LMFDB - Embedded newform 900.2.be.f.857.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(257,900)] 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("900.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 10, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0,0,0,0,-12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			857.7
Character	$\chi$	$=$	900.857
Dual form			900.2.be.f.293.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.45262 - 0.943342i) q^{3} +(0.349759 - 0.0937177i) q^{7} +(1.22021 - 2.74064i) q^{9} +(3.66769 + 2.11754i) q^{11} +(0.817828 + 0.219136i) q^{13} +(0.443477 - 0.443477i) q^{17} -2.85410i q^{19} +(0.419659 - 0.466079i) q^{21} +(-0.262645 + 0.980206i) q^{23} +(-0.812857 - 5.13218i) q^{27} +(0.511841 - 0.886534i) q^{29} +(4.24803 + 7.35780i) q^{31} +(7.32532 - 0.383904i) q^{33} +(-4.97633 - 4.97633i) q^{37} +(1.39471 - 0.453170i) q^{39} +(8.74911 - 5.05130i) q^{41} +(-2.75637 - 10.2869i) q^{43} +(-2.03279 - 7.58648i) q^{47} +(-5.94863 + 3.43444i) q^{49} +(0.225853 - 1.06255i) q^{51} +(7.52500 + 7.52500i) q^{53} +(-2.69240 - 4.14593i) q^{57} +(6.10629 + 10.5764i) q^{59} +(-5.68247 + 9.84233i) q^{61} +(0.169933 - 1.07292i) q^{63} +(0.761142 - 2.84062i) q^{67} +(0.543146 + 1.67163i) q^{69} -2.71873i q^{71} +(2.35741 - 2.35741i) q^{73} +(1.48126 + 0.396902i) q^{77} +(-6.28431 - 3.62825i) q^{79} +(-6.02218 - 6.68830i) q^{81} +(-14.4405 + 3.86932i) q^{83} +(-0.0927953 - 1.77064i) q^{87} -3.50111 q^{89} +0.306580 q^{91} +(13.1117 + 6.68074i) q^{93} +(-5.86166 + 1.57063i) q^{97} +(10.2788 - 7.46795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 12 q^{11} + 12 q^{21} + 8 q^{31} + 60 q^{41} + 36 q^{51} + 52 q^{61} - 36 q^{81} + 120 q^{91}+O(q^{100}) $ 32 * q - 12 * q^11 + 12 * q^21 + 8 * q^31 + 60 * q^41 + 36 * q^51 + 52 * q^61 - 36 * q^81 + 120 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	1.45262	−	0.943342i	0.838671	−	0.544639i
$3$	1.45262	−	0.943342i	0.838671	−	0.544639i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.349759	−	0.0937177i	0.132196	−	0.0354219i	−0.192114	−	0.981373i	$-0.561534\pi$
$7$	0.349759	−	0.0937177i	0.132196	−	0.0354219i	0.324311	+	0.945951i	$0.394868\pi$
$8$		0			0
$9$	1.22021	−	2.74064i	0.406737	−	0.913545i
$10$		0			0
$11$	3.66769	+	2.11754i	1.10585	+	0.638462i	0.937751	−	0.347308i	$-0.112904\pi$
$11$	3.66769	+	2.11754i	1.10585	+	0.638462i	0.168098	+	0.985770i	$0.446237\pi$
$12$		0			0
$13$	0.817828	+	0.219136i	0.226825	+	0.0607775i	0.370441	−	0.928856i	$-0.379207\pi$
$13$	0.817828	+	0.219136i	0.226825	+	0.0607775i	−0.143616	+	0.989633i	$0.545873\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.443477	−	0.443477i	0.107559	−	0.107559i	−0.651279	−	0.758838i	$-0.725767\pi$
$17$	0.443477	−	0.443477i	0.107559	−	0.107559i	0.758838	+	0.651279i	$0.225767\pi$
$18$		0			0
$19$		−	2.85410i		−	0.654776i	−0.944890	−	0.327388i	$-0.893832\pi$
$19$		−	2.85410i		−	0.654776i	0.944890	−	0.327388i	$-0.106168\pi$
$20$		0			0
$21$	0.419659	−	0.466079i	0.0915771	−	0.101707i
$22$		0			0
$23$	−0.262645	+	0.980206i	−0.0547653	+	0.204387i	−0.987887	−	0.155173i	$-0.950407\pi$
$23$	−0.262645	+	0.980206i	−0.0547653	+	0.204387i	0.933122	+	0.359560i	$0.117073\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.812857	−	5.13218i	−0.156434	−	0.987688i
$28$		0			0
$29$	0.511841	−	0.886534i	0.0950465	−	0.164625i	−0.814582	−	0.580049i	$-0.803033\pi$
$29$	0.511841	−	0.886534i	0.0950465	−	0.164625i	0.909628	+	0.415424i	$0.136367\pi$
$30$		0			0
$31$	4.24803	+	7.35780i	0.762968	+	1.32150i	0.941314	+	0.337532i	$0.109592\pi$
$31$	4.24803	+	7.35780i	0.762968	+	1.32150i	−0.178346	+	0.983968i	$0.557075\pi$
$32$		0			0
$33$	7.32532	−	0.383904i	1.27517	−	0.0668291i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.97633	−	4.97633i	−0.818104	−	0.818104i	0.167729	−	0.985833i	$-0.446357\pi$
$37$	−4.97633	−	4.97633i	−0.818104	−	0.818104i	−0.985833	+	0.167729i	$0.946357\pi$
$38$		0			0
$39$	1.39471	−	0.453170i	0.223333	−	0.0725653i
$40$		0			0
$41$	8.74911	−	5.05130i	1.36638	−	0.788880i	0.375917	−	0.926653i	$-0.377328\pi$
$41$	8.74911	−	5.05130i	1.36638	−	0.788880i	0.990464	+	0.137773i	$0.0439944\pi$
$42$		0			0
$43$	−2.75637	−	10.2869i	−0.420342	−	1.56874i	−0.773889	−	0.633322i	$-0.781691\pi$
$43$	−2.75637	−	10.2869i	−0.420342	−	1.56874i	0.353547	−	0.935417i	$-0.384976\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.03279	−	7.58648i	−0.296513	−	1.10660i	−0.940008	−	0.341152i	$-0.889183\pi$
$47$	−2.03279	−	7.58648i	−0.296513	−	1.10660i	0.643495	−	0.765450i	$-0.277484\pi$
$48$		0			0
$49$	−5.94863	+	3.43444i	−0.849804	+	0.490635i
$50$		0			0
$51$	0.225853	−	1.06255i	0.0316257	−	0.148787i
$52$		0			0
$53$	7.52500	+	7.52500i	1.03364	+	1.03364i	0.999414	+	0.0342238i	$0.0108959\pi$
$53$	7.52500	+	7.52500i	1.03364	+	1.03364i	0.0342238	+	0.999414i	$0.489104\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.69240	−	4.14593i	−0.356617	−	0.549141i
$58$		0			0
$59$	6.10629	+	10.5764i	0.794971	+	1.37693i	0.922858	+	0.385141i	$0.125847\pi$
$59$	6.10629	+	10.5764i	0.794971	+	1.37693i	−0.127887	+	0.991789i	$0.540820\pi$
$60$		0			0
$61$	−5.68247	+	9.84233i	−0.727566	+	1.26018i	0.230343	+	0.973109i	$0.426015\pi$
$61$	−5.68247	+	9.84233i	−0.727566	+	1.26018i	−0.957909	+	0.287072i	$0.907318\pi$
$62$		0			0
$63$	0.169933	−	1.07292i	0.0214096	−	0.135175i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.761142	−	2.84062i	0.0929883	−	0.347037i	−0.903718	−	0.428127i	$-0.859174\pi$
$67$	0.761142	−	2.84062i	0.0929883	−	0.347037i	0.996707	+	0.0810902i	$0.0258402\pi$
$68$		0			0
$69$	0.543146	+	1.67163i	0.0653871	+	0.201241i
$70$		0			0
$71$		−	2.71873i		−	0.322654i	−0.986901	−	0.161327i	$-0.948423\pi$
$71$		−	2.71873i		−	0.322654i	0.986901	−	0.161327i	$-0.0515773\pi$
$72$		0			0
$73$	2.35741	−	2.35741i	0.275914	−	0.275914i	−0.555561	−	0.831475i	$-0.687497\pi$
$73$	2.35741	−	2.35741i	0.275914	−	0.275914i	0.831475	+	0.555561i	$0.187497\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.48126	+	0.396902i	0.168805	+	0.0452312i
$78$		0			0
$79$	−6.28431	−	3.62825i	−0.707040	−	0.408210i	0.102924	−	0.994689i	$-0.467180\pi$
$79$	−6.28431	−	3.62825i	−0.707040	−	0.408210i	−0.809964	+	0.586479i	$0.800514\pi$
$80$		0			0
$81$	−6.02218	−	6.68830i	−0.669131	−	0.743145i
$82$		0			0
$83$	−14.4405	+	3.86932i	−1.58505	+	0.424713i	−0.940485	−	0.339834i	$-0.889629\pi$
