0.301392	+	0.174009i
$550$		0			0
$551$	3.23707	+	5.60677i	0.137904	+	0.238857i
$552$		0			0
$553$	14.3399	−	2.00235i	0.609794	−	0.0851485i
$554$		0			0
$555$	5.28975	−	3.05404i	0.224537	−	0.129637i
$556$		0			0
$557$	36.7321	+	21.2073i	1.55639	+	0.898583i	0.997598	+	0.0692757i	$0.0220688\pi$
$557$	36.7321	+	21.2073i	1.55639	+	0.898583i	0.558793	+	0.829307i	$0.311265\pi$
$558$		0			0
$559$	21.5704			0.912333
$560$		0			0
$561$	3.56417			0.150479
$562$		0			0
$563$	−10.2656	−	5.92685i	−0.432644	−	0.249787i	0.267828	−	0.963467i	$-0.413694\pi$
$563$	−10.2656	−	5.92685i	−0.432644	−	0.249787i	−0.700472	+	0.713680i	$0.747027\pi$
$564$		0			0
$565$	42.9985	−	24.8252i	1.80896	−	1.04440i
$566$		0			0
$567$	−1.62703	−	2.08633i	−0.0683290	−	0.0876175i
$568$		0			0
$569$	−2.71207	−	4.69744i	−0.113696	−	0.196927i	0.803562	−	0.595221i	$-0.202936\pi$
$569$	−2.71207	−	4.69744i	−0.113696	−	0.196927i	−0.917258	+	0.398294i	$0.869602\pi$
$570$		0			0
$571$	16.9613	+	9.79262i	0.709809	+	0.409809i	0.810990	−	0.585059i	$-0.198929\pi$
$571$	16.9613	+	9.79262i	0.709809	+	0.409809i	−0.101181	+	0.994868i	$0.532262\pi$
$572$		0			0
$573$		−	14.0300i		−	0.586113i
$574$		0			0
$575$	23.3031			0.971804
$576$		0			0
$577$	−3.11174	+	5.38970i	−0.129544	+	0.224376i	−0.923500	−	0.383599i	$-0.874685\pi$
$577$	−3.11174	+	5.38970i	−0.129544	+	0.224376i	0.793956	+	0.607975i	$0.208018\pi$
$578$		0			0
$579$	0.675669	−	0.390098i	0.0280798	−	0.0162119i
$580$		0			0
$581$	2.93188	+	1.18759i	0.121635	+	0.0492694i
$582$		0			0
$583$	3.57560	+	6.19312i	0.148086	+	0.256493i
$584$		0			0
$585$	−11.0037	+	19.0590i	−0.454947	+	0.787991i
$586$		0			0
$587$			0.894279i			0.0369108i	0.999830	+	0.0184554i	$0.00587487\pi$
$587$			0.894279i			0.0369108i	−0.999830	+	0.0184554i	$0.994125\pi$
$588$		0			0
$589$		−	25.8693i		−	1.06593i
$590$		0			0
$591$	1.18818	−	2.05799i	0.0488753	−	0.0846545i
$592$		0			0
$593$	11.3498	+	19.6584i	0.466080	+	0.807275i	0.999250	−	0.0387338i	$-0.0123324\pi$
$593$	11.3498	+	19.6584i	0.466080	+	0.807275i	−0.533169	+	0.846009i	$0.678999\pi$
$594$		0			0
$595$	−33.1965	−	13.4466i	−1.36092	−	0.551256i
$596$		0			0
$597$	11.7640	−	6.79196i	0.481469	−	0.277976i
$598$		0			0
$599$	−19.5178	+	33.8058i	−0.797476	+	1.38127i	0.123780	+	0.992310i	$0.460498\pi$
$599$	−19.5178	+	33.8058i	−0.797476	+	1.38127i	−0.921255	+	0.388959i	$0.872835\pi$
$600$		0			0
$601$	−0.397117			−0.0161987			−0.00809936	−	0.999967i	$-0.502578\pi$
$601$	−0.397117			−0.0161987			−0.00809936	+	0.999967i	$0.502578\pi$
$602$		0			0
$603$		−	3.97580i		−	0.161907i
$604$		0			0
$605$	31.3335	+	18.0904i	1.27389	+	0.735480i
$606$		0			0
$607$	10.9157	+	18.9066i	0.443056	+	0.767395i	0.997915	−	0.0645493i	$-0.0205610\pi$
$607$	10.9157	+	18.9066i	0.443056	+	0.767395i	−0.554859	+	0.831945i	$0.687228\pi$
$608$		0			0
$609$	4.36249	+	5.59397i	0.176777	+	0.226679i
$610$		0			0
$611$	−36.4682	+	21.0549i	−1.47535	+	0.851791i
$612$		0			0
$613$	−21.6460	−	12.4973i	−0.874275	−	0.504763i	−0.00550856	−	0.999985i	$-0.501753\pi$
