LMFDB - Embedded newform 380.2.bh.a.193.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(13,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("380.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bh (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.9
Character	$\chi$	$=$	380.193
Dual form			380.2.bh.a.317.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11039 - 2.38123i) q^{3} +(-0.922332 - 2.03698i) q^{5} +(-2.08587 - 0.558906i) q^{7} +(-2.50894 - 2.99004i) q^{9} +O(q^{10})$	\(q+(1.11039 - 2.38123i) q^{3} +(-0.922332 - 2.03698i) q^{5} +(-2.08587 - 0.558906i) q^{7} +(-2.50894 - 2.99004i) q^{9} +(-0.730936 + 1.26602i) q^{11} +(0.748918 - 0.349226i) q^{13} +(-5.87467 - 0.0655530i) q^{15} +(-2.71062 + 0.237149i) q^{17} +(4.25189 + 0.959893i) q^{19} +(-3.64700 + 4.34633i) q^{21} +(3.96759 - 5.66631i) q^{23} +(-3.29861 + 3.75755i) q^{25} +(-2.29224 + 0.614204i) q^{27} +(1.39280 - 1.16870i) q^{29} +(-1.26371 + 0.729601i) q^{31} +(2.20306 + 3.14629i) q^{33} +(0.785379 + 4.76437i) q^{35} +(-0.309697 - 0.309697i) q^{37} -2.17112i q^{39} +(0.339156 + 0.931825i) q^{41} +(8.06488 - 5.64709i) q^{43} +(-3.77658 + 7.86847i) q^{45} +(0.955306 - 10.9192i) q^{47} +(-2.02372 - 1.16839i) q^{49} +(-2.44513 + 6.71794i) q^{51} +(-7.82119 - 5.47646i) q^{53} +(3.25302 + 0.321215i) q^{55} +(7.00697 - 9.05889i) q^{57} +(4.73412 + 3.97240i) q^{59} +(0.0111039 + 0.0629732i) q^{61} +(3.56216 + 7.63907i) q^{63} +(-1.40212 - 1.20343i) q^{65} +(2.01623 + 0.176397i) q^{67} +(-9.08722 - 15.7395i) q^{69} +(13.0287 + 2.29730i) q^{71} +(13.5919 + 6.33800i) q^{73} +(5.28487 + 12.0271i) q^{75} +(2.23222 - 2.23222i) q^{77} +(-2.02226 + 0.736043i) q^{79} +(0.950647 - 5.39139i) q^{81} +(-3.25291 + 12.1400i) q^{83} +(2.98316 + 5.30276i) q^{85} +(-1.23639 - 4.61428i) q^{87} +(-11.7510 - 4.27701i) q^{89} +(-1.75733 + 0.309864i) q^{91} +(0.334147 + 3.81931i) q^{93} +(-1.96637 - 9.54638i) q^{95} +(0.868480 + 9.92678i) q^{97} +(5.61931 - 0.990836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.11039	−	2.38123i	0.641082	−	1.37480i	−0.270113	−	0.962829i	$-0.587061\pi$
$3$	1.11039	−	2.38123i	0.641082	−	1.37480i	0.911195	−	0.411975i	$-0.135161\pi$
$4$		0			0
$5$	−0.922332	−	2.03698i	−0.412479	−	0.910967i
$5$	−0.922332	−	2.03698i	−0.412479	−	0.910967i
$6$		0			0
$7$	−2.08587	−	0.558906i	−0.788383	−	0.211247i	−0.157906	−	0.987454i	$-0.550474\pi$
$7$	−2.08587	−	0.558906i	−0.788383	−	0.211247i	−0.630477	+	0.776208i	$0.717141\pi$
$8$		0			0
$9$	−2.50894	−	2.99004i	−0.836313	−	0.996679i
$10$		0			0
$11$	−0.730936	+	1.26602i	−0.220385	+	0.381719i	−0.954925	−	0.296847i	$-0.904065\pi$
$11$	−0.730936	+	1.26602i	−0.220385	+	0.381719i	0.734540	+	0.678566i	$0.237398\pi$
$12$		0			0
$13$	0.748918	−	0.349226i	0.207712	−	0.0968579i	−0.315978	−	0.948766i	$-0.602333\pi$
$13$	0.748918	−	0.349226i	0.207712	−	0.0968579i	0.523691	+	0.851909i	$0.324555\pi$
$14$		0			0
$15$	−5.87467	−	0.0655530i	−1.51683	−	0.0169257i
$16$		0			0
$17$	−2.71062	+	0.237149i	−0.657422	+	0.0575170i	−0.410985	−	0.911642i	$-0.634815\pi$
$17$	−2.71062	+	0.237149i	−0.657422	+	0.0575170i	−0.246437	+	0.969159i	$0.579260\pi$
$18$		0			0
$19$	4.25189	+	0.959893i	0.975451	+	0.220214i
$19$	4.25189	+	0.959893i	0.975451	+	0.220214i
$20$		0			0
$21$	−3.64700	+	4.34633i	−0.795841	+	0.948446i
$22$		0			0
$23$	3.96759	−	5.66631i	0.827300	−	1.18151i	−0.153819	−	0.988099i	$-0.549157\pi$
$23$	3.96759	−	5.66631i	0.827300	−	1.18151i	0.981119	−	0.193407i	$-0.0619539\pi$
$24$		0			0
$25$	−3.29861	+	3.75755i	−0.659721	+	0.751510i
$26$		0			0
$27$	−2.29224	+	0.614204i	−0.441142	+	0.118204i
$28$		0			0
$29$	1.39280	−	1.16870i	0.258636	−	0.217022i	−0.504244	−	0.863561i	$-0.668229\pi$
$29$	1.39280	−	1.16870i	0.258636	−	0.217022i	0.762881	+	0.646539i	$0.223784\pi$
$30$		0			0
$31$	−1.26371	+	0.729601i	−0.226968	+	0.131040i	−0.609173	−	0.793038i	$-0.708498\pi$
$31$	−1.26371	+	0.729601i	−0.226968	+	0.131040i	0.382204	+	0.924078i	$0.375165\pi$
$32$		0			0
$33$	2.20306	+	3.14629i	0.383503	+	0.547700i
$34$		0			0
$35$	0.785379	+	4.76437i	0.132753	+	0.805326i
$36$		0			0
$37$	−0.309697	−	0.309697i	−0.0509138	−	0.0509138i	0.681191	−	0.732105i	$-0.261462\pi$
$37$	−0.309697	−	0.309697i	−0.0509138	−	0.0509138i	−0.732105	+	0.681191i	$0.761462\pi$
$38$		0			0
$39$		−	2.17112i		−	0.347658i
$40$		0			0
$41$	0.339156	+	0.931825i	0.0529673	+	0.145527i	0.963355	−	0.268230i	$-0.0864387\pi$
$41$	0.339156	+	0.931825i	0.0529673	+	0.145527i	−0.910388	+	0.413757i	$0.864216\pi$
$42$		0			0
$43$	8.06488	−	5.64709i	1.22988	−	0.861173i	0.236015	−	0.971749i	$-0.424159\pi$
$43$	8.06488	−	5.64709i	1.22988	−	0.861173i	0.993868	+	0.110576i	$0.0352697\pi$
$44$		0			0
$45$	−3.77658	+	7.86847i	−0.562979	+	1.17296i
$46$		0			0
$47$	0.955306	−	10.9192i	0.139346	−	1.59273i	−0.528831	−	0.848727i	$-0.677370\pi$
$47$	0.955306	−	10.9192i	0.139346	−	1.59273i	0.668177	−	0.744002i	$-0.267075\pi$
$48$		0			0
$49$	−2.02372	−	1.16839i	−0.289102	−	0.166913i
$50$		0			0
$51$	−2.44513	+	6.71794i	−0.342387	+	0.940699i
$52$		0			0
$53$	−7.82119	−	5.47646i	−1.07432	−	0.752249i	−0.104126	−	0.994564i	$-0.533204\pi$
$53$	−7.82119	−	5.47646i	−1.07432	−	0.752249i	−0.970198	+	0.242315i	$0.922093\pi$
$54$		0			0
$55$	3.25302	+	0.321215i	0.438638	+	0.0433127i
$56$		0			0
$57$	7.00697	−	9.05889i	0.928096	−	1.19988i
$58$		0			0
$59$	4.73412	+	3.97240i	0.616330	+	0.517162i	0.896647	−	0.442745i	$-0.145995\pi$
$59$	4.73412	+	3.97240i	0.616330	+	0.517162i	−0.280318	+	0.959907i	$0.590440\pi$
$60$		0			0
$61$	0.0111039	+	0.0629732i	0.00142171	+	0.00806290i	0.985510	−	0.169615i	$-0.0542525\pi$
$61$	0.0111039	+	0.0629732i	0.00142171	+	0.00806290i	−0.984089	+	0.177678i	$0.943141\pi$
$62$		0			0
$63$	3.56216	+	7.63907i	0.448790	+	0.962433i
$64$		0			0
$65$	−1.40212	−	1.20343i	−0.173911	−	0.149267i
$66$		0			0
$67$	2.01623	+	0.176397i	0.246322	+	0.0215504i	0.209648	−	0.977777i	$-0.432768\pi$
$67$	2.01623	+	0.176397i	0.246322	+	0.0215504i	0.0366737	+	0.999327i	$0.488324\pi$
$68$		0			0
$69$	−9.08722	−	15.7395i	−1.09397	−	1.89482i
$70$		0			0
$71$	13.0287	+	2.29730i	1.54622	+	0.272640i	0.880675	−	0.473720i	$-0.157089\pi$
$71$	13.0287	+	2.29730i	1.54622	+	0.272640i	0.665542	+	0.746360i	$0.268200\pi$
$72$		0			0
$73$	13.5919	+	6.33800i	1.59081	+	0.741807i	0.997981	−	0.0635204i	$-0.0202328\pi$
$73$	13.5919	+	6.33800i	1.59081	+	0.741807i	0.592830	+	0.805328i	$0.298011\pi$
$74$		0			0
$75$	5.28487	+	12.0271i	0.610244	+	1.38877i
$76$		0			0
$77$	2.23222	−	2.23222i	0.254385	−	0.254385i
$78$		0			0
$79$	−2.02226	+	0.736043i	−0.227522	+	0.0828113i	−0.453266	−	0.891375i	$-0.649741\pi$
$79$	−2.02226	+	0.736043i	−0.227522	+	0.0828113i	0.225743	+	0.974187i	$0.427519\pi$
$80$		0			0
$81$	0.950647	−	5.39139i	0.105627	−	0.599043i
$82$		0			0