$83$	−14.4405	+	3.86932i	−1.58505	+	0.424713i	−0.644567	+	0.764548i	$0.722962\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.0927953	−	1.77064i	−0.00994870	−	0.189832i
$88$		0			0
$89$	−3.50111			−0.371116			−0.185558	−	0.982633i	$-0.559409\pi$
$89$	−3.50111			−0.371116			−0.185558	+	0.982633i	$0.559409\pi$
$90$		0			0
$91$	0.306580			0.0321383
$92$		0			0
$93$	13.1117	+	6.68074i	1.35962	+	0.692761i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.86166	+	1.57063i	−0.595161	+	0.159473i	−0.543811	−	0.839208i	$-0.683019\pi$
$97$	−5.86166	+	1.57063i	−0.595161	+	0.159473i	−0.0513503	+	0.998681i	$0.516353\pi$
$98$		0			0
$99$	10.2788	−	7.46795i	1.03305	−	0.750558i
$100$		0			0
$101$	7.97102	+	4.60207i	0.793146	+	0.457923i	0.841069	−	0.540928i	$-0.181927\pi$
$101$	7.97102	+	4.60207i	0.793146	+	0.457923i	−0.0479231	+	0.998851i	$0.515260\pi$
$102$		0			0
$103$	−14.7196	−	3.94411i	−1.45037	−	0.388625i	−0.554216	−	0.832373i	$-0.686982\pi$
$103$	−14.7196	−	3.94411i	−1.45037	−	0.388625i	−0.896152	+	0.443748i	$0.853649\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.0927119	+	0.0927119i	−0.00896280	+	0.00896280i	−0.711574	−	0.702611i	$-0.752017\pi$
$107$	−0.0927119	+	0.0927119i	−0.00896280	+	0.00896280i	0.702611	+	0.711574i	$0.252017\pi$
$108$		0			0
$109$			4.38761i			0.420257i	0.977674	+	0.210129i	$0.0673883\pi$
$109$			4.38761i			0.420257i	−0.977674	+	0.210129i	$0.932612\pi$
$110$		0			0
$111$	−11.9231	−	2.53433i	−1.13169	−	0.240548i
$112$		0			0
$113$	−2.12725	+	7.93899i	−0.200114	+	0.746837i	0.790769	+	0.612115i	$0.209681\pi$
$113$	−2.12725	+	7.93899i	−0.200114	+	0.746837i	−0.990883	+	0.134722i	$0.956986\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.59849	−	1.97398i	0.147781	−	0.182494i
$118$		0			0
$119$	0.113548	−	0.196672i	0.0104090	−	0.0180289i
$120$		0			0
$121$	3.46795	+	6.00667i	0.315269	+	0.546061i
$122$		0			0
$123$	7.94402	−	15.5910i	0.716288	−	1.40580i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	9.86606	+	9.86606i	0.875471	+	0.875471i	0.993062	−	0.117591i	$-0.0375172\pi$
$127$	9.86606	+	9.86606i	0.875471	+	0.875471i	−0.117591	+	0.993062i	$0.537517\pi$
$128$		0			0
$129$	−13.7080	−	12.3428i	−1.20692	−	1.08672i
$130$		0			0
$131$	13.4118	−	7.74329i	1.17179	−	0.676534i	0.217690	−	0.976018i	$-0.430148\pi$
$131$	13.4118	−	7.74329i	1.17179	−	0.676534i	0.954101	+	0.299483i	$0.0968143\pi$
$132$		0			0
$133$	−0.267480	−	0.998248i	−0.0231934	−	0.0865591i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.89739	+	14.5453i	0.332977	+	1.24269i	0.906046	+	0.423179i	$0.139086\pi$
$137$	3.89739	+	14.5453i	0.332977	+	1.24269i	−0.573070	+	0.819507i	$0.694248\pi$
$138$		0			0
$139$	2.19342	−	1.26637i	0.186043	−	0.107412i	−0.404086	−	0.914721i	$-0.632410\pi$
$139$	2.19342	−	1.26637i	0.186043	−	0.107412i	0.590129	+	0.807309i	$0.299077\pi$
$140$		0			0
$141$	−10.1095	−	9.10265i	−0.851375	−	0.766582i
$142$		0			0
$143$	2.53551	+	2.53551i	0.212030	+	0.212030i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.40124	+	10.6005i	−0.445487	+	0.874317i
$148$		0			0
$149$	6.25871	+	10.8404i	0.512733	+	0.888080i	0.999891	+	0.0147659i	$0.00470032\pi$
$149$	6.25871	+	10.8404i	0.512733	+	0.888080i	−0.487158	+	0.873314i	$0.661966\pi$
$150$		0			0
$151$	−3.73432	+	6.46804i	−0.303895	+	0.526361i	−0.977015	−	0.213172i	$-0.931621\pi$
$151$	−3.73432	+	6.46804i	−0.303895	+	0.526361i	0.673120	+	0.739533i	$0.264954\pi$
$152$		0			0
$153$	−0.674274	−	1.75654i	−0.0545118	−	0.142008i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.67663	+	13.7214i	−0.293427	+	1.09509i	0.649031	+	0.760762i	$0.275174\pi$
$157$	−3.67663	+	13.7214i	−0.293427	+	1.09509i	−0.942458	+	0.334323i	$0.891492\pi$
$158$		0			0
$159$	18.0296	+	3.83231i	1.42984	+	0.303922i
$160$		0			0
$161$			0.367450i			0.0289591i
$162$		0			0
$163$	0.845478	−	0.845478i	0.0662229	−	0.0662229i	−0.673220	−	0.739443i	$-0.735089\pi$
$163$	0.845478	−	0.845478i	0.0662229	−	0.0662229i	0.739443	+	0.673220i	$0.235089\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	21.8840	+	5.86380i	1.69343	+	0.453754i	0.971272	−	0.237971i	$-0.0764823\pi$
$167$	21.8840	+	5.86380i	1.69343	+	0.453754i	0.722161	+	0.691725i	$0.243149\pi$
$168$		0			0
$169$	−10.6375	−	6.14157i	−0.818270	−	0.472428i
$170$		0			0
$171$	−7.82206	−	3.48260i	−0.598168	−	0.266321i
$172$		0			0
$173$	−18.4716	+	4.94946i	−1.40437	+	0.376300i	−0.879912	−	0.475136i	$-0.842399\pi$
$173$	−18.4716	+	4.94946i	−1.40437	+	0.376300i	−0.524459	+	0.851436i	$0.675732\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	18.8473	+	9.60317i	1.41665	+	0.721818i
$178$		0			0
$179$	−8.34494			−0.623730			−0.311865	−	0.950126i	$-0.600954\pi$
$179$	−8.34494			−0.623730			−0.311865	+	0.950126i	$0.600954\pi$
$180$		0			0
$181$	−10.9499			−0.813901			−0.406951	−	0.913450i	$-0.633408\pi$
$181$	−10.9499			−0.813901			−0.406951	+	0.913450i	$0.633408\pi$
$182$		0			0
$183$	1.03022	+	19.6577i	0.0761557	+	1.45314i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.56561	−	0.687454i	0.187616	−	0.0502716i
$188$		0			0
$189$	−0.765280	−	1.71885i	−0.0556659	−	0.125028i
$190$		0			0
$191$	−13.7169	−	7.91945i	−0.992519	−	0.573031i	−0.0864928	−	0.996252i	$-0.527566\pi$
$191$	−13.7169	−	7.91945i	−0.992519	−	0.573031i	−0.906026	+	0.423221i	$0.860899\pi$
$192$		0			0
$193$	−15.5248	−	4.15986i	−1.11750	−	0.299433i	−0.347629	−	0.937632i	$-0.613013\pi$
$193$	−15.5248	−	4.15986i	−1.11750	−	0.299433i	−0.769871	+	0.638199i	$0.779680\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−17.5320	+	17.5320i	−1.24910	+	1.24910i	−0.292986	+	0.956117i	$0.594649\pi$
$197$	−17.5320	+	17.5320i	−1.24910	+	1.24910i	−0.956117	+	0.292986i	$0.905351\pi$
$198$		0			0
$199$		−	4.00216i		−	0.283705i	−0.989888	−	0.141853i	$-0.954694\pi$
$199$		−	4.00216i		−	0.283705i	0.989888	−	0.141853i	$-0.0453059\pi$
$200$		0			0
$201$	−1.57403	−	4.84436i	−0.111023	−	0.341695i
$202$		0			0
$203$	0.0959371	−	0.358042i	0.00673346	−	0.0251296i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.36591	+	1.91587i	0.164442	+	0.133162i
$208$		0			0
$209$	6.04368	−	10.4680i	0.418050	−	0.724083i
$210$		0			0
$211$	−2.30619	−	3.99444i	−0.158765	−	0.274989i	0.775659	−	0.631153i	$-0.217418\pi$
$211$	−2.30619	−	3.99444i	−0.158765	−	0.274989i	−0.934424	+	0.356164i	$0.884085\pi$
$212$		0			0