$613$	−21.6460	−	12.4973i	−0.874275	−	0.504763i	−0.868767	+	0.495222i	$0.835087\pi$
$614$		0			0
$615$	−16.3146			−0.657867
$616$		0			0
$617$	−17.0538			−0.686560			−0.343280	−	0.939233i	$-0.611538\pi$
$617$	−17.0538			−0.686560			−0.343280	+	0.939233i	$0.611538\pi$
$618$		0			0
$619$	4.32061	+	2.49451i	0.173660	+	0.100263i	0.584311	−	0.811530i	$-0.301365\pi$
$619$	4.32061	+	2.49451i	0.173660	+	0.100263i	−0.410650	+	0.911793i	$0.634698\pi$
$620$		0			0
$621$	2.58719	−	1.49371i	0.103820	−	0.0599407i
$622$		0			0
$623$	−4.77167	+	0.666291i	−0.191173	+	0.0266944i
$624$		0			0
$625$	1.57804	+	2.73324i	0.0631215	+	0.109330i
$626$		0			0
$627$	1.96975	+	1.13723i	0.0786642	+	0.0454168i
$628$		0			0
$629$		−	6.45975i		−	0.257567i
$630$		0			0
$631$	−15.7236			−0.625947			−0.312973	−	0.949762i	$-0.601325\pi$
$631$	−15.7236			−0.625947			−0.312973	+	0.949762i	$0.601325\pi$
$632$		0			0
$633$	−7.09662	+	12.2917i	−0.282065	+	0.488551i
$634$		0			0
$635$	24.0869	−	13.9066i	0.955859	−	0.551865i
$636$		0			0
$637$	−29.9657	+	30.9203i	−1.18728	+	1.22511i
$638$		0			0
$639$	1.96286	+	3.39977i	0.0776495	+	0.134493i
$640$		0			0
$641$	−12.3353	+	21.3654i	−0.487216	+	0.843884i	−0.999892	−	0.0146989i	$-0.995321\pi$
$641$	−12.3353	+	21.3654i	−0.487216	+	0.843884i	0.512676	+	0.858582i	$0.328654\pi$
$642$		0			0
$643$			47.6908i			1.88074i	0.340150	+	0.940371i	$0.389522\pi$
$643$			47.6908i			1.88074i	−0.340150	+	0.940371i	$0.610478\pi$
$644$		0			0
$645$			12.5462i			0.494007i
$646$		0			0
$647$	−9.64727	+	16.7096i	−0.379273	+	0.656921i	−0.990957	−	0.134182i	$-0.957159\pi$
$647$	−9.64727	+	16.7096i	−0.379273	+	0.656921i	0.611683	+	0.791103i	$0.290493\pi$
$648$		0			0
$649$	−0.0547233	−	0.0947835i	−0.00214808	−	0.00372058i
$650$		0			0
$651$	−3.92004	−	28.0735i	−0.153638	−	1.10029i
$652$		0			0
$653$	−35.9797	+	20.7729i	−1.40799	+	0.812905i	−0.995195	−	0.0979172i	$-0.968782\pi$
$653$	−35.9797	+	20.7729i	−1.40799	+	0.812905i	−0.412799	+	0.910822i	$0.635449\pi$
$654$		0			0
$655$	12.6030	−	21.8291i	0.492442	−	0.852934i
$656$		0			0
$657$	−6.22876			−0.243007
$658$		0			0
$659$			21.7026i			0.845414i	0.906266	+	0.422707i	$0.138920\pi$
$659$			21.7026i			0.845414i	−0.906266	+	0.422707i	$0.861080\pi$
$660$		0			0
$661$	12.7886	+	7.38348i	0.497417	+	0.287184i	0.727646	−	0.685952i	$-0.240614\pi$
$661$	12.7886	+	7.38348i	0.497417	+	0.287184i	−0.230229	+	0.973136i	$0.573948\pi$
$662$		0			0
$663$	11.6372	+	20.1563i	0.451953	+	0.782805i
$664$		0			0
$665$	−14.0557	−	18.0235i	−0.545056	−	0.698919i
$666$		0			0
$667$	−6.93691	+	4.00503i	−0.268598	+	0.155075i
$668$		0			0
$669$	−0.171627	−	0.0990889i	−0.00663548	−	0.00383100i
$670$		0			0
$671$	−7.68110			−0.296526
$672$		0			0
$673$	3.09088			0.119145			0.0595724	−	0.998224i	$-0.481026\pi$
$673$	3.09088			0.119145			0.0595724	+	0.998224i	$0.481026\pi$
$674$		0			0
$675$	−6.75532	−	3.90019i	−0.260012	−	0.150118i
$676$		0			0
