LMFDB - Embedded newform 804.2.s.b.161.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(5,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 5]))

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

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

chi := DirichletCharacter("804.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.s (of order $22$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$20$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			161.12
Character	$\chi$	$=$	804.161
Dual form			804.2.s.b.5.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.185769 - 1.72206i) q^{3} +(-2.83063 - 0.831147i) q^{5} +(-2.86249 + 2.48036i) q^{7} +(-2.93098 - 0.639810i) q^{9} +O(q^{10})$	\(q+(0.185769 - 1.72206i) q^{3} +(-2.83063 - 0.831147i) q^{5} +(-2.86249 + 2.48036i) q^{7} +(-2.93098 - 0.639810i) q^{9} +(3.88931 + 1.14200i) q^{11} +(-0.777890 + 1.21042i) q^{13} +(-1.95713 + 4.72011i) q^{15} +(5.27916 - 0.759028i) q^{17} +(-0.130434 + 0.150529i) q^{19} +(3.73957 + 5.39016i) q^{21} +(-0.694228 - 0.317043i) q^{23} +(3.11537 + 2.00213i) q^{25} +(-1.64628 + 4.92847i) q^{27} +8.71464i q^{29} +(3.86518 + 6.01434i) q^{31} +(2.68911 - 6.48548i) q^{33} +(10.1642 - 4.64183i) q^{35} -2.50144 q^{37} +(1.93991 + 1.56443i) q^{39} +(0.0416445 + 0.289644i) q^{41} +(-6.85998 + 0.986316i) q^{43} +(7.76473 + 4.24714i) q^{45} +(6.89272 + 3.14780i) q^{47} +(1.04545 - 7.27129i) q^{49} +(-0.326389 - 9.23202i) q^{51} +(0.173569 - 1.20720i) q^{53} +(-10.0600 - 6.46518i) q^{55} +(0.234989 + 0.252578i) q^{57} +(-0.206913 - 0.321963i) q^{59} +(3.48314 + 11.8625i) q^{61} +(9.97687 - 5.43844i) q^{63} +(3.20795 - 2.77971i) q^{65} +(-8.15987 - 0.645356i) q^{67} +(-0.674933 + 1.13660i) q^{69} +(0.756392 + 0.108753i) q^{71} +(-11.2432 + 3.30131i) q^{73} +(4.02652 - 4.99292i) q^{75} +(-13.9657 + 6.37792i) q^{77} +(8.00157 - 12.4507i) q^{79} +(8.18129 + 3.75054i) q^{81} +(3.51473 - 11.9701i) q^{83} +(-15.5742 - 2.23923i) q^{85} +(15.0071 + 1.61891i) q^{87} +(0.0142974 - 0.00652940i) q^{89} +(-0.775578 - 5.39427i) q^{91} +(11.0751 - 5.53880i) q^{93} +(0.494321 - 0.317681i) q^{95} +15.9958i q^{97} +(-10.6688 - 5.83561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 10 q^{9}+O(q^{10}) $ 200 * q - 10 * q^9	$ 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) $ 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{17}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.185769	−	1.72206i	0.107254	−	0.994232i
$3$	0.185769	−	1.72206i	0.107254	−	0.994232i
$4$		0			0
$5$	−2.83063	−	0.831147i	−1.26589	−	0.371700i	−0.421209	−	0.906964i	$-0.638394\pi$
$5$	−2.83063	−	0.831147i	−1.26589	−	0.371700i	−0.844685	+	0.535263i	$0.820212\pi$
$6$		0			0
$7$	−2.86249	+	2.48036i	−1.08192	+	0.937489i	−0.998258	−	0.0590050i	$-0.981207\pi$
$7$	−2.86249	+	2.48036i	−1.08192	+	0.937489i	−0.0836625	+	0.996494i	$0.526662\pi$
$8$		0			0
$9$	−2.93098	−	0.639810i	−0.976993	−	0.213270i
$10$		0			0
$11$	3.88931	+	1.14200i	1.17267	+	0.344327i	0.809344	−	0.587334i	$-0.199823\pi$
$11$	3.88931	+	1.14200i	1.17267	+	0.344327i	0.363327	+	0.931662i	$0.381641\pi$
$12$		0			0
$13$	−0.777890	+	1.21042i	−0.215748	+	0.335710i	−0.932211	−	0.361914i	$-0.882123\pi$
$13$	−0.777890	+	1.21042i	−0.215748	+	0.335710i	0.716464	+	0.697625i	$0.245760\pi$
$14$		0			0
$15$	−1.95713	+	4.72011i	−0.505328	+	1.21873i
$16$		0			0
$17$	5.27916	−	0.759028i	1.28038	−	0.184091i	0.531651	−	0.846964i	$-0.321572\pi$
$17$	5.27916	−	0.759028i	1.28038	−	0.184091i	0.748732	+	0.662872i	$0.230663\pi$
$18$		0			0
$19$	−0.130434	+	0.150529i	−0.0299236	+	0.0345336i	−0.770514	−	0.637423i	$-0.780000\pi$
$19$	−0.130434	+	0.150529i	−0.0299236	+	0.0345336i	0.740591	+	0.671957i	$0.234546\pi$
$20$		0			0
$21$	3.73957	+	5.39016i	0.816042	+	1.17623i
$22$		0			0
$23$	−0.694228	−	0.317043i	−0.144756	−	0.0661081i	0.341720	−	0.939802i	$-0.388991\pi$
$23$	−0.694228	−	0.317043i	−0.144756	−	0.0661081i	−0.486476	+	0.873694i	$0.661718\pi$
$24$		0			0
$25$	3.11537	+	2.00213i	0.623074	+	0.400425i
$26$		0			0
$27$	−1.64628	+	4.92847i	−0.316826	+	0.948484i
$28$		0			0
$29$			8.71464i			1.61827i	0.587624	+	0.809134i	$0.300063\pi$
$29$			8.71464i			1.61827i	−0.587624	+	0.809134i	$0.699937\pi$
$30$		0			0
$31$	3.86518	+	6.01434i	0.694207	+	1.08021i	0.992081	+	0.125602i	$0.0400864\pi$
$31$	3.86518	+	6.01434i	0.694207	+	1.08021i	−0.297873	+	0.954605i	$0.596277\pi$
$32$		0			0
$33$	2.68911	−	6.48548i	0.468114	−	1.12898i
$34$		0			0
$35$	10.1642	−	4.64183i	1.71806	−	0.784612i
$36$		0			0
$37$	−2.50144			−0.411234			−0.205617	−	0.978633i	$-0.565920\pi$
$37$	−2.50144			−0.411234			−0.205617	+	0.978633i	$0.565920\pi$
$38$		0			0
$39$	1.93991	+	1.56443i	0.310634	+	0.250509i
$40$		0			0
$41$	0.0416445	+	0.289644i	0.00650378	+	0.0452348i	0.992815	−	0.119660i	$-0.0381805\pi$
$41$	0.0416445	+	0.289644i	0.00650378	+	0.0452348i	−0.986311	+	0.164895i	$0.947271\pi$
$42$		0			0
$43$	−6.85998	+	0.986316i	−1.04614	+	0.150412i	−0.643889	−	0.765119i	$-0.722680\pi$
$43$	−6.85998	+	0.986316i	−1.04614	+	0.150412i	−0.402248	+	0.915531i	$0.631771\pi$
$44$		0			0
$45$	7.76473	+	4.24714i	1.15750	+	0.633126i
$46$		0			0
$47$	6.89272	+	3.14780i	1.00541	+	0.459154i	0.848917	−	0.528526i	$-0.177255\pi$
$47$	6.89272	+	3.14780i	1.00541	+	0.459154i	0.156489	+	0.987680i	$0.449982\pi$
$48$		0			0
$49$	1.04545	−	7.27129i	0.149351	−	1.03876i
$50$		0			0
$51$	−0.326389	−	9.23202i	−0.0457036	−	1.29274i
$52$		0			0
$53$	0.173569	−	1.20720i	0.0238415	−	0.165821i	−0.974422	−	0.224725i	$-0.927852\pi$
$53$	0.173569	−	1.20720i	0.0238415	−	0.165821i	0.998264	+	0.0589041i	$0.0187606\pi$
$54$		0			0
$55$	−10.0600	−	6.46518i	−1.35649	−	0.871764i
$56$		0			0
$57$	0.234989	+	0.252578i	0.0311250	+	0.0334548i
$58$		0			0
$59$	−0.206913	−	0.321963i	−0.0269378	−	0.0419160i	0.827524	−	0.561431i	$-0.189749\pi$
$59$	−0.206913	−	0.321963i	−0.0269378	−	0.0419160i	−0.854461	+	0.519515i	$0.826113\pi$
$60$		0			0
$61$	3.48314	+	11.8625i	0.445970	+	1.51883i	0.809425	+	0.587223i	$0.199779\pi$
$61$	3.48314	+	11.8625i	0.445970	+	1.51883i	−0.363456	+	0.931612i	$0.618403\pi$
$62$		0			0
$63$	9.97687	−	5.43844i	1.25697	−	0.685180i
$64$		0			0
$65$	3.20795	−	2.77971i	0.397897	−	0.344780i
$66$		0			0
$67$	−8.15987	−	0.645356i	−0.996887	−	0.0788428i
$67$	−8.15987	−	0.645356i	−0.996887	−	0.0788428i
$68$		0			0
$69$	−0.674933	+	1.13660i	−0.0812524	+	0.136831i
$70$		0			0
$71$	0.756392	+	0.108753i	0.0897672	+	0.0129066i	0.187052	−	0.982350i	$-0.440107\pi$
$71$	0.756392	+	0.108753i	0.0897672	+	0.0129066i	−0.0972849	+	0.995257i	$0.531016\pi$
$72$		0			0
$73$	−11.2432	+	3.30131i	−1.31592	+	0.386390i	−0.863020	−	0.505170i	$-0.831430\pi$
$73$	−11.2432	+	3.30131i	−1.31592	+	0.386390i	−0.452903	+	0.891560i	$0.649612\pi$
$74$		0			0
$75$	4.02652	−	4.99292i	0.464943	−	0.576533i
