LMFDB - Embedded newform 405.2.f.a.242.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(242,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("405.242");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.f (of order $4$, degree $2$, 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			242.7
Root			$0.430324 + 1.60599i$ of defining polynomial
Character	$\chi$	$=$	405.242
Dual form			405.2.f.a.323.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17567 - 1.17567i) q^{2} -0.764383i q^{4} +(-0.981675 + 2.00906i) q^{5} +(1.27193 + 1.27193i) q^{7} +(1.45267 + 1.45267i) q^{8} +O(q^{10})$	\(q+(1.17567 - 1.17567i) q^{2} -0.764383i q^{4} +(-0.981675 + 2.00906i) q^{5} +(1.27193 + 1.27193i) q^{7} +(1.45267 + 1.45267i) q^{8} +(1.20786 + 3.51610i) q^{10} +3.61002i q^{11} +(0.935928 - 0.935928i) q^{13} +2.99073 q^{14} +4.94448 q^{16} +(-0.277007 + 0.277007i) q^{17} -6.25273i q^{19} +(1.53569 + 0.750376i) q^{20} +(4.24417 + 4.24417i) q^{22} +(-1.58377 - 1.58377i) q^{23} +(-3.07263 - 3.94448i) q^{25} -2.20068i q^{26} +(0.972242 - 0.972242i) q^{28} -3.13665 q^{29} +4.85211 q^{31} +(2.90772 - 2.90772i) q^{32} +0.651336i q^{34} +(-3.80401 + 1.30676i) q^{35} +(5.55242 + 5.55242i) q^{37} +(-7.35112 - 7.35112i) q^{38} +(-4.34456 + 1.49245i) q^{40} -1.48998i q^{41} +(-3.00856 + 3.00856i) q^{43} +2.75943 q^{44} -3.72396 q^{46} +(2.79674 - 2.79674i) q^{47} -3.76438i q^{49} +(-8.24978 - 1.02501i) q^{50} +(-0.715408 - 0.715408i) q^{52} +(-7.48222 - 7.48222i) q^{53} +(-7.25273 - 3.54386i) q^{55} +3.69540i q^{56} +(-3.68765 + 3.68765i) q^{58} +0.558755 q^{59} +5.92473 q^{61} +(5.70446 - 5.70446i) q^{62} +3.05196i q^{64} +(0.961557 + 2.79911i) q^{65} +(-7.93182 - 7.93182i) q^{67} +(0.211740 + 0.211740i) q^{68} +(-2.93593 + 6.00856i) q^{70} +8.01611i q^{71} +(-1.29315 + 1.29315i) q^{73} +13.0556 q^{74} -4.77948 q^{76} +(-4.59169 + 4.59169i) q^{77} -8.04731i q^{79} +(-4.85388 + 9.93376i) q^{80} +(-1.75172 - 1.75172i) q^{82} +(-0.410471 - 0.410471i) q^{83} +(-0.284592 - 0.828454i) q^{85} +7.07412i q^{86} +(-5.24417 + 5.24417i) q^{88} +16.4343 q^{89} +2.38087 q^{91} +(-1.21060 + 1.21060i) q^{92} -6.57607i q^{94} +(12.5621 + 6.13815i) q^{95} +(-3.76438 - 3.76438i) q^{97} +(-4.42566 - 4.42566i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7}+O(q^{10}) $ 16 * q + 4 * q^7	$ 16 q + 4 q^{7} - 8 q^{10} + 4 q^{13} + 16 q^{16} + 20 q^{22} - 8 q^{25} - 16 q^{28} + 8 q^{31} + 4 q^{37} - 12 q^{40} + 4 q^{43} + 32 q^{46} + 28 q^{52} - 16 q^{55} + 12 q^{58} - 16 q^{61} - 8 q^{67} - 36 q^{70} - 8 q^{73} - 48 q^{76} + 32 q^{82} - 44 q^{85} - 36 q^{88} - 40 q^{91} - 56 q^{97}+O(q^{100}) $ 16 * q + 4 * q^7 - 8 * q^10 + 4 * q^13 + 16 * q^16 + 20 * q^22 - 8 * q^25 - 16 * q^28 + 8 * q^31 + 4 * q^37 - 12 * q^40 + 4 * q^43 + 32 * q^46 + 28 * q^52 - 16 * q^55 + 12 * q^58 - 16 * q^61 - 8 * q^67 - 36 * q^70 - 8 * q^73 - 48 * q^76 + 32 * q^82 - 44 * q^85 - 36 * q^88 - 40 * q^91 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.17567	−	1.17567i	0.831322	−	0.831322i	−0.156376	−	0.987698i	$-0.549981\pi$
$2$	1.17567	−	1.17567i	0.831322	−	0.831322i	0.987698	+	0.156376i	$0.0499811\pi$
$3$		0			0
$3$		0			0
$4$		−	0.764383i		−	0.382191i
$5$	−0.981675	+	2.00906i	−0.439018	+	0.898478i
$5$	−0.981675	+	2.00906i	−0.439018	+	0.898478i
$6$		0			0
$7$	1.27193	+	1.27193i	0.480745	+	0.480745i	0.905369	−	0.424625i	$-0.139594\pi$
$7$	1.27193	+	1.27193i	0.480745	+	0.480745i	−0.424625	+	0.905369i	$0.639594\pi$
$8$	1.45267	+	1.45267i	0.513598	+	0.513598i
$9$		0			0
$10$	1.20786	+	3.51610i	0.381959	+	1.11189i
$11$			3.61002i			1.08846i	0.838936	+	0.544230i	$0.183178\pi$
$11$			3.61002i			1.08846i	−0.838936	+	0.544230i	$0.816822\pi$
$12$		0			0
$13$	0.935928	−	0.935928i	0.259580	−	0.259580i	−0.565303	−	0.824883i	$-0.691241\pi$
$13$	0.935928	−	0.935928i	0.259580	−	0.259580i	0.824883	+	0.565303i	$0.191241\pi$
$14$	2.99073			0.799307
$15$		0			0
$16$	4.94448			1.23612
$17$	−0.277007	+	0.277007i	−0.0671841	+	0.0671841i	−0.739900	−	0.672716i	$-0.765127\pi$
$17$	−0.277007	+	0.277007i	−0.0671841	+	0.0671841i	0.672716	+	0.739900i	$0.265127\pi$
$18$		0			0
$19$		−	6.25273i		−	1.43447i	−0.696829	−	0.717237i	$-0.745406\pi$
$19$		−	6.25273i		−	1.43447i	0.696829	−	0.717237i	$-0.254594\pi$
$20$	1.53569	+	0.750376i	0.343391	+	0.167789i
$21$		0			0
$22$	4.24417	+	4.24417i	0.904861	+	0.904861i
$23$	−1.58377	−	1.58377i	−0.330238	−	0.330238i	0.522439	−	0.852677i	$-0.325022\pi$
$23$	−1.58377	−	1.58377i	−0.330238	−	0.330238i	−0.852677	+	0.522439i	$0.825022\pi$
$24$		0			0
$25$	−3.07263	−	3.94448i	−0.614526	−	0.788897i
$26$		−	2.20068i		−	0.431589i
$27$		0			0
$28$	0.972242	−	0.972242i	0.183737	−	0.183737i
$29$	−3.13665			−0.582461			−0.291230	−	0.956653i	$-0.594065\pi$
$29$	−3.13665			−0.582461			−0.291230	+	0.956653i	$0.594065\pi$
$30$		0			0
$31$	4.85211			0.871464			0.435732	−	0.900076i	$-0.356490\pi$
$31$	4.85211			0.871464			0.435732	+	0.900076i	$0.356490\pi$
$32$	2.90772	−	2.90772i	0.514017	−	0.514017i
$33$		0			0
$34$			0.651336i			0.111703i
$35$	−3.80401	+	1.30676i	−0.642994	+	0.220883i
$36$		0			0
$37$	5.55242	+	5.55242i	0.912812	+	0.912812i	0.996493	−	0.0836807i	$-0.0266676\pi$
$37$	5.55242	+	5.55242i	0.912812	+	0.912812i	−0.0836807	+	0.996493i	$0.526668\pi$
$38$	−7.35112	−	7.35112i	−1.19251	−	1.19251i
$39$		0			0
$40$	−4.34456	+	1.49245i	−0.686935	+	0.235977i
$41$		−	1.48998i		−	0.232696i	−0.993209	−	0.116348i	$-0.962881\pi$
$41$		−	1.48998i		−	0.232696i	0.993209	−	0.116348i	$-0.0371188\pi$
$42$		0			0
$43$	−3.00856	+	3.00856i	−0.458801	+	0.458801i	−0.898262	−	0.439461i	$-0.855169\pi$
$43$	−3.00856	+	3.00856i	−0.458801	+	0.458801i	0.439461	+	0.898262i	$0.355169\pi$
$44$	2.75943			0.416000
$45$		0			0
$46$	−3.72396			−0.549069
$47$	2.79674	−	2.79674i	0.407947	−	0.407947i	−0.473075	−	0.881022i	$-0.656856\pi$
$47$	2.79674	−	2.79674i	0.407947	−	0.407947i	0.881022	+	0.473075i	$0.156856\pi$
$48$		0			0
$49$		−	3.76438i		−	0.537769i
$50$	−8.24978	−	1.02501i	−1.16670	−	0.144959i
$51$		0			0
$52$	−0.715408	−	0.715408i	−0.0992092	−	0.0992092i
$53$	−7.48222	−	7.48222i	−1.02776	−	1.02776i	−0.999603	−	0.0281581i	$-0.991036\pi$
$53$	−7.48222	−	7.48222i	−1.02776	−	1.02776i	−0.0281581	−	0.999603i	$-0.508964\pi$
$54$		0			0
$55$	−7.25273	−	3.54386i	−0.977958	−	0.477854i
$56$			3.69540i			0.493819i
$57$		0			0
$58$	−3.68765	+	3.68765i	−0.484212	+	0.484212i
$59$	0.558755			0.0727436			0.0363718	−	0.999338i	$-0.488420\pi$
$59$	0.558755			0.0727436			0.0363718	+	0.999338i	$0.488420\pi$
$60$		0			0
$61$	5.92473			0.758585			0.379292	−	0.925277i	$-0.376167\pi$
$61$	5.92473			0.758585			0.379292	+	0.925277i	$0.376167\pi$
$62$	5.70446	−	5.70446i	0.724467	−	0.724467i
$63$		0			0
$64$			3.05196i			0.381495i
$65$	0.961557	+	2.79911i	0.119266	+	0.347187i
$66$		0			0
$67$	−7.93182	−	7.93182i	−0.969026	−	0.969026i	0.0305081	−	0.999535i	$-0.490287\pi$
$67$	−7.93182	−	7.93182i	−0.969026	−	0.969026i	−0.999535	+	0.0305081i	$0.990287\pi$
$68$	0.211740	+	0.211740i	0.0256772	+	0.0256772i
$69$		0			0
$70$	−2.93593	+	6.00856i	−0.350911	+	0.718160i
$71$			8.01611i			0.951338i	0.879624	+	0.475669i	$0.157794\pi$