$677$	−33.6034	+	19.4009i	−1.29148	+	0.745638i	−0.978917	−	0.204258i	$-0.934522\pi$
$677$	−33.6034	+	19.4009i	−1.29148	+	0.745638i	−0.312566	+	0.949896i	$0.601188\pi$
$678$		0			0
$679$	−11.9435	+	29.4857i	−0.458349	+	1.13156i
$680$		0			0
$681$	12.8780	+	22.3054i	0.493487	+	0.854744i
$682$		0			0
$683$	−22.5229	−	13.0036i	−0.861817	−	0.497570i	0.00280354	−	0.999996i	$-0.499108\pi$
$683$	−22.5229	−	13.0036i	−0.861817	−	0.497570i	−0.864620	+	0.502426i	$0.832441\pi$
$684$		0			0
$685$			64.7846i			2.47529i
$686$		0			0
$687$	16.1617			0.616609
$688$		0			0
$689$	−23.3491	+	40.4418i	−0.889530	+	1.54071i
$690$		0			0
$691$	8.60842	−	4.97007i	0.327480	−	0.189070i	−0.327242	−	0.944941i	$-0.606119\pi$
$691$	8.60842	−	4.97007i	0.327480	−	0.189070i	0.654722	+	0.755870i	$0.272786\pi$
$692$		0			0
$693$	2.30991	+	0.935652i	0.0877461	+	0.0355425i
$694$		0			0
$695$	−14.8964	−	25.8013i	−0.565052	−	0.978698i
$696$		0			0
$697$	−8.62694	+	14.9423i	−0.326769	+	0.565980i
$698$		0			0
$699$			25.1239i			0.950272i
$700$		0			0
$701$		−	32.3250i		−	1.22090i	−0.792056	−	0.610449i	$-0.790989\pi$
$701$		−	32.3250i		−	1.22090i	0.792056	−	0.610449i	$-0.209011\pi$
$702$		0			0
$703$	2.06114	−	3.57000i	0.0777374	−	0.134645i
$704$		0			0
$705$	−12.2464	−	21.2113i	−0.461225	−	0.798865i
$706$		0			0
$707$	3.71576	−	2.89776i	0.139746	−	0.108981i
$708$		0			0
$709$	38.2056	−	22.0580i	1.43484	−	0.828406i	0.437357	−	0.899288i	$-0.355915\pi$
$709$	38.2056	−	22.0580i	1.43484	−	0.828406i	0.997485	+	0.0708817i	$0.0225813\pi$
$710$		0			0
$711$	2.73628	−	4.73937i	0.102618	−	0.177740i
$712$		0			0
$713$	32.0065			1.19865
$714$		0			0
$715$		−	20.7303i		−	0.775268i
$716$		0			0
$717$	13.8901	+	8.01946i	0.518736	+	0.299492i
$718$		0			0
$719$	−3.22929	−	5.59330i	−0.120432	−	0.208595i	0.799506	−	0.600658i	$-0.205095\pi$
$719$	−3.22929	−	5.59330i	−0.120432	−	0.208595i	−0.919938	+	0.392063i	$0.871761\pi$
$720$		0			0
$721$	32.5523	−	4.54544i	1.21231	−	0.169281i
$722$		0			0
$723$	−11.4047	+	6.58453i	−0.424147	+	0.244881i
$724$		0			0
$725$	18.1127	+	10.4574i	0.672690	+	0.388378i
$726$		0			0
$727$	25.6040			0.949600			0.474800	−	0.880094i	$-0.342520\pi$
$727$	25.6040			0.949600			0.474800	+	0.880094i	$0.342520\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	11.4909	+	6.63428i	0.425007	+	0.245378i
$732$		0			0
$733$	8.94596	−	5.16495i	0.330426	−	0.190772i	−0.325604	−	0.945506i	$-0.605568\pi$
$733$	8.94596	−	5.16495i	0.330426	−	0.190772i	0.656030	+	0.754734i	$0.272234\pi$
$734$		0			0
$735$	−17.9844	−	17.4292i	−0.663366	−	0.642887i
$736$		0			0
$737$	1.87254	+	3.24333i	0.0689757	+	0.119470i
$738$		0			0
$739$	40.1335	+	23.1711i	1.47633	+	0.852362i	0.999643	−	0.0267085i	$-0.00850260\pi$
$739$	40.1335	+	23.1711i	1.47633	+	0.852362i	0.476691	+	0.879071i	$0.341836\pi$
$740$		0			0
$741$			14.8526i			0.545623i
$742$		0			0
$743$	38.1002			1.39776			0.698880	−	0.715239i	$-0.253682\pi$
$743$	38.1002			1.39776			0.698880	+	0.715239i	$0.253682\pi$
$744$		0			0
$745$	−37.0398	+	64.1548i	−1.35703	+	2.35045i