$83$	−3.25291	+	12.1400i	−0.357053	+	1.33254i	0.520829	+	0.853661i	$0.325623\pi$
$83$	−3.25291	+	12.1400i	−0.357053	+	1.33254i	−0.877882	+	0.478878i	$0.841044\pi$
$84$		0			0
$85$	2.98316	+	5.30276i	0.323569	+	0.575165i
$86$		0			0
$87$	−1.23639	−	4.61428i	−0.132555	−	0.494703i
$88$		0			0
$89$	−11.7510	−	4.27701i	−1.24560	−	0.453362i	−0.366688	−	0.930344i	$-0.619508\pi$
$89$	−11.7510	−	4.27701i	−1.24560	−	0.453362i	−0.878913	+	0.476982i	$0.841731\pi$
$90$		0			0
$91$	−1.75733	+	0.309864i	−0.184218	+	0.0324826i
$92$		0			0
$93$	0.334147	+	3.81931i	0.0346494	+	0.396044i
$94$		0			0
$95$	−1.96637	−	9.54638i	−0.201746	−	0.979438i
$96$		0			0
$97$	0.868480	+	9.92678i	0.0881808	+	1.00791i	0.903411	+	0.428775i	$0.141055\pi$
$97$	0.868480	+	9.92678i	0.0881808	+	1.00791i	−0.815231	+	0.579137i	$0.803390\pi$
$98$		0			0
$99$	5.61931	−	0.990836i	0.564762	−	0.0995828i
$100$		0			0
$101$	−6.98936	−	2.54392i	−0.695468	−	0.253130i	−0.0299932	−	0.999550i	$-0.509549\pi$
$101$	−6.98936	−	2.54392i	−0.695468	−	0.253130i	−0.665475	+	0.746421i	$0.731771\pi$
$102$		0			0
$103$	3.50166	+	13.0684i	0.345029	+	1.28767i	0.892578	+	0.450893i	$0.148894\pi$
$103$	3.50166	+	13.0684i	0.345029	+	1.28767i	−0.547549	+	0.836774i	$0.684439\pi$
$104$		0			0
$105$	12.2171	+	3.42013i	1.19227	+	0.333770i
$106$		0			0
$107$	−0.536140	+	2.00090i	−0.0518306	+	0.193435i	−0.986987	−	0.160801i	$-0.948592\pi$
$107$	−0.536140	+	2.00090i	−0.0518306	+	0.193435i	0.935156	+	0.354236i	$0.115259\pi$
$108$		0			0
$109$	−3.56668	+	20.2276i	−0.341626	+	1.93746i	0.00642372	+	0.999979i	$0.497955\pi$
$109$	−3.56668	+	20.2276i	−0.341626	+	1.93746i	−0.348049	+	0.937476i	$0.613156\pi$
$110$		0			0
$111$	−1.08134	+	0.393576i	−0.102636	+	0.0373566i
$112$		0			0
$113$	13.3811	−	13.3811i	1.25879	−	1.25879i	0.307122	−	0.951670i	$-0.400634\pi$
$113$	13.3811	−	13.3811i	1.25879	−	1.25879i	0.951670	−	0.307122i	$-0.0993659\pi$
$114$		0			0
$115$	−15.2016	−	2.85570i	−1.41756	−	0.266296i
$116$		0			0
$117$	−2.92319	−	1.36310i	−0.270249	−	0.126019i
$118$		0			0
$119$	5.78654	+	1.02032i	0.530451	+	0.0935328i
$120$		0			0
$121$	4.43147	+	7.67552i	0.402861	+	0.697775i
$122$		0			0
$123$	2.59548	+	0.227075i	0.234027	+	0.0204747i
$124$		0			0
$125$	10.6965	+	3.25350i	0.956723	+	0.291002i
$126$		0			0
$127$	5.33846	+	11.4484i	0.473712	+	1.01588i	0.987450	+	0.157931i	$0.0504825\pi$
$127$	5.33846	+	11.4484i	0.473712	+	1.01588i	−0.513738	+	0.857947i	$0.671740\pi$
$128$		0			0
$129$	−4.49189	−	25.4748i	−0.395489	−	2.24293i
$130$		0			0
$131$	10.5177	+	8.82537i	0.918933	+	0.771076i	0.973797	−	0.227418i	$-0.0730283\pi$
$131$	10.5177	+	8.82537i	0.918933	+	0.771076i	−0.0548646	+	0.998494i	$0.517473\pi$
$132$		0			0
$133$	−8.33239	−	4.37862i	−0.722510	−	0.379674i
$134$		0			0
$135$	3.36533	+	4.10276i	0.289642	+	0.353109i
$136$		0			0
$137$	5.66550	+	3.96702i	0.484036	+	0.338926i	0.789989	−	0.613121i	$-0.210086\pi$
$137$	5.66550	+	3.96702i	0.484036	+	0.338926i	−0.305953	+	0.952047i	$0.598975\pi$
$138$		0			0
$139$	−6.75859	+	18.5691i	−0.573256	+	1.57501i	0.226069	+	0.974111i	$0.427412\pi$
$139$	−6.75859	+	18.5691i	−0.573256	+	1.57501i	−0.799326	+	0.600898i	$0.794810\pi$
$140$		0			0
$141$	−24.9404	−	14.3993i	−2.10036	−	1.21264i
$142$		0			0
$143$	−0.105284	+	1.20341i	−0.00880432	+	0.100634i
$144$		0			0
$145$	−3.66524	−	1.75918i	−0.304382	−	0.146092i
$146$		0			0
$147$	−5.02932	+	3.52157i	−0.414811	+	0.290454i
$148$		0			0
$149$	−4.11924	−	11.3175i	−0.337461	−	0.927167i	−0.986112	−	0.166081i	$-0.946889\pi$
$149$	−4.11924	−	11.3175i	−0.337461	−	0.927167i	0.648651	−	0.761086i	$-0.275334\pi$
$150$		0			0
$151$		−	21.7280i		−	1.76820i	−0.467296	−	0.884101i	$-0.654772\pi$
$151$		−	21.7280i		−	1.76820i	0.467296	−	0.884101i	$-0.345228\pi$
$152$		0			0
$153$	7.50986	+	7.50986i	0.607136	+	0.607136i
$154$		0			0
$155$	2.65174	+	1.90121i	0.212993	+	0.152709i
$156$		0			0
$157$	−4.57305	−	6.53099i	−0.364969	−	0.521230i	0.594104	−	0.804388i	$-0.297507\pi$
$157$	−4.57305	−	6.53099i	−0.364969	−	0.521230i	−0.959073	+	0.283158i	$0.908618\pi$
$158$		0			0
$159$	−21.7253	+	12.5431i	−1.72292	+	0.994731i
$160$		0			0
$161$	−11.4428	+	9.60165i	−0.901819	+	0.756716i
$162$		0			0
$163$	−5.25745	+	1.40873i	−0.411795	+	0.110340i	−0.458768	−	0.888556i	$-0.651709\pi$
$163$	−5.25745	+	1.40873i	−0.411795	+	0.110340i	0.0469731	+	0.998896i	$0.485042\pi$
$164$		0			0
$165$	4.37700	−	7.38953i	0.340749	−	0.575274i
$166$		0			0
$167$	10.6739	−	15.2439i	0.825973	−	1.17961i	−0.155467	−	0.987841i	$-0.549688\pi$
$167$	10.6739	−	15.2439i	0.825973	−	1.17961i	0.981440	−	0.191770i	$-0.0614229\pi$
$168$		0			0
$169$	−7.91732	+	9.43549i	−0.609025	+	0.725807i
$170$		0			0
$171$	−7.79763	−	15.1216i	−0.596299	−	1.15638i
$172$		0			0
$173$	−12.7401	+	1.11462i	−0.968616	+	0.0847429i	−0.560471	−	0.828174i	$-0.689380\pi$
$173$	−12.7401	+	1.11462i	−0.968616	+	0.0847429i	−0.408145	+	0.912917i	$0.633824\pi$
$174$		0			0
$175$	8.98057	−	5.99414i	0.678867	−	0.453114i
$176$		0			0
$177$	14.7159	−	6.86213i	1.10611	−	0.515789i
$178$		0			0
$179$	6.86857	−	11.8967i	0.513381	−	0.889202i	−0.486499	−	0.873681i	$-0.661726\pi$
$179$	6.86857	−	11.8967i	0.513381	−	0.889202i	0.999880	−	0.0155204i	$-0.00494048\pi$
$180$		0			0
$181$	−1.26467	−	1.50718i	−0.0940024	−	0.112028i	0.716993	−	0.697081i	$-0.245518\pi$
$181$	−1.26467	−	1.50718i	−0.0940024	−	0.112028i	−0.810995	+	0.585053i	$0.801074\pi$
$182$		0			0
$183$	0.162283	+	0.0434837i	0.0119963	+	0.00321441i
$184$		0			0
$185$	−0.345204	+	0.916490i	−0.0253799	+	0.0673817i
$186$		0			0
$187$	1.68106	−	3.60503i	0.122931	−	0.263626i
$188$		0			0
$189$	5.12459			0.372759
$190$		0			0
$191$	−7.72276			−0.558799			−0.279400	−	0.960175i	$-0.590135\pi$
$191$	−7.72276			−0.558799			−0.279400	+	0.960175i	$0.590135\pi$
$192$		0			0
$193$	0.727748	−	1.56066i	0.0523845	−	0.112339i	−0.878373	−	0.477975i	$-0.841371\pi$
$193$	0.727748	−	1.56066i	0.0523845	−	0.112339i	0.930758	+	0.365636i	$0.119149\pi$
$194$		0			0
$195$	−4.42254	+	2.00250i	−0.316705	+	0.143402i
$196$		0			0
$197$	2.61779	+	0.701434i	0.186510	+	0.0499751i	0.350865	−	0.936426i	$-0.385888\pi$
$197$	2.61779	+	0.701434i	0.186510	+	0.0499751i	−0.164355	+	0.986401i	$0.552554\pi$
$198$		0			0
$199$	−10.4768	−	12.4858i	−0.742680	−	0.885091i	0.253942	−	0.967219i	$-0.418273\pi$
$199$	−10.4768	−	12.4858i	−0.742680	−	0.885091i	−0.996622	+	0.0821280i	$0.973828\pi$
$200$		0			0
$201$	2.65884	−	4.60524i	0.187540	−	0.324828i
$202$		0			0
$203$	−3.55839	+	1.65930i	−0.249750	+	0.116460i
$204$		0			0
$205$	1.58530	−	1.55031i	0.110722	−	0.108278i
$206$		0			0
$207$	−26.8969	+	2.35317i	−1.86946	+	0.163557i
$208$		0			0
$209$	−4.32310	+	4.68135i	−0.299035	+	0.323816i
$210$		0			0
$211$	8.61100	−	10.2622i	0.592806	−	0.706479i	−0.383337	−	0.923609i	$-0.625225\pi$