$213$	−2.56469	−	3.94928i	−0.175730	−	0.270600i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.17534	+	2.17534i	0.147672	+	0.147672i
$218$		0			0
$219$	1.20058	−	5.64827i	0.0811274	−	0.381675i
$220$		0			0
$221$	0.459870	−	0.265506i	0.0309342	−	0.0178599i
$222$		0			0
$223$	−2.93579	−	10.9565i	−0.196595	−	0.733703i	−0.991848	−	0.127425i	$-0.959329\pi$
$223$	−2.93579	−	10.9565i	−0.196595	−	0.733703i	0.795253	−	0.606278i	$-0.207338\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.04978	−	18.8460i	−0.335165	−	1.25085i	−0.903690	−	0.428188i	$-0.859152\pi$
$227$	−5.04978	−	18.8460i	−0.335165	−	1.25085i	0.568524	−	0.822667i	$-0.307515\pi$
$228$		0			0
$229$	−9.00807	+	5.20081i	−0.595270	+	0.343679i	−0.767179	−	0.641434i	$-0.778340\pi$
$229$	−9.00807	+	5.20081i	−0.595270	+	0.343679i	0.171908	+	0.985113i	$0.445007\pi$
$230$		0			0
$231$	2.52612	−	0.820786i	0.166206	−	0.0540037i
$232$		0			0
$233$	18.6324	+	18.6324i	1.22065	+	1.22065i	0.967402	+	0.253245i	$0.0814980\pi$
$233$	18.6324	+	18.6324i	1.22065	+	1.22065i	0.253245	+	0.967402i	$0.418502\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−12.5514	+	0.657791i	−0.815301	+	0.0427281i
$238$		0			0
$239$	11.2711	+	19.5222i	0.729069	+	1.26278i	0.957277	+	0.289172i	$0.0933800\pi$
$239$	11.2711	+	19.5222i	0.729069	+	1.26278i	−0.228208	+	0.973612i	$0.573287\pi$
$240$		0			0
$241$	−8.47496	+	14.6791i	−0.545920	+	0.945561i	0.452628	+	0.891699i	$0.350486\pi$
$241$	−8.47496	+	14.6791i	−0.545920	+	0.945561i	−0.998548	+	0.0538621i	$0.982847\pi$
$242$		0			0
$243$	−15.0573	−	4.03459i	−0.965926	−	0.258819i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.625438	−	2.33416i	0.0397956	−	0.148519i
$248$		0			0
$249$	−17.3265	+	19.2430i	−1.09802	+	1.21948i
$250$		0			0
$251$		−	20.0265i		−	1.26406i	−0.774943	−	0.632031i	$-0.782222\pi$
$251$		−	20.0265i		−	1.26406i	0.774943	−	0.632031i	$-0.217778\pi$
$252$		0			0
$253$	−3.03893	+	3.03893i	−0.191056	+	0.191056i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.0479	+	2.69234i	0.626773	+	0.167943i	0.558205	−	0.829703i	$-0.311490\pi$
$257$	10.0479	+	2.69234i	0.626773	+	0.167943i	0.0685683	+	0.997646i	$0.478157\pi$
$258$		0			0
$259$	−2.20689	−	1.27415i	−0.137129	−	0.0791717i
$260$		0			0
$261$	−1.80512	−	2.48453i	−0.111734	−	0.153788i
$262$		0			0
$263$	−16.2798	+	4.36216i	−1.00386	+	0.268982i	−0.723060	−	0.690785i	$-0.757265\pi$
$263$	−16.2798	+	4.36216i	−1.00386	+	0.268982i	−0.280796	+	0.959767i	$0.590598\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.08578	+	3.30274i	−0.311244	+	0.202125i
$268$		0			0
$269$	−10.2671			−0.625995			−0.312998	−	0.949754i	$-0.601333\pi$
$269$	−10.2671			−0.625995			−0.312998	+	0.949754i	$0.601333\pi$
$270$		0			0
$271$	−7.86673			−0.477870			−0.238935	−	0.971036i	$-0.576798\pi$
$271$	−7.86673			−0.477870			−0.238935	+	0.971036i	$0.576798\pi$
$272$		0			0
$273$	0.445344	−	0.289210i	0.0269534	−	0.0175038i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−12.4729	+	3.34209i	−0.749421	+	0.200807i	−0.613261	−	0.789880i	$-0.710143\pi$
$277$	−12.4729	+	3.34209i	−0.749421	+	0.200807i	−0.136160	+	0.990687i	$0.543476\pi$
$278$		0			0
$279$	25.3485	−	2.66424i	1.51758	−	0.159504i
$280$		0			0
$281$	−0.778091	−	0.449231i	−0.0464170	−	0.0267989i	0.476612	−	0.879114i	$-0.341865\pi$
$281$	−0.778091	−	0.449231i	−0.0464170	−	0.0267989i	−0.523029	+	0.852315i	$0.675198\pi$
$282$		0			0
$283$	4.88814	+	1.30977i	0.290570	+	0.0778580i	0.401160	−	0.916008i	$-0.368607\pi$
$283$	4.88814	+	1.30977i	0.290570	+	0.0778580i	−0.110590	+	0.993866i	$0.535274\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.58668	−	2.58668i	0.152687	−	0.152687i
$288$		0			0
$289$			16.6067i			0.976862i
$290$		0			0
$291$	−7.03312	+	7.81108i	−0.412289	+	0.457893i
$292$		0			0
$293$	6.81992	−	25.4523i	0.398424	−	1.48694i	−0.417445	−	0.908702i	$-0.637074\pi$
$293$	6.81992	−	25.4523i	0.398424	−	1.48694i	0.815869	−	0.578237i	$-0.196259\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	7.88629	−	20.5445i	0.457609	−	1.19211i
$298$		0			0
$299$	−0.429597	+	0.744085i	−0.0248443	+	0.0430315i
$300$		0			0
$301$	−1.92813	−	3.33962i	−0.111136	−	0.192492i
$302$		0			0
$303$	15.9202	−	0.834341i	0.914591	−	0.0479317i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−0.731912	−	0.731912i	−0.0417724	−	0.0417724i	0.685912	−	0.727684i	$-0.259403\pi$
$307$	−0.731912	−	0.731912i	−0.0417724	−	0.0417724i	−0.727684	+	0.685912i	$0.759403\pi$
$308$		0			0
$309$	−25.1027	+	8.15635i	−1.42804	+	0.463999i
$310$		0			0
$311$	−14.1899	+	8.19252i	−0.804633	+	0.464555i	−0.845089	−	0.534626i	$-0.820452\pi$
$311$	−14.1899	+	8.19252i	−0.804633	+	0.464555i	0.0404554	+	0.999181i	$0.487119\pi$
$312$		0			0
$313$	2.62294	+	9.78893i	0.148257	+	0.553303i	0.999589	+	0.0286753i	$0.00912888\pi$
$313$	2.62294	+	9.78893i	0.148257	+	0.553303i	−0.851332	+	0.524628i	$0.824204\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.759869	+	2.83587i	0.0426785	+	0.159278i	0.983976	−	0.178299i	$-0.0570593\pi$
$317$	0.759869	+	2.83587i	0.0426785	+	0.159278i	−0.941298	+	0.337577i	$0.890393\pi$
$318$		0			0
$319$	3.75454	−	2.16769i	0.210214	−	0.121367i
$320$		0			0
$321$	−0.0472161	+	0.222134i	−0.00263534	+	0.0123983i
$322$		0			0
$323$	−1.26573	−	1.26573i	−0.0704270	−	0.0704270i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	4.13902	+	6.37353i	0.228888	+	0.352457i
$328$		0			0
$329$	−1.42197	−	2.46293i	−0.0783960	−	0.135786i
$330$		0			0
$331$	16.0229	−	27.7524i	0.880696	−	1.52541i	0.0301284	−	0.999546i	$-0.490408\pi$
$331$	16.0229	−	27.7524i	0.880696	−	1.52541i	0.850568	−	0.525865i	$-0.176258\pi$
$332$		0			0
$333$	−19.7105	+	7.56615i	−1.08013	+	0.414622i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.19941	−	4.47628i	0.0653363	−	0.243838i	−0.925532	−	0.378668i	$-0.876382\pi$
$337$	1.19941	−	4.47628i	0.0653363	−	0.243838i	0.990869	+	0.134830i	$0.0430488\pi$
$338$		0			0
$339$	4.39910	+	13.5391i	0.238927	+	0.735340i
$340$		0			0
$341$			35.9815i			1.94851i
$342$		0			0
$343$	−3.55101	+	3.55101i	−0.191736	+	0.191736i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.8128	−	3.70113i	−0.741511	−	0.198687i	−0.131761	−	0.991281i	$-0.542063\pi$
$347$	−13.8128	−	3.70113i	−0.741511	−	0.198687i	−0.609749	+	0.792594i	$0.708730\pi$
$348$		0			0
$349$	26.8777	+	15.5178i	1.43873	+	0.830651i	0.997762	−	0.0668713i	$-0.0213017\pi$
$349$	26.8777	+	15.5178i	1.43873	+	0.830651i	0.440969	+	0.897523i	$0.354635\pi$