$746$		0			0
$747$	1.03542	−	0.597802i	0.0378841	−	0.0218724i
$748$		0			0
$749$	3.55429	+	25.4542i	0.129871	+	0.930075i
$750$		0			0
$751$	−3.76000	−	6.51250i	−0.137204	−	0.237645i	0.789233	−	0.614094i	$-0.210478\pi$
$751$	−3.76000	−	6.51250i	−0.137204	−	0.237645i	−0.926437	+	0.376449i	$0.877145\pi$
$752$		0			0
$753$	4.32352	−	7.48855i	0.157558	−	0.272898i
$754$		0			0
$755$			14.1524i			0.515059i
$756$		0			0
$757$		−	41.2006i		−	1.49746i	−0.662873	−	0.748731i	$-0.730663\pi$
$757$		−	41.2006i		−	1.49746i	0.662873	−	0.748731i	$-0.269337\pi$
$758$		0			0
$759$	−1.40703	+	2.43705i	−0.0510720	+	0.0884592i
$760$		0			0
$761$	−14.3106	−	24.7867i	−0.518759	−	0.898517i	−0.999762	−	0.0217985i	$-0.993061\pi$
$761$	−14.3106	−	24.7867i	−0.518759	−	0.898517i	0.481003	−	0.876719i	$-0.340273\pi$
$762$		0			0
$763$	−29.7875	+	23.2299i	−1.07838	+	0.840980i
$764$		0			0
$765$	−11.7237	+	6.76867i	−0.423871	+	0.244722i
$766$		0			0
$767$	0.357350	−	0.618949i	0.0129032	−	0.0223489i
$768$		0			0
$769$	−14.6303			−0.527581			−0.263791	−	0.964580i	$-0.584973\pi$
$769$	−14.6303			−0.527581			−0.263791	+	0.964580i	$0.584973\pi$
$770$		0			0
$771$		−	14.4651i		−	0.520947i
$772$		0			0
$773$	−36.7815	−	21.2358i	−1.32294	−	0.763798i	−0.338741	−	0.940880i	$-0.610001\pi$
$773$	−36.7815	−	21.2358i	−1.32294	−	0.763798i	−0.984196	+	0.177082i	$0.943334\pi$
$774$		0			0
$775$	−41.7855	−	72.3746i	−1.50098	−	2.59977i
$776$		0			0
$777$	1.69579	−	4.18651i	0.0608361	−	0.150190i
$778$		0			0
$779$	−9.53541	+	5.50527i	−0.341642	+	0.197247i
$780$		0			0
$781$	−3.20247	−	1.84895i	−0.114594	−	0.0661606i
$782$		0			0
$783$	2.68125			0.0958202
$784$		0			0
$785$	42.4703			1.51583
$786$		0			0
$787$	6.55295	+	3.78335i	0.233588	+	0.134862i	0.612226	−	0.790683i	$-0.290274\pi$
$787$	6.55295	+	3.78335i	0.233588	+	0.134862i	−0.378638	+	0.925545i	$0.623608\pi$
$788$		0			0
$789$	−17.2310	+	9.94833i	−0.613440	+	0.354170i
$790$		0			0
$791$	13.7844	−	34.0306i	0.490119	−	1.20999i
$792$		0			0
$793$	−25.0793	−	43.4386i	−0.890591	−	1.54255i
$794$		0			0
$795$	−23.5226	−	13.5808i	−0.834259	−	0.481660i
$796$		0			0
$797$		−	11.4622i		−	0.406013i	−0.979177	−	0.203007i	$-0.934929\pi$
$797$		−	11.4622i		−	0.406013i	0.979177	−	0.203007i	$-0.0650713\pi$
$798$		0			0
$799$	−25.9029			−0.916379
$800$		0			0
$801$	−0.910509	+	1.57705i	−0.0321713	+	0.0557222i
$802$		0			0
$803$	5.08122	−	2.93365i	0.179312	−	0.103526i
$804$		0			0
$805$	22.2993	−	17.3902i	0.785947	−	0.612925i
$806$		0			0
$807$	−8.48299	−	14.6930i	−0.298616	−	0.517217i
$808$		0			0
$809$	−8.54103	+	14.7935i	−0.300287	+	0.520112i	−0.976201	−	0.216869i	$-0.930416\pi$
$809$	−8.54103	+	14.7935i	−0.300287	+	0.520112i	0.675914	+	0.736980i	$0.263749\pi$
$810$		0			0
$811$		−	16.6693i		−	0.585338i	−0.956214	−	0.292669i	$-0.905457\pi$
$811$		−	16.6693i		−	0.585338i	0.956214	−	0.292669i	$-0.0945434\pi$
$812$		0			0
$813$		−	1.07637i		−	0.0377500i
$814$		0			0
$815$	−30.5058	+	52.8375i	−1.06857	+	1.85082i