$76$		0			0
$77$	−13.9657	+	6.37792i	−1.59154	+	0.726832i
$78$		0			0
$79$	8.00157	−	12.4507i	0.900247	−	1.40081i	−0.0158579	−	0.999874i	$-0.505048\pi$
$79$	8.00157	−	12.4507i	0.900247	−	1.40081i	0.916105	−	0.400938i	$-0.131316\pi$
$80$		0			0
$81$	8.18129	+	3.75054i	0.909032	+	0.416727i
$82$		0			0
$83$	3.51473	−	11.9701i	0.385792	−	1.31389i	−0.506428	−	0.862282i	$-0.669034\pi$
$83$	3.51473	−	11.9701i	0.385792	−	1.31389i	0.892219	−	0.451603i	$-0.149148\pi$
$84$		0			0
$85$	−15.5742	−	2.23923i	−1.68926	−	0.242878i
$86$		0			0
$87$	15.0071	+	1.61891i	1.60893	+	0.173565i
$88$		0			0
$89$	0.0142974	−	0.00652940i	0.00151552	−	0.000692115i	−0.414657	−	0.909978i	$-0.636098\pi$
$89$	0.0142974	−	0.00652940i	0.00151552	−	0.000692115i	0.416173	+	0.909286i	$0.363371\pi$
$90$		0			0
$91$	−0.775578	−	5.39427i	−0.0813027	−	0.565473i
$92$		0			0
$93$	11.0751	−	5.53880i	1.14843	−	0.574347i
$94$		0			0
$95$	0.494321	−	0.317681i	0.0507162	−	0.0325933i
$96$		0			0
$97$			15.9958i			1.62413i	0.583566	+	0.812066i	$0.301657\pi$
$97$			15.9958i			1.62413i	−0.583566	+	0.812066i	$0.698343\pi$
$98$		0			0
$99$	−10.6688	−	5.83561i	−1.07226	−	0.586501i
$100$		0			0
$101$	−9.07482	+	10.4729i	−0.902979	+	1.04209i	0.0959301	+	0.995388i	$0.469417\pi$
$101$	−9.07482	+	10.4729i	−0.902979	+	1.04209i	−0.998909	+	0.0467048i	$0.985128\pi$
$102$		0			0
$103$	0.156435	−	0.100534i	0.0154140	−	0.00990596i	−0.532911	−	0.846171i	$-0.678902\pi$
$103$	0.156435	−	0.100534i	0.0154140	−	0.00990596i	0.548325	+	0.836265i	$0.315266\pi$
$104$		0			0
$105$	−6.10532	−	18.3656i	−0.595818	−	1.79230i
$106$		0			0
$107$	3.20448	+	10.9135i	0.309789	+	1.05504i	0.956360	+	0.292191i	$0.0943842\pi$
$107$	3.20448	+	10.9135i	0.309789	+	1.05504i	−0.646571	+	0.762854i	$0.723798\pi$
$108$		0			0
$109$	−7.91640	+	12.3182i	−0.758254	+	1.17987i	0.220612	+	0.975362i	$0.429195\pi$
$109$	−7.91640	+	12.3182i	−0.758254	+	1.17987i	−0.978866	+	0.204504i	$0.934442\pi$
$110$		0			0
$111$	−0.464689	+	4.30763i	−0.0441064	+	0.408862i
$112$		0			0
$113$	−13.2015	+	3.87631i	−1.24189	+	0.364653i	−0.835726	−	0.549147i	$-0.814953\pi$
$113$	−13.2015	+	3.87631i	−1.24189	+	0.364653i	−0.406166	+	0.913799i	$0.633135\pi$
$114$		0			0
$115$	1.70159	+	1.47444i	0.158674	+	0.137492i
$116$		0			0
$117$	3.05442	−	3.05002i	0.282381	−	0.281974i
$118$		0			0
$119$	−13.2289	+	15.2669i	−1.21269	+	1.39952i
$120$		0			0
$121$	4.56877	+	2.93617i	0.415343	+	0.266925i
$122$		0			0
$123$	0.506521	−	0.0179076i	0.0456714	−	0.00161467i
$124$		0			0
$125$	2.50523	+	2.89118i	0.224074	+	0.258595i
$126$		0			0
$127$	2.59056	+	2.98967i	0.229875	+	0.265290i	0.858956	−	0.512050i	$-0.171114\pi$
$127$	2.59056	+	2.98967i	0.229875	+	0.265290i	−0.629080	+	0.777340i	$0.716568\pi$
$128$		0			0
$129$	0.424125	+	11.9965i	0.0373422	+	1.05623i
$130$		0			0
$131$	−3.04712	−	1.39157i	−0.266228	−	0.121582i	0.277829	−	0.960631i	$-0.410385\pi$
$131$	−3.04712	−	1.39157i	−0.266228	−	0.121582i	−0.544057	+	0.839048i	$0.683112\pi$
$132$		0			0
$133$		−	0.754410i		−	0.0654157i
$134$		0			0
$135$	8.75627	−	12.5823i	0.753620	−	1.08292i
$136$		0			0
$137$	6.27585	−	13.7422i	0.536182	−	1.17407i	−0.426760	−	0.904365i	$-0.640345\pi$
$137$	6.27585	−	13.7422i	0.536182	−	1.17407i	0.962942	−	0.269710i	$-0.0869277\pi$
$138$		0			0
$139$	−4.37634	+	14.9044i	−0.371196	+	1.26418i	0.536268	+	0.844048i	$0.319834\pi$
$139$	−4.37634	+	14.9044i	−0.371196	+	1.26418i	−0.907464	+	0.420130i	$0.861985\pi$
$140$		0			0
$141$	6.70115	−	11.2849i	0.564339	−	0.950361i
$142$		0			0
$143$	−4.40776	+	3.81935i	−0.368595	+	0.319390i
$144$		0			0
$145$	7.24315	−	24.6679i	0.601510	−	2.04856i
$146$		0			0
$147$	−12.3274	−	3.15111i	−1.01675	−	0.259899i
$148$		0			0
$149$	−13.7776	−	11.9383i	−1.12870	−	0.978026i	−0.128795	−	0.991671i	$-0.541111\pi$
$149$	−13.7776	−	11.9383i	−1.12870	−	0.978026i	−0.999907	+	0.0136454i	$0.995656\pi$
$150$		0			0
$151$	−0.470875	−	3.27501i	−0.0383192	−	0.266516i	0.961651	−	0.274277i	$-0.0884386\pi$
$151$	−0.470875	−	3.27501i	−0.0383192	−	0.266516i	−0.999970	+	0.00776115i	$0.997530\pi$
$152$		0			0
$153$	−15.9587	−	1.15296i	−1.29019	−	0.0932113i
$154$		0			0
$155$	−5.94209	−	20.2369i	−0.477280	−	1.62547i
$156$		0			0
$157$	−4.94188	+	10.8212i	−0.394405	+	0.863626i	0.603402	+	0.797437i	$0.293811\pi$
$157$	−4.94188	+	10.8212i	−0.394405	+	0.863626i	−0.997807	+	0.0661893i	$0.978916\pi$
$158$		0			0
$159$	−2.04662	−	0.523155i	−0.162308	−	0.0414889i
$160$		0			0
$161$	2.77360	−	0.814403i	0.218591	−	0.0641840i
$162$		0			0
$163$	17.8684			1.39956			0.699781	−	0.714357i	$-0.253281\pi$
$163$	17.8684			1.39956			0.699781	+	0.714357i	$0.253281\pi$
$164$		0			0
$165$	−13.0023	+	16.1229i	−1.01222	+	1.25517i
$166$		0			0
$167$	−0.518218	−	0.449039i	−0.0401009	−	0.0347477i	0.634580	−	0.772857i	$-0.281173\pi$
$167$	−0.518218	−	0.449039i	−0.0401009	−	0.0347477i	−0.674681	+	0.738110i	$0.735719\pi$
$168$		0			0
$169$	4.54039	+	9.94207i	0.349261	+	0.764775i
$170$		0			0
$171$	0.478609	−	0.357744i	0.0366001	−	0.0273573i
$172$		0			0
$173$	−11.6014	−	18.0521i	−0.882037	−	1.37248i	−0.927624	−	0.373516i	$-0.878152\pi$
$173$	−11.6014	−	18.0521i	−0.882037	−	1.37248i	0.0455864	−	0.998960i	$-0.485484\pi$
$174$		0			0
$175$	−13.8837	+	1.99618i	−1.04951	+	0.150897i
$176$		0			0
$177$	−0.592878	+	0.296506i	−0.0445634	+	0.0222868i
$178$		0			0
$179$	1.38815	+	3.03963i	0.103755	+	0.227192i	0.954389	−	0.298567i	$-0.0965086\pi$
$179$	1.38815	+	3.03963i	0.103755	+	0.227192i	−0.850633	+	0.525759i	$0.823781\pi$
$180$		0			0
$181$	−1.03125	+	2.25813i	−0.0766526	+	0.167846i	−0.944079	−	0.329720i	$-0.893046\pi$
$181$	−1.03125	+	2.25813i	−0.0766526	+	0.167846i	0.867426	+	0.497566i	$0.165773\pi$
$182$		0			0
$183$	21.0749	−	3.79449i	1.55790	−	0.280497i
$184$		0			0
$185$	7.08064	+	2.07906i	0.520579	+	0.152856i
$186$		0			0
$187$	21.3991	+	3.07672i	1.56486	+	0.224992i
$188$		0			0
$189$	−7.51194	−	18.1911i	−0.546413	−	1.32320i
$190$		0			0
$191$	−2.31794	−	5.07558i	−0.167720	−	0.367256i	0.807045	−	0.590491i	$-0.201066\pi$
$191$	−2.31794	−	5.07558i	−0.167720	−	0.367256i	−0.974765	+	0.223235i	$0.928338\pi$
$192$		0			0
$193$	17.2923	−	11.1131i	1.24473	−	0.799938i	0.258609	−	0.965982i	$-0.416736\pi$
$193$	17.2923	−	11.1131i	1.24473	−	0.799938i	0.986118	+	0.166044i	$0.0530994\pi$
$194$		0			0
$195$	−4.19088	−	6.04067i	−0.300115	−	0.432581i
$196$		0			0
$197$	0.352396	−	2.45097i	0.0251072	−	0.174624i	−0.973409	−	0.229072i	$-0.926431\pi$
$197$	0.352396	−	2.45097i	0.0251072	−	0.174624i	0.998517	+	0.0544480i	$0.0173399\pi$
$198$		0			0
$199$	−3.29690	−	3.80483i	−0.233711	−	0.269717i	0.626764	−	0.779209i	$-0.284379\pi$
$199$	−3.29690	−	3.80483i	−0.233711	−	0.269717i	−0.860476	+	0.509492i	$0.829833\pi$
$200$		0			0
$201$	−2.62719	+	13.9319i	−0.185308	+	0.982681i
$202$		0			0