$71$			8.01611i			0.951338i	−0.879624	+	0.475669i	$0.842206\pi$
$72$		0			0
$73$	−1.29315	+	1.29315i	−0.151352	+	0.151352i	−0.778721	−	0.627370i	$-0.784131\pi$
$73$	−1.29315	+	1.29315i	−0.151352	+	0.151352i	0.627370	+	0.778721i	$0.284131\pi$
$74$	13.0556			1.51768
$75$		0			0
$76$	−4.77948			−0.548244
$77$	−4.59169	+	4.59169i	−0.523272	+	0.523272i
$78$		0			0
$79$		−	8.04731i		−	0.905393i	−0.891665	−	0.452696i	$-0.850462\pi$
$79$		−	8.04731i		−	0.905393i	0.891665	−	0.452696i	$-0.149538\pi$
$80$	−4.85388	+	9.93376i	−0.542680	+	1.11063i
$81$		0			0
$82$	−1.75172	−	1.75172i	−0.193445	−	0.193445i
$83$	−0.410471	−	0.410471i	−0.0450550	−	0.0450550i	0.684220	−	0.729275i	$-0.260143\pi$
$83$	−0.410471	−	0.410471i	−0.0450550	−	0.0450550i	−0.729275	+	0.684220i	$0.760143\pi$
$84$		0			0
$85$	−0.284592	−	0.828454i	−0.0308684	−	0.0898585i
$86$			7.07412i			0.762822i
$87$		0			0
$88$	−5.24417	+	5.24417i	−0.559031	+	0.559031i
$89$	16.4343			1.74203			0.871016	−	0.491255i	$-0.163462\pi$
$89$	16.4343			1.74203			0.871016	+	0.491255i	$0.163462\pi$
$90$		0			0
$91$	2.38087			0.249583
$92$	−1.21060	+	1.21060i	−0.126214	+	0.126214i
$93$		0			0
$94$		−	6.57607i		−	0.678270i
$95$	12.5621	+	6.13815i	1.28884	+	0.629761i
$96$		0			0
$97$	−3.76438	−	3.76438i	−0.382215	−	0.382215i	0.489685	−	0.871900i	$-0.337112\pi$
$97$	−3.76438	−	3.76438i	−0.382215	−	0.382215i	−0.871900	+	0.489685i	$0.837112\pi$
$98$	−4.42566	−	4.42566i	−0.447059	−	0.447059i
$99$		0			0
$100$	−3.01510	+	2.34866i	−0.301510	+	0.234866i
$101$		−	5.46183i		−	0.543473i	−0.962372	−	0.271736i	$-0.912402\pi$
$101$		−	5.46183i		−	0.543473i	0.962372	−	0.271736i	$-0.0875978\pi$
$102$		0			0
$103$	−3.68521	+	3.68521i	−0.363115	+	0.363115i	−0.864958	−	0.501843i	$-0.832655\pi$
$103$	−3.68521	+	3.68521i	−0.363115	+	0.363115i	0.501843	+	0.864958i	$0.332655\pi$
$104$	2.71920			0.266639
$105$		0			0
$106$	−17.5932			−1.70880
$107$	−4.07498	+	4.07498i	−0.393944	+	0.393944i	−0.876090	−	0.482147i	$-0.839857\pi$
$107$	−4.07498	+	4.07498i	−0.393944	+	0.393944i	0.482147	+	0.876090i	$0.339857\pi$
$108$		0			0
$109$		−	1.10747i		−	0.106077i	−0.998592	−	0.0530384i	$-0.983109\pi$
$109$		−	1.10747i		−	0.106077i	0.998592	−	0.0530384i	$-0.0168906\pi$
$110$	−12.6932	+	4.36039i	−1.21025	+	0.415747i
$111$		0			0
$112$	6.28904	+	6.28904i	0.594259	+	0.594259i
$113$	−5.90082	−	5.90082i	−0.555102	−	0.555102i	0.372807	−	0.927909i	$-0.378395\pi$
$113$	−5.90082	−	5.90082i	−0.555102	−	0.555102i	−0.927909	+	0.372807i	$0.878395\pi$
$114$		0			0
$115$	4.73663	−	1.62714i	0.441693	−	0.151731i
$116$			2.39760i			0.222611i
$117$		0			0
$118$	0.656909	−	0.656909i	0.0604734	−	0.0604734i
$119$	−0.704668			−0.0645968
$120$		0			0
$121$	−2.03221			−0.184746
$122$	6.96551	−	6.96551i	0.630628	−	0.630628i
$123$		0			0
$124$		−	3.70887i		−	0.333066i
$125$	10.9410	−	2.30088i	0.978595	−	0.205797i
$126$		0			0
$127$	−11.5887	−	11.5887i	−1.02833	−	1.02833i	−0.999587	−	0.0287470i	$-0.990848\pi$
$127$	−11.5887	−	11.5887i	−1.02833	−	1.02833i	−0.0287470	−	0.999587i	$-0.509152\pi$
$128$	9.40352	+	9.40352i	0.831162	+	0.831162i
$129$		0			0
$130$	4.42129	+	2.16035i	0.387773	+	0.189475i
$131$		−	5.01603i		−	0.438253i	−0.975696	−	0.219126i	$-0.929679\pi$
$131$		−	5.01603i		−	0.438253i	0.975696	−	0.219126i	$-0.0703207\pi$
$132$		0			0
$133$	7.95304	−	7.95304i	0.689616	−	0.689616i
$134$	−18.6504			−1.61115
$135$		0			0
$136$	−0.804802			−0.0690112
$137$	0.322715	−	0.322715i	0.0275714	−	0.0275714i	−0.693187	−	0.720758i	$-0.743794\pi$
$137$	0.322715	−	0.322715i	0.0275714	−	0.0275714i	0.720758	+	0.693187i	$0.243794\pi$
$138$		0			0
$139$			16.0342i			1.36001i	0.733210	+	0.680003i	$0.238021\pi$
$139$			16.0342i			1.36001i	−0.733210	+	0.680003i	$0.761979\pi$
$140$	0.998865	+	2.90772i	0.0844195	+	0.245747i
$141$		0			0
$142$	9.42428	+	9.42428i	0.790868	+	0.790868i
$143$	3.37872	+	3.37872i	0.282542	+	0.282542i
$144$		0			0
$145$	3.07917	−	6.30170i	0.255711	−	0.523328i
$146$			3.04062i			0.251644i
$147$		0			0
$148$	4.24417	−	4.24417i	0.348869	−	0.348869i
$149$	6.88305			0.563882			0.281941	−	0.959432i	$-0.409022\pi$
$149$	6.88305			0.563882			0.281941	+	0.959432i	$0.409022\pi$
$150$		0			0
$151$	−8.61293			−0.700911			−0.350455	−	0.936579i	$-0.613973\pi$
$151$	−8.61293			−0.700911			−0.350455	+	0.936579i	$0.613973\pi$
$152$	9.08317	−	9.08317i	0.736743	−	0.736743i
$153$		0			0
$154$			10.7966i			0.870014i
$155$	−4.76319	+	9.74816i	−0.382589	+	0.782991i
$156$		0			0
$157$	1.17809	+	1.17809i	0.0940215	+	0.0940215i	0.752553	−	0.658532i	$-0.228822\pi$
$157$	1.17809	+	1.17809i	0.0940215	+	0.0940215i	−0.658532	+	0.752553i	$0.728822\pi$
$158$	−9.46095	−	9.46095i	−0.752672	−	0.752672i
$159$		0			0
$160$	2.98734	+	8.69621i	0.236170	+	0.687495i
$161$		−	4.02889i		−	0.317521i
$162$		0			0
$163$	−10.5120	+	10.5120i	−0.823363	+	0.823363i	−0.986589	−	0.163225i	$-0.947810\pi$
$163$	−10.5120	+	10.5120i	−0.823363	+	0.823363i	0.163225	+	0.986589i	$0.447810\pi$
$164$	−1.13892			−0.0889344
$165$		0			0
$166$	−0.965154			−0.0749105
$167$	6.87539	−	6.87539i	0.532033	−	0.532033i	−0.389144	−	0.921177i	$-0.627229\pi$
$167$	6.87539	−	6.87539i	0.532033	−	0.532033i	0.921177	+	0.389144i	$0.127229\pi$
$168$		0			0
$169$			11.2481i			0.865237i
$170$	−1.30857	−	0.639400i	−0.100363	−	0.0490398i
$171$		0			0
$172$	2.29969	+	2.29969i	0.175350	+	0.175350i
$173$	−10.6095	−	10.6095i	−0.806627	−	0.806627i	0.177495	−	0.984122i	$-0.443201\pi$
$173$	−10.6095	−	10.6095i	−0.806627	−	0.806627i	−0.984122	+	0.177495i	$0.943201\pi$
$174$		0			0
$175$	1.10894	−	8.92528i	0.0838281	−	0.674688i
$176$			17.8497i			1.34547i
$177$		0			0
$178$	19.3213	−	19.3213i	1.44819	−	1.44819i
$179$	−4.21995			−0.315414			−0.157707	−	0.987486i	$-0.550410\pi$
$179$	−4.21995			−0.315414			−0.157707	+	0.987486i	$0.550410\pi$
$180$		0			0
$181$	23.7930			1.76852			0.884261	−	0.466993i	$-0.154663\pi$
$181$	23.7930			1.76852			0.884261	+	0.466993i	$0.154663\pi$
$182$	2.79911	−	2.79911i	0.207484	−	0.207484i
$183$		0			0
$184$		−	4.60139i		−	0.339219i
$185$	−16.6058	+	5.70446i	−1.22088	+	0.419400i
$186$		0			0
$187$	−1.00000	−	1.00000i	−0.0731272	−	0.0731272i
$188$	−2.13778	−	2.13778i	−0.155914	−	0.155914i
$189$		0			0
$190$	21.9852	−	7.55242i	1.59498	−	0.547910i
$191$		−	23.2724i		−	1.68393i	−0.539532	−	0.841965i	$-0.681399\pi$
$191$		−	23.2724i		−	1.68393i	0.539532	−	0.841965i	$-0.318601\pi$
$192$		0			0
$193$	14.6619	−	14.6619i	1.05539	−	1.05539i	0.0570139	−	0.998373i	$-0.481842\pi$
$193$	14.6619	−	14.6619i	1.05539	−	1.05539i	0.998373	−	0.0570139i	$-0.0181579\pi$
$194$	−8.85132			−0.635488
$195$		0			0
$196$	−2.87743			−0.205531
$197$	−6.52613	+	6.52613i	−0.464968	+	0.464968i	−0.900280	−	0.435312i	$-0.856638\pi$
$197$	−6.52613	+	6.52613i	−0.464968	+	0.464968i	0.435312	+	0.900280i	$0.356638\pi$
$198$		0			0
$199$			4.03778i			0.286231i	0.989706	+	0.143115i	$0.0457120\pi$
$199$			4.03778i			0.286231i	−0.989706	+	0.143115i	$0.954288\pi$
$200$	1.26652	−	10.1936i	0.0895567	−	0.720794i
$201$		0			0
$202$	−6.42129	−	6.42129i	−0.451801	−	0.451801i
$203$	−3.98960	−	3.98960i	−0.280015	−	0.280015i
$204$		0			0