$816$		0			0
$817$	4.23366	+	7.33291i	0.148117	+	0.256546i
$818$		0			0
$819$	2.25065	+	16.1181i	0.0786439	+	0.563211i
$820$		0			0
$821$	37.2593	−	21.5117i	1.30036	−	0.750762i	0.319893	−	0.947454i	$-0.396353\pi$
$821$	37.2593	−	21.5117i	1.30036	−	0.750762i	0.980465	+	0.196691i	$0.0630197\pi$
$822$		0			0
$823$	17.3255	−	30.0086i	0.603928	−	1.04603i	−0.388292	−	0.921536i	$-0.626935\pi$
$823$	17.3255	−	30.0086i	0.603928	−	1.04603i	0.992220	−	0.124497i	$-0.0397317\pi$
$824$		0			0
$825$	7.34769			0.255814
$826$		0			0
$827$		−	36.5937i		−	1.27249i	−0.771489	−	0.636243i	$-0.780487\pi$
$827$		−	36.5937i		−	1.27249i	0.771489	−	0.636243i	$-0.219513\pi$
$828$		0			0
$829$	−6.54607	−	3.77938i	−0.227354	−	0.131263i	0.381997	−	0.924164i	$-0.375237\pi$
$829$	−6.54607	−	3.77938i	−0.227354	−	0.131263i	−0.609351	+	0.792901i	$0.708570\pi$
$830$		0			0
$831$	−2.44572	−	4.23611i	−0.0848410	−	0.146949i
$832$		0			0
$833$	−25.4731	+	7.25534i	−0.882592	+	0.251383i
$834$		0			0
$835$	32.3286	−	18.6649i	1.11878	−	0.645926i
$836$		0			0
$837$	−9.27835	−	5.35686i	−0.320707	−	0.185160i
$838$		0			0
$839$	33.3899			1.15275			0.576374	−	0.817186i	$-0.304467\pi$
$839$	33.3899			1.15275			0.576374	+	0.817186i	$0.304467\pi$
$840$		0			0
$841$	21.8109			0.752099
$842$		0			0
$843$	0.653146	+	0.377094i	0.0224956	+	0.0129878i
$844$		0			0
$845$	76.9553	−	44.4302i	2.64734	−	1.52844i
$846$		0			0
$847$	26.4986	−	3.70013i	0.910503	−	0.127138i
$848$		0			0
$849$	9.71510	+	16.8270i	0.333421	+	0.577503i
$850$		0			0
$851$	4.41694	+	2.55012i	0.151411	+	0.0874171i
$852$		0			0
$853$			18.6855i			0.639779i	0.947455	+	0.319889i	$0.103646\pi$
$853$			18.6855i			0.639779i	−0.947455	+	0.319889i	$0.896354\pi$
$854$		0			0
$855$	−8.63884			−0.295442
$856$		0			0
$857$	15.4441	−	26.7499i	0.527559	−	0.913759i	−0.471925	−	0.881639i	$-0.656441\pi$
$857$	15.4441	−	26.7499i	0.527559	−	0.913759i	0.999484	−	0.0321205i	$-0.0102260\pi$
$858$		0			0
$859$	35.3861	−	20.4302i	1.20736	−	0.697069i	0.245178	−	0.969478i	$-0.421154\pi$
$859$	35.3861	−	20.4302i	1.20736	−	0.697069i	0.962182	+	0.272409i	$0.0878203\pi$
$860$		0			0
$861$	−9.51365	+	7.41927i	−0.324224	+	0.252848i
$862$		0			0
$863$	1.87676	+	3.25064i	0.0638857	+	0.110653i	0.896199	−	0.443652i	$-0.146317\pi$
$863$	1.87676	+	3.25064i	0.0638857	+	0.110653i	−0.832313	+	0.554305i	$0.812984\pi$
$864$		0			0
$865$	26.0714	−	45.1571i	0.886455	−	1.53539i
$866$		0			0
$867$		−	2.68324i		−	0.0911277i
$868$		0			0
$869$			5.15496i			0.174870i
$870$		0			0
$871$	−12.2279	+	21.1793i	−0.414327	+	0.717635i
$872$		0			0
$873$	6.01205	+	10.4132i	0.203477	+	0.352433i
$874$		0			0
$875$	−24.5689	−	9.95188i	−0.830580	−	0.336435i
$876$		0			0
$877$	−26.0217	+	15.0236i	−0.878689	+	0.507311i	−0.870226	−	0.492653i	$-0.836027\pi$
$877$	−26.0217	+	15.0236i	−0.878689	+	0.507311i	−0.00846311	+	0.999964i	$0.502694\pi$
$878$		0			0
$879$	−10.9717	+	19.0035i	−0.370065	+	0.640972i
$880$		0			0
$881$	42.4160			1.42903			0.714516	−	0.699619i	$-0.246647\pi$