$203$	−21.6155	−	24.9456i	−1.51711	−	1.75084i
$204$		0			0
$205$	0.122857	−	0.854487i	0.00858068	−	0.0596800i
$206$		0			0
$207$	1.83192	+	1.37342i	0.127327	+	0.0954593i
$208$		0			0
$209$	−0.679202	+	0.436497i	−0.0469814	+	0.0301931i
$210$		0			0
$211$	−9.04523	−	19.8063i	−0.622699	−	1.36352i	−0.913540	−	0.406750i	$-0.866662\pi$
$211$	−9.04523	−	19.8063i	−0.622699	−	1.36352i	0.290840	−	0.956772i	$-0.406065\pi$
$212$		0			0
$213$	0.327793	−	1.28235i	0.0224600	−	0.0878651i
$214$		0			0
$215$	20.2378	+	2.90976i	1.38021	+	0.198444i
$216$		0			0
$217$	−25.9818	−	7.62895i	−1.76376	−	0.517887i
$218$		0			0
$219$	3.59642	+	19.9748i	0.243023	+	1.34977i
$220$		0			0
$221$	−3.18786	+	6.98043i	−0.214439	+	0.469555i
$222$		0			0
$223$	9.31921	+	20.4062i	0.624060	+	1.36650i	0.912529	+	0.409012i	$0.134127\pi$
$223$	9.31921	+	20.4062i	0.624060	+	1.36650i	−0.288469	+	0.957489i	$0.593146\pi$
$224$		0			0
$225$	−7.85011	−	7.86144i	−0.523340	−	0.524096i
$226$		0			0
$227$	4.40653	−	0.633564i	0.292472	−	0.0420511i	0.00548275	−	0.999985i	$-0.498255\pi$
$227$	4.40653	−	0.633564i	0.292472	−	0.0420511i	0.286989	+	0.957934i	$0.407346\pi$
$228$		0			0
$229$	8.29963	+	12.9145i	0.548455	+	0.853413i	0.999230	−	0.0392245i	$-0.0124888\pi$
$229$	8.29963	+	12.9145i	0.548455	+	0.853413i	−0.450775	+	0.892638i	$0.648852\pi$
$230$		0			0
$231$	8.38877	+	25.2346i	0.551941	+	1.66031i
$232$		0			0
$233$	5.70613	+	12.4947i	0.373821	+	0.818553i	0.999267	+	0.0382859i	$0.0121898\pi$
$233$	5.70613	+	12.4947i	0.373821	+	0.818553i	−0.625446	+	0.780267i	$0.715083\pi$
$234$		0			0
$235$	−16.8944	−	14.6391i	−1.10207	−	0.954950i
$236$		0			0
$237$	−19.9544	−	16.0921i	−1.29618	−	1.04530i
$238$		0			0
$239$	23.3595			1.51100			0.755500	−	0.655148i	$-0.227394\pi$
$239$	23.3595			1.51100			0.755500	+	0.655148i	$0.227394\pi$
$240$		0			0
$241$	2.15759	−	0.633526i	0.138983	−	0.0408090i	−0.211501	−	0.977378i	$-0.567835\pi$
$241$	2.15759	−	0.633526i	0.138983	−	0.0408090i	0.350484	+	0.936569i	$0.386017\pi$
$242$		0			0
$243$	7.97848	−	13.3919i	0.511820	−	0.859093i
$244$		0			0
$245$	−9.00280	+	19.7134i	−0.575168	+	1.25944i
$246$		0			0
$247$	−0.0807398	−	0.274974i	−0.00513735	−	0.0174962i
$248$		0			0
$249$	−19.9602	−	8.27624i	−1.26493	−	0.524485i
$250$		0			0
$251$	−2.12352	−	14.7694i	−0.134035	−	0.932237i	−0.940219	−	0.340571i	$-0.889380\pi$
$251$	−2.12352	−	14.7694i	−0.134035	−	0.932237i	0.806183	−	0.591666i	$-0.201530\pi$
$252$		0			0
$253$	−2.33800	−	2.02589i	−0.146989	−	0.127367i
$254$		0			0
$255$	−6.74928	+	26.4037i	−0.422656	+	1.65346i
$256$		0			0
$257$	−3.22142	+	10.9711i	−0.200947	+	0.684361i	0.795930	+	0.605389i	$0.206982\pi$
$257$	−3.22142	+	10.9711i	−0.200947	+	0.684361i	−0.996877	+	0.0789730i	$0.974836\pi$
$258$		0			0
$259$	7.16035	−	6.20448i	0.444923	−	0.385528i
$260$		0			0
$261$	5.57571	−	25.5424i	0.345128	−	1.58104i
$262$		0			0
$263$	4.21240	−	14.3461i	0.259747	−	0.884619i	−0.721589	−	0.692321i	$-0.756588\pi$
$263$	4.21240	−	14.3461i	0.259747	−	0.884619i	0.981337	−	0.192297i	$-0.0615938\pi$
$264$		0			0
$265$	−1.49466	+	3.27286i	−0.0918165	+	0.201050i
$266$		0			0
$267$	−0.00858801	−	0.0258339i	−0.000525578	−	0.00158101i
$268$		0			0
$269$		−	20.8104i		−	1.26884i	−0.772990	−	0.634418i	$-0.781240\pi$
$269$		−	20.8104i		−	1.26884i	0.772990	−	0.634418i	$-0.218760\pi$
$270$		0			0
$271$	−26.4716	−	12.0892i	−1.60804	−	0.734366i	−0.609734	−	0.792606i	$-0.708724\pi$
$271$	−26.4716	−	12.0892i	−1.60804	−	0.734366i	−0.998303	+	0.0582400i	$0.981451\pi$
$272$		0			0
$273$	−9.43333	+	0.333506i	−0.570931	+	0.0201847i
$274$		0			0
$275$	9.83020	+	11.3447i	0.592784	+	0.684109i
$276$		0			0
$277$	−16.1014	−	18.5820i	−0.967440	−	1.11648i	−0.993154	−	0.116815i	$-0.962731\pi$
$277$	−16.1014	−	18.5820i	−0.967440	−	1.11648i	0.0257141	−	0.999669i	$-0.491814\pi$
$278$		0			0
$279$	−7.48074	−	20.1009i	−0.447860	−	1.20341i
$280$		0			0
$281$	27.7394	+	17.8271i	1.65480	+	1.06347i	0.925116	+	0.379685i	$0.123968\pi$
$281$	27.7394	+	17.8271i	1.65480	+	1.06347i	0.729681	+	0.683788i	$0.239669\pi$
$282$		0			0
$283$	3.38795	−	3.90990i	0.201393	−	0.232420i	−0.646065	−	0.763282i	$-0.723587\pi$
$283$	3.38795	−	3.90990i	0.201393	−	0.232420i	0.847458	+	0.530863i	$0.178132\pi$
$284$		0			0
$285$	−0.455236	−	0.910265i	−0.0269658	−	0.0539194i
$286$		0			0
$287$	−0.837630	−	0.725810i	−0.0494437	−	0.0428432i
$288$		0			0
$289$	10.9820	−	3.22460i	0.645999	−	0.189682i
$290$		0			0
$291$	27.5458	+	2.97153i	1.61476	+	0.174194i
$292$		0			0
$293$	1.03101	−	1.60428i	0.0602322	−	0.0937231i	−0.809831	−	0.586663i	$-0.800441\pi$
$293$	1.03101	−	1.60428i	0.0602322	−	0.0937231i	0.870063	+	0.492940i	$0.164078\pi$
$294$		0			0
$295$	0.318095	+	1.08333i	0.0185202	+	0.0630741i
$296$		0			0
$297$	−12.0312	+	17.2883i	−0.698121	+	1.00317i
$298$		0			0
$299$	0.923788	−	0.593682i	0.0534240	−	0.0343335i
$300$		0			0
$301$	17.1902	−	19.8386i	0.990827	−	1.14348i
$302$		0			0
$303$	16.3491	+	17.5729i	0.939234	+	1.00954i
$304$		0			0
$305$		−	36.4732i		−	2.08845i
$306$		0			0
$307$	2.28977	−	1.47155i	0.130684	−	0.0839857i	−0.473665	−	0.880705i	$-0.657069\pi$
$307$	2.28977	−	1.47155i	0.130684	−	0.0839857i	0.604350	+	0.796719i	$0.293433\pi$
$308$		0			0
$309$	−0.144066	−	0.288066i	−0.00819561	−	0.0163875i
$310$		0			0
$311$	0.224559	+	1.56184i	0.0127336	+	0.0885639i	0.995197	−	0.0978904i	$-0.0312095\pi$
$311$	0.224559	+	1.56184i	0.0127336	+	0.0885639i	−0.982464	+	0.186454i	$0.940300\pi$
$312$		0			0
$313$	2.15289	−	0.983191i	0.121688	−	0.0555732i	−0.353640	−	0.935381i	$-0.615056\pi$
$313$	2.15289	−	0.983191i	0.121688	−	0.0555732i	0.475329	+	0.879808i	$0.342329\pi$
$314$		0			0
$315$	−32.7609	+	7.10196i	−1.84587	+	0.400150i
$316$		0			0
$317$	−1.60985	−	0.231462i	−0.0904183	−	0.0130002i	0.0969572	−	0.995289i	$-0.469089\pi$
$317$	−1.60985	−	0.231462i	−0.0904183	−	0.0130002i	−0.187375	+	0.982288i	$0.559998\pi$
$318$		0			0
$319$	−9.95216	+	33.8939i	−0.557214	+	1.89770i
$320$		0			0
$321$	19.3889	−	3.49093i	1.08218	−	0.194845i
$322$		0			0
$323$	−0.574325	+	0.893667i	−0.0319563	+	0.0497250i
$324$		0			0
$325$	−4.84683	+	2.21347i	−0.268854	+	0.122781i
$326$		0			0
$327$	19.7420	+	15.9208i	1.09173	+	0.880425i
$328$		0			0
$329$	−27.5380	+	8.08590i	−1.51822	+	0.445790i
$330$		0			0
$331$	28.3260	+	4.07266i	1.55694	+	0.223853i	0.866365	−	0.499412i	$-0.166450\pi$
$331$	28.3260	+	4.07266i	1.55694	+	0.223853i	0.690570	+	0.723265i	$0.257360\pi$
$332$		0			0
$333$	7.33167	+	1.60045i	0.401773	+	0.0877039i
$334$		0			0
$335$	22.5612	+	8.60881i	1.23265	+	0.470350i
$336$		0			0
$337$	−15.2316	+	13.1983i	−0.829719	+	0.718956i	−0.962234	−	0.272225i	$-0.912240\pi$
$337$	−15.2316	+	13.1983i	−0.829719	+	0.718956i	0.132514	+	0.991181i	$0.457695\pi$
$338$		0			0
$339$	4.22281	+	23.4539i	0.229352	+	1.27384i
$340$		0			0