$205$	2.99346	+	1.46268i	0.209072	+	0.102158i
$206$			8.66517i			0.603731i
$207$		0			0
$208$	4.62768	−	4.62768i	0.320872	−	0.320872i
$209$	22.5724			1.56137
$210$		0			0
$211$	−1.30623			−0.0899245			−0.0449623	−	0.998989i	$-0.514317\pi$
$211$	−1.30623			−0.0899245			−0.0449623	+	0.998989i	$0.514317\pi$
$212$	−5.71928	+	5.71928i	−0.392802	+	0.392802i
$213$		0			0
$214$			9.58164i			0.654988i
$215$	−3.09094	−	8.99779i	−0.210800	−	0.613644i
$216$		0			0
$217$	6.17155	+	6.17155i	0.418952	+	0.418952i
$218$	−1.30202	−	1.30202i	−0.0881839	−	0.0881839i
$219$		0			0
$220$	−2.70887	+	5.54386i	−0.182632	+	0.373767i
$221$			0.518518i			0.0348793i
$222$		0			0
$223$	−5.86477	+	5.86477i	−0.392734	+	0.392734i	−0.875661	−	0.482927i	$-0.839574\pi$
$223$	−5.86477	+	5.86477i	−0.392734	+	0.392734i	0.482927	+	0.875661i	$0.339574\pi$
$224$	7.39683			0.494222
$225$		0			0
$226$	−13.8748			−0.922937
$227$	−6.52066	+	6.52066i	−0.432791	+	0.432791i	−0.889577	−	0.456785i	$-0.849001\pi$
$227$	−6.52066	+	6.52066i	−0.432791	+	0.432791i	0.456785	+	0.889577i	$0.349001\pi$
$228$		0			0
$229$			19.8646i			1.31269i	0.754462	+	0.656344i	$0.227898\pi$
$229$			19.8646i			1.31269i	−0.754462	+	0.656344i	$0.772102\pi$
$230$	3.65572	−	7.48166i	0.241051	−	0.493326i
$231$		0			0
$232$	−4.55652	−	4.55652i	−0.299150	−	0.299150i
$233$	−5.45304	−	5.45304i	−0.357241	−	0.357241i	0.505554	−	0.862795i	$-0.331288\pi$
$233$	−5.45304	−	5.45304i	−0.357241	−	0.357241i	−0.862795	+	0.505554i	$0.831288\pi$
$234$		0			0
$235$	2.87332	+	8.36431i	0.187435	+	0.545627i
$236$		−	0.427102i		−	0.0278020i
$237$		0			0
$238$	−0.828454	+	0.828454i	−0.0537007	+	0.0537007i
$239$	−6.96370			−0.450444			−0.225222	−	0.974307i	$-0.572311\pi$
$239$	−6.96370			−0.450444			−0.225222	+	0.974307i	$0.572311\pi$
$240$		0			0
$241$	23.5321			1.51584			0.757918	−	0.652350i	$-0.226217\pi$
$241$	23.5321			1.51584			0.757918	+	0.652350i	$0.226217\pi$
$242$	−2.38920	+	2.38920i	−0.153584	+	0.153584i
$243$		0			0
$244$		−	4.52877i		−	0.289925i
$245$	7.56286	+	3.69540i	0.483174	+	0.236091i
$246$		0			0
$247$	−5.85211	−	5.85211i	−0.372361	−	0.372361i
$248$	7.04853	+	7.04853i	0.447582	+	0.447582i
$249$		0			0
$250$	10.1579	−	15.5681i	0.642443	−	0.984611i
$251$		−	20.7941i		−	1.31251i	−0.754537	−	0.656257i	$-0.772139\pi$
$251$		−	20.7941i		−	1.31251i	0.754537	−	0.656257i	$-0.227861\pi$
$252$		0			0
$253$	5.71742	−	5.71742i	0.359451	−	0.359451i
$254$	−27.2490			−1.70975
$255$		0			0
$256$	16.0069			1.00043
$257$	7.43121	−	7.43121i	0.463546	−	0.463546i	−0.436270	−	0.899816i	$-0.643701\pi$
$257$	7.43121	−	7.43121i	0.463546	−	0.463546i	0.899816	+	0.436270i	$0.143701\pi$
$258$		0			0
$259$			14.1246i			0.877659i
$260$	2.13959	−	0.734997i	0.132692	−	0.0455826i
$261$		0			0
$262$	−5.89718	−	5.89718i	−0.364329	−	0.364329i
$263$	10.5638	+	10.5638i	0.651392	+	0.651392i	0.953328	−	0.301936i	$-0.0976329\pi$
$263$	10.5638	+	10.5638i	0.651392	+	0.651392i	−0.301936	+	0.953328i	$0.597633\pi$
$264$		0			0
$265$	22.3773	−	7.68710i	1.37463	−	0.472215i
$266$		−	18.7002i		−	1.14659i
$267$		0			0
$268$	−6.06295	+	6.06295i	−0.370354	+	0.370354i
$269$	0.781994			0.0476790			0.0238395	−	0.999716i	$-0.492411\pi$
$269$	0.781994			0.0476790			0.0238395	+	0.999716i	$0.492411\pi$
$270$		0			0
$271$	−12.4677			−0.757357			−0.378679	−	0.925528i	$-0.623621\pi$
$271$	−12.4677			−0.757357			−0.378679	+	0.925528i	$0.623621\pi$
$272$	−1.36966	+	1.36966i	−0.0830477	+	0.0830477i
$273$		0			0
$274$		−	0.758810i		−	0.0458414i
$275$	14.2396	−	11.0922i	0.858683	−	0.668887i
$276$		0			0
$277$	−6.64216	−	6.64216i	−0.399089	−	0.399089i	0.478823	−	0.877912i	$-0.341064\pi$
$277$	−6.64216	−	6.64216i	−0.399089	−	0.399089i	−0.877912	+	0.478823i	$0.841064\pi$
$278$	18.8509	+	18.8509i	1.13060	+	1.13060i
$279$		0			0
$280$	−7.42428	−	3.62768i	−0.443685	−	0.216796i
$281$			30.7178i			1.83247i	0.400638	+	0.916237i	$0.368789\pi$
$281$			30.7178i			1.83247i	−0.400638	+	0.916237i	$0.631211\pi$
$282$		0			0
$283$	−13.3006	+	13.3006i	−0.790638	+	0.790638i	−0.981598	−	0.190960i	$-0.938840\pi$
$283$	−13.3006	+	13.3006i	−0.790638	+	0.790638i	0.190960	+	0.981598i	$0.438840\pi$
$284$	6.12738			0.363593
$285$		0			0
$286$	7.94448			0.469767
$287$	1.89515	−	1.89515i	0.111867	−	0.111867i
$288$		0			0
$289$			16.8465i			0.990973i
$290$	−3.78863	−	11.0288i	−0.222476	−	0.647632i
$291$		0			0
$292$	0.988461	+	0.988461i	0.0578453	+	0.0578453i
$293$	23.9004	+	23.9004i	1.39628	+	1.39628i	0.810395	+	0.585885i	$0.199253\pi$
$293$	23.9004	+	23.9004i	1.39628	+	1.39628i	0.585885	+	0.810395i	$0.300747\pi$
$294$		0			0
$295$	−0.548515	+	1.12257i	−0.0319358	+	0.0653586i
$296$			16.1317i			0.937636i
$297$		0			0
$298$	8.09218	−	8.09218i	0.468767	−	0.468767i
$299$	−2.96459			−0.171446
$300$		0			0
$301$	−7.65335			−0.441132
$302$	−10.1259	+	10.1259i	−0.582682	+	0.582682i
$303$		0			0
$304$		−	30.9165i		−	1.77318i
$305$	−5.81616	+	11.9031i	−0.333033	+	0.681572i
$306$		0			0
$307$	−2.26728	−	2.26728i	−0.129400	−	0.129400i	0.639440	−	0.768841i	$-0.279166\pi$
$307$	−2.26728	−	2.26728i	−0.129400	−	0.129400i	−0.768841	+	0.639440i	$0.779166\pi$
$308$	3.50981	+	3.50981i	0.199990	+	0.199990i
$309$		0			0
$310$	5.86066	+	17.0605i	0.332863	+	0.968972i
$311$			2.15570i			0.122239i	0.998130	+	0.0611193i	$0.0194670\pi$
$311$			2.15570i			0.122239i	−0.998130	+	0.0611193i	$0.980533\pi$
$312$		0			0
$313$	−15.3661	+	15.3661i	−0.868545	+	0.868545i	−0.992311	−	0.123767i	$-0.960503\pi$
$313$	−15.3661	+	15.3661i	−0.868545	+	0.868545i	0.123767	+	0.992311i	$0.460503\pi$
$314$	2.77007			0.156324
$315$		0			0
$316$	−6.15122			−0.346033
$317$	−3.27851	+	3.27851i	−0.184139	+	0.184139i	−0.793157	−	0.609017i	$-0.791564\pi$
$317$	−3.27851	+	3.27851i	−0.184139	+	0.184139i	0.609017	+	0.793157i	$0.291564\pi$
$318$		0			0
$319$		−	11.3233i		−	0.633985i
$320$	−6.13156	−	2.99603i	−0.342765	−	0.167483i
$321$		0			0
$322$	−4.73663	−	4.73663i	−0.263962	−	0.263962i
$323$	1.73205	+	1.73205i	0.0963739	+	0.0963739i
$324$		0			0
$325$	−6.56751	−	0.815995i	−0.364300	−	0.0452633i
$326$			24.7172i			1.36896i
$327$		0			0
$328$	2.16446	−	2.16446i	0.119512	−	0.119512i
$329$	7.11453			0.392236
$330$		0			0
$331$	−29.1097			−1.60001			−0.800007	−	0.599991i	$-0.795171\pi$
$331$	−29.1097			−1.60001			−0.800007	+	0.599991i	$0.795171\pi$
$332$	−0.313757	+	0.313757i	−0.0172197	+	0.0172197i
$333$		0			0
$334$		−	16.1663i		−	0.884582i
$335$	23.7220	−	8.14902i	1.29607	−	0.445228i
$336$		0			0
$337$	17.7027	+	17.7027i	0.964326	+	0.964326i	0.999385	−	0.0350592i	$-0.0111620\pi$
$337$	17.7027	+	17.7027i	0.964326	+	0.964326i	−0.0350592	+	0.999385i	$0.511162\pi$
$338$	13.2240	+	13.2240i	0.719290	+	0.719290i
$339$		0			0
$340$	−0.633256	+	0.217538i	−0.0343431	+	0.0117976i
$341$			17.5162i			0.948554i
$342$		0			0
$343$	13.6916	−	13.6916i	0.739274	−	0.739274i
$344$	−8.74090			−0.471278
$345$		0			0
$346$	−24.9465			−1.34113
$347$	−24.7322	+	24.7322i	−1.32769	+	1.32769i	−0.420312	+	0.907379i	$0.638080\pi$
$347$	−24.7322	+	24.7322i	−1.32769	+	1.32769i	−0.907379	+	0.420312i	$0.861920\pi$
$348$		0			0
$349$			19.7375i			1.05653i	0.849081	+	0.528263i	$0.177156\pi$