$881$	42.4160			1.42903			0.714516	+	0.699619i	$0.246647\pi$
$882$		0			0
$883$		−	20.3124i		−	0.683568i	−0.939779	−	0.341784i	$-0.888969\pi$
$883$		−	20.3124i		−	0.683568i	0.939779	−	0.341784i	$-0.111031\pi$
$884$		0			0
$885$	0.360005	+	0.207849i	0.0121014	+	0.00698676i
$886$		0			0
$887$	8.69219	+	15.0553i	0.291855	+	0.505508i	0.974248	−	0.225477i	$-0.0723941\pi$
$887$	8.69219	+	15.0553i	0.291855	+	0.505508i	−0.682393	+	0.730985i	$0.739061\pi$
$888$		0			0
$889$	7.72177	−	19.0633i	0.258980	−	0.639362i
$890$		0			0
$891$	0.815768	−	0.470984i	0.0273292	−	0.0157785i
$892$		0			0
$893$	−14.3153	−	8.26496i	−0.479044	−	0.276576i
$894$		0			0
$895$	−13.5225			−0.452008
$896$		0			0
$897$	−18.3762			−0.613563
$898$		0			0
$899$	24.8776	+	14.3631i	0.829715	+	0.479036i
$900$		0			0
$901$	−24.8769	+	14.3627i	−0.828769	+	0.478490i
$902$		0			0
$903$	5.70556	+	7.31617i	0.189869	+	0.243467i
$904$		0			0
$905$	−2.01004	−	3.48150i	−0.0668161	−	0.115729i
$906$		0			0
$907$	18.8970	+	10.9102i	0.627464	+	0.362266i	0.779769	−	0.626067i	$-0.215336\pi$
$907$	18.8970	+	10.9102i	0.627464	+	0.362266i	−0.152306	+	0.988333i	$0.548670\pi$
$908$		0			0
$909$		−	1.78101i		−	0.0590723i
$910$		0			0
$911$	−11.9139			−0.394727			−0.197363	−	0.980330i	$-0.563238\pi$
$911$	−11.9139			−0.394727			−0.197363	+	0.980330i	$0.563238\pi$
$912$		0			0
$913$	−0.563109	+	0.975334i	−0.0186362	+	0.0322789i
$914$		0			0
$915$	25.2656	−	14.5871i	0.835255	−	0.482234i
$916$		0			0
$917$	−2.57777	−	18.4608i	−0.0851254	−	0.609629i
$918$		0			0
$919$	−18.8832	−	32.7067i	−0.622900	−	1.07890i	−0.988943	−	0.148297i	$-0.952621\pi$
$919$	−18.8832	−	32.7067i	−0.622900	−	1.07890i	0.366042	−	0.930598i	$-0.380712\pi$
$920$		0			0
$921$	1.09277	−	1.89274i	0.0360081	−	0.0623679i
$922$		0			0
$923$		−	24.1477i		−	0.794833i
$924$		0			0
$925$		−	13.3171i		−	0.437863i
$926$		0			0
$927$	6.21150	−	10.7586i	0.204012	−	0.353360i
$928$		0			0
$929$	17.2547	+	29.8860i	0.566108	+	0.980528i	0.996946	+	0.0780988i	$0.0248849\pi$
$929$	17.2547	+	29.8860i	0.566108	+	0.980528i	−0.430837	+	0.902430i	$0.641782\pi$
$930$		0			0
$931$	−16.3928	−	4.11814i	−0.537253	−	0.134967i
$932$		0			0
$933$	−23.6152	+	13.6343i	−0.773129	+	0.446366i
$934$		0			0
$935$	6.37587	−	11.0433i	0.208513	−	0.361156i
$936$		0			0
$937$	2.63475			0.0860735			0.0430367	−	0.999073i	$-0.486297\pi$
$937$	2.63475			0.0860735			0.0430367	+	0.999073i	$0.486297\pi$
$938$		0			0
$939$		−	1.36654i		−	0.0445952i
$940$		0			0
$941$	−17.7673	−	10.2579i	−0.579197	−	0.334399i	0.181617	−	0.983369i	$-0.441867\pi$
$941$	−17.7673	−	10.2579i	−0.579197	−	0.334399i	−0.760814	+	0.648970i	$0.775200\pi$
$942$		0			0
$943$	−6.81133	−	11.7976i	−0.221808	−	0.384182i
$944$		0			0
$945$	−9.37491	+	1.30906i	−0.304966	+	0.0425839i
$946$		0			0
$947$	−27.2353	+	15.7243i	−0.885029	+	0.510972i	−0.872313	−	0.488947i	$-0.837381\pi$
$947$	−27.2353	+	15.7243i	−0.885029	+	0.510972i	−0.0127161	+	0.999919i	$0.504048\pi$
$948$		0			0