$211$	8.61100	−	10.2622i	0.592806	−	0.706479i	0.976143	+	0.217130i	$0.0696696\pi$
$212$		0			0
$213$	19.9372	−	28.4733i	1.36608	−	1.95096i
$214$		0			0
$215$	−18.9415	−	11.2195i	−1.29180	−	0.765166i
$216$		0			0
$217$	3.04370	−	0.815557i	0.206620	−	0.0553636i
$218$		0			0
$219$	30.1845	−	25.3278i	2.03968	−	1.71149i
$220$		0			0
$221$	−1.94721	+	1.12422i	−0.130984	+	0.0756235i
$222$		0			0
$223$	−4.16608	−	5.94978i	−0.278982	−	0.398427i	0.655068	−	0.755570i	$-0.272640\pi$
$223$	−4.16608	−	5.94978i	−0.278982	−	0.398427i	−0.934050	+	0.357143i	$0.883751\pi$
$224$		0			0
$225$	19.5112	+	0.435489i	1.30075	+	0.0290326i
$226$		0			0
$227$	−11.2519	−	11.2519i	−0.746813	−	0.746813i	0.227067	−	0.973879i	$-0.427087\pi$
$227$	−11.2519	−	11.2519i	−0.746813	−	0.746813i	−0.973879	+	0.227067i	$0.927087\pi$
$228$		0			0
$229$			17.1090i			1.13059i	0.824888	+	0.565296i	$0.191238\pi$
$229$			17.1090i			1.13059i	−0.824888	+	0.565296i	$0.808762\pi$
$230$		0			0
$231$	−2.83680	−	7.79405i	−0.186648	−	0.512811i
$232$		0			0
$233$	−11.2710	+	7.89205i	−0.738389	+	0.517025i	−0.881211	−	0.472723i	$-0.843271\pi$
$233$	−11.2710	+	7.89205i	−0.738389	+	0.517025i	0.142822	+	0.989748i	$0.454382\pi$
$234$		0			0
$235$	−23.1233	+	8.12519i	−1.50840	+	0.530029i
$236$		0			0
$237$	−0.492803	+	5.63276i	−0.0320110	+	0.365887i
$238$		0			0
$239$	10.0336	+	5.79288i	0.649017	+	0.374710i	0.788080	−	0.615573i	$-0.211076\pi$
$239$	10.0336	+	5.79288i	0.649017	+	0.374710i	−0.139062	+	0.990284i	$0.544409\pi$
$240$		0			0
$241$	−1.49523	+	4.10811i	−0.0963161	+	0.264626i	−0.978489	−	0.206300i	$-0.933858\pi$
$241$	−1.49523	+	4.10811i	−0.0963161	+	0.264626i	0.882173	+	0.470926i	$0.156080\pi$
$242$		0			0
$243$	−17.6144	−	12.3337i	−1.12996	−	0.791207i
$244$		0			0
$245$	−0.513460	+	5.19993i	−0.0328037	+	0.332211i
$246$		0			0
$247$	3.51954	−	0.765992i	0.223943	−	0.0487389i
$248$		0			0
$249$	25.2962	+	21.2260i	1.60308	+	1.34514i
$250$		0			0
$251$	4.34823	+	24.6600i	0.274458	+	1.55653i	0.740679	+	0.671859i	$0.234504\pi$
$251$	4.34823	+	24.6600i	0.274458	+	1.55653i	−0.466221	+	0.884668i	$0.654385\pi$
$252$		0			0
$253$	4.27359	+	9.16475i	0.268678	+	0.576183i
$254$		0			0
$255$	15.9396	−	1.21548i	0.998174	−	0.0761164i
$256$		0			0
$257$	−14.0206	−	1.22664i	−0.874579	−	0.0765157i	−0.358979	−	0.933346i	$-0.616875\pi$
$257$	−14.0206	−	1.22664i	−0.874579	−	0.0765157i	−0.515599	+	0.856830i	$0.672431\pi$
$258$		0			0
$259$	0.472894	+	0.819077i	0.0293842	+	0.0508950i
$260$		0			0
$261$	−6.98890	−	1.23233i	−0.432602	−	0.0762794i
$262$		0			0
$263$	−0.120737	−	0.0563004i	−0.00744493	−	0.00347163i	0.418892	−	0.908036i	$-0.362419\pi$
$263$	−0.120737	−	0.0563004i	−0.00744493	−	0.00347163i	−0.426337	+	0.904564i	$0.640196\pi$
$264$		0			0
$265$	−3.94172	+	20.9828i	−0.242138	+	1.28896i
$266$		0			0
$267$	−23.2327	+	23.2327i	−1.42182	+	1.42182i
$268$		0			0
$269$	−4.35873	+	1.58645i	−0.265756	+	0.0967274i	−0.471462	−	0.881887i	$-0.656273\pi$
$269$	−4.35873	+	1.58645i	−0.265756	+	0.0967274i	0.205705	+	0.978614i	$0.434051\pi$
$270$		0			0
$271$	−1.42075	+	8.05748i	−0.0863045	+	0.489457i	0.910763	+	0.412930i	$0.135494\pi$
$271$	−1.42075	+	8.05748i	−0.0863045	+	0.489457i	−0.997067	+	0.0765276i	$0.975617\pi$
$272$		0			0
$273$	−1.21345	+	4.52867i	−0.0734415	+	0.274088i
$274$		0			0
$275$	−2.34606	−	6.92262i	−0.141473	−	0.417450i
$276$		0			0
$277$	7.12181	+	26.5790i	0.427908	+	1.59697i	0.757489	+	0.652848i	$0.226426\pi$
$277$	7.12181	+	26.5790i	0.427908	+	1.59697i	−0.329581	+	0.944127i	$0.606908\pi$
$278$		0			0
$279$	5.35209	+	1.94800i	0.320421	+	0.116624i
$280$		0			0
$281$	23.1580	−	4.08337i	1.38149	−	0.243594i	0.566973	−	0.823736i	$-0.308114\pi$
$281$	23.1580	−	4.08337i	1.38149	−	0.243594i	0.814515	+	0.580143i	$0.197003\pi$
$282$		0			0
$283$	−1.37605	−	15.7284i	−0.0817980	−	0.934955i	−0.920597	−	0.390514i	$-0.872297\pi$
$283$	−1.37605	−	15.7284i	−0.0817980	−	0.934955i	0.838799	−	0.544441i	$-0.183258\pi$
$284$		0			0
$285$	−24.9156	−	5.91778i	−1.47587	−	0.350539i
$286$		0			0
$287$	−0.186632	−	2.13322i	−0.0110166	−	0.125920i
$288$		0			0
$289$	−9.45051	+	1.66638i	−0.555912	+	0.0980223i
$290$		0			0
$291$	24.6023	+	8.95450i	1.44221	+	0.524922i
$292$		0			0
$293$	−1.88836	−	7.04746i	−0.110319	−	0.411717i	0.888575	−	0.458732i	$-0.151696\pi$
$293$	−1.88836	−	7.04746i	−0.110319	−	0.411717i	−0.998894	+	0.0470143i	$0.985029\pi$
$294$		0			0
$295$	3.72528	−	13.3072i	0.216894	−	0.774775i
$296$		0			0
$297$	0.897888	−	3.35096i	0.0521007	−	0.194443i
$298$		0			0
$299$	0.992577	−	5.62918i	0.0574022	−	0.325544i
$300$		0			0
$301$	−19.9785	+	7.27156i	−1.15154	+	0.419126i
$302$		0			0
$303$	−13.8186	+	13.8186i	−0.793855	+	0.793855i
$304$		0			0
$305$	0.118034	−	0.0807007i	0.00675861	−	0.00462091i
$306$		0			0
$307$	−11.5978	−	5.40813i	−0.661920	−	0.308658i	0.0624721	−	0.998047i	$-0.480102\pi$
$307$	−11.5978	−	5.40813i	−0.661920	−	0.308658i	−0.724392	+	0.689388i	$0.757879\pi$
$308$		0			0
$309$	35.0070	+	6.17269i	1.99148	+	0.351152i
$310$		0			0
$311$	−0.789525	−	1.36750i	−0.0447699	−	0.0775437i	0.842772	−	0.538271i	$-0.180922\pi$
$311$	−0.789525	−	1.36750i	−0.0447699	−	0.0775437i	−0.887542	+	0.460727i	$0.847589\pi$
$312$		0			0
$313$	−0.498136	−	0.0435813i	−0.0281563	−	0.00246336i	0.0730689	−	0.997327i	$-0.476721\pi$
$313$	−0.498136	−	0.0435813i	−0.0281563	−	0.00246336i	−0.101225	+	0.994864i	$0.532276\pi$
$314$		0			0
$315$	12.2752	−	14.3018i	0.691628	−	0.805817i
$316$		0			0
$317$	3.62724	+	7.77864i	0.203726	+	0.436892i	0.981451	−	0.191713i	$-0.0614042\pi$
$317$	3.62724	+	7.77864i	0.203726	+	0.436892i	−0.777725	+	0.628605i	$0.783626\pi$
$318$		0			0
$319$	0.461545	+	2.61755i	0.0258416	+	0.146555i
$320$		0			0
$321$	4.16929	+	3.49845i	0.232707	+	0.195264i
$322$		0			0
$323$	−11.7529	−	1.59357i	−0.653949	−	0.0886688i
$324$		0			0
$325$	−1.15815	+	3.96606i	−0.0642426	+	0.219997i
$326$		0			0
$327$	44.2063	+	30.9536i	2.44461	+	1.71174i
$328$		0			0
$329$	−8.09545	+	22.2421i	−0.446317	+	1.22624i
$330$		0			0
$331$	28.8818	+	16.6749i	1.58749	+	0.916535i	0.993720	+	0.111897i	$0.0356927\pi$
$331$	28.8818	+	16.6749i	1.58749	+	0.916535i	0.593766	+	0.804638i	$0.297641\pi$
$332$		0			0
$333$	−0.148994	+	1.70301i	−0.00816484	+	0.0933246i
$334$		0			0
$335$	−1.50032	−	4.26972i	−0.0819710	−	0.233280i
$336$		0			0
$337$	4.69991	−	3.29091i	0.256020	−	0.179267i	−0.438519	−	0.898722i	$-0.644497\pi$
$337$	4.69991	−	3.29091i	0.256020	−	0.179267i	0.694540	+	0.719454i	$0.255608\pi$
$338$		0			0
$339$	−17.0053	−	46.7218i	−0.923604	−	2.53758i
$340$		0			0
$341$		−	2.13317i		−	0.115517i
$342$		0			0
$343$	14.2569	+	14.2569i	0.769800	+	0.769800i
$344$		0			0
$345$	−23.6797	+	33.0276i	−1.27487	+	1.77815i
$346$		0			0
$347$	−14.8215	−	21.1673i	−0.795659	−	1.13632i	−0.987918	−	0.154975i	$-0.950470\pi$