$341$	8.16449	+	27.8057i	0.442132	+	1.50576i
$342$		0			0
$343$	0.708644	+	1.10267i	0.0382632	+	0.0595387i
$344$		0			0
$345$	2.85517	−	2.65633i	0.153717	−	0.143012i
$346$		0			0
$347$	−24.7044	−	15.8765i	−1.32620	−	0.852297i	−0.330399	−	0.943841i	$-0.607183\pi$
$347$	−24.7044	−	15.8765i	−1.32620	−	0.852297i	−0.995801	+	0.0915445i	$0.970820\pi$
$348$		0			0
$349$	−2.66838	+	18.5590i	−0.142835	+	0.993439i	0.784746	+	0.619817i	$0.212793\pi$
$349$	−2.66838	+	18.5590i	−0.142835	+	0.993439i	−0.927581	+	0.373622i	$0.878116\pi$
$350$		0			0
$351$	−4.68489	−	5.82649i	−0.250061	−	0.310995i
$352$		0			0
$353$	−1.25495	+	8.72836i	−0.0667942	+	0.464564i	0.928784	+	0.370623i	$0.120856\pi$
$353$	−1.25495	+	8.72836i	−0.0667942	+	0.464564i	−0.995578	+	0.0939411i	$0.970053\pi$
$354$		0			0
$355$	−2.05067	−	0.936511i	−0.108838	−	0.0497048i
$356$		0			0
$357$	23.8331	+	25.6170i	1.26138	+	1.35580i
$358$		0			0
$359$	−4.63866	+	0.666939i	−0.244819	+	0.0351997i	−0.263632	−	0.964623i	$-0.584920\pi$
$359$	−4.63866	+	0.666939i	−0.244819	+	0.0351997i	0.0188128	+	0.999823i	$0.494011\pi$
$360$		0			0
$361$	2.69834	+	18.7673i	0.142018	+	0.987755i
$362$		0			0
$363$	5.90500	−	7.32225i	0.309932	−	0.384318i
$364$		0			0
$365$	34.5693			1.80944
$366$		0			0
$367$	10.3001	−	4.70390i	0.537661	−	0.245541i	−0.128029	−	0.991770i	$-0.540865\pi$
$367$	10.3001	−	4.70390i	0.537661	−	0.245541i	0.665689	+	0.746229i	$0.268138\pi$
$368$		0			0
$369$	0.0632579	−	0.875586i	0.00329307	−	0.0455812i
$370$		0			0
$371$	2.49745	+	3.88610i	0.129661	+	0.201756i
$372$		0			0
$373$		−	27.8273i		−	1.44084i	−0.693538	−	0.720420i	$-0.743949\pi$
$373$		−	27.8273i		−	1.44084i	0.693538	−	0.720420i	$-0.256051\pi$
$374$		0			0
$375$	5.44418	−	3.77706i	0.281136	−	0.195046i
$376$		0			0
$377$	−10.5484	−	6.77903i	−0.543269	−	0.349138i
$378$		0			0
$379$	33.4407	+	15.2718i	1.71773	+	0.784461i	0.995704	+	0.0925970i	$0.0295168\pi$
$379$	33.4407	+	15.2718i	1.71773	+	0.784461i	0.722027	+	0.691865i	$0.243210\pi$
$380$		0			0
$381$	5.62963	−	3.90572i	0.288415	−	0.200096i
$382$		0			0
$383$	−12.5766	+	14.5142i	−0.642634	+	0.741639i	−0.979838	−	0.199793i	$-0.935973\pi$
$383$	−12.5766	+	14.5142i	−0.642634	+	0.741639i	0.337205	+	0.941431i	$0.390519\pi$
$384$		0			0
$385$	44.8327	−	6.44597i	2.28488	−	0.328517i
$386$		0			0
$387$	20.7375	+	1.49821i	1.05415	+	0.0761583i
$388$		0			0
$389$	−10.8893	+	16.9441i	−0.552109	+	0.859098i	−0.999377	−	0.0353022i	$-0.988761\pi$
$389$	−10.8893	+	16.9441i	−0.552109	+	0.859098i	0.447268	+	0.894400i	$0.352397\pi$
$390$		0			0
$391$	−3.90558	−	1.14678i	−0.197514	−	0.0579952i
$392$		0			0
$393$	−2.96243	+	4.98881i	−0.149435	+	0.251652i
$394$		0			0
$395$	−32.9978	+	28.5928i	−1.66030	+	1.43866i
$396$		0			0
$397$	−12.5930	−	3.69765i	−0.632026	−	0.185580i	−0.0499993	−	0.998749i	$-0.515922\pi$
$397$	−12.5930	−	3.69765i	−0.632026	−	0.185580i	−0.582027	+	0.813170i	$0.697740\pi$
$398$		0			0
$399$	−1.29914	−	0.140146i	−0.0650383	−	0.00701607i
$400$		0			0
$401$	30.6091			1.52854			0.764272	−	0.644894i	$-0.223099\pi$
$401$	30.6091			1.52854			0.764272	+	0.644894i	$0.223099\pi$
$402$		0			0
$403$	−10.2866			−0.512410
$404$		0			0
$405$	−20.0409	−	17.4162i	−0.995841	−	0.865419i
$406$		0			0
$407$	−9.72888	−	2.85666i	−0.482243	−	0.141599i
$408$		0			0
$409$	6.14065	−	5.32091i	0.303636	−	0.263102i	−0.489694	−	0.871895i	$-0.662891\pi$
$409$	6.14065	−	5.32091i	0.303636	−	0.263102i	0.793329	+	0.608793i	$0.208346\pi$
$410$		0			0
$411$	−22.4990	−	13.3603i	−1.10979	−	0.659013i
$412$		0			0
$413$	1.39087	+	0.408397i	0.0684404	+	0.0200959i
$414$		0			0
$415$	−19.8978	+	30.9615i	−0.976743	+	1.51984i
$416$		0			0
$417$	24.8533	+	10.3051i	1.21707	+	0.504642i
$418$		0			0
$419$	19.7307	−	2.83685i	0.963908	−	0.138589i	0.357649	−	0.933856i	$-0.383579\pi$
$419$	19.7307	−	2.83685i	0.963908	−	0.138589i	0.606259	+	0.795267i	$0.292669\pi$
$420$		0			0
$421$	−4.74306	+	5.47379i	−0.231163	+	0.266776i	−0.859467	−	0.511192i	$-0.829204\pi$
$421$	−4.74306	+	5.47379i	−0.231163	+	0.266776i	0.628304	+	0.777968i	$0.283750\pi$
$422$		0			0
$423$	−18.1884	−	13.6362i	−0.884352	−	0.663013i
$424$		0			0
$425$	17.9662	+	8.20488i	0.871488	+	0.397995i
$426$		0			0
$427$	−39.3937	−	25.3168i	−1.90639	−	1.22517i
$428$		0			0
$429$	5.75832	+	8.29994i	0.278014	+	0.400725i
$430$		0			0
$431$			10.6012i			0.510640i	0.966857	+	0.255320i	$0.0821809\pi$
$431$			10.6012i			0.510640i	−0.966857	+	0.255320i	$0.917819\pi$
$432$		0			0
$433$	12.1735	+	18.9423i	0.585021	+	0.910310i	1.00000		0.000479079i	$0.000152496\pi$
$433$	12.1735	+	18.9423i	0.585021	+	0.910310i	−0.414979	+	0.909831i	$0.636211\pi$
$434$		0			0
$435$	−41.1340	−	17.0557i	−1.97223	−	0.817756i
$436$		0			0
$437$	0.138275	−	0.0631480i	0.00661458	−	0.00302078i
$438$		0			0
$439$	−13.7539			−0.656438			−0.328219	−	0.944602i	$-0.606448\pi$
$439$	−13.7539			−0.656438			−0.328219	+	0.944602i	$0.606448\pi$
$440$		0			0
$441$	−7.71645	+	20.6431i	−0.367450	+	0.983005i
$442$		0			0
$443$	−2.76881	−	19.2575i	−0.131550	−	0.914950i	−0.943535	−	0.331272i	$-0.892522\pi$
$443$	−2.76881	−	19.2575i	−0.131550	−	0.914950i	0.811985	−	0.583678i	$-0.198387\pi$
$444$		0			0
$445$	−0.0458975	+	0.00659906i	−0.00217575	+	0.000312825i
$446$		0			0
$447$	−23.1180	+	21.5080i	−1.09344	+	1.01729i
$448$		0			0
$449$	38.1025	+	17.4008i	1.79817	+	0.821196i	0.962163	+	0.272473i	$0.0878417\pi$
$449$	38.1025	+	17.4008i	1.79817	+	0.821196i	0.836005	+	0.548722i	$0.184886\pi$
$450$		0			0
$451$	−0.168806	+	1.17407i	−0.00794878	+	0.0552850i
$452$		0			0
$453$	−5.72723	+	0.202481i	−0.269089	+	0.00951337i
$454$		0			0
$455$	−2.28805	+	15.9138i	−0.107266	+	0.746049i
$456$		0			0
$457$	−11.0054	−	7.07271i	−0.514809	−	0.330848i	0.257307	−	0.966330i	$-0.417165\pi$
$457$	−11.0054	−	7.07271i	−0.514809	−	0.330848i	−0.772115	+	0.635482i	$0.780801\pi$
$458$		0			0
$459$	−4.95010	+	27.2677i	−0.231051	+	1.27275i
$460$		0			0
$461$	11.9303	+	18.5639i	0.555649	+	0.864607i	0.999504	−	0.0314915i	$-0.0100257\pi$
$461$	11.9303	+	18.5639i	0.555649	+	0.864607i	−0.443855	+	0.896099i	$0.646389\pi$
$462$		0			0
$463$	−11.2952	−	38.4680i	−0.524934	−	1.78776i	−0.611185	−	0.791488i	$-0.709307\pi$
$463$	−11.2952	−	38.4680i	−0.524934	−	1.78776i	0.0862514	−	0.996273i	$-0.472511\pi$
$464$		0			0
$465$	−35.9530	+	6.47325i	−1.66728	+	0.300190i
$466$		0			0
$467$	−17.4693	+	15.1372i	−0.808382	+	0.700467i	−0.957525	−	0.288349i	$-0.906894\pi$
$467$	−17.4693	+	15.1372i	−0.808382	+	0.700467i	0.149144	+	0.988816i	$0.452348\pi$
$468$		0			0
$469$	24.9583	−	18.3921i	1.15247	−	0.849269i
$470$		0			0
$471$	17.7167	+	10.5205i	0.816343	+	0.484757i
$472$		0			0
$473$	−27.8070	−	3.99804i	−1.27857	−	0.183830i
$474$		0			0
$475$	−0.707727	+	0.207807i	−0.0324727	+	0.00953486i
$476$		0			0
$477$	−1.28110	+	3.42722i	−0.0586576	+	0.156921i