$349$			19.7375i			1.05653i	−0.849081	+	0.528263i	$0.822844\pi$
$350$	−9.18941	−	11.7969i	−0.491195	−	0.630571i
$351$		0			0
$352$	10.4969	+	10.4969i	0.559487	+	0.559487i
$353$	−5.35141	−	5.35141i	−0.284827	−	0.284827i	0.550204	−	0.835031i	$-0.314550\pi$
$353$	−5.35141	−	5.35141i	−0.284827	−	0.284827i	−0.835031	+	0.550204i	$0.814550\pi$
$354$		0			0
$355$	−16.1048	−	7.86922i	−0.854756	−	0.417655i
$356$		−	12.5621i		−	0.665790i
$357$		0			0
$358$	−4.96125	+	4.96125i	−0.262210	+	0.262210i
$359$	8.47760			0.447430			0.223715	−	0.974655i	$-0.428181\pi$
$359$	8.47760			0.447430			0.223715	+	0.974655i	$0.428181\pi$
$360$		0			0
$361$	−20.0966			−1.05772
$362$	27.9727	−	27.9727i	1.47021	−	1.47021i
$363$		0			0
$364$		−	1.81990i		−	0.0953886i
$365$	−1.32856	−	3.86746i	−0.0695399	−	0.202432i
$366$		0			0
$367$	−5.80577	−	5.80577i	−0.303059	−	0.303059i	0.539151	−	0.842209i	$-0.318745\pi$
$367$	−5.80577	−	5.80577i	−0.303059	−	0.303059i	−0.842209	+	0.539151i	$0.818745\pi$
$368$	−7.83091	−	7.83091i	−0.408215	−	0.408215i
$369$		0			0
$370$	−12.8163	+	26.2294i	−0.666290	+	1.36360i
$371$		−	19.0337i		−	0.988182i
$372$		0			0
$373$	−15.2159	+	15.2159i	−0.787848	+	0.787848i	−0.981141	−	0.193293i	$-0.938083\pi$
$373$	−15.2159	+	15.2159i	−0.787848	+	0.787848i	0.193293	+	0.981141i	$0.438083\pi$
$374$	−2.35133			−0.121585
$375$		0			0
$376$	8.12551			0.419041
$377$	−2.93568	+	2.93568i	−0.151195	+	0.151195i
$378$		0			0
$379$			11.1614i			0.573325i	0.958032	+	0.286663i	$0.0925458\pi$
$379$			11.1614i			0.573325i	−0.958032	+	0.286663i	$0.907454\pi$
$380$	4.69190	−	9.60225i	0.240689	−	0.492585i
$381$		0			0
$382$	−27.3605	−	27.3605i	−1.39989	−	1.39989i
$383$	−10.7595	−	10.7595i	−0.549784	−	0.549784i	0.376595	−	0.926378i	$-0.377095\pi$
$383$	−10.7595	−	10.7595i	−0.549784	−	0.549784i	−0.926378	+	0.376595i	$0.877095\pi$
$384$		0			0
$385$	−4.71742	−	13.7325i	−0.240422	−	0.699874i
$386$		−	34.4750i		−	1.75473i
$387$		0			0
$388$	−2.87743	+	2.87743i	−0.146079	+	0.146079i
$389$	−25.4791			−1.29184			−0.645920	−	0.763405i	$-0.723526\pi$
$389$	−25.4791			−1.29184			−0.645920	+	0.763405i	$0.723526\pi$
$390$		0			0
$391$	0.877430			0.0443735
$392$	5.46842	−	5.46842i	0.276197	−	0.276197i
$393$		0			0
$394$			15.3451i			0.773075i
$395$	16.1675	+	7.89984i	0.813475	+	0.397484i
$396$		0			0
$397$	−5.96779	−	5.96779i	−0.299515	−	0.299515i	0.541309	−	0.840824i	$-0.317929\pi$
$397$	−5.96779	−	5.96779i	−0.299515	−	0.299515i	−0.840824	+	0.541309i	$0.817929\pi$
$398$	4.74708	+	4.74708i	0.237950	+	0.237950i
$399$		0			0
$400$	−15.1926	−	19.5034i	−0.759628	−	0.975172i
$401$		−	27.3439i		−	1.36549i	−0.730658	−	0.682744i	$-0.760786\pi$
$401$		−	27.3439i		−	1.36549i	0.730658	−	0.682744i	$-0.239214\pi$
$402$		0			0
$403$	4.54122	−	4.54122i	0.226215	−	0.226215i
$404$	−4.17493			−0.207711
$405$		0			0
$406$	−9.38087			−0.465565
$407$	−20.0443	+	20.0443i	−0.993560	+	0.993560i
$408$		0			0
$409$		−	27.1864i		−	1.34428i	−0.740424	−	0.672140i	$-0.765375\pi$
$409$		−	27.1864i		−	1.34428i	0.740424	−	0.672140i	$-0.234625\pi$
$410$	5.23893	−	1.79969i	0.258732	−	0.0888803i
$411$		0			0
$412$	2.81692	+	2.81692i	0.138779	+	0.138779i
$413$	0.710697	+	0.710697i	0.0349711	+	0.0349711i
$414$		0			0
$415$	1.22761	−	0.421711i	0.0602610	−	0.0207010i
$416$		−	5.44283i		−	0.266857i
$417$		0			0
$418$	26.5377	−	26.5377i	1.29800	−	1.29800i
$419$	−31.4036			−1.53417			−0.767084	−	0.641546i	$-0.778293\pi$
$419$	−31.4036			−1.53417			−0.767084	+	0.641546i	$0.778293\pi$
$420$		0			0
$421$	30.8657			1.50430			0.752150	−	0.658992i	$-0.229017\pi$
$421$	30.8657			1.50430			0.752150	+	0.658992i	$0.229017\pi$
$422$	−1.53569	+	1.53569i	−0.0747562	+	0.0747562i
$423$		0			0
$424$		−	21.7384i		−	1.05571i
$425$	1.94379	+	0.241511i	0.0942877	+	0.0117150i
$426$		0			0
$427$	7.53585	+	7.53585i	0.364686	+	0.364686i
$428$	3.11485	+	3.11485i	0.150562	+	0.150562i
$429$		0			0
$430$	−14.2123	−	6.94448i	−0.685378	−	0.334893i
$431$		−	32.6869i		−	1.57447i	−0.616652	−	0.787236i	$-0.711511\pi$
$431$		−	32.6869i		−	1.57447i	0.616652	−	0.787236i	$-0.288489\pi$
$432$		0			0
$433$	−7.25927	+	7.25927i	−0.348858	+	0.348858i	−0.859684	−	0.510826i	$-0.829340\pi$
$433$	−7.25927	+	7.25927i	−0.348858	+	0.348858i	0.510826	+	0.859684i	$0.329340\pi$
$434$	14.5114			0.696567
$435$		0			0
$436$	−0.846534			−0.0405416
$437$	−9.90287	+	9.90287i	−0.473718	+	0.473718i
$438$		0			0
$439$		−	22.4801i		−	1.07292i	−0.843926	−	0.536459i	$-0.819762\pi$
$439$		−	22.4801i		−	1.07292i	0.843926	−	0.536459i	$-0.180238\pi$
$440$	−5.38777	−	15.6839i	−0.256852	−	0.747702i
$441$		0			0
$442$	0.609604	+	0.609604i	0.0289959	+	0.0289959i
$443$	−5.46493	−	5.46493i	−0.259647	−	0.259647i	0.565264	−	0.824910i	$-0.308774\pi$
$443$	−5.46493	−	5.46493i	−0.259647	−	0.259647i	−0.824910	+	0.565264i	$0.808774\pi$
$444$		0			0
$445$	−16.1331	+	33.0175i	−0.764784	+	1.56518i
$446$			13.7900i			0.652976i
$447$		0			0
$448$	−3.88188	+	3.88188i	−0.183402	+	0.183402i
$449$	−38.1502			−1.80042			−0.900209	−	0.435458i	$-0.856586\pi$
$449$	−38.1502			−1.80042			−0.900209	+	0.435458i	$0.856586\pi$
$450$		0			0
$451$	5.37886			0.253280
$452$	−4.51049	+	4.51049i	−0.212155	+	0.212155i
$453$		0			0
$454$			15.3322i			0.719578i
$455$	−2.33724	+	4.78331i	−0.109572	+	0.224245i
$456$		0			0
$457$	19.6941	+	19.6941i	0.921252	+	0.921252i	0.997118	−	0.0758661i	$-0.0241722\pi$
$457$	19.6941	+	19.6941i	0.921252	+	0.921252i	−0.0758661	+	0.997118i	$0.524172\pi$
$458$	23.3541	+	23.3541i	1.09127	+	1.09127i
$459$		0			0
$460$	−1.24375	−	3.62060i	−0.0579903	−	0.168811i
$461$		−	24.5144i		−	1.14175i	−0.821037	−	0.570874i	$-0.806604\pi$
$461$		−	24.5144i		−	1.14175i	0.821037	−	0.570874i	$-0.193396\pi$
$462$		0			0
$463$	−12.6422	+	12.6422i	−0.587531	+	0.587531i	−0.936962	−	0.349431i	$-0.886375\pi$
$463$	−12.6422	+	12.6422i	−0.587531	+	0.587531i	0.349431	+	0.936962i	$0.386375\pi$
$464$	−15.5091			−0.719992
$465$		0			0
$466$	−12.8219			−0.593964
$467$	−22.2894	+	22.2894i	−1.03143	+	1.03143i	−0.0319412	+	0.999490i	$0.510169\pi$
$467$	−22.2894	+	22.2894i	−1.03143	+	1.03143i	−0.999490	+	0.0319412i	$0.989831\pi$
$468$		0			0
$469$		−	20.1775i		−	0.931709i
$470$	13.2117	+	6.45557i	0.609411	+	0.297773i
$471$		0			0
$472$	0.811688	+	0.811688i	0.0373610	+	0.0373610i
$473$	−10.8609	−	10.8609i	−0.499386	−	0.499386i
$474$		0			0
$475$	−24.6638	+	19.2123i	−1.13165	+	0.881521i
$476$			0.538636i			0.0246883i
$477$		0			0
$478$	−8.18699	+	8.18699i	−0.374464	+	0.374464i
$479$	−13.5255			−0.617994			−0.308997	−	0.951063i	$-0.599993\pi$
$479$	−13.5255			−0.617994			−0.308997	+	0.951063i	$0.599993\pi$
$480$		0			0
$481$	10.3933			0.473895
$482$	27.6659	−	27.6659i	1.26015	−	1.26015i
$483$		0			0
$484$			1.55339i			0.0706084i
$485$	11.2583	−	3.86746i	0.511211	−	0.175612i
$486$		0			0
$487$	17.7890	+	17.7890i	0.806094	+	0.806094i	0.984040	−	0.177946i	$-0.0569452\pi$
$487$	17.7890	+	17.7890i	0.806094	+	0.806094i	−0.177946	+	0.984040i	$0.556945\pi$
$488$	8.60671	+	8.60671i	0.389607	+	0.389607i
$489$		0			0
$490$	13.2360	−	4.54685i	0.597940	−	0.205406i