$350$		0			0
$351$	0.459870	−	4.37537i	0.0245460	−	0.233540i
$352$		0			0
$353$	−6.35852	+	1.70376i	−0.338430	+	0.0906819i	−0.424031	−	0.905647i	$-0.639385\pi$
$353$	−6.35852	+	1.70376i	−0.338430	+	0.0906819i	0.0856018	+	0.996329i	$0.472719\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.0205860	−	0.392804i	−0.00108953	−	0.0207894i
$358$		0			0
$359$	−21.5812			−1.13901			−0.569506	−	0.821987i	$-0.692865\pi$
$359$	−21.5812			−1.13901			−0.569506	+	0.821987i	$0.692865\pi$
$360$		0			0
$361$	10.8541			0.571269
$362$		0			0
$363$	10.7040	+	5.45394i	0.561813	+	0.286258i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	28.5467	−	7.64906i	1.49012	−	0.399278i	0.580345	−	0.814371i	$-0.302918\pi$
$367$	28.5467	−	7.64906i	1.49012	−	0.399278i	0.909779	+	0.415093i	$0.136251\pi$
$368$		0			0
$369$	−3.16803	−	30.1418i	−0.164921	−	1.56912i
$370$		0			0
$371$	3.33716	+	1.92671i	0.173257	+	0.100030i
$372$		0			0
$373$	29.6506	+	7.94485i	1.53525	+	0.411369i	0.924727	−	0.380631i	$-0.124293\pi$
$373$	29.6506	+	7.94485i	1.53525	+	0.411369i	0.610522	+	0.791999i	$0.290960\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.612870	−	0.612870i	0.0315644	−	0.0315644i
$378$		0			0
$379$		−	27.4359i		−	1.40929i	−0.709560	−	0.704645i	$-0.751106\pi$
$379$		−	27.4359i		−	1.40929i	0.709560	−	0.704645i	$-0.248894\pi$
$380$		0			0
$381$	23.6387	+	5.02456i	1.21105	+	0.257416i
$382$		0			0
$383$	4.66313	−	17.4030i	0.238275	−	0.889253i	−0.738371	−	0.674395i	$-0.764404\pi$
$383$	4.66313	−	17.4030i	0.238275	−	0.889253i	0.976645	−	0.214858i	$-0.0689289\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−31.5560	−	4.99798i	−1.60408	−	0.254062i
$388$		0			0
$389$	16.4239	−	28.4471i	0.832725	−	1.44232i	−0.0631434	−	0.998004i	$-0.520113\pi$
$389$	16.4239	−	28.4471i	0.832725	−	1.44232i	0.895869	−	0.444318i	$-0.146554\pi$
$390$		0			0
$391$	0.318221	+	0.551175i	0.0160931	+	0.0278741i
$392$		0			0
$393$	12.1776	−	23.9000i	0.614280	−	1.20559i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−22.4277	−	22.4277i	−1.12561	−	1.12561i	−0.990882	−	0.134729i	$-0.956984\pi$
$397$	−22.4277	−	22.4277i	−1.12561	−	1.12561i	−0.134729	−	0.990882i	$-0.543016\pi$
$398$		0			0
$399$	−1.33024	−	1.19775i	−0.0665951	−	0.0599625i
$400$		0			0
$401$	17.5401	−	10.1268i	0.875912	−	0.505708i	0.00660386	−	0.999978i	$-0.497898\pi$
$401$	17.5401	−	10.1268i	0.875912	−	0.505708i	0.869308	+	0.494270i	$0.164565\pi$
$402$		0			0
$403$	1.86179	+	6.94831i	0.0927426	+	0.346120i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.71405	−	28.7892i	−0.382371	−	1.42703i
$408$		0			0
$409$	3.50934	−	2.02612i	0.173526	−	0.100185i	−0.410722	−	0.911761i	$-0.634723\pi$
$409$	3.50934	−	2.02612i	0.173526	−	0.100185i	0.584247	+	0.811576i	$0.301390\pi$
$410$		0			0
$411$	19.3826	+	17.4522i	0.956073	+	0.860852i
$412$		0			0
$413$	3.12692	+	3.12692i	0.153866	+	0.153866i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.99158	−	3.90870i	0.0975281	−	0.191410i
$418$		0			0
$419$	−2.21902	−	3.84346i	−0.108406	−	0.187765i	0.806718	−	0.590936i	$-0.201241\pi$
$419$	−2.21902	−	3.84346i	−0.108406	−	0.187765i	−0.915125	+	0.403171i	$0.867908\pi$
$420$		0			0
$421$	7.06970	−	12.2451i	0.344556	−	0.596788i	−0.640717	−	0.767777i	$-0.721363\pi$
$421$	7.06970	−	12.2451i	0.344556	−	0.596788i	0.985273	+	0.170989i	$0.0546961\pi$
$422$		0			0
$423$	−23.2722	−	3.68596i	−1.13153	−	0.179217i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.06510	+	3.97499i	−0.0515436	+	0.192363i
$428$		0			0
$429$	6.07498	+	1.29128i	0.293303	+	0.0623434i
$430$		0			0
$431$			9.06378i			0.436587i	0.975883	+	0.218294i	$0.0700490\pi$
$431$			9.06378i			0.436587i	−0.975883	+	0.218294i	$0.929951\pi$
$432$		0			0
$433$	−6.33694	+	6.33694i	−0.304534	+	0.304534i	−0.842785	−	0.538251i	$-0.819085\pi$
$433$	−6.33694	+	6.33694i	−0.304534	+	0.304534i	0.538251	+	0.842785i	$0.319085\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.79761	+	0.749617i	0.133828	+	0.0358590i
$438$		0			0
$439$	−1.33899	−	0.773069i	−0.0639067	−	0.0368966i	0.467706	−	0.883884i	$-0.345081\pi$
$439$	−1.33899	−	0.773069i	−0.0639067	−	0.0368966i	−0.531613	+	0.846987i	$0.678414\pi$
$440$		0			0
$441$	2.15398	+	20.4938i	0.102571	+	0.975894i
$442$		0			0
$443$	22.2365	−	5.95825i	1.05649	−	0.283085i	0.311557	−	0.950227i	$-0.399149\pi$
$443$	22.2365	−	5.95825i	1.05649	−	0.283085i	0.744930	+	0.667142i	$0.232483\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	19.3177	+	9.84287i	0.913697	+	0.465552i
$448$		0			0
$449$	7.58683			0.358045			0.179022	−	0.983845i	$-0.442707\pi$
$449$	7.58683			0.358045			0.179022	+	0.983845i	$0.442707\pi$
$450$		0			0
$451$	42.7853			2.01468
$452$		0			0
$453$	0.677022	+	12.9183i	0.0318093	+	0.606957i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.54550	+	0.682064i	−0.119073	+	0.0319056i	−0.317864	−	0.948136i	$-0.602965\pi$
$457$	−2.54550	+	0.682064i	−0.119073	+	0.0319056i	0.198790	+	0.980042i	$0.436299\pi$
$458$		0			0
$459$	−2.63649	−	1.91552i	−0.123061	−	0.0894088i
$460$		0			0
$461$	−7.70782	−	4.45011i	−0.358989	−	0.207262i	0.309648	−	0.950851i	$-0.399789\pi$
$461$	−7.70782	−	4.45011i	−0.358989	−	0.207262i	−0.668637	+	0.743589i	$0.733122\pi$
$462$		0			0
$463$	31.1175	+	8.33790i	1.44615	+	0.387495i	0.894683	−	0.446701i	$-0.147401\pi$
$463$	31.1175	+	8.33790i	1.44615	+	0.387495i	0.551468	+	0.834196i	$0.314068\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.9540	+	10.9540i	−0.506891	+	0.506891i	−0.913571	−	0.406680i	$-0.866687\pi$
$467$	−10.9540	+	10.9540i	−0.506891	+	0.506891i	0.406680	+	0.913571i	$0.366687\pi$
$468$		0			0
$469$		−	1.06486i		−	0.0491709i
$470$		0			0
$471$	7.60321	+	23.4003i	0.350337	+	1.07823i
$472$		0			0
$473$	11.6734	−	43.5659i	0.536745	−	2.00316i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	29.8054	−	11.4412i	1.36469	−	0.523857i
$478$		0			0
$479$	6.16179	−	10.6725i	0.281539	−	0.487641i	−0.690225	−	0.723595i	$-0.742488\pi$
$479$	6.16179	−	10.6725i	0.281539	−	0.487641i	0.971764	+	0.235955i	$0.0758216\pi$
$480$		0			0
$481$	−2.97929	−	5.16028i	−0.135844	−	0.235289i
$482$		0			0
$483$	0.346632	+	0.533766i	0.0157723	+	0.0242872i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	14.7058	+	14.7058i	0.666383	+	0.666383i	0.956877	−	0.290494i	$-0.0938196\pi$
$487$	14.7058	+	14.7058i	0.666383	+	0.666383i	−0.290494	+	0.956877i	$0.593820\pi$