$347$	−14.8215	−	21.1673i	−0.795659	−	1.13632i	0.192259	−	0.981344i	$-0.438419\pi$
$348$		0			0
$349$	13.6620	−	7.88776i	0.731310	−	0.422222i	−0.0875913	−	0.996156i	$-0.527917\pi$
$349$	13.6620	−	7.88776i	0.731310	−	0.422222i	0.818901	+	0.573935i	$0.194584\pi$
$350$		0			0
$351$	−1.50220	+	1.26050i	−0.0801817	+	0.0672805i
$352$		0			0
$353$	−5.55725	+	1.48906i	−0.295783	+	0.0792547i	−0.403659	−	0.914910i	$-0.632262\pi$
$353$	−5.55725	+	1.48906i	−0.295783	+	0.0792547i	0.107876	+	0.994164i	$0.465595\pi$
$354$		0			0
$355$	−7.33718	−	28.6580i	−0.389417	−	1.52101i
$356$		0			0
$357$	8.85491	−	12.6461i	0.468651	−	0.669304i
$358$		0			0
$359$	−2.00499	+	2.38946i	−0.105820	+	0.126111i	−0.816355	−	0.577551i	$-0.804008\pi$
$359$	−2.00499	+	2.38946i	−0.105820	+	0.126111i	0.710535	+	0.703662i	$0.248453\pi$
$360$		0			0
$361$	17.1572	+	8.16273i	0.903011	+	0.429617i
$362$		0			0
$363$	23.1978	−	2.02955i	1.21757	−	0.106524i
$364$		0			0
$365$	0.374172	−	33.5322i	0.0195850	−	1.75516i
$366$		0			0
$367$	3.58028	−	1.66951i	0.186889	−	0.0871478i	−0.326921	−	0.945052i	$-0.606011\pi$
$367$	3.58028	−	1.66951i	0.186889	−	0.0871478i	0.513810	+	0.857904i	$0.328233\pi$
$368$		0			0
$369$	1.93527	−	3.35198i	0.100746	−	0.174497i
$370$		0			0
$371$	13.2531	+	15.7945i	0.688068	+	0.820008i
$372$		0			0
$373$	−10.2605	−	2.74928i	−0.531266	−	0.142352i	−0.0167934	−	0.999859i	$-0.505346\pi$
$373$	−10.2605	−	2.74928i	−0.531266	−	0.142352i	−0.514473	+	0.857507i	$0.672012\pi$
$374$		0			0
$375$	19.6246	−	21.8582i	1.01341	−	1.12875i
$376$		0			0
$377$	0.634953	−	1.36166i	0.0327017	−	0.0701291i
$378$		0			0
$379$	1.77489			0.0911701			0.0455850	−	0.998960i	$-0.485485\pi$
$379$	1.77489			0.0911701			0.0455850	+	0.998960i	$0.485485\pi$
$380$		0			0
$381$	33.1890			1.70032
$382$		0			0
$383$	−11.3345	+	24.3069i	−0.579165	+	1.24202i	0.370522	+	0.928824i	$0.379179\pi$
$383$	−11.3345	+	24.3069i	−0.579165	+	1.24202i	−0.949687	+	0.313200i	$0.898599\pi$
$384$		0			0
$385$	−6.60584	−	2.48815i	−0.336665	−	0.126808i
$386$		0			0
$387$	−37.1193	−	9.94608i	−1.88688	−	0.505588i
$388$		0			0
$389$	11.1104	+	13.2408i	0.563318	+	0.671336i	0.970245	−	0.242125i	$-0.0778443\pi$
$389$	11.1104	+	13.2408i	0.563318	+	0.671336i	−0.406928	+	0.913460i	$0.633400\pi$
$390$		0			0
$391$	−9.41088	+	16.3001i	−0.475928	+	0.824332i
$392$		0			0
$393$	32.6939	−	15.2454i	1.64919	−	0.769030i
$394$		0			0
$395$	3.36450	+	3.44044i	0.169287	+	0.173107i
$396$		0			0
$397$	4.55004	−	0.398077i	0.228360	−	0.0199789i	0.0275986	−	0.999619i	$-0.491214\pi$
$397$	4.55004	−	0.398077i	0.228360	−	0.0199789i	0.200761	+	0.979640i	$0.435658\pi$
$398$		0			0
$399$	−19.6787	+	14.9794i	−0.985166	+	0.749907i
$400$		0			0
$401$	9.78469	−	11.6609i	0.488624	−	0.582320i	−0.464243	−	0.885708i	$-0.653673\pi$
$401$	9.78469	−	11.6609i	0.488624	−	0.582320i	0.952867	+	0.303388i	$0.0981179\pi$
$402$		0			0
$403$	−0.691616	+	0.987730i	−0.0344519	+	0.0492023i
$404$		0			0
$405$	−11.8590	+	3.03620i	−0.589278	+	0.150870i
$406$		0			0
$407$	0.618450	−	0.165713i	0.0306554	−	0.00821409i
$408$		0			0
$409$	19.0672	−	15.9993i	0.942812	−	0.791113i	−0.0352604	−	0.999378i	$-0.511226\pi$
$409$	19.0672	−	15.9993i	0.942812	−	0.791113i	0.978072	+	0.208265i	$0.0667816\pi$
$410$		0			0
$411$	15.7373	−	9.08593i	0.776263	−	0.448176i
$412$		0			0
$413$	−7.65454	−	10.9318i	−0.376655	−	0.537919i
$414$		0			0
$415$	27.7293	−	4.57100i	1.36118	−	0.224382i
$416$		0			0
$417$	36.7126	+	36.7126i	1.79782	+	1.79782i
$418$		0			0
$419$			17.8878i			0.873877i	0.899491	+	0.436939i	$0.143937\pi$
$419$			17.8878i			0.873877i	−0.899491	+	0.436939i	$0.856063\pi$
$420$		0			0
$421$	−8.99524	−	24.7142i	−0.438401	−	1.20450i	−0.940532	−	0.339706i	$-0.889673\pi$
$421$	−8.99524	−	24.7142i	−0.438401	−	1.20450i	0.502130	−	0.864792i	$-0.332550\pi$
$422$		0			0
$423$	−35.0456	+	24.5392i	−1.70398	+	1.19314i
$424$		0			0
$425$	8.05017	−	10.9676i	0.390491	−	0.532005i
$426$		0			0
$427$	0.0120349	−	0.137560i	0.000582411	−	0.00665698i
$428$		0			0
$429$	2.74868	+	1.58695i	0.132707	+	0.0766187i
$430$		0			0
$431$	−3.69543	+	10.1531i	−0.178002	+	0.489058i	−0.996320	−	0.0857084i	$-0.972685\pi$
$431$	−3.69543	+	10.1531i	−0.178002	+	0.489058i	0.818318	+	0.574766i	$0.194907\pi$
$432$		0			0
$433$	−23.2915	−	16.3089i	−1.11932	−	0.783756i	−0.140826	−	0.990034i	$-0.544976\pi$
$433$	−23.2915	−	16.3089i	−1.11932	−	0.783756i	−0.978493	+	0.206278i	$0.933865\pi$
$434$		0			0
$435$	−8.25886	+	6.77442i	−0.395982	+	0.324808i
$436$		0			0
$437$	22.3088	−	20.2841i	1.06718	−	0.970319i
$438$		0			0
$439$	18.3174	+	15.3701i	0.874241	+	0.733575i	0.964987	−	0.262299i	$-0.0844806\pi$
$439$	18.3174	+	15.3701i	0.874241	+	0.733575i	−0.0907456	+	0.995874i	$0.528925\pi$
$440$		0			0
$441$	1.58384	+	8.98241i	0.0754210	+	0.427734i
$442$		0			0
$443$	−7.66199	−	16.4312i	−0.364032	−	0.780670i	−0.999960	−	0.00892130i	$-0.997160\pi$
$443$	−7.66199	−	16.4312i	−0.364032	−	0.780670i	0.635928	−	0.771748i	$-0.280618\pi$
$444$		0			0
$445$	2.12611	+	27.8814i	0.100787	+	1.32170i
$446$		0			0
$447$	−31.5236	−	2.75795i	−1.49101	−	0.130447i
$448$		0			0
$449$	5.71905	+	9.90569i	0.269899	+	0.467478i	0.968835	−	0.247705i	$-0.0796765\pi$
$449$	5.71905	+	9.90569i	0.269899	+	0.467478i	−0.698937	+	0.715183i	$0.746343\pi$
$450$		0			0
$451$	−1.42761	−	0.251726i	−0.0672234	−	0.0118533i
$452$		0			0
$453$	−51.7394	−	24.1265i	−2.43093	−	1.13356i
$454$		0			0
$455$	2.25203	+	3.29385i	0.105577	+	0.154418i
$456$		0			0
$457$	13.9205	−	13.9205i	0.651173	−	0.651173i	−0.302102	−	0.953276i	$-0.597688\pi$
$457$	13.9205	−	13.9205i	0.651173	−	0.651173i	0.953276	+	0.302102i	$0.0976884\pi$
$458$		0			0
$459$	6.06774	−	2.20848i	0.283218	−	0.103083i
$460$		0			0
$461$	−2.37062	+	13.4444i	−0.110411	+	0.626170i	0.878510	+	0.477724i	$0.158538\pi$
$461$	−2.37062	+	13.4444i	−0.110411	+	0.626170i	−0.988921	+	0.148446i	$0.952573\pi$
$462$		0			0
$463$	9.46574	−	35.3266i	0.439910	−	1.64177i	−0.289126	−	0.957291i	$-0.593365\pi$
$463$	9.46574	−	35.3266i	0.439910	−	1.64177i	0.729036	−	0.684476i	$-0.239969\pi$
$464$		0			0
$465$	7.47168	−	4.20333i	0.346491	−	0.194925i
$466$		0			0
$467$	1.15756	+	4.32009i	0.0535657	+	0.199910i	0.987523	−	0.157475i	$-0.0503353\pi$
$467$	1.15756	+	4.32009i	0.0535657	+	0.199910i	−0.933957	+	0.357384i	$0.883669\pi$
$468$		0			0
$469$	−4.10700	−	1.49482i	−0.189643	−	0.0690246i
$470$		0			0
$471$	−20.6296	+	3.63756i	−0.950564	+	0.167610i
$472$		0			0
$473$	1.25441	+	14.3379i	0.0576777	+	0.659259i
$474$		0			0
$475$	−17.6322	+	12.8104i	−0.809020	+	0.587782i
$476$		0			0
$477$	3.24808	+	37.1257i	0.148719	+	1.69987i
$478$		0			0
$479$	−15.7074	+	2.76964i	−0.717691	+	0.126548i	−0.520555	−	0.853828i	$-0.674275\pi$