$478$		0			0
$479$	23.8724	−	10.9021i	1.09076	−	0.498132i	0.212909	−	0.977072i	$-0.431706\pi$
$479$	23.8724	−	10.9021i	1.09076	−	0.498132i	0.877848	+	0.478940i	$0.158979\pi$
$480$		0			0
$481$	1.94584	−	3.02779i	0.0887229	−	0.138055i
$482$		0			0
$483$	−0.887202	−	4.92760i	−0.0403691	−	0.224214i
$484$		0			0
$485$	13.2949	−	45.2782i	0.603690	−	2.05598i
$486$		0			0
$487$	−1.33732	−	0.192278i	−0.0605997	−	0.00871293i	0.111948	−	0.993714i	$-0.464291\pi$
$487$	−1.33732	−	0.192278i	−0.0605997	−	0.00871293i	−0.172548	+	0.985001i	$0.555200\pi$
$488$		0			0
$489$	3.31939	−	30.7705i	0.150108	−	1.39149i
$490$		0			0
$491$	−29.2186	+	13.3437i	−1.31862	+	0.602193i	−0.945509	−	0.325595i	$-0.894435\pi$
$491$	−29.2186	+	13.3437i	−1.31862	+	0.602193i	−0.373109	+	0.927788i	$0.621708\pi$
$492$		0			0
$493$	6.61466	+	46.0059i	0.297909	+	2.07200i
$494$		0			0
$495$	25.3492	+	25.3858i	1.13936	+	1.14101i
$496$		0			0
$497$	−2.43491	+	1.56482i	−0.109221	+	0.0701919i
$498$		0			0
$499$			12.9260i			0.578646i	0.957231	+	0.289323i	$0.0934302\pi$
$499$			12.9260i			0.578646i	−0.957231	+	0.289323i	$0.906570\pi$
$500$		0			0
$501$	−0.869541	+	0.808986i	−0.0388482	+	0.0361428i
$502$		0			0
$503$	−12.5972	+	14.5380i	−0.561682	+	0.648215i	−0.963565	−	0.267476i	$-0.913810\pi$
$503$	−12.5972	+	14.5380i	−0.561682	+	0.648215i	0.401883	+	0.915691i	$0.368356\pi$
$504$		0			0
$505$	34.3919	−	22.1024i	1.53042	−	0.983542i
$506$		0			0
$507$	17.9643	−	5.97190i	0.797823	−	0.265221i
$508$		0			0
$509$	−5.63479	−	19.1903i	−0.249758	−	0.850597i	−0.984965	−	0.172754i	$-0.944733\pi$
$509$	−5.63479	−	19.1903i	−0.249758	−	0.850597i	0.735207	−	0.677842i	$-0.237085\pi$
$510$		0			0
$511$	23.9952	−	37.3373i	1.06149	−	1.65171i
$512$		0			0
$513$	−0.527145	−	0.890650i	−0.0232740	−	0.0393232i
$514$		0			0
$515$	−0.526367	+	0.154555i	−0.0231945	+	0.00681052i
$516$		0			0
$517$	23.2131	+	20.1143i	1.02091	+	0.884625i
$518$		0			0
$519$	−33.2420	+	16.6248i	−1.45916	+	0.729746i
$520$		0			0
$521$	−14.3488	+	16.5594i	−0.628632	+	0.725480i	−0.977322	−	0.211758i	$-0.932081\pi$
$521$	−14.3488	+	16.5594i	−0.628632	+	0.725480i	0.348690	+	0.937238i	$0.386627\pi$
$522$		0			0
$523$	−1.74778	−	1.12323i	−0.0764251	−	0.0491154i	0.501870	−	0.864943i	$-0.332645\pi$
$523$	−1.74778	−	1.12323i	−0.0764251	−	0.0491154i	−0.578295	+	0.815828i	$0.696282\pi$
$524$		0			0
$525$	0.858376	+	24.2794i	0.0374626	+	1.05964i
$526$		0			0
$527$	24.9700	+	28.8169i	1.08771	+	1.25528i
$528$		0			0
$529$	−14.6804	−	16.9420i	−0.638277	−	0.736610i
$530$		0			0
$531$	0.400463	+	1.07605i	0.0173786	+	0.0466967i
$532$		0			0
$533$	−0.382986	−	0.174904i	−0.0165890	−	0.00757592i
$534$		0			0
$535$		−	33.5553i		−	1.45072i
$536$		0			0
$537$	5.49229	−	1.82581i	0.237010	−	0.0787895i
$538$		0			0
$539$	12.3699	−	27.0864i	0.532811	−	1.16669i
$540$		0			0
$541$	−10.1591	+	34.5988i	−0.436775	+	1.48752i	0.387788	+	0.921748i	$0.373239\pi$
$541$	−10.1591	+	34.5988i	−0.436775	+	1.48752i	−0.824563	+	0.565770i	$0.808579\pi$
$542$		0			0
$543$	3.69707	+	2.19537i	0.158656	+	0.0942125i
$544$		0			0
$545$	32.6466	−	28.2884i	1.39843	−	1.21174i
$546$		0			0
$547$	7.92881	−	27.0031i	0.339012	−	1.15457i	−0.596895	−	0.802319i	$-0.703599\pi$
$547$	7.92881	−	27.0031i	0.339012	−	1.15457i	0.935907	−	0.352248i	$-0.114583\pi$
$548$		0			0
$549$	−2.61928	−	36.9972i	−0.111788	−	1.57900i
$550$		0			0
$551$	−1.31180	−	1.13668i	−0.0558847	−	0.0484244i
$552$		0			0
$553$	7.97780	+	55.4868i	0.339251	+	2.35954i
$554$		0			0
$555$	4.89563	−	11.8071i	0.207808	−	0.501182i
$556$		0			0
$557$	−6.49987	−	22.1365i	−0.275409	−	0.937955i	−0.974775	−	0.223192i	$-0.928352\pi$
$557$	−6.49987	−	22.1365i	−0.275409	−	0.937955i	0.699366	−	0.714764i	$-0.253466\pi$
$558$		0			0
$559$	4.14245	−	9.07070i	0.175207	−	0.383650i
$560$		0			0
$561$	9.27359	−	36.2789i	0.391531	−	1.53170i
$562$		0			0
$563$	23.5092	−	6.90294i	0.990797	−	0.290924i	0.254123	−	0.967172i	$-0.418213\pi$
$563$	23.5092	−	6.90294i	0.990797	−	0.290924i	0.736674	+	0.676248i	$0.236395\pi$
$564$		0			0
$565$	40.5903			1.70765
$566$		0			0
$567$	−32.7216	+	9.55667i	−1.37418	+	0.401343i
$568$		0			0
$569$	−4.98397	−	4.31864i	−0.208939	−	0.181047i	0.544104	−	0.839018i	$-0.316870\pi$
$569$	−4.98397	−	4.31864i	−0.208939	−	0.181047i	−0.753043	+	0.657971i	$0.771415\pi$
$570$		0			0
$571$	8.65212	+	18.9455i	0.362080	+	0.792844i	0.999746	+	0.0225316i	$0.00717263\pi$
$571$	8.65212	+	18.9455i	0.362080	+	0.792844i	−0.637666	+	0.770313i	$0.720100\pi$
$572$		0			0
$573$	−9.17105	+	3.04875i	−0.383126	+	0.127363i
$574$		0			0
$575$	−1.52802	−	2.37764i	−0.0637226	−	0.0991544i
$576$		0			0
$577$	20.2236	−	2.90771i	0.841918	−	0.121049i	0.292156	−	0.956371i	$-0.405627\pi$
$577$	20.2236	−	2.90771i	0.841918	−	0.121049i	0.549762	+	0.835321i	$0.314718\pi$
$578$		0			0
$579$	−15.9250	−	31.8429i	−0.661822	−	1.32334i
$580$		0			0
$581$	19.6292	+	42.9820i	0.814358	+	1.78319i
$582$		0			0
$583$	2.05369	−	4.49694i	0.0850550	−	0.186244i
$584$		0			0
$585$	−11.1809	+	6.09478i	−0.462274	+	0.251988i
$586$		0			0
$587$	13.5582	+	3.98104i	0.559606	+	0.164315i	0.549290	−	0.835632i	$-0.314898\pi$
$587$	13.5582	+	3.98104i	0.559606	+	0.164315i	0.0103159	+	0.999947i	$0.496716\pi$
$588$		0			0
$589$	−1.40948	−	0.202653i	−0.0580767	−	0.00835017i
$590$		0			0
$591$	−4.15525	−	1.06216i	−0.170924	−	0.0436914i
$592$		0			0
$593$	−8.23739	−	18.0374i	−0.338269	−	0.740706i	0.661690	−	0.749778i	$-0.269840\pi$
$593$	−8.23739	−	18.0374i	−0.338269	−	0.740706i	−0.999959	+	0.00907163i	$0.997112\pi$
$594$		0			0
$595$	50.1351	−	32.2198i	2.05534	−	1.32088i
$596$		0			0
$597$	−7.16460	+	4.97064i	−0.293228	+	0.203435i
$598$		0			0
$599$	3.41470	−	23.7497i	0.139521	−	0.970388i	−0.792987	−	0.609239i	$-0.791475\pi$
$599$	3.41470	−	23.7497i	0.139521	−	0.970388i	0.932508	−	0.361150i	$-0.117616\pi$
$600$		0			0
$601$	−13.9003	−	16.0418i	−0.567004	−	0.654358i	0.397755	−	0.917492i	$-0.369789\pi$
$601$	−13.9003	−	16.0418i	−0.567004	−	0.654358i	−0.964759	+	0.263134i	$0.915244\pi$
$602$		0			0
$603$	23.5035	+	7.11229i	0.957137	+	0.289635i
$604$		0			0
$605$	−10.4921	−	12.1085i	−0.426564	−	0.492281i
$606$		0			0
$607$	2.80749	−	19.5266i	0.113953	−	0.792558i	−0.850057	−	0.526691i	$-0.823433\pi$
$607$	2.80749	−	19.5266i	0.113953	−	0.792558i	0.964010	−	0.265867i	$-0.0856583\pi$
$608$		0			0
$609$	−46.9733	+	32.5890i	−1.90345	+	1.32057i
$610$		0			0
$611$	−9.17194	+	5.89445i	−0.371057	+	0.238464i
$612$		0			0
$613$	−3.16626	−	6.93315i	−0.127884	−	0.280027i	0.834850	−	0.550478i	$-0.185555\pi$
$613$	−3.16626	−	6.93315i	−0.127884	−	0.280027i	−0.962734	+	0.270451i	$0.912827\pi$
$614$		0			0
$615$	−1.44865	−	0.370304i	−0.0584154	−	0.0149321i
$616$		0			0
$617$	−3.30061	−	0.474556i	−0.132877	−	0.0191049i	0.0755552	−	0.997142i	$-0.475927\pi$