$488$		0			0
$489$	0.430583	−	2.02573i	0.0194716	−	0.0916068i
$490$		0			0
$491$	−26.3427	+	15.2089i	−1.18883	+	0.686370i	−0.958040	−	0.286634i	$-0.907464\pi$
$491$	−26.3427	+	15.2089i	−1.18883	+	0.686370i	−0.230787	+	0.973004i	$0.574130\pi$
$492$		0			0
$493$	−0.166168	−	0.620147i	−0.00748382	−	0.0279300i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.254793	−	0.950900i	−0.0114290	−	0.0426537i
$498$		0			0
$499$	9.76122	−	5.63564i	0.436972	−	0.252286i	−0.265340	−	0.964155i	$-0.585484\pi$
$499$	9.76122	−	5.63564i	0.436972	−	0.252286i	0.702312	+	0.711869i	$0.252151\pi$
$500$		0			0
$501$	37.3207	−	12.1262i	1.66736	−	0.541760i
$502$		0			0
$503$	10.7406	+	10.7406i	0.478899	+	0.478899i	0.904779	−	0.425881i	$-0.140036\pi$
$503$	10.7406	+	10.7406i	0.478899	+	0.478899i	−0.425881	+	0.904779i	$0.640036\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−21.2459	+	1.11345i	−0.943562	+	0.0494500i
$508$		0			0
$509$	−8.89519	−	15.4069i	−0.394272	−	0.682900i	0.598736	−	0.800947i	$-0.295670\pi$
$509$	−8.89519	−	15.4069i	−0.394272	−	0.682900i	−0.993008	+	0.118047i	$0.962337\pi$
$510$		0			0
$511$	0.603595	−	1.04546i	0.0267015	−	0.0462483i
$512$		0			0
$513$	−14.6478	+	2.31998i	−0.646715	+	0.102430i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	8.60903	−	32.1294i	0.378625	−	1.41305i
$518$		0			0
$519$	−22.1632	+	24.6147i	−0.972857	+	1.08047i
$520$		0			0
$521$			7.18091i			0.314601i	0.987551	+	0.157301i	$0.0502792\pi$
$521$			7.18091i			0.314601i	−0.987551	+	0.157301i	$0.949721\pi$
$522$		0			0
$523$	19.7187	−	19.7187i	0.862240	−	0.862240i	−0.129358	−	0.991598i	$-0.541292\pi$
$523$	19.7187	−	19.7187i	0.862240	−	0.862240i	0.991598	+	0.129358i	$0.0412916\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.14691	+	1.37911i	0.224203	+	0.0600750i
$528$		0			0
$529$	19.0268	+	10.9851i	0.827251	+	0.477613i
$530$		0			0
$531$	36.4370	−	3.82968i	1.58123	−	0.166194i
$532$		0			0
$533$	8.26219	−	2.21385i	0.357875	−	0.0958923i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−12.1220	+	7.87214i	−0.523104	+	0.339708i
$538$		0			0
$539$	−29.0903			−1.25301
$540$		0			0
$541$	−36.2098			−1.55678			−0.778390	−	0.627781i	$-0.783963\pi$
$541$	−36.2098			−1.55678			−0.778390	+	0.627781i	$0.783963\pi$
$542$		0			0
$543$	−15.9061	+	10.3295i	−0.682595	+	0.443282i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−11.5435	+	3.09306i	−0.493562	+	0.132250i	−0.497011	−	0.867744i	$-0.665569\pi$
$547$	−11.5435	+	3.09306i	−0.493562	+	0.132250i	0.00344834	+	0.999994i	$0.498902\pi$
$548$		0			0
$549$	20.0404	+	27.5833i	0.855305	+	1.17723i
$550$		0			0
$551$	−2.53026	−	1.46085i	−0.107793	−	0.0622341i
$552$		0			0
$553$	−2.53803	−	0.680062i	−0.107928	−	0.0289192i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.42031	−	7.42031i	0.314409	−	0.314409i	−0.532206	−	0.846615i	$-0.678637\pi$
$557$	7.42031	−	7.42031i	0.314409	−	0.314409i	0.846615	+	0.532206i	$0.178637\pi$
$558$		0			0
$559$		−	9.01694i		−	0.381376i
$560$		0			0
$561$	3.07836	−	3.41886i	0.129968	−	0.144344i
$562$		0			0
$563$	6.13083	−	22.8806i	0.258383	−	0.964300i	−0.707793	−	0.706420i	$-0.750309\pi$
$563$	6.13083	−	22.8806i	0.258383	−	0.964300i	0.966177	−	0.257881i	$-0.0830241\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.73312	−	1.77491i	−0.114780	−	0.0745392i
$568$		0			0
$569$	19.9559	−	34.5646i	0.836593	−	1.44902i	−0.0561334	−	0.998423i	$-0.517877\pi$
$569$	19.9559	−	34.5646i	0.836593	−	1.44902i	0.892727	−	0.450599i	$-0.148789\pi$
$570$		0			0
$571$	−1.46164	−	2.53164i	−0.0611677	−	0.105946i	0.833820	−	0.552037i	$-0.186149\pi$
$571$	−1.46164	−	2.53164i	−0.0611677	−	0.105946i	−0.894988	+	0.446091i	$0.852816\pi$
$572$		0			0
$573$	−27.3962	+	1.43577i	−1.14449	+	0.0599803i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−14.0335	−	14.0335i	−0.584223	−	0.584223i	0.351838	−	0.936061i	$-0.385557\pi$
$577$	−14.0335	−	14.0335i	−0.584223	−	0.584223i	−0.936061	+	0.351838i	$0.885557\pi$
$578$		0			0
$579$	−26.4758	+	8.60252i	−1.10030	+	0.357508i
$580$		0			0
$581$	−4.68808	+	2.70666i	−0.194494	+	0.112291i
$582$		0			0
$583$	11.6649	+	43.5338i	0.483109	+	1.80299i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.8018	−	44.0450i	−0.487114	−	1.81793i	−0.570348	−	0.821403i	$-0.693192\pi$
$587$	−11.8018	−	44.0450i	−0.487114	−	1.81793i	0.0832347	−	0.996530i	$-0.473475\pi$
$588$		0			0
$589$	20.9999	−	12.1243i	0.865286	−	0.499573i
$590$		0			0
$591$	−8.92865	+	42.0060i	−0.367276	+	1.72790i
$592$		0			0
$593$	11.4862	+	11.4862i	0.471680	+	0.471680i	0.902458	−	0.430778i	$-0.141761\pi$
$593$	11.4862	+	11.4862i	0.471680	+	0.471680i	−0.430778	+	0.902458i	$0.641761\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.77540	−	5.81361i	−0.154517	−	0.237935i
$598$		0			0
$599$	10.8461	+	18.7860i	0.443160	+	0.767575i	0.997922	−	0.0644337i	$-0.0205241\pi$
$599$	10.8461	+	18.7860i	0.443160	+	0.767575i	−0.554762	+	0.832009i	$0.687191\pi$
$600$		0			0
$601$	17.6688	−	30.6032i	0.720724	−	1.24833i	−0.239986	−	0.970776i	$-0.577143\pi$
$601$	17.6688	−	30.6032i	0.720724	−	1.24833i	0.960710	−	0.277554i	$-0.0895238\pi$
$602$		0			0
$603$	−6.85635	−	5.55217i	−0.279212	−	0.226102i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−0.244062	+	0.910852i	−0.00990617	+	0.0369703i	−0.970702	−	0.240286i	$-0.922759\pi$
$607$	−0.244062	+	0.910852i	−0.00990617	+	0.0369703i	0.960796	+	0.277257i	$0.0894253\pi$
$608$		0			0
$609$	−0.198396	−	0.610600i	−0.00803942	−	0.0247428i
$610$		0			0
$611$		−	6.64989i		−	0.269026i
$612$		0			0
$613$	0.288873	−	0.288873i	0.0116675	−	0.0116675i	−0.701249	−	0.712916i	$-0.747374\pi$
$613$	0.288873	−	0.288873i	0.0116675	−	0.0116675i	0.712916	+	0.701249i	$0.247374\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−10.3841	−	2.78241i	−0.418048	−	0.112016i	0.0436626	−	0.999046i	$-0.486097\pi$
$617$	−10.3841	−	2.78241i	−0.418048	−	0.112016i	−0.461710	+	0.887031i	$0.652764\pi$
$618$		0			0
$619$	−19.6462	−	11.3428i	−0.789649	−	0.455904i	0.0501897	−	0.998740i	$-0.484017\pi$
$619$	−19.6462	−	11.3428i	−0.789649	−	0.455904i	−0.839839	+	0.542835i	$0.817351\pi$
$620$		0			0
$621$	5.24408	+	0.551175i	0.210438	+	0.0221179i
$622$		0			0
$623$	−1.22454	+	0.328115i	−0.0490603	+	0.0131457i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.09570	−	20.9072i	−0.0437581	−	0.834954i
$628$		0			0
$629$	−4.41378			−0.175989