$479$	−15.7074	+	2.76964i	−0.717691	+	0.126548i	−0.197136	+	0.980376i	$0.563164\pi$
$480$		0			0
$481$	−0.340091	−	0.123783i	−0.0155068	−	0.00564403i
$482$		0			0
$483$	10.1578	+	37.9095i	0.462196	+	1.72494i
$484$		0			0
$485$	19.4197	−	10.9249i	0.881801	−	0.496073i
$486$		0			0
$487$	−9.99684	+	37.3087i	−0.453000	+	1.69062i	0.240902	+	0.970549i	$0.422557\pi$
$487$	−9.99684	+	37.3087i	−0.453000	+	1.69062i	−0.693902	+	0.720069i	$0.744110\pi$
$488$		0			0
$489$	−2.48329	+	14.0834i	−0.112298	+	0.636874i
$490$		0			0
$491$	−27.1611	+	9.88583i	−1.22576	+	0.446141i	−0.872145	−	0.489248i	$-0.837271\pi$
$491$	−27.1611	+	9.88583i	−1.22576	+	0.446141i	−0.353619	+	0.935390i	$0.615049\pi$
$492$		0			0
$493$	−3.49820	+	3.49820i	−0.157551	+	0.157551i
$494$		0			0
$495$	−7.20119	−	10.5326i	−0.323669	−	0.473404i
$496$		0			0
$497$	−25.8921	−	12.0737i	−1.16142	−	0.541578i
$498$		0			0
$499$	−16.1470	−	2.84716i	−0.722841	−	0.127456i	−0.199889	−	0.979819i	$-0.564058\pi$
$499$	−16.1470	−	2.84716i	−0.722841	−	0.127456i	−0.522952	+	0.852362i	$0.675169\pi$
$500$		0			0
$501$	−24.4472	−	42.3437i	−1.09222	−	1.89178i
$502$		0			0
$503$	−12.7996	−	1.11982i	−0.570708	−	0.0499305i	−0.201850	−	0.979416i	$-0.564695\pi$
$503$	−12.7996	−	1.11982i	−0.570708	−	0.0499305i	−0.368858	+	0.929486i	$0.620251\pi$
$504$		0			0
$505$	1.26459	+	16.5836i	0.0562735	+	0.737959i
$506$		0			0
$507$	13.6768	+	29.3300i	0.607408	+	1.30259i
$508$		0			0
$509$	5.32090	+	30.1763i	0.235845	+	1.33754i	0.840828	+	0.541303i	$0.182069\pi$
$509$	5.32090	+	30.1763i	0.235845	+	1.33754i	−0.604983	+	0.796238i	$0.706820\pi$
$510$		0			0
$511$	−24.8085	−	20.8168i	−1.09746	−	0.920882i
$512$		0			0
$513$	−10.3359	+	0.411226i	−0.456343	+	0.0181561i
$514$		0			0
$515$	23.3904	−	19.1862i	1.03070	−	0.845446i
$516$		0			0
$517$	13.1256	+	9.19067i	0.577265	+	0.404205i
$518$		0			0
$519$	−11.4923	+	31.5749i	−0.504457	+	1.38598i
$520$		0			0
$521$	−32.1106	−	18.5391i	−1.40679	−	0.812211i	−0.411714	−	0.911313i	$-0.635070\pi$
$521$	−32.1106	−	18.5391i	−1.40679	−	0.812211i	−0.995077	+	0.0991015i	$0.968403\pi$
$522$		0			0
$523$	0.489130	−	5.59078i	0.0213882	−	0.244468i	−0.977973	−	0.208731i	$-0.933067\pi$
$523$	0.489130	−	5.59078i	0.0213882	−	0.244468i	0.999361	−	0.0357367i	$-0.0113778\pi$
$524$		0			0
$525$	−4.30152	−	28.0406i	−0.187734	−	1.22379i
$526$		0			0
$527$	3.25240	−	2.27736i	0.141677	−	0.0992032i
$528$		0			0
$529$	−8.49879	−	23.3502i	−0.369513	−	1.01523i
$530$		0			0
$531$		−	24.1217i		−	1.04679i
$532$		0			0
$533$	0.579418	+	0.579418i	0.0250974	+	0.0250974i
$534$		0			0
$535$	4.57031	−	0.753388i	0.197592	−	0.0325718i
$536$		0			0
$537$	−20.7020	−	29.5656i	−0.893359	−	1.27585i
$538$		0			0
$539$	2.95841	−	1.70804i	0.127428	−	0.0735705i
$540$		0			0
$541$	12.9275	−	10.8475i	0.555796	−	0.466369i	−0.321102	−	0.947045i	$-0.604053\pi$
$541$	12.9275	−	10.8475i	0.555796	−	0.466369i	0.876898	+	0.480676i	$0.159609\pi$
$542$		0			0
$543$	−4.99321	+	1.33793i	−0.214279	+	0.0574160i
$544$		0			0
$545$	44.4930	−	11.3913i	1.90587	−	0.487951i
$546$		0			0
$547$	13.3805	−	19.1093i	0.572109	−	0.817056i	−0.423956	−	0.905683i	$-0.639359\pi$
$547$	13.3805	−	19.1093i	0.572109	−	0.817056i	0.996065	+	0.0886268i	$0.0282479\pi$
$548$		0			0
$549$	0.160433	−	0.191197i	0.00684713	−	0.00816009i
$550$		0			0
$551$	7.04386	−	3.63224i	0.300079	−	0.154739i
$552$		0			0
$553$	4.62955	−	0.405033i	0.196868	−	0.0172237i
$554$		0			0
$555$	1.79906	+	1.83967i	0.0763660	+	0.0780895i
$556$		0			0
$557$	−15.6212	+	7.28427i	−0.661890	+	0.308645i	−0.724380	−	0.689401i	$-0.757874\pi$
$557$	−15.6212	+	7.28427i	−0.661890	+	0.308645i	0.0624895	+	0.998046i	$0.480096\pi$
$558$		0			0
$559$	4.06782	−	7.04567i	0.172051	−	0.298000i
$560$		0			0
$561$	−6.71780	−	8.00596i	−0.283626	−	0.338012i
$562$		0			0
$563$	20.3871	+	5.46271i	0.859214	+	0.230226i	0.661418	−	0.750017i	$-0.269955\pi$
$563$	20.3871	+	5.46271i	0.859214	+	0.230226i	0.197796	+	0.980243i	$0.436622\pi$
$564$		0			0
$565$	−39.5990	−	14.9153i	−1.66594	−	0.627492i
$566$		0			0
$567$	−4.99620	+	10.7144i	−0.209821	+	0.449962i
$568$		0			0
$569$	19.7637			0.828537			0.414269	−	0.910155i	$-0.364037\pi$
$569$	19.7637			0.828537			0.414269	+	0.910155i	$0.364037\pi$
$570$		0			0
$571$	11.4004			0.477090			0.238545	−	0.971131i	$-0.423330\pi$
$571$	11.4004			0.477090			0.238545	+	0.971131i	$0.423330\pi$
$572$		0			0
$573$	−8.57524	+	18.3897i	−0.358236	+	0.768239i
$574$		0			0
$575$	8.20392	+	33.5993i	0.342127	+	1.40119i
$576$		0			0
$577$	36.7485	+	9.84673i	1.52986	+	0.409925i	0.922973	−	0.384864i	$-0.125752\pi$
$577$	36.7485	+	9.84673i	1.52986	+	0.409925i	0.606886	+	0.794789i	$0.292418\pi$
$578$		0			0
$579$	−2.90821	−	3.46587i	−0.120861	−	0.144037i
$580$		0			0
$581$	13.5702	−	23.5044i	0.562989	−	0.975125i
$582$		0			0
$583$	12.6501	−	5.89883i	0.523913	−	0.244305i
$584$		0			0
$585$	−0.0804725	+	7.21172i	−0.00332713	+	0.298168i
$586$		0			0
$587$	0.0608415	−	0.00532294i	0.00251120	−	0.000219701i	−0.0859001	−	0.996304i	$-0.527377\pi$
$587$	0.0608415	−	0.00532294i	0.00251120	−	0.000219701i	0.0884113	+	0.996084i	$0.471821\pi$
$588$		0			0
$589$	−6.07348	+	1.88916i	−0.250253	+	0.0778416i
$590$		0			0
$591$	4.57703	−	5.45469i	0.188274	−	0.224376i
$592$		0			0
$593$	0.327194	−	0.467281i	0.0134362	−	0.0191889i	−0.812378	−	0.583132i	$-0.801827\pi$
$593$	0.327194	−	0.467281i	0.0134362	−	0.0191889i	0.825814	+	0.563943i	$0.190716\pi$
$594$		0			0
$595$	−3.25873	−	12.7282i	−0.133595	−	0.521803i
$596$		0			0
$597$	−41.3647	+	11.0836i	−1.69295	+	0.453623i
$598$		0			0
$599$	32.9504	−	27.6487i	1.34632	−	1.12970i	0.366364	−	0.930472i	$-0.380602\pi$
$599$	32.9504	−	27.6487i	1.34632	−	1.12970i	0.979954	−	0.199224i	$-0.0638420\pi$
$600$		0			0
$601$	25.2979	−	14.6058i	1.03192	−	0.595782i	0.114389	−	0.993436i	$-0.463509\pi$
$601$	25.2979	−	14.6058i	1.03192	−	0.595782i	0.917535	+	0.397655i	$0.130176\pi$
$602$		0			0
$603$	−4.53116	−	6.47117i	−0.184523	−	0.263526i
$604$		0			0
$605$	11.5476	−	16.1062i	0.469478	−	0.654810i
$606$		0			0
$607$	−21.0882	−	21.0882i	−0.855943	−	0.855943i	0.134914	−	0.990857i	$-0.456924\pi$
$607$	−21.0882	−	21.0882i	−0.855943	−	0.855943i	−0.990857	+	0.134914i	$0.956924\pi$
$608$		0			0
$609$			10.3158i			0.418018i
$610$		0			0
$611$	−3.09782	−	8.51120i	−0.125325	−	0.344326i
$612$		0			0
$613$	−18.0625	+	12.6475i	−0.729538	+	0.510828i	−0.878338	−	0.478039i	$-0.841348\pi$
$613$	−18.0625	+	12.6475i	−0.729538	+	0.510828i	0.148801	+	0.988867i	$0.452459\pi$
$614$		0			0
$615$	−1.93135	−	5.49640i	−0.0778795	−	0.221636i
$616$		0			0
$617$	1.86169	−	21.2792i	0.0749489	−	0.856670i	−0.861932	−	0.507023i	$-0.830746\pi$
$617$	1.86169	−	21.2792i	0.0749489	−	0.856670i	0.936881	−	0.349647i	$-0.113699\pi$
$618$		0			0
$619$	−12.8655	−	7.42787i	−0.517106	−	0.298551i	0.218644	−	0.975805i	$-0.429837\pi$