$491$			20.7598i			0.936876i	0.883496	+	0.468438i	$0.155183\pi$
$491$			20.7598i			0.936876i	−0.883496	+	0.468438i	$0.844817\pi$
$492$		0			0
$493$	0.868874	−	0.868874i	0.0391321	−	0.0391321i
$494$	−13.7603			−0.619103
$495$		0			0
$496$	23.9912			1.07724
$497$	−10.1959	+	10.1959i	−0.457351	+	0.457351i
$498$		0			0
$499$			9.88603i			0.442560i	0.975210	+	0.221280i	$0.0710234\pi$
$499$			9.88603i			0.442560i	−0.975210	+	0.221280i	$0.928977\pi$
$500$	−1.75876	−	8.36313i	−0.0786540	−	0.374010i
$501$		0			0
$502$	−24.4470	−	24.4470i	−1.09112	−	1.09112i
$503$	16.8084	+	16.8084i	0.749450	+	0.749450i	0.974376	−	0.224926i	$-0.0722140\pi$
$503$	16.8084	+	16.8084i	0.749450	+	0.749450i	−0.224926	+	0.974376i	$0.572214\pi$
$504$		0			0
$505$	10.9731	+	5.36174i	0.488298	+	0.238594i
$506$		−	13.4436i		−	0.597639i
$507$		0			0
$508$	−8.85823	+	8.85823i	−0.393020	+	0.393020i
$509$	40.3590			1.78888			0.894442	−	0.447185i	$-0.147573\pi$
$509$	40.3590			1.78888			0.894442	+	0.447185i	$0.147573\pi$
$510$		0			0
$511$	−3.28959			−0.145523
$512$	0.0117190	−	0.0117190i	0.000517913	−	0.000517913i
$513$		0			0
$514$		−	17.4733i		−	0.770712i
$515$	−3.78613	−	11.0215i	−0.166837	−	0.485665i
$516$		0			0
$517$	10.0963	+	10.0963i	0.444034	+	0.444034i
$518$	16.6058	+	16.6058i	0.729617	+	0.729617i
$519$		0			0
$520$	−2.66937	+	5.46302i	−0.117060	+	0.239569i
$521$			11.5144i			0.504456i	0.967668	+	0.252228i	$0.0811633\pi$
$521$			11.5144i			0.504456i	−0.967668	+	0.252228i	$0.918837\pi$
$522$		0			0
$523$	−29.5457	+	29.5457i	−1.29194	+	1.29194i	−0.358358	+	0.933584i	$0.616663\pi$
$523$	−29.5457	+	29.5457i	−1.29194	+	1.29194i	−0.933584	+	0.358358i	$0.883337\pi$
$524$	−3.83417			−0.167496
$525$		0			0
$526$	24.8390			1.08303
$527$	−1.34407	+	1.34407i	−0.0585485	+	0.0585485i
$528$		0			0
$529$		−	17.9834i		−	0.781885i
$530$	17.2708	−	35.3457i	0.750195	−	1.53532i
$531$		0			0
$532$	−6.07917	−	6.07917i	−0.263565	−	0.263565i
$533$	−1.39452	−	1.39452i	−0.0604032	−	0.0604032i
$534$		0			0
$535$	−4.18657	−	12.1872i	−0.181001	−	0.526898i
$536$		−	23.0447i		−	0.995379i
$537$		0			0
$538$	0.919364	−	0.919364i	0.0396366	−	0.0396366i
$539$	13.5895			0.585340
$540$		0			0
$541$	6.30670			0.271146			0.135573	−	0.990767i	$-0.456712\pi$
$541$	6.30670			0.271146			0.135573	+	0.990767i	$0.456712\pi$
$542$	−14.6578	+	14.6578i	−0.629608	+	0.629608i
$543$		0			0
$544$			1.61092i			0.0690675i
$545$	2.22498	+	1.08718i	0.0953076	+	0.0465697i
$546$		0			0
$547$	21.8527	+	21.8527i	0.934352	+	0.934352i	0.997974	−	0.0636220i	$-0.0202652\pi$
$547$	21.8527	+	21.8527i	0.934352	+	0.934352i	−0.0636220	+	0.997974i	$0.520265\pi$
$548$	−0.246678	−	0.246678i	−0.0105375	−	0.0105375i
$549$		0			0
$550$	3.70031	−	29.7818i	0.157782	−	1.26990i
$551$			19.6126i			0.835525i
$552$		0			0
$553$	10.2356	−	10.2356i	0.435263	−	0.435263i
$554$	−15.6179			−0.663542
$555$		0			0
$556$	12.2563			0.519782
$557$	6.63181	−	6.63181i	0.280999	−	0.280999i	−0.552509	−	0.833507i	$-0.686329\pi$
$557$	6.63181	−	6.63181i	0.280999	−	0.280999i	0.833507	+	0.552509i	$0.186329\pi$
$558$		0			0
$559$			5.63159i			0.238191i
$560$	−18.8089	+	6.46126i	−0.794819	+	0.273038i
$561$		0			0
$562$	36.1139	+	36.1139i	1.52337	+	1.52337i
$563$	13.3256	+	13.3256i	0.561608	+	0.561608i	0.929764	−	0.368156i	$-0.120011\pi$
$563$	13.3256	+	13.3256i	0.561608	+	0.561608i	−0.368156	+	0.929764i	$0.620011\pi$
$564$		0			0
$565$	17.6478	−	6.06240i	0.742448	−	0.255047i
$566$			31.2741i			1.31455i
$567$		0			0
$568$	−11.6448	+	11.6448i	−0.488605	+	0.488605i
$569$	20.9755			0.879340			0.439670	−	0.898159i	$-0.355095\pi$
$569$	20.9755			0.879340			0.439670	+	0.898159i	$0.355095\pi$
$570$		0			0
$571$	24.4812			1.02451			0.512254	−	0.858834i	$-0.328811\pi$
$571$	24.4812			1.02451			0.512254	+	0.858834i	$0.328811\pi$
$572$	2.58263	−	2.58263i	0.107985	−	0.107985i
$573$		0			0
$574$		−	4.45614i		−	0.185996i
$575$	−1.38082	+	11.1135i	−0.0575841	+	0.463464i
$576$		0			0
$577$	−12.4198	−	12.4198i	−0.517041	−	0.517041i	0.399634	−	0.916675i	$-0.369137\pi$
$577$	−12.4198	−	12.4198i	−0.517041	−	0.517041i	−0.916675	+	0.399634i	$0.869137\pi$
$578$	19.8059	+	19.8059i	0.823817	+	0.823817i
$579$		0			0
$580$	−4.81692	−	2.35366i	−0.200012	−	0.0977305i
$581$		−	1.04418i		−	0.0433200i
$582$		0			0
$583$	27.0109	−	27.0109i	1.11868	−	1.11868i
$584$	−3.75705			−0.155468
$585$		0			0
$586$	56.1979			2.32151
$587$	−10.7006	+	10.7006i	−0.441661	+	0.441661i	−0.892570	−	0.450909i	$-0.851100\pi$
$587$	−10.7006	+	10.7006i	−0.441661	+	0.441661i	0.450909	+	0.892570i	$0.351100\pi$
$588$		0			0
$589$		−	30.3389i		−	1.25009i
$590$	0.674897	+	1.96464i	0.0277851	+	0.0808829i
$591$		0			0
$592$	27.4538	+	27.4538i	1.12835	+	1.12835i
$593$	−12.8270	−	12.8270i	−0.526744	−	0.526744i	0.392856	−	0.919600i	$-0.371487\pi$
$593$	−12.8270	−	12.8270i	−0.526744	−	0.526744i	−0.919600	+	0.392856i	$0.871487\pi$
$594$		0			0
$595$	0.691755	−	1.41572i	0.0283592	−	0.0580388i
$596$		−	5.26129i		−	0.215511i
$597$		0			0
$598$	−3.48536	+	3.48536i	−0.142527	+	0.142527i
$599$	6.90114			0.281973			0.140987	−	0.990012i	$-0.454973\pi$
$599$	6.90114			0.281973			0.140987	+	0.990012i	$0.454973\pi$
$600$		0			0
$601$	−12.5994			−0.513939			−0.256970	−	0.966419i	$-0.582724\pi$
$601$	−12.5994			−0.513939			−0.256970	+	0.966419i	$0.582724\pi$
$602$	−8.99779	+	8.99779i	−0.366722	+	0.366722i
$603$		0			0
$604$			6.58358i			0.267882i
$605$	1.99497	−	4.08283i	0.0811070	−	0.165990i
$606$		0			0
$607$	−26.3138	−	26.3138i	−1.06804	−	1.06804i	−0.997509	−	0.0705345i	$-0.977529\pi$
$607$	−26.3138	−	26.3138i	−1.06804	−	1.06804i	−0.0705345	−	0.997509i	$-0.522471\pi$
$608$	−18.1812	−	18.1812i	−0.737344	−	0.737344i
$609$		0			0
$610$	7.15625	+	20.8320i	0.289748	+	0.843462i
$611$		−	5.23510i		−	0.211789i
$612$		0			0
$613$	12.4072	−	12.4072i	0.501121	−	0.501121i	−0.410665	−	0.911786i	$-0.634704\pi$
$613$	12.4072	−	12.4072i	0.501121	−	0.501121i	0.911786	+	0.410665i	$0.134704\pi$
$614$	−5.33112			−0.215147
$615$		0			0
$616$	−13.3405			−0.537502
$617$	−7.26298	+	7.26298i	−0.292396	+	0.292396i	−0.838026	−	0.545630i	$-0.816290\pi$
$617$	−7.26298	+	7.26298i	−0.292396	+	0.292396i	0.545630	+	0.838026i	$0.316290\pi$
$618$		0			0
$619$		−	22.1286i		−	0.889424i	−0.895674	−	0.444712i	$-0.853306\pi$
$619$		−	22.1286i		−	0.889424i	0.895674	−	0.444712i	$-0.146694\pi$
$620$	7.45133	+	3.64090i	0.299253	+	0.146222i
$621$		0			0
$622$	2.53439	+	2.53439i	0.101620	+	0.101620i
$623$	20.9033	+	20.9033i	0.837473	+	0.837473i
$624$		0			0
$625$	−6.11792	+	24.2399i	−0.244717	+	0.969595i
$626$			36.1309i			1.44408i
$627$		0			0
$628$	0.900509	−	0.900509i	0.0359342	−	0.0359342i
$629$	−3.07612			−0.122653
$630$		0			0
$631$	8.15013			0.324451			0.162226	−	0.986754i	$-0.448133\pi$
$631$	8.15013			0.324451			0.162226	+	0.986754i	$0.448133\pi$
$632$	11.6901	−	11.6901i	0.465007	−	0.465007i
$633$		0			0
$634$			7.70887i			0.306158i
$635$	34.6588	−	11.9061i	1.37539	−	0.472478i
$636$		0			0
$637$	−3.52319	−	3.52319i	−0.139594	−	0.139594i
$638$	−13.3125	−	13.3125i	−0.527046	−	0.527046i
$639$		0			0
$640$	−28.1234	+	9.66101i	−1.11168	+	0.381885i