$630$		0			0
$631$	19.9499			0.794194			0.397097	−	0.917777i	$-0.370018\pi$
$631$	19.9499			0.794194			0.397097	+	0.917777i	$0.370018\pi$
$632$		0			0
$633$	−7.11815	−	3.62688i	−0.282921	−	0.144156i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−5.61757	+	1.50522i	−0.222576	+	0.0596391i
$638$		0			0
$639$	−7.45105	−	3.31742i	−0.294759	−	0.131235i
$640$		0			0
$641$	−25.3896	−	14.6587i	−1.00283	−	0.578983i	−0.0937447	−	0.995596i	$-0.529884\pi$
$641$	−25.3896	−	14.6587i	−1.00283	−	0.578983i	−0.909084	+	0.416613i	$0.863217\pi$
$642$		0			0
$643$	−14.5444	−	3.89715i	−0.573574	−	0.153689i	−0.0396389	−	0.999214i	$-0.512621\pi$
$643$	−14.5444	−	3.89715i	−0.573574	−	0.153689i	−0.533935	+	0.845525i	$0.679287\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.8603	+	15.8603i	−0.623531	+	0.623531i	−0.946433	−	0.322901i	$-0.895342\pi$
$647$	−15.8603	+	15.8603i	−0.623531	+	0.623531i	0.322901	+	0.946433i	$0.395342\pi$
$648$		0			0
$649$			51.7212i			2.03024i
$650$		0			0
$651$	5.21204	+	1.10785i	0.204276	+	0.0434202i
$652$		0			0
$653$	5.87165	−	21.9133i	0.229775	−	0.857533i	−0.750659	−	0.660689i	$-0.770264\pi$
$653$	5.87165	−	21.9133i	0.229775	−	0.857533i	0.980435	−	0.196844i	$-0.0630692\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−3.58427	−	9.33734i	−0.139836	−	0.364284i
$658$		0			0
$659$	−9.73561	+	16.8626i	−0.379246	+	0.656873i	−0.990953	−	0.134212i	$-0.957150\pi$
$659$	−9.73561	+	16.8626i	−0.379246	+	0.656873i	0.611707	+	0.791084i	$0.290483\pi$
$660$		0			0
$661$	−17.0942	−	29.6081i	−0.664889	−	1.15162i	−0.979315	−	0.202340i	$-0.935146\pi$
$661$	−17.0942	−	29.6081i	−0.664889	−	1.15162i	0.314426	−	0.949282i	$-0.398188\pi$
$662$		0			0
$663$	0.417553	−	0.819494i	0.0162164	−	0.0318265i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.734553	+	0.734553i	0.0284420	+	0.0284420i
$668$		0			0
$669$	−14.6003	−	13.1462i	−0.564482	−	0.508262i
$670$		0			0
$671$	−41.6831	+	24.0657i	−1.60916	+	0.929047i
$672$		0			0
$673$	7.66046	+	28.5892i	0.295289	+	1.10203i	0.940988	+	0.338441i	$0.109900\pi$
$673$	7.66046	+	28.5892i	0.295289	+	1.10203i	−0.645699	+	0.763592i	$0.723434\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.50754	+	28.0185i	0.288538	+	1.07684i	0.946215	+	0.323539i	$0.104873\pi$
$677$	7.50754	+	28.0185i	0.288538	+	1.07684i	−0.657677	+	0.753300i	$0.728461\pi$
$678$		0			0
$679$	−1.90297	+	1.09868i	−0.0730294	+	0.0421635i
$680$		0			0
$681$	−25.1137	−	22.6124i	−0.962358	−	0.866511i
$682$		0			0
$683$	−19.6240	−	19.6240i	−0.750892	−	0.750892i	0.223754	−	0.974646i	$-0.428169\pi$
$683$	−19.6240	−	19.6240i	−0.750892	−	0.750892i	−0.974646	+	0.223754i	$0.928169\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−8.17916	+	16.0525i	−0.312054	+	0.612441i
$688$		0			0
$689$	4.50515	+	7.80316i	0.171633	+	0.297277i
$690$		0			0
$691$	1.96293	−	3.39990i	0.0746734	−	0.129338i	−0.826271	−	0.563273i	$-0.809542\pi$
$691$	1.96293	−	3.39990i	0.0746734	−	0.129338i	0.900944	+	0.433935i	$0.142875\pi$
$692$		0			0
$693$	2.89521	−	3.57529i	0.109980	−	0.135814i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.63989	−	6.12016i	0.0621153	−	0.231818i
$698$		0			0
$699$	44.6425	+	9.48905i	1.68853	+	0.358909i
$700$		0			0
$701$			22.9088i			0.865253i	0.901573	+	0.432627i	$0.142413\pi$
$701$			22.9088i			0.865253i	−0.901573	+	0.432627i	$0.857587\pi$
$702$		0			0
$703$	−14.2030	+	14.2030i	−0.535675	+	0.535675i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.21923	+	0.862590i	0.121072	+	0.0324410i
$708$		0			0
$709$	22.4427	+	12.9573i	0.842854	+	0.486622i	0.858233	−	0.513260i	$-0.171562\pi$
$709$	22.4427	+	12.9573i	0.842854	+	0.486622i	−0.0153793	+	0.999882i	$0.504896\pi$
$710$		0			0
$711$	−17.6119	+	12.7958i	−0.660498	+	0.479880i
$712$		0			0
$713$	−8.32788	+	2.23145i	−0.311882	+	0.0835684i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	34.7888	+	17.7258i	1.29921	+	0.661981i
$718$		0			0
$719$	−41.9600			−1.56484			−0.782422	−	0.622748i	$-0.786016\pi$
$719$	−41.9600			−1.56484			−0.782422	+	0.622748i	$0.786016\pi$
$720$		0			0
$721$	−5.51795			−0.205499
$722$		0			0
$723$	1.53649	+	29.3179i	0.0571425	+	1.09034i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	35.2940	−	9.45700i	1.30898	−	0.350741i	0.464142	−	0.885761i	$-0.346363\pi$
$727$	35.2940	−	9.45700i	1.30898	−	0.350741i	0.844839	+	0.535020i	$0.179696\pi$
$728$		0			0
$729$	−25.6785	+	8.34346i	−0.951057	+	0.309017i
$730$		0			0
$731$	−5.78439	−	3.33962i	−0.213943	−	0.123520i
$732$		0			0
$733$	20.5975	+	5.51909i	0.760787	+	0.203852i	0.618298	−	0.785944i	$-0.287823\pi$
$733$	20.5975	+	5.51909i	0.760787	+	0.203852i	0.142490	+	0.989796i	$0.454489\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.80676	−	8.80676i	0.324401	−	0.324401i
$738$		0			0
$739$			11.8977i			0.437663i	0.975763	+	0.218832i	$0.0702245\pi$
$739$			11.8977i			0.437663i	−0.975763	+	0.218832i	$0.929775\pi$
$740$		0			0
$741$	−1.29339	−	3.98066i	−0.0475140	−	0.146233i
$742$		0			0
$743$	−5.49496	+	20.5075i	−0.201591	+	0.752346i	0.788871	+	0.614559i	$0.210666\pi$
$743$	−5.49496	+	20.5075i	−0.201591	+	0.752346i	−0.990462	+	0.137788i	$0.956001\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−7.01605	+	44.2976i	−0.256704	+	1.62076i
$748$		0			0
$749$	−0.0237381	+	0.0411156i	−0.000867371	+	0.00150233i
$750$		0			0
$751$	−25.4044	−	44.0017i	−0.927019	−	1.60564i	−0.788281	−	0.615315i	$-0.789029\pi$
$751$	−25.4044	−	44.0017i	−0.927019	−	1.60564i	−0.138738	−	0.990329i	$-0.544304\pi$
$752$		0			0
$753$	−18.8918	−	29.0909i	−0.688457	−	1.06013i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	30.3660	+	30.3660i	1.10367	+	1.10367i	0.993964	+	0.109705i	$0.0349908\pi$
$757$	30.3660	+	30.3660i	1.10367	+	1.10367i	0.109705	+	0.993964i	$0.465009\pi$
$758$		0			0
$759$	−1.54766	+	7.28115i	−0.0561764	+	0.264289i
$760$		0			0
$761$	−2.14551	+	1.23871i	−0.0777747	+	0.0449033i	−0.538383	−	0.842700i	$-0.680965\pi$
$761$	−2.14551	+	1.23871i	−0.0777747	+	0.0449033i	0.460608	+	0.887604i	$0.347631\pi$
$762$		0			0
$763$	0.411197	+	1.53461i	0.0148863	+	0.0555565i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.67622	+	9.98778i	0.0966326	+	0.360638i
$768$		0			0
$769$	23.4800	−	13.5562i	0.846712	−	0.488849i	−0.0128282	−	0.999918i	$-0.504083\pi$
$769$	23.4800	−	13.5562i	0.846712	−	0.488849i	0.859540	+	0.511068i	$0.170750\pi$
$770$		0			0