$617$	−3.30061	−	0.474556i	−0.132877	−	0.0191049i	−0.208433	+	0.978037i	$0.566836\pi$
$618$		0			0
$619$	45.2582	+	13.2890i	1.81908	+	0.534130i	0.999259	−	0.0384883i	$-0.0122542\pi$
$619$	45.2582	+	13.2890i	1.81908	+	0.534130i	0.819822	+	0.572619i	$0.194072\pi$
$620$		0			0
$621$	2.70543	−	2.89954i	0.108565	−	0.116354i
$622$		0			0
$623$	−0.0247309	+	0.0541531i	−0.000990822	+	0.00216960i
$624$		0			0
$625$	−12.3803	−	27.1090i	−0.495211	−	1.08436i
$626$		0			0
$627$	0.625499	+	1.25071i	0.0249800	+	0.0499487i
$628$		0			0
$629$	−13.2055	+	1.89866i	−0.526537	+	0.0757046i
$630$		0			0
$631$	−19.5180	−	30.3706i	−0.776999	−	1.20903i	−0.973535	−	0.228537i	$-0.926606\pi$
$631$	−19.5180	−	30.3706i	−0.776999	−	1.20903i	0.196537	−	0.980496i	$-0.437031\pi$
$632$		0			0
$633$	−35.7879	+	11.8970i	−1.42244	+	0.472865i
$634$		0			0
$635$	−4.84806	−	10.6158i	−0.192389	−	0.421274i
$636$		0			0
$637$	7.98807	+	6.92170i	0.316499	+	0.274248i
$638$		0			0
$639$	−2.14739	−	0.802699i	−0.0849493	−	0.0317543i
$640$		0			0
$641$	−19.0369			−0.751914			−0.375957	−	0.926637i	$-0.622686\pi$
$641$	−19.0369			−0.751914			−0.375957	+	0.926637i	$0.622686\pi$
$642$		0			0
$643$	−26.1566	+	7.68027i	−1.03152	+	0.302880i	−0.753327	−	0.657646i	$-0.771552\pi$
$643$	−26.1566	+	7.68027i	−1.03152	+	0.302880i	−0.278189	+	0.960526i	$0.589734\pi$
$644$		0			0
$645$	8.77033	−	34.3102i	0.345331	−	1.35096i
$646$		0			0
$647$	−19.9666	+	43.7207i	−0.784968	+	1.71884i	−0.0944441	+	0.995530i	$0.530107\pi$
$647$	−19.9666	+	43.7207i	−0.784968	+	1.71884i	−0.690524	+	0.723310i	$0.742620\pi$
$648$		0			0
$649$	−0.437066	−	1.48851i	−0.0171564	−	0.0584292i
$650$		0			0
$651$	−17.9641	+	43.3250i	−0.704069	+	1.69804i
$652$		0			0
$653$	−1.49965	−	10.4303i	−0.0586860	−	0.408170i	−0.997896	−	0.0648281i	$-0.979350\pi$
$653$	−1.49965	−	10.4303i	−0.0586860	−	0.408170i	0.939210	−	0.343342i	$-0.111559\pi$
$654$		0			0
$655$	7.46865	+	6.47162i	0.291824	+	0.252867i
$656$		0			0
$657$	35.0659	−	2.48255i	1.36805	−	0.0968534i
$658$		0			0
$659$	−3.84876	+	13.1077i	−0.149926	+	0.510602i	−0.999868	−	0.0162753i	$-0.994819\pi$
$659$	−3.84876	+	13.1077i	−0.149926	+	0.510602i	0.849941	+	0.526878i	$0.176637\pi$
$660$		0			0
$661$	−6.20052	+	5.37278i	−0.241172	+	0.208977i	−0.767057	−	0.641579i	$-0.778280\pi$
$661$	−6.20052	+	5.37278i	−0.241172	+	0.208977i	0.525885	+	0.850556i	$0.323734\pi$
$662$		0			0
$663$	11.4285	+	6.78643i	0.443847	+	0.263563i
$664$		0			0
$665$	−0.627026	+	2.13545i	−0.0243150	+	0.0828093i
$666$		0			0
$667$	2.76292	−	6.04994i	0.106981	−	0.234255i
$668$		0			0
$669$	36.8719	−	12.2574i	1.42555	−	0.473898i
$670$		0			0
$671$			50.1146i			1.93465i
$672$		0			0
$673$	12.7092	+	5.80409i	0.489903	+	0.223731i	0.645021	−	0.764165i	$-0.276849\pi$
$673$	12.7092	+	5.80409i	0.489903	+	0.223731i	−0.155118	+	0.987896i	$0.549576\pi$
$674$		0			0
$675$	−14.9962	+	12.0579i	−0.577203	+	0.464110i
$676$		0			0
$677$	−1.10341	−	1.27340i	−0.0424073	−	0.0489407i	0.734150	−	0.678988i	$-0.237581\pi$
$677$	−1.10341	−	1.27340i	−0.0424073	−	0.0489407i	−0.776557	+	0.630047i	$0.783036\pi$
$678$		0			0
$679$	−39.6755	−	45.7880i	−1.52261	−	1.75718i
$680$		0			0
$681$	−0.272438	−	7.70601i	−0.0104399	−	0.295295i
$682$		0			0
$683$	−12.0221	−	7.72614i	−0.460013	−	0.295633i	0.290035	−	0.957016i	$-0.406333\pi$
$683$	−12.0221	−	7.72614i	−0.460013	−	0.295633i	−0.750048	+	0.661384i	$0.769970\pi$
$684$		0			0
$685$	−29.1864	+	33.6828i	−1.11515	+	1.28696i
$686$		0			0
$687$	23.7813	−	11.8934i	0.907314	−	0.453760i
$688$		0			0
$689$	1.32620	+	1.14916i	0.0505241	+	0.0437794i
$690$		0			0
$691$	−16.0896	+	4.72433i	−0.612077	+	0.179722i	−0.573056	−	0.819516i	$-0.694242\pi$
$691$	−16.0896	+	4.72433i	−0.612077	+	0.179722i	−0.0390213	+	0.999238i	$0.512424\pi$
$692$		0			0
$693$	45.0139	−	9.75817i	1.70994	−	0.370682i
$694$		0			0
$695$	24.7755	−	38.5515i	0.939790	−	1.46234i
$696$		0			0
$697$	0.439696	+	1.49747i	0.0166547	+	0.0567206i
$698$		0			0
$699$	22.5766	−	7.50517i	0.853925	−	0.283872i
$700$		0			0
$701$	−14.5696	+	9.36331i	−0.550286	+	0.353647i	−0.786050	−	0.618163i	$-0.787877\pi$
$701$	−14.5696	+	9.36331i	−0.550286	+	0.353647i	0.235764	+	0.971810i	$0.424241\pi$
$702$		0			0
$703$	0.326272	−	0.376538i	0.0123056	−	0.0142014i
$704$		0			0
$705$	−28.3479	+	26.3737i	−1.06764	+	0.993292i
$706$		0			0
$707$		−	52.4875i		−	1.97399i
$708$		0			0
$709$	20.9318	−	13.4520i	0.786110	−	0.505202i	−0.0849464	−	0.996386i	$-0.527072\pi$
$709$	20.9318	−	13.4520i	0.786110	−	0.505202i	0.871056	+	0.491183i	$0.163436\pi$
$710$		0			0
$711$	−31.4185	+	31.3732i	−1.17829	+	1.17659i
$712$		0			0
$713$	−0.776511	−	5.40075i	−0.0290806	−	0.202260i
$714$		0			0
$715$	15.6512	−	7.14764i	0.585320	−	0.267307i
$716$		0			0
$717$	4.33947	−	40.2265i	0.162060	−	1.50228i
$718$		0			0
$719$	6.05908	+	0.871164i	0.225966	+	0.0324889i	0.254367	−	0.967108i	$-0.418133\pi$
$719$	6.05908	+	0.871164i	0.225966	+	0.0324889i	−0.0284019	+	0.999597i	$0.509042\pi$
$720$		0			0
$721$	−0.198431	+	0.675794i	−0.00738996	+	0.0251679i
$722$		0			0
$723$	−0.690157	−	3.83319i	−0.0256672	−	0.142558i
$724$		0			0
$725$	−17.4478	+	27.1493i	−0.647996	+	1.00830i
$726$		0			0
$727$	−14.1305	+	6.45316i	−0.524070	+	0.239335i	−0.659840	−	0.751406i	$-0.729376\pi$
$727$	−14.1305	+	6.45316i	−0.524070	+	0.239335i	0.135771	+	0.990740i	$0.456649\pi$
$728$		0			0
$729$	−21.5796	−	16.2272i	−0.799243	−	0.601008i
$730$		0			0
$731$	−35.4663	+	10.4138i	−1.31177	+	0.385169i
$732$		0			0
$733$	−25.2314	−	3.62773i	−0.931944	−	0.133993i	−0.340414	−	0.940276i	$-0.610567\pi$
$733$	−25.2314	−	3.62773i	−0.931944	−	0.133993i	−0.591531	+	0.806282i	$0.701476\pi$
$734$		0			0
$735$	32.2752	+	19.1655i	1.19049	+	0.706929i
$736$		0			0
$737$	−30.9993	−	11.8286i	−1.14187	−	0.435712i
$738$		0			0
$739$	−14.2599	+	12.3563i	−0.524558	+	0.454532i	−0.876439	−	0.481512i	$-0.840088\pi$
$739$	−14.2599	+	12.3563i	−0.524558	+	0.454532i	0.351881	+	0.936045i	$0.385542\pi$
$740$		0			0
$741$	−0.488521	+	0.0879570i	−0.0179463	+	0.00323118i
$742$		0			0
$743$	−11.9043	−	40.5424i	−0.436728	−	1.48736i	−0.824638	−	0.565661i	$-0.808621\pi$
$743$	−11.9043	−	40.5424i	−0.436728	−	1.48736i	0.387910	−	0.921697i	$-0.373197\pi$
$744$		0			0
$745$	29.0766	+	45.2441i	1.06529	+	1.65762i
$746$		0			0
$747$	−17.9602	+	32.8353i	−0.657128	+	1.20138i
$748$		0			0
$749$	−36.2422	−	23.2914i	−1.32426	−	0.851050i
$750$		0			0
$751$	0.861200	−	5.98978i	0.0314256	−	0.218570i	−0.968057	−	0.250730i	$-0.919329\pi$
$751$	0.861200	−	5.98978i	0.0314256	−	0.218570i	0.999483	+	0.0321598i	$0.0102385\pi$
$752$		0			0
$753$	−25.8283	+	0.913135i	−0.941236	+	0.0332765i
$754$		0			0
$755$	−1.38914	+	9.66168i	−0.0505560	+	0.351625i
$756$		0			0
$757$	0.504090	+	0.230210i	0.0183215	+	0.00836714i	0.424555	−	0.905402i	$-0.360431\pi$