$619$	−12.8655	−	7.42787i	−0.517106	−	0.298551i	−0.735750	+	0.677253i	$0.763170\pi$
$620$		0			0
$621$	−5.61441	+	15.4255i	−0.225298	+	0.619002i
$622$		0			0
$623$	22.1205	+	15.4890i	0.886240	+	0.620552i
$624$		0			0
$625$	−3.23839	−	24.7894i	−0.129535	−	0.991575i
$626$		0			0
$627$	6.34707	+	15.4924i	0.253478	+	0.618707i
$628$		0			0
$629$	0.912914	+	0.766026i	0.0364003	+	0.0305435i
$630$		0			0
$631$	−4.05803	−	23.0142i	−0.161548	−	0.916182i	−0.952553	−	0.304373i	$-0.901553\pi$
$631$	−4.05803	−	23.0142i	−0.161548	−	0.916182i	0.791005	−	0.611809i	$-0.209558\pi$
$632$		0			0
$633$	−14.8751	−	31.8998i	−0.591233	−	1.26790i
$634$		0			0
$635$	18.3963	−	21.4336i	0.730035	−	0.850565i
$636$		0			0
$637$	−1.92363	−	0.168296i	−0.0762170	−	0.00666813i
$638$		0			0
$639$	−25.8191	−	44.7199i	−1.02139	−	1.76909i
$640$		0			0
$641$	−28.6687	−	5.05507i	−1.13235	−	0.199663i	−0.424091	−	0.905620i	$-0.639406\pi$
$641$	−28.6687	−	5.05507i	−1.13235	−	0.199663i	−0.708255	+	0.705957i	$0.750517\pi$
$642$		0			0
$643$	8.94126	+	4.16938i	0.352609	+	0.164424i	0.590849	−	0.806782i	$-0.298793\pi$
$643$	8.94126	+	4.16938i	0.352609	+	0.164424i	−0.238240	+	0.971206i	$0.576571\pi$
$644$		0			0
$645$	−47.7487	+	32.6461i	−1.88010	+	1.28544i
$646$		0			0
$647$	−29.2498	+	29.2498i	−1.14993	+	1.14993i	−0.163361	+	0.986566i	$0.552233\pi$
$647$	−29.2498	+	29.2498i	−1.14993	+	1.14993i	−0.986566	+	0.163361i	$0.947767\pi$
$648$		0			0
$649$	−8.48946	+	3.08991i	−0.333241	+	0.121290i
$650$		0			0
$651$	1.43765	−	8.15333i	0.0563460	−	0.319554i
$652$		0			0
$653$	−9.53310	+	35.5780i	−0.373059	+	1.39227i	0.483101	+	0.875564i	$0.339510\pi$
$653$	−9.53310	+	35.5780i	−0.373059	+	1.39227i	−0.856160	+	0.516710i	$0.827156\pi$
$654$		0			0
$655$	8.27635	−	29.5642i	0.323384	−	1.15517i
$656$		0			0
$657$	−15.1504	−	56.5419i	−0.591072	−	2.20591i
$658$		0			0
$659$	−8.42325	−	3.06581i	−0.328123	−	0.119427i	0.172705	−	0.984974i	$-0.444749\pi$
$659$	−8.42325	−	3.06581i	−0.328123	−	0.119427i	−0.500829	+	0.865546i	$0.666971\pi$
$660$		0			0
$661$	28.3996	−	5.00761i	1.10462	−	0.194774i	0.408539	−	0.912741i	$-0.366038\pi$
$661$	28.3996	−	5.00761i	1.10462	−	0.194774i	0.696077	+	0.717967i	$0.254927\pi$
$662$		0			0
$663$	0.514878	+	5.88509i	0.0199962	+	0.228558i
$664$		0			0
$665$	−1.23394	+	21.0115i	−0.0478501	+	0.814791i
$666$		0			0
$667$	−1.09614	−	12.5289i	−0.0424427	−	0.485123i
$668$		0			0
$669$	−18.7938	+	3.31385i	−0.726609	+	0.128121i
$670$		0			0
$671$	−0.0878415	−	0.0319717i	−0.00339108	−	0.00123425i
$672$		0			0
$673$	−4.34513	−	16.2163i	−0.167493	−	0.625091i	−0.997709	−	0.0676498i	$-0.978450\pi$
$673$	−4.34513	−	16.2163i	−0.167493	−	0.625091i	0.830217	−	0.557441i	$-0.188217\pi$
$674$		0			0
$675$	5.25330	−	10.6392i	0.202200	−	0.409504i
$676$		0			0
$677$	−5.34238	+	19.9380i	−0.205324	+	0.766280i	0.784026	+	0.620728i	$0.213163\pi$
$677$	−5.34238	+	19.9380i	−0.205324	+	0.766280i	−0.989351	+	0.145553i	$0.953504\pi$
$678$		0			0
$679$	3.73660	−	21.1913i	0.143398	−	0.813248i
$680$		0			0
$681$	−39.2872	+	14.2994i	−1.50549	+	0.547953i
$682$		0			0
$683$	−18.1397	+	18.1397i	−0.694095	+	0.694095i	−0.963130	−	0.269036i	$-0.913295\pi$
$683$	−18.1397	+	18.1397i	−0.694095	+	0.694095i	0.269036	+	0.963130i	$0.413295\pi$
$684$		0			0
$685$	2.85529	−	15.1994i	0.109095	−	0.580741i
$686$		0			0
$687$	40.7404	+	18.9976i	1.55434	+	0.724802i
$688$		0			0
$689$	−7.76995	−	1.37005i	−0.296012	−	0.0521948i
$690$		0			0
$691$	2.68880	+	4.65714i	0.102287	+	0.177166i	0.912626	−	0.408795i	$-0.134051\pi$
$691$	2.68880	+	4.65714i	0.102287	+	0.177166i	−0.810340	+	0.585960i	$0.800717\pi$
$692$		0			0
$693$	−12.2749	−	1.07392i	−0.466285	−	0.0407947i
$694$		0			0
$695$	44.0586	−	3.35972i	1.67124	−	0.127441i
$696$		0			0
$697$	−1.14031	−	2.44539i	−0.0431921	−	0.0926258i
$698$		0			0
$699$	6.27761	+	35.6021i	0.237441	+	1.34660i
$700$		0			0
$701$	23.7726	+	19.9476i	0.897878	+	0.753409i	0.969774	−	0.244003i	$-0.0784607\pi$
$701$	23.7726	+	19.9476i	0.897878	+	0.753409i	−0.0718966	+	0.997412i	$0.522905\pi$
$702$		0			0
$703$	−1.01952	−	1.61407i	−0.0384520	−	0.0608759i
$704$		0			0
$705$	−6.32790	+	64.0841i	−0.238322	+	2.41355i
$706$		0			0
$707$	13.1571	+	9.21268i	0.494822	+	0.346478i
$708$		0			0
$709$	−10.9635	+	30.1220i	−0.411744	+	1.13126i	0.544519	+	0.838748i	$0.316712\pi$
$709$	−10.9635	+	30.1220i	−0.411744	+	1.13126i	−0.956263	+	0.292508i	$0.905510\pi$
$710$		0			0
$711$	7.27452	+	4.19995i	0.272816	+	0.157510i
$712$		0			0
$713$	−0.879725	+	10.0553i	−0.0329460	+	0.376574i
$714$		0			0
$715$	2.54842	−	0.895477i	0.0953057	−	0.0334889i
$716$		0			0
$717$	24.9353	−	17.4599i	0.931226	−	0.652052i
$718$		0			0
$719$	4.98770	+	13.7036i	0.186010	+	0.511058i	0.997288	−	0.0736030i	$-0.0234498\pi$
$719$	4.98770	+	13.7036i	0.186010	+	0.511058i	−0.811278	+	0.584661i	$0.801228\pi$
$720$		0			0
$721$		−	29.2160i		−	1.08806i
$722$		0			0
$723$	8.12207	+	8.12207i	0.302063	+	0.302063i
$724$		0			0
$725$	−0.202857	+	9.08859i	−0.00753391	+	0.337542i
$726$		0			0
$727$	11.3169	+	16.1621i	0.419719	+	0.599420i	0.972214	−	0.234096i	$-0.0752130\pi$
$727$	11.3169	+	16.1621i	0.419719	+	0.599420i	−0.552495	+	0.833516i	$0.686324\pi$
$728$		0			0
$729$	−34.7048	+	20.0368i	−1.28536	+	0.742104i
$730$		0			0
$731$	−20.5216	+	17.2197i	−0.759020	+	0.636893i
$732$		0			0
$733$	0.897220	−	0.240409i	0.0331396	−	0.00887972i	−0.242211	−	0.970224i	$-0.577873\pi$
$733$	0.897220	−	0.240409i	0.0331396	−	0.00887972i	0.275351	+	0.961344i	$0.411206\pi$
$734$		0			0
$735$	11.8121	+	6.99659i	0.435695	+	0.258073i
$736$		0			0
$737$	−1.69706	+	2.42365i	−0.0625119	+	0.0892762i
$738$		0			0
$739$	27.7319	−	33.0495i	1.02013	−	1.21575i	0.0438973	−	0.999036i	$-0.486023\pi$
$739$	27.7319	−	33.0495i	1.02013	−	1.21575i	0.976236	−	0.216711i	$-0.0695330\pi$
$740$		0			0
$741$	2.08404	−	9.23138i	0.0765593	−	0.339123i
$742$		0			0
$743$	37.2986	−	3.26320i	1.36835	−	0.119715i	0.620827	−	0.783948i	$-0.286797\pi$
$743$	37.2986	−	3.26320i	1.36835	−	0.119715i	0.747526	+	0.664232i	$0.231241\pi$
$744$		0			0
$745$	−19.2543	+	18.8293i	−0.705423	+	0.689853i
$746$		0			0
$747$	44.4604	−	20.7322i	1.62672	−	0.758552i
$748$		0			0
$749$	2.23663	−	3.87396i	0.0817248	−	0.141552i
$750$		0			0
$751$	−8.92461	−	10.6359i	−0.325664	−	0.388111i	0.578226	−	0.815877i	$-0.303745\pi$
$751$	−8.92461	−	10.6359i	−0.325664	−	0.388111i	−0.903890	+	0.427766i	$0.859301\pi$
$752$		0			0
$753$	63.5494	+	17.0280i	2.31587	+	0.620536i
$754$		0			0
$755$	−44.2596	+	20.0405i	−1.61077	+	0.729347i
$756$		0			0
$757$	−1.11571	+	2.39265i	−0.0405513	+	0.0869625i	−0.925540	−	0.378650i	$-0.876388\pi$
$757$	−1.11571	+	2.39265i	−0.0405513	+	0.0869625i	0.884989	+	0.465613i	$0.154166\pi$
$758$		0			0
$759$	26.5687			0.964383