$641$		−	2.87588i		−	0.113590i	−0.998386	−	0.0567952i	$-0.981912\pi$
$641$		−	2.87588i		−	0.113590i	0.998386	−	0.0567952i	$-0.0180882\pi$
$642$		0			0
$643$	6.95652	−	6.95652i	0.274339	−	0.274339i	−0.556505	−	0.830844i	$-0.687858\pi$
$643$	6.95652	−	6.95652i	0.274339	−	0.274339i	0.830844	+	0.556505i	$0.187858\pi$
$644$	−3.07961			−0.121354
$645$		0			0
$646$	4.07263			0.160235
$647$	14.2662	−	14.2662i	0.560862	−	0.560862i	−0.368691	−	0.929552i	$-0.620194\pi$
$647$	14.2662	−	14.2662i	0.560862	−	0.560862i	0.929552	+	0.368691i	$0.120194\pi$
$648$		0			0
$649$			2.01711i			0.0791786i
$650$	−8.68054	+	6.76187i	−0.340479	+	0.265222i
$651$		0			0
$652$	8.03519	+	8.03519i	0.314682	+	0.314682i
$653$	−28.0800	−	28.0800i	−1.09885	−	1.09885i	−0.994545	−	0.104310i	$-0.966737\pi$
$653$	−28.0800	−	28.0800i	−1.09885	−	1.09885i	−0.104310	−	0.994545i	$-0.533263\pi$
$654$		0			0
$655$	10.0775	+	4.92411i	0.393760	+	0.192401i
$656$		−	7.36719i		−	0.287641i
$657$		0			0
$658$	8.36431	−	8.36431i	0.326075	−	0.326075i
$659$	46.7378			1.82065			0.910324	−	0.413896i	$-0.135832\pi$
$659$	46.7378			1.82065			0.910324	+	0.413896i	$0.135832\pi$
$660$		0			0
$661$	5.62865			0.218929			0.109465	−	0.993991i	$-0.465086\pi$
$661$	5.62865			0.218929			0.109465	+	0.993991i	$0.465086\pi$
$662$	−34.2233	+	34.2233i	−1.33013	+	1.33013i
$663$		0			0
$664$		−	1.19256i		−	0.0462803i
$665$	8.17082	+	23.7854i	0.316851	+	0.922359i
$666$		0			0
$667$	4.96772	+	4.96772i	0.192351	+	0.192351i
$668$	−5.25543	−	5.25543i	−0.203339	−	0.203339i
$669$		0			0
$670$	18.3086	−	37.4696i	0.707323	−	1.44758i
$671$			21.3884i			0.825689i
$672$		0			0
$673$	−21.0785	+	21.0785i	−0.812518	+	0.812518i	−0.985011	−	0.172493i	$-0.944818\pi$
$673$	−21.0785	+	21.0785i	−0.812518	+	0.812518i	0.172493	+	0.985011i	$0.444818\pi$
$674$	41.6249			1.60333
$675$		0			0
$676$	8.59784			0.330686
$677$	35.3463	−	35.3463i	1.35847	−	1.35847i	0.482660	−	0.875808i	$-0.339671\pi$
$677$	35.3463	−	35.3463i	1.35847	−	1.35847i	0.875808	−	0.482660i	$-0.160329\pi$
$678$		0			0
$679$		−	9.57607i		−	0.367496i
$680$	0.790054	−	1.61689i	0.0302972	−	0.0620050i
$681$		0			0
$682$	20.5932	+	20.5932i	0.788554	+	0.788554i
$683$	4.38271	+	4.38271i	0.167700	+	0.167700i	0.785968	−	0.618268i	$-0.212165\pi$
$683$	4.38271	+	4.38271i	0.167700	+	0.167700i	−0.618268	+	0.785968i	$0.712165\pi$
$684$		0			0
$685$	0.331552	+	0.965154i	0.0126679	+	0.0368766i
$686$		−	32.1934i		−	1.22915i
$687$		0			0
$688$	−14.8758	+	14.8758i	−0.567133	+	0.567133i
$689$	−14.0056			−0.533572
$690$		0			0
$691$	0.693296			0.0263742			0.0131871	−	0.999913i	$-0.495802\pi$
$691$	0.693296			0.0263742			0.0131871	+	0.999913i	$0.495802\pi$
$692$	−8.10973	+	8.10973i	−0.308286	+	0.308286i
$693$		0			0
$694$			58.1535i			2.20748i
$695$	−32.2137	−	15.7404i	−1.22193	−	0.597067i
$696$		0			0
$697$	0.412736	+	0.412736i	0.0156335	+	0.0156335i
$698$	23.2047	+	23.2047i	0.878312	+	0.878312i
$699$		0			0
$700$	−6.82233	−	0.847656i	−0.257860	−	0.0320384i
$701$			8.36037i			0.315767i	0.987458	+	0.157883i	$0.0504670\pi$
$701$			8.36037i			0.315767i	−0.987458	+	0.157883i	$0.949533\pi$
$702$		0			0
$703$	34.7178	−	34.7178i	1.30941	−	1.30941i
$704$	−11.0176			−0.415242
$705$		0			0
$706$	−12.5830			−0.473566
$707$	6.94707	−	6.94707i	0.261272	−	0.261272i
$708$		0			0
$709$			5.30469i			0.199222i	0.995026	+	0.0996109i	$0.0317598\pi$
$709$			5.30469i			0.199222i	−0.995026	+	0.0996109i	$0.968240\pi$
$710$	−28.1855	+	9.68234i	−1.05778	+	0.363372i
$711$		0			0
$712$	23.8737	+	23.8737i	0.894704	+	0.894704i
$713$	−7.68461	−	7.68461i	−0.287791	−	0.287791i
$714$		0			0
$715$	−10.1048	+	3.47123i	−0.377899	+	0.129817i
$716$			3.22566i			0.120548i
$717$		0			0
$718$	9.96682	−	9.96682i	0.371959	−	0.371959i
$719$	−28.3121			−1.05586			−0.527932	−	0.849286i	$-0.677033\pi$
$719$	−28.3121			−1.05586			−0.527932	+	0.849286i	$0.677033\pi$
$720$		0			0
$721$	−9.37468			−0.349131
$722$	−23.6269	+	23.6269i	−0.879303	+	0.879303i
$723$		0			0
$724$		−	18.1870i		−	0.675914i
$725$	9.63775	+	12.3725i	0.357937	+	0.459501i
$726$		0			0
$727$	−31.8237	−	31.8237i	−1.18028	−	1.18028i	−0.979672	−	0.200604i	$-0.935709\pi$
$727$	−31.8237	−	31.8237i	−1.18028	−	1.18028i	−0.200604	−	0.979672i	$-0.564291\pi$
$728$	3.45863	+	3.45863i	0.128185	+	0.128185i
$729$		0			0
$730$	−6.10879	−	2.98490i	−0.226096	−	0.110476i
$731$		−	1.66678i		−	0.0616482i
$732$		0			0
$733$	17.0982	−	17.0982i	0.631535	−	0.631535i	−0.316918	−	0.948453i	$-0.602648\pi$
$733$	17.0982	−	17.0982i	0.631535	−	0.631535i	0.948453	+	0.316918i	$0.102648\pi$
$734$	−13.6513			−0.503879
$735$		0			0
$736$	−9.21029			−0.339496
$737$	28.6340	−	28.6340i	1.05475	−	1.05475i
$738$		0			0
$739$			5.60736i			0.206270i	0.994667	+	0.103135i	$0.0328874\pi$
$739$			5.60736i			0.206270i	−0.994667	+	0.103135i	$0.967113\pi$
$740$	4.36039	+	12.6932i	0.160291	+	0.466611i
$741$		0			0
$742$	−22.3773	−	22.3773i	−0.821497	−	0.821497i
$743$	6.03833	+	6.03833i	0.221525	+	0.221525i	0.809140	−	0.587615i	$-0.199933\pi$
$743$	6.03833	+	6.03833i	0.221525	+	0.221525i	−0.587615	+	0.809140i	$0.699933\pi$
$744$		0			0
$745$	−6.75692	+	13.8285i	−0.247555	+	0.506635i
$746$			35.7776i			1.30991i
$747$		0			0
$748$	−0.764383	+	0.764383i	−0.0279486	+	0.0279486i
$749$	−10.3662			−0.378773
$750$		0			0
$751$	−4.64537			−0.169512			−0.0847560	−	0.996402i	$-0.527011\pi$
$751$	−4.64537			−0.169512			−0.0847560	+	0.996402i	$0.527011\pi$
$752$	13.8284	−	13.8284i	0.504272	−	0.504272i
$753$		0			0
$754$			6.90275i			0.251383i
$755$	8.45510	−	17.3039i	0.307713	−	0.629753i
$756$		0			0
$757$	−3.09830	−	3.09830i	−0.112609	−	0.112609i	0.648557	−	0.761166i	$-0.275373\pi$
$757$	−3.09830	−	3.09830i	−0.112609	−	0.112609i	−0.761166	+	0.648557i	$0.775373\pi$
$758$	13.1221	+	13.1221i	0.476618	+	0.476618i
$759$		0			0
$760$	9.33190	+	27.1654i	0.338503	+	0.985391i
$761$		−	45.0190i		−	1.63194i	−0.578097	−	0.815968i	$-0.696204\pi$
$761$		−	45.0190i		−	1.63194i	0.578097	−	0.815968i	$-0.303796\pi$
$762$		0			0
$763$	1.40863	−	1.40863i	0.0509958	−	0.0509958i
$764$	−17.7890			−0.643584
$765$		0			0
$766$	−25.2991			−0.914094
$767$	0.522954	−	0.522954i	0.0188828	−	0.0188828i
$768$		0			0
$769$			6.24119i			0.225063i	0.993648	+	0.112532i	$0.0358959\pi$
$769$			6.24119i			0.225063i	−0.993648	+	0.112532i	$0.964104\pi$
$770$	−21.6910	−	10.5987i	−0.781689	−	0.381952i
$771$		0			0
$772$	−11.2073	−	11.2073i	−0.403360	−	0.403360i
$773$	−19.5366	−	19.5366i	−0.702681	−	0.702681i	0.262304	−	0.964985i	$-0.415518\pi$
$773$	−19.5366	−	19.5366i	−0.702681	−	0.702681i	−0.964985	+	0.262304i	$0.915518\pi$
$774$		0			0
$775$	−14.9087	−	19.1391i	−0.535537	−	0.687495i
$776$		−	10.9368i		−	0.392610i
$777$		0			0
$778$	−29.9549	+	29.9549i	−1.07394	+	1.07394i
$779$	−9.31645			−0.333797
$780$		0			0
$781$	−28.9383			−1.03549
$782$	1.03156	−	1.03156i	0.0368887	−	0.0368887i
$783$		0			0
$784$		−	18.6129i		−	0.664748i
$785$	−3.52334	+	1.21035i	−0.125753	+	0.0431991i
$786$		0			0
$787$	20.7470	+	20.7470i	0.739550	+	0.739550i	0.972491	−	0.232940i	$-0.0748347\pi$
$787$	20.7470	+	20.7470i	0.739550	+	0.739550i	−0.232940	+	0.972491i	$0.574835\pi$