$757$	0.504090	+	0.230210i	0.0183215	+	0.00836714i	−0.406233	+	0.913769i	$0.633158\pi$
$758$		0			0
$759$	−3.92303	+	3.64983i	−0.142397	+	0.132481i
$760$		0			0
$761$	−1.51723	+	0.218144i	−0.0549995	+	0.00790773i	−0.169760	−	0.985485i	$-0.554299\pi$
$761$	−1.51723	+	0.218144i	−0.0549995	+	0.00790773i	0.114760	+	0.993393i	$0.463390\pi$
$762$		0			0
$763$	−7.89288	−	54.8962i	−0.285741	−	1.98738i
$764$		0			0
$765$	44.2149	+	16.5276i	1.59859	+	0.597558i
$766$		0			0
$767$	0.550666			0.0198834
$768$		0			0
$769$	5.52872	−	2.52488i	0.199371	−	0.0910496i	−0.313228	−	0.949678i	$-0.601410\pi$
$769$	5.52872	−	2.52488i	0.199371	−	0.0910496i	0.512598	+	0.858629i	$0.328683\pi$
$770$		0			0
$771$	18.2945	+	7.58558i	0.658862	+	0.273188i
$772$		0			0
$773$	16.8998	+	26.2967i	0.607845	+	0.945825i	0.999668	+	0.0257841i	$0.00820825\pi$
$773$	16.8998	+	26.2967i	0.607845	+	0.945825i	−0.391823	+	0.920041i	$0.628155\pi$
$774$		0			0
$775$			26.4755i			0.951028i
$776$		0			0
$777$	−9.35432	−	13.4832i	−0.335584	−	0.483705i
$778$		0			0
$779$	−0.0490316	−	0.0315107i	−0.00175674	−	0.00112899i
$780$		0			0
$781$	2.81765	+	1.28678i	0.100823	+	0.0460445i
$782$		0			0
$783$	−42.9498	−	14.3467i	−1.53490	−	0.512709i
$784$		0			0
$785$	22.9826	−	26.5234i	0.820285	−	0.946659i
$786$		0			0
$787$	−24.4189	+	3.51090i	−0.870438	+	0.125150i	−0.563039	−	0.826430i	$-0.690368\pi$
$787$	−24.4189	+	3.51090i	−0.870438	+	0.125150i	−0.307399	+	0.951581i	$0.599459\pi$
$788$		0			0
$789$	−23.9223	−	9.91906i	−0.851657	−	0.353128i
$790$		0			0
$791$	28.1745	−	43.8404i	1.00177	−	1.55879i
$792$		0			0
$793$	−17.0681	−	5.01164i	−0.606105	−	0.177968i
$794$		0			0
$795$	5.35840	+	3.18190i	0.190043	+	0.112850i
$796$		0			0
$797$	37.9773	−	32.9075i	1.34522	−	1.16564i	0.374013	−	0.927423i	$-0.377981\pi$
$797$	37.9773	−	32.9075i	1.34522	−	1.16564i	0.971211	−	0.238220i	$-0.0765640\pi$
$798$		0			0
$799$	38.7770	+	11.3860i	1.37183	+	0.402806i
$800$		0			0
$801$	−0.0460830	+	0.00998993i	−0.00162826	+	0.000352977i
$802$		0			0
$803$	−47.4986			−1.67619
$804$		0			0
$805$	−8.52792			−0.300570
$806$		0			0
$807$	−35.8368	−	3.86593i	−1.26152	−	0.136087i
$808$		0			0
$809$	−15.9590	−	4.68600i	−0.561090	−	0.164751i	−0.0111243	−	0.999938i	$-0.503541\pi$
$809$	−15.9590	−	4.68600i	−0.561090	−	0.164751i	−0.549966	+	0.835187i	$0.685359\pi$
$810$		0			0
$811$	−31.8586	+	27.6056i	−1.11871	+	0.969365i	−0.999723	−	0.0235312i	$-0.992509\pi$
$811$	−31.8586	+	27.6056i	−1.11871	+	0.969365i	−0.118984	+	0.992896i	$0.537964\pi$
$812$		0			0
$813$	−25.7359	+	43.3399i	−0.902598	+	1.52000i
$814$		0			0
$815$	−50.5788	−	14.8513i	−1.77170	−	0.520218i
$816$		0			0
$817$	0.746304	−	1.16127i	0.0261099	−	0.0406278i
$818$		0			0
$819$	−1.17810	+	16.3067i	−0.0411662	+	0.569802i
$820$		0			0
$821$	33.2770	−	4.78451i	1.16137	−	0.166980i	0.465436	−	0.885082i	$-0.345898\pi$
$821$	33.2770	−	4.78451i	1.16137	−	0.166980i	0.695939	+	0.718101i	$0.254989\pi$
$822$		0			0
$823$	5.30667	−	6.12422i	0.184979	−	0.213477i	−0.655685	−	0.755035i	$-0.727620\pi$
$823$	5.30667	−	6.12422i	0.184979	−	0.213477i	0.840663	+	0.541558i	$0.182165\pi$
$824$		0			0
$825$	21.3623	−	14.8207i	0.743741	−	0.515991i
$826$		0			0
$827$	24.7893	+	11.3209i	0.862008	+	0.393666i	0.796827	−	0.604208i	$-0.206510\pi$
$827$	24.7893	+	11.3209i	0.862008	+	0.393666i	0.0651809	+	0.997873i	$0.479238\pi$
$828$		0			0
$829$	−2.65572	−	1.70673i	−0.0922369	−	0.0592771i	0.493709	−	0.869627i	$-0.335641\pi$
$829$	−2.65572	−	1.70673i	−0.0922369	−	0.0592771i	−0.585946	+	0.810350i	$0.699277\pi$
$830$		0			0
$831$	−34.9905	+	24.2756i	−1.21381	+	0.842112i
$832$		0			0
$833$		−	39.1798i		−	1.35750i
$834$		0			0
$835$	1.09367	+	1.70178i	0.0378478	+	0.0588924i
$836$		0			0
$837$	−36.0046	+	9.14816i	−1.24450	+	0.316207i
$838$		0			0
$839$	21.6673	−	9.89514i	0.748040	−	0.341618i	−0.00465394	−	0.999989i	$-0.501481\pi$
$839$	21.6673	−	9.89514i	0.748040	−	0.341618i	0.752694	+	0.658371i	$0.228754\pi$
$840$		0			0
$841$	−46.9450			−1.61879
$842$		0			0
$843$	35.8524	−	44.4573i	1.23482	−	1.53119i
$844$		0			0
$845$	−4.58883	−	31.9160i	−0.157861	−	1.09794i
$846$		0			0
$847$	−20.3608	+	2.92745i	−0.699607	+	0.100588i
$848$		0			0
$849$	−6.10371	−	6.56059i	−0.209479	−	0.225159i
$850$		0			0
$851$	1.73657	+	0.793064i	0.0595288	+	0.0271859i
$852$		0			0
$853$	5.84235	−	40.6345i	0.200038	−	1.39130i	−0.604125	−	0.796889i	$-0.706477\pi$
$853$	5.84235	−	40.6345i	0.200038	−	1.39130i	0.804164	−	0.594408i	$-0.202614\pi$
$854$		0			0
$855$	−1.65210	+	0.614844i	−0.0565006	+	0.0210272i
$856$		0			0
$857$	−6.06500	+	42.1830i	−0.207177	+	1.44094i	0.575136	+	0.818058i	$0.304949\pi$
$857$	−6.06500	+	42.1830i	−0.207177	+	1.44094i	−0.782312	+	0.622886i	$0.785960\pi$
$858$		0			0
$859$	15.5190	+	9.97347i	0.529502	+	0.340290i	0.777921	−	0.628362i	$-0.216275\pi$
$859$	15.5190	+	9.97347i	0.529502	+	0.340290i	−0.248419	+	0.968653i	$0.579911\pi$
$860$		0			0
$861$	−1.40549	+	1.30762i	−0.0478991	+	0.0445634i
$862$		0			0
$863$	7.30510	+	11.3670i	0.248668	+	0.386936i	0.943039	−	0.332682i	$-0.107954\pi$
$863$	7.30510	+	11.3670i	0.248668	+	0.386936i	−0.694371	+	0.719618i	$0.744317\pi$
$864$		0			0
$865$	17.8352	+	60.7412i	0.606416	+	2.06526i
$866$		0			0
$867$	−3.51284	−	19.5107i	−0.119302	−	0.662616i
$868$		0			0
$869$	45.3393	−	39.2868i	1.53803	−	1.33271i
$870$		0			0
$871$	7.12863	−	9.37486i	0.241544	−	0.317655i
$872$		0			0
$873$	10.2343	−	46.8835i	0.346378	−	1.58677i
$874$		0			0
$875$	−14.3424	−	2.06212i	−0.484861	−	0.0697124i
$876$		0			0
$877$	−15.3290	+	4.50101i	−0.517624	+	0.151988i	−0.530102	−	0.847934i	$-0.677846\pi$
$877$	−15.3290	+	4.50101i	−0.517624	+	0.151988i	0.0124776	+	0.999922i	$0.496028\pi$
$878$		0			0
$879$	−2.57114	−	2.07348i	−0.0867223	−	0.0699369i
$880$		0			0
$881$	15.1214	−	6.90569i	0.509452	−	0.232659i	−0.144069	−	0.989568i	$-0.546019\pi$
$881$	15.1214	−	6.90569i	0.509452	−	0.232659i	0.653520	+	0.756909i	$0.273291\pi$
$882$		0			0
$883$	−13.6674	+	21.2668i	−0.459943	+	0.715686i	−0.991323	−	0.131448i	$-0.958037\pi$
$883$	−13.6674	+	21.2668i	−0.459943	+	0.715686i	0.531380	+	0.847134i	$0.321674\pi$
$884$		0			0
$885$	1.92466	−	0.346530i	0.0646966	−	0.0116485i
$886$		0			0
$887$	−14.8180	+	50.4653i	−0.497538	+	1.69446i	0.201595	+	0.979469i	$0.435387\pi$
$887$	−14.8180	+	50.4653i	−0.497538	+	1.69446i	−0.699134	+	0.714991i	$0.746431\pi$
$888$		0			0
$889$	−14.8309	−	2.13237i	−0.497413	−	0.0715172i
$890$		0			0
$891$	27.5364	+	23.9301i	0.922505	+	0.801688i
$892$		0			0
$893$	−1.37288	+	0.626972i	−0.0459416	+	0.0209808i
$894$		0			0
$895$	−1.40296	−	9.75780i	−0.0468958	−	0.326167i
$896$		0			0
$897$	−0.850746	−	1.70111i	−0.0284056	−	0.0567983i
$898$		0			0
$899$	−52.4128	+	33.6837i	−1.74807	+	1.12341i
$900$		0			0
$901$		−	6.50472i		−	0.216704i