$760$		0			0
$761$	26.9984			0.978690			0.489345	−	0.872090i	$-0.337236\pi$
$761$	26.9984			0.978690			0.489345	+	0.872090i	$0.337236\pi$
$762$		0			0
$763$	18.7450	−	40.1987i	0.678613	−	1.45529i
$764$		0			0
$765$	8.37088	−	22.2241i	0.302650	−	0.803512i
$766$		0			0
$767$	4.93273	+	1.32172i	0.178111	+	0.0477246i
$768$		0			0
$769$	−13.2323	−	15.7696i	−0.477167	−	0.568666i	0.472738	−	0.881203i	$-0.343266\pi$
$769$	−13.2323	−	15.7696i	−0.477167	−	0.568666i	−0.949906	+	0.312537i	$0.898821\pi$
$770$		0			0
$771$	−18.4891	+	32.0241i	−0.665870	+	1.15332i
$772$		0			0
$773$	−9.80824	+	4.57366i	−0.352778	+	0.164503i	−0.590926	−	0.806726i	$-0.701237\pi$
$773$	−9.80824	+	4.57366i	−0.352778	+	0.164503i	0.238148	+	0.971229i	$0.423460\pi$
$774$		0			0
$775$	1.42696	−	7.15511i	0.0512578	−	0.257019i
$776$		0			0
$777$	2.47551	−	0.216579i	0.0888083	−	0.00776972i
$778$		0			0
$779$	0.547606	+	4.28757i	0.0196200	+	0.153618i
$780$		0			0
$781$	−12.4315	+	14.8153i	−0.444836	+	0.530134i
$782$		0			0
$783$	−2.47481	+	3.53440i	−0.0884426	+	0.126309i
$784$		0			0
$785$	−9.08565	+	15.3390i	−0.324281	+	0.547471i
$786$		0			0
$787$	−26.5456	+	7.11287i	−0.946248	+	0.253546i	−0.698769	−	0.715347i	$-0.746269\pi$
$787$	−26.5456	+	7.11287i	−0.946248	+	0.253546i	−0.247479	+	0.968893i	$0.579602\pi$
$788$		0			0
$789$	−0.268128	+	0.224986i	−0.00954562	+	0.00800973i
$790$		0			0
$791$	−35.3901	+	20.4325i	−1.25833	+	0.726495i
$792$		0			0
$793$	0.0303078	+	0.0432840i	0.00107626	+	0.00153706i
$794$		0			0
$795$	45.5879	+	32.6851i	1.61684	+	1.15922i
$796$		0			0
$797$	−4.21605	−	4.21605i	−0.149340	−	0.149340i	0.628483	−	0.777823i	$-0.283676\pi$
$797$	−4.21605	−	4.21605i	−0.149340	−	0.149340i	−0.777823	+	0.628483i	$0.783676\pi$
$798$		0			0
$799$			29.8244i			1.05511i
$800$		0			0
$801$	16.6941	+	45.8666i	0.589856	+	1.62062i
$802$		0			0
$803$	−17.9588	+	12.5749i	−0.633753	+	0.443759i
$804$		0			0
$805$	30.1125	+	14.4529i	1.06132	+	0.509397i
$806$		0			0
$807$	−1.06217	+	12.1407i	−0.0373903	+	0.427373i
$808$		0			0
$809$	15.0726	+	8.70219i	0.529926	+	0.305953i	0.740986	−	0.671520i	$-0.234358\pi$
$809$	15.0726	+	8.70219i	0.529926	+	0.305953i	−0.211061	+	0.977473i	$0.567692\pi$
$810$		0			0
$811$	−7.14119	+	19.6203i	−0.250761	+	0.688961i	0.748894	+	0.662690i	$0.230585\pi$
$811$	−7.14119	+	19.6203i	−0.250761	+	0.688961i	−0.999655	+	0.0262705i	$0.991637\pi$
$812$		0			0
$813$	17.6091	+	12.3301i	0.617579	+	0.432434i
$814$		0			0
$815$	7.71867	+	9.41002i	0.270373	+	0.329619i
$816$		0			0
$817$	39.7116	−	16.2694i	1.38933	−	0.569195i
$818$		0			0
$819$	5.33553	+	4.47704i	0.186438	+	0.156440i
$820$		0			0
$821$	2.18333	+	12.3823i	0.0761988	+	0.432145i	0.998911	+	0.0466553i	$0.0148562\pi$
$821$	2.18333	+	12.3823i	0.0761988	+	0.432145i	−0.922712	+	0.385489i	$0.874033\pi$
$822$		0			0
$823$	−4.97919	−	10.6779i	−0.173564	−	0.372208i	0.800213	−	0.599716i	$-0.204720\pi$
$823$	−4.97919	−	10.6779i	−0.173564	−	0.372208i	−0.973776	+	0.227508i	$0.926942\pi$
$824$		0			0
$825$	−19.0894	−	2.10028i	−0.664607	−	0.0731224i
$826$		0			0
$827$	2.52806	+	0.221177i	0.0879094	+	0.00769108i	0.131026	−	0.991379i	$-0.458173\pi$
$827$	2.52806	+	0.221177i	0.0879094	+	0.00769108i	−0.0431162	+	0.999070i	$0.513729\pi$
$828$		0			0
$829$	−26.4688	−	45.8453i	−0.919300	−	1.59227i	−0.800481	−	0.599359i	$-0.795422\pi$
$829$	−26.4688	−	45.8453i	−0.919300	−	1.59227i	−0.118820	−	0.992916i	$-0.537911\pi$
$830$		0			0
$831$	71.1986	+	12.5542i	2.46985	+	0.435501i
$832$		0			0
$833$	5.76261	+	2.68715i	0.199663	+	0.0931042i
$834$		0			0
$835$	−40.8966	−	7.68263i	−1.41528	−	0.265868i
$836$		0			0
$837$	2.44859	−	2.44859i	0.0846358	−	0.0846358i
$838$		0			0
$839$	9.49943	−	3.45751i	0.327957	−	0.119366i	−0.172794	−	0.984958i	$-0.555280\pi$
$839$	9.49943	−	3.45751i	0.327957	−	0.119366i	0.500751	+	0.865591i	$0.333057\pi$
$840$		0			0
$841$	−4.46176	+	25.3039i	−0.153854	+	0.872548i
$842$		0			0
$843$	15.9908	−	59.6786i	0.550753	−	2.05544i
$844$		0			0
$845$	26.5223	+	7.42479i	0.912397	+	0.255421i
$846$		0			0
$847$	−4.95355	−	18.4869i	−0.170206	−	0.635217i
$848$		0			0
$849$	−38.9808	−	14.1879i	−1.33782	−	0.486926i
$850$		0			0
$851$	−2.98359	+	0.526087i	−0.102276	+	0.0180340i
$852$		0			0
$853$	4.22925	+	48.3405i	0.144807	+	1.65515i	0.626953	+	0.779057i	$0.284302\pi$
$853$	4.22925	+	48.3405i	0.144807	+	1.65515i	−0.482146	+	0.876091i	$0.660142\pi$
$854$		0			0
$855$	−23.6105	+	29.8308i	−0.807462	+	1.02019i
$856$		0			0
$857$	−3.94672	−	45.1112i	−0.134817	−	1.54097i	−0.698881	−	0.715238i	$-0.746318\pi$
$857$	−3.94672	−	45.1112i	−0.134817	−	1.54097i	0.564064	−	0.825731i	$-0.309237\pi$
$858$		0			0
$859$	−7.61198	+	1.34220i	−0.259717	+	0.0457952i	−0.301991	−	0.953311i	$-0.597651\pi$
$859$	−7.61198	+	1.34220i	−0.259717	+	0.0457952i	0.0422732	+	0.999106i	$0.486540\pi$
$860$		0			0
$861$	−5.28692	−	1.92428i	−0.180178	−	0.0655793i
$862$		0			0
$863$	−1.43525	−	5.35643i	−0.0488565	−	0.182335i	0.937186	−	0.348831i	$-0.113421\pi$
$863$	−1.43525	−	5.35643i	−0.0488565	−	0.182335i	−0.986042	+	0.166496i	$0.946755\pi$
$864$		0			0
$865$	14.0211	+	24.9234i	0.476732	+	0.847422i
$866$		0			0
$867$	−6.52568	+	24.3542i	−0.221624	+	0.827111i
$868$		0			0
$869$	0.546300	−	3.09822i	0.0185319	−	0.105100i
$870$		0			0
$871$	1.57159	−	0.572013i	0.0532514	−	0.0193819i
$872$		0			0
$873$	27.5024	−	27.5024i	0.930817	−	0.930817i
$874$		0			0
$875$	−20.4930	−	12.7647i	−0.692791	−	0.431525i
$876$		0			0
$877$	21.6315	+	10.0870i	0.730445	+	0.340612i	0.752007	−	0.659155i	$-0.229086\pi$
$877$	21.6315	+	10.0870i	0.730445	+	0.340612i	−0.0215614	+	0.999768i	$0.506864\pi$
$878$		0			0
$879$	−18.8784	−	3.32878i	−0.636754	−	0.112277i
$880$		0			0
$881$	15.9927	+	27.7001i	0.538807	+	0.933241i	0.998969	+	0.0454056i	$0.0144580\pi$
$881$	15.9927	+	27.7001i	0.538807	+	0.933241i	−0.460162	+	0.887835i	$0.652209\pi$
$882$		0			0
$883$	5.16340	+	0.451739i	0.173762	+	0.0152022i	0.173705	−	0.984798i	$-0.444426\pi$
$883$	5.16340	+	0.451739i	0.173762	+	0.0152022i	5.74846e−5		1.00000i	$0.499982\pi$
$884$		0			0
$885$	−27.5510	−	23.6469i	−0.926116	−	0.794881i
$886$		0			0
$887$	−19.9594	−	42.8030i	−0.670171	−	1.43719i	−0.887370	−	0.461058i	$-0.847470\pi$
$887$	−19.9594	−	42.8030i	−0.670171	−	1.43719i	0.217199	−	0.976127i	$-0.430308\pi$
$888$		0			0
$889$	−4.73675	−	26.8635i	−0.158866	−	0.900972i
$890$		0			0
$891$	6.13073	+	5.14430i	0.205387	+	0.172340i
$892$		0			0
$893$	14.5431	−	45.5103i	0.486667	−	1.52294i
$894$		0			0
$895$	−30.5685	−	3.01844i	−1.02179	−	0.100895i
$896$		0			0
$897$	−12.3022	−	8.61412i	−0.410760	−	0.287617i
$898$		0			0
$899$	−0.907406	+	2.49308i	−0.0302637	+	0.0831488i
$900$		0			0
$901$	22.4990	+	12.9898i	0.749551	+	0.432753i
$902$		0			0
$903$	−4.86853	+	55.6475i	−0.162014	+	1.85183i