$788$	4.98846	+	4.98846i	0.177707	+	0.177707i
$789$		0			0
$790$	28.2952	−	9.72001i	1.00670	−	0.345823i
$791$		−	15.0109i		−	0.533725i
$792$		0			0
$793$	5.54513	−	5.54513i	0.196913	−	0.196913i
$794$	−14.0323			−0.497986
$795$		0			0
$796$	3.08641			0.109395
$797$	1.24054	−	1.24054i	0.0439423	−	0.0439423i	−0.684794	−	0.728736i	$-0.740108\pi$
$797$	1.24054	−	1.24054i	0.0439423	−	0.0439423i	0.728736	+	0.684794i	$0.240108\pi$
$798$		0			0
$799$			1.54944i			0.0548151i
$800$	−20.4038	−	2.53511i	−0.721382	−	0.0896298i
$801$		0			0
$802$	−32.1473	−	32.1473i	−1.13516	−	1.13516i
$803$	−4.66829	−	4.66829i	−0.164740	−	0.164740i
$804$		0			0
$805$	8.09426	+	3.95506i	0.285285	+	0.139397i
$806$		−	10.6779i		−	0.376114i
$807$		0			0
$808$	7.93426	−	7.93426i	0.279126	−	0.279126i
$809$	27.5870			0.969908			0.484954	−	0.874540i	$-0.338836\pi$
$809$	27.5870			0.969908			0.484954	+	0.874540i	$0.338836\pi$
$810$		0			0
$811$	−44.5699			−1.56506			−0.782530	−	0.622613i	$-0.786071\pi$
$811$	−44.5699			−1.56506			−0.782530	+	0.622613i	$0.786071\pi$
$812$	−3.04958	+	3.04958i	−0.107019	+	0.107019i
$813$		0			0
$814$			47.1309i			1.65194i
$815$	−10.7998	−	31.4386i	−0.378302	−	1.10125i
$816$		0			0
$817$	18.8117	+	18.8117i	0.658138	+	0.658138i
$818$	−31.9621	−	31.9621i	−1.11753	−	1.11753i
$819$		0			0
$820$	1.11805	−	2.28815i	0.0390439	−	0.0799056i
$821$			44.4188i			1.55023i	0.631822	+	0.775114i	$0.282307\pi$
$821$			44.4188i			1.55023i	−0.631822	+	0.775114i	$0.717693\pi$
$822$		0			0
$823$	22.3777	−	22.3777i	0.780039	−	0.780039i	−0.199798	−	0.979837i	$-0.564029\pi$
$823$	22.3777	−	22.3777i	0.780039	−	0.780039i	0.979837	+	0.199798i	$0.0640287\pi$
$824$	−10.7068			−0.372990
$825$		0			0
$826$	1.67109			0.0581445
$827$	−2.06846	+	2.06846i	−0.0719275	+	0.0719275i	−0.742155	−	0.670228i	$-0.766196\pi$
$827$	−2.06846	+	2.06846i	−0.0719275	+	0.0719275i	0.670228	+	0.742155i	$0.266196\pi$
$828$		0			0
$829$		−	12.9618i		−	0.450182i	−0.974338	−	0.225091i	$-0.927732\pi$
$829$		−	12.9618i		−	0.450182i	0.974338	−	0.225091i	$-0.0722680\pi$
$830$	0.947468	−	1.93905i	0.0328871	−	0.0673054i
$831$		0			0
$832$	2.85641	+	2.85641i	0.0990284	+	0.0990284i
$833$	1.04276	+	1.04276i	0.0361295	+	0.0361295i
$834$		0			0
$835$	7.06365	+	20.5624i	0.244448	+	0.711593i
$836$		−	17.2540i		−	0.596742i
$837$		0			0
$838$	−36.9202	+	36.9202i	−1.27539	+	1.27539i
$839$	−18.3905			−0.634911			−0.317455	−	0.948273i	$-0.602828\pi$
$839$	−18.3905			−0.634911			−0.317455	+	0.948273i	$0.602828\pi$
$840$		0			0
$841$	−19.1614			−0.660740
$842$	36.2877	−	36.2877i	1.25056	−	1.25056i
$843$		0			0
$844$			0.998459i			0.0343684i
$845$	−22.5980	−	11.0420i	−0.777396	−	0.379855i
$846$		0			0
$847$	−2.58483	−	2.58483i	−0.0888158	−	0.0888158i
$848$	−36.9957	−	36.9957i	−1.27044	−	1.27044i
$849$		0			0
$850$	2.56918	−	2.00131i	0.0881223	−	0.0686445i
$851$		−	17.5875i		−	0.602891i
$852$		0			0
$853$	9.76829	−	9.76829i	0.334460	−	0.334460i	−0.519818	−	0.854277i	$-0.674000\pi$
$853$	9.76829	−	9.76829i	0.334460	−	0.334460i	0.854277	+	0.519818i	$0.174000\pi$
$854$	17.7193			0.606342
$855$		0			0
$856$	−11.8392			−0.404657
$857$	−4.31399	+	4.31399i	−0.147363	+	0.147363i	−0.776939	−	0.629576i	$-0.783229\pi$
$857$	−4.31399	+	4.31399i	−0.147363	+	0.147363i	0.629576	+	0.776939i	$0.283229\pi$
$858$		0			0
$859$			18.6501i			0.636333i	0.948035	+	0.318166i	$0.103067\pi$
$859$			18.6501i			0.636333i	−0.948035	+	0.318166i	$0.896933\pi$
$860$	−6.87776	+	2.36266i	−0.234530	+	0.0805661i
$861$		0			0
$862$	−38.4289	−	38.4289i	−1.30889	−	1.30889i
$863$	9.43441	+	9.43441i	0.321151	+	0.321151i	0.849209	−	0.528058i	$-0.177079\pi$
$863$	9.43441	+	9.43441i	0.321151	+	0.321151i	−0.528058	+	0.849209i	$0.677079\pi$
$864$		0			0
$865$	31.7302	−	10.9000i	1.07886	−	0.370612i
$866$			17.0690i			0.580027i
$867$		0			0
$868$	4.71742	−	4.71742i	0.160120	−	0.160120i
$869$	29.0509			0.985484
$870$		0			0
$871$	−14.8472			−0.503079
$872$	1.60880	−	1.60880i	0.0544808	−	0.0544808i
$873$		0			0
$874$			23.2849i			0.787625i
$875$	16.8428	+	10.9897i	0.569390	+	0.371518i
$876$		0			0
$877$	−34.7554	−	34.7554i	−1.17361	−	1.17361i	−0.981343	−	0.192264i	$-0.938417\pi$
$877$	−34.7554	−	34.7554i	−1.17361	−	1.17361i	−0.192264	−	0.981343i	$-0.561583\pi$
$878$	−26.4291	−	26.4291i	−0.891940	−	0.891940i
$879$		0			0
$880$	−35.8610	−	17.5226i	−1.20887	−	0.590686i
$881$		−	17.7562i		−	0.598222i	−0.954218	−	0.299111i	$-0.903310\pi$
$881$		−	17.7562i		−	0.598222i	0.954218	−	0.299111i	$-0.0966901\pi$
$882$		0			0
$883$	8.09196	−	8.09196i	0.272316	−	0.272316i	−0.557716	−	0.830032i	$-0.688322\pi$
$883$	8.09196	−	8.09196i	0.272316	−	0.272316i	0.830032	+	0.557716i	$0.188322\pi$
$884$	0.396346			0.0133306
$885$		0			0
$886$	−12.8499			−0.431700
$887$	7.51255	−	7.51255i	0.252247	−	0.252247i	−0.569645	−	0.821891i	$-0.692919\pi$
$887$	7.51255	−	7.51255i	0.252247	−	0.252247i	0.821891	+	0.569645i	$0.192919\pi$
$888$		0			0
$889$		−	29.4801i		−	0.988732i
$890$	19.8503	+	57.7847i	0.665384	+	1.93695i
$891$		0			0
$892$	4.48293	+	4.48293i	0.150100	+	0.150100i
$893$	−17.4873	−	17.4873i	−0.585189	−	0.585189i
$894$		0			0
$895$	4.14262	−	8.47812i	0.138472	−	0.283392i
$896$			23.9213i			0.799153i
$897$		0			0
$898$	−44.8519	+	44.8519i	−1.49673	+	1.49673i
$899$	−15.2193			−0.507594
$900$		0			0
$901$	4.14526			0.138098
$902$	6.32374	−	6.32374i	0.210558	−	0.210558i
$903$		0			0
$904$		−	17.1439i		−	0.570199i
$905$	−23.3570	+	47.8016i	−0.776414	+	1.58898i
$906$		0			0
$907$	−5.48745	−	5.48745i	−0.182208	−	0.182208i	0.610109	−	0.792317i	$-0.291125\pi$
$907$	−5.48745	−	5.48745i	−0.182208	−	0.182208i	−0.792317	+	0.610109i	$0.791125\pi$
$908$	4.98428	+	4.98428i	0.165409	+	0.165409i
$909$		0			0
$910$	2.87576	+	8.37140i	0.0953305	+	0.277509i
$911$		−	12.8566i		−	0.425958i	−0.977057	−	0.212979i	$-0.931683\pi$
$911$		−	12.8566i		−	0.425958i	0.977057	−	0.212979i	$-0.0683166\pi$
$912$		0			0
$913$	1.48181	−	1.48181i	0.0490406	−	0.0490406i
$914$	46.3074			1.53171
$915$		0			0
$916$	15.1841			0.501698
$917$	6.38005	−	6.38005i	0.210688	−	0.210688i
$918$		0			0
$919$		−	30.7848i		−	1.01550i	−0.861505	−	0.507749i	$-0.830478\pi$
$919$		−	30.7848i		−	1.01550i	0.861505	−	0.507749i	$-0.169522\pi$
$920$	9.24447	+	4.51707i	0.304781	+	0.148924i
$921$		0			0
$922$	−28.8207	−	28.8207i	−0.949161	−	0.949161i
$923$	7.50251	+	7.50251i	0.246948	+	0.246948i
$924$		0			0
$925$	4.84091	−	38.9619i	0.159168	−	1.28106i
$926$			29.7259i			0.976854i
$927$		0			0
$928$	−9.12048	+	9.12048i	−0.299394	+	0.299394i
$929$	24.2893			0.796906			0.398453	−	0.917189i	$-0.369547\pi$
$929$	24.2893			0.796906			0.398453	+	0.917189i	$0.369547\pi$
$930$		0			0
$931$	−23.5377			−0.771416
$932$	−4.16821	+	4.16821i	−0.136534	+	0.136534i
$933$		0			0
$934$			52.4098i			1.71490i
$935$	2.99073	−	1.02738i	0.0978074	−	0.0335990i
$936$		0			0
$937$	−18.4403	−	18.4403i	−0.602420	−	0.602420i	0.338534	−	0.940954i	$-0.390069\pi$
$937$	−18.4403	−	18.4403i	−0.602420	−	0.602420i	−0.940954	+	0.338534i	$0.890069\pi$
$938$	−23.7220	−	23.7220i	−0.774550	−	0.774550i
$939$		0			0
$940$	6.39353	−	2.19632i	0.208534	−	0.0716361i