$902$		0			0
$903$	−30.9698	−	33.2880i	−1.03061	−	1.10775i
$904$		0			0
$905$	4.79594	−	5.53481i	0.159422	−	0.183983i
$906$		0			0
$907$	41.5788	−	26.7211i	1.38060	−	0.887259i	0.381294	−	0.924454i	$-0.375478\pi$
$907$	41.5788	−	26.7211i	1.38060	−	0.887259i	0.999308	+	0.0371944i	$0.0118421\pi$
$908$		0			0
$909$	33.2988	−	24.8897i	1.10445	−	0.825540i
$910$		0			0
$911$	−8.68233	−	29.5693i	−0.287659	−	0.979675i	−0.968866	−	0.247585i	$-0.920363\pi$
$911$	−8.68233	−	29.5693i	−0.287659	−	0.979675i	0.681208	−	0.732090i	$-0.261455\pi$
$912$		0			0
$913$	27.3397	−	42.5415i	0.904813	−	1.40792i
$914$		0			0
$915$	−62.8091	−	6.77559i	−2.07640	−	0.223994i
$916$		0			0
$917$	12.1740	−	3.57460i	0.402019	−	0.118044i
$918$		0			0
$919$	35.9822	+	31.1787i	1.18694	+	1.02849i	0.998926	+	0.0463247i	$0.0147509\pi$
$919$	35.9822	+	31.1787i	1.18694	+	1.02849i	0.188015	+	0.982166i	$0.439795\pi$
$920$		0			0
$921$	−2.10873	−	4.21649i	−0.0694849	−	0.138938i
$922$		0			0
$923$	−0.720026	+	0.830954i	−0.0236999	+	0.0273512i
$924$		0			0
$925$	−7.79291	−	5.00820i	−0.256229	−	0.164669i
$926$		0			0
$927$	−0.522830	+	0.194576i	−0.0171720	+	0.00639072i
$928$		0			0
$929$	34.8473	+	40.2159i	1.14330	+	1.31944i	0.940332	+	0.340258i	$0.110514\pi$
$929$	34.8473	+	40.2159i	1.14330	+	1.31944i	0.202971	+	0.979185i	$0.434940\pi$
$930$		0			0
$931$	0.958175	+	1.10579i	0.0314029	+	0.0362409i
$932$		0			0
$933$	2.73130	−	0.0965624i	0.0894187	−	0.00316131i
$934$		0			0
$935$	−58.0156	−	26.4948i	−1.89731	−	0.866474i
$936$		0			0
$937$		−	23.3787i		−	0.763748i	−0.924214	−	0.381874i	$-0.875279\pi$
$937$		−	23.3787i		−	0.763748i	0.924214	−	0.381874i	$-0.124721\pi$
$938$		0			0
$939$	−1.29317	−	3.89005i	−0.0422012	−	0.126947i
$940$		0			0
$941$	6.54190	−	14.3248i	0.213260	−	0.466974i	−0.772526	−	0.634984i	$-0.781007\pi$
$941$	6.54190	−	14.3248i	0.213260	−	0.466974i	0.985785	+	0.168010i	$0.0537341\pi$
$942$		0			0
$943$	0.0629189	−	0.214282i	0.00204892	−	0.00697798i
$944$		0			0
$945$	6.14404	+	57.7356i	0.199866	+	1.87814i
$946$		0			0
$947$	1.36387	−	1.18180i	0.0443198	−	0.0384034i	−0.632419	−	0.774626i	$-0.717938\pi$
$947$	1.36387	−	1.18180i	0.0443198	−	0.0384034i	0.676739	+	0.736223i	$0.263393\pi$
$948$		0			0
$949$	4.75003	−	16.1771i	0.154192	−	0.525131i
$950$		0			0
$951$	−0.697651	+	2.72926i	−0.0226229	+	0.0885024i
$952$		0			0
$953$	−26.8276	−	23.2462i	−0.869031	−	0.753020i	0.101286	−	0.994857i	$-0.467704\pi$
$953$	−26.8276	−	23.2462i	−0.869031	−	0.753020i	−0.970317	+	0.241838i	$0.922250\pi$
$954$		0			0
$955$	2.34267	+	16.2936i	0.0758069	+	0.527249i
$956$		0			0
$957$	56.5186	+	23.4347i	1.82699	+	0.757535i
$958$		0			0
$959$	16.1211	+	54.9033i	0.520576	+	1.77292i
$960$		0			0
$961$	−8.35481	+	18.2945i	−0.269510	+	0.590145i
$962$		0			0
$963$	−2.40973	−	34.0374i	−0.0776525	−	1.09684i
$964$		0			0
$965$	−58.1847	+	17.0846i	−1.87303	+	0.549972i
$966$		0			0
$967$	−21.1933			−0.681530			−0.340765	−	0.940149i	$-0.610686\pi$
$967$	−21.1933			−0.681530			−0.340765	+	0.940149i	$0.610686\pi$
$968$		0			0
$969$	1.43226	+	1.15504i	0.0460107	+	0.0371051i
$970$		0			0
$971$	13.2617	+	11.4913i	0.425587	+	0.368774i	0.841160	−	0.540787i	$-0.181873\pi$
$971$	13.2617	+	11.4913i	0.425587	+	0.368774i	−0.415573	+	0.909560i	$0.636419\pi$
$972$		0			0
$973$	−24.4412	−	53.5187i	−0.783548	−	1.71573i
$974$		0			0
$975$	2.91134	+	8.75772i	0.0932376	+	0.280472i
$976$		0			0
$977$	−7.36138	−	11.4545i	−0.235511	−	0.366463i	0.703301	−	0.710892i	$-0.251709\pi$
$977$	−7.36138	−	11.4545i	−0.235511	−	0.366463i	−0.938812	+	0.344429i	$0.888072\pi$
$978$		0			0
$979$	0.0630636	−	0.00906718i	0.00201552	−	0.000289788i
$980$		0			0
$981$	31.0841	−	31.0393i	0.992439	−	0.991008i
$982$		0			0
$983$	19.7227	+	43.1868i	0.629058	+	1.37744i	0.908744	+	0.417353i	$0.137042\pi$
$983$	19.7227	+	43.1868i	0.629058	+	1.37744i	−0.279686	+	0.960091i	$0.590230\pi$
$984$		0			0
$985$	−3.03462	+	6.64488i	−0.0966909	+	0.211723i
$986$		0			0
$987$	8.80869	+	48.9243i	0.280384	+	1.55728i
$988$		0			0
$989$	5.07509	+	1.49018i	0.161379	+	0.0473850i
$990$		0			0
$991$	13.7419	+	1.97579i	0.436527	+	0.0627631i	0.357075	−	0.934076i	$-0.383774\pi$
$991$	13.7419	+	1.97579i	0.436527	+	0.0627631i	0.0794517	+	0.996839i	$0.474683\pi$
$992$		0			0
$993$	12.2754	−	48.0224i	0.389549	−	1.52395i
$994$		0			0
$995$	6.16993	+	13.5103i	0.195600	+	0.428304i
$996$		0			0
$997$	2.72231	−	1.74952i	0.0862165	−	0.0554080i	−0.496822	−	0.867852i	$-0.665500\pi$
$997$	2.72231	−	1.74952i	0.0862165	−	0.0554080i	0.583039	+	0.812444i	$0.301864\pi$
$998$		0			0
$999$	4.11806	−	12.3283i	0.130290	−	0.390049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.s.b.161.12	yes	200
3.2	odd	2	inner	804.2.s.b.161.6	yes	200
67.5	odd	22	inner	804.2.s.b.5.6	✓	200
201.5	even	22	inner	804.2.s.b.5.12	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.6	✓	200	67.5	odd	22	inner
804.2.s.b.5.12	yes	200	201.5	even	22	inner
804.2.s.b.161.6	yes	200	3.2	odd	2	inner
804.2.s.b.161.12	yes	200	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.185769 - 1.72206i) q^{3} +(-2.83063 - 0.831147i) q^{5} +(-2.86249 + 2.48036i) q^{7} +(-2.93098 - 0.639810i) q^{9} +O(q^{10})\)	\(q+(0.185769 - 1.72206i) q^{3} +(-2.83063 - 0.831147i) q^{5} +(-2.86249 + 2.48036i) q^{7} +(-2.93098 - 0.639810i) q^{9} +(3.88931 + 1.14200i) q^{11} +(-0.777890 + 1.21042i) q^{13} +(-1.95713 + 4.72011i) q^{15} +(5.27916 - 0.759028i) q^{17} +(-0.130434 + 0.150529i) q^{19} +(3.73957 + 5.39016i) q^{21} +(-0.694228 - 0.317043i) q^{23} +(3.11537 + 2.00213i) q^{25} +(-1.64628 + 4.92847i) q^{27} +8.71464i q^{29} +(3.86518 + 6.01434i) q^{31} +(2.68911 - 6.48548i) q^{33} +(10.1642 - 4.64183i) q^{35} -2.50144 q^{37} +(1.93991 + 1.56443i) q^{39} +(0.0416445 + 0.289644i) q^{41} +(-6.85998 + 0.986316i) q^{43} +(7.76473 + 4.24714i) q^{45} +(6.89272 + 3.14780i) q^{47} +(1.04545 - 7.27129i) q^{49} +(-0.326389 - 9.23202i) q^{51} +(0.173569 - 1.20720i) q^{53} +(-10.0600 - 6.46518i) q^{55} +(0.234989 + 0.252578i) q^{57} +(-0.206913 - 0.321963i) q^{59} +(3.48314 + 11.8625i) q^{61} +(9.97687 - 5.43844i) q^{63} +(3.20795 - 2.77971i) q^{65} +(-8.15987 - 0.645356i) q^{67} +(-0.674933 + 1.13660i) q^{69} +(0.756392 + 0.108753i) q^{71} +(-11.2432 + 3.30131i) q^{73} +(4.02652 - 4.99292i) q^{75} +(-13.9657 + 6.37792i) q^{77} +(8.00157 - 12.4507i) q^{79} +(8.18129 + 3.75054i) q^{81} +(3.51473 - 11.9701i) q^{83} +(-15.5742 - 2.23923i) q^{85} +(15.0071 + 1.61891i) q^{87} +(0.0142974 - 0.00652940i) q^{89} +(-0.775578 - 5.39427i) q^{91} +(11.0751 - 5.53880i) q^{93} +(0.494321 - 0.317681i) q^{95} +15.9958i q^{97} +(-10.6688 - 5.83561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 200 * q - 10 * q^9	\( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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