$904$		0			0
$905$	−1.90365	+	3.96624i	−0.0632795	+	0.131842i
$906$		0			0
$907$	−21.0967	+	14.7721i	−0.700505	+	0.490499i	−0.868753	−	0.495246i	$-0.835078\pi$
$907$	−21.0967	+	14.7721i	−0.700505	+	0.490499i	0.168248	+	0.985745i	$0.446189\pi$
$908$		0			0
$909$	9.92947	+	27.2810i	0.329340	+	0.904853i
$910$		0			0
$911$		−	9.95400i		−	0.329791i	−0.986311	−	0.164895i	$-0.947271\pi$
$911$		−	9.95400i		−	0.329791i	0.986311	−	0.164895i	$-0.0527286\pi$
$912$		0			0
$913$	−12.9918	−	12.9918i	−0.429966	−	0.429966i
$914$		0			0
$915$	−0.0611036	−	0.370675i	−0.00202002	−	0.0122541i
$916$		0			0
$917$	−17.0059	−	24.2869i	−0.561584	−	0.802025i
$918$		0			0
$919$	30.8227	−	17.7955i	1.01675	−	0.587019i	0.103587	−	0.994620i	$-0.466968\pi$
$919$	30.8227	−	17.7955i	1.01675	−	0.587019i	0.913160	+	0.407601i	$0.133635\pi$
$920$		0			0
$921$	−25.7560	+	21.6119i	−0.848689	+	0.712135i
$922$		0			0
$923$	10.5597	−	2.82946i	0.347576	−	0.0931327i
$924$		0			0
$925$	2.18527	−	0.142134i	0.0718512	−	0.00467333i
$926$		0			0
$927$	30.2895	−	43.2579i	0.994837	−	1.42077i
$928$		0			0
$929$	18.8656	−	22.4832i	0.618961	−	0.737649i	−0.361930	−	0.932205i	$-0.617882\pi$
$929$	18.8656	−	22.4832i	0.618961	−	0.737649i	0.980891	+	0.194556i	$0.0623266\pi$
$930$		0			0
$931$	−7.48310	−	6.91044i	−0.245249	−	0.226480i
$932$		0			0
$933$	−4.13301	+	0.361591i	−0.135309	+	0.0118380i
$934$		0			0
$935$	−8.89389	−	0.0992431i	−0.290861	−	0.00324560i
$936$		0			0
$937$	14.7165	−	6.86241i	0.480767	−	0.224185i	−0.167098	−	0.985940i	$-0.553440\pi$
$937$	14.7165	−	6.86241i	0.480767	−	0.224185i	0.647865	+	0.761755i	$0.275662\pi$
$938$		0			0
$939$	−0.656900	+	1.13778i	−0.0214371	+	0.0371302i
$940$		0			0
$941$	22.2530	+	26.5201i	0.725427	+	0.864531i	0.995146	−	0.0984084i	$-0.0313752\pi$
$941$	22.2530	+	26.5201i	0.725427	+	0.864531i	−0.269719	+	0.962939i	$0.586931\pi$
$942$		0			0
$943$	6.62564	+	1.77533i	0.215760	+	0.0578128i
$944$		0			0
$945$	−4.72657	−	10.4387i	−0.153755	−	0.339571i
$946$		0			0
$947$	6.86827	−	14.7291i	0.223189	−	0.478630i	−0.762546	−	0.646934i	$-0.776051\pi$
$947$	6.86827	−	14.7291i	0.223189	−	0.478630i	0.985735	+	0.168303i	$0.0538289\pi$
$948$		0			0
$949$	12.3926			0.402281
$950$		0			0
$951$	22.5504			0.731245
$952$		0			0
$953$	−7.21045	+	15.4629i	−0.233570	+	0.500891i	−0.987802	−	0.155716i	$-0.950231\pi$
$953$	−7.21045	+	15.4629i	−0.233570	+	0.500891i	0.754232	+	0.656608i	$0.228009\pi$
$954$		0			0
$955$	7.12295	+	15.7311i	0.230493	+	0.509048i
$956$		0			0
$957$	6.74549	+	1.80745i	0.218051	+	0.0584265i
$958$		0			0
$959$	−9.60027	−	11.4412i	−0.310009	−	0.369454i
$960$		0			0
$961$	−14.4354	+	25.0028i	−0.465657	+	0.806541i
$962$		0			0
$963$	7.32791	−	3.41706i	0.236139	−	0.110113i
$964$		0			0
$965$	−3.85027	−	0.0429635i	−0.123944	−	0.00138304i
$966$		0			0
$967$	−0.947199	+	0.0828692i	−0.0304599	+	0.00266489i	−0.102375	−	0.994746i	$-0.532644\pi$
$967$	−0.947199	+	0.0828692i	−0.0304599	+	0.00266489i	0.0719156	+	0.997411i	$0.477089\pi$
$968$		0			0
$969$	−16.8449	+	26.2169i	−0.541137	+	0.842208i
$970$		0			0
$971$	−20.6691	+	24.6324i	−0.663302	+	0.790492i	−0.987856	−	0.155375i	$-0.950341\pi$
$971$	−20.6691	+	24.6324i	−0.663302	+	0.790492i	0.324554	+	0.945867i	$0.394786\pi$
$972$		0			0
$973$	24.4759	−	34.9552i	0.784661	−	1.12061i
$974$		0			0
$975$	8.15810	+	7.16168i	0.261268	+	0.229357i
$976$		0			0
$977$	−57.0899	+	15.2972i	−1.82647	+	0.489401i	−0.997549	−	0.0699682i	$-0.977710\pi$
$977$	−57.0899	+	15.2972i	−1.82647	+	0.489401i	−0.828919	+	0.559369i	$0.811044\pi$
$978$		0			0
$979$	14.0040	−	11.7507i	0.447569	−	0.375555i
$980$		0			0
$981$	69.4299	−	40.0854i	2.21673	−	1.27983i
$982$		0			0
$983$	26.2541	+	37.4947i	0.837376	+	1.19590i	0.978570	+	0.205915i	$0.0660169\pi$
$983$	26.2541	+	37.4947i	0.837376	+	1.19590i	−0.141194	+	0.989982i	$0.545094\pi$
$984$		0			0
$985$	−0.985659	−	5.97934i	−0.0314057	−	0.190518i
$986$		0			0
$987$	43.9744	+	43.9744i	1.39972	+	1.39972i
$988$		0			0
$989$		−	68.1034i		−	2.16556i
$990$		0			0
$991$	−8.36088	−	22.9713i	−0.265592	−	0.729709i	−0.998766	−	0.0496671i	$-0.984184\pi$
$991$	−8.36088	−	22.9713i	−0.265592	−	0.729709i	0.733174	−	0.680042i	$-0.238038\pi$
$992$		0			0
$993$	71.7767	−	50.2586i	2.27776	−	1.59491i
$994$		0			0
$995$	−15.7702	+	32.8571i	−0.499949	+	1.04164i
$996$		0			0
$997$	2.24042	−	25.6081i	0.0709549	−	0.811018i	−0.874449	−	0.485117i	$-0.838777\pi$
$997$	2.24042	−	25.6081i	0.0709549	−	0.811018i	0.945404	−	0.325901i	$-0.105668\pi$
$998$		0			0
$999$	0.900116	+	0.519682i	0.0284784	+	0.0164420i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.193.9	yes	120
5.2	odd	4	inner	380.2.bh.a.117.2	yes	120
19.13	odd	18	inner	380.2.bh.a.13.2	✓	120
95.32	even	36	inner	380.2.bh.a.317.9	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.13.2	✓	120	19.13	odd	18	inner
380.2.bh.a.117.2	yes	120	5.2	odd	4	inner
380.2.bh.a.193.9	yes	120	1.1	even	1	trivial
380.2.bh.a.317.9	yes	120	95.32	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11039 - 2.38123i) q^{3} +(-0.922332 - 2.03698i) q^{5} +(-2.08587 - 0.558906i) q^{7} +(-2.50894 - 2.99004i) q^{9} +O(q^{10})\)	\(q+(1.11039 - 2.38123i) q^{3} +(-0.922332 - 2.03698i) q^{5} +(-2.08587 - 0.558906i) q^{7} +(-2.50894 - 2.99004i) q^{9} +(-0.730936 + 1.26602i) q^{11} +(0.748918 - 0.349226i) q^{13} +(-5.87467 - 0.0655530i) q^{15} +(-2.71062 + 0.237149i) q^{17} +(4.25189 + 0.959893i) q^{19} +(-3.64700 + 4.34633i) q^{21} +(3.96759 - 5.66631i) q^{23} +(-3.29861 + 3.75755i) q^{25} +(-2.29224 + 0.614204i) q^{27} +(1.39280 - 1.16870i) q^{29} +(-1.26371 + 0.729601i) q^{31} +(2.20306 + 3.14629i) q^{33} +(0.785379 + 4.76437i) q^{35} +(-0.309697 - 0.309697i) q^{37} -2.17112i q^{39} +(0.339156 + 0.931825i) q^{41} +(8.06488 - 5.64709i) q^{43} +(-3.77658 + 7.86847i) q^{45} +(0.955306 - 10.9192i) q^{47} +(-2.02372 - 1.16839i) q^{49} +(-2.44513 + 6.71794i) q^{51} +(-7.82119 - 5.47646i) q^{53} +(3.25302 + 0.321215i) q^{55} +(7.00697 - 9.05889i) q^{57} +(4.73412 + 3.97240i) q^{59} +(0.0111039 + 0.0629732i) q^{61} +(3.56216 + 7.63907i) q^{63} +(-1.40212 - 1.20343i) q^{65} +(2.01623 + 0.176397i) q^{67} +(-9.08722 - 15.7395i) q^{69} +(13.0287 + 2.29730i) q^{71} +(13.5919 + 6.33800i) q^{73} +(5.28487 + 12.0271i) q^{75} +(2.23222 - 2.23222i) q^{77} +(-2.02226 + 0.736043i) q^{79} +(0.950647 - 5.39139i) q^{81} +(-3.25291 + 12.1400i) q^{83} +(2.98316 + 5.30276i) q^{85} +(-1.23639 - 4.61428i) q^{87} +(-11.7510 - 4.27701i) q^{89} +(-1.75733 + 0.309864i) q^{91} +(0.334147 + 3.81931i) q^{93} +(-1.96637 - 9.54638i) q^{95} +(0.868480 + 9.92678i) q^{97} +(5.61931 - 0.990836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 120 * q + 6 * q^7	\( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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