$941$			39.5834i			1.29038i	0.764021	+	0.645191i	$0.223222\pi$
$941$			39.5834i			1.29038i	−0.764021	+	0.645191i	$0.776778\pi$
$942$		0			0
$943$	−2.35978	+	2.35978i	−0.0768452	+	0.0768452i
$944$	2.76275			0.0899200
$945$		0			0
$946$	−25.5377			−0.830301
$947$	29.2710	−	29.2710i	0.951181	−	0.951181i	−0.0476819	−	0.998863i	$-0.515183\pi$
$947$	29.2710	−	29.2710i	0.951181	−	0.951181i	0.998863	+	0.0476819i	$0.0151834\pi$
$948$		0			0
$949$			2.42059i			0.0785756i
$950$	−6.40913	+	51.5837i	−0.207940	+	1.67359i
$951$		0			0
$952$	−1.02365	−	1.02365i	−0.0331768	−	0.0331768i
$953$	17.2048	+	17.2048i	0.557319	+	0.557319i	0.928543	−	0.371224i	$-0.121062\pi$
$953$	17.2048	+	17.2048i	0.557319	+	0.557319i	−0.371224	+	0.928543i	$0.621062\pi$
$954$		0			0
$955$	46.7556	+	22.8459i	1.51297	+	0.739276i
$956$			5.32293i			0.172156i
$957$		0			0
$958$	−15.9014	+	15.9014i	−0.513752	+	0.513752i
$959$	0.820942			0.0265096
$960$		0			0
$961$	−7.45706			−0.240550
$962$	12.2191	−	12.2191i	0.393959	−	0.393959i
$963$		0			0
$964$		−	17.9875i		−	0.579339i
$965$	15.0634	+	43.8499i	0.484908	+	1.41158i
$966$		0			0
$967$	15.6255	+	15.6255i	0.502481	+	0.502481i	0.912208	−	0.409727i	$-0.134376\pi$
$967$	15.6255	+	15.6255i	0.502481	+	0.502481i	−0.409727	+	0.912208i	$0.634376\pi$
$968$	−2.95214	−	2.95214i	−0.0948852	−	0.0948852i
$969$		0			0
$970$	8.68912	−	17.7828i	0.278991	−	0.570972i
$971$			3.58038i			0.114900i	0.998348	+	0.0574499i	$0.0182969\pi$
$971$			3.58038i			0.114900i	−0.998348	+	0.0574499i	$0.981703\pi$
$972$		0			0
$973$	−20.3944	+	20.3944i	−0.653815	+	0.653815i
$974$	41.8278			1.34025
$975$		0			0
$976$	29.2948			0.937702
$977$	−14.5653	+	14.5653i	−0.465985	+	0.465985i	−0.900611	−	0.434626i	$-0.856881\pi$
$977$	−14.5653	+	14.5653i	−0.465985	+	0.465985i	0.434626	+	0.900611i	$0.356881\pi$
$978$		0			0
$979$			59.3281i			1.89613i
$980$	2.82470	−	5.78092i	0.0902318	−	0.184665i
$981$		0			0
$982$	24.4066	+	24.4066i	0.778846	+	0.778846i
$983$	20.7122	+	20.7122i	0.660618	+	0.660618i	0.955526	−	0.294908i	$-0.0952890\pi$
$983$	20.7122	+	20.7122i	0.660618	+	0.660618i	−0.294908	+	0.955526i	$0.595289\pi$
$984$		0			0
$985$	−6.70484	−	19.5179i	−0.213634	−	0.621893i
$986$		−	2.04301i		−	0.0650627i
$987$		0			0
$988$	−4.47325	+	4.47325i	−0.142313	+	0.142313i
$989$	9.52971			0.303027
$990$		0			0
$991$	−21.0816			−0.669679			−0.334840	−	0.942275i	$-0.608682\pi$
$991$	−21.0816			−0.669679			−0.334840	+	0.942275i	$0.608682\pi$
$992$	14.1086	−	14.1086i	0.447947	−	0.447947i
$993$		0			0
$994$			23.9741i			0.760411i
$995$	−8.11214	−	3.96379i	−0.257172	−	0.125661i
$996$		0			0
$997$	−36.5710	−	36.5710i	−1.15821	−	1.15821i	−0.984859	−	0.173355i	$-0.944539\pi$
$997$	−36.5710	−	36.5710i	−1.15821	−	1.15821i	−0.173355	−	0.984859i	$-0.555461\pi$
$998$	11.6227	+	11.6227i	0.367909	+	0.367909i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.f.a.242.7		16
3.2	odd	2	inner	405.2.f.a.242.2		16
5.3	odd	4	inner	405.2.f.a.323.2		16
9.2	odd	6		135.2.m.a.17.3		16
9.4	even	3		135.2.m.a.62.3		16
9.5	odd	6		45.2.l.a.2.2	✓	16
9.7	even	3		45.2.l.a.32.2	yes	16
15.8	even	4	inner	405.2.f.a.323.7		16
36.7	odd	6		720.2.cu.c.257.3		16
36.23	even	6		720.2.cu.c.497.1		16
45.2	even	12		675.2.q.a.368.2		16
45.4	even	6		675.2.q.a.332.2		16
45.7	odd	12		225.2.p.b.68.3		16
45.13	odd	12		135.2.m.a.8.3		16
45.14	odd	6		225.2.p.b.182.3		16
45.22	odd	12		675.2.q.a.143.2		16
45.23	even	12		45.2.l.a.38.2	yes	16
45.29	odd	6		675.2.q.a.557.2		16
45.32	even	12		225.2.p.b.218.3		16
45.34	even	6		225.2.p.b.32.3		16
45.38	even	12		135.2.m.a.98.3		16
45.43	odd	12		45.2.l.a.23.2	yes	16
180.23	odd	12		720.2.cu.c.353.3		16
180.43	even	12		720.2.cu.c.113.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.2	✓	16	9.5	odd	6
45.2.l.a.23.2	yes	16	45.43	odd	12
45.2.l.a.32.2	yes	16	9.7	even	3
45.2.l.a.38.2	yes	16	45.23	even	12
135.2.m.a.8.3		16	45.13	odd	12
135.2.m.a.17.3		16	9.2	odd	6
135.2.m.a.62.3		16	9.4	even	3
135.2.m.a.98.3		16	45.38	even	12
225.2.p.b.32.3		16	45.34	even	6
225.2.p.b.68.3		16	45.7	odd	12
225.2.p.b.182.3		16	45.14	odd	6
225.2.p.b.218.3		16	45.32	even	12
405.2.f.a.242.2		16	3.2	odd	2	inner
405.2.f.a.242.7		16	1.1	even	1	trivial
405.2.f.a.323.2		16	5.3	odd	4	inner
405.2.f.a.323.7		16	15.8	even	4	inner
675.2.q.a.143.2		16	45.22	odd	12
675.2.q.a.332.2		16	45.4	even	6
675.2.q.a.368.2		16	45.2	even	12
675.2.q.a.557.2		16	45.29	odd	6
720.2.cu.c.113.1		16	180.43	even	12
720.2.cu.c.257.3		16	36.7	odd	6
720.2.cu.c.353.3		16	180.23	odd	12
720.2.cu.c.497.1		16	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17567 - 1.17567i) q^{2} -0.764383i q^{4} +(-0.981675 + 2.00906i) q^{5} +(1.27193 + 1.27193i) q^{7} +(1.45267 + 1.45267i) q^{8} +O(q^{10})\)	\(q+(1.17567 - 1.17567i) q^{2} -0.764383i q^{4} +(-0.981675 + 2.00906i) q^{5} +(1.27193 + 1.27193i) q^{7} +(1.45267 + 1.45267i) q^{8} +(1.20786 + 3.51610i) q^{10} +3.61002i q^{11} +(0.935928 - 0.935928i) q^{13} +2.99073 q^{14} +4.94448 q^{16} +(-0.277007 + 0.277007i) q^{17} -6.25273i q^{19} +(1.53569 + 0.750376i) q^{20} +(4.24417 + 4.24417i) q^{22} +(-1.58377 - 1.58377i) q^{23} +(-3.07263 - 3.94448i) q^{25} -2.20068i q^{26} +(0.972242 - 0.972242i) q^{28} -3.13665 q^{29} +4.85211 q^{31} +(2.90772 - 2.90772i) q^{32} +0.651336i q^{34} +(-3.80401 + 1.30676i) q^{35} +(5.55242 + 5.55242i) q^{37} +(-7.35112 - 7.35112i) q^{38} +(-4.34456 + 1.49245i) q^{40} -1.48998i q^{41} +(-3.00856 + 3.00856i) q^{43} +2.75943 q^{44} -3.72396 q^{46} +(2.79674 - 2.79674i) q^{47} -3.76438i q^{49} +(-8.24978 - 1.02501i) q^{50} +(-0.715408 - 0.715408i) q^{52} +(-7.48222 - 7.48222i) q^{53} +(-7.25273 - 3.54386i) q^{55} +3.69540i q^{56} +(-3.68765 + 3.68765i) q^{58} +0.558755 q^{59} +5.92473 q^{61} +(5.70446 - 5.70446i) q^{62} +3.05196i q^{64} +(0.961557 + 2.79911i) q^{65} +(-7.93182 - 7.93182i) q^{67} +(0.211740 + 0.211740i) q^{68} +(-2.93593 + 6.00856i) q^{70} +8.01611i q^{71} +(-1.29315 + 1.29315i) q^{73} +13.0556 q^{74} -4.77948 q^{76} +(-4.59169 + 4.59169i) q^{77} -8.04731i q^{79} +(-4.85388 + 9.93376i) q^{80} +(-1.75172 - 1.75172i) q^{82} +(-0.410471 - 0.410471i) q^{83} +(-0.284592 - 0.828454i) q^{85} +7.07412i q^{86} +(-5.24417 + 5.24417i) q^{88} +16.4343 q^{89} +2.38087 q^{91} +(-1.21060 + 1.21060i) q^{92} -6.57607i q^{94} +(12.5621 + 6.13815i) q^{95} +(-3.76438 - 3.76438i) q^{97} +(-4.42566 - 4.42566i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7}+O(q^{10}) \) 16 * q + 4 * q^7	\( 16 q + 4 q^{7} - 8 q^{10} + 4 q^{13} + 16 q^{16} + 20 q^{22} - 8 q^{25} - 16 q^{28} + 8 q^{31} + 4 q^{37} - 12 q^{40} + 4 q^{43} + 32 q^{46} + 28 q^{52} - 16 q^{55} + 12 q^{58} - 16 q^{61} - 8 q^{67} - 36 q^{70} - 8 q^{73} - 48 q^{76} + 32 q^{82} - 44 q^{85} - 36 q^{88} - 40 q^{91} - 56 q^{97}+O(q^{100}) \) 16 * q + 4 * q^7 - 8 * q^10 + 4 * q^13 + 16 * q^16 + 20 * q^22 - 8 * q^25 - 16 * q^28 + 8 * q^31 + 4 * q^37 - 12 * q^40 + 4 * q^43 + 32 * q^46 + 28 * q^52 - 16 * q^55 + 12 * q^58 - 16 * q^61 - 8 * q^67 - 36 * q^70 - 8 * q^73 - 48 * q^76 + 32 * q^82 - 44 * q^85 - 36 * q^88 - 40 * q^91 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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