$771$	17.1356	−	5.56771i	0.617125	−	0.200516i
$772$		0			0
$773$	−32.7753	−	32.7753i	−1.17885	−	1.17885i	−0.980038	−	0.198809i	$-0.936293\pi$
$773$	−32.7753	−	32.7753i	−1.17885	−	1.17885i	−0.198809	−	0.980038i	$-0.563707\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−4.40773	+	0.230999i	−0.158126	+	0.00828705i
$778$		0			0
$779$	−14.4169	−	24.9708i	−0.516540	−	0.894673i
$780$		0			0
$781$	5.75702	−	9.97145i	0.206002	−	0.356806i
$782$		0			0
$783$	−4.96591	−	1.90623i	−0.177467	−	0.0681232i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−7.48454	+	27.9327i	−0.266795	+	0.995693i	0.694347	+	0.719640i	$0.255693\pi$
$787$	−7.48454	+	27.9327i	−0.266795	+	0.995693i	−0.961142	+	0.276053i	$0.910973\pi$
$788$		0			0
$789$	−19.5334	+	21.6940i	−0.695406	+	0.772327i
$790$		0			0
$791$			2.97609i			0.105818i
$792$		0			0
$793$	−6.80410	+	6.80410i	−0.241621	+	0.241621i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.91209	−	1.58414i	−0.209417	−	0.0561131i	0.152585	−	0.988290i	$-0.451240\pi$
$797$	−5.91209	−	1.58414i	−0.209417	−	0.0561131i	−0.362002	+	0.932177i	$0.617907\pi$
$798$		0			0
$799$	−4.26592	−	2.46293i	−0.150917	−	0.0871323i
$800$		0			0
$801$	−4.27208	+	9.59526i	−0.150947	+	0.339032i
$802$		0			0
$803$	13.6382	−	3.65433i	0.481280	−	0.128959i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−14.9142	+	9.68538i	−0.525004	+	0.340941i
$808$		0			0
$809$	48.6392			1.71006			0.855032	−	0.518574i	$-0.173537\pi$
$809$	48.6392			1.71006			0.855032	+	0.518574i	$0.173537\pi$
$810$		0			0
$811$	−14.8894			−0.522838			−0.261419	−	0.965225i	$-0.584190\pi$
$811$	−14.8894			−0.522838			−0.261419	+	0.965225i	$0.584190\pi$
$812$		0			0
$813$	−11.4274	+	7.42102i	−0.400775	+	0.260267i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−29.3599	+	7.86696i	−1.02717	+	0.275230i
$818$		0			0
$819$	0.374092	−	0.840223i	0.0130718	−	0.0293598i
$820$		0			0
$821$	−13.5079	−	7.79880i	−0.471429	−	0.272180i	0.245409	−	0.969420i	$-0.421078\pi$
$821$	−13.5079	−	7.79880i	−0.471429	−	0.272180i	−0.716838	+	0.697240i	$0.754411\pi$
$822$		0			0
$823$	14.6686	+	3.93044i	0.511315	+	0.137006i	0.505246	−	0.862975i	$-0.331402\pi$
$823$	14.6686	+	3.93044i	0.511315	+	0.137006i	0.00606868	+	0.999982i	$0.498068\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−19.9628	+	19.9628i	−0.694175	+	0.694175i	−0.963148	−	0.268973i	$-0.913316\pi$
$827$	−19.9628	+	19.9628i	−0.694175	+	0.694175i	0.268973	+	0.963148i	$0.413316\pi$
$828$		0			0
$829$		−	30.9272i		−	1.07415i	−0.843535	−	0.537074i	$-0.819530\pi$
$829$		−	30.9272i		−	1.07415i	0.843535	−	0.537074i	$-0.180470\pi$
$830$		0			0
$831$	−14.9656	+	16.6210i	−0.519150	+	0.576575i
$832$		0			0
$833$	−1.11498	+	4.16117i	−0.0386319	+	0.144176i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	34.3085	−	27.7825i	1.18588	−	0.960303i
$838$		0			0
$839$	−4.62581	+	8.01213i	−0.159701	+	0.276609i	−0.934761	−	0.355278i	$-0.884386\pi$
$839$	−4.62581	+	8.01213i	−0.159701	+	0.276609i	0.775060	+	0.631887i	$0.217720\pi$
$840$		0			0
$841$	13.9760	+	24.2072i	0.481932	+	0.834731i
$842$		0			0
$843$	−1.55405	+	0.0814443i	−0.0535243	+	0.00280509i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.77588	+	1.77588i	0.0610199	+	0.0610199i
$848$		0			0
$849$	8.33618	−	2.70859i	0.286097	−	0.0929586i
$850$		0			0
$851$	6.18484	−	3.57082i	0.212014	−	0.122406i
$852$		0			0
$853$	−3.74693	−	13.9837i	−0.128293	−	0.478794i	0.871643	−	0.490141i	$-0.163055\pi$
$853$	−3.74693	−	13.9837i	−0.128293	−	0.478794i	−0.999936	+	0.0113469i	$0.996388\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.19758	+	34.3258i	0.314183	+	1.17255i	0.924748	+	0.380581i	$0.124276\pi$
$857$	9.19758	+	34.3258i	0.314183	+	1.17255i	−0.610564	+	0.791967i	$0.709057\pi$
$858$		0			0
$859$	−22.0478	+	12.7293i	−0.752261	+	0.434318i	−0.826510	−	0.562922i	$-0.809677\pi$
$859$	−22.0478	+	12.7293i	−0.752261	+	0.434318i	0.0742492	+	0.997240i	$0.476344\pi$
$860$		0			0
$861$	1.31734	−	6.19760i	0.0448948	−	0.211214i
$862$		0			0
$863$	12.7951	+	12.7951i	0.435551	+	0.435551i	0.890512	−	0.454960i	$-0.150347\pi$
$863$	12.7951	+	12.7951i	0.435551	+	0.435551i	−0.454960	+	0.890512i	$0.650347\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	15.6658	+	24.1232i	0.532037	+	0.819266i
$868$		0			0
$869$	−15.3659	−	26.6146i	−0.521253	−	0.902837i
$870$		0			0
$871$	1.24497	−	2.15634i	0.0421841	−	0.0730649i
$872$		0			0
$873$	−2.84794	+	17.9812i	−0.0963881	+	0.608570i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.42491	−	5.31783i	0.0481157	−	0.179570i	−0.937686	−	0.347484i	$-0.887036\pi$
$877$	1.42491	−	5.31783i	0.0481157	−	0.179570i	0.985802	+	0.167913i	$0.0537029\pi$
$878$		0			0
$879$	−14.1035	−	43.4060i	−0.475699	−	1.46405i
$880$		0			0
$881$		−	28.8632i		−	0.972425i	−0.873840	−	0.486213i	$-0.838378\pi$
$881$		−	28.8632i		−	0.972425i	0.873840	−	0.486213i	$-0.161622\pi$
$882$		0			0
$883$	4.77501	−	4.77501i	0.160692	−	0.160692i	−0.622181	−	0.782873i	$-0.713753\pi$
$883$	4.77501	−	4.77501i	0.160692	−	0.160692i	0.782873	+	0.622181i	$0.213753\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	47.5840	+	12.7501i	1.59772	+	0.428107i	0.944352	−	0.328937i	$-0.106690\pi$
$887$	47.5840	+	12.7501i	1.59772	+	0.428107i	0.653364	+	0.757044i	$0.273357\pi$
$888$		0			0
$889$	4.37537	+	2.52612i	0.146745	+	0.0847233i
$890$		0			0
$891$	−7.92470	−	37.2828i	−0.265488	−	1.24902i
$892$		0			0
$893$	−21.6526	+	5.80179i	−0.724576	+	0.194150i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.0778848	+	1.48613i	0.00260050	+	0.0496204i
$898$		0			0
$899$	8.69726			0.290070
$900$		0			0
$901$	6.67432			0.222354
$902$		0			0
$903$	−5.95124	−	3.03231i	−0.198045	−	0.100909i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−7.86434	+	2.10724i	−0.261131	+	0.0699698i	−0.387009	−	0.922076i	$-0.626492\pi$
$907$	−7.86434	+	2.10724i	−0.261131	+	0.0699698i	0.125878	+	0.992046i	$0.459825\pi$
$908$		0			0
$909$	22.3389	−	16.2302i	0.740935	−	0.538321i
$910$		0			0
$911$	−9.07444	−	5.23913i	−0.300650	−	0.173580i	0.342085	−	0.939669i	$-0.388867\pi$
$911$	−9.07444	−	5.23913i	−0.300650	−	0.173580i	−0.642735	+	0.766089i	$0.722200\pi$
$912$		0			0
$913$	−61.1567	−	16.3869i	−2.02399	−	0.542327i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.96521	−	3.96521i	0.130943	−	0.130943i
$918$		0			0
$919$		−	7.87147i		−	0.259656i	−0.991537	−	0.129828i	$-0.958558\pi$