$949$	33.1810	+	19.1571i	1.07710	+	0.621865i
$950$		0			0
$951$	−8.19107			−0.265614
$952$		0			0
$953$	7.69660			0.249317			0.124659	−	0.992200i	$-0.460216\pi$
$953$	7.69660			0.249317			0.124659	+	0.992200i	$0.460216\pi$
$954$		0			0
$955$	−43.4711	−	25.0980i	−1.40669	−	0.812154i
$956$		0			0
$957$	−2.18728	+	1.26283i	−0.0707048	+	0.0408214i
$958$		0			0
$959$	29.4617	+	37.7784i	0.951367	+	1.21993i
$960$		0			0
$961$	−41.8919	−	72.5589i	−1.35135	−	2.34061i
$962$		0			0
$963$	8.41266	+	4.85705i	0.271094	+	0.156516i
$964$		0			0
$965$		−	2.79135i		−	0.0898568i
$966$		0			0
$967$	58.4850			1.88075			0.940375	−	0.340140i	$-0.110474\pi$
$967$	58.4850			1.88075			0.940375	+	0.340140i	$0.110474\pi$
$968$		0			0
$969$	−4.56811	+	7.91220i	−0.146749	+	0.254177i
$970$		0			0
$971$	−40.3828	+	23.3150i	−1.29595	+	0.748215i	−0.979701	−	0.200463i	$-0.935755\pi$
$971$	−40.3828	+	23.3150i	−1.29595	+	0.748215i	−0.316245	+	0.948678i	$0.602422\pi$
$972$		0			0
$973$	−20.4201	−	8.27137i	−0.654639	−	0.265168i
$974$		0			0
$975$	23.9907	+	41.5531i	0.768317	+	1.33076i
$976$		0			0
$977$	0.754805	−	1.30736i	0.0241484	−	0.0418262i	−0.853699	−	0.520767i	$-0.825646\pi$
$977$	0.754805	−	1.30736i	0.0241484	−	0.0418262i	0.877847	+	0.478941i	$0.158979\pi$
$978$		0			0
$979$		−	1.71534i		−	0.0548225i
$980$		0			0
$981$			14.2775i			0.455845i
$982$		0			0
$983$	11.0830	−	19.1964i	0.353494	−	0.612270i	−0.633365	−	0.773853i	$-0.718327\pi$
$983$	11.0830	−	19.1964i	0.353494	−	0.612270i	0.986859	+	0.161584i	$0.0516601\pi$
$984$		0			0
$985$	−4.25103	−	7.36301i	−0.135449	−	0.234605i
$986$		0			0
$987$	−16.7875	−	6.79993i	−0.534351	−	0.216444i
$988$		0			0
$989$	−9.07256	+	5.23805i	−0.288491	+	0.166560i
$990$		0			0
$991$	−28.9420	+	50.1291i	−0.919374	+	1.59240i	−0.119007	+	0.992893i	$0.537971\pi$
$991$	−28.9420	+	50.1291i	−0.919374	+	1.59240i	−0.800368	+	0.599510i	$0.795362\pi$
$992$		0			0
$993$	15.4318			0.489713
$994$		0			0
$995$		−	48.6000i		−	1.54072i
$996$		0			0
$997$	−44.1522	−	25.4913i	−1.39831	−	0.807317i	−0.404098	−	0.914716i	$-0.632414\pi$
$997$	−44.1522	−	25.4913i	−1.39831	−	0.807317i	−0.994216	+	0.107399i	$0.965748\pi$
$998$		0			0
$999$	−0.853618	−	1.47851i	−0.0270073	−	0.0467780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bk.a.529.1		32
3.2	odd	2		2016.2.cr.e.1873.16		32
4.3	odd	2		168.2.bc.a.109.15	yes	32
7.2	even	3	inner	672.2.bk.a.625.16		32
7.3	odd	6		4704.2.c.f.2353.8		16
7.4	even	3		4704.2.c.e.2353.9		16
8.3	odd	2		168.2.bc.a.109.7	yes	32
8.5	even	2	inner	672.2.bk.a.529.16		32
12.11	even	2		504.2.cj.e.109.2		32
21.2	odd	6		2016.2.cr.e.1297.1		32
24.5	odd	2		2016.2.cr.e.1873.1		32
24.11	even	2		504.2.cj.e.109.10		32
28.3	even	6		1176.2.c.f.589.6		16
28.11	odd	6		1176.2.c.e.589.6		16
28.23	odd	6		168.2.bc.a.37.7	✓	32
56.3	even	6		1176.2.c.f.589.5		16
56.11	odd	6		1176.2.c.e.589.5		16
56.37	even	6	inner	672.2.bk.a.625.1		32
56.45	odd	6		4704.2.c.f.2353.9		16
56.51	odd	6		168.2.bc.a.37.15	yes	32
56.53	even	6		4704.2.c.e.2353.8		16
84.23	even	6		504.2.cj.e.37.10		32
168.107	even	6		504.2.cj.e.37.2		32
168.149	odd	6		2016.2.cr.e.1297.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.7	✓	32	28.23	odd	6
168.2.bc.a.37.15	yes	32	56.51	odd	6
168.2.bc.a.109.7	yes	32	8.3	odd	2
168.2.bc.a.109.15	yes	32	4.3	odd	2
504.2.cj.e.37.2		32	168.107	even	6
504.2.cj.e.37.10		32	84.23	even	6
504.2.cj.e.109.2		32	12.11	even	2
504.2.cj.e.109.10		32	24.11	even	2
672.2.bk.a.529.1		32	1.1	even	1	trivial
672.2.bk.a.529.16		32	8.5	even	2	inner
672.2.bk.a.625.1		32	56.37	even	6	inner
672.2.bk.a.625.16		32	7.2	even	3	inner
1176.2.c.e.589.5		16	56.11	odd	6
1176.2.c.e.589.6		16	28.11	odd	6
1176.2.c.f.589.5		16	56.3	even	6
1176.2.c.f.589.6		16	28.3	even	6
2016.2.cr.e.1297.1		32	21.2	odd	6
2016.2.cr.e.1297.16		32	168.149	odd	6
2016.2.cr.e.1873.1		32	24.5	odd	2
2016.2.cr.e.1873.16		32	3.2	odd	2
4704.2.c.e.2353.8		16	56.53	even	6
4704.2.c.e.2353.9		16	7.4	even	3
4704.2.c.f.2353.8		16	7.3	odd	6
4704.2.c.f.2353.9		16	56.45	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bk (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-3.09843 + 1.78888i) q^{5} +(-0.993295 + 2.45222i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-3.09843 + 1.78888i) q^{5} +(-0.993295 + 2.45222i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-0.815768 - 0.470984i) q^{11} -6.15117i q^{13} +3.57776 q^{15} +(1.89187 - 3.27682i) q^{17} +(2.09110 - 1.20730i) q^{19} +(2.08633 - 1.62703i) q^{21} +(1.49371 + 2.58719i) q^{23} +(3.90019 - 6.75532i) q^{25} -1.00000i q^{27} +2.68125i q^{29} +(5.35686 - 9.27835i) q^{31} +(0.470984 + 0.815768i) q^{33} +(-1.30906 - 9.37491i) q^{35} +(1.47851 - 0.853618i) q^{37} +(-3.07558 + 5.32707i) q^{39} -4.56000 q^{41} +3.50672i q^{43} +(-3.09843 - 1.78888i) q^{45} +(-3.42292 - 5.92866i) q^{47} +(-5.02673 - 4.87155i) q^{49} +(-3.27682 + 1.89187i) q^{51} +(-6.57466 - 3.79588i) q^{53} +3.37013 q^{55} -2.41460 q^{57} +(0.100623 + 0.0580947i) q^{59} +(7.06184 - 4.07716i) q^{61} +(-2.62033 + 0.365889i) q^{63} +(11.0037 + 19.0590i) q^{65} +(-3.44314 - 1.98790i) q^{67} -2.98743i q^{69} +3.92572 q^{71} +(-3.11438 + 5.39427i) q^{73} +(-6.75532 + 3.90019i) q^{75} +(1.96525 - 1.53261i) q^{77} +(-2.73628 - 4.73937i) q^{79} +(-0.500000 + 0.866025i) q^{81} -1.19560i q^{83} +13.5373i q^{85} +(1.34063 - 2.32203i) q^{87} +(0.910509 + 1.57705i) q^{89} +(15.0840 + 6.10992i) q^{91} +(-9.27835 + 5.35686i) q^{93} +(-4.31942 + 7.48146i) q^{95} +12.0241 q^{97} -0.941967i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^9	\( 32 q + 16 q^{9} + 8 q^{23} + 16 q^{25} + 24 q^{31} + 24 q^{47} + 8 q^{49} + 64 q^{55} - 16 q^{57} + 80 q^{71} + 8 q^{73} - 8 q^{79} - 16 q^{81} - 24 q^{87} - 24 q^{95} - 48 q^{97}+O(q^{100}) \) 32 * q + 16 * q^9 + 8 * q^23 + 16 * q^25 + 24 * q^31 + 24 * q^47 + 8 * q^49 + 64 * q^55 - 16 * q^57 + 80 * q^71 + 8 * q^73 - 8 * q^79 - 16 * q^81 - 24 * q^87 - 24 * q^95 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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