$919$		−	7.87147i		−	0.259656i	0.991537	−	0.129828i	$-0.0414425\pi$
$920$		0			0
$921$	−1.75363	−	0.372746i	−0.0577842	−	0.0122824i
$922$		0			0
$923$	0.595772	−	2.22345i	0.0196101	−	0.0731858i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−28.7704	+	35.5285i	−0.944944	+	1.16691i
$928$		0			0
$929$	4.96149	−	8.59355i	0.162781	−	0.281945i	−0.773084	−	0.634304i	$-0.781287\pi$
$929$	4.96149	−	8.59355i	0.162781	−	0.281945i	0.935865	+	0.352358i	$0.114620\pi$
$930$		0			0
$931$	9.80225	+	16.9780i	0.321256	+	0.556431i
$932$		0			0
$933$	−12.8841	+	25.2865i	−0.421807	+	0.827844i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	19.0704	+	19.0704i	0.623002	+	0.623002i	0.946298	−	0.323296i	$-0.104791\pi$
$937$	19.0704	+	19.0704i	0.623002	+	0.623002i	−0.323296	+	0.946298i	$0.604791\pi$
$938$		0			0
$939$	13.0444	+	11.7453i	0.425689	+	0.383292i
$940$		0			0
$941$	−7.88359	+	4.55159i	−0.256998	+	0.148378i	−0.622964	−	0.782250i	$-0.714072\pi$
$941$	−7.88359	+	4.55159i	−0.256998	+	0.148378i	0.365967	+	0.930628i	$0.380738\pi$
$942$		0			0
$943$	2.65340	+	9.90262i	0.0864066	+	0.322474i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.54027	+	9.48040i	0.0825476	+	0.308072i	0.994838	−	0.101471i	$-0.0323549\pi$
$947$	2.54027	+	9.48040i	0.0825476	+	0.308072i	−0.912291	+	0.409543i	$0.865688\pi$
$948$		0			0
$949$	2.44455	−	1.41136i	0.0793535	−	0.0458148i
$950$		0			0
$951$	3.77900	+	3.40262i	0.122542	+	0.110338i
$952$		0			0
$953$	34.0291	+	34.0291i	1.10231	+	1.10231i	0.994131	+	0.108179i	$0.0345019\pi$
$953$	34.0291	+	34.0291i	1.10231	+	1.10231i	0.108179	+	0.994131i	$0.465498\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	3.40906	−	6.69065i	0.110199	−	0.216278i
$958$		0			0
$959$	2.72630	+	4.72208i	0.0880367	+	0.152484i
$960$		0			0
$961$	−20.5915	+	35.6655i	−0.664242	+	1.15050i
$962$		0			0
$963$	0.140962	+	0.367218i	0.00454242	+	0.0118334i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−11.3258	+	42.2686i	−0.364214	+	1.35927i	0.504268	+	0.863547i	$0.331762\pi$
$967$	−11.3258	+	42.2686i	−0.364214	+	1.35927i	−0.868483	+	0.495719i	$0.834904\pi$
$968$		0			0
$969$	−3.03264	−	0.644607i	−0.0974223	−	0.0207078i
$970$		0			0
$971$		−	35.4120i		−	1.13643i	−0.822882	−	0.568213i	$-0.807635\pi$
$971$		−	35.4120i		−	1.13643i	0.822882	−	0.568213i	$-0.192365\pi$
$972$		0			0
$973$	0.648486	−	0.648486i	0.0207895	−	0.0207895i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.7120	−	5.01386i	−0.598649	−	0.160408i	−0.0532459	−	0.998581i	$-0.516957\pi$
$977$	−18.7120	−	5.01386i	−0.598649	−	0.160408i	−0.545403	+	0.838174i	$0.683623\pi$
$978$		0			0
$979$	−12.8410	−	7.41373i	−0.410399	−	0.236944i
$980$		0			0
$981$	12.0249	+	5.35381i	0.383924	+	0.170934i
$982$		0			0
$983$	−10.6318	+	2.84879i	−0.339103	+	0.0908624i	−0.424352	−	0.905497i	$-0.639498\pi$
$983$	−10.6318	+	2.84879i	−0.339103	+	0.0908624i	0.0852489	+	0.996360i	$0.472831\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.38898	−	2.23630i	−0.139703	−	0.0711821i
$988$		0			0
$989$	10.8072			0.343650
$990$		0			0
$991$	−44.8001			−1.42312			−0.711561	−	0.702624i	$-0.752011\pi$
$991$	−44.8001			−1.42312			−0.711561	+	0.702624i	$0.752011\pi$
$992$		0			0
$993$	−2.90490	−	55.4288i	−0.0921842	−	1.75898i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	44.1081	−	11.8187i	1.39692	−	0.374303i	0.519681	−	0.854360i	$-0.326051\pi$
$997$	44.1081	−	11.8187i	1.39692	−	0.374303i	0.877237	+	0.480057i	$0.159384\pi$
$998$		0			0
$999$	−21.4944	+	29.5845i	−0.680052	+	0.936012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.be.f.857.7	yes	32
3.2	odd	2		2700.2.bf.f.2357.5		32
5.2	odd	4	inner	900.2.be.f.893.3	yes	32
5.3	odd	4	inner	900.2.be.f.893.6	yes	32
5.4	even	2	inner	900.2.be.f.857.2	yes	32
9.4	even	3		2700.2.bf.f.557.4		32
9.5	odd	6	inner	900.2.be.f.257.6	yes	32
15.2	even	4		2700.2.bf.f.1493.5		32
15.8	even	4		2700.2.bf.f.1493.4		32
15.14	odd	2		2700.2.bf.f.2357.4		32
45.4	even	6		2700.2.bf.f.557.5		32
45.13	odd	12		2700.2.bf.f.2393.5		32
45.14	odd	6	inner	900.2.be.f.257.3	✓	32
45.22	odd	12		2700.2.bf.f.2393.4		32
45.23	even	12	inner	900.2.be.f.293.7	yes	32
45.32	even	12	inner	900.2.be.f.293.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.be.f.257.3	✓	32	45.14	odd	6	inner
900.2.be.f.257.6	yes	32	9.5	odd	6	inner
900.2.be.f.293.2	yes	32	45.32	even	12	inner
900.2.be.f.293.7	yes	32	45.23	even	12	inner
900.2.be.f.857.2	yes	32	5.4	even	2	inner
900.2.be.f.857.7	yes	32	1.1	even	1	trivial
900.2.be.f.893.3	yes	32	5.2	odd	4	inner
900.2.be.f.893.6	yes	32	5.3	odd	4	inner
2700.2.bf.f.557.4		32	9.4	even	3
2700.2.bf.f.557.5		32	45.4	even	6
2700.2.bf.f.1493.4		32	15.8	even	4
2700.2.bf.f.1493.5		32	15.2	even	4
2700.2.bf.f.2357.4		32	15.14	odd	2
2700.2.bf.f.2357.5		32	3.2	odd	2
2700.2.bf.f.2393.4		32	45.22	odd	12
2700.2.bf.f.2393.5		32	45.13	odd	12

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45262 - 0.943342i) q^{3} +(0.349759 - 0.0937177i) q^{7} +(1.22021 - 2.74064i) q^{9} +(3.66769 + 2.11754i) q^{11} +(0.817828 + 0.219136i) q^{13} +(0.443477 - 0.443477i) q^{17} -2.85410i q^{19} +(0.419659 - 0.466079i) q^{21} +(-0.262645 + 0.980206i) q^{23} +(-0.812857 - 5.13218i) q^{27} +(0.511841 - 0.886534i) q^{29} +(4.24803 + 7.35780i) q^{31} +(7.32532 - 0.383904i) q^{33} +(-4.97633 - 4.97633i) q^{37} +(1.39471 - 0.453170i) q^{39} +(8.74911 - 5.05130i) q^{41} +(-2.75637 - 10.2869i) q^{43} +(-2.03279 - 7.58648i) q^{47} +(-5.94863 + 3.43444i) q^{49} +(0.225853 - 1.06255i) q^{51} +(7.52500 + 7.52500i) q^{53} +(-2.69240 - 4.14593i) q^{57} +(6.10629 + 10.5764i) q^{59} +(-5.68247 + 9.84233i) q^{61} +(0.169933 - 1.07292i) q^{63} +(0.761142 - 2.84062i) q^{67} +(0.543146 + 1.67163i) q^{69} -2.71873i q^{71} +(2.35741 - 2.35741i) q^{73} +(1.48126 + 0.396902i) q^{77} +(-6.28431 - 3.62825i) q^{79} +(-6.02218 - 6.68830i) q^{81} +(-14.4405 + 3.86932i) q^{83} +(-0.0927953 - 1.77064i) q^{87} -3.50111 q^{89} +0.306580 q^{91} +(13.1117 + 6.68074i) q^{93} +(-5.86166 + 1.57063i) q^{97} +(10.2788 - 7.46795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 12 q^{11} + 12 q^{21} + 8 q^{31} + 60 q^{41} + 36 q^{51} + 52 q^{61} - 36 q^{81} + 120 q^{91}+O(q^{100}) \) 32 * q - 12 * q^11 + 12 * q^21 + 8 * q^31 + 60 * q^41 + 36 * q^51 + 52 * q^61 - 36 * q^81 + 